TSTP Solution File: SEU811^1 by Zipperpin---2.1.9999
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU811^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.XA1kiZNYb4 true
% Computer : n016.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 19:18:10 EDT 2023
% Result : Theorem 96.58s 13.12s
% Output : Refutation 98.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU811^1 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.XA1kiZNYb4 true
% 0.13/0.34 % Computer : n016.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 24 00:48:08 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % Running portfolio for 300 s
% 0.13/0.34 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.35 % Number of cores: 8
% 0.13/0.35 % Python version: Python 3.6.8
% 0.13/0.35 % Running in HO mode
% 0.21/0.67 % Total configuration time : 828
% 0.21/0.67 % Estimated wc time : 1656
% 0.21/0.67 % Estimated cpu time (8 cpus) : 207.0
% 0.21/0.70 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.21/0.75 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.21/0.75 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.21/0.75 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.21/0.75 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.21/0.78 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.21/0.79 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.21/0.80 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 96.58/13.12 % Solved by lams/40_b.comb.sh.
% 96.58/13.12 % done 186 iterations in 11.934s
% 96.58/13.12 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 96.58/13.12 % SZS output start Refutation
% 96.58/13.12 thf(setadjoinAx_type, type, setadjoinAx: $o).
% 96.58/13.12 thf('#sk50_type', type, '#sk50': $i).
% 96.58/13.12 thf(cartprodfstpairEq_type, type, cartprodfstpairEq: $o).
% 96.58/13.12 thf(notdexE_type, type, notdexE: $o).
% 96.58/13.12 thf(setunionAx_type, type, setunionAx: $o).
% 96.58/13.12 thf(setminusELneg_type, type, setminusELneg: $o).
% 96.58/13.12 thf(breln1unionEcases_type, type, breln1unionEcases: $o).
% 96.58/13.12 thf(powersetE_type, type, powersetE: $o).
% 96.58/13.12 thf(woz1_1_type, type, woz1_1: $o).
% 96.58/13.12 thf(omegaSAx_type, type, omegaSAx: $o).
% 96.58/13.12 thf(breln1unionI_type, type, breln1unionI: $o).
% 96.58/13.12 thf(complementSubsetComplementIntersect_type, type, complementSubsetComplementIntersect:
% 96.58/13.12 $o).
% 96.58/13.12 thf(surjCantorThm_type, type, surjCantorThm: $o).
% 96.58/13.12 thf(exuI1_type, type, exuI1: $o).
% 96.58/13.12 thf(exuI2_type, type, exuI2: $o).
% 96.58/13.12 thf(notequalI2_type, type, notequalI2: $o).
% 96.58/13.12 thf(kfstsingleton_type, type, kfstsingleton: $o).
% 96.58/13.12 thf(kpairiskpair_type, type, kpairiskpair: $o).
% 96.58/13.12 thf(upairsubunion_type, type, upairsubunion: $o).
% 96.58/13.12 thf(binunionTE_type, type, binunionTE: $o).
% 96.58/13.12 thf(binunionTEcontra_type, type, binunionTEcontra: $o).
% 96.58/13.12 thf(powerset__Cong_type, type, powerset__Cong: $o).
% 96.58/13.12 thf(omegaS_type, type, omegaS: $i > $i).
% 96.58/13.12 thf(setukpairinjR2_type, type, setukpairinjR2: $o).
% 96.58/13.12 thf(singletonsuniq_type, type, singletonsuniq: $o).
% 96.58/13.12 thf(setminusILneg_type, type, setminusILneg: $o).
% 96.58/13.12 thf(wellorderingAx_type, type, wellorderingAx: $o).
% 96.58/13.12 thf(kpairsurjEq_type, type, kpairsurjEq: $o).
% 96.58/13.12 thf(funcextLem_type, type, funcextLem: $o).
% 96.58/13.12 thf(setadjoinSub2_type, type, setadjoinSub2: $o).
% 96.58/13.12 thf(binintersectSubset5_type, type, binintersectSubset5: $o).
% 96.58/13.12 thf(upairinpowunion_type, type, upairinpowunion: $o).
% 96.58/13.12 thf(eta1_type, type, eta1: $o).
% 96.58/13.12 thf(complementTnotintersectT_type, type, complementTnotintersectT: $o).
% 96.58/13.12 thf(setoftrueEq_type, type, setoftrueEq: $o).
% 96.58/13.12 thf(notinself_type, type, notinself: $o).
% 96.58/13.12 thf(apProp_type, type, apProp: $o).
% 96.58/13.12 thf(setextT_type, type, setextT: $o).
% 96.58/13.12 thf(inIntersectImpInIntersectUnions_type, type, inIntersectImpInIntersectUnions:
% 96.58/13.12 $o).
% 96.58/13.12 thf(emptyset__Cong_type, type, emptyset__Cong: $o).
% 96.58/13.12 thf(cartprodmempaircEq_type, type, cartprodmempaircEq: $o).
% 96.58/13.12 thf(breln1invprop_type, type, breln1invprop: $o).
% 96.58/13.12 thf(lamProp_type, type, lamProp: $o).
% 96.58/13.12 thf(dpsetconstrSub_type, type, dpsetconstrSub: $o).
% 96.58/13.12 thf(ex1E1_type, type, ex1E1: $o).
% 96.58/13.12 thf(sepInPowerset_type, type, sepInPowerset: $o).
% 96.58/13.12 thf(setukpairIR_type, type, setukpairIR: $o).
% 96.58/13.12 thf(brelnall1_type, type, brelnall1: $o).
% 96.58/13.12 thf(binunionE_type, type, binunionE: $o).
% 96.58/13.12 thf(setext_type, type, setext: $o).
% 96.58/13.12 thf(complementTcontraSubset_type, type, complementTcontraSubset: $o).
% 96.58/13.12 thf(emptyinPowerset_type, type, emptyinPowerset: $o).
% 96.58/13.12 thf(binintersectTELcontra_type, type, binintersectTELcontra: $o).
% 96.58/13.12 thf(ubforcartprodlem1_type, type, ubforcartprodlem1: $o).
% 96.58/13.12 thf(iftrue_type, type, iftrue: $o).
% 96.58/13.12 thf(woz13rule4_type, type, woz13rule4: $o).
% 96.58/13.12 thf(descr__Cong_type, type, descr__Cong: $o).
% 96.58/13.12 thf(funcGraphProp2_type, type, funcGraphProp2: $o).
% 96.58/13.12 thf(theprop_type, type, theprop: $o).
% 96.58/13.12 thf(image1I_type, type, image1I: $o).
% 96.58/13.12 thf(binintersectSubset1_type, type, binintersectSubset1: $o).
% 96.58/13.12 thf(in_type, type, in: $i > $i > $o).
% 96.58/13.12 thf(cartprodsndpairEq_type, type, cartprodsndpairEq: $o).
% 96.58/13.12 thf(quantDeMorgan1_type, type, quantDeMorgan1: $o).
% 96.58/13.12 thf(setukpairinjL2_type, type, setukpairinjL2: $o).
% 96.58/13.12 thf(demorgan1_type, type, demorgan1: $o).
% 96.58/13.12 thf(setadjoinIR_type, type, setadjoinIR: $o).
% 96.58/13.12 thf(complementInPowersetComplementIntersect_type, type, complementInPowersetComplementIntersect:
% 96.58/13.12 $o).
% 96.58/13.12 thf(inIntersectImpInUnion_type, type, inIntersectImpInUnion: $o).
% 96.58/13.12 thf(breln1SetBreln1_type, type, breln1SetBreln1: $o).
% 96.58/13.12 thf(setadjoin__Cong_type, type, setadjoin__Cong: $o).
% 96.58/13.12 thf(ksndpairEq_type, type, ksndpairEq: $o).
% 96.58/13.12 thf(ex1I2_type, type, ex1I2: $o).
% 96.58/13.12 thf(foundation2_type, type, foundation2: $o).
% 96.58/13.12 thf(symdiffI2_type, type, symdiffI2: $o).
% 96.58/13.12 thf(ap2apEq2_type, type, ap2apEq2: $o).
% 96.58/13.12 thf(ifSingleton_type, type, ifSingleton: $o).
% 96.58/13.12 thf(upairset2IR_type, type, upairset2IR: $o).
% 96.58/13.12 thf(iftrueProp1_type, type, iftrueProp1: $o).
% 96.58/13.12 thf(complementTI1_type, type, complementTI1: $o).
% 96.58/13.12 thf(subsetE_type, type, subsetE: $o).
% 96.58/13.12 thf(prop2set2propI_type, type, prop2set2propI: $o).
% 96.58/13.12 thf(doubleComplementSub2_type, type, doubleComplementSub2: $o).
% 96.58/13.12 thf(complementUnionInPowersetComplement_type, type, complementUnionInPowersetComplement:
% 96.58/13.12 $o).
% 96.58/13.12 thf(iffalse_type, type, iffalse: $o).
% 96.58/13.12 thf(dsetconstrEL_type, type, dsetconstrEL: $o).
% 96.58/13.12 thf(setbeta_type, type, setbeta: $o).
% 96.58/13.12 thf(eqinunit_type, type, eqinunit: $o).
% 96.58/13.12 thf(upairsetIL_type, type, upairsetIL: $o).
% 96.58/13.12 thf(powersetI1_type, type, powersetI1: $o).
% 96.58/13.12 thf(cartprodfstin_type, type, cartprodfstin: $o).
% 96.58/13.12 thf(lamp_type, type, lamp: $o).
% 96.58/13.12 thf(iffalseProp1_type, type, iffalseProp1: $o).
% 96.58/13.12 thf(breln1invI_type, type, breln1invI: $o).
% 96.58/13.12 thf(binintersectSubset3_type, type, binintersectSubset3: $o).
% 96.58/13.12 thf(breln1unionE_type, type, breln1unionE: $o).
% 96.58/13.12 thf(ksndsingleton_type, type, ksndsingleton: $o).
% 96.58/13.12 thf(setminusIRneg_type, type, setminusIRneg: $o).
% 96.58/13.12 thf(lam2lamEq_type, type, lam2lamEq: $o).
% 96.58/13.12 thf(omegaSclos_type, type, omegaSclos: $o).
% 96.58/13.12 thf(powersetAx_type, type, powersetAx: $o).
% 96.58/13.12 thf(woz2Ex_type, type, woz2Ex: $o).
% 96.58/13.12 thf(eta2_type, type, eta2: $o).
% 96.58/13.12 thf(binintersectSubset4_type, type, binintersectSubset4: $o).
% 96.58/13.12 thf(singletoninpowunion_type, type, singletoninpowunion: $o).
% 96.58/13.12 thf(image1Ex_type, type, image1Ex: $o).
% 96.58/13.12 thf(powersetI_type, type, powersetI: $o).
% 96.58/13.12 thf(cartprodmempair_type, type, cartprodmempair: $o).
% 96.58/13.12 thf(powersetTE1_type, type, powersetTE1: $o).
% 96.58/13.12 thf(upairsetIR_type, type, upairsetIR: $o).
% 96.58/13.12 thf(cartprodpairsurjEq_type, type, cartprodpairsurjEq: $o).
% 96.58/13.12 thf(lam2p_type, type, lam2p: $o).
% 96.58/13.12 thf(contraSubsetComplement_type, type, contraSubsetComplement: $o).
% 96.58/13.12 thf(doubleComplementSub1_type, type, doubleComplementSub1: $o).
% 96.58/13.12 thf(cartprodpairmemEL_type, type, cartprodpairmemEL: $o).
% 96.58/13.12 thf(setOfPairsIsBReln1_type, type, setOfPairsIsBReln1: $o).
% 96.58/13.12 thf(inCongP_type, type, inCongP: $o).
% 96.58/13.12 thf(setukpairinjR11_type, type, setukpairinjR11: $o).
% 96.58/13.12 thf(setadjoinSub_type, type, setadjoinSub: $o).
% 96.58/13.12 thf(exuE3e_type, type, exuE3e: $o).
% 96.58/13.12 thf(emptysetE_type, type, emptysetE: $o).
% 96.58/13.12 thf(woz13rule2_type, type, woz13rule2: $o).
% 96.58/13.12 thf(binintersectSubset2_type, type, binintersectSubset2: $o).
% 96.58/13.12 thf(image1E_type, type, image1E: $o).
% 96.58/13.12 thf(setunionI_type, type, setunionI: $o).
% 96.58/13.12 thf(breln1unionIR_type, type, breln1unionIR: $o).
% 96.58/13.12 thf(binintersectTERcontra_type, type, binintersectTERcontra: $o).
% 96.58/13.12 thf(setunion__Cong_type, type, setunion__Cong: $o).
% 96.58/13.12 thf(injFuncSetFuncInj_type, type, injFuncSetFuncInj: $o).
% 96.58/13.12 thf(prop2setI_type, type, prop2setI: $o).
% 96.58/13.12 thf(nonemptyImpWitness_type, type, nonemptyImpWitness: $o).
% 96.58/13.12 thf(setminusER_type, type, setminusER: $o).
% 96.58/13.12 thf(exuE2_type, type, exuE2: $o).
% 96.58/13.12 thf(woz1_2_type, type, woz1_2: $o).
% 96.58/13.12 thf(emptyset_type, type, emptyset: $i).
% 96.58/13.12 thf(setukpairinjR12_type, type, setukpairinjR12: $o).
% 96.58/13.12 thf(funcGraphProp1_type, type, funcGraphProp1: $o).
% 96.58/13.12 thf(powersetsubset_type, type, powersetsubset: $o).
% 96.58/13.12 thf(upairequniteq_type, type, upairequniteq: $o).
% 96.58/13.12 thf(dpsetconstrEL1_type, type, dpsetconstrEL1: $o).
% 96.58/13.12 thf(injFuncInInjFuncSet_type, type, injFuncInInjFuncSet: $o).
% 96.58/13.12 thf(subPowSU_type, type, subPowSU: $o).
% 96.58/13.12 thf(breln1compprop_type, type, breln1compprop: $o).
% 96.58/13.12 thf(woz2B_type, type, woz2B: $o).
% 96.58/13.12 thf(notequalI1_type, type, notequalI1: $o).
% 96.58/13.12 thf(demorgan2b_type, type, demorgan2b: $o).
% 96.58/13.12 thf(notinemptyset_type, type, notinemptyset: $o).
% 96.58/13.12 thf(nonemptyI1_type, type, nonemptyI1: $o).
% 96.58/13.12 thf(breln1unionIL_type, type, breln1unionIL: $o).
% 96.58/13.12 thf(subsetTrans_type, type, subsetTrans: $o).
% 96.58/13.12 thf(setukpairinjR_type, type, setukpairinjR: $o).
% 96.58/13.12 thf(infuncsetfunc_type, type, infuncsetfunc: $o).
% 96.58/13.12 thf(kpairp_type, type, kpairp: $o).
% 96.58/13.12 thf(setukpairinjR1_type, type, setukpairinjR1: $o).
% 96.58/13.12 thf(setminusI_type, type, setminusI: $o).
% 96.58/13.12 thf(notinself2_type, type, notinself2: $o).
% 96.58/13.12 thf(binunionIL_type, type, binunionIL: $o).
% 96.58/13.12 thf(setOfPairsIsBReln_type, type, setOfPairsIsBReln: $o).
% 96.58/13.12 thf(setukpairinjL1_type, type, setukpairinjL1: $o).
% 96.58/13.12 thf(setunionsingleton_type, type, setunionsingleton: $o).
% 96.58/13.12 thf(powersetTI1_type, type, powersetTI1: $o).
% 96.58/13.12 thf(subsetE2_type, type, subsetE2: $o).
% 96.58/13.12 thf(image1Ex1_type, type, image1Ex1: $o).
% 96.58/13.12 thf(singletonsswitch_type, type, singletonsswitch: $o).
% 96.58/13.12 thf(ubforcartprodlem3_type, type, ubforcartprodlem3: $o).
% 96.58/13.12 thf(setextsub_type, type, setextsub: $o).
% 96.58/13.12 thf(binunionLsub_type, type, binunionLsub: $o).
% 96.58/13.12 thf(contrasubsetT1_type, type, contrasubsetT1: $o).
% 96.58/13.12 thf(setunionsingleton1_type, type, setunionsingleton1: $o).
% 96.58/13.12 thf(breln1compE_type, type, breln1compE: $o).
% 96.58/13.12 thf(emptysetsubset_type, type, emptysetsubset: $o).
% 96.58/13.12 thf(quantDeMorgan3_type, type, quantDeMorgan3: $o).
% 96.58/13.12 thf(dpsetconstrERa_type, type, dpsetconstrERa: $o).
% 96.58/13.12 thf(setunionE_type, type, setunionE: $o).
% 96.58/13.12 thf(setminusSubset1_type, type, setminusSubset1: $o).
% 96.58/13.12 thf(complementT_lem_type, type, complementT_lem: $o).
% 96.58/13.12 thf(binintersectT_lem_type, type, binintersectT_lem: $o).
% 96.58/13.12 thf(emptyinunitempty_type, type, emptyinunitempty: $o).
% 96.58/13.12 thf(binunionIR_type, type, binunionIR: $o).
% 96.58/13.12 thf(injFuncSetFuncIn_type, type, injFuncSetFuncIn: $o).
% 96.58/13.12 thf(setadjoinE_type, type, setadjoinE: $o).
% 96.58/13.12 thf(doubleComplementEq_type, type, doubleComplementEq: $o).
% 96.58/13.12 thf(eqbreln1_type, type, eqbreln1: $o).
% 96.58/13.12 thf(cartprodpairmemER_type, type, cartprodpairmemER: $o).
% 96.58/13.12 thf(dpsetconstrER_type, type, dpsetconstrER: $o).
% 96.58/13.12 thf(leftInvIsSurj_type, type, leftInvIsSurj: $o).
% 96.58/13.12 thf(doubleComplementE1_type, type, doubleComplementE1: $o).
% 96.58/13.12 thf(setadjoinIL_type, type, setadjoinIL: $o).
% 96.58/13.12 thf(exuE1_type, type, exuE1: $o).
% 96.58/13.12 thf(ubforcartprodlem2_type, type, ubforcartprodlem2: $o).
% 96.58/13.12 thf(binintersectRsub_type, type, binintersectRsub: $o).
% 96.58/13.12 thf(setminusLsub_type, type, setminusLsub: $o).
% 96.58/13.12 thf(notinsingleton_type, type, notinsingleton: $o).
% 96.58/13.12 thf(intersectInPowersetIntersectUnions_type, type, intersectInPowersetIntersectUnions:
% 96.58/13.12 $o).
% 96.58/13.12 thf(dpsetconstrEL2_type, type, dpsetconstrEL2: $o).
% 96.58/13.12 thf(eqimpsubset2_type, type, eqimpsubset2: $o).
% 96.58/13.12 thf(exuEu_type, type, exuEu: $o).
% 96.58/13.12 thf(emptysetimpfalse_type, type, emptysetimpfalse: $o).
% 96.58/13.12 thf(upairsetE_type, type, upairsetE: $o).
% 96.58/13.12 thf(omega0Ax_type, type, omega0Ax: $o).
% 96.58/13.12 thf(breln1invE_type, type, breln1invE: $o).
% 96.58/13.12 thf(breln1unionCommutes_type, type, breln1unionCommutes: $o).
% 96.58/13.12 thf(funcGraphProp3_type, type, funcGraphProp3: $o).
% 96.58/13.12 thf(app_type, type, app: $o).
% 96.58/13.12 thf('#sk51_type', type, '#sk51': $i).
% 96.58/13.12 thf(funcImageSingleton_type, type, funcImageSingleton: $o).
% 96.58/13.12 thf(dpsetconstrI_type, type, dpsetconstrI: $o).
% 96.58/13.12 thf(notsubsetI_type, type, notsubsetI: $o).
% 96.58/13.12 thf(powersetT_lem_type, type, powersetT_lem: $o).
% 96.58/13.12 thf(woz2W_type, type, woz2W: $o).
% 96.58/13.12 thf(iffalseProp2_type, type, iffalseProp2: $o).
% 96.58/13.12 thf(quantDeMorgan4_type, type, quantDeMorgan4: $o).
% 96.58/13.12 thf(setextAx_type, type, setextAx: $o).
% 96.58/13.12 thf(breln1all1_type, type, breln1all1: $o).
% 96.58/13.12 thf(choice2fnsingleton_type, type, choice2fnsingleton: $o).
% 96.58/13.12 thf(breln1compI_type, type, breln1compI: $o).
% 96.58/13.12 thf(demorgan2a1_type, type, demorgan2a1: $o).
% 96.58/13.12 thf(powersetE1_type, type, powersetE1: $o).
% 96.58/13.12 thf(bs114d_type, type, bs114d: $o).
% 96.58/13.12 thf(complementTE1_type, type, complementTE1: $o).
% 96.58/13.12 thf(noeltsimpempty_type, type, noeltsimpempty: $o).
% 96.58/13.12 thf(breln1all2_type, type, breln1all2: $o).
% 96.58/13.12 thf(contrasubsetT2_type, type, contrasubsetT2: $o).
% 96.58/13.12 thf(inIntersectImpInUnion2_type, type, inIntersectImpInUnion2: $o).
% 96.58/13.12 thf(demorgan2b2_type, type, demorgan2b2: $o).
% 96.58/13.12 thf(binintersectLsub_type, type, binintersectLsub: $o).
% 96.58/13.12 thf(subsetI1_type, type, subsetI1: $o).
% 96.58/13.12 thf(symdiffE_type, type, symdiffE: $o).
% 96.58/13.12 thf(woz13rule1_type, type, woz13rule1: $o).
% 96.58/13.12 thf(breln1unionprop_type, type, breln1unionprop: $o).
% 96.58/13.12 thf(descrp_type, type, descrp: $o).
% 96.58/13.12 thf(dsetconstr__Cong_type, type, dsetconstr__Cong: $o).
% 96.58/13.12 thf(foundationAx_type, type, foundationAx: $o).
% 96.58/13.12 thf(brelnall2_type, type, brelnall2: $o).
% 96.58/13.12 thf(emptysetAx_type, type, emptysetAx: $o).
% 96.58/13.12 thf(emptyI_type, type, emptyI: $o).
% 96.58/13.12 thf(setadjoinOr_type, type, setadjoinOr: $o).
% 96.58/13.12 thf(binintersectEL_type, type, binintersectEL: $o).
% 96.58/13.12 thf(emptyE1_type, type, emptyE1: $o).
% 96.58/13.12 thf(demorgan2a_type, type, demorgan2a: $o).
% 96.58/13.12 thf(woz1_3_type, type, woz1_3: $o).
% 96.58/13.12 thf(emptyInPowerset_type, type, emptyInPowerset: $o).
% 96.58/13.12 thf(omegaSp_type, type, omegaSp: $o).
% 96.58/13.12 thf(vacuousDall_type, type, vacuousDall: $o).
% 96.58/13.12 thf(dsetconstrER_type, type, dsetconstrER: $o).
% 96.58/13.12 thf(demorgan1a_type, type, demorgan1a: $o).
% 96.58/13.12 thf(ifp_type, type, ifp: $o).
% 96.58/13.12 thf(binintersectI_type, type, binintersectI: $o).
% 96.58/13.12 thf(beta1_type, type, beta1: $o).
% 96.58/13.12 thf(funcext2_type, type, funcext2: $o).
% 96.58/13.12 thf(subbreln_type, type, subbreln: $o).
% 96.58/13.12 thf(cartprodpairin_type, type, cartprodpairin: $o).
% 96.58/13.12 thf(cartprodmempair1_type, type, cartprodmempair1: $o).
% 96.58/13.12 thf(subbreln1_type, type, subbreln1: $o).
% 96.58/13.12 thf(demorgan2a2_type, type, demorgan2a2: $o).
% 96.58/13.12 thf(image1Equiv_type, type, image1Equiv: $o).
% 96.58/13.12 thf(subsetTI_type, type, subsetTI: $o).
% 96.58/13.12 thf(setminusT_lem_type, type, setminusT_lem: $o).
% 96.58/13.12 thf(ap2p_type, type, ap2p: $o).
% 96.58/13.12 thf(doubleComplementI1_type, type, doubleComplementI1: $o).
% 96.58/13.12 thf(binunionT_lem_type, type, binunionT_lem: $o).
% 96.58/13.12 thf(symdiffI1_type, type, symdiffI1: $o).
% 96.58/13.12 thf(woz1_4_type, type, woz1_4: $o).
% 96.58/13.12 thf(kfstpairEq_type, type, kfstpairEq: $o).
% 96.58/13.12 thf(subsetI2_type, type, subsetI2: $o).
% 96.58/13.12 thf(symdiffIneg1_type, type, symdiffIneg1: $o).
% 96.58/13.12 thf(theeq_type, type, theeq: $o).
% 96.58/13.12 thf(setminusERneg_type, type, setminusERneg: $o).
% 96.58/13.12 thf(symdiffIneg2_type, type, symdiffIneg2: $o).
% 96.58/13.12 thf(binunionTIRcontra_type, type, binunionTIRcontra: $o).
% 96.58/13.12 thf(omega__Cong_type, type, omega__Cong: $o).
% 96.58/13.12 thf(demorgan1b_type, type, demorgan1b: $o).
% 96.58/13.12 thf(subsetRefl_type, type, subsetRefl: $o).
% 96.58/13.12 thf(uniqinunit_type, type, uniqinunit: $o).
% 96.58/13.12 thf(eqbreln_type, type, eqbreln: $o).
% 96.58/13.12 thf(inComplementUnionImpNotIn1_type, type, inComplementUnionImpNotIn1: $o).
% 96.58/13.12 thf(funcinfuncset_type, type, funcinfuncset: $o).
% 96.58/13.12 thf(breln1compEex_type, type, breln1compEex: $o).
% 96.58/13.12 thf(contrasubsetT_type, type, contrasubsetT: $o).
% 96.58/13.12 thf(setminusSubset2_type, type, setminusSubset2: $o).
% 96.58/13.12 thf(prop2setE_type, type, prop2setE: $o).
% 96.58/13.12 thf(binunionEcases_type, type, binunionEcases: $o).
% 96.58/13.12 thf(omega_type, type, omega: $i).
% 96.58/13.12 thf(nonemptyI_type, type, nonemptyI: $o).
% 96.58/13.12 thf(disjointsetsI1_type, type, disjointsetsI1: $o).
% 96.58/13.12 thf(woz2A_type, type, woz2A: $o).
% 96.58/13.12 thf(exuE3u_type, type, exuE3u: $o).
% 96.58/13.12 thf(setminusEL_type, type, setminusEL: $o).
% 96.58/13.12 thf(funcGraphProp4_type, type, funcGraphProp4: $o).
% 96.58/13.12 thf(woz1_5_type, type, woz1_5: $o).
% 96.58/13.12 thf(demorgan2_type, type, demorgan2: $o).
% 96.58/13.12 thf(setunionsingleton2_type, type, setunionsingleton2: $o).
% 96.58/13.12 thf(sepSubset_type, type, sepSubset: $o).
% 96.58/13.12 thf(inComplementUnionImpInComplement1_type, type, inComplementUnionImpInComplement1:
% 96.58/13.12 $o).
% 96.58/13.12 thf(funcext_type, type, funcext: $o).
% 96.58/13.12 thf(surjFuncSetFuncSurj_type, type, surjFuncSetFuncSurj: $o).
% 96.58/13.12 thf(upairset2E_type, type, upairset2E: $o).
% 96.58/13.12 thf(eqimpsubset1_type, type, eqimpsubset1: $o).
% 96.58/13.12 thf(exuI3_type, type, exuI3: $o).
% 96.58/13.12 thf(notdallE_type, type, notdallE: $o).
% 96.58/13.12 thf(peano0notS_type, type, peano0notS: $o).
% 96.58/13.12 thf(iftrueProp2_type, type, iftrueProp2: $o).
% 96.58/13.12 thf(binintersectER_type, type, binintersectER: $o).
% 96.58/13.12 thf(woz13rule0_type, type, woz13rule0: $o).
% 96.58/13.12 thf(dsetconstrI_type, type, dsetconstrI: $o).
% 96.58/13.12 thf(beta2_type, type, beta2: $o).
% 96.58/13.12 thf(setadjoin_type, type, setadjoin: $i > $i > $i).
% 96.58/13.12 thf(exu__Cong_type, type, exu__Cong: $o).
% 96.58/13.12 thf(cartprodsndin_type, type, cartprodsndin: $o).
% 96.58/13.12 thf(iftrueorfalse_type, type, iftrueorfalse: $o).
% 96.58/13.12 thf(surjFuncSetFuncIn_type, type, surjFuncSetFuncIn: $o).
% 96.58/13.12 thf(quantDeMorgan2_type, type, quantDeMorgan2: $o).
% 96.58/13.12 thf(ex1I_type, type, ex1I: $o).
% 96.58/13.12 thf(secondinupair_type, type, secondinupair: $o).
% 96.58/13.12 thf(singletonprop_type, type, singletonprop: $o).
% 96.58/13.12 thf(singletonsubset_type, type, singletonsubset: $o).
% 96.58/13.12 thf(singletoninpowerset_type, type, singletoninpowerset: $o).
% 96.58/13.12 thf(subsetemptysetimpeq_type, type, subsetemptysetimpeq: $o).
% 96.58/13.12 thf(ex1E2_type, type, ex1E2: $o).
% 96.58/13.12 thf(replAx_type, type, replAx: $o).
% 96.58/13.12 thf(nonemptyE1_type, type, nonemptyE1: $o).
% 96.58/13.12 thf(omegaIndAx_type, type, omegaIndAx: $o).
% 96.58/13.12 thf(setukpairIL_type, type, setukpairIL: $o).
% 96.58/13.12 thf(setunionE2_type, type, setunionE2: $o).
% 96.58/13.12 thf(inPowerset_type, type, inPowerset: $o).
% 96.58/13.12 thf(binunionTILcontra_type, type, binunionTILcontra: $o).
% 96.58/13.12 thf(ap2apEq1_type, type, ap2apEq1: $o).
% 96.58/13.12 thf(contrasubsetT3_type, type, contrasubsetT3: $o).
% 96.58/13.12 thf(woz13rule3_type, type, woz13rule3: $o).
% 96.58/13.12 thf(complementImpComplementIntersect_type, type, complementImpComplementIntersect:
% 96.58/13.12 $o).
% 96.58/13.12 thf(in__Cong_type, type, in__Cong: $o).
% 96.58/13.12 thf(setukpairinjL_type, type, setukpairinjL: $o).
% 96.58/13.12 thf(binunionRsub_type, type, binunionRsub: $o).
% 96.58/13.12 thf(subset2powerset_type, type, subset2powerset: $o).
% 96.58/13.12 thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)).
% 96.58/13.12 thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)).
% 96.58/13.12 thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)).
% 96.58/13.12 thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)).
% 96.58/13.12 thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)).
% 96.58/13.12 thf(peanoSinj, conjecture,
% 96.58/13.12 (( setextAx ) =>
% 96.58/13.12 ( ( emptysetAx ) =>
% 96.58/13.12 ( ( setadjoinAx ) =>
% 96.58/13.12 ( ( powersetAx ) =>
% 96.58/13.12 ( ( setunionAx ) =>
% 96.58/13.12 ( ( omega0Ax ) =>
% 96.58/13.12 ( ( omegaSAx ) =>
% 96.58/13.12 ( ( omegaIndAx ) =>
% 96.58/13.12 ( ( replAx ) =>
% 96.58/13.12 ( ( foundationAx ) =>
% 96.58/13.12 ( ( wellorderingAx ) =>
% 96.58/13.12 ( ( descrp ) =>
% 96.58/13.12 ( ( dsetconstrI ) =>
% 96.58/13.12 ( ( dsetconstrEL ) =>
% 96.58/13.12 ( ( dsetconstrER ) =>
% 96.58/13.12 ( ( exuE1 ) =>
% 96.58/13.12 ( ( prop2setE ) =>
% 96.58/13.12 ( ( emptysetE ) =>
% 96.58/13.12 ( ( emptysetimpfalse ) =>
% 96.58/13.12 ( ( notinemptyset ) =>
% 96.58/13.12 ( ( exuE3e ) =>
% 96.58/13.12 ( ( setext ) =>
% 96.58/13.12 ( ( emptyI ) =>
% 96.58/13.12 ( ( noeltsimpempty ) =>
% 96.58/13.12 ( ( setbeta ) =>
% 96.58/13.12 ( ( nonemptyE1 ) =>
% 96.58/13.12 ( ( nonemptyI ) =>
% 96.58/13.12 ( ( nonemptyI1 ) =>
% 96.58/13.12 ( ( setadjoinIL ) =>
% 96.58/13.12 ( ( emptyinunitempty ) =>
% 96.58/13.12 ( ( setadjoinIR ) =>
% 96.58/13.12 ( ( setadjoinE ) =>
% 96.58/13.12 ( (
% 96.58/13.12 setadjoinOr ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 setoftrueEq ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 powersetI ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 emptyinPowerset ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 emptyInPowerset ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 powersetE ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 setunionI ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 setunionE ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 subPowSU ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 exuE2 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 nonemptyImpWitness ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 uniqinunit ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 notinsingleton ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 eqinunit ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 singletonsswitch ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 upairsetE ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 upairsetIL ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 upairsetIR ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 emptyE1 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 vacuousDall ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 quantDeMorgan1 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 quantDeMorgan2 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 quantDeMorgan3 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 quantDeMorgan4 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 prop2setI ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 prop2set2propI ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 notdexE ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 notdallE ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 exuI1 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 exuI3 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 exuI2 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 inCongP ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 in__Cong ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 exuE3u ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 exu__Cong ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 emptyset__Cong ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 setadjoin__Cong ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 powerset__Cong ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 setunion__Cong ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 omega__Cong ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 exuEu ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 descr__Cong ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 dsetconstr__Cong ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 subsetI1 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 eqimpsubset2 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 eqimpsubset1 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 subsetI2 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 emptysetsubset ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 subsetE ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 subsetE2 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 notsubsetI ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 notequalI1 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 notequalI2 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 subsetRefl ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 subsetTrans ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 setadjoinSub ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 setadjoinSub2 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 subset2powerset ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 setextsub ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 subsetemptysetimpeq ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 powersetI1 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 powersetE1 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 inPowerset ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 powersetsubset ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 sepInPowerset ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 sepSubset ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 binunionIL ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 upairset2IR ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 binunionIR ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 binunionEcases ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 binunionE ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 binunionLsub ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 binunionRsub ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 binintersectI ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 binintersectSubset5 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 binintersectEL ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 binintersectLsub ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 binintersectSubset2 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 binintersectSubset3 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 binintersectER ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 disjointsetsI1 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 binintersectRsub ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 binintersectSubset4 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 binintersectSubset1 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 bs114d ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 setminusI ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 setminusEL ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 setminusER ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 setminusSubset2 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 setminusERneg ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 setminusELneg ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 setminusILneg ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 setminusIRneg ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 setminusLsub ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 setminusSubset1 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 symdiffE ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 symdiffI1 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 symdiffI2 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 symdiffIneg1 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 symdiffIneg2 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 secondinupair ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 setukpairIL ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 setukpairIR ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 kpairiskpair ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 kpairp ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 singletonsubset ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 singletoninpowerset ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 singletoninpowunion ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 upairset2E ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 upairsubunion ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 upairinpowunion ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 ubforcartprodlem1 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 ubforcartprodlem2 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 ubforcartprodlem3 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 cartprodpairin ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 cartprodmempair1 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 cartprodmempair ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 setunionE2 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 setunionsingleton1 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 setunionsingleton2 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 setunionsingleton ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 singletonprop ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 ex1E1 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 ex1I ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 ex1I2 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 singletonsuniq ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 setukpairinjL1 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 kfstsingleton ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 theprop ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 kfstpairEq ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 cartprodfstin ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 setukpairinjL2 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 setukpairinjL ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 setukpairinjR11 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 setukpairinjR12 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 setukpairinjR1 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 upairequniteq ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 setukpairinjR2 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 setukpairinjR ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 ksndsingleton ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 ksndpairEq ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 kpairsurjEq ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 cartprodsndin ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 cartprodpairmemEL ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 cartprodpairmemER ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 cartprodmempaircEq ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 cartprodfstpairEq ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 cartprodsndpairEq ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 cartprodpairsurjEq ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 dpsetconstrI ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 dpsetconstrSub ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 setOfPairsIsBReln ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 dpsetconstrERa ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 dpsetconstrEL1 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 dpsetconstrEL2 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 dpsetconstrER ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 funcImageSingleton ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 apProp ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 app ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 infuncsetfunc ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 ap2p ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 funcinfuncset ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 lamProp ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 lamp ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 lam2p ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 brelnall1 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 brelnall2 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 ex1E2 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 funcGraphProp1 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 funcGraphProp3 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 funcGraphProp2 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 funcextLem ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 funcGraphProp4 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 subbreln ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 eqbreln ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 funcext ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 funcext2 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 ap2apEq1 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 ap2apEq2 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 beta1 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 eta1 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 lam2lamEq ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 beta2 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 eta2 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 iffalseProp1 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 iffalseProp2 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 iftrueProp1 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 iftrueProp2 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 ifSingleton ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 ifp ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 theeq ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 iftrue ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 iffalse ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 iftrueorfalse ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 binintersectT_lem ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 binunionT_lem ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 powersetT_lem ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 setminusT_lem ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 complementT_lem ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 setextT ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 subsetTI ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 powersetTI1 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 powersetTE1 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 complementTI1 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 complementTE1 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 binintersectTELcontra ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 binintersectTERcontra ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 contrasubsetT ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 contrasubsetT1 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 contrasubsetT2 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 contrasubsetT3 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 doubleComplementI1 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 doubleComplementE1 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 doubleComplementSub1 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 doubleComplementSub2 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 doubleComplementEq ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 complementTnotintersectT ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 complementImpComplementIntersect ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 complementSubsetComplementIntersect ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 complementInPowersetComplementIntersect ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 contraSubsetComplement ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 complementTcontraSubset ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 binunionTILcontra ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 binunionTIRcontra ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 inIntersectImpInUnion ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 inIntersectImpInUnion2 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 inIntersectImpInIntersectUnions ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 intersectInPowersetIntersectUnions ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 inComplementUnionImpNotIn1 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 inComplementUnionImpInComplement1 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 binunionTE ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 binunionTEcontra ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 demorgan2a1 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 complementUnionInPowersetComplement ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 demorgan2a2 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 demorgan1a ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 demorgan1b ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 demorgan1 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 demorgan2a ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 demorgan2b2 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 demorgan2b ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 demorgan2 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 woz13rule0 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 woz13rule1 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 woz13rule2 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 woz13rule3 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 woz13rule4 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 woz1_1 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 woz1_2 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 woz1_3 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 woz1_4 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 woz1_5 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 breln1all2 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 breln1SetBreln1 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 choice2fnsingleton ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 setOfPairsIsBReln1 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 breln1all1 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 subbreln1 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 eqbreln1 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 breln1invprop ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 breln1invI ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 breln1invE ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 breln1compprop ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 breln1compI ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 breln1compE ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 breln1compEex ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 breln1unionprop ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 breln1unionIL ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 breln1unionIR ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 breln1unionI ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 breln1unionE ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 breln1unionEcases ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 breln1unionCommutes ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 woz2Ex ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 woz2W ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 woz2A ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 woz2B ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 image1Ex ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 image1Ex1 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 image1Equiv ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 image1E ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 image1I ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 injFuncInInjFuncSet ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 injFuncSetFuncIn ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 injFuncSetFuncInj ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 surjFuncSetFuncIn ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 surjFuncSetFuncSurj ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 leftInvIsSurj ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 surjCantorThm ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 foundation2 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 notinself ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 notinself2 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 omegaSp ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 omegaSclos ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 peano0notS ) =>
% 96.58/13.12 (
% 96.58/13.12 ![
% 96.58/13.12 Xx:$i]:
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 in @
% 96.58/13.12 Xx @ omega ) =>
% 96.58/13.12 (
% 96.58/13.12 ![
% 96.58/13.12 Xy:$i]:
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 in @
% 96.58/13.12 Xy @ omega ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 omegaS @
% 96.58/13.12 Xx ) =
% 96.58/13.12 (
% 96.58/13.12 omegaS @
% 96.58/13.12 Xy ) ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 Xx ) =
% 96.58/13.12 (
% 96.58/13.12 Xy ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 96.58/13.12 thf(zf_stmt_0, negated_conjecture,
% 96.58/13.12 (~( ( setextAx ) =>
% 96.58/13.12 ( ( emptysetAx ) =>
% 96.58/13.12 ( ( setadjoinAx ) =>
% 96.58/13.12 ( ( powersetAx ) =>
% 96.58/13.12 ( ( setunionAx ) =>
% 96.58/13.12 ( ( omega0Ax ) =>
% 96.58/13.12 ( ( omegaSAx ) =>
% 96.58/13.12 ( ( omegaIndAx ) =>
% 96.58/13.12 ( ( replAx ) =>
% 96.58/13.12 ( ( foundationAx ) =>
% 96.58/13.12 ( ( wellorderingAx ) =>
% 96.58/13.12 ( ( descrp ) =>
% 96.58/13.12 ( ( dsetconstrI ) =>
% 96.58/13.12 ( ( dsetconstrEL ) =>
% 96.58/13.12 ( ( dsetconstrER ) =>
% 96.58/13.12 ( ( exuE1 ) =>
% 96.58/13.12 ( ( prop2setE ) =>
% 96.58/13.12 ( ( emptysetE ) =>
% 96.58/13.12 ( ( emptysetimpfalse ) =>
% 96.58/13.12 ( ( notinemptyset ) =>
% 96.58/13.12 ( ( exuE3e ) =>
% 96.58/13.12 ( ( setext ) =>
% 96.58/13.12 ( ( emptyI ) =>
% 96.58/13.12 ( ( noeltsimpempty ) =>
% 96.58/13.12 ( ( setbeta ) =>
% 96.58/13.12 ( ( nonemptyE1 ) =>
% 96.58/13.12 ( ( nonemptyI ) =>
% 96.58/13.12 ( ( nonemptyI1 ) =>
% 96.58/13.12 ( ( setadjoinIL ) =>
% 96.58/13.12 ( ( emptyinunitempty ) =>
% 96.58/13.12 ( ( setadjoinIR ) =>
% 96.58/13.12 ( (
% 96.58/13.12 setadjoinE ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 setadjoinOr ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 setoftrueEq ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 powersetI ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 emptyinPowerset ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 emptyInPowerset ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 powersetE ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 setunionI ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 setunionE ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 subPowSU ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 exuE2 ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 nonemptyImpWitness ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 uniqinunit ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 notinsingleton ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 eqinunit ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 singletonsswitch ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 upairsetE ) =>
% 96.58/13.12 (
% 96.58/13.12 (
% 96.58/13.12 upairsetIL ) =>
% 96.58/13.12 (
% 96.58/13.13 (
% 96.58/13.13 upairsetIR ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 emptyE1 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 vacuousDall ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 quantDeMorgan1 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 quantDeMorgan2 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 quantDeMorgan3 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 quantDeMorgan4 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 prop2setI ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 prop2set2propI ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 notdexE ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 notdallE ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 exuI1 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 exuI3 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 exuI2 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 inCongP ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 in__Cong ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 exuE3u ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 exu__Cong ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 emptyset__Cong ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 setadjoin__Cong ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 powerset__Cong ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 setunion__Cong ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 omega__Cong ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 exuEu ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 descr__Cong ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 dsetconstr__Cong ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 subsetI1 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 eqimpsubset2 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 eqimpsubset1 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 subsetI2 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 emptysetsubset ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 subsetE ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 subsetE2 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 notsubsetI ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 notequalI1 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 notequalI2 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 subsetRefl ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 subsetTrans ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 setadjoinSub ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 setadjoinSub2 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 subset2powerset ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 setextsub ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 subsetemptysetimpeq ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 powersetI1 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 powersetE1 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 inPowerset ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 powersetsubset ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 sepInPowerset ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 sepSubset ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 binunionIL ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 upairset2IR ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 binunionIR ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 binunionEcases ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 binunionE ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 binunionLsub ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 binunionRsub ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 binintersectI ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 binintersectSubset5 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 binintersectEL ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 binintersectLsub ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 binintersectSubset2 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 binintersectSubset3 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 binintersectER ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 disjointsetsI1 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 binintersectRsub ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 binintersectSubset4 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 binintersectSubset1 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 bs114d ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 setminusI ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 setminusEL ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 setminusER ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 setminusSubset2 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 setminusERneg ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 setminusELneg ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 setminusILneg ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 setminusIRneg ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 setminusLsub ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 setminusSubset1 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 symdiffE ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 symdiffI1 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 symdiffI2 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 symdiffIneg1 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 symdiffIneg2 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 secondinupair ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 setukpairIL ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 setukpairIR ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 kpairiskpair ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 kpairp ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 singletonsubset ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 singletoninpowerset ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 singletoninpowunion ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 upairset2E ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 upairsubunion ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 upairinpowunion ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 ubforcartprodlem1 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 ubforcartprodlem2 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 ubforcartprodlem3 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 cartprodpairin ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 cartprodmempair1 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 cartprodmempair ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 setunionE2 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 setunionsingleton1 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 setunionsingleton2 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 setunionsingleton ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 singletonprop ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 ex1E1 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 ex1I ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 ex1I2 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 singletonsuniq ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 setukpairinjL1 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 kfstsingleton ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 theprop ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 kfstpairEq ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 cartprodfstin ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 setukpairinjL2 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 setukpairinjL ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 setukpairinjR11 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 setukpairinjR12 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 setukpairinjR1 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 upairequniteq ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 setukpairinjR2 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 setukpairinjR ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 ksndsingleton ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 ksndpairEq ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 kpairsurjEq ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 cartprodsndin ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 cartprodpairmemEL ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 cartprodpairmemER ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 cartprodmempaircEq ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 cartprodfstpairEq ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 cartprodsndpairEq ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 cartprodpairsurjEq ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 dpsetconstrI ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 dpsetconstrSub ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 setOfPairsIsBReln ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 dpsetconstrERa ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 dpsetconstrEL1 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 dpsetconstrEL2 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 dpsetconstrER ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 funcImageSingleton ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 apProp ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 app ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 infuncsetfunc ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 ap2p ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 funcinfuncset ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 lamProp ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 lamp ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 lam2p ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 brelnall1 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 brelnall2 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 ex1E2 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 funcGraphProp1 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 funcGraphProp3 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 funcGraphProp2 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 funcextLem ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 funcGraphProp4 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 subbreln ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 eqbreln ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 funcext ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 funcext2 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 ap2apEq1 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 ap2apEq2 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 beta1 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 eta1 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 lam2lamEq ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 beta2 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 eta2 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 iffalseProp1 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 iffalseProp2 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 iftrueProp1 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 iftrueProp2 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 ifSingleton ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 ifp ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 theeq ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 iftrue ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 iffalse ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 iftrueorfalse ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 binintersectT_lem ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 binunionT_lem ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 powersetT_lem ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 setminusT_lem ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 complementT_lem ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 setextT ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 subsetTI ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 powersetTI1 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 powersetTE1 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 complementTI1 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 complementTE1 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 binintersectTELcontra ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 binintersectTERcontra ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 contrasubsetT ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 contrasubsetT1 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 contrasubsetT2 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 contrasubsetT3 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 doubleComplementI1 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 doubleComplementE1 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 doubleComplementSub1 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 doubleComplementSub2 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 doubleComplementEq ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 complementTnotintersectT ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 complementImpComplementIntersect ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 complementSubsetComplementIntersect ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 complementInPowersetComplementIntersect ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 contraSubsetComplement ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 complementTcontraSubset ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 binunionTILcontra ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 binunionTIRcontra ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 inIntersectImpInUnion ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 inIntersectImpInUnion2 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 inIntersectImpInIntersectUnions ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 intersectInPowersetIntersectUnions ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 inComplementUnionImpNotIn1 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 inComplementUnionImpInComplement1 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 binunionTE ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 binunionTEcontra ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 demorgan2a1 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 complementUnionInPowersetComplement ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 demorgan2a2 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 demorgan1a ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 demorgan1b ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 demorgan1 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 demorgan2a ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 demorgan2b2 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 demorgan2b ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 demorgan2 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 woz13rule0 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 woz13rule1 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 woz13rule2 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 woz13rule3 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 woz13rule4 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 woz1_1 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 woz1_2 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 woz1_3 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 woz1_4 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 woz1_5 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 breln1all2 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 breln1SetBreln1 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 choice2fnsingleton ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 setOfPairsIsBReln1 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 breln1all1 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 subbreln1 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 eqbreln1 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 breln1invprop ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 breln1invI ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 breln1invE ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 breln1compprop ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 breln1compI ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 breln1compE ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 breln1compEex ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 breln1unionprop ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 breln1unionIL ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 breln1unionIR ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 breln1unionI ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 breln1unionE ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 breln1unionEcases ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 breln1unionCommutes ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 woz2Ex ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 woz2W ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 woz2A ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 woz2B ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 image1Ex ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 image1Ex1 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 image1Equiv ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 image1E ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 image1I ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 injFuncInInjFuncSet ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 injFuncSetFuncIn ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 injFuncSetFuncInj ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 surjFuncSetFuncIn ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 surjFuncSetFuncSurj ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 leftInvIsSurj ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 surjCantorThm ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 foundation2 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 notinself ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 notinself2 ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 omegaSp ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 omegaSclos ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 peano0notS ) =>
% 96.58/13.13 (
% 96.58/13.13 ![
% 96.58/13.13 Xx:$i]:
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 in @
% 96.58/13.13 Xx @
% 96.58/13.13 omega ) =>
% 96.58/13.13 (
% 96.58/13.13 ![
% 96.58/13.13 Xy:$i]:
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 in @
% 96.58/13.13 Xy @
% 96.58/13.13 omega ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 omegaS @
% 96.58/13.13 Xx ) =
% 96.58/13.13 (
% 96.58/13.13 omegaS @
% 96.58/13.13 Xy ) ) =>
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 Xx ) =
% 96.58/13.13 (
% 96.58/13.13 Xy ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )),
% 96.58/13.13 inference('cnf.neg', [status(esa)], [peanoSinj])).
% 96.58/13.13 thf(zip_derived_cl0, plain,
% 96.58/13.13 (~ (((setextAx) =>
% 96.58/13.13 (((emptysetAx) =>
% 96.58/13.13 (((setadjoinAx) =>
% 96.58/13.13 (((powersetAx) =>
% 96.58/13.13 (((setunionAx) =>
% 96.58/13.13 (((omega0Ax) =>
% 96.58/13.13 (((omegaSAx) =>
% 96.58/13.13 (((omegaIndAx) =>
% 96.58/13.13 (((replAx) =>
% 96.58/13.13 (((foundationAx) =>
% 96.58/13.13 (((wellorderingAx) =>
% 96.58/13.13 (((descrp) =>
% 96.58/13.13 (((dsetconstrI) =>
% 96.58/13.13 (((dsetconstrEL) =>
% 96.58/13.13 (((dsetconstrER) =>
% 96.58/13.13 (((exuE1) =>
% 96.58/13.13 (((prop2setE) =>
% 96.58/13.13 (((emptysetE) =>
% 96.58/13.13 (((emptysetimpfalse) =>
% 96.58/13.13 (((notinemptyset) =>
% 96.58/13.13 (((exuE3e) =>
% 96.58/13.13 (((setext) =>
% 96.58/13.13 (((emptyI) =>
% 96.58/13.13 (((noeltsimpempty) =>
% 96.58/13.13 (((setbeta) =>
% 96.58/13.13 (((nonemptyE1) =>
% 96.58/13.13 (((nonemptyI) =>
% 96.58/13.13 (((nonemptyI1) =>
% 96.58/13.13 (((setadjoinIL) =>
% 96.58/13.13 (((emptyinunitempty) =>
% 96.58/13.13 ((
% 96.58/13.13 (setadjoinIR) =>
% 96.58/13.13 ((
% 96.58/13.13 (setadjoinE) =>
% 96.58/13.13 ((
% 96.58/13.13 (setadjoinOr) =>
% 96.58/13.13 ((
% 96.58/13.13 (setoftrueEq) =>
% 96.58/13.13 ((
% 96.58/13.13 (powersetI) =>
% 96.58/13.13 ((
% 96.58/13.13 (emptyinPowerset) =>
% 96.58/13.13 ((
% 96.58/13.13 (emptyInPowerset) =>
% 96.58/13.13 ((
% 96.58/13.13 (powersetE) =>
% 96.58/13.13 ((
% 96.58/13.13 (setunionI) =>
% 96.58/13.13 ((
% 96.58/13.13 (setunionE) =>
% 96.58/13.13 ((
% 96.58/13.13 (subPowSU) =>
% 96.58/13.13 ((
% 96.58/13.13 (exuE2) =>
% 96.58/13.13 ((
% 96.58/13.13 (nonemptyImpWitness) =>
% 96.58/13.13 ((
% 96.58/13.13 (uniqinunit) =>
% 96.58/13.13 ((
% 96.58/13.13 (notinsingleton) =>
% 96.58/13.13 ((
% 96.58/13.13 (eqinunit) =>
% 96.58/13.13 ((
% 96.58/13.13 (singletonsswitch) =>
% 96.58/13.13 ((
% 96.58/13.13 (upairsetE) =>
% 96.58/13.13 ((
% 96.58/13.13 (upairsetIL) =>
% 96.58/13.13 ((
% 96.58/13.13 (upairsetIR) =>
% 96.58/13.13 ((
% 96.58/13.13 (emptyE1) =>
% 96.58/13.13 ((
% 96.58/13.13 (vacuousDall) =>
% 96.58/13.13 ((
% 96.58/13.13 (quantDeMorgan1) =>
% 96.58/13.13 ((
% 96.58/13.13 (quantDeMorgan2) =>
% 96.58/13.13 ((
% 96.58/13.13 (quantDeMorgan3) =>
% 96.58/13.13 ((
% 96.58/13.13 (quantDeMorgan4) =>
% 96.58/13.13 ((
% 96.58/13.13 (prop2setI) =>
% 96.58/13.13 ((
% 96.58/13.13 (prop2set2propI) =>
% 96.58/13.13 ((
% 96.58/13.13 (notdexE) =>
% 96.58/13.13 ((
% 96.58/13.13 (notdallE) =>
% 96.58/13.13 ((
% 96.58/13.13 (exuI1) =>
% 96.58/13.13 ((
% 96.58/13.13 (exuI3) =>
% 96.58/13.13 ((
% 96.58/13.13 (exuI2) =>
% 96.58/13.13 ((
% 96.58/13.13 (inCongP) =>
% 96.58/13.13 ((
% 96.58/13.13 (in__Cong) =>
% 96.58/13.13 ((
% 96.58/13.13 (exuE3u) =>
% 96.58/13.13 ((
% 96.58/13.13 (exu__Cong) =>
% 96.58/13.13 ((
% 96.58/13.13 (emptyset__Cong) =>
% 96.58/13.13 ((
% 96.58/13.13 (setadjoin__Cong) =>
% 96.58/13.13 ((
% 96.58/13.13 (powerset__Cong) =>
% 96.58/13.13 ((
% 96.58/13.13 (setunion__Cong) =>
% 96.58/13.13 ((
% 96.58/13.13 (omega__Cong) =>
% 96.58/13.13 ((
% 96.58/13.13 (exuEu) =>
% 96.58/13.13 ((
% 96.58/13.13 (descr__Cong) =>
% 96.58/13.13 ((
% 96.58/13.13 (dsetconstr__Cong) =>
% 96.58/13.13 ((
% 96.58/13.13 (subsetI1) =>
% 96.58/13.13 ((
% 96.58/13.13 (eqimpsubset2) =>
% 96.58/13.13 ((
% 96.58/13.13 (eqimpsubset1) =>
% 96.58/13.13 ((
% 96.58/13.13 (subsetI2) =>
% 96.58/13.13 ((
% 96.58/13.13 (emptysetsubset) =>
% 96.58/13.13 ((
% 96.58/13.13 (subsetE) =>
% 96.58/13.13 ((
% 96.58/13.13 (subsetE2) =>
% 96.58/13.13 ((
% 96.58/13.13 (notsubsetI) =>
% 96.58/13.13 ((
% 96.58/13.13 (notequalI1) =>
% 96.58/13.13 ((
% 96.58/13.13 (notequalI2) =>
% 96.58/13.13 ((
% 96.58/13.13 (subsetRefl) =>
% 96.58/13.13 ((
% 96.58/13.13 (subsetTrans) =>
% 96.58/13.13 ((
% 96.58/13.13 (setadjoinSub) =>
% 96.58/13.13 ((
% 96.58/13.13 (setadjoinSub2) =>
% 96.58/13.13 ((
% 96.58/13.13 (subset2powerset) =>
% 96.58/13.13 ((
% 96.58/13.13 (setextsub) =>
% 96.58/13.13 ((
% 96.58/13.13 (subsetemptysetimpeq) =>
% 96.58/13.13 ((
% 96.58/13.13 (powersetI1) =>
% 96.58/13.13 ((
% 96.58/13.13 (powersetE1) =>
% 96.58/13.13 ((
% 96.58/13.13 (inPowerset) =>
% 96.58/13.13 ((
% 96.58/13.13 (powersetsubset) =>
% 96.58/13.13 ((
% 96.58/13.13 (sepInPowerset) =>
% 96.58/13.13 ((
% 96.58/13.13 (sepSubset) =>
% 96.58/13.13 ((
% 96.58/13.13 (binunionIL) =>
% 96.58/13.13 ((
% 96.58/13.13 (upairset2IR) =>
% 96.58/13.13 ((
% 96.58/13.13 (binunionIR) =>
% 96.58/13.13 ((
% 96.58/13.13 (binunionEcases) =>
% 96.58/13.13 ((
% 96.58/13.13 (binunionE) =>
% 96.58/13.13 ((
% 96.58/13.13 (binunionLsub) =>
% 96.58/13.13 ((
% 96.58/13.13 (binunionRsub) =>
% 96.58/13.13 ((
% 96.58/13.13 (binintersectI) =>
% 96.58/13.13 ((
% 96.58/13.13 (binintersectSubset5) =>
% 96.58/13.13 ((
% 96.58/13.13 (binintersectEL) =>
% 96.58/13.13 ((
% 96.58/13.13 (binintersectLsub) =>
% 96.58/13.13 ((
% 96.58/13.13 (binintersectSubset2) =>
% 96.58/13.13 ((
% 96.58/13.13 (binintersectSubset3) =>
% 96.58/13.13 ((
% 96.58/13.13 (binintersectER) =>
% 96.58/13.13 ((
% 96.58/13.13 (disjointsetsI1) =>
% 96.58/13.13 ((
% 96.58/13.13 (binintersectRsub) =>
% 96.58/13.13 ((
% 96.58/13.13 (binintersectSubset4) =>
% 96.58/13.13 ((
% 96.58/13.13 (binintersectSubset1) =>
% 96.58/13.13 ((
% 96.58/13.13 (bs114d) =>
% 96.58/13.13 ((
% 96.58/13.13 (setminusI) =>
% 96.58/13.13 ((
% 96.58/13.13 (setminusEL) =>
% 96.58/13.13 ((
% 96.58/13.13 (setminusER) =>
% 96.58/13.13 ((
% 96.58/13.13 (setminusSubset2) =>
% 96.58/13.13 ((
% 96.58/13.13 (setminusERneg) =>
% 96.58/13.13 ((
% 96.58/13.13 (setminusELneg) =>
% 96.58/13.13 ((
% 96.58/13.13 (setminusILneg) =>
% 96.58/13.13 ((
% 96.58/13.13 (setminusIRneg) =>
% 96.58/13.13 ((
% 96.58/13.13 (setminusLsub) =>
% 96.58/13.13 ((
% 96.58/13.13 (setminusSubset1) =>
% 96.58/13.13 ((
% 96.58/13.13 (symdiffE) =>
% 96.58/13.13 ((
% 96.58/13.13 (symdiffI1) =>
% 96.58/13.13 ((
% 96.58/13.13 (symdiffI2) =>
% 96.58/13.13 ((
% 96.58/13.13 (symdiffIneg1) =>
% 96.58/13.13 ((
% 96.58/13.13 (symdiffIneg2) =>
% 96.58/13.13 ((
% 96.58/13.13 (secondinupair) =>
% 96.58/13.13 ((
% 96.58/13.13 (setukpairIL) =>
% 96.58/13.13 ((
% 96.58/13.13 (setukpairIR) =>
% 96.58/13.13 ((
% 96.58/13.13 (kpairiskpair) =>
% 96.58/13.13 ((
% 96.58/13.13 (kpairp) =>
% 96.58/13.13 ((
% 96.58/13.13 (singletonsubset) =>
% 96.58/13.13 ((
% 96.58/13.13 (singletoninpowerset) =>
% 96.58/13.13 ((
% 96.58/13.13 (singletoninpowunion) =>
% 96.58/13.13 ((
% 96.58/13.13 (upairset2E) =>
% 96.58/13.13 ((
% 96.58/13.13 (upairsubunion) =>
% 96.58/13.13 ((
% 96.58/13.13 (upairinpowunion) =>
% 96.58/13.13 ((
% 96.58/13.13 (ubforcartprodlem1) =>
% 96.58/13.13 ((
% 96.58/13.13 (ubforcartprodlem2) =>
% 96.58/13.13 ((
% 96.58/13.13 (ubforcartprodlem3) =>
% 96.58/13.13 ((
% 96.58/13.13 (cartprodpairin) =>
% 96.58/13.13 ((
% 96.58/13.13 (cartprodmempair1) =>
% 96.58/13.13 ((
% 96.58/13.13 (cartprodmempair) =>
% 96.58/13.13 ((
% 96.58/13.13 (setunionE2) =>
% 96.58/13.13 ((
% 96.58/13.13 (setunionsingleton1) =>
% 96.58/13.13 ((
% 96.58/13.13 (setunionsingleton2) =>
% 96.58/13.13 ((
% 96.58/13.13 (setunionsingleton) =>
% 96.58/13.13 ((
% 96.58/13.13 (singletonprop) =>
% 96.58/13.13 ((
% 96.58/13.13 (ex1E1) =>
% 96.58/13.13 ((
% 96.58/13.13 (ex1I) =>
% 96.58/13.13 ((
% 96.58/13.13 (ex1I2) =>
% 96.58/13.13 ((
% 96.58/13.13 (singletonsuniq) =>
% 96.58/13.13 ((
% 96.58/13.13 (setukpairinjL1) =>
% 96.58/13.13 ((
% 96.58/13.13 (kfstsingleton) =>
% 96.58/13.13 ((
% 96.58/13.13 (theprop) =>
% 96.58/13.13 ((
% 96.58/13.13 (kfstpairEq) =>
% 96.58/13.13 ((
% 96.58/13.13 (cartprodfstin) =>
% 96.58/13.13 ((
% 96.58/13.13 (setukpairinjL2) =>
% 96.58/13.13 ((
% 96.58/13.13 (setukpairinjL) =>
% 96.58/13.13 ((
% 96.58/13.13 (setukpairinjR11) =>
% 96.58/13.13 ((
% 96.58/13.13 (setukpairinjR12) =>
% 96.58/13.13 ((
% 96.58/13.13 (setukpairinjR1) =>
% 96.58/13.13 ((
% 96.58/13.13 (upairequniteq) =>
% 96.58/13.13 ((
% 96.58/13.13 (setukpairinjR2) =>
% 96.58/13.13 ((
% 96.58/13.13 (setukpairinjR) =>
% 96.58/13.13 ((
% 96.58/13.13 (ksndsingleton) =>
% 96.58/13.13 ((
% 96.58/13.13 (ksndpairEq) =>
% 96.58/13.13 ((
% 96.58/13.13 (kpairsurjEq) =>
% 96.58/13.13 ((
% 96.58/13.13 (cartprodsndin) =>
% 96.58/13.13 ((
% 96.58/13.13 (cartprodpairmemEL) =>
% 96.58/13.13 ((
% 96.58/13.13 (cartprodpairmemER) =>
% 96.58/13.13 ((
% 96.58/13.13 (cartprodmempaircEq) =>
% 96.58/13.13 ((
% 96.58/13.13 (cartprodfstpairEq) =>
% 96.58/13.13 ((
% 96.58/13.13 (cartprodsndpairEq) =>
% 96.58/13.13 ((
% 96.58/13.13 (cartprodpairsurjEq) =>
% 96.58/13.13 ((
% 96.58/13.13 (dpsetconstrI) =>
% 96.58/13.13 ((
% 96.58/13.13 (dpsetconstrSub) =>
% 96.58/13.13 ((
% 96.58/13.13 (setOfPairsIsBReln) =>
% 96.58/13.13 ((
% 96.58/13.13 (dpsetconstrERa) =>
% 96.58/13.13 ((
% 96.58/13.13 (dpsetconstrEL1) =>
% 96.58/13.13 ((
% 96.58/13.13 (dpsetconstrEL2) =>
% 96.58/13.13 ((
% 96.58/13.13 (dpsetconstrER) =>
% 96.58/13.13 ((
% 96.58/13.13 (funcImageSingleton) =>
% 96.58/13.13 ((
% 96.58/13.13 (apProp) =>
% 96.58/13.13 ((
% 96.58/13.13 (app) =>
% 96.58/13.13 ((
% 96.58/13.13 (infuncsetfunc) =>
% 96.58/13.13 ((
% 96.58/13.13 (ap2p) =>
% 96.58/13.13 ((
% 96.58/13.13 (funcinfuncset) =>
% 96.58/13.13 ((
% 96.58/13.13 (lamProp) =>
% 96.58/13.13 ((
% 96.58/13.13 (lamp) =>
% 96.58/13.13 ((
% 96.58/13.13 (lam2p) =>
% 96.58/13.13 ((
% 96.58/13.13 (brelnall1) =>
% 96.58/13.13 ((
% 96.58/13.13 (brelnall2) =>
% 96.58/13.13 ((
% 96.58/13.13 (ex1E2) =>
% 96.58/13.13 ((
% 96.58/13.13 (funcGraphProp1) =>
% 96.58/13.13 ((
% 96.58/13.13 (funcGraphProp3) =>
% 96.58/13.13 ((
% 96.58/13.13 (funcGraphProp2) =>
% 96.58/13.13 ((
% 96.58/13.13 (funcextLem) =>
% 96.58/13.13 ((
% 96.58/13.13 (funcGraphProp4) =>
% 96.58/13.13 ((
% 96.58/13.13 (subbreln) =>
% 96.58/13.13 ((
% 96.58/13.13 (eqbreln) =>
% 96.58/13.13 ((
% 96.58/13.13 (funcext) =>
% 96.58/13.13 ((
% 96.58/13.13 (funcext2) =>
% 96.58/13.13 ((
% 96.58/13.13 (ap2apEq1) =>
% 96.58/13.13 ((
% 96.58/13.13 (ap2apEq2) =>
% 96.58/13.13 ((
% 96.58/13.13 (beta1) =>
% 96.58/13.13 ((
% 96.58/13.13 (eta1) =>
% 96.58/13.13 ((
% 96.58/13.13 (lam2lamEq) =>
% 96.58/13.13 ((
% 96.58/13.13 (beta2) =>
% 96.58/13.13 ((
% 96.58/13.13 (eta2) =>
% 96.58/13.13 ((
% 96.58/13.13 (iffalseProp1) =>
% 96.58/13.13 ((
% 96.58/13.13 (iffalseProp2) =>
% 96.58/13.13 ((
% 96.58/13.13 (iftrueProp1) =>
% 96.58/13.13 ((
% 96.58/13.13 (iftrueProp2) =>
% 96.58/13.13 ((
% 96.58/13.13 (ifSingleton) =>
% 96.58/13.13 ((
% 96.58/13.13 (ifp) =>
% 96.58/13.13 ((
% 96.58/13.13 (theeq) =>
% 96.58/13.13 ((
% 96.58/13.13 (iftrue) =>
% 96.58/13.13 ((
% 96.58/13.13 (iffalse) =>
% 96.58/13.13 ((
% 96.58/13.13 (iftrueorfalse) =>
% 96.58/13.13 ((
% 96.58/13.13 (binintersectT_lem) =>
% 96.58/13.13 ((
% 96.58/13.13 (binunionT_lem) =>
% 96.58/13.13 ((
% 96.58/13.13 (powersetT_lem) =>
% 96.58/13.13 ((
% 96.58/13.13 (setminusT_lem) =>
% 96.58/13.13 ((
% 96.58/13.13 (complementT_lem) =>
% 96.58/13.13 ((
% 96.58/13.13 (setextT) =>
% 96.58/13.13 ((
% 96.58/13.13 (subsetTI) =>
% 96.58/13.13 ((
% 96.58/13.13 (powersetTI1) =>
% 96.58/13.13 ((
% 96.58/13.13 (powersetTE1) =>
% 96.58/13.13 ((
% 96.58/13.13 (complementTI1) =>
% 96.58/13.13 ((
% 96.58/13.13 (complementTE1) =>
% 96.58/13.13 ((
% 96.58/13.13 (binintersectTELcontra) =>
% 96.58/13.13 ((
% 96.58/13.13 (binintersectTERcontra) =>
% 96.58/13.13 ((
% 96.58/13.13 (contrasubsetT) =>
% 96.58/13.13 ((
% 96.58/13.13 (contrasubsetT1) =>
% 96.58/13.13 ((
% 96.58/13.13 (contrasubsetT2) =>
% 96.58/13.13 ((
% 96.58/13.13 (contrasubsetT3) =>
% 96.58/13.13 ((
% 96.58/13.13 (doubleComplementI1) =>
% 96.58/13.13 ((
% 96.58/13.13 (doubleComplementE1) =>
% 96.58/13.13 ((
% 96.58/13.13 (doubleComplementSub1) =>
% 96.58/13.13 ((
% 96.58/13.13 (doubleComplementSub2) =>
% 96.58/13.13 ((
% 96.58/13.13 (doubleComplementEq) =>
% 96.58/13.13 ((
% 96.58/13.13 (complementTnotintersectT) =>
% 96.58/13.13 ((
% 96.58/13.13 (complementImpComplementIntersect) =>
% 96.58/13.13 ((
% 96.58/13.13 (complementSubsetComplementIntersect) =>
% 96.58/13.13 ((
% 96.58/13.13 (complementInPowersetComplementIntersect) =>
% 96.58/13.13 ((
% 96.58/13.13 (contraSubsetComplement) =>
% 96.58/13.13 ((
% 96.58/13.13 (complementTcontraSubset) =>
% 96.58/13.13 ((
% 96.58/13.13 (binunionTILcontra) =>
% 96.58/13.13 ((
% 96.58/13.13 (binunionTIRcontra) =>
% 96.58/13.13 ((
% 96.58/13.13 (inIntersectImpInUnion) =>
% 96.58/13.13 ((
% 96.58/13.13 (inIntersectImpInUnion2) =>
% 96.58/13.13 ((
% 96.58/13.13 (inIntersectImpInIntersectUnions) =>
% 96.58/13.13 ((
% 96.58/13.13 (intersectInPowersetIntersectUnions) =>
% 96.58/13.13 ((
% 96.58/13.13 (inComplementUnionImpNotIn1) =>
% 96.58/13.13 ((
% 96.58/13.13 (inComplementUnionImpInComplement1) =>
% 96.58/13.13 ((
% 96.58/13.13 (binunionTE) =>
% 96.58/13.13 ((
% 96.58/13.13 (binunionTEcontra) =>
% 96.58/13.13 ((
% 96.58/13.13 (demorgan2a1) =>
% 96.58/13.13 ((
% 96.58/13.13 (complementUnionInPowersetComplement) =>
% 96.58/13.13 ((
% 96.58/13.13 (demorgan2a2) =>
% 96.58/13.13 ((
% 96.58/13.13 (demorgan1a) =>
% 96.58/13.13 ((
% 96.58/13.13 (demorgan1b) =>
% 96.58/13.13 ((
% 96.58/13.13 (demorgan1) =>
% 96.58/13.13 ((
% 96.58/13.13 (demorgan2a) =>
% 96.58/13.13 ((
% 96.58/13.13 (demorgan2b2) =>
% 96.58/13.13 ((
% 96.58/13.13 (demorgan2b) =>
% 96.58/13.13 ((
% 96.58/13.13 (demorgan2) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz13rule0) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz13rule1) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz13rule2) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz13rule3) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz13rule4) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz1_1) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz1_2) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz1_3) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz1_4) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz1_5) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1all2) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1SetBreln1) =>
% 96.58/13.13 ((
% 96.58/13.13 (choice2fnsingleton) =>
% 96.58/13.13 ((
% 96.58/13.13 (setOfPairsIsBReln1) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1all1) =>
% 96.58/13.13 ((
% 96.58/13.13 (subbreln1) =>
% 96.58/13.13 ((
% 96.58/13.13 (eqbreln1) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1invprop) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1invI) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1invE) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1compprop) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1compI) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1compE) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1compEex) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1unionprop) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1unionIL) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1unionIR) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1unionI) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1unionE) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1unionEcases) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1unionCommutes) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz2Ex) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz2W) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz2A) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz2B) =>
% 96.58/13.13 ((
% 96.58/13.13 (image1Ex) =>
% 96.58/13.13 ((
% 96.58/13.13 (image1Ex1) =>
% 96.58/13.13 ((
% 96.58/13.13 (image1Equiv) =>
% 96.58/13.13 ((
% 96.58/13.13 (image1E) =>
% 96.58/13.13 ((
% 96.58/13.13 (image1I) =>
% 96.58/13.13 ((
% 96.58/13.13 (injFuncInInjFuncSet) =>
% 96.58/13.13 ((
% 96.58/13.13 (injFuncSetFuncIn) =>
% 96.58/13.13 ((
% 96.58/13.13 (injFuncSetFuncInj) =>
% 96.58/13.13 ((
% 96.58/13.13 (surjFuncSetFuncIn) =>
% 96.58/13.13 ((
% 96.58/13.13 (surjFuncSetFuncSurj) =>
% 96.58/13.13 ((
% 96.58/13.13 (leftInvIsSurj) =>
% 96.58/13.13 ((
% 96.58/13.13 (surjCantorThm) =>
% 96.58/13.13 ((
% 96.58/13.13 (foundation2) =>
% 96.58/13.13 ((
% 96.58/13.13 (notinself) =>
% 96.58/13.13 ((
% 96.58/13.13 (notinself2) =>
% 96.58/13.13 ((
% 96.58/13.13 (omegaSp) =>
% 96.58/13.13 ((
% 96.58/13.13 (omegaSclos) =>
% 96.58/13.13 ((
% 96.58/13.13 (peano0notS) =>
% 96.58/13.13 ((
% 96.58/13.13 (!!) @ (
% 96.58/13.13 ^[Y0 : $i]:
% 96.58/13.13 ((
% 96.58/13.13 (in @
% 96.58/13.13 Y0 @
% 96.58/13.13 omega) =>
% 96.58/13.13 ((
% 96.58/13.13 (!!) @ (
% 96.58/13.13 ^[Y1 : $i]:
% 96.58/13.13 ((
% 96.58/13.13 (in @
% 96.58/13.13 Y1 @
% 96.58/13.13 omega) =>
% 96.58/13.13 ((
% 96.58/13.13 ((
% 96.58/13.13 (omegaS @
% 96.58/13.13 Y0) =
% 96.58/13.13 (omegaS @
% 96.58/13.13 Y1))) =>
% 96.58/13.13 ((
% 96.58/13.13 (Y0) =
% 96.58/13.13 (Y1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 96.58/13.13 inference('cnf', [status(esa)], [zf_stmt_0])).
% 96.58/13.13 thf(zip_derived_cl1, plain,
% 96.58/13.13 (~ (((setextAx) =>
% 96.58/13.13 (((emptysetAx) =>
% 96.58/13.13 (((setadjoinAx) =>
% 96.58/13.13 (((powersetAx) =>
% 96.58/13.13 (((setunionAx) =>
% 96.58/13.13 (((omega0Ax) =>
% 96.58/13.13 (((omegaSAx) =>
% 96.58/13.13 (((omegaIndAx) =>
% 96.58/13.13 (((replAx) =>
% 96.58/13.13 (((foundationAx) =>
% 96.58/13.13 (((wellorderingAx) =>
% 96.58/13.13 (((descrp) =>
% 96.58/13.13 (((dsetconstrI) =>
% 96.58/13.13 (((dsetconstrEL) =>
% 96.58/13.13 (((dsetconstrER) =>
% 96.58/13.13 (((exuE1) =>
% 96.58/13.13 (((prop2setE) =>
% 96.58/13.13 (((emptysetE) =>
% 96.58/13.13 (((emptysetimpfalse) =>
% 96.58/13.13 (((notinemptyset) =>
% 96.58/13.13 (((exuE3e) =>
% 96.58/13.13 (((setext) =>
% 96.58/13.13 (((emptyI) =>
% 96.58/13.13 (((noeltsimpempty) =>
% 96.58/13.13 (((setbeta) =>
% 96.58/13.13 (((nonemptyE1) =>
% 96.58/13.13 (((nonemptyI) =>
% 96.58/13.13 (((nonemptyI1) =>
% 96.58/13.13 (((setadjoinIL) =>
% 96.58/13.13 (((emptyinunitempty) =>
% 96.58/13.13 ((
% 96.58/13.13 (setadjoinIR) =>
% 96.58/13.13 ((
% 96.58/13.13 (setadjoinE) =>
% 96.58/13.13 ((
% 96.58/13.13 (setadjoinOr) =>
% 96.58/13.13 ((
% 96.58/13.13 (setoftrueEq) =>
% 96.58/13.13 ((
% 96.58/13.13 (powersetI) =>
% 96.58/13.13 ((
% 96.58/13.13 (emptyinPowerset) =>
% 96.58/13.13 ((
% 96.58/13.13 (emptyInPowerset) =>
% 96.58/13.13 ((
% 96.58/13.13 (powersetE) =>
% 96.58/13.13 ((
% 96.58/13.13 (setunionI) =>
% 96.58/13.13 ((
% 96.58/13.13 (setunionE) =>
% 96.58/13.13 ((
% 96.58/13.13 (subPowSU) =>
% 96.58/13.13 ((
% 96.58/13.13 (exuE2) =>
% 96.58/13.13 ((
% 96.58/13.13 (nonemptyImpWitness) =>
% 96.58/13.13 ((
% 96.58/13.13 (uniqinunit) =>
% 96.58/13.13 ((
% 96.58/13.13 (notinsingleton) =>
% 96.58/13.13 ((
% 96.58/13.13 (eqinunit) =>
% 96.58/13.13 ((
% 96.58/13.13 (singletonsswitch) =>
% 96.58/13.13 ((
% 96.58/13.13 (upairsetE) =>
% 96.58/13.13 ((
% 96.58/13.13 (upairsetIL) =>
% 96.58/13.13 ((
% 96.58/13.13 (upairsetIR) =>
% 96.58/13.13 ((
% 96.58/13.13 (emptyE1) =>
% 96.58/13.13 ((
% 96.58/13.13 (vacuousDall) =>
% 96.58/13.13 ((
% 96.58/13.13 (quantDeMorgan1) =>
% 96.58/13.13 ((
% 96.58/13.13 (quantDeMorgan2) =>
% 96.58/13.13 ((
% 96.58/13.13 (quantDeMorgan3) =>
% 96.58/13.13 ((
% 96.58/13.13 (quantDeMorgan4) =>
% 96.58/13.13 ((
% 96.58/13.13 (prop2setI) =>
% 96.58/13.13 ((
% 96.58/13.13 (prop2set2propI) =>
% 96.58/13.13 ((
% 96.58/13.13 (notdexE) =>
% 96.58/13.13 ((
% 96.58/13.13 (notdallE) =>
% 96.58/13.13 ((
% 96.58/13.13 (exuI1) =>
% 96.58/13.13 ((
% 96.58/13.13 (exuI3) =>
% 96.58/13.13 ((
% 96.58/13.13 (exuI2) =>
% 96.58/13.13 ((
% 96.58/13.13 (inCongP) =>
% 96.58/13.13 ((
% 96.58/13.13 (in__Cong) =>
% 96.58/13.13 ((
% 96.58/13.13 (exuE3u) =>
% 96.58/13.13 ((
% 96.58/13.13 (exu__Cong) =>
% 96.58/13.13 ((
% 96.58/13.13 (emptyset__Cong) =>
% 96.58/13.13 ((
% 96.58/13.13 (setadjoin__Cong) =>
% 96.58/13.13 ((
% 96.58/13.13 (powerset__Cong) =>
% 96.58/13.13 ((
% 96.58/13.13 (setunion__Cong) =>
% 96.58/13.13 ((
% 96.58/13.13 (omega__Cong) =>
% 96.58/13.13 ((
% 96.58/13.13 (exuEu) =>
% 96.58/13.13 ((
% 96.58/13.13 (descr__Cong) =>
% 96.58/13.13 ((
% 96.58/13.13 (dsetconstr__Cong) =>
% 96.58/13.13 ((
% 96.58/13.13 (subsetI1) =>
% 96.58/13.13 ((
% 96.58/13.13 (eqimpsubset2) =>
% 96.58/13.13 ((
% 96.58/13.13 (eqimpsubset1) =>
% 96.58/13.13 ((
% 96.58/13.13 (subsetI2) =>
% 96.58/13.13 ((
% 96.58/13.13 (emptysetsubset) =>
% 96.58/13.13 ((
% 96.58/13.13 (subsetE) =>
% 96.58/13.13 ((
% 96.58/13.13 (subsetE2) =>
% 96.58/13.13 ((
% 96.58/13.13 (notsubsetI) =>
% 96.58/13.13 ((
% 96.58/13.13 (notequalI1) =>
% 96.58/13.13 ((
% 96.58/13.13 (notequalI2) =>
% 96.58/13.13 ((
% 96.58/13.13 (subsetRefl) =>
% 96.58/13.13 ((
% 96.58/13.13 (subsetTrans) =>
% 96.58/13.13 ((
% 96.58/13.13 (setadjoinSub) =>
% 96.58/13.13 ((
% 96.58/13.13 (setadjoinSub2) =>
% 96.58/13.13 ((
% 96.58/13.13 (subset2powerset) =>
% 96.58/13.13 ((
% 96.58/13.13 (setextsub) =>
% 96.58/13.13 ((
% 96.58/13.13 (subsetemptysetimpeq) =>
% 96.58/13.13 ((
% 96.58/13.13 (powersetI1) =>
% 96.58/13.13 ((
% 96.58/13.13 (powersetE1) =>
% 96.58/13.13 ((
% 96.58/13.13 (inPowerset) =>
% 96.58/13.13 ((
% 96.58/13.13 (powersetsubset) =>
% 96.58/13.13 ((
% 96.58/13.13 (sepInPowerset) =>
% 96.58/13.13 ((
% 96.58/13.13 (sepSubset) =>
% 96.58/13.13 ((
% 96.58/13.13 (binunionIL) =>
% 96.58/13.13 ((
% 96.58/13.13 (upairset2IR) =>
% 96.58/13.13 ((
% 96.58/13.13 (binunionIR) =>
% 96.58/13.13 ((
% 96.58/13.13 (binunionEcases) =>
% 96.58/13.13 ((
% 96.58/13.13 (binunionE) =>
% 96.58/13.13 ((
% 96.58/13.13 (binunionLsub) =>
% 96.58/13.13 ((
% 96.58/13.13 (binunionRsub) =>
% 96.58/13.13 ((
% 96.58/13.13 (binintersectI) =>
% 96.58/13.13 ((
% 96.58/13.13 (binintersectSubset5) =>
% 96.58/13.13 ((
% 96.58/13.13 (binintersectEL) =>
% 96.58/13.13 ((
% 96.58/13.13 (binintersectLsub) =>
% 96.58/13.13 ((
% 96.58/13.13 (binintersectSubset2) =>
% 96.58/13.13 ((
% 96.58/13.13 (binintersectSubset3) =>
% 96.58/13.13 ((
% 96.58/13.13 (binintersectER) =>
% 96.58/13.13 ((
% 96.58/13.13 (disjointsetsI1) =>
% 96.58/13.13 ((
% 96.58/13.13 (binintersectRsub) =>
% 96.58/13.13 ((
% 96.58/13.13 (binintersectSubset4) =>
% 96.58/13.13 ((
% 96.58/13.13 (binintersectSubset1) =>
% 96.58/13.13 ((
% 96.58/13.13 (bs114d) =>
% 96.58/13.13 ((
% 96.58/13.13 (setminusI) =>
% 96.58/13.13 ((
% 96.58/13.13 (setminusEL) =>
% 96.58/13.13 ((
% 96.58/13.13 (setminusER) =>
% 96.58/13.13 ((
% 96.58/13.13 (setminusSubset2) =>
% 96.58/13.13 ((
% 96.58/13.13 (setminusERneg) =>
% 96.58/13.13 ((
% 96.58/13.13 (setminusELneg) =>
% 96.58/13.13 ((
% 96.58/13.13 (setminusILneg) =>
% 96.58/13.13 ((
% 96.58/13.13 (setminusIRneg) =>
% 96.58/13.13 ((
% 96.58/13.13 (setminusLsub) =>
% 96.58/13.13 ((
% 96.58/13.13 (setminusSubset1) =>
% 96.58/13.13 ((
% 96.58/13.13 (symdiffE) =>
% 96.58/13.13 ((
% 96.58/13.13 (symdiffI1) =>
% 96.58/13.13 ((
% 96.58/13.13 (symdiffI2) =>
% 96.58/13.13 ((
% 96.58/13.13 (symdiffIneg1) =>
% 96.58/13.13 ((
% 96.58/13.13 (symdiffIneg2) =>
% 96.58/13.13 ((
% 96.58/13.13 (secondinupair) =>
% 96.58/13.13 ((
% 96.58/13.13 (setukpairIL) =>
% 96.58/13.13 ((
% 96.58/13.13 (setukpairIR) =>
% 96.58/13.13 ((
% 96.58/13.13 (kpairiskpair) =>
% 96.58/13.13 ((
% 96.58/13.13 (kpairp) =>
% 96.58/13.13 ((
% 96.58/13.13 (singletonsubset) =>
% 96.58/13.13 ((
% 96.58/13.13 (singletoninpowerset) =>
% 96.58/13.13 ((
% 96.58/13.13 (singletoninpowunion) =>
% 96.58/13.13 ((
% 96.58/13.13 (upairset2E) =>
% 96.58/13.13 ((
% 96.58/13.13 (upairsubunion) =>
% 96.58/13.13 ((
% 96.58/13.13 (upairinpowunion) =>
% 96.58/13.13 ((
% 96.58/13.13 (ubforcartprodlem1) =>
% 96.58/13.13 ((
% 96.58/13.13 (ubforcartprodlem2) =>
% 96.58/13.13 ((
% 96.58/13.13 (ubforcartprodlem3) =>
% 96.58/13.13 ((
% 96.58/13.13 (cartprodpairin) =>
% 96.58/13.13 ((
% 96.58/13.13 (cartprodmempair1) =>
% 96.58/13.13 ((
% 96.58/13.13 (cartprodmempair) =>
% 96.58/13.13 ((
% 96.58/13.13 (setunionE2) =>
% 96.58/13.13 ((
% 96.58/13.13 (setunionsingleton1) =>
% 96.58/13.13 ((
% 96.58/13.13 (setunionsingleton2) =>
% 96.58/13.13 ((
% 96.58/13.13 (setunionsingleton) =>
% 96.58/13.13 ((
% 96.58/13.13 (singletonprop) =>
% 96.58/13.13 ((
% 96.58/13.13 (ex1E1) =>
% 96.58/13.13 ((
% 96.58/13.13 (ex1I) =>
% 96.58/13.13 ((
% 96.58/13.13 (ex1I2) =>
% 96.58/13.13 ((
% 96.58/13.13 (singletonsuniq) =>
% 96.58/13.13 ((
% 96.58/13.13 (setukpairinjL1) =>
% 96.58/13.13 ((
% 96.58/13.13 (kfstsingleton) =>
% 96.58/13.13 ((
% 96.58/13.13 (theprop) =>
% 96.58/13.13 ((
% 96.58/13.13 (kfstpairEq) =>
% 96.58/13.13 ((
% 96.58/13.13 (cartprodfstin) =>
% 96.58/13.13 ((
% 96.58/13.13 (setukpairinjL2) =>
% 96.58/13.13 ((
% 96.58/13.13 (setukpairinjL) =>
% 96.58/13.13 ((
% 96.58/13.13 (setukpairinjR11) =>
% 96.58/13.13 ((
% 96.58/13.13 (setukpairinjR12) =>
% 96.58/13.13 ((
% 96.58/13.13 (setukpairinjR1) =>
% 96.58/13.13 ((
% 96.58/13.13 (upairequniteq) =>
% 96.58/13.13 ((
% 96.58/13.13 (setukpairinjR2) =>
% 96.58/13.13 ((
% 96.58/13.13 (setukpairinjR) =>
% 96.58/13.13 ((
% 96.58/13.13 (ksndsingleton) =>
% 96.58/13.13 ((
% 96.58/13.13 (ksndpairEq) =>
% 96.58/13.13 ((
% 96.58/13.13 (kpairsurjEq) =>
% 96.58/13.13 ((
% 96.58/13.13 (cartprodsndin) =>
% 96.58/13.13 ((
% 96.58/13.13 (cartprodpairmemEL) =>
% 96.58/13.13 ((
% 96.58/13.13 (cartprodpairmemER) =>
% 96.58/13.13 ((
% 96.58/13.13 (cartprodmempaircEq) =>
% 96.58/13.13 ((
% 96.58/13.13 (cartprodfstpairEq) =>
% 96.58/13.13 ((
% 96.58/13.13 (cartprodsndpairEq) =>
% 96.58/13.13 ((
% 96.58/13.13 (cartprodpairsurjEq) =>
% 96.58/13.13 ((
% 96.58/13.13 (dpsetconstrI) =>
% 96.58/13.13 ((
% 96.58/13.13 (dpsetconstrSub) =>
% 96.58/13.13 ((
% 96.58/13.13 (setOfPairsIsBReln) =>
% 96.58/13.13 ((
% 96.58/13.13 (dpsetconstrERa) =>
% 96.58/13.13 ((
% 96.58/13.13 (dpsetconstrEL1) =>
% 96.58/13.13 ((
% 96.58/13.13 (dpsetconstrEL2) =>
% 96.58/13.13 ((
% 96.58/13.13 (dpsetconstrER) =>
% 96.58/13.13 ((
% 96.58/13.13 (funcImageSingleton) =>
% 96.58/13.13 ((
% 96.58/13.13 (apProp) =>
% 96.58/13.13 ((
% 96.58/13.13 (app) =>
% 96.58/13.13 ((
% 96.58/13.13 (infuncsetfunc) =>
% 96.58/13.13 ((
% 96.58/13.13 (ap2p) =>
% 96.58/13.13 ((
% 96.58/13.13 (funcinfuncset) =>
% 96.58/13.13 ((
% 96.58/13.13 (lamProp) =>
% 96.58/13.13 ((
% 96.58/13.13 (lamp) =>
% 96.58/13.13 ((
% 96.58/13.13 (lam2p) =>
% 96.58/13.13 ((
% 96.58/13.13 (brelnall1) =>
% 96.58/13.13 ((
% 96.58/13.13 (brelnall2) =>
% 96.58/13.13 ((
% 96.58/13.13 (ex1E2) =>
% 96.58/13.13 ((
% 96.58/13.13 (funcGraphProp1) =>
% 96.58/13.13 ((
% 96.58/13.13 (funcGraphProp3) =>
% 96.58/13.13 ((
% 96.58/13.13 (funcGraphProp2) =>
% 96.58/13.13 ((
% 96.58/13.13 (funcextLem) =>
% 96.58/13.13 ((
% 96.58/13.13 (funcGraphProp4) =>
% 96.58/13.13 ((
% 96.58/13.13 (subbreln) =>
% 96.58/13.13 ((
% 96.58/13.13 (eqbreln) =>
% 96.58/13.13 ((
% 96.58/13.13 (funcext) =>
% 96.58/13.13 ((
% 96.58/13.13 (funcext2) =>
% 96.58/13.13 ((
% 96.58/13.13 (ap2apEq1) =>
% 96.58/13.13 ((
% 96.58/13.13 (ap2apEq2) =>
% 96.58/13.13 ((
% 96.58/13.13 (beta1) =>
% 96.58/13.13 ((
% 96.58/13.13 (eta1) =>
% 96.58/13.13 ((
% 96.58/13.13 (lam2lamEq) =>
% 96.58/13.13 ((
% 96.58/13.13 (beta2) =>
% 96.58/13.13 ((
% 96.58/13.13 (eta2) =>
% 96.58/13.13 ((
% 96.58/13.13 (iffalseProp1) =>
% 96.58/13.13 ((
% 96.58/13.13 (iffalseProp2) =>
% 96.58/13.13 ((
% 96.58/13.13 (iftrueProp1) =>
% 96.58/13.13 ((
% 96.58/13.13 (iftrueProp2) =>
% 96.58/13.13 ((
% 96.58/13.13 (ifSingleton) =>
% 96.58/13.13 ((
% 96.58/13.13 (ifp) =>
% 96.58/13.13 ((
% 96.58/13.13 (theeq) =>
% 96.58/13.13 ((
% 96.58/13.13 (iftrue) =>
% 96.58/13.13 ((
% 96.58/13.13 (iffalse) =>
% 96.58/13.13 ((
% 96.58/13.13 (iftrueorfalse) =>
% 96.58/13.13 ((
% 96.58/13.13 (binintersectT_lem) =>
% 96.58/13.13 ((
% 96.58/13.13 (binunionT_lem) =>
% 96.58/13.13 ((
% 96.58/13.13 (powersetT_lem) =>
% 96.58/13.13 ((
% 96.58/13.13 (setminusT_lem) =>
% 96.58/13.13 ((
% 96.58/13.13 (complementT_lem) =>
% 96.58/13.13 ((
% 96.58/13.13 (setextT) =>
% 96.58/13.13 ((
% 96.58/13.13 (subsetTI) =>
% 96.58/13.13 ((
% 96.58/13.13 (powersetTI1) =>
% 96.58/13.13 ((
% 96.58/13.13 (powersetTE1) =>
% 96.58/13.13 ((
% 96.58/13.13 (complementTI1) =>
% 96.58/13.13 ((
% 96.58/13.13 (complementTE1) =>
% 96.58/13.13 ((
% 96.58/13.13 (binintersectTELcontra) =>
% 96.58/13.13 ((
% 96.58/13.13 (binintersectTERcontra) =>
% 96.58/13.13 ((
% 96.58/13.13 (contrasubsetT) =>
% 96.58/13.13 ((
% 96.58/13.13 (contrasubsetT1) =>
% 96.58/13.13 ((
% 96.58/13.13 (contrasubsetT2) =>
% 96.58/13.13 ((
% 96.58/13.13 (contrasubsetT3) =>
% 96.58/13.13 ((
% 96.58/13.13 (doubleComplementI1) =>
% 96.58/13.13 ((
% 96.58/13.13 (doubleComplementE1) =>
% 96.58/13.13 ((
% 96.58/13.13 (doubleComplementSub1) =>
% 96.58/13.13 ((
% 96.58/13.13 (doubleComplementSub2) =>
% 96.58/13.13 ((
% 96.58/13.13 (doubleComplementEq) =>
% 96.58/13.13 ((
% 96.58/13.13 (complementTnotintersectT) =>
% 96.58/13.13 ((
% 96.58/13.13 (complementImpComplementIntersect) =>
% 96.58/13.13 ((
% 96.58/13.13 (complementSubsetComplementIntersect) =>
% 96.58/13.13 ((
% 96.58/13.13 (complementInPowersetComplementIntersect) =>
% 96.58/13.13 ((
% 96.58/13.13 (contraSubsetComplement) =>
% 96.58/13.13 ((
% 96.58/13.13 (complementTcontraSubset) =>
% 96.58/13.13 ((
% 96.58/13.13 (binunionTILcontra) =>
% 96.58/13.13 ((
% 96.58/13.13 (binunionTIRcontra) =>
% 96.58/13.13 ((
% 96.58/13.13 (inIntersectImpInUnion) =>
% 96.58/13.13 ((
% 96.58/13.13 (inIntersectImpInUnion2) =>
% 96.58/13.13 ((
% 96.58/13.13 (inIntersectImpInIntersectUnions) =>
% 96.58/13.13 ((
% 96.58/13.13 (intersectInPowersetIntersectUnions) =>
% 96.58/13.13 ((
% 96.58/13.13 (inComplementUnionImpNotIn1) =>
% 96.58/13.13 ((
% 96.58/13.13 (inComplementUnionImpInComplement1) =>
% 96.58/13.13 ((
% 96.58/13.13 (binunionTE) =>
% 96.58/13.13 ((
% 96.58/13.13 (binunionTEcontra) =>
% 96.58/13.13 ((
% 96.58/13.13 (demorgan2a1) =>
% 96.58/13.13 ((
% 96.58/13.13 (complementUnionInPowersetComplement) =>
% 96.58/13.13 ((
% 96.58/13.13 (demorgan2a2) =>
% 96.58/13.13 ((
% 96.58/13.13 (demorgan1a) =>
% 96.58/13.13 ((
% 96.58/13.13 (demorgan1b) =>
% 96.58/13.13 ((
% 96.58/13.13 (demorgan1) =>
% 96.58/13.13 ((
% 96.58/13.13 (demorgan2a) =>
% 96.58/13.13 ((
% 96.58/13.13 (demorgan2b2) =>
% 96.58/13.13 ((
% 96.58/13.13 (demorgan2b) =>
% 96.58/13.13 ((
% 96.58/13.13 (demorgan2) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz13rule0) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz13rule1) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz13rule2) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz13rule3) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz13rule4) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz1_1) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz1_2) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz1_3) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz1_4) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz1_5) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1all2) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1SetBreln1) =>
% 96.58/13.13 ((
% 96.58/13.13 (choice2fnsingleton) =>
% 96.58/13.13 ((
% 96.58/13.13 (setOfPairsIsBReln1) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1all1) =>
% 96.58/13.13 ((
% 96.58/13.13 (subbreln1) =>
% 96.58/13.13 ((
% 96.58/13.13 (eqbreln1) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1invprop) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1invI) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1invE) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1compprop) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1compI) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1compE) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1compEex) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1unionprop) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1unionIL) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1unionIR) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1unionI) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1unionE) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1unionEcases) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1unionCommutes) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz2Ex) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz2W) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz2A) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz2B) =>
% 96.58/13.13 ((
% 96.58/13.13 (image1Ex) =>
% 96.58/13.13 ((
% 96.58/13.13 (image1Ex1) =>
% 96.58/13.13 ((
% 96.58/13.13 (image1Equiv) =>
% 96.58/13.13 ((
% 96.58/13.13 (image1E) =>
% 96.58/13.13 ((
% 96.58/13.13 (image1I) =>
% 96.58/13.13 ((
% 96.58/13.13 (injFuncInInjFuncSet) =>
% 96.58/13.13 ((
% 96.58/13.13 (injFuncSetFuncIn) =>
% 96.58/13.13 ((
% 96.58/13.13 (injFuncSetFuncInj) =>
% 96.58/13.13 ((
% 96.58/13.13 (surjFuncSetFuncIn) =>
% 96.58/13.13 ((
% 96.58/13.13 (surjFuncSetFuncSurj) =>
% 96.58/13.13 ((
% 96.58/13.13 (leftInvIsSurj) =>
% 96.58/13.13 ((
% 96.58/13.13 (surjCantorThm) =>
% 96.58/13.13 ((
% 96.58/13.13 (foundation2) =>
% 96.58/13.13 ((
% 96.58/13.13 (notinself) =>
% 96.58/13.13 ((
% 96.58/13.13 (notinself2) =>
% 96.58/13.13 ((
% 96.58/13.13 (omegaSp) =>
% 96.58/13.13 ((
% 96.58/13.13 (omegaSclos) =>
% 96.58/13.13 ((
% 96.58/13.13 (peano0notS) =>
% 96.58/13.13 ((
% 96.58/13.13 (!!) @ (
% 96.58/13.13 (('#S') @ (
% 96.58/13.13 (
% 96.58/13.13 ('#B') @ (
% 96.58/13.13 =>) @
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 ('#C') @ in @
% 96.58/13.13 omega)))) @
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 ('#B') @ (
% 96.58/13.13 !!) @
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 ('#B') @ (
% 96.58/13.13 (
% 96.58/13.13 ('#S') @ (
% 96.58/13.13 (
% 96.58/13.13 ('#B') @ (
% 96.58/13.13 =>) @
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 ('#C') @ in @
% 96.58/13.13 omega)))))) @
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 ('#S') @ (
% 96.58/13.13 (
% 96.58/13.13 ('#B') @ (
% 96.58/13.13 '#S') @
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 ('#B') @ (
% 96.58/13.13 (
% 96.58/13.13 ('#B') @ (
% 96.58/13.13 =>))) @
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 ('#C') @ (
% 96.58/13.13 (
% 96.58/13.13 ('#B') @ (
% 96.58/13.13 '#B') @
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 ('#B') @ (
% 96.58/13.13 =) @
% 96.58/13.13 omegaS)))) @
% 96.58/13.13 omegaS)))))) @
% 96.58/13.13 (
% 96.58/13.13 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 96.58/13.13 inference('lams2combs', [status(thm)], [zip_derived_cl0])).
% 96.58/13.13 thf(omega0Ax, axiom,(( omega0Ax ) = ((in @ emptyset @ omega)))).
% 96.58/13.13 thf('0', plain, (( omega0Ax ) = ( in @ emptyset @ omega )),
% 96.58/13.13 define([status(thm)])).
% 96.58/13.13 thf(emptyinunitempty, axiom,(( emptyinunitempty ) =
% 96.58/13.13 ((in @ emptyset @ (setadjoin @ emptyset @ emptyset))))).
% 96.58/13.13 thf('1', plain,
% 96.58/13.13 (( emptyinunitempty ) =
% 96.58/13.13 ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )),
% 96.58/13.13 define([status(thm)])).
% 96.58/13.13 thf(emptyset__Cong, axiom,(( emptyset__Cong ) =
% 96.58/13.13 ((((emptyset) = (emptyset)))))).
% 96.58/13.13 thf('2', plain, (( emptyset__Cong ) = ( ( emptyset ) = ( emptyset ) )),
% 96.58/13.13 define([status(thm)])).
% 96.58/13.13 thf(omega__Cong, axiom,(( omega__Cong ) = ((((omega) = (omega)))))).
% 96.58/13.13 thf('3', plain, (( omega__Cong ) = ( ( omega ) = ( omega ) )),
% 96.58/13.13 define([status(thm)])).
% 96.58/13.13 thf(zip_derived_cl2, plain,
% 96.58/13.13 (~ (((setextAx) =>
% 96.58/13.13 (((emptysetAx) =>
% 96.58/13.13 (((setadjoinAx) =>
% 96.58/13.13 (((powersetAx) =>
% 96.58/13.13 (((setunionAx) =>
% 96.58/13.13 (((in @ emptyset @ omega) =>
% 96.58/13.13 (((omegaSAx) =>
% 96.58/13.13 (((omegaIndAx) =>
% 96.58/13.13 (((replAx) =>
% 96.58/13.13 (((foundationAx) =>
% 96.58/13.13 (((wellorderingAx) =>
% 96.58/13.13 (((descrp) =>
% 96.58/13.13 (((dsetconstrI) =>
% 96.58/13.13 (((dsetconstrEL) =>
% 96.58/13.13 (((dsetconstrER) =>
% 96.58/13.13 (((exuE1) =>
% 96.58/13.13 (((prop2setE) =>
% 96.58/13.13 (((emptysetE) =>
% 96.58/13.13 (((emptysetimpfalse) =>
% 96.58/13.13 (((notinemptyset) =>
% 96.58/13.13 (((exuE3e) =>
% 96.58/13.13 (((setext) =>
% 96.58/13.13 (((emptyI) =>
% 96.58/13.13 (((noeltsimpempty) =>
% 96.58/13.13 (((setbeta) =>
% 96.58/13.13 (((nonemptyE1) =>
% 96.58/13.13 (((nonemptyI) =>
% 96.58/13.13 (((nonemptyI1) =>
% 96.58/13.13 (((setadjoinIL) =>
% 96.58/13.13 (((in @
% 96.58/13.13 emptyset @
% 96.58/13.13 (setadjoin @
% 96.58/13.13 emptyset @
% 96.58/13.13 emptyset)) =>
% 96.58/13.13 ((
% 96.58/13.13 (setadjoinIR) =>
% 96.58/13.13 ((
% 96.58/13.13 (setadjoinE) =>
% 96.58/13.13 ((
% 96.58/13.13 (setadjoinOr) =>
% 96.58/13.13 ((
% 96.58/13.13 (setoftrueEq) =>
% 96.58/13.13 ((
% 96.58/13.13 (powersetI) =>
% 96.58/13.13 ((
% 96.58/13.13 (emptyinPowerset) =>
% 96.58/13.13 ((
% 96.58/13.13 (emptyInPowerset) =>
% 96.58/13.13 ((
% 96.58/13.13 (powersetE) =>
% 96.58/13.13 ((
% 96.58/13.13 (setunionI) =>
% 96.58/13.13 ((
% 96.58/13.13 (setunionE) =>
% 96.58/13.13 ((
% 96.58/13.13 (subPowSU) =>
% 96.58/13.13 ((
% 96.58/13.13 (exuE2) =>
% 96.58/13.13 ((
% 96.58/13.13 (nonemptyImpWitness) =>
% 96.58/13.13 ((
% 96.58/13.13 (uniqinunit) =>
% 96.58/13.13 ((
% 96.58/13.13 (notinsingleton) =>
% 96.58/13.13 ((
% 96.58/13.13 (eqinunit) =>
% 96.58/13.13 ((
% 96.58/13.13 (singletonsswitch) =>
% 96.58/13.13 ((
% 96.58/13.13 (upairsetE) =>
% 96.58/13.13 ((
% 96.58/13.13 (upairsetIL) =>
% 96.58/13.13 ((
% 96.58/13.13 (upairsetIR) =>
% 96.58/13.13 ((
% 96.58/13.13 (emptyE1) =>
% 96.58/13.13 ((
% 96.58/13.13 (vacuousDall) =>
% 96.58/13.13 ((
% 96.58/13.13 (quantDeMorgan1) =>
% 96.58/13.13 ((
% 96.58/13.13 (quantDeMorgan2) =>
% 96.58/13.13 ((
% 96.58/13.13 (quantDeMorgan3) =>
% 96.58/13.13 ((
% 96.58/13.13 (quantDeMorgan4) =>
% 96.58/13.13 ((
% 96.58/13.13 (prop2setI) =>
% 96.58/13.13 ((
% 96.58/13.13 (prop2set2propI) =>
% 96.58/13.13 ((
% 96.58/13.13 (notdexE) =>
% 96.58/13.13 ((
% 96.58/13.13 (notdallE) =>
% 96.58/13.13 ((
% 96.58/13.13 (exuI1) =>
% 96.58/13.13 ((
% 96.58/13.13 (exuI3) =>
% 96.58/13.13 ((
% 96.58/13.13 (exuI2) =>
% 96.58/13.13 ((
% 96.58/13.13 (inCongP) =>
% 96.58/13.13 ((
% 96.58/13.13 (in__Cong) =>
% 96.58/13.13 ((
% 96.58/13.13 (exuE3u) =>
% 96.58/13.13 ((
% 96.58/13.13 (exu__Cong) =>
% 96.58/13.13 ((
% 96.58/13.13 ((
% 96.58/13.13 (emptyset) =
% 96.58/13.13 (emptyset))) =>
% 96.58/13.13 ((
% 96.58/13.13 (setadjoin__Cong) =>
% 96.58/13.13 ((
% 96.58/13.13 (powerset__Cong) =>
% 96.58/13.13 ((
% 96.58/13.13 (setunion__Cong) =>
% 96.58/13.13 ((
% 96.58/13.13 ((
% 96.58/13.13 (omega) =
% 96.58/13.13 (omega))) =>
% 96.58/13.13 ((
% 96.58/13.13 (exuEu) =>
% 96.58/13.13 ((
% 96.58/13.13 (descr__Cong) =>
% 96.58/13.13 ((
% 96.58/13.13 (dsetconstr__Cong) =>
% 96.58/13.13 ((
% 96.58/13.13 (subsetI1) =>
% 96.58/13.13 ((
% 96.58/13.13 (eqimpsubset2) =>
% 96.58/13.13 ((
% 96.58/13.13 (eqimpsubset1) =>
% 96.58/13.13 ((
% 96.58/13.13 (subsetI2) =>
% 96.58/13.13 ((
% 96.58/13.13 (emptysetsubset) =>
% 96.58/13.13 ((
% 96.58/13.13 (subsetE) =>
% 96.58/13.13 ((
% 96.58/13.13 (subsetE2) =>
% 96.58/13.13 ((
% 96.58/13.13 (notsubsetI) =>
% 96.58/13.13 ((
% 96.58/13.13 (notequalI1) =>
% 96.58/13.13 ((
% 96.58/13.13 (notequalI2) =>
% 96.58/13.13 ((
% 96.58/13.13 (subsetRefl) =>
% 96.58/13.13 ((
% 96.58/13.13 (subsetTrans) =>
% 96.58/13.13 ((
% 96.58/13.13 (setadjoinSub) =>
% 96.58/13.13 ((
% 96.58/13.13 (setadjoinSub2) =>
% 96.58/13.13 ((
% 96.58/13.13 (subset2powerset) =>
% 96.58/13.13 ((
% 96.58/13.13 (setextsub) =>
% 96.58/13.13 ((
% 96.58/13.13 (subsetemptysetimpeq) =>
% 96.58/13.13 ((
% 96.58/13.13 (powersetI1) =>
% 96.58/13.13 ((
% 96.58/13.13 (powersetE1) =>
% 96.58/13.13 ((
% 96.58/13.13 (inPowerset) =>
% 96.58/13.13 ((
% 96.58/13.13 (powersetsubset) =>
% 96.58/13.13 ((
% 96.58/13.13 (sepInPowerset) =>
% 96.58/13.13 ((
% 96.58/13.13 (sepSubset) =>
% 96.58/13.13 ((
% 96.58/13.13 (binunionIL) =>
% 96.58/13.13 ((
% 96.58/13.13 (upairset2IR) =>
% 96.58/13.13 ((
% 96.58/13.13 (binunionIR) =>
% 96.58/13.13 ((
% 96.58/13.13 (binunionEcases) =>
% 96.58/13.13 ((
% 96.58/13.13 (binunionE) =>
% 96.58/13.13 ((
% 96.58/13.13 (binunionLsub) =>
% 96.58/13.13 ((
% 96.58/13.13 (binunionRsub) =>
% 96.58/13.13 ((
% 96.58/13.13 (binintersectI) =>
% 96.58/13.13 ((
% 96.58/13.13 (binintersectSubset5) =>
% 96.58/13.13 ((
% 96.58/13.13 (binintersectEL) =>
% 96.58/13.13 ((
% 96.58/13.13 (binintersectLsub) =>
% 96.58/13.13 ((
% 96.58/13.13 (binintersectSubset2) =>
% 96.58/13.13 ((
% 96.58/13.13 (binintersectSubset3) =>
% 96.58/13.13 ((
% 96.58/13.13 (binintersectER) =>
% 96.58/13.13 ((
% 96.58/13.13 (disjointsetsI1) =>
% 96.58/13.13 ((
% 96.58/13.13 (binintersectRsub) =>
% 96.58/13.13 ((
% 96.58/13.13 (binintersectSubset4) =>
% 96.58/13.13 ((
% 96.58/13.13 (binintersectSubset1) =>
% 96.58/13.13 ((
% 96.58/13.13 (bs114d) =>
% 96.58/13.13 ((
% 96.58/13.13 (setminusI) =>
% 96.58/13.13 ((
% 96.58/13.13 (setminusEL) =>
% 96.58/13.13 ((
% 96.58/13.13 (setminusER) =>
% 96.58/13.13 ((
% 96.58/13.13 (setminusSubset2) =>
% 96.58/13.13 ((
% 96.58/13.13 (setminusERneg) =>
% 96.58/13.13 ((
% 96.58/13.13 (setminusELneg) =>
% 96.58/13.13 ((
% 96.58/13.13 (setminusILneg) =>
% 96.58/13.13 ((
% 96.58/13.13 (setminusIRneg) =>
% 96.58/13.13 ((
% 96.58/13.13 (setminusLsub) =>
% 96.58/13.13 ((
% 96.58/13.13 (setminusSubset1) =>
% 96.58/13.13 ((
% 96.58/13.13 (symdiffE) =>
% 96.58/13.13 ((
% 96.58/13.13 (symdiffI1) =>
% 96.58/13.13 ((
% 96.58/13.13 (symdiffI2) =>
% 96.58/13.13 ((
% 96.58/13.13 (symdiffIneg1) =>
% 96.58/13.13 ((
% 96.58/13.13 (symdiffIneg2) =>
% 96.58/13.13 ((
% 96.58/13.13 (secondinupair) =>
% 96.58/13.13 ((
% 96.58/13.13 (setukpairIL) =>
% 96.58/13.13 ((
% 96.58/13.13 (setukpairIR) =>
% 96.58/13.13 ((
% 96.58/13.13 (kpairiskpair) =>
% 96.58/13.13 ((
% 96.58/13.13 (kpairp) =>
% 96.58/13.13 ((
% 96.58/13.13 (singletonsubset) =>
% 96.58/13.13 ((
% 96.58/13.13 (singletoninpowerset) =>
% 96.58/13.13 ((
% 96.58/13.13 (singletoninpowunion) =>
% 96.58/13.13 ((
% 96.58/13.13 (upairset2E) =>
% 96.58/13.13 ((
% 96.58/13.13 (upairsubunion) =>
% 96.58/13.13 ((
% 96.58/13.13 (upairinpowunion) =>
% 96.58/13.13 ((
% 96.58/13.13 (ubforcartprodlem1) =>
% 96.58/13.13 ((
% 96.58/13.13 (ubforcartprodlem2) =>
% 96.58/13.13 ((
% 96.58/13.13 (ubforcartprodlem3) =>
% 96.58/13.13 ((
% 96.58/13.13 (cartprodpairin) =>
% 96.58/13.13 ((
% 96.58/13.13 (cartprodmempair1) =>
% 96.58/13.13 ((
% 96.58/13.13 (cartprodmempair) =>
% 96.58/13.13 ((
% 96.58/13.13 (setunionE2) =>
% 96.58/13.13 ((
% 96.58/13.13 (setunionsingleton1) =>
% 96.58/13.13 ((
% 96.58/13.13 (setunionsingleton2) =>
% 96.58/13.13 ((
% 96.58/13.13 (setunionsingleton) =>
% 96.58/13.13 ((
% 96.58/13.13 (singletonprop) =>
% 96.58/13.13 ((
% 96.58/13.13 (ex1E1) =>
% 96.58/13.13 ((
% 96.58/13.13 (ex1I) =>
% 96.58/13.13 ((
% 96.58/13.13 (ex1I2) =>
% 96.58/13.13 ((
% 96.58/13.13 (singletonsuniq) =>
% 96.58/13.13 ((
% 96.58/13.13 (setukpairinjL1) =>
% 96.58/13.13 ((
% 96.58/13.13 (kfstsingleton) =>
% 96.58/13.13 ((
% 96.58/13.13 (theprop) =>
% 96.58/13.13 ((
% 96.58/13.13 (kfstpairEq) =>
% 96.58/13.13 ((
% 96.58/13.13 (cartprodfstin) =>
% 96.58/13.13 ((
% 96.58/13.13 (setukpairinjL2) =>
% 96.58/13.13 ((
% 96.58/13.13 (setukpairinjL) =>
% 96.58/13.13 ((
% 96.58/13.13 (setukpairinjR11) =>
% 96.58/13.13 ((
% 96.58/13.13 (setukpairinjR12) =>
% 96.58/13.13 ((
% 96.58/13.13 (setukpairinjR1) =>
% 96.58/13.13 ((
% 96.58/13.13 (upairequniteq) =>
% 96.58/13.13 ((
% 96.58/13.13 (setukpairinjR2) =>
% 96.58/13.13 ((
% 96.58/13.13 (setukpairinjR) =>
% 96.58/13.13 ((
% 96.58/13.13 (ksndsingleton) =>
% 96.58/13.13 ((
% 96.58/13.13 (ksndpairEq) =>
% 96.58/13.13 ((
% 96.58/13.13 (kpairsurjEq) =>
% 96.58/13.13 ((
% 96.58/13.13 (cartprodsndin) =>
% 96.58/13.13 ((
% 96.58/13.13 (cartprodpairmemEL) =>
% 96.58/13.13 ((
% 96.58/13.13 (cartprodpairmemER) =>
% 96.58/13.13 ((
% 96.58/13.13 (cartprodmempaircEq) =>
% 96.58/13.13 ((
% 96.58/13.13 (cartprodfstpairEq) =>
% 96.58/13.13 ((
% 96.58/13.13 (cartprodsndpairEq) =>
% 96.58/13.13 ((
% 96.58/13.13 (cartprodpairsurjEq) =>
% 96.58/13.13 ((
% 96.58/13.13 (dpsetconstrI) =>
% 96.58/13.13 ((
% 96.58/13.13 (dpsetconstrSub) =>
% 96.58/13.13 ((
% 96.58/13.13 (setOfPairsIsBReln) =>
% 96.58/13.13 ((
% 96.58/13.13 (dpsetconstrERa) =>
% 96.58/13.13 ((
% 96.58/13.13 (dpsetconstrEL1) =>
% 96.58/13.13 ((
% 96.58/13.13 (dpsetconstrEL2) =>
% 96.58/13.13 ((
% 96.58/13.13 (dpsetconstrER) =>
% 96.58/13.13 ((
% 96.58/13.13 (funcImageSingleton) =>
% 96.58/13.13 ((
% 96.58/13.13 (apProp) =>
% 96.58/13.13 ((
% 96.58/13.13 (app) =>
% 96.58/13.13 ((
% 96.58/13.13 (infuncsetfunc) =>
% 96.58/13.13 ((
% 96.58/13.13 (ap2p) =>
% 96.58/13.13 ((
% 96.58/13.13 (funcinfuncset) =>
% 96.58/13.13 ((
% 96.58/13.13 (lamProp) =>
% 96.58/13.13 ((
% 96.58/13.13 (lamp) =>
% 96.58/13.13 ((
% 96.58/13.13 (lam2p) =>
% 96.58/13.13 ((
% 96.58/13.13 (brelnall1) =>
% 96.58/13.13 ((
% 96.58/13.13 (brelnall2) =>
% 96.58/13.13 ((
% 96.58/13.13 (ex1E2) =>
% 96.58/13.13 ((
% 96.58/13.13 (funcGraphProp1) =>
% 96.58/13.13 ((
% 96.58/13.13 (funcGraphProp3) =>
% 96.58/13.13 ((
% 96.58/13.13 (funcGraphProp2) =>
% 96.58/13.13 ((
% 96.58/13.13 (funcextLem) =>
% 96.58/13.13 ((
% 96.58/13.13 (funcGraphProp4) =>
% 96.58/13.13 ((
% 96.58/13.13 (subbreln) =>
% 96.58/13.13 ((
% 96.58/13.13 (eqbreln) =>
% 96.58/13.13 ((
% 96.58/13.13 (funcext) =>
% 96.58/13.13 ((
% 96.58/13.13 (funcext2) =>
% 96.58/13.13 ((
% 96.58/13.13 (ap2apEq1) =>
% 96.58/13.13 ((
% 96.58/13.13 (ap2apEq2) =>
% 96.58/13.13 ((
% 96.58/13.13 (beta1) =>
% 96.58/13.13 ((
% 96.58/13.13 (eta1) =>
% 96.58/13.13 ((
% 96.58/13.13 (lam2lamEq) =>
% 96.58/13.13 ((
% 96.58/13.13 (beta2) =>
% 96.58/13.13 ((
% 96.58/13.13 (eta2) =>
% 96.58/13.13 ((
% 96.58/13.13 (iffalseProp1) =>
% 96.58/13.13 ((
% 96.58/13.13 (iffalseProp2) =>
% 96.58/13.13 ((
% 96.58/13.13 (iftrueProp1) =>
% 96.58/13.13 ((
% 96.58/13.13 (iftrueProp2) =>
% 96.58/13.13 ((
% 96.58/13.13 (ifSingleton) =>
% 96.58/13.13 ((
% 96.58/13.13 (ifp) =>
% 96.58/13.13 ((
% 96.58/13.13 (theeq) =>
% 96.58/13.13 ((
% 96.58/13.13 (iftrue) =>
% 96.58/13.13 ((
% 96.58/13.13 (iffalse) =>
% 96.58/13.13 ((
% 96.58/13.13 (iftrueorfalse) =>
% 96.58/13.13 ((
% 96.58/13.13 (binintersectT_lem) =>
% 96.58/13.13 ((
% 96.58/13.13 (binunionT_lem) =>
% 96.58/13.13 ((
% 96.58/13.13 (powersetT_lem) =>
% 96.58/13.13 ((
% 96.58/13.13 (setminusT_lem) =>
% 96.58/13.13 ((
% 96.58/13.13 (complementT_lem) =>
% 96.58/13.13 ((
% 96.58/13.13 (setextT) =>
% 96.58/13.13 ((
% 96.58/13.13 (subsetTI) =>
% 96.58/13.13 ((
% 96.58/13.13 (powersetTI1) =>
% 96.58/13.13 ((
% 96.58/13.13 (powersetTE1) =>
% 96.58/13.13 ((
% 96.58/13.13 (complementTI1) =>
% 96.58/13.13 ((
% 96.58/13.13 (complementTE1) =>
% 96.58/13.13 ((
% 96.58/13.13 (binintersectTELcontra) =>
% 96.58/13.13 ((
% 96.58/13.13 (binintersectTERcontra) =>
% 96.58/13.13 ((
% 96.58/13.13 (contrasubsetT) =>
% 96.58/13.13 ((
% 96.58/13.13 (contrasubsetT1) =>
% 96.58/13.13 ((
% 96.58/13.13 (contrasubsetT2) =>
% 96.58/13.13 ((
% 96.58/13.13 (contrasubsetT3) =>
% 96.58/13.13 ((
% 96.58/13.13 (doubleComplementI1) =>
% 96.58/13.13 ((
% 96.58/13.13 (doubleComplementE1) =>
% 96.58/13.13 ((
% 96.58/13.13 (doubleComplementSub1) =>
% 96.58/13.13 ((
% 96.58/13.13 (doubleComplementSub2) =>
% 96.58/13.13 ((
% 96.58/13.13 (doubleComplementEq) =>
% 96.58/13.13 ((
% 96.58/13.13 (complementTnotintersectT) =>
% 96.58/13.13 ((
% 96.58/13.13 (complementImpComplementIntersect) =>
% 96.58/13.13 ((
% 96.58/13.13 (complementSubsetComplementIntersect) =>
% 96.58/13.13 ((
% 96.58/13.13 (complementInPowersetComplementIntersect) =>
% 96.58/13.13 ((
% 96.58/13.13 (contraSubsetComplement) =>
% 96.58/13.13 ((
% 96.58/13.13 (complementTcontraSubset) =>
% 96.58/13.13 ((
% 96.58/13.13 (binunionTILcontra) =>
% 96.58/13.13 ((
% 96.58/13.13 (binunionTIRcontra) =>
% 96.58/13.13 ((
% 96.58/13.13 (inIntersectImpInUnion) =>
% 96.58/13.13 ((
% 96.58/13.13 (inIntersectImpInUnion2) =>
% 96.58/13.13 ((
% 96.58/13.13 (inIntersectImpInIntersectUnions) =>
% 96.58/13.13 ((
% 96.58/13.13 (intersectInPowersetIntersectUnions) =>
% 96.58/13.13 ((
% 96.58/13.13 (inComplementUnionImpNotIn1) =>
% 96.58/13.13 ((
% 96.58/13.13 (inComplementUnionImpInComplement1) =>
% 96.58/13.13 ((
% 96.58/13.13 (binunionTE) =>
% 96.58/13.13 ((
% 96.58/13.13 (binunionTEcontra) =>
% 96.58/13.13 ((
% 96.58/13.13 (demorgan2a1) =>
% 96.58/13.13 ((
% 96.58/13.13 (complementUnionInPowersetComplement) =>
% 96.58/13.13 ((
% 96.58/13.13 (demorgan2a2) =>
% 96.58/13.13 ((
% 96.58/13.13 (demorgan1a) =>
% 96.58/13.13 ((
% 96.58/13.13 (demorgan1b) =>
% 96.58/13.13 ((
% 96.58/13.13 (demorgan1) =>
% 96.58/13.13 ((
% 96.58/13.13 (demorgan2a) =>
% 96.58/13.13 ((
% 96.58/13.13 (demorgan2b2) =>
% 96.58/13.13 ((
% 96.58/13.13 (demorgan2b) =>
% 96.58/13.13 ((
% 96.58/13.13 (demorgan2) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz13rule0) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz13rule1) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz13rule2) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz13rule3) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz13rule4) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz1_1) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz1_2) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz1_3) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz1_4) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz1_5) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1all2) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1SetBreln1) =>
% 96.58/13.13 ((
% 96.58/13.13 (choice2fnsingleton) =>
% 96.58/13.13 ((
% 96.58/13.13 (setOfPairsIsBReln1) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1all1) =>
% 96.58/13.13 ((
% 96.58/13.13 (subbreln1) =>
% 96.58/13.13 ((
% 96.58/13.13 (eqbreln1) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1invprop) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1invI) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1invE) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1compprop) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1compI) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1compE) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1compEex) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1unionprop) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1unionIL) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1unionIR) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1unionI) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1unionE) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1unionEcases) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1unionCommutes) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz2Ex) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz2W) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz2A) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz2B) =>
% 96.58/13.13 ((
% 96.58/13.13 (image1Ex) =>
% 96.58/13.13 ((
% 96.58/13.13 (image1Ex1) =>
% 96.58/13.13 ((
% 96.58/13.13 (image1Equiv) =>
% 96.58/13.13 ((
% 96.58/13.13 (image1E) =>
% 96.58/13.13 ((
% 96.58/13.13 (image1I) =>
% 96.58/13.13 ((
% 96.58/13.13 (injFuncInInjFuncSet) =>
% 96.58/13.13 ((
% 96.58/13.13 (injFuncSetFuncIn) =>
% 96.58/13.13 ((
% 96.58/13.13 (injFuncSetFuncInj) =>
% 96.58/13.13 ((
% 96.58/13.13 (surjFuncSetFuncIn) =>
% 96.58/13.13 ((
% 96.58/13.13 (surjFuncSetFuncSurj) =>
% 96.58/13.13 ((
% 96.58/13.13 (leftInvIsSurj) =>
% 96.58/13.13 ((
% 96.58/13.13 (surjCantorThm) =>
% 96.58/13.13 ((
% 96.58/13.13 (foundation2) =>
% 96.58/13.13 ((
% 96.58/13.13 (notinself) =>
% 96.58/13.13 ((
% 96.58/13.13 (notinself2) =>
% 96.58/13.13 ((
% 96.58/13.13 (omegaSp) =>
% 96.58/13.13 ((
% 96.58/13.13 (omegaSclos) =>
% 96.58/13.13 ((
% 96.58/13.13 (peano0notS) =>
% 96.58/13.13 ((
% 96.58/13.13 (!!) @ (
% 96.58/13.13 (('#S') @ (
% 96.58/13.13 (
% 96.58/13.13 ('#B') @ (
% 96.58/13.13 =>) @
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 ('#C') @ in @
% 96.58/13.13 omega)))) @
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 ('#B') @ (
% 96.58/13.13 !!) @
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 ('#B') @ (
% 96.58/13.13 (
% 96.58/13.13 ('#S') @ (
% 96.58/13.13 (
% 96.58/13.13 ('#B') @ (
% 96.58/13.13 =>) @
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 ('#C') @ in @
% 96.58/13.13 omega)))))) @
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 ('#S') @ (
% 96.58/13.13 (
% 96.58/13.13 ('#B') @ (
% 96.58/13.13 '#S') @
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 ('#B') @ (
% 96.58/13.13 (
% 96.58/13.13 ('#B') @ (
% 96.58/13.13 =>))) @
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 ('#C') @ (
% 96.58/13.13 (
% 96.58/13.13 ('#B') @ (
% 96.58/13.13 '#B') @
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 ('#B') @ (
% 96.58/13.13 =) @
% 96.58/13.13 omegaS)))) @
% 96.58/13.13 omegaS)))))) @
% 96.58/13.13 (
% 96.58/13.13 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 96.58/13.13 inference('rw', [status(thm)], [zip_derived_cl1, '0', '1', '2', '3'])).
% 96.58/13.13 thf(zip_derived_cl3, plain,
% 96.58/13.13 (~ (((setextAx) =>
% 96.58/13.13 (((emptysetAx) =>
% 96.58/13.13 (((setadjoinAx) =>
% 96.58/13.13 (((powersetAx) =>
% 96.58/13.13 (((setunionAx) =>
% 96.58/13.13 (((in @ emptyset @ omega) =>
% 96.58/13.13 (((omegaSAx) =>
% 96.58/13.13 (((omegaIndAx) =>
% 96.58/13.13 (((replAx) =>
% 96.58/13.13 (((foundationAx) =>
% 96.58/13.13 (((wellorderingAx) =>
% 96.58/13.13 (((descrp) =>
% 96.58/13.13 (((dsetconstrI) =>
% 96.58/13.13 (((dsetconstrEL) =>
% 96.58/13.13 (((dsetconstrER) =>
% 96.58/13.13 (((exuE1) =>
% 96.58/13.13 (((prop2setE) =>
% 96.58/13.13 (((emptysetE) =>
% 96.58/13.13 (((emptysetimpfalse) =>
% 96.58/13.13 (((notinemptyset) =>
% 96.58/13.13 (((exuE3e) =>
% 96.58/13.13 (((setext) =>
% 96.58/13.13 (((emptyI) =>
% 96.58/13.13 (((noeltsimpempty) =>
% 96.58/13.13 (((setbeta) =>
% 96.58/13.13 (((nonemptyE1) =>
% 96.58/13.13 (((nonemptyI) =>
% 96.58/13.13 (((nonemptyI1) =>
% 96.58/13.13 (((setadjoinIL) =>
% 96.58/13.13 (((in @
% 96.58/13.13 emptyset @
% 96.58/13.13 (setadjoin @
% 96.58/13.13 emptyset @
% 96.58/13.13 emptyset)) =>
% 96.58/13.13 ((
% 96.58/13.13 (setadjoinIR) =>
% 96.58/13.13 ((
% 96.58/13.13 (setadjoinE) =>
% 96.58/13.13 ((
% 96.58/13.13 (setadjoinOr) =>
% 96.58/13.13 ((
% 96.58/13.13 (setoftrueEq) =>
% 96.58/13.13 ((
% 96.58/13.13 (powersetI) =>
% 96.58/13.13 ((
% 96.58/13.13 (emptyinPowerset) =>
% 96.58/13.13 ((
% 96.58/13.13 (emptyInPowerset) =>
% 96.58/13.13 ((
% 96.58/13.13 (powersetE) =>
% 96.58/13.13 ((
% 96.58/13.13 (setunionI) =>
% 96.58/13.13 ((
% 96.58/13.13 (setunionE) =>
% 96.58/13.13 ((
% 96.58/13.13 (subPowSU) =>
% 96.58/13.13 ((
% 96.58/13.13 (exuE2) =>
% 96.58/13.13 ((
% 96.58/13.13 (nonemptyImpWitness) =>
% 96.58/13.13 ((
% 96.58/13.13 (uniqinunit) =>
% 96.58/13.13 ((
% 96.58/13.13 (notinsingleton) =>
% 96.58/13.13 ((
% 96.58/13.13 (eqinunit) =>
% 96.58/13.13 ((
% 96.58/13.13 (singletonsswitch) =>
% 96.58/13.13 ((
% 96.58/13.13 (upairsetE) =>
% 96.58/13.13 ((
% 96.58/13.13 (upairsetIL) =>
% 96.58/13.13 ((
% 96.58/13.13 (upairsetIR) =>
% 96.58/13.13 ((
% 96.58/13.13 (emptyE1) =>
% 96.58/13.13 ((
% 96.58/13.13 (vacuousDall) =>
% 96.58/13.13 ((
% 96.58/13.13 (quantDeMorgan1) =>
% 96.58/13.13 ((
% 96.58/13.13 (quantDeMorgan2) =>
% 96.58/13.13 ((
% 96.58/13.13 (quantDeMorgan3) =>
% 96.58/13.13 ((
% 96.58/13.13 (quantDeMorgan4) =>
% 96.58/13.13 ((
% 96.58/13.13 (prop2setI) =>
% 96.58/13.13 ((
% 96.58/13.13 (prop2set2propI) =>
% 96.58/13.13 ((
% 96.58/13.13 (notdexE) =>
% 96.58/13.13 ((
% 96.58/13.13 (notdallE) =>
% 96.58/13.13 ((
% 96.58/13.13 (exuI1) =>
% 96.58/13.13 ((
% 96.58/13.13 (exuI3) =>
% 96.58/13.13 ((
% 96.58/13.13 (exuI2) =>
% 96.58/13.13 ((
% 96.58/13.13 (inCongP) =>
% 96.58/13.13 ((
% 96.58/13.13 (in__Cong) =>
% 96.58/13.13 ((
% 96.58/13.13 (exuE3u) =>
% 96.58/13.13 ((
% 96.58/13.13 (exu__Cong) =>
% 96.58/13.13 ((
% 96.58/13.13 (setadjoin__Cong) =>
% 96.58/13.13 ((
% 96.58/13.13 (powerset__Cong) =>
% 96.58/13.13 ((
% 96.58/13.13 (setunion__Cong) =>
% 96.58/13.13 ((
% 96.58/13.13 (exuEu) =>
% 96.58/13.13 ((
% 96.58/13.13 (descr__Cong) =>
% 96.58/13.13 ((
% 96.58/13.13 (dsetconstr__Cong) =>
% 96.58/13.13 ((
% 96.58/13.13 (subsetI1) =>
% 96.58/13.13 ((
% 96.58/13.13 (eqimpsubset2) =>
% 96.58/13.13 ((
% 96.58/13.13 (eqimpsubset1) =>
% 96.58/13.13 ((
% 96.58/13.13 (subsetI2) =>
% 96.58/13.13 ((
% 96.58/13.13 (emptysetsubset) =>
% 96.58/13.13 ((
% 96.58/13.13 (subsetE) =>
% 96.58/13.13 ((
% 96.58/13.13 (subsetE2) =>
% 96.58/13.13 ((
% 96.58/13.13 (notsubsetI) =>
% 96.58/13.13 ((
% 96.58/13.13 (notequalI1) =>
% 96.58/13.13 ((
% 96.58/13.13 (notequalI2) =>
% 96.58/13.13 ((
% 96.58/13.13 (subsetRefl) =>
% 96.58/13.13 ((
% 96.58/13.13 (subsetTrans) =>
% 96.58/13.13 ((
% 96.58/13.13 (setadjoinSub) =>
% 96.58/13.13 ((
% 96.58/13.13 (setadjoinSub2) =>
% 96.58/13.13 ((
% 96.58/13.13 (subset2powerset) =>
% 96.58/13.13 ((
% 96.58/13.13 (setextsub) =>
% 96.58/13.13 ((
% 96.58/13.13 (subsetemptysetimpeq) =>
% 96.58/13.13 ((
% 96.58/13.13 (powersetI1) =>
% 96.58/13.13 ((
% 96.58/13.13 (powersetE1) =>
% 96.58/13.13 ((
% 96.58/13.13 (inPowerset) =>
% 96.58/13.13 ((
% 96.58/13.13 (powersetsubset) =>
% 96.58/13.13 ((
% 96.58/13.13 (sepInPowerset) =>
% 96.58/13.13 ((
% 96.58/13.13 (sepSubset) =>
% 96.58/13.13 ((
% 96.58/13.13 (binunionIL) =>
% 96.58/13.13 ((
% 96.58/13.13 (upairset2IR) =>
% 96.58/13.13 ((
% 96.58/13.13 (binunionIR) =>
% 96.58/13.13 ((
% 96.58/13.13 (binunionEcases) =>
% 96.58/13.13 ((
% 96.58/13.13 (binunionE) =>
% 96.58/13.13 ((
% 96.58/13.13 (binunionLsub) =>
% 96.58/13.13 ((
% 96.58/13.13 (binunionRsub) =>
% 96.58/13.13 ((
% 96.58/13.13 (binintersectI) =>
% 96.58/13.13 ((
% 96.58/13.13 (binintersectSubset5) =>
% 96.58/13.13 ((
% 96.58/13.13 (binintersectEL) =>
% 96.58/13.13 ((
% 96.58/13.13 (binintersectLsub) =>
% 96.58/13.13 ((
% 96.58/13.13 (binintersectSubset2) =>
% 96.58/13.13 ((
% 96.58/13.13 (binintersectSubset3) =>
% 96.58/13.13 ((
% 96.58/13.13 (binintersectER) =>
% 96.58/13.13 ((
% 96.58/13.13 (disjointsetsI1) =>
% 96.58/13.13 ((
% 96.58/13.13 (binintersectRsub) =>
% 96.58/13.13 ((
% 96.58/13.13 (binintersectSubset4) =>
% 96.58/13.13 ((
% 96.58/13.13 (binintersectSubset1) =>
% 96.58/13.13 ((
% 96.58/13.13 (bs114d) =>
% 96.58/13.13 ((
% 96.58/13.13 (setminusI) =>
% 96.58/13.13 ((
% 96.58/13.13 (setminusEL) =>
% 96.58/13.13 ((
% 96.58/13.13 (setminusER) =>
% 96.58/13.13 ((
% 96.58/13.13 (setminusSubset2) =>
% 96.58/13.13 ((
% 96.58/13.13 (setminusERneg) =>
% 96.58/13.13 ((
% 96.58/13.13 (setminusELneg) =>
% 96.58/13.13 ((
% 96.58/13.13 (setminusILneg) =>
% 96.58/13.13 ((
% 96.58/13.13 (setminusIRneg) =>
% 96.58/13.13 ((
% 96.58/13.13 (setminusLsub) =>
% 96.58/13.13 ((
% 96.58/13.13 (setminusSubset1) =>
% 96.58/13.13 ((
% 96.58/13.13 (symdiffE) =>
% 96.58/13.13 ((
% 96.58/13.13 (symdiffI1) =>
% 96.58/13.13 ((
% 96.58/13.13 (symdiffI2) =>
% 96.58/13.13 ((
% 96.58/13.13 (symdiffIneg1) =>
% 96.58/13.13 ((
% 96.58/13.13 (symdiffIneg2) =>
% 96.58/13.13 ((
% 96.58/13.13 (secondinupair) =>
% 96.58/13.13 ((
% 96.58/13.13 (setukpairIL) =>
% 96.58/13.13 ((
% 96.58/13.13 (setukpairIR) =>
% 96.58/13.13 ((
% 96.58/13.13 (kpairiskpair) =>
% 96.58/13.13 ((
% 96.58/13.13 (kpairp) =>
% 96.58/13.13 ((
% 96.58/13.13 (singletonsubset) =>
% 96.58/13.13 ((
% 96.58/13.13 (singletoninpowerset) =>
% 96.58/13.13 ((
% 96.58/13.13 (singletoninpowunion) =>
% 96.58/13.13 ((
% 96.58/13.13 (upairset2E) =>
% 96.58/13.13 ((
% 96.58/13.13 (upairsubunion) =>
% 96.58/13.13 ((
% 96.58/13.13 (upairinpowunion) =>
% 96.58/13.13 ((
% 96.58/13.13 (ubforcartprodlem1) =>
% 96.58/13.13 ((
% 96.58/13.13 (ubforcartprodlem2) =>
% 96.58/13.13 ((
% 96.58/13.13 (ubforcartprodlem3) =>
% 96.58/13.13 ((
% 96.58/13.13 (cartprodpairin) =>
% 96.58/13.13 ((
% 96.58/13.13 (cartprodmempair1) =>
% 96.58/13.13 ((
% 96.58/13.13 (cartprodmempair) =>
% 96.58/13.13 ((
% 96.58/13.13 (setunionE2) =>
% 96.58/13.13 ((
% 96.58/13.13 (setunionsingleton1) =>
% 96.58/13.13 ((
% 96.58/13.13 (setunionsingleton2) =>
% 96.58/13.13 ((
% 96.58/13.13 (setunionsingleton) =>
% 96.58/13.13 ((
% 96.58/13.13 (singletonprop) =>
% 96.58/13.13 ((
% 96.58/13.13 (ex1E1) =>
% 96.58/13.13 ((
% 96.58/13.13 (ex1I) =>
% 96.58/13.13 ((
% 96.58/13.13 (ex1I2) =>
% 96.58/13.13 ((
% 96.58/13.13 (singletonsuniq) =>
% 96.58/13.13 ((
% 96.58/13.13 (setukpairinjL1) =>
% 96.58/13.13 ((
% 96.58/13.13 (kfstsingleton) =>
% 96.58/13.13 ((
% 96.58/13.13 (theprop) =>
% 96.58/13.13 ((
% 96.58/13.13 (kfstpairEq) =>
% 96.58/13.13 ((
% 96.58/13.13 (cartprodfstin) =>
% 96.58/13.13 ((
% 96.58/13.13 (setukpairinjL2) =>
% 96.58/13.13 ((
% 96.58/13.13 (setukpairinjL) =>
% 96.58/13.13 ((
% 96.58/13.13 (setukpairinjR11) =>
% 96.58/13.13 ((
% 96.58/13.13 (setukpairinjR12) =>
% 96.58/13.13 ((
% 96.58/13.13 (setukpairinjR1) =>
% 96.58/13.13 ((
% 96.58/13.13 (upairequniteq) =>
% 96.58/13.13 ((
% 96.58/13.13 (setukpairinjR2) =>
% 96.58/13.13 ((
% 96.58/13.13 (setukpairinjR) =>
% 96.58/13.13 ((
% 96.58/13.13 (ksndsingleton) =>
% 96.58/13.13 ((
% 96.58/13.13 (ksndpairEq) =>
% 96.58/13.13 ((
% 96.58/13.13 (kpairsurjEq) =>
% 96.58/13.13 ((
% 96.58/13.13 (cartprodsndin) =>
% 96.58/13.13 ((
% 96.58/13.13 (cartprodpairmemEL) =>
% 96.58/13.13 ((
% 96.58/13.13 (cartprodpairmemER) =>
% 96.58/13.13 ((
% 96.58/13.13 (cartprodmempaircEq) =>
% 96.58/13.13 ((
% 96.58/13.13 (cartprodfstpairEq) =>
% 96.58/13.13 ((
% 96.58/13.13 (cartprodsndpairEq) =>
% 96.58/13.13 ((
% 96.58/13.13 (cartprodpairsurjEq) =>
% 96.58/13.13 ((
% 96.58/13.13 (dpsetconstrI) =>
% 96.58/13.13 ((
% 96.58/13.13 (dpsetconstrSub) =>
% 96.58/13.13 ((
% 96.58/13.13 (setOfPairsIsBReln) =>
% 96.58/13.13 ((
% 96.58/13.13 (dpsetconstrERa) =>
% 96.58/13.13 ((
% 96.58/13.13 (dpsetconstrEL1) =>
% 96.58/13.13 ((
% 96.58/13.13 (dpsetconstrEL2) =>
% 96.58/13.13 ((
% 96.58/13.13 (dpsetconstrER) =>
% 96.58/13.13 ((
% 96.58/13.13 (funcImageSingleton) =>
% 96.58/13.13 ((
% 96.58/13.13 (apProp) =>
% 96.58/13.13 ((
% 96.58/13.13 (app) =>
% 96.58/13.13 ((
% 96.58/13.13 (infuncsetfunc) =>
% 96.58/13.13 ((
% 96.58/13.13 (ap2p) =>
% 96.58/13.13 ((
% 96.58/13.13 (funcinfuncset) =>
% 96.58/13.13 ((
% 96.58/13.13 (lamProp) =>
% 96.58/13.13 ((
% 96.58/13.13 (lamp) =>
% 96.58/13.13 ((
% 96.58/13.13 (lam2p) =>
% 96.58/13.13 ((
% 96.58/13.13 (brelnall1) =>
% 96.58/13.13 ((
% 96.58/13.13 (brelnall2) =>
% 96.58/13.13 ((
% 96.58/13.13 (ex1E2) =>
% 96.58/13.13 ((
% 96.58/13.13 (funcGraphProp1) =>
% 96.58/13.13 ((
% 96.58/13.13 (funcGraphProp3) =>
% 96.58/13.13 ((
% 96.58/13.13 (funcGraphProp2) =>
% 96.58/13.13 ((
% 96.58/13.13 (funcextLem) =>
% 96.58/13.13 ((
% 96.58/13.13 (funcGraphProp4) =>
% 96.58/13.13 ((
% 96.58/13.13 (subbreln) =>
% 96.58/13.13 ((
% 96.58/13.13 (eqbreln) =>
% 96.58/13.13 ((
% 96.58/13.13 (funcext) =>
% 96.58/13.13 ((
% 96.58/13.13 (funcext2) =>
% 96.58/13.13 ((
% 96.58/13.13 (ap2apEq1) =>
% 96.58/13.13 ((
% 96.58/13.13 (ap2apEq2) =>
% 96.58/13.13 ((
% 96.58/13.13 (beta1) =>
% 96.58/13.13 ((
% 96.58/13.13 (eta1) =>
% 96.58/13.13 ((
% 96.58/13.13 (lam2lamEq) =>
% 96.58/13.13 ((
% 96.58/13.13 (beta2) =>
% 96.58/13.13 ((
% 96.58/13.13 (eta2) =>
% 96.58/13.13 ((
% 96.58/13.13 (iffalseProp1) =>
% 96.58/13.13 ((
% 96.58/13.13 (iffalseProp2) =>
% 96.58/13.13 ((
% 96.58/13.13 (iftrueProp1) =>
% 96.58/13.13 ((
% 96.58/13.13 (iftrueProp2) =>
% 96.58/13.13 ((
% 96.58/13.13 (ifSingleton) =>
% 96.58/13.13 ((
% 96.58/13.13 (ifp) =>
% 96.58/13.13 ((
% 96.58/13.13 (theeq) =>
% 96.58/13.13 ((
% 96.58/13.13 (iftrue) =>
% 96.58/13.13 ((
% 96.58/13.13 (iffalse) =>
% 96.58/13.13 ((
% 96.58/13.13 (iftrueorfalse) =>
% 96.58/13.13 ((
% 96.58/13.13 (binintersectT_lem) =>
% 96.58/13.13 ((
% 96.58/13.13 (binunionT_lem) =>
% 96.58/13.13 ((
% 96.58/13.13 (powersetT_lem) =>
% 96.58/13.13 ((
% 96.58/13.13 (setminusT_lem) =>
% 96.58/13.13 ((
% 96.58/13.13 (complementT_lem) =>
% 96.58/13.13 ((
% 96.58/13.13 (setextT) =>
% 96.58/13.13 ((
% 96.58/13.13 (subsetTI) =>
% 96.58/13.13 ((
% 96.58/13.13 (powersetTI1) =>
% 96.58/13.13 ((
% 96.58/13.13 (powersetTE1) =>
% 96.58/13.13 ((
% 96.58/13.13 (complementTI1) =>
% 96.58/13.13 ((
% 96.58/13.13 (complementTE1) =>
% 96.58/13.13 ((
% 96.58/13.13 (binintersectTELcontra) =>
% 96.58/13.13 ((
% 96.58/13.13 (binintersectTERcontra) =>
% 96.58/13.13 ((
% 96.58/13.13 (contrasubsetT) =>
% 96.58/13.13 ((
% 96.58/13.13 (contrasubsetT1) =>
% 96.58/13.13 ((
% 96.58/13.13 (contrasubsetT2) =>
% 96.58/13.13 ((
% 96.58/13.13 (contrasubsetT3) =>
% 96.58/13.13 ((
% 96.58/13.13 (doubleComplementI1) =>
% 96.58/13.13 ((
% 96.58/13.13 (doubleComplementE1) =>
% 96.58/13.13 ((
% 96.58/13.13 (doubleComplementSub1) =>
% 96.58/13.13 ((
% 96.58/13.13 (doubleComplementSub2) =>
% 96.58/13.13 ((
% 96.58/13.13 (doubleComplementEq) =>
% 96.58/13.13 ((
% 96.58/13.13 (complementTnotintersectT) =>
% 96.58/13.13 ((
% 96.58/13.13 (complementImpComplementIntersect) =>
% 96.58/13.13 ((
% 96.58/13.13 (complementSubsetComplementIntersect) =>
% 96.58/13.13 ((
% 96.58/13.13 (complementInPowersetComplementIntersect) =>
% 96.58/13.13 ((
% 96.58/13.13 (contraSubsetComplement) =>
% 96.58/13.13 ((
% 96.58/13.13 (complementTcontraSubset) =>
% 96.58/13.13 ((
% 96.58/13.13 (binunionTILcontra) =>
% 96.58/13.13 ((
% 96.58/13.13 (binunionTIRcontra) =>
% 96.58/13.13 ((
% 96.58/13.13 (inIntersectImpInUnion) =>
% 96.58/13.13 ((
% 96.58/13.13 (inIntersectImpInUnion2) =>
% 96.58/13.13 ((
% 96.58/13.13 (inIntersectImpInIntersectUnions) =>
% 96.58/13.13 ((
% 96.58/13.13 (intersectInPowersetIntersectUnions) =>
% 96.58/13.13 ((
% 96.58/13.13 (inComplementUnionImpNotIn1) =>
% 96.58/13.13 ((
% 96.58/13.13 (inComplementUnionImpInComplement1) =>
% 96.58/13.13 ((
% 96.58/13.13 (binunionTE) =>
% 96.58/13.13 ((
% 96.58/13.13 (binunionTEcontra) =>
% 96.58/13.13 ((
% 96.58/13.13 (demorgan2a1) =>
% 96.58/13.13 ((
% 96.58/13.13 (complementUnionInPowersetComplement) =>
% 96.58/13.13 ((
% 96.58/13.13 (demorgan2a2) =>
% 96.58/13.13 ((
% 96.58/13.13 (demorgan1a) =>
% 96.58/13.13 ((
% 96.58/13.13 (demorgan1b) =>
% 96.58/13.13 ((
% 96.58/13.13 (demorgan1) =>
% 96.58/13.13 ((
% 96.58/13.13 (demorgan2a) =>
% 96.58/13.13 ((
% 96.58/13.13 (demorgan2b2) =>
% 96.58/13.13 ((
% 96.58/13.13 (demorgan2b) =>
% 96.58/13.13 ((
% 96.58/13.13 (demorgan2) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz13rule0) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz13rule1) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz13rule2) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz13rule3) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz13rule4) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz1_1) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz1_2) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz1_3) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz1_4) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz1_5) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1all2) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1SetBreln1) =>
% 96.58/13.13 ((
% 96.58/13.13 (choice2fnsingleton) =>
% 96.58/13.13 ((
% 96.58/13.13 (setOfPairsIsBReln1) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1all1) =>
% 96.58/13.13 ((
% 96.58/13.13 (subbreln1) =>
% 96.58/13.13 ((
% 96.58/13.13 (eqbreln1) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1invprop) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1invI) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1invE) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1compprop) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1compI) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1compE) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1compEex) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1unionprop) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1unionIL) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1unionIR) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1unionI) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1unionE) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1unionEcases) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1unionCommutes) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz2Ex) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz2W) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz2A) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz2B) =>
% 96.58/13.13 ((
% 96.58/13.13 (image1Ex) =>
% 96.58/13.13 ((
% 96.58/13.13 (image1Ex1) =>
% 96.58/13.13 ((
% 96.58/13.13 (image1Equiv) =>
% 96.58/13.13 ((
% 96.58/13.13 (image1E) =>
% 96.58/13.13 ((
% 96.58/13.13 (image1I) =>
% 96.58/13.13 ((
% 96.58/13.13 (injFuncInInjFuncSet) =>
% 96.58/13.13 ((
% 96.58/13.13 (injFuncSetFuncIn) =>
% 96.58/13.13 ((
% 96.58/13.13 (injFuncSetFuncInj) =>
% 96.58/13.13 ((
% 96.58/13.13 (surjFuncSetFuncIn) =>
% 96.58/13.13 ((
% 96.58/13.13 (surjFuncSetFuncSurj) =>
% 96.58/13.13 ((
% 96.58/13.13 (leftInvIsSurj) =>
% 96.58/13.13 ((
% 96.58/13.13 (surjCantorThm) =>
% 96.58/13.13 ((
% 96.58/13.13 (foundation2) =>
% 96.58/13.13 ((
% 96.58/13.13 (notinself) =>
% 96.58/13.13 ((
% 96.58/13.13 (notinself2) =>
% 96.58/13.13 ((
% 96.58/13.13 (omegaSp) =>
% 96.58/13.13 ((
% 96.58/13.13 (omegaSclos) =>
% 96.58/13.13 ((
% 96.58/13.13 (peano0notS) =>
% 96.58/13.13 ((
% 96.58/13.13 (!!) @ (
% 96.58/13.13 (('#S') @ (
% 96.58/13.13 (
% 96.58/13.13 ('#B') @ (
% 96.58/13.13 =>) @
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 ('#C') @ in @
% 96.58/13.13 omega)))) @
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 ('#B') @ (
% 96.58/13.13 !!) @
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 ('#B') @ (
% 96.58/13.13 (
% 96.58/13.13 ('#S') @ (
% 96.58/13.13 (
% 96.58/13.13 ('#B') @ (
% 96.58/13.13 =>) @
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 ('#C') @ in @
% 96.58/13.13 omega)))))) @
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 ('#S') @ (
% 96.58/13.13 (
% 96.58/13.13 ('#B') @ (
% 96.58/13.13 '#S') @
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 ('#B') @ (
% 96.58/13.13 (
% 96.58/13.13 ('#B') @ (
% 96.58/13.13 =>))) @
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 ('#C') @ (
% 96.58/13.13 (
% 96.58/13.13 ('#B') @ (
% 96.58/13.13 '#B') @
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 ('#B') @ (
% 96.58/13.13 =) @
% 96.58/13.13 omegaS)))) @
% 96.58/13.13 omegaS)))))) @
% 96.58/13.13 (
% 96.58/13.13 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 96.58/13.13 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl2])).
% 96.58/13.13 thf(zip_derived_cl5, plain,
% 96.58/13.13 (~ (((emptysetAx) =>
% 96.58/13.13 (((setadjoinAx) =>
% 96.58/13.13 (((powersetAx) =>
% 96.58/13.13 (((setunionAx) =>
% 96.58/13.13 (((in @ emptyset @ omega) =>
% 96.58/13.13 (((omegaSAx) =>
% 96.58/13.13 (((omegaIndAx) =>
% 96.58/13.13 (((replAx) =>
% 96.58/13.13 (((foundationAx) =>
% 96.58/13.13 (((wellorderingAx) =>
% 96.58/13.13 (((descrp) =>
% 96.58/13.13 (((dsetconstrI) =>
% 96.58/13.13 (((dsetconstrEL) =>
% 96.58/13.13 (((dsetconstrER) =>
% 96.58/13.13 (((exuE1) =>
% 96.58/13.13 (((prop2setE) =>
% 96.58/13.13 (((emptysetE) =>
% 96.58/13.13 (((emptysetimpfalse) =>
% 96.58/13.13 (((notinemptyset) =>
% 96.58/13.13 (((exuE3e) =>
% 96.58/13.13 (((setext) =>
% 96.58/13.13 (((emptyI) =>
% 96.58/13.13 (((noeltsimpempty) =>
% 96.58/13.13 (((setbeta) =>
% 96.58/13.13 (((nonemptyE1) =>
% 96.58/13.13 (((nonemptyI) =>
% 96.58/13.13 (((nonemptyI1) =>
% 96.58/13.13 (((setadjoinIL) =>
% 96.58/13.13 (((in @
% 96.58/13.13 emptyset @
% 96.58/13.13 (setadjoin @
% 96.58/13.13 emptyset @
% 96.58/13.13 emptyset)) =>
% 96.58/13.13 (((setadjoinIR) =>
% 96.58/13.13 ((
% 96.58/13.13 (setadjoinE) =>
% 96.58/13.13 ((
% 96.58/13.13 (setadjoinOr) =>
% 96.58/13.13 ((
% 96.58/13.13 (setoftrueEq) =>
% 96.58/13.13 ((
% 96.58/13.13 (powersetI) =>
% 96.58/13.13 ((
% 96.58/13.13 (emptyinPowerset) =>
% 96.58/13.13 ((
% 96.58/13.13 (emptyInPowerset) =>
% 96.58/13.13 ((
% 96.58/13.13 (powersetE) =>
% 96.58/13.13 ((
% 96.58/13.13 (setunionI) =>
% 96.58/13.13 ((
% 96.58/13.13 (setunionE) =>
% 96.58/13.13 ((
% 96.58/13.13 (subPowSU) =>
% 96.58/13.13 ((
% 96.58/13.13 (exuE2) =>
% 96.58/13.13 ((
% 96.58/13.13 (nonemptyImpWitness) =>
% 96.58/13.13 ((
% 96.58/13.13 (uniqinunit) =>
% 96.58/13.13 ((
% 96.58/13.13 (notinsingleton) =>
% 96.58/13.13 ((
% 96.58/13.13 (eqinunit) =>
% 96.58/13.13 ((
% 96.58/13.13 (singletonsswitch) =>
% 96.58/13.13 ((
% 96.58/13.13 (upairsetE) =>
% 96.58/13.13 ((
% 96.58/13.13 (upairsetIL) =>
% 96.58/13.13 ((
% 96.58/13.13 (upairsetIR) =>
% 96.58/13.13 ((
% 96.58/13.13 (emptyE1) =>
% 96.58/13.13 ((
% 96.58/13.13 (vacuousDall) =>
% 96.58/13.13 ((
% 96.58/13.13 (quantDeMorgan1) =>
% 96.58/13.13 ((
% 96.58/13.13 (quantDeMorgan2) =>
% 96.58/13.13 ((
% 96.58/13.13 (quantDeMorgan3) =>
% 96.58/13.13 ((
% 96.58/13.13 (quantDeMorgan4) =>
% 96.58/13.13 ((
% 96.58/13.13 (prop2setI) =>
% 96.58/13.13 ((
% 96.58/13.13 (prop2set2propI) =>
% 96.58/13.13 ((
% 96.58/13.13 (notdexE) =>
% 96.58/13.13 ((
% 96.58/13.13 (notdallE) =>
% 96.58/13.13 ((
% 96.58/13.13 (exuI1) =>
% 96.58/13.13 ((
% 96.58/13.13 (exuI3) =>
% 96.58/13.13 ((
% 96.58/13.13 (exuI2) =>
% 96.58/13.13 ((
% 96.58/13.13 (inCongP) =>
% 96.58/13.13 ((
% 96.58/13.13 (in__Cong) =>
% 96.58/13.13 ((
% 96.58/13.13 (exuE3u) =>
% 96.58/13.13 ((
% 96.58/13.13 (exu__Cong) =>
% 96.58/13.13 ((
% 96.58/13.13 (setadjoin__Cong) =>
% 96.58/13.13 ((
% 96.58/13.13 (powerset__Cong) =>
% 96.58/13.13 ((
% 96.58/13.13 (setunion__Cong) =>
% 96.58/13.13 ((
% 96.58/13.13 (exuEu) =>
% 96.58/13.13 ((
% 96.58/13.13 (descr__Cong) =>
% 96.58/13.13 ((
% 96.58/13.13 (dsetconstr__Cong) =>
% 96.58/13.13 ((
% 96.58/13.13 (subsetI1) =>
% 96.58/13.13 ((
% 96.58/13.13 (eqimpsubset2) =>
% 96.58/13.13 ((
% 96.58/13.13 (eqimpsubset1) =>
% 96.58/13.13 ((
% 96.58/13.13 (subsetI2) =>
% 96.58/13.13 ((
% 96.58/13.13 (emptysetsubset) =>
% 96.58/13.13 ((
% 96.58/13.13 (subsetE) =>
% 96.58/13.13 ((
% 96.58/13.13 (subsetE2) =>
% 96.58/13.13 ((
% 96.58/13.13 (notsubsetI) =>
% 96.58/13.13 ((
% 96.58/13.13 (notequalI1) =>
% 96.58/13.13 ((
% 96.58/13.13 (notequalI2) =>
% 96.58/13.13 ((
% 96.58/13.13 (subsetRefl) =>
% 96.58/13.13 ((
% 96.58/13.13 (subsetTrans) =>
% 96.58/13.13 ((
% 96.58/13.13 (setadjoinSub) =>
% 96.58/13.13 ((
% 96.58/13.13 (setadjoinSub2) =>
% 96.58/13.13 ((
% 96.58/13.13 (subset2powerset) =>
% 96.58/13.13 ((
% 96.58/13.13 (setextsub) =>
% 96.58/13.13 ((
% 96.58/13.13 (subsetemptysetimpeq) =>
% 96.58/13.13 ((
% 96.58/13.13 (powersetI1) =>
% 96.58/13.13 ((
% 96.58/13.13 (powersetE1) =>
% 96.58/13.13 ((
% 96.58/13.13 (inPowerset) =>
% 96.58/13.13 ((
% 96.58/13.13 (powersetsubset) =>
% 96.58/13.13 ((
% 96.58/13.13 (sepInPowerset) =>
% 96.58/13.13 ((
% 96.58/13.13 (sepSubset) =>
% 96.58/13.13 ((
% 96.58/13.13 (binunionIL) =>
% 96.58/13.13 ((
% 96.58/13.13 (upairset2IR) =>
% 96.58/13.13 ((
% 96.58/13.13 (binunionIR) =>
% 96.58/13.13 ((
% 96.58/13.13 (binunionEcases) =>
% 96.58/13.13 ((
% 96.58/13.13 (binunionE) =>
% 96.58/13.13 ((
% 96.58/13.13 (binunionLsub) =>
% 96.58/13.13 ((
% 96.58/13.13 (binunionRsub) =>
% 96.58/13.13 ((
% 96.58/13.13 (binintersectI) =>
% 96.58/13.13 ((
% 96.58/13.13 (binintersectSubset5) =>
% 96.58/13.13 ((
% 96.58/13.13 (binintersectEL) =>
% 96.58/13.13 ((
% 96.58/13.13 (binintersectLsub) =>
% 96.58/13.13 ((
% 96.58/13.13 (binintersectSubset2) =>
% 96.58/13.13 ((
% 96.58/13.13 (binintersectSubset3) =>
% 96.58/13.13 ((
% 96.58/13.13 (binintersectER) =>
% 96.58/13.13 ((
% 96.58/13.13 (disjointsetsI1) =>
% 96.58/13.13 ((
% 96.58/13.13 (binintersectRsub) =>
% 96.58/13.13 ((
% 96.58/13.13 (binintersectSubset4) =>
% 96.58/13.13 ((
% 96.58/13.13 (binintersectSubset1) =>
% 96.58/13.13 ((
% 96.58/13.13 (bs114d) =>
% 96.58/13.13 ((
% 96.58/13.13 (setminusI) =>
% 96.58/13.13 ((
% 96.58/13.13 (setminusEL) =>
% 96.58/13.13 ((
% 96.58/13.13 (setminusER) =>
% 96.58/13.13 ((
% 96.58/13.13 (setminusSubset2) =>
% 96.58/13.13 ((
% 96.58/13.13 (setminusERneg) =>
% 96.58/13.13 ((
% 96.58/13.13 (setminusELneg) =>
% 96.58/13.13 ((
% 96.58/13.13 (setminusILneg) =>
% 96.58/13.13 ((
% 96.58/13.13 (setminusIRneg) =>
% 96.58/13.13 ((
% 96.58/13.13 (setminusLsub) =>
% 96.58/13.13 ((
% 96.58/13.13 (setminusSubset1) =>
% 96.58/13.13 ((
% 96.58/13.13 (symdiffE) =>
% 96.58/13.13 ((
% 96.58/13.13 (symdiffI1) =>
% 96.58/13.13 ((
% 96.58/13.13 (symdiffI2) =>
% 96.58/13.13 ((
% 96.58/13.13 (symdiffIneg1) =>
% 96.58/13.13 ((
% 96.58/13.13 (symdiffIneg2) =>
% 96.58/13.13 ((
% 96.58/13.13 (secondinupair) =>
% 96.58/13.13 ((
% 96.58/13.13 (setukpairIL) =>
% 96.58/13.13 ((
% 96.58/13.13 (setukpairIR) =>
% 96.58/13.13 ((
% 96.58/13.13 (kpairiskpair) =>
% 96.58/13.13 ((
% 96.58/13.13 (kpairp) =>
% 96.58/13.13 ((
% 96.58/13.13 (singletonsubset) =>
% 96.58/13.13 ((
% 96.58/13.13 (singletoninpowerset) =>
% 96.58/13.13 ((
% 96.58/13.13 (singletoninpowunion) =>
% 96.58/13.13 ((
% 96.58/13.13 (upairset2E) =>
% 96.58/13.13 ((
% 96.58/13.13 (upairsubunion) =>
% 96.58/13.13 ((
% 96.58/13.13 (upairinpowunion) =>
% 96.58/13.13 ((
% 96.58/13.13 (ubforcartprodlem1) =>
% 96.58/13.13 ((
% 96.58/13.13 (ubforcartprodlem2) =>
% 96.58/13.13 ((
% 96.58/13.13 (ubforcartprodlem3) =>
% 96.58/13.13 ((
% 96.58/13.13 (cartprodpairin) =>
% 96.58/13.13 ((
% 96.58/13.13 (cartprodmempair1) =>
% 96.58/13.13 ((
% 96.58/13.13 (cartprodmempair) =>
% 96.58/13.13 ((
% 96.58/13.13 (setunionE2) =>
% 96.58/13.13 ((
% 96.58/13.13 (setunionsingleton1) =>
% 96.58/13.13 ((
% 96.58/13.13 (setunionsingleton2) =>
% 96.58/13.13 ((
% 96.58/13.13 (setunionsingleton) =>
% 96.58/13.13 ((
% 96.58/13.13 (singletonprop) =>
% 96.58/13.13 ((
% 96.58/13.13 (ex1E1) =>
% 96.58/13.13 ((
% 96.58/13.13 (ex1I) =>
% 96.58/13.13 ((
% 96.58/13.13 (ex1I2) =>
% 96.58/13.13 ((
% 96.58/13.13 (singletonsuniq) =>
% 96.58/13.13 ((
% 96.58/13.13 (setukpairinjL1) =>
% 96.58/13.13 ((
% 96.58/13.13 (kfstsingleton) =>
% 96.58/13.13 ((
% 96.58/13.13 (theprop) =>
% 96.58/13.13 ((
% 96.58/13.13 (kfstpairEq) =>
% 96.58/13.13 ((
% 96.58/13.13 (cartprodfstin) =>
% 96.58/13.13 ((
% 96.58/13.13 (setukpairinjL2) =>
% 96.58/13.13 ((
% 96.58/13.13 (setukpairinjL) =>
% 96.58/13.13 ((
% 96.58/13.13 (setukpairinjR11) =>
% 96.58/13.13 ((
% 96.58/13.13 (setukpairinjR12) =>
% 96.58/13.13 ((
% 96.58/13.13 (setukpairinjR1) =>
% 96.58/13.13 ((
% 96.58/13.13 (upairequniteq) =>
% 96.58/13.13 ((
% 96.58/13.13 (setukpairinjR2) =>
% 96.58/13.13 ((
% 96.58/13.13 (setukpairinjR) =>
% 96.58/13.13 ((
% 96.58/13.13 (ksndsingleton) =>
% 96.58/13.13 ((
% 96.58/13.13 (ksndpairEq) =>
% 96.58/13.13 ((
% 96.58/13.13 (kpairsurjEq) =>
% 96.58/13.13 ((
% 96.58/13.13 (cartprodsndin) =>
% 96.58/13.13 ((
% 96.58/13.13 (cartprodpairmemEL) =>
% 96.58/13.13 ((
% 96.58/13.13 (cartprodpairmemER) =>
% 96.58/13.13 ((
% 96.58/13.13 (cartprodmempaircEq) =>
% 96.58/13.13 ((
% 96.58/13.13 (cartprodfstpairEq) =>
% 96.58/13.13 ((
% 96.58/13.13 (cartprodsndpairEq) =>
% 96.58/13.13 ((
% 96.58/13.13 (cartprodpairsurjEq) =>
% 96.58/13.13 ((
% 96.58/13.13 (dpsetconstrI) =>
% 96.58/13.13 ((
% 96.58/13.13 (dpsetconstrSub) =>
% 96.58/13.13 ((
% 96.58/13.13 (setOfPairsIsBReln) =>
% 96.58/13.13 ((
% 96.58/13.13 (dpsetconstrERa) =>
% 96.58/13.13 ((
% 96.58/13.13 (dpsetconstrEL1) =>
% 96.58/13.13 ((
% 96.58/13.13 (dpsetconstrEL2) =>
% 96.58/13.13 ((
% 96.58/13.13 (dpsetconstrER) =>
% 96.58/13.13 ((
% 96.58/13.13 (funcImageSingleton) =>
% 96.58/13.13 ((
% 96.58/13.13 (apProp) =>
% 96.58/13.13 ((
% 96.58/13.13 (app) =>
% 96.58/13.13 ((
% 96.58/13.13 (infuncsetfunc) =>
% 96.58/13.13 ((
% 96.58/13.13 (ap2p) =>
% 96.58/13.13 ((
% 96.58/13.13 (funcinfuncset) =>
% 96.58/13.13 ((
% 96.58/13.13 (lamProp) =>
% 96.58/13.13 ((
% 96.58/13.13 (lamp) =>
% 96.58/13.13 ((
% 96.58/13.13 (lam2p) =>
% 96.58/13.13 ((
% 96.58/13.13 (brelnall1) =>
% 96.58/13.13 ((
% 96.58/13.13 (brelnall2) =>
% 96.58/13.13 ((
% 96.58/13.13 (ex1E2) =>
% 96.58/13.13 ((
% 96.58/13.13 (funcGraphProp1) =>
% 96.58/13.13 ((
% 96.58/13.13 (funcGraphProp3) =>
% 96.58/13.13 ((
% 96.58/13.13 (funcGraphProp2) =>
% 96.58/13.13 ((
% 96.58/13.13 (funcextLem) =>
% 96.58/13.13 ((
% 96.58/13.13 (funcGraphProp4) =>
% 96.58/13.13 ((
% 96.58/13.13 (subbreln) =>
% 96.58/13.13 ((
% 96.58/13.13 (eqbreln) =>
% 96.58/13.13 ((
% 96.58/13.13 (funcext) =>
% 96.58/13.13 ((
% 96.58/13.13 (funcext2) =>
% 96.58/13.13 ((
% 96.58/13.13 (ap2apEq1) =>
% 96.58/13.13 ((
% 96.58/13.13 (ap2apEq2) =>
% 96.58/13.13 ((
% 96.58/13.13 (beta1) =>
% 96.58/13.13 ((
% 96.58/13.13 (eta1) =>
% 96.58/13.13 ((
% 96.58/13.13 (lam2lamEq) =>
% 96.58/13.13 ((
% 96.58/13.13 (beta2) =>
% 96.58/13.13 ((
% 96.58/13.13 (eta2) =>
% 96.58/13.13 ((
% 96.58/13.13 (iffalseProp1) =>
% 96.58/13.13 ((
% 96.58/13.13 (iffalseProp2) =>
% 96.58/13.13 ((
% 96.58/13.13 (iftrueProp1) =>
% 96.58/13.13 ((
% 96.58/13.13 (iftrueProp2) =>
% 96.58/13.13 ((
% 96.58/13.13 (ifSingleton) =>
% 96.58/13.13 ((
% 96.58/13.13 (ifp) =>
% 96.58/13.13 ((
% 96.58/13.13 (theeq) =>
% 96.58/13.13 ((
% 96.58/13.13 (iftrue) =>
% 96.58/13.13 ((
% 96.58/13.13 (iffalse) =>
% 96.58/13.13 ((
% 96.58/13.13 (iftrueorfalse) =>
% 96.58/13.13 ((
% 96.58/13.13 (binintersectT_lem) =>
% 96.58/13.13 ((
% 96.58/13.13 (binunionT_lem) =>
% 96.58/13.13 ((
% 96.58/13.13 (powersetT_lem) =>
% 96.58/13.13 ((
% 96.58/13.13 (setminusT_lem) =>
% 96.58/13.13 ((
% 96.58/13.13 (complementT_lem) =>
% 96.58/13.13 ((
% 96.58/13.13 (setextT) =>
% 96.58/13.13 ((
% 96.58/13.13 (subsetTI) =>
% 96.58/13.13 ((
% 96.58/13.13 (powersetTI1) =>
% 96.58/13.13 ((
% 96.58/13.13 (powersetTE1) =>
% 96.58/13.13 ((
% 96.58/13.13 (complementTI1) =>
% 96.58/13.13 ((
% 96.58/13.13 (complementTE1) =>
% 96.58/13.13 ((
% 96.58/13.13 (binintersectTELcontra) =>
% 96.58/13.13 ((
% 96.58/13.13 (binintersectTERcontra) =>
% 96.58/13.13 ((
% 96.58/13.13 (contrasubsetT) =>
% 96.58/13.13 ((
% 96.58/13.13 (contrasubsetT1) =>
% 96.58/13.13 ((
% 96.58/13.13 (contrasubsetT2) =>
% 96.58/13.13 ((
% 96.58/13.13 (contrasubsetT3) =>
% 96.58/13.13 ((
% 96.58/13.13 (doubleComplementI1) =>
% 96.58/13.13 ((
% 96.58/13.13 (doubleComplementE1) =>
% 96.58/13.13 ((
% 96.58/13.13 (doubleComplementSub1) =>
% 96.58/13.13 ((
% 96.58/13.13 (doubleComplementSub2) =>
% 96.58/13.13 ((
% 96.58/13.13 (doubleComplementEq) =>
% 96.58/13.13 ((
% 96.58/13.13 (complementTnotintersectT) =>
% 96.58/13.13 ((
% 96.58/13.13 (complementImpComplementIntersect) =>
% 96.58/13.13 ((
% 96.58/13.13 (complementSubsetComplementIntersect) =>
% 96.58/13.13 ((
% 96.58/13.13 (complementInPowersetComplementIntersect) =>
% 96.58/13.13 ((
% 96.58/13.13 (contraSubsetComplement) =>
% 96.58/13.13 ((
% 96.58/13.13 (complementTcontraSubset) =>
% 96.58/13.13 ((
% 96.58/13.13 (binunionTILcontra) =>
% 96.58/13.13 ((
% 96.58/13.13 (binunionTIRcontra) =>
% 96.58/13.13 ((
% 96.58/13.13 (inIntersectImpInUnion) =>
% 96.58/13.13 ((
% 96.58/13.13 (inIntersectImpInUnion2) =>
% 96.58/13.13 ((
% 96.58/13.13 (inIntersectImpInIntersectUnions) =>
% 96.58/13.13 ((
% 96.58/13.13 (intersectInPowersetIntersectUnions) =>
% 96.58/13.13 ((
% 96.58/13.13 (inComplementUnionImpNotIn1) =>
% 96.58/13.13 ((
% 96.58/13.13 (inComplementUnionImpInComplement1) =>
% 96.58/13.13 ((
% 96.58/13.13 (binunionTE) =>
% 96.58/13.13 ((
% 96.58/13.13 (binunionTEcontra) =>
% 96.58/13.13 ((
% 96.58/13.13 (demorgan2a1) =>
% 96.58/13.13 ((
% 96.58/13.13 (complementUnionInPowersetComplement) =>
% 96.58/13.13 ((
% 96.58/13.13 (demorgan2a2) =>
% 96.58/13.13 ((
% 96.58/13.13 (demorgan1a) =>
% 96.58/13.13 ((
% 96.58/13.13 (demorgan1b) =>
% 96.58/13.13 ((
% 96.58/13.13 (demorgan1) =>
% 96.58/13.13 ((
% 96.58/13.13 (demorgan2a) =>
% 96.58/13.13 ((
% 96.58/13.13 (demorgan2b2) =>
% 96.58/13.13 ((
% 96.58/13.13 (demorgan2b) =>
% 96.58/13.13 ((
% 96.58/13.13 (demorgan2) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz13rule0) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz13rule1) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz13rule2) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz13rule3) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz13rule4) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz1_1) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz1_2) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz1_3) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz1_4) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz1_5) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1all2) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1SetBreln1) =>
% 96.58/13.13 ((
% 96.58/13.13 (choice2fnsingleton) =>
% 96.58/13.13 ((
% 96.58/13.13 (setOfPairsIsBReln1) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1all1) =>
% 96.58/13.13 ((
% 96.58/13.13 (subbreln1) =>
% 96.58/13.13 ((
% 96.58/13.13 (eqbreln1) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1invprop) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1invI) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1invE) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1compprop) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1compI) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1compE) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1compEex) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1unionprop) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1unionIL) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1unionIR) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1unionI) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1unionE) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1unionEcases) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1unionCommutes) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz2Ex) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz2W) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz2A) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz2B) =>
% 96.58/13.13 ((
% 96.58/13.13 (image1Ex) =>
% 96.58/13.13 ((
% 96.58/13.13 (image1Ex1) =>
% 96.58/13.13 ((
% 96.58/13.13 (image1Equiv) =>
% 96.58/13.13 ((
% 96.58/13.13 (image1E) =>
% 96.58/13.13 ((
% 96.58/13.13 (image1I) =>
% 96.58/13.13 ((
% 96.58/13.13 (injFuncInInjFuncSet) =>
% 96.58/13.13 ((
% 96.58/13.13 (injFuncSetFuncIn) =>
% 96.58/13.13 ((
% 96.58/13.13 (injFuncSetFuncInj) =>
% 96.58/13.13 ((
% 96.58/13.13 (surjFuncSetFuncIn) =>
% 96.58/13.13 ((
% 96.58/13.13 (surjFuncSetFuncSurj) =>
% 96.58/13.13 ((
% 96.58/13.13 (leftInvIsSurj) =>
% 96.58/13.13 ((
% 96.58/13.13 (surjCantorThm) =>
% 96.58/13.13 ((
% 96.58/13.13 (foundation2) =>
% 96.58/13.13 ((
% 96.58/13.13 (notinself) =>
% 96.58/13.13 ((
% 96.58/13.13 (notinself2) =>
% 96.58/13.13 ((
% 96.58/13.13 (omegaSp) =>
% 96.58/13.13 ((
% 96.58/13.13 (omegaSclos) =>
% 96.58/13.13 ((
% 96.58/13.13 (peano0notS) =>
% 96.58/13.13 ((
% 96.58/13.13 (!!) @ (
% 96.58/13.13 (('#S') @ (
% 96.58/13.13 (
% 96.58/13.13 ('#B') @ (
% 96.58/13.13 =>) @
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 ('#C') @ in @
% 96.58/13.13 omega)))) @
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 ('#B') @ (
% 96.58/13.13 !!) @
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 ('#B') @ (
% 96.58/13.13 (
% 96.58/13.13 ('#S') @ (
% 96.58/13.13 (
% 96.58/13.13 ('#B') @ (
% 96.58/13.13 =>) @
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 ('#C') @ in @
% 96.58/13.13 omega)))))) @
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 ('#S') @ (
% 96.58/13.13 (
% 96.58/13.13 ('#B') @ (
% 96.58/13.13 '#S') @
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 ('#B') @ (
% 96.58/13.13 (
% 96.58/13.13 ('#B') @ (
% 96.58/13.13 =>))) @
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 ('#C') @ (
% 96.58/13.13 (
% 96.58/13.13 ('#B') @ (
% 96.58/13.13 '#B') @
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 ('#B') @ (
% 96.58/13.13 =) @
% 96.58/13.13 omegaS)))) @
% 96.58/13.13 omegaS)))))) @
% 96.58/13.13 (
% 96.58/13.13 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 96.58/13.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3])).
% 96.58/13.13 thf(zip_derived_cl8, plain,
% 96.58/13.13 (~ (((setadjoinAx) =>
% 96.58/13.13 (((powersetAx) =>
% 96.58/13.13 (((setunionAx) =>
% 96.58/13.13 (((in @ emptyset @ omega) =>
% 96.58/13.13 (((omegaSAx) =>
% 96.58/13.13 (((omegaIndAx) =>
% 96.58/13.13 (((replAx) =>
% 96.58/13.13 (((foundationAx) =>
% 96.58/13.13 (((wellorderingAx) =>
% 96.58/13.13 (((descrp) =>
% 96.58/13.13 (((dsetconstrI) =>
% 96.58/13.13 (((dsetconstrEL) =>
% 96.58/13.13 (((dsetconstrER) =>
% 96.58/13.13 (((exuE1) =>
% 96.58/13.13 (((prop2setE) =>
% 96.58/13.13 (((emptysetE) =>
% 96.58/13.13 (((emptysetimpfalse) =>
% 96.58/13.13 (((notinemptyset) =>
% 96.58/13.13 (((exuE3e) =>
% 96.58/13.13 (((setext) =>
% 96.58/13.13 (((emptyI) =>
% 96.58/13.13 (((noeltsimpempty) =>
% 96.58/13.13 (((setbeta) =>
% 96.58/13.13 (((nonemptyE1) =>
% 96.58/13.13 (((nonemptyI) =>
% 96.58/13.13 (((nonemptyI1) =>
% 96.58/13.13 (((setadjoinIL) =>
% 96.58/13.13 (((in @
% 96.58/13.13 emptyset @
% 96.58/13.13 (setadjoin @
% 96.58/13.13 emptyset @
% 96.58/13.13 emptyset)) =>
% 96.58/13.13 (((setadjoinIR) =>
% 96.58/13.13 (((setadjoinE) =>
% 96.58/13.13 ((
% 96.58/13.13 (setadjoinOr) =>
% 96.58/13.13 ((
% 96.58/13.13 (setoftrueEq) =>
% 96.58/13.13 ((
% 96.58/13.13 (powersetI) =>
% 96.58/13.13 ((
% 96.58/13.13 (emptyinPowerset) =>
% 96.58/13.13 ((
% 96.58/13.13 (emptyInPowerset) =>
% 96.58/13.13 ((
% 96.58/13.13 (powersetE) =>
% 96.58/13.13 ((
% 96.58/13.13 (setunionI) =>
% 96.58/13.13 ((
% 96.58/13.13 (setunionE) =>
% 96.58/13.13 ((
% 96.58/13.13 (subPowSU) =>
% 96.58/13.13 ((
% 96.58/13.13 (exuE2) =>
% 96.58/13.13 ((
% 96.58/13.13 (nonemptyImpWitness) =>
% 96.58/13.13 ((
% 96.58/13.13 (uniqinunit) =>
% 96.58/13.13 ((
% 96.58/13.13 (notinsingleton) =>
% 96.58/13.13 ((
% 96.58/13.13 (eqinunit) =>
% 96.58/13.13 ((
% 96.58/13.13 (singletonsswitch) =>
% 96.58/13.13 ((
% 96.58/13.13 (upairsetE) =>
% 96.58/13.13 ((
% 96.58/13.13 (upairsetIL) =>
% 96.58/13.13 ((
% 96.58/13.13 (upairsetIR) =>
% 96.58/13.13 ((
% 96.58/13.13 (emptyE1) =>
% 96.58/13.13 ((
% 96.58/13.13 (vacuousDall) =>
% 96.58/13.13 ((
% 96.58/13.13 (quantDeMorgan1) =>
% 96.58/13.13 ((
% 96.58/13.13 (quantDeMorgan2) =>
% 96.58/13.13 ((
% 96.58/13.13 (quantDeMorgan3) =>
% 96.58/13.13 ((
% 96.58/13.13 (quantDeMorgan4) =>
% 96.58/13.13 ((
% 96.58/13.13 (prop2setI) =>
% 96.58/13.13 ((
% 96.58/13.13 (prop2set2propI) =>
% 96.58/13.13 ((
% 96.58/13.13 (notdexE) =>
% 96.58/13.13 ((
% 96.58/13.13 (notdallE) =>
% 96.58/13.13 ((
% 96.58/13.13 (exuI1) =>
% 96.58/13.13 ((
% 96.58/13.13 (exuI3) =>
% 96.58/13.13 ((
% 96.58/13.13 (exuI2) =>
% 96.58/13.13 ((
% 96.58/13.13 (inCongP) =>
% 96.58/13.13 ((
% 96.58/13.13 (in__Cong) =>
% 96.58/13.13 ((
% 96.58/13.13 (exuE3u) =>
% 96.58/13.13 ((
% 96.58/13.13 (exu__Cong) =>
% 96.58/13.13 ((
% 96.58/13.13 (setadjoin__Cong) =>
% 96.58/13.13 ((
% 96.58/13.13 (powerset__Cong) =>
% 96.58/13.13 ((
% 96.58/13.13 (setunion__Cong) =>
% 96.58/13.13 ((
% 96.58/13.13 (exuEu) =>
% 96.58/13.13 ((
% 96.58/13.13 (descr__Cong) =>
% 96.58/13.13 ((
% 96.58/13.13 (dsetconstr__Cong) =>
% 96.58/13.13 ((
% 96.58/13.13 (subsetI1) =>
% 96.58/13.13 ((
% 96.58/13.13 (eqimpsubset2) =>
% 96.58/13.13 ((
% 96.58/13.13 (eqimpsubset1) =>
% 96.58/13.13 ((
% 96.58/13.13 (subsetI2) =>
% 96.58/13.13 ((
% 96.58/13.13 (emptysetsubset) =>
% 96.58/13.13 ((
% 96.58/13.13 (subsetE) =>
% 96.58/13.13 ((
% 96.58/13.13 (subsetE2) =>
% 96.58/13.13 ((
% 96.58/13.13 (notsubsetI) =>
% 96.58/13.13 ((
% 96.58/13.13 (notequalI1) =>
% 96.58/13.13 ((
% 96.58/13.13 (notequalI2) =>
% 96.58/13.13 ((
% 96.58/13.13 (subsetRefl) =>
% 96.58/13.13 ((
% 96.58/13.13 (subsetTrans) =>
% 96.58/13.13 ((
% 96.58/13.13 (setadjoinSub) =>
% 96.58/13.13 ((
% 96.58/13.13 (setadjoinSub2) =>
% 96.58/13.13 ((
% 96.58/13.13 (subset2powerset) =>
% 96.58/13.13 ((
% 96.58/13.13 (setextsub) =>
% 96.58/13.13 ((
% 96.58/13.13 (subsetemptysetimpeq) =>
% 96.58/13.13 ((
% 96.58/13.13 (powersetI1) =>
% 96.58/13.13 ((
% 96.58/13.13 (powersetE1) =>
% 96.58/13.13 ((
% 96.58/13.13 (inPowerset) =>
% 96.58/13.13 ((
% 96.58/13.13 (powersetsubset) =>
% 96.58/13.13 ((
% 96.58/13.13 (sepInPowerset) =>
% 96.58/13.13 ((
% 96.58/13.13 (sepSubset) =>
% 96.58/13.13 ((
% 96.58/13.13 (binunionIL) =>
% 96.58/13.13 ((
% 96.58/13.13 (upairset2IR) =>
% 96.58/13.13 ((
% 96.58/13.13 (binunionIR) =>
% 96.58/13.13 ((
% 96.58/13.13 (binunionEcases) =>
% 96.58/13.13 ((
% 96.58/13.13 (binunionE) =>
% 96.58/13.13 ((
% 96.58/13.13 (binunionLsub) =>
% 96.58/13.13 ((
% 96.58/13.13 (binunionRsub) =>
% 96.58/13.13 ((
% 96.58/13.13 (binintersectI) =>
% 96.58/13.13 ((
% 96.58/13.13 (binintersectSubset5) =>
% 96.58/13.13 ((
% 96.58/13.13 (binintersectEL) =>
% 96.58/13.13 ((
% 96.58/13.13 (binintersectLsub) =>
% 96.58/13.13 ((
% 96.58/13.13 (binintersectSubset2) =>
% 96.58/13.13 ((
% 96.58/13.13 (binintersectSubset3) =>
% 96.58/13.13 ((
% 96.58/13.13 (binintersectER) =>
% 96.58/13.13 ((
% 96.58/13.13 (disjointsetsI1) =>
% 96.58/13.13 ((
% 96.58/13.13 (binintersectRsub) =>
% 96.58/13.13 ((
% 96.58/13.13 (binintersectSubset4) =>
% 96.58/13.13 ((
% 96.58/13.13 (binintersectSubset1) =>
% 96.58/13.13 ((
% 96.58/13.13 (bs114d) =>
% 96.58/13.13 ((
% 96.58/13.13 (setminusI) =>
% 96.58/13.13 ((
% 96.58/13.13 (setminusEL) =>
% 96.58/13.13 ((
% 96.58/13.13 (setminusER) =>
% 96.58/13.13 ((
% 96.58/13.13 (setminusSubset2) =>
% 96.58/13.13 ((
% 96.58/13.13 (setminusERneg) =>
% 96.58/13.13 ((
% 96.58/13.13 (setminusELneg) =>
% 96.58/13.13 ((
% 96.58/13.13 (setminusILneg) =>
% 96.58/13.13 ((
% 96.58/13.13 (setminusIRneg) =>
% 96.58/13.13 ((
% 96.58/13.13 (setminusLsub) =>
% 96.58/13.13 ((
% 96.58/13.13 (setminusSubset1) =>
% 96.58/13.13 ((
% 96.58/13.13 (symdiffE) =>
% 96.58/13.13 ((
% 96.58/13.13 (symdiffI1) =>
% 96.58/13.13 ((
% 96.58/13.13 (symdiffI2) =>
% 96.58/13.13 ((
% 96.58/13.13 (symdiffIneg1) =>
% 96.58/13.13 ((
% 96.58/13.13 (symdiffIneg2) =>
% 96.58/13.13 ((
% 96.58/13.13 (secondinupair) =>
% 96.58/13.13 ((
% 96.58/13.13 (setukpairIL) =>
% 96.58/13.13 ((
% 96.58/13.13 (setukpairIR) =>
% 96.58/13.13 ((
% 96.58/13.13 (kpairiskpair) =>
% 96.58/13.13 ((
% 96.58/13.13 (kpairp) =>
% 96.58/13.13 ((
% 96.58/13.13 (singletonsubset) =>
% 96.58/13.13 ((
% 96.58/13.13 (singletoninpowerset) =>
% 96.58/13.13 ((
% 96.58/13.13 (singletoninpowunion) =>
% 96.58/13.13 ((
% 96.58/13.13 (upairset2E) =>
% 96.58/13.13 ((
% 96.58/13.13 (upairsubunion) =>
% 96.58/13.13 ((
% 96.58/13.13 (upairinpowunion) =>
% 96.58/13.13 ((
% 96.58/13.13 (ubforcartprodlem1) =>
% 96.58/13.13 ((
% 96.58/13.13 (ubforcartprodlem2) =>
% 96.58/13.13 ((
% 96.58/13.13 (ubforcartprodlem3) =>
% 96.58/13.13 ((
% 96.58/13.13 (cartprodpairin) =>
% 96.58/13.13 ((
% 96.58/13.13 (cartprodmempair1) =>
% 96.58/13.13 ((
% 96.58/13.13 (cartprodmempair) =>
% 96.58/13.13 ((
% 96.58/13.13 (setunionE2) =>
% 96.58/13.13 ((
% 96.58/13.13 (setunionsingleton1) =>
% 96.58/13.13 ((
% 96.58/13.13 (setunionsingleton2) =>
% 96.58/13.13 ((
% 96.58/13.13 (setunionsingleton) =>
% 96.58/13.13 ((
% 96.58/13.13 (singletonprop) =>
% 96.58/13.13 ((
% 96.58/13.13 (ex1E1) =>
% 96.58/13.13 ((
% 96.58/13.13 (ex1I) =>
% 96.58/13.13 ((
% 96.58/13.13 (ex1I2) =>
% 96.58/13.13 ((
% 96.58/13.13 (singletonsuniq) =>
% 96.58/13.13 ((
% 96.58/13.13 (setukpairinjL1) =>
% 96.58/13.13 ((
% 96.58/13.13 (kfstsingleton) =>
% 96.58/13.13 ((
% 96.58/13.13 (theprop) =>
% 96.58/13.13 ((
% 96.58/13.13 (kfstpairEq) =>
% 96.58/13.13 ((
% 96.58/13.13 (cartprodfstin) =>
% 96.58/13.13 ((
% 96.58/13.13 (setukpairinjL2) =>
% 96.58/13.13 ((
% 96.58/13.13 (setukpairinjL) =>
% 96.58/13.13 ((
% 96.58/13.13 (setukpairinjR11) =>
% 96.58/13.13 ((
% 96.58/13.13 (setukpairinjR12) =>
% 96.58/13.13 ((
% 96.58/13.13 (setukpairinjR1) =>
% 96.58/13.13 ((
% 96.58/13.13 (upairequniteq) =>
% 96.58/13.13 ((
% 96.58/13.13 (setukpairinjR2) =>
% 96.58/13.13 ((
% 96.58/13.13 (setukpairinjR) =>
% 96.58/13.13 ((
% 96.58/13.13 (ksndsingleton) =>
% 96.58/13.13 ((
% 96.58/13.13 (ksndpairEq) =>
% 96.58/13.13 ((
% 96.58/13.13 (kpairsurjEq) =>
% 96.58/13.13 ((
% 96.58/13.13 (cartprodsndin) =>
% 96.58/13.13 ((
% 96.58/13.13 (cartprodpairmemEL) =>
% 96.58/13.13 ((
% 96.58/13.13 (cartprodpairmemER) =>
% 96.58/13.13 ((
% 96.58/13.13 (cartprodmempaircEq) =>
% 96.58/13.13 ((
% 96.58/13.13 (cartprodfstpairEq) =>
% 96.58/13.13 ((
% 96.58/13.13 (cartprodsndpairEq) =>
% 96.58/13.13 ((
% 96.58/13.13 (cartprodpairsurjEq) =>
% 96.58/13.13 ((
% 96.58/13.13 (dpsetconstrI) =>
% 96.58/13.13 ((
% 96.58/13.13 (dpsetconstrSub) =>
% 96.58/13.13 ((
% 96.58/13.13 (setOfPairsIsBReln) =>
% 96.58/13.13 ((
% 96.58/13.13 (dpsetconstrERa) =>
% 96.58/13.13 ((
% 96.58/13.13 (dpsetconstrEL1) =>
% 96.58/13.13 ((
% 96.58/13.13 (dpsetconstrEL2) =>
% 96.58/13.13 ((
% 96.58/13.13 (dpsetconstrER) =>
% 96.58/13.13 ((
% 96.58/13.13 (funcImageSingleton) =>
% 96.58/13.13 ((
% 96.58/13.13 (apProp) =>
% 96.58/13.13 ((
% 96.58/13.13 (app) =>
% 96.58/13.13 ((
% 96.58/13.13 (infuncsetfunc) =>
% 96.58/13.13 ((
% 96.58/13.13 (ap2p) =>
% 96.58/13.13 ((
% 96.58/13.13 (funcinfuncset) =>
% 96.58/13.13 ((
% 96.58/13.13 (lamProp) =>
% 96.58/13.13 ((
% 96.58/13.13 (lamp) =>
% 96.58/13.13 ((
% 96.58/13.13 (lam2p) =>
% 96.58/13.13 ((
% 96.58/13.13 (brelnall1) =>
% 96.58/13.13 ((
% 96.58/13.13 (brelnall2) =>
% 96.58/13.13 ((
% 96.58/13.13 (ex1E2) =>
% 96.58/13.13 ((
% 96.58/13.13 (funcGraphProp1) =>
% 96.58/13.13 ((
% 96.58/13.13 (funcGraphProp3) =>
% 96.58/13.13 ((
% 96.58/13.13 (funcGraphProp2) =>
% 96.58/13.13 ((
% 96.58/13.13 (funcextLem) =>
% 96.58/13.13 ((
% 96.58/13.13 (funcGraphProp4) =>
% 96.58/13.13 ((
% 96.58/13.13 (subbreln) =>
% 96.58/13.13 ((
% 96.58/13.13 (eqbreln) =>
% 96.58/13.13 ((
% 96.58/13.13 (funcext) =>
% 96.58/13.13 ((
% 96.58/13.13 (funcext2) =>
% 96.58/13.13 ((
% 96.58/13.13 (ap2apEq1) =>
% 96.58/13.13 ((
% 96.58/13.13 (ap2apEq2) =>
% 96.58/13.13 ((
% 96.58/13.13 (beta1) =>
% 96.58/13.13 ((
% 96.58/13.13 (eta1) =>
% 96.58/13.13 ((
% 96.58/13.13 (lam2lamEq) =>
% 96.58/13.13 ((
% 96.58/13.13 (beta2) =>
% 96.58/13.13 ((
% 96.58/13.13 (eta2) =>
% 96.58/13.13 ((
% 96.58/13.13 (iffalseProp1) =>
% 96.58/13.13 ((
% 96.58/13.13 (iffalseProp2) =>
% 96.58/13.13 ((
% 96.58/13.13 (iftrueProp1) =>
% 96.58/13.13 ((
% 96.58/13.13 (iftrueProp2) =>
% 96.58/13.13 ((
% 96.58/13.13 (ifSingleton) =>
% 96.58/13.13 ((
% 96.58/13.13 (ifp) =>
% 96.58/13.13 ((
% 96.58/13.13 (theeq) =>
% 96.58/13.13 ((
% 96.58/13.13 (iftrue) =>
% 96.58/13.13 ((
% 96.58/13.13 (iffalse) =>
% 96.58/13.13 ((
% 96.58/13.13 (iftrueorfalse) =>
% 96.58/13.13 ((
% 96.58/13.13 (binintersectT_lem) =>
% 96.58/13.13 ((
% 96.58/13.13 (binunionT_lem) =>
% 96.58/13.13 ((
% 96.58/13.13 (powersetT_lem) =>
% 96.58/13.13 ((
% 96.58/13.13 (setminusT_lem) =>
% 96.58/13.13 ((
% 96.58/13.13 (complementT_lem) =>
% 96.58/13.13 ((
% 96.58/13.13 (setextT) =>
% 96.58/13.13 ((
% 96.58/13.13 (subsetTI) =>
% 96.58/13.13 ((
% 96.58/13.13 (powersetTI1) =>
% 96.58/13.13 ((
% 96.58/13.13 (powersetTE1) =>
% 96.58/13.13 ((
% 96.58/13.13 (complementTI1) =>
% 96.58/13.13 ((
% 96.58/13.13 (complementTE1) =>
% 96.58/13.13 ((
% 96.58/13.13 (binintersectTELcontra) =>
% 96.58/13.13 ((
% 96.58/13.13 (binintersectTERcontra) =>
% 96.58/13.13 ((
% 96.58/13.13 (contrasubsetT) =>
% 96.58/13.13 ((
% 96.58/13.13 (contrasubsetT1) =>
% 96.58/13.13 ((
% 96.58/13.13 (contrasubsetT2) =>
% 96.58/13.13 ((
% 96.58/13.13 (contrasubsetT3) =>
% 96.58/13.13 ((
% 96.58/13.13 (doubleComplementI1) =>
% 96.58/13.13 ((
% 96.58/13.13 (doubleComplementE1) =>
% 96.58/13.13 ((
% 96.58/13.13 (doubleComplementSub1) =>
% 96.58/13.13 ((
% 96.58/13.13 (doubleComplementSub2) =>
% 96.58/13.13 ((
% 96.58/13.13 (doubleComplementEq) =>
% 96.58/13.13 ((
% 96.58/13.13 (complementTnotintersectT) =>
% 96.58/13.13 ((
% 96.58/13.13 (complementImpComplementIntersect) =>
% 96.58/13.13 ((
% 96.58/13.13 (complementSubsetComplementIntersect) =>
% 96.58/13.13 ((
% 96.58/13.13 (complementInPowersetComplementIntersect) =>
% 96.58/13.13 ((
% 96.58/13.13 (contraSubsetComplement) =>
% 96.58/13.13 ((
% 96.58/13.13 (complementTcontraSubset) =>
% 96.58/13.13 ((
% 96.58/13.13 (binunionTILcontra) =>
% 96.58/13.13 ((
% 96.58/13.13 (binunionTIRcontra) =>
% 96.58/13.13 ((
% 96.58/13.13 (inIntersectImpInUnion) =>
% 96.58/13.13 ((
% 96.58/13.13 (inIntersectImpInUnion2) =>
% 96.58/13.13 ((
% 96.58/13.13 (inIntersectImpInIntersectUnions) =>
% 96.58/13.13 ((
% 96.58/13.13 (intersectInPowersetIntersectUnions) =>
% 96.58/13.13 ((
% 96.58/13.13 (inComplementUnionImpNotIn1) =>
% 96.58/13.13 ((
% 96.58/13.13 (inComplementUnionImpInComplement1) =>
% 96.58/13.13 ((
% 96.58/13.13 (binunionTE) =>
% 96.58/13.13 ((
% 96.58/13.13 (binunionTEcontra) =>
% 96.58/13.13 ((
% 96.58/13.13 (demorgan2a1) =>
% 96.58/13.13 ((
% 96.58/13.13 (complementUnionInPowersetComplement) =>
% 96.58/13.13 ((
% 96.58/13.13 (demorgan2a2) =>
% 96.58/13.13 ((
% 96.58/13.13 (demorgan1a) =>
% 96.58/13.13 ((
% 96.58/13.13 (demorgan1b) =>
% 96.58/13.13 ((
% 96.58/13.13 (demorgan1) =>
% 96.58/13.13 ((
% 96.58/13.13 (demorgan2a) =>
% 96.58/13.13 ((
% 96.58/13.13 (demorgan2b2) =>
% 96.58/13.13 ((
% 96.58/13.13 (demorgan2b) =>
% 96.58/13.13 ((
% 96.58/13.13 (demorgan2) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz13rule0) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz13rule1) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz13rule2) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz13rule3) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz13rule4) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz1_1) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz1_2) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz1_3) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz1_4) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz1_5) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1all2) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1SetBreln1) =>
% 96.58/13.13 ((
% 96.58/13.13 (choice2fnsingleton) =>
% 96.58/13.13 ((
% 96.58/13.13 (setOfPairsIsBReln1) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1all1) =>
% 96.58/13.13 ((
% 96.58/13.13 (subbreln1) =>
% 96.58/13.13 ((
% 96.58/13.13 (eqbreln1) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1invprop) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1invI) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1invE) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1compprop) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1compI) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1compE) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1compEex) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1unionprop) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1unionIL) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1unionIR) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1unionI) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1unionE) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1unionEcases) =>
% 96.58/13.13 ((
% 96.58/13.13 (breln1unionCommutes) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz2Ex) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz2W) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz2A) =>
% 96.58/13.13 ((
% 96.58/13.13 (woz2B) =>
% 96.58/13.13 ((
% 96.58/13.13 (image1Ex) =>
% 96.58/13.13 ((
% 96.58/13.13 (image1Ex1) =>
% 96.58/13.13 ((
% 96.58/13.13 (image1Equiv) =>
% 96.58/13.13 ((
% 96.58/13.13 (image1E) =>
% 96.58/13.13 ((
% 96.58/13.13 (image1I) =>
% 96.58/13.13 ((
% 96.58/13.13 (injFuncInInjFuncSet) =>
% 96.58/13.13 ((
% 96.58/13.13 (injFuncSetFuncIn) =>
% 96.58/13.13 ((
% 96.58/13.13 (injFuncSetFuncInj) =>
% 96.58/13.13 ((
% 96.58/13.13 (surjFuncSetFuncIn) =>
% 96.58/13.13 ((
% 96.58/13.13 (surjFuncSetFuncSurj) =>
% 96.58/13.13 ((
% 96.58/13.13 (leftInvIsSurj) =>
% 96.58/13.13 ((
% 96.58/13.13 (surjCantorThm) =>
% 96.58/13.13 ((
% 96.58/13.13 (foundation2) =>
% 96.58/13.13 ((
% 96.58/13.13 (notinself) =>
% 96.58/13.13 ((
% 96.58/13.13 (notinself2) =>
% 96.58/13.13 ((
% 96.58/13.13 (omegaSp) =>
% 96.58/13.13 ((
% 96.58/13.13 (omegaSclos) =>
% 96.58/13.13 ((
% 96.58/13.13 (peano0notS) =>
% 96.58/13.13 ((
% 96.58/13.13 (!!) @ (
% 96.58/13.13 (('#S') @ (
% 96.58/13.13 (
% 96.58/13.13 ('#B') @ (
% 96.58/13.13 =>) @
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 ('#C') @ in @
% 96.58/13.13 omega)))) @
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 ('#B') @ (
% 96.58/13.13 !!) @
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 ('#B') @ (
% 96.58/13.13 (
% 96.58/13.13 ('#S') @ (
% 96.58/13.13 (
% 96.58/13.13 ('#B') @ (
% 96.58/13.13 =>) @
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 ('#C') @ in @
% 96.58/13.13 omega)))))) @
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 ('#S') @ (
% 96.58/13.13 (
% 96.58/13.13 ('#B') @ (
% 96.58/13.13 '#S') @
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 ('#B') @ (
% 96.58/13.13 (
% 96.58/13.13 ('#B') @ (
% 96.58/13.13 =>))) @
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 ('#C') @ (
% 96.58/13.13 (
% 96.58/13.13 ('#B') @ (
% 96.58/13.13 '#B') @
% 96.58/13.13 (
% 96.58/13.13 (
% 96.58/13.13 ('#B') @ (
% 96.58/13.13 =) @
% 96.58/13.13 omegaS)))) @
% 96.58/13.13 omegaS)))))) @
% 96.58/13.13 (
% 96.58/13.13 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 96.58/13.13 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl5])).
% 96.58/13.13 thf(zip_derived_cl13, plain,
% 96.58/13.13 (~ (((powersetAx) =>
% 96.58/13.13 (((setunionAx) =>
% 96.58/13.13 (((in @ emptyset @ omega) =>
% 96.58/13.13 (((omegaSAx) =>
% 96.58/13.13 (((omegaIndAx) =>
% 96.58/13.13 (((replAx) =>
% 96.58/13.13 (((foundationAx) =>
% 96.58/13.13 (((wellorderingAx) =>
% 96.58/13.13 (((descrp) =>
% 96.58/13.13 (((dsetconstrI) =>
% 96.58/13.13 (((dsetconstrEL) =>
% 96.58/13.13 (((dsetconstrER) =>
% 96.58/13.13 (((exuE1) =>
% 96.58/13.13 (((prop2setE) =>
% 96.58/13.13 (((emptysetE) =>
% 96.58/13.13 (((emptysetimpfalse) =>
% 96.58/13.13 (((notinemptyset) =>
% 96.58/13.13 (((exuE3e) =>
% 96.58/13.13 (((setext) =>
% 96.58/13.13 (((emptyI) =>
% 96.58/13.13 (((noeltsimpempty) =>
% 96.58/13.13 (((setbeta) =>
% 96.58/13.13 (((nonemptyE1) =>
% 96.58/13.13 (((nonemptyI) =>
% 96.58/13.13 (((nonemptyI1) =>
% 96.58/13.13 (((setadjoinIL) =>
% 96.58/13.13 (((in @
% 96.58/13.13 emptyset @
% 96.58/13.13 (setadjoin @
% 96.58/13.13 emptyset @
% 96.58/13.13 emptyset)) =>
% 96.58/13.13 (((setadjoinIR) =>
% 96.58/13.13 (((setadjoinE) =>
% 96.58/13.13 (((setadjoinOr) =>
% 96.58/13.13 ((
% 96.58/13.13 (setoftrueEq) =>
% 96.58/13.13 ((
% 96.58/13.13 (powersetI) =>
% 96.58/13.13 ((
% 96.58/13.13 (emptyinPowerset) =>
% 96.58/13.13 ((
% 96.58/13.13 (emptyInPowerset) =>
% 96.58/13.13 ((
% 96.58/13.13 (powersetE) =>
% 96.58/13.13 ((
% 96.58/13.13 (setunionI) =>
% 96.58/13.13 ((
% 96.58/13.13 (setunionE) =>
% 96.58/13.13 ((
% 96.58/13.13 (subPowSU) =>
% 96.58/13.13 ((
% 96.58/13.13 (exuE2) =>
% 96.58/13.13 ((
% 96.58/13.13 (nonemptyImpWitness) =>
% 96.58/13.13 ((
% 96.58/13.13 (uniqinunit) =>
% 96.58/13.13 ((
% 96.58/13.13 (notinsingleton) =>
% 96.58/13.13 ((
% 96.58/13.13 (eqinunit) =>
% 96.58/13.13 ((
% 96.58/13.13 (singletonsswitch) =>
% 96.58/13.13 ((
% 96.58/13.13 (upairsetE) =>
% 96.58/13.13 ((
% 96.58/13.13 (upairsetIL) =>
% 96.58/13.13 ((
% 96.58/13.13 (upairsetIR) =>
% 96.58/13.13 ((
% 96.58/13.13 (emptyE1) =>
% 96.58/13.13 ((
% 96.58/13.13 (vacuousDall) =>
% 96.58/13.13 ((
% 96.58/13.13 (quantDeMorgan1) =>
% 96.58/13.13 ((
% 96.58/13.13 (quantDeMorgan2) =>
% 96.58/13.13 ((
% 96.58/13.13 (quantDeMorgan3) =>
% 96.58/13.13 ((
% 96.58/13.13 (quantDeMorgan4) =>
% 96.58/13.13 ((
% 96.58/13.13 (prop2setI) =>
% 96.58/13.13 ((
% 96.58/13.13 (prop2set2propI) =>
% 96.58/13.13 ((
% 96.58/13.13 (notdexE) =>
% 96.58/13.13 ((
% 96.58/13.13 (notdallE) =>
% 96.58/13.13 ((
% 96.58/13.13 (exuI1) =>
% 96.58/13.13 ((
% 96.58/13.13 (exuI3) =>
% 96.58/13.13 ((
% 96.58/13.13 (exuI2) =>
% 96.58/13.13 ((
% 96.58/13.13 (inCongP) =>
% 96.58/13.13 ((
% 96.58/13.13 (in__Cong) =>
% 96.58/13.13 ((
% 96.58/13.13 (exuE3u) =>
% 96.58/13.13 ((
% 96.58/13.13 (exu__Cong) =>
% 96.58/13.13 ((
% 96.58/13.13 (setadjoin__Cong) =>
% 96.58/13.13 ((
% 96.58/13.13 (powerset__Cong) =>
% 96.58/13.14 ((
% 96.58/13.14 (setunion__Cong) =>
% 96.58/13.14 ((
% 96.58/13.14 (exuEu) =>
% 96.58/13.14 ((
% 96.58/13.14 (descr__Cong) =>
% 96.58/13.14 ((
% 96.58/13.14 (dsetconstr__Cong) =>
% 96.58/13.14 ((
% 96.58/13.14 (subsetI1) =>
% 96.58/13.14 ((
% 96.58/13.14 (eqimpsubset2) =>
% 96.58/13.14 ((
% 96.58/13.14 (eqimpsubset1) =>
% 96.58/13.14 ((
% 96.58/13.14 (subsetI2) =>
% 96.58/13.14 ((
% 96.58/13.14 (emptysetsubset) =>
% 96.58/13.14 ((
% 96.58/13.14 (subsetE) =>
% 96.58/13.14 ((
% 96.58/13.14 (subsetE2) =>
% 96.58/13.14 ((
% 96.58/13.14 (notsubsetI) =>
% 96.58/13.14 ((
% 96.58/13.14 (notequalI1) =>
% 96.58/13.14 ((
% 96.58/13.14 (notequalI2) =>
% 96.58/13.14 ((
% 96.58/13.14 (subsetRefl) =>
% 96.58/13.14 ((
% 96.58/13.14 (subsetTrans) =>
% 96.58/13.14 ((
% 96.58/13.14 (setadjoinSub) =>
% 96.58/13.14 ((
% 96.58/13.14 (setadjoinSub2) =>
% 96.58/13.14 ((
% 96.58/13.14 (subset2powerset) =>
% 96.58/13.14 ((
% 96.58/13.14 (setextsub) =>
% 96.58/13.14 ((
% 96.58/13.14 (subsetemptysetimpeq) =>
% 96.58/13.14 ((
% 96.58/13.14 (powersetI1) =>
% 96.58/13.14 ((
% 96.58/13.14 (powersetE1) =>
% 96.58/13.14 ((
% 96.58/13.14 (inPowerset) =>
% 96.58/13.14 ((
% 96.58/13.14 (powersetsubset) =>
% 96.58/13.14 ((
% 96.58/13.14 (sepInPowerset) =>
% 96.58/13.14 ((
% 96.58/13.14 (sepSubset) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionIL) =>
% 96.58/13.14 ((
% 96.58/13.14 (upairset2IR) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionIR) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionEcases) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionE) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionLsub) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionRsub) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectI) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectSubset5) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectEL) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectLsub) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectSubset2) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectSubset3) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectER) =>
% 96.58/13.14 ((
% 96.58/13.14 (disjointsetsI1) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectRsub) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectSubset4) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectSubset1) =>
% 96.58/13.14 ((
% 96.58/13.14 (bs114d) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusI) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusEL) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusER) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusSubset2) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusERneg) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusELneg) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusILneg) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusIRneg) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusLsub) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusSubset1) =>
% 96.58/13.14 ((
% 96.58/13.14 (symdiffE) =>
% 96.58/13.14 ((
% 96.58/13.14 (symdiffI1) =>
% 96.58/13.14 ((
% 96.58/13.14 (symdiffI2) =>
% 96.58/13.14 ((
% 96.58/13.14 (symdiffIneg1) =>
% 96.58/13.14 ((
% 96.58/13.14 (symdiffIneg2) =>
% 96.58/13.14 ((
% 96.58/13.14 (secondinupair) =>
% 96.58/13.14 ((
% 96.58/13.14 (setukpairIL) =>
% 96.58/13.14 ((
% 96.58/13.14 (setukpairIR) =>
% 96.58/13.14 ((
% 96.58/13.14 (kpairiskpair) =>
% 96.58/13.14 ((
% 96.58/13.14 (kpairp) =>
% 96.58/13.14 ((
% 96.58/13.14 (singletonsubset) =>
% 96.58/13.14 ((
% 96.58/13.14 (singletoninpowerset) =>
% 96.58/13.14 ((
% 96.58/13.14 (singletoninpowunion) =>
% 96.58/13.14 ((
% 96.58/13.14 (upairset2E) =>
% 96.58/13.14 ((
% 96.58/13.14 (upairsubunion) =>
% 96.58/13.14 ((
% 96.58/13.14 (upairinpowunion) =>
% 96.58/13.14 ((
% 96.58/13.14 (ubforcartprodlem1) =>
% 96.58/13.14 ((
% 96.58/13.14 (ubforcartprodlem2) =>
% 96.58/13.14 ((
% 96.58/13.14 (ubforcartprodlem3) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodpairin) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodmempair1) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodmempair) =>
% 96.58/13.14 ((
% 96.58/13.14 (setunionE2) =>
% 96.58/13.14 ((
% 96.58/13.14 (setunionsingleton1) =>
% 96.58/13.14 ((
% 96.58/13.14 (setunionsingleton2) =>
% 96.58/13.14 ((
% 96.58/13.14 (setunionsingleton) =>
% 96.58/13.14 ((
% 96.58/13.14 (singletonprop) =>
% 96.58/13.14 ((
% 96.58/13.14 (ex1E1) =>
% 96.58/13.14 ((
% 96.58/13.14 (ex1I) =>
% 96.58/13.14 ((
% 96.58/13.14 (ex1I2) =>
% 96.58/13.14 ((
% 96.58/13.14 (singletonsuniq) =>
% 96.58/13.14 ((
% 96.58/13.14 (setukpairinjL1) =>
% 96.58/13.14 ((
% 96.58/13.14 (kfstsingleton) =>
% 96.58/13.14 ((
% 96.58/13.14 (theprop) =>
% 96.58/13.14 ((
% 96.58/13.14 (kfstpairEq) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodfstin) =>
% 96.58/13.14 ((
% 96.58/13.14 (setukpairinjL2) =>
% 96.58/13.14 ((
% 96.58/13.14 (setukpairinjL) =>
% 96.58/13.14 ((
% 96.58/13.14 (setukpairinjR11) =>
% 96.58/13.14 ((
% 96.58/13.14 (setukpairinjR12) =>
% 96.58/13.14 ((
% 96.58/13.14 (setukpairinjR1) =>
% 96.58/13.14 ((
% 96.58/13.14 (upairequniteq) =>
% 96.58/13.14 ((
% 96.58/13.14 (setukpairinjR2) =>
% 96.58/13.14 ((
% 96.58/13.14 (setukpairinjR) =>
% 96.58/13.14 ((
% 96.58/13.14 (ksndsingleton) =>
% 96.58/13.14 ((
% 96.58/13.14 (ksndpairEq) =>
% 96.58/13.14 ((
% 96.58/13.14 (kpairsurjEq) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodsndin) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodpairmemEL) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodpairmemER) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodmempaircEq) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodfstpairEq) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodsndpairEq) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodpairsurjEq) =>
% 96.58/13.14 ((
% 96.58/13.14 (dpsetconstrI) =>
% 96.58/13.14 ((
% 96.58/13.14 (dpsetconstrSub) =>
% 96.58/13.14 ((
% 96.58/13.14 (setOfPairsIsBReln) =>
% 96.58/13.14 ((
% 96.58/13.14 (dpsetconstrERa) =>
% 96.58/13.14 ((
% 96.58/13.14 (dpsetconstrEL1) =>
% 96.58/13.14 ((
% 96.58/13.14 (dpsetconstrEL2) =>
% 96.58/13.14 ((
% 96.58/13.14 (dpsetconstrER) =>
% 96.58/13.14 ((
% 96.58/13.14 (funcImageSingleton) =>
% 96.58/13.14 ((
% 96.58/13.14 (apProp) =>
% 96.58/13.14 ((
% 96.58/13.14 (app) =>
% 96.58/13.14 ((
% 96.58/13.14 (infuncsetfunc) =>
% 96.58/13.14 ((
% 96.58/13.14 (ap2p) =>
% 96.58/13.14 ((
% 96.58/13.14 (funcinfuncset) =>
% 96.58/13.14 ((
% 96.58/13.14 (lamProp) =>
% 96.58/13.14 ((
% 96.58/13.14 (lamp) =>
% 96.58/13.14 ((
% 96.58/13.14 (lam2p) =>
% 96.58/13.14 ((
% 96.58/13.14 (brelnall1) =>
% 96.58/13.14 ((
% 96.58/13.14 (brelnall2) =>
% 96.58/13.14 ((
% 96.58/13.14 (ex1E2) =>
% 96.58/13.14 ((
% 96.58/13.14 (funcGraphProp1) =>
% 96.58/13.14 ((
% 96.58/13.14 (funcGraphProp3) =>
% 96.58/13.14 ((
% 96.58/13.14 (funcGraphProp2) =>
% 96.58/13.14 ((
% 96.58/13.14 (funcextLem) =>
% 96.58/13.14 ((
% 96.58/13.14 (funcGraphProp4) =>
% 96.58/13.14 ((
% 96.58/13.14 (subbreln) =>
% 96.58/13.14 ((
% 96.58/13.14 (eqbreln) =>
% 96.58/13.14 ((
% 96.58/13.14 (funcext) =>
% 96.58/13.14 ((
% 96.58/13.14 (funcext2) =>
% 96.58/13.14 ((
% 96.58/13.14 (ap2apEq1) =>
% 96.58/13.14 ((
% 96.58/13.14 (ap2apEq2) =>
% 96.58/13.14 ((
% 96.58/13.14 (beta1) =>
% 96.58/13.14 ((
% 96.58/13.14 (eta1) =>
% 96.58/13.14 ((
% 96.58/13.14 (lam2lamEq) =>
% 96.58/13.14 ((
% 96.58/13.14 (beta2) =>
% 96.58/13.14 ((
% 96.58/13.14 (eta2) =>
% 96.58/13.14 ((
% 96.58/13.14 (iffalseProp1) =>
% 96.58/13.14 ((
% 96.58/13.14 (iffalseProp2) =>
% 96.58/13.14 ((
% 96.58/13.14 (iftrueProp1) =>
% 96.58/13.14 ((
% 96.58/13.14 (iftrueProp2) =>
% 96.58/13.14 ((
% 96.58/13.14 (ifSingleton) =>
% 96.58/13.14 ((
% 96.58/13.14 (ifp) =>
% 96.58/13.14 ((
% 96.58/13.14 (theeq) =>
% 96.58/13.14 ((
% 96.58/13.14 (iftrue) =>
% 96.58/13.14 ((
% 96.58/13.14 (iffalse) =>
% 96.58/13.14 ((
% 96.58/13.14 (iftrueorfalse) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectT_lem) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionT_lem) =>
% 96.58/13.14 ((
% 96.58/13.14 (powersetT_lem) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusT_lem) =>
% 96.58/13.14 ((
% 96.58/13.14 (complementT_lem) =>
% 96.58/13.14 ((
% 96.58/13.14 (setextT) =>
% 96.58/13.14 ((
% 96.58/13.14 (subsetTI) =>
% 96.58/13.14 ((
% 96.58/13.14 (powersetTI1) =>
% 96.58/13.14 ((
% 96.58/13.14 (powersetTE1) =>
% 96.58/13.14 ((
% 96.58/13.14 (complementTI1) =>
% 96.58/13.14 ((
% 96.58/13.14 (complementTE1) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectTELcontra) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectTERcontra) =>
% 96.58/13.14 ((
% 96.58/13.14 (contrasubsetT) =>
% 96.58/13.14 ((
% 96.58/13.14 (contrasubsetT1) =>
% 96.58/13.14 ((
% 96.58/13.14 (contrasubsetT2) =>
% 96.58/13.14 ((
% 96.58/13.14 (contrasubsetT3) =>
% 96.58/13.14 ((
% 96.58/13.14 (doubleComplementI1) =>
% 96.58/13.14 ((
% 96.58/13.14 (doubleComplementE1) =>
% 96.58/13.14 ((
% 96.58/13.14 (doubleComplementSub1) =>
% 96.58/13.14 ((
% 96.58/13.14 (doubleComplementSub2) =>
% 96.58/13.14 ((
% 96.58/13.14 (doubleComplementEq) =>
% 96.58/13.14 ((
% 96.58/13.14 (complementTnotintersectT) =>
% 96.58/13.14 ((
% 96.58/13.14 (complementImpComplementIntersect) =>
% 96.58/13.14 ((
% 96.58/13.14 (complementSubsetComplementIntersect) =>
% 96.58/13.14 ((
% 96.58/13.14 (complementInPowersetComplementIntersect) =>
% 96.58/13.14 ((
% 96.58/13.14 (contraSubsetComplement) =>
% 96.58/13.14 ((
% 96.58/13.14 (complementTcontraSubset) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionTILcontra) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionTIRcontra) =>
% 96.58/13.14 ((
% 96.58/13.14 (inIntersectImpInUnion) =>
% 96.58/13.14 ((
% 96.58/13.14 (inIntersectImpInUnion2) =>
% 96.58/13.14 ((
% 96.58/13.14 (inIntersectImpInIntersectUnions) =>
% 96.58/13.14 ((
% 96.58/13.14 (intersectInPowersetIntersectUnions) =>
% 96.58/13.14 ((
% 96.58/13.14 (inComplementUnionImpNotIn1) =>
% 96.58/13.14 ((
% 96.58/13.14 (inComplementUnionImpInComplement1) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionTE) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionTEcontra) =>
% 96.58/13.14 ((
% 96.58/13.14 (demorgan2a1) =>
% 96.58/13.14 ((
% 96.58/13.14 (complementUnionInPowersetComplement) =>
% 96.58/13.14 ((
% 96.58/13.14 (demorgan2a2) =>
% 96.58/13.14 ((
% 96.58/13.14 (demorgan1a) =>
% 96.58/13.14 ((
% 96.58/13.14 (demorgan1b) =>
% 96.58/13.14 ((
% 96.58/13.14 (demorgan1) =>
% 96.58/13.14 ((
% 96.58/13.14 (demorgan2a) =>
% 96.58/13.14 ((
% 96.58/13.14 (demorgan2b2) =>
% 96.58/13.14 ((
% 96.58/13.14 (demorgan2b) =>
% 96.58/13.14 ((
% 96.58/13.14 (demorgan2) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz13rule0) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz13rule1) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz13rule2) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz13rule3) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz13rule4) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz1_1) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz1_2) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz1_3) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz1_4) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz1_5) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1all2) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1SetBreln1) =>
% 96.58/13.14 ((
% 96.58/13.14 (choice2fnsingleton) =>
% 96.58/13.14 ((
% 96.58/13.14 (setOfPairsIsBReln1) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1all1) =>
% 96.58/13.14 ((
% 96.58/13.14 (subbreln1) =>
% 96.58/13.14 ((
% 96.58/13.14 (eqbreln1) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1invprop) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1invI) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1invE) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1compprop) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1compI) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1compE) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1compEex) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1unionprop) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1unionIL) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1unionIR) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1unionI) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1unionE) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1unionEcases) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1unionCommutes) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz2Ex) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz2W) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz2A) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz2B) =>
% 96.58/13.14 ((
% 96.58/13.14 (image1Ex) =>
% 96.58/13.14 ((
% 96.58/13.14 (image1Ex1) =>
% 96.58/13.14 ((
% 96.58/13.14 (image1Equiv) =>
% 96.58/13.14 ((
% 96.58/13.14 (image1E) =>
% 96.58/13.14 ((
% 96.58/13.14 (image1I) =>
% 96.58/13.14 ((
% 96.58/13.14 (injFuncInInjFuncSet) =>
% 96.58/13.14 ((
% 96.58/13.14 (injFuncSetFuncIn) =>
% 96.58/13.14 ((
% 96.58/13.14 (injFuncSetFuncInj) =>
% 96.58/13.14 ((
% 96.58/13.14 (surjFuncSetFuncIn) =>
% 96.58/13.14 ((
% 96.58/13.14 (surjFuncSetFuncSurj) =>
% 96.58/13.14 ((
% 96.58/13.14 (leftInvIsSurj) =>
% 96.58/13.14 ((
% 96.58/13.14 (surjCantorThm) =>
% 96.58/13.14 ((
% 96.58/13.14 (foundation2) =>
% 96.58/13.14 ((
% 96.58/13.14 (notinself) =>
% 96.58/13.14 ((
% 96.58/13.14 (notinself2) =>
% 96.58/13.14 ((
% 96.58/13.14 (omegaSp) =>
% 96.58/13.14 ((
% 96.58/13.14 (omegaSclos) =>
% 96.58/13.14 ((
% 96.58/13.14 (peano0notS) =>
% 96.58/13.14 ((
% 96.58/13.14 (!!) @ (
% 96.58/13.14 (('#S') @ (
% 96.58/13.14 (
% 96.58/13.14 ('#B') @ (
% 96.58/13.14 =>) @
% 96.58/13.14 (
% 96.58/13.14 (
% 96.58/13.14 ('#C') @ in @
% 96.58/13.14 omega)))) @
% 96.58/13.14 (
% 96.58/13.14 (
% 96.58/13.14 ('#B') @ (
% 96.58/13.14 !!) @
% 96.58/13.14 (
% 96.58/13.14 (
% 96.58/13.14 ('#B') @ (
% 96.58/13.14 (
% 96.58/13.14 ('#S') @ (
% 96.58/13.14 (
% 96.58/13.14 ('#B') @ (
% 96.58/13.14 =>) @
% 96.58/13.14 (
% 96.58/13.14 (
% 96.58/13.14 ('#C') @ in @
% 96.58/13.14 omega)))))) @
% 96.58/13.14 (
% 96.58/13.14 (
% 96.58/13.14 ('#S') @ (
% 96.58/13.14 (
% 96.58/13.14 ('#B') @ (
% 96.58/13.14 '#S') @
% 96.58/13.14 (
% 96.58/13.14 (
% 96.58/13.14 ('#B') @ (
% 96.58/13.14 (
% 96.58/13.14 ('#B') @ (
% 96.58/13.14 =>))) @
% 96.58/13.14 (
% 96.58/13.14 (
% 96.58/13.14 ('#C') @ (
% 96.58/13.14 (
% 96.58/13.14 ('#B') @ (
% 96.58/13.14 '#B') @
% 96.58/13.14 (
% 96.58/13.14 (
% 96.58/13.14 ('#B') @ (
% 96.58/13.14 =) @
% 96.58/13.14 omegaS)))) @
% 96.58/13.14 omegaS)))))) @
% 96.58/13.14 (
% 96.58/13.14 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 96.58/13.14 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl8])).
% 96.58/13.14 thf(zip_derived_cl19, plain,
% 96.58/13.14 (~ (((setunionAx) =>
% 96.58/13.14 (((in @ emptyset @ omega) =>
% 96.58/13.14 (((omegaSAx) =>
% 96.58/13.14 (((omegaIndAx) =>
% 96.58/13.14 (((replAx) =>
% 96.58/13.14 (((foundationAx) =>
% 96.58/13.14 (((wellorderingAx) =>
% 96.58/13.14 (((descrp) =>
% 96.58/13.14 (((dsetconstrI) =>
% 96.58/13.14 (((dsetconstrEL) =>
% 96.58/13.14 (((dsetconstrER) =>
% 96.58/13.14 (((exuE1) =>
% 96.58/13.14 (((prop2setE) =>
% 96.58/13.14 (((emptysetE) =>
% 96.58/13.14 (((emptysetimpfalse) =>
% 96.58/13.14 (((notinemptyset) =>
% 96.58/13.14 (((exuE3e) =>
% 96.58/13.14 (((setext) =>
% 96.58/13.14 (((emptyI) =>
% 96.58/13.14 (((noeltsimpempty) =>
% 96.58/13.14 (((setbeta) =>
% 96.58/13.14 (((nonemptyE1) =>
% 96.58/13.14 (((nonemptyI) =>
% 96.58/13.14 (((nonemptyI1) =>
% 96.58/13.14 (((setadjoinIL) =>
% 96.58/13.14 (((in @ emptyset @
% 96.58/13.14 (setadjoin @
% 96.58/13.14 emptyset @
% 96.58/13.14 emptyset)) =>
% 96.58/13.14 (((setadjoinIR) =>
% 96.58/13.14 (((setadjoinE) =>
% 96.58/13.14 (((setadjoinOr) =>
% 96.58/13.14 (((setoftrueEq) =>
% 96.58/13.14 ((
% 96.58/13.14 (powersetI) =>
% 96.58/13.14 ((
% 96.58/13.14 (emptyinPowerset) =>
% 96.58/13.14 ((
% 96.58/13.14 (emptyInPowerset) =>
% 96.58/13.14 ((
% 96.58/13.14 (powersetE) =>
% 96.58/13.14 ((
% 96.58/13.14 (setunionI) =>
% 96.58/13.14 ((
% 96.58/13.14 (setunionE) =>
% 96.58/13.14 ((
% 96.58/13.14 (subPowSU) =>
% 96.58/13.14 ((
% 96.58/13.14 (exuE2) =>
% 96.58/13.14 ((
% 96.58/13.14 (nonemptyImpWitness) =>
% 96.58/13.14 ((
% 96.58/13.14 (uniqinunit) =>
% 96.58/13.14 ((
% 96.58/13.14 (notinsingleton) =>
% 96.58/13.14 ((
% 96.58/13.14 (eqinunit) =>
% 96.58/13.14 ((
% 96.58/13.14 (singletonsswitch) =>
% 96.58/13.14 ((
% 96.58/13.14 (upairsetE) =>
% 96.58/13.14 ((
% 96.58/13.14 (upairsetIL) =>
% 96.58/13.14 ((
% 96.58/13.14 (upairsetIR) =>
% 96.58/13.14 ((
% 96.58/13.14 (emptyE1) =>
% 96.58/13.14 ((
% 96.58/13.14 (vacuousDall) =>
% 96.58/13.14 ((
% 96.58/13.14 (quantDeMorgan1) =>
% 96.58/13.14 ((
% 96.58/13.14 (quantDeMorgan2) =>
% 96.58/13.14 ((
% 96.58/13.14 (quantDeMorgan3) =>
% 96.58/13.14 ((
% 96.58/13.14 (quantDeMorgan4) =>
% 96.58/13.14 ((
% 96.58/13.14 (prop2setI) =>
% 96.58/13.14 ((
% 96.58/13.14 (prop2set2propI) =>
% 96.58/13.14 ((
% 96.58/13.14 (notdexE) =>
% 96.58/13.14 ((
% 96.58/13.14 (notdallE) =>
% 96.58/13.14 ((
% 96.58/13.14 (exuI1) =>
% 96.58/13.14 ((
% 96.58/13.14 (exuI3) =>
% 96.58/13.14 ((
% 96.58/13.14 (exuI2) =>
% 96.58/13.14 ((
% 96.58/13.14 (inCongP) =>
% 96.58/13.14 ((
% 96.58/13.14 (in__Cong) =>
% 96.58/13.14 ((
% 96.58/13.14 (exuE3u) =>
% 96.58/13.14 ((
% 96.58/13.14 (exu__Cong) =>
% 96.58/13.14 ((
% 96.58/13.14 (setadjoin__Cong) =>
% 96.58/13.14 ((
% 96.58/13.14 (powerset__Cong) =>
% 96.58/13.14 ((
% 96.58/13.14 (setunion__Cong) =>
% 96.58/13.14 ((
% 96.58/13.14 (exuEu) =>
% 96.58/13.14 ((
% 96.58/13.14 (descr__Cong) =>
% 96.58/13.14 ((
% 96.58/13.14 (dsetconstr__Cong) =>
% 96.58/13.14 ((
% 96.58/13.14 (subsetI1) =>
% 96.58/13.14 ((
% 96.58/13.14 (eqimpsubset2) =>
% 96.58/13.14 ((
% 96.58/13.14 (eqimpsubset1) =>
% 96.58/13.14 ((
% 96.58/13.14 (subsetI2) =>
% 96.58/13.14 ((
% 96.58/13.14 (emptysetsubset) =>
% 96.58/13.14 ((
% 96.58/13.14 (subsetE) =>
% 96.58/13.14 ((
% 96.58/13.14 (subsetE2) =>
% 96.58/13.14 ((
% 96.58/13.14 (notsubsetI) =>
% 96.58/13.14 ((
% 96.58/13.14 (notequalI1) =>
% 96.58/13.14 ((
% 96.58/13.14 (notequalI2) =>
% 96.58/13.14 ((
% 96.58/13.14 (subsetRefl) =>
% 96.58/13.14 ((
% 96.58/13.14 (subsetTrans) =>
% 96.58/13.14 ((
% 96.58/13.14 (setadjoinSub) =>
% 96.58/13.14 ((
% 96.58/13.14 (setadjoinSub2) =>
% 96.58/13.14 ((
% 96.58/13.14 (subset2powerset) =>
% 96.58/13.14 ((
% 96.58/13.14 (setextsub) =>
% 96.58/13.14 ((
% 96.58/13.14 (subsetemptysetimpeq) =>
% 96.58/13.14 ((
% 96.58/13.14 (powersetI1) =>
% 96.58/13.14 ((
% 96.58/13.14 (powersetE1) =>
% 96.58/13.14 ((
% 96.58/13.14 (inPowerset) =>
% 96.58/13.14 ((
% 96.58/13.14 (powersetsubset) =>
% 96.58/13.14 ((
% 96.58/13.14 (sepInPowerset) =>
% 96.58/13.14 ((
% 96.58/13.14 (sepSubset) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionIL) =>
% 96.58/13.14 ((
% 96.58/13.14 (upairset2IR) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionIR) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionEcases) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionE) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionLsub) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionRsub) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectI) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectSubset5) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectEL) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectLsub) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectSubset2) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectSubset3) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectER) =>
% 96.58/13.14 ((
% 96.58/13.14 (disjointsetsI1) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectRsub) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectSubset4) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectSubset1) =>
% 96.58/13.14 ((
% 96.58/13.14 (bs114d) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusI) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusEL) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusER) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusSubset2) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusERneg) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusELneg) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusILneg) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusIRneg) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusLsub) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusSubset1) =>
% 96.58/13.14 ((
% 96.58/13.14 (symdiffE) =>
% 96.58/13.14 ((
% 96.58/13.14 (symdiffI1) =>
% 96.58/13.14 ((
% 96.58/13.14 (symdiffI2) =>
% 96.58/13.14 ((
% 96.58/13.14 (symdiffIneg1) =>
% 96.58/13.14 ((
% 96.58/13.14 (symdiffIneg2) =>
% 96.58/13.14 ((
% 96.58/13.14 (secondinupair) =>
% 96.58/13.14 ((
% 96.58/13.14 (setukpairIL) =>
% 96.58/13.14 ((
% 96.58/13.14 (setukpairIR) =>
% 96.58/13.14 ((
% 96.58/13.14 (kpairiskpair) =>
% 96.58/13.14 ((
% 96.58/13.14 (kpairp) =>
% 96.58/13.14 ((
% 96.58/13.14 (singletonsubset) =>
% 96.58/13.14 ((
% 96.58/13.14 (singletoninpowerset) =>
% 96.58/13.14 ((
% 96.58/13.14 (singletoninpowunion) =>
% 96.58/13.14 ((
% 96.58/13.14 (upairset2E) =>
% 96.58/13.14 ((
% 96.58/13.14 (upairsubunion) =>
% 96.58/13.14 ((
% 96.58/13.14 (upairinpowunion) =>
% 96.58/13.14 ((
% 96.58/13.14 (ubforcartprodlem1) =>
% 96.58/13.14 ((
% 96.58/13.14 (ubforcartprodlem2) =>
% 96.58/13.14 ((
% 96.58/13.14 (ubforcartprodlem3) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodpairin) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodmempair1) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodmempair) =>
% 96.58/13.14 ((
% 96.58/13.14 (setunionE2) =>
% 96.58/13.14 ((
% 96.58/13.14 (setunionsingleton1) =>
% 96.58/13.14 ((
% 96.58/13.14 (setunionsingleton2) =>
% 96.58/13.14 ((
% 96.58/13.14 (setunionsingleton) =>
% 96.58/13.14 ((
% 96.58/13.14 (singletonprop) =>
% 96.58/13.14 ((
% 96.58/13.14 (ex1E1) =>
% 96.58/13.14 ((
% 96.58/13.14 (ex1I) =>
% 96.58/13.14 ((
% 96.58/13.14 (ex1I2) =>
% 96.58/13.14 ((
% 96.58/13.14 (singletonsuniq) =>
% 96.58/13.14 ((
% 96.58/13.14 (setukpairinjL1) =>
% 96.58/13.14 ((
% 96.58/13.14 (kfstsingleton) =>
% 96.58/13.14 ((
% 96.58/13.14 (theprop) =>
% 96.58/13.14 ((
% 96.58/13.14 (kfstpairEq) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodfstin) =>
% 96.58/13.14 ((
% 96.58/13.14 (setukpairinjL2) =>
% 96.58/13.14 ((
% 96.58/13.14 (setukpairinjL) =>
% 96.58/13.14 ((
% 96.58/13.14 (setukpairinjR11) =>
% 96.58/13.14 ((
% 96.58/13.14 (setukpairinjR12) =>
% 96.58/13.14 ((
% 96.58/13.14 (setukpairinjR1) =>
% 96.58/13.14 ((
% 96.58/13.14 (upairequniteq) =>
% 96.58/13.14 ((
% 96.58/13.14 (setukpairinjR2) =>
% 96.58/13.14 ((
% 96.58/13.14 (setukpairinjR) =>
% 96.58/13.14 ((
% 96.58/13.14 (ksndsingleton) =>
% 96.58/13.14 ((
% 96.58/13.14 (ksndpairEq) =>
% 96.58/13.14 ((
% 96.58/13.14 (kpairsurjEq) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodsndin) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodpairmemEL) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodpairmemER) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodmempaircEq) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodfstpairEq) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodsndpairEq) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodpairsurjEq) =>
% 96.58/13.14 ((
% 96.58/13.14 (dpsetconstrI) =>
% 96.58/13.14 ((
% 96.58/13.14 (dpsetconstrSub) =>
% 96.58/13.14 ((
% 96.58/13.14 (setOfPairsIsBReln) =>
% 96.58/13.14 ((
% 96.58/13.14 (dpsetconstrERa) =>
% 96.58/13.14 ((
% 96.58/13.14 (dpsetconstrEL1) =>
% 96.58/13.14 ((
% 96.58/13.14 (dpsetconstrEL2) =>
% 96.58/13.14 ((
% 96.58/13.14 (dpsetconstrER) =>
% 96.58/13.14 ((
% 96.58/13.14 (funcImageSingleton) =>
% 96.58/13.14 ((
% 96.58/13.14 (apProp) =>
% 96.58/13.14 ((
% 96.58/13.14 (app) =>
% 96.58/13.14 ((
% 96.58/13.14 (infuncsetfunc) =>
% 96.58/13.14 ((
% 96.58/13.14 (ap2p) =>
% 96.58/13.14 ((
% 96.58/13.14 (funcinfuncset) =>
% 96.58/13.14 ((
% 96.58/13.14 (lamProp) =>
% 96.58/13.14 ((
% 96.58/13.14 (lamp) =>
% 96.58/13.14 ((
% 96.58/13.14 (lam2p) =>
% 96.58/13.14 ((
% 96.58/13.14 (brelnall1) =>
% 96.58/13.14 ((
% 96.58/13.14 (brelnall2) =>
% 96.58/13.14 ((
% 96.58/13.14 (ex1E2) =>
% 96.58/13.14 ((
% 96.58/13.14 (funcGraphProp1) =>
% 96.58/13.14 ((
% 96.58/13.14 (funcGraphProp3) =>
% 96.58/13.14 ((
% 96.58/13.14 (funcGraphProp2) =>
% 96.58/13.14 ((
% 96.58/13.14 (funcextLem) =>
% 96.58/13.14 ((
% 96.58/13.14 (funcGraphProp4) =>
% 96.58/13.14 ((
% 96.58/13.14 (subbreln) =>
% 96.58/13.14 ((
% 96.58/13.14 (eqbreln) =>
% 96.58/13.14 ((
% 96.58/13.14 (funcext) =>
% 96.58/13.14 ((
% 96.58/13.14 (funcext2) =>
% 96.58/13.14 ((
% 96.58/13.14 (ap2apEq1) =>
% 96.58/13.14 ((
% 96.58/13.14 (ap2apEq2) =>
% 96.58/13.14 ((
% 96.58/13.14 (beta1) =>
% 96.58/13.14 ((
% 96.58/13.14 (eta1) =>
% 96.58/13.14 ((
% 96.58/13.14 (lam2lamEq) =>
% 96.58/13.14 ((
% 96.58/13.14 (beta2) =>
% 96.58/13.14 ((
% 96.58/13.14 (eta2) =>
% 96.58/13.14 ((
% 96.58/13.14 (iffalseProp1) =>
% 96.58/13.14 ((
% 96.58/13.14 (iffalseProp2) =>
% 96.58/13.14 ((
% 96.58/13.14 (iftrueProp1) =>
% 96.58/13.14 ((
% 96.58/13.14 (iftrueProp2) =>
% 96.58/13.14 ((
% 96.58/13.14 (ifSingleton) =>
% 96.58/13.14 ((
% 96.58/13.14 (ifp) =>
% 96.58/13.14 ((
% 96.58/13.14 (theeq) =>
% 96.58/13.14 ((
% 96.58/13.14 (iftrue) =>
% 96.58/13.14 ((
% 96.58/13.14 (iffalse) =>
% 96.58/13.14 ((
% 96.58/13.14 (iftrueorfalse) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectT_lem) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionT_lem) =>
% 96.58/13.14 ((
% 96.58/13.14 (powersetT_lem) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusT_lem) =>
% 96.58/13.14 ((
% 96.58/13.14 (complementT_lem) =>
% 96.58/13.14 ((
% 96.58/13.14 (setextT) =>
% 96.58/13.14 ((
% 96.58/13.14 (subsetTI) =>
% 96.58/13.14 ((
% 96.58/13.14 (powersetTI1) =>
% 96.58/13.14 ((
% 96.58/13.14 (powersetTE1) =>
% 96.58/13.14 ((
% 96.58/13.14 (complementTI1) =>
% 96.58/13.14 ((
% 96.58/13.14 (complementTE1) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectTELcontra) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectTERcontra) =>
% 96.58/13.14 ((
% 96.58/13.14 (contrasubsetT) =>
% 96.58/13.14 ((
% 96.58/13.14 (contrasubsetT1) =>
% 96.58/13.14 ((
% 96.58/13.14 (contrasubsetT2) =>
% 96.58/13.14 ((
% 96.58/13.14 (contrasubsetT3) =>
% 96.58/13.14 ((
% 96.58/13.14 (doubleComplementI1) =>
% 96.58/13.14 ((
% 96.58/13.14 (doubleComplementE1) =>
% 96.58/13.14 ((
% 96.58/13.14 (doubleComplementSub1) =>
% 96.58/13.14 ((
% 96.58/13.14 (doubleComplementSub2) =>
% 96.58/13.14 ((
% 96.58/13.14 (doubleComplementEq) =>
% 96.58/13.14 ((
% 96.58/13.14 (complementTnotintersectT) =>
% 96.58/13.14 ((
% 96.58/13.14 (complementImpComplementIntersect) =>
% 96.58/13.14 ((
% 96.58/13.14 (complementSubsetComplementIntersect) =>
% 96.58/13.14 ((
% 96.58/13.14 (complementInPowersetComplementIntersect) =>
% 96.58/13.14 ((
% 96.58/13.14 (contraSubsetComplement) =>
% 96.58/13.14 ((
% 96.58/13.14 (complementTcontraSubset) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionTILcontra) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionTIRcontra) =>
% 96.58/13.14 ((
% 96.58/13.14 (inIntersectImpInUnion) =>
% 96.58/13.14 ((
% 96.58/13.14 (inIntersectImpInUnion2) =>
% 96.58/13.14 ((
% 96.58/13.14 (inIntersectImpInIntersectUnions) =>
% 96.58/13.14 ((
% 96.58/13.14 (intersectInPowersetIntersectUnions) =>
% 96.58/13.14 ((
% 96.58/13.14 (inComplementUnionImpNotIn1) =>
% 96.58/13.14 ((
% 96.58/13.14 (inComplementUnionImpInComplement1) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionTE) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionTEcontra) =>
% 96.58/13.14 ((
% 96.58/13.14 (demorgan2a1) =>
% 96.58/13.14 ((
% 96.58/13.14 (complementUnionInPowersetComplement) =>
% 96.58/13.14 ((
% 96.58/13.14 (demorgan2a2) =>
% 96.58/13.14 ((
% 96.58/13.14 (demorgan1a) =>
% 96.58/13.14 ((
% 96.58/13.14 (demorgan1b) =>
% 96.58/13.14 ((
% 96.58/13.14 (demorgan1) =>
% 96.58/13.14 ((
% 96.58/13.14 (demorgan2a) =>
% 96.58/13.14 ((
% 96.58/13.14 (demorgan2b2) =>
% 96.58/13.14 ((
% 96.58/13.14 (demorgan2b) =>
% 96.58/13.14 ((
% 96.58/13.14 (demorgan2) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz13rule0) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz13rule1) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz13rule2) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz13rule3) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz13rule4) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz1_1) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz1_2) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz1_3) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz1_4) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz1_5) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1all2) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1SetBreln1) =>
% 96.58/13.14 ((
% 96.58/13.14 (choice2fnsingleton) =>
% 96.58/13.14 ((
% 96.58/13.14 (setOfPairsIsBReln1) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1all1) =>
% 96.58/13.14 ((
% 96.58/13.14 (subbreln1) =>
% 96.58/13.14 ((
% 96.58/13.14 (eqbreln1) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1invprop) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1invI) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1invE) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1compprop) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1compI) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1compE) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1compEex) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1unionprop) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1unionIL) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1unionIR) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1unionI) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1unionE) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1unionEcases) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1unionCommutes) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz2Ex) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz2W) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz2A) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz2B) =>
% 96.58/13.14 ((
% 96.58/13.14 (image1Ex) =>
% 96.58/13.14 ((
% 96.58/13.14 (image1Ex1) =>
% 96.58/13.14 ((
% 96.58/13.14 (image1Equiv) =>
% 96.58/13.14 ((
% 96.58/13.14 (image1E) =>
% 96.58/13.14 ((
% 96.58/13.14 (image1I) =>
% 96.58/13.14 ((
% 96.58/13.14 (injFuncInInjFuncSet) =>
% 96.58/13.14 ((
% 96.58/13.14 (injFuncSetFuncIn) =>
% 96.58/13.14 ((
% 96.58/13.14 (injFuncSetFuncInj) =>
% 96.58/13.14 ((
% 96.58/13.14 (surjFuncSetFuncIn) =>
% 96.58/13.14 ((
% 96.58/13.14 (surjFuncSetFuncSurj) =>
% 96.58/13.14 ((
% 96.58/13.14 (leftInvIsSurj) =>
% 96.58/13.14 ((
% 96.58/13.14 (surjCantorThm) =>
% 96.58/13.14 ((
% 96.58/13.14 (foundation2) =>
% 96.58/13.14 ((
% 96.58/13.14 (notinself) =>
% 96.58/13.14 ((
% 96.58/13.14 (notinself2) =>
% 96.58/13.14 ((
% 96.58/13.14 (omegaSp) =>
% 96.58/13.14 ((
% 96.58/13.14 (omegaSclos) =>
% 96.58/13.14 ((
% 96.58/13.14 (peano0notS) =>
% 96.58/13.14 ((
% 96.58/13.14 (!!) @ (
% 96.58/13.14 (('#S') @ (
% 96.58/13.14 (
% 96.58/13.14 ('#B') @ (
% 96.58/13.14 =>) @
% 96.58/13.14 (
% 96.58/13.14 (
% 96.58/13.14 ('#C') @ in @
% 96.58/13.14 omega)))) @
% 96.58/13.14 (
% 96.58/13.14 (
% 96.58/13.14 ('#B') @ (
% 96.58/13.14 !!) @
% 96.58/13.14 (
% 96.58/13.14 (
% 96.58/13.14 ('#B') @ (
% 96.58/13.14 (
% 96.58/13.14 ('#S') @ (
% 96.58/13.14 (
% 96.58/13.14 ('#B') @ (
% 96.58/13.14 =>) @
% 96.58/13.14 (
% 96.58/13.14 (
% 96.58/13.14 ('#C') @ in @
% 96.58/13.14 omega)))))) @
% 96.58/13.14 (
% 96.58/13.14 (
% 96.58/13.14 ('#S') @ (
% 96.58/13.14 (
% 96.58/13.14 ('#B') @ (
% 96.58/13.14 '#S') @
% 96.58/13.14 (
% 96.58/13.14 (
% 96.58/13.14 ('#B') @ (
% 96.58/13.14 (
% 96.58/13.14 ('#B') @ (
% 96.58/13.14 =>))) @
% 96.58/13.14 (
% 96.58/13.14 (
% 96.58/13.14 ('#C') @ (
% 96.58/13.14 (
% 96.58/13.14 ('#B') @ (
% 96.58/13.14 '#B') @
% 96.58/13.14 (
% 96.58/13.14 (
% 96.58/13.14 ('#B') @ (
% 96.58/13.14 =) @
% 96.58/13.14 omegaS)))) @
% 96.58/13.14 omegaS)))))) @
% 96.58/13.14 (
% 96.58/13.14 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 96.58/13.14 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl13])).
% 96.58/13.14 thf(zip_derived_cl25, plain,
% 96.58/13.14 (~ (((in @ emptyset @ omega) =>
% 96.58/13.14 (((omegaSAx) =>
% 96.58/13.14 (((omegaIndAx) =>
% 96.58/13.14 (((replAx) =>
% 96.58/13.14 (((foundationAx) =>
% 96.58/13.14 (((wellorderingAx) =>
% 96.58/13.14 (((descrp) =>
% 96.58/13.14 (((dsetconstrI) =>
% 96.58/13.14 (((dsetconstrEL) =>
% 96.58/13.14 (((dsetconstrER) =>
% 96.58/13.14 (((exuE1) =>
% 96.58/13.14 (((prop2setE) =>
% 96.58/13.14 (((emptysetE) =>
% 96.58/13.14 (((emptysetimpfalse) =>
% 96.58/13.14 (((notinemptyset) =>
% 96.58/13.14 (((exuE3e) =>
% 96.58/13.14 (((setext) =>
% 96.58/13.14 (((emptyI) =>
% 96.58/13.14 (((noeltsimpempty) =>
% 96.58/13.14 (((setbeta) =>
% 96.58/13.14 (((nonemptyE1) =>
% 96.58/13.14 (((nonemptyI) =>
% 96.58/13.14 (((nonemptyI1) =>
% 96.58/13.14 (((setadjoinIL) =>
% 96.58/13.14 (((in @ emptyset @
% 96.58/13.14 (setadjoin @
% 96.58/13.14 emptyset @ emptyset)) =>
% 96.58/13.14 (((setadjoinIR) =>
% 96.58/13.14 (((setadjoinE) =>
% 96.58/13.14 (((setadjoinOr) =>
% 96.58/13.14 (((setoftrueEq) =>
% 96.58/13.14 (((powersetI) =>
% 96.58/13.14 ((
% 96.58/13.14 (emptyinPowerset) =>
% 96.58/13.14 ((
% 96.58/13.14 (emptyInPowerset) =>
% 96.58/13.14 ((
% 96.58/13.14 (powersetE) =>
% 96.58/13.14 ((
% 96.58/13.14 (setunionI) =>
% 96.58/13.14 ((
% 96.58/13.14 (setunionE) =>
% 96.58/13.14 ((
% 96.58/13.14 (subPowSU) =>
% 96.58/13.14 ((
% 96.58/13.14 (exuE2) =>
% 96.58/13.14 ((
% 96.58/13.14 (nonemptyImpWitness) =>
% 96.58/13.14 ((
% 96.58/13.14 (uniqinunit) =>
% 96.58/13.14 ((
% 96.58/13.14 (notinsingleton) =>
% 96.58/13.14 ((
% 96.58/13.14 (eqinunit) =>
% 96.58/13.14 ((
% 96.58/13.14 (singletonsswitch) =>
% 96.58/13.14 ((
% 96.58/13.14 (upairsetE) =>
% 96.58/13.14 ((
% 96.58/13.14 (upairsetIL) =>
% 96.58/13.14 ((
% 96.58/13.14 (upairsetIR) =>
% 96.58/13.14 ((
% 96.58/13.14 (emptyE1) =>
% 96.58/13.14 ((
% 96.58/13.14 (vacuousDall) =>
% 96.58/13.14 ((
% 96.58/13.14 (quantDeMorgan1) =>
% 96.58/13.14 ((
% 96.58/13.14 (quantDeMorgan2) =>
% 96.58/13.14 ((
% 96.58/13.14 (quantDeMorgan3) =>
% 96.58/13.14 ((
% 96.58/13.14 (quantDeMorgan4) =>
% 96.58/13.14 ((
% 96.58/13.14 (prop2setI) =>
% 96.58/13.14 ((
% 96.58/13.14 (prop2set2propI) =>
% 96.58/13.14 ((
% 96.58/13.14 (notdexE) =>
% 96.58/13.14 ((
% 96.58/13.14 (notdallE) =>
% 96.58/13.14 ((
% 96.58/13.14 (exuI1) =>
% 96.58/13.14 ((
% 96.58/13.14 (exuI3) =>
% 96.58/13.14 ((
% 96.58/13.14 (exuI2) =>
% 96.58/13.14 ((
% 96.58/13.14 (inCongP) =>
% 96.58/13.14 ((
% 96.58/13.14 (in__Cong) =>
% 96.58/13.14 ((
% 96.58/13.14 (exuE3u) =>
% 96.58/13.14 ((
% 96.58/13.14 (exu__Cong) =>
% 96.58/13.14 ((
% 96.58/13.14 (setadjoin__Cong) =>
% 96.58/13.14 ((
% 96.58/13.14 (powerset__Cong) =>
% 96.58/13.14 ((
% 96.58/13.14 (setunion__Cong) =>
% 96.58/13.14 ((
% 96.58/13.14 (exuEu) =>
% 96.58/13.14 ((
% 96.58/13.14 (descr__Cong) =>
% 96.58/13.14 ((
% 96.58/13.14 (dsetconstr__Cong) =>
% 96.58/13.14 ((
% 96.58/13.14 (subsetI1) =>
% 96.58/13.14 ((
% 96.58/13.14 (eqimpsubset2) =>
% 96.58/13.14 ((
% 96.58/13.14 (eqimpsubset1) =>
% 96.58/13.14 ((
% 96.58/13.14 (subsetI2) =>
% 96.58/13.14 ((
% 96.58/13.14 (emptysetsubset) =>
% 96.58/13.14 ((
% 96.58/13.14 (subsetE) =>
% 96.58/13.14 ((
% 96.58/13.14 (subsetE2) =>
% 96.58/13.14 ((
% 96.58/13.14 (notsubsetI) =>
% 96.58/13.14 ((
% 96.58/13.14 (notequalI1) =>
% 96.58/13.14 ((
% 96.58/13.14 (notequalI2) =>
% 96.58/13.14 ((
% 96.58/13.14 (subsetRefl) =>
% 96.58/13.14 ((
% 96.58/13.14 (subsetTrans) =>
% 96.58/13.14 ((
% 96.58/13.14 (setadjoinSub) =>
% 96.58/13.14 ((
% 96.58/13.14 (setadjoinSub2) =>
% 96.58/13.14 ((
% 96.58/13.14 (subset2powerset) =>
% 96.58/13.14 ((
% 96.58/13.14 (setextsub) =>
% 96.58/13.14 ((
% 96.58/13.14 (subsetemptysetimpeq) =>
% 96.58/13.14 ((
% 96.58/13.14 (powersetI1) =>
% 96.58/13.14 ((
% 96.58/13.14 (powersetE1) =>
% 96.58/13.14 ((
% 96.58/13.14 (inPowerset) =>
% 96.58/13.14 ((
% 96.58/13.14 (powersetsubset) =>
% 96.58/13.14 ((
% 96.58/13.14 (sepInPowerset) =>
% 96.58/13.14 ((
% 96.58/13.14 (sepSubset) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionIL) =>
% 96.58/13.14 ((
% 96.58/13.14 (upairset2IR) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionIR) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionEcases) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionE) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionLsub) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionRsub) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectI) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectSubset5) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectEL) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectLsub) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectSubset2) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectSubset3) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectER) =>
% 96.58/13.14 ((
% 96.58/13.14 (disjointsetsI1) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectRsub) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectSubset4) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectSubset1) =>
% 96.58/13.14 ((
% 96.58/13.14 (bs114d) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusI) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusEL) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusER) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusSubset2) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusERneg) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusELneg) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusILneg) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusIRneg) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusLsub) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusSubset1) =>
% 96.58/13.14 ((
% 96.58/13.14 (symdiffE) =>
% 96.58/13.14 ((
% 96.58/13.14 (symdiffI1) =>
% 96.58/13.14 ((
% 96.58/13.14 (symdiffI2) =>
% 96.58/13.14 ((
% 96.58/13.14 (symdiffIneg1) =>
% 96.58/13.14 ((
% 96.58/13.14 (symdiffIneg2) =>
% 96.58/13.14 ((
% 96.58/13.14 (secondinupair) =>
% 96.58/13.14 ((
% 96.58/13.14 (setukpairIL) =>
% 96.58/13.14 ((
% 96.58/13.14 (setukpairIR) =>
% 96.58/13.14 ((
% 96.58/13.14 (kpairiskpair) =>
% 96.58/13.14 ((
% 96.58/13.14 (kpairp) =>
% 96.58/13.14 ((
% 96.58/13.14 (singletonsubset) =>
% 96.58/13.14 ((
% 96.58/13.14 (singletoninpowerset) =>
% 96.58/13.14 ((
% 96.58/13.14 (singletoninpowunion) =>
% 96.58/13.14 ((
% 96.58/13.14 (upairset2E) =>
% 96.58/13.14 ((
% 96.58/13.14 (upairsubunion) =>
% 96.58/13.14 ((
% 96.58/13.14 (upairinpowunion) =>
% 96.58/13.14 ((
% 96.58/13.14 (ubforcartprodlem1) =>
% 96.58/13.14 ((
% 96.58/13.14 (ubforcartprodlem2) =>
% 96.58/13.14 ((
% 96.58/13.14 (ubforcartprodlem3) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodpairin) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodmempair1) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodmempair) =>
% 96.58/13.14 ((
% 96.58/13.14 (setunionE2) =>
% 96.58/13.14 ((
% 96.58/13.14 (setunionsingleton1) =>
% 96.58/13.14 ((
% 96.58/13.14 (setunionsingleton2) =>
% 96.58/13.14 ((
% 96.58/13.14 (setunionsingleton) =>
% 96.58/13.14 ((
% 96.58/13.14 (singletonprop) =>
% 96.58/13.14 ((
% 96.58/13.14 (ex1E1) =>
% 96.58/13.14 ((
% 96.58/13.14 (ex1I) =>
% 96.58/13.14 ((
% 96.58/13.14 (ex1I2) =>
% 96.58/13.14 ((
% 96.58/13.14 (singletonsuniq) =>
% 96.58/13.14 ((
% 96.58/13.14 (setukpairinjL1) =>
% 96.58/13.14 ((
% 96.58/13.14 (kfstsingleton) =>
% 96.58/13.14 ((
% 96.58/13.14 (theprop) =>
% 96.58/13.14 ((
% 96.58/13.14 (kfstpairEq) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodfstin) =>
% 96.58/13.14 ((
% 96.58/13.14 (setukpairinjL2) =>
% 96.58/13.14 ((
% 96.58/13.14 (setukpairinjL) =>
% 96.58/13.14 ((
% 96.58/13.14 (setukpairinjR11) =>
% 96.58/13.14 ((
% 96.58/13.14 (setukpairinjR12) =>
% 96.58/13.14 ((
% 96.58/13.14 (setukpairinjR1) =>
% 96.58/13.14 ((
% 96.58/13.14 (upairequniteq) =>
% 96.58/13.14 ((
% 96.58/13.14 (setukpairinjR2) =>
% 96.58/13.14 ((
% 96.58/13.14 (setukpairinjR) =>
% 96.58/13.14 ((
% 96.58/13.14 (ksndsingleton) =>
% 96.58/13.14 ((
% 96.58/13.14 (ksndpairEq) =>
% 96.58/13.14 ((
% 96.58/13.14 (kpairsurjEq) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodsndin) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodpairmemEL) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodpairmemER) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodmempaircEq) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodfstpairEq) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodsndpairEq) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodpairsurjEq) =>
% 96.58/13.14 ((
% 96.58/13.14 (dpsetconstrI) =>
% 96.58/13.14 ((
% 96.58/13.14 (dpsetconstrSub) =>
% 96.58/13.14 ((
% 96.58/13.14 (setOfPairsIsBReln) =>
% 96.58/13.14 ((
% 96.58/13.14 (dpsetconstrERa) =>
% 96.58/13.14 ((
% 96.58/13.14 (dpsetconstrEL1) =>
% 96.58/13.14 ((
% 96.58/13.14 (dpsetconstrEL2) =>
% 96.58/13.14 ((
% 96.58/13.14 (dpsetconstrER) =>
% 96.58/13.14 ((
% 96.58/13.14 (funcImageSingleton) =>
% 96.58/13.14 ((
% 96.58/13.14 (apProp) =>
% 96.58/13.14 ((
% 96.58/13.14 (app) =>
% 96.58/13.14 ((
% 96.58/13.14 (infuncsetfunc) =>
% 96.58/13.14 ((
% 96.58/13.14 (ap2p) =>
% 96.58/13.14 ((
% 96.58/13.14 (funcinfuncset) =>
% 96.58/13.14 ((
% 96.58/13.14 (lamProp) =>
% 96.58/13.14 ((
% 96.58/13.14 (lamp) =>
% 96.58/13.14 ((
% 96.58/13.14 (lam2p) =>
% 96.58/13.14 ((
% 96.58/13.14 (brelnall1) =>
% 96.58/13.14 ((
% 96.58/13.14 (brelnall2) =>
% 96.58/13.14 ((
% 96.58/13.14 (ex1E2) =>
% 96.58/13.14 ((
% 96.58/13.14 (funcGraphProp1) =>
% 96.58/13.14 ((
% 96.58/13.14 (funcGraphProp3) =>
% 96.58/13.14 ((
% 96.58/13.14 (funcGraphProp2) =>
% 96.58/13.14 ((
% 96.58/13.14 (funcextLem) =>
% 96.58/13.14 ((
% 96.58/13.14 (funcGraphProp4) =>
% 96.58/13.14 ((
% 96.58/13.14 (subbreln) =>
% 96.58/13.14 ((
% 96.58/13.14 (eqbreln) =>
% 96.58/13.14 ((
% 96.58/13.14 (funcext) =>
% 96.58/13.14 ((
% 96.58/13.14 (funcext2) =>
% 96.58/13.14 ((
% 96.58/13.14 (ap2apEq1) =>
% 96.58/13.14 ((
% 96.58/13.14 (ap2apEq2) =>
% 96.58/13.14 ((
% 96.58/13.14 (beta1) =>
% 96.58/13.14 ((
% 96.58/13.14 (eta1) =>
% 96.58/13.14 ((
% 96.58/13.14 (lam2lamEq) =>
% 96.58/13.14 ((
% 96.58/13.14 (beta2) =>
% 96.58/13.14 ((
% 96.58/13.14 (eta2) =>
% 96.58/13.14 ((
% 96.58/13.14 (iffalseProp1) =>
% 96.58/13.14 ((
% 96.58/13.14 (iffalseProp2) =>
% 96.58/13.14 ((
% 96.58/13.14 (iftrueProp1) =>
% 96.58/13.14 ((
% 96.58/13.14 (iftrueProp2) =>
% 96.58/13.14 ((
% 96.58/13.14 (ifSingleton) =>
% 96.58/13.14 ((
% 96.58/13.14 (ifp) =>
% 96.58/13.14 ((
% 96.58/13.14 (theeq) =>
% 96.58/13.14 ((
% 96.58/13.14 (iftrue) =>
% 96.58/13.14 ((
% 96.58/13.14 (iffalse) =>
% 96.58/13.14 ((
% 96.58/13.14 (iftrueorfalse) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectT_lem) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionT_lem) =>
% 96.58/13.14 ((
% 96.58/13.14 (powersetT_lem) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusT_lem) =>
% 96.58/13.14 ((
% 96.58/13.14 (complementT_lem) =>
% 96.58/13.14 ((
% 96.58/13.14 (setextT) =>
% 96.58/13.14 ((
% 96.58/13.14 (subsetTI) =>
% 96.58/13.14 ((
% 96.58/13.14 (powersetTI1) =>
% 96.58/13.14 ((
% 96.58/13.14 (powersetTE1) =>
% 96.58/13.14 ((
% 96.58/13.14 (complementTI1) =>
% 96.58/13.14 ((
% 96.58/13.14 (complementTE1) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectTELcontra) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectTERcontra) =>
% 96.58/13.14 ((
% 96.58/13.14 (contrasubsetT) =>
% 96.58/13.14 ((
% 96.58/13.14 (contrasubsetT1) =>
% 96.58/13.14 ((
% 96.58/13.14 (contrasubsetT2) =>
% 96.58/13.14 ((
% 96.58/13.14 (contrasubsetT3) =>
% 96.58/13.14 ((
% 96.58/13.14 (doubleComplementI1) =>
% 96.58/13.14 ((
% 96.58/13.14 (doubleComplementE1) =>
% 96.58/13.14 ((
% 96.58/13.14 (doubleComplementSub1) =>
% 96.58/13.14 ((
% 96.58/13.14 (doubleComplementSub2) =>
% 96.58/13.14 ((
% 96.58/13.14 (doubleComplementEq) =>
% 96.58/13.14 ((
% 96.58/13.14 (complementTnotintersectT) =>
% 96.58/13.14 ((
% 96.58/13.14 (complementImpComplementIntersect) =>
% 96.58/13.14 ((
% 96.58/13.14 (complementSubsetComplementIntersect) =>
% 96.58/13.14 ((
% 96.58/13.14 (complementInPowersetComplementIntersect) =>
% 96.58/13.14 ((
% 96.58/13.14 (contraSubsetComplement) =>
% 96.58/13.14 ((
% 96.58/13.14 (complementTcontraSubset) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionTILcontra) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionTIRcontra) =>
% 96.58/13.14 ((
% 96.58/13.14 (inIntersectImpInUnion) =>
% 96.58/13.14 ((
% 96.58/13.14 (inIntersectImpInUnion2) =>
% 96.58/13.14 ((
% 96.58/13.14 (inIntersectImpInIntersectUnions) =>
% 96.58/13.14 ((
% 96.58/13.14 (intersectInPowersetIntersectUnions) =>
% 96.58/13.14 ((
% 96.58/13.14 (inComplementUnionImpNotIn1) =>
% 96.58/13.14 ((
% 96.58/13.14 (inComplementUnionImpInComplement1) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionTE) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionTEcontra) =>
% 96.58/13.14 ((
% 96.58/13.14 (demorgan2a1) =>
% 96.58/13.14 ((
% 96.58/13.14 (complementUnionInPowersetComplement) =>
% 96.58/13.14 ((
% 96.58/13.14 (demorgan2a2) =>
% 96.58/13.14 ((
% 96.58/13.14 (demorgan1a) =>
% 96.58/13.14 ((
% 96.58/13.14 (demorgan1b) =>
% 96.58/13.14 ((
% 96.58/13.14 (demorgan1) =>
% 96.58/13.14 ((
% 96.58/13.14 (demorgan2a) =>
% 96.58/13.14 ((
% 96.58/13.14 (demorgan2b2) =>
% 96.58/13.14 ((
% 96.58/13.14 (demorgan2b) =>
% 96.58/13.14 ((
% 96.58/13.14 (demorgan2) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz13rule0) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz13rule1) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz13rule2) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz13rule3) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz13rule4) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz1_1) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz1_2) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz1_3) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz1_4) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz1_5) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1all2) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1SetBreln1) =>
% 96.58/13.14 ((
% 96.58/13.14 (choice2fnsingleton) =>
% 96.58/13.14 ((
% 96.58/13.14 (setOfPairsIsBReln1) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1all1) =>
% 96.58/13.14 ((
% 96.58/13.14 (subbreln1) =>
% 96.58/13.14 ((
% 96.58/13.14 (eqbreln1) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1invprop) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1invI) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1invE) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1compprop) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1compI) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1compE) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1compEex) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1unionprop) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1unionIL) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1unionIR) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1unionI) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1unionE) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1unionEcases) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1unionCommutes) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz2Ex) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz2W) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz2A) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz2B) =>
% 96.58/13.14 ((
% 96.58/13.14 (image1Ex) =>
% 96.58/13.14 ((
% 96.58/13.14 (image1Ex1) =>
% 96.58/13.14 ((
% 96.58/13.14 (image1Equiv) =>
% 96.58/13.14 ((
% 96.58/13.14 (image1E) =>
% 96.58/13.14 ((
% 96.58/13.14 (image1I) =>
% 96.58/13.14 ((
% 96.58/13.14 (injFuncInInjFuncSet) =>
% 96.58/13.14 ((
% 96.58/13.14 (injFuncSetFuncIn) =>
% 96.58/13.14 ((
% 96.58/13.14 (injFuncSetFuncInj) =>
% 96.58/13.14 ((
% 96.58/13.14 (surjFuncSetFuncIn) =>
% 96.58/13.14 ((
% 96.58/13.14 (surjFuncSetFuncSurj) =>
% 96.58/13.14 ((
% 96.58/13.14 (leftInvIsSurj) =>
% 96.58/13.14 ((
% 96.58/13.14 (surjCantorThm) =>
% 96.58/13.14 ((
% 96.58/13.14 (foundation2) =>
% 96.58/13.14 ((
% 96.58/13.14 (notinself) =>
% 96.58/13.14 ((
% 96.58/13.14 (notinself2) =>
% 96.58/13.14 ((
% 96.58/13.14 (omegaSp) =>
% 96.58/13.14 ((
% 96.58/13.14 (omegaSclos) =>
% 96.58/13.14 ((
% 96.58/13.14 (peano0notS) =>
% 96.58/13.14 ((
% 96.58/13.14 (!!) @ (
% 96.58/13.14 (('#S') @ (
% 96.58/13.14 (
% 96.58/13.14 ('#B') @ (
% 96.58/13.14 =>) @
% 96.58/13.14 (
% 96.58/13.14 (
% 96.58/13.14 ('#C') @ in @
% 96.58/13.14 omega)))) @
% 96.58/13.14 (
% 96.58/13.14 (
% 96.58/13.14 ('#B') @ (
% 96.58/13.14 !!) @
% 96.58/13.14 (
% 96.58/13.14 (
% 96.58/13.14 ('#B') @ (
% 96.58/13.14 (
% 96.58/13.14 ('#S') @ (
% 96.58/13.14 (
% 96.58/13.14 ('#B') @ (
% 96.58/13.14 =>) @
% 96.58/13.14 (
% 96.58/13.14 (
% 96.58/13.14 ('#C') @ in @
% 96.58/13.14 omega)))))) @
% 96.58/13.14 (
% 96.58/13.14 (
% 96.58/13.14 ('#S') @ (
% 96.58/13.14 (
% 96.58/13.14 ('#B') @ (
% 96.58/13.14 '#S') @
% 96.58/13.14 (
% 96.58/13.14 (
% 96.58/13.14 ('#B') @ (
% 96.58/13.14 (
% 96.58/13.14 ('#B') @ (
% 96.58/13.14 =>))) @
% 96.58/13.14 (
% 96.58/13.14 (
% 96.58/13.14 ('#C') @ (
% 96.58/13.14 (
% 96.58/13.14 ('#B') @ (
% 96.58/13.14 '#B') @
% 96.58/13.14 (
% 96.58/13.14 (
% 96.58/13.14 ('#B') @ (
% 96.58/13.14 =) @
% 96.58/13.14 omegaS)))) @
% 96.58/13.14 omegaS)))))) @
% 96.58/13.14 (
% 96.58/13.14 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 96.58/13.14 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl19])).
% 96.58/13.14 thf(zip_derived_cl33, plain,
% 96.58/13.14 (~ (((omegaSAx) =>
% 96.58/13.14 (((omegaIndAx) =>
% 96.58/13.14 (((replAx) =>
% 96.58/13.14 (((foundationAx) =>
% 96.58/13.14 (((wellorderingAx) =>
% 96.58/13.14 (((descrp) =>
% 96.58/13.14 (((dsetconstrI) =>
% 96.58/13.14 (((dsetconstrEL) =>
% 96.58/13.14 (((dsetconstrER) =>
% 96.58/13.14 (((exuE1) =>
% 96.58/13.14 (((prop2setE) =>
% 96.58/13.14 (((emptysetE) =>
% 96.58/13.14 (((emptysetimpfalse) =>
% 96.58/13.14 (((notinemptyset) =>
% 96.58/13.14 (((exuE3e) =>
% 96.58/13.14 (((setext) =>
% 96.58/13.14 (((emptyI) =>
% 96.58/13.14 (((noeltsimpempty) =>
% 96.58/13.14 (((setbeta) =>
% 96.58/13.14 (((nonemptyE1) =>
% 96.58/13.14 (((nonemptyI) =>
% 96.58/13.14 (((nonemptyI1) =>
% 96.58/13.14 (((setadjoinIL) =>
% 96.58/13.14 (((in @ emptyset @
% 96.58/13.14 (setadjoin @
% 96.58/13.14 emptyset @ emptyset)) =>
% 96.58/13.14 (((setadjoinIR) =>
% 96.58/13.14 (((setadjoinE) =>
% 96.58/13.14 (((setadjoinOr) =>
% 96.58/13.14 (((setoftrueEq) =>
% 96.58/13.14 (((powersetI) =>
% 96.58/13.14 (((emptyinPowerset) =>
% 96.58/13.14 ((
% 96.58/13.14 (emptyInPowerset) =>
% 96.58/13.14 ((
% 96.58/13.14 (powersetE) =>
% 96.58/13.14 ((
% 96.58/13.14 (setunionI) =>
% 96.58/13.14 ((
% 96.58/13.14 (setunionE) =>
% 96.58/13.14 ((
% 96.58/13.14 (subPowSU) =>
% 96.58/13.14 ((
% 96.58/13.14 (exuE2) =>
% 96.58/13.14 ((
% 96.58/13.14 (nonemptyImpWitness) =>
% 96.58/13.14 ((
% 96.58/13.14 (uniqinunit) =>
% 96.58/13.14 ((
% 96.58/13.14 (notinsingleton) =>
% 96.58/13.14 ((
% 96.58/13.14 (eqinunit) =>
% 96.58/13.14 ((
% 96.58/13.14 (singletonsswitch) =>
% 96.58/13.14 ((
% 96.58/13.14 (upairsetE) =>
% 96.58/13.14 ((
% 96.58/13.14 (upairsetIL) =>
% 96.58/13.14 ((
% 96.58/13.14 (upairsetIR) =>
% 96.58/13.14 ((
% 96.58/13.14 (emptyE1) =>
% 96.58/13.14 ((
% 96.58/13.14 (vacuousDall) =>
% 96.58/13.14 ((
% 96.58/13.14 (quantDeMorgan1) =>
% 96.58/13.14 ((
% 96.58/13.14 (quantDeMorgan2) =>
% 96.58/13.14 ((
% 96.58/13.14 (quantDeMorgan3) =>
% 96.58/13.14 ((
% 96.58/13.14 (quantDeMorgan4) =>
% 96.58/13.14 ((
% 96.58/13.14 (prop2setI) =>
% 96.58/13.14 ((
% 96.58/13.14 (prop2set2propI) =>
% 96.58/13.14 ((
% 96.58/13.14 (notdexE) =>
% 96.58/13.14 ((
% 96.58/13.14 (notdallE) =>
% 96.58/13.14 ((
% 96.58/13.14 (exuI1) =>
% 96.58/13.14 ((
% 96.58/13.14 (exuI3) =>
% 96.58/13.14 ((
% 96.58/13.14 (exuI2) =>
% 96.58/13.14 ((
% 96.58/13.14 (inCongP) =>
% 96.58/13.14 ((
% 96.58/13.14 (in__Cong) =>
% 96.58/13.14 ((
% 96.58/13.14 (exuE3u) =>
% 96.58/13.14 ((
% 96.58/13.14 (exu__Cong) =>
% 96.58/13.14 ((
% 96.58/13.14 (setadjoin__Cong) =>
% 96.58/13.14 ((
% 96.58/13.14 (powerset__Cong) =>
% 96.58/13.14 ((
% 96.58/13.14 (setunion__Cong) =>
% 96.58/13.14 ((
% 96.58/13.14 (exuEu) =>
% 96.58/13.14 ((
% 96.58/13.14 (descr__Cong) =>
% 96.58/13.14 ((
% 96.58/13.14 (dsetconstr__Cong) =>
% 96.58/13.14 ((
% 96.58/13.14 (subsetI1) =>
% 96.58/13.14 ((
% 96.58/13.14 (eqimpsubset2) =>
% 96.58/13.14 ((
% 96.58/13.14 (eqimpsubset1) =>
% 96.58/13.14 ((
% 96.58/13.14 (subsetI2) =>
% 96.58/13.14 ((
% 96.58/13.14 (emptysetsubset) =>
% 96.58/13.14 ((
% 96.58/13.14 (subsetE) =>
% 96.58/13.14 ((
% 96.58/13.14 (subsetE2) =>
% 96.58/13.14 ((
% 96.58/13.14 (notsubsetI) =>
% 96.58/13.14 ((
% 96.58/13.14 (notequalI1) =>
% 96.58/13.14 ((
% 96.58/13.14 (notequalI2) =>
% 96.58/13.14 ((
% 96.58/13.14 (subsetRefl) =>
% 96.58/13.14 ((
% 96.58/13.14 (subsetTrans) =>
% 96.58/13.14 ((
% 96.58/13.14 (setadjoinSub) =>
% 96.58/13.14 ((
% 96.58/13.14 (setadjoinSub2) =>
% 96.58/13.14 ((
% 96.58/13.14 (subset2powerset) =>
% 96.58/13.14 ((
% 96.58/13.14 (setextsub) =>
% 96.58/13.14 ((
% 96.58/13.14 (subsetemptysetimpeq) =>
% 96.58/13.14 ((
% 96.58/13.14 (powersetI1) =>
% 96.58/13.14 ((
% 96.58/13.14 (powersetE1) =>
% 96.58/13.14 ((
% 96.58/13.14 (inPowerset) =>
% 96.58/13.14 ((
% 96.58/13.14 (powersetsubset) =>
% 96.58/13.14 ((
% 96.58/13.14 (sepInPowerset) =>
% 96.58/13.14 ((
% 96.58/13.14 (sepSubset) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionIL) =>
% 96.58/13.14 ((
% 96.58/13.14 (upairset2IR) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionIR) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionEcases) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionE) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionLsub) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionRsub) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectI) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectSubset5) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectEL) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectLsub) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectSubset2) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectSubset3) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectER) =>
% 96.58/13.14 ((
% 96.58/13.14 (disjointsetsI1) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectRsub) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectSubset4) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectSubset1) =>
% 96.58/13.14 ((
% 96.58/13.14 (bs114d) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusI) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusEL) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusER) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusSubset2) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusERneg) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusELneg) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusILneg) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusIRneg) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusLsub) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusSubset1) =>
% 96.58/13.14 ((
% 96.58/13.14 (symdiffE) =>
% 96.58/13.14 ((
% 96.58/13.14 (symdiffI1) =>
% 96.58/13.14 ((
% 96.58/13.14 (symdiffI2) =>
% 96.58/13.14 ((
% 96.58/13.14 (symdiffIneg1) =>
% 96.58/13.14 ((
% 96.58/13.14 (symdiffIneg2) =>
% 96.58/13.14 ((
% 96.58/13.14 (secondinupair) =>
% 96.58/13.14 ((
% 96.58/13.14 (setukpairIL) =>
% 96.58/13.14 ((
% 96.58/13.14 (setukpairIR) =>
% 96.58/13.14 ((
% 96.58/13.14 (kpairiskpair) =>
% 96.58/13.14 ((
% 96.58/13.14 (kpairp) =>
% 96.58/13.14 ((
% 96.58/13.14 (singletonsubset) =>
% 96.58/13.14 ((
% 96.58/13.14 (singletoninpowerset) =>
% 96.58/13.14 ((
% 96.58/13.14 (singletoninpowunion) =>
% 96.58/13.14 ((
% 96.58/13.14 (upairset2E) =>
% 96.58/13.14 ((
% 96.58/13.14 (upairsubunion) =>
% 96.58/13.14 ((
% 96.58/13.14 (upairinpowunion) =>
% 96.58/13.14 ((
% 96.58/13.14 (ubforcartprodlem1) =>
% 96.58/13.14 ((
% 96.58/13.14 (ubforcartprodlem2) =>
% 96.58/13.14 ((
% 96.58/13.14 (ubforcartprodlem3) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodpairin) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodmempair1) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodmempair) =>
% 96.58/13.14 ((
% 96.58/13.14 (setunionE2) =>
% 96.58/13.14 ((
% 96.58/13.14 (setunionsingleton1) =>
% 96.58/13.14 ((
% 96.58/13.14 (setunionsingleton2) =>
% 96.58/13.14 ((
% 96.58/13.14 (setunionsingleton) =>
% 96.58/13.14 ((
% 96.58/13.14 (singletonprop) =>
% 96.58/13.14 ((
% 96.58/13.14 (ex1E1) =>
% 96.58/13.14 ((
% 96.58/13.14 (ex1I) =>
% 96.58/13.14 ((
% 96.58/13.14 (ex1I2) =>
% 96.58/13.14 ((
% 96.58/13.14 (singletonsuniq) =>
% 96.58/13.14 ((
% 96.58/13.14 (setukpairinjL1) =>
% 96.58/13.14 ((
% 96.58/13.14 (kfstsingleton) =>
% 96.58/13.14 ((
% 96.58/13.14 (theprop) =>
% 96.58/13.14 ((
% 96.58/13.14 (kfstpairEq) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodfstin) =>
% 96.58/13.14 ((
% 96.58/13.14 (setukpairinjL2) =>
% 96.58/13.14 ((
% 96.58/13.14 (setukpairinjL) =>
% 96.58/13.14 ((
% 96.58/13.14 (setukpairinjR11) =>
% 96.58/13.14 ((
% 96.58/13.14 (setukpairinjR12) =>
% 96.58/13.14 ((
% 96.58/13.14 (setukpairinjR1) =>
% 96.58/13.14 ((
% 96.58/13.14 (upairequniteq) =>
% 96.58/13.14 ((
% 96.58/13.14 (setukpairinjR2) =>
% 96.58/13.14 ((
% 96.58/13.14 (setukpairinjR) =>
% 96.58/13.14 ((
% 96.58/13.14 (ksndsingleton) =>
% 96.58/13.14 ((
% 96.58/13.14 (ksndpairEq) =>
% 96.58/13.14 ((
% 96.58/13.14 (kpairsurjEq) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodsndin) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodpairmemEL) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodpairmemER) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodmempaircEq) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodfstpairEq) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodsndpairEq) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodpairsurjEq) =>
% 96.58/13.14 ((
% 96.58/13.14 (dpsetconstrI) =>
% 96.58/13.14 ((
% 96.58/13.14 (dpsetconstrSub) =>
% 96.58/13.14 ((
% 96.58/13.14 (setOfPairsIsBReln) =>
% 96.58/13.14 ((
% 96.58/13.14 (dpsetconstrERa) =>
% 96.58/13.14 ((
% 96.58/13.14 (dpsetconstrEL1) =>
% 96.58/13.14 ((
% 96.58/13.14 (dpsetconstrEL2) =>
% 96.58/13.14 ((
% 96.58/13.14 (dpsetconstrER) =>
% 96.58/13.14 ((
% 96.58/13.14 (funcImageSingleton) =>
% 96.58/13.14 ((
% 96.58/13.14 (apProp) =>
% 96.58/13.14 ((
% 96.58/13.14 (app) =>
% 96.58/13.14 ((
% 96.58/13.14 (infuncsetfunc) =>
% 96.58/13.14 ((
% 96.58/13.14 (ap2p) =>
% 96.58/13.14 ((
% 96.58/13.14 (funcinfuncset) =>
% 96.58/13.14 ((
% 96.58/13.14 (lamProp) =>
% 96.58/13.14 ((
% 96.58/13.14 (lamp) =>
% 96.58/13.14 ((
% 96.58/13.14 (lam2p) =>
% 96.58/13.14 ((
% 96.58/13.14 (brelnall1) =>
% 96.58/13.14 ((
% 96.58/13.14 (brelnall2) =>
% 96.58/13.14 ((
% 96.58/13.14 (ex1E2) =>
% 96.58/13.14 ((
% 96.58/13.14 (funcGraphProp1) =>
% 96.58/13.14 ((
% 96.58/13.14 (funcGraphProp3) =>
% 96.58/13.14 ((
% 96.58/13.14 (funcGraphProp2) =>
% 96.58/13.14 ((
% 96.58/13.14 (funcextLem) =>
% 96.58/13.14 ((
% 96.58/13.14 (funcGraphProp4) =>
% 96.58/13.14 ((
% 96.58/13.14 (subbreln) =>
% 96.58/13.14 ((
% 96.58/13.14 (eqbreln) =>
% 96.58/13.14 ((
% 96.58/13.14 (funcext) =>
% 96.58/13.14 ((
% 96.58/13.14 (funcext2) =>
% 96.58/13.14 ((
% 96.58/13.14 (ap2apEq1) =>
% 96.58/13.14 ((
% 96.58/13.14 (ap2apEq2) =>
% 96.58/13.14 ((
% 96.58/13.14 (beta1) =>
% 96.58/13.14 ((
% 96.58/13.14 (eta1) =>
% 96.58/13.14 ((
% 96.58/13.14 (lam2lamEq) =>
% 96.58/13.14 ((
% 96.58/13.14 (beta2) =>
% 96.58/13.14 ((
% 96.58/13.14 (eta2) =>
% 96.58/13.14 ((
% 96.58/13.14 (iffalseProp1) =>
% 96.58/13.14 ((
% 96.58/13.14 (iffalseProp2) =>
% 96.58/13.14 ((
% 96.58/13.14 (iftrueProp1) =>
% 96.58/13.14 ((
% 96.58/13.14 (iftrueProp2) =>
% 96.58/13.14 ((
% 96.58/13.14 (ifSingleton) =>
% 96.58/13.14 ((
% 96.58/13.14 (ifp) =>
% 96.58/13.14 ((
% 96.58/13.14 (theeq) =>
% 96.58/13.14 ((
% 96.58/13.14 (iftrue) =>
% 96.58/13.14 ((
% 96.58/13.14 (iffalse) =>
% 96.58/13.14 ((
% 96.58/13.14 (iftrueorfalse) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectT_lem) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionT_lem) =>
% 96.58/13.14 ((
% 96.58/13.14 (powersetT_lem) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusT_lem) =>
% 96.58/13.14 ((
% 96.58/13.14 (complementT_lem) =>
% 96.58/13.14 ((
% 96.58/13.14 (setextT) =>
% 96.58/13.14 ((
% 96.58/13.14 (subsetTI) =>
% 96.58/13.14 ((
% 96.58/13.14 (powersetTI1) =>
% 96.58/13.14 ((
% 96.58/13.14 (powersetTE1) =>
% 96.58/13.14 ((
% 96.58/13.14 (complementTI1) =>
% 96.58/13.14 ((
% 96.58/13.14 (complementTE1) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectTELcontra) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectTERcontra) =>
% 96.58/13.14 ((
% 96.58/13.14 (contrasubsetT) =>
% 96.58/13.14 ((
% 96.58/13.14 (contrasubsetT1) =>
% 96.58/13.14 ((
% 96.58/13.14 (contrasubsetT2) =>
% 96.58/13.14 ((
% 96.58/13.14 (contrasubsetT3) =>
% 96.58/13.14 ((
% 96.58/13.14 (doubleComplementI1) =>
% 96.58/13.14 ((
% 96.58/13.14 (doubleComplementE1) =>
% 96.58/13.14 ((
% 96.58/13.14 (doubleComplementSub1) =>
% 96.58/13.14 ((
% 96.58/13.14 (doubleComplementSub2) =>
% 96.58/13.14 ((
% 96.58/13.14 (doubleComplementEq) =>
% 96.58/13.14 ((
% 96.58/13.14 (complementTnotintersectT) =>
% 96.58/13.14 ((
% 96.58/13.14 (complementImpComplementIntersect) =>
% 96.58/13.14 ((
% 96.58/13.14 (complementSubsetComplementIntersect) =>
% 96.58/13.14 ((
% 96.58/13.14 (complementInPowersetComplementIntersect) =>
% 96.58/13.14 ((
% 96.58/13.14 (contraSubsetComplement) =>
% 96.58/13.14 ((
% 96.58/13.14 (complementTcontraSubset) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionTILcontra) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionTIRcontra) =>
% 96.58/13.14 ((
% 96.58/13.14 (inIntersectImpInUnion) =>
% 96.58/13.14 ((
% 96.58/13.14 (inIntersectImpInUnion2) =>
% 96.58/13.14 ((
% 96.58/13.14 (inIntersectImpInIntersectUnions) =>
% 96.58/13.14 ((
% 96.58/13.14 (intersectInPowersetIntersectUnions) =>
% 96.58/13.14 ((
% 96.58/13.14 (inComplementUnionImpNotIn1) =>
% 96.58/13.14 ((
% 96.58/13.14 (inComplementUnionImpInComplement1) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionTE) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionTEcontra) =>
% 96.58/13.14 ((
% 96.58/13.14 (demorgan2a1) =>
% 96.58/13.14 ((
% 96.58/13.14 (complementUnionInPowersetComplement) =>
% 96.58/13.14 ((
% 96.58/13.14 (demorgan2a2) =>
% 96.58/13.14 ((
% 96.58/13.14 (demorgan1a) =>
% 96.58/13.14 ((
% 96.58/13.14 (demorgan1b) =>
% 96.58/13.14 ((
% 96.58/13.14 (demorgan1) =>
% 96.58/13.14 ((
% 96.58/13.14 (demorgan2a) =>
% 96.58/13.14 ((
% 96.58/13.14 (demorgan2b2) =>
% 96.58/13.14 ((
% 96.58/13.14 (demorgan2b) =>
% 96.58/13.14 ((
% 96.58/13.14 (demorgan2) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz13rule0) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz13rule1) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz13rule2) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz13rule3) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz13rule4) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz1_1) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz1_2) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz1_3) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz1_4) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz1_5) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1all2) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1SetBreln1) =>
% 96.58/13.14 ((
% 96.58/13.14 (choice2fnsingleton) =>
% 96.58/13.14 ((
% 96.58/13.14 (setOfPairsIsBReln1) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1all1) =>
% 96.58/13.14 ((
% 96.58/13.14 (subbreln1) =>
% 96.58/13.14 ((
% 96.58/13.14 (eqbreln1) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1invprop) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1invI) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1invE) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1compprop) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1compI) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1compE) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1compEex) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1unionprop) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1unionIL) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1unionIR) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1unionI) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1unionE) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1unionEcases) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1unionCommutes) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz2Ex) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz2W) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz2A) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz2B) =>
% 96.58/13.14 ((
% 96.58/13.14 (image1Ex) =>
% 96.58/13.14 ((
% 96.58/13.14 (image1Ex1) =>
% 96.58/13.14 ((
% 96.58/13.14 (image1Equiv) =>
% 96.58/13.14 ((
% 96.58/13.14 (image1E) =>
% 96.58/13.14 ((
% 96.58/13.14 (image1I) =>
% 96.58/13.14 ((
% 96.58/13.14 (injFuncInInjFuncSet) =>
% 96.58/13.14 ((
% 96.58/13.14 (injFuncSetFuncIn) =>
% 96.58/13.14 ((
% 96.58/13.14 (injFuncSetFuncInj) =>
% 96.58/13.14 ((
% 96.58/13.14 (surjFuncSetFuncIn) =>
% 96.58/13.14 ((
% 96.58/13.14 (surjFuncSetFuncSurj) =>
% 96.58/13.14 ((
% 96.58/13.14 (leftInvIsSurj) =>
% 96.58/13.14 ((
% 96.58/13.14 (surjCantorThm) =>
% 96.58/13.14 ((
% 96.58/13.14 (foundation2) =>
% 96.58/13.14 ((
% 96.58/13.14 (notinself) =>
% 96.58/13.14 ((
% 96.58/13.14 (notinself2) =>
% 96.58/13.14 ((
% 96.58/13.14 (omegaSp) =>
% 96.58/13.14 ((
% 96.58/13.14 (omegaSclos) =>
% 96.58/13.14 ((
% 96.58/13.14 (peano0notS) =>
% 96.58/13.14 ((
% 96.58/13.14 (!!) @ (
% 96.58/13.14 (('#S') @ (
% 96.58/13.14 (
% 96.58/13.14 ('#B') @ (
% 96.58/13.14 =>) @
% 96.58/13.14 (
% 96.58/13.14 (
% 96.58/13.14 ('#C') @ in @
% 96.58/13.14 omega)))) @
% 96.58/13.14 (
% 96.58/13.14 (
% 96.58/13.14 ('#B') @ (
% 96.58/13.14 !!) @
% 96.58/13.14 (
% 96.58/13.14 (
% 96.58/13.14 ('#B') @ (
% 96.58/13.14 (
% 96.58/13.14 ('#S') @ (
% 96.58/13.14 (
% 96.58/13.14 ('#B') @ (
% 96.58/13.14 =>) @
% 96.58/13.14 (
% 96.58/13.14 (
% 96.58/13.14 ('#C') @ in @
% 96.58/13.14 omega)))))) @
% 96.58/13.14 (
% 96.58/13.14 (
% 96.58/13.14 ('#S') @ (
% 96.58/13.14 (
% 96.58/13.14 ('#B') @ (
% 96.58/13.14 '#S') @
% 96.58/13.14 (
% 96.58/13.14 (
% 96.58/13.14 ('#B') @ (
% 96.58/13.14 (
% 96.58/13.14 ('#B') @ (
% 96.58/13.14 =>))) @
% 96.58/13.14 (
% 96.58/13.14 (
% 96.58/13.14 ('#C') @ (
% 96.58/13.14 (
% 96.58/13.14 ('#B') @ (
% 96.58/13.14 '#B') @
% 96.58/13.14 (
% 96.58/13.14 (
% 96.58/13.14 ('#B') @ (
% 96.58/13.14 =) @
% 96.58/13.14 omegaS)))) @
% 96.58/13.14 omegaS)))))) @
% 96.58/13.14 (
% 96.58/13.14 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 96.58/13.14 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl25])).
% 96.58/13.14 thf(zip_derived_cl40, plain,
% 96.58/13.14 (~ (((omegaIndAx) =>
% 96.58/13.14 (((replAx) =>
% 96.58/13.14 (((foundationAx) =>
% 96.58/13.14 (((wellorderingAx) =>
% 96.58/13.14 (((descrp) =>
% 96.58/13.14 (((dsetconstrI) =>
% 96.58/13.14 (((dsetconstrEL) =>
% 96.58/13.14 (((dsetconstrER) =>
% 96.58/13.14 (((exuE1) =>
% 96.58/13.14 (((prop2setE) =>
% 96.58/13.14 (((emptysetE) =>
% 96.58/13.14 (((emptysetimpfalse) =>
% 96.58/13.14 (((notinemptyset) =>
% 96.58/13.14 (((exuE3e) =>
% 96.58/13.14 (((setext) =>
% 96.58/13.14 (((emptyI) =>
% 96.58/13.14 (((noeltsimpempty) =>
% 96.58/13.14 (((setbeta) =>
% 96.58/13.14 (((nonemptyE1) =>
% 96.58/13.14 (((nonemptyI) =>
% 96.58/13.14 (((nonemptyI1) =>
% 96.58/13.14 (((setadjoinIL) =>
% 96.58/13.14 (((in @ emptyset @
% 96.58/13.14 (setadjoin @ emptyset @
% 96.58/13.14 emptyset)) =>
% 96.58/13.14 (((setadjoinIR) =>
% 96.58/13.14 (((setadjoinE) =>
% 96.58/13.14 (((setadjoinOr) =>
% 96.58/13.14 (((setoftrueEq) =>
% 96.58/13.14 (((powersetI) =>
% 96.58/13.14 (((emptyinPowerset) =>
% 96.58/13.14 (((emptyInPowerset) =>
% 96.58/13.14 ((
% 96.58/13.14 (powersetE) =>
% 96.58/13.14 ((
% 96.58/13.14 (setunionI) =>
% 96.58/13.14 ((
% 96.58/13.14 (setunionE) =>
% 96.58/13.14 ((
% 96.58/13.14 (subPowSU) =>
% 96.58/13.14 ((
% 96.58/13.14 (exuE2) =>
% 96.58/13.14 ((
% 96.58/13.14 (nonemptyImpWitness) =>
% 96.58/13.14 ((
% 96.58/13.14 (uniqinunit) =>
% 96.58/13.14 ((
% 96.58/13.14 (notinsingleton) =>
% 96.58/13.14 ((
% 96.58/13.14 (eqinunit) =>
% 96.58/13.14 ((
% 96.58/13.14 (singletonsswitch) =>
% 96.58/13.14 ((
% 96.58/13.14 (upairsetE) =>
% 96.58/13.14 ((
% 96.58/13.14 (upairsetIL) =>
% 96.58/13.14 ((
% 96.58/13.14 (upairsetIR) =>
% 96.58/13.14 ((
% 96.58/13.14 (emptyE1) =>
% 96.58/13.14 ((
% 96.58/13.14 (vacuousDall) =>
% 96.58/13.14 ((
% 96.58/13.14 (quantDeMorgan1) =>
% 96.58/13.14 ((
% 96.58/13.14 (quantDeMorgan2) =>
% 96.58/13.14 ((
% 96.58/13.14 (quantDeMorgan3) =>
% 96.58/13.14 ((
% 96.58/13.14 (quantDeMorgan4) =>
% 96.58/13.14 ((
% 96.58/13.14 (prop2setI) =>
% 96.58/13.14 ((
% 96.58/13.14 (prop2set2propI) =>
% 96.58/13.14 ((
% 96.58/13.14 (notdexE) =>
% 96.58/13.14 ((
% 96.58/13.14 (notdallE) =>
% 96.58/13.14 ((
% 96.58/13.14 (exuI1) =>
% 96.58/13.14 ((
% 96.58/13.14 (exuI3) =>
% 96.58/13.14 ((
% 96.58/13.14 (exuI2) =>
% 96.58/13.14 ((
% 96.58/13.14 (inCongP) =>
% 96.58/13.14 ((
% 96.58/13.14 (in__Cong) =>
% 96.58/13.14 ((
% 96.58/13.14 (exuE3u) =>
% 96.58/13.14 ((
% 96.58/13.14 (exu__Cong) =>
% 96.58/13.14 ((
% 96.58/13.14 (setadjoin__Cong) =>
% 96.58/13.14 ((
% 96.58/13.14 (powerset__Cong) =>
% 96.58/13.14 ((
% 96.58/13.14 (setunion__Cong) =>
% 96.58/13.14 ((
% 96.58/13.14 (exuEu) =>
% 96.58/13.14 ((
% 96.58/13.14 (descr__Cong) =>
% 96.58/13.14 ((
% 96.58/13.14 (dsetconstr__Cong) =>
% 96.58/13.14 ((
% 96.58/13.14 (subsetI1) =>
% 96.58/13.14 ((
% 96.58/13.14 (eqimpsubset2) =>
% 96.58/13.14 ((
% 96.58/13.14 (eqimpsubset1) =>
% 96.58/13.14 ((
% 96.58/13.14 (subsetI2) =>
% 96.58/13.14 ((
% 96.58/13.14 (emptysetsubset) =>
% 96.58/13.14 ((
% 96.58/13.14 (subsetE) =>
% 96.58/13.14 ((
% 96.58/13.14 (subsetE2) =>
% 96.58/13.14 ((
% 96.58/13.14 (notsubsetI) =>
% 96.58/13.14 ((
% 96.58/13.14 (notequalI1) =>
% 96.58/13.14 ((
% 96.58/13.14 (notequalI2) =>
% 96.58/13.14 ((
% 96.58/13.14 (subsetRefl) =>
% 96.58/13.14 ((
% 96.58/13.14 (subsetTrans) =>
% 96.58/13.14 ((
% 96.58/13.14 (setadjoinSub) =>
% 96.58/13.14 ((
% 96.58/13.14 (setadjoinSub2) =>
% 96.58/13.14 ((
% 96.58/13.14 (subset2powerset) =>
% 96.58/13.14 ((
% 96.58/13.14 (setextsub) =>
% 96.58/13.14 ((
% 96.58/13.14 (subsetemptysetimpeq) =>
% 96.58/13.14 ((
% 96.58/13.14 (powersetI1) =>
% 96.58/13.14 ((
% 96.58/13.14 (powersetE1) =>
% 96.58/13.14 ((
% 96.58/13.14 (inPowerset) =>
% 96.58/13.14 ((
% 96.58/13.14 (powersetsubset) =>
% 96.58/13.14 ((
% 96.58/13.14 (sepInPowerset) =>
% 96.58/13.14 ((
% 96.58/13.14 (sepSubset) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionIL) =>
% 96.58/13.14 ((
% 96.58/13.14 (upairset2IR) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionIR) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionEcases) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionE) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionLsub) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionRsub) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectI) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectSubset5) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectEL) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectLsub) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectSubset2) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectSubset3) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectER) =>
% 96.58/13.14 ((
% 96.58/13.14 (disjointsetsI1) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectRsub) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectSubset4) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectSubset1) =>
% 96.58/13.14 ((
% 96.58/13.14 (bs114d) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusI) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusEL) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusER) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusSubset2) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusERneg) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusELneg) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusILneg) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusIRneg) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusLsub) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusSubset1) =>
% 96.58/13.14 ((
% 96.58/13.14 (symdiffE) =>
% 96.58/13.14 ((
% 96.58/13.14 (symdiffI1) =>
% 96.58/13.14 ((
% 96.58/13.14 (symdiffI2) =>
% 96.58/13.14 ((
% 96.58/13.14 (symdiffIneg1) =>
% 96.58/13.14 ((
% 96.58/13.14 (symdiffIneg2) =>
% 96.58/13.14 ((
% 96.58/13.14 (secondinupair) =>
% 96.58/13.14 ((
% 96.58/13.14 (setukpairIL) =>
% 96.58/13.14 ((
% 96.58/13.14 (setukpairIR) =>
% 96.58/13.14 ((
% 96.58/13.14 (kpairiskpair) =>
% 96.58/13.14 ((
% 96.58/13.14 (kpairp) =>
% 96.58/13.14 ((
% 96.58/13.14 (singletonsubset) =>
% 96.58/13.14 ((
% 96.58/13.14 (singletoninpowerset) =>
% 96.58/13.14 ((
% 96.58/13.14 (singletoninpowunion) =>
% 96.58/13.14 ((
% 96.58/13.14 (upairset2E) =>
% 96.58/13.14 ((
% 96.58/13.14 (upairsubunion) =>
% 96.58/13.14 ((
% 96.58/13.14 (upairinpowunion) =>
% 96.58/13.14 ((
% 96.58/13.14 (ubforcartprodlem1) =>
% 96.58/13.14 ((
% 96.58/13.14 (ubforcartprodlem2) =>
% 96.58/13.14 ((
% 96.58/13.14 (ubforcartprodlem3) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodpairin) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodmempair1) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodmempair) =>
% 96.58/13.14 ((
% 96.58/13.14 (setunionE2) =>
% 96.58/13.14 ((
% 96.58/13.14 (setunionsingleton1) =>
% 96.58/13.14 ((
% 96.58/13.14 (setunionsingleton2) =>
% 96.58/13.14 ((
% 96.58/13.14 (setunionsingleton) =>
% 96.58/13.14 ((
% 96.58/13.14 (singletonprop) =>
% 96.58/13.14 ((
% 96.58/13.14 (ex1E1) =>
% 96.58/13.14 ((
% 96.58/13.14 (ex1I) =>
% 96.58/13.14 ((
% 96.58/13.14 (ex1I2) =>
% 96.58/13.14 ((
% 96.58/13.14 (singletonsuniq) =>
% 96.58/13.14 ((
% 96.58/13.14 (setukpairinjL1) =>
% 96.58/13.14 ((
% 96.58/13.14 (kfstsingleton) =>
% 96.58/13.14 ((
% 96.58/13.14 (theprop) =>
% 96.58/13.14 ((
% 96.58/13.14 (kfstpairEq) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodfstin) =>
% 96.58/13.14 ((
% 96.58/13.14 (setukpairinjL2) =>
% 96.58/13.14 ((
% 96.58/13.14 (setukpairinjL) =>
% 96.58/13.14 ((
% 96.58/13.14 (setukpairinjR11) =>
% 96.58/13.14 ((
% 96.58/13.14 (setukpairinjR12) =>
% 96.58/13.14 ((
% 96.58/13.14 (setukpairinjR1) =>
% 96.58/13.14 ((
% 96.58/13.14 (upairequniteq) =>
% 96.58/13.14 ((
% 96.58/13.14 (setukpairinjR2) =>
% 96.58/13.14 ((
% 96.58/13.14 (setukpairinjR) =>
% 96.58/13.14 ((
% 96.58/13.14 (ksndsingleton) =>
% 96.58/13.14 ((
% 96.58/13.14 (ksndpairEq) =>
% 96.58/13.14 ((
% 96.58/13.14 (kpairsurjEq) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodsndin) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodpairmemEL) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodpairmemER) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodmempaircEq) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodfstpairEq) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodsndpairEq) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodpairsurjEq) =>
% 96.58/13.14 ((
% 96.58/13.14 (dpsetconstrI) =>
% 96.58/13.14 ((
% 96.58/13.14 (dpsetconstrSub) =>
% 96.58/13.14 ((
% 96.58/13.14 (setOfPairsIsBReln) =>
% 96.58/13.14 ((
% 96.58/13.14 (dpsetconstrERa) =>
% 96.58/13.14 ((
% 96.58/13.14 (dpsetconstrEL1) =>
% 96.58/13.14 ((
% 96.58/13.14 (dpsetconstrEL2) =>
% 96.58/13.14 ((
% 96.58/13.14 (dpsetconstrER) =>
% 96.58/13.14 ((
% 96.58/13.14 (funcImageSingleton) =>
% 96.58/13.14 ((
% 96.58/13.14 (apProp) =>
% 96.58/13.14 ((
% 96.58/13.14 (app) =>
% 96.58/13.14 ((
% 96.58/13.14 (infuncsetfunc) =>
% 96.58/13.14 ((
% 96.58/13.14 (ap2p) =>
% 96.58/13.14 ((
% 96.58/13.14 (funcinfuncset) =>
% 96.58/13.14 ((
% 96.58/13.14 (lamProp) =>
% 96.58/13.14 ((
% 96.58/13.14 (lamp) =>
% 96.58/13.14 ((
% 96.58/13.14 (lam2p) =>
% 96.58/13.14 ((
% 96.58/13.14 (brelnall1) =>
% 96.58/13.14 ((
% 96.58/13.14 (brelnall2) =>
% 96.58/13.14 ((
% 96.58/13.14 (ex1E2) =>
% 96.58/13.14 ((
% 96.58/13.14 (funcGraphProp1) =>
% 96.58/13.14 ((
% 96.58/13.14 (funcGraphProp3) =>
% 96.58/13.14 ((
% 96.58/13.14 (funcGraphProp2) =>
% 96.58/13.14 ((
% 96.58/13.14 (funcextLem) =>
% 96.58/13.14 ((
% 96.58/13.14 (funcGraphProp4) =>
% 96.58/13.14 ((
% 96.58/13.14 (subbreln) =>
% 96.58/13.14 ((
% 96.58/13.14 (eqbreln) =>
% 96.58/13.14 ((
% 96.58/13.14 (funcext) =>
% 96.58/13.14 ((
% 96.58/13.14 (funcext2) =>
% 96.58/13.14 ((
% 96.58/13.14 (ap2apEq1) =>
% 96.58/13.14 ((
% 96.58/13.14 (ap2apEq2) =>
% 96.58/13.14 ((
% 96.58/13.14 (beta1) =>
% 96.58/13.14 ((
% 96.58/13.14 (eta1) =>
% 96.58/13.14 ((
% 96.58/13.14 (lam2lamEq) =>
% 96.58/13.14 ((
% 96.58/13.14 (beta2) =>
% 96.58/13.14 ((
% 96.58/13.14 (eta2) =>
% 96.58/13.14 ((
% 96.58/13.14 (iffalseProp1) =>
% 96.58/13.14 ((
% 96.58/13.14 (iffalseProp2) =>
% 96.58/13.14 ((
% 96.58/13.14 (iftrueProp1) =>
% 96.58/13.14 ((
% 96.58/13.14 (iftrueProp2) =>
% 96.58/13.14 ((
% 96.58/13.14 (ifSingleton) =>
% 96.58/13.14 ((
% 96.58/13.14 (ifp) =>
% 96.58/13.14 ((
% 96.58/13.14 (theeq) =>
% 96.58/13.14 ((
% 96.58/13.14 (iftrue) =>
% 96.58/13.14 ((
% 96.58/13.14 (iffalse) =>
% 96.58/13.14 ((
% 96.58/13.14 (iftrueorfalse) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectT_lem) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionT_lem) =>
% 96.58/13.14 ((
% 96.58/13.14 (powersetT_lem) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusT_lem) =>
% 96.58/13.14 ((
% 96.58/13.14 (complementT_lem) =>
% 96.58/13.14 ((
% 96.58/13.14 (setextT) =>
% 96.58/13.14 ((
% 96.58/13.14 (subsetTI) =>
% 96.58/13.14 ((
% 96.58/13.14 (powersetTI1) =>
% 96.58/13.14 ((
% 96.58/13.14 (powersetTE1) =>
% 96.58/13.14 ((
% 96.58/13.14 (complementTI1) =>
% 96.58/13.14 ((
% 96.58/13.14 (complementTE1) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectTELcontra) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectTERcontra) =>
% 96.58/13.14 ((
% 96.58/13.14 (contrasubsetT) =>
% 96.58/13.14 ((
% 96.58/13.14 (contrasubsetT1) =>
% 96.58/13.14 ((
% 96.58/13.14 (contrasubsetT2) =>
% 96.58/13.14 ((
% 96.58/13.14 (contrasubsetT3) =>
% 96.58/13.14 ((
% 96.58/13.14 (doubleComplementI1) =>
% 96.58/13.14 ((
% 96.58/13.14 (doubleComplementE1) =>
% 96.58/13.14 ((
% 96.58/13.14 (doubleComplementSub1) =>
% 96.58/13.14 ((
% 96.58/13.14 (doubleComplementSub2) =>
% 96.58/13.14 ((
% 96.58/13.14 (doubleComplementEq) =>
% 96.58/13.14 ((
% 96.58/13.14 (complementTnotintersectT) =>
% 96.58/13.14 ((
% 96.58/13.14 (complementImpComplementIntersect) =>
% 96.58/13.14 ((
% 96.58/13.14 (complementSubsetComplementIntersect) =>
% 96.58/13.14 ((
% 96.58/13.14 (complementInPowersetComplementIntersect) =>
% 96.58/13.14 ((
% 96.58/13.14 (contraSubsetComplement) =>
% 96.58/13.14 ((
% 96.58/13.14 (complementTcontraSubset) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionTILcontra) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionTIRcontra) =>
% 96.58/13.14 ((
% 96.58/13.14 (inIntersectImpInUnion) =>
% 96.58/13.14 ((
% 96.58/13.14 (inIntersectImpInUnion2) =>
% 96.58/13.14 ((
% 96.58/13.14 (inIntersectImpInIntersectUnions) =>
% 96.58/13.14 ((
% 96.58/13.14 (intersectInPowersetIntersectUnions) =>
% 96.58/13.14 ((
% 96.58/13.14 (inComplementUnionImpNotIn1) =>
% 96.58/13.14 ((
% 96.58/13.14 (inComplementUnionImpInComplement1) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionTE) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionTEcontra) =>
% 96.58/13.14 ((
% 96.58/13.14 (demorgan2a1) =>
% 96.58/13.14 ((
% 96.58/13.14 (complementUnionInPowersetComplement) =>
% 96.58/13.14 ((
% 96.58/13.14 (demorgan2a2) =>
% 96.58/13.14 ((
% 96.58/13.14 (demorgan1a) =>
% 96.58/13.14 ((
% 96.58/13.14 (demorgan1b) =>
% 96.58/13.14 ((
% 96.58/13.14 (demorgan1) =>
% 96.58/13.14 ((
% 96.58/13.14 (demorgan2a) =>
% 96.58/13.14 ((
% 96.58/13.14 (demorgan2b2) =>
% 96.58/13.14 ((
% 96.58/13.14 (demorgan2b) =>
% 96.58/13.14 ((
% 96.58/13.14 (demorgan2) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz13rule0) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz13rule1) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz13rule2) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz13rule3) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz13rule4) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz1_1) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz1_2) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz1_3) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz1_4) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz1_5) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1all2) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1SetBreln1) =>
% 96.58/13.14 ((
% 96.58/13.14 (choice2fnsingleton) =>
% 96.58/13.14 ((
% 96.58/13.14 (setOfPairsIsBReln1) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1all1) =>
% 96.58/13.14 ((
% 96.58/13.14 (subbreln1) =>
% 96.58/13.14 ((
% 96.58/13.14 (eqbreln1) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1invprop) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1invI) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1invE) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1compprop) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1compI) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1compE) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1compEex) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1unionprop) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1unionIL) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1unionIR) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1unionI) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1unionE) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1unionEcases) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1unionCommutes) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz2Ex) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz2W) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz2A) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz2B) =>
% 96.58/13.14 ((
% 96.58/13.14 (image1Ex) =>
% 96.58/13.14 ((
% 96.58/13.14 (image1Ex1) =>
% 96.58/13.14 ((
% 96.58/13.14 (image1Equiv) =>
% 96.58/13.14 ((
% 96.58/13.14 (image1E) =>
% 96.58/13.14 ((
% 96.58/13.14 (image1I) =>
% 96.58/13.14 ((
% 96.58/13.14 (injFuncInInjFuncSet) =>
% 96.58/13.14 ((
% 96.58/13.14 (injFuncSetFuncIn) =>
% 96.58/13.14 ((
% 96.58/13.14 (injFuncSetFuncInj) =>
% 96.58/13.14 ((
% 96.58/13.14 (surjFuncSetFuncIn) =>
% 96.58/13.14 ((
% 96.58/13.14 (surjFuncSetFuncSurj) =>
% 96.58/13.14 ((
% 96.58/13.14 (leftInvIsSurj) =>
% 96.58/13.14 ((
% 96.58/13.14 (surjCantorThm) =>
% 96.58/13.14 ((
% 96.58/13.14 (foundation2) =>
% 96.58/13.14 ((
% 96.58/13.14 (notinself) =>
% 96.58/13.14 ((
% 96.58/13.14 (notinself2) =>
% 96.58/13.14 ((
% 96.58/13.14 (omegaSp) =>
% 96.58/13.14 ((
% 96.58/13.14 (omegaSclos) =>
% 96.58/13.14 ((
% 96.58/13.14 (peano0notS) =>
% 96.58/13.14 ((
% 96.58/13.14 (!!) @ (
% 96.58/13.14 (('#S') @ (
% 96.58/13.14 (
% 96.58/13.14 ('#B') @ (
% 96.58/13.14 =>) @
% 96.58/13.14 (
% 96.58/13.14 (
% 96.58/13.14 ('#C') @ in @
% 96.58/13.14 omega)))) @
% 96.58/13.14 (
% 96.58/13.14 (
% 96.58/13.14 ('#B') @ (
% 96.58/13.14 !!) @
% 96.58/13.14 (
% 96.58/13.14 (
% 96.58/13.14 ('#B') @ (
% 96.58/13.14 (
% 96.58/13.14 ('#S') @ (
% 96.58/13.14 (
% 96.58/13.14 ('#B') @ (
% 96.58/13.14 =>) @
% 96.58/13.14 (
% 96.58/13.14 (
% 96.58/13.14 ('#C') @ in @
% 96.58/13.14 omega)))))) @
% 96.58/13.14 (
% 96.58/13.14 (
% 96.58/13.14 ('#S') @ (
% 96.58/13.14 (
% 96.58/13.14 ('#B') @ (
% 96.58/13.14 '#S') @
% 96.58/13.14 (
% 96.58/13.14 (
% 96.58/13.14 ('#B') @ (
% 96.58/13.14 (
% 96.58/13.14 ('#B') @ (
% 96.58/13.14 =>))) @
% 96.58/13.14 (
% 96.58/13.14 (
% 96.58/13.14 ('#C') @ (
% 96.58/13.14 (
% 96.58/13.14 ('#B') @ (
% 96.58/13.14 '#B') @
% 96.58/13.14 (
% 96.58/13.14 (
% 96.58/13.14 ('#B') @ (
% 96.58/13.14 =) @
% 96.58/13.14 omegaS)))) @
% 96.58/13.14 omegaS)))))) @
% 96.58/13.14 (
% 96.58/13.14 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 96.58/13.14 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl33])).
% 96.58/13.14 thf(zip_derived_cl46, plain,
% 96.58/13.14 (~ (((replAx) =>
% 96.58/13.14 (((foundationAx) =>
% 96.58/13.14 (((wellorderingAx) =>
% 96.58/13.14 (((descrp) =>
% 96.58/13.14 (((dsetconstrI) =>
% 96.58/13.14 (((dsetconstrEL) =>
% 96.58/13.14 (((dsetconstrER) =>
% 96.58/13.14 (((exuE1) =>
% 96.58/13.14 (((prop2setE) =>
% 96.58/13.14 (((emptysetE) =>
% 96.58/13.14 (((emptysetimpfalse) =>
% 96.58/13.14 (((notinemptyset) =>
% 96.58/13.14 (((exuE3e) =>
% 96.58/13.14 (((setext) =>
% 96.58/13.14 (((emptyI) =>
% 96.58/13.14 (((noeltsimpempty) =>
% 96.58/13.14 (((setbeta) =>
% 96.58/13.14 (((nonemptyE1) =>
% 96.58/13.14 (((nonemptyI) =>
% 96.58/13.14 (((nonemptyI1) =>
% 96.58/13.14 (((setadjoinIL) =>
% 96.58/13.14 (((in @ emptyset @
% 96.58/13.14 (setadjoin @ emptyset @
% 96.58/13.14 emptyset)) =>
% 96.58/13.14 (((setadjoinIR) =>
% 96.58/13.14 (((setadjoinE) =>
% 96.58/13.14 (((setadjoinOr) =>
% 96.58/13.14 (((setoftrueEq) =>
% 96.58/13.14 (((powersetI) =>
% 96.58/13.14 (((emptyinPowerset) =>
% 96.58/13.14 (((emptyInPowerset) =>
% 96.58/13.14 (((powersetE) =>
% 96.58/13.14 ((
% 96.58/13.14 (setunionI) =>
% 96.58/13.14 ((
% 96.58/13.14 (setunionE) =>
% 96.58/13.14 ((
% 96.58/13.14 (subPowSU) =>
% 96.58/13.14 ((
% 96.58/13.14 (exuE2) =>
% 96.58/13.14 ((
% 96.58/13.14 (nonemptyImpWitness) =>
% 96.58/13.14 ((
% 96.58/13.14 (uniqinunit) =>
% 96.58/13.14 ((
% 96.58/13.14 (notinsingleton) =>
% 96.58/13.14 ((
% 96.58/13.14 (eqinunit) =>
% 96.58/13.14 ((
% 96.58/13.14 (singletonsswitch) =>
% 96.58/13.14 ((
% 96.58/13.14 (upairsetE) =>
% 96.58/13.14 ((
% 96.58/13.14 (upairsetIL) =>
% 96.58/13.14 ((
% 96.58/13.14 (upairsetIR) =>
% 96.58/13.14 ((
% 96.58/13.14 (emptyE1) =>
% 96.58/13.14 ((
% 96.58/13.14 (vacuousDall) =>
% 96.58/13.14 ((
% 96.58/13.14 (quantDeMorgan1) =>
% 96.58/13.14 ((
% 96.58/13.14 (quantDeMorgan2) =>
% 96.58/13.14 ((
% 96.58/13.14 (quantDeMorgan3) =>
% 96.58/13.14 ((
% 96.58/13.14 (quantDeMorgan4) =>
% 96.58/13.14 ((
% 96.58/13.14 (prop2setI) =>
% 96.58/13.14 ((
% 96.58/13.14 (prop2set2propI) =>
% 96.58/13.14 ((
% 96.58/13.14 (notdexE) =>
% 96.58/13.14 ((
% 96.58/13.14 (notdallE) =>
% 96.58/13.14 ((
% 96.58/13.14 (exuI1) =>
% 96.58/13.14 ((
% 96.58/13.14 (exuI3) =>
% 96.58/13.14 ((
% 96.58/13.14 (exuI2) =>
% 96.58/13.14 ((
% 96.58/13.14 (inCongP) =>
% 96.58/13.14 ((
% 96.58/13.14 (in__Cong) =>
% 96.58/13.14 ((
% 96.58/13.14 (exuE3u) =>
% 96.58/13.14 ((
% 96.58/13.14 (exu__Cong) =>
% 96.58/13.14 ((
% 96.58/13.14 (setadjoin__Cong) =>
% 96.58/13.14 ((
% 96.58/13.14 (powerset__Cong) =>
% 96.58/13.14 ((
% 96.58/13.14 (setunion__Cong) =>
% 96.58/13.14 ((
% 96.58/13.14 (exuEu) =>
% 96.58/13.14 ((
% 96.58/13.14 (descr__Cong) =>
% 96.58/13.14 ((
% 96.58/13.14 (dsetconstr__Cong) =>
% 96.58/13.14 ((
% 96.58/13.14 (subsetI1) =>
% 96.58/13.14 ((
% 96.58/13.14 (eqimpsubset2) =>
% 96.58/13.14 ((
% 96.58/13.14 (eqimpsubset1) =>
% 96.58/13.14 ((
% 96.58/13.14 (subsetI2) =>
% 96.58/13.14 ((
% 96.58/13.14 (emptysetsubset) =>
% 96.58/13.14 ((
% 96.58/13.14 (subsetE) =>
% 96.58/13.14 ((
% 96.58/13.14 (subsetE2) =>
% 96.58/13.14 ((
% 96.58/13.14 (notsubsetI) =>
% 96.58/13.14 ((
% 96.58/13.14 (notequalI1) =>
% 96.58/13.14 ((
% 96.58/13.14 (notequalI2) =>
% 96.58/13.14 ((
% 96.58/13.14 (subsetRefl) =>
% 96.58/13.14 ((
% 96.58/13.14 (subsetTrans) =>
% 96.58/13.14 ((
% 96.58/13.14 (setadjoinSub) =>
% 96.58/13.14 ((
% 96.58/13.14 (setadjoinSub2) =>
% 96.58/13.14 ((
% 96.58/13.14 (subset2powerset) =>
% 96.58/13.14 ((
% 96.58/13.14 (setextsub) =>
% 96.58/13.14 ((
% 96.58/13.14 (subsetemptysetimpeq) =>
% 96.58/13.14 ((
% 96.58/13.14 (powersetI1) =>
% 96.58/13.14 ((
% 96.58/13.14 (powersetE1) =>
% 96.58/13.14 ((
% 96.58/13.14 (inPowerset) =>
% 96.58/13.14 ((
% 96.58/13.14 (powersetsubset) =>
% 96.58/13.14 ((
% 96.58/13.14 (sepInPowerset) =>
% 96.58/13.14 ((
% 96.58/13.14 (sepSubset) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionIL) =>
% 96.58/13.14 ((
% 96.58/13.14 (upairset2IR) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionIR) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionEcases) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionE) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionLsub) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionRsub) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectI) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectSubset5) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectEL) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectLsub) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectSubset2) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectSubset3) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectER) =>
% 96.58/13.14 ((
% 96.58/13.14 (disjointsetsI1) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectRsub) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectSubset4) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectSubset1) =>
% 96.58/13.14 ((
% 96.58/13.14 (bs114d) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusI) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusEL) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusER) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusSubset2) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusERneg) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusELneg) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusILneg) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusIRneg) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusLsub) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusSubset1) =>
% 96.58/13.14 ((
% 96.58/13.14 (symdiffE) =>
% 96.58/13.14 ((
% 96.58/13.14 (symdiffI1) =>
% 96.58/13.14 ((
% 96.58/13.14 (symdiffI2) =>
% 96.58/13.14 ((
% 96.58/13.14 (symdiffIneg1) =>
% 96.58/13.14 ((
% 96.58/13.14 (symdiffIneg2) =>
% 96.58/13.14 ((
% 96.58/13.14 (secondinupair) =>
% 96.58/13.14 ((
% 96.58/13.14 (setukpairIL) =>
% 96.58/13.14 ((
% 96.58/13.14 (setukpairIR) =>
% 96.58/13.14 ((
% 96.58/13.14 (kpairiskpair) =>
% 96.58/13.14 ((
% 96.58/13.14 (kpairp) =>
% 96.58/13.14 ((
% 96.58/13.14 (singletonsubset) =>
% 96.58/13.14 ((
% 96.58/13.14 (singletoninpowerset) =>
% 96.58/13.14 ((
% 96.58/13.14 (singletoninpowunion) =>
% 96.58/13.14 ((
% 96.58/13.14 (upairset2E) =>
% 96.58/13.14 ((
% 96.58/13.14 (upairsubunion) =>
% 96.58/13.14 ((
% 96.58/13.14 (upairinpowunion) =>
% 96.58/13.14 ((
% 96.58/13.14 (ubforcartprodlem1) =>
% 96.58/13.14 ((
% 96.58/13.14 (ubforcartprodlem2) =>
% 96.58/13.14 ((
% 96.58/13.14 (ubforcartprodlem3) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodpairin) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodmempair1) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodmempair) =>
% 96.58/13.14 ((
% 96.58/13.14 (setunionE2) =>
% 96.58/13.14 ((
% 96.58/13.14 (setunionsingleton1) =>
% 96.58/13.14 ((
% 96.58/13.14 (setunionsingleton2) =>
% 96.58/13.14 ((
% 96.58/13.14 (setunionsingleton) =>
% 96.58/13.14 ((
% 96.58/13.14 (singletonprop) =>
% 96.58/13.14 ((
% 96.58/13.14 (ex1E1) =>
% 96.58/13.14 ((
% 96.58/13.14 (ex1I) =>
% 96.58/13.14 ((
% 96.58/13.14 (ex1I2) =>
% 96.58/13.14 ((
% 96.58/13.14 (singletonsuniq) =>
% 96.58/13.14 ((
% 96.58/13.14 (setukpairinjL1) =>
% 96.58/13.14 ((
% 96.58/13.14 (kfstsingleton) =>
% 96.58/13.14 ((
% 96.58/13.14 (theprop) =>
% 96.58/13.14 ((
% 96.58/13.14 (kfstpairEq) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodfstin) =>
% 96.58/13.14 ((
% 96.58/13.14 (setukpairinjL2) =>
% 96.58/13.14 ((
% 96.58/13.14 (setukpairinjL) =>
% 96.58/13.14 ((
% 96.58/13.14 (setukpairinjR11) =>
% 96.58/13.14 ((
% 96.58/13.14 (setukpairinjR12) =>
% 96.58/13.14 ((
% 96.58/13.14 (setukpairinjR1) =>
% 96.58/13.14 ((
% 96.58/13.14 (upairequniteq) =>
% 96.58/13.14 ((
% 96.58/13.14 (setukpairinjR2) =>
% 96.58/13.14 ((
% 96.58/13.14 (setukpairinjR) =>
% 96.58/13.14 ((
% 96.58/13.14 (ksndsingleton) =>
% 96.58/13.14 ((
% 96.58/13.14 (ksndpairEq) =>
% 96.58/13.14 ((
% 96.58/13.14 (kpairsurjEq) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodsndin) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodpairmemEL) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodpairmemER) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodmempaircEq) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodfstpairEq) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodsndpairEq) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodpairsurjEq) =>
% 96.58/13.14 ((
% 96.58/13.14 (dpsetconstrI) =>
% 96.58/13.14 ((
% 96.58/13.14 (dpsetconstrSub) =>
% 96.58/13.14 ((
% 96.58/13.14 (setOfPairsIsBReln) =>
% 96.58/13.14 ((
% 96.58/13.14 (dpsetconstrERa) =>
% 96.58/13.14 ((
% 96.58/13.14 (dpsetconstrEL1) =>
% 96.58/13.14 ((
% 96.58/13.14 (dpsetconstrEL2) =>
% 96.58/13.14 ((
% 96.58/13.14 (dpsetconstrER) =>
% 96.58/13.14 ((
% 96.58/13.14 (funcImageSingleton) =>
% 96.58/13.14 ((
% 96.58/13.14 (apProp) =>
% 96.58/13.14 ((
% 96.58/13.14 (app) =>
% 96.58/13.14 ((
% 96.58/13.14 (infuncsetfunc) =>
% 96.58/13.14 ((
% 96.58/13.14 (ap2p) =>
% 96.58/13.14 ((
% 96.58/13.14 (funcinfuncset) =>
% 96.58/13.14 ((
% 96.58/13.14 (lamProp) =>
% 96.58/13.14 ((
% 96.58/13.14 (lamp) =>
% 96.58/13.14 ((
% 96.58/13.14 (lam2p) =>
% 96.58/13.14 ((
% 96.58/13.14 (brelnall1) =>
% 96.58/13.14 ((
% 96.58/13.14 (brelnall2) =>
% 96.58/13.14 ((
% 96.58/13.14 (ex1E2) =>
% 96.58/13.14 ((
% 96.58/13.14 (funcGraphProp1) =>
% 96.58/13.14 ((
% 96.58/13.14 (funcGraphProp3) =>
% 96.58/13.14 ((
% 96.58/13.14 (funcGraphProp2) =>
% 96.58/13.14 ((
% 96.58/13.14 (funcextLem) =>
% 96.58/13.14 ((
% 96.58/13.14 (funcGraphProp4) =>
% 96.58/13.14 ((
% 96.58/13.14 (subbreln) =>
% 96.58/13.14 ((
% 96.58/13.14 (eqbreln) =>
% 96.58/13.14 ((
% 96.58/13.14 (funcext) =>
% 96.58/13.14 ((
% 96.58/13.14 (funcext2) =>
% 96.58/13.14 ((
% 96.58/13.14 (ap2apEq1) =>
% 96.58/13.14 ((
% 96.58/13.14 (ap2apEq2) =>
% 96.58/13.14 ((
% 96.58/13.14 (beta1) =>
% 96.58/13.14 ((
% 96.58/13.14 (eta1) =>
% 96.58/13.14 ((
% 96.58/13.14 (lam2lamEq) =>
% 96.58/13.14 ((
% 96.58/13.14 (beta2) =>
% 96.58/13.14 ((
% 96.58/13.14 (eta2) =>
% 96.58/13.14 ((
% 96.58/13.14 (iffalseProp1) =>
% 96.58/13.14 ((
% 96.58/13.14 (iffalseProp2) =>
% 96.58/13.14 ((
% 96.58/13.14 (iftrueProp1) =>
% 96.58/13.14 ((
% 96.58/13.14 (iftrueProp2) =>
% 96.58/13.14 ((
% 96.58/13.14 (ifSingleton) =>
% 96.58/13.14 ((
% 96.58/13.14 (ifp) =>
% 96.58/13.14 ((
% 96.58/13.14 (theeq) =>
% 96.58/13.14 ((
% 96.58/13.14 (iftrue) =>
% 96.58/13.14 ((
% 96.58/13.14 (iffalse) =>
% 96.58/13.14 ((
% 96.58/13.14 (iftrueorfalse) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectT_lem) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionT_lem) =>
% 96.58/13.14 ((
% 96.58/13.14 (powersetT_lem) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusT_lem) =>
% 96.58/13.14 ((
% 96.58/13.14 (complementT_lem) =>
% 96.58/13.14 ((
% 96.58/13.14 (setextT) =>
% 96.58/13.14 ((
% 96.58/13.14 (subsetTI) =>
% 96.58/13.14 ((
% 96.58/13.14 (powersetTI1) =>
% 96.58/13.14 ((
% 96.58/13.14 (powersetTE1) =>
% 96.58/13.14 ((
% 96.58/13.14 (complementTI1) =>
% 96.58/13.14 ((
% 96.58/13.14 (complementTE1) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectTELcontra) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectTERcontra) =>
% 96.58/13.14 ((
% 96.58/13.14 (contrasubsetT) =>
% 96.58/13.14 ((
% 96.58/13.14 (contrasubsetT1) =>
% 96.58/13.14 ((
% 96.58/13.14 (contrasubsetT2) =>
% 96.58/13.14 ((
% 96.58/13.14 (contrasubsetT3) =>
% 96.58/13.14 ((
% 96.58/13.14 (doubleComplementI1) =>
% 96.58/13.14 ((
% 96.58/13.14 (doubleComplementE1) =>
% 96.58/13.14 ((
% 96.58/13.14 (doubleComplementSub1) =>
% 96.58/13.14 ((
% 96.58/13.14 (doubleComplementSub2) =>
% 96.58/13.14 ((
% 96.58/13.14 (doubleComplementEq) =>
% 96.58/13.14 ((
% 96.58/13.14 (complementTnotintersectT) =>
% 96.58/13.14 ((
% 96.58/13.14 (complementImpComplementIntersect) =>
% 96.58/13.14 ((
% 96.58/13.14 (complementSubsetComplementIntersect) =>
% 96.58/13.14 ((
% 96.58/13.14 (complementInPowersetComplementIntersect) =>
% 96.58/13.14 ((
% 96.58/13.14 (contraSubsetComplement) =>
% 96.58/13.14 ((
% 96.58/13.14 (complementTcontraSubset) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionTILcontra) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionTIRcontra) =>
% 96.58/13.14 ((
% 96.58/13.14 (inIntersectImpInUnion) =>
% 96.58/13.14 ((
% 96.58/13.14 (inIntersectImpInUnion2) =>
% 96.58/13.14 ((
% 96.58/13.14 (inIntersectImpInIntersectUnions) =>
% 96.58/13.14 ((
% 96.58/13.14 (intersectInPowersetIntersectUnions) =>
% 96.58/13.14 ((
% 96.58/13.14 (inComplementUnionImpNotIn1) =>
% 96.58/13.14 ((
% 96.58/13.14 (inComplementUnionImpInComplement1) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionTE) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionTEcontra) =>
% 96.58/13.14 ((
% 96.58/13.14 (demorgan2a1) =>
% 96.58/13.14 ((
% 96.58/13.14 (complementUnionInPowersetComplement) =>
% 96.58/13.14 ((
% 96.58/13.14 (demorgan2a2) =>
% 96.58/13.14 ((
% 96.58/13.14 (demorgan1a) =>
% 96.58/13.14 ((
% 96.58/13.14 (demorgan1b) =>
% 96.58/13.14 ((
% 96.58/13.14 (demorgan1) =>
% 96.58/13.14 ((
% 96.58/13.14 (demorgan2a) =>
% 96.58/13.14 ((
% 96.58/13.14 (demorgan2b2) =>
% 96.58/13.14 ((
% 96.58/13.14 (demorgan2b) =>
% 96.58/13.14 ((
% 96.58/13.14 (demorgan2) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz13rule0) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz13rule1) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz13rule2) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz13rule3) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz13rule4) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz1_1) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz1_2) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz1_3) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz1_4) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz1_5) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1all2) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1SetBreln1) =>
% 96.58/13.14 ((
% 96.58/13.14 (choice2fnsingleton) =>
% 96.58/13.14 ((
% 96.58/13.14 (setOfPairsIsBReln1) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1all1) =>
% 96.58/13.14 ((
% 96.58/13.14 (subbreln1) =>
% 96.58/13.14 ((
% 96.58/13.14 (eqbreln1) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1invprop) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1invI) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1invE) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1compprop) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1compI) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1compE) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1compEex) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1unionprop) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1unionIL) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1unionIR) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1unionI) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1unionE) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1unionEcases) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1unionCommutes) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz2Ex) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz2W) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz2A) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz2B) =>
% 96.58/13.14 ((
% 96.58/13.14 (image1Ex) =>
% 96.58/13.14 ((
% 96.58/13.14 (image1Ex1) =>
% 96.58/13.14 ((
% 96.58/13.14 (image1Equiv) =>
% 96.58/13.14 ((
% 96.58/13.14 (image1E) =>
% 96.58/13.14 ((
% 96.58/13.14 (image1I) =>
% 96.58/13.14 ((
% 96.58/13.14 (injFuncInInjFuncSet) =>
% 96.58/13.14 ((
% 96.58/13.14 (injFuncSetFuncIn) =>
% 96.58/13.14 ((
% 96.58/13.14 (injFuncSetFuncInj) =>
% 96.58/13.14 ((
% 96.58/13.14 (surjFuncSetFuncIn) =>
% 96.58/13.14 ((
% 96.58/13.14 (surjFuncSetFuncSurj) =>
% 96.58/13.14 ((
% 96.58/13.14 (leftInvIsSurj) =>
% 96.58/13.14 ((
% 96.58/13.14 (surjCantorThm) =>
% 96.58/13.14 ((
% 96.58/13.14 (foundation2) =>
% 96.58/13.14 ((
% 96.58/13.14 (notinself) =>
% 96.58/13.14 ((
% 96.58/13.14 (notinself2) =>
% 96.58/13.14 ((
% 96.58/13.14 (omegaSp) =>
% 96.58/13.14 ((
% 96.58/13.14 (omegaSclos) =>
% 96.58/13.14 ((
% 96.58/13.14 (peano0notS) =>
% 96.58/13.14 ((
% 96.58/13.14 (!!) @ (
% 96.58/13.14 (('#S') @ (
% 96.58/13.14 (
% 96.58/13.14 ('#B') @ (
% 96.58/13.14 =>) @
% 96.58/13.14 (
% 96.58/13.14 (
% 96.58/13.14 ('#C') @ in @
% 96.58/13.14 omega)))) @
% 96.58/13.14 (
% 96.58/13.14 (
% 96.58/13.14 ('#B') @ (
% 96.58/13.14 !!) @
% 96.58/13.14 (
% 96.58/13.14 (
% 96.58/13.14 ('#B') @ (
% 96.58/13.14 (
% 96.58/13.14 ('#S') @ (
% 96.58/13.14 (
% 96.58/13.14 ('#B') @ (
% 96.58/13.14 =>) @
% 96.58/13.14 (
% 96.58/13.14 (
% 96.58/13.14 ('#C') @ in @
% 96.58/13.14 omega)))))) @
% 96.58/13.14 (
% 96.58/13.14 (
% 96.58/13.14 ('#S') @ (
% 96.58/13.14 (
% 96.58/13.14 ('#B') @ (
% 96.58/13.14 '#S') @
% 96.58/13.14 (
% 96.58/13.14 (
% 96.58/13.14 ('#B') @ (
% 96.58/13.14 (
% 96.58/13.14 ('#B') @ (
% 96.58/13.14 =>))) @
% 96.58/13.14 (
% 96.58/13.14 (
% 96.58/13.14 ('#C') @ (
% 96.58/13.14 (
% 96.58/13.14 ('#B') @ (
% 96.58/13.14 '#B') @
% 96.58/13.14 (
% 96.58/13.14 (
% 96.58/13.14 ('#B') @ (
% 96.58/13.14 =) @
% 96.58/13.14 omegaS)))) @
% 96.58/13.14 omegaS)))))) @
% 96.58/13.14 (
% 96.58/13.14 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 96.58/13.14 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl40])).
% 96.58/13.14 thf(zip_derived_cl52, plain,
% 96.58/13.14 (~ (((foundationAx) =>
% 96.58/13.14 (((wellorderingAx) =>
% 96.58/13.14 (((descrp) =>
% 96.58/13.14 (((dsetconstrI) =>
% 96.58/13.14 (((dsetconstrEL) =>
% 96.58/13.14 (((dsetconstrER) =>
% 96.58/13.14 (((exuE1) =>
% 96.58/13.14 (((prop2setE) =>
% 96.58/13.14 (((emptysetE) =>
% 96.58/13.14 (((emptysetimpfalse) =>
% 96.58/13.14 (((notinemptyset) =>
% 96.58/13.14 (((exuE3e) =>
% 96.58/13.14 (((setext) =>
% 96.58/13.14 (((emptyI) =>
% 96.58/13.14 (((noeltsimpempty) =>
% 96.58/13.14 (((setbeta) =>
% 96.58/13.14 (((nonemptyE1) =>
% 96.58/13.14 (((nonemptyI) =>
% 96.58/13.14 (((nonemptyI1) =>
% 96.58/13.14 (((setadjoinIL) =>
% 96.58/13.14 (((in @ emptyset @
% 96.58/13.14 (setadjoin @ emptyset @
% 96.58/13.14 emptyset)) =>
% 96.58/13.14 (((setadjoinIR) =>
% 96.58/13.14 (((setadjoinE) =>
% 96.58/13.14 (((setadjoinOr) =>
% 96.58/13.14 (((setoftrueEq) =>
% 96.58/13.14 (((powersetI) =>
% 96.58/13.14 (((emptyinPowerset) =>
% 96.58/13.14 (((emptyInPowerset) =>
% 96.58/13.14 (((powersetE) =>
% 96.58/13.14 (((setunionI) =>
% 96.58/13.14 ((
% 96.58/13.14 (setunionE) =>
% 96.58/13.14 ((
% 96.58/13.14 (subPowSU) =>
% 96.58/13.14 ((
% 96.58/13.14 (exuE2) =>
% 96.58/13.14 ((
% 96.58/13.14 (nonemptyImpWitness) =>
% 96.58/13.14 ((
% 96.58/13.14 (uniqinunit) =>
% 96.58/13.14 ((
% 96.58/13.14 (notinsingleton) =>
% 96.58/13.14 ((
% 96.58/13.14 (eqinunit) =>
% 96.58/13.14 ((
% 96.58/13.14 (singletonsswitch) =>
% 96.58/13.14 ((
% 96.58/13.14 (upairsetE) =>
% 96.58/13.14 ((
% 96.58/13.14 (upairsetIL) =>
% 96.58/13.14 ((
% 96.58/13.14 (upairsetIR) =>
% 96.58/13.14 ((
% 96.58/13.14 (emptyE1) =>
% 96.58/13.14 ((
% 96.58/13.14 (vacuousDall) =>
% 96.58/13.14 ((
% 96.58/13.14 (quantDeMorgan1) =>
% 96.58/13.14 ((
% 96.58/13.14 (quantDeMorgan2) =>
% 96.58/13.14 ((
% 96.58/13.14 (quantDeMorgan3) =>
% 96.58/13.14 ((
% 96.58/13.14 (quantDeMorgan4) =>
% 96.58/13.14 ((
% 96.58/13.14 (prop2setI) =>
% 96.58/13.14 ((
% 96.58/13.14 (prop2set2propI) =>
% 96.58/13.14 ((
% 96.58/13.14 (notdexE) =>
% 96.58/13.14 ((
% 96.58/13.14 (notdallE) =>
% 96.58/13.14 ((
% 96.58/13.14 (exuI1) =>
% 96.58/13.14 ((
% 96.58/13.14 (exuI3) =>
% 96.58/13.14 ((
% 96.58/13.14 (exuI2) =>
% 96.58/13.14 ((
% 96.58/13.14 (inCongP) =>
% 96.58/13.14 ((
% 96.58/13.14 (in__Cong) =>
% 96.58/13.14 ((
% 96.58/13.14 (exuE3u) =>
% 96.58/13.14 ((
% 96.58/13.14 (exu__Cong) =>
% 96.58/13.14 ((
% 96.58/13.14 (setadjoin__Cong) =>
% 96.58/13.14 ((
% 96.58/13.14 (powerset__Cong) =>
% 96.58/13.14 ((
% 96.58/13.14 (setunion__Cong) =>
% 96.58/13.14 ((
% 96.58/13.14 (exuEu) =>
% 96.58/13.14 ((
% 96.58/13.14 (descr__Cong) =>
% 96.58/13.14 ((
% 96.58/13.14 (dsetconstr__Cong) =>
% 96.58/13.14 ((
% 96.58/13.14 (subsetI1) =>
% 96.58/13.14 ((
% 96.58/13.14 (eqimpsubset2) =>
% 96.58/13.14 ((
% 96.58/13.14 (eqimpsubset1) =>
% 96.58/13.14 ((
% 96.58/13.14 (subsetI2) =>
% 96.58/13.14 ((
% 96.58/13.14 (emptysetsubset) =>
% 96.58/13.14 ((
% 96.58/13.14 (subsetE) =>
% 96.58/13.14 ((
% 96.58/13.14 (subsetE2) =>
% 96.58/13.14 ((
% 96.58/13.14 (notsubsetI) =>
% 96.58/13.14 ((
% 96.58/13.14 (notequalI1) =>
% 96.58/13.14 ((
% 96.58/13.14 (notequalI2) =>
% 96.58/13.14 ((
% 96.58/13.14 (subsetRefl) =>
% 96.58/13.14 ((
% 96.58/13.14 (subsetTrans) =>
% 96.58/13.14 ((
% 96.58/13.14 (setadjoinSub) =>
% 96.58/13.14 ((
% 96.58/13.14 (setadjoinSub2) =>
% 96.58/13.14 ((
% 96.58/13.14 (subset2powerset) =>
% 96.58/13.14 ((
% 96.58/13.14 (setextsub) =>
% 96.58/13.14 ((
% 96.58/13.14 (subsetemptysetimpeq) =>
% 96.58/13.14 ((
% 96.58/13.14 (powersetI1) =>
% 96.58/13.14 ((
% 96.58/13.14 (powersetE1) =>
% 96.58/13.14 ((
% 96.58/13.14 (inPowerset) =>
% 96.58/13.14 ((
% 96.58/13.14 (powersetsubset) =>
% 96.58/13.14 ((
% 96.58/13.14 (sepInPowerset) =>
% 96.58/13.14 ((
% 96.58/13.14 (sepSubset) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionIL) =>
% 96.58/13.14 ((
% 96.58/13.14 (upairset2IR) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionIR) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionEcases) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionE) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionLsub) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionRsub) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectI) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectSubset5) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectEL) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectLsub) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectSubset2) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectSubset3) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectER) =>
% 96.58/13.14 ((
% 96.58/13.14 (disjointsetsI1) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectRsub) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectSubset4) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectSubset1) =>
% 96.58/13.14 ((
% 96.58/13.14 (bs114d) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusI) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusEL) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusER) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusSubset2) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusERneg) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusELneg) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusILneg) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusIRneg) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusLsub) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusSubset1) =>
% 96.58/13.14 ((
% 96.58/13.14 (symdiffE) =>
% 96.58/13.14 ((
% 96.58/13.14 (symdiffI1) =>
% 96.58/13.14 ((
% 96.58/13.14 (symdiffI2) =>
% 96.58/13.14 ((
% 96.58/13.14 (symdiffIneg1) =>
% 96.58/13.14 ((
% 96.58/13.14 (symdiffIneg2) =>
% 96.58/13.14 ((
% 96.58/13.14 (secondinupair) =>
% 96.58/13.14 ((
% 96.58/13.14 (setukpairIL) =>
% 96.58/13.14 ((
% 96.58/13.14 (setukpairIR) =>
% 96.58/13.14 ((
% 96.58/13.14 (kpairiskpair) =>
% 96.58/13.14 ((
% 96.58/13.14 (kpairp) =>
% 96.58/13.14 ((
% 96.58/13.14 (singletonsubset) =>
% 96.58/13.14 ((
% 96.58/13.14 (singletoninpowerset) =>
% 96.58/13.14 ((
% 96.58/13.14 (singletoninpowunion) =>
% 96.58/13.14 ((
% 96.58/13.14 (upairset2E) =>
% 96.58/13.14 ((
% 96.58/13.14 (upairsubunion) =>
% 96.58/13.14 ((
% 96.58/13.14 (upairinpowunion) =>
% 96.58/13.14 ((
% 96.58/13.14 (ubforcartprodlem1) =>
% 96.58/13.14 ((
% 96.58/13.14 (ubforcartprodlem2) =>
% 96.58/13.14 ((
% 96.58/13.14 (ubforcartprodlem3) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodpairin) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodmempair1) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodmempair) =>
% 96.58/13.14 ((
% 96.58/13.14 (setunionE2) =>
% 96.58/13.14 ((
% 96.58/13.14 (setunionsingleton1) =>
% 96.58/13.14 ((
% 96.58/13.14 (setunionsingleton2) =>
% 96.58/13.14 ((
% 96.58/13.14 (setunionsingleton) =>
% 96.58/13.14 ((
% 96.58/13.14 (singletonprop) =>
% 96.58/13.14 ((
% 96.58/13.14 (ex1E1) =>
% 96.58/13.14 ((
% 96.58/13.14 (ex1I) =>
% 96.58/13.14 ((
% 96.58/13.14 (ex1I2) =>
% 96.58/13.14 ((
% 96.58/13.14 (singletonsuniq) =>
% 96.58/13.14 ((
% 96.58/13.14 (setukpairinjL1) =>
% 96.58/13.14 ((
% 96.58/13.14 (kfstsingleton) =>
% 96.58/13.14 ((
% 96.58/13.14 (theprop) =>
% 96.58/13.14 ((
% 96.58/13.14 (kfstpairEq) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodfstin) =>
% 96.58/13.14 ((
% 96.58/13.14 (setukpairinjL2) =>
% 96.58/13.14 ((
% 96.58/13.14 (setukpairinjL) =>
% 96.58/13.14 ((
% 96.58/13.14 (setukpairinjR11) =>
% 96.58/13.14 ((
% 96.58/13.14 (setukpairinjR12) =>
% 96.58/13.14 ((
% 96.58/13.14 (setukpairinjR1) =>
% 96.58/13.14 ((
% 96.58/13.14 (upairequniteq) =>
% 96.58/13.14 ((
% 96.58/13.14 (setukpairinjR2) =>
% 96.58/13.14 ((
% 96.58/13.14 (setukpairinjR) =>
% 96.58/13.14 ((
% 96.58/13.14 (ksndsingleton) =>
% 96.58/13.14 ((
% 96.58/13.14 (ksndpairEq) =>
% 96.58/13.14 ((
% 96.58/13.14 (kpairsurjEq) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodsndin) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodpairmemEL) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodpairmemER) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodmempaircEq) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodfstpairEq) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodsndpairEq) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodpairsurjEq) =>
% 96.58/13.14 ((
% 96.58/13.14 (dpsetconstrI) =>
% 96.58/13.14 ((
% 96.58/13.14 (dpsetconstrSub) =>
% 96.58/13.14 ((
% 96.58/13.14 (setOfPairsIsBReln) =>
% 96.58/13.14 ((
% 96.58/13.14 (dpsetconstrERa) =>
% 96.58/13.14 ((
% 96.58/13.14 (dpsetconstrEL1) =>
% 96.58/13.14 ((
% 96.58/13.14 (dpsetconstrEL2) =>
% 96.58/13.14 ((
% 96.58/13.14 (dpsetconstrER) =>
% 96.58/13.14 ((
% 96.58/13.14 (funcImageSingleton) =>
% 96.58/13.14 ((
% 96.58/13.14 (apProp) =>
% 96.58/13.14 ((
% 96.58/13.14 (app) =>
% 96.58/13.14 ((
% 96.58/13.14 (infuncsetfunc) =>
% 96.58/13.14 ((
% 96.58/13.14 (ap2p) =>
% 96.58/13.14 ((
% 96.58/13.14 (funcinfuncset) =>
% 96.58/13.14 ((
% 96.58/13.14 (lamProp) =>
% 96.58/13.14 ((
% 96.58/13.14 (lamp) =>
% 96.58/13.14 ((
% 96.58/13.14 (lam2p) =>
% 96.58/13.14 ((
% 96.58/13.14 (brelnall1) =>
% 96.58/13.14 ((
% 96.58/13.14 (brelnall2) =>
% 96.58/13.14 ((
% 96.58/13.14 (ex1E2) =>
% 96.58/13.14 ((
% 96.58/13.14 (funcGraphProp1) =>
% 96.58/13.14 ((
% 96.58/13.14 (funcGraphProp3) =>
% 96.58/13.14 ((
% 96.58/13.14 (funcGraphProp2) =>
% 96.58/13.14 ((
% 96.58/13.14 (funcextLem) =>
% 96.58/13.14 ((
% 96.58/13.14 (funcGraphProp4) =>
% 96.58/13.14 ((
% 96.58/13.14 (subbreln) =>
% 96.58/13.14 ((
% 96.58/13.14 (eqbreln) =>
% 96.58/13.14 ((
% 96.58/13.14 (funcext) =>
% 96.58/13.14 ((
% 96.58/13.14 (funcext2) =>
% 96.58/13.14 ((
% 96.58/13.14 (ap2apEq1) =>
% 96.58/13.14 ((
% 96.58/13.14 (ap2apEq2) =>
% 96.58/13.14 ((
% 96.58/13.14 (beta1) =>
% 96.58/13.14 ((
% 96.58/13.14 (eta1) =>
% 96.58/13.14 ((
% 96.58/13.14 (lam2lamEq) =>
% 96.58/13.14 ((
% 96.58/13.14 (beta2) =>
% 96.58/13.14 ((
% 96.58/13.14 (eta2) =>
% 96.58/13.14 ((
% 96.58/13.14 (iffalseProp1) =>
% 96.58/13.14 ((
% 96.58/13.14 (iffalseProp2) =>
% 96.58/13.14 ((
% 96.58/13.14 (iftrueProp1) =>
% 96.58/13.14 ((
% 96.58/13.14 (iftrueProp2) =>
% 96.58/13.14 ((
% 96.58/13.14 (ifSingleton) =>
% 96.58/13.14 ((
% 96.58/13.14 (ifp) =>
% 96.58/13.14 ((
% 96.58/13.14 (theeq) =>
% 96.58/13.14 ((
% 96.58/13.14 (iftrue) =>
% 96.58/13.14 ((
% 96.58/13.14 (iffalse) =>
% 96.58/13.14 ((
% 96.58/13.14 (iftrueorfalse) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectT_lem) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionT_lem) =>
% 96.58/13.14 ((
% 96.58/13.14 (powersetT_lem) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusT_lem) =>
% 96.58/13.14 ((
% 96.58/13.14 (complementT_lem) =>
% 96.58/13.14 ((
% 96.58/13.14 (setextT) =>
% 96.58/13.14 ((
% 96.58/13.14 (subsetTI) =>
% 96.58/13.14 ((
% 96.58/13.14 (powersetTI1) =>
% 96.58/13.14 ((
% 96.58/13.14 (powersetTE1) =>
% 96.58/13.14 ((
% 96.58/13.14 (complementTI1) =>
% 96.58/13.14 ((
% 96.58/13.14 (complementTE1) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectTELcontra) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectTERcontra) =>
% 96.58/13.14 ((
% 96.58/13.14 (contrasubsetT) =>
% 96.58/13.14 ((
% 96.58/13.14 (contrasubsetT1) =>
% 96.58/13.14 ((
% 96.58/13.14 (contrasubsetT2) =>
% 96.58/13.14 ((
% 96.58/13.14 (contrasubsetT3) =>
% 96.58/13.14 ((
% 96.58/13.14 (doubleComplementI1) =>
% 96.58/13.14 ((
% 96.58/13.14 (doubleComplementE1) =>
% 96.58/13.14 ((
% 96.58/13.14 (doubleComplementSub1) =>
% 96.58/13.14 ((
% 96.58/13.14 (doubleComplementSub2) =>
% 96.58/13.14 ((
% 96.58/13.14 (doubleComplementEq) =>
% 96.58/13.14 ((
% 96.58/13.14 (complementTnotintersectT) =>
% 96.58/13.14 ((
% 96.58/13.14 (complementImpComplementIntersect) =>
% 96.58/13.14 ((
% 96.58/13.14 (complementSubsetComplementIntersect) =>
% 96.58/13.14 ((
% 96.58/13.14 (complementInPowersetComplementIntersect) =>
% 96.58/13.14 ((
% 96.58/13.14 (contraSubsetComplement) =>
% 96.58/13.14 ((
% 96.58/13.14 (complementTcontraSubset) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionTILcontra) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionTIRcontra) =>
% 96.58/13.14 ((
% 96.58/13.14 (inIntersectImpInUnion) =>
% 96.58/13.14 ((
% 96.58/13.14 (inIntersectImpInUnion2) =>
% 96.58/13.14 ((
% 96.58/13.14 (inIntersectImpInIntersectUnions) =>
% 96.58/13.14 ((
% 96.58/13.14 (intersectInPowersetIntersectUnions) =>
% 96.58/13.14 ((
% 96.58/13.14 (inComplementUnionImpNotIn1) =>
% 96.58/13.14 ((
% 96.58/13.14 (inComplementUnionImpInComplement1) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionTE) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionTEcontra) =>
% 96.58/13.14 ((
% 96.58/13.14 (demorgan2a1) =>
% 96.58/13.14 ((
% 96.58/13.14 (complementUnionInPowersetComplement) =>
% 96.58/13.14 ((
% 96.58/13.14 (demorgan2a2) =>
% 96.58/13.14 ((
% 96.58/13.14 (demorgan1a) =>
% 96.58/13.14 ((
% 96.58/13.14 (demorgan1b) =>
% 96.58/13.14 ((
% 96.58/13.14 (demorgan1) =>
% 96.58/13.14 ((
% 96.58/13.14 (demorgan2a) =>
% 96.58/13.14 ((
% 96.58/13.14 (demorgan2b2) =>
% 96.58/13.14 ((
% 96.58/13.14 (demorgan2b) =>
% 96.58/13.14 ((
% 96.58/13.14 (demorgan2) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz13rule0) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz13rule1) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz13rule2) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz13rule3) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz13rule4) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz1_1) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz1_2) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz1_3) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz1_4) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz1_5) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1all2) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1SetBreln1) =>
% 96.58/13.14 ((
% 96.58/13.14 (choice2fnsingleton) =>
% 96.58/13.14 ((
% 96.58/13.14 (setOfPairsIsBReln1) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1all1) =>
% 96.58/13.14 ((
% 96.58/13.14 (subbreln1) =>
% 96.58/13.14 ((
% 96.58/13.14 (eqbreln1) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1invprop) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1invI) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1invE) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1compprop) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1compI) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1compE) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1compEex) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1unionprop) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1unionIL) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1unionIR) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1unionI) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1unionE) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1unionEcases) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1unionCommutes) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz2Ex) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz2W) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz2A) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz2B) =>
% 96.58/13.14 ((
% 96.58/13.14 (image1Ex) =>
% 96.58/13.14 ((
% 96.58/13.14 (image1Ex1) =>
% 96.58/13.14 ((
% 96.58/13.14 (image1Equiv) =>
% 96.58/13.14 ((
% 96.58/13.14 (image1E) =>
% 96.58/13.14 ((
% 96.58/13.14 (image1I) =>
% 96.58/13.14 ((
% 96.58/13.14 (injFuncInInjFuncSet) =>
% 96.58/13.14 ((
% 96.58/13.14 (injFuncSetFuncIn) =>
% 96.58/13.14 ((
% 96.58/13.14 (injFuncSetFuncInj) =>
% 96.58/13.14 ((
% 96.58/13.14 (surjFuncSetFuncIn) =>
% 96.58/13.14 ((
% 96.58/13.14 (surjFuncSetFuncSurj) =>
% 96.58/13.14 ((
% 96.58/13.14 (leftInvIsSurj) =>
% 96.58/13.14 ((
% 96.58/13.14 (surjCantorThm) =>
% 96.58/13.14 ((
% 96.58/13.14 (foundation2) =>
% 96.58/13.14 ((
% 96.58/13.14 (notinself) =>
% 96.58/13.14 ((
% 96.58/13.14 (notinself2) =>
% 96.58/13.14 ((
% 96.58/13.14 (omegaSp) =>
% 96.58/13.14 ((
% 96.58/13.14 (omegaSclos) =>
% 96.58/13.14 ((
% 96.58/13.14 (peano0notS) =>
% 96.58/13.14 ((
% 96.58/13.14 (!!) @ (
% 96.58/13.14 (('#S') @ (
% 96.58/13.14 (
% 96.58/13.14 ('#B') @ (
% 96.58/13.14 =>) @
% 96.58/13.14 (
% 96.58/13.14 (
% 96.58/13.14 ('#C') @ in @
% 96.58/13.14 omega)))) @
% 96.58/13.14 (
% 96.58/13.14 (
% 96.58/13.14 ('#B') @ (
% 96.58/13.14 !!) @
% 96.58/13.14 (
% 96.58/13.14 (
% 96.58/13.14 ('#B') @ (
% 96.58/13.14 (
% 96.58/13.14 ('#S') @ (
% 96.58/13.14 (
% 96.58/13.14 ('#B') @ (
% 96.58/13.14 =>) @
% 96.58/13.14 (
% 96.58/13.14 (
% 96.58/13.14 ('#C') @ in @
% 96.58/13.14 omega)))))) @
% 96.58/13.14 (
% 96.58/13.14 (
% 96.58/13.14 ('#S') @ (
% 96.58/13.14 (
% 96.58/13.14 ('#B') @ (
% 96.58/13.14 '#S') @
% 96.58/13.14 (
% 96.58/13.14 (
% 96.58/13.14 ('#B') @ (
% 96.58/13.14 (
% 96.58/13.14 ('#B') @ (
% 96.58/13.14 =>))) @
% 96.58/13.14 (
% 96.58/13.14 (
% 96.58/13.14 ('#C') @ (
% 96.58/13.14 (
% 96.58/13.14 ('#B') @ (
% 96.58/13.14 '#B') @
% 96.58/13.14 (
% 96.58/13.14 (
% 96.58/13.14 ('#B') @ (
% 96.58/13.14 =) @
% 96.58/13.14 omegaS)))) @
% 96.58/13.14 omegaS)))))) @
% 96.58/13.14 (
% 96.58/13.14 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 96.58/13.14 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl46])).
% 96.58/13.14 thf(zip_derived_cl58, plain,
% 96.58/13.14 (~ (((wellorderingAx) =>
% 96.58/13.14 (((descrp) =>
% 96.58/13.14 (((dsetconstrI) =>
% 96.58/13.14 (((dsetconstrEL) =>
% 96.58/13.14 (((dsetconstrER) =>
% 96.58/13.14 (((exuE1) =>
% 96.58/13.14 (((prop2setE) =>
% 96.58/13.14 (((emptysetE) =>
% 96.58/13.14 (((emptysetimpfalse) =>
% 96.58/13.14 (((notinemptyset) =>
% 96.58/13.14 (((exuE3e) =>
% 96.58/13.14 (((setext) =>
% 96.58/13.14 (((emptyI) =>
% 96.58/13.14 (((noeltsimpempty) =>
% 96.58/13.14 (((setbeta) =>
% 96.58/13.14 (((nonemptyE1) =>
% 96.58/13.14 (((nonemptyI) =>
% 96.58/13.14 (((nonemptyI1) =>
% 96.58/13.14 (((setadjoinIL) =>
% 96.58/13.14 (((in @ emptyset @
% 96.58/13.14 (setadjoin @ emptyset @
% 96.58/13.14 emptyset)) =>
% 96.58/13.14 (((setadjoinIR) =>
% 96.58/13.14 (((setadjoinE) =>
% 96.58/13.14 (((setadjoinOr) =>
% 96.58/13.14 (((setoftrueEq) =>
% 96.58/13.14 (((powersetI) =>
% 96.58/13.14 (((emptyinPowerset) =>
% 96.58/13.14 (((emptyInPowerset) =>
% 96.58/13.14 (((powersetE) =>
% 96.58/13.14 (((setunionI) =>
% 96.58/13.14 (((setunionE) =>
% 96.58/13.14 ((
% 96.58/13.14 (subPowSU) =>
% 96.58/13.14 ((
% 96.58/13.14 (exuE2) =>
% 96.58/13.14 ((
% 96.58/13.14 (nonemptyImpWitness) =>
% 96.58/13.14 ((
% 96.58/13.14 (uniqinunit) =>
% 96.58/13.14 ((
% 96.58/13.14 (notinsingleton) =>
% 96.58/13.14 ((
% 96.58/13.14 (eqinunit) =>
% 96.58/13.14 ((
% 96.58/13.14 (singletonsswitch) =>
% 96.58/13.14 ((
% 96.58/13.14 (upairsetE) =>
% 96.58/13.14 ((
% 96.58/13.14 (upairsetIL) =>
% 96.58/13.14 ((
% 96.58/13.14 (upairsetIR) =>
% 96.58/13.14 ((
% 96.58/13.14 (emptyE1) =>
% 96.58/13.14 ((
% 96.58/13.14 (vacuousDall) =>
% 96.58/13.14 ((
% 96.58/13.14 (quantDeMorgan1) =>
% 96.58/13.14 ((
% 96.58/13.14 (quantDeMorgan2) =>
% 96.58/13.14 ((
% 96.58/13.14 (quantDeMorgan3) =>
% 96.58/13.14 ((
% 96.58/13.14 (quantDeMorgan4) =>
% 96.58/13.14 ((
% 96.58/13.14 (prop2setI) =>
% 96.58/13.14 ((
% 96.58/13.14 (prop2set2propI) =>
% 96.58/13.14 ((
% 96.58/13.14 (notdexE) =>
% 96.58/13.14 ((
% 96.58/13.14 (notdallE) =>
% 96.58/13.14 ((
% 96.58/13.14 (exuI1) =>
% 96.58/13.14 ((
% 96.58/13.14 (exuI3) =>
% 96.58/13.14 ((
% 96.58/13.14 (exuI2) =>
% 96.58/13.14 ((
% 96.58/13.14 (inCongP) =>
% 96.58/13.14 ((
% 96.58/13.14 (in__Cong) =>
% 96.58/13.14 ((
% 96.58/13.14 (exuE3u) =>
% 96.58/13.14 ((
% 96.58/13.14 (exu__Cong) =>
% 96.58/13.14 ((
% 96.58/13.14 (setadjoin__Cong) =>
% 96.58/13.14 ((
% 96.58/13.14 (powerset__Cong) =>
% 96.58/13.14 ((
% 96.58/13.14 (setunion__Cong) =>
% 96.58/13.14 ((
% 96.58/13.14 (exuEu) =>
% 96.58/13.14 ((
% 96.58/13.14 (descr__Cong) =>
% 96.58/13.14 ((
% 96.58/13.14 (dsetconstr__Cong) =>
% 96.58/13.14 ((
% 96.58/13.14 (subsetI1) =>
% 96.58/13.14 ((
% 96.58/13.14 (eqimpsubset2) =>
% 96.58/13.14 ((
% 96.58/13.14 (eqimpsubset1) =>
% 96.58/13.14 ((
% 96.58/13.14 (subsetI2) =>
% 96.58/13.14 ((
% 96.58/13.14 (emptysetsubset) =>
% 96.58/13.14 ((
% 96.58/13.14 (subsetE) =>
% 96.58/13.14 ((
% 96.58/13.14 (subsetE2) =>
% 96.58/13.14 ((
% 96.58/13.14 (notsubsetI) =>
% 96.58/13.14 ((
% 96.58/13.14 (notequalI1) =>
% 96.58/13.14 ((
% 96.58/13.14 (notequalI2) =>
% 96.58/13.14 ((
% 96.58/13.14 (subsetRefl) =>
% 96.58/13.14 ((
% 96.58/13.14 (subsetTrans) =>
% 96.58/13.14 ((
% 96.58/13.14 (setadjoinSub) =>
% 96.58/13.14 ((
% 96.58/13.14 (setadjoinSub2) =>
% 96.58/13.14 ((
% 96.58/13.14 (subset2powerset) =>
% 96.58/13.14 ((
% 96.58/13.14 (setextsub) =>
% 96.58/13.14 ((
% 96.58/13.14 (subsetemptysetimpeq) =>
% 96.58/13.14 ((
% 96.58/13.14 (powersetI1) =>
% 96.58/13.14 ((
% 96.58/13.14 (powersetE1) =>
% 96.58/13.14 ((
% 96.58/13.14 (inPowerset) =>
% 96.58/13.14 ((
% 96.58/13.14 (powersetsubset) =>
% 96.58/13.14 ((
% 96.58/13.14 (sepInPowerset) =>
% 96.58/13.14 ((
% 96.58/13.14 (sepSubset) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionIL) =>
% 96.58/13.14 ((
% 96.58/13.14 (upairset2IR) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionIR) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionEcases) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionE) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionLsub) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionRsub) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectI) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectSubset5) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectEL) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectLsub) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectSubset2) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectSubset3) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectER) =>
% 96.58/13.14 ((
% 96.58/13.14 (disjointsetsI1) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectRsub) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectSubset4) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectSubset1) =>
% 96.58/13.14 ((
% 96.58/13.14 (bs114d) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusI) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusEL) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusER) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusSubset2) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusERneg) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusELneg) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusILneg) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusIRneg) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusLsub) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusSubset1) =>
% 96.58/13.14 ((
% 96.58/13.14 (symdiffE) =>
% 96.58/13.14 ((
% 96.58/13.14 (symdiffI1) =>
% 96.58/13.14 ((
% 96.58/13.14 (symdiffI2) =>
% 96.58/13.14 ((
% 96.58/13.14 (symdiffIneg1) =>
% 96.58/13.14 ((
% 96.58/13.14 (symdiffIneg2) =>
% 96.58/13.14 ((
% 96.58/13.14 (secondinupair) =>
% 96.58/13.14 ((
% 96.58/13.14 (setukpairIL) =>
% 96.58/13.14 ((
% 96.58/13.14 (setukpairIR) =>
% 96.58/13.14 ((
% 96.58/13.14 (kpairiskpair) =>
% 96.58/13.14 ((
% 96.58/13.14 (kpairp) =>
% 96.58/13.14 ((
% 96.58/13.14 (singletonsubset) =>
% 96.58/13.14 ((
% 96.58/13.14 (singletoninpowerset) =>
% 96.58/13.14 ((
% 96.58/13.14 (singletoninpowunion) =>
% 96.58/13.14 ((
% 96.58/13.14 (upairset2E) =>
% 96.58/13.14 ((
% 96.58/13.14 (upairsubunion) =>
% 96.58/13.14 ((
% 96.58/13.14 (upairinpowunion) =>
% 96.58/13.14 ((
% 96.58/13.14 (ubforcartprodlem1) =>
% 96.58/13.14 ((
% 96.58/13.14 (ubforcartprodlem2) =>
% 96.58/13.14 ((
% 96.58/13.14 (ubforcartprodlem3) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodpairin) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodmempair1) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodmempair) =>
% 96.58/13.14 ((
% 96.58/13.14 (setunionE2) =>
% 96.58/13.14 ((
% 96.58/13.14 (setunionsingleton1) =>
% 96.58/13.14 ((
% 96.58/13.14 (setunionsingleton2) =>
% 96.58/13.14 ((
% 96.58/13.14 (setunionsingleton) =>
% 96.58/13.14 ((
% 96.58/13.14 (singletonprop) =>
% 96.58/13.14 ((
% 96.58/13.14 (ex1E1) =>
% 96.58/13.14 ((
% 96.58/13.14 (ex1I) =>
% 96.58/13.14 ((
% 96.58/13.14 (ex1I2) =>
% 96.58/13.14 ((
% 96.58/13.14 (singletonsuniq) =>
% 96.58/13.14 ((
% 96.58/13.14 (setukpairinjL1) =>
% 96.58/13.14 ((
% 96.58/13.14 (kfstsingleton) =>
% 96.58/13.14 ((
% 96.58/13.14 (theprop) =>
% 96.58/13.14 ((
% 96.58/13.14 (kfstpairEq) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodfstin) =>
% 96.58/13.14 ((
% 96.58/13.14 (setukpairinjL2) =>
% 96.58/13.14 ((
% 96.58/13.14 (setukpairinjL) =>
% 96.58/13.14 ((
% 96.58/13.14 (setukpairinjR11) =>
% 96.58/13.14 ((
% 96.58/13.14 (setukpairinjR12) =>
% 96.58/13.14 ((
% 96.58/13.14 (setukpairinjR1) =>
% 96.58/13.14 ((
% 96.58/13.14 (upairequniteq) =>
% 96.58/13.14 ((
% 96.58/13.14 (setukpairinjR2) =>
% 96.58/13.14 ((
% 96.58/13.14 (setukpairinjR) =>
% 96.58/13.14 ((
% 96.58/13.14 (ksndsingleton) =>
% 96.58/13.14 ((
% 96.58/13.14 (ksndpairEq) =>
% 96.58/13.14 ((
% 96.58/13.14 (kpairsurjEq) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodsndin) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodpairmemEL) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodpairmemER) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodmempaircEq) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodfstpairEq) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodsndpairEq) =>
% 96.58/13.14 ((
% 96.58/13.14 (cartprodpairsurjEq) =>
% 96.58/13.14 ((
% 96.58/13.14 (dpsetconstrI) =>
% 96.58/13.14 ((
% 96.58/13.14 (dpsetconstrSub) =>
% 96.58/13.14 ((
% 96.58/13.14 (setOfPairsIsBReln) =>
% 96.58/13.14 ((
% 96.58/13.14 (dpsetconstrERa) =>
% 96.58/13.14 ((
% 96.58/13.14 (dpsetconstrEL1) =>
% 96.58/13.14 ((
% 96.58/13.14 (dpsetconstrEL2) =>
% 96.58/13.14 ((
% 96.58/13.14 (dpsetconstrER) =>
% 96.58/13.14 ((
% 96.58/13.14 (funcImageSingleton) =>
% 96.58/13.14 ((
% 96.58/13.14 (apProp) =>
% 96.58/13.14 ((
% 96.58/13.14 (app) =>
% 96.58/13.14 ((
% 96.58/13.14 (infuncsetfunc) =>
% 96.58/13.14 ((
% 96.58/13.14 (ap2p) =>
% 96.58/13.14 ((
% 96.58/13.14 (funcinfuncset) =>
% 96.58/13.14 ((
% 96.58/13.14 (lamProp) =>
% 96.58/13.14 ((
% 96.58/13.14 (lamp) =>
% 96.58/13.14 ((
% 96.58/13.14 (lam2p) =>
% 96.58/13.14 ((
% 96.58/13.14 (brelnall1) =>
% 96.58/13.14 ((
% 96.58/13.14 (brelnall2) =>
% 96.58/13.14 ((
% 96.58/13.14 (ex1E2) =>
% 96.58/13.14 ((
% 96.58/13.14 (funcGraphProp1) =>
% 96.58/13.14 ((
% 96.58/13.14 (funcGraphProp3) =>
% 96.58/13.14 ((
% 96.58/13.14 (funcGraphProp2) =>
% 96.58/13.14 ((
% 96.58/13.14 (funcextLem) =>
% 96.58/13.14 ((
% 96.58/13.14 (funcGraphProp4) =>
% 96.58/13.14 ((
% 96.58/13.14 (subbreln) =>
% 96.58/13.14 ((
% 96.58/13.14 (eqbreln) =>
% 96.58/13.14 ((
% 96.58/13.14 (funcext) =>
% 96.58/13.14 ((
% 96.58/13.14 (funcext2) =>
% 96.58/13.14 ((
% 96.58/13.14 (ap2apEq1) =>
% 96.58/13.14 ((
% 96.58/13.14 (ap2apEq2) =>
% 96.58/13.14 ((
% 96.58/13.14 (beta1) =>
% 96.58/13.14 ((
% 96.58/13.14 (eta1) =>
% 96.58/13.14 ((
% 96.58/13.14 (lam2lamEq) =>
% 96.58/13.14 ((
% 96.58/13.14 (beta2) =>
% 96.58/13.14 ((
% 96.58/13.14 (eta2) =>
% 96.58/13.14 ((
% 96.58/13.14 (iffalseProp1) =>
% 96.58/13.14 ((
% 96.58/13.14 (iffalseProp2) =>
% 96.58/13.14 ((
% 96.58/13.14 (iftrueProp1) =>
% 96.58/13.14 ((
% 96.58/13.14 (iftrueProp2) =>
% 96.58/13.14 ((
% 96.58/13.14 (ifSingleton) =>
% 96.58/13.14 ((
% 96.58/13.14 (ifp) =>
% 96.58/13.14 ((
% 96.58/13.14 (theeq) =>
% 96.58/13.14 ((
% 96.58/13.14 (iftrue) =>
% 96.58/13.14 ((
% 96.58/13.14 (iffalse) =>
% 96.58/13.14 ((
% 96.58/13.14 (iftrueorfalse) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectT_lem) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionT_lem) =>
% 96.58/13.14 ((
% 96.58/13.14 (powersetT_lem) =>
% 96.58/13.14 ((
% 96.58/13.14 (setminusT_lem) =>
% 96.58/13.14 ((
% 96.58/13.14 (complementT_lem) =>
% 96.58/13.14 ((
% 96.58/13.14 (setextT) =>
% 96.58/13.14 ((
% 96.58/13.14 (subsetTI) =>
% 96.58/13.14 ((
% 96.58/13.14 (powersetTI1) =>
% 96.58/13.14 ((
% 96.58/13.14 (powersetTE1) =>
% 96.58/13.14 ((
% 96.58/13.14 (complementTI1) =>
% 96.58/13.14 ((
% 96.58/13.14 (complementTE1) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectTELcontra) =>
% 96.58/13.14 ((
% 96.58/13.14 (binintersectTERcontra) =>
% 96.58/13.14 ((
% 96.58/13.14 (contrasubsetT) =>
% 96.58/13.14 ((
% 96.58/13.14 (contrasubsetT1) =>
% 96.58/13.14 ((
% 96.58/13.14 (contrasubsetT2) =>
% 96.58/13.14 ((
% 96.58/13.14 (contrasubsetT3) =>
% 96.58/13.14 ((
% 96.58/13.14 (doubleComplementI1) =>
% 96.58/13.14 ((
% 96.58/13.14 (doubleComplementE1) =>
% 96.58/13.14 ((
% 96.58/13.14 (doubleComplementSub1) =>
% 96.58/13.14 ((
% 96.58/13.14 (doubleComplementSub2) =>
% 96.58/13.14 ((
% 96.58/13.14 (doubleComplementEq) =>
% 96.58/13.14 ((
% 96.58/13.14 (complementTnotintersectT) =>
% 96.58/13.14 ((
% 96.58/13.14 (complementImpComplementIntersect) =>
% 96.58/13.14 ((
% 96.58/13.14 (complementSubsetComplementIntersect) =>
% 96.58/13.14 ((
% 96.58/13.14 (complementInPowersetComplementIntersect) =>
% 96.58/13.14 ((
% 96.58/13.14 (contraSubsetComplement) =>
% 96.58/13.14 ((
% 96.58/13.14 (complementTcontraSubset) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionTILcontra) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionTIRcontra) =>
% 96.58/13.14 ((
% 96.58/13.14 (inIntersectImpInUnion) =>
% 96.58/13.14 ((
% 96.58/13.14 (inIntersectImpInUnion2) =>
% 96.58/13.14 ((
% 96.58/13.14 (inIntersectImpInIntersectUnions) =>
% 96.58/13.14 ((
% 96.58/13.14 (intersectInPowersetIntersectUnions) =>
% 96.58/13.14 ((
% 96.58/13.14 (inComplementUnionImpNotIn1) =>
% 96.58/13.14 ((
% 96.58/13.14 (inComplementUnionImpInComplement1) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionTE) =>
% 96.58/13.14 ((
% 96.58/13.14 (binunionTEcontra) =>
% 96.58/13.14 ((
% 96.58/13.14 (demorgan2a1) =>
% 96.58/13.14 ((
% 96.58/13.14 (complementUnionInPowersetComplement) =>
% 96.58/13.14 ((
% 96.58/13.14 (demorgan2a2) =>
% 96.58/13.14 ((
% 96.58/13.14 (demorgan1a) =>
% 96.58/13.14 ((
% 96.58/13.14 (demorgan1b) =>
% 96.58/13.14 ((
% 96.58/13.14 (demorgan1) =>
% 96.58/13.14 ((
% 96.58/13.14 (demorgan2a) =>
% 96.58/13.14 ((
% 96.58/13.14 (demorgan2b2) =>
% 96.58/13.14 ((
% 96.58/13.14 (demorgan2b) =>
% 96.58/13.14 ((
% 96.58/13.14 (demorgan2) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz13rule0) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz13rule1) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz13rule2) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz13rule3) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz13rule4) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz1_1) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz1_2) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz1_3) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz1_4) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz1_5) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1all2) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1SetBreln1) =>
% 96.58/13.14 ((
% 96.58/13.14 (choice2fnsingleton) =>
% 96.58/13.14 ((
% 96.58/13.14 (setOfPairsIsBReln1) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1all1) =>
% 96.58/13.14 ((
% 96.58/13.14 (subbreln1) =>
% 96.58/13.14 ((
% 96.58/13.14 (eqbreln1) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1invprop) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1invI) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1invE) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1compprop) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1compI) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1compE) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1compEex) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1unionprop) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1unionIL) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1unionIR) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1unionI) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1unionE) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1unionEcases) =>
% 96.58/13.14 ((
% 96.58/13.14 (breln1unionCommutes) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz2Ex) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz2W) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz2A) =>
% 96.58/13.14 ((
% 96.58/13.14 (woz2B) =>
% 96.58/13.14 ((
% 96.58/13.14 (image1Ex) =>
% 96.58/13.14 ((
% 96.58/13.14 (image1Ex1) =>
% 96.58/13.14 ((
% 96.58/13.14 (image1Equiv) =>
% 96.58/13.14 ((
% 96.58/13.14 (image1E) =>
% 96.58/13.14 ((
% 96.58/13.14 (image1I) =>
% 96.58/13.14 ((
% 96.58/13.14 (injFuncInInjFuncSet) =>
% 96.58/13.14 ((
% 96.58/13.14 (injFuncSetFuncIn) =>
% 96.58/13.14 ((
% 96.58/13.14 (injFuncSetFuncInj) =>
% 96.58/13.14 ((
% 96.58/13.14 (surjFuncSetFuncIn) =>
% 96.58/13.14 ((
% 96.58/13.14 (surjFuncSetFuncSurj) =>
% 96.58/13.14 ((
% 96.58/13.14 (leftInvIsSurj) =>
% 96.58/13.14 ((
% 96.58/13.14 (surjCantorThm) =>
% 96.58/13.14 ((
% 96.58/13.14 (foundation2) =>
% 96.58/13.14 ((
% 96.58/13.14 (notinself) =>
% 96.58/13.14 ((
% 96.58/13.14 (notinself2) =>
% 96.58/13.14 ((
% 96.58/13.14 (omegaSp) =>
% 96.58/13.14 ((
% 96.58/13.14 (omegaSclos) =>
% 96.58/13.14 ((
% 96.58/13.14 (peano0notS) =>
% 96.58/13.14 ((
% 96.58/13.14 (!!) @ (
% 96.58/13.14 (('#S') @ (
% 96.58/13.14 (
% 96.58/13.14 ('#B') @ (
% 96.58/13.14 =>) @
% 96.58/13.14 (
% 96.58/13.14 (
% 96.58/13.14 ('#C') @ in @
% 96.58/13.14 omega)))) @
% 96.58/13.14 (
% 96.58/13.14 (
% 96.58/13.14 ('#B') @ (
% 96.58/13.14 !!) @
% 96.58/13.14 (
% 96.58/13.14 (
% 96.58/13.14 ('#B') @ (
% 96.58/13.14 (
% 96.58/13.14 ('#S') @ (
% 96.58/13.14 (
% 96.58/13.14 ('#B') @ (
% 96.58/13.14 =>) @
% 96.58/13.14 (
% 96.58/13.14 (
% 96.58/13.14 ('#C') @ in @
% 96.58/13.14 omega)))))) @
% 96.58/13.14 (
% 96.58/13.14 (
% 96.58/13.14 ('#S') @ (
% 96.58/13.14 (
% 96.58/13.14 ('#B') @ (
% 96.58/13.14 '#S') @
% 96.58/13.14 (
% 96.58/13.14 (
% 96.58/13.14 ('#B') @ (
% 96.58/13.14 (
% 96.58/13.14 ('#B') @ (
% 96.58/13.14 =>))) @
% 96.58/13.14 (
% 96.58/13.14 (
% 96.58/13.14 ('#C') @ (
% 96.58/13.14 (
% 96.58/13.14 ('#B') @ (
% 96.58/13.14 '#B') @
% 96.58/13.14 (
% 96.58/13.14 (
% 96.58/13.14 ('#B') @ (
% 96.58/13.14 =) @
% 96.58/13.14 omegaS)))) @
% 96.58/13.14 omegaS)))))) @
% 96.58/13.14 (
% 96.58/13.14 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 96.58/13.14 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl52])).
% 96.58/13.14 thf(zip_derived_cl64, plain,
% 96.58/13.14 (~ (((descrp) =>
% 96.58/13.14 (((dsetconstrI) =>
% 96.58/13.14 (((dsetconstrEL) =>
% 96.58/13.14 (((dsetconstrER) =>
% 96.58/13.14 (((exuE1) =>
% 96.58/13.14 (((prop2setE) =>
% 96.58/13.14 (((emptysetE) =>
% 96.58/13.14 (((emptysetimpfalse) =>
% 96.58/13.14 (((notinemptyset) =>
% 96.58/13.14 (((exuE3e) =>
% 96.58/13.14 (((setext) =>
% 96.58/13.14 (((emptyI) =>
% 96.58/13.14 (((noeltsimpempty) =>
% 96.58/13.14 (((setbeta) =>
% 96.58/13.14 (((nonemptyE1) =>
% 96.58/13.14 (((nonemptyI) =>
% 96.58/13.14 (((nonemptyI1) =>
% 96.58/13.14 (((setadjoinIL) =>
% 96.58/13.14 (((in @ emptyset @
% 96.58/13.14 (setadjoin @ emptyset @ emptyset)) =>
% 96.58/13.14 (((setadjoinIR) =>
% 96.58/13.14 (((setadjoinE) =>
% 96.58/13.14 (((setadjoinOr) =>
% 96.58/13.14 (((setoftrueEq) =>
% 96.58/13.14 (((powersetI) =>
% 96.58/13.14 (((emptyinPowerset) =>
% 96.58/13.14 (((emptyInPowerset) =>
% 96.58/13.14 (((powersetE) =>
% 96.58/13.14 (((setunionI) =>
% 96.58/13.14 (((setunionE) =>
% 96.58/13.14 (((subPowSU) =>
% 96.58/13.14 ((
% 96.58/13.14 (exuE2) =>
% 96.58/13.14 ((
% 96.58/13.14 (nonemptyImpWitness) =>
% 96.58/13.14 ((
% 96.58/13.14 (uniqinunit) =>
% 96.58/13.14 ((
% 96.58/13.14 (notinsingleton) =>
% 96.58/13.14 ((
% 96.58/13.14 (eqinunit) =>
% 96.58/13.14 ((
% 96.58/13.14 (singletonsswitch) =>
% 96.58/13.14 ((
% 96.58/13.14 (upairsetE) =>
% 96.58/13.14 ((
% 96.58/13.14 (upairsetIL) =>
% 96.58/13.14 ((
% 96.58/13.14 (upairsetIR) =>
% 96.58/13.14 ((
% 96.58/13.14 (emptyE1) =>
% 96.58/13.14 ((
% 96.58/13.14 (vacuousDall) =>
% 96.58/13.14 ((
% 96.58/13.14 (quantDeMorgan1) =>
% 96.58/13.14 ((
% 96.58/13.14 (quantDeMorgan2) =>
% 96.58/13.14 ((
% 96.58/13.14 (quantDeMorgan3) =>
% 96.58/13.14 ((
% 96.58/13.14 (quantDeMorgan4) =>
% 96.58/13.14 ((
% 96.58/13.14 (prop2setI) =>
% 96.58/13.14 ((
% 96.58/13.14 (prop2set2propI) =>
% 96.58/13.14 ((
% 96.58/13.14 (notdexE) =>
% 96.58/13.14 ((
% 96.58/13.14 (notdallE) =>
% 96.58/13.14 ((
% 96.58/13.14 (exuI1) =>
% 96.58/13.14 ((
% 96.58/13.14 (exuI3) =>
% 96.58/13.14 ((
% 96.58/13.14 (exuI2) =>
% 96.58/13.14 ((
% 96.58/13.14 (inCongP) =>
% 96.58/13.14 ((
% 96.58/13.14 (in__Cong) =>
% 96.58/13.14 ((
% 96.58/13.14 (exuE3u) =>
% 96.58/13.14 ((
% 96.58/13.14 (exu__Cong) =>
% 96.58/13.14 ((
% 96.58/13.14 (setadjoin__Cong) =>
% 96.58/13.14 ((
% 96.58/13.14 (powerset__Cong) =>
% 96.58/13.14 ((
% 96.58/13.14 (setunion__Cong) =>
% 96.58/13.14 ((
% 96.58/13.14 (exuEu) =>
% 96.58/13.14 ((
% 96.58/13.14 (descr__Cong) =>
% 96.58/13.14 ((
% 96.58/13.14 (dsetconstr__Cong) =>
% 96.58/13.14 ((
% 96.58/13.14 (subsetI1) =>
% 96.58/13.14 ((
% 96.58/13.14 (eqimpsubset2) =>
% 96.58/13.14 ((
% 96.58/13.14 (eqimpsubset1) =>
% 96.58/13.14 ((
% 96.58/13.14 (subsetI2) =>
% 96.58/13.14 ((
% 96.58/13.14 (emptysetsubset) =>
% 96.58/13.14 ((
% 96.58/13.14 (subsetE) =>
% 96.58/13.14 ((
% 96.58/13.14 (subsetE2) =>
% 96.58/13.14 ((
% 96.58/13.14 (notsubsetI) =>
% 96.58/13.14 ((
% 96.58/13.14 (notequalI1) =>
% 96.58/13.14 ((
% 96.58/13.14 (notequalI2) =>
% 96.58/13.14 ((
% 96.58/13.14 (subsetRefl) =>
% 96.58/13.14 ((
% 96.58/13.14 (subsetTrans) =>
% 96.58/13.14 ((
% 96.58/13.14 (setadjoinSub) =>
% 96.58/13.14 ((
% 96.58/13.14 (setadjoinSub2) =>
% 96.58/13.14 ((
% 96.58/13.14 (subset2powerset) =>
% 96.58/13.15 ((
% 96.58/13.15 (setextsub) =>
% 96.58/13.15 ((
% 96.58/13.15 (subsetemptysetimpeq) =>
% 96.58/13.15 ((
% 96.58/13.15 (powersetI1) =>
% 96.58/13.15 ((
% 96.58/13.15 (powersetE1) =>
% 96.58/13.15 ((
% 96.58/13.15 (inPowerset) =>
% 96.58/13.15 ((
% 96.58/13.15 (powersetsubset) =>
% 96.58/13.15 ((
% 96.58/13.15 (sepInPowerset) =>
% 96.58/13.15 ((
% 96.58/13.15 (sepSubset) =>
% 96.58/13.15 ((
% 96.58/13.15 (binunionIL) =>
% 96.58/13.15 ((
% 96.58/13.15 (upairset2IR) =>
% 96.58/13.15 ((
% 96.58/13.15 (binunionIR) =>
% 96.58/13.15 ((
% 96.58/13.15 (binunionEcases) =>
% 96.58/13.15 ((
% 96.58/13.15 (binunionE) =>
% 96.58/13.15 ((
% 96.58/13.15 (binunionLsub) =>
% 96.58/13.15 ((
% 96.58/13.15 (binunionRsub) =>
% 96.58/13.15 ((
% 96.58/13.15 (binintersectI) =>
% 96.58/13.15 ((
% 96.58/13.15 (binintersectSubset5) =>
% 96.58/13.15 ((
% 96.58/13.15 (binintersectEL) =>
% 96.58/13.15 ((
% 96.58/13.15 (binintersectLsub) =>
% 96.58/13.15 ((
% 96.58/13.15 (binintersectSubset2) =>
% 96.58/13.15 ((
% 96.58/13.15 (binintersectSubset3) =>
% 96.58/13.15 ((
% 96.58/13.15 (binintersectER) =>
% 96.58/13.15 ((
% 96.58/13.15 (disjointsetsI1) =>
% 96.58/13.15 ((
% 96.58/13.15 (binintersectRsub) =>
% 96.58/13.15 ((
% 96.58/13.15 (binintersectSubset4) =>
% 96.58/13.15 ((
% 96.58/13.15 (binintersectSubset1) =>
% 96.58/13.15 ((
% 96.58/13.15 (bs114d) =>
% 96.58/13.15 ((
% 96.58/13.15 (setminusI) =>
% 96.58/13.15 ((
% 96.58/13.15 (setminusEL) =>
% 96.58/13.15 ((
% 96.58/13.15 (setminusER) =>
% 96.58/13.15 ((
% 96.58/13.15 (setminusSubset2) =>
% 96.58/13.15 ((
% 96.58/13.15 (setminusERneg) =>
% 96.58/13.15 ((
% 96.58/13.15 (setminusELneg) =>
% 96.58/13.15 ((
% 96.58/13.15 (setminusILneg) =>
% 96.58/13.15 ((
% 96.58/13.15 (setminusIRneg) =>
% 96.58/13.15 ((
% 96.58/13.15 (setminusLsub) =>
% 96.58/13.15 ((
% 96.58/13.15 (setminusSubset1) =>
% 96.58/13.15 ((
% 96.58/13.15 (symdiffE) =>
% 96.58/13.15 ((
% 96.58/13.15 (symdiffI1) =>
% 96.58/13.15 ((
% 96.58/13.15 (symdiffI2) =>
% 96.58/13.15 ((
% 96.58/13.15 (symdiffIneg1) =>
% 96.58/13.15 ((
% 96.58/13.15 (symdiffIneg2) =>
% 96.58/13.15 ((
% 96.58/13.15 (secondinupair) =>
% 96.58/13.15 ((
% 96.58/13.15 (setukpairIL) =>
% 96.58/13.15 ((
% 96.58/13.15 (setukpairIR) =>
% 96.58/13.15 ((
% 96.58/13.15 (kpairiskpair) =>
% 96.58/13.15 ((
% 96.58/13.15 (kpairp) =>
% 96.58/13.15 ((
% 96.58/13.15 (singletonsubset) =>
% 96.58/13.15 ((
% 96.58/13.15 (singletoninpowerset) =>
% 96.58/13.15 ((
% 96.58/13.15 (singletoninpowunion) =>
% 96.58/13.15 ((
% 96.58/13.15 (upairset2E) =>
% 96.58/13.15 ((
% 96.58/13.15 (upairsubunion) =>
% 96.58/13.15 ((
% 96.58/13.15 (upairinpowunion) =>
% 96.58/13.15 ((
% 96.58/13.15 (ubforcartprodlem1) =>
% 96.58/13.15 ((
% 96.58/13.15 (ubforcartprodlem2) =>
% 96.58/13.15 ((
% 96.58/13.15 (ubforcartprodlem3) =>
% 96.58/13.15 ((
% 96.58/13.15 (cartprodpairin) =>
% 96.58/13.15 ((
% 96.58/13.15 (cartprodmempair1) =>
% 96.58/13.15 ((
% 96.58/13.15 (cartprodmempair) =>
% 96.58/13.15 ((
% 96.58/13.15 (setunionE2) =>
% 96.58/13.15 ((
% 96.58/13.15 (setunionsingleton1) =>
% 96.58/13.15 ((
% 96.58/13.15 (setunionsingleton2) =>
% 96.58/13.15 ((
% 96.58/13.15 (setunionsingleton) =>
% 96.58/13.15 ((
% 96.58/13.15 (singletonprop) =>
% 96.58/13.15 ((
% 96.58/13.15 (ex1E1) =>
% 96.58/13.15 ((
% 96.58/13.15 (ex1I) =>
% 96.58/13.15 ((
% 96.58/13.15 (ex1I2) =>
% 96.58/13.15 ((
% 96.58/13.15 (singletonsuniq) =>
% 96.58/13.15 ((
% 96.58/13.15 (setukpairinjL1) =>
% 96.58/13.15 ((
% 96.58/13.15 (kfstsingleton) =>
% 96.58/13.15 ((
% 96.58/13.15 (theprop) =>
% 96.58/13.15 ((
% 96.58/13.15 (kfstpairEq) =>
% 96.58/13.15 ((
% 96.58/13.15 (cartprodfstin) =>
% 96.58/13.15 ((
% 96.58/13.15 (setukpairinjL2) =>
% 96.58/13.15 ((
% 96.58/13.15 (setukpairinjL) =>
% 96.58/13.15 ((
% 96.58/13.15 (setukpairinjR11) =>
% 96.58/13.15 ((
% 96.58/13.15 (setukpairinjR12) =>
% 96.58/13.15 ((
% 96.58/13.15 (setukpairinjR1) =>
% 96.58/13.15 ((
% 96.58/13.15 (upairequniteq) =>
% 96.58/13.15 ((
% 96.58/13.15 (setukpairinjR2) =>
% 96.58/13.15 ((
% 96.58/13.15 (setukpairinjR) =>
% 96.58/13.15 ((
% 96.58/13.15 (ksndsingleton) =>
% 96.58/13.15 ((
% 96.58/13.15 (ksndpairEq) =>
% 96.58/13.15 ((
% 96.58/13.15 (kpairsurjEq) =>
% 96.58/13.15 ((
% 96.58/13.15 (cartprodsndin) =>
% 96.58/13.15 ((
% 96.58/13.15 (cartprodpairmemEL) =>
% 96.58/13.15 ((
% 96.58/13.15 (cartprodpairmemER) =>
% 96.58/13.15 ((
% 96.58/13.15 (cartprodmempaircEq) =>
% 96.58/13.15 ((
% 96.58/13.15 (cartprodfstpairEq) =>
% 96.58/13.15 ((
% 96.58/13.15 (cartprodsndpairEq) =>
% 96.58/13.15 ((
% 96.58/13.15 (cartprodpairsurjEq) =>
% 96.58/13.15 ((
% 96.58/13.15 (dpsetconstrI) =>
% 96.58/13.15 ((
% 96.58/13.15 (dpsetconstrSub) =>
% 96.58/13.15 ((
% 96.58/13.15 (setOfPairsIsBReln) =>
% 96.58/13.15 ((
% 96.58/13.15 (dpsetconstrERa) =>
% 96.58/13.15 ((
% 96.58/13.15 (dpsetconstrEL1) =>
% 96.58/13.15 ((
% 96.58/13.15 (dpsetconstrEL2) =>
% 96.58/13.15 ((
% 96.58/13.15 (dpsetconstrER) =>
% 96.58/13.15 ((
% 96.58/13.15 (funcImageSingleton) =>
% 96.58/13.15 ((
% 96.58/13.15 (apProp) =>
% 96.58/13.15 ((
% 96.58/13.15 (app) =>
% 96.58/13.15 ((
% 96.58/13.15 (infuncsetfunc) =>
% 96.58/13.15 ((
% 96.58/13.15 (ap2p) =>
% 96.58/13.15 ((
% 96.58/13.15 (funcinfuncset) =>
% 96.58/13.15 ((
% 96.58/13.15 (lamProp) =>
% 96.58/13.15 ((
% 96.58/13.15 (lamp) =>
% 96.58/13.15 ((
% 96.58/13.15 (lam2p) =>
% 96.58/13.15 ((
% 96.58/13.15 (brelnall1) =>
% 96.58/13.15 ((
% 96.58/13.15 (brelnall2) =>
% 96.58/13.15 ((
% 96.58/13.15 (ex1E2) =>
% 96.58/13.15 ((
% 96.58/13.15 (funcGraphProp1) =>
% 96.58/13.15 ((
% 96.58/13.15 (funcGraphProp3) =>
% 96.58/13.15 ((
% 96.58/13.15 (funcGraphProp2) =>
% 96.58/13.15 ((
% 96.58/13.15 (funcextLem) =>
% 96.58/13.15 ((
% 96.58/13.15 (funcGraphProp4) =>
% 96.58/13.15 ((
% 96.58/13.15 (subbreln) =>
% 96.58/13.15 ((
% 96.58/13.15 (eqbreln) =>
% 96.58/13.15 ((
% 96.58/13.15 (funcext) =>
% 96.58/13.15 ((
% 96.58/13.15 (funcext2) =>
% 96.58/13.15 ((
% 96.58/13.15 (ap2apEq1) =>
% 96.58/13.15 ((
% 96.58/13.15 (ap2apEq2) =>
% 96.58/13.15 ((
% 96.58/13.15 (beta1) =>
% 96.58/13.15 ((
% 96.58/13.15 (eta1) =>
% 96.58/13.15 ((
% 96.58/13.15 (lam2lamEq) =>
% 96.58/13.15 ((
% 96.58/13.15 (beta2) =>
% 96.58/13.15 ((
% 96.58/13.15 (eta2) =>
% 96.58/13.15 ((
% 96.58/13.15 (iffalseProp1) =>
% 96.58/13.15 ((
% 96.58/13.15 (iffalseProp2) =>
% 96.58/13.15 ((
% 96.58/13.15 (iftrueProp1) =>
% 96.58/13.15 ((
% 96.58/13.15 (iftrueProp2) =>
% 96.58/13.15 ((
% 96.58/13.15 (ifSingleton) =>
% 96.58/13.15 ((
% 96.58/13.15 (ifp) =>
% 96.58/13.15 ((
% 96.58/13.15 (theeq) =>
% 96.58/13.15 ((
% 96.58/13.15 (iftrue) =>
% 96.58/13.15 ((
% 96.58/13.15 (iffalse) =>
% 96.58/13.15 ((
% 96.58/13.15 (iftrueorfalse) =>
% 96.58/13.15 ((
% 96.58/13.15 (binintersectT_lem) =>
% 96.58/13.15 ((
% 96.58/13.15 (binunionT_lem) =>
% 96.58/13.15 ((
% 96.58/13.15 (powersetT_lem) =>
% 96.58/13.15 ((
% 96.58/13.15 (setminusT_lem) =>
% 96.58/13.15 ((
% 96.58/13.15 (complementT_lem) =>
% 96.58/13.15 ((
% 96.58/13.15 (setextT) =>
% 96.58/13.15 ((
% 96.58/13.15 (subsetTI) =>
% 96.58/13.15 ((
% 96.58/13.15 (powersetTI1) =>
% 96.58/13.15 ((
% 96.58/13.15 (powersetTE1) =>
% 96.58/13.15 ((
% 96.58/13.15 (complementTI1) =>
% 96.58/13.15 ((
% 96.58/13.15 (complementTE1) =>
% 96.58/13.15 ((
% 96.58/13.15 (binintersectTELcontra) =>
% 96.58/13.15 ((
% 96.58/13.15 (binintersectTERcontra) =>
% 96.58/13.15 ((
% 96.58/13.15 (contrasubsetT) =>
% 96.58/13.15 ((
% 96.58/13.15 (contrasubsetT1) =>
% 96.58/13.15 ((
% 96.58/13.15 (contrasubsetT2) =>
% 96.58/13.15 ((
% 96.58/13.15 (contrasubsetT3) =>
% 96.58/13.15 ((
% 96.58/13.15 (doubleComplementI1) =>
% 96.58/13.15 ((
% 96.58/13.15 (doubleComplementE1) =>
% 96.58/13.15 ((
% 96.58/13.15 (doubleComplementSub1) =>
% 96.58/13.15 ((
% 96.58/13.15 (doubleComplementSub2) =>
% 96.58/13.15 ((
% 96.58/13.15 (doubleComplementEq) =>
% 96.58/13.15 ((
% 96.58/13.15 (complementTnotintersectT) =>
% 96.58/13.15 ((
% 96.58/13.15 (complementImpComplementIntersect) =>
% 96.58/13.15 ((
% 96.58/13.15 (complementSubsetComplementIntersect) =>
% 96.58/13.15 ((
% 96.58/13.15 (complementInPowersetComplementIntersect) =>
% 96.58/13.15 ((
% 96.58/13.15 (contraSubsetComplement) =>
% 96.58/13.15 ((
% 96.58/13.15 (complementTcontraSubset) =>
% 96.58/13.15 ((
% 96.58/13.15 (binunionTILcontra) =>
% 96.58/13.15 ((
% 96.58/13.15 (binunionTIRcontra) =>
% 96.58/13.15 ((
% 96.58/13.15 (inIntersectImpInUnion) =>
% 96.58/13.15 ((
% 96.58/13.15 (inIntersectImpInUnion2) =>
% 96.58/13.15 ((
% 96.58/13.15 (inIntersectImpInIntersectUnions) =>
% 96.58/13.15 ((
% 96.58/13.15 (intersectInPowersetIntersectUnions) =>
% 96.58/13.15 ((
% 96.58/13.15 (inComplementUnionImpNotIn1) =>
% 96.58/13.15 ((
% 96.58/13.15 (inComplementUnionImpInComplement1) =>
% 96.58/13.15 ((
% 96.58/13.15 (binunionTE) =>
% 96.58/13.15 ((
% 96.58/13.15 (binunionTEcontra) =>
% 96.58/13.15 ((
% 96.58/13.15 (demorgan2a1) =>
% 96.58/13.15 ((
% 96.58/13.15 (complementUnionInPowersetComplement) =>
% 96.58/13.15 ((
% 96.58/13.15 (demorgan2a2) =>
% 96.58/13.15 ((
% 96.58/13.15 (demorgan1a) =>
% 96.58/13.15 ((
% 96.58/13.15 (demorgan1b) =>
% 96.58/13.15 ((
% 96.58/13.15 (demorgan1) =>
% 96.58/13.15 ((
% 96.58/13.15 (demorgan2a) =>
% 96.58/13.15 ((
% 96.58/13.15 (demorgan2b2) =>
% 96.58/13.15 ((
% 96.58/13.15 (demorgan2b) =>
% 96.58/13.15 ((
% 96.58/13.15 (demorgan2) =>
% 96.58/13.15 ((
% 96.58/13.15 (woz13rule0) =>
% 96.58/13.15 ((
% 96.58/13.15 (woz13rule1) =>
% 96.58/13.15 ((
% 96.58/13.15 (woz13rule2) =>
% 96.58/13.15 ((
% 96.58/13.15 (woz13rule3) =>
% 96.58/13.15 ((
% 96.58/13.15 (woz13rule4) =>
% 96.58/13.15 ((
% 96.58/13.15 (woz1_1) =>
% 96.58/13.15 ((
% 96.58/13.15 (woz1_2) =>
% 96.58/13.15 ((
% 96.58/13.15 (woz1_3) =>
% 96.58/13.15 ((
% 96.58/13.15 (woz1_4) =>
% 96.58/13.15 ((
% 96.58/13.15 (woz1_5) =>
% 96.58/13.15 ((
% 96.58/13.15 (breln1all2) =>
% 96.58/13.15 ((
% 96.58/13.15 (breln1SetBreln1) =>
% 96.58/13.15 ((
% 96.58/13.15 (choice2fnsingleton) =>
% 96.58/13.15 ((
% 96.58/13.15 (setOfPairsIsBReln1) =>
% 96.58/13.15 ((
% 96.58/13.15 (breln1all1) =>
% 96.58/13.15 ((
% 96.58/13.15 (subbreln1) =>
% 96.58/13.15 ((
% 96.58/13.15 (eqbreln1) =>
% 96.58/13.15 ((
% 96.58/13.15 (breln1invprop) =>
% 96.58/13.15 ((
% 96.58/13.15 (breln1invI) =>
% 96.58/13.15 ((
% 96.58/13.15 (breln1invE) =>
% 96.58/13.15 ((
% 96.58/13.15 (breln1compprop) =>
% 96.58/13.15 ((
% 96.58/13.15 (breln1compI) =>
% 96.58/13.15 ((
% 96.58/13.15 (breln1compE) =>
% 96.58/13.15 ((
% 96.58/13.15 (breln1compEex) =>
% 96.58/13.15 ((
% 96.58/13.15 (breln1unionprop) =>
% 96.58/13.15 ((
% 96.58/13.15 (breln1unionIL) =>
% 96.58/13.15 ((
% 96.58/13.15 (breln1unionIR) =>
% 96.58/13.15 ((
% 96.58/13.15 (breln1unionI) =>
% 96.58/13.15 ((
% 96.58/13.15 (breln1unionE) =>
% 96.58/13.15 ((
% 96.58/13.15 (breln1unionEcases) =>
% 96.58/13.15 ((
% 96.58/13.15 (breln1unionCommutes) =>
% 96.58/13.15 ((
% 96.58/13.15 (woz2Ex) =>
% 96.58/13.15 ((
% 96.58/13.15 (woz2W) =>
% 96.58/13.15 ((
% 96.58/13.15 (woz2A) =>
% 96.58/13.15 ((
% 96.58/13.15 (woz2B) =>
% 96.58/13.15 ((
% 96.58/13.15 (image1Ex) =>
% 96.58/13.15 ((
% 96.58/13.15 (image1Ex1) =>
% 96.58/13.15 ((
% 96.58/13.15 (image1Equiv) =>
% 96.58/13.15 ((
% 96.58/13.15 (image1E) =>
% 96.58/13.15 ((
% 96.58/13.15 (image1I) =>
% 96.58/13.15 ((
% 96.58/13.15 (injFuncInInjFuncSet) =>
% 96.58/13.15 ((
% 96.58/13.15 (injFuncSetFuncIn) =>
% 96.58/13.15 ((
% 96.58/13.15 (injFuncSetFuncInj) =>
% 96.58/13.15 ((
% 96.58/13.15 (surjFuncSetFuncIn) =>
% 96.58/13.15 ((
% 96.58/13.15 (surjFuncSetFuncSurj) =>
% 96.58/13.15 ((
% 96.58/13.15 (leftInvIsSurj) =>
% 96.58/13.15 ((
% 96.58/13.15 (surjCantorThm) =>
% 96.58/13.15 ((
% 96.58/13.15 (foundation2) =>
% 96.58/13.15 ((
% 96.58/13.15 (notinself) =>
% 96.58/13.15 ((
% 96.58/13.15 (notinself2) =>
% 96.58/13.15 ((
% 96.58/13.15 (omegaSp) =>
% 96.58/13.15 ((
% 96.58/13.15 (omegaSclos) =>
% 96.58/13.15 ((
% 96.58/13.15 (peano0notS) =>
% 96.58/13.15 ((
% 96.58/13.15 (!!) @ (
% 96.58/13.15 (('#S') @ (
% 96.58/13.15 (
% 96.58/13.15 ('#B') @ (
% 96.58/13.15 =>) @
% 96.58/13.15 (
% 96.58/13.15 (
% 96.58/13.15 ('#C') @ in @
% 96.58/13.15 omega)))) @
% 96.58/13.15 (
% 96.58/13.15 (
% 96.58/13.15 ('#B') @ (
% 96.58/13.15 !!) @
% 96.58/13.15 (
% 96.58/13.15 (
% 96.58/13.15 ('#B') @ (
% 96.58/13.15 (
% 96.58/13.15 ('#S') @ (
% 96.58/13.15 (
% 96.58/13.15 ('#B') @ (
% 96.58/13.15 =>) @
% 96.58/13.15 (
% 96.58/13.15 (
% 96.58/13.15 ('#C') @ in @
% 96.58/13.15 omega)))))) @
% 96.58/13.15 (
% 96.58/13.15 (
% 96.58/13.15 ('#S') @ (
% 96.58/13.15 (
% 96.58/13.15 ('#B') @ (
% 96.58/13.15 '#S') @
% 96.58/13.15 (
% 96.58/13.15 (
% 96.58/13.15 ('#B') @ (
% 96.58/13.15 (
% 96.58/13.15 ('#B') @ (
% 96.58/13.15 =>))) @
% 96.58/13.15 (
% 96.58/13.15 (
% 96.58/13.15 ('#C') @ (
% 96.58/13.15 (
% 96.58/13.15 ('#B') @ (
% 96.58/13.15 '#B') @
% 96.58/13.15 (
% 96.58/13.15 (
% 96.58/13.15 ('#B') @ (
% 96.58/13.15 =) @
% 96.58/13.15 omegaS)))) @
% 96.58/13.15 omegaS)))))) @
% 96.58/13.15 (
% 96.58/13.15 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 96.58/13.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl58])).
% 96.58/13.15 thf(zip_derived_cl71, plain,
% 96.58/13.15 (~ (((dsetconstrI) =>
% 96.58/13.15 (((dsetconstrEL) =>
% 96.58/13.15 (((dsetconstrER) =>
% 96.58/13.15 (((exuE1) =>
% 96.58/13.15 (((prop2setE) =>
% 96.58/13.15 (((emptysetE) =>
% 96.58/13.15 (((emptysetimpfalse) =>
% 96.58/13.15 (((notinemptyset) =>
% 96.58/13.15 (((exuE3e) =>
% 96.58/13.15 (((setext) =>
% 96.58/13.15 (((emptyI) =>
% 96.58/13.15 (((noeltsimpempty) =>
% 96.58/13.15 (((setbeta) =>
% 96.58/13.15 (((nonemptyE1) =>
% 96.58/13.15 (((nonemptyI) =>
% 96.58/13.15 (((nonemptyI1) =>
% 96.58/13.15 (((setadjoinIL) =>
% 96.58/13.15 (((in @ emptyset @
% 96.58/13.15 (setadjoin @ emptyset @ emptyset)) =>
% 96.58/13.15 (((setadjoinIR) =>
% 96.58/13.15 (((setadjoinE) =>
% 96.58/13.15 (((setadjoinOr) =>
% 96.58/13.15 (((setoftrueEq) =>
% 96.58/13.15 (((powersetI) =>
% 96.58/13.15 (((emptyinPowerset) =>
% 96.58/13.15 (((emptyInPowerset) =>
% 96.58/13.15 (((powersetE) =>
% 96.58/13.15 (((setunionI) =>
% 96.58/13.15 (((setunionE) =>
% 96.58/13.15 (((subPowSU) =>
% 96.58/13.15 (((exuE2) =>
% 96.58/13.15 ((
% 96.58/13.15 (nonemptyImpWitness) =>
% 96.58/13.15 ((
% 96.58/13.15 (uniqinunit) =>
% 96.58/13.15 ((
% 96.58/13.15 (notinsingleton) =>
% 96.58/13.15 ((
% 96.58/13.15 (eqinunit) =>
% 96.58/13.15 ((
% 96.58/13.15 (singletonsswitch) =>
% 96.58/13.15 ((
% 96.58/13.15 (upairsetE) =>
% 96.58/13.15 ((
% 96.58/13.15 (upairsetIL) =>
% 96.58/13.15 ((
% 96.58/13.15 (upairsetIR) =>
% 96.58/13.15 ((
% 96.58/13.15 (emptyE1) =>
% 96.58/13.15 ((
% 96.58/13.15 (vacuousDall) =>
% 96.58/13.15 ((
% 96.58/13.15 (quantDeMorgan1) =>
% 96.58/13.15 ((
% 96.58/13.15 (quantDeMorgan2) =>
% 96.58/13.15 ((
% 96.58/13.15 (quantDeMorgan3) =>
% 96.58/13.15 ((
% 96.58/13.15 (quantDeMorgan4) =>
% 96.58/13.15 ((
% 96.58/13.15 (prop2setI) =>
% 96.58/13.15 ((
% 96.58/13.15 (prop2set2propI) =>
% 96.58/13.15 ((
% 96.58/13.15 (notdexE) =>
% 96.58/13.15 ((
% 96.58/13.15 (notdallE) =>
% 96.58/13.15 ((
% 96.58/13.15 (exuI1) =>
% 96.58/13.15 ((
% 96.58/13.15 (exuI3) =>
% 96.58/13.15 ((
% 96.58/13.15 (exuI2) =>
% 96.58/13.15 ((
% 96.58/13.15 (inCongP) =>
% 96.58/13.15 ((
% 96.58/13.15 (in__Cong) =>
% 96.58/13.15 ((
% 96.58/13.15 (exuE3u) =>
% 96.58/13.15 ((
% 96.58/13.15 (exu__Cong) =>
% 96.58/13.15 ((
% 96.58/13.15 (setadjoin__Cong) =>
% 96.58/13.15 ((
% 96.58/13.15 (powerset__Cong) =>
% 96.58/13.15 ((
% 96.58/13.15 (setunion__Cong) =>
% 96.58/13.15 ((
% 96.58/13.15 (exuEu) =>
% 96.58/13.15 ((
% 96.58/13.15 (descr__Cong) =>
% 96.58/13.15 ((
% 96.58/13.15 (dsetconstr__Cong) =>
% 96.58/13.15 ((
% 96.58/13.15 (subsetI1) =>
% 96.58/13.15 ((
% 96.58/13.15 (eqimpsubset2) =>
% 96.58/13.15 ((
% 96.58/13.15 (eqimpsubset1) =>
% 96.58/13.15 ((
% 96.58/13.15 (subsetI2) =>
% 96.58/13.15 ((
% 96.58/13.15 (emptysetsubset) =>
% 96.58/13.15 ((
% 96.58/13.15 (subsetE) =>
% 96.58/13.15 ((
% 96.58/13.15 (subsetE2) =>
% 96.58/13.15 ((
% 96.58/13.15 (notsubsetI) =>
% 96.58/13.15 ((
% 96.58/13.15 (notequalI1) =>
% 96.58/13.15 ((
% 96.58/13.15 (notequalI2) =>
% 96.58/13.15 ((
% 96.58/13.15 (subsetRefl) =>
% 96.58/13.15 ((
% 96.58/13.15 (subsetTrans) =>
% 96.58/13.15 ((
% 96.58/13.15 (setadjoinSub) =>
% 96.58/13.15 ((
% 96.58/13.15 (setadjoinSub2) =>
% 96.58/13.15 ((
% 96.58/13.15 (subset2powerset) =>
% 96.58/13.15 ((
% 96.58/13.15 (setextsub) =>
% 96.58/13.15 ((
% 96.58/13.15 (subsetemptysetimpeq) =>
% 96.58/13.15 ((
% 96.58/13.15 (powersetI1) =>
% 96.58/13.15 ((
% 96.58/13.15 (powersetE1) =>
% 96.58/13.15 ((
% 96.58/13.15 (inPowerset) =>
% 96.58/13.15 ((
% 96.58/13.15 (powersetsubset) =>
% 96.58/13.15 ((
% 96.58/13.15 (sepInPowerset) =>
% 96.58/13.15 ((
% 96.58/13.15 (sepSubset) =>
% 96.58/13.15 ((
% 96.58/13.15 (binunionIL) =>
% 96.58/13.15 ((
% 96.58/13.15 (upairset2IR) =>
% 96.58/13.15 ((
% 96.58/13.15 (binunionIR) =>
% 96.58/13.15 ((
% 96.58/13.15 (binunionEcases) =>
% 96.58/13.15 ((
% 96.58/13.15 (binunionE) =>
% 96.58/13.15 ((
% 96.58/13.15 (binunionLsub) =>
% 96.58/13.15 ((
% 96.58/13.15 (binunionRsub) =>
% 96.58/13.15 ((
% 96.58/13.15 (binintersectI) =>
% 96.58/13.15 ((
% 96.58/13.15 (binintersectSubset5) =>
% 96.58/13.15 ((
% 96.58/13.15 (binintersectEL) =>
% 96.58/13.15 ((
% 96.58/13.15 (binintersectLsub) =>
% 96.58/13.15 ((
% 96.58/13.15 (binintersectSubset2) =>
% 96.58/13.15 ((
% 96.58/13.15 (binintersectSubset3) =>
% 96.58/13.15 ((
% 96.58/13.15 (binintersectER) =>
% 96.58/13.15 ((
% 96.58/13.15 (disjointsetsI1) =>
% 96.58/13.15 ((
% 96.58/13.15 (binintersectRsub) =>
% 96.58/13.15 ((
% 96.58/13.15 (binintersectSubset4) =>
% 96.58/13.15 ((
% 96.58/13.15 (binintersectSubset1) =>
% 96.58/13.15 ((
% 96.58/13.15 (bs114d) =>
% 96.58/13.15 ((
% 96.58/13.15 (setminusI) =>
% 96.58/13.15 ((
% 96.58/13.15 (setminusEL) =>
% 96.58/13.15 ((
% 96.58/13.15 (setminusER) =>
% 96.58/13.15 ((
% 96.58/13.15 (setminusSubset2) =>
% 96.58/13.15 ((
% 96.58/13.15 (setminusERneg) =>
% 96.58/13.15 ((
% 96.58/13.15 (setminusELneg) =>
% 96.58/13.15 ((
% 96.58/13.15 (setminusILneg) =>
% 96.58/13.15 ((
% 96.58/13.15 (setminusIRneg) =>
% 96.58/13.15 ((
% 96.58/13.15 (setminusLsub) =>
% 96.58/13.15 ((
% 96.58/13.15 (setminusSubset1) =>
% 96.58/13.15 ((
% 96.58/13.15 (symdiffE) =>
% 96.58/13.15 ((
% 96.58/13.15 (symdiffI1) =>
% 96.58/13.15 ((
% 96.58/13.15 (symdiffI2) =>
% 96.58/13.15 ((
% 96.58/13.15 (symdiffIneg1) =>
% 96.58/13.15 ((
% 96.58/13.15 (symdiffIneg2) =>
% 96.58/13.15 ((
% 96.58/13.15 (secondinupair) =>
% 96.58/13.15 ((
% 96.58/13.15 (setukpairIL) =>
% 96.58/13.15 ((
% 96.58/13.15 (setukpairIR) =>
% 96.58/13.15 ((
% 96.58/13.15 (kpairiskpair) =>
% 96.58/13.15 ((
% 96.58/13.15 (kpairp) =>
% 96.58/13.15 ((
% 96.58/13.15 (singletonsubset) =>
% 96.58/13.15 ((
% 96.58/13.15 (singletoninpowerset) =>
% 96.58/13.15 ((
% 96.58/13.15 (singletoninpowunion) =>
% 96.58/13.15 ((
% 96.58/13.15 (upairset2E) =>
% 96.58/13.15 ((
% 96.58/13.15 (upairsubunion) =>
% 96.58/13.15 ((
% 96.58/13.15 (upairinpowunion) =>
% 96.58/13.15 ((
% 96.58/13.15 (ubforcartprodlem1) =>
% 96.58/13.15 ((
% 96.58/13.15 (ubforcartprodlem2) =>
% 96.58/13.15 ((
% 96.58/13.15 (ubforcartprodlem3) =>
% 96.58/13.15 ((
% 96.58/13.15 (cartprodpairin) =>
% 96.58/13.15 ((
% 96.58/13.15 (cartprodmempair1) =>
% 96.58/13.15 ((
% 96.58/13.15 (cartprodmempair) =>
% 96.58/13.15 ((
% 96.58/13.15 (setunionE2) =>
% 96.58/13.15 ((
% 96.58/13.15 (setunionsingleton1) =>
% 96.58/13.15 ((
% 96.58/13.15 (setunionsingleton2) =>
% 96.58/13.15 ((
% 96.58/13.15 (setunionsingleton) =>
% 96.58/13.15 ((
% 96.58/13.15 (singletonprop) =>
% 96.58/13.15 ((
% 96.58/13.15 (ex1E1) =>
% 96.58/13.15 ((
% 96.58/13.15 (ex1I) =>
% 96.58/13.15 ((
% 96.58/13.15 (ex1I2) =>
% 96.58/13.15 ((
% 96.58/13.15 (singletonsuniq) =>
% 96.58/13.15 ((
% 96.58/13.15 (setukpairinjL1) =>
% 96.58/13.15 ((
% 96.58/13.15 (kfstsingleton) =>
% 96.58/13.15 ((
% 96.58/13.15 (theprop) =>
% 96.58/13.15 ((
% 96.58/13.15 (kfstpairEq) =>
% 96.58/13.15 ((
% 96.58/13.15 (cartprodfstin) =>
% 96.58/13.15 ((
% 96.58/13.15 (setukpairinjL2) =>
% 96.58/13.15 ((
% 96.58/13.15 (setukpairinjL) =>
% 96.58/13.15 ((
% 96.58/13.15 (setukpairinjR11) =>
% 96.58/13.15 ((
% 96.58/13.15 (setukpairinjR12) =>
% 96.58/13.15 ((
% 96.58/13.15 (setukpairinjR1) =>
% 96.58/13.15 ((
% 96.58/13.15 (upairequniteq) =>
% 96.58/13.15 ((
% 96.58/13.15 (setukpairinjR2) =>
% 96.58/13.15 ((
% 96.58/13.15 (setukpairinjR) =>
% 96.58/13.15 ((
% 96.58/13.15 (ksndsingleton) =>
% 96.58/13.15 ((
% 96.58/13.15 (ksndpairEq) =>
% 96.58/13.15 ((
% 96.58/13.15 (kpairsurjEq) =>
% 96.58/13.15 ((
% 96.58/13.15 (cartprodsndin) =>
% 96.58/13.15 ((
% 96.58/13.15 (cartprodpairmemEL) =>
% 96.58/13.15 ((
% 96.58/13.15 (cartprodpairmemER) =>
% 96.58/13.15 ((
% 96.58/13.15 (cartprodmempaircEq) =>
% 96.58/13.15 ((
% 96.58/13.15 (cartprodfstpairEq) =>
% 96.58/13.15 ((
% 96.58/13.15 (cartprodsndpairEq) =>
% 96.58/13.15 ((
% 96.58/13.15 (cartprodpairsurjEq) =>
% 96.58/13.15 ((
% 96.58/13.15 (dpsetconstrI) =>
% 96.58/13.15 ((
% 96.58/13.15 (dpsetconstrSub) =>
% 96.58/13.15 ((
% 96.58/13.15 (setOfPairsIsBReln) =>
% 96.58/13.15 ((
% 96.58/13.15 (dpsetconstrERa) =>
% 96.58/13.15 ((
% 96.58/13.15 (dpsetconstrEL1) =>
% 96.58/13.15 ((
% 96.58/13.15 (dpsetconstrEL2) =>
% 96.58/13.15 ((
% 96.58/13.15 (dpsetconstrER) =>
% 96.58/13.15 ((
% 96.58/13.15 (funcImageSingleton) =>
% 96.58/13.15 ((
% 96.58/13.15 (apProp) =>
% 96.58/13.15 ((
% 96.58/13.15 (app) =>
% 96.58/13.15 ((
% 96.58/13.15 (infuncsetfunc) =>
% 96.58/13.15 ((
% 96.58/13.15 (ap2p) =>
% 96.58/13.15 ((
% 96.58/13.15 (funcinfuncset) =>
% 96.58/13.15 ((
% 96.58/13.15 (lamProp) =>
% 96.58/13.15 ((
% 96.58/13.15 (lamp) =>
% 96.58/13.15 ((
% 96.58/13.15 (lam2p) =>
% 96.58/13.15 ((
% 96.58/13.15 (brelnall1) =>
% 96.58/13.15 ((
% 96.58/13.15 (brelnall2) =>
% 96.58/13.15 ((
% 96.58/13.15 (ex1E2) =>
% 96.58/13.15 ((
% 96.58/13.15 (funcGraphProp1) =>
% 96.58/13.15 ((
% 96.58/13.15 (funcGraphProp3) =>
% 96.58/13.15 ((
% 96.58/13.15 (funcGraphProp2) =>
% 96.58/13.15 ((
% 96.58/13.15 (funcextLem) =>
% 96.58/13.15 ((
% 96.58/13.15 (funcGraphProp4) =>
% 96.58/13.15 ((
% 96.58/13.15 (subbreln) =>
% 96.58/13.15 ((
% 96.58/13.15 (eqbreln) =>
% 96.58/13.15 ((
% 96.58/13.15 (funcext) =>
% 96.58/13.15 ((
% 96.58/13.15 (funcext2) =>
% 96.58/13.15 ((
% 96.58/13.15 (ap2apEq1) =>
% 96.58/13.15 ((
% 96.58/13.15 (ap2apEq2) =>
% 96.58/13.15 ((
% 96.58/13.15 (beta1) =>
% 96.58/13.15 ((
% 96.58/13.15 (eta1) =>
% 96.58/13.15 ((
% 96.58/13.15 (lam2lamEq) =>
% 96.58/13.15 ((
% 96.58/13.15 (beta2) =>
% 96.58/13.15 ((
% 96.58/13.15 (eta2) =>
% 96.58/13.15 ((
% 96.58/13.15 (iffalseProp1) =>
% 96.58/13.15 ((
% 96.58/13.15 (iffalseProp2) =>
% 96.58/13.15 ((
% 96.58/13.15 (iftrueProp1) =>
% 96.58/13.15 ((
% 96.58/13.15 (iftrueProp2) =>
% 96.58/13.15 ((
% 96.58/13.15 (ifSingleton) =>
% 96.58/13.15 ((
% 96.58/13.15 (ifp) =>
% 96.58/13.15 ((
% 96.58/13.15 (theeq) =>
% 96.58/13.15 ((
% 96.58/13.15 (iftrue) =>
% 96.58/13.15 ((
% 96.58/13.15 (iffalse) =>
% 96.58/13.15 ((
% 96.58/13.15 (iftrueorfalse) =>
% 96.58/13.15 ((
% 96.58/13.15 (binintersectT_lem) =>
% 96.58/13.15 ((
% 96.58/13.15 (binunionT_lem) =>
% 96.58/13.15 ((
% 96.58/13.15 (powersetT_lem) =>
% 96.58/13.15 ((
% 96.58/13.15 (setminusT_lem) =>
% 96.58/13.15 ((
% 96.58/13.15 (complementT_lem) =>
% 96.58/13.15 ((
% 96.58/13.15 (setextT) =>
% 96.58/13.15 ((
% 96.58/13.15 (subsetTI) =>
% 96.58/13.15 ((
% 96.58/13.15 (powersetTI1) =>
% 96.58/13.15 ((
% 96.58/13.15 (powersetTE1) =>
% 96.58/13.15 ((
% 96.58/13.15 (complementTI1) =>
% 96.58/13.15 ((
% 96.58/13.15 (complementTE1) =>
% 96.58/13.15 ((
% 96.58/13.15 (binintersectTELcontra) =>
% 96.58/13.15 ((
% 96.58/13.15 (binintersectTERcontra) =>
% 96.58/13.15 ((
% 96.58/13.15 (contrasubsetT) =>
% 96.58/13.15 ((
% 96.58/13.15 (contrasubsetT1) =>
% 96.58/13.15 ((
% 96.58/13.15 (contrasubsetT2) =>
% 96.58/13.15 ((
% 96.58/13.15 (contrasubsetT3) =>
% 96.58/13.15 ((
% 96.58/13.15 (doubleComplementI1) =>
% 96.58/13.15 ((
% 96.58/13.15 (doubleComplementE1) =>
% 96.58/13.15 ((
% 96.58/13.15 (doubleComplementSub1) =>
% 96.58/13.15 ((
% 96.58/13.15 (doubleComplementSub2) =>
% 96.58/13.15 ((
% 96.58/13.15 (doubleComplementEq) =>
% 96.58/13.15 ((
% 96.58/13.15 (complementTnotintersectT) =>
% 96.58/13.15 ((
% 96.58/13.15 (complementImpComplementIntersect) =>
% 96.58/13.15 ((
% 96.58/13.15 (complementSubsetComplementIntersect) =>
% 96.58/13.15 ((
% 96.58/13.15 (complementInPowersetComplementIntersect) =>
% 96.58/13.15 ((
% 96.58/13.15 (contraSubsetComplement) =>
% 96.58/13.15 ((
% 96.58/13.15 (complementTcontraSubset) =>
% 96.58/13.15 ((
% 96.58/13.15 (binunionTILcontra) =>
% 96.58/13.15 ((
% 96.58/13.15 (binunionTIRcontra) =>
% 96.58/13.15 ((
% 96.58/13.15 (inIntersectImpInUnion) =>
% 96.58/13.15 ((
% 96.58/13.15 (inIntersectImpInUnion2) =>
% 96.58/13.15 ((
% 96.58/13.15 (inIntersectImpInIntersectUnions) =>
% 96.58/13.15 ((
% 96.58/13.15 (intersectInPowersetIntersectUnions) =>
% 96.58/13.15 ((
% 96.58/13.15 (inComplementUnionImpNotIn1) =>
% 96.58/13.15 ((
% 96.58/13.15 (inComplementUnionImpInComplement1) =>
% 96.58/13.15 ((
% 96.58/13.15 (binunionTE) =>
% 96.58/13.15 ((
% 96.58/13.15 (binunionTEcontra) =>
% 96.58/13.15 ((
% 96.58/13.15 (demorgan2a1) =>
% 96.58/13.15 ((
% 96.58/13.15 (complementUnionInPowersetComplement) =>
% 96.58/13.15 ((
% 96.58/13.15 (demorgan2a2) =>
% 96.58/13.15 ((
% 96.58/13.15 (demorgan1a) =>
% 96.58/13.15 ((
% 96.58/13.15 (demorgan1b) =>
% 96.58/13.15 ((
% 96.58/13.15 (demorgan1) =>
% 96.58/13.15 ((
% 96.58/13.15 (demorgan2a) =>
% 96.58/13.15 ((
% 96.58/13.15 (demorgan2b2) =>
% 96.58/13.15 ((
% 96.58/13.15 (demorgan2b) =>
% 96.58/13.15 ((
% 96.58/13.15 (demorgan2) =>
% 96.58/13.15 ((
% 96.58/13.15 (woz13rule0) =>
% 96.58/13.15 ((
% 96.58/13.15 (woz13rule1) =>
% 96.58/13.15 ((
% 96.58/13.15 (woz13rule2) =>
% 96.58/13.15 ((
% 96.58/13.15 (woz13rule3) =>
% 96.58/13.15 ((
% 96.58/13.15 (woz13rule4) =>
% 96.58/13.15 ((
% 96.58/13.15 (woz1_1) =>
% 96.58/13.15 ((
% 96.58/13.15 (woz1_2) =>
% 96.58/13.15 ((
% 96.58/13.15 (woz1_3) =>
% 96.58/13.15 ((
% 96.58/13.15 (woz1_4) =>
% 96.58/13.15 ((
% 96.58/13.15 (woz1_5) =>
% 96.58/13.15 ((
% 96.58/13.15 (breln1all2) =>
% 96.58/13.15 ((
% 96.58/13.15 (breln1SetBreln1) =>
% 96.58/13.15 ((
% 96.58/13.15 (choice2fnsingleton) =>
% 96.58/13.15 ((
% 96.58/13.15 (setOfPairsIsBReln1) =>
% 96.58/13.15 ((
% 96.58/13.15 (breln1all1) =>
% 96.58/13.15 ((
% 96.58/13.15 (subbreln1) =>
% 96.58/13.15 ((
% 96.58/13.15 (eqbreln1) =>
% 96.58/13.15 ((
% 96.58/13.15 (breln1invprop) =>
% 96.58/13.15 ((
% 96.58/13.15 (breln1invI) =>
% 96.58/13.15 ((
% 96.58/13.15 (breln1invE) =>
% 96.58/13.15 ((
% 96.58/13.15 (breln1compprop) =>
% 96.58/13.15 ((
% 96.58/13.15 (breln1compI) =>
% 96.58/13.15 ((
% 96.58/13.15 (breln1compE) =>
% 96.58/13.15 ((
% 96.58/13.15 (breln1compEex) =>
% 96.58/13.15 ((
% 96.58/13.15 (breln1unionprop) =>
% 96.58/13.15 ((
% 96.58/13.15 (breln1unionIL) =>
% 96.58/13.15 ((
% 96.58/13.15 (breln1unionIR) =>
% 96.58/13.15 ((
% 96.58/13.15 (breln1unionI) =>
% 96.58/13.15 ((
% 96.58/13.15 (breln1unionE) =>
% 96.58/13.15 ((
% 96.58/13.15 (breln1unionEcases) =>
% 96.58/13.15 ((
% 96.58/13.15 (breln1unionCommutes) =>
% 96.58/13.15 ((
% 96.58/13.15 (woz2Ex) =>
% 96.58/13.15 ((
% 96.58/13.15 (woz2W) =>
% 96.58/13.15 ((
% 96.58/13.15 (woz2A) =>
% 96.58/13.15 ((
% 96.58/13.15 (woz2B) =>
% 96.58/13.15 ((
% 96.58/13.15 (image1Ex) =>
% 96.58/13.15 ((
% 96.58/13.15 (image1Ex1) =>
% 96.58/13.15 ((
% 96.58/13.15 (image1Equiv) =>
% 96.58/13.15 ((
% 96.58/13.15 (image1E) =>
% 96.58/13.15 ((
% 96.58/13.15 (image1I) =>
% 96.58/13.15 ((
% 96.58/13.15 (injFuncInInjFuncSet) =>
% 96.58/13.15 ((
% 96.58/13.15 (injFuncSetFuncIn) =>
% 96.58/13.15 ((
% 96.58/13.15 (injFuncSetFuncInj) =>
% 96.58/13.15 ((
% 96.58/13.15 (surjFuncSetFuncIn) =>
% 96.58/13.15 ((
% 96.58/13.15 (surjFuncSetFuncSurj) =>
% 96.58/13.15 ((
% 96.58/13.15 (leftInvIsSurj) =>
% 96.58/13.15 ((
% 96.58/13.15 (surjCantorThm) =>
% 96.58/13.15 ((
% 96.58/13.15 (foundation2) =>
% 96.58/13.15 ((
% 96.58/13.15 (notinself) =>
% 96.58/13.15 ((
% 96.58/13.15 (notinself2) =>
% 96.58/13.15 ((
% 96.58/13.15 (omegaSp) =>
% 96.58/13.15 ((
% 96.58/13.15 (omegaSclos) =>
% 96.58/13.15 ((
% 96.58/13.15 (peano0notS) =>
% 96.58/13.15 ((
% 96.58/13.15 (!!) @ (
% 96.58/13.15 (('#S') @ (
% 96.58/13.15 (
% 96.58/13.15 ('#B') @ (
% 96.58/13.15 =>) @
% 96.58/13.15 (
% 96.58/13.15 (
% 96.58/13.15 ('#C') @ in @
% 96.58/13.15 omega)))) @
% 96.58/13.15 (
% 96.58/13.15 (
% 96.58/13.15 ('#B') @ (
% 96.58/13.15 !!) @
% 96.58/13.15 (
% 96.58/13.15 (
% 96.58/13.15 ('#B') @ (
% 96.58/13.15 (
% 96.58/13.15 ('#S') @ (
% 96.58/13.15 (
% 96.58/13.15 ('#B') @ (
% 96.58/13.15 =>) @
% 96.58/13.15 (
% 96.58/13.15 (
% 96.58/13.15 ('#C') @ in @
% 96.58/13.15 omega)))))) @
% 96.58/13.15 (
% 96.58/13.15 (
% 96.58/13.15 ('#S') @ (
% 96.58/13.15 (
% 96.58/13.15 ('#B') @ (
% 96.58/13.15 '#S') @
% 96.58/13.15 (
% 96.58/13.15 (
% 96.58/13.15 ('#B') @ (
% 96.58/13.15 (
% 96.58/13.15 ('#B') @ (
% 96.58/13.15 =>))) @
% 96.58/13.15 (
% 96.58/13.15 (
% 96.58/13.15 ('#C') @ (
% 96.58/13.15 (
% 96.58/13.15 ('#B') @ (
% 96.58/13.15 '#B') @
% 96.58/13.15 (
% 96.58/13.15 (
% 96.58/13.15 ('#B') @ (
% 96.58/13.15 =) @
% 96.58/13.15 omegaS)))) @
% 96.58/13.15 omegaS)))))) @
% 96.58/13.15 (
% 96.58/13.15 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 96.58/13.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl64])).
% 96.58/13.15 thf(zip_derived_cl79, plain,
% 96.58/13.15 (~ (((dsetconstrEL) =>
% 96.58/13.15 (((dsetconstrER) =>
% 96.58/13.15 (((exuE1) =>
% 96.58/13.15 (((prop2setE) =>
% 96.58/13.15 (((emptysetE) =>
% 96.58/13.15 (((emptysetimpfalse) =>
% 96.58/13.15 (((notinemptyset) =>
% 96.58/13.15 (((exuE3e) =>
% 96.58/13.15 (((setext) =>
% 96.58/13.15 (((emptyI) =>
% 96.58/13.15 (((noeltsimpempty) =>
% 96.58/13.15 (((setbeta) =>
% 96.58/13.15 (((nonemptyE1) =>
% 96.58/13.15 (((nonemptyI) =>
% 96.58/13.15 (((nonemptyI1) =>
% 96.58/13.15 (((setadjoinIL) =>
% 96.58/13.15 (((in @ emptyset @
% 96.58/13.15 (setadjoin @ emptyset @ emptyset)) =>
% 96.58/13.15 (((setadjoinIR) =>
% 96.58/13.15 (((setadjoinE) =>
% 96.58/13.15 (((setadjoinOr) =>
% 96.58/13.15 (((setoftrueEq) =>
% 96.58/13.15 (((powersetI) =>
% 96.58/13.15 (((emptyinPowerset) =>
% 96.58/13.15 (((emptyInPowerset) =>
% 96.58/13.15 (((powersetE) =>
% 96.58/13.15 (((setunionI) =>
% 96.58/13.15 (((setunionE) =>
% 96.58/13.15 (((subPowSU) =>
% 96.58/13.15 (((exuE2) =>
% 96.58/13.15 (((nonemptyImpWitness) =>
% 96.58/13.15 ((
% 96.58/13.15 (uniqinunit) =>
% 96.58/13.15 ((
% 96.58/13.15 (notinsingleton) =>
% 96.58/13.15 ((
% 96.58/13.15 (eqinunit) =>
% 96.58/13.15 ((
% 96.58/13.15 (singletonsswitch) =>
% 96.58/13.15 ((
% 96.58/13.15 (upairsetE) =>
% 96.58/13.15 ((
% 96.58/13.15 (upairsetIL) =>
% 96.58/13.15 ((
% 96.58/13.15 (upairsetIR) =>
% 96.58/13.15 ((
% 96.58/13.15 (emptyE1) =>
% 96.58/13.15 ((
% 96.58/13.15 (vacuousDall) =>
% 96.58/13.15 ((
% 96.58/13.15 (quantDeMorgan1) =>
% 96.58/13.15 ((
% 96.58/13.15 (quantDeMorgan2) =>
% 96.58/13.15 ((
% 96.58/13.15 (quantDeMorgan3) =>
% 96.58/13.15 ((
% 96.58/13.15 (quantDeMorgan4) =>
% 96.58/13.15 ((
% 96.58/13.15 (prop2setI) =>
% 96.58/13.15 ((
% 96.58/13.15 (prop2set2propI) =>
% 96.58/13.15 ((
% 96.58/13.15 (notdexE) =>
% 96.58/13.15 ((
% 96.58/13.15 (notdallE) =>
% 96.58/13.15 ((
% 96.58/13.15 (exuI1) =>
% 96.58/13.15 ((
% 96.58/13.15 (exuI3) =>
% 96.58/13.15 ((
% 96.58/13.15 (exuI2) =>
% 96.58/13.15 ((
% 96.58/13.15 (inCongP) =>
% 96.58/13.15 ((
% 96.58/13.15 (in__Cong) =>
% 96.58/13.15 ((
% 96.58/13.15 (exuE3u) =>
% 96.58/13.15 ((
% 96.58/13.15 (exu__Cong) =>
% 96.58/13.15 ((
% 96.58/13.15 (setadjoin__Cong) =>
% 96.58/13.15 ((
% 96.58/13.15 (powerset__Cong) =>
% 96.58/13.15 ((
% 96.58/13.15 (setunion__Cong) =>
% 96.58/13.15 ((
% 96.58/13.15 (exuEu) =>
% 96.58/13.15 ((
% 96.58/13.15 (descr__Cong) =>
% 96.58/13.15 ((
% 96.58/13.15 (dsetconstr__Cong) =>
% 96.58/13.15 ((
% 96.58/13.15 (subsetI1) =>
% 96.58/13.15 ((
% 96.58/13.15 (eqimpsubset2) =>
% 96.58/13.15 ((
% 96.58/13.15 (eqimpsubset1) =>
% 96.58/13.15 ((
% 96.58/13.15 (subsetI2) =>
% 96.58/13.15 ((
% 96.58/13.15 (emptysetsubset) =>
% 96.58/13.15 ((
% 96.58/13.15 (subsetE) =>
% 96.58/13.15 ((
% 96.58/13.15 (subsetE2) =>
% 96.58/13.15 ((
% 96.58/13.15 (notsubsetI) =>
% 96.58/13.15 ((
% 96.58/13.15 (notequalI1) =>
% 96.58/13.15 ((
% 96.58/13.15 (notequalI2) =>
% 96.58/13.15 ((
% 96.58/13.15 (subsetRefl) =>
% 96.58/13.15 ((
% 96.58/13.15 (subsetTrans) =>
% 96.58/13.15 ((
% 96.58/13.15 (setadjoinSub) =>
% 96.58/13.15 ((
% 96.58/13.15 (setadjoinSub2) =>
% 96.58/13.15 ((
% 96.58/13.15 (subset2powerset) =>
% 96.58/13.15 ((
% 96.58/13.15 (setextsub) =>
% 96.58/13.15 ((
% 96.58/13.15 (subsetemptysetimpeq) =>
% 96.58/13.15 ((
% 96.58/13.15 (powersetI1) =>
% 96.58/13.15 ((
% 96.58/13.15 (powersetE1) =>
% 96.58/13.15 ((
% 96.58/13.15 (inPowerset) =>
% 96.58/13.15 ((
% 96.58/13.15 (powersetsubset) =>
% 96.58/13.15 ((
% 96.58/13.15 (sepInPowerset) =>
% 96.58/13.15 ((
% 96.58/13.15 (sepSubset) =>
% 96.58/13.15 ((
% 96.58/13.15 (binunionIL) =>
% 96.58/13.15 ((
% 96.58/13.15 (upairset2IR) =>
% 96.58/13.15 ((
% 96.58/13.15 (binunionIR) =>
% 96.58/13.15 ((
% 96.58/13.15 (binunionEcases) =>
% 96.58/13.15 ((
% 96.58/13.15 (binunionE) =>
% 96.58/13.15 ((
% 96.58/13.15 (binunionLsub) =>
% 96.58/13.15 ((
% 96.58/13.15 (binunionRsub) =>
% 96.58/13.15 ((
% 96.58/13.15 (binintersectI) =>
% 96.58/13.15 ((
% 96.58/13.15 (binintersectSubset5) =>
% 96.58/13.15 ((
% 96.58/13.15 (binintersectEL) =>
% 96.58/13.15 ((
% 96.58/13.15 (binintersectLsub) =>
% 96.58/13.15 ((
% 96.58/13.15 (binintersectSubset2) =>
% 96.58/13.15 ((
% 96.58/13.15 (binintersectSubset3) =>
% 96.58/13.15 ((
% 96.58/13.15 (binintersectER) =>
% 96.58/13.15 ((
% 96.58/13.15 (disjointsetsI1) =>
% 96.58/13.15 ((
% 96.58/13.15 (binintersectRsub) =>
% 96.58/13.15 ((
% 96.58/13.15 (binintersectSubset4) =>
% 96.58/13.15 ((
% 96.58/13.15 (binintersectSubset1) =>
% 96.58/13.15 ((
% 96.58/13.15 (bs114d) =>
% 96.58/13.15 ((
% 96.58/13.15 (setminusI) =>
% 96.58/13.15 ((
% 96.58/13.15 (setminusEL) =>
% 96.58/13.15 ((
% 96.58/13.15 (setminusER) =>
% 96.58/13.15 ((
% 96.58/13.15 (setminusSubset2) =>
% 96.58/13.15 ((
% 96.58/13.15 (setminusERneg) =>
% 96.58/13.15 ((
% 96.58/13.15 (setminusELneg) =>
% 96.58/13.15 ((
% 96.58/13.15 (setminusILneg) =>
% 96.58/13.15 ((
% 96.58/13.15 (setminusIRneg) =>
% 96.58/13.15 ((
% 96.58/13.15 (setminusLsub) =>
% 96.58/13.15 ((
% 96.58/13.15 (setminusSubset1) =>
% 96.58/13.15 ((
% 96.58/13.15 (symdiffE) =>
% 96.58/13.15 ((
% 96.58/13.15 (symdiffI1) =>
% 96.58/13.15 ((
% 96.58/13.15 (symdiffI2) =>
% 96.58/13.15 ((
% 96.58/13.15 (symdiffIneg1) =>
% 96.58/13.15 ((
% 96.58/13.15 (symdiffIneg2) =>
% 96.58/13.15 ((
% 96.58/13.15 (secondinupair) =>
% 96.58/13.15 ((
% 96.58/13.15 (setukpairIL) =>
% 96.58/13.15 ((
% 96.58/13.15 (setukpairIR) =>
% 96.58/13.15 ((
% 96.58/13.15 (kpairiskpair) =>
% 96.58/13.15 ((
% 96.58/13.15 (kpairp) =>
% 96.58/13.15 ((
% 96.58/13.15 (singletonsubset) =>
% 96.58/13.15 ((
% 96.58/13.15 (singletoninpowerset) =>
% 96.58/13.15 ((
% 96.58/13.15 (singletoninpowunion) =>
% 96.58/13.15 ((
% 96.58/13.15 (upairset2E) =>
% 96.58/13.15 ((
% 96.58/13.15 (upairsubunion) =>
% 96.58/13.15 ((
% 96.58/13.15 (upairinpowunion) =>
% 96.58/13.15 ((
% 96.58/13.15 (ubforcartprodlem1) =>
% 96.58/13.15 ((
% 96.58/13.15 (ubforcartprodlem2) =>
% 96.58/13.15 ((
% 96.58/13.15 (ubforcartprodlem3) =>
% 96.58/13.15 ((
% 96.58/13.15 (cartprodpairin) =>
% 96.58/13.15 ((
% 96.58/13.15 (cartprodmempair1) =>
% 96.58/13.15 ((
% 96.58/13.15 (cartprodmempair) =>
% 96.58/13.15 ((
% 96.58/13.15 (setunionE2) =>
% 96.58/13.15 ((
% 96.58/13.15 (setunionsingleton1) =>
% 96.58/13.15 ((
% 96.58/13.15 (setunionsingleton2) =>
% 96.58/13.15 ((
% 96.58/13.15 (setunionsingleton) =>
% 96.58/13.15 ((
% 96.58/13.15 (singletonprop) =>
% 96.58/13.15 ((
% 96.58/13.15 (ex1E1) =>
% 96.58/13.15 ((
% 96.58/13.15 (ex1I) =>
% 96.58/13.15 ((
% 96.58/13.15 (ex1I2) =>
% 96.58/13.15 ((
% 96.58/13.15 (singletonsuniq) =>
% 96.58/13.15 ((
% 96.58/13.15 (setukpairinjL1) =>
% 96.58/13.15 ((
% 96.58/13.15 (kfstsingleton) =>
% 96.58/13.15 ((
% 96.58/13.15 (theprop) =>
% 96.58/13.15 ((
% 96.58/13.15 (kfstpairEq) =>
% 96.58/13.15 ((
% 96.58/13.15 (cartprodfstin) =>
% 96.58/13.15 ((
% 96.58/13.15 (setukpairinjL2) =>
% 96.58/13.15 ((
% 96.58/13.15 (setukpairinjL) =>
% 96.58/13.15 ((
% 96.58/13.15 (setukpairinjR11) =>
% 96.58/13.15 ((
% 96.58/13.15 (setukpairinjR12) =>
% 96.58/13.15 ((
% 96.58/13.15 (setukpairinjR1) =>
% 96.58/13.15 ((
% 96.58/13.15 (upairequniteq) =>
% 96.58/13.15 ((
% 96.58/13.15 (setukpairinjR2) =>
% 96.58/13.15 ((
% 96.58/13.15 (setukpairinjR) =>
% 96.58/13.15 ((
% 96.58/13.15 (ksndsingleton) =>
% 96.58/13.15 ((
% 96.58/13.15 (ksndpairEq) =>
% 96.58/13.15 ((
% 96.58/13.15 (kpairsurjEq) =>
% 96.58/13.15 ((
% 96.58/13.15 (cartprodsndin) =>
% 96.58/13.15 ((
% 96.58/13.15 (cartprodpairmemEL) =>
% 96.58/13.15 ((
% 96.58/13.15 (cartprodpairmemER) =>
% 96.58/13.15 ((
% 96.58/13.15 (cartprodmempaircEq) =>
% 96.58/13.15 ((
% 96.58/13.15 (cartprodfstpairEq) =>
% 96.58/13.15 ((
% 96.58/13.15 (cartprodsndpairEq) =>
% 96.58/13.15 ((
% 96.58/13.15 (cartprodpairsurjEq) =>
% 96.58/13.15 ((
% 96.58/13.15 (dpsetconstrI) =>
% 96.58/13.15 ((
% 96.58/13.15 (dpsetconstrSub) =>
% 96.58/13.15 ((
% 96.58/13.15 (setOfPairsIsBReln) =>
% 96.58/13.15 ((
% 96.58/13.15 (dpsetconstrERa) =>
% 96.58/13.15 ((
% 96.58/13.15 (dpsetconstrEL1) =>
% 96.58/13.15 ((
% 96.58/13.15 (dpsetconstrEL2) =>
% 96.58/13.15 ((
% 96.58/13.15 (dpsetconstrER) =>
% 96.58/13.15 ((
% 96.58/13.15 (funcImageSingleton) =>
% 96.58/13.15 ((
% 96.58/13.15 (apProp) =>
% 96.58/13.15 ((
% 96.58/13.15 (app) =>
% 96.58/13.15 ((
% 96.58/13.15 (infuncsetfunc) =>
% 96.58/13.15 ((
% 96.58/13.15 (ap2p) =>
% 96.58/13.15 ((
% 96.58/13.15 (funcinfuncset) =>
% 96.58/13.15 ((
% 96.58/13.15 (lamProp) =>
% 96.58/13.15 ((
% 96.58/13.15 (lamp) =>
% 96.58/13.15 ((
% 96.58/13.15 (lam2p) =>
% 96.58/13.15 ((
% 96.58/13.15 (brelnall1) =>
% 96.58/13.15 ((
% 96.58/13.15 (brelnall2) =>
% 96.58/13.15 ((
% 96.58/13.15 (ex1E2) =>
% 96.58/13.15 ((
% 96.58/13.15 (funcGraphProp1) =>
% 96.58/13.15 ((
% 96.58/13.15 (funcGraphProp3) =>
% 96.58/13.15 ((
% 96.58/13.15 (funcGraphProp2) =>
% 96.58/13.15 ((
% 96.58/13.15 (funcextLem) =>
% 96.58/13.15 ((
% 96.58/13.15 (funcGraphProp4) =>
% 96.58/13.15 ((
% 96.58/13.15 (subbreln) =>
% 96.58/13.15 ((
% 96.58/13.15 (eqbreln) =>
% 96.58/13.15 ((
% 96.58/13.15 (funcext) =>
% 96.58/13.15 ((
% 96.58/13.15 (funcext2) =>
% 96.58/13.15 ((
% 96.58/13.15 (ap2apEq1) =>
% 96.58/13.15 ((
% 96.58/13.15 (ap2apEq2) =>
% 96.58/13.15 ((
% 96.58/13.15 (beta1) =>
% 96.58/13.15 ((
% 96.58/13.15 (eta1) =>
% 96.58/13.15 ((
% 96.58/13.15 (lam2lamEq) =>
% 96.58/13.15 ((
% 96.58/13.15 (beta2) =>
% 96.58/13.15 ((
% 96.58/13.15 (eta2) =>
% 96.58/13.15 ((
% 96.58/13.15 (iffalseProp1) =>
% 96.58/13.15 ((
% 96.58/13.15 (iffalseProp2) =>
% 96.58/13.15 ((
% 96.58/13.15 (iftrueProp1) =>
% 96.58/13.15 ((
% 96.58/13.15 (iftrueProp2) =>
% 96.58/13.15 ((
% 96.58/13.15 (ifSingleton) =>
% 96.58/13.15 ((
% 96.58/13.15 (ifp) =>
% 96.58/13.15 ((
% 96.58/13.15 (theeq) =>
% 96.58/13.15 ((
% 96.58/13.15 (iftrue) =>
% 96.58/13.15 ((
% 96.58/13.15 (iffalse) =>
% 96.58/13.15 ((
% 96.58/13.15 (iftrueorfalse) =>
% 96.58/13.15 ((
% 96.58/13.15 (binintersectT_lem) =>
% 96.58/13.15 ((
% 96.58/13.15 (binunionT_lem) =>
% 96.58/13.15 ((
% 96.58/13.15 (powersetT_lem) =>
% 96.58/13.15 ((
% 96.58/13.15 (setminusT_lem) =>
% 96.58/13.15 ((
% 96.58/13.15 (complementT_lem) =>
% 96.58/13.15 ((
% 96.58/13.15 (setextT) =>
% 96.58/13.15 ((
% 96.58/13.15 (subsetTI) =>
% 96.58/13.15 ((
% 96.58/13.15 (powersetTI1) =>
% 96.58/13.15 ((
% 96.58/13.15 (powersetTE1) =>
% 96.58/13.15 ((
% 96.58/13.15 (complementTI1) =>
% 96.58/13.15 ((
% 96.58/13.15 (complementTE1) =>
% 96.58/13.15 ((
% 96.58/13.15 (binintersectTELcontra) =>
% 96.58/13.15 ((
% 96.58/13.15 (binintersectTERcontra) =>
% 96.58/13.15 ((
% 96.58/13.15 (contrasubsetT) =>
% 96.58/13.15 ((
% 96.58/13.15 (contrasubsetT1) =>
% 96.58/13.15 ((
% 96.58/13.15 (contrasubsetT2) =>
% 96.58/13.15 ((
% 96.58/13.15 (contrasubsetT3) =>
% 96.58/13.15 ((
% 96.58/13.15 (doubleComplementI1) =>
% 96.58/13.15 ((
% 96.58/13.15 (doubleComplementE1) =>
% 96.58/13.15 ((
% 96.58/13.15 (doubleComplementSub1) =>
% 96.58/13.15 ((
% 96.58/13.15 (doubleComplementSub2) =>
% 96.58/13.15 ((
% 96.58/13.15 (doubleComplementEq) =>
% 96.58/13.15 ((
% 96.58/13.15 (complementTnotintersectT) =>
% 96.58/13.15 ((
% 96.58/13.15 (complementImpComplementIntersect) =>
% 96.58/13.15 ((
% 96.58/13.15 (complementSubsetComplementIntersect) =>
% 96.58/13.15 ((
% 96.58/13.15 (complementInPowersetComplementIntersect) =>
% 96.58/13.15 ((
% 96.58/13.15 (contraSubsetComplement) =>
% 96.58/13.15 ((
% 96.58/13.15 (complementTcontraSubset) =>
% 96.58/13.15 ((
% 96.58/13.15 (binunionTILcontra) =>
% 96.58/13.15 ((
% 96.58/13.15 (binunionTIRcontra) =>
% 96.58/13.15 ((
% 96.58/13.15 (inIntersectImpInUnion) =>
% 96.58/13.15 ((
% 96.58/13.15 (inIntersectImpInUnion2) =>
% 96.58/13.15 ((
% 96.58/13.15 (inIntersectImpInIntersectUnions) =>
% 96.58/13.15 ((
% 96.58/13.15 (intersectInPowersetIntersectUnions) =>
% 96.58/13.15 ((
% 96.58/13.15 (inComplementUnionImpNotIn1) =>
% 96.58/13.15 ((
% 96.58/13.15 (inComplementUnionImpInComplement1) =>
% 96.58/13.15 ((
% 96.58/13.15 (binunionTE) =>
% 96.58/13.15 ((
% 96.58/13.15 (binunionTEcontra) =>
% 96.58/13.15 ((
% 96.58/13.15 (demorgan2a1) =>
% 96.58/13.15 ((
% 96.58/13.15 (complementUnionInPowersetComplement) =>
% 96.58/13.15 ((
% 96.58/13.15 (demorgan2a2) =>
% 96.58/13.15 ((
% 96.58/13.15 (demorgan1a) =>
% 96.58/13.15 ((
% 96.58/13.15 (demorgan1b) =>
% 96.58/13.15 ((
% 96.58/13.15 (demorgan1) =>
% 96.58/13.15 ((
% 96.58/13.15 (demorgan2a) =>
% 96.58/13.15 ((
% 96.58/13.15 (demorgan2b2) =>
% 96.58/13.15 ((
% 96.58/13.15 (demorgan2b) =>
% 96.58/13.15 ((
% 96.58/13.15 (demorgan2) =>
% 96.58/13.15 ((
% 96.58/13.15 (woz13rule0) =>
% 96.58/13.15 ((
% 96.58/13.15 (woz13rule1) =>
% 96.58/13.15 ((
% 96.58/13.15 (woz13rule2) =>
% 96.58/13.15 ((
% 96.58/13.15 (woz13rule3) =>
% 96.58/13.15 ((
% 96.58/13.15 (woz13rule4) =>
% 96.58/13.15 ((
% 96.58/13.15 (woz1_1) =>
% 96.58/13.15 ((
% 96.58/13.15 (woz1_2) =>
% 96.58/13.15 ((
% 96.58/13.15 (woz1_3) =>
% 96.58/13.15 ((
% 96.58/13.15 (woz1_4) =>
% 96.58/13.15 ((
% 96.58/13.15 (woz1_5) =>
% 96.58/13.15 ((
% 96.58/13.15 (breln1all2) =>
% 96.58/13.15 ((
% 96.58/13.15 (breln1SetBreln1) =>
% 96.58/13.15 ((
% 96.58/13.15 (choice2fnsingleton) =>
% 96.58/13.15 ((
% 96.58/13.15 (setOfPairsIsBReln1) =>
% 96.58/13.15 ((
% 96.58/13.15 (breln1all1) =>
% 96.58/13.15 ((
% 96.58/13.15 (subbreln1) =>
% 96.58/13.15 ((
% 96.58/13.15 (eqbreln1) =>
% 96.58/13.15 ((
% 96.58/13.15 (breln1invprop) =>
% 96.58/13.15 ((
% 96.58/13.15 (breln1invI) =>
% 96.58/13.15 ((
% 96.58/13.15 (breln1invE) =>
% 96.58/13.15 ((
% 96.58/13.15 (breln1compprop) =>
% 96.58/13.15 ((
% 96.58/13.15 (breln1compI) =>
% 96.58/13.15 ((
% 96.58/13.15 (breln1compE) =>
% 96.58/13.15 ((
% 96.58/13.15 (breln1compEex) =>
% 96.58/13.15 ((
% 96.58/13.15 (breln1unionprop) =>
% 96.58/13.15 ((
% 96.58/13.15 (breln1unionIL) =>
% 96.58/13.15 ((
% 96.58/13.15 (breln1unionIR) =>
% 96.58/13.15 ((
% 96.58/13.15 (breln1unionI) =>
% 96.58/13.15 ((
% 96.58/13.15 (breln1unionE) =>
% 96.58/13.15 ((
% 96.58/13.15 (breln1unionEcases) =>
% 96.58/13.15 ((
% 96.58/13.15 (breln1unionCommutes) =>
% 96.58/13.15 ((
% 96.58/13.15 (woz2Ex) =>
% 96.58/13.15 ((
% 96.58/13.15 (woz2W) =>
% 96.58/13.15 ((
% 96.58/13.15 (woz2A) =>
% 96.58/13.15 ((
% 96.58/13.15 (woz2B) =>
% 96.58/13.15 ((
% 96.58/13.15 (image1Ex) =>
% 96.58/13.15 ((
% 96.58/13.15 (image1Ex1) =>
% 96.58/13.15 ((
% 96.58/13.15 (image1Equiv) =>
% 96.58/13.15 ((
% 96.58/13.15 (image1E) =>
% 96.58/13.15 ((
% 96.58/13.15 (image1I) =>
% 96.58/13.15 ((
% 96.58/13.15 (injFuncInInjFuncSet) =>
% 96.58/13.15 ((
% 96.58/13.15 (injFuncSetFuncIn) =>
% 96.58/13.15 ((
% 96.58/13.15 (injFuncSetFuncInj) =>
% 96.58/13.15 ((
% 96.58/13.15 (surjFuncSetFuncIn) =>
% 96.58/13.15 ((
% 96.58/13.15 (surjFuncSetFuncSurj) =>
% 96.58/13.15 ((
% 96.58/13.15 (leftInvIsSurj) =>
% 96.58/13.15 ((
% 96.58/13.15 (surjCantorThm) =>
% 96.58/13.15 ((
% 96.58/13.15 (foundation2) =>
% 96.58/13.15 ((
% 96.58/13.15 (notinself) =>
% 96.58/13.15 ((
% 96.58/13.15 (notinself2) =>
% 96.58/13.15 ((
% 96.58/13.15 (omegaSp) =>
% 96.58/13.15 ((
% 96.58/13.15 (omegaSclos) =>
% 96.58/13.15 ((
% 96.58/13.15 (peano0notS) =>
% 96.58/13.15 ((
% 96.58/13.15 (!!) @ (
% 96.58/13.15 (('#S') @ (
% 96.58/13.15 (
% 96.58/13.15 ('#B') @ (
% 96.58/13.15 =>) @
% 96.58/13.15 (
% 96.58/13.15 (
% 96.58/13.15 ('#C') @ in @
% 96.58/13.15 omega)))) @
% 96.58/13.15 (
% 96.58/13.15 (
% 96.58/13.15 ('#B') @ (
% 96.58/13.15 !!) @
% 96.58/13.15 (
% 96.58/13.15 (
% 96.58/13.15 ('#B') @ (
% 96.58/13.15 (
% 96.58/13.15 ('#S') @ (
% 96.58/13.15 (
% 96.58/13.15 ('#B') @ (
% 96.58/13.15 =>) @
% 96.58/13.15 (
% 96.58/13.15 (
% 96.58/13.15 ('#C') @ in @
% 96.58/13.15 omega)))))) @
% 96.58/13.15 (
% 96.58/13.15 (
% 96.58/13.15 ('#S') @ (
% 96.58/13.15 (
% 96.58/13.15 ('#B') @ (
% 96.58/13.15 '#S') @
% 96.58/13.15 (
% 96.58/13.15 (
% 96.58/13.15 ('#B') @ (
% 96.58/13.15 (
% 96.58/13.15 ('#B') @ (
% 96.58/13.15 =>))) @
% 96.58/13.15 (
% 96.58/13.15 (
% 96.58/13.15 ('#C') @ (
% 96.58/13.15 (
% 96.58/13.15 ('#B') @ (
% 96.58/13.15 '#B') @
% 96.58/13.15 (
% 96.58/13.15 (
% 96.58/13.15 ('#B') @ (
% 96.58/13.15 =) @
% 96.58/13.15 omegaS)))) @
% 96.58/13.15 omegaS)))))) @
% 96.58/13.15 (
% 96.58/13.15 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 96.58/13.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl71])).
% 96.58/13.15 thf(zip_derived_cl89, plain,
% 96.58/13.15 (~ (((dsetconstrER) =>
% 96.58/13.15 (((exuE1) =>
% 96.58/13.15 (((prop2setE) =>
% 96.58/13.15 (((emptysetE) =>
% 96.58/13.15 (((emptysetimpfalse) =>
% 96.58/13.15 (((notinemptyset) =>
% 96.58/13.15 (((exuE3e) =>
% 96.58/13.15 (((setext) =>
% 96.58/13.15 (((emptyI) =>
% 96.58/13.15 (((noeltsimpempty) =>
% 96.58/13.15 (((setbeta) =>
% 96.58/13.15 (((nonemptyE1) =>
% 96.58/13.15 (((nonemptyI) =>
% 96.58/13.15 (((nonemptyI1) =>
% 96.58/13.15 (((setadjoinIL) =>
% 96.58/13.15 (((in @ emptyset @
% 96.58/13.15 (setadjoin @ emptyset @ emptyset)) =>
% 96.58/13.15 (((setadjoinIR) =>
% 96.58/13.15 (((setadjoinE) =>
% 96.58/13.15 (((setadjoinOr) =>
% 96.58/13.15 (((setoftrueEq) =>
% 96.58/13.15 (((powersetI) =>
% 96.58/13.15 (((emptyinPowerset) =>
% 96.58/13.15 (((emptyInPowerset) =>
% 96.58/13.15 (((powersetE) =>
% 96.58/13.15 (((setunionI) =>
% 96.58/13.15 (((setunionE) =>
% 96.58/13.15 (((subPowSU) =>
% 96.58/13.15 (((exuE2) =>
% 96.58/13.15 (((nonemptyImpWitness) =>
% 96.58/13.15 (((uniqinunit) =>
% 96.58/13.15 ((
% 96.58/13.15 (notinsingleton) =>
% 96.58/13.15 ((
% 96.58/13.15 (eqinunit) =>
% 96.58/13.15 ((
% 96.58/13.15 (singletonsswitch) =>
% 96.58/13.15 ((
% 96.58/13.15 (upairsetE) =>
% 96.58/13.15 ((
% 96.58/13.15 (upairsetIL) =>
% 96.58/13.15 ((
% 96.58/13.15 (upairsetIR) =>
% 96.58/13.15 ((
% 96.58/13.15 (emptyE1) =>
% 96.58/13.15 ((
% 96.58/13.15 (vacuousDall) =>
% 96.58/13.15 ((
% 96.58/13.15 (quantDeMorgan1) =>
% 96.58/13.15 ((
% 96.58/13.15 (quantDeMorgan2) =>
% 96.58/13.15 ((
% 96.58/13.15 (quantDeMorgan3) =>
% 96.58/13.15 ((
% 96.58/13.15 (quantDeMorgan4) =>
% 96.58/13.15 ((
% 96.58/13.15 (prop2setI) =>
% 96.58/13.15 ((
% 96.58/13.15 (prop2set2propI) =>
% 96.58/13.15 ((
% 96.58/13.15 (notdexE) =>
% 96.58/13.15 ((
% 96.58/13.15 (notdallE) =>
% 96.58/13.15 ((
% 96.58/13.15 (exuI1) =>
% 96.58/13.15 ((
% 96.58/13.15 (exuI3) =>
% 96.58/13.15 ((
% 96.58/13.15 (exuI2) =>
% 96.58/13.15 ((
% 96.58/13.15 (inCongP) =>
% 96.58/13.15 ((
% 96.58/13.15 (in__Cong) =>
% 96.58/13.15 ((
% 96.58/13.15 (exuE3u) =>
% 96.58/13.15 ((
% 96.58/13.15 (exu__Cong) =>
% 96.58/13.15 ((
% 96.58/13.15 (setadjoin__Cong) =>
% 96.58/13.15 ((
% 96.58/13.15 (powerset__Cong) =>
% 96.58/13.15 ((
% 96.58/13.15 (setunion__Cong) =>
% 96.58/13.15 ((
% 96.58/13.15 (exuEu) =>
% 96.58/13.15 ((
% 96.58/13.15 (descr__Cong) =>
% 96.58/13.15 ((
% 96.58/13.15 (dsetconstr__Cong) =>
% 96.58/13.15 ((
% 96.58/13.15 (subsetI1) =>
% 96.58/13.15 ((
% 96.58/13.15 (eqimpsubset2) =>
% 96.58/13.15 ((
% 96.58/13.15 (eqimpsubset1) =>
% 96.58/13.15 ((
% 96.58/13.15 (subsetI2) =>
% 96.58/13.15 ((
% 96.58/13.15 (emptysetsubset) =>
% 96.58/13.15 ((
% 96.58/13.15 (subsetE) =>
% 96.58/13.15 ((
% 96.58/13.15 (subsetE2) =>
% 96.58/13.15 ((
% 96.58/13.15 (notsubsetI) =>
% 96.58/13.15 ((
% 96.58/13.15 (notequalI1) =>
% 96.58/13.15 ((
% 96.58/13.15 (notequalI2) =>
% 96.58/13.15 ((
% 96.58/13.15 (subsetRefl) =>
% 96.58/13.15 ((
% 96.58/13.15 (subsetTrans) =>
% 96.58/13.15 ((
% 96.58/13.15 (setadjoinSub) =>
% 96.58/13.15 ((
% 96.58/13.15 (setadjoinSub2) =>
% 96.58/13.15 ((
% 96.58/13.15 (subset2powerset) =>
% 96.58/13.15 ((
% 96.58/13.15 (setextsub) =>
% 96.58/13.15 ((
% 96.58/13.15 (subsetemptysetimpeq) =>
% 96.58/13.15 ((
% 96.58/13.15 (powersetI1) =>
% 96.58/13.15 ((
% 96.58/13.15 (powersetE1) =>
% 96.58/13.15 ((
% 96.58/13.15 (inPowerset) =>
% 96.58/13.15 ((
% 96.58/13.15 (powersetsubset) =>
% 96.58/13.15 ((
% 96.58/13.15 (sepInPowerset) =>
% 96.58/13.15 ((
% 96.58/13.15 (sepSubset) =>
% 96.58/13.15 ((
% 96.58/13.15 (binunionIL) =>
% 96.58/13.15 ((
% 96.58/13.15 (upairset2IR) =>
% 96.58/13.15 ((
% 96.58/13.15 (binunionIR) =>
% 96.58/13.15 ((
% 96.58/13.15 (binunionEcases) =>
% 96.58/13.15 ((
% 96.58/13.15 (binunionE) =>
% 96.58/13.15 ((
% 96.58/13.15 (binunionLsub) =>
% 96.58/13.15 ((
% 96.58/13.15 (binunionRsub) =>
% 96.58/13.15 ((
% 96.58/13.15 (binintersectI) =>
% 96.58/13.15 ((
% 96.58/13.15 (binintersectSubset5) =>
% 96.58/13.15 ((
% 96.58/13.15 (binintersectEL) =>
% 96.58/13.15 ((
% 96.58/13.15 (binintersectLsub) =>
% 96.58/13.15 ((
% 96.58/13.15 (binintersectSubset2) =>
% 96.58/13.15 ((
% 96.58/13.15 (binintersectSubset3) =>
% 96.58/13.15 ((
% 96.58/13.15 (binintersectER) =>
% 96.58/13.15 ((
% 96.58/13.15 (disjointsetsI1) =>
% 96.58/13.15 ((
% 96.58/13.15 (binintersectRsub) =>
% 96.58/13.15 ((
% 96.58/13.15 (binintersectSubset4) =>
% 96.58/13.15 ((
% 96.58/13.15 (binintersectSubset1) =>
% 96.58/13.15 ((
% 96.58/13.15 (bs114d) =>
% 96.58/13.15 ((
% 96.58/13.15 (setminusI) =>
% 96.58/13.15 ((
% 96.58/13.15 (setminusEL) =>
% 96.58/13.15 ((
% 96.58/13.15 (setminusER) =>
% 96.58/13.15 ((
% 96.58/13.15 (setminusSubset2) =>
% 96.58/13.15 ((
% 96.58/13.15 (setminusERneg) =>
% 96.58/13.15 ((
% 96.58/13.15 (setminusELneg) =>
% 96.58/13.15 ((
% 96.58/13.15 (setminusILneg) =>
% 96.58/13.15 ((
% 96.58/13.15 (setminusIRneg) =>
% 96.58/13.15 ((
% 96.58/13.15 (setminusLsub) =>
% 96.58/13.15 ((
% 96.58/13.15 (setminusSubset1) =>
% 96.58/13.15 ((
% 96.58/13.15 (symdiffE) =>
% 96.58/13.15 ((
% 96.58/13.15 (symdiffI1) =>
% 96.58/13.15 ((
% 96.58/13.15 (symdiffI2) =>
% 96.58/13.15 ((
% 96.58/13.15 (symdiffIneg1) =>
% 96.58/13.15 ((
% 96.58/13.15 (symdiffIneg2) =>
% 96.58/13.15 ((
% 96.58/13.15 (secondinupair) =>
% 96.58/13.15 ((
% 96.58/13.15 (setukpairIL) =>
% 96.58/13.15 ((
% 96.58/13.15 (setukpairIR) =>
% 96.58/13.15 ((
% 96.58/13.15 (kpairiskpair) =>
% 96.58/13.15 ((
% 96.58/13.15 (kpairp) =>
% 96.58/13.15 ((
% 96.58/13.15 (singletonsubset) =>
% 96.58/13.15 ((
% 96.58/13.15 (singletoninpowerset) =>
% 96.58/13.15 ((
% 96.58/13.15 (singletoninpowunion) =>
% 96.58/13.15 ((
% 96.58/13.15 (upairset2E) =>
% 96.58/13.15 ((
% 96.58/13.15 (upairsubunion) =>
% 96.58/13.15 ((
% 96.58/13.15 (upairinpowunion) =>
% 96.58/13.15 ((
% 96.58/13.15 (ubforcartprodlem1) =>
% 96.58/13.15 ((
% 96.58/13.15 (ubforcartprodlem2) =>
% 96.58/13.15 ((
% 96.58/13.15 (ubforcartprodlem3) =>
% 96.58/13.15 ((
% 96.58/13.15 (cartprodpairin) =>
% 96.58/13.15 ((
% 96.58/13.15 (cartprodmempair1) =>
% 96.58/13.15 ((
% 96.58/13.15 (cartprodmempair) =>
% 96.58/13.15 ((
% 96.58/13.15 (setunionE2) =>
% 96.58/13.15 ((
% 96.58/13.15 (setunionsingleton1) =>
% 96.58/13.15 ((
% 96.58/13.15 (setunionsingleton2) =>
% 96.58/13.15 ((
% 96.58/13.15 (setunionsingleton) =>
% 96.58/13.15 ((
% 96.58/13.15 (singletonprop) =>
% 96.58/13.15 ((
% 96.58/13.15 (ex1E1) =>
% 96.58/13.15 ((
% 96.58/13.15 (ex1I) =>
% 96.58/13.15 ((
% 96.58/13.15 (ex1I2) =>
% 96.58/13.15 ((
% 96.58/13.15 (singletonsuniq) =>
% 96.58/13.15 ((
% 96.58/13.15 (setukpairinjL1) =>
% 96.58/13.15 ((
% 96.58/13.15 (kfstsingleton) =>
% 96.58/13.15 ((
% 96.58/13.15 (theprop) =>
% 96.58/13.15 ((
% 96.58/13.15 (kfstpairEq) =>
% 96.58/13.15 ((
% 96.58/13.15 (cartprodfstin) =>
% 96.58/13.15 ((
% 96.58/13.15 (setukpairinjL2) =>
% 96.58/13.15 ((
% 96.58/13.15 (setukpairinjL) =>
% 96.58/13.15 ((
% 96.58/13.15 (setukpairinjR11) =>
% 96.58/13.15 ((
% 96.58/13.15 (setukpairinjR12) =>
% 96.58/13.15 ((
% 96.58/13.15 (setukpairinjR1) =>
% 96.58/13.15 ((
% 96.58/13.15 (upairequniteq) =>
% 96.58/13.15 ((
% 96.58/13.15 (setukpairinjR2) =>
% 96.58/13.15 ((
% 96.58/13.15 (setukpairinjR) =>
% 96.58/13.15 ((
% 96.58/13.15 (ksndsingleton) =>
% 96.58/13.15 ((
% 96.58/13.15 (ksndpairEq) =>
% 96.58/13.15 ((
% 96.58/13.15 (kpairsurjEq) =>
% 96.58/13.15 ((
% 96.58/13.15 (cartprodsndin) =>
% 96.58/13.15 ((
% 96.58/13.15 (cartprodpairmemEL) =>
% 96.58/13.15 ((
% 96.58/13.15 (cartprodpairmemER) =>
% 96.58/13.15 ((
% 96.58/13.15 (cartprodmempaircEq) =>
% 96.58/13.15 ((
% 96.58/13.15 (cartprodfstpairEq) =>
% 96.58/13.15 ((
% 96.58/13.15 (cartprodsndpairEq) =>
% 96.58/13.15 ((
% 96.58/13.15 (cartprodpairsurjEq) =>
% 96.58/13.15 ((
% 96.58/13.15 (dpsetconstrI) =>
% 96.58/13.15 ((
% 96.58/13.15 (dpsetconstrSub) =>
% 96.58/13.15 ((
% 96.58/13.15 (setOfPairsIsBReln) =>
% 96.58/13.15 ((
% 96.58/13.15 (dpsetconstrERa) =>
% 96.58/13.15 ((
% 96.58/13.15 (dpsetconstrEL1) =>
% 96.58/13.15 ((
% 96.58/13.15 (dpsetconstrEL2) =>
% 96.58/13.15 ((
% 96.58/13.15 (dpsetconstrER) =>
% 96.58/13.15 ((
% 96.58/13.15 (funcImageSingleton) =>
% 96.58/13.15 ((
% 96.58/13.15 (apProp) =>
% 96.58/13.15 ((
% 96.58/13.15 (app) =>
% 96.58/13.15 ((
% 96.58/13.15 (infuncsetfunc) =>
% 96.58/13.15 ((
% 96.58/13.15 (ap2p) =>
% 96.58/13.15 ((
% 96.58/13.15 (funcinfuncset) =>
% 96.58/13.15 ((
% 96.58/13.15 (lamProp) =>
% 96.58/13.15 ((
% 96.58/13.15 (lamp) =>
% 96.58/13.15 ((
% 96.58/13.15 (lam2p) =>
% 96.58/13.15 ((
% 96.58/13.15 (brelnall1) =>
% 96.58/13.15 ((
% 96.58/13.15 (brelnall2) =>
% 96.58/13.15 ((
% 96.58/13.15 (ex1E2) =>
% 96.58/13.15 ((
% 96.58/13.15 (funcGraphProp1) =>
% 96.58/13.15 ((
% 96.58/13.15 (funcGraphProp3) =>
% 96.58/13.15 ((
% 96.58/13.15 (funcGraphProp2) =>
% 96.58/13.15 ((
% 96.58/13.15 (funcextLem) =>
% 96.58/13.15 ((
% 96.58/13.15 (funcGraphProp4) =>
% 96.58/13.15 ((
% 96.58/13.15 (subbreln) =>
% 96.58/13.15 ((
% 96.58/13.15 (eqbreln) =>
% 96.58/13.15 ((
% 96.58/13.15 (funcext) =>
% 96.58/13.15 ((
% 96.58/13.15 (funcext2) =>
% 96.58/13.15 ((
% 96.58/13.15 (ap2apEq1) =>
% 96.58/13.15 ((
% 96.58/13.15 (ap2apEq2) =>
% 96.58/13.15 ((
% 96.58/13.15 (beta1) =>
% 96.58/13.15 ((
% 96.58/13.15 (eta1) =>
% 96.58/13.15 ((
% 96.58/13.15 (lam2lamEq) =>
% 96.58/13.15 ((
% 96.58/13.15 (beta2) =>
% 96.58/13.15 ((
% 96.58/13.15 (eta2) =>
% 96.58/13.15 ((
% 96.58/13.15 (iffalseProp1) =>
% 96.58/13.15 ((
% 96.58/13.15 (iffalseProp2) =>
% 96.58/13.15 ((
% 96.58/13.15 (iftrueProp1) =>
% 96.58/13.15 ((
% 96.58/13.15 (iftrueProp2) =>
% 96.58/13.15 ((
% 96.58/13.15 (ifSingleton) =>
% 96.58/13.15 ((
% 96.58/13.15 (ifp) =>
% 96.58/13.15 ((
% 96.58/13.15 (theeq) =>
% 96.58/13.15 ((
% 96.58/13.15 (iftrue) =>
% 96.58/13.15 ((
% 96.58/13.15 (iffalse) =>
% 96.58/13.15 ((
% 96.58/13.15 (iftrueorfalse) =>
% 96.58/13.15 ((
% 96.58/13.15 (binintersectT_lem) =>
% 96.58/13.15 ((
% 96.58/13.15 (binunionT_lem) =>
% 96.58/13.15 ((
% 96.58/13.15 (powersetT_lem) =>
% 96.58/13.15 ((
% 96.58/13.15 (setminusT_lem) =>
% 96.58/13.15 ((
% 96.58/13.15 (complementT_lem) =>
% 96.58/13.15 ((
% 96.58/13.15 (setextT) =>
% 96.58/13.15 ((
% 96.58/13.15 (subsetTI) =>
% 96.58/13.15 ((
% 96.58/13.15 (powersetTI1) =>
% 96.58/13.15 ((
% 96.58/13.15 (powersetTE1) =>
% 96.58/13.15 ((
% 96.58/13.15 (complementTI1) =>
% 96.58/13.15 ((
% 96.58/13.15 (complementTE1) =>
% 96.58/13.15 ((
% 96.58/13.15 (binintersectTELcontra) =>
% 96.58/13.15 ((
% 96.58/13.15 (binintersectTERcontra) =>
% 96.58/13.15 ((
% 96.58/13.15 (contrasubsetT) =>
% 96.58/13.15 ((
% 96.58/13.15 (contrasubsetT1) =>
% 96.58/13.15 ((
% 96.58/13.15 (contrasubsetT2) =>
% 96.58/13.15 ((
% 96.58/13.15 (contrasubsetT3) =>
% 96.58/13.15 ((
% 96.58/13.15 (doubleComplementI1) =>
% 96.58/13.15 ((
% 96.58/13.15 (doubleComplementE1) =>
% 96.58/13.15 ((
% 96.58/13.15 (doubleComplementSub1) =>
% 96.58/13.15 ((
% 96.58/13.15 (doubleComplementSub2) =>
% 96.58/13.15 ((
% 96.58/13.15 (doubleComplementEq) =>
% 96.58/13.15 ((
% 96.58/13.15 (complementTnotintersectT) =>
% 96.58/13.15 ((
% 96.58/13.15 (complementImpComplementIntersect) =>
% 96.58/13.15 ((
% 96.58/13.15 (complementSubsetComplementIntersect) =>
% 96.58/13.15 ((
% 96.58/13.15 (complementInPowersetComplementIntersect) =>
% 96.58/13.15 ((
% 96.58/13.15 (contraSubsetComplement) =>
% 96.58/13.15 ((
% 96.58/13.15 (complementTcontraSubset) =>
% 97.31/13.15 ((
% 97.31/13.15 (binunionTILcontra) =>
% 97.31/13.15 ((
% 97.31/13.15 (binunionTIRcontra) =>
% 97.31/13.15 ((
% 97.31/13.15 (inIntersectImpInUnion) =>
% 97.31/13.15 ((
% 97.31/13.15 (inIntersectImpInUnion2) =>
% 97.31/13.15 ((
% 97.31/13.15 (inIntersectImpInIntersectUnions) =>
% 97.31/13.15 ((
% 97.31/13.15 (intersectInPowersetIntersectUnions) =>
% 97.31/13.15 ((
% 97.31/13.15 (inComplementUnionImpNotIn1) =>
% 97.31/13.15 ((
% 97.31/13.15 (inComplementUnionImpInComplement1) =>
% 97.31/13.15 ((
% 97.31/13.15 (binunionTE) =>
% 97.31/13.15 ((
% 97.31/13.15 (binunionTEcontra) =>
% 97.31/13.15 ((
% 97.31/13.15 (demorgan2a1) =>
% 97.31/13.15 ((
% 97.31/13.15 (complementUnionInPowersetComplement) =>
% 97.31/13.15 ((
% 97.31/13.15 (demorgan2a2) =>
% 97.31/13.15 ((
% 97.31/13.15 (demorgan1a) =>
% 97.31/13.15 ((
% 97.31/13.15 (demorgan1b) =>
% 97.31/13.15 ((
% 97.31/13.15 (demorgan1) =>
% 97.31/13.15 ((
% 97.31/13.15 (demorgan2a) =>
% 97.31/13.15 ((
% 97.31/13.15 (demorgan2b2) =>
% 97.31/13.15 ((
% 97.31/13.15 (demorgan2b) =>
% 97.31/13.15 ((
% 97.31/13.15 (demorgan2) =>
% 97.31/13.15 ((
% 97.31/13.15 (woz13rule0) =>
% 97.31/13.15 ((
% 97.31/13.15 (woz13rule1) =>
% 97.31/13.15 ((
% 97.31/13.15 (woz13rule2) =>
% 97.31/13.15 ((
% 97.31/13.15 (woz13rule3) =>
% 97.31/13.15 ((
% 97.31/13.15 (woz13rule4) =>
% 97.31/13.15 ((
% 97.31/13.15 (woz1_1) =>
% 97.31/13.15 ((
% 97.31/13.15 (woz1_2) =>
% 97.31/13.15 ((
% 97.31/13.15 (woz1_3) =>
% 97.31/13.15 ((
% 97.31/13.15 (woz1_4) =>
% 97.31/13.15 ((
% 97.31/13.15 (woz1_5) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1all2) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1SetBreln1) =>
% 97.31/13.15 ((
% 97.31/13.15 (choice2fnsingleton) =>
% 97.31/13.15 ((
% 97.31/13.15 (setOfPairsIsBReln1) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1all1) =>
% 97.31/13.15 ((
% 97.31/13.15 (subbreln1) =>
% 97.31/13.15 ((
% 97.31/13.15 (eqbreln1) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1invprop) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1invI) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1invE) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1compprop) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1compI) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1compE) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1compEex) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1unionprop) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1unionIL) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1unionIR) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1unionI) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1unionE) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1unionEcases) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1unionCommutes) =>
% 97.31/13.15 ((
% 97.31/13.15 (woz2Ex) =>
% 97.31/13.15 ((
% 97.31/13.15 (woz2W) =>
% 97.31/13.15 ((
% 97.31/13.15 (woz2A) =>
% 97.31/13.15 ((
% 97.31/13.15 (woz2B) =>
% 97.31/13.15 ((
% 97.31/13.15 (image1Ex) =>
% 97.31/13.15 ((
% 97.31/13.15 (image1Ex1) =>
% 97.31/13.15 ((
% 97.31/13.15 (image1Equiv) =>
% 97.31/13.15 ((
% 97.31/13.15 (image1E) =>
% 97.31/13.15 ((
% 97.31/13.15 (image1I) =>
% 97.31/13.15 ((
% 97.31/13.15 (injFuncInInjFuncSet) =>
% 97.31/13.15 ((
% 97.31/13.15 (injFuncSetFuncIn) =>
% 97.31/13.15 ((
% 97.31/13.15 (injFuncSetFuncInj) =>
% 97.31/13.15 ((
% 97.31/13.15 (surjFuncSetFuncIn) =>
% 97.31/13.15 ((
% 97.31/13.15 (surjFuncSetFuncSurj) =>
% 97.31/13.15 ((
% 97.31/13.15 (leftInvIsSurj) =>
% 97.31/13.15 ((
% 97.31/13.15 (surjCantorThm) =>
% 97.31/13.15 ((
% 97.31/13.15 (foundation2) =>
% 97.31/13.15 ((
% 97.31/13.15 (notinself) =>
% 97.31/13.15 ((
% 97.31/13.15 (notinself2) =>
% 97.31/13.15 ((
% 97.31/13.15 (omegaSp) =>
% 97.31/13.15 ((
% 97.31/13.15 (omegaSclos) =>
% 97.31/13.15 ((
% 97.31/13.15 (peano0notS) =>
% 97.31/13.15 ((
% 97.31/13.15 (!!) @ (
% 97.31/13.15 (('#S') @ (
% 97.31/13.15 (
% 97.31/13.15 ('#B') @ (
% 97.31/13.15 =>) @
% 97.31/13.15 (
% 97.31/13.15 (
% 97.31/13.15 ('#C') @ in @
% 97.31/13.15 omega)))) @
% 97.31/13.15 (
% 97.31/13.15 (
% 97.31/13.15 ('#B') @ (
% 97.31/13.15 !!) @
% 97.31/13.15 (
% 97.31/13.15 (
% 97.31/13.15 ('#B') @ (
% 97.31/13.15 (
% 97.31/13.15 ('#S') @ (
% 97.31/13.15 (
% 97.31/13.15 ('#B') @ (
% 97.31/13.15 =>) @
% 97.31/13.15 (
% 97.31/13.15 (
% 97.31/13.15 ('#C') @ in @
% 97.31/13.15 omega)))))) @
% 97.31/13.15 (
% 97.31/13.15 (
% 97.31/13.15 ('#S') @ (
% 97.31/13.15 (
% 97.31/13.15 ('#B') @ (
% 97.31/13.15 '#S') @
% 97.31/13.15 (
% 97.31/13.15 (
% 97.31/13.15 ('#B') @ (
% 97.31/13.15 (
% 97.31/13.15 ('#B') @ (
% 97.31/13.15 =>))) @
% 97.31/13.15 (
% 97.31/13.15 (
% 97.31/13.15 ('#C') @ (
% 97.31/13.15 (
% 97.31/13.15 ('#B') @ (
% 97.31/13.15 '#B') @
% 97.31/13.15 (
% 97.31/13.15 (
% 97.31/13.15 ('#B') @ (
% 97.31/13.15 =) @
% 97.31/13.15 omegaS)))) @
% 97.31/13.15 omegaS)))))) @
% 97.31/13.15 (
% 97.31/13.15 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.31/13.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl79])).
% 97.31/13.15 thf(zip_derived_cl105, plain,
% 97.31/13.15 (~ (((exuE1) =>
% 97.31/13.15 (((prop2setE) =>
% 97.31/13.15 (((emptysetE) =>
% 97.31/13.15 (((emptysetimpfalse) =>
% 97.31/13.15 (((notinemptyset) =>
% 97.31/13.15 (((exuE3e) =>
% 97.31/13.15 (((setext) =>
% 97.31/13.15 (((emptyI) =>
% 97.31/13.15 (((noeltsimpempty) =>
% 97.31/13.15 (((setbeta) =>
% 97.31/13.15 (((nonemptyE1) =>
% 97.31/13.15 (((nonemptyI) =>
% 97.31/13.15 (((nonemptyI1) =>
% 97.31/13.15 (((setadjoinIL) =>
% 97.31/13.15 (((in @ emptyset @
% 97.31/13.15 (setadjoin @ emptyset @ emptyset)) =>
% 97.31/13.15 (((setadjoinIR) =>
% 97.31/13.15 (((setadjoinE) =>
% 97.31/13.15 (((setadjoinOr) =>
% 97.31/13.15 (((setoftrueEq) =>
% 97.31/13.15 (((powersetI) =>
% 97.31/13.15 (((emptyinPowerset) =>
% 97.31/13.15 (((emptyInPowerset) =>
% 97.31/13.15 (((powersetE) =>
% 97.31/13.15 (((setunionI) =>
% 97.31/13.15 (((setunionE) =>
% 97.31/13.15 (((subPowSU) =>
% 97.31/13.15 (((exuE2) =>
% 97.31/13.15 (((nonemptyImpWitness) =>
% 97.31/13.15 (((uniqinunit) =>
% 97.31/13.15 (((notinsingleton) =>
% 97.31/13.15 ((
% 97.31/13.15 (eqinunit) =>
% 97.31/13.15 ((
% 97.31/13.15 (singletonsswitch) =>
% 97.31/13.15 ((
% 97.31/13.15 (upairsetE) =>
% 97.31/13.15 ((
% 97.31/13.15 (upairsetIL) =>
% 97.31/13.15 ((
% 97.31/13.15 (upairsetIR) =>
% 97.31/13.15 ((
% 97.31/13.15 (emptyE1) =>
% 97.31/13.15 ((
% 97.31/13.15 (vacuousDall) =>
% 97.31/13.15 ((
% 97.31/13.15 (quantDeMorgan1) =>
% 97.31/13.15 ((
% 97.31/13.15 (quantDeMorgan2) =>
% 97.31/13.15 ((
% 97.31/13.15 (quantDeMorgan3) =>
% 97.31/13.15 ((
% 97.31/13.15 (quantDeMorgan4) =>
% 97.31/13.15 ((
% 97.31/13.15 (prop2setI) =>
% 97.31/13.15 ((
% 97.31/13.15 (prop2set2propI) =>
% 97.31/13.15 ((
% 97.31/13.15 (notdexE) =>
% 97.31/13.15 ((
% 97.31/13.15 (notdallE) =>
% 97.31/13.15 ((
% 97.31/13.15 (exuI1) =>
% 97.31/13.15 ((
% 97.31/13.15 (exuI3) =>
% 97.31/13.15 ((
% 97.31/13.15 (exuI2) =>
% 97.31/13.15 ((
% 97.31/13.15 (inCongP) =>
% 97.31/13.15 ((
% 97.31/13.15 (in__Cong) =>
% 97.31/13.15 ((
% 97.31/13.15 (exuE3u) =>
% 97.31/13.15 ((
% 97.31/13.15 (exu__Cong) =>
% 97.31/13.15 ((
% 97.31/13.15 (setadjoin__Cong) =>
% 97.31/13.15 ((
% 97.31/13.15 (powerset__Cong) =>
% 97.31/13.15 ((
% 97.31/13.15 (setunion__Cong) =>
% 97.31/13.15 ((
% 97.31/13.15 (exuEu) =>
% 97.31/13.15 ((
% 97.31/13.15 (descr__Cong) =>
% 97.31/13.15 ((
% 97.31/13.15 (dsetconstr__Cong) =>
% 97.31/13.15 ((
% 97.31/13.15 (subsetI1) =>
% 97.31/13.15 ((
% 97.31/13.15 (eqimpsubset2) =>
% 97.31/13.15 ((
% 97.31/13.15 (eqimpsubset1) =>
% 97.31/13.15 ((
% 97.31/13.15 (subsetI2) =>
% 97.31/13.15 ((
% 97.31/13.15 (emptysetsubset) =>
% 97.31/13.15 ((
% 97.31/13.15 (subsetE) =>
% 97.31/13.15 ((
% 97.31/13.15 (subsetE2) =>
% 97.31/13.15 ((
% 97.31/13.15 (notsubsetI) =>
% 97.31/13.15 ((
% 97.31/13.15 (notequalI1) =>
% 97.31/13.15 ((
% 97.31/13.15 (notequalI2) =>
% 97.31/13.15 ((
% 97.31/13.15 (subsetRefl) =>
% 97.31/13.15 ((
% 97.31/13.15 (subsetTrans) =>
% 97.31/13.15 ((
% 97.31/13.15 (setadjoinSub) =>
% 97.31/13.15 ((
% 97.31/13.15 (setadjoinSub2) =>
% 97.31/13.15 ((
% 97.31/13.15 (subset2powerset) =>
% 97.31/13.15 ((
% 97.31/13.15 (setextsub) =>
% 97.31/13.15 ((
% 97.31/13.15 (subsetemptysetimpeq) =>
% 97.31/13.15 ((
% 97.31/13.15 (powersetI1) =>
% 97.31/13.15 ((
% 97.31/13.15 (powersetE1) =>
% 97.31/13.15 ((
% 97.31/13.15 (inPowerset) =>
% 97.31/13.15 ((
% 97.31/13.15 (powersetsubset) =>
% 97.31/13.15 ((
% 97.31/13.15 (sepInPowerset) =>
% 97.31/13.15 ((
% 97.31/13.15 (sepSubset) =>
% 97.31/13.15 ((
% 97.31/13.15 (binunionIL) =>
% 97.31/13.15 ((
% 97.31/13.15 (upairset2IR) =>
% 97.31/13.15 ((
% 97.31/13.15 (binunionIR) =>
% 97.31/13.15 ((
% 97.31/13.15 (binunionEcases) =>
% 97.31/13.15 ((
% 97.31/13.15 (binunionE) =>
% 97.31/13.15 ((
% 97.31/13.15 (binunionLsub) =>
% 97.31/13.15 ((
% 97.31/13.15 (binunionRsub) =>
% 97.31/13.15 ((
% 97.31/13.15 (binintersectI) =>
% 97.31/13.15 ((
% 97.31/13.15 (binintersectSubset5) =>
% 97.31/13.15 ((
% 97.31/13.15 (binintersectEL) =>
% 97.31/13.15 ((
% 97.31/13.15 (binintersectLsub) =>
% 97.31/13.15 ((
% 97.31/13.15 (binintersectSubset2) =>
% 97.31/13.15 ((
% 97.31/13.15 (binintersectSubset3) =>
% 97.31/13.15 ((
% 97.31/13.15 (binintersectER) =>
% 97.31/13.15 ((
% 97.31/13.15 (disjointsetsI1) =>
% 97.31/13.15 ((
% 97.31/13.15 (binintersectRsub) =>
% 97.31/13.15 ((
% 97.31/13.15 (binintersectSubset4) =>
% 97.31/13.15 ((
% 97.31/13.15 (binintersectSubset1) =>
% 97.31/13.15 ((
% 97.31/13.15 (bs114d) =>
% 97.31/13.15 ((
% 97.31/13.15 (setminusI) =>
% 97.31/13.15 ((
% 97.31/13.15 (setminusEL) =>
% 97.31/13.15 ((
% 97.31/13.15 (setminusER) =>
% 97.31/13.15 ((
% 97.31/13.15 (setminusSubset2) =>
% 97.31/13.15 ((
% 97.31/13.15 (setminusERneg) =>
% 97.31/13.15 ((
% 97.31/13.15 (setminusELneg) =>
% 97.31/13.15 ((
% 97.31/13.15 (setminusILneg) =>
% 97.31/13.15 ((
% 97.31/13.15 (setminusIRneg) =>
% 97.31/13.15 ((
% 97.31/13.15 (setminusLsub) =>
% 97.31/13.15 ((
% 97.31/13.15 (setminusSubset1) =>
% 97.31/13.15 ((
% 97.31/13.15 (symdiffE) =>
% 97.31/13.15 ((
% 97.31/13.15 (symdiffI1) =>
% 97.31/13.15 ((
% 97.31/13.15 (symdiffI2) =>
% 97.31/13.15 ((
% 97.31/13.15 (symdiffIneg1) =>
% 97.31/13.15 ((
% 97.31/13.15 (symdiffIneg2) =>
% 97.31/13.15 ((
% 97.31/13.15 (secondinupair) =>
% 97.31/13.15 ((
% 97.31/13.15 (setukpairIL) =>
% 97.31/13.15 ((
% 97.31/13.15 (setukpairIR) =>
% 97.31/13.15 ((
% 97.31/13.15 (kpairiskpair) =>
% 97.31/13.15 ((
% 97.31/13.15 (kpairp) =>
% 97.31/13.15 ((
% 97.31/13.15 (singletonsubset) =>
% 97.31/13.15 ((
% 97.31/13.15 (singletoninpowerset) =>
% 97.31/13.15 ((
% 97.31/13.15 (singletoninpowunion) =>
% 97.31/13.15 ((
% 97.31/13.15 (upairset2E) =>
% 97.31/13.15 ((
% 97.31/13.15 (upairsubunion) =>
% 97.31/13.15 ((
% 97.31/13.15 (upairinpowunion) =>
% 97.31/13.15 ((
% 97.31/13.15 (ubforcartprodlem1) =>
% 97.31/13.15 ((
% 97.31/13.15 (ubforcartprodlem2) =>
% 97.31/13.15 ((
% 97.31/13.15 (ubforcartprodlem3) =>
% 97.31/13.15 ((
% 97.31/13.15 (cartprodpairin) =>
% 97.31/13.15 ((
% 97.31/13.15 (cartprodmempair1) =>
% 97.31/13.15 ((
% 97.31/13.15 (cartprodmempair) =>
% 97.31/13.15 ((
% 97.31/13.15 (setunionE2) =>
% 97.31/13.15 ((
% 97.31/13.15 (setunionsingleton1) =>
% 97.31/13.15 ((
% 97.31/13.15 (setunionsingleton2) =>
% 97.31/13.15 ((
% 97.31/13.15 (setunionsingleton) =>
% 97.31/13.15 ((
% 97.31/13.15 (singletonprop) =>
% 97.31/13.15 ((
% 97.31/13.15 (ex1E1) =>
% 97.31/13.15 ((
% 97.31/13.15 (ex1I) =>
% 97.31/13.15 ((
% 97.31/13.15 (ex1I2) =>
% 97.31/13.15 ((
% 97.31/13.15 (singletonsuniq) =>
% 97.31/13.15 ((
% 97.31/13.15 (setukpairinjL1) =>
% 97.31/13.15 ((
% 97.31/13.15 (kfstsingleton) =>
% 97.31/13.15 ((
% 97.31/13.15 (theprop) =>
% 97.31/13.15 ((
% 97.31/13.15 (kfstpairEq) =>
% 97.31/13.15 ((
% 97.31/13.15 (cartprodfstin) =>
% 97.31/13.15 ((
% 97.31/13.15 (setukpairinjL2) =>
% 97.31/13.15 ((
% 97.31/13.15 (setukpairinjL) =>
% 97.31/13.15 ((
% 97.31/13.15 (setukpairinjR11) =>
% 97.31/13.15 ((
% 97.31/13.15 (setukpairinjR12) =>
% 97.31/13.15 ((
% 97.31/13.15 (setukpairinjR1) =>
% 97.31/13.15 ((
% 97.31/13.15 (upairequniteq) =>
% 97.31/13.15 ((
% 97.31/13.15 (setukpairinjR2) =>
% 97.31/13.15 ((
% 97.31/13.15 (setukpairinjR) =>
% 97.31/13.15 ((
% 97.31/13.15 (ksndsingleton) =>
% 97.31/13.15 ((
% 97.31/13.15 (ksndpairEq) =>
% 97.31/13.15 ((
% 97.31/13.15 (kpairsurjEq) =>
% 97.31/13.15 ((
% 97.31/13.15 (cartprodsndin) =>
% 97.31/13.15 ((
% 97.31/13.15 (cartprodpairmemEL) =>
% 97.31/13.15 ((
% 97.31/13.15 (cartprodpairmemER) =>
% 97.31/13.15 ((
% 97.31/13.15 (cartprodmempaircEq) =>
% 97.31/13.15 ((
% 97.31/13.15 (cartprodfstpairEq) =>
% 97.31/13.15 ((
% 97.31/13.15 (cartprodsndpairEq) =>
% 97.31/13.15 ((
% 97.31/13.15 (cartprodpairsurjEq) =>
% 97.31/13.15 ((
% 97.31/13.15 (dpsetconstrI) =>
% 97.31/13.15 ((
% 97.31/13.15 (dpsetconstrSub) =>
% 97.31/13.15 ((
% 97.31/13.15 (setOfPairsIsBReln) =>
% 97.31/13.15 ((
% 97.31/13.15 (dpsetconstrERa) =>
% 97.31/13.15 ((
% 97.31/13.15 (dpsetconstrEL1) =>
% 97.31/13.15 ((
% 97.31/13.15 (dpsetconstrEL2) =>
% 97.31/13.15 ((
% 97.31/13.15 (dpsetconstrER) =>
% 97.31/13.15 ((
% 97.31/13.15 (funcImageSingleton) =>
% 97.31/13.15 ((
% 97.31/13.15 (apProp) =>
% 97.31/13.15 ((
% 97.31/13.15 (app) =>
% 97.31/13.15 ((
% 97.31/13.15 (infuncsetfunc) =>
% 97.31/13.15 ((
% 97.31/13.15 (ap2p) =>
% 97.31/13.15 ((
% 97.31/13.15 (funcinfuncset) =>
% 97.31/13.15 ((
% 97.31/13.15 (lamProp) =>
% 97.31/13.15 ((
% 97.31/13.15 (lamp) =>
% 97.31/13.15 ((
% 97.31/13.15 (lam2p) =>
% 97.31/13.15 ((
% 97.31/13.15 (brelnall1) =>
% 97.31/13.15 ((
% 97.31/13.15 (brelnall2) =>
% 97.31/13.15 ((
% 97.31/13.15 (ex1E2) =>
% 97.31/13.15 ((
% 97.31/13.15 (funcGraphProp1) =>
% 97.31/13.15 ((
% 97.31/13.15 (funcGraphProp3) =>
% 97.31/13.15 ((
% 97.31/13.15 (funcGraphProp2) =>
% 97.31/13.15 ((
% 97.31/13.15 (funcextLem) =>
% 97.31/13.15 ((
% 97.31/13.15 (funcGraphProp4) =>
% 97.31/13.15 ((
% 97.31/13.15 (subbreln) =>
% 97.31/13.15 ((
% 97.31/13.15 (eqbreln) =>
% 97.31/13.15 ((
% 97.31/13.15 (funcext) =>
% 97.31/13.15 ((
% 97.31/13.15 (funcext2) =>
% 97.31/13.15 ((
% 97.31/13.15 (ap2apEq1) =>
% 97.31/13.15 ((
% 97.31/13.15 (ap2apEq2) =>
% 97.31/13.15 ((
% 97.31/13.15 (beta1) =>
% 97.31/13.15 ((
% 97.31/13.15 (eta1) =>
% 97.31/13.15 ((
% 97.31/13.15 (lam2lamEq) =>
% 97.31/13.15 ((
% 97.31/13.15 (beta2) =>
% 97.31/13.15 ((
% 97.31/13.15 (eta2) =>
% 97.31/13.15 ((
% 97.31/13.15 (iffalseProp1) =>
% 97.31/13.15 ((
% 97.31/13.15 (iffalseProp2) =>
% 97.31/13.15 ((
% 97.31/13.15 (iftrueProp1) =>
% 97.31/13.15 ((
% 97.31/13.15 (iftrueProp2) =>
% 97.31/13.15 ((
% 97.31/13.15 (ifSingleton) =>
% 97.31/13.15 ((
% 97.31/13.15 (ifp) =>
% 97.31/13.15 ((
% 97.31/13.15 (theeq) =>
% 97.31/13.15 ((
% 97.31/13.15 (iftrue) =>
% 97.31/13.15 ((
% 97.31/13.15 (iffalse) =>
% 97.31/13.15 ((
% 97.31/13.15 (iftrueorfalse) =>
% 97.31/13.15 ((
% 97.31/13.15 (binintersectT_lem) =>
% 97.31/13.15 ((
% 97.31/13.15 (binunionT_lem) =>
% 97.31/13.15 ((
% 97.31/13.15 (powersetT_lem) =>
% 97.31/13.15 ((
% 97.31/13.15 (setminusT_lem) =>
% 97.31/13.15 ((
% 97.31/13.15 (complementT_lem) =>
% 97.31/13.15 ((
% 97.31/13.15 (setextT) =>
% 97.31/13.15 ((
% 97.31/13.15 (subsetTI) =>
% 97.31/13.15 ((
% 97.31/13.15 (powersetTI1) =>
% 97.31/13.15 ((
% 97.31/13.15 (powersetTE1) =>
% 97.31/13.15 ((
% 97.31/13.15 (complementTI1) =>
% 97.31/13.15 ((
% 97.31/13.15 (complementTE1) =>
% 97.31/13.15 ((
% 97.31/13.15 (binintersectTELcontra) =>
% 97.31/13.15 ((
% 97.31/13.15 (binintersectTERcontra) =>
% 97.31/13.15 ((
% 97.31/13.15 (contrasubsetT) =>
% 97.31/13.15 ((
% 97.31/13.15 (contrasubsetT1) =>
% 97.31/13.15 ((
% 97.31/13.15 (contrasubsetT2) =>
% 97.31/13.15 ((
% 97.31/13.15 (contrasubsetT3) =>
% 97.31/13.15 ((
% 97.31/13.15 (doubleComplementI1) =>
% 97.31/13.15 ((
% 97.31/13.15 (doubleComplementE1) =>
% 97.31/13.15 ((
% 97.31/13.15 (doubleComplementSub1) =>
% 97.31/13.15 ((
% 97.31/13.15 (doubleComplementSub2) =>
% 97.31/13.15 ((
% 97.31/13.15 (doubleComplementEq) =>
% 97.31/13.15 ((
% 97.31/13.15 (complementTnotintersectT) =>
% 97.31/13.15 ((
% 97.31/13.15 (complementImpComplementIntersect) =>
% 97.31/13.15 ((
% 97.31/13.15 (complementSubsetComplementIntersect) =>
% 97.31/13.15 ((
% 97.31/13.15 (complementInPowersetComplementIntersect) =>
% 97.31/13.15 ((
% 97.31/13.15 (contraSubsetComplement) =>
% 97.31/13.15 ((
% 97.31/13.15 (complementTcontraSubset) =>
% 97.31/13.15 ((
% 97.31/13.15 (binunionTILcontra) =>
% 97.31/13.15 ((
% 97.31/13.15 (binunionTIRcontra) =>
% 97.31/13.15 ((
% 97.31/13.15 (inIntersectImpInUnion) =>
% 97.31/13.15 ((
% 97.31/13.15 (inIntersectImpInUnion2) =>
% 97.31/13.15 ((
% 97.31/13.15 (inIntersectImpInIntersectUnions) =>
% 97.31/13.15 ((
% 97.31/13.15 (intersectInPowersetIntersectUnions) =>
% 97.31/13.15 ((
% 97.31/13.15 (inComplementUnionImpNotIn1) =>
% 97.31/13.15 ((
% 97.31/13.15 (inComplementUnionImpInComplement1) =>
% 97.31/13.15 ((
% 97.31/13.15 (binunionTE) =>
% 97.31/13.15 ((
% 97.31/13.15 (binunionTEcontra) =>
% 97.31/13.15 ((
% 97.31/13.15 (demorgan2a1) =>
% 97.31/13.15 ((
% 97.31/13.15 (complementUnionInPowersetComplement) =>
% 97.31/13.15 ((
% 97.31/13.15 (demorgan2a2) =>
% 97.31/13.15 ((
% 97.31/13.15 (demorgan1a) =>
% 97.31/13.15 ((
% 97.31/13.15 (demorgan1b) =>
% 97.31/13.15 ((
% 97.31/13.15 (demorgan1) =>
% 97.31/13.15 ((
% 97.31/13.15 (demorgan2a) =>
% 97.31/13.15 ((
% 97.31/13.15 (demorgan2b2) =>
% 97.31/13.15 ((
% 97.31/13.15 (demorgan2b) =>
% 97.31/13.15 ((
% 97.31/13.15 (demorgan2) =>
% 97.31/13.15 ((
% 97.31/13.15 (woz13rule0) =>
% 97.31/13.15 ((
% 97.31/13.15 (woz13rule1) =>
% 97.31/13.15 ((
% 97.31/13.15 (woz13rule2) =>
% 97.31/13.15 ((
% 97.31/13.15 (woz13rule3) =>
% 97.31/13.15 ((
% 97.31/13.15 (woz13rule4) =>
% 97.31/13.15 ((
% 97.31/13.15 (woz1_1) =>
% 97.31/13.15 ((
% 97.31/13.15 (woz1_2) =>
% 97.31/13.15 ((
% 97.31/13.15 (woz1_3) =>
% 97.31/13.15 ((
% 97.31/13.15 (woz1_4) =>
% 97.31/13.15 ((
% 97.31/13.15 (woz1_5) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1all2) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1SetBreln1) =>
% 97.31/13.15 ((
% 97.31/13.15 (choice2fnsingleton) =>
% 97.31/13.15 ((
% 97.31/13.15 (setOfPairsIsBReln1) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1all1) =>
% 97.31/13.15 ((
% 97.31/13.15 (subbreln1) =>
% 97.31/13.15 ((
% 97.31/13.15 (eqbreln1) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1invprop) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1invI) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1invE) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1compprop) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1compI) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1compE) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1compEex) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1unionprop) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1unionIL) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1unionIR) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1unionI) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1unionE) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1unionEcases) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1unionCommutes) =>
% 97.31/13.15 ((
% 97.31/13.15 (woz2Ex) =>
% 97.31/13.15 ((
% 97.31/13.15 (woz2W) =>
% 97.31/13.15 ((
% 97.31/13.15 (woz2A) =>
% 97.31/13.15 ((
% 97.31/13.15 (woz2B) =>
% 97.31/13.15 ((
% 97.31/13.15 (image1Ex) =>
% 97.31/13.15 ((
% 97.31/13.15 (image1Ex1) =>
% 97.31/13.15 ((
% 97.31/13.15 (image1Equiv) =>
% 97.31/13.15 ((
% 97.31/13.15 (image1E) =>
% 97.31/13.15 ((
% 97.31/13.15 (image1I) =>
% 97.31/13.15 ((
% 97.31/13.15 (injFuncInInjFuncSet) =>
% 97.31/13.15 ((
% 97.31/13.15 (injFuncSetFuncIn) =>
% 97.31/13.15 ((
% 97.31/13.15 (injFuncSetFuncInj) =>
% 97.31/13.15 ((
% 97.31/13.15 (surjFuncSetFuncIn) =>
% 97.31/13.15 ((
% 97.31/13.15 (surjFuncSetFuncSurj) =>
% 97.31/13.15 ((
% 97.31/13.15 (leftInvIsSurj) =>
% 97.31/13.15 ((
% 97.31/13.15 (surjCantorThm) =>
% 97.31/13.15 ((
% 97.31/13.15 (foundation2) =>
% 97.31/13.15 ((
% 97.31/13.15 (notinself) =>
% 97.31/13.15 ((
% 97.31/13.15 (notinself2) =>
% 97.31/13.15 ((
% 97.31/13.15 (omegaSp) =>
% 97.31/13.15 ((
% 97.31/13.15 (omegaSclos) =>
% 97.31/13.15 ((
% 97.31/13.15 (peano0notS) =>
% 97.31/13.15 ((
% 97.31/13.15 (!!) @ (
% 97.31/13.15 (('#S') @ (
% 97.31/13.15 (
% 97.31/13.15 ('#B') @ (
% 97.31/13.15 =>) @
% 97.31/13.15 (
% 97.31/13.15 (
% 97.31/13.15 ('#C') @ in @
% 97.31/13.15 omega)))) @
% 97.31/13.15 (
% 97.31/13.15 (
% 97.31/13.15 ('#B') @ (
% 97.31/13.15 !!) @
% 97.31/13.15 (
% 97.31/13.15 (
% 97.31/13.15 ('#B') @ (
% 97.31/13.15 (
% 97.31/13.15 ('#S') @ (
% 97.31/13.15 (
% 97.31/13.15 ('#B') @ (
% 97.31/13.15 =>) @
% 97.31/13.15 (
% 97.31/13.15 (
% 97.31/13.15 ('#C') @ in @
% 97.31/13.15 omega)))))) @
% 97.31/13.15 (
% 97.31/13.15 (
% 97.31/13.15 ('#S') @ (
% 97.31/13.15 (
% 97.31/13.15 ('#B') @ (
% 97.31/13.15 '#S') @
% 97.31/13.15 (
% 97.31/13.15 (
% 97.31/13.15 ('#B') @ (
% 97.31/13.15 (
% 97.31/13.15 ('#B') @ (
% 97.31/13.15 =>))) @
% 97.31/13.15 (
% 97.31/13.15 (
% 97.31/13.15 ('#C') @ (
% 97.31/13.15 (
% 97.31/13.15 ('#B') @ (
% 97.31/13.15 '#B') @
% 97.31/13.15 (
% 97.31/13.15 (
% 97.31/13.15 ('#B') @ (
% 97.31/13.15 =) @
% 97.31/13.15 omegaS)))) @
% 97.31/13.15 omegaS)))))) @
% 97.31/13.15 (
% 97.31/13.15 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.31/13.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl89])).
% 97.31/13.15 thf(zip_derived_cl123, plain,
% 97.31/13.15 (~ (((prop2setE) =>
% 97.31/13.15 (((emptysetE) =>
% 97.31/13.15 (((emptysetimpfalse) =>
% 97.31/13.15 (((notinemptyset) =>
% 97.31/13.15 (((exuE3e) =>
% 97.31/13.15 (((setext) =>
% 97.31/13.15 (((emptyI) =>
% 97.31/13.15 (((noeltsimpempty) =>
% 97.31/13.15 (((setbeta) =>
% 97.31/13.15 (((nonemptyE1) =>
% 97.31/13.15 (((nonemptyI) =>
% 97.31/13.15 (((nonemptyI1) =>
% 97.31/13.15 (((setadjoinIL) =>
% 97.31/13.15 (((in @ emptyset @
% 97.31/13.15 (setadjoin @ emptyset @ emptyset)) =>
% 97.31/13.15 (((setadjoinIR) =>
% 97.31/13.15 (((setadjoinE) =>
% 97.31/13.15 (((setadjoinOr) =>
% 97.31/13.15 (((setoftrueEq) =>
% 97.31/13.15 (((powersetI) =>
% 97.31/13.15 (((emptyinPowerset) =>
% 97.31/13.15 (((emptyInPowerset) =>
% 97.31/13.15 (((powersetE) =>
% 97.31/13.15 (((setunionI) =>
% 97.31/13.15 (((setunionE) =>
% 97.31/13.15 (((subPowSU) =>
% 97.31/13.15 (((exuE2) =>
% 97.31/13.15 (((nonemptyImpWitness) =>
% 97.31/13.15 (((uniqinunit) =>
% 97.31/13.15 (((notinsingleton) =>
% 97.31/13.15 (((eqinunit) =>
% 97.31/13.15 ((
% 97.31/13.15 (singletonsswitch) =>
% 97.31/13.15 ((
% 97.31/13.15 (upairsetE) =>
% 97.31/13.15 ((
% 97.31/13.15 (upairsetIL) =>
% 97.31/13.15 ((
% 97.31/13.15 (upairsetIR) =>
% 97.31/13.15 ((
% 97.31/13.15 (emptyE1) =>
% 97.31/13.15 ((
% 97.31/13.15 (vacuousDall) =>
% 97.31/13.15 ((
% 97.31/13.15 (quantDeMorgan1) =>
% 97.31/13.15 ((
% 97.31/13.15 (quantDeMorgan2) =>
% 97.31/13.15 ((
% 97.31/13.15 (quantDeMorgan3) =>
% 97.31/13.15 ((
% 97.31/13.15 (quantDeMorgan4) =>
% 97.31/13.15 ((
% 97.31/13.15 (prop2setI) =>
% 97.31/13.15 ((
% 97.31/13.15 (prop2set2propI) =>
% 97.31/13.15 ((
% 97.31/13.15 (notdexE) =>
% 97.31/13.15 ((
% 97.31/13.15 (notdallE) =>
% 97.31/13.15 ((
% 97.31/13.15 (exuI1) =>
% 97.31/13.15 ((
% 97.31/13.15 (exuI3) =>
% 97.31/13.15 ((
% 97.31/13.15 (exuI2) =>
% 97.31/13.15 ((
% 97.31/13.15 (inCongP) =>
% 97.31/13.15 ((
% 97.31/13.15 (in__Cong) =>
% 97.31/13.15 ((
% 97.31/13.15 (exuE3u) =>
% 97.31/13.15 ((
% 97.31/13.15 (exu__Cong) =>
% 97.31/13.15 ((
% 97.31/13.15 (setadjoin__Cong) =>
% 97.31/13.15 ((
% 97.31/13.15 (powerset__Cong) =>
% 97.31/13.15 ((
% 97.31/13.15 (setunion__Cong) =>
% 97.31/13.15 ((
% 97.31/13.15 (exuEu) =>
% 97.31/13.15 ((
% 97.31/13.15 (descr__Cong) =>
% 97.31/13.15 ((
% 97.31/13.15 (dsetconstr__Cong) =>
% 97.31/13.15 ((
% 97.31/13.15 (subsetI1) =>
% 97.31/13.15 ((
% 97.31/13.15 (eqimpsubset2) =>
% 97.31/13.15 ((
% 97.31/13.15 (eqimpsubset1) =>
% 97.31/13.15 ((
% 97.31/13.15 (subsetI2) =>
% 97.31/13.15 ((
% 97.31/13.15 (emptysetsubset) =>
% 97.31/13.15 ((
% 97.31/13.15 (subsetE) =>
% 97.31/13.15 ((
% 97.31/13.15 (subsetE2) =>
% 97.31/13.15 ((
% 97.31/13.15 (notsubsetI) =>
% 97.31/13.15 ((
% 97.31/13.15 (notequalI1) =>
% 97.31/13.15 ((
% 97.31/13.15 (notequalI2) =>
% 97.31/13.15 ((
% 97.31/13.15 (subsetRefl) =>
% 97.31/13.15 ((
% 97.31/13.15 (subsetTrans) =>
% 97.31/13.15 ((
% 97.31/13.15 (setadjoinSub) =>
% 97.31/13.15 ((
% 97.31/13.15 (setadjoinSub2) =>
% 97.31/13.15 ((
% 97.31/13.15 (subset2powerset) =>
% 97.31/13.15 ((
% 97.31/13.15 (setextsub) =>
% 97.31/13.15 ((
% 97.31/13.15 (subsetemptysetimpeq) =>
% 97.31/13.15 ((
% 97.31/13.15 (powersetI1) =>
% 97.31/13.15 ((
% 97.31/13.15 (powersetE1) =>
% 97.31/13.15 ((
% 97.31/13.15 (inPowerset) =>
% 97.31/13.15 ((
% 97.31/13.15 (powersetsubset) =>
% 97.31/13.15 ((
% 97.31/13.15 (sepInPowerset) =>
% 97.31/13.15 ((
% 97.31/13.15 (sepSubset) =>
% 97.31/13.15 ((
% 97.31/13.15 (binunionIL) =>
% 97.31/13.15 ((
% 97.31/13.15 (upairset2IR) =>
% 97.31/13.15 ((
% 97.31/13.15 (binunionIR) =>
% 97.31/13.15 ((
% 97.31/13.15 (binunionEcases) =>
% 97.31/13.15 ((
% 97.31/13.15 (binunionE) =>
% 97.31/13.15 ((
% 97.31/13.15 (binunionLsub) =>
% 97.31/13.15 ((
% 97.31/13.15 (binunionRsub) =>
% 97.31/13.15 ((
% 97.31/13.15 (binintersectI) =>
% 97.31/13.15 ((
% 97.31/13.15 (binintersectSubset5) =>
% 97.31/13.15 ((
% 97.31/13.15 (binintersectEL) =>
% 97.31/13.15 ((
% 97.31/13.15 (binintersectLsub) =>
% 97.31/13.15 ((
% 97.31/13.15 (binintersectSubset2) =>
% 97.31/13.15 ((
% 97.31/13.15 (binintersectSubset3) =>
% 97.31/13.15 ((
% 97.31/13.15 (binintersectER) =>
% 97.31/13.15 ((
% 97.31/13.15 (disjointsetsI1) =>
% 97.31/13.15 ((
% 97.31/13.15 (binintersectRsub) =>
% 97.31/13.15 ((
% 97.31/13.15 (binintersectSubset4) =>
% 97.31/13.15 ((
% 97.31/13.15 (binintersectSubset1) =>
% 97.31/13.15 ((
% 97.31/13.15 (bs114d) =>
% 97.31/13.15 ((
% 97.31/13.15 (setminusI) =>
% 97.31/13.15 ((
% 97.31/13.15 (setminusEL) =>
% 97.31/13.15 ((
% 97.31/13.15 (setminusER) =>
% 97.31/13.15 ((
% 97.31/13.15 (setminusSubset2) =>
% 97.31/13.15 ((
% 97.31/13.15 (setminusERneg) =>
% 97.31/13.15 ((
% 97.31/13.15 (setminusELneg) =>
% 97.31/13.15 ((
% 97.31/13.15 (setminusILneg) =>
% 97.31/13.15 ((
% 97.31/13.15 (setminusIRneg) =>
% 97.31/13.15 ((
% 97.31/13.15 (setminusLsub) =>
% 97.31/13.15 ((
% 97.31/13.15 (setminusSubset1) =>
% 97.31/13.15 ((
% 97.31/13.15 (symdiffE) =>
% 97.31/13.15 ((
% 97.31/13.15 (symdiffI1) =>
% 97.31/13.15 ((
% 97.31/13.15 (symdiffI2) =>
% 97.31/13.15 ((
% 97.31/13.15 (symdiffIneg1) =>
% 97.31/13.15 ((
% 97.31/13.15 (symdiffIneg2) =>
% 97.31/13.15 ((
% 97.31/13.15 (secondinupair) =>
% 97.31/13.15 ((
% 97.31/13.15 (setukpairIL) =>
% 97.31/13.15 ((
% 97.31/13.15 (setukpairIR) =>
% 97.31/13.15 ((
% 97.31/13.15 (kpairiskpair) =>
% 97.31/13.15 ((
% 97.31/13.15 (kpairp) =>
% 97.31/13.15 ((
% 97.31/13.15 (singletonsubset) =>
% 97.31/13.15 ((
% 97.31/13.15 (singletoninpowerset) =>
% 97.31/13.15 ((
% 97.31/13.15 (singletoninpowunion) =>
% 97.31/13.15 ((
% 97.31/13.15 (upairset2E) =>
% 97.31/13.15 ((
% 97.31/13.15 (upairsubunion) =>
% 97.31/13.15 ((
% 97.31/13.15 (upairinpowunion) =>
% 97.31/13.15 ((
% 97.31/13.15 (ubforcartprodlem1) =>
% 97.31/13.15 ((
% 97.31/13.15 (ubforcartprodlem2) =>
% 97.31/13.15 ((
% 97.31/13.15 (ubforcartprodlem3) =>
% 97.31/13.15 ((
% 97.31/13.15 (cartprodpairin) =>
% 97.31/13.15 ((
% 97.31/13.15 (cartprodmempair1) =>
% 97.31/13.15 ((
% 97.31/13.15 (cartprodmempair) =>
% 97.31/13.15 ((
% 97.31/13.15 (setunionE2) =>
% 97.31/13.15 ((
% 97.31/13.15 (setunionsingleton1) =>
% 97.31/13.15 ((
% 97.31/13.15 (setunionsingleton2) =>
% 97.31/13.15 ((
% 97.31/13.15 (setunionsingleton) =>
% 97.31/13.15 ((
% 97.31/13.15 (singletonprop) =>
% 97.31/13.15 ((
% 97.31/13.15 (ex1E1) =>
% 97.31/13.15 ((
% 97.31/13.15 (ex1I) =>
% 97.31/13.15 ((
% 97.31/13.15 (ex1I2) =>
% 97.31/13.15 ((
% 97.31/13.15 (singletonsuniq) =>
% 97.31/13.15 ((
% 97.31/13.15 (setukpairinjL1) =>
% 97.31/13.15 ((
% 97.31/13.15 (kfstsingleton) =>
% 97.31/13.15 ((
% 97.31/13.15 (theprop) =>
% 97.31/13.15 ((
% 97.31/13.15 (kfstpairEq) =>
% 97.31/13.15 ((
% 97.31/13.15 (cartprodfstin) =>
% 97.31/13.15 ((
% 97.31/13.15 (setukpairinjL2) =>
% 97.31/13.15 ((
% 97.31/13.15 (setukpairinjL) =>
% 97.31/13.15 ((
% 97.31/13.15 (setukpairinjR11) =>
% 97.31/13.15 ((
% 97.31/13.15 (setukpairinjR12) =>
% 97.31/13.15 ((
% 97.31/13.15 (setukpairinjR1) =>
% 97.31/13.15 ((
% 97.31/13.15 (upairequniteq) =>
% 97.31/13.15 ((
% 97.31/13.15 (setukpairinjR2) =>
% 97.31/13.15 ((
% 97.31/13.15 (setukpairinjR) =>
% 97.31/13.15 ((
% 97.31/13.15 (ksndsingleton) =>
% 97.31/13.15 ((
% 97.31/13.15 (ksndpairEq) =>
% 97.31/13.15 ((
% 97.31/13.15 (kpairsurjEq) =>
% 97.31/13.15 ((
% 97.31/13.15 (cartprodsndin) =>
% 97.31/13.15 ((
% 97.31/13.15 (cartprodpairmemEL) =>
% 97.31/13.15 ((
% 97.31/13.15 (cartprodpairmemER) =>
% 97.31/13.15 ((
% 97.31/13.15 (cartprodmempaircEq) =>
% 97.31/13.15 ((
% 97.31/13.15 (cartprodfstpairEq) =>
% 97.31/13.15 ((
% 97.31/13.15 (cartprodsndpairEq) =>
% 97.31/13.15 ((
% 97.31/13.15 (cartprodpairsurjEq) =>
% 97.31/13.15 ((
% 97.31/13.15 (dpsetconstrI) =>
% 97.31/13.15 ((
% 97.31/13.15 (dpsetconstrSub) =>
% 97.31/13.15 ((
% 97.31/13.15 (setOfPairsIsBReln) =>
% 97.31/13.15 ((
% 97.31/13.15 (dpsetconstrERa) =>
% 97.31/13.15 ((
% 97.31/13.15 (dpsetconstrEL1) =>
% 97.31/13.15 ((
% 97.31/13.15 (dpsetconstrEL2) =>
% 97.31/13.15 ((
% 97.31/13.15 (dpsetconstrER) =>
% 97.31/13.15 ((
% 97.31/13.15 (funcImageSingleton) =>
% 97.31/13.15 ((
% 97.31/13.15 (apProp) =>
% 97.31/13.15 ((
% 97.31/13.15 (app) =>
% 97.31/13.15 ((
% 97.31/13.15 (infuncsetfunc) =>
% 97.31/13.15 ((
% 97.31/13.15 (ap2p) =>
% 97.31/13.15 ((
% 97.31/13.15 (funcinfuncset) =>
% 97.31/13.15 ((
% 97.31/13.15 (lamProp) =>
% 97.31/13.15 ((
% 97.31/13.15 (lamp) =>
% 97.31/13.15 ((
% 97.31/13.15 (lam2p) =>
% 97.31/13.15 ((
% 97.31/13.15 (brelnall1) =>
% 97.31/13.15 ((
% 97.31/13.15 (brelnall2) =>
% 97.31/13.15 ((
% 97.31/13.15 (ex1E2) =>
% 97.31/13.15 ((
% 97.31/13.15 (funcGraphProp1) =>
% 97.31/13.15 ((
% 97.31/13.15 (funcGraphProp3) =>
% 97.31/13.15 ((
% 97.31/13.15 (funcGraphProp2) =>
% 97.31/13.15 ((
% 97.31/13.15 (funcextLem) =>
% 97.31/13.15 ((
% 97.31/13.15 (funcGraphProp4) =>
% 97.31/13.15 ((
% 97.31/13.15 (subbreln) =>
% 97.31/13.15 ((
% 97.31/13.15 (eqbreln) =>
% 97.31/13.15 ((
% 97.31/13.15 (funcext) =>
% 97.31/13.15 ((
% 97.31/13.15 (funcext2) =>
% 97.31/13.15 ((
% 97.31/13.15 (ap2apEq1) =>
% 97.31/13.15 ((
% 97.31/13.15 (ap2apEq2) =>
% 97.31/13.15 ((
% 97.31/13.15 (beta1) =>
% 97.31/13.15 ((
% 97.31/13.15 (eta1) =>
% 97.31/13.15 ((
% 97.31/13.15 (lam2lamEq) =>
% 97.31/13.15 ((
% 97.31/13.15 (beta2) =>
% 97.31/13.15 ((
% 97.31/13.15 (eta2) =>
% 97.31/13.15 ((
% 97.31/13.15 (iffalseProp1) =>
% 97.31/13.15 ((
% 97.31/13.15 (iffalseProp2) =>
% 97.31/13.15 ((
% 97.31/13.15 (iftrueProp1) =>
% 97.31/13.15 ((
% 97.31/13.15 (iftrueProp2) =>
% 97.31/13.15 ((
% 97.31/13.15 (ifSingleton) =>
% 97.31/13.15 ((
% 97.31/13.15 (ifp) =>
% 97.31/13.15 ((
% 97.31/13.15 (theeq) =>
% 97.31/13.15 ((
% 97.31/13.15 (iftrue) =>
% 97.31/13.15 ((
% 97.31/13.15 (iffalse) =>
% 97.31/13.15 ((
% 97.31/13.15 (iftrueorfalse) =>
% 97.31/13.15 ((
% 97.31/13.15 (binintersectT_lem) =>
% 97.31/13.15 ((
% 97.31/13.15 (binunionT_lem) =>
% 97.31/13.15 ((
% 97.31/13.15 (powersetT_lem) =>
% 97.31/13.15 ((
% 97.31/13.15 (setminusT_lem) =>
% 97.31/13.15 ((
% 97.31/13.15 (complementT_lem) =>
% 97.31/13.15 ((
% 97.31/13.15 (setextT) =>
% 97.31/13.15 ((
% 97.31/13.15 (subsetTI) =>
% 97.31/13.15 ((
% 97.31/13.15 (powersetTI1) =>
% 97.31/13.15 ((
% 97.31/13.15 (powersetTE1) =>
% 97.31/13.15 ((
% 97.31/13.15 (complementTI1) =>
% 97.31/13.15 ((
% 97.31/13.15 (complementTE1) =>
% 97.31/13.15 ((
% 97.31/13.15 (binintersectTELcontra) =>
% 97.31/13.15 ((
% 97.31/13.15 (binintersectTERcontra) =>
% 97.31/13.15 ((
% 97.31/13.15 (contrasubsetT) =>
% 97.31/13.15 ((
% 97.31/13.15 (contrasubsetT1) =>
% 97.31/13.15 ((
% 97.31/13.15 (contrasubsetT2) =>
% 97.31/13.15 ((
% 97.31/13.15 (contrasubsetT3) =>
% 97.31/13.15 ((
% 97.31/13.15 (doubleComplementI1) =>
% 97.31/13.15 ((
% 97.31/13.15 (doubleComplementE1) =>
% 97.31/13.15 ((
% 97.31/13.15 (doubleComplementSub1) =>
% 97.31/13.15 ((
% 97.31/13.15 (doubleComplementSub2) =>
% 97.31/13.15 ((
% 97.31/13.15 (doubleComplementEq) =>
% 97.31/13.15 ((
% 97.31/13.15 (complementTnotintersectT) =>
% 97.31/13.15 ((
% 97.31/13.15 (complementImpComplementIntersect) =>
% 97.31/13.15 ((
% 97.31/13.15 (complementSubsetComplementIntersect) =>
% 97.31/13.15 ((
% 97.31/13.15 (complementInPowersetComplementIntersect) =>
% 97.31/13.15 ((
% 97.31/13.15 (contraSubsetComplement) =>
% 97.31/13.15 ((
% 97.31/13.15 (complementTcontraSubset) =>
% 97.31/13.15 ((
% 97.31/13.15 (binunionTILcontra) =>
% 97.31/13.15 ((
% 97.31/13.15 (binunionTIRcontra) =>
% 97.31/13.15 ((
% 97.31/13.15 (inIntersectImpInUnion) =>
% 97.31/13.15 ((
% 97.31/13.15 (inIntersectImpInUnion2) =>
% 97.31/13.15 ((
% 97.31/13.15 (inIntersectImpInIntersectUnions) =>
% 97.31/13.15 ((
% 97.31/13.15 (intersectInPowersetIntersectUnions) =>
% 97.31/13.15 ((
% 97.31/13.15 (inComplementUnionImpNotIn1) =>
% 97.31/13.15 ((
% 97.31/13.15 (inComplementUnionImpInComplement1) =>
% 97.31/13.15 ((
% 97.31/13.15 (binunionTE) =>
% 97.31/13.15 ((
% 97.31/13.15 (binunionTEcontra) =>
% 97.31/13.15 ((
% 97.31/13.15 (demorgan2a1) =>
% 97.31/13.15 ((
% 97.31/13.15 (complementUnionInPowersetComplement) =>
% 97.31/13.15 ((
% 97.31/13.15 (demorgan2a2) =>
% 97.31/13.15 ((
% 97.31/13.15 (demorgan1a) =>
% 97.31/13.15 ((
% 97.31/13.15 (demorgan1b) =>
% 97.31/13.15 ((
% 97.31/13.15 (demorgan1) =>
% 97.31/13.15 ((
% 97.31/13.15 (demorgan2a) =>
% 97.31/13.15 ((
% 97.31/13.15 (demorgan2b2) =>
% 97.31/13.15 ((
% 97.31/13.15 (demorgan2b) =>
% 97.31/13.15 ((
% 97.31/13.15 (demorgan2) =>
% 97.31/13.15 ((
% 97.31/13.15 (woz13rule0) =>
% 97.31/13.15 ((
% 97.31/13.15 (woz13rule1) =>
% 97.31/13.15 ((
% 97.31/13.15 (woz13rule2) =>
% 97.31/13.15 ((
% 97.31/13.15 (woz13rule3) =>
% 97.31/13.15 ((
% 97.31/13.15 (woz13rule4) =>
% 97.31/13.15 ((
% 97.31/13.15 (woz1_1) =>
% 97.31/13.15 ((
% 97.31/13.15 (woz1_2) =>
% 97.31/13.15 ((
% 97.31/13.15 (woz1_3) =>
% 97.31/13.15 ((
% 97.31/13.15 (woz1_4) =>
% 97.31/13.15 ((
% 97.31/13.15 (woz1_5) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1all2) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1SetBreln1) =>
% 97.31/13.15 ((
% 97.31/13.15 (choice2fnsingleton) =>
% 97.31/13.15 ((
% 97.31/13.15 (setOfPairsIsBReln1) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1all1) =>
% 97.31/13.15 ((
% 97.31/13.15 (subbreln1) =>
% 97.31/13.15 ((
% 97.31/13.15 (eqbreln1) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1invprop) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1invI) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1invE) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1compprop) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1compI) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1compE) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1compEex) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1unionprop) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1unionIL) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1unionIR) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1unionI) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1unionE) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1unionEcases) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1unionCommutes) =>
% 97.31/13.15 ((
% 97.31/13.15 (woz2Ex) =>
% 97.31/13.15 ((
% 97.31/13.15 (woz2W) =>
% 97.31/13.15 ((
% 97.31/13.15 (woz2A) =>
% 97.31/13.15 ((
% 97.31/13.15 (woz2B) =>
% 97.31/13.15 ((
% 97.31/13.15 (image1Ex) =>
% 97.31/13.15 ((
% 97.31/13.15 (image1Ex1) =>
% 97.31/13.15 ((
% 97.31/13.15 (image1Equiv) =>
% 97.31/13.15 ((
% 97.31/13.15 (image1E) =>
% 97.31/13.15 ((
% 97.31/13.15 (image1I) =>
% 97.31/13.15 ((
% 97.31/13.15 (injFuncInInjFuncSet) =>
% 97.31/13.15 ((
% 97.31/13.15 (injFuncSetFuncIn) =>
% 97.31/13.15 ((
% 97.31/13.15 (injFuncSetFuncInj) =>
% 97.31/13.15 ((
% 97.31/13.15 (surjFuncSetFuncIn) =>
% 97.31/13.15 ((
% 97.31/13.15 (surjFuncSetFuncSurj) =>
% 97.31/13.15 ((
% 97.31/13.15 (leftInvIsSurj) =>
% 97.31/13.15 ((
% 97.31/13.15 (surjCantorThm) =>
% 97.31/13.15 ((
% 97.31/13.15 (foundation2) =>
% 97.31/13.15 ((
% 97.31/13.15 (notinself) =>
% 97.31/13.15 ((
% 97.31/13.15 (notinself2) =>
% 97.31/13.15 ((
% 97.31/13.15 (omegaSp) =>
% 97.31/13.15 ((
% 97.31/13.15 (omegaSclos) =>
% 97.31/13.15 ((
% 97.31/13.15 (peano0notS) =>
% 97.31/13.15 ((
% 97.31/13.15 (!!) @ (
% 97.31/13.15 (('#S') @ (
% 97.31/13.15 (
% 97.31/13.15 ('#B') @ (
% 97.31/13.15 =>) @
% 97.31/13.15 (
% 97.31/13.15 (
% 97.31/13.15 ('#C') @ in @
% 97.31/13.15 omega)))) @
% 97.31/13.15 (
% 97.31/13.15 (
% 97.31/13.15 ('#B') @ (
% 97.31/13.15 !!) @
% 97.31/13.15 (
% 97.31/13.15 (
% 97.31/13.15 ('#B') @ (
% 97.31/13.15 (
% 97.31/13.15 ('#S') @ (
% 97.31/13.15 (
% 97.31/13.15 ('#B') @ (
% 97.31/13.15 =>) @
% 97.31/13.15 (
% 97.31/13.15 (
% 97.31/13.15 ('#C') @ in @
% 97.31/13.15 omega)))))) @
% 97.31/13.15 (
% 97.31/13.15 (
% 97.31/13.15 ('#S') @ (
% 97.31/13.15 (
% 97.31/13.15 ('#B') @ (
% 97.31/13.15 '#S') @
% 97.31/13.15 (
% 97.31/13.15 (
% 97.31/13.15 ('#B') @ (
% 97.31/13.15 (
% 97.31/13.15 ('#B') @ (
% 97.31/13.15 =>))) @
% 97.31/13.15 (
% 97.31/13.15 (
% 97.31/13.15 ('#C') @ (
% 97.31/13.15 (
% 97.31/13.15 ('#B') @ (
% 97.31/13.15 '#B') @
% 97.31/13.15 (
% 97.31/13.15 (
% 97.31/13.15 ('#B') @ (
% 97.31/13.15 =) @
% 97.31/13.15 omegaS)))) @
% 97.31/13.15 omegaS)))))) @
% 97.31/13.15 (
% 97.31/13.15 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.31/13.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl105])).
% 97.31/13.15 thf(zip_derived_cl142, plain,
% 97.31/13.15 (~ (((emptysetE) =>
% 97.31/13.15 (((emptysetimpfalse) =>
% 97.31/13.15 (((notinemptyset) =>
% 97.31/13.15 (((exuE3e) =>
% 97.31/13.15 (((setext) =>
% 97.31/13.15 (((emptyI) =>
% 97.31/13.15 (((noeltsimpempty) =>
% 97.31/13.15 (((setbeta) =>
% 97.31/13.15 (((nonemptyE1) =>
% 97.31/13.15 (((nonemptyI) =>
% 97.31/13.15 (((nonemptyI1) =>
% 97.31/13.15 (((setadjoinIL) =>
% 97.31/13.15 (((in @ emptyset @
% 97.31/13.15 (setadjoin @ emptyset @ emptyset)) =>
% 97.31/13.15 (((setadjoinIR) =>
% 97.31/13.15 (((setadjoinE) =>
% 97.31/13.15 (((setadjoinOr) =>
% 97.31/13.15 (((setoftrueEq) =>
% 97.31/13.15 (((powersetI) =>
% 97.31/13.15 (((emptyinPowerset) =>
% 97.31/13.15 (((emptyInPowerset) =>
% 97.31/13.15 (((powersetE) =>
% 97.31/13.15 (((setunionI) =>
% 97.31/13.15 (((setunionE) =>
% 97.31/13.15 (((subPowSU) =>
% 97.31/13.15 (((exuE2) =>
% 97.31/13.15 (((nonemptyImpWitness) =>
% 97.31/13.15 (((uniqinunit) =>
% 97.31/13.15 (((notinsingleton) =>
% 97.31/13.15 (((eqinunit) =>
% 97.31/13.15 (((singletonsswitch) =>
% 97.31/13.15 ((
% 97.31/13.15 (upairsetE) =>
% 97.31/13.15 ((
% 97.31/13.15 (upairsetIL) =>
% 97.31/13.15 ((
% 97.31/13.15 (upairsetIR) =>
% 97.31/13.15 ((
% 97.31/13.15 (emptyE1) =>
% 97.31/13.15 ((
% 97.31/13.15 (vacuousDall) =>
% 97.31/13.15 ((
% 97.31/13.15 (quantDeMorgan1) =>
% 97.31/13.15 ((
% 97.31/13.15 (quantDeMorgan2) =>
% 97.31/13.15 ((
% 97.31/13.15 (quantDeMorgan3) =>
% 97.31/13.15 ((
% 97.31/13.15 (quantDeMorgan4) =>
% 97.31/13.15 ((
% 97.31/13.15 (prop2setI) =>
% 97.31/13.15 ((
% 97.31/13.15 (prop2set2propI) =>
% 97.31/13.15 ((
% 97.31/13.15 (notdexE) =>
% 97.31/13.15 ((
% 97.31/13.15 (notdallE) =>
% 97.31/13.15 ((
% 97.31/13.15 (exuI1) =>
% 97.31/13.15 ((
% 97.31/13.15 (exuI3) =>
% 97.31/13.15 ((
% 97.31/13.15 (exuI2) =>
% 97.31/13.15 ((
% 97.31/13.15 (inCongP) =>
% 97.31/13.15 ((
% 97.31/13.15 (in__Cong) =>
% 97.31/13.15 ((
% 97.31/13.15 (exuE3u) =>
% 97.31/13.15 ((
% 97.31/13.15 (exu__Cong) =>
% 97.31/13.15 ((
% 97.31/13.15 (setadjoin__Cong) =>
% 97.31/13.15 ((
% 97.31/13.15 (powerset__Cong) =>
% 97.31/13.15 ((
% 97.31/13.15 (setunion__Cong) =>
% 97.31/13.15 ((
% 97.31/13.15 (exuEu) =>
% 97.31/13.15 ((
% 97.31/13.15 (descr__Cong) =>
% 97.31/13.15 ((
% 97.31/13.15 (dsetconstr__Cong) =>
% 97.31/13.15 ((
% 97.31/13.15 (subsetI1) =>
% 97.31/13.15 ((
% 97.31/13.15 (eqimpsubset2) =>
% 97.31/13.15 ((
% 97.31/13.15 (eqimpsubset1) =>
% 97.31/13.15 ((
% 97.31/13.15 (subsetI2) =>
% 97.31/13.15 ((
% 97.31/13.15 (emptysetsubset) =>
% 97.31/13.15 ((
% 97.31/13.15 (subsetE) =>
% 97.31/13.15 ((
% 97.31/13.15 (subsetE2) =>
% 97.31/13.15 ((
% 97.31/13.15 (notsubsetI) =>
% 97.31/13.15 ((
% 97.31/13.15 (notequalI1) =>
% 97.31/13.15 ((
% 97.31/13.15 (notequalI2) =>
% 97.31/13.15 ((
% 97.31/13.15 (subsetRefl) =>
% 97.31/13.15 ((
% 97.31/13.15 (subsetTrans) =>
% 97.31/13.15 ((
% 97.31/13.15 (setadjoinSub) =>
% 97.31/13.15 ((
% 97.31/13.15 (setadjoinSub2) =>
% 97.31/13.15 ((
% 97.31/13.15 (subset2powerset) =>
% 97.31/13.15 ((
% 97.31/13.15 (setextsub) =>
% 97.31/13.15 ((
% 97.31/13.15 (subsetemptysetimpeq) =>
% 97.31/13.15 ((
% 97.31/13.15 (powersetI1) =>
% 97.31/13.15 ((
% 97.31/13.15 (powersetE1) =>
% 97.31/13.15 ((
% 97.31/13.15 (inPowerset) =>
% 97.31/13.15 ((
% 97.31/13.15 (powersetsubset) =>
% 97.31/13.15 ((
% 97.31/13.15 (sepInPowerset) =>
% 97.31/13.15 ((
% 97.31/13.15 (sepSubset) =>
% 97.31/13.15 ((
% 97.31/13.15 (binunionIL) =>
% 97.31/13.15 ((
% 97.31/13.15 (upairset2IR) =>
% 97.31/13.15 ((
% 97.31/13.15 (binunionIR) =>
% 97.31/13.15 ((
% 97.31/13.15 (binunionEcases) =>
% 97.31/13.15 ((
% 97.31/13.15 (binunionE) =>
% 97.31/13.15 ((
% 97.31/13.15 (binunionLsub) =>
% 97.31/13.15 ((
% 97.31/13.15 (binunionRsub) =>
% 97.31/13.15 ((
% 97.31/13.15 (binintersectI) =>
% 97.31/13.15 ((
% 97.31/13.15 (binintersectSubset5) =>
% 97.31/13.15 ((
% 97.31/13.15 (binintersectEL) =>
% 97.31/13.15 ((
% 97.31/13.15 (binintersectLsub) =>
% 97.31/13.15 ((
% 97.31/13.15 (binintersectSubset2) =>
% 97.31/13.15 ((
% 97.31/13.15 (binintersectSubset3) =>
% 97.31/13.15 ((
% 97.31/13.15 (binintersectER) =>
% 97.31/13.15 ((
% 97.31/13.15 (disjointsetsI1) =>
% 97.31/13.15 ((
% 97.31/13.15 (binintersectRsub) =>
% 97.31/13.15 ((
% 97.31/13.15 (binintersectSubset4) =>
% 97.31/13.15 ((
% 97.31/13.15 (binintersectSubset1) =>
% 97.31/13.15 ((
% 97.31/13.15 (bs114d) =>
% 97.31/13.15 ((
% 97.31/13.15 (setminusI) =>
% 97.31/13.15 ((
% 97.31/13.15 (setminusEL) =>
% 97.31/13.15 ((
% 97.31/13.15 (setminusER) =>
% 97.31/13.15 ((
% 97.31/13.15 (setminusSubset2) =>
% 97.31/13.15 ((
% 97.31/13.15 (setminusERneg) =>
% 97.31/13.15 ((
% 97.31/13.15 (setminusELneg) =>
% 97.31/13.15 ((
% 97.31/13.15 (setminusILneg) =>
% 97.31/13.15 ((
% 97.31/13.15 (setminusIRneg) =>
% 97.31/13.15 ((
% 97.31/13.15 (setminusLsub) =>
% 97.31/13.15 ((
% 97.31/13.15 (setminusSubset1) =>
% 97.31/13.15 ((
% 97.31/13.15 (symdiffE) =>
% 97.31/13.15 ((
% 97.31/13.15 (symdiffI1) =>
% 97.31/13.15 ((
% 97.31/13.15 (symdiffI2) =>
% 97.31/13.15 ((
% 97.31/13.15 (symdiffIneg1) =>
% 97.31/13.15 ((
% 97.31/13.15 (symdiffIneg2) =>
% 97.31/13.15 ((
% 97.31/13.15 (secondinupair) =>
% 97.31/13.15 ((
% 97.31/13.15 (setukpairIL) =>
% 97.31/13.15 ((
% 97.31/13.15 (setukpairIR) =>
% 97.31/13.15 ((
% 97.31/13.15 (kpairiskpair) =>
% 97.31/13.15 ((
% 97.31/13.15 (kpairp) =>
% 97.31/13.15 ((
% 97.31/13.15 (singletonsubset) =>
% 97.31/13.15 ((
% 97.31/13.15 (singletoninpowerset) =>
% 97.31/13.15 ((
% 97.31/13.15 (singletoninpowunion) =>
% 97.31/13.15 ((
% 97.31/13.15 (upairset2E) =>
% 97.31/13.15 ((
% 97.31/13.15 (upairsubunion) =>
% 97.31/13.15 ((
% 97.31/13.15 (upairinpowunion) =>
% 97.31/13.15 ((
% 97.31/13.15 (ubforcartprodlem1) =>
% 97.31/13.15 ((
% 97.31/13.15 (ubforcartprodlem2) =>
% 97.31/13.15 ((
% 97.31/13.15 (ubforcartprodlem3) =>
% 97.31/13.15 ((
% 97.31/13.15 (cartprodpairin) =>
% 97.31/13.15 ((
% 97.31/13.15 (cartprodmempair1) =>
% 97.31/13.15 ((
% 97.31/13.15 (cartprodmempair) =>
% 97.31/13.15 ((
% 97.31/13.15 (setunionE2) =>
% 97.31/13.15 ((
% 97.31/13.15 (setunionsingleton1) =>
% 97.31/13.15 ((
% 97.31/13.15 (setunionsingleton2) =>
% 97.31/13.15 ((
% 97.31/13.15 (setunionsingleton) =>
% 97.31/13.15 ((
% 97.31/13.15 (singletonprop) =>
% 97.31/13.15 ((
% 97.31/13.15 (ex1E1) =>
% 97.31/13.15 ((
% 97.31/13.15 (ex1I) =>
% 97.31/13.15 ((
% 97.31/13.15 (ex1I2) =>
% 97.31/13.15 ((
% 97.31/13.15 (singletonsuniq) =>
% 97.31/13.15 ((
% 97.31/13.15 (setukpairinjL1) =>
% 97.31/13.15 ((
% 97.31/13.15 (kfstsingleton) =>
% 97.31/13.15 ((
% 97.31/13.15 (theprop) =>
% 97.31/13.15 ((
% 97.31/13.15 (kfstpairEq) =>
% 97.31/13.15 ((
% 97.31/13.15 (cartprodfstin) =>
% 97.31/13.15 ((
% 97.31/13.15 (setukpairinjL2) =>
% 97.31/13.15 ((
% 97.31/13.15 (setukpairinjL) =>
% 97.31/13.15 ((
% 97.31/13.15 (setukpairinjR11) =>
% 97.31/13.15 ((
% 97.31/13.15 (setukpairinjR12) =>
% 97.31/13.15 ((
% 97.31/13.15 (setukpairinjR1) =>
% 97.31/13.15 ((
% 97.31/13.15 (upairequniteq) =>
% 97.31/13.15 ((
% 97.31/13.15 (setukpairinjR2) =>
% 97.31/13.15 ((
% 97.31/13.15 (setukpairinjR) =>
% 97.31/13.15 ((
% 97.31/13.15 (ksndsingleton) =>
% 97.31/13.15 ((
% 97.31/13.15 (ksndpairEq) =>
% 97.31/13.15 ((
% 97.31/13.15 (kpairsurjEq) =>
% 97.31/13.15 ((
% 97.31/13.15 (cartprodsndin) =>
% 97.31/13.15 ((
% 97.31/13.15 (cartprodpairmemEL) =>
% 97.31/13.15 ((
% 97.31/13.15 (cartprodpairmemER) =>
% 97.31/13.15 ((
% 97.31/13.15 (cartprodmempaircEq) =>
% 97.31/13.15 ((
% 97.31/13.15 (cartprodfstpairEq) =>
% 97.31/13.15 ((
% 97.31/13.15 (cartprodsndpairEq) =>
% 97.31/13.15 ((
% 97.31/13.15 (cartprodpairsurjEq) =>
% 97.31/13.15 ((
% 97.31/13.15 (dpsetconstrI) =>
% 97.31/13.15 ((
% 97.31/13.15 (dpsetconstrSub) =>
% 97.31/13.15 ((
% 97.31/13.15 (setOfPairsIsBReln) =>
% 97.31/13.15 ((
% 97.31/13.15 (dpsetconstrERa) =>
% 97.31/13.15 ((
% 97.31/13.15 (dpsetconstrEL1) =>
% 97.31/13.15 ((
% 97.31/13.15 (dpsetconstrEL2) =>
% 97.31/13.15 ((
% 97.31/13.15 (dpsetconstrER) =>
% 97.31/13.15 ((
% 97.31/13.15 (funcImageSingleton) =>
% 97.31/13.15 ((
% 97.31/13.15 (apProp) =>
% 97.31/13.15 ((
% 97.31/13.15 (app) =>
% 97.31/13.15 ((
% 97.31/13.15 (infuncsetfunc) =>
% 97.31/13.15 ((
% 97.31/13.15 (ap2p) =>
% 97.31/13.15 ((
% 97.31/13.15 (funcinfuncset) =>
% 97.31/13.15 ((
% 97.31/13.15 (lamProp) =>
% 97.31/13.15 ((
% 97.31/13.15 (lamp) =>
% 97.31/13.15 ((
% 97.31/13.15 (lam2p) =>
% 97.31/13.15 ((
% 97.31/13.15 (brelnall1) =>
% 97.31/13.15 ((
% 97.31/13.15 (brelnall2) =>
% 97.31/13.15 ((
% 97.31/13.15 (ex1E2) =>
% 97.31/13.15 ((
% 97.31/13.15 (funcGraphProp1) =>
% 97.31/13.15 ((
% 97.31/13.15 (funcGraphProp3) =>
% 97.31/13.15 ((
% 97.31/13.15 (funcGraphProp2) =>
% 97.31/13.15 ((
% 97.31/13.15 (funcextLem) =>
% 97.31/13.15 ((
% 97.31/13.15 (funcGraphProp4) =>
% 97.31/13.15 ((
% 97.31/13.15 (subbreln) =>
% 97.31/13.15 ((
% 97.31/13.15 (eqbreln) =>
% 97.31/13.15 ((
% 97.31/13.15 (funcext) =>
% 97.31/13.15 ((
% 97.31/13.15 (funcext2) =>
% 97.31/13.15 ((
% 97.31/13.15 (ap2apEq1) =>
% 97.31/13.15 ((
% 97.31/13.15 (ap2apEq2) =>
% 97.31/13.15 ((
% 97.31/13.15 (beta1) =>
% 97.31/13.15 ((
% 97.31/13.15 (eta1) =>
% 97.31/13.15 ((
% 97.31/13.15 (lam2lamEq) =>
% 97.31/13.15 ((
% 97.31/13.15 (beta2) =>
% 97.31/13.15 ((
% 97.31/13.15 (eta2) =>
% 97.31/13.15 ((
% 97.31/13.15 (iffalseProp1) =>
% 97.31/13.15 ((
% 97.31/13.15 (iffalseProp2) =>
% 97.31/13.15 ((
% 97.31/13.15 (iftrueProp1) =>
% 97.31/13.15 ((
% 97.31/13.15 (iftrueProp2) =>
% 97.31/13.15 ((
% 97.31/13.15 (ifSingleton) =>
% 97.31/13.15 ((
% 97.31/13.15 (ifp) =>
% 97.31/13.15 ((
% 97.31/13.15 (theeq) =>
% 97.31/13.15 ((
% 97.31/13.15 (iftrue) =>
% 97.31/13.15 ((
% 97.31/13.15 (iffalse) =>
% 97.31/13.15 ((
% 97.31/13.15 (iftrueorfalse) =>
% 97.31/13.15 ((
% 97.31/13.15 (binintersectT_lem) =>
% 97.31/13.15 ((
% 97.31/13.15 (binunionT_lem) =>
% 97.31/13.15 ((
% 97.31/13.15 (powersetT_lem) =>
% 97.31/13.15 ((
% 97.31/13.15 (setminusT_lem) =>
% 97.31/13.15 ((
% 97.31/13.15 (complementT_lem) =>
% 97.31/13.15 ((
% 97.31/13.15 (setextT) =>
% 97.31/13.15 ((
% 97.31/13.15 (subsetTI) =>
% 97.31/13.15 ((
% 97.31/13.15 (powersetTI1) =>
% 97.31/13.15 ((
% 97.31/13.15 (powersetTE1) =>
% 97.31/13.15 ((
% 97.31/13.15 (complementTI1) =>
% 97.31/13.15 ((
% 97.31/13.15 (complementTE1) =>
% 97.31/13.15 ((
% 97.31/13.15 (binintersectTELcontra) =>
% 97.31/13.15 ((
% 97.31/13.15 (binintersectTERcontra) =>
% 97.31/13.15 ((
% 97.31/13.15 (contrasubsetT) =>
% 97.31/13.15 ((
% 97.31/13.15 (contrasubsetT1) =>
% 97.31/13.15 ((
% 97.31/13.15 (contrasubsetT2) =>
% 97.31/13.15 ((
% 97.31/13.15 (contrasubsetT3) =>
% 97.31/13.15 ((
% 97.31/13.15 (doubleComplementI1) =>
% 97.31/13.15 ((
% 97.31/13.15 (doubleComplementE1) =>
% 97.31/13.15 ((
% 97.31/13.15 (doubleComplementSub1) =>
% 97.31/13.15 ((
% 97.31/13.15 (doubleComplementSub2) =>
% 97.31/13.15 ((
% 97.31/13.15 (doubleComplementEq) =>
% 97.31/13.15 ((
% 97.31/13.15 (complementTnotintersectT) =>
% 97.31/13.15 ((
% 97.31/13.15 (complementImpComplementIntersect) =>
% 97.31/13.15 ((
% 97.31/13.15 (complementSubsetComplementIntersect) =>
% 97.31/13.15 ((
% 97.31/13.15 (complementInPowersetComplementIntersect) =>
% 97.31/13.15 ((
% 97.31/13.15 (contraSubsetComplement) =>
% 97.31/13.15 ((
% 97.31/13.15 (complementTcontraSubset) =>
% 97.31/13.15 ((
% 97.31/13.15 (binunionTILcontra) =>
% 97.31/13.15 ((
% 97.31/13.15 (binunionTIRcontra) =>
% 97.31/13.15 ((
% 97.31/13.15 (inIntersectImpInUnion) =>
% 97.31/13.15 ((
% 97.31/13.15 (inIntersectImpInUnion2) =>
% 97.31/13.15 ((
% 97.31/13.15 (inIntersectImpInIntersectUnions) =>
% 97.31/13.15 ((
% 97.31/13.15 (intersectInPowersetIntersectUnions) =>
% 97.31/13.15 ((
% 97.31/13.15 (inComplementUnionImpNotIn1) =>
% 97.31/13.15 ((
% 97.31/13.15 (inComplementUnionImpInComplement1) =>
% 97.31/13.15 ((
% 97.31/13.15 (binunionTE) =>
% 97.31/13.15 ((
% 97.31/13.15 (binunionTEcontra) =>
% 97.31/13.15 ((
% 97.31/13.15 (demorgan2a1) =>
% 97.31/13.15 ((
% 97.31/13.15 (complementUnionInPowersetComplement) =>
% 97.31/13.15 ((
% 97.31/13.15 (demorgan2a2) =>
% 97.31/13.15 ((
% 97.31/13.15 (demorgan1a) =>
% 97.31/13.15 ((
% 97.31/13.15 (demorgan1b) =>
% 97.31/13.15 ((
% 97.31/13.15 (demorgan1) =>
% 97.31/13.15 ((
% 97.31/13.15 (demorgan2a) =>
% 97.31/13.15 ((
% 97.31/13.15 (demorgan2b2) =>
% 97.31/13.15 ((
% 97.31/13.15 (demorgan2b) =>
% 97.31/13.15 ((
% 97.31/13.15 (demorgan2) =>
% 97.31/13.15 ((
% 97.31/13.15 (woz13rule0) =>
% 97.31/13.15 ((
% 97.31/13.15 (woz13rule1) =>
% 97.31/13.15 ((
% 97.31/13.15 (woz13rule2) =>
% 97.31/13.15 ((
% 97.31/13.15 (woz13rule3) =>
% 97.31/13.15 ((
% 97.31/13.15 (woz13rule4) =>
% 97.31/13.15 ((
% 97.31/13.15 (woz1_1) =>
% 97.31/13.15 ((
% 97.31/13.15 (woz1_2) =>
% 97.31/13.15 ((
% 97.31/13.15 (woz1_3) =>
% 97.31/13.15 ((
% 97.31/13.15 (woz1_4) =>
% 97.31/13.15 ((
% 97.31/13.15 (woz1_5) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1all2) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1SetBreln1) =>
% 97.31/13.15 ((
% 97.31/13.15 (choice2fnsingleton) =>
% 97.31/13.15 ((
% 97.31/13.15 (setOfPairsIsBReln1) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1all1) =>
% 97.31/13.15 ((
% 97.31/13.15 (subbreln1) =>
% 97.31/13.15 ((
% 97.31/13.15 (eqbreln1) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1invprop) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1invI) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1invE) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1compprop) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1compI) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1compE) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1compEex) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1unionprop) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1unionIL) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1unionIR) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1unionI) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1unionE) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1unionEcases) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1unionCommutes) =>
% 97.31/13.15 ((
% 97.31/13.15 (woz2Ex) =>
% 97.31/13.15 ((
% 97.31/13.15 (woz2W) =>
% 97.31/13.15 ((
% 97.31/13.15 (woz2A) =>
% 97.31/13.15 ((
% 97.31/13.15 (woz2B) =>
% 97.31/13.15 ((
% 97.31/13.15 (image1Ex) =>
% 97.31/13.15 ((
% 97.31/13.15 (image1Ex1) =>
% 97.31/13.15 ((
% 97.31/13.15 (image1Equiv) =>
% 97.31/13.15 ((
% 97.31/13.15 (image1E) =>
% 97.31/13.15 ((
% 97.31/13.15 (image1I) =>
% 97.31/13.15 ((
% 97.31/13.15 (injFuncInInjFuncSet) =>
% 97.31/13.15 ((
% 97.31/13.15 (injFuncSetFuncIn) =>
% 97.31/13.15 ((
% 97.31/13.15 (injFuncSetFuncInj) =>
% 97.31/13.15 ((
% 97.31/13.15 (surjFuncSetFuncIn) =>
% 97.31/13.15 ((
% 97.31/13.15 (surjFuncSetFuncSurj) =>
% 97.31/13.15 ((
% 97.31/13.15 (leftInvIsSurj) =>
% 97.31/13.15 ((
% 97.31/13.15 (surjCantorThm) =>
% 97.31/13.15 ((
% 97.31/13.15 (foundation2) =>
% 97.31/13.15 ((
% 97.31/13.15 (notinself) =>
% 97.31/13.15 ((
% 97.31/13.15 (notinself2) =>
% 97.31/13.15 ((
% 97.31/13.15 (omegaSp) =>
% 97.31/13.15 ((
% 97.31/13.15 (omegaSclos) =>
% 97.31/13.15 ((
% 97.31/13.15 (peano0notS) =>
% 97.31/13.15 ((
% 97.31/13.15 (!!) @ (
% 97.31/13.15 (('#S') @ (
% 97.31/13.15 (
% 97.31/13.15 ('#B') @ (
% 97.31/13.15 =>) @
% 97.31/13.15 (
% 97.31/13.15 (
% 97.31/13.15 ('#C') @ in @
% 97.31/13.15 omega)))) @
% 97.31/13.15 (
% 97.31/13.15 (
% 97.31/13.15 ('#B') @ (
% 97.31/13.15 !!) @
% 97.31/13.15 (
% 97.31/13.15 (
% 97.31/13.15 ('#B') @ (
% 97.31/13.15 (
% 97.31/13.15 ('#S') @ (
% 97.31/13.15 (
% 97.31/13.15 ('#B') @ (
% 97.31/13.15 =>) @
% 97.31/13.15 (
% 97.31/13.15 (
% 97.31/13.15 ('#C') @ in @
% 97.31/13.15 omega)))))) @
% 97.31/13.15 (
% 97.31/13.15 (
% 97.31/13.15 ('#S') @ (
% 97.31/13.15 (
% 97.31/13.15 ('#B') @ (
% 97.31/13.15 '#S') @
% 97.31/13.15 (
% 97.31/13.15 (
% 97.31/13.15 ('#B') @ (
% 97.31/13.15 (
% 97.31/13.15 ('#B') @ (
% 97.31/13.15 =>))) @
% 97.31/13.15 (
% 97.31/13.15 (
% 97.31/13.15 ('#C') @ (
% 97.31/13.15 (
% 97.31/13.15 ('#B') @ (
% 97.31/13.15 '#B') @
% 97.31/13.15 (
% 97.31/13.15 (
% 97.31/13.15 ('#B') @ (
% 97.31/13.15 =) @
% 97.31/13.15 omegaS)))) @
% 97.31/13.15 omegaS)))))) @
% 97.31/13.15 (
% 97.31/13.15 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.31/13.15 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl123])).
% 97.31/13.15 thf(zip_derived_cl158, plain,
% 97.31/13.15 (~ (((emptysetimpfalse) =>
% 97.31/13.15 (((notinemptyset) =>
% 97.31/13.15 (((exuE3e) =>
% 97.31/13.15 (((setext) =>
% 97.31/13.15 (((emptyI) =>
% 97.31/13.15 (((noeltsimpempty) =>
% 97.31/13.15 (((setbeta) =>
% 97.31/13.15 (((nonemptyE1) =>
% 97.31/13.15 (((nonemptyI) =>
% 97.31/13.15 (((nonemptyI1) =>
% 97.31/13.15 (((setadjoinIL) =>
% 97.31/13.15 (((in @ emptyset @
% 97.31/13.15 (setadjoin @ emptyset @ emptyset)) =>
% 97.31/13.15 (((setadjoinIR) =>
% 97.31/13.15 (((setadjoinE) =>
% 97.31/13.15 (((setadjoinOr) =>
% 97.31/13.15 (((setoftrueEq) =>
% 97.31/13.15 (((powersetI) =>
% 97.31/13.15 (((emptyinPowerset) =>
% 97.31/13.15 (((emptyInPowerset) =>
% 97.31/13.15 (((powersetE) =>
% 97.31/13.15 (((setunionI) =>
% 97.31/13.15 (((setunionE) =>
% 97.31/13.15 (((subPowSU) =>
% 97.31/13.15 (((exuE2) =>
% 97.31/13.15 (((nonemptyImpWitness) =>
% 97.31/13.15 (((uniqinunit) =>
% 97.31/13.15 (((notinsingleton) =>
% 97.31/13.15 (((eqinunit) =>
% 97.31/13.15 (((singletonsswitch) =>
% 97.31/13.15 (((upairsetE) =>
% 97.31/13.15 ((
% 97.31/13.15 (upairsetIL) =>
% 97.31/13.15 ((
% 97.31/13.15 (upairsetIR) =>
% 97.31/13.15 ((
% 97.31/13.15 (emptyE1) =>
% 97.31/13.15 ((
% 97.31/13.15 (vacuousDall) =>
% 97.31/13.15 ((
% 97.31/13.15 (quantDeMorgan1) =>
% 97.31/13.15 ((
% 97.31/13.15 (quantDeMorgan2) =>
% 97.31/13.15 ((
% 97.31/13.15 (quantDeMorgan3) =>
% 97.31/13.15 ((
% 97.31/13.15 (quantDeMorgan4) =>
% 97.31/13.15 ((
% 97.31/13.15 (prop2setI) =>
% 97.31/13.15 ((
% 97.31/13.15 (prop2set2propI) =>
% 97.31/13.15 ((
% 97.31/13.15 (notdexE) =>
% 97.31/13.15 ((
% 97.31/13.15 (notdallE) =>
% 97.31/13.15 ((
% 97.31/13.15 (exuI1) =>
% 97.31/13.15 ((
% 97.31/13.15 (exuI3) =>
% 97.31/13.15 ((
% 97.31/13.15 (exuI2) =>
% 97.31/13.15 ((
% 97.31/13.15 (inCongP) =>
% 97.31/13.15 ((
% 97.31/13.15 (in__Cong) =>
% 97.31/13.15 ((
% 97.31/13.15 (exuE3u) =>
% 97.31/13.15 ((
% 97.31/13.15 (exu__Cong) =>
% 97.31/13.15 ((
% 97.31/13.15 (setadjoin__Cong) =>
% 97.31/13.15 ((
% 97.31/13.15 (powerset__Cong) =>
% 97.31/13.15 ((
% 97.31/13.15 (setunion__Cong) =>
% 97.31/13.15 ((
% 97.31/13.15 (exuEu) =>
% 97.31/13.15 ((
% 97.31/13.15 (descr__Cong) =>
% 97.31/13.15 ((
% 97.31/13.15 (dsetconstr__Cong) =>
% 97.31/13.15 ((
% 97.31/13.15 (subsetI1) =>
% 97.31/13.15 ((
% 97.31/13.15 (eqimpsubset2) =>
% 97.31/13.15 ((
% 97.31/13.15 (eqimpsubset1) =>
% 97.31/13.15 ((
% 97.31/13.15 (subsetI2) =>
% 97.31/13.15 ((
% 97.31/13.15 (emptysetsubset) =>
% 97.31/13.15 ((
% 97.31/13.15 (subsetE) =>
% 97.31/13.15 ((
% 97.31/13.15 (subsetE2) =>
% 97.31/13.15 ((
% 97.31/13.15 (notsubsetI) =>
% 97.31/13.15 ((
% 97.31/13.15 (notequalI1) =>
% 97.31/13.15 ((
% 97.31/13.15 (notequalI2) =>
% 97.31/13.15 ((
% 97.31/13.15 (subsetRefl) =>
% 97.31/13.15 ((
% 97.31/13.15 (subsetTrans) =>
% 97.31/13.15 ((
% 97.31/13.15 (setadjoinSub) =>
% 97.31/13.15 ((
% 97.31/13.15 (setadjoinSub2) =>
% 97.31/13.15 ((
% 97.31/13.15 (subset2powerset) =>
% 97.31/13.15 ((
% 97.31/13.15 (setextsub) =>
% 97.31/13.15 ((
% 97.31/13.15 (subsetemptysetimpeq) =>
% 97.31/13.15 ((
% 97.31/13.15 (powersetI1) =>
% 97.31/13.15 ((
% 97.31/13.15 (powersetE1) =>
% 97.31/13.15 ((
% 97.31/13.15 (inPowerset) =>
% 97.31/13.15 ((
% 97.31/13.15 (powersetsubset) =>
% 97.31/13.15 ((
% 97.31/13.15 (sepInPowerset) =>
% 97.31/13.15 ((
% 97.31/13.15 (sepSubset) =>
% 97.31/13.15 ((
% 97.31/13.15 (binunionIL) =>
% 97.31/13.15 ((
% 97.31/13.15 (upairset2IR) =>
% 97.31/13.15 ((
% 97.31/13.15 (binunionIR) =>
% 97.31/13.15 ((
% 97.31/13.15 (binunionEcases) =>
% 97.31/13.15 ((
% 97.31/13.15 (binunionE) =>
% 97.31/13.15 ((
% 97.31/13.15 (binunionLsub) =>
% 97.31/13.15 ((
% 97.31/13.15 (binunionRsub) =>
% 97.31/13.15 ((
% 97.31/13.15 (binintersectI) =>
% 97.31/13.15 ((
% 97.31/13.15 (binintersectSubset5) =>
% 97.31/13.15 ((
% 97.31/13.15 (binintersectEL) =>
% 97.31/13.15 ((
% 97.31/13.15 (binintersectLsub) =>
% 97.31/13.15 ((
% 97.31/13.15 (binintersectSubset2) =>
% 97.31/13.15 ((
% 97.31/13.15 (binintersectSubset3) =>
% 97.31/13.15 ((
% 97.31/13.15 (binintersectER) =>
% 97.31/13.15 ((
% 97.31/13.15 (disjointsetsI1) =>
% 97.31/13.15 ((
% 97.31/13.15 (binintersectRsub) =>
% 97.31/13.15 ((
% 97.31/13.15 (binintersectSubset4) =>
% 97.31/13.15 ((
% 97.31/13.15 (binintersectSubset1) =>
% 97.31/13.15 ((
% 97.31/13.15 (bs114d) =>
% 97.31/13.15 ((
% 97.31/13.15 (setminusI) =>
% 97.31/13.15 ((
% 97.31/13.15 (setminusEL) =>
% 97.31/13.15 ((
% 97.31/13.15 (setminusER) =>
% 97.31/13.15 ((
% 97.31/13.15 (setminusSubset2) =>
% 97.31/13.15 ((
% 97.31/13.15 (setminusERneg) =>
% 97.31/13.15 ((
% 97.31/13.15 (setminusELneg) =>
% 97.31/13.15 ((
% 97.31/13.15 (setminusILneg) =>
% 97.31/13.15 ((
% 97.31/13.15 (setminusIRneg) =>
% 97.31/13.15 ((
% 97.31/13.15 (setminusLsub) =>
% 97.31/13.15 ((
% 97.31/13.15 (setminusSubset1) =>
% 97.31/13.15 ((
% 97.31/13.15 (symdiffE) =>
% 97.31/13.15 ((
% 97.31/13.15 (symdiffI1) =>
% 97.31/13.15 ((
% 97.31/13.15 (symdiffI2) =>
% 97.31/13.15 ((
% 97.31/13.15 (symdiffIneg1) =>
% 97.31/13.15 ((
% 97.31/13.15 (symdiffIneg2) =>
% 97.31/13.15 ((
% 97.31/13.15 (secondinupair) =>
% 97.31/13.15 ((
% 97.31/13.15 (setukpairIL) =>
% 97.31/13.15 ((
% 97.31/13.15 (setukpairIR) =>
% 97.31/13.15 ((
% 97.31/13.15 (kpairiskpair) =>
% 97.31/13.15 ((
% 97.31/13.15 (kpairp) =>
% 97.31/13.15 ((
% 97.31/13.15 (singletonsubset) =>
% 97.31/13.15 ((
% 97.31/13.15 (singletoninpowerset) =>
% 97.31/13.15 ((
% 97.31/13.15 (singletoninpowunion) =>
% 97.31/13.15 ((
% 97.31/13.15 (upairset2E) =>
% 97.31/13.15 ((
% 97.31/13.15 (upairsubunion) =>
% 97.31/13.15 ((
% 97.31/13.15 (upairinpowunion) =>
% 97.31/13.15 ((
% 97.31/13.15 (ubforcartprodlem1) =>
% 97.31/13.15 ((
% 97.31/13.15 (ubforcartprodlem2) =>
% 97.31/13.15 ((
% 97.31/13.15 (ubforcartprodlem3) =>
% 97.31/13.15 ((
% 97.31/13.15 (cartprodpairin) =>
% 97.31/13.15 ((
% 97.31/13.15 (cartprodmempair1) =>
% 97.31/13.15 ((
% 97.31/13.15 (cartprodmempair) =>
% 97.31/13.15 ((
% 97.31/13.15 (setunionE2) =>
% 97.31/13.15 ((
% 97.31/13.15 (setunionsingleton1) =>
% 97.31/13.15 ((
% 97.31/13.15 (setunionsingleton2) =>
% 97.31/13.15 ((
% 97.31/13.15 (setunionsingleton) =>
% 97.31/13.15 ((
% 97.31/13.15 (singletonprop) =>
% 97.31/13.15 ((
% 97.31/13.15 (ex1E1) =>
% 97.31/13.15 ((
% 97.31/13.15 (ex1I) =>
% 97.31/13.15 ((
% 97.31/13.15 (ex1I2) =>
% 97.31/13.15 ((
% 97.31/13.15 (singletonsuniq) =>
% 97.31/13.15 ((
% 97.31/13.15 (setukpairinjL1) =>
% 97.31/13.15 ((
% 97.31/13.15 (kfstsingleton) =>
% 97.31/13.15 ((
% 97.31/13.15 (theprop) =>
% 97.31/13.15 ((
% 97.31/13.15 (kfstpairEq) =>
% 97.31/13.15 ((
% 97.31/13.15 (cartprodfstin) =>
% 97.31/13.15 ((
% 97.31/13.15 (setukpairinjL2) =>
% 97.31/13.15 ((
% 97.31/13.15 (setukpairinjL) =>
% 97.31/13.15 ((
% 97.31/13.15 (setukpairinjR11) =>
% 97.31/13.15 ((
% 97.31/13.15 (setukpairinjR12) =>
% 97.31/13.15 ((
% 97.31/13.15 (setukpairinjR1) =>
% 97.31/13.15 ((
% 97.31/13.15 (upairequniteq) =>
% 97.31/13.15 ((
% 97.31/13.15 (setukpairinjR2) =>
% 97.31/13.15 ((
% 97.31/13.15 (setukpairinjR) =>
% 97.31/13.15 ((
% 97.31/13.15 (ksndsingleton) =>
% 97.31/13.15 ((
% 97.31/13.15 (ksndpairEq) =>
% 97.31/13.15 ((
% 97.31/13.15 (kpairsurjEq) =>
% 97.31/13.15 ((
% 97.31/13.15 (cartprodsndin) =>
% 97.31/13.15 ((
% 97.31/13.15 (cartprodpairmemEL) =>
% 97.31/13.15 ((
% 97.31/13.15 (cartprodpairmemER) =>
% 97.31/13.15 ((
% 97.31/13.15 (cartprodmempaircEq) =>
% 97.31/13.15 ((
% 97.31/13.15 (cartprodfstpairEq) =>
% 97.31/13.15 ((
% 97.31/13.15 (cartprodsndpairEq) =>
% 97.31/13.15 ((
% 97.31/13.15 (cartprodpairsurjEq) =>
% 97.31/13.15 ((
% 97.31/13.15 (dpsetconstrI) =>
% 97.31/13.15 ((
% 97.31/13.15 (dpsetconstrSub) =>
% 97.31/13.15 ((
% 97.31/13.15 (setOfPairsIsBReln) =>
% 97.31/13.15 ((
% 97.31/13.15 (dpsetconstrERa) =>
% 97.31/13.15 ((
% 97.31/13.15 (dpsetconstrEL1) =>
% 97.31/13.15 ((
% 97.31/13.15 (dpsetconstrEL2) =>
% 97.31/13.15 ((
% 97.31/13.15 (dpsetconstrER) =>
% 97.31/13.15 ((
% 97.31/13.15 (funcImageSingleton) =>
% 97.31/13.15 ((
% 97.31/13.15 (apProp) =>
% 97.31/13.15 ((
% 97.31/13.15 (app) =>
% 97.31/13.15 ((
% 97.31/13.15 (infuncsetfunc) =>
% 97.31/13.15 ((
% 97.31/13.15 (ap2p) =>
% 97.31/13.15 ((
% 97.31/13.15 (funcinfuncset) =>
% 97.31/13.15 ((
% 97.31/13.15 (lamProp) =>
% 97.31/13.15 ((
% 97.31/13.15 (lamp) =>
% 97.31/13.15 ((
% 97.31/13.15 (lam2p) =>
% 97.31/13.15 ((
% 97.31/13.15 (brelnall1) =>
% 97.31/13.15 ((
% 97.31/13.15 (brelnall2) =>
% 97.31/13.15 ((
% 97.31/13.15 (ex1E2) =>
% 97.31/13.15 ((
% 97.31/13.15 (funcGraphProp1) =>
% 97.31/13.15 ((
% 97.31/13.15 (funcGraphProp3) =>
% 97.31/13.15 ((
% 97.31/13.15 (funcGraphProp2) =>
% 97.31/13.15 ((
% 97.31/13.15 (funcextLem) =>
% 97.31/13.15 ((
% 97.31/13.15 (funcGraphProp4) =>
% 97.31/13.15 ((
% 97.31/13.15 (subbreln) =>
% 97.31/13.15 ((
% 97.31/13.15 (eqbreln) =>
% 97.31/13.15 ((
% 97.31/13.15 (funcext) =>
% 97.31/13.15 ((
% 97.31/13.15 (funcext2) =>
% 97.31/13.15 ((
% 97.31/13.15 (ap2apEq1) =>
% 97.31/13.15 ((
% 97.31/13.15 (ap2apEq2) =>
% 97.31/13.15 ((
% 97.31/13.15 (beta1) =>
% 97.31/13.15 ((
% 97.31/13.15 (eta1) =>
% 97.31/13.15 ((
% 97.31/13.15 (lam2lamEq) =>
% 97.31/13.15 ((
% 97.31/13.15 (beta2) =>
% 97.31/13.15 ((
% 97.31/13.15 (eta2) =>
% 97.31/13.15 ((
% 97.31/13.15 (iffalseProp1) =>
% 97.31/13.15 ((
% 97.31/13.15 (iffalseProp2) =>
% 97.31/13.15 ((
% 97.31/13.15 (iftrueProp1) =>
% 97.31/13.15 ((
% 97.31/13.15 (iftrueProp2) =>
% 97.31/13.15 ((
% 97.31/13.15 (ifSingleton) =>
% 97.31/13.15 ((
% 97.31/13.15 (ifp) =>
% 97.31/13.15 ((
% 97.31/13.15 (theeq) =>
% 97.31/13.15 ((
% 97.31/13.15 (iftrue) =>
% 97.31/13.15 ((
% 97.31/13.15 (iffalse) =>
% 97.31/13.15 ((
% 97.31/13.15 (iftrueorfalse) =>
% 97.31/13.15 ((
% 97.31/13.15 (binintersectT_lem) =>
% 97.31/13.15 ((
% 97.31/13.15 (binunionT_lem) =>
% 97.31/13.15 ((
% 97.31/13.15 (powersetT_lem) =>
% 97.31/13.15 ((
% 97.31/13.15 (setminusT_lem) =>
% 97.31/13.15 ((
% 97.31/13.15 (complementT_lem) =>
% 97.31/13.15 ((
% 97.31/13.15 (setextT) =>
% 97.31/13.15 ((
% 97.31/13.15 (subsetTI) =>
% 97.31/13.15 ((
% 97.31/13.15 (powersetTI1) =>
% 97.31/13.15 ((
% 97.31/13.15 (powersetTE1) =>
% 97.31/13.15 ((
% 97.31/13.15 (complementTI1) =>
% 97.31/13.15 ((
% 97.31/13.15 (complementTE1) =>
% 97.31/13.15 ((
% 97.31/13.15 (binintersectTELcontra) =>
% 97.31/13.15 ((
% 97.31/13.15 (binintersectTERcontra) =>
% 97.31/13.15 ((
% 97.31/13.15 (contrasubsetT) =>
% 97.31/13.15 ((
% 97.31/13.15 (contrasubsetT1) =>
% 97.31/13.15 ((
% 97.31/13.15 (contrasubsetT2) =>
% 97.31/13.15 ((
% 97.31/13.15 (contrasubsetT3) =>
% 97.31/13.15 ((
% 97.31/13.15 (doubleComplementI1) =>
% 97.31/13.15 ((
% 97.31/13.15 (doubleComplementE1) =>
% 97.31/13.15 ((
% 97.31/13.15 (doubleComplementSub1) =>
% 97.31/13.15 ((
% 97.31/13.15 (doubleComplementSub2) =>
% 97.31/13.15 ((
% 97.31/13.15 (doubleComplementEq) =>
% 97.31/13.15 ((
% 97.31/13.15 (complementTnotintersectT) =>
% 97.31/13.15 ((
% 97.31/13.15 (complementImpComplementIntersect) =>
% 97.31/13.15 ((
% 97.31/13.15 (complementSubsetComplementIntersect) =>
% 97.31/13.15 ((
% 97.31/13.15 (complementInPowersetComplementIntersect) =>
% 97.31/13.15 ((
% 97.31/13.15 (contraSubsetComplement) =>
% 97.31/13.15 ((
% 97.31/13.15 (complementTcontraSubset) =>
% 97.31/13.15 ((
% 97.31/13.15 (binunionTILcontra) =>
% 97.31/13.15 ((
% 97.31/13.15 (binunionTIRcontra) =>
% 97.31/13.15 ((
% 97.31/13.15 (inIntersectImpInUnion) =>
% 97.31/13.15 ((
% 97.31/13.15 (inIntersectImpInUnion2) =>
% 97.31/13.15 ((
% 97.31/13.15 (inIntersectImpInIntersectUnions) =>
% 97.31/13.15 ((
% 97.31/13.15 (intersectInPowersetIntersectUnions) =>
% 97.31/13.15 ((
% 97.31/13.15 (inComplementUnionImpNotIn1) =>
% 97.31/13.15 ((
% 97.31/13.15 (inComplementUnionImpInComplement1) =>
% 97.31/13.15 ((
% 97.31/13.15 (binunionTE) =>
% 97.31/13.15 ((
% 97.31/13.15 (binunionTEcontra) =>
% 97.31/13.15 ((
% 97.31/13.15 (demorgan2a1) =>
% 97.31/13.15 ((
% 97.31/13.15 (complementUnionInPowersetComplement) =>
% 97.31/13.15 ((
% 97.31/13.15 (demorgan2a2) =>
% 97.31/13.15 ((
% 97.31/13.15 (demorgan1a) =>
% 97.31/13.15 ((
% 97.31/13.15 (demorgan1b) =>
% 97.31/13.15 ((
% 97.31/13.15 (demorgan1) =>
% 97.31/13.15 ((
% 97.31/13.15 (demorgan2a) =>
% 97.31/13.15 ((
% 97.31/13.15 (demorgan2b2) =>
% 97.31/13.15 ((
% 97.31/13.15 (demorgan2b) =>
% 97.31/13.15 ((
% 97.31/13.15 (demorgan2) =>
% 97.31/13.15 ((
% 97.31/13.15 (woz13rule0) =>
% 97.31/13.15 ((
% 97.31/13.15 (woz13rule1) =>
% 97.31/13.15 ((
% 97.31/13.15 (woz13rule2) =>
% 97.31/13.15 ((
% 97.31/13.15 (woz13rule3) =>
% 97.31/13.15 ((
% 97.31/13.15 (woz13rule4) =>
% 97.31/13.15 ((
% 97.31/13.15 (woz1_1) =>
% 97.31/13.15 ((
% 97.31/13.15 (woz1_2) =>
% 97.31/13.15 ((
% 97.31/13.15 (woz1_3) =>
% 97.31/13.15 ((
% 97.31/13.15 (woz1_4) =>
% 97.31/13.15 ((
% 97.31/13.15 (woz1_5) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1all2) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1SetBreln1) =>
% 97.31/13.15 ((
% 97.31/13.15 (choice2fnsingleton) =>
% 97.31/13.15 ((
% 97.31/13.15 (setOfPairsIsBReln1) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1all1) =>
% 97.31/13.15 ((
% 97.31/13.15 (subbreln1) =>
% 97.31/13.15 ((
% 97.31/13.15 (eqbreln1) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1invprop) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1invI) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1invE) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1compprop) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1compI) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1compE) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1compEex) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1unionprop) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1unionIL) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1unionIR) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1unionI) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1unionE) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1unionEcases) =>
% 97.31/13.15 ((
% 97.31/13.15 (breln1unionCommutes) =>
% 97.31/13.15 ((
% 97.31/13.15 (woz2Ex) =>
% 97.31/13.15 ((
% 97.31/13.15 (woz2W) =>
% 97.31/13.15 ((
% 97.31/13.15 (woz2A) =>
% 97.31/13.15 ((
% 97.31/13.15 (woz2B) =>
% 97.31/13.15 ((
% 97.31/13.15 (image1Ex) =>
% 97.31/13.15 ((
% 97.31/13.15 (image1Ex1) =>
% 97.31/13.15 ((
% 97.31/13.15 (image1Equiv) =>
% 97.31/13.15 ((
% 97.31/13.15 (image1E) =>
% 97.31/13.15 ((
% 97.31/13.15 (image1I) =>
% 97.31/13.15 ((
% 97.31/13.15 (injFuncInInjFuncSet) =>
% 97.31/13.15 ((
% 97.31/13.15 (injFuncSetFuncIn) =>
% 97.31/13.15 ((
% 97.31/13.15 (injFuncSetFuncInj) =>
% 97.31/13.15 ((
% 97.31/13.15 (surjFuncSetFuncIn) =>
% 97.31/13.15 ((
% 97.31/13.15 (surjFuncSetFuncSurj) =>
% 97.31/13.15 ((
% 97.31/13.15 (leftInvIsSurj) =>
% 97.31/13.15 ((
% 97.31/13.15 (surjCantorThm) =>
% 97.31/13.15 ((
% 97.31/13.15 (foundation2) =>
% 97.31/13.15 ((
% 97.31/13.15 (notinself) =>
% 97.31/13.15 ((
% 97.31/13.15 (notinself2) =>
% 97.31/13.15 ((
% 97.31/13.15 (omegaSp) =>
% 97.31/13.15 ((
% 97.31/13.15 (omegaSclos) =>
% 97.31/13.15 ((
% 97.31/13.15 (peano0notS) =>
% 97.31/13.15 ((
% 97.31/13.15 (!!) @ (
% 97.31/13.15 (('#S') @ (
% 97.31/13.15 (
% 97.31/13.15 ('#B') @ (
% 97.31/13.15 =>) @
% 97.31/13.15 (
% 97.31/13.15 (
% 97.31/13.15 ('#C') @ in @
% 97.31/13.15 omega)))) @
% 97.31/13.15 (
% 97.31/13.15 (
% 97.31/13.15 ('#B') @ (
% 97.31/13.15 !!) @
% 97.31/13.15 (
% 97.31/13.15 (
% 97.31/13.15 ('#B') @ (
% 97.31/13.15 (
% 97.31/13.15 ('#S') @ (
% 97.31/13.15 (
% 97.31/13.15 ('#B') @ (
% 97.31/13.15 =>) @
% 97.31/13.15 (
% 97.31/13.15 (
% 97.31/13.15 ('#C') @ in @
% 97.31/13.15 omega)))))) @
% 97.31/13.15 (
% 97.31/13.15 (
% 97.31/13.15 ('#S') @ (
% 97.31/13.15 (
% 97.31/13.15 ('#B') @ (
% 97.31/13.15 '#S') @
% 97.31/13.15 (
% 97.31/13.15 (
% 97.31/13.15 ('#B') @ (
% 97.31/13.15 (
% 97.31/13.15 ('#B') @ (
% 97.31/13.15 =>))) @
% 97.31/13.15 (
% 97.31/13.15 (
% 97.31/13.15 ('#C') @ (
% 97.31/13.15 (
% 97.31/13.16 ('#B') @ (
% 97.31/13.16 '#B') @
% 97.31/13.16 (
% 97.31/13.16 (
% 97.31/13.16 ('#B') @ (
% 97.31/13.16 =) @
% 97.31/13.16 omegaS)))) @
% 97.31/13.16 omegaS)))))) @
% 97.31/13.16 (
% 97.31/13.16 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.31/13.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl142])).
% 97.31/13.16 thf(zip_derived_cl174, plain,
% 97.31/13.16 (~ (((notinemptyset) =>
% 97.31/13.16 (((exuE3e) =>
% 97.31/13.16 (((setext) =>
% 97.31/13.16 (((emptyI) =>
% 97.31/13.16 (((noeltsimpempty) =>
% 97.31/13.16 (((setbeta) =>
% 97.31/13.16 (((nonemptyE1) =>
% 97.31/13.16 (((nonemptyI) =>
% 97.31/13.16 (((nonemptyI1) =>
% 97.31/13.16 (((setadjoinIL) =>
% 97.31/13.16 (((in @ emptyset @
% 97.31/13.16 (setadjoin @ emptyset @ emptyset)) =>
% 97.31/13.16 (((setadjoinIR) =>
% 97.31/13.16 (((setadjoinE) =>
% 97.31/13.16 (((setadjoinOr) =>
% 97.31/13.16 (((setoftrueEq) =>
% 97.31/13.16 (((powersetI) =>
% 97.31/13.16 (((emptyinPowerset) =>
% 97.31/13.16 (((emptyInPowerset) =>
% 97.31/13.16 (((powersetE) =>
% 97.31/13.16 (((setunionI) =>
% 97.31/13.16 (((setunionE) =>
% 97.31/13.16 (((subPowSU) =>
% 97.31/13.16 (((exuE2) =>
% 97.31/13.16 (((nonemptyImpWitness) =>
% 97.31/13.16 (((uniqinunit) =>
% 97.31/13.16 (((notinsingleton) =>
% 97.31/13.16 (((eqinunit) =>
% 97.31/13.16 (((singletonsswitch) =>
% 97.31/13.16 (((upairsetE) =>
% 97.31/13.16 (((upairsetIL) =>
% 97.31/13.16 ((
% 97.31/13.16 (upairsetIR) =>
% 97.31/13.16 ((
% 97.31/13.16 (emptyE1) =>
% 97.31/13.16 ((
% 97.31/13.16 (vacuousDall) =>
% 97.31/13.16 ((
% 97.31/13.16 (quantDeMorgan1) =>
% 97.31/13.16 ((
% 97.31/13.16 (quantDeMorgan2) =>
% 97.31/13.16 ((
% 97.31/13.16 (quantDeMorgan3) =>
% 97.31/13.16 ((
% 97.31/13.16 (quantDeMorgan4) =>
% 97.31/13.16 ((
% 97.31/13.16 (prop2setI) =>
% 97.31/13.16 ((
% 97.31/13.16 (prop2set2propI) =>
% 97.31/13.16 ((
% 97.31/13.16 (notdexE) =>
% 97.31/13.16 ((
% 97.31/13.16 (notdallE) =>
% 97.31/13.16 ((
% 97.31/13.16 (exuI1) =>
% 97.31/13.16 ((
% 97.31/13.16 (exuI3) =>
% 97.31/13.16 ((
% 97.31/13.16 (exuI2) =>
% 97.31/13.16 ((
% 97.31/13.16 (inCongP) =>
% 97.31/13.16 ((
% 97.31/13.16 (in__Cong) =>
% 97.31/13.16 ((
% 97.31/13.16 (exuE3u) =>
% 97.31/13.16 ((
% 97.31/13.16 (exu__Cong) =>
% 97.31/13.16 ((
% 97.31/13.16 (setadjoin__Cong) =>
% 97.31/13.16 ((
% 97.31/13.16 (powerset__Cong) =>
% 97.31/13.16 ((
% 97.31/13.16 (setunion__Cong) =>
% 97.31/13.16 ((
% 97.31/13.16 (exuEu) =>
% 97.31/13.16 ((
% 97.31/13.16 (descr__Cong) =>
% 97.31/13.16 ((
% 97.31/13.16 (dsetconstr__Cong) =>
% 97.31/13.16 ((
% 97.31/13.16 (subsetI1) =>
% 97.31/13.16 ((
% 97.31/13.16 (eqimpsubset2) =>
% 97.31/13.16 ((
% 97.31/13.16 (eqimpsubset1) =>
% 97.31/13.16 ((
% 97.31/13.16 (subsetI2) =>
% 97.31/13.16 ((
% 97.31/13.16 (emptysetsubset) =>
% 97.31/13.16 ((
% 97.31/13.16 (subsetE) =>
% 97.31/13.16 ((
% 97.31/13.16 (subsetE2) =>
% 97.31/13.16 ((
% 97.31/13.16 (notsubsetI) =>
% 97.31/13.16 ((
% 97.31/13.16 (notequalI1) =>
% 97.31/13.16 ((
% 97.31/13.16 (notequalI2) =>
% 97.31/13.16 ((
% 97.31/13.16 (subsetRefl) =>
% 97.31/13.16 ((
% 97.31/13.16 (subsetTrans) =>
% 97.31/13.16 ((
% 97.31/13.16 (setadjoinSub) =>
% 97.31/13.16 ((
% 97.31/13.16 (setadjoinSub2) =>
% 97.31/13.16 ((
% 97.31/13.16 (subset2powerset) =>
% 97.31/13.16 ((
% 97.31/13.16 (setextsub) =>
% 97.31/13.16 ((
% 97.31/13.16 (subsetemptysetimpeq) =>
% 97.31/13.16 ((
% 97.31/13.16 (powersetI1) =>
% 97.31/13.16 ((
% 97.31/13.16 (powersetE1) =>
% 97.31/13.16 ((
% 97.31/13.16 (inPowerset) =>
% 97.31/13.16 ((
% 97.31/13.16 (powersetsubset) =>
% 97.31/13.16 ((
% 97.31/13.16 (sepInPowerset) =>
% 97.31/13.16 ((
% 97.31/13.16 (sepSubset) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionIL) =>
% 97.31/13.16 ((
% 97.31/13.16 (upairset2IR) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionIR) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionEcases) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionE) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionLsub) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionRsub) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectI) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectSubset5) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectEL) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectLsub) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectSubset2) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectSubset3) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectER) =>
% 97.31/13.16 ((
% 97.31/13.16 (disjointsetsI1) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectRsub) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectSubset4) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectSubset1) =>
% 97.31/13.16 ((
% 97.31/13.16 (bs114d) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusI) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusEL) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusER) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusSubset2) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusERneg) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusELneg) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusILneg) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusIRneg) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusLsub) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusSubset1) =>
% 97.31/13.16 ((
% 97.31/13.16 (symdiffE) =>
% 97.31/13.16 ((
% 97.31/13.16 (symdiffI1) =>
% 97.31/13.16 ((
% 97.31/13.16 (symdiffI2) =>
% 97.31/13.16 ((
% 97.31/13.16 (symdiffIneg1) =>
% 97.31/13.16 ((
% 97.31/13.16 (symdiffIneg2) =>
% 97.31/13.16 ((
% 97.31/13.16 (secondinupair) =>
% 97.31/13.16 ((
% 97.31/13.16 (setukpairIL) =>
% 97.31/13.16 ((
% 97.31/13.16 (setukpairIR) =>
% 97.31/13.16 ((
% 97.31/13.16 (kpairiskpair) =>
% 97.31/13.16 ((
% 97.31/13.16 (kpairp) =>
% 97.31/13.16 ((
% 97.31/13.16 (singletonsubset) =>
% 97.31/13.16 ((
% 97.31/13.16 (singletoninpowerset) =>
% 97.31/13.16 ((
% 97.31/13.16 (singletoninpowunion) =>
% 97.31/13.16 ((
% 97.31/13.16 (upairset2E) =>
% 97.31/13.16 ((
% 97.31/13.16 (upairsubunion) =>
% 97.31/13.16 ((
% 97.31/13.16 (upairinpowunion) =>
% 97.31/13.16 ((
% 97.31/13.16 (ubforcartprodlem1) =>
% 97.31/13.16 ((
% 97.31/13.16 (ubforcartprodlem2) =>
% 97.31/13.16 ((
% 97.31/13.16 (ubforcartprodlem3) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodpairin) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodmempair1) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodmempair) =>
% 97.31/13.16 ((
% 97.31/13.16 (setunionE2) =>
% 97.31/13.16 ((
% 97.31/13.16 (setunionsingleton1) =>
% 97.31/13.16 ((
% 97.31/13.16 (setunionsingleton2) =>
% 97.31/13.16 ((
% 97.31/13.16 (setunionsingleton) =>
% 97.31/13.16 ((
% 97.31/13.16 (singletonprop) =>
% 97.31/13.16 ((
% 97.31/13.16 (ex1E1) =>
% 97.31/13.16 ((
% 97.31/13.16 (ex1I) =>
% 97.31/13.16 ((
% 97.31/13.16 (ex1I2) =>
% 97.31/13.16 ((
% 97.31/13.16 (singletonsuniq) =>
% 97.31/13.16 ((
% 97.31/13.16 (setukpairinjL1) =>
% 97.31/13.16 ((
% 97.31/13.16 (kfstsingleton) =>
% 97.31/13.16 ((
% 97.31/13.16 (theprop) =>
% 97.31/13.16 ((
% 97.31/13.16 (kfstpairEq) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodfstin) =>
% 97.31/13.16 ((
% 97.31/13.16 (setukpairinjL2) =>
% 97.31/13.16 ((
% 97.31/13.16 (setukpairinjL) =>
% 97.31/13.16 ((
% 97.31/13.16 (setukpairinjR11) =>
% 97.31/13.16 ((
% 97.31/13.16 (setukpairinjR12) =>
% 97.31/13.16 ((
% 97.31/13.16 (setukpairinjR1) =>
% 97.31/13.16 ((
% 97.31/13.16 (upairequniteq) =>
% 97.31/13.16 ((
% 97.31/13.16 (setukpairinjR2) =>
% 97.31/13.16 ((
% 97.31/13.16 (setukpairinjR) =>
% 97.31/13.16 ((
% 97.31/13.16 (ksndsingleton) =>
% 97.31/13.16 ((
% 97.31/13.16 (ksndpairEq) =>
% 97.31/13.16 ((
% 97.31/13.16 (kpairsurjEq) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodsndin) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodpairmemEL) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodpairmemER) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodmempaircEq) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodfstpairEq) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodsndpairEq) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodpairsurjEq) =>
% 97.31/13.16 ((
% 97.31/13.16 (dpsetconstrI) =>
% 97.31/13.16 ((
% 97.31/13.16 (dpsetconstrSub) =>
% 97.31/13.16 ((
% 97.31/13.16 (setOfPairsIsBReln) =>
% 97.31/13.16 ((
% 97.31/13.16 (dpsetconstrERa) =>
% 97.31/13.16 ((
% 97.31/13.16 (dpsetconstrEL1) =>
% 97.31/13.16 ((
% 97.31/13.16 (dpsetconstrEL2) =>
% 97.31/13.16 ((
% 97.31/13.16 (dpsetconstrER) =>
% 97.31/13.16 ((
% 97.31/13.16 (funcImageSingleton) =>
% 97.31/13.16 ((
% 97.31/13.16 (apProp) =>
% 97.31/13.16 ((
% 97.31/13.16 (app) =>
% 97.31/13.16 ((
% 97.31/13.16 (infuncsetfunc) =>
% 97.31/13.16 ((
% 97.31/13.16 (ap2p) =>
% 97.31/13.16 ((
% 97.31/13.16 (funcinfuncset) =>
% 97.31/13.16 ((
% 97.31/13.16 (lamProp) =>
% 97.31/13.16 ((
% 97.31/13.16 (lamp) =>
% 97.31/13.16 ((
% 97.31/13.16 (lam2p) =>
% 97.31/13.16 ((
% 97.31/13.16 (brelnall1) =>
% 97.31/13.16 ((
% 97.31/13.16 (brelnall2) =>
% 97.31/13.16 ((
% 97.31/13.16 (ex1E2) =>
% 97.31/13.16 ((
% 97.31/13.16 (funcGraphProp1) =>
% 97.31/13.16 ((
% 97.31/13.16 (funcGraphProp3) =>
% 97.31/13.16 ((
% 97.31/13.16 (funcGraphProp2) =>
% 97.31/13.16 ((
% 97.31/13.16 (funcextLem) =>
% 97.31/13.16 ((
% 97.31/13.16 (funcGraphProp4) =>
% 97.31/13.16 ((
% 97.31/13.16 (subbreln) =>
% 97.31/13.16 ((
% 97.31/13.16 (eqbreln) =>
% 97.31/13.16 ((
% 97.31/13.16 (funcext) =>
% 97.31/13.16 ((
% 97.31/13.16 (funcext2) =>
% 97.31/13.16 ((
% 97.31/13.16 (ap2apEq1) =>
% 97.31/13.16 ((
% 97.31/13.16 (ap2apEq2) =>
% 97.31/13.16 ((
% 97.31/13.16 (beta1) =>
% 97.31/13.16 ((
% 97.31/13.16 (eta1) =>
% 97.31/13.16 ((
% 97.31/13.16 (lam2lamEq) =>
% 97.31/13.16 ((
% 97.31/13.16 (beta2) =>
% 97.31/13.16 ((
% 97.31/13.16 (eta2) =>
% 97.31/13.16 ((
% 97.31/13.16 (iffalseProp1) =>
% 97.31/13.16 ((
% 97.31/13.16 (iffalseProp2) =>
% 97.31/13.16 ((
% 97.31/13.16 (iftrueProp1) =>
% 97.31/13.16 ((
% 97.31/13.16 (iftrueProp2) =>
% 97.31/13.16 ((
% 97.31/13.16 (ifSingleton) =>
% 97.31/13.16 ((
% 97.31/13.16 (ifp) =>
% 97.31/13.16 ((
% 97.31/13.16 (theeq) =>
% 97.31/13.16 ((
% 97.31/13.16 (iftrue) =>
% 97.31/13.16 ((
% 97.31/13.16 (iffalse) =>
% 97.31/13.16 ((
% 97.31/13.16 (iftrueorfalse) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectT_lem) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionT_lem) =>
% 97.31/13.16 ((
% 97.31/13.16 (powersetT_lem) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusT_lem) =>
% 97.31/13.16 ((
% 97.31/13.16 (complementT_lem) =>
% 97.31/13.16 ((
% 97.31/13.16 (setextT) =>
% 97.31/13.16 ((
% 97.31/13.16 (subsetTI) =>
% 97.31/13.16 ((
% 97.31/13.16 (powersetTI1) =>
% 97.31/13.16 ((
% 97.31/13.16 (powersetTE1) =>
% 97.31/13.16 ((
% 97.31/13.16 (complementTI1) =>
% 97.31/13.16 ((
% 97.31/13.16 (complementTE1) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectTELcontra) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectTERcontra) =>
% 97.31/13.16 ((
% 97.31/13.16 (contrasubsetT) =>
% 97.31/13.16 ((
% 97.31/13.16 (contrasubsetT1) =>
% 97.31/13.16 ((
% 97.31/13.16 (contrasubsetT2) =>
% 97.31/13.16 ((
% 97.31/13.16 (contrasubsetT3) =>
% 97.31/13.16 ((
% 97.31/13.16 (doubleComplementI1) =>
% 97.31/13.16 ((
% 97.31/13.16 (doubleComplementE1) =>
% 97.31/13.16 ((
% 97.31/13.16 (doubleComplementSub1) =>
% 97.31/13.16 ((
% 97.31/13.16 (doubleComplementSub2) =>
% 97.31/13.16 ((
% 97.31/13.16 (doubleComplementEq) =>
% 97.31/13.16 ((
% 97.31/13.16 (complementTnotintersectT) =>
% 97.31/13.16 ((
% 97.31/13.16 (complementImpComplementIntersect) =>
% 97.31/13.16 ((
% 97.31/13.16 (complementSubsetComplementIntersect) =>
% 97.31/13.16 ((
% 97.31/13.16 (complementInPowersetComplementIntersect) =>
% 97.31/13.16 ((
% 97.31/13.16 (contraSubsetComplement) =>
% 97.31/13.16 ((
% 97.31/13.16 (complementTcontraSubset) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionTILcontra) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionTIRcontra) =>
% 97.31/13.16 ((
% 97.31/13.16 (inIntersectImpInUnion) =>
% 97.31/13.16 ((
% 97.31/13.16 (inIntersectImpInUnion2) =>
% 97.31/13.16 ((
% 97.31/13.16 (inIntersectImpInIntersectUnions) =>
% 97.31/13.16 ((
% 97.31/13.16 (intersectInPowersetIntersectUnions) =>
% 97.31/13.16 ((
% 97.31/13.16 (inComplementUnionImpNotIn1) =>
% 97.31/13.16 ((
% 97.31/13.16 (inComplementUnionImpInComplement1) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionTE) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionTEcontra) =>
% 97.31/13.16 ((
% 97.31/13.16 (demorgan2a1) =>
% 97.31/13.16 ((
% 97.31/13.16 (complementUnionInPowersetComplement) =>
% 97.31/13.16 ((
% 97.31/13.16 (demorgan2a2) =>
% 97.31/13.16 ((
% 97.31/13.16 (demorgan1a) =>
% 97.31/13.16 ((
% 97.31/13.16 (demorgan1b) =>
% 97.31/13.16 ((
% 97.31/13.16 (demorgan1) =>
% 97.31/13.16 ((
% 97.31/13.16 (demorgan2a) =>
% 97.31/13.16 ((
% 97.31/13.16 (demorgan2b2) =>
% 97.31/13.16 ((
% 97.31/13.16 (demorgan2b) =>
% 97.31/13.16 ((
% 97.31/13.16 (demorgan2) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz13rule0) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz13rule1) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz13rule2) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz13rule3) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz13rule4) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz1_1) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz1_2) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz1_3) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz1_4) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz1_5) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1all2) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1SetBreln1) =>
% 97.31/13.16 ((
% 97.31/13.16 (choice2fnsingleton) =>
% 97.31/13.16 ((
% 97.31/13.16 (setOfPairsIsBReln1) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1all1) =>
% 97.31/13.16 ((
% 97.31/13.16 (subbreln1) =>
% 97.31/13.16 ((
% 97.31/13.16 (eqbreln1) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1invprop) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1invI) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1invE) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1compprop) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1compI) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1compE) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1compEex) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1unionprop) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1unionIL) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1unionIR) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1unionI) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1unionE) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1unionEcases) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1unionCommutes) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz2Ex) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz2W) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz2A) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz2B) =>
% 97.31/13.16 ((
% 97.31/13.16 (image1Ex) =>
% 97.31/13.16 ((
% 97.31/13.16 (image1Ex1) =>
% 97.31/13.16 ((
% 97.31/13.16 (image1Equiv) =>
% 97.31/13.16 ((
% 97.31/13.16 (image1E) =>
% 97.31/13.16 ((
% 97.31/13.16 (image1I) =>
% 97.31/13.16 ((
% 97.31/13.16 (injFuncInInjFuncSet) =>
% 97.31/13.16 ((
% 97.31/13.16 (injFuncSetFuncIn) =>
% 97.31/13.16 ((
% 97.31/13.16 (injFuncSetFuncInj) =>
% 97.31/13.16 ((
% 97.31/13.16 (surjFuncSetFuncIn) =>
% 97.31/13.16 ((
% 97.31/13.16 (surjFuncSetFuncSurj) =>
% 97.31/13.16 ((
% 97.31/13.16 (leftInvIsSurj) =>
% 97.31/13.16 ((
% 97.31/13.16 (surjCantorThm) =>
% 97.31/13.16 ((
% 97.31/13.16 (foundation2) =>
% 97.31/13.16 ((
% 97.31/13.16 (notinself) =>
% 97.31/13.16 ((
% 97.31/13.16 (notinself2) =>
% 97.31/13.16 ((
% 97.31/13.16 (omegaSp) =>
% 97.31/13.16 ((
% 97.31/13.16 (omegaSclos) =>
% 97.31/13.16 ((
% 97.31/13.16 (peano0notS) =>
% 97.31/13.16 ((
% 97.31/13.16 (!!) @ (
% 97.31/13.16 (('#S') @ (
% 97.31/13.16 (
% 97.31/13.16 ('#B') @ (
% 97.31/13.16 =>) @
% 97.31/13.16 (
% 97.31/13.16 (
% 97.31/13.16 ('#C') @ in @
% 97.31/13.16 omega)))) @
% 97.31/13.16 (
% 97.31/13.16 (
% 97.31/13.16 ('#B') @ (
% 97.31/13.16 !!) @
% 97.31/13.16 (
% 97.31/13.16 (
% 97.31/13.16 ('#B') @ (
% 97.31/13.16 (
% 97.31/13.16 ('#S') @ (
% 97.31/13.16 (
% 97.31/13.16 ('#B') @ (
% 97.31/13.16 =>) @
% 97.31/13.16 (
% 97.31/13.16 (
% 97.31/13.16 ('#C') @ in @
% 97.31/13.16 omega)))))) @
% 97.31/13.16 (
% 97.31/13.16 (
% 97.31/13.16 ('#S') @ (
% 97.31/13.16 (
% 97.31/13.16 ('#B') @ (
% 97.31/13.16 '#S') @
% 97.31/13.16 (
% 97.31/13.16 (
% 97.31/13.16 ('#B') @ (
% 97.31/13.16 (
% 97.31/13.16 ('#B') @ (
% 97.31/13.16 =>))) @
% 97.31/13.16 (
% 97.31/13.16 (
% 97.31/13.16 ('#C') @ (
% 97.31/13.16 (
% 97.31/13.16 ('#B') @ (
% 97.31/13.16 '#B') @
% 97.31/13.16 (
% 97.31/13.16 (
% 97.31/13.16 ('#B') @ (
% 97.31/13.16 =) @
% 97.31/13.16 omegaS)))) @
% 97.31/13.16 omegaS)))))) @
% 97.31/13.16 (
% 97.31/13.16 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.31/13.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl158])).
% 97.31/13.16 thf(zip_derived_cl189, plain,
% 97.31/13.16 (~ (((exuE3e) =>
% 97.31/13.16 (((setext) =>
% 97.31/13.16 (((emptyI) =>
% 97.31/13.16 (((noeltsimpempty) =>
% 97.31/13.16 (((setbeta) =>
% 97.31/13.16 (((nonemptyE1) =>
% 97.31/13.16 (((nonemptyI) =>
% 97.31/13.16 (((nonemptyI1) =>
% 97.31/13.16 (((setadjoinIL) =>
% 97.31/13.16 (((in @ emptyset @
% 97.31/13.16 (setadjoin @ emptyset @ emptyset)) =>
% 97.31/13.16 (((setadjoinIR) =>
% 97.31/13.16 (((setadjoinE) =>
% 97.31/13.16 (((setadjoinOr) =>
% 97.31/13.16 (((setoftrueEq) =>
% 97.31/13.16 (((powersetI) =>
% 97.31/13.16 (((emptyinPowerset) =>
% 97.31/13.16 (((emptyInPowerset) =>
% 97.31/13.16 (((powersetE) =>
% 97.31/13.16 (((setunionI) =>
% 97.31/13.16 (((setunionE) =>
% 97.31/13.16 (((subPowSU) =>
% 97.31/13.16 (((exuE2) =>
% 97.31/13.16 (((nonemptyImpWitness) =>
% 97.31/13.16 (((uniqinunit) =>
% 97.31/13.16 (((notinsingleton) =>
% 97.31/13.16 (((eqinunit) =>
% 97.31/13.16 (((singletonsswitch) =>
% 97.31/13.16 (((upairsetE) =>
% 97.31/13.16 (((upairsetIL) =>
% 97.31/13.16 (((upairsetIR) =>
% 97.31/13.16 ((
% 97.31/13.16 (emptyE1) =>
% 97.31/13.16 ((
% 97.31/13.16 (vacuousDall) =>
% 97.31/13.16 ((
% 97.31/13.16 (quantDeMorgan1) =>
% 97.31/13.16 ((
% 97.31/13.16 (quantDeMorgan2) =>
% 97.31/13.16 ((
% 97.31/13.16 (quantDeMorgan3) =>
% 97.31/13.16 ((
% 97.31/13.16 (quantDeMorgan4) =>
% 97.31/13.16 ((
% 97.31/13.16 (prop2setI) =>
% 97.31/13.16 ((
% 97.31/13.16 (prop2set2propI) =>
% 97.31/13.16 ((
% 97.31/13.16 (notdexE) =>
% 97.31/13.16 ((
% 97.31/13.16 (notdallE) =>
% 97.31/13.16 ((
% 97.31/13.16 (exuI1) =>
% 97.31/13.16 ((
% 97.31/13.16 (exuI3) =>
% 97.31/13.16 ((
% 97.31/13.16 (exuI2) =>
% 97.31/13.16 ((
% 97.31/13.16 (inCongP) =>
% 97.31/13.16 ((
% 97.31/13.16 (in__Cong) =>
% 97.31/13.16 ((
% 97.31/13.16 (exuE3u) =>
% 97.31/13.16 ((
% 97.31/13.16 (exu__Cong) =>
% 97.31/13.16 ((
% 97.31/13.16 (setadjoin__Cong) =>
% 97.31/13.16 ((
% 97.31/13.16 (powerset__Cong) =>
% 97.31/13.16 ((
% 97.31/13.16 (setunion__Cong) =>
% 97.31/13.16 ((
% 97.31/13.16 (exuEu) =>
% 97.31/13.16 ((
% 97.31/13.16 (descr__Cong) =>
% 97.31/13.16 ((
% 97.31/13.16 (dsetconstr__Cong) =>
% 97.31/13.16 ((
% 97.31/13.16 (subsetI1) =>
% 97.31/13.16 ((
% 97.31/13.16 (eqimpsubset2) =>
% 97.31/13.16 ((
% 97.31/13.16 (eqimpsubset1) =>
% 97.31/13.16 ((
% 97.31/13.16 (subsetI2) =>
% 97.31/13.16 ((
% 97.31/13.16 (emptysetsubset) =>
% 97.31/13.16 ((
% 97.31/13.16 (subsetE) =>
% 97.31/13.16 ((
% 97.31/13.16 (subsetE2) =>
% 97.31/13.16 ((
% 97.31/13.16 (notsubsetI) =>
% 97.31/13.16 ((
% 97.31/13.16 (notequalI1) =>
% 97.31/13.16 ((
% 97.31/13.16 (notequalI2) =>
% 97.31/13.16 ((
% 97.31/13.16 (subsetRefl) =>
% 97.31/13.16 ((
% 97.31/13.16 (subsetTrans) =>
% 97.31/13.16 ((
% 97.31/13.16 (setadjoinSub) =>
% 97.31/13.16 ((
% 97.31/13.16 (setadjoinSub2) =>
% 97.31/13.16 ((
% 97.31/13.16 (subset2powerset) =>
% 97.31/13.16 ((
% 97.31/13.16 (setextsub) =>
% 97.31/13.16 ((
% 97.31/13.16 (subsetemptysetimpeq) =>
% 97.31/13.16 ((
% 97.31/13.16 (powersetI1) =>
% 97.31/13.16 ((
% 97.31/13.16 (powersetE1) =>
% 97.31/13.16 ((
% 97.31/13.16 (inPowerset) =>
% 97.31/13.16 ((
% 97.31/13.16 (powersetsubset) =>
% 97.31/13.16 ((
% 97.31/13.16 (sepInPowerset) =>
% 97.31/13.16 ((
% 97.31/13.16 (sepSubset) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionIL) =>
% 97.31/13.16 ((
% 97.31/13.16 (upairset2IR) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionIR) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionEcases) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionE) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionLsub) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionRsub) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectI) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectSubset5) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectEL) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectLsub) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectSubset2) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectSubset3) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectER) =>
% 97.31/13.16 ((
% 97.31/13.16 (disjointsetsI1) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectRsub) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectSubset4) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectSubset1) =>
% 97.31/13.16 ((
% 97.31/13.16 (bs114d) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusI) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusEL) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusER) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusSubset2) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusERneg) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusELneg) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusILneg) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusIRneg) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusLsub) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusSubset1) =>
% 97.31/13.16 ((
% 97.31/13.16 (symdiffE) =>
% 97.31/13.16 ((
% 97.31/13.16 (symdiffI1) =>
% 97.31/13.16 ((
% 97.31/13.16 (symdiffI2) =>
% 97.31/13.16 ((
% 97.31/13.16 (symdiffIneg1) =>
% 97.31/13.16 ((
% 97.31/13.16 (symdiffIneg2) =>
% 97.31/13.16 ((
% 97.31/13.16 (secondinupair) =>
% 97.31/13.16 ((
% 97.31/13.16 (setukpairIL) =>
% 97.31/13.16 ((
% 97.31/13.16 (setukpairIR) =>
% 97.31/13.16 ((
% 97.31/13.16 (kpairiskpair) =>
% 97.31/13.16 ((
% 97.31/13.16 (kpairp) =>
% 97.31/13.16 ((
% 97.31/13.16 (singletonsubset) =>
% 97.31/13.16 ((
% 97.31/13.16 (singletoninpowerset) =>
% 97.31/13.16 ((
% 97.31/13.16 (singletoninpowunion) =>
% 97.31/13.16 ((
% 97.31/13.16 (upairset2E) =>
% 97.31/13.16 ((
% 97.31/13.16 (upairsubunion) =>
% 97.31/13.16 ((
% 97.31/13.16 (upairinpowunion) =>
% 97.31/13.16 ((
% 97.31/13.16 (ubforcartprodlem1) =>
% 97.31/13.16 ((
% 97.31/13.16 (ubforcartprodlem2) =>
% 97.31/13.16 ((
% 97.31/13.16 (ubforcartprodlem3) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodpairin) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodmempair1) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodmempair) =>
% 97.31/13.16 ((
% 97.31/13.16 (setunionE2) =>
% 97.31/13.16 ((
% 97.31/13.16 (setunionsingleton1) =>
% 97.31/13.16 ((
% 97.31/13.16 (setunionsingleton2) =>
% 97.31/13.16 ((
% 97.31/13.16 (setunionsingleton) =>
% 97.31/13.16 ((
% 97.31/13.16 (singletonprop) =>
% 97.31/13.16 ((
% 97.31/13.16 (ex1E1) =>
% 97.31/13.16 ((
% 97.31/13.16 (ex1I) =>
% 97.31/13.16 ((
% 97.31/13.16 (ex1I2) =>
% 97.31/13.16 ((
% 97.31/13.16 (singletonsuniq) =>
% 97.31/13.16 ((
% 97.31/13.16 (setukpairinjL1) =>
% 97.31/13.16 ((
% 97.31/13.16 (kfstsingleton) =>
% 97.31/13.16 ((
% 97.31/13.16 (theprop) =>
% 97.31/13.16 ((
% 97.31/13.16 (kfstpairEq) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodfstin) =>
% 97.31/13.16 ((
% 97.31/13.16 (setukpairinjL2) =>
% 97.31/13.16 ((
% 97.31/13.16 (setukpairinjL) =>
% 97.31/13.16 ((
% 97.31/13.16 (setukpairinjR11) =>
% 97.31/13.16 ((
% 97.31/13.16 (setukpairinjR12) =>
% 97.31/13.16 ((
% 97.31/13.16 (setukpairinjR1) =>
% 97.31/13.16 ((
% 97.31/13.16 (upairequniteq) =>
% 97.31/13.16 ((
% 97.31/13.16 (setukpairinjR2) =>
% 97.31/13.16 ((
% 97.31/13.16 (setukpairinjR) =>
% 97.31/13.16 ((
% 97.31/13.16 (ksndsingleton) =>
% 97.31/13.16 ((
% 97.31/13.16 (ksndpairEq) =>
% 97.31/13.16 ((
% 97.31/13.16 (kpairsurjEq) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodsndin) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodpairmemEL) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodpairmemER) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodmempaircEq) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodfstpairEq) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodsndpairEq) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodpairsurjEq) =>
% 97.31/13.16 ((
% 97.31/13.16 (dpsetconstrI) =>
% 97.31/13.16 ((
% 97.31/13.16 (dpsetconstrSub) =>
% 97.31/13.16 ((
% 97.31/13.16 (setOfPairsIsBReln) =>
% 97.31/13.16 ((
% 97.31/13.16 (dpsetconstrERa) =>
% 97.31/13.16 ((
% 97.31/13.16 (dpsetconstrEL1) =>
% 97.31/13.16 ((
% 97.31/13.16 (dpsetconstrEL2) =>
% 97.31/13.16 ((
% 97.31/13.16 (dpsetconstrER) =>
% 97.31/13.16 ((
% 97.31/13.16 (funcImageSingleton) =>
% 97.31/13.16 ((
% 97.31/13.16 (apProp) =>
% 97.31/13.16 ((
% 97.31/13.16 (app) =>
% 97.31/13.16 ((
% 97.31/13.16 (infuncsetfunc) =>
% 97.31/13.16 ((
% 97.31/13.16 (ap2p) =>
% 97.31/13.16 ((
% 97.31/13.16 (funcinfuncset) =>
% 97.31/13.16 ((
% 97.31/13.16 (lamProp) =>
% 97.31/13.16 ((
% 97.31/13.16 (lamp) =>
% 97.31/13.16 ((
% 97.31/13.16 (lam2p) =>
% 97.31/13.16 ((
% 97.31/13.16 (brelnall1) =>
% 97.31/13.16 ((
% 97.31/13.16 (brelnall2) =>
% 97.31/13.16 ((
% 97.31/13.16 (ex1E2) =>
% 97.31/13.16 ((
% 97.31/13.16 (funcGraphProp1) =>
% 97.31/13.16 ((
% 97.31/13.16 (funcGraphProp3) =>
% 97.31/13.16 ((
% 97.31/13.16 (funcGraphProp2) =>
% 97.31/13.16 ((
% 97.31/13.16 (funcextLem) =>
% 97.31/13.16 ((
% 97.31/13.16 (funcGraphProp4) =>
% 97.31/13.16 ((
% 97.31/13.16 (subbreln) =>
% 97.31/13.16 ((
% 97.31/13.16 (eqbreln) =>
% 97.31/13.16 ((
% 97.31/13.16 (funcext) =>
% 97.31/13.16 ((
% 97.31/13.16 (funcext2) =>
% 97.31/13.16 ((
% 97.31/13.16 (ap2apEq1) =>
% 97.31/13.16 ((
% 97.31/13.16 (ap2apEq2) =>
% 97.31/13.16 ((
% 97.31/13.16 (beta1) =>
% 97.31/13.16 ((
% 97.31/13.16 (eta1) =>
% 97.31/13.16 ((
% 97.31/13.16 (lam2lamEq) =>
% 97.31/13.16 ((
% 97.31/13.16 (beta2) =>
% 97.31/13.16 ((
% 97.31/13.16 (eta2) =>
% 97.31/13.16 ((
% 97.31/13.16 (iffalseProp1) =>
% 97.31/13.16 ((
% 97.31/13.16 (iffalseProp2) =>
% 97.31/13.16 ((
% 97.31/13.16 (iftrueProp1) =>
% 97.31/13.16 ((
% 97.31/13.16 (iftrueProp2) =>
% 97.31/13.16 ((
% 97.31/13.16 (ifSingleton) =>
% 97.31/13.16 ((
% 97.31/13.16 (ifp) =>
% 97.31/13.16 ((
% 97.31/13.16 (theeq) =>
% 97.31/13.16 ((
% 97.31/13.16 (iftrue) =>
% 97.31/13.16 ((
% 97.31/13.16 (iffalse) =>
% 97.31/13.16 ((
% 97.31/13.16 (iftrueorfalse) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectT_lem) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionT_lem) =>
% 97.31/13.16 ((
% 97.31/13.16 (powersetT_lem) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusT_lem) =>
% 97.31/13.16 ((
% 97.31/13.16 (complementT_lem) =>
% 97.31/13.16 ((
% 97.31/13.16 (setextT) =>
% 97.31/13.16 ((
% 97.31/13.16 (subsetTI) =>
% 97.31/13.16 ((
% 97.31/13.16 (powersetTI1) =>
% 97.31/13.16 ((
% 97.31/13.16 (powersetTE1) =>
% 97.31/13.16 ((
% 97.31/13.16 (complementTI1) =>
% 97.31/13.16 ((
% 97.31/13.16 (complementTE1) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectTELcontra) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectTERcontra) =>
% 97.31/13.16 ((
% 97.31/13.16 (contrasubsetT) =>
% 97.31/13.16 ((
% 97.31/13.16 (contrasubsetT1) =>
% 97.31/13.16 ((
% 97.31/13.16 (contrasubsetT2) =>
% 97.31/13.16 ((
% 97.31/13.16 (contrasubsetT3) =>
% 97.31/13.16 ((
% 97.31/13.16 (doubleComplementI1) =>
% 97.31/13.16 ((
% 97.31/13.16 (doubleComplementE1) =>
% 97.31/13.16 ((
% 97.31/13.16 (doubleComplementSub1) =>
% 97.31/13.16 ((
% 97.31/13.16 (doubleComplementSub2) =>
% 97.31/13.16 ((
% 97.31/13.16 (doubleComplementEq) =>
% 97.31/13.16 ((
% 97.31/13.16 (complementTnotintersectT) =>
% 97.31/13.16 ((
% 97.31/13.16 (complementImpComplementIntersect) =>
% 97.31/13.16 ((
% 97.31/13.16 (complementSubsetComplementIntersect) =>
% 97.31/13.16 ((
% 97.31/13.16 (complementInPowersetComplementIntersect) =>
% 97.31/13.16 ((
% 97.31/13.16 (contraSubsetComplement) =>
% 97.31/13.16 ((
% 97.31/13.16 (complementTcontraSubset) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionTILcontra) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionTIRcontra) =>
% 97.31/13.16 ((
% 97.31/13.16 (inIntersectImpInUnion) =>
% 97.31/13.16 ((
% 97.31/13.16 (inIntersectImpInUnion2) =>
% 97.31/13.16 ((
% 97.31/13.16 (inIntersectImpInIntersectUnions) =>
% 97.31/13.16 ((
% 97.31/13.16 (intersectInPowersetIntersectUnions) =>
% 97.31/13.16 ((
% 97.31/13.16 (inComplementUnionImpNotIn1) =>
% 97.31/13.16 ((
% 97.31/13.16 (inComplementUnionImpInComplement1) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionTE) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionTEcontra) =>
% 97.31/13.16 ((
% 97.31/13.16 (demorgan2a1) =>
% 97.31/13.16 ((
% 97.31/13.16 (complementUnionInPowersetComplement) =>
% 97.31/13.16 ((
% 97.31/13.16 (demorgan2a2) =>
% 97.31/13.16 ((
% 97.31/13.16 (demorgan1a) =>
% 97.31/13.16 ((
% 97.31/13.16 (demorgan1b) =>
% 97.31/13.16 ((
% 97.31/13.16 (demorgan1) =>
% 97.31/13.16 ((
% 97.31/13.16 (demorgan2a) =>
% 97.31/13.16 ((
% 97.31/13.16 (demorgan2b2) =>
% 97.31/13.16 ((
% 97.31/13.16 (demorgan2b) =>
% 97.31/13.16 ((
% 97.31/13.16 (demorgan2) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz13rule0) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz13rule1) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz13rule2) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz13rule3) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz13rule4) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz1_1) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz1_2) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz1_3) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz1_4) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz1_5) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1all2) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1SetBreln1) =>
% 97.31/13.16 ((
% 97.31/13.16 (choice2fnsingleton) =>
% 97.31/13.16 ((
% 97.31/13.16 (setOfPairsIsBReln1) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1all1) =>
% 97.31/13.16 ((
% 97.31/13.16 (subbreln1) =>
% 97.31/13.16 ((
% 97.31/13.16 (eqbreln1) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1invprop) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1invI) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1invE) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1compprop) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1compI) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1compE) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1compEex) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1unionprop) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1unionIL) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1unionIR) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1unionI) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1unionE) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1unionEcases) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1unionCommutes) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz2Ex) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz2W) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz2A) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz2B) =>
% 97.31/13.16 ((
% 97.31/13.16 (image1Ex) =>
% 97.31/13.16 ((
% 97.31/13.16 (image1Ex1) =>
% 97.31/13.16 ((
% 97.31/13.16 (image1Equiv) =>
% 97.31/13.16 ((
% 97.31/13.16 (image1E) =>
% 97.31/13.16 ((
% 97.31/13.16 (image1I) =>
% 97.31/13.16 ((
% 97.31/13.16 (injFuncInInjFuncSet) =>
% 97.31/13.16 ((
% 97.31/13.16 (injFuncSetFuncIn) =>
% 97.31/13.16 ((
% 97.31/13.16 (injFuncSetFuncInj) =>
% 97.31/13.16 ((
% 97.31/13.16 (surjFuncSetFuncIn) =>
% 97.31/13.16 ((
% 97.31/13.16 (surjFuncSetFuncSurj) =>
% 97.31/13.16 ((
% 97.31/13.16 (leftInvIsSurj) =>
% 97.31/13.16 ((
% 97.31/13.16 (surjCantorThm) =>
% 97.31/13.16 ((
% 97.31/13.16 (foundation2) =>
% 97.31/13.16 ((
% 97.31/13.16 (notinself) =>
% 97.31/13.16 ((
% 97.31/13.16 (notinself2) =>
% 97.31/13.16 ((
% 97.31/13.16 (omegaSp) =>
% 97.31/13.16 ((
% 97.31/13.16 (omegaSclos) =>
% 97.31/13.16 ((
% 97.31/13.16 (peano0notS) =>
% 97.31/13.16 ((
% 97.31/13.16 (!!) @ (
% 97.31/13.16 (('#S') @ (
% 97.31/13.16 (
% 97.31/13.16 ('#B') @ (
% 97.31/13.16 =>) @
% 97.31/13.16 (
% 97.31/13.16 (
% 97.31/13.16 ('#C') @ in @
% 97.31/13.16 omega)))) @
% 97.31/13.16 (
% 97.31/13.16 (
% 97.31/13.16 ('#B') @ (
% 97.31/13.16 !!) @
% 97.31/13.16 (
% 97.31/13.16 (
% 97.31/13.16 ('#B') @ (
% 97.31/13.16 (
% 97.31/13.16 ('#S') @ (
% 97.31/13.16 (
% 97.31/13.16 ('#B') @ (
% 97.31/13.16 =>) @
% 97.31/13.16 (
% 97.31/13.16 (
% 97.31/13.16 ('#C') @ in @
% 97.31/13.16 omega)))))) @
% 97.31/13.16 (
% 97.31/13.16 (
% 97.31/13.16 ('#S') @ (
% 97.31/13.16 (
% 97.31/13.16 ('#B') @ (
% 97.31/13.16 '#S') @
% 97.31/13.16 (
% 97.31/13.16 (
% 97.31/13.16 ('#B') @ (
% 97.31/13.16 (
% 97.31/13.16 ('#B') @ (
% 97.31/13.16 =>))) @
% 97.31/13.16 (
% 97.31/13.16 (
% 97.31/13.16 ('#C') @ (
% 97.31/13.16 (
% 97.31/13.16 ('#B') @ (
% 97.31/13.16 '#B') @
% 97.31/13.16 (
% 97.31/13.16 (
% 97.31/13.16 ('#B') @ (
% 97.31/13.16 =) @
% 97.31/13.16 omegaS)))) @
% 97.31/13.16 omegaS)))))) @
% 97.31/13.16 (
% 97.31/13.16 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.31/13.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl174])).
% 97.31/13.16 thf(zip_derived_cl206, plain,
% 97.31/13.16 (~ (((setext) =>
% 97.31/13.16 (((emptyI) =>
% 97.31/13.16 (((noeltsimpempty) =>
% 97.31/13.16 (((setbeta) =>
% 97.31/13.16 (((nonemptyE1) =>
% 97.31/13.16 (((nonemptyI) =>
% 97.31/13.16 (((nonemptyI1) =>
% 97.31/13.16 (((setadjoinIL) =>
% 97.31/13.16 (((in @ emptyset @
% 97.31/13.16 (setadjoin @ emptyset @ emptyset)) =>
% 97.31/13.16 (((setadjoinIR) =>
% 97.31/13.16 (((setadjoinE) =>
% 97.31/13.16 (((setadjoinOr) =>
% 97.31/13.16 (((setoftrueEq) =>
% 97.31/13.16 (((powersetI) =>
% 97.31/13.16 (((emptyinPowerset) =>
% 97.31/13.16 (((emptyInPowerset) =>
% 97.31/13.16 (((powersetE) =>
% 97.31/13.16 (((setunionI) =>
% 97.31/13.16 (((setunionE) =>
% 97.31/13.16 (((subPowSU) =>
% 97.31/13.16 (((exuE2) =>
% 97.31/13.16 (((nonemptyImpWitness) =>
% 97.31/13.16 (((uniqinunit) =>
% 97.31/13.16 (((notinsingleton) =>
% 97.31/13.16 (((eqinunit) =>
% 97.31/13.16 (((singletonsswitch) =>
% 97.31/13.16 (((upairsetE) =>
% 97.31/13.16 (((upairsetIL) =>
% 97.31/13.16 (((upairsetIR) =>
% 97.31/13.16 (((emptyE1) =>
% 97.31/13.16 ((
% 97.31/13.16 (vacuousDall) =>
% 97.31/13.16 ((
% 97.31/13.16 (quantDeMorgan1) =>
% 97.31/13.16 ((
% 97.31/13.16 (quantDeMorgan2) =>
% 97.31/13.16 ((
% 97.31/13.16 (quantDeMorgan3) =>
% 97.31/13.16 ((
% 97.31/13.16 (quantDeMorgan4) =>
% 97.31/13.16 ((
% 97.31/13.16 (prop2setI) =>
% 97.31/13.16 ((
% 97.31/13.16 (prop2set2propI) =>
% 97.31/13.16 ((
% 97.31/13.16 (notdexE) =>
% 97.31/13.16 ((
% 97.31/13.16 (notdallE) =>
% 97.31/13.16 ((
% 97.31/13.16 (exuI1) =>
% 97.31/13.16 ((
% 97.31/13.16 (exuI3) =>
% 97.31/13.16 ((
% 97.31/13.16 (exuI2) =>
% 97.31/13.16 ((
% 97.31/13.16 (inCongP) =>
% 97.31/13.16 ((
% 97.31/13.16 (in__Cong) =>
% 97.31/13.16 ((
% 97.31/13.16 (exuE3u) =>
% 97.31/13.16 ((
% 97.31/13.16 (exu__Cong) =>
% 97.31/13.16 ((
% 97.31/13.16 (setadjoin__Cong) =>
% 97.31/13.16 ((
% 97.31/13.16 (powerset__Cong) =>
% 97.31/13.16 ((
% 97.31/13.16 (setunion__Cong) =>
% 97.31/13.16 ((
% 97.31/13.16 (exuEu) =>
% 97.31/13.16 ((
% 97.31/13.16 (descr__Cong) =>
% 97.31/13.16 ((
% 97.31/13.16 (dsetconstr__Cong) =>
% 97.31/13.16 ((
% 97.31/13.16 (subsetI1) =>
% 97.31/13.16 ((
% 97.31/13.16 (eqimpsubset2) =>
% 97.31/13.16 ((
% 97.31/13.16 (eqimpsubset1) =>
% 97.31/13.16 ((
% 97.31/13.16 (subsetI2) =>
% 97.31/13.16 ((
% 97.31/13.16 (emptysetsubset) =>
% 97.31/13.16 ((
% 97.31/13.16 (subsetE) =>
% 97.31/13.16 ((
% 97.31/13.16 (subsetE2) =>
% 97.31/13.16 ((
% 97.31/13.16 (notsubsetI) =>
% 97.31/13.16 ((
% 97.31/13.16 (notequalI1) =>
% 97.31/13.16 ((
% 97.31/13.16 (notequalI2) =>
% 97.31/13.16 ((
% 97.31/13.16 (subsetRefl) =>
% 97.31/13.16 ((
% 97.31/13.16 (subsetTrans) =>
% 97.31/13.16 ((
% 97.31/13.16 (setadjoinSub) =>
% 97.31/13.16 ((
% 97.31/13.16 (setadjoinSub2) =>
% 97.31/13.16 ((
% 97.31/13.16 (subset2powerset) =>
% 97.31/13.16 ((
% 97.31/13.16 (setextsub) =>
% 97.31/13.16 ((
% 97.31/13.16 (subsetemptysetimpeq) =>
% 97.31/13.16 ((
% 97.31/13.16 (powersetI1) =>
% 97.31/13.16 ((
% 97.31/13.16 (powersetE1) =>
% 97.31/13.16 ((
% 97.31/13.16 (inPowerset) =>
% 97.31/13.16 ((
% 97.31/13.16 (powersetsubset) =>
% 97.31/13.16 ((
% 97.31/13.16 (sepInPowerset) =>
% 97.31/13.16 ((
% 97.31/13.16 (sepSubset) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionIL) =>
% 97.31/13.16 ((
% 97.31/13.16 (upairset2IR) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionIR) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionEcases) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionE) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionLsub) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionRsub) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectI) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectSubset5) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectEL) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectLsub) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectSubset2) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectSubset3) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectER) =>
% 97.31/13.16 ((
% 97.31/13.16 (disjointsetsI1) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectRsub) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectSubset4) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectSubset1) =>
% 97.31/13.16 ((
% 97.31/13.16 (bs114d) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusI) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusEL) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusER) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusSubset2) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusERneg) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusELneg) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusILneg) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusIRneg) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusLsub) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusSubset1) =>
% 97.31/13.16 ((
% 97.31/13.16 (symdiffE) =>
% 97.31/13.16 ((
% 97.31/13.16 (symdiffI1) =>
% 97.31/13.16 ((
% 97.31/13.16 (symdiffI2) =>
% 97.31/13.16 ((
% 97.31/13.16 (symdiffIneg1) =>
% 97.31/13.16 ((
% 97.31/13.16 (symdiffIneg2) =>
% 97.31/13.16 ((
% 97.31/13.16 (secondinupair) =>
% 97.31/13.16 ((
% 97.31/13.16 (setukpairIL) =>
% 97.31/13.16 ((
% 97.31/13.16 (setukpairIR) =>
% 97.31/13.16 ((
% 97.31/13.16 (kpairiskpair) =>
% 97.31/13.16 ((
% 97.31/13.16 (kpairp) =>
% 97.31/13.16 ((
% 97.31/13.16 (singletonsubset) =>
% 97.31/13.16 ((
% 97.31/13.16 (singletoninpowerset) =>
% 97.31/13.16 ((
% 97.31/13.16 (singletoninpowunion) =>
% 97.31/13.16 ((
% 97.31/13.16 (upairset2E) =>
% 97.31/13.16 ((
% 97.31/13.16 (upairsubunion) =>
% 97.31/13.16 ((
% 97.31/13.16 (upairinpowunion) =>
% 97.31/13.16 ((
% 97.31/13.16 (ubforcartprodlem1) =>
% 97.31/13.16 ((
% 97.31/13.16 (ubforcartprodlem2) =>
% 97.31/13.16 ((
% 97.31/13.16 (ubforcartprodlem3) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodpairin) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodmempair1) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodmempair) =>
% 97.31/13.16 ((
% 97.31/13.16 (setunionE2) =>
% 97.31/13.16 ((
% 97.31/13.16 (setunionsingleton1) =>
% 97.31/13.16 ((
% 97.31/13.16 (setunionsingleton2) =>
% 97.31/13.16 ((
% 97.31/13.16 (setunionsingleton) =>
% 97.31/13.16 ((
% 97.31/13.16 (singletonprop) =>
% 97.31/13.16 ((
% 97.31/13.16 (ex1E1) =>
% 97.31/13.16 ((
% 97.31/13.16 (ex1I) =>
% 97.31/13.16 ((
% 97.31/13.16 (ex1I2) =>
% 97.31/13.16 ((
% 97.31/13.16 (singletonsuniq) =>
% 97.31/13.16 ((
% 97.31/13.16 (setukpairinjL1) =>
% 97.31/13.16 ((
% 97.31/13.16 (kfstsingleton) =>
% 97.31/13.16 ((
% 97.31/13.16 (theprop) =>
% 97.31/13.16 ((
% 97.31/13.16 (kfstpairEq) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodfstin) =>
% 97.31/13.16 ((
% 97.31/13.16 (setukpairinjL2) =>
% 97.31/13.16 ((
% 97.31/13.16 (setukpairinjL) =>
% 97.31/13.16 ((
% 97.31/13.16 (setukpairinjR11) =>
% 97.31/13.16 ((
% 97.31/13.16 (setukpairinjR12) =>
% 97.31/13.16 ((
% 97.31/13.16 (setukpairinjR1) =>
% 97.31/13.16 ((
% 97.31/13.16 (upairequniteq) =>
% 97.31/13.16 ((
% 97.31/13.16 (setukpairinjR2) =>
% 97.31/13.16 ((
% 97.31/13.16 (setukpairinjR) =>
% 97.31/13.16 ((
% 97.31/13.16 (ksndsingleton) =>
% 97.31/13.16 ((
% 97.31/13.16 (ksndpairEq) =>
% 97.31/13.16 ((
% 97.31/13.16 (kpairsurjEq) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodsndin) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodpairmemEL) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodpairmemER) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodmempaircEq) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodfstpairEq) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodsndpairEq) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodpairsurjEq) =>
% 97.31/13.16 ((
% 97.31/13.16 (dpsetconstrI) =>
% 97.31/13.16 ((
% 97.31/13.16 (dpsetconstrSub) =>
% 97.31/13.16 ((
% 97.31/13.16 (setOfPairsIsBReln) =>
% 97.31/13.16 ((
% 97.31/13.16 (dpsetconstrERa) =>
% 97.31/13.16 ((
% 97.31/13.16 (dpsetconstrEL1) =>
% 97.31/13.16 ((
% 97.31/13.16 (dpsetconstrEL2) =>
% 97.31/13.16 ((
% 97.31/13.16 (dpsetconstrER) =>
% 97.31/13.16 ((
% 97.31/13.16 (funcImageSingleton) =>
% 97.31/13.16 ((
% 97.31/13.16 (apProp) =>
% 97.31/13.16 ((
% 97.31/13.16 (app) =>
% 97.31/13.16 ((
% 97.31/13.16 (infuncsetfunc) =>
% 97.31/13.16 ((
% 97.31/13.16 (ap2p) =>
% 97.31/13.16 ((
% 97.31/13.16 (funcinfuncset) =>
% 97.31/13.16 ((
% 97.31/13.16 (lamProp) =>
% 97.31/13.16 ((
% 97.31/13.16 (lamp) =>
% 97.31/13.16 ((
% 97.31/13.16 (lam2p) =>
% 97.31/13.16 ((
% 97.31/13.16 (brelnall1) =>
% 97.31/13.16 ((
% 97.31/13.16 (brelnall2) =>
% 97.31/13.16 ((
% 97.31/13.16 (ex1E2) =>
% 97.31/13.16 ((
% 97.31/13.16 (funcGraphProp1) =>
% 97.31/13.16 ((
% 97.31/13.16 (funcGraphProp3) =>
% 97.31/13.16 ((
% 97.31/13.16 (funcGraphProp2) =>
% 97.31/13.16 ((
% 97.31/13.16 (funcextLem) =>
% 97.31/13.16 ((
% 97.31/13.16 (funcGraphProp4) =>
% 97.31/13.16 ((
% 97.31/13.16 (subbreln) =>
% 97.31/13.16 ((
% 97.31/13.16 (eqbreln) =>
% 97.31/13.16 ((
% 97.31/13.16 (funcext) =>
% 97.31/13.16 ((
% 97.31/13.16 (funcext2) =>
% 97.31/13.16 ((
% 97.31/13.16 (ap2apEq1) =>
% 97.31/13.16 ((
% 97.31/13.16 (ap2apEq2) =>
% 97.31/13.16 ((
% 97.31/13.16 (beta1) =>
% 97.31/13.16 ((
% 97.31/13.16 (eta1) =>
% 97.31/13.16 ((
% 97.31/13.16 (lam2lamEq) =>
% 97.31/13.16 ((
% 97.31/13.16 (beta2) =>
% 97.31/13.16 ((
% 97.31/13.16 (eta2) =>
% 97.31/13.16 ((
% 97.31/13.16 (iffalseProp1) =>
% 97.31/13.16 ((
% 97.31/13.16 (iffalseProp2) =>
% 97.31/13.16 ((
% 97.31/13.16 (iftrueProp1) =>
% 97.31/13.16 ((
% 97.31/13.16 (iftrueProp2) =>
% 97.31/13.16 ((
% 97.31/13.16 (ifSingleton) =>
% 97.31/13.16 ((
% 97.31/13.16 (ifp) =>
% 97.31/13.16 ((
% 97.31/13.16 (theeq) =>
% 97.31/13.16 ((
% 97.31/13.16 (iftrue) =>
% 97.31/13.16 ((
% 97.31/13.16 (iffalse) =>
% 97.31/13.16 ((
% 97.31/13.16 (iftrueorfalse) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectT_lem) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionT_lem) =>
% 97.31/13.16 ((
% 97.31/13.16 (powersetT_lem) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusT_lem) =>
% 97.31/13.16 ((
% 97.31/13.16 (complementT_lem) =>
% 97.31/13.16 ((
% 97.31/13.16 (setextT) =>
% 97.31/13.16 ((
% 97.31/13.16 (subsetTI) =>
% 97.31/13.16 ((
% 97.31/13.16 (powersetTI1) =>
% 97.31/13.16 ((
% 97.31/13.16 (powersetTE1) =>
% 97.31/13.16 ((
% 97.31/13.16 (complementTI1) =>
% 97.31/13.16 ((
% 97.31/13.16 (complementTE1) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectTELcontra) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectTERcontra) =>
% 97.31/13.16 ((
% 97.31/13.16 (contrasubsetT) =>
% 97.31/13.16 ((
% 97.31/13.16 (contrasubsetT1) =>
% 97.31/13.16 ((
% 97.31/13.16 (contrasubsetT2) =>
% 97.31/13.16 ((
% 97.31/13.16 (contrasubsetT3) =>
% 97.31/13.16 ((
% 97.31/13.16 (doubleComplementI1) =>
% 97.31/13.16 ((
% 97.31/13.16 (doubleComplementE1) =>
% 97.31/13.16 ((
% 97.31/13.16 (doubleComplementSub1) =>
% 97.31/13.16 ((
% 97.31/13.16 (doubleComplementSub2) =>
% 97.31/13.16 ((
% 97.31/13.16 (doubleComplementEq) =>
% 97.31/13.16 ((
% 97.31/13.16 (complementTnotintersectT) =>
% 97.31/13.16 ((
% 97.31/13.16 (complementImpComplementIntersect) =>
% 97.31/13.16 ((
% 97.31/13.16 (complementSubsetComplementIntersect) =>
% 97.31/13.16 ((
% 97.31/13.16 (complementInPowersetComplementIntersect) =>
% 97.31/13.16 ((
% 97.31/13.16 (contraSubsetComplement) =>
% 97.31/13.16 ((
% 97.31/13.16 (complementTcontraSubset) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionTILcontra) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionTIRcontra) =>
% 97.31/13.16 ((
% 97.31/13.16 (inIntersectImpInUnion) =>
% 97.31/13.16 ((
% 97.31/13.16 (inIntersectImpInUnion2) =>
% 97.31/13.16 ((
% 97.31/13.16 (inIntersectImpInIntersectUnions) =>
% 97.31/13.16 ((
% 97.31/13.16 (intersectInPowersetIntersectUnions) =>
% 97.31/13.16 ((
% 97.31/13.16 (inComplementUnionImpNotIn1) =>
% 97.31/13.16 ((
% 97.31/13.16 (inComplementUnionImpInComplement1) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionTE) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionTEcontra) =>
% 97.31/13.16 ((
% 97.31/13.16 (demorgan2a1) =>
% 97.31/13.16 ((
% 97.31/13.16 (complementUnionInPowersetComplement) =>
% 97.31/13.16 ((
% 97.31/13.16 (demorgan2a2) =>
% 97.31/13.16 ((
% 97.31/13.16 (demorgan1a) =>
% 97.31/13.16 ((
% 97.31/13.16 (demorgan1b) =>
% 97.31/13.16 ((
% 97.31/13.16 (demorgan1) =>
% 97.31/13.16 ((
% 97.31/13.16 (demorgan2a) =>
% 97.31/13.16 ((
% 97.31/13.16 (demorgan2b2) =>
% 97.31/13.16 ((
% 97.31/13.16 (demorgan2b) =>
% 97.31/13.16 ((
% 97.31/13.16 (demorgan2) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz13rule0) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz13rule1) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz13rule2) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz13rule3) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz13rule4) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz1_1) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz1_2) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz1_3) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz1_4) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz1_5) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1all2) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1SetBreln1) =>
% 97.31/13.16 ((
% 97.31/13.16 (choice2fnsingleton) =>
% 97.31/13.16 ((
% 97.31/13.16 (setOfPairsIsBReln1) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1all1) =>
% 97.31/13.16 ((
% 97.31/13.16 (subbreln1) =>
% 97.31/13.16 ((
% 97.31/13.16 (eqbreln1) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1invprop) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1invI) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1invE) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1compprop) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1compI) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1compE) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1compEex) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1unionprop) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1unionIL) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1unionIR) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1unionI) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1unionE) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1unionEcases) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1unionCommutes) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz2Ex) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz2W) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz2A) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz2B) =>
% 97.31/13.16 ((
% 97.31/13.16 (image1Ex) =>
% 97.31/13.16 ((
% 97.31/13.16 (image1Ex1) =>
% 97.31/13.16 ((
% 97.31/13.16 (image1Equiv) =>
% 97.31/13.16 ((
% 97.31/13.16 (image1E) =>
% 97.31/13.16 ((
% 97.31/13.16 (image1I) =>
% 97.31/13.16 ((
% 97.31/13.16 (injFuncInInjFuncSet) =>
% 97.31/13.16 ((
% 97.31/13.16 (injFuncSetFuncIn) =>
% 97.31/13.16 ((
% 97.31/13.16 (injFuncSetFuncInj) =>
% 97.31/13.16 ((
% 97.31/13.16 (surjFuncSetFuncIn) =>
% 97.31/13.16 ((
% 97.31/13.16 (surjFuncSetFuncSurj) =>
% 97.31/13.16 ((
% 97.31/13.16 (leftInvIsSurj) =>
% 97.31/13.16 ((
% 97.31/13.16 (surjCantorThm) =>
% 97.31/13.16 ((
% 97.31/13.16 (foundation2) =>
% 97.31/13.16 ((
% 97.31/13.16 (notinself) =>
% 97.31/13.16 ((
% 97.31/13.16 (notinself2) =>
% 97.31/13.16 ((
% 97.31/13.16 (omegaSp) =>
% 97.31/13.16 ((
% 97.31/13.16 (omegaSclos) =>
% 97.31/13.16 ((
% 97.31/13.16 (peano0notS) =>
% 97.31/13.16 ((
% 97.31/13.16 (!!) @ (
% 97.31/13.16 (('#S') @ (
% 97.31/13.16 (
% 97.31/13.16 ('#B') @ (
% 97.31/13.16 =>) @
% 97.31/13.16 (
% 97.31/13.16 (
% 97.31/13.16 ('#C') @ in @
% 97.31/13.16 omega)))) @
% 97.31/13.16 (
% 97.31/13.16 (
% 97.31/13.16 ('#B') @ (
% 97.31/13.16 !!) @
% 97.31/13.16 (
% 97.31/13.16 (
% 97.31/13.16 ('#B') @ (
% 97.31/13.16 (
% 97.31/13.16 ('#S') @ (
% 97.31/13.16 (
% 97.31/13.16 ('#B') @ (
% 97.31/13.16 =>) @
% 97.31/13.16 (
% 97.31/13.16 (
% 97.31/13.16 ('#C') @ in @
% 97.31/13.16 omega)))))) @
% 97.31/13.16 (
% 97.31/13.16 (
% 97.31/13.16 ('#S') @ (
% 97.31/13.16 (
% 97.31/13.16 ('#B') @ (
% 97.31/13.16 '#S') @
% 97.31/13.16 (
% 97.31/13.16 (
% 97.31/13.16 ('#B') @ (
% 97.31/13.16 (
% 97.31/13.16 ('#B') @ (
% 97.31/13.16 =>))) @
% 97.31/13.16 (
% 97.31/13.16 (
% 97.31/13.16 ('#C') @ (
% 97.31/13.16 (
% 97.31/13.16 ('#B') @ (
% 97.31/13.16 '#B') @
% 97.31/13.16 (
% 97.31/13.16 (
% 97.31/13.16 ('#B') @ (
% 97.31/13.16 =) @
% 97.31/13.16 omegaS)))) @
% 97.31/13.16 omegaS)))))) @
% 97.31/13.16 (
% 97.31/13.16 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.31/13.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl189])).
% 97.31/13.16 thf(zip_derived_cl222, plain,
% 97.31/13.16 (~ (((emptyI) =>
% 97.31/13.16 (((noeltsimpempty) =>
% 97.31/13.16 (((setbeta) =>
% 97.31/13.16 (((nonemptyE1) =>
% 97.31/13.16 (((nonemptyI) =>
% 97.31/13.16 (((nonemptyI1) =>
% 97.31/13.16 (((setadjoinIL) =>
% 97.31/13.16 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 97.31/13.16 (((setadjoinIR) =>
% 97.31/13.16 (((setadjoinE) =>
% 97.31/13.16 (((setadjoinOr) =>
% 97.31/13.16 (((setoftrueEq) =>
% 97.31/13.16 (((powersetI) =>
% 97.31/13.16 (((emptyinPowerset) =>
% 97.31/13.16 (((emptyInPowerset) =>
% 97.31/13.16 (((powersetE) =>
% 97.31/13.16 (((setunionI) =>
% 97.31/13.16 (((setunionE) =>
% 97.31/13.16 (((subPowSU) =>
% 97.31/13.16 (((exuE2) =>
% 97.31/13.16 (((nonemptyImpWitness) =>
% 97.31/13.16 (((uniqinunit) =>
% 97.31/13.16 (((notinsingleton) =>
% 97.31/13.16 (((eqinunit) =>
% 97.31/13.16 (((singletonsswitch) =>
% 97.31/13.16 (((upairsetE) =>
% 97.31/13.16 (((upairsetIL) =>
% 97.31/13.16 (((upairsetIR) =>
% 97.31/13.16 (((emptyE1) =>
% 97.31/13.16 (((vacuousDall) =>
% 97.31/13.16 ((
% 97.31/13.16 (quantDeMorgan1) =>
% 97.31/13.16 ((
% 97.31/13.16 (quantDeMorgan2) =>
% 97.31/13.16 ((
% 97.31/13.16 (quantDeMorgan3) =>
% 97.31/13.16 ((
% 97.31/13.16 (quantDeMorgan4) =>
% 97.31/13.16 ((
% 97.31/13.16 (prop2setI) =>
% 97.31/13.16 ((
% 97.31/13.16 (prop2set2propI) =>
% 97.31/13.16 ((
% 97.31/13.16 (notdexE) =>
% 97.31/13.16 ((
% 97.31/13.16 (notdallE) =>
% 97.31/13.16 ((
% 97.31/13.16 (exuI1) =>
% 97.31/13.16 ((
% 97.31/13.16 (exuI3) =>
% 97.31/13.16 ((
% 97.31/13.16 (exuI2) =>
% 97.31/13.16 ((
% 97.31/13.16 (inCongP) =>
% 97.31/13.16 ((
% 97.31/13.16 (in__Cong) =>
% 97.31/13.16 ((
% 97.31/13.16 (exuE3u) =>
% 97.31/13.16 ((
% 97.31/13.16 (exu__Cong) =>
% 97.31/13.16 ((
% 97.31/13.16 (setadjoin__Cong) =>
% 97.31/13.16 ((
% 97.31/13.16 (powerset__Cong) =>
% 97.31/13.16 ((
% 97.31/13.16 (setunion__Cong) =>
% 97.31/13.16 ((
% 97.31/13.16 (exuEu) =>
% 97.31/13.16 ((
% 97.31/13.16 (descr__Cong) =>
% 97.31/13.16 ((
% 97.31/13.16 (dsetconstr__Cong) =>
% 97.31/13.16 ((
% 97.31/13.16 (subsetI1) =>
% 97.31/13.16 ((
% 97.31/13.16 (eqimpsubset2) =>
% 97.31/13.16 ((
% 97.31/13.16 (eqimpsubset1) =>
% 97.31/13.16 ((
% 97.31/13.16 (subsetI2) =>
% 97.31/13.16 ((
% 97.31/13.16 (emptysetsubset) =>
% 97.31/13.16 ((
% 97.31/13.16 (subsetE) =>
% 97.31/13.16 ((
% 97.31/13.16 (subsetE2) =>
% 97.31/13.16 ((
% 97.31/13.16 (notsubsetI) =>
% 97.31/13.16 ((
% 97.31/13.16 (notequalI1) =>
% 97.31/13.16 ((
% 97.31/13.16 (notequalI2) =>
% 97.31/13.16 ((
% 97.31/13.16 (subsetRefl) =>
% 97.31/13.16 ((
% 97.31/13.16 (subsetTrans) =>
% 97.31/13.16 ((
% 97.31/13.16 (setadjoinSub) =>
% 97.31/13.16 ((
% 97.31/13.16 (setadjoinSub2) =>
% 97.31/13.16 ((
% 97.31/13.16 (subset2powerset) =>
% 97.31/13.16 ((
% 97.31/13.16 (setextsub) =>
% 97.31/13.16 ((
% 97.31/13.16 (subsetemptysetimpeq) =>
% 97.31/13.16 ((
% 97.31/13.16 (powersetI1) =>
% 97.31/13.16 ((
% 97.31/13.16 (powersetE1) =>
% 97.31/13.16 ((
% 97.31/13.16 (inPowerset) =>
% 97.31/13.16 ((
% 97.31/13.16 (powersetsubset) =>
% 97.31/13.16 ((
% 97.31/13.16 (sepInPowerset) =>
% 97.31/13.16 ((
% 97.31/13.16 (sepSubset) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionIL) =>
% 97.31/13.16 ((
% 97.31/13.16 (upairset2IR) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionIR) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionEcases) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionE) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionLsub) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionRsub) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectI) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectSubset5) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectEL) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectLsub) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectSubset2) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectSubset3) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectER) =>
% 97.31/13.16 ((
% 97.31/13.16 (disjointsetsI1) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectRsub) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectSubset4) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectSubset1) =>
% 97.31/13.16 ((
% 97.31/13.16 (bs114d) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusI) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusEL) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusER) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusSubset2) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusERneg) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusELneg) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusILneg) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusIRneg) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusLsub) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusSubset1) =>
% 97.31/13.16 ((
% 97.31/13.16 (symdiffE) =>
% 97.31/13.16 ((
% 97.31/13.16 (symdiffI1) =>
% 97.31/13.16 ((
% 97.31/13.16 (symdiffI2) =>
% 97.31/13.16 ((
% 97.31/13.16 (symdiffIneg1) =>
% 97.31/13.16 ((
% 97.31/13.16 (symdiffIneg2) =>
% 97.31/13.16 ((
% 97.31/13.16 (secondinupair) =>
% 97.31/13.16 ((
% 97.31/13.16 (setukpairIL) =>
% 97.31/13.16 ((
% 97.31/13.16 (setukpairIR) =>
% 97.31/13.16 ((
% 97.31/13.16 (kpairiskpair) =>
% 97.31/13.16 ((
% 97.31/13.16 (kpairp) =>
% 97.31/13.16 ((
% 97.31/13.16 (singletonsubset) =>
% 97.31/13.16 ((
% 97.31/13.16 (singletoninpowerset) =>
% 97.31/13.16 ((
% 97.31/13.16 (singletoninpowunion) =>
% 97.31/13.16 ((
% 97.31/13.16 (upairset2E) =>
% 97.31/13.16 ((
% 97.31/13.16 (upairsubunion) =>
% 97.31/13.16 ((
% 97.31/13.16 (upairinpowunion) =>
% 97.31/13.16 ((
% 97.31/13.16 (ubforcartprodlem1) =>
% 97.31/13.16 ((
% 97.31/13.16 (ubforcartprodlem2) =>
% 97.31/13.16 ((
% 97.31/13.16 (ubforcartprodlem3) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodpairin) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodmempair1) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodmempair) =>
% 97.31/13.16 ((
% 97.31/13.16 (setunionE2) =>
% 97.31/13.16 ((
% 97.31/13.16 (setunionsingleton1) =>
% 97.31/13.16 ((
% 97.31/13.16 (setunionsingleton2) =>
% 97.31/13.16 ((
% 97.31/13.16 (setunionsingleton) =>
% 97.31/13.16 ((
% 97.31/13.16 (singletonprop) =>
% 97.31/13.16 ((
% 97.31/13.16 (ex1E1) =>
% 97.31/13.16 ((
% 97.31/13.16 (ex1I) =>
% 97.31/13.16 ((
% 97.31/13.16 (ex1I2) =>
% 97.31/13.16 ((
% 97.31/13.16 (singletonsuniq) =>
% 97.31/13.16 ((
% 97.31/13.16 (setukpairinjL1) =>
% 97.31/13.16 ((
% 97.31/13.16 (kfstsingleton) =>
% 97.31/13.16 ((
% 97.31/13.16 (theprop) =>
% 97.31/13.16 ((
% 97.31/13.16 (kfstpairEq) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodfstin) =>
% 97.31/13.16 ((
% 97.31/13.16 (setukpairinjL2) =>
% 97.31/13.16 ((
% 97.31/13.16 (setukpairinjL) =>
% 97.31/13.16 ((
% 97.31/13.16 (setukpairinjR11) =>
% 97.31/13.16 ((
% 97.31/13.16 (setukpairinjR12) =>
% 97.31/13.16 ((
% 97.31/13.16 (setukpairinjR1) =>
% 97.31/13.16 ((
% 97.31/13.16 (upairequniteq) =>
% 97.31/13.16 ((
% 97.31/13.16 (setukpairinjR2) =>
% 97.31/13.16 ((
% 97.31/13.16 (setukpairinjR) =>
% 97.31/13.16 ((
% 97.31/13.16 (ksndsingleton) =>
% 97.31/13.16 ((
% 97.31/13.16 (ksndpairEq) =>
% 97.31/13.16 ((
% 97.31/13.16 (kpairsurjEq) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodsndin) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodpairmemEL) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodpairmemER) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodmempaircEq) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodfstpairEq) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodsndpairEq) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodpairsurjEq) =>
% 97.31/13.16 ((
% 97.31/13.16 (dpsetconstrI) =>
% 97.31/13.16 ((
% 97.31/13.16 (dpsetconstrSub) =>
% 97.31/13.16 ((
% 97.31/13.16 (setOfPairsIsBReln) =>
% 97.31/13.16 ((
% 97.31/13.16 (dpsetconstrERa) =>
% 97.31/13.16 ((
% 97.31/13.16 (dpsetconstrEL1) =>
% 97.31/13.16 ((
% 97.31/13.16 (dpsetconstrEL2) =>
% 97.31/13.16 ((
% 97.31/13.16 (dpsetconstrER) =>
% 97.31/13.16 ((
% 97.31/13.16 (funcImageSingleton) =>
% 97.31/13.16 ((
% 97.31/13.16 (apProp) =>
% 97.31/13.16 ((
% 97.31/13.16 (app) =>
% 97.31/13.16 ((
% 97.31/13.16 (infuncsetfunc) =>
% 97.31/13.16 ((
% 97.31/13.16 (ap2p) =>
% 97.31/13.16 ((
% 97.31/13.16 (funcinfuncset) =>
% 97.31/13.16 ((
% 97.31/13.16 (lamProp) =>
% 97.31/13.16 ((
% 97.31/13.16 (lamp) =>
% 97.31/13.16 ((
% 97.31/13.16 (lam2p) =>
% 97.31/13.16 ((
% 97.31/13.16 (brelnall1) =>
% 97.31/13.16 ((
% 97.31/13.16 (brelnall2) =>
% 97.31/13.16 ((
% 97.31/13.16 (ex1E2) =>
% 97.31/13.16 ((
% 97.31/13.16 (funcGraphProp1) =>
% 97.31/13.16 ((
% 97.31/13.16 (funcGraphProp3) =>
% 97.31/13.16 ((
% 97.31/13.16 (funcGraphProp2) =>
% 97.31/13.16 ((
% 97.31/13.16 (funcextLem) =>
% 97.31/13.16 ((
% 97.31/13.16 (funcGraphProp4) =>
% 97.31/13.16 ((
% 97.31/13.16 (subbreln) =>
% 97.31/13.16 ((
% 97.31/13.16 (eqbreln) =>
% 97.31/13.16 ((
% 97.31/13.16 (funcext) =>
% 97.31/13.16 ((
% 97.31/13.16 (funcext2) =>
% 97.31/13.16 ((
% 97.31/13.16 (ap2apEq1) =>
% 97.31/13.16 ((
% 97.31/13.16 (ap2apEq2) =>
% 97.31/13.16 ((
% 97.31/13.16 (beta1) =>
% 97.31/13.16 ((
% 97.31/13.16 (eta1) =>
% 97.31/13.16 ((
% 97.31/13.16 (lam2lamEq) =>
% 97.31/13.16 ((
% 97.31/13.16 (beta2) =>
% 97.31/13.16 ((
% 97.31/13.16 (eta2) =>
% 97.31/13.16 ((
% 97.31/13.16 (iffalseProp1) =>
% 97.31/13.16 ((
% 97.31/13.16 (iffalseProp2) =>
% 97.31/13.16 ((
% 97.31/13.16 (iftrueProp1) =>
% 97.31/13.16 ((
% 97.31/13.16 (iftrueProp2) =>
% 97.31/13.16 ((
% 97.31/13.16 (ifSingleton) =>
% 97.31/13.16 ((
% 97.31/13.16 (ifp) =>
% 97.31/13.16 ((
% 97.31/13.16 (theeq) =>
% 97.31/13.16 ((
% 97.31/13.16 (iftrue) =>
% 97.31/13.16 ((
% 97.31/13.16 (iffalse) =>
% 97.31/13.16 ((
% 97.31/13.16 (iftrueorfalse) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectT_lem) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionT_lem) =>
% 97.31/13.16 ((
% 97.31/13.16 (powersetT_lem) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusT_lem) =>
% 97.31/13.16 ((
% 97.31/13.16 (complementT_lem) =>
% 97.31/13.16 ((
% 97.31/13.16 (setextT) =>
% 97.31/13.16 ((
% 97.31/13.16 (subsetTI) =>
% 97.31/13.16 ((
% 97.31/13.16 (powersetTI1) =>
% 97.31/13.16 ((
% 97.31/13.16 (powersetTE1) =>
% 97.31/13.16 ((
% 97.31/13.16 (complementTI1) =>
% 97.31/13.16 ((
% 97.31/13.16 (complementTE1) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectTELcontra) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectTERcontra) =>
% 97.31/13.16 ((
% 97.31/13.16 (contrasubsetT) =>
% 97.31/13.16 ((
% 97.31/13.16 (contrasubsetT1) =>
% 97.31/13.16 ((
% 97.31/13.16 (contrasubsetT2) =>
% 97.31/13.16 ((
% 97.31/13.16 (contrasubsetT3) =>
% 97.31/13.16 ((
% 97.31/13.16 (doubleComplementI1) =>
% 97.31/13.16 ((
% 97.31/13.16 (doubleComplementE1) =>
% 97.31/13.16 ((
% 97.31/13.16 (doubleComplementSub1) =>
% 97.31/13.16 ((
% 97.31/13.16 (doubleComplementSub2) =>
% 97.31/13.16 ((
% 97.31/13.16 (doubleComplementEq) =>
% 97.31/13.16 ((
% 97.31/13.16 (complementTnotintersectT) =>
% 97.31/13.16 ((
% 97.31/13.16 (complementImpComplementIntersect) =>
% 97.31/13.16 ((
% 97.31/13.16 (complementSubsetComplementIntersect) =>
% 97.31/13.16 ((
% 97.31/13.16 (complementInPowersetComplementIntersect) =>
% 97.31/13.16 ((
% 97.31/13.16 (contraSubsetComplement) =>
% 97.31/13.16 ((
% 97.31/13.16 (complementTcontraSubset) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionTILcontra) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionTIRcontra) =>
% 97.31/13.16 ((
% 97.31/13.16 (inIntersectImpInUnion) =>
% 97.31/13.16 ((
% 97.31/13.16 (inIntersectImpInUnion2) =>
% 97.31/13.16 ((
% 97.31/13.16 (inIntersectImpInIntersectUnions) =>
% 97.31/13.16 ((
% 97.31/13.16 (intersectInPowersetIntersectUnions) =>
% 97.31/13.16 ((
% 97.31/13.16 (inComplementUnionImpNotIn1) =>
% 97.31/13.16 ((
% 97.31/13.16 (inComplementUnionImpInComplement1) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionTE) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionTEcontra) =>
% 97.31/13.16 ((
% 97.31/13.16 (demorgan2a1) =>
% 97.31/13.16 ((
% 97.31/13.16 (complementUnionInPowersetComplement) =>
% 97.31/13.16 ((
% 97.31/13.16 (demorgan2a2) =>
% 97.31/13.16 ((
% 97.31/13.16 (demorgan1a) =>
% 97.31/13.16 ((
% 97.31/13.16 (demorgan1b) =>
% 97.31/13.16 ((
% 97.31/13.16 (demorgan1) =>
% 97.31/13.16 ((
% 97.31/13.16 (demorgan2a) =>
% 97.31/13.16 ((
% 97.31/13.16 (demorgan2b2) =>
% 97.31/13.16 ((
% 97.31/13.16 (demorgan2b) =>
% 97.31/13.16 ((
% 97.31/13.16 (demorgan2) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz13rule0) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz13rule1) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz13rule2) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz13rule3) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz13rule4) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz1_1) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz1_2) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz1_3) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz1_4) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz1_5) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1all2) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1SetBreln1) =>
% 97.31/13.16 ((
% 97.31/13.16 (choice2fnsingleton) =>
% 97.31/13.16 ((
% 97.31/13.16 (setOfPairsIsBReln1) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1all1) =>
% 97.31/13.16 ((
% 97.31/13.16 (subbreln1) =>
% 97.31/13.16 ((
% 97.31/13.16 (eqbreln1) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1invprop) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1invI) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1invE) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1compprop) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1compI) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1compE) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1compEex) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1unionprop) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1unionIL) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1unionIR) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1unionI) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1unionE) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1unionEcases) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1unionCommutes) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz2Ex) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz2W) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz2A) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz2B) =>
% 97.31/13.16 ((
% 97.31/13.16 (image1Ex) =>
% 97.31/13.16 ((
% 97.31/13.16 (image1Ex1) =>
% 97.31/13.16 ((
% 97.31/13.16 (image1Equiv) =>
% 97.31/13.16 ((
% 97.31/13.16 (image1E) =>
% 97.31/13.16 ((
% 97.31/13.16 (image1I) =>
% 97.31/13.16 ((
% 97.31/13.16 (injFuncInInjFuncSet) =>
% 97.31/13.16 ((
% 97.31/13.16 (injFuncSetFuncIn) =>
% 97.31/13.16 ((
% 97.31/13.16 (injFuncSetFuncInj) =>
% 97.31/13.16 ((
% 97.31/13.16 (surjFuncSetFuncIn) =>
% 97.31/13.16 ((
% 97.31/13.16 (surjFuncSetFuncSurj) =>
% 97.31/13.16 ((
% 97.31/13.16 (leftInvIsSurj) =>
% 97.31/13.16 ((
% 97.31/13.16 (surjCantorThm) =>
% 97.31/13.16 ((
% 97.31/13.16 (foundation2) =>
% 97.31/13.16 ((
% 97.31/13.16 (notinself) =>
% 97.31/13.16 ((
% 97.31/13.16 (notinself2) =>
% 97.31/13.16 ((
% 97.31/13.16 (omegaSp) =>
% 97.31/13.16 ((
% 97.31/13.16 (omegaSclos) =>
% 97.31/13.16 ((
% 97.31/13.16 (peano0notS) =>
% 97.31/13.16 ((
% 97.31/13.16 (!!) @ (
% 97.31/13.16 (('#S') @ (
% 97.31/13.16 (
% 97.31/13.16 ('#B') @ (
% 97.31/13.16 =>) @
% 97.31/13.16 (
% 97.31/13.16 (
% 97.31/13.16 ('#C') @ in @
% 97.31/13.16 omega)))) @
% 97.31/13.16 (
% 97.31/13.16 (
% 97.31/13.16 ('#B') @ (
% 97.31/13.16 !!) @
% 97.31/13.16 (
% 97.31/13.16 (
% 97.31/13.16 ('#B') @ (
% 97.31/13.16 (
% 97.31/13.16 ('#S') @ (
% 97.31/13.16 (
% 97.31/13.16 ('#B') @ (
% 97.31/13.16 =>) @
% 97.31/13.16 (
% 97.31/13.16 (
% 97.31/13.16 ('#C') @ in @
% 97.31/13.16 omega)))))) @
% 97.31/13.16 (
% 97.31/13.16 (
% 97.31/13.16 ('#S') @ (
% 97.31/13.16 (
% 97.31/13.16 ('#B') @ (
% 97.31/13.16 '#S') @
% 97.31/13.16 (
% 97.31/13.16 (
% 97.31/13.16 ('#B') @ (
% 97.31/13.16 (
% 97.31/13.16 ('#B') @ (
% 97.31/13.16 =>))) @
% 97.31/13.16 (
% 97.31/13.16 (
% 97.31/13.16 ('#C') @ (
% 97.31/13.16 (
% 97.31/13.16 ('#B') @ (
% 97.31/13.16 '#B') @
% 97.31/13.16 (
% 97.31/13.16 (
% 97.31/13.16 ('#B') @ (
% 97.31/13.16 =) @
% 97.31/13.16 omegaS)))) @
% 97.31/13.16 omegaS)))))) @
% 97.31/13.16 (
% 97.31/13.16 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.31/13.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl206])).
% 97.31/13.16 thf(zip_derived_cl236, plain,
% 97.31/13.16 (~ (((noeltsimpempty) =>
% 97.31/13.16 (((setbeta) =>
% 97.31/13.16 (((nonemptyE1) =>
% 97.31/13.16 (((nonemptyI) =>
% 97.31/13.16 (((nonemptyI1) =>
% 97.31/13.16 (((setadjoinIL) =>
% 97.31/13.16 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 97.31/13.16 (((setadjoinIR) =>
% 97.31/13.16 (((setadjoinE) =>
% 97.31/13.16 (((setadjoinOr) =>
% 97.31/13.16 (((setoftrueEq) =>
% 97.31/13.16 (((powersetI) =>
% 97.31/13.16 (((emptyinPowerset) =>
% 97.31/13.16 (((emptyInPowerset) =>
% 97.31/13.16 (((powersetE) =>
% 97.31/13.16 (((setunionI) =>
% 97.31/13.16 (((setunionE) =>
% 97.31/13.16 (((subPowSU) =>
% 97.31/13.16 (((exuE2) =>
% 97.31/13.16 (((nonemptyImpWitness) =>
% 97.31/13.16 (((uniqinunit) =>
% 97.31/13.16 (((notinsingleton) =>
% 97.31/13.16 (((eqinunit) =>
% 97.31/13.16 (((singletonsswitch) =>
% 97.31/13.16 (((upairsetE) =>
% 97.31/13.16 (((upairsetIL) =>
% 97.31/13.16 (((upairsetIR) =>
% 97.31/13.16 (((emptyE1) =>
% 97.31/13.16 (((vacuousDall) =>
% 97.31/13.16 (((quantDeMorgan1) =>
% 97.31/13.16 ((
% 97.31/13.16 (quantDeMorgan2) =>
% 97.31/13.16 ((
% 97.31/13.16 (quantDeMorgan3) =>
% 97.31/13.16 ((
% 97.31/13.16 (quantDeMorgan4) =>
% 97.31/13.16 ((
% 97.31/13.16 (prop2setI) =>
% 97.31/13.16 ((
% 97.31/13.16 (prop2set2propI) =>
% 97.31/13.16 ((
% 97.31/13.16 (notdexE) =>
% 97.31/13.16 ((
% 97.31/13.16 (notdallE) =>
% 97.31/13.16 ((
% 97.31/13.16 (exuI1) =>
% 97.31/13.16 ((
% 97.31/13.16 (exuI3) =>
% 97.31/13.16 ((
% 97.31/13.16 (exuI2) =>
% 97.31/13.16 ((
% 97.31/13.16 (inCongP) =>
% 97.31/13.16 ((
% 97.31/13.16 (in__Cong) =>
% 97.31/13.16 ((
% 97.31/13.16 (exuE3u) =>
% 97.31/13.16 ((
% 97.31/13.16 (exu__Cong) =>
% 97.31/13.16 ((
% 97.31/13.16 (setadjoin__Cong) =>
% 97.31/13.16 ((
% 97.31/13.16 (powerset__Cong) =>
% 97.31/13.16 ((
% 97.31/13.16 (setunion__Cong) =>
% 97.31/13.16 ((
% 97.31/13.16 (exuEu) =>
% 97.31/13.16 ((
% 97.31/13.16 (descr__Cong) =>
% 97.31/13.16 ((
% 97.31/13.16 (dsetconstr__Cong) =>
% 97.31/13.16 ((
% 97.31/13.16 (subsetI1) =>
% 97.31/13.16 ((
% 97.31/13.16 (eqimpsubset2) =>
% 97.31/13.16 ((
% 97.31/13.16 (eqimpsubset1) =>
% 97.31/13.16 ((
% 97.31/13.16 (subsetI2) =>
% 97.31/13.16 ((
% 97.31/13.16 (emptysetsubset) =>
% 97.31/13.16 ((
% 97.31/13.16 (subsetE) =>
% 97.31/13.16 ((
% 97.31/13.16 (subsetE2) =>
% 97.31/13.16 ((
% 97.31/13.16 (notsubsetI) =>
% 97.31/13.16 ((
% 97.31/13.16 (notequalI1) =>
% 97.31/13.16 ((
% 97.31/13.16 (notequalI2) =>
% 97.31/13.16 ((
% 97.31/13.16 (subsetRefl) =>
% 97.31/13.16 ((
% 97.31/13.16 (subsetTrans) =>
% 97.31/13.16 ((
% 97.31/13.16 (setadjoinSub) =>
% 97.31/13.16 ((
% 97.31/13.16 (setadjoinSub2) =>
% 97.31/13.16 ((
% 97.31/13.16 (subset2powerset) =>
% 97.31/13.16 ((
% 97.31/13.16 (setextsub) =>
% 97.31/13.16 ((
% 97.31/13.16 (subsetemptysetimpeq) =>
% 97.31/13.16 ((
% 97.31/13.16 (powersetI1) =>
% 97.31/13.16 ((
% 97.31/13.16 (powersetE1) =>
% 97.31/13.16 ((
% 97.31/13.16 (inPowerset) =>
% 97.31/13.16 ((
% 97.31/13.16 (powersetsubset) =>
% 97.31/13.16 ((
% 97.31/13.16 (sepInPowerset) =>
% 97.31/13.16 ((
% 97.31/13.16 (sepSubset) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionIL) =>
% 97.31/13.16 ((
% 97.31/13.16 (upairset2IR) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionIR) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionEcases) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionE) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionLsub) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionRsub) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectI) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectSubset5) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectEL) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectLsub) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectSubset2) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectSubset3) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectER) =>
% 97.31/13.16 ((
% 97.31/13.16 (disjointsetsI1) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectRsub) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectSubset4) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectSubset1) =>
% 97.31/13.16 ((
% 97.31/13.16 (bs114d) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusI) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusEL) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusER) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusSubset2) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusERneg) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusELneg) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusILneg) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusIRneg) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusLsub) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusSubset1) =>
% 97.31/13.16 ((
% 97.31/13.16 (symdiffE) =>
% 97.31/13.16 ((
% 97.31/13.16 (symdiffI1) =>
% 97.31/13.16 ((
% 97.31/13.16 (symdiffI2) =>
% 97.31/13.16 ((
% 97.31/13.16 (symdiffIneg1) =>
% 97.31/13.16 ((
% 97.31/13.16 (symdiffIneg2) =>
% 97.31/13.16 ((
% 97.31/13.16 (secondinupair) =>
% 97.31/13.16 ((
% 97.31/13.16 (setukpairIL) =>
% 97.31/13.16 ((
% 97.31/13.16 (setukpairIR) =>
% 97.31/13.16 ((
% 97.31/13.16 (kpairiskpair) =>
% 97.31/13.16 ((
% 97.31/13.16 (kpairp) =>
% 97.31/13.16 ((
% 97.31/13.16 (singletonsubset) =>
% 97.31/13.16 ((
% 97.31/13.16 (singletoninpowerset) =>
% 97.31/13.16 ((
% 97.31/13.16 (singletoninpowunion) =>
% 97.31/13.16 ((
% 97.31/13.16 (upairset2E) =>
% 97.31/13.16 ((
% 97.31/13.16 (upairsubunion) =>
% 97.31/13.16 ((
% 97.31/13.16 (upairinpowunion) =>
% 97.31/13.16 ((
% 97.31/13.16 (ubforcartprodlem1) =>
% 97.31/13.16 ((
% 97.31/13.16 (ubforcartprodlem2) =>
% 97.31/13.16 ((
% 97.31/13.16 (ubforcartprodlem3) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodpairin) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodmempair1) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodmempair) =>
% 97.31/13.16 ((
% 97.31/13.16 (setunionE2) =>
% 97.31/13.16 ((
% 97.31/13.16 (setunionsingleton1) =>
% 97.31/13.16 ((
% 97.31/13.16 (setunionsingleton2) =>
% 97.31/13.16 ((
% 97.31/13.16 (setunionsingleton) =>
% 97.31/13.16 ((
% 97.31/13.16 (singletonprop) =>
% 97.31/13.16 ((
% 97.31/13.16 (ex1E1) =>
% 97.31/13.16 ((
% 97.31/13.16 (ex1I) =>
% 97.31/13.16 ((
% 97.31/13.16 (ex1I2) =>
% 97.31/13.16 ((
% 97.31/13.16 (singletonsuniq) =>
% 97.31/13.16 ((
% 97.31/13.16 (setukpairinjL1) =>
% 97.31/13.16 ((
% 97.31/13.16 (kfstsingleton) =>
% 97.31/13.16 ((
% 97.31/13.16 (theprop) =>
% 97.31/13.16 ((
% 97.31/13.16 (kfstpairEq) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodfstin) =>
% 97.31/13.16 ((
% 97.31/13.16 (setukpairinjL2) =>
% 97.31/13.16 ((
% 97.31/13.16 (setukpairinjL) =>
% 97.31/13.16 ((
% 97.31/13.16 (setukpairinjR11) =>
% 97.31/13.16 ((
% 97.31/13.16 (setukpairinjR12) =>
% 97.31/13.16 ((
% 97.31/13.16 (setukpairinjR1) =>
% 97.31/13.16 ((
% 97.31/13.16 (upairequniteq) =>
% 97.31/13.16 ((
% 97.31/13.16 (setukpairinjR2) =>
% 97.31/13.16 ((
% 97.31/13.16 (setukpairinjR) =>
% 97.31/13.16 ((
% 97.31/13.16 (ksndsingleton) =>
% 97.31/13.16 ((
% 97.31/13.16 (ksndpairEq) =>
% 97.31/13.16 ((
% 97.31/13.16 (kpairsurjEq) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodsndin) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodpairmemEL) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodpairmemER) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodmempaircEq) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodfstpairEq) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodsndpairEq) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodpairsurjEq) =>
% 97.31/13.16 ((
% 97.31/13.16 (dpsetconstrI) =>
% 97.31/13.16 ((
% 97.31/13.16 (dpsetconstrSub) =>
% 97.31/13.16 ((
% 97.31/13.16 (setOfPairsIsBReln) =>
% 97.31/13.16 ((
% 97.31/13.16 (dpsetconstrERa) =>
% 97.31/13.16 ((
% 97.31/13.16 (dpsetconstrEL1) =>
% 97.31/13.16 ((
% 97.31/13.16 (dpsetconstrEL2) =>
% 97.31/13.16 ((
% 97.31/13.16 (dpsetconstrER) =>
% 97.31/13.16 ((
% 97.31/13.16 (funcImageSingleton) =>
% 97.31/13.16 ((
% 97.31/13.16 (apProp) =>
% 97.31/13.16 ((
% 97.31/13.16 (app) =>
% 97.31/13.16 ((
% 97.31/13.16 (infuncsetfunc) =>
% 97.31/13.16 ((
% 97.31/13.16 (ap2p) =>
% 97.31/13.16 ((
% 97.31/13.16 (funcinfuncset) =>
% 97.31/13.16 ((
% 97.31/13.16 (lamProp) =>
% 97.31/13.16 ((
% 97.31/13.16 (lamp) =>
% 97.31/13.16 ((
% 97.31/13.16 (lam2p) =>
% 97.31/13.16 ((
% 97.31/13.16 (brelnall1) =>
% 97.31/13.16 ((
% 97.31/13.16 (brelnall2) =>
% 97.31/13.16 ((
% 97.31/13.16 (ex1E2) =>
% 97.31/13.16 ((
% 97.31/13.16 (funcGraphProp1) =>
% 97.31/13.16 ((
% 97.31/13.16 (funcGraphProp3) =>
% 97.31/13.16 ((
% 97.31/13.16 (funcGraphProp2) =>
% 97.31/13.16 ((
% 97.31/13.16 (funcextLem) =>
% 97.31/13.16 ((
% 97.31/13.16 (funcGraphProp4) =>
% 97.31/13.16 ((
% 97.31/13.16 (subbreln) =>
% 97.31/13.16 ((
% 97.31/13.16 (eqbreln) =>
% 97.31/13.16 ((
% 97.31/13.16 (funcext) =>
% 97.31/13.16 ((
% 97.31/13.16 (funcext2) =>
% 97.31/13.16 ((
% 97.31/13.16 (ap2apEq1) =>
% 97.31/13.16 ((
% 97.31/13.16 (ap2apEq2) =>
% 97.31/13.16 ((
% 97.31/13.16 (beta1) =>
% 97.31/13.16 ((
% 97.31/13.16 (eta1) =>
% 97.31/13.16 ((
% 97.31/13.16 (lam2lamEq) =>
% 97.31/13.16 ((
% 97.31/13.16 (beta2) =>
% 97.31/13.16 ((
% 97.31/13.16 (eta2) =>
% 97.31/13.16 ((
% 97.31/13.16 (iffalseProp1) =>
% 97.31/13.16 ((
% 97.31/13.16 (iffalseProp2) =>
% 97.31/13.16 ((
% 97.31/13.16 (iftrueProp1) =>
% 97.31/13.16 ((
% 97.31/13.16 (iftrueProp2) =>
% 97.31/13.16 ((
% 97.31/13.16 (ifSingleton) =>
% 97.31/13.16 ((
% 97.31/13.16 (ifp) =>
% 97.31/13.16 ((
% 97.31/13.16 (theeq) =>
% 97.31/13.16 ((
% 97.31/13.16 (iftrue) =>
% 97.31/13.16 ((
% 97.31/13.16 (iffalse) =>
% 97.31/13.16 ((
% 97.31/13.16 (iftrueorfalse) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectT_lem) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionT_lem) =>
% 97.31/13.16 ((
% 97.31/13.16 (powersetT_lem) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusT_lem) =>
% 97.31/13.16 ((
% 97.31/13.16 (complementT_lem) =>
% 97.31/13.16 ((
% 97.31/13.16 (setextT) =>
% 97.31/13.16 ((
% 97.31/13.16 (subsetTI) =>
% 97.31/13.16 ((
% 97.31/13.16 (powersetTI1) =>
% 97.31/13.16 ((
% 97.31/13.16 (powersetTE1) =>
% 97.31/13.16 ((
% 97.31/13.16 (complementTI1) =>
% 97.31/13.16 ((
% 97.31/13.16 (complementTE1) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectTELcontra) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectTERcontra) =>
% 97.31/13.16 ((
% 97.31/13.16 (contrasubsetT) =>
% 97.31/13.16 ((
% 97.31/13.16 (contrasubsetT1) =>
% 97.31/13.16 ((
% 97.31/13.16 (contrasubsetT2) =>
% 97.31/13.16 ((
% 97.31/13.16 (contrasubsetT3) =>
% 97.31/13.16 ((
% 97.31/13.16 (doubleComplementI1) =>
% 97.31/13.16 ((
% 97.31/13.16 (doubleComplementE1) =>
% 97.31/13.16 ((
% 97.31/13.16 (doubleComplementSub1) =>
% 97.31/13.16 ((
% 97.31/13.16 (doubleComplementSub2) =>
% 97.31/13.16 ((
% 97.31/13.16 (doubleComplementEq) =>
% 97.31/13.16 ((
% 97.31/13.16 (complementTnotintersectT) =>
% 97.31/13.16 ((
% 97.31/13.16 (complementImpComplementIntersect) =>
% 97.31/13.16 ((
% 97.31/13.16 (complementSubsetComplementIntersect) =>
% 97.31/13.16 ((
% 97.31/13.16 (complementInPowersetComplementIntersect) =>
% 97.31/13.16 ((
% 97.31/13.16 (contraSubsetComplement) =>
% 97.31/13.16 ((
% 97.31/13.16 (complementTcontraSubset) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionTILcontra) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionTIRcontra) =>
% 97.31/13.16 ((
% 97.31/13.16 (inIntersectImpInUnion) =>
% 97.31/13.16 ((
% 97.31/13.16 (inIntersectImpInUnion2) =>
% 97.31/13.16 ((
% 97.31/13.16 (inIntersectImpInIntersectUnions) =>
% 97.31/13.16 ((
% 97.31/13.16 (intersectInPowersetIntersectUnions) =>
% 97.31/13.16 ((
% 97.31/13.16 (inComplementUnionImpNotIn1) =>
% 97.31/13.16 ((
% 97.31/13.16 (inComplementUnionImpInComplement1) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionTE) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionTEcontra) =>
% 97.31/13.16 ((
% 97.31/13.16 (demorgan2a1) =>
% 97.31/13.16 ((
% 97.31/13.16 (complementUnionInPowersetComplement) =>
% 97.31/13.16 ((
% 97.31/13.16 (demorgan2a2) =>
% 97.31/13.16 ((
% 97.31/13.16 (demorgan1a) =>
% 97.31/13.16 ((
% 97.31/13.16 (demorgan1b) =>
% 97.31/13.16 ((
% 97.31/13.16 (demorgan1) =>
% 97.31/13.16 ((
% 97.31/13.16 (demorgan2a) =>
% 97.31/13.16 ((
% 97.31/13.16 (demorgan2b2) =>
% 97.31/13.16 ((
% 97.31/13.16 (demorgan2b) =>
% 97.31/13.16 ((
% 97.31/13.16 (demorgan2) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz13rule0) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz13rule1) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz13rule2) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz13rule3) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz13rule4) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz1_1) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz1_2) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz1_3) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz1_4) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz1_5) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1all2) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1SetBreln1) =>
% 97.31/13.16 ((
% 97.31/13.16 (choice2fnsingleton) =>
% 97.31/13.16 ((
% 97.31/13.16 (setOfPairsIsBReln1) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1all1) =>
% 97.31/13.16 ((
% 97.31/13.16 (subbreln1) =>
% 97.31/13.16 ((
% 97.31/13.16 (eqbreln1) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1invprop) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1invI) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1invE) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1compprop) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1compI) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1compE) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1compEex) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1unionprop) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1unionIL) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1unionIR) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1unionI) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1unionE) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1unionEcases) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1unionCommutes) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz2Ex) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz2W) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz2A) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz2B) =>
% 97.31/13.16 ((
% 97.31/13.16 (image1Ex) =>
% 97.31/13.16 ((
% 97.31/13.16 (image1Ex1) =>
% 97.31/13.16 ((
% 97.31/13.16 (image1Equiv) =>
% 97.31/13.16 ((
% 97.31/13.16 (image1E) =>
% 97.31/13.16 ((
% 97.31/13.16 (image1I) =>
% 97.31/13.16 ((
% 97.31/13.16 (injFuncInInjFuncSet) =>
% 97.31/13.16 ((
% 97.31/13.16 (injFuncSetFuncIn) =>
% 97.31/13.16 ((
% 97.31/13.16 (injFuncSetFuncInj) =>
% 97.31/13.16 ((
% 97.31/13.16 (surjFuncSetFuncIn) =>
% 97.31/13.16 ((
% 97.31/13.16 (surjFuncSetFuncSurj) =>
% 97.31/13.16 ((
% 97.31/13.16 (leftInvIsSurj) =>
% 97.31/13.16 ((
% 97.31/13.16 (surjCantorThm) =>
% 97.31/13.16 ((
% 97.31/13.16 (foundation2) =>
% 97.31/13.16 ((
% 97.31/13.16 (notinself) =>
% 97.31/13.16 ((
% 97.31/13.16 (notinself2) =>
% 97.31/13.16 ((
% 97.31/13.16 (omegaSp) =>
% 97.31/13.16 ((
% 97.31/13.16 (omegaSclos) =>
% 97.31/13.16 ((
% 97.31/13.16 (peano0notS) =>
% 97.31/13.16 ((
% 97.31/13.16 (!!) @ (
% 97.31/13.16 (('#S') @ (
% 97.31/13.16 (
% 97.31/13.16 ('#B') @ (
% 97.31/13.16 =>) @
% 97.31/13.16 (
% 97.31/13.16 (
% 97.31/13.16 ('#C') @ in @
% 97.31/13.16 omega)))) @
% 97.31/13.16 (
% 97.31/13.16 (
% 97.31/13.16 ('#B') @ (
% 97.31/13.16 !!) @
% 97.31/13.16 (
% 97.31/13.16 (
% 97.31/13.16 ('#B') @ (
% 97.31/13.16 (
% 97.31/13.16 ('#S') @ (
% 97.31/13.16 (
% 97.31/13.16 ('#B') @ (
% 97.31/13.16 =>) @
% 97.31/13.16 (
% 97.31/13.16 (
% 97.31/13.16 ('#C') @ in @
% 97.31/13.16 omega)))))) @
% 97.31/13.16 (
% 97.31/13.16 (
% 97.31/13.16 ('#S') @ (
% 97.31/13.16 (
% 97.31/13.16 ('#B') @ (
% 97.31/13.16 '#S') @
% 97.31/13.16 (
% 97.31/13.16 (
% 97.31/13.16 ('#B') @ (
% 97.31/13.16 (
% 97.31/13.16 ('#B') @ (
% 97.31/13.16 =>))) @
% 97.31/13.16 (
% 97.31/13.16 (
% 97.31/13.16 ('#C') @ (
% 97.31/13.16 (
% 97.31/13.16 ('#B') @ (
% 97.31/13.16 '#B') @
% 97.31/13.16 (
% 97.31/13.16 (
% 97.31/13.16 ('#B') @ (
% 97.31/13.16 =) @
% 97.31/13.16 omegaS)))) @
% 97.31/13.16 omegaS)))))) @
% 97.31/13.16 (
% 97.31/13.16 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.31/13.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl222])).
% 97.31/13.16 thf(zip_derived_cl251, plain,
% 97.31/13.16 (~ (((setbeta) =>
% 97.31/13.16 (((nonemptyE1) =>
% 97.31/13.16 (((nonemptyI) =>
% 97.31/13.16 (((nonemptyI1) =>
% 97.31/13.16 (((setadjoinIL) =>
% 97.31/13.16 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 97.31/13.16 (((setadjoinIR) =>
% 97.31/13.16 (((setadjoinE) =>
% 97.31/13.16 (((setadjoinOr) =>
% 97.31/13.16 (((setoftrueEq) =>
% 97.31/13.16 (((powersetI) =>
% 97.31/13.16 (((emptyinPowerset) =>
% 97.31/13.16 (((emptyInPowerset) =>
% 97.31/13.16 (((powersetE) =>
% 97.31/13.16 (((setunionI) =>
% 97.31/13.16 (((setunionE) =>
% 97.31/13.16 (((subPowSU) =>
% 97.31/13.16 (((exuE2) =>
% 97.31/13.16 (((nonemptyImpWitness) =>
% 97.31/13.16 (((uniqinunit) =>
% 97.31/13.16 (((notinsingleton) =>
% 97.31/13.16 (((eqinunit) =>
% 97.31/13.16 (((singletonsswitch) =>
% 97.31/13.16 (((upairsetE) =>
% 97.31/13.16 (((upairsetIL) =>
% 97.31/13.16 (((upairsetIR) =>
% 97.31/13.16 (((emptyE1) =>
% 97.31/13.16 (((vacuousDall) =>
% 97.31/13.16 (((quantDeMorgan1) =>
% 97.31/13.16 (((quantDeMorgan2) =>
% 97.31/13.16 ((
% 97.31/13.16 (quantDeMorgan3) =>
% 97.31/13.16 ((
% 97.31/13.16 (quantDeMorgan4) =>
% 97.31/13.16 ((
% 97.31/13.16 (prop2setI) =>
% 97.31/13.16 ((
% 97.31/13.16 (prop2set2propI) =>
% 97.31/13.16 ((
% 97.31/13.16 (notdexE) =>
% 97.31/13.16 ((
% 97.31/13.16 (notdallE) =>
% 97.31/13.16 ((
% 97.31/13.16 (exuI1) =>
% 97.31/13.16 ((
% 97.31/13.16 (exuI3) =>
% 97.31/13.16 ((
% 97.31/13.16 (exuI2) =>
% 97.31/13.16 ((
% 97.31/13.16 (inCongP) =>
% 97.31/13.16 ((
% 97.31/13.16 (in__Cong) =>
% 97.31/13.16 ((
% 97.31/13.16 (exuE3u) =>
% 97.31/13.16 ((
% 97.31/13.16 (exu__Cong) =>
% 97.31/13.16 ((
% 97.31/13.16 (setadjoin__Cong) =>
% 97.31/13.16 ((
% 97.31/13.16 (powerset__Cong) =>
% 97.31/13.16 ((
% 97.31/13.16 (setunion__Cong) =>
% 97.31/13.16 ((
% 97.31/13.16 (exuEu) =>
% 97.31/13.16 ((
% 97.31/13.16 (descr__Cong) =>
% 97.31/13.16 ((
% 97.31/13.16 (dsetconstr__Cong) =>
% 97.31/13.16 ((
% 97.31/13.16 (subsetI1) =>
% 97.31/13.16 ((
% 97.31/13.16 (eqimpsubset2) =>
% 97.31/13.16 ((
% 97.31/13.16 (eqimpsubset1) =>
% 97.31/13.16 ((
% 97.31/13.16 (subsetI2) =>
% 97.31/13.16 ((
% 97.31/13.16 (emptysetsubset) =>
% 97.31/13.16 ((
% 97.31/13.16 (subsetE) =>
% 97.31/13.16 ((
% 97.31/13.16 (subsetE2) =>
% 97.31/13.16 ((
% 97.31/13.16 (notsubsetI) =>
% 97.31/13.16 ((
% 97.31/13.16 (notequalI1) =>
% 97.31/13.16 ((
% 97.31/13.16 (notequalI2) =>
% 97.31/13.16 ((
% 97.31/13.16 (subsetRefl) =>
% 97.31/13.16 ((
% 97.31/13.16 (subsetTrans) =>
% 97.31/13.16 ((
% 97.31/13.16 (setadjoinSub) =>
% 97.31/13.16 ((
% 97.31/13.16 (setadjoinSub2) =>
% 97.31/13.16 ((
% 97.31/13.16 (subset2powerset) =>
% 97.31/13.16 ((
% 97.31/13.16 (setextsub) =>
% 97.31/13.16 ((
% 97.31/13.16 (subsetemptysetimpeq) =>
% 97.31/13.16 ((
% 97.31/13.16 (powersetI1) =>
% 97.31/13.16 ((
% 97.31/13.16 (powersetE1) =>
% 97.31/13.16 ((
% 97.31/13.16 (inPowerset) =>
% 97.31/13.16 ((
% 97.31/13.16 (powersetsubset) =>
% 97.31/13.16 ((
% 97.31/13.16 (sepInPowerset) =>
% 97.31/13.16 ((
% 97.31/13.16 (sepSubset) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionIL) =>
% 97.31/13.16 ((
% 97.31/13.16 (upairset2IR) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionIR) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionEcases) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionE) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionLsub) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionRsub) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectI) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectSubset5) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectEL) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectLsub) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectSubset2) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectSubset3) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectER) =>
% 97.31/13.16 ((
% 97.31/13.16 (disjointsetsI1) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectRsub) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectSubset4) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectSubset1) =>
% 97.31/13.16 ((
% 97.31/13.16 (bs114d) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusI) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusEL) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusER) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusSubset2) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusERneg) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusELneg) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusILneg) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusIRneg) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusLsub) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusSubset1) =>
% 97.31/13.16 ((
% 97.31/13.16 (symdiffE) =>
% 97.31/13.16 ((
% 97.31/13.16 (symdiffI1) =>
% 97.31/13.16 ((
% 97.31/13.16 (symdiffI2) =>
% 97.31/13.16 ((
% 97.31/13.16 (symdiffIneg1) =>
% 97.31/13.16 ((
% 97.31/13.16 (symdiffIneg2) =>
% 97.31/13.16 ((
% 97.31/13.16 (secondinupair) =>
% 97.31/13.16 ((
% 97.31/13.16 (setukpairIL) =>
% 97.31/13.16 ((
% 97.31/13.16 (setukpairIR) =>
% 97.31/13.16 ((
% 97.31/13.16 (kpairiskpair) =>
% 97.31/13.16 ((
% 97.31/13.16 (kpairp) =>
% 97.31/13.16 ((
% 97.31/13.16 (singletonsubset) =>
% 97.31/13.16 ((
% 97.31/13.16 (singletoninpowerset) =>
% 97.31/13.16 ((
% 97.31/13.16 (singletoninpowunion) =>
% 97.31/13.16 ((
% 97.31/13.16 (upairset2E) =>
% 97.31/13.16 ((
% 97.31/13.16 (upairsubunion) =>
% 97.31/13.16 ((
% 97.31/13.16 (upairinpowunion) =>
% 97.31/13.16 ((
% 97.31/13.16 (ubforcartprodlem1) =>
% 97.31/13.16 ((
% 97.31/13.16 (ubforcartprodlem2) =>
% 97.31/13.16 ((
% 97.31/13.16 (ubforcartprodlem3) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodpairin) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodmempair1) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodmempair) =>
% 97.31/13.16 ((
% 97.31/13.16 (setunionE2) =>
% 97.31/13.16 ((
% 97.31/13.16 (setunionsingleton1) =>
% 97.31/13.16 ((
% 97.31/13.16 (setunionsingleton2) =>
% 97.31/13.16 ((
% 97.31/13.16 (setunionsingleton) =>
% 97.31/13.16 ((
% 97.31/13.16 (singletonprop) =>
% 97.31/13.16 ((
% 97.31/13.16 (ex1E1) =>
% 97.31/13.16 ((
% 97.31/13.16 (ex1I) =>
% 97.31/13.16 ((
% 97.31/13.16 (ex1I2) =>
% 97.31/13.16 ((
% 97.31/13.16 (singletonsuniq) =>
% 97.31/13.16 ((
% 97.31/13.16 (setukpairinjL1) =>
% 97.31/13.16 ((
% 97.31/13.16 (kfstsingleton) =>
% 97.31/13.16 ((
% 97.31/13.16 (theprop) =>
% 97.31/13.16 ((
% 97.31/13.16 (kfstpairEq) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodfstin) =>
% 97.31/13.16 ((
% 97.31/13.16 (setukpairinjL2) =>
% 97.31/13.16 ((
% 97.31/13.16 (setukpairinjL) =>
% 97.31/13.16 ((
% 97.31/13.16 (setukpairinjR11) =>
% 97.31/13.16 ((
% 97.31/13.16 (setukpairinjR12) =>
% 97.31/13.16 ((
% 97.31/13.16 (setukpairinjR1) =>
% 97.31/13.16 ((
% 97.31/13.16 (upairequniteq) =>
% 97.31/13.16 ((
% 97.31/13.16 (setukpairinjR2) =>
% 97.31/13.16 ((
% 97.31/13.16 (setukpairinjR) =>
% 97.31/13.16 ((
% 97.31/13.16 (ksndsingleton) =>
% 97.31/13.16 ((
% 97.31/13.16 (ksndpairEq) =>
% 97.31/13.16 ((
% 97.31/13.16 (kpairsurjEq) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodsndin) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodpairmemEL) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodpairmemER) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodmempaircEq) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodfstpairEq) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodsndpairEq) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodpairsurjEq) =>
% 97.31/13.16 ((
% 97.31/13.16 (dpsetconstrI) =>
% 97.31/13.16 ((
% 97.31/13.16 (dpsetconstrSub) =>
% 97.31/13.16 ((
% 97.31/13.16 (setOfPairsIsBReln) =>
% 97.31/13.16 ((
% 97.31/13.16 (dpsetconstrERa) =>
% 97.31/13.16 ((
% 97.31/13.16 (dpsetconstrEL1) =>
% 97.31/13.16 ((
% 97.31/13.16 (dpsetconstrEL2) =>
% 97.31/13.16 ((
% 97.31/13.16 (dpsetconstrER) =>
% 97.31/13.16 ((
% 97.31/13.16 (funcImageSingleton) =>
% 97.31/13.16 ((
% 97.31/13.16 (apProp) =>
% 97.31/13.16 ((
% 97.31/13.16 (app) =>
% 97.31/13.16 ((
% 97.31/13.16 (infuncsetfunc) =>
% 97.31/13.16 ((
% 97.31/13.16 (ap2p) =>
% 97.31/13.16 ((
% 97.31/13.16 (funcinfuncset) =>
% 97.31/13.16 ((
% 97.31/13.16 (lamProp) =>
% 97.31/13.16 ((
% 97.31/13.16 (lamp) =>
% 97.31/13.16 ((
% 97.31/13.16 (lam2p) =>
% 97.31/13.16 ((
% 97.31/13.16 (brelnall1) =>
% 97.31/13.16 ((
% 97.31/13.16 (brelnall2) =>
% 97.31/13.16 ((
% 97.31/13.16 (ex1E2) =>
% 97.31/13.16 ((
% 97.31/13.16 (funcGraphProp1) =>
% 97.31/13.16 ((
% 97.31/13.16 (funcGraphProp3) =>
% 97.31/13.16 ((
% 97.31/13.16 (funcGraphProp2) =>
% 97.31/13.16 ((
% 97.31/13.16 (funcextLem) =>
% 97.31/13.16 ((
% 97.31/13.16 (funcGraphProp4) =>
% 97.31/13.16 ((
% 97.31/13.16 (subbreln) =>
% 97.31/13.16 ((
% 97.31/13.16 (eqbreln) =>
% 97.31/13.16 ((
% 97.31/13.16 (funcext) =>
% 97.31/13.16 ((
% 97.31/13.16 (funcext2) =>
% 97.31/13.16 ((
% 97.31/13.16 (ap2apEq1) =>
% 97.31/13.16 ((
% 97.31/13.16 (ap2apEq2) =>
% 97.31/13.16 ((
% 97.31/13.16 (beta1) =>
% 97.31/13.16 ((
% 97.31/13.16 (eta1) =>
% 97.31/13.16 ((
% 97.31/13.16 (lam2lamEq) =>
% 97.31/13.16 ((
% 97.31/13.16 (beta2) =>
% 97.31/13.16 ((
% 97.31/13.16 (eta2) =>
% 97.31/13.16 ((
% 97.31/13.16 (iffalseProp1) =>
% 97.31/13.16 ((
% 97.31/13.16 (iffalseProp2) =>
% 97.31/13.16 ((
% 97.31/13.16 (iftrueProp1) =>
% 97.31/13.16 ((
% 97.31/13.16 (iftrueProp2) =>
% 97.31/13.16 ((
% 97.31/13.16 (ifSingleton) =>
% 97.31/13.16 ((
% 97.31/13.16 (ifp) =>
% 97.31/13.16 ((
% 97.31/13.16 (theeq) =>
% 97.31/13.16 ((
% 97.31/13.16 (iftrue) =>
% 97.31/13.16 ((
% 97.31/13.16 (iffalse) =>
% 97.31/13.16 ((
% 97.31/13.16 (iftrueorfalse) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectT_lem) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionT_lem) =>
% 97.31/13.16 ((
% 97.31/13.16 (powersetT_lem) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusT_lem) =>
% 97.31/13.16 ((
% 97.31/13.16 (complementT_lem) =>
% 97.31/13.16 ((
% 97.31/13.16 (setextT) =>
% 97.31/13.16 ((
% 97.31/13.16 (subsetTI) =>
% 97.31/13.16 ((
% 97.31/13.16 (powersetTI1) =>
% 97.31/13.16 ((
% 97.31/13.16 (powersetTE1) =>
% 97.31/13.16 ((
% 97.31/13.16 (complementTI1) =>
% 97.31/13.16 ((
% 97.31/13.16 (complementTE1) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectTELcontra) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectTERcontra) =>
% 97.31/13.16 ((
% 97.31/13.16 (contrasubsetT) =>
% 97.31/13.16 ((
% 97.31/13.16 (contrasubsetT1) =>
% 97.31/13.16 ((
% 97.31/13.16 (contrasubsetT2) =>
% 97.31/13.16 ((
% 97.31/13.16 (contrasubsetT3) =>
% 97.31/13.16 ((
% 97.31/13.16 (doubleComplementI1) =>
% 97.31/13.16 ((
% 97.31/13.16 (doubleComplementE1) =>
% 97.31/13.16 ((
% 97.31/13.16 (doubleComplementSub1) =>
% 97.31/13.16 ((
% 97.31/13.16 (doubleComplementSub2) =>
% 97.31/13.16 ((
% 97.31/13.16 (doubleComplementEq) =>
% 97.31/13.16 ((
% 97.31/13.16 (complementTnotintersectT) =>
% 97.31/13.16 ((
% 97.31/13.16 (complementImpComplementIntersect) =>
% 97.31/13.16 ((
% 97.31/13.16 (complementSubsetComplementIntersect) =>
% 97.31/13.16 ((
% 97.31/13.16 (complementInPowersetComplementIntersect) =>
% 97.31/13.16 ((
% 97.31/13.16 (contraSubsetComplement) =>
% 97.31/13.16 ((
% 97.31/13.16 (complementTcontraSubset) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionTILcontra) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionTIRcontra) =>
% 97.31/13.16 ((
% 97.31/13.16 (inIntersectImpInUnion) =>
% 97.31/13.16 ((
% 97.31/13.16 (inIntersectImpInUnion2) =>
% 97.31/13.16 ((
% 97.31/13.16 (inIntersectImpInIntersectUnions) =>
% 97.31/13.16 ((
% 97.31/13.16 (intersectInPowersetIntersectUnions) =>
% 97.31/13.16 ((
% 97.31/13.16 (inComplementUnionImpNotIn1) =>
% 97.31/13.16 ((
% 97.31/13.16 (inComplementUnionImpInComplement1) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionTE) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionTEcontra) =>
% 97.31/13.16 ((
% 97.31/13.16 (demorgan2a1) =>
% 97.31/13.16 ((
% 97.31/13.16 (complementUnionInPowersetComplement) =>
% 97.31/13.16 ((
% 97.31/13.16 (demorgan2a2) =>
% 97.31/13.16 ((
% 97.31/13.16 (demorgan1a) =>
% 97.31/13.16 ((
% 97.31/13.16 (demorgan1b) =>
% 97.31/13.16 ((
% 97.31/13.16 (demorgan1) =>
% 97.31/13.16 ((
% 97.31/13.16 (demorgan2a) =>
% 97.31/13.16 ((
% 97.31/13.16 (demorgan2b2) =>
% 97.31/13.16 ((
% 97.31/13.16 (demorgan2b) =>
% 97.31/13.16 ((
% 97.31/13.16 (demorgan2) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz13rule0) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz13rule1) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz13rule2) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz13rule3) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz13rule4) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz1_1) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz1_2) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz1_3) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz1_4) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz1_5) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1all2) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1SetBreln1) =>
% 97.31/13.16 ((
% 97.31/13.16 (choice2fnsingleton) =>
% 97.31/13.16 ((
% 97.31/13.16 (setOfPairsIsBReln1) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1all1) =>
% 97.31/13.16 ((
% 97.31/13.16 (subbreln1) =>
% 97.31/13.16 ((
% 97.31/13.16 (eqbreln1) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1invprop) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1invI) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1invE) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1compprop) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1compI) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1compE) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1compEex) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1unionprop) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1unionIL) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1unionIR) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1unionI) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1unionE) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1unionEcases) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1unionCommutes) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz2Ex) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz2W) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz2A) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz2B) =>
% 97.31/13.16 ((
% 97.31/13.16 (image1Ex) =>
% 97.31/13.16 ((
% 97.31/13.16 (image1Ex1) =>
% 97.31/13.16 ((
% 97.31/13.16 (image1Equiv) =>
% 97.31/13.16 ((
% 97.31/13.16 (image1E) =>
% 97.31/13.16 ((
% 97.31/13.16 (image1I) =>
% 97.31/13.16 ((
% 97.31/13.16 (injFuncInInjFuncSet) =>
% 97.31/13.16 ((
% 97.31/13.16 (injFuncSetFuncIn) =>
% 97.31/13.16 ((
% 97.31/13.16 (injFuncSetFuncInj) =>
% 97.31/13.16 ((
% 97.31/13.16 (surjFuncSetFuncIn) =>
% 97.31/13.16 ((
% 97.31/13.16 (surjFuncSetFuncSurj) =>
% 97.31/13.16 ((
% 97.31/13.16 (leftInvIsSurj) =>
% 97.31/13.16 ((
% 97.31/13.16 (surjCantorThm) =>
% 97.31/13.16 ((
% 97.31/13.16 (foundation2) =>
% 97.31/13.16 ((
% 97.31/13.16 (notinself) =>
% 97.31/13.16 ((
% 97.31/13.16 (notinself2) =>
% 97.31/13.16 ((
% 97.31/13.16 (omegaSp) =>
% 97.31/13.16 ((
% 97.31/13.16 (omegaSclos) =>
% 97.31/13.16 ((
% 97.31/13.16 (peano0notS) =>
% 97.31/13.16 ((
% 97.31/13.16 (!!) @ (
% 97.31/13.16 (('#S') @ (
% 97.31/13.16 (
% 97.31/13.16 ('#B') @ (
% 97.31/13.16 =>) @
% 97.31/13.16 (
% 97.31/13.16 (
% 97.31/13.16 ('#C') @ in @
% 97.31/13.16 omega)))) @
% 97.31/13.16 (
% 97.31/13.16 (
% 97.31/13.16 ('#B') @ (
% 97.31/13.16 !!) @
% 97.31/13.16 (
% 97.31/13.16 (
% 97.31/13.16 ('#B') @ (
% 97.31/13.16 (
% 97.31/13.16 ('#S') @ (
% 97.31/13.16 (
% 97.31/13.16 ('#B') @ (
% 97.31/13.16 =>) @
% 97.31/13.16 (
% 97.31/13.16 (
% 97.31/13.16 ('#C') @ in @
% 97.31/13.16 omega)))))) @
% 97.31/13.16 (
% 97.31/13.16 (
% 97.31/13.16 ('#S') @ (
% 97.31/13.16 (
% 97.31/13.16 ('#B') @ (
% 97.31/13.16 '#S') @
% 97.31/13.16 (
% 97.31/13.16 (
% 97.31/13.16 ('#B') @ (
% 97.31/13.16 (
% 97.31/13.16 ('#B') @ (
% 97.31/13.16 =>))) @
% 97.31/13.16 (
% 97.31/13.16 (
% 97.31/13.16 ('#C') @ (
% 97.31/13.16 (
% 97.31/13.16 ('#B') @ (
% 97.31/13.16 '#B') @
% 97.31/13.16 (
% 97.31/13.16 (
% 97.31/13.16 ('#B') @ (
% 97.31/13.16 =) @
% 97.31/13.16 omegaS)))) @
% 97.31/13.16 omegaS)))))) @
% 97.31/13.16 (
% 97.31/13.16 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.31/13.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl236])).
% 97.31/13.16 thf(zip_derived_cl264, plain,
% 97.31/13.16 (~ (((nonemptyE1) =>
% 97.31/13.16 (((nonemptyI) =>
% 97.31/13.16 (((nonemptyI1) =>
% 97.31/13.16 (((setadjoinIL) =>
% 97.31/13.16 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 97.31/13.16 (((setadjoinIR) =>
% 97.31/13.16 (((setadjoinE) =>
% 97.31/13.16 (((setadjoinOr) =>
% 97.31/13.16 (((setoftrueEq) =>
% 97.31/13.16 (((powersetI) =>
% 97.31/13.16 (((emptyinPowerset) =>
% 97.31/13.16 (((emptyInPowerset) =>
% 97.31/13.16 (((powersetE) =>
% 97.31/13.16 (((setunionI) =>
% 97.31/13.16 (((setunionE) =>
% 97.31/13.16 (((subPowSU) =>
% 97.31/13.16 (((exuE2) =>
% 97.31/13.16 (((nonemptyImpWitness) =>
% 97.31/13.16 (((uniqinunit) =>
% 97.31/13.16 (((notinsingleton) =>
% 97.31/13.16 (((eqinunit) =>
% 97.31/13.16 (((singletonsswitch) =>
% 97.31/13.16 (((upairsetE) =>
% 97.31/13.16 (((upairsetIL) =>
% 97.31/13.16 (((upairsetIR) =>
% 97.31/13.16 (((emptyE1) =>
% 97.31/13.16 (((vacuousDall) =>
% 97.31/13.16 (((quantDeMorgan1) =>
% 97.31/13.16 (((quantDeMorgan2) =>
% 97.31/13.16 (((quantDeMorgan3) =>
% 97.31/13.16 ((
% 97.31/13.16 (quantDeMorgan4) =>
% 97.31/13.16 ((
% 97.31/13.16 (prop2setI) =>
% 97.31/13.16 ((
% 97.31/13.16 (prop2set2propI) =>
% 97.31/13.16 ((
% 97.31/13.16 (notdexE) =>
% 97.31/13.16 ((
% 97.31/13.16 (notdallE) =>
% 97.31/13.16 ((
% 97.31/13.16 (exuI1) =>
% 97.31/13.16 ((
% 97.31/13.16 (exuI3) =>
% 97.31/13.16 ((
% 97.31/13.16 (exuI2) =>
% 97.31/13.16 ((
% 97.31/13.16 (inCongP) =>
% 97.31/13.16 ((
% 97.31/13.16 (in__Cong) =>
% 97.31/13.16 ((
% 97.31/13.16 (exuE3u) =>
% 97.31/13.16 ((
% 97.31/13.16 (exu__Cong) =>
% 97.31/13.16 ((
% 97.31/13.16 (setadjoin__Cong) =>
% 97.31/13.16 ((
% 97.31/13.16 (powerset__Cong) =>
% 97.31/13.16 ((
% 97.31/13.16 (setunion__Cong) =>
% 97.31/13.16 ((
% 97.31/13.16 (exuEu) =>
% 97.31/13.16 ((
% 97.31/13.16 (descr__Cong) =>
% 97.31/13.16 ((
% 97.31/13.16 (dsetconstr__Cong) =>
% 97.31/13.16 ((
% 97.31/13.16 (subsetI1) =>
% 97.31/13.16 ((
% 97.31/13.16 (eqimpsubset2) =>
% 97.31/13.16 ((
% 97.31/13.16 (eqimpsubset1) =>
% 97.31/13.16 ((
% 97.31/13.16 (subsetI2) =>
% 97.31/13.16 ((
% 97.31/13.16 (emptysetsubset) =>
% 97.31/13.16 ((
% 97.31/13.16 (subsetE) =>
% 97.31/13.16 ((
% 97.31/13.16 (subsetE2) =>
% 97.31/13.16 ((
% 97.31/13.16 (notsubsetI) =>
% 97.31/13.16 ((
% 97.31/13.16 (notequalI1) =>
% 97.31/13.16 ((
% 97.31/13.16 (notequalI2) =>
% 97.31/13.16 ((
% 97.31/13.16 (subsetRefl) =>
% 97.31/13.16 ((
% 97.31/13.16 (subsetTrans) =>
% 97.31/13.16 ((
% 97.31/13.16 (setadjoinSub) =>
% 97.31/13.16 ((
% 97.31/13.16 (setadjoinSub2) =>
% 97.31/13.16 ((
% 97.31/13.16 (subset2powerset) =>
% 97.31/13.16 ((
% 97.31/13.16 (setextsub) =>
% 97.31/13.16 ((
% 97.31/13.16 (subsetemptysetimpeq) =>
% 97.31/13.16 ((
% 97.31/13.16 (powersetI1) =>
% 97.31/13.16 ((
% 97.31/13.16 (powersetE1) =>
% 97.31/13.16 ((
% 97.31/13.16 (inPowerset) =>
% 97.31/13.16 ((
% 97.31/13.16 (powersetsubset) =>
% 97.31/13.16 ((
% 97.31/13.16 (sepInPowerset) =>
% 97.31/13.16 ((
% 97.31/13.16 (sepSubset) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionIL) =>
% 97.31/13.16 ((
% 97.31/13.16 (upairset2IR) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionIR) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionEcases) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionE) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionLsub) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionRsub) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectI) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectSubset5) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectEL) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectLsub) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectSubset2) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectSubset3) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectER) =>
% 97.31/13.16 ((
% 97.31/13.16 (disjointsetsI1) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectRsub) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectSubset4) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectSubset1) =>
% 97.31/13.16 ((
% 97.31/13.16 (bs114d) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusI) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusEL) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusER) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusSubset2) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusERneg) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusELneg) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusILneg) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusIRneg) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusLsub) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusSubset1) =>
% 97.31/13.16 ((
% 97.31/13.16 (symdiffE) =>
% 97.31/13.16 ((
% 97.31/13.16 (symdiffI1) =>
% 97.31/13.16 ((
% 97.31/13.16 (symdiffI2) =>
% 97.31/13.16 ((
% 97.31/13.16 (symdiffIneg1) =>
% 97.31/13.16 ((
% 97.31/13.16 (symdiffIneg2) =>
% 97.31/13.16 ((
% 97.31/13.16 (secondinupair) =>
% 97.31/13.16 ((
% 97.31/13.16 (setukpairIL) =>
% 97.31/13.16 ((
% 97.31/13.16 (setukpairIR) =>
% 97.31/13.16 ((
% 97.31/13.16 (kpairiskpair) =>
% 97.31/13.16 ((
% 97.31/13.16 (kpairp) =>
% 97.31/13.16 ((
% 97.31/13.16 (singletonsubset) =>
% 97.31/13.16 ((
% 97.31/13.16 (singletoninpowerset) =>
% 97.31/13.16 ((
% 97.31/13.16 (singletoninpowunion) =>
% 97.31/13.16 ((
% 97.31/13.16 (upairset2E) =>
% 97.31/13.16 ((
% 97.31/13.16 (upairsubunion) =>
% 97.31/13.16 ((
% 97.31/13.16 (upairinpowunion) =>
% 97.31/13.16 ((
% 97.31/13.16 (ubforcartprodlem1) =>
% 97.31/13.16 ((
% 97.31/13.16 (ubforcartprodlem2) =>
% 97.31/13.16 ((
% 97.31/13.16 (ubforcartprodlem3) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodpairin) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodmempair1) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodmempair) =>
% 97.31/13.16 ((
% 97.31/13.16 (setunionE2) =>
% 97.31/13.16 ((
% 97.31/13.16 (setunionsingleton1) =>
% 97.31/13.16 ((
% 97.31/13.16 (setunionsingleton2) =>
% 97.31/13.16 ((
% 97.31/13.16 (setunionsingleton) =>
% 97.31/13.16 ((
% 97.31/13.16 (singletonprop) =>
% 97.31/13.16 ((
% 97.31/13.16 (ex1E1) =>
% 97.31/13.16 ((
% 97.31/13.16 (ex1I) =>
% 97.31/13.16 ((
% 97.31/13.16 (ex1I2) =>
% 97.31/13.16 ((
% 97.31/13.16 (singletonsuniq) =>
% 97.31/13.16 ((
% 97.31/13.16 (setukpairinjL1) =>
% 97.31/13.16 ((
% 97.31/13.16 (kfstsingleton) =>
% 97.31/13.16 ((
% 97.31/13.16 (theprop) =>
% 97.31/13.16 ((
% 97.31/13.16 (kfstpairEq) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodfstin) =>
% 97.31/13.16 ((
% 97.31/13.16 (setukpairinjL2) =>
% 97.31/13.16 ((
% 97.31/13.16 (setukpairinjL) =>
% 97.31/13.16 ((
% 97.31/13.16 (setukpairinjR11) =>
% 97.31/13.16 ((
% 97.31/13.16 (setukpairinjR12) =>
% 97.31/13.16 ((
% 97.31/13.16 (setukpairinjR1) =>
% 97.31/13.16 ((
% 97.31/13.16 (upairequniteq) =>
% 97.31/13.16 ((
% 97.31/13.16 (setukpairinjR2) =>
% 97.31/13.16 ((
% 97.31/13.16 (setukpairinjR) =>
% 97.31/13.16 ((
% 97.31/13.16 (ksndsingleton) =>
% 97.31/13.16 ((
% 97.31/13.16 (ksndpairEq) =>
% 97.31/13.16 ((
% 97.31/13.16 (kpairsurjEq) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodsndin) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodpairmemEL) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodpairmemER) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodmempaircEq) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodfstpairEq) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodsndpairEq) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodpairsurjEq) =>
% 97.31/13.16 ((
% 97.31/13.16 (dpsetconstrI) =>
% 97.31/13.16 ((
% 97.31/13.16 (dpsetconstrSub) =>
% 97.31/13.16 ((
% 97.31/13.16 (setOfPairsIsBReln) =>
% 97.31/13.16 ((
% 97.31/13.16 (dpsetconstrERa) =>
% 97.31/13.16 ((
% 97.31/13.16 (dpsetconstrEL1) =>
% 97.31/13.16 ((
% 97.31/13.16 (dpsetconstrEL2) =>
% 97.31/13.16 ((
% 97.31/13.16 (dpsetconstrER) =>
% 97.31/13.16 ((
% 97.31/13.16 (funcImageSingleton) =>
% 97.31/13.16 ((
% 97.31/13.16 (apProp) =>
% 97.31/13.16 ((
% 97.31/13.16 (app) =>
% 97.31/13.16 ((
% 97.31/13.16 (infuncsetfunc) =>
% 97.31/13.16 ((
% 97.31/13.16 (ap2p) =>
% 97.31/13.16 ((
% 97.31/13.16 (funcinfuncset) =>
% 97.31/13.16 ((
% 97.31/13.16 (lamProp) =>
% 97.31/13.16 ((
% 97.31/13.16 (lamp) =>
% 97.31/13.16 ((
% 97.31/13.16 (lam2p) =>
% 97.31/13.16 ((
% 97.31/13.16 (brelnall1) =>
% 97.31/13.16 ((
% 97.31/13.16 (brelnall2) =>
% 97.31/13.16 ((
% 97.31/13.16 (ex1E2) =>
% 97.31/13.16 ((
% 97.31/13.16 (funcGraphProp1) =>
% 97.31/13.16 ((
% 97.31/13.16 (funcGraphProp3) =>
% 97.31/13.16 ((
% 97.31/13.16 (funcGraphProp2) =>
% 97.31/13.16 ((
% 97.31/13.16 (funcextLem) =>
% 97.31/13.16 ((
% 97.31/13.16 (funcGraphProp4) =>
% 97.31/13.16 ((
% 97.31/13.16 (subbreln) =>
% 97.31/13.16 ((
% 97.31/13.16 (eqbreln) =>
% 97.31/13.16 ((
% 97.31/13.16 (funcext) =>
% 97.31/13.16 ((
% 97.31/13.16 (funcext2) =>
% 97.31/13.16 ((
% 97.31/13.16 (ap2apEq1) =>
% 97.31/13.16 ((
% 97.31/13.16 (ap2apEq2) =>
% 97.31/13.16 ((
% 97.31/13.16 (beta1) =>
% 97.31/13.16 ((
% 97.31/13.16 (eta1) =>
% 97.31/13.16 ((
% 97.31/13.16 (lam2lamEq) =>
% 97.31/13.16 ((
% 97.31/13.16 (beta2) =>
% 97.31/13.16 ((
% 97.31/13.16 (eta2) =>
% 97.31/13.16 ((
% 97.31/13.16 (iffalseProp1) =>
% 97.31/13.16 ((
% 97.31/13.16 (iffalseProp2) =>
% 97.31/13.16 ((
% 97.31/13.16 (iftrueProp1) =>
% 97.31/13.16 ((
% 97.31/13.16 (iftrueProp2) =>
% 97.31/13.16 ((
% 97.31/13.16 (ifSingleton) =>
% 97.31/13.16 ((
% 97.31/13.16 (ifp) =>
% 97.31/13.16 ((
% 97.31/13.16 (theeq) =>
% 97.31/13.16 ((
% 97.31/13.16 (iftrue) =>
% 97.31/13.16 ((
% 97.31/13.16 (iffalse) =>
% 97.31/13.16 ((
% 97.31/13.16 (iftrueorfalse) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectT_lem) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionT_lem) =>
% 97.31/13.16 ((
% 97.31/13.16 (powersetT_lem) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusT_lem) =>
% 97.31/13.16 ((
% 97.31/13.16 (complementT_lem) =>
% 97.31/13.16 ((
% 97.31/13.16 (setextT) =>
% 97.31/13.16 ((
% 97.31/13.16 (subsetTI) =>
% 97.31/13.16 ((
% 97.31/13.16 (powersetTI1) =>
% 97.31/13.16 ((
% 97.31/13.16 (powersetTE1) =>
% 97.31/13.16 ((
% 97.31/13.16 (complementTI1) =>
% 97.31/13.16 ((
% 97.31/13.16 (complementTE1) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectTELcontra) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectTERcontra) =>
% 97.31/13.16 ((
% 97.31/13.16 (contrasubsetT) =>
% 97.31/13.16 ((
% 97.31/13.16 (contrasubsetT1) =>
% 97.31/13.16 ((
% 97.31/13.16 (contrasubsetT2) =>
% 97.31/13.16 ((
% 97.31/13.16 (contrasubsetT3) =>
% 97.31/13.16 ((
% 97.31/13.16 (doubleComplementI1) =>
% 97.31/13.16 ((
% 97.31/13.16 (doubleComplementE1) =>
% 97.31/13.16 ((
% 97.31/13.16 (doubleComplementSub1) =>
% 97.31/13.16 ((
% 97.31/13.16 (doubleComplementSub2) =>
% 97.31/13.16 ((
% 97.31/13.16 (doubleComplementEq) =>
% 97.31/13.16 ((
% 97.31/13.16 (complementTnotintersectT) =>
% 97.31/13.16 ((
% 97.31/13.16 (complementImpComplementIntersect) =>
% 97.31/13.16 ((
% 97.31/13.16 (complementSubsetComplementIntersect) =>
% 97.31/13.16 ((
% 97.31/13.16 (complementInPowersetComplementIntersect) =>
% 97.31/13.16 ((
% 97.31/13.16 (contraSubsetComplement) =>
% 97.31/13.16 ((
% 97.31/13.16 (complementTcontraSubset) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionTILcontra) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionTIRcontra) =>
% 97.31/13.16 ((
% 97.31/13.16 (inIntersectImpInUnion) =>
% 97.31/13.16 ((
% 97.31/13.16 (inIntersectImpInUnion2) =>
% 97.31/13.16 ((
% 97.31/13.16 (inIntersectImpInIntersectUnions) =>
% 97.31/13.16 ((
% 97.31/13.16 (intersectInPowersetIntersectUnions) =>
% 97.31/13.16 ((
% 97.31/13.16 (inComplementUnionImpNotIn1) =>
% 97.31/13.16 ((
% 97.31/13.16 (inComplementUnionImpInComplement1) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionTE) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionTEcontra) =>
% 97.31/13.16 ((
% 97.31/13.16 (demorgan2a1) =>
% 97.31/13.16 ((
% 97.31/13.16 (complementUnionInPowersetComplement) =>
% 97.31/13.16 ((
% 97.31/13.16 (demorgan2a2) =>
% 97.31/13.16 ((
% 97.31/13.16 (demorgan1a) =>
% 97.31/13.16 ((
% 97.31/13.16 (demorgan1b) =>
% 97.31/13.16 ((
% 97.31/13.16 (demorgan1) =>
% 97.31/13.16 ((
% 97.31/13.16 (demorgan2a) =>
% 97.31/13.16 ((
% 97.31/13.16 (demorgan2b2) =>
% 97.31/13.16 ((
% 97.31/13.16 (demorgan2b) =>
% 97.31/13.16 ((
% 97.31/13.16 (demorgan2) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz13rule0) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz13rule1) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz13rule2) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz13rule3) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz13rule4) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz1_1) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz1_2) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz1_3) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz1_4) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz1_5) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1all2) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1SetBreln1) =>
% 97.31/13.16 ((
% 97.31/13.16 (choice2fnsingleton) =>
% 97.31/13.16 ((
% 97.31/13.16 (setOfPairsIsBReln1) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1all1) =>
% 97.31/13.16 ((
% 97.31/13.16 (subbreln1) =>
% 97.31/13.16 ((
% 97.31/13.16 (eqbreln1) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1invprop) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1invI) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1invE) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1compprop) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1compI) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1compE) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1compEex) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1unionprop) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1unionIL) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1unionIR) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1unionI) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1unionE) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1unionEcases) =>
% 97.31/13.16 ((
% 97.31/13.16 (breln1unionCommutes) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz2Ex) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz2W) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz2A) =>
% 97.31/13.16 ((
% 97.31/13.16 (woz2B) =>
% 97.31/13.16 ((
% 97.31/13.16 (image1Ex) =>
% 97.31/13.16 ((
% 97.31/13.16 (image1Ex1) =>
% 97.31/13.16 ((
% 97.31/13.16 (image1Equiv) =>
% 97.31/13.16 ((
% 97.31/13.16 (image1E) =>
% 97.31/13.16 ((
% 97.31/13.16 (image1I) =>
% 97.31/13.16 ((
% 97.31/13.16 (injFuncInInjFuncSet) =>
% 97.31/13.16 ((
% 97.31/13.16 (injFuncSetFuncIn) =>
% 97.31/13.16 ((
% 97.31/13.16 (injFuncSetFuncInj) =>
% 97.31/13.16 ((
% 97.31/13.16 (surjFuncSetFuncIn) =>
% 97.31/13.16 ((
% 97.31/13.16 (surjFuncSetFuncSurj) =>
% 97.31/13.16 ((
% 97.31/13.16 (leftInvIsSurj) =>
% 97.31/13.16 ((
% 97.31/13.16 (surjCantorThm) =>
% 97.31/13.16 ((
% 97.31/13.16 (foundation2) =>
% 97.31/13.16 ((
% 97.31/13.16 (notinself) =>
% 97.31/13.16 ((
% 97.31/13.16 (notinself2) =>
% 97.31/13.16 ((
% 97.31/13.16 (omegaSp) =>
% 97.31/13.16 ((
% 97.31/13.16 (omegaSclos) =>
% 97.31/13.16 ((
% 97.31/13.16 (peano0notS) =>
% 97.31/13.16 ((
% 97.31/13.16 (!!) @ (
% 97.31/13.16 (('#S') @ (
% 97.31/13.16 (
% 97.31/13.16 ('#B') @ (
% 97.31/13.16 =>) @
% 97.31/13.16 (
% 97.31/13.16 (
% 97.31/13.16 ('#C') @ in @
% 97.31/13.16 omega)))) @
% 97.31/13.16 (
% 97.31/13.16 (
% 97.31/13.16 ('#B') @ (
% 97.31/13.16 !!) @
% 97.31/13.16 (
% 97.31/13.16 (
% 97.31/13.16 ('#B') @ (
% 97.31/13.16 (
% 97.31/13.16 ('#S') @ (
% 97.31/13.16 (
% 97.31/13.16 ('#B') @ (
% 97.31/13.16 =>) @
% 97.31/13.16 (
% 97.31/13.16 (
% 97.31/13.16 ('#C') @ in @
% 97.31/13.16 omega)))))) @
% 97.31/13.16 (
% 97.31/13.16 (
% 97.31/13.16 ('#S') @ (
% 97.31/13.16 (
% 97.31/13.16 ('#B') @ (
% 97.31/13.16 '#S') @
% 97.31/13.16 (
% 97.31/13.16 (
% 97.31/13.16 ('#B') @ (
% 97.31/13.16 (
% 97.31/13.16 ('#B') @ (
% 97.31/13.16 =>))) @
% 97.31/13.16 (
% 97.31/13.16 (
% 97.31/13.16 ('#C') @ (
% 97.31/13.16 (
% 97.31/13.16 ('#B') @ (
% 97.31/13.16 '#B') @
% 97.31/13.16 (
% 97.31/13.16 (
% 97.31/13.16 ('#B') @ (
% 97.31/13.16 =) @
% 97.31/13.16 omegaS)))) @
% 97.31/13.16 omegaS)))))) @
% 97.31/13.16 (
% 97.31/13.16 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.31/13.16 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl251])).
% 97.31/13.16 thf(zip_derived_cl280, plain,
% 97.31/13.16 (~ (((nonemptyI) =>
% 97.31/13.16 (((nonemptyI1) =>
% 97.31/13.16 (((setadjoinIL) =>
% 97.31/13.16 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 97.31/13.16 (((setadjoinIR) =>
% 97.31/13.16 (((setadjoinE) =>
% 97.31/13.16 (((setadjoinOr) =>
% 97.31/13.16 (((setoftrueEq) =>
% 97.31/13.16 (((powersetI) =>
% 97.31/13.16 (((emptyinPowerset) =>
% 97.31/13.16 (((emptyInPowerset) =>
% 97.31/13.16 (((powersetE) =>
% 97.31/13.16 (((setunionI) =>
% 97.31/13.16 (((setunionE) =>
% 97.31/13.16 (((subPowSU) =>
% 97.31/13.16 (((exuE2) =>
% 97.31/13.16 (((nonemptyImpWitness) =>
% 97.31/13.16 (((uniqinunit) =>
% 97.31/13.16 (((notinsingleton) =>
% 97.31/13.16 (((eqinunit) =>
% 97.31/13.16 (((singletonsswitch) =>
% 97.31/13.16 (((upairsetE) =>
% 97.31/13.16 (((upairsetIL) =>
% 97.31/13.16 (((upairsetIR) =>
% 97.31/13.16 (((emptyE1) =>
% 97.31/13.16 (((vacuousDall) =>
% 97.31/13.16 (((quantDeMorgan1) =>
% 97.31/13.16 (((quantDeMorgan2) =>
% 97.31/13.16 (((quantDeMorgan3) =>
% 97.31/13.16 (((quantDeMorgan4) =>
% 97.31/13.16 ((
% 97.31/13.16 (prop2setI) =>
% 97.31/13.16 ((
% 97.31/13.16 (prop2set2propI) =>
% 97.31/13.16 ((
% 97.31/13.16 (notdexE) =>
% 97.31/13.16 ((
% 97.31/13.16 (notdallE) =>
% 97.31/13.16 ((
% 97.31/13.16 (exuI1) =>
% 97.31/13.16 ((
% 97.31/13.16 (exuI3) =>
% 97.31/13.16 ((
% 97.31/13.16 (exuI2) =>
% 97.31/13.16 ((
% 97.31/13.16 (inCongP) =>
% 97.31/13.16 ((
% 97.31/13.16 (in__Cong) =>
% 97.31/13.16 ((
% 97.31/13.16 (exuE3u) =>
% 97.31/13.16 ((
% 97.31/13.16 (exu__Cong) =>
% 97.31/13.16 ((
% 97.31/13.16 (setadjoin__Cong) =>
% 97.31/13.16 ((
% 97.31/13.16 (powerset__Cong) =>
% 97.31/13.16 ((
% 97.31/13.16 (setunion__Cong) =>
% 97.31/13.16 ((
% 97.31/13.16 (exuEu) =>
% 97.31/13.16 ((
% 97.31/13.16 (descr__Cong) =>
% 97.31/13.16 ((
% 97.31/13.16 (dsetconstr__Cong) =>
% 97.31/13.16 ((
% 97.31/13.16 (subsetI1) =>
% 97.31/13.16 ((
% 97.31/13.16 (eqimpsubset2) =>
% 97.31/13.16 ((
% 97.31/13.16 (eqimpsubset1) =>
% 97.31/13.16 ((
% 97.31/13.16 (subsetI2) =>
% 97.31/13.16 ((
% 97.31/13.16 (emptysetsubset) =>
% 97.31/13.16 ((
% 97.31/13.16 (subsetE) =>
% 97.31/13.16 ((
% 97.31/13.16 (subsetE2) =>
% 97.31/13.16 ((
% 97.31/13.16 (notsubsetI) =>
% 97.31/13.16 ((
% 97.31/13.16 (notequalI1) =>
% 97.31/13.16 ((
% 97.31/13.16 (notequalI2) =>
% 97.31/13.16 ((
% 97.31/13.16 (subsetRefl) =>
% 97.31/13.16 ((
% 97.31/13.16 (subsetTrans) =>
% 97.31/13.16 ((
% 97.31/13.16 (setadjoinSub) =>
% 97.31/13.16 ((
% 97.31/13.16 (setadjoinSub2) =>
% 97.31/13.16 ((
% 97.31/13.16 (subset2powerset) =>
% 97.31/13.16 ((
% 97.31/13.16 (setextsub) =>
% 97.31/13.16 ((
% 97.31/13.16 (subsetemptysetimpeq) =>
% 97.31/13.16 ((
% 97.31/13.16 (powersetI1) =>
% 97.31/13.16 ((
% 97.31/13.16 (powersetE1) =>
% 97.31/13.16 ((
% 97.31/13.16 (inPowerset) =>
% 97.31/13.16 ((
% 97.31/13.16 (powersetsubset) =>
% 97.31/13.16 ((
% 97.31/13.16 (sepInPowerset) =>
% 97.31/13.16 ((
% 97.31/13.16 (sepSubset) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionIL) =>
% 97.31/13.16 ((
% 97.31/13.16 (upairset2IR) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionIR) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionEcases) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionE) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionLsub) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionRsub) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectI) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectSubset5) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectEL) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectLsub) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectSubset2) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectSubset3) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectER) =>
% 97.31/13.16 ((
% 97.31/13.16 (disjointsetsI1) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectRsub) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectSubset4) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectSubset1) =>
% 97.31/13.16 ((
% 97.31/13.16 (bs114d) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusI) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusEL) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusER) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusSubset2) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusERneg) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusELneg) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusILneg) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusIRneg) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusLsub) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusSubset1) =>
% 97.31/13.16 ((
% 97.31/13.16 (symdiffE) =>
% 97.31/13.16 ((
% 97.31/13.16 (symdiffI1) =>
% 97.31/13.16 ((
% 97.31/13.16 (symdiffI2) =>
% 97.31/13.16 ((
% 97.31/13.16 (symdiffIneg1) =>
% 97.31/13.16 ((
% 97.31/13.16 (symdiffIneg2) =>
% 97.31/13.16 ((
% 97.31/13.16 (secondinupair) =>
% 97.31/13.16 ((
% 97.31/13.16 (setukpairIL) =>
% 97.31/13.16 ((
% 97.31/13.16 (setukpairIR) =>
% 97.31/13.16 ((
% 97.31/13.16 (kpairiskpair) =>
% 97.31/13.16 ((
% 97.31/13.16 (kpairp) =>
% 97.31/13.16 ((
% 97.31/13.16 (singletonsubset) =>
% 97.31/13.16 ((
% 97.31/13.16 (singletoninpowerset) =>
% 97.31/13.16 ((
% 97.31/13.16 (singletoninpowunion) =>
% 97.31/13.16 ((
% 97.31/13.16 (upairset2E) =>
% 97.31/13.16 ((
% 97.31/13.16 (upairsubunion) =>
% 97.31/13.16 ((
% 97.31/13.16 (upairinpowunion) =>
% 97.31/13.16 ((
% 97.31/13.16 (ubforcartprodlem1) =>
% 97.31/13.16 ((
% 97.31/13.16 (ubforcartprodlem2) =>
% 97.31/13.16 ((
% 97.31/13.16 (ubforcartprodlem3) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodpairin) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodmempair1) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodmempair) =>
% 97.31/13.16 ((
% 97.31/13.16 (setunionE2) =>
% 97.31/13.16 ((
% 97.31/13.16 (setunionsingleton1) =>
% 97.31/13.16 ((
% 97.31/13.16 (setunionsingleton2) =>
% 97.31/13.16 ((
% 97.31/13.16 (setunionsingleton) =>
% 97.31/13.16 ((
% 97.31/13.16 (singletonprop) =>
% 97.31/13.16 ((
% 97.31/13.16 (ex1E1) =>
% 97.31/13.16 ((
% 97.31/13.16 (ex1I) =>
% 97.31/13.16 ((
% 97.31/13.16 (ex1I2) =>
% 97.31/13.16 ((
% 97.31/13.16 (singletonsuniq) =>
% 97.31/13.16 ((
% 97.31/13.16 (setukpairinjL1) =>
% 97.31/13.16 ((
% 97.31/13.16 (kfstsingleton) =>
% 97.31/13.16 ((
% 97.31/13.16 (theprop) =>
% 97.31/13.16 ((
% 97.31/13.16 (kfstpairEq) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodfstin) =>
% 97.31/13.16 ((
% 97.31/13.16 (setukpairinjL2) =>
% 97.31/13.16 ((
% 97.31/13.16 (setukpairinjL) =>
% 97.31/13.16 ((
% 97.31/13.16 (setukpairinjR11) =>
% 97.31/13.16 ((
% 97.31/13.16 (setukpairinjR12) =>
% 97.31/13.16 ((
% 97.31/13.16 (setukpairinjR1) =>
% 97.31/13.16 ((
% 97.31/13.16 (upairequniteq) =>
% 97.31/13.16 ((
% 97.31/13.16 (setukpairinjR2) =>
% 97.31/13.16 ((
% 97.31/13.16 (setukpairinjR) =>
% 97.31/13.16 ((
% 97.31/13.16 (ksndsingleton) =>
% 97.31/13.16 ((
% 97.31/13.16 (ksndpairEq) =>
% 97.31/13.16 ((
% 97.31/13.16 (kpairsurjEq) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodsndin) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodpairmemEL) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodpairmemER) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodmempaircEq) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodfstpairEq) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodsndpairEq) =>
% 97.31/13.16 ((
% 97.31/13.16 (cartprodpairsurjEq) =>
% 97.31/13.16 ((
% 97.31/13.16 (dpsetconstrI) =>
% 97.31/13.16 ((
% 97.31/13.16 (dpsetconstrSub) =>
% 97.31/13.16 ((
% 97.31/13.16 (setOfPairsIsBReln) =>
% 97.31/13.16 ((
% 97.31/13.16 (dpsetconstrERa) =>
% 97.31/13.16 ((
% 97.31/13.16 (dpsetconstrEL1) =>
% 97.31/13.16 ((
% 97.31/13.16 (dpsetconstrEL2) =>
% 97.31/13.16 ((
% 97.31/13.16 (dpsetconstrER) =>
% 97.31/13.16 ((
% 97.31/13.16 (funcImageSingleton) =>
% 97.31/13.16 ((
% 97.31/13.16 (apProp) =>
% 97.31/13.16 ((
% 97.31/13.16 (app) =>
% 97.31/13.16 ((
% 97.31/13.16 (infuncsetfunc) =>
% 97.31/13.16 ((
% 97.31/13.16 (ap2p) =>
% 97.31/13.16 ((
% 97.31/13.16 (funcinfuncset) =>
% 97.31/13.16 ((
% 97.31/13.16 (lamProp) =>
% 97.31/13.16 ((
% 97.31/13.16 (lamp) =>
% 97.31/13.16 ((
% 97.31/13.16 (lam2p) =>
% 97.31/13.16 ((
% 97.31/13.16 (brelnall1) =>
% 97.31/13.16 ((
% 97.31/13.16 (brelnall2) =>
% 97.31/13.16 ((
% 97.31/13.16 (ex1E2) =>
% 97.31/13.16 ((
% 97.31/13.16 (funcGraphProp1) =>
% 97.31/13.16 ((
% 97.31/13.16 (funcGraphProp3) =>
% 97.31/13.16 ((
% 97.31/13.16 (funcGraphProp2) =>
% 97.31/13.16 ((
% 97.31/13.16 (funcextLem) =>
% 97.31/13.16 ((
% 97.31/13.16 (funcGraphProp4) =>
% 97.31/13.16 ((
% 97.31/13.16 (subbreln) =>
% 97.31/13.16 ((
% 97.31/13.16 (eqbreln) =>
% 97.31/13.16 ((
% 97.31/13.16 (funcext) =>
% 97.31/13.16 ((
% 97.31/13.16 (funcext2) =>
% 97.31/13.16 ((
% 97.31/13.16 (ap2apEq1) =>
% 97.31/13.16 ((
% 97.31/13.16 (ap2apEq2) =>
% 97.31/13.16 ((
% 97.31/13.16 (beta1) =>
% 97.31/13.16 ((
% 97.31/13.16 (eta1) =>
% 97.31/13.16 ((
% 97.31/13.16 (lam2lamEq) =>
% 97.31/13.16 ((
% 97.31/13.16 (beta2) =>
% 97.31/13.16 ((
% 97.31/13.16 (eta2) =>
% 97.31/13.16 ((
% 97.31/13.16 (iffalseProp1) =>
% 97.31/13.16 ((
% 97.31/13.16 (iffalseProp2) =>
% 97.31/13.16 ((
% 97.31/13.16 (iftrueProp1) =>
% 97.31/13.16 ((
% 97.31/13.16 (iftrueProp2) =>
% 97.31/13.16 ((
% 97.31/13.16 (ifSingleton) =>
% 97.31/13.16 ((
% 97.31/13.16 (ifp) =>
% 97.31/13.16 ((
% 97.31/13.16 (theeq) =>
% 97.31/13.16 ((
% 97.31/13.16 (iftrue) =>
% 97.31/13.16 ((
% 97.31/13.16 (iffalse) =>
% 97.31/13.16 ((
% 97.31/13.16 (iftrueorfalse) =>
% 97.31/13.16 ((
% 97.31/13.16 (binintersectT_lem) =>
% 97.31/13.16 ((
% 97.31/13.16 (binunionT_lem) =>
% 97.31/13.16 ((
% 97.31/13.16 (powersetT_lem) =>
% 97.31/13.16 ((
% 97.31/13.16 (setminusT_lem) =>
% 97.31/13.16 ((
% 97.31/13.16 (complementT_lem) =>
% 97.31/13.16 ((
% 97.31/13.16 (setextT) =>
% 97.31/13.16 ((
% 97.31/13.16 (subsetTI) =>
% 97.31/13.16 ((
% 97.31/13.16 (powersetTI1) =>
% 97.31/13.16 ((
% 97.31/13.17 (powersetTE1) =>
% 97.31/13.17 ((
% 97.31/13.17 (complementTI1) =>
% 97.31/13.17 ((
% 97.31/13.17 (complementTE1) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectTELcontra) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectTERcontra) =>
% 97.31/13.17 ((
% 97.31/13.17 (contrasubsetT) =>
% 97.31/13.17 ((
% 97.31/13.17 (contrasubsetT1) =>
% 97.31/13.17 ((
% 97.31/13.17 (contrasubsetT2) =>
% 97.31/13.17 ((
% 97.31/13.17 (contrasubsetT3) =>
% 97.31/13.17 ((
% 97.31/13.17 (doubleComplementI1) =>
% 97.31/13.17 ((
% 97.31/13.17 (doubleComplementE1) =>
% 97.31/13.17 ((
% 97.31/13.17 (doubleComplementSub1) =>
% 97.31/13.17 ((
% 97.31/13.17 (doubleComplementSub2) =>
% 97.31/13.17 ((
% 97.31/13.17 (doubleComplementEq) =>
% 97.31/13.17 ((
% 97.31/13.17 (complementTnotintersectT) =>
% 97.31/13.17 ((
% 97.31/13.17 (complementImpComplementIntersect) =>
% 97.31/13.17 ((
% 97.31/13.17 (complementSubsetComplementIntersect) =>
% 97.31/13.17 ((
% 97.31/13.17 (complementInPowersetComplementIntersect) =>
% 97.31/13.17 ((
% 97.31/13.17 (contraSubsetComplement) =>
% 97.31/13.17 ((
% 97.31/13.17 (complementTcontraSubset) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionTILcontra) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionTIRcontra) =>
% 97.31/13.17 ((
% 97.31/13.17 (inIntersectImpInUnion) =>
% 97.31/13.17 ((
% 97.31/13.17 (inIntersectImpInUnion2) =>
% 97.31/13.17 ((
% 97.31/13.17 (inIntersectImpInIntersectUnions) =>
% 97.31/13.17 ((
% 97.31/13.17 (intersectInPowersetIntersectUnions) =>
% 97.31/13.17 ((
% 97.31/13.17 (inComplementUnionImpNotIn1) =>
% 97.31/13.17 ((
% 97.31/13.17 (inComplementUnionImpInComplement1) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionTE) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionTEcontra) =>
% 97.31/13.17 ((
% 97.31/13.17 (demorgan2a1) =>
% 97.31/13.17 ((
% 97.31/13.17 (complementUnionInPowersetComplement) =>
% 97.31/13.17 ((
% 97.31/13.17 (demorgan2a2) =>
% 97.31/13.17 ((
% 97.31/13.17 (demorgan1a) =>
% 97.31/13.17 ((
% 97.31/13.17 (demorgan1b) =>
% 97.31/13.17 ((
% 97.31/13.17 (demorgan1) =>
% 97.31/13.17 ((
% 97.31/13.17 (demorgan2a) =>
% 97.31/13.17 ((
% 97.31/13.17 (demorgan2b2) =>
% 97.31/13.17 ((
% 97.31/13.17 (demorgan2b) =>
% 97.31/13.17 ((
% 97.31/13.17 (demorgan2) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz13rule0) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz13rule1) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz13rule2) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz13rule3) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz13rule4) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz1_1) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz1_2) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz1_3) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz1_4) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz1_5) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1all2) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1SetBreln1) =>
% 97.31/13.17 ((
% 97.31/13.17 (choice2fnsingleton) =>
% 97.31/13.17 ((
% 97.31/13.17 (setOfPairsIsBReln1) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1all1) =>
% 97.31/13.17 ((
% 97.31/13.17 (subbreln1) =>
% 97.31/13.17 ((
% 97.31/13.17 (eqbreln1) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1invprop) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1invI) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1invE) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1compprop) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1compI) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1compE) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1compEex) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1unionprop) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1unionIL) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1unionIR) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1unionI) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1unionE) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1unionEcases) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1unionCommutes) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz2Ex) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz2W) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz2A) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz2B) =>
% 97.31/13.17 ((
% 97.31/13.17 (image1Ex) =>
% 97.31/13.17 ((
% 97.31/13.17 (image1Ex1) =>
% 97.31/13.17 ((
% 97.31/13.17 (image1Equiv) =>
% 97.31/13.17 ((
% 97.31/13.17 (image1E) =>
% 97.31/13.17 ((
% 97.31/13.17 (image1I) =>
% 97.31/13.17 ((
% 97.31/13.17 (injFuncInInjFuncSet) =>
% 97.31/13.17 ((
% 97.31/13.17 (injFuncSetFuncIn) =>
% 97.31/13.17 ((
% 97.31/13.17 (injFuncSetFuncInj) =>
% 97.31/13.17 ((
% 97.31/13.17 (surjFuncSetFuncIn) =>
% 97.31/13.17 ((
% 97.31/13.17 (surjFuncSetFuncSurj) =>
% 97.31/13.17 ((
% 97.31/13.17 (leftInvIsSurj) =>
% 97.31/13.17 ((
% 97.31/13.17 (surjCantorThm) =>
% 97.31/13.17 ((
% 97.31/13.17 (foundation2) =>
% 97.31/13.17 ((
% 97.31/13.17 (notinself) =>
% 97.31/13.17 ((
% 97.31/13.17 (notinself2) =>
% 97.31/13.17 ((
% 97.31/13.17 (omegaSp) =>
% 97.31/13.17 ((
% 97.31/13.17 (omegaSclos) =>
% 97.31/13.17 ((
% 97.31/13.17 (peano0notS) =>
% 97.31/13.17 ((
% 97.31/13.17 (!!) @ (
% 97.31/13.17 (('#S') @ (
% 97.31/13.17 (
% 97.31/13.17 ('#B') @ (
% 97.31/13.17 =>) @
% 97.31/13.17 (
% 97.31/13.17 (
% 97.31/13.17 ('#C') @ in @
% 97.31/13.17 omega)))) @
% 97.31/13.17 (
% 97.31/13.17 (
% 97.31/13.17 ('#B') @ (
% 97.31/13.17 !!) @
% 97.31/13.17 (
% 97.31/13.17 (
% 97.31/13.17 ('#B') @ (
% 97.31/13.17 (
% 97.31/13.17 ('#S') @ (
% 97.31/13.17 (
% 97.31/13.17 ('#B') @ (
% 97.31/13.17 =>) @
% 97.31/13.17 (
% 97.31/13.17 (
% 97.31/13.17 ('#C') @ in @
% 97.31/13.17 omega)))))) @
% 97.31/13.17 (
% 97.31/13.17 (
% 97.31/13.17 ('#S') @ (
% 97.31/13.17 (
% 97.31/13.17 ('#B') @ (
% 97.31/13.17 '#S') @
% 97.31/13.17 (
% 97.31/13.17 (
% 97.31/13.17 ('#B') @ (
% 97.31/13.17 (
% 97.31/13.17 ('#B') @ (
% 97.31/13.17 =>))) @
% 97.31/13.17 (
% 97.31/13.17 (
% 97.31/13.17 ('#C') @ (
% 97.31/13.17 (
% 97.31/13.17 ('#B') @ (
% 97.31/13.17 '#B') @
% 97.31/13.17 (
% 97.31/13.17 (
% 97.31/13.17 ('#B') @ (
% 97.31/13.17 =) @
% 97.31/13.17 omegaS)))) @
% 97.31/13.17 omegaS)))))) @
% 97.31/13.17 (
% 97.31/13.17 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.31/13.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl264])).
% 97.31/13.17 thf(zip_derived_cl293, plain,
% 97.31/13.17 (~ (((nonemptyI1) =>
% 97.31/13.17 (((setadjoinIL) =>
% 97.31/13.17 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 97.31/13.17 (((setadjoinIR) =>
% 97.31/13.17 (((setadjoinE) =>
% 97.31/13.17 (((setadjoinOr) =>
% 97.31/13.17 (((setoftrueEq) =>
% 97.31/13.17 (((powersetI) =>
% 97.31/13.17 (((emptyinPowerset) =>
% 97.31/13.17 (((emptyInPowerset) =>
% 97.31/13.17 (((powersetE) =>
% 97.31/13.17 (((setunionI) =>
% 97.31/13.17 (((setunionE) =>
% 97.31/13.17 (((subPowSU) =>
% 97.31/13.17 (((exuE2) =>
% 97.31/13.17 (((nonemptyImpWitness) =>
% 97.31/13.17 (((uniqinunit) =>
% 97.31/13.17 (((notinsingleton) =>
% 97.31/13.17 (((eqinunit) =>
% 97.31/13.17 (((singletonsswitch) =>
% 97.31/13.17 (((upairsetE) =>
% 97.31/13.17 (((upairsetIL) =>
% 97.31/13.17 (((upairsetIR) =>
% 97.31/13.17 (((emptyE1) =>
% 97.31/13.17 (((vacuousDall) =>
% 97.31/13.17 (((quantDeMorgan1) =>
% 97.31/13.17 (((quantDeMorgan2) =>
% 97.31/13.17 (((quantDeMorgan3) =>
% 97.31/13.17 (((quantDeMorgan4) =>
% 97.31/13.17 (((prop2setI) =>
% 97.31/13.17 ((
% 97.31/13.17 (prop2set2propI) =>
% 97.31/13.17 ((
% 97.31/13.17 (notdexE) =>
% 97.31/13.17 ((
% 97.31/13.17 (notdallE) =>
% 97.31/13.17 ((
% 97.31/13.17 (exuI1) =>
% 97.31/13.17 ((
% 97.31/13.17 (exuI3) =>
% 97.31/13.17 ((
% 97.31/13.17 (exuI2) =>
% 97.31/13.17 ((
% 97.31/13.17 (inCongP) =>
% 97.31/13.17 ((
% 97.31/13.17 (in__Cong) =>
% 97.31/13.17 ((
% 97.31/13.17 (exuE3u) =>
% 97.31/13.17 ((
% 97.31/13.17 (exu__Cong) =>
% 97.31/13.17 ((
% 97.31/13.17 (setadjoin__Cong) =>
% 97.31/13.17 ((
% 97.31/13.17 (powerset__Cong) =>
% 97.31/13.17 ((
% 97.31/13.17 (setunion__Cong) =>
% 97.31/13.17 ((
% 97.31/13.17 (exuEu) =>
% 97.31/13.17 ((
% 97.31/13.17 (descr__Cong) =>
% 97.31/13.17 ((
% 97.31/13.17 (dsetconstr__Cong) =>
% 97.31/13.17 ((
% 97.31/13.17 (subsetI1) =>
% 97.31/13.17 ((
% 97.31/13.17 (eqimpsubset2) =>
% 97.31/13.17 ((
% 97.31/13.17 (eqimpsubset1) =>
% 97.31/13.17 ((
% 97.31/13.17 (subsetI2) =>
% 97.31/13.17 ((
% 97.31/13.17 (emptysetsubset) =>
% 97.31/13.17 ((
% 97.31/13.17 (subsetE) =>
% 97.31/13.17 ((
% 97.31/13.17 (subsetE2) =>
% 97.31/13.17 ((
% 97.31/13.17 (notsubsetI) =>
% 97.31/13.17 ((
% 97.31/13.17 (notequalI1) =>
% 97.31/13.17 ((
% 97.31/13.17 (notequalI2) =>
% 97.31/13.17 ((
% 97.31/13.17 (subsetRefl) =>
% 97.31/13.17 ((
% 97.31/13.17 (subsetTrans) =>
% 97.31/13.17 ((
% 97.31/13.17 (setadjoinSub) =>
% 97.31/13.17 ((
% 97.31/13.17 (setadjoinSub2) =>
% 97.31/13.17 ((
% 97.31/13.17 (subset2powerset) =>
% 97.31/13.17 ((
% 97.31/13.17 (setextsub) =>
% 97.31/13.17 ((
% 97.31/13.17 (subsetemptysetimpeq) =>
% 97.31/13.17 ((
% 97.31/13.17 (powersetI1) =>
% 97.31/13.17 ((
% 97.31/13.17 (powersetE1) =>
% 97.31/13.17 ((
% 97.31/13.17 (inPowerset) =>
% 97.31/13.17 ((
% 97.31/13.17 (powersetsubset) =>
% 97.31/13.17 ((
% 97.31/13.17 (sepInPowerset) =>
% 97.31/13.17 ((
% 97.31/13.17 (sepSubset) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionIL) =>
% 97.31/13.17 ((
% 97.31/13.17 (upairset2IR) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionIR) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionEcases) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionE) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionLsub) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionRsub) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectI) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectSubset5) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectEL) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectLsub) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectSubset2) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectSubset3) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectER) =>
% 97.31/13.17 ((
% 97.31/13.17 (disjointsetsI1) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectRsub) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectSubset4) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectSubset1) =>
% 97.31/13.17 ((
% 97.31/13.17 (bs114d) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusI) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusEL) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusER) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusSubset2) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusERneg) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusELneg) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusILneg) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusIRneg) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusLsub) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusSubset1) =>
% 97.31/13.17 ((
% 97.31/13.17 (symdiffE) =>
% 97.31/13.17 ((
% 97.31/13.17 (symdiffI1) =>
% 97.31/13.17 ((
% 97.31/13.17 (symdiffI2) =>
% 97.31/13.17 ((
% 97.31/13.17 (symdiffIneg1) =>
% 97.31/13.17 ((
% 97.31/13.17 (symdiffIneg2) =>
% 97.31/13.17 ((
% 97.31/13.17 (secondinupair) =>
% 97.31/13.17 ((
% 97.31/13.17 (setukpairIL) =>
% 97.31/13.17 ((
% 97.31/13.17 (setukpairIR) =>
% 97.31/13.17 ((
% 97.31/13.17 (kpairiskpair) =>
% 97.31/13.17 ((
% 97.31/13.17 (kpairp) =>
% 97.31/13.17 ((
% 97.31/13.17 (singletonsubset) =>
% 97.31/13.17 ((
% 97.31/13.17 (singletoninpowerset) =>
% 97.31/13.17 ((
% 97.31/13.17 (singletoninpowunion) =>
% 97.31/13.17 ((
% 97.31/13.17 (upairset2E) =>
% 97.31/13.17 ((
% 97.31/13.17 (upairsubunion) =>
% 97.31/13.17 ((
% 97.31/13.17 (upairinpowunion) =>
% 97.31/13.17 ((
% 97.31/13.17 (ubforcartprodlem1) =>
% 97.31/13.17 ((
% 97.31/13.17 (ubforcartprodlem2) =>
% 97.31/13.17 ((
% 97.31/13.17 (ubforcartprodlem3) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodpairin) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodmempair1) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodmempair) =>
% 97.31/13.17 ((
% 97.31/13.17 (setunionE2) =>
% 97.31/13.17 ((
% 97.31/13.17 (setunionsingleton1) =>
% 97.31/13.17 ((
% 97.31/13.17 (setunionsingleton2) =>
% 97.31/13.17 ((
% 97.31/13.17 (setunionsingleton) =>
% 97.31/13.17 ((
% 97.31/13.17 (singletonprop) =>
% 97.31/13.17 ((
% 97.31/13.17 (ex1E1) =>
% 97.31/13.17 ((
% 97.31/13.17 (ex1I) =>
% 97.31/13.17 ((
% 97.31/13.17 (ex1I2) =>
% 97.31/13.17 ((
% 97.31/13.17 (singletonsuniq) =>
% 97.31/13.17 ((
% 97.31/13.17 (setukpairinjL1) =>
% 97.31/13.17 ((
% 97.31/13.17 (kfstsingleton) =>
% 97.31/13.17 ((
% 97.31/13.17 (theprop) =>
% 97.31/13.17 ((
% 97.31/13.17 (kfstpairEq) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodfstin) =>
% 97.31/13.17 ((
% 97.31/13.17 (setukpairinjL2) =>
% 97.31/13.17 ((
% 97.31/13.17 (setukpairinjL) =>
% 97.31/13.17 ((
% 97.31/13.17 (setukpairinjR11) =>
% 97.31/13.17 ((
% 97.31/13.17 (setukpairinjR12) =>
% 97.31/13.17 ((
% 97.31/13.17 (setukpairinjR1) =>
% 97.31/13.17 ((
% 97.31/13.17 (upairequniteq) =>
% 97.31/13.17 ((
% 97.31/13.17 (setukpairinjR2) =>
% 97.31/13.17 ((
% 97.31/13.17 (setukpairinjR) =>
% 97.31/13.17 ((
% 97.31/13.17 (ksndsingleton) =>
% 97.31/13.17 ((
% 97.31/13.17 (ksndpairEq) =>
% 97.31/13.17 ((
% 97.31/13.17 (kpairsurjEq) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodsndin) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodpairmemEL) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodpairmemER) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodmempaircEq) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodfstpairEq) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodsndpairEq) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodpairsurjEq) =>
% 97.31/13.17 ((
% 97.31/13.17 (dpsetconstrI) =>
% 97.31/13.17 ((
% 97.31/13.17 (dpsetconstrSub) =>
% 97.31/13.17 ((
% 97.31/13.17 (setOfPairsIsBReln) =>
% 97.31/13.17 ((
% 97.31/13.17 (dpsetconstrERa) =>
% 97.31/13.17 ((
% 97.31/13.17 (dpsetconstrEL1) =>
% 97.31/13.17 ((
% 97.31/13.17 (dpsetconstrEL2) =>
% 97.31/13.17 ((
% 97.31/13.17 (dpsetconstrER) =>
% 97.31/13.17 ((
% 97.31/13.17 (funcImageSingleton) =>
% 97.31/13.17 ((
% 97.31/13.17 (apProp) =>
% 97.31/13.17 ((
% 97.31/13.17 (app) =>
% 97.31/13.17 ((
% 97.31/13.17 (infuncsetfunc) =>
% 97.31/13.17 ((
% 97.31/13.17 (ap2p) =>
% 97.31/13.17 ((
% 97.31/13.17 (funcinfuncset) =>
% 97.31/13.17 ((
% 97.31/13.17 (lamProp) =>
% 97.31/13.17 ((
% 97.31/13.17 (lamp) =>
% 97.31/13.17 ((
% 97.31/13.17 (lam2p) =>
% 97.31/13.17 ((
% 97.31/13.17 (brelnall1) =>
% 97.31/13.17 ((
% 97.31/13.17 (brelnall2) =>
% 97.31/13.17 ((
% 97.31/13.17 (ex1E2) =>
% 97.31/13.17 ((
% 97.31/13.17 (funcGraphProp1) =>
% 97.31/13.17 ((
% 97.31/13.17 (funcGraphProp3) =>
% 97.31/13.17 ((
% 97.31/13.17 (funcGraphProp2) =>
% 97.31/13.17 ((
% 97.31/13.17 (funcextLem) =>
% 97.31/13.17 ((
% 97.31/13.17 (funcGraphProp4) =>
% 97.31/13.17 ((
% 97.31/13.17 (subbreln) =>
% 97.31/13.17 ((
% 97.31/13.17 (eqbreln) =>
% 97.31/13.17 ((
% 97.31/13.17 (funcext) =>
% 97.31/13.17 ((
% 97.31/13.17 (funcext2) =>
% 97.31/13.17 ((
% 97.31/13.17 (ap2apEq1) =>
% 97.31/13.17 ((
% 97.31/13.17 (ap2apEq2) =>
% 97.31/13.17 ((
% 97.31/13.17 (beta1) =>
% 97.31/13.17 ((
% 97.31/13.17 (eta1) =>
% 97.31/13.17 ((
% 97.31/13.17 (lam2lamEq) =>
% 97.31/13.17 ((
% 97.31/13.17 (beta2) =>
% 97.31/13.17 ((
% 97.31/13.17 (eta2) =>
% 97.31/13.17 ((
% 97.31/13.17 (iffalseProp1) =>
% 97.31/13.17 ((
% 97.31/13.17 (iffalseProp2) =>
% 97.31/13.17 ((
% 97.31/13.17 (iftrueProp1) =>
% 97.31/13.17 ((
% 97.31/13.17 (iftrueProp2) =>
% 97.31/13.17 ((
% 97.31/13.17 (ifSingleton) =>
% 97.31/13.17 ((
% 97.31/13.17 (ifp) =>
% 97.31/13.17 ((
% 97.31/13.17 (theeq) =>
% 97.31/13.17 ((
% 97.31/13.17 (iftrue) =>
% 97.31/13.17 ((
% 97.31/13.17 (iffalse) =>
% 97.31/13.17 ((
% 97.31/13.17 (iftrueorfalse) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectT_lem) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionT_lem) =>
% 97.31/13.17 ((
% 97.31/13.17 (powersetT_lem) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusT_lem) =>
% 97.31/13.17 ((
% 97.31/13.17 (complementT_lem) =>
% 97.31/13.17 ((
% 97.31/13.17 (setextT) =>
% 97.31/13.17 ((
% 97.31/13.17 (subsetTI) =>
% 97.31/13.17 ((
% 97.31/13.17 (powersetTI1) =>
% 97.31/13.17 ((
% 97.31/13.17 (powersetTE1) =>
% 97.31/13.17 ((
% 97.31/13.17 (complementTI1) =>
% 97.31/13.17 ((
% 97.31/13.17 (complementTE1) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectTELcontra) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectTERcontra) =>
% 97.31/13.17 ((
% 97.31/13.17 (contrasubsetT) =>
% 97.31/13.17 ((
% 97.31/13.17 (contrasubsetT1) =>
% 97.31/13.17 ((
% 97.31/13.17 (contrasubsetT2) =>
% 97.31/13.17 ((
% 97.31/13.17 (contrasubsetT3) =>
% 97.31/13.17 ((
% 97.31/13.17 (doubleComplementI1) =>
% 97.31/13.17 ((
% 97.31/13.17 (doubleComplementE1) =>
% 97.31/13.17 ((
% 97.31/13.17 (doubleComplementSub1) =>
% 97.31/13.17 ((
% 97.31/13.17 (doubleComplementSub2) =>
% 97.31/13.17 ((
% 97.31/13.17 (doubleComplementEq) =>
% 97.31/13.17 ((
% 97.31/13.17 (complementTnotintersectT) =>
% 97.31/13.17 ((
% 97.31/13.17 (complementImpComplementIntersect) =>
% 97.31/13.17 ((
% 97.31/13.17 (complementSubsetComplementIntersect) =>
% 97.31/13.17 ((
% 97.31/13.17 (complementInPowersetComplementIntersect) =>
% 97.31/13.17 ((
% 97.31/13.17 (contraSubsetComplement) =>
% 97.31/13.17 ((
% 97.31/13.17 (complementTcontraSubset) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionTILcontra) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionTIRcontra) =>
% 97.31/13.17 ((
% 97.31/13.17 (inIntersectImpInUnion) =>
% 97.31/13.17 ((
% 97.31/13.17 (inIntersectImpInUnion2) =>
% 97.31/13.17 ((
% 97.31/13.17 (inIntersectImpInIntersectUnions) =>
% 97.31/13.17 ((
% 97.31/13.17 (intersectInPowersetIntersectUnions) =>
% 97.31/13.17 ((
% 97.31/13.17 (inComplementUnionImpNotIn1) =>
% 97.31/13.17 ((
% 97.31/13.17 (inComplementUnionImpInComplement1) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionTE) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionTEcontra) =>
% 97.31/13.17 ((
% 97.31/13.17 (demorgan2a1) =>
% 97.31/13.17 ((
% 97.31/13.17 (complementUnionInPowersetComplement) =>
% 97.31/13.17 ((
% 97.31/13.17 (demorgan2a2) =>
% 97.31/13.17 ((
% 97.31/13.17 (demorgan1a) =>
% 97.31/13.17 ((
% 97.31/13.17 (demorgan1b) =>
% 97.31/13.17 ((
% 97.31/13.17 (demorgan1) =>
% 97.31/13.17 ((
% 97.31/13.17 (demorgan2a) =>
% 97.31/13.17 ((
% 97.31/13.17 (demorgan2b2) =>
% 97.31/13.17 ((
% 97.31/13.17 (demorgan2b) =>
% 97.31/13.17 ((
% 97.31/13.17 (demorgan2) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz13rule0) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz13rule1) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz13rule2) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz13rule3) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz13rule4) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz1_1) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz1_2) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz1_3) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz1_4) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz1_5) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1all2) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1SetBreln1) =>
% 97.31/13.17 ((
% 97.31/13.17 (choice2fnsingleton) =>
% 97.31/13.17 ((
% 97.31/13.17 (setOfPairsIsBReln1) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1all1) =>
% 97.31/13.17 ((
% 97.31/13.17 (subbreln1) =>
% 97.31/13.17 ((
% 97.31/13.17 (eqbreln1) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1invprop) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1invI) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1invE) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1compprop) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1compI) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1compE) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1compEex) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1unionprop) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1unionIL) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1unionIR) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1unionI) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1unionE) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1unionEcases) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1unionCommutes) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz2Ex) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz2W) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz2A) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz2B) =>
% 97.31/13.17 ((
% 97.31/13.17 (image1Ex) =>
% 97.31/13.17 ((
% 97.31/13.17 (image1Ex1) =>
% 97.31/13.17 ((
% 97.31/13.17 (image1Equiv) =>
% 97.31/13.17 ((
% 97.31/13.17 (image1E) =>
% 97.31/13.17 ((
% 97.31/13.17 (image1I) =>
% 97.31/13.17 ((
% 97.31/13.17 (injFuncInInjFuncSet) =>
% 97.31/13.17 ((
% 97.31/13.17 (injFuncSetFuncIn) =>
% 97.31/13.17 ((
% 97.31/13.17 (injFuncSetFuncInj) =>
% 97.31/13.17 ((
% 97.31/13.17 (surjFuncSetFuncIn) =>
% 97.31/13.17 ((
% 97.31/13.17 (surjFuncSetFuncSurj) =>
% 97.31/13.17 ((
% 97.31/13.17 (leftInvIsSurj) =>
% 97.31/13.17 ((
% 97.31/13.17 (surjCantorThm) =>
% 97.31/13.17 ((
% 97.31/13.17 (foundation2) =>
% 97.31/13.17 ((
% 97.31/13.17 (notinself) =>
% 97.31/13.17 ((
% 97.31/13.17 (notinself2) =>
% 97.31/13.17 ((
% 97.31/13.17 (omegaSp) =>
% 97.31/13.17 ((
% 97.31/13.17 (omegaSclos) =>
% 97.31/13.17 ((
% 97.31/13.17 (peano0notS) =>
% 97.31/13.17 ((
% 97.31/13.17 (!!) @ (
% 97.31/13.17 (('#S') @ (
% 97.31/13.17 (
% 97.31/13.17 ('#B') @ (
% 97.31/13.17 =>) @
% 97.31/13.17 (
% 97.31/13.17 (
% 97.31/13.17 ('#C') @ in @
% 97.31/13.17 omega)))) @
% 97.31/13.17 (
% 97.31/13.17 (
% 97.31/13.17 ('#B') @ (
% 97.31/13.17 !!) @
% 97.31/13.17 (
% 97.31/13.17 (
% 97.31/13.17 ('#B') @ (
% 97.31/13.17 (
% 97.31/13.17 ('#S') @ (
% 97.31/13.17 (
% 97.31/13.17 ('#B') @ (
% 97.31/13.17 =>) @
% 97.31/13.17 (
% 97.31/13.17 (
% 97.31/13.17 ('#C') @ in @
% 97.31/13.17 omega)))))) @
% 97.31/13.17 (
% 97.31/13.17 (
% 97.31/13.17 ('#S') @ (
% 97.31/13.17 (
% 97.31/13.17 ('#B') @ (
% 97.31/13.17 '#S') @
% 97.31/13.17 (
% 97.31/13.17 (
% 97.31/13.17 ('#B') @ (
% 97.31/13.17 (
% 97.31/13.17 ('#B') @ (
% 97.31/13.17 =>))) @
% 97.31/13.17 (
% 97.31/13.17 (
% 97.31/13.17 ('#C') @ (
% 97.31/13.17 (
% 97.31/13.17 ('#B') @ (
% 97.31/13.17 '#B') @
% 97.31/13.17 (
% 97.31/13.17 (
% 97.31/13.17 ('#B') @ (
% 97.31/13.17 =) @
% 97.31/13.17 omegaS)))) @
% 97.31/13.17 omegaS)))))) @
% 97.31/13.17 (
% 97.31/13.17 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.31/13.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl280])).
% 97.31/13.17 thf(zip_derived_cl307, plain,
% 97.31/13.17 (~ (((setadjoinIL) =>
% 97.31/13.17 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 97.31/13.17 (((setadjoinIR) =>
% 97.31/13.17 (((setadjoinE) =>
% 97.31/13.17 (((setadjoinOr) =>
% 97.31/13.17 (((setoftrueEq) =>
% 97.31/13.17 (((powersetI) =>
% 97.31/13.17 (((emptyinPowerset) =>
% 97.31/13.17 (((emptyInPowerset) =>
% 97.31/13.17 (((powersetE) =>
% 97.31/13.17 (((setunionI) =>
% 97.31/13.17 (((setunionE) =>
% 97.31/13.17 (((subPowSU) =>
% 97.31/13.17 (((exuE2) =>
% 97.31/13.17 (((nonemptyImpWitness) =>
% 97.31/13.17 (((uniqinunit) =>
% 97.31/13.17 (((notinsingleton) =>
% 97.31/13.17 (((eqinunit) =>
% 97.31/13.17 (((singletonsswitch) =>
% 97.31/13.17 (((upairsetE) =>
% 97.31/13.17 (((upairsetIL) =>
% 97.31/13.17 (((upairsetIR) =>
% 97.31/13.17 (((emptyE1) =>
% 97.31/13.17 (((vacuousDall) =>
% 97.31/13.17 (((quantDeMorgan1) =>
% 97.31/13.17 (((quantDeMorgan2) =>
% 97.31/13.17 (((quantDeMorgan3) =>
% 97.31/13.17 (((quantDeMorgan4) =>
% 97.31/13.17 (((prop2setI) =>
% 97.31/13.17 (((prop2set2propI) =>
% 97.31/13.17 ((
% 97.31/13.17 (notdexE) =>
% 97.31/13.17 ((
% 97.31/13.17 (notdallE) =>
% 97.31/13.17 ((
% 97.31/13.17 (exuI1) =>
% 97.31/13.17 ((
% 97.31/13.17 (exuI3) =>
% 97.31/13.17 ((
% 97.31/13.17 (exuI2) =>
% 97.31/13.17 ((
% 97.31/13.17 (inCongP) =>
% 97.31/13.17 ((
% 97.31/13.17 (in__Cong) =>
% 97.31/13.17 ((
% 97.31/13.17 (exuE3u) =>
% 97.31/13.17 ((
% 97.31/13.17 (exu__Cong) =>
% 97.31/13.17 ((
% 97.31/13.17 (setadjoin__Cong) =>
% 97.31/13.17 ((
% 97.31/13.17 (powerset__Cong) =>
% 97.31/13.17 ((
% 97.31/13.17 (setunion__Cong) =>
% 97.31/13.17 ((
% 97.31/13.17 (exuEu) =>
% 97.31/13.17 ((
% 97.31/13.17 (descr__Cong) =>
% 97.31/13.17 ((
% 97.31/13.17 (dsetconstr__Cong) =>
% 97.31/13.17 ((
% 97.31/13.17 (subsetI1) =>
% 97.31/13.17 ((
% 97.31/13.17 (eqimpsubset2) =>
% 97.31/13.17 ((
% 97.31/13.17 (eqimpsubset1) =>
% 97.31/13.17 ((
% 97.31/13.17 (subsetI2) =>
% 97.31/13.17 ((
% 97.31/13.17 (emptysetsubset) =>
% 97.31/13.17 ((
% 97.31/13.17 (subsetE) =>
% 97.31/13.17 ((
% 97.31/13.17 (subsetE2) =>
% 97.31/13.17 ((
% 97.31/13.17 (notsubsetI) =>
% 97.31/13.17 ((
% 97.31/13.17 (notequalI1) =>
% 97.31/13.17 ((
% 97.31/13.17 (notequalI2) =>
% 97.31/13.17 ((
% 97.31/13.17 (subsetRefl) =>
% 97.31/13.17 ((
% 97.31/13.17 (subsetTrans) =>
% 97.31/13.17 ((
% 97.31/13.17 (setadjoinSub) =>
% 97.31/13.17 ((
% 97.31/13.17 (setadjoinSub2) =>
% 97.31/13.17 ((
% 97.31/13.17 (subset2powerset) =>
% 97.31/13.17 ((
% 97.31/13.17 (setextsub) =>
% 97.31/13.17 ((
% 97.31/13.17 (subsetemptysetimpeq) =>
% 97.31/13.17 ((
% 97.31/13.17 (powersetI1) =>
% 97.31/13.17 ((
% 97.31/13.17 (powersetE1) =>
% 97.31/13.17 ((
% 97.31/13.17 (inPowerset) =>
% 97.31/13.17 ((
% 97.31/13.17 (powersetsubset) =>
% 97.31/13.17 ((
% 97.31/13.17 (sepInPowerset) =>
% 97.31/13.17 ((
% 97.31/13.17 (sepSubset) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionIL) =>
% 97.31/13.17 ((
% 97.31/13.17 (upairset2IR) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionIR) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionEcases) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionE) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionLsub) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionRsub) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectI) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectSubset5) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectEL) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectLsub) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectSubset2) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectSubset3) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectER) =>
% 97.31/13.17 ((
% 97.31/13.17 (disjointsetsI1) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectRsub) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectSubset4) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectSubset1) =>
% 97.31/13.17 ((
% 97.31/13.17 (bs114d) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusI) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusEL) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusER) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusSubset2) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusERneg) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusELneg) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusILneg) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusIRneg) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusLsub) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusSubset1) =>
% 97.31/13.17 ((
% 97.31/13.17 (symdiffE) =>
% 97.31/13.17 ((
% 97.31/13.17 (symdiffI1) =>
% 97.31/13.17 ((
% 97.31/13.17 (symdiffI2) =>
% 97.31/13.17 ((
% 97.31/13.17 (symdiffIneg1) =>
% 97.31/13.17 ((
% 97.31/13.17 (symdiffIneg2) =>
% 97.31/13.17 ((
% 97.31/13.17 (secondinupair) =>
% 97.31/13.17 ((
% 97.31/13.17 (setukpairIL) =>
% 97.31/13.17 ((
% 97.31/13.17 (setukpairIR) =>
% 97.31/13.17 ((
% 97.31/13.17 (kpairiskpair) =>
% 97.31/13.17 ((
% 97.31/13.17 (kpairp) =>
% 97.31/13.17 ((
% 97.31/13.17 (singletonsubset) =>
% 97.31/13.17 ((
% 97.31/13.17 (singletoninpowerset) =>
% 97.31/13.17 ((
% 97.31/13.17 (singletoninpowunion) =>
% 97.31/13.17 ((
% 97.31/13.17 (upairset2E) =>
% 97.31/13.17 ((
% 97.31/13.17 (upairsubunion) =>
% 97.31/13.17 ((
% 97.31/13.17 (upairinpowunion) =>
% 97.31/13.17 ((
% 97.31/13.17 (ubforcartprodlem1) =>
% 97.31/13.17 ((
% 97.31/13.17 (ubforcartprodlem2) =>
% 97.31/13.17 ((
% 97.31/13.17 (ubforcartprodlem3) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodpairin) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodmempair1) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodmempair) =>
% 97.31/13.17 ((
% 97.31/13.17 (setunionE2) =>
% 97.31/13.17 ((
% 97.31/13.17 (setunionsingleton1) =>
% 97.31/13.17 ((
% 97.31/13.17 (setunionsingleton2) =>
% 97.31/13.17 ((
% 97.31/13.17 (setunionsingleton) =>
% 97.31/13.17 ((
% 97.31/13.17 (singletonprop) =>
% 97.31/13.17 ((
% 97.31/13.17 (ex1E1) =>
% 97.31/13.17 ((
% 97.31/13.17 (ex1I) =>
% 97.31/13.17 ((
% 97.31/13.17 (ex1I2) =>
% 97.31/13.17 ((
% 97.31/13.17 (singletonsuniq) =>
% 97.31/13.17 ((
% 97.31/13.17 (setukpairinjL1) =>
% 97.31/13.17 ((
% 97.31/13.17 (kfstsingleton) =>
% 97.31/13.17 ((
% 97.31/13.17 (theprop) =>
% 97.31/13.17 ((
% 97.31/13.17 (kfstpairEq) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodfstin) =>
% 97.31/13.17 ((
% 97.31/13.17 (setukpairinjL2) =>
% 97.31/13.17 ((
% 97.31/13.17 (setukpairinjL) =>
% 97.31/13.17 ((
% 97.31/13.17 (setukpairinjR11) =>
% 97.31/13.17 ((
% 97.31/13.17 (setukpairinjR12) =>
% 97.31/13.17 ((
% 97.31/13.17 (setukpairinjR1) =>
% 97.31/13.17 ((
% 97.31/13.17 (upairequniteq) =>
% 97.31/13.17 ((
% 97.31/13.17 (setukpairinjR2) =>
% 97.31/13.17 ((
% 97.31/13.17 (setukpairinjR) =>
% 97.31/13.17 ((
% 97.31/13.17 (ksndsingleton) =>
% 97.31/13.17 ((
% 97.31/13.17 (ksndpairEq) =>
% 97.31/13.17 ((
% 97.31/13.17 (kpairsurjEq) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodsndin) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodpairmemEL) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodpairmemER) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodmempaircEq) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodfstpairEq) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodsndpairEq) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodpairsurjEq) =>
% 97.31/13.17 ((
% 97.31/13.17 (dpsetconstrI) =>
% 97.31/13.17 ((
% 97.31/13.17 (dpsetconstrSub) =>
% 97.31/13.17 ((
% 97.31/13.17 (setOfPairsIsBReln) =>
% 97.31/13.17 ((
% 97.31/13.17 (dpsetconstrERa) =>
% 97.31/13.17 ((
% 97.31/13.17 (dpsetconstrEL1) =>
% 97.31/13.17 ((
% 97.31/13.17 (dpsetconstrEL2) =>
% 97.31/13.17 ((
% 97.31/13.17 (dpsetconstrER) =>
% 97.31/13.17 ((
% 97.31/13.17 (funcImageSingleton) =>
% 97.31/13.17 ((
% 97.31/13.17 (apProp) =>
% 97.31/13.17 ((
% 97.31/13.17 (app) =>
% 97.31/13.17 ((
% 97.31/13.17 (infuncsetfunc) =>
% 97.31/13.17 ((
% 97.31/13.17 (ap2p) =>
% 97.31/13.17 ((
% 97.31/13.17 (funcinfuncset) =>
% 97.31/13.17 ((
% 97.31/13.17 (lamProp) =>
% 97.31/13.17 ((
% 97.31/13.17 (lamp) =>
% 97.31/13.17 ((
% 97.31/13.17 (lam2p) =>
% 97.31/13.17 ((
% 97.31/13.17 (brelnall1) =>
% 97.31/13.17 ((
% 97.31/13.17 (brelnall2) =>
% 97.31/13.17 ((
% 97.31/13.17 (ex1E2) =>
% 97.31/13.17 ((
% 97.31/13.17 (funcGraphProp1) =>
% 97.31/13.17 ((
% 97.31/13.17 (funcGraphProp3) =>
% 97.31/13.17 ((
% 97.31/13.17 (funcGraphProp2) =>
% 97.31/13.17 ((
% 97.31/13.17 (funcextLem) =>
% 97.31/13.17 ((
% 97.31/13.17 (funcGraphProp4) =>
% 97.31/13.17 ((
% 97.31/13.17 (subbreln) =>
% 97.31/13.17 ((
% 97.31/13.17 (eqbreln) =>
% 97.31/13.17 ((
% 97.31/13.17 (funcext) =>
% 97.31/13.17 ((
% 97.31/13.17 (funcext2) =>
% 97.31/13.17 ((
% 97.31/13.17 (ap2apEq1) =>
% 97.31/13.17 ((
% 97.31/13.17 (ap2apEq2) =>
% 97.31/13.17 ((
% 97.31/13.17 (beta1) =>
% 97.31/13.17 ((
% 97.31/13.17 (eta1) =>
% 97.31/13.17 ((
% 97.31/13.17 (lam2lamEq) =>
% 97.31/13.17 ((
% 97.31/13.17 (beta2) =>
% 97.31/13.17 ((
% 97.31/13.17 (eta2) =>
% 97.31/13.17 ((
% 97.31/13.17 (iffalseProp1) =>
% 97.31/13.17 ((
% 97.31/13.17 (iffalseProp2) =>
% 97.31/13.17 ((
% 97.31/13.17 (iftrueProp1) =>
% 97.31/13.17 ((
% 97.31/13.17 (iftrueProp2) =>
% 97.31/13.17 ((
% 97.31/13.17 (ifSingleton) =>
% 97.31/13.17 ((
% 97.31/13.17 (ifp) =>
% 97.31/13.17 ((
% 97.31/13.17 (theeq) =>
% 97.31/13.17 ((
% 97.31/13.17 (iftrue) =>
% 97.31/13.17 ((
% 97.31/13.17 (iffalse) =>
% 97.31/13.17 ((
% 97.31/13.17 (iftrueorfalse) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectT_lem) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionT_lem) =>
% 97.31/13.17 ((
% 97.31/13.17 (powersetT_lem) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusT_lem) =>
% 97.31/13.17 ((
% 97.31/13.17 (complementT_lem) =>
% 97.31/13.17 ((
% 97.31/13.17 (setextT) =>
% 97.31/13.17 ((
% 97.31/13.17 (subsetTI) =>
% 97.31/13.17 ((
% 97.31/13.17 (powersetTI1) =>
% 97.31/13.17 ((
% 97.31/13.17 (powersetTE1) =>
% 97.31/13.17 ((
% 97.31/13.17 (complementTI1) =>
% 97.31/13.17 ((
% 97.31/13.17 (complementTE1) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectTELcontra) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectTERcontra) =>
% 97.31/13.17 ((
% 97.31/13.17 (contrasubsetT) =>
% 97.31/13.17 ((
% 97.31/13.17 (contrasubsetT1) =>
% 97.31/13.17 ((
% 97.31/13.17 (contrasubsetT2) =>
% 97.31/13.17 ((
% 97.31/13.17 (contrasubsetT3) =>
% 97.31/13.17 ((
% 97.31/13.17 (doubleComplementI1) =>
% 97.31/13.17 ((
% 97.31/13.17 (doubleComplementE1) =>
% 97.31/13.17 ((
% 97.31/13.17 (doubleComplementSub1) =>
% 97.31/13.17 ((
% 97.31/13.17 (doubleComplementSub2) =>
% 97.31/13.17 ((
% 97.31/13.17 (doubleComplementEq) =>
% 97.31/13.17 ((
% 97.31/13.17 (complementTnotintersectT) =>
% 97.31/13.17 ((
% 97.31/13.17 (complementImpComplementIntersect) =>
% 97.31/13.17 ((
% 97.31/13.17 (complementSubsetComplementIntersect) =>
% 97.31/13.17 ((
% 97.31/13.17 (complementInPowersetComplementIntersect) =>
% 97.31/13.17 ((
% 97.31/13.17 (contraSubsetComplement) =>
% 97.31/13.17 ((
% 97.31/13.17 (complementTcontraSubset) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionTILcontra) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionTIRcontra) =>
% 97.31/13.17 ((
% 97.31/13.17 (inIntersectImpInUnion) =>
% 97.31/13.17 ((
% 97.31/13.17 (inIntersectImpInUnion2) =>
% 97.31/13.17 ((
% 97.31/13.17 (inIntersectImpInIntersectUnions) =>
% 97.31/13.17 ((
% 97.31/13.17 (intersectInPowersetIntersectUnions) =>
% 97.31/13.17 ((
% 97.31/13.17 (inComplementUnionImpNotIn1) =>
% 97.31/13.17 ((
% 97.31/13.17 (inComplementUnionImpInComplement1) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionTE) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionTEcontra) =>
% 97.31/13.17 ((
% 97.31/13.17 (demorgan2a1) =>
% 97.31/13.17 ((
% 97.31/13.17 (complementUnionInPowersetComplement) =>
% 97.31/13.17 ((
% 97.31/13.17 (demorgan2a2) =>
% 97.31/13.17 ((
% 97.31/13.17 (demorgan1a) =>
% 97.31/13.17 ((
% 97.31/13.17 (demorgan1b) =>
% 97.31/13.17 ((
% 97.31/13.17 (demorgan1) =>
% 97.31/13.17 ((
% 97.31/13.17 (demorgan2a) =>
% 97.31/13.17 ((
% 97.31/13.17 (demorgan2b2) =>
% 97.31/13.17 ((
% 97.31/13.17 (demorgan2b) =>
% 97.31/13.17 ((
% 97.31/13.17 (demorgan2) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz13rule0) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz13rule1) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz13rule2) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz13rule3) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz13rule4) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz1_1) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz1_2) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz1_3) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz1_4) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz1_5) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1all2) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1SetBreln1) =>
% 97.31/13.17 ((
% 97.31/13.17 (choice2fnsingleton) =>
% 97.31/13.17 ((
% 97.31/13.17 (setOfPairsIsBReln1) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1all1) =>
% 97.31/13.17 ((
% 97.31/13.17 (subbreln1) =>
% 97.31/13.17 ((
% 97.31/13.17 (eqbreln1) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1invprop) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1invI) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1invE) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1compprop) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1compI) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1compE) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1compEex) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1unionprop) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1unionIL) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1unionIR) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1unionI) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1unionE) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1unionEcases) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1unionCommutes) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz2Ex) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz2W) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz2A) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz2B) =>
% 97.31/13.17 ((
% 97.31/13.17 (image1Ex) =>
% 97.31/13.17 ((
% 97.31/13.17 (image1Ex1) =>
% 97.31/13.17 ((
% 97.31/13.17 (image1Equiv) =>
% 97.31/13.17 ((
% 97.31/13.17 (image1E) =>
% 97.31/13.17 ((
% 97.31/13.17 (image1I) =>
% 97.31/13.17 ((
% 97.31/13.17 (injFuncInInjFuncSet) =>
% 97.31/13.17 ((
% 97.31/13.17 (injFuncSetFuncIn) =>
% 97.31/13.17 ((
% 97.31/13.17 (injFuncSetFuncInj) =>
% 97.31/13.17 ((
% 97.31/13.17 (surjFuncSetFuncIn) =>
% 97.31/13.17 ((
% 97.31/13.17 (surjFuncSetFuncSurj) =>
% 97.31/13.17 ((
% 97.31/13.17 (leftInvIsSurj) =>
% 97.31/13.17 ((
% 97.31/13.17 (surjCantorThm) =>
% 97.31/13.17 ((
% 97.31/13.17 (foundation2) =>
% 97.31/13.17 ((
% 97.31/13.17 (notinself) =>
% 97.31/13.17 ((
% 97.31/13.17 (notinself2) =>
% 97.31/13.17 ((
% 97.31/13.17 (omegaSp) =>
% 97.31/13.17 ((
% 97.31/13.17 (omegaSclos) =>
% 97.31/13.17 ((
% 97.31/13.17 (peano0notS) =>
% 97.31/13.17 ((
% 97.31/13.17 (!!) @ (
% 97.31/13.17 (('#S') @ (
% 97.31/13.17 (
% 97.31/13.17 ('#B') @ (
% 97.31/13.17 =>) @
% 97.31/13.17 (
% 97.31/13.17 (
% 97.31/13.17 ('#C') @ in @
% 97.31/13.17 omega)))) @
% 97.31/13.17 (
% 97.31/13.17 (
% 97.31/13.17 ('#B') @ (
% 97.31/13.17 !!) @
% 97.31/13.17 (
% 97.31/13.17 (
% 97.31/13.17 ('#B') @ (
% 97.31/13.17 (
% 97.31/13.17 ('#S') @ (
% 97.31/13.17 (
% 97.31/13.17 ('#B') @ (
% 97.31/13.17 =>) @
% 97.31/13.17 (
% 97.31/13.17 (
% 97.31/13.17 ('#C') @ in @
% 97.31/13.17 omega)))))) @
% 97.31/13.17 (
% 97.31/13.17 (
% 97.31/13.17 ('#S') @ (
% 97.31/13.17 (
% 97.31/13.17 ('#B') @ (
% 97.31/13.17 '#S') @
% 97.31/13.17 (
% 97.31/13.17 (
% 97.31/13.17 ('#B') @ (
% 97.31/13.17 (
% 97.31/13.17 ('#B') @ (
% 97.31/13.17 =>))) @
% 97.31/13.17 (
% 97.31/13.17 (
% 97.31/13.17 ('#C') @ (
% 97.31/13.17 (
% 97.31/13.17 ('#B') @ (
% 97.31/13.17 '#B') @
% 97.31/13.17 (
% 97.31/13.17 (
% 97.31/13.17 ('#B') @ (
% 97.31/13.17 =) @
% 97.31/13.17 omegaS)))) @
% 97.31/13.17 omegaS)))))) @
% 97.31/13.17 (
% 97.31/13.17 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.31/13.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl293])).
% 97.31/13.17 thf(zip_derived_cl322, plain,
% 97.31/13.17 (~ (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 97.31/13.17 (((setadjoinIR) =>
% 97.31/13.17 (((setadjoinE) =>
% 97.31/13.17 (((setadjoinOr) =>
% 97.31/13.17 (((setoftrueEq) =>
% 97.31/13.17 (((powersetI) =>
% 97.31/13.17 (((emptyinPowerset) =>
% 97.31/13.17 (((emptyInPowerset) =>
% 97.31/13.17 (((powersetE) =>
% 97.31/13.17 (((setunionI) =>
% 97.31/13.17 (((setunionE) =>
% 97.31/13.17 (((subPowSU) =>
% 97.31/13.17 (((exuE2) =>
% 97.31/13.17 (((nonemptyImpWitness) =>
% 97.31/13.17 (((uniqinunit) =>
% 97.31/13.17 (((notinsingleton) =>
% 97.31/13.17 (((eqinunit) =>
% 97.31/13.17 (((singletonsswitch) =>
% 97.31/13.17 (((upairsetE) =>
% 97.31/13.17 (((upairsetIL) =>
% 97.31/13.17 (((upairsetIR) =>
% 97.31/13.17 (((emptyE1) =>
% 97.31/13.17 (((vacuousDall) =>
% 97.31/13.17 (((quantDeMorgan1) =>
% 97.31/13.17 (((quantDeMorgan2) =>
% 97.31/13.17 (((quantDeMorgan3) =>
% 97.31/13.17 (((quantDeMorgan4) =>
% 97.31/13.17 (((prop2setI) =>
% 97.31/13.17 (((prop2set2propI) =>
% 97.31/13.17 (((notdexE) =>
% 97.31/13.17 ((
% 97.31/13.17 (notdallE) =>
% 97.31/13.17 ((
% 97.31/13.17 (exuI1) =>
% 97.31/13.17 ((
% 97.31/13.17 (exuI3) =>
% 97.31/13.17 ((
% 97.31/13.17 (exuI2) =>
% 97.31/13.17 ((
% 97.31/13.17 (inCongP) =>
% 97.31/13.17 ((
% 97.31/13.17 (in__Cong) =>
% 97.31/13.17 ((
% 97.31/13.17 (exuE3u) =>
% 97.31/13.17 ((
% 97.31/13.17 (exu__Cong) =>
% 97.31/13.17 ((
% 97.31/13.17 (setadjoin__Cong) =>
% 97.31/13.17 ((
% 97.31/13.17 (powerset__Cong) =>
% 97.31/13.17 ((
% 97.31/13.17 (setunion__Cong) =>
% 97.31/13.17 ((
% 97.31/13.17 (exuEu) =>
% 97.31/13.17 ((
% 97.31/13.17 (descr__Cong) =>
% 97.31/13.17 ((
% 97.31/13.17 (dsetconstr__Cong) =>
% 97.31/13.17 ((
% 97.31/13.17 (subsetI1) =>
% 97.31/13.17 ((
% 97.31/13.17 (eqimpsubset2) =>
% 97.31/13.17 ((
% 97.31/13.17 (eqimpsubset1) =>
% 97.31/13.17 ((
% 97.31/13.17 (subsetI2) =>
% 97.31/13.17 ((
% 97.31/13.17 (emptysetsubset) =>
% 97.31/13.17 ((
% 97.31/13.17 (subsetE) =>
% 97.31/13.17 ((
% 97.31/13.17 (subsetE2) =>
% 97.31/13.17 ((
% 97.31/13.17 (notsubsetI) =>
% 97.31/13.17 ((
% 97.31/13.17 (notequalI1) =>
% 97.31/13.17 ((
% 97.31/13.17 (notequalI2) =>
% 97.31/13.17 ((
% 97.31/13.17 (subsetRefl) =>
% 97.31/13.17 ((
% 97.31/13.17 (subsetTrans) =>
% 97.31/13.17 ((
% 97.31/13.17 (setadjoinSub) =>
% 97.31/13.17 ((
% 97.31/13.17 (setadjoinSub2) =>
% 97.31/13.17 ((
% 97.31/13.17 (subset2powerset) =>
% 97.31/13.17 ((
% 97.31/13.17 (setextsub) =>
% 97.31/13.17 ((
% 97.31/13.17 (subsetemptysetimpeq) =>
% 97.31/13.17 ((
% 97.31/13.17 (powersetI1) =>
% 97.31/13.17 ((
% 97.31/13.17 (powersetE1) =>
% 97.31/13.17 ((
% 97.31/13.17 (inPowerset) =>
% 97.31/13.17 ((
% 97.31/13.17 (powersetsubset) =>
% 97.31/13.17 ((
% 97.31/13.17 (sepInPowerset) =>
% 97.31/13.17 ((
% 97.31/13.17 (sepSubset) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionIL) =>
% 97.31/13.17 ((
% 97.31/13.17 (upairset2IR) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionIR) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionEcases) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionE) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionLsub) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionRsub) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectI) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectSubset5) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectEL) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectLsub) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectSubset2) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectSubset3) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectER) =>
% 97.31/13.17 ((
% 97.31/13.17 (disjointsetsI1) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectRsub) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectSubset4) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectSubset1) =>
% 97.31/13.17 ((
% 97.31/13.17 (bs114d) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusI) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusEL) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusER) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusSubset2) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusERneg) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusELneg) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusILneg) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusIRneg) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusLsub) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusSubset1) =>
% 97.31/13.17 ((
% 97.31/13.17 (symdiffE) =>
% 97.31/13.17 ((
% 97.31/13.17 (symdiffI1) =>
% 97.31/13.17 ((
% 97.31/13.17 (symdiffI2) =>
% 97.31/13.17 ((
% 97.31/13.17 (symdiffIneg1) =>
% 97.31/13.17 ((
% 97.31/13.17 (symdiffIneg2) =>
% 97.31/13.17 ((
% 97.31/13.17 (secondinupair) =>
% 97.31/13.17 ((
% 97.31/13.17 (setukpairIL) =>
% 97.31/13.17 ((
% 97.31/13.17 (setukpairIR) =>
% 97.31/13.17 ((
% 97.31/13.17 (kpairiskpair) =>
% 97.31/13.17 ((
% 97.31/13.17 (kpairp) =>
% 97.31/13.17 ((
% 97.31/13.17 (singletonsubset) =>
% 97.31/13.17 ((
% 97.31/13.17 (singletoninpowerset) =>
% 97.31/13.17 ((
% 97.31/13.17 (singletoninpowunion) =>
% 97.31/13.17 ((
% 97.31/13.17 (upairset2E) =>
% 97.31/13.17 ((
% 97.31/13.17 (upairsubunion) =>
% 97.31/13.17 ((
% 97.31/13.17 (upairinpowunion) =>
% 97.31/13.17 ((
% 97.31/13.17 (ubforcartprodlem1) =>
% 97.31/13.17 ((
% 97.31/13.17 (ubforcartprodlem2) =>
% 97.31/13.17 ((
% 97.31/13.17 (ubforcartprodlem3) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodpairin) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodmempair1) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodmempair) =>
% 97.31/13.17 ((
% 97.31/13.17 (setunionE2) =>
% 97.31/13.17 ((
% 97.31/13.17 (setunionsingleton1) =>
% 97.31/13.17 ((
% 97.31/13.17 (setunionsingleton2) =>
% 97.31/13.17 ((
% 97.31/13.17 (setunionsingleton) =>
% 97.31/13.17 ((
% 97.31/13.17 (singletonprop) =>
% 97.31/13.17 ((
% 97.31/13.17 (ex1E1) =>
% 97.31/13.17 ((
% 97.31/13.17 (ex1I) =>
% 97.31/13.17 ((
% 97.31/13.17 (ex1I2) =>
% 97.31/13.17 ((
% 97.31/13.17 (singletonsuniq) =>
% 97.31/13.17 ((
% 97.31/13.17 (setukpairinjL1) =>
% 97.31/13.17 ((
% 97.31/13.17 (kfstsingleton) =>
% 97.31/13.17 ((
% 97.31/13.17 (theprop) =>
% 97.31/13.17 ((
% 97.31/13.17 (kfstpairEq) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodfstin) =>
% 97.31/13.17 ((
% 97.31/13.17 (setukpairinjL2) =>
% 97.31/13.17 ((
% 97.31/13.17 (setukpairinjL) =>
% 97.31/13.17 ((
% 97.31/13.17 (setukpairinjR11) =>
% 97.31/13.17 ((
% 97.31/13.17 (setukpairinjR12) =>
% 97.31/13.17 ((
% 97.31/13.17 (setukpairinjR1) =>
% 97.31/13.17 ((
% 97.31/13.17 (upairequniteq) =>
% 97.31/13.17 ((
% 97.31/13.17 (setukpairinjR2) =>
% 97.31/13.17 ((
% 97.31/13.17 (setukpairinjR) =>
% 97.31/13.17 ((
% 97.31/13.17 (ksndsingleton) =>
% 97.31/13.17 ((
% 97.31/13.17 (ksndpairEq) =>
% 97.31/13.17 ((
% 97.31/13.17 (kpairsurjEq) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodsndin) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodpairmemEL) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodpairmemER) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodmempaircEq) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodfstpairEq) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodsndpairEq) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodpairsurjEq) =>
% 97.31/13.17 ((
% 97.31/13.17 (dpsetconstrI) =>
% 97.31/13.17 ((
% 97.31/13.17 (dpsetconstrSub) =>
% 97.31/13.17 ((
% 97.31/13.17 (setOfPairsIsBReln) =>
% 97.31/13.17 ((
% 97.31/13.17 (dpsetconstrERa) =>
% 97.31/13.17 ((
% 97.31/13.17 (dpsetconstrEL1) =>
% 97.31/13.17 ((
% 97.31/13.17 (dpsetconstrEL2) =>
% 97.31/13.17 ((
% 97.31/13.17 (dpsetconstrER) =>
% 97.31/13.17 ((
% 97.31/13.17 (funcImageSingleton) =>
% 97.31/13.17 ((
% 97.31/13.17 (apProp) =>
% 97.31/13.17 ((
% 97.31/13.17 (app) =>
% 97.31/13.17 ((
% 97.31/13.17 (infuncsetfunc) =>
% 97.31/13.17 ((
% 97.31/13.17 (ap2p) =>
% 97.31/13.17 ((
% 97.31/13.17 (funcinfuncset) =>
% 97.31/13.17 ((
% 97.31/13.17 (lamProp) =>
% 97.31/13.17 ((
% 97.31/13.17 (lamp) =>
% 97.31/13.17 ((
% 97.31/13.17 (lam2p) =>
% 97.31/13.17 ((
% 97.31/13.17 (brelnall1) =>
% 97.31/13.17 ((
% 97.31/13.17 (brelnall2) =>
% 97.31/13.17 ((
% 97.31/13.17 (ex1E2) =>
% 97.31/13.17 ((
% 97.31/13.17 (funcGraphProp1) =>
% 97.31/13.17 ((
% 97.31/13.17 (funcGraphProp3) =>
% 97.31/13.17 ((
% 97.31/13.17 (funcGraphProp2) =>
% 97.31/13.17 ((
% 97.31/13.17 (funcextLem) =>
% 97.31/13.17 ((
% 97.31/13.17 (funcGraphProp4) =>
% 97.31/13.17 ((
% 97.31/13.17 (subbreln) =>
% 97.31/13.17 ((
% 97.31/13.17 (eqbreln) =>
% 97.31/13.17 ((
% 97.31/13.17 (funcext) =>
% 97.31/13.17 ((
% 97.31/13.17 (funcext2) =>
% 97.31/13.17 ((
% 97.31/13.17 (ap2apEq1) =>
% 97.31/13.17 ((
% 97.31/13.17 (ap2apEq2) =>
% 97.31/13.17 ((
% 97.31/13.17 (beta1) =>
% 97.31/13.17 ((
% 97.31/13.17 (eta1) =>
% 97.31/13.17 ((
% 97.31/13.17 (lam2lamEq) =>
% 97.31/13.17 ((
% 97.31/13.17 (beta2) =>
% 97.31/13.17 ((
% 97.31/13.17 (eta2) =>
% 97.31/13.17 ((
% 97.31/13.17 (iffalseProp1) =>
% 97.31/13.17 ((
% 97.31/13.17 (iffalseProp2) =>
% 97.31/13.17 ((
% 97.31/13.17 (iftrueProp1) =>
% 97.31/13.17 ((
% 97.31/13.17 (iftrueProp2) =>
% 97.31/13.17 ((
% 97.31/13.17 (ifSingleton) =>
% 97.31/13.17 ((
% 97.31/13.17 (ifp) =>
% 97.31/13.17 ((
% 97.31/13.17 (theeq) =>
% 97.31/13.17 ((
% 97.31/13.17 (iftrue) =>
% 97.31/13.17 ((
% 97.31/13.17 (iffalse) =>
% 97.31/13.17 ((
% 97.31/13.17 (iftrueorfalse) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectT_lem) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionT_lem) =>
% 97.31/13.17 ((
% 97.31/13.17 (powersetT_lem) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusT_lem) =>
% 97.31/13.17 ((
% 97.31/13.17 (complementT_lem) =>
% 97.31/13.17 ((
% 97.31/13.17 (setextT) =>
% 97.31/13.17 ((
% 97.31/13.17 (subsetTI) =>
% 97.31/13.17 ((
% 97.31/13.17 (powersetTI1) =>
% 97.31/13.17 ((
% 97.31/13.17 (powersetTE1) =>
% 97.31/13.17 ((
% 97.31/13.17 (complementTI1) =>
% 97.31/13.17 ((
% 97.31/13.17 (complementTE1) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectTELcontra) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectTERcontra) =>
% 97.31/13.17 ((
% 97.31/13.17 (contrasubsetT) =>
% 97.31/13.17 ((
% 97.31/13.17 (contrasubsetT1) =>
% 97.31/13.17 ((
% 97.31/13.17 (contrasubsetT2) =>
% 97.31/13.17 ((
% 97.31/13.17 (contrasubsetT3) =>
% 97.31/13.17 ((
% 97.31/13.17 (doubleComplementI1) =>
% 97.31/13.17 ((
% 97.31/13.17 (doubleComplementE1) =>
% 97.31/13.17 ((
% 97.31/13.17 (doubleComplementSub1) =>
% 97.31/13.17 ((
% 97.31/13.17 (doubleComplementSub2) =>
% 97.31/13.17 ((
% 97.31/13.17 (doubleComplementEq) =>
% 97.31/13.17 ((
% 97.31/13.17 (complementTnotintersectT) =>
% 97.31/13.17 ((
% 97.31/13.17 (complementImpComplementIntersect) =>
% 97.31/13.17 ((
% 97.31/13.17 (complementSubsetComplementIntersect) =>
% 97.31/13.17 ((
% 97.31/13.17 (complementInPowersetComplementIntersect) =>
% 97.31/13.17 ((
% 97.31/13.17 (contraSubsetComplement) =>
% 97.31/13.17 ((
% 97.31/13.17 (complementTcontraSubset) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionTILcontra) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionTIRcontra) =>
% 97.31/13.17 ((
% 97.31/13.17 (inIntersectImpInUnion) =>
% 97.31/13.17 ((
% 97.31/13.17 (inIntersectImpInUnion2) =>
% 97.31/13.17 ((
% 97.31/13.17 (inIntersectImpInIntersectUnions) =>
% 97.31/13.17 ((
% 97.31/13.17 (intersectInPowersetIntersectUnions) =>
% 97.31/13.17 ((
% 97.31/13.17 (inComplementUnionImpNotIn1) =>
% 97.31/13.17 ((
% 97.31/13.17 (inComplementUnionImpInComplement1) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionTE) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionTEcontra) =>
% 97.31/13.17 ((
% 97.31/13.17 (demorgan2a1) =>
% 97.31/13.17 ((
% 97.31/13.17 (complementUnionInPowersetComplement) =>
% 97.31/13.17 ((
% 97.31/13.17 (demorgan2a2) =>
% 97.31/13.17 ((
% 97.31/13.17 (demorgan1a) =>
% 97.31/13.17 ((
% 97.31/13.17 (demorgan1b) =>
% 97.31/13.17 ((
% 97.31/13.17 (demorgan1) =>
% 97.31/13.17 ((
% 97.31/13.17 (demorgan2a) =>
% 97.31/13.17 ((
% 97.31/13.17 (demorgan2b2) =>
% 97.31/13.17 ((
% 97.31/13.17 (demorgan2b) =>
% 97.31/13.17 ((
% 97.31/13.17 (demorgan2) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz13rule0) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz13rule1) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz13rule2) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz13rule3) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz13rule4) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz1_1) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz1_2) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz1_3) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz1_4) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz1_5) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1all2) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1SetBreln1) =>
% 97.31/13.17 ((
% 97.31/13.17 (choice2fnsingleton) =>
% 97.31/13.17 ((
% 97.31/13.17 (setOfPairsIsBReln1) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1all1) =>
% 97.31/13.17 ((
% 97.31/13.17 (subbreln1) =>
% 97.31/13.17 ((
% 97.31/13.17 (eqbreln1) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1invprop) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1invI) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1invE) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1compprop) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1compI) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1compE) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1compEex) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1unionprop) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1unionIL) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1unionIR) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1unionI) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1unionE) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1unionEcases) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1unionCommutes) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz2Ex) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz2W) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz2A) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz2B) =>
% 97.31/13.17 ((
% 97.31/13.17 (image1Ex) =>
% 97.31/13.17 ((
% 97.31/13.17 (image1Ex1) =>
% 97.31/13.17 ((
% 97.31/13.17 (image1Equiv) =>
% 97.31/13.17 ((
% 97.31/13.17 (image1E) =>
% 97.31/13.17 ((
% 97.31/13.17 (image1I) =>
% 97.31/13.17 ((
% 97.31/13.17 (injFuncInInjFuncSet) =>
% 97.31/13.17 ((
% 97.31/13.17 (injFuncSetFuncIn) =>
% 97.31/13.17 ((
% 97.31/13.17 (injFuncSetFuncInj) =>
% 97.31/13.17 ((
% 97.31/13.17 (surjFuncSetFuncIn) =>
% 97.31/13.17 ((
% 97.31/13.17 (surjFuncSetFuncSurj) =>
% 97.31/13.17 ((
% 97.31/13.17 (leftInvIsSurj) =>
% 97.31/13.17 ((
% 97.31/13.17 (surjCantorThm) =>
% 97.31/13.17 ((
% 97.31/13.17 (foundation2) =>
% 97.31/13.17 ((
% 97.31/13.17 (notinself) =>
% 97.31/13.17 ((
% 97.31/13.17 (notinself2) =>
% 97.31/13.17 ((
% 97.31/13.17 (omegaSp) =>
% 97.31/13.17 ((
% 97.31/13.17 (omegaSclos) =>
% 97.31/13.17 ((
% 97.31/13.17 (peano0notS) =>
% 97.31/13.17 ((
% 97.31/13.17 (!!) @ (
% 97.31/13.17 (('#S') @ (
% 97.31/13.17 (
% 97.31/13.17 ('#B') @ (
% 97.31/13.17 =>) @
% 97.31/13.17 (
% 97.31/13.17 (
% 97.31/13.17 ('#C') @ in @
% 97.31/13.17 omega)))) @
% 97.31/13.17 (
% 97.31/13.17 (
% 97.31/13.17 ('#B') @ (
% 97.31/13.17 !!) @
% 97.31/13.17 (
% 97.31/13.17 (
% 97.31/13.17 ('#B') @ (
% 97.31/13.17 (
% 97.31/13.17 ('#S') @ (
% 97.31/13.17 (
% 97.31/13.17 ('#B') @ (
% 97.31/13.17 =>) @
% 97.31/13.17 (
% 97.31/13.17 (
% 97.31/13.17 ('#C') @ in @
% 97.31/13.17 omega)))))) @
% 97.31/13.17 (
% 97.31/13.17 (
% 97.31/13.17 ('#S') @ (
% 97.31/13.17 (
% 97.31/13.17 ('#B') @ (
% 97.31/13.17 '#S') @
% 97.31/13.17 (
% 97.31/13.17 (
% 97.31/13.17 ('#B') @ (
% 97.31/13.17 (
% 97.31/13.17 ('#B') @ (
% 97.31/13.17 =>))) @
% 97.31/13.17 (
% 97.31/13.17 (
% 97.31/13.17 ('#C') @ (
% 97.31/13.17 (
% 97.31/13.17 ('#B') @ (
% 97.31/13.17 '#B') @
% 97.31/13.17 (
% 97.31/13.17 (
% 97.31/13.17 ('#B') @ (
% 97.31/13.17 =) @
% 97.31/13.17 omegaS)))) @
% 97.31/13.17 omegaS)))))) @
% 97.31/13.17 (
% 97.31/13.17 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.31/13.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl307])).
% 97.31/13.17 thf(zip_derived_cl337, plain,
% 97.31/13.17 (~ (((setadjoinIR) =>
% 97.31/13.17 (((setadjoinE) =>
% 97.31/13.17 (((setadjoinOr) =>
% 97.31/13.17 (((setoftrueEq) =>
% 97.31/13.17 (((powersetI) =>
% 97.31/13.17 (((emptyinPowerset) =>
% 97.31/13.17 (((emptyInPowerset) =>
% 97.31/13.17 (((powersetE) =>
% 97.31/13.17 (((setunionI) =>
% 97.31/13.17 (((setunionE) =>
% 97.31/13.17 (((subPowSU) =>
% 97.31/13.17 (((exuE2) =>
% 97.31/13.17 (((nonemptyImpWitness) =>
% 97.31/13.17 (((uniqinunit) =>
% 97.31/13.17 (((notinsingleton) =>
% 97.31/13.17 (((eqinunit) =>
% 97.31/13.17 (((singletonsswitch) =>
% 97.31/13.17 (((upairsetE) =>
% 97.31/13.17 (((upairsetIL) =>
% 97.31/13.17 (((upairsetIR) =>
% 97.31/13.17 (((emptyE1) =>
% 97.31/13.17 (((vacuousDall) =>
% 97.31/13.17 (((quantDeMorgan1) =>
% 97.31/13.17 (((quantDeMorgan2) =>
% 97.31/13.17 (((quantDeMorgan3) =>
% 97.31/13.17 (((quantDeMorgan4) =>
% 97.31/13.17 (((prop2setI) =>
% 97.31/13.17 (((prop2set2propI) =>
% 97.31/13.17 (((notdexE) =>
% 97.31/13.17 (((notdallE) =>
% 97.31/13.17 ((
% 97.31/13.17 (exuI1) =>
% 97.31/13.17 ((
% 97.31/13.17 (exuI3) =>
% 97.31/13.17 ((
% 97.31/13.17 (exuI2) =>
% 97.31/13.17 ((
% 97.31/13.17 (inCongP) =>
% 97.31/13.17 ((
% 97.31/13.17 (in__Cong) =>
% 97.31/13.17 ((
% 97.31/13.17 (exuE3u) =>
% 97.31/13.17 ((
% 97.31/13.17 (exu__Cong) =>
% 97.31/13.17 ((
% 97.31/13.17 (setadjoin__Cong) =>
% 97.31/13.17 ((
% 97.31/13.17 (powerset__Cong) =>
% 97.31/13.17 ((
% 97.31/13.17 (setunion__Cong) =>
% 97.31/13.17 ((
% 97.31/13.17 (exuEu) =>
% 97.31/13.17 ((
% 97.31/13.17 (descr__Cong) =>
% 97.31/13.17 ((
% 97.31/13.17 (dsetconstr__Cong) =>
% 97.31/13.17 ((
% 97.31/13.17 (subsetI1) =>
% 97.31/13.17 ((
% 97.31/13.17 (eqimpsubset2) =>
% 97.31/13.17 ((
% 97.31/13.17 (eqimpsubset1) =>
% 97.31/13.17 ((
% 97.31/13.17 (subsetI2) =>
% 97.31/13.17 ((
% 97.31/13.17 (emptysetsubset) =>
% 97.31/13.17 ((
% 97.31/13.17 (subsetE) =>
% 97.31/13.17 ((
% 97.31/13.17 (subsetE2) =>
% 97.31/13.17 ((
% 97.31/13.17 (notsubsetI) =>
% 97.31/13.17 ((
% 97.31/13.17 (notequalI1) =>
% 97.31/13.17 ((
% 97.31/13.17 (notequalI2) =>
% 97.31/13.17 ((
% 97.31/13.17 (subsetRefl) =>
% 97.31/13.17 ((
% 97.31/13.17 (subsetTrans) =>
% 97.31/13.17 ((
% 97.31/13.17 (setadjoinSub) =>
% 97.31/13.17 ((
% 97.31/13.17 (setadjoinSub2) =>
% 97.31/13.17 ((
% 97.31/13.17 (subset2powerset) =>
% 97.31/13.17 ((
% 97.31/13.17 (setextsub) =>
% 97.31/13.17 ((
% 97.31/13.17 (subsetemptysetimpeq) =>
% 97.31/13.17 ((
% 97.31/13.17 (powersetI1) =>
% 97.31/13.17 ((
% 97.31/13.17 (powersetE1) =>
% 97.31/13.17 ((
% 97.31/13.17 (inPowerset) =>
% 97.31/13.17 ((
% 97.31/13.17 (powersetsubset) =>
% 97.31/13.17 ((
% 97.31/13.17 (sepInPowerset) =>
% 97.31/13.17 ((
% 97.31/13.17 (sepSubset) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionIL) =>
% 97.31/13.17 ((
% 97.31/13.17 (upairset2IR) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionIR) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionEcases) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionE) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionLsub) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionRsub) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectI) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectSubset5) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectEL) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectLsub) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectSubset2) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectSubset3) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectER) =>
% 97.31/13.17 ((
% 97.31/13.17 (disjointsetsI1) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectRsub) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectSubset4) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectSubset1) =>
% 97.31/13.17 ((
% 97.31/13.17 (bs114d) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusI) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusEL) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusER) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusSubset2) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusERneg) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusELneg) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusILneg) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusIRneg) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusLsub) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusSubset1) =>
% 97.31/13.17 ((
% 97.31/13.17 (symdiffE) =>
% 97.31/13.17 ((
% 97.31/13.17 (symdiffI1) =>
% 97.31/13.17 ((
% 97.31/13.17 (symdiffI2) =>
% 97.31/13.17 ((
% 97.31/13.17 (symdiffIneg1) =>
% 97.31/13.17 ((
% 97.31/13.17 (symdiffIneg2) =>
% 97.31/13.17 ((
% 97.31/13.17 (secondinupair) =>
% 97.31/13.17 ((
% 97.31/13.17 (setukpairIL) =>
% 97.31/13.17 ((
% 97.31/13.17 (setukpairIR) =>
% 97.31/13.17 ((
% 97.31/13.17 (kpairiskpair) =>
% 97.31/13.17 ((
% 97.31/13.17 (kpairp) =>
% 97.31/13.17 ((
% 97.31/13.17 (singletonsubset) =>
% 97.31/13.17 ((
% 97.31/13.17 (singletoninpowerset) =>
% 97.31/13.17 ((
% 97.31/13.17 (singletoninpowunion) =>
% 97.31/13.17 ((
% 97.31/13.17 (upairset2E) =>
% 97.31/13.17 ((
% 97.31/13.17 (upairsubunion) =>
% 97.31/13.17 ((
% 97.31/13.17 (upairinpowunion) =>
% 97.31/13.17 ((
% 97.31/13.17 (ubforcartprodlem1) =>
% 97.31/13.17 ((
% 97.31/13.17 (ubforcartprodlem2) =>
% 97.31/13.17 ((
% 97.31/13.17 (ubforcartprodlem3) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodpairin) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodmempair1) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodmempair) =>
% 97.31/13.17 ((
% 97.31/13.17 (setunionE2) =>
% 97.31/13.17 ((
% 97.31/13.17 (setunionsingleton1) =>
% 97.31/13.17 ((
% 97.31/13.17 (setunionsingleton2) =>
% 97.31/13.17 ((
% 97.31/13.17 (setunionsingleton) =>
% 97.31/13.17 ((
% 97.31/13.17 (singletonprop) =>
% 97.31/13.17 ((
% 97.31/13.17 (ex1E1) =>
% 97.31/13.17 ((
% 97.31/13.17 (ex1I) =>
% 97.31/13.17 ((
% 97.31/13.17 (ex1I2) =>
% 97.31/13.17 ((
% 97.31/13.17 (singletonsuniq) =>
% 97.31/13.17 ((
% 97.31/13.17 (setukpairinjL1) =>
% 97.31/13.17 ((
% 97.31/13.17 (kfstsingleton) =>
% 97.31/13.17 ((
% 97.31/13.17 (theprop) =>
% 97.31/13.17 ((
% 97.31/13.17 (kfstpairEq) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodfstin) =>
% 97.31/13.17 ((
% 97.31/13.17 (setukpairinjL2) =>
% 97.31/13.17 ((
% 97.31/13.17 (setukpairinjL) =>
% 97.31/13.17 ((
% 97.31/13.17 (setukpairinjR11) =>
% 97.31/13.17 ((
% 97.31/13.17 (setukpairinjR12) =>
% 97.31/13.17 ((
% 97.31/13.17 (setukpairinjR1) =>
% 97.31/13.17 ((
% 97.31/13.17 (upairequniteq) =>
% 97.31/13.17 ((
% 97.31/13.17 (setukpairinjR2) =>
% 97.31/13.17 ((
% 97.31/13.17 (setukpairinjR) =>
% 97.31/13.17 ((
% 97.31/13.17 (ksndsingleton) =>
% 97.31/13.17 ((
% 97.31/13.17 (ksndpairEq) =>
% 97.31/13.17 ((
% 97.31/13.17 (kpairsurjEq) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodsndin) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodpairmemEL) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodpairmemER) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodmempaircEq) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodfstpairEq) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodsndpairEq) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodpairsurjEq) =>
% 97.31/13.17 ((
% 97.31/13.17 (dpsetconstrI) =>
% 97.31/13.17 ((
% 97.31/13.17 (dpsetconstrSub) =>
% 97.31/13.17 ((
% 97.31/13.17 (setOfPairsIsBReln) =>
% 97.31/13.17 ((
% 97.31/13.17 (dpsetconstrERa) =>
% 97.31/13.17 ((
% 97.31/13.17 (dpsetconstrEL1) =>
% 97.31/13.17 ((
% 97.31/13.17 (dpsetconstrEL2) =>
% 97.31/13.17 ((
% 97.31/13.17 (dpsetconstrER) =>
% 97.31/13.17 ((
% 97.31/13.17 (funcImageSingleton) =>
% 97.31/13.17 ((
% 97.31/13.17 (apProp) =>
% 97.31/13.17 ((
% 97.31/13.17 (app) =>
% 97.31/13.17 ((
% 97.31/13.17 (infuncsetfunc) =>
% 97.31/13.17 ((
% 97.31/13.17 (ap2p) =>
% 97.31/13.17 ((
% 97.31/13.17 (funcinfuncset) =>
% 97.31/13.17 ((
% 97.31/13.17 (lamProp) =>
% 97.31/13.17 ((
% 97.31/13.17 (lamp) =>
% 97.31/13.17 ((
% 97.31/13.17 (lam2p) =>
% 97.31/13.17 ((
% 97.31/13.17 (brelnall1) =>
% 97.31/13.17 ((
% 97.31/13.17 (brelnall2) =>
% 97.31/13.17 ((
% 97.31/13.17 (ex1E2) =>
% 97.31/13.17 ((
% 97.31/13.17 (funcGraphProp1) =>
% 97.31/13.17 ((
% 97.31/13.17 (funcGraphProp3) =>
% 97.31/13.17 ((
% 97.31/13.17 (funcGraphProp2) =>
% 97.31/13.17 ((
% 97.31/13.17 (funcextLem) =>
% 97.31/13.17 ((
% 97.31/13.17 (funcGraphProp4) =>
% 97.31/13.17 ((
% 97.31/13.17 (subbreln) =>
% 97.31/13.17 ((
% 97.31/13.17 (eqbreln) =>
% 97.31/13.17 ((
% 97.31/13.17 (funcext) =>
% 97.31/13.17 ((
% 97.31/13.17 (funcext2) =>
% 97.31/13.17 ((
% 97.31/13.17 (ap2apEq1) =>
% 97.31/13.17 ((
% 97.31/13.17 (ap2apEq2) =>
% 97.31/13.17 ((
% 97.31/13.17 (beta1) =>
% 97.31/13.17 ((
% 97.31/13.17 (eta1) =>
% 97.31/13.17 ((
% 97.31/13.17 (lam2lamEq) =>
% 97.31/13.17 ((
% 97.31/13.17 (beta2) =>
% 97.31/13.17 ((
% 97.31/13.17 (eta2) =>
% 97.31/13.17 ((
% 97.31/13.17 (iffalseProp1) =>
% 97.31/13.17 ((
% 97.31/13.17 (iffalseProp2) =>
% 97.31/13.17 ((
% 97.31/13.17 (iftrueProp1) =>
% 97.31/13.17 ((
% 97.31/13.17 (iftrueProp2) =>
% 97.31/13.17 ((
% 97.31/13.17 (ifSingleton) =>
% 97.31/13.17 ((
% 97.31/13.17 (ifp) =>
% 97.31/13.17 ((
% 97.31/13.17 (theeq) =>
% 97.31/13.17 ((
% 97.31/13.17 (iftrue) =>
% 97.31/13.17 ((
% 97.31/13.17 (iffalse) =>
% 97.31/13.17 ((
% 97.31/13.17 (iftrueorfalse) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectT_lem) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionT_lem) =>
% 97.31/13.17 ((
% 97.31/13.17 (powersetT_lem) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusT_lem) =>
% 97.31/13.17 ((
% 97.31/13.17 (complementT_lem) =>
% 97.31/13.17 ((
% 97.31/13.17 (setextT) =>
% 97.31/13.17 ((
% 97.31/13.17 (subsetTI) =>
% 97.31/13.17 ((
% 97.31/13.17 (powersetTI1) =>
% 97.31/13.17 ((
% 97.31/13.17 (powersetTE1) =>
% 97.31/13.17 ((
% 97.31/13.17 (complementTI1) =>
% 97.31/13.17 ((
% 97.31/13.17 (complementTE1) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectTELcontra) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectTERcontra) =>
% 97.31/13.17 ((
% 97.31/13.17 (contrasubsetT) =>
% 97.31/13.17 ((
% 97.31/13.17 (contrasubsetT1) =>
% 97.31/13.17 ((
% 97.31/13.17 (contrasubsetT2) =>
% 97.31/13.17 ((
% 97.31/13.17 (contrasubsetT3) =>
% 97.31/13.17 ((
% 97.31/13.17 (doubleComplementI1) =>
% 97.31/13.17 ((
% 97.31/13.17 (doubleComplementE1) =>
% 97.31/13.17 ((
% 97.31/13.17 (doubleComplementSub1) =>
% 97.31/13.17 ((
% 97.31/13.17 (doubleComplementSub2) =>
% 97.31/13.17 ((
% 97.31/13.17 (doubleComplementEq) =>
% 97.31/13.17 ((
% 97.31/13.17 (complementTnotintersectT) =>
% 97.31/13.17 ((
% 97.31/13.17 (complementImpComplementIntersect) =>
% 97.31/13.17 ((
% 97.31/13.17 (complementSubsetComplementIntersect) =>
% 97.31/13.17 ((
% 97.31/13.17 (complementInPowersetComplementIntersect) =>
% 97.31/13.17 ((
% 97.31/13.17 (contraSubsetComplement) =>
% 97.31/13.17 ((
% 97.31/13.17 (complementTcontraSubset) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionTILcontra) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionTIRcontra) =>
% 97.31/13.17 ((
% 97.31/13.17 (inIntersectImpInUnion) =>
% 97.31/13.17 ((
% 97.31/13.17 (inIntersectImpInUnion2) =>
% 97.31/13.17 ((
% 97.31/13.17 (inIntersectImpInIntersectUnions) =>
% 97.31/13.17 ((
% 97.31/13.17 (intersectInPowersetIntersectUnions) =>
% 97.31/13.17 ((
% 97.31/13.17 (inComplementUnionImpNotIn1) =>
% 97.31/13.17 ((
% 97.31/13.17 (inComplementUnionImpInComplement1) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionTE) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionTEcontra) =>
% 97.31/13.17 ((
% 97.31/13.17 (demorgan2a1) =>
% 97.31/13.17 ((
% 97.31/13.17 (complementUnionInPowersetComplement) =>
% 97.31/13.17 ((
% 97.31/13.17 (demorgan2a2) =>
% 97.31/13.17 ((
% 97.31/13.17 (demorgan1a) =>
% 97.31/13.17 ((
% 97.31/13.17 (demorgan1b) =>
% 97.31/13.17 ((
% 97.31/13.17 (demorgan1) =>
% 97.31/13.17 ((
% 97.31/13.17 (demorgan2a) =>
% 97.31/13.17 ((
% 97.31/13.17 (demorgan2b2) =>
% 97.31/13.17 ((
% 97.31/13.17 (demorgan2b) =>
% 97.31/13.17 ((
% 97.31/13.17 (demorgan2) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz13rule0) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz13rule1) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz13rule2) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz13rule3) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz13rule4) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz1_1) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz1_2) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz1_3) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz1_4) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz1_5) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1all2) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1SetBreln1) =>
% 97.31/13.17 ((
% 97.31/13.17 (choice2fnsingleton) =>
% 97.31/13.17 ((
% 97.31/13.17 (setOfPairsIsBReln1) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1all1) =>
% 97.31/13.17 ((
% 97.31/13.17 (subbreln1) =>
% 97.31/13.17 ((
% 97.31/13.17 (eqbreln1) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1invprop) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1invI) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1invE) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1compprop) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1compI) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1compE) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1compEex) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1unionprop) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1unionIL) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1unionIR) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1unionI) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1unionE) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1unionEcases) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1unionCommutes) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz2Ex) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz2W) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz2A) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz2B) =>
% 97.31/13.17 ((
% 97.31/13.17 (image1Ex) =>
% 97.31/13.17 ((
% 97.31/13.17 (image1Ex1) =>
% 97.31/13.17 ((
% 97.31/13.17 (image1Equiv) =>
% 97.31/13.17 ((
% 97.31/13.17 (image1E) =>
% 97.31/13.17 ((
% 97.31/13.17 (image1I) =>
% 97.31/13.17 ((
% 97.31/13.17 (injFuncInInjFuncSet) =>
% 97.31/13.17 ((
% 97.31/13.17 (injFuncSetFuncIn) =>
% 97.31/13.17 ((
% 97.31/13.17 (injFuncSetFuncInj) =>
% 97.31/13.17 ((
% 97.31/13.17 (surjFuncSetFuncIn) =>
% 97.31/13.17 ((
% 97.31/13.17 (surjFuncSetFuncSurj) =>
% 97.31/13.17 ((
% 97.31/13.17 (leftInvIsSurj) =>
% 97.31/13.17 ((
% 97.31/13.17 (surjCantorThm) =>
% 97.31/13.17 ((
% 97.31/13.17 (foundation2) =>
% 97.31/13.17 ((
% 97.31/13.17 (notinself) =>
% 97.31/13.17 ((
% 97.31/13.17 (notinself2) =>
% 97.31/13.17 ((
% 97.31/13.17 (omegaSp) =>
% 97.31/13.17 ((
% 97.31/13.17 (omegaSclos) =>
% 97.31/13.17 ((
% 97.31/13.17 (peano0notS) =>
% 97.31/13.17 ((
% 97.31/13.17 (!!) @ (
% 97.31/13.17 (('#S') @ (
% 97.31/13.17 (
% 97.31/13.17 ('#B') @ (
% 97.31/13.17 =>) @
% 97.31/13.17 (
% 97.31/13.17 (
% 97.31/13.17 ('#C') @ in @
% 97.31/13.17 omega)))) @
% 97.31/13.17 (
% 97.31/13.17 (
% 97.31/13.17 ('#B') @ (
% 97.31/13.17 !!) @
% 97.31/13.17 (
% 97.31/13.17 (
% 97.31/13.17 ('#B') @ (
% 97.31/13.17 (
% 97.31/13.17 ('#S') @ (
% 97.31/13.17 (
% 97.31/13.17 ('#B') @ (
% 97.31/13.17 =>) @
% 97.31/13.17 (
% 97.31/13.17 (
% 97.31/13.17 ('#C') @ in @
% 97.31/13.17 omega)))))) @
% 97.31/13.17 (
% 97.31/13.17 (
% 97.31/13.17 ('#S') @ (
% 97.31/13.17 (
% 97.31/13.17 ('#B') @ (
% 97.31/13.17 '#S') @
% 97.31/13.17 (
% 97.31/13.17 (
% 97.31/13.17 ('#B') @ (
% 97.31/13.17 (
% 97.31/13.17 ('#B') @ (
% 97.31/13.17 =>))) @
% 97.31/13.17 (
% 97.31/13.17 (
% 97.31/13.17 ('#C') @ (
% 97.31/13.17 (
% 97.31/13.17 ('#B') @ (
% 97.31/13.17 '#B') @
% 97.31/13.17 (
% 97.31/13.17 (
% 97.31/13.17 ('#B') @ (
% 97.31/13.17 =) @
% 97.31/13.17 omegaS)))) @
% 97.31/13.17 omegaS)))))) @
% 97.31/13.17 (
% 97.31/13.17 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.31/13.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl322])).
% 97.31/13.17 thf(zip_derived_cl349, plain,
% 97.31/13.17 (~ (((setadjoinE) =>
% 97.31/13.17 (((setadjoinOr) =>
% 97.31/13.17 (((setoftrueEq) =>
% 97.31/13.17 (((powersetI) =>
% 97.31/13.17 (((emptyinPowerset) =>
% 97.31/13.17 (((emptyInPowerset) =>
% 97.31/13.17 (((powersetE) =>
% 97.31/13.17 (((setunionI) =>
% 97.31/13.17 (((setunionE) =>
% 97.31/13.17 (((subPowSU) =>
% 97.31/13.17 (((exuE2) =>
% 97.31/13.17 (((nonemptyImpWitness) =>
% 97.31/13.17 (((uniqinunit) =>
% 97.31/13.17 (((notinsingleton) =>
% 97.31/13.17 (((eqinunit) =>
% 97.31/13.17 (((singletonsswitch) =>
% 97.31/13.17 (((upairsetE) =>
% 97.31/13.17 (((upairsetIL) =>
% 97.31/13.17 (((upairsetIR) =>
% 97.31/13.17 (((emptyE1) =>
% 97.31/13.17 (((vacuousDall) =>
% 97.31/13.17 (((quantDeMorgan1) =>
% 97.31/13.17 (((quantDeMorgan2) =>
% 97.31/13.17 (((quantDeMorgan3) =>
% 97.31/13.17 (((quantDeMorgan4) =>
% 97.31/13.17 (((prop2setI) =>
% 97.31/13.17 (((prop2set2propI) =>
% 97.31/13.17 (((notdexE) =>
% 97.31/13.17 (((notdallE) =>
% 97.31/13.17 (((exuI1) =>
% 97.31/13.17 ((
% 97.31/13.17 (exuI3) =>
% 97.31/13.17 ((
% 97.31/13.17 (exuI2) =>
% 97.31/13.17 ((
% 97.31/13.17 (inCongP) =>
% 97.31/13.17 ((
% 97.31/13.17 (in__Cong) =>
% 97.31/13.17 ((
% 97.31/13.17 (exuE3u) =>
% 97.31/13.17 ((
% 97.31/13.17 (exu__Cong) =>
% 97.31/13.17 ((
% 97.31/13.17 (setadjoin__Cong) =>
% 97.31/13.17 ((
% 97.31/13.17 (powerset__Cong) =>
% 97.31/13.17 ((
% 97.31/13.17 (setunion__Cong) =>
% 97.31/13.17 ((
% 97.31/13.17 (exuEu) =>
% 97.31/13.17 ((
% 97.31/13.17 (descr__Cong) =>
% 97.31/13.17 ((
% 97.31/13.17 (dsetconstr__Cong) =>
% 97.31/13.17 ((
% 97.31/13.17 (subsetI1) =>
% 97.31/13.17 ((
% 97.31/13.17 (eqimpsubset2) =>
% 97.31/13.17 ((
% 97.31/13.17 (eqimpsubset1) =>
% 97.31/13.17 ((
% 97.31/13.17 (subsetI2) =>
% 97.31/13.17 ((
% 97.31/13.17 (emptysetsubset) =>
% 97.31/13.17 ((
% 97.31/13.17 (subsetE) =>
% 97.31/13.17 ((
% 97.31/13.17 (subsetE2) =>
% 97.31/13.17 ((
% 97.31/13.17 (notsubsetI) =>
% 97.31/13.17 ((
% 97.31/13.17 (notequalI1) =>
% 97.31/13.17 ((
% 97.31/13.17 (notequalI2) =>
% 97.31/13.17 ((
% 97.31/13.17 (subsetRefl) =>
% 97.31/13.17 ((
% 97.31/13.17 (subsetTrans) =>
% 97.31/13.17 ((
% 97.31/13.17 (setadjoinSub) =>
% 97.31/13.17 ((
% 97.31/13.17 (setadjoinSub2) =>
% 97.31/13.17 ((
% 97.31/13.17 (subset2powerset) =>
% 97.31/13.17 ((
% 97.31/13.17 (setextsub) =>
% 97.31/13.17 ((
% 97.31/13.17 (subsetemptysetimpeq) =>
% 97.31/13.17 ((
% 97.31/13.17 (powersetI1) =>
% 97.31/13.17 ((
% 97.31/13.17 (powersetE1) =>
% 97.31/13.17 ((
% 97.31/13.17 (inPowerset) =>
% 97.31/13.17 ((
% 97.31/13.17 (powersetsubset) =>
% 97.31/13.17 ((
% 97.31/13.17 (sepInPowerset) =>
% 97.31/13.17 ((
% 97.31/13.17 (sepSubset) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionIL) =>
% 97.31/13.17 ((
% 97.31/13.17 (upairset2IR) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionIR) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionEcases) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionE) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionLsub) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionRsub) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectI) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectSubset5) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectEL) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectLsub) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectSubset2) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectSubset3) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectER) =>
% 97.31/13.17 ((
% 97.31/13.17 (disjointsetsI1) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectRsub) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectSubset4) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectSubset1) =>
% 97.31/13.17 ((
% 97.31/13.17 (bs114d) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusI) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusEL) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusER) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusSubset2) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusERneg) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusELneg) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusILneg) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusIRneg) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusLsub) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusSubset1) =>
% 97.31/13.17 ((
% 97.31/13.17 (symdiffE) =>
% 97.31/13.17 ((
% 97.31/13.17 (symdiffI1) =>
% 97.31/13.17 ((
% 97.31/13.17 (symdiffI2) =>
% 97.31/13.17 ((
% 97.31/13.17 (symdiffIneg1) =>
% 97.31/13.17 ((
% 97.31/13.17 (symdiffIneg2) =>
% 97.31/13.17 ((
% 97.31/13.17 (secondinupair) =>
% 97.31/13.17 ((
% 97.31/13.17 (setukpairIL) =>
% 97.31/13.17 ((
% 97.31/13.17 (setukpairIR) =>
% 97.31/13.17 ((
% 97.31/13.17 (kpairiskpair) =>
% 97.31/13.17 ((
% 97.31/13.17 (kpairp) =>
% 97.31/13.17 ((
% 97.31/13.17 (singletonsubset) =>
% 97.31/13.17 ((
% 97.31/13.17 (singletoninpowerset) =>
% 97.31/13.17 ((
% 97.31/13.17 (singletoninpowunion) =>
% 97.31/13.17 ((
% 97.31/13.17 (upairset2E) =>
% 97.31/13.17 ((
% 97.31/13.17 (upairsubunion) =>
% 97.31/13.17 ((
% 97.31/13.17 (upairinpowunion) =>
% 97.31/13.17 ((
% 97.31/13.17 (ubforcartprodlem1) =>
% 97.31/13.17 ((
% 97.31/13.17 (ubforcartprodlem2) =>
% 97.31/13.17 ((
% 97.31/13.17 (ubforcartprodlem3) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodpairin) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodmempair1) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodmempair) =>
% 97.31/13.17 ((
% 97.31/13.17 (setunionE2) =>
% 97.31/13.17 ((
% 97.31/13.17 (setunionsingleton1) =>
% 97.31/13.17 ((
% 97.31/13.17 (setunionsingleton2) =>
% 97.31/13.17 ((
% 97.31/13.17 (setunionsingleton) =>
% 97.31/13.17 ((
% 97.31/13.17 (singletonprop) =>
% 97.31/13.17 ((
% 97.31/13.17 (ex1E1) =>
% 97.31/13.17 ((
% 97.31/13.17 (ex1I) =>
% 97.31/13.17 ((
% 97.31/13.17 (ex1I2) =>
% 97.31/13.17 ((
% 97.31/13.17 (singletonsuniq) =>
% 97.31/13.17 ((
% 97.31/13.17 (setukpairinjL1) =>
% 97.31/13.17 ((
% 97.31/13.17 (kfstsingleton) =>
% 97.31/13.17 ((
% 97.31/13.17 (theprop) =>
% 97.31/13.17 ((
% 97.31/13.17 (kfstpairEq) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodfstin) =>
% 97.31/13.17 ((
% 97.31/13.17 (setukpairinjL2) =>
% 97.31/13.17 ((
% 97.31/13.17 (setukpairinjL) =>
% 97.31/13.17 ((
% 97.31/13.17 (setukpairinjR11) =>
% 97.31/13.17 ((
% 97.31/13.17 (setukpairinjR12) =>
% 97.31/13.17 ((
% 97.31/13.17 (setukpairinjR1) =>
% 97.31/13.17 ((
% 97.31/13.17 (upairequniteq) =>
% 97.31/13.17 ((
% 97.31/13.17 (setukpairinjR2) =>
% 97.31/13.17 ((
% 97.31/13.17 (setukpairinjR) =>
% 97.31/13.17 ((
% 97.31/13.17 (ksndsingleton) =>
% 97.31/13.17 ((
% 97.31/13.17 (ksndpairEq) =>
% 97.31/13.17 ((
% 97.31/13.17 (kpairsurjEq) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodsndin) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodpairmemEL) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodpairmemER) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodmempaircEq) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodfstpairEq) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodsndpairEq) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodpairsurjEq) =>
% 97.31/13.17 ((
% 97.31/13.17 (dpsetconstrI) =>
% 97.31/13.17 ((
% 97.31/13.17 (dpsetconstrSub) =>
% 97.31/13.17 ((
% 97.31/13.17 (setOfPairsIsBReln) =>
% 97.31/13.17 ((
% 97.31/13.17 (dpsetconstrERa) =>
% 97.31/13.17 ((
% 97.31/13.17 (dpsetconstrEL1) =>
% 97.31/13.17 ((
% 97.31/13.17 (dpsetconstrEL2) =>
% 97.31/13.17 ((
% 97.31/13.17 (dpsetconstrER) =>
% 97.31/13.17 ((
% 97.31/13.17 (funcImageSingleton) =>
% 97.31/13.17 ((
% 97.31/13.17 (apProp) =>
% 97.31/13.17 ((
% 97.31/13.17 (app) =>
% 97.31/13.17 ((
% 97.31/13.17 (infuncsetfunc) =>
% 97.31/13.17 ((
% 97.31/13.17 (ap2p) =>
% 97.31/13.17 ((
% 97.31/13.17 (funcinfuncset) =>
% 97.31/13.17 ((
% 97.31/13.17 (lamProp) =>
% 97.31/13.17 ((
% 97.31/13.17 (lamp) =>
% 97.31/13.17 ((
% 97.31/13.17 (lam2p) =>
% 97.31/13.17 ((
% 97.31/13.17 (brelnall1) =>
% 97.31/13.17 ((
% 97.31/13.17 (brelnall2) =>
% 97.31/13.17 ((
% 97.31/13.17 (ex1E2) =>
% 97.31/13.17 ((
% 97.31/13.17 (funcGraphProp1) =>
% 97.31/13.17 ((
% 97.31/13.17 (funcGraphProp3) =>
% 97.31/13.17 ((
% 97.31/13.17 (funcGraphProp2) =>
% 97.31/13.17 ((
% 97.31/13.17 (funcextLem) =>
% 97.31/13.17 ((
% 97.31/13.17 (funcGraphProp4) =>
% 97.31/13.17 ((
% 97.31/13.17 (subbreln) =>
% 97.31/13.17 ((
% 97.31/13.17 (eqbreln) =>
% 97.31/13.17 ((
% 97.31/13.17 (funcext) =>
% 97.31/13.17 ((
% 97.31/13.17 (funcext2) =>
% 97.31/13.17 ((
% 97.31/13.17 (ap2apEq1) =>
% 97.31/13.17 ((
% 97.31/13.17 (ap2apEq2) =>
% 97.31/13.17 ((
% 97.31/13.17 (beta1) =>
% 97.31/13.17 ((
% 97.31/13.17 (eta1) =>
% 97.31/13.17 ((
% 97.31/13.17 (lam2lamEq) =>
% 97.31/13.17 ((
% 97.31/13.17 (beta2) =>
% 97.31/13.17 ((
% 97.31/13.17 (eta2) =>
% 97.31/13.17 ((
% 97.31/13.17 (iffalseProp1) =>
% 97.31/13.17 ((
% 97.31/13.17 (iffalseProp2) =>
% 97.31/13.17 ((
% 97.31/13.17 (iftrueProp1) =>
% 97.31/13.17 ((
% 97.31/13.17 (iftrueProp2) =>
% 97.31/13.17 ((
% 97.31/13.17 (ifSingleton) =>
% 97.31/13.17 ((
% 97.31/13.17 (ifp) =>
% 97.31/13.17 ((
% 97.31/13.17 (theeq) =>
% 97.31/13.17 ((
% 97.31/13.17 (iftrue) =>
% 97.31/13.17 ((
% 97.31/13.17 (iffalse) =>
% 97.31/13.17 ((
% 97.31/13.17 (iftrueorfalse) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectT_lem) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionT_lem) =>
% 97.31/13.17 ((
% 97.31/13.17 (powersetT_lem) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusT_lem) =>
% 97.31/13.17 ((
% 97.31/13.17 (complementT_lem) =>
% 97.31/13.17 ((
% 97.31/13.17 (setextT) =>
% 97.31/13.17 ((
% 97.31/13.17 (subsetTI) =>
% 97.31/13.17 ((
% 97.31/13.17 (powersetTI1) =>
% 97.31/13.17 ((
% 97.31/13.17 (powersetTE1) =>
% 97.31/13.17 ((
% 97.31/13.17 (complementTI1) =>
% 97.31/13.17 ((
% 97.31/13.17 (complementTE1) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectTELcontra) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectTERcontra) =>
% 97.31/13.17 ((
% 97.31/13.17 (contrasubsetT) =>
% 97.31/13.17 ((
% 97.31/13.17 (contrasubsetT1) =>
% 97.31/13.17 ((
% 97.31/13.17 (contrasubsetT2) =>
% 97.31/13.17 ((
% 97.31/13.17 (contrasubsetT3) =>
% 97.31/13.17 ((
% 97.31/13.17 (doubleComplementI1) =>
% 97.31/13.17 ((
% 97.31/13.17 (doubleComplementE1) =>
% 97.31/13.17 ((
% 97.31/13.17 (doubleComplementSub1) =>
% 97.31/13.17 ((
% 97.31/13.17 (doubleComplementSub2) =>
% 97.31/13.17 ((
% 97.31/13.17 (doubleComplementEq) =>
% 97.31/13.17 ((
% 97.31/13.17 (complementTnotintersectT) =>
% 97.31/13.17 ((
% 97.31/13.17 (complementImpComplementIntersect) =>
% 97.31/13.17 ((
% 97.31/13.17 (complementSubsetComplementIntersect) =>
% 97.31/13.17 ((
% 97.31/13.17 (complementInPowersetComplementIntersect) =>
% 97.31/13.17 ((
% 97.31/13.17 (contraSubsetComplement) =>
% 97.31/13.17 ((
% 97.31/13.17 (complementTcontraSubset) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionTILcontra) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionTIRcontra) =>
% 97.31/13.17 ((
% 97.31/13.17 (inIntersectImpInUnion) =>
% 97.31/13.17 ((
% 97.31/13.17 (inIntersectImpInUnion2) =>
% 97.31/13.17 ((
% 97.31/13.17 (inIntersectImpInIntersectUnions) =>
% 97.31/13.17 ((
% 97.31/13.17 (intersectInPowersetIntersectUnions) =>
% 97.31/13.17 ((
% 97.31/13.17 (inComplementUnionImpNotIn1) =>
% 97.31/13.17 ((
% 97.31/13.17 (inComplementUnionImpInComplement1) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionTE) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionTEcontra) =>
% 97.31/13.17 ((
% 97.31/13.17 (demorgan2a1) =>
% 97.31/13.17 ((
% 97.31/13.17 (complementUnionInPowersetComplement) =>
% 97.31/13.17 ((
% 97.31/13.17 (demorgan2a2) =>
% 97.31/13.17 ((
% 97.31/13.17 (demorgan1a) =>
% 97.31/13.17 ((
% 97.31/13.17 (demorgan1b) =>
% 97.31/13.17 ((
% 97.31/13.17 (demorgan1) =>
% 97.31/13.17 ((
% 97.31/13.17 (demorgan2a) =>
% 97.31/13.17 ((
% 97.31/13.17 (demorgan2b2) =>
% 97.31/13.17 ((
% 97.31/13.17 (demorgan2b) =>
% 97.31/13.17 ((
% 97.31/13.17 (demorgan2) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz13rule0) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz13rule1) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz13rule2) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz13rule3) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz13rule4) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz1_1) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz1_2) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz1_3) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz1_4) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz1_5) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1all2) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1SetBreln1) =>
% 97.31/13.17 ((
% 97.31/13.17 (choice2fnsingleton) =>
% 97.31/13.17 ((
% 97.31/13.17 (setOfPairsIsBReln1) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1all1) =>
% 97.31/13.17 ((
% 97.31/13.17 (subbreln1) =>
% 97.31/13.17 ((
% 97.31/13.17 (eqbreln1) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1invprop) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1invI) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1invE) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1compprop) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1compI) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1compE) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1compEex) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1unionprop) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1unionIL) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1unionIR) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1unionI) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1unionE) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1unionEcases) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1unionCommutes) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz2Ex) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz2W) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz2A) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz2B) =>
% 97.31/13.17 ((
% 97.31/13.17 (image1Ex) =>
% 97.31/13.17 ((
% 97.31/13.17 (image1Ex1) =>
% 97.31/13.17 ((
% 97.31/13.17 (image1Equiv) =>
% 97.31/13.17 ((
% 97.31/13.17 (image1E) =>
% 97.31/13.17 ((
% 97.31/13.17 (image1I) =>
% 97.31/13.17 ((
% 97.31/13.17 (injFuncInInjFuncSet) =>
% 97.31/13.17 ((
% 97.31/13.17 (injFuncSetFuncIn) =>
% 97.31/13.17 ((
% 97.31/13.17 (injFuncSetFuncInj) =>
% 97.31/13.17 ((
% 97.31/13.17 (surjFuncSetFuncIn) =>
% 97.31/13.17 ((
% 97.31/13.17 (surjFuncSetFuncSurj) =>
% 97.31/13.17 ((
% 97.31/13.17 (leftInvIsSurj) =>
% 97.31/13.17 ((
% 97.31/13.17 (surjCantorThm) =>
% 97.31/13.17 ((
% 97.31/13.17 (foundation2) =>
% 97.31/13.17 ((
% 97.31/13.17 (notinself) =>
% 97.31/13.17 ((
% 97.31/13.17 (notinself2) =>
% 97.31/13.17 ((
% 97.31/13.17 (omegaSp) =>
% 97.31/13.17 ((
% 97.31/13.17 (omegaSclos) =>
% 97.31/13.17 ((
% 97.31/13.17 (peano0notS) =>
% 97.31/13.17 ((
% 97.31/13.17 (!!) @ (
% 97.31/13.17 (('#S') @ (
% 97.31/13.17 (
% 97.31/13.17 ('#B') @ (
% 97.31/13.17 =>) @
% 97.31/13.17 (
% 97.31/13.17 (
% 97.31/13.17 ('#C') @ in @
% 97.31/13.17 omega)))) @
% 97.31/13.17 (
% 97.31/13.17 (
% 97.31/13.17 ('#B') @ (
% 97.31/13.17 !!) @
% 97.31/13.17 (
% 97.31/13.17 (
% 97.31/13.17 ('#B') @ (
% 97.31/13.17 (
% 97.31/13.17 ('#S') @ (
% 97.31/13.17 (
% 97.31/13.17 ('#B') @ (
% 97.31/13.17 =>) @
% 97.31/13.17 (
% 97.31/13.17 (
% 97.31/13.17 ('#C') @ in @
% 97.31/13.17 omega)))))) @
% 97.31/13.17 (
% 97.31/13.17 (
% 97.31/13.17 ('#S') @ (
% 97.31/13.17 (
% 97.31/13.17 ('#B') @ (
% 97.31/13.17 '#S') @
% 97.31/13.17 (
% 97.31/13.17 (
% 97.31/13.17 ('#B') @ (
% 97.31/13.17 (
% 97.31/13.17 ('#B') @ (
% 97.31/13.17 =>))) @
% 97.31/13.17 (
% 97.31/13.17 (
% 97.31/13.17 ('#C') @ (
% 97.31/13.17 (
% 97.31/13.17 ('#B') @ (
% 97.31/13.17 '#B') @
% 97.31/13.17 (
% 97.31/13.17 (
% 97.31/13.17 ('#B') @ (
% 97.31/13.17 =) @
% 97.31/13.17 omegaS)))) @
% 97.31/13.17 omegaS)))))) @
% 97.31/13.17 (
% 97.31/13.17 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.31/13.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl337])).
% 97.31/13.17 thf(zip_derived_cl355, plain,
% 97.31/13.17 (~ (((setadjoinOr) =>
% 97.31/13.17 (((setoftrueEq) =>
% 97.31/13.17 (((powersetI) =>
% 97.31/13.17 (((emptyinPowerset) =>
% 97.31/13.17 (((emptyInPowerset) =>
% 97.31/13.17 (((powersetE) =>
% 97.31/13.17 (((setunionI) =>
% 97.31/13.17 (((setunionE) =>
% 97.31/13.17 (((subPowSU) =>
% 97.31/13.17 (((exuE2) =>
% 97.31/13.17 (((nonemptyImpWitness) =>
% 97.31/13.17 (((uniqinunit) =>
% 97.31/13.17 (((notinsingleton) =>
% 97.31/13.17 (((eqinunit) =>
% 97.31/13.17 (((singletonsswitch) =>
% 97.31/13.17 (((upairsetE) =>
% 97.31/13.17 (((upairsetIL) =>
% 97.31/13.17 (((upairsetIR) =>
% 97.31/13.17 (((emptyE1) =>
% 97.31/13.17 (((vacuousDall) =>
% 97.31/13.17 (((quantDeMorgan1) =>
% 97.31/13.17 (((quantDeMorgan2) =>
% 97.31/13.17 (((quantDeMorgan3) =>
% 97.31/13.17 (((quantDeMorgan4) =>
% 97.31/13.17 (((prop2setI) =>
% 97.31/13.17 (((prop2set2propI) =>
% 97.31/13.17 (((notdexE) =>
% 97.31/13.17 (((notdallE) =>
% 97.31/13.17 (((exuI1) =>
% 97.31/13.17 (((exuI3) =>
% 97.31/13.17 ((
% 97.31/13.17 (exuI2) =>
% 97.31/13.17 ((
% 97.31/13.17 (inCongP) =>
% 97.31/13.17 ((
% 97.31/13.17 (in__Cong) =>
% 97.31/13.17 ((
% 97.31/13.17 (exuE3u) =>
% 97.31/13.17 ((
% 97.31/13.17 (exu__Cong) =>
% 97.31/13.17 ((
% 97.31/13.17 (setadjoin__Cong) =>
% 97.31/13.17 ((
% 97.31/13.17 (powerset__Cong) =>
% 97.31/13.17 ((
% 97.31/13.17 (setunion__Cong) =>
% 97.31/13.17 ((
% 97.31/13.17 (exuEu) =>
% 97.31/13.17 ((
% 97.31/13.17 (descr__Cong) =>
% 97.31/13.17 ((
% 97.31/13.17 (dsetconstr__Cong) =>
% 97.31/13.17 ((
% 97.31/13.17 (subsetI1) =>
% 97.31/13.17 ((
% 97.31/13.17 (eqimpsubset2) =>
% 97.31/13.17 ((
% 97.31/13.17 (eqimpsubset1) =>
% 97.31/13.17 ((
% 97.31/13.17 (subsetI2) =>
% 97.31/13.17 ((
% 97.31/13.17 (emptysetsubset) =>
% 97.31/13.17 ((
% 97.31/13.17 (subsetE) =>
% 97.31/13.17 ((
% 97.31/13.17 (subsetE2) =>
% 97.31/13.17 ((
% 97.31/13.17 (notsubsetI) =>
% 97.31/13.17 ((
% 97.31/13.17 (notequalI1) =>
% 97.31/13.17 ((
% 97.31/13.17 (notequalI2) =>
% 97.31/13.17 ((
% 97.31/13.17 (subsetRefl) =>
% 97.31/13.17 ((
% 97.31/13.17 (subsetTrans) =>
% 97.31/13.17 ((
% 97.31/13.17 (setadjoinSub) =>
% 97.31/13.17 ((
% 97.31/13.17 (setadjoinSub2) =>
% 97.31/13.17 ((
% 97.31/13.17 (subset2powerset) =>
% 97.31/13.17 ((
% 97.31/13.17 (setextsub) =>
% 97.31/13.17 ((
% 97.31/13.17 (subsetemptysetimpeq) =>
% 97.31/13.17 ((
% 97.31/13.17 (powersetI1) =>
% 97.31/13.17 ((
% 97.31/13.17 (powersetE1) =>
% 97.31/13.17 ((
% 97.31/13.17 (inPowerset) =>
% 97.31/13.17 ((
% 97.31/13.17 (powersetsubset) =>
% 97.31/13.17 ((
% 97.31/13.17 (sepInPowerset) =>
% 97.31/13.17 ((
% 97.31/13.17 (sepSubset) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionIL) =>
% 97.31/13.17 ((
% 97.31/13.17 (upairset2IR) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionIR) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionEcases) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionE) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionLsub) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionRsub) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectI) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectSubset5) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectEL) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectLsub) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectSubset2) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectSubset3) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectER) =>
% 97.31/13.17 ((
% 97.31/13.17 (disjointsetsI1) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectRsub) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectSubset4) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectSubset1) =>
% 97.31/13.17 ((
% 97.31/13.17 (bs114d) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusI) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusEL) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusER) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusSubset2) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusERneg) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusELneg) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusILneg) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusIRneg) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusLsub) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusSubset1) =>
% 97.31/13.17 ((
% 97.31/13.17 (symdiffE) =>
% 97.31/13.17 ((
% 97.31/13.17 (symdiffI1) =>
% 97.31/13.17 ((
% 97.31/13.17 (symdiffI2) =>
% 97.31/13.17 ((
% 97.31/13.17 (symdiffIneg1) =>
% 97.31/13.17 ((
% 97.31/13.17 (symdiffIneg2) =>
% 97.31/13.17 ((
% 97.31/13.17 (secondinupair) =>
% 97.31/13.17 ((
% 97.31/13.17 (setukpairIL) =>
% 97.31/13.17 ((
% 97.31/13.17 (setukpairIR) =>
% 97.31/13.17 ((
% 97.31/13.17 (kpairiskpair) =>
% 97.31/13.17 ((
% 97.31/13.17 (kpairp) =>
% 97.31/13.17 ((
% 97.31/13.17 (singletonsubset) =>
% 97.31/13.17 ((
% 97.31/13.17 (singletoninpowerset) =>
% 97.31/13.17 ((
% 97.31/13.17 (singletoninpowunion) =>
% 97.31/13.17 ((
% 97.31/13.17 (upairset2E) =>
% 97.31/13.17 ((
% 97.31/13.17 (upairsubunion) =>
% 97.31/13.17 ((
% 97.31/13.17 (upairinpowunion) =>
% 97.31/13.17 ((
% 97.31/13.17 (ubforcartprodlem1) =>
% 97.31/13.17 ((
% 97.31/13.17 (ubforcartprodlem2) =>
% 97.31/13.17 ((
% 97.31/13.17 (ubforcartprodlem3) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodpairin) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodmempair1) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodmempair) =>
% 97.31/13.17 ((
% 97.31/13.17 (setunionE2) =>
% 97.31/13.17 ((
% 97.31/13.17 (setunionsingleton1) =>
% 97.31/13.17 ((
% 97.31/13.17 (setunionsingleton2) =>
% 97.31/13.17 ((
% 97.31/13.17 (setunionsingleton) =>
% 97.31/13.17 ((
% 97.31/13.17 (singletonprop) =>
% 97.31/13.17 ((
% 97.31/13.17 (ex1E1) =>
% 97.31/13.17 ((
% 97.31/13.17 (ex1I) =>
% 97.31/13.17 ((
% 97.31/13.17 (ex1I2) =>
% 97.31/13.17 ((
% 97.31/13.17 (singletonsuniq) =>
% 97.31/13.17 ((
% 97.31/13.17 (setukpairinjL1) =>
% 97.31/13.17 ((
% 97.31/13.17 (kfstsingleton) =>
% 97.31/13.17 ((
% 97.31/13.17 (theprop) =>
% 97.31/13.17 ((
% 97.31/13.17 (kfstpairEq) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodfstin) =>
% 97.31/13.17 ((
% 97.31/13.17 (setukpairinjL2) =>
% 97.31/13.17 ((
% 97.31/13.17 (setukpairinjL) =>
% 97.31/13.17 ((
% 97.31/13.17 (setukpairinjR11) =>
% 97.31/13.17 ((
% 97.31/13.17 (setukpairinjR12) =>
% 97.31/13.17 ((
% 97.31/13.17 (setukpairinjR1) =>
% 97.31/13.17 ((
% 97.31/13.17 (upairequniteq) =>
% 97.31/13.17 ((
% 97.31/13.17 (setukpairinjR2) =>
% 97.31/13.17 ((
% 97.31/13.17 (setukpairinjR) =>
% 97.31/13.17 ((
% 97.31/13.17 (ksndsingleton) =>
% 97.31/13.17 ((
% 97.31/13.17 (ksndpairEq) =>
% 97.31/13.17 ((
% 97.31/13.17 (kpairsurjEq) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodsndin) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodpairmemEL) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodpairmemER) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodmempaircEq) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodfstpairEq) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodsndpairEq) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodpairsurjEq) =>
% 97.31/13.17 ((
% 97.31/13.17 (dpsetconstrI) =>
% 97.31/13.17 ((
% 97.31/13.17 (dpsetconstrSub) =>
% 97.31/13.17 ((
% 97.31/13.17 (setOfPairsIsBReln) =>
% 97.31/13.17 ((
% 97.31/13.17 (dpsetconstrERa) =>
% 97.31/13.17 ((
% 97.31/13.17 (dpsetconstrEL1) =>
% 97.31/13.17 ((
% 97.31/13.17 (dpsetconstrEL2) =>
% 97.31/13.17 ((
% 97.31/13.17 (dpsetconstrER) =>
% 97.31/13.17 ((
% 97.31/13.17 (funcImageSingleton) =>
% 97.31/13.17 ((
% 97.31/13.17 (apProp) =>
% 97.31/13.17 ((
% 97.31/13.17 (app) =>
% 97.31/13.17 ((
% 97.31/13.17 (infuncsetfunc) =>
% 97.31/13.17 ((
% 97.31/13.17 (ap2p) =>
% 97.31/13.17 ((
% 97.31/13.17 (funcinfuncset) =>
% 97.31/13.17 ((
% 97.31/13.17 (lamProp) =>
% 97.31/13.17 ((
% 97.31/13.17 (lamp) =>
% 97.31/13.17 ((
% 97.31/13.17 (lam2p) =>
% 97.31/13.17 ((
% 97.31/13.17 (brelnall1) =>
% 97.31/13.17 ((
% 97.31/13.17 (brelnall2) =>
% 97.31/13.17 ((
% 97.31/13.17 (ex1E2) =>
% 97.31/13.17 ((
% 97.31/13.17 (funcGraphProp1) =>
% 97.31/13.17 ((
% 97.31/13.17 (funcGraphProp3) =>
% 97.31/13.17 ((
% 97.31/13.17 (funcGraphProp2) =>
% 97.31/13.17 ((
% 97.31/13.17 (funcextLem) =>
% 97.31/13.17 ((
% 97.31/13.17 (funcGraphProp4) =>
% 97.31/13.17 ((
% 97.31/13.17 (subbreln) =>
% 97.31/13.17 ((
% 97.31/13.17 (eqbreln) =>
% 97.31/13.17 ((
% 97.31/13.17 (funcext) =>
% 97.31/13.17 ((
% 97.31/13.17 (funcext2) =>
% 97.31/13.17 ((
% 97.31/13.17 (ap2apEq1) =>
% 97.31/13.17 ((
% 97.31/13.17 (ap2apEq2) =>
% 97.31/13.17 ((
% 97.31/13.17 (beta1) =>
% 97.31/13.17 ((
% 97.31/13.17 (eta1) =>
% 97.31/13.17 ((
% 97.31/13.17 (lam2lamEq) =>
% 97.31/13.17 ((
% 97.31/13.17 (beta2) =>
% 97.31/13.17 ((
% 97.31/13.17 (eta2) =>
% 97.31/13.17 ((
% 97.31/13.17 (iffalseProp1) =>
% 97.31/13.17 ((
% 97.31/13.17 (iffalseProp2) =>
% 97.31/13.17 ((
% 97.31/13.17 (iftrueProp1) =>
% 97.31/13.17 ((
% 97.31/13.17 (iftrueProp2) =>
% 97.31/13.17 ((
% 97.31/13.17 (ifSingleton) =>
% 97.31/13.17 ((
% 97.31/13.17 (ifp) =>
% 97.31/13.17 ((
% 97.31/13.17 (theeq) =>
% 97.31/13.17 ((
% 97.31/13.17 (iftrue) =>
% 97.31/13.17 ((
% 97.31/13.17 (iffalse) =>
% 97.31/13.17 ((
% 97.31/13.17 (iftrueorfalse) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectT_lem) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionT_lem) =>
% 97.31/13.17 ((
% 97.31/13.17 (powersetT_lem) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusT_lem) =>
% 97.31/13.17 ((
% 97.31/13.17 (complementT_lem) =>
% 97.31/13.17 ((
% 97.31/13.17 (setextT) =>
% 97.31/13.17 ((
% 97.31/13.17 (subsetTI) =>
% 97.31/13.17 ((
% 97.31/13.17 (powersetTI1) =>
% 97.31/13.17 ((
% 97.31/13.17 (powersetTE1) =>
% 97.31/13.17 ((
% 97.31/13.17 (complementTI1) =>
% 97.31/13.17 ((
% 97.31/13.17 (complementTE1) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectTELcontra) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectTERcontra) =>
% 97.31/13.17 ((
% 97.31/13.17 (contrasubsetT) =>
% 97.31/13.17 ((
% 97.31/13.17 (contrasubsetT1) =>
% 97.31/13.17 ((
% 97.31/13.17 (contrasubsetT2) =>
% 97.31/13.17 ((
% 97.31/13.17 (contrasubsetT3) =>
% 97.31/13.17 ((
% 97.31/13.17 (doubleComplementI1) =>
% 97.31/13.17 ((
% 97.31/13.17 (doubleComplementE1) =>
% 97.31/13.17 ((
% 97.31/13.17 (doubleComplementSub1) =>
% 97.31/13.17 ((
% 97.31/13.17 (doubleComplementSub2) =>
% 97.31/13.17 ((
% 97.31/13.17 (doubleComplementEq) =>
% 97.31/13.17 ((
% 97.31/13.17 (complementTnotintersectT) =>
% 97.31/13.17 ((
% 97.31/13.17 (complementImpComplementIntersect) =>
% 97.31/13.17 ((
% 97.31/13.17 (complementSubsetComplementIntersect) =>
% 97.31/13.17 ((
% 97.31/13.17 (complementInPowersetComplementIntersect) =>
% 97.31/13.17 ((
% 97.31/13.17 (contraSubsetComplement) =>
% 97.31/13.17 ((
% 97.31/13.17 (complementTcontraSubset) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionTILcontra) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionTIRcontra) =>
% 97.31/13.17 ((
% 97.31/13.17 (inIntersectImpInUnion) =>
% 97.31/13.17 ((
% 97.31/13.17 (inIntersectImpInUnion2) =>
% 97.31/13.17 ((
% 97.31/13.17 (inIntersectImpInIntersectUnions) =>
% 97.31/13.17 ((
% 97.31/13.17 (intersectInPowersetIntersectUnions) =>
% 97.31/13.17 ((
% 97.31/13.17 (inComplementUnionImpNotIn1) =>
% 97.31/13.17 ((
% 97.31/13.17 (inComplementUnionImpInComplement1) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionTE) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionTEcontra) =>
% 97.31/13.17 ((
% 97.31/13.17 (demorgan2a1) =>
% 97.31/13.17 ((
% 97.31/13.17 (complementUnionInPowersetComplement) =>
% 97.31/13.17 ((
% 97.31/13.17 (demorgan2a2) =>
% 97.31/13.17 ((
% 97.31/13.17 (demorgan1a) =>
% 97.31/13.17 ((
% 97.31/13.17 (demorgan1b) =>
% 97.31/13.17 ((
% 97.31/13.17 (demorgan1) =>
% 97.31/13.17 ((
% 97.31/13.17 (demorgan2a) =>
% 97.31/13.17 ((
% 97.31/13.17 (demorgan2b2) =>
% 97.31/13.17 ((
% 97.31/13.17 (demorgan2b) =>
% 97.31/13.17 ((
% 97.31/13.17 (demorgan2) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz13rule0) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz13rule1) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz13rule2) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz13rule3) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz13rule4) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz1_1) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz1_2) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz1_3) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz1_4) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz1_5) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1all2) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1SetBreln1) =>
% 97.31/13.17 ((
% 97.31/13.17 (choice2fnsingleton) =>
% 97.31/13.17 ((
% 97.31/13.17 (setOfPairsIsBReln1) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1all1) =>
% 97.31/13.17 ((
% 97.31/13.17 (subbreln1) =>
% 97.31/13.17 ((
% 97.31/13.17 (eqbreln1) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1invprop) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1invI) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1invE) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1compprop) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1compI) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1compE) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1compEex) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1unionprop) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1unionIL) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1unionIR) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1unionI) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1unionE) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1unionEcases) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1unionCommutes) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz2Ex) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz2W) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz2A) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz2B) =>
% 97.31/13.17 ((
% 97.31/13.17 (image1Ex) =>
% 97.31/13.17 ((
% 97.31/13.17 (image1Ex1) =>
% 97.31/13.17 ((
% 97.31/13.17 (image1Equiv) =>
% 97.31/13.17 ((
% 97.31/13.17 (image1E) =>
% 97.31/13.17 ((
% 97.31/13.17 (image1I) =>
% 97.31/13.17 ((
% 97.31/13.17 (injFuncInInjFuncSet) =>
% 97.31/13.17 ((
% 97.31/13.17 (injFuncSetFuncIn) =>
% 97.31/13.17 ((
% 97.31/13.17 (injFuncSetFuncInj) =>
% 97.31/13.17 ((
% 97.31/13.17 (surjFuncSetFuncIn) =>
% 97.31/13.17 ((
% 97.31/13.17 (surjFuncSetFuncSurj) =>
% 97.31/13.17 ((
% 97.31/13.17 (leftInvIsSurj) =>
% 97.31/13.17 ((
% 97.31/13.17 (surjCantorThm) =>
% 97.31/13.17 ((
% 97.31/13.17 (foundation2) =>
% 97.31/13.17 ((
% 97.31/13.17 (notinself) =>
% 97.31/13.17 ((
% 97.31/13.17 (notinself2) =>
% 97.31/13.17 ((
% 97.31/13.17 (omegaSp) =>
% 97.31/13.17 ((
% 97.31/13.17 (omegaSclos) =>
% 97.31/13.17 ((
% 97.31/13.17 (peano0notS) =>
% 97.31/13.17 ((
% 97.31/13.17 (!!) @ (
% 97.31/13.17 (('#S') @ (
% 97.31/13.17 (
% 97.31/13.17 ('#B') @ (
% 97.31/13.17 =>) @
% 97.31/13.17 (
% 97.31/13.17 (
% 97.31/13.17 ('#C') @ in @
% 97.31/13.17 omega)))) @
% 97.31/13.17 (
% 97.31/13.17 (
% 97.31/13.17 ('#B') @ (
% 97.31/13.17 !!) @
% 97.31/13.17 (
% 97.31/13.17 (
% 97.31/13.17 ('#B') @ (
% 97.31/13.17 (
% 97.31/13.17 ('#S') @ (
% 97.31/13.17 (
% 97.31/13.17 ('#B') @ (
% 97.31/13.17 =>) @
% 97.31/13.17 (
% 97.31/13.17 (
% 97.31/13.17 ('#C') @ in @
% 97.31/13.17 omega)))))) @
% 97.31/13.17 (
% 97.31/13.17 (
% 97.31/13.17 ('#S') @ (
% 97.31/13.17 (
% 97.31/13.17 ('#B') @ (
% 97.31/13.17 '#S') @
% 97.31/13.17 (
% 97.31/13.17 (
% 97.31/13.17 ('#B') @ (
% 97.31/13.17 (
% 97.31/13.17 ('#B') @ (
% 97.31/13.17 =>))) @
% 97.31/13.17 (
% 97.31/13.17 (
% 97.31/13.17 ('#C') @ (
% 97.31/13.17 (
% 97.31/13.17 ('#B') @ (
% 97.31/13.17 '#B') @
% 97.31/13.17 (
% 97.31/13.17 (
% 97.31/13.17 ('#B') @ (
% 97.31/13.17 =) @
% 97.31/13.17 omegaS)))) @
% 97.31/13.17 omegaS)))))) @
% 97.31/13.17 (
% 97.31/13.17 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.31/13.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl349])).
% 97.31/13.17 thf(zip_derived_cl362, plain,
% 97.31/13.17 (~ (((setoftrueEq) =>
% 97.31/13.17 (((powersetI) =>
% 97.31/13.17 (((emptyinPowerset) =>
% 97.31/13.17 (((emptyInPowerset) =>
% 97.31/13.17 (((powersetE) =>
% 97.31/13.17 (((setunionI) =>
% 97.31/13.17 (((setunionE) =>
% 97.31/13.17 (((subPowSU) =>
% 97.31/13.17 (((exuE2) =>
% 97.31/13.17 (((nonemptyImpWitness) =>
% 97.31/13.17 (((uniqinunit) =>
% 97.31/13.17 (((notinsingleton) =>
% 97.31/13.17 (((eqinunit) =>
% 97.31/13.17 (((singletonsswitch) =>
% 97.31/13.17 (((upairsetE) =>
% 97.31/13.17 (((upairsetIL) =>
% 97.31/13.17 (((upairsetIR) =>
% 97.31/13.17 (((emptyE1) =>
% 97.31/13.17 (((vacuousDall) =>
% 97.31/13.17 (((quantDeMorgan1) =>
% 97.31/13.17 (((quantDeMorgan2) =>
% 97.31/13.17 (((quantDeMorgan3) =>
% 97.31/13.17 (((quantDeMorgan4) =>
% 97.31/13.17 (((prop2setI) =>
% 97.31/13.17 (((prop2set2propI) =>
% 97.31/13.17 (((notdexE) =>
% 97.31/13.17 (((notdallE) =>
% 97.31/13.17 (((exuI1) =>
% 97.31/13.17 (((exuI3) =>
% 97.31/13.17 (((exuI2) =>
% 97.31/13.17 ((
% 97.31/13.17 (inCongP) =>
% 97.31/13.17 ((
% 97.31/13.17 (in__Cong) =>
% 97.31/13.17 ((
% 97.31/13.17 (exuE3u) =>
% 97.31/13.17 ((
% 97.31/13.17 (exu__Cong) =>
% 97.31/13.17 ((
% 97.31/13.17 (setadjoin__Cong) =>
% 97.31/13.17 ((
% 97.31/13.17 (powerset__Cong) =>
% 97.31/13.17 ((
% 97.31/13.17 (setunion__Cong) =>
% 97.31/13.17 ((
% 97.31/13.17 (exuEu) =>
% 97.31/13.17 ((
% 97.31/13.17 (descr__Cong) =>
% 97.31/13.17 ((
% 97.31/13.17 (dsetconstr__Cong) =>
% 97.31/13.17 ((
% 97.31/13.17 (subsetI1) =>
% 97.31/13.17 ((
% 97.31/13.17 (eqimpsubset2) =>
% 97.31/13.17 ((
% 97.31/13.17 (eqimpsubset1) =>
% 97.31/13.17 ((
% 97.31/13.17 (subsetI2) =>
% 97.31/13.17 ((
% 97.31/13.17 (emptysetsubset) =>
% 97.31/13.17 ((
% 97.31/13.17 (subsetE) =>
% 97.31/13.17 ((
% 97.31/13.17 (subsetE2) =>
% 97.31/13.17 ((
% 97.31/13.17 (notsubsetI) =>
% 97.31/13.17 ((
% 97.31/13.17 (notequalI1) =>
% 97.31/13.17 ((
% 97.31/13.17 (notequalI2) =>
% 97.31/13.17 ((
% 97.31/13.17 (subsetRefl) =>
% 97.31/13.17 ((
% 97.31/13.17 (subsetTrans) =>
% 97.31/13.17 ((
% 97.31/13.17 (setadjoinSub) =>
% 97.31/13.17 ((
% 97.31/13.17 (setadjoinSub2) =>
% 97.31/13.17 ((
% 97.31/13.17 (subset2powerset) =>
% 97.31/13.17 ((
% 97.31/13.17 (setextsub) =>
% 97.31/13.17 ((
% 97.31/13.17 (subsetemptysetimpeq) =>
% 97.31/13.17 ((
% 97.31/13.17 (powersetI1) =>
% 97.31/13.17 ((
% 97.31/13.17 (powersetE1) =>
% 97.31/13.17 ((
% 97.31/13.17 (inPowerset) =>
% 97.31/13.17 ((
% 97.31/13.17 (powersetsubset) =>
% 97.31/13.17 ((
% 97.31/13.17 (sepInPowerset) =>
% 97.31/13.17 ((
% 97.31/13.17 (sepSubset) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionIL) =>
% 97.31/13.17 ((
% 97.31/13.17 (upairset2IR) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionIR) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionEcases) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionE) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionLsub) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionRsub) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectI) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectSubset5) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectEL) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectLsub) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectSubset2) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectSubset3) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectER) =>
% 97.31/13.17 ((
% 97.31/13.17 (disjointsetsI1) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectRsub) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectSubset4) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectSubset1) =>
% 97.31/13.17 ((
% 97.31/13.17 (bs114d) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusI) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusEL) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusER) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusSubset2) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusERneg) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusELneg) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusILneg) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusIRneg) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusLsub) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusSubset1) =>
% 97.31/13.17 ((
% 97.31/13.17 (symdiffE) =>
% 97.31/13.17 ((
% 97.31/13.17 (symdiffI1) =>
% 97.31/13.17 ((
% 97.31/13.17 (symdiffI2) =>
% 97.31/13.17 ((
% 97.31/13.17 (symdiffIneg1) =>
% 97.31/13.17 ((
% 97.31/13.17 (symdiffIneg2) =>
% 97.31/13.17 ((
% 97.31/13.17 (secondinupair) =>
% 97.31/13.17 ((
% 97.31/13.17 (setukpairIL) =>
% 97.31/13.17 ((
% 97.31/13.17 (setukpairIR) =>
% 97.31/13.17 ((
% 97.31/13.17 (kpairiskpair) =>
% 97.31/13.17 ((
% 97.31/13.17 (kpairp) =>
% 97.31/13.17 ((
% 97.31/13.17 (singletonsubset) =>
% 97.31/13.17 ((
% 97.31/13.17 (singletoninpowerset) =>
% 97.31/13.17 ((
% 97.31/13.17 (singletoninpowunion) =>
% 97.31/13.17 ((
% 97.31/13.17 (upairset2E) =>
% 97.31/13.17 ((
% 97.31/13.17 (upairsubunion) =>
% 97.31/13.17 ((
% 97.31/13.17 (upairinpowunion) =>
% 97.31/13.17 ((
% 97.31/13.17 (ubforcartprodlem1) =>
% 97.31/13.17 ((
% 97.31/13.17 (ubforcartprodlem2) =>
% 97.31/13.17 ((
% 97.31/13.17 (ubforcartprodlem3) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodpairin) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodmempair1) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodmempair) =>
% 97.31/13.17 ((
% 97.31/13.17 (setunionE2) =>
% 97.31/13.17 ((
% 97.31/13.17 (setunionsingleton1) =>
% 97.31/13.17 ((
% 97.31/13.17 (setunionsingleton2) =>
% 97.31/13.17 ((
% 97.31/13.17 (setunionsingleton) =>
% 97.31/13.17 ((
% 97.31/13.17 (singletonprop) =>
% 97.31/13.17 ((
% 97.31/13.17 (ex1E1) =>
% 97.31/13.17 ((
% 97.31/13.17 (ex1I) =>
% 97.31/13.17 ((
% 97.31/13.17 (ex1I2) =>
% 97.31/13.17 ((
% 97.31/13.17 (singletonsuniq) =>
% 97.31/13.17 ((
% 97.31/13.17 (setukpairinjL1) =>
% 97.31/13.17 ((
% 97.31/13.17 (kfstsingleton) =>
% 97.31/13.17 ((
% 97.31/13.17 (theprop) =>
% 97.31/13.17 ((
% 97.31/13.17 (kfstpairEq) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodfstin) =>
% 97.31/13.17 ((
% 97.31/13.17 (setukpairinjL2) =>
% 97.31/13.17 ((
% 97.31/13.17 (setukpairinjL) =>
% 97.31/13.17 ((
% 97.31/13.17 (setukpairinjR11) =>
% 97.31/13.17 ((
% 97.31/13.17 (setukpairinjR12) =>
% 97.31/13.17 ((
% 97.31/13.17 (setukpairinjR1) =>
% 97.31/13.17 ((
% 97.31/13.17 (upairequniteq) =>
% 97.31/13.17 ((
% 97.31/13.17 (setukpairinjR2) =>
% 97.31/13.17 ((
% 97.31/13.17 (setukpairinjR) =>
% 97.31/13.17 ((
% 97.31/13.17 (ksndsingleton) =>
% 97.31/13.17 ((
% 97.31/13.17 (ksndpairEq) =>
% 97.31/13.17 ((
% 97.31/13.17 (kpairsurjEq) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodsndin) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodpairmemEL) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodpairmemER) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodmempaircEq) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodfstpairEq) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodsndpairEq) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodpairsurjEq) =>
% 97.31/13.17 ((
% 97.31/13.17 (dpsetconstrI) =>
% 97.31/13.17 ((
% 97.31/13.17 (dpsetconstrSub) =>
% 97.31/13.17 ((
% 97.31/13.17 (setOfPairsIsBReln) =>
% 97.31/13.17 ((
% 97.31/13.17 (dpsetconstrERa) =>
% 97.31/13.17 ((
% 97.31/13.17 (dpsetconstrEL1) =>
% 97.31/13.17 ((
% 97.31/13.17 (dpsetconstrEL2) =>
% 97.31/13.17 ((
% 97.31/13.17 (dpsetconstrER) =>
% 97.31/13.17 ((
% 97.31/13.17 (funcImageSingleton) =>
% 97.31/13.17 ((
% 97.31/13.17 (apProp) =>
% 97.31/13.17 ((
% 97.31/13.17 (app) =>
% 97.31/13.17 ((
% 97.31/13.17 (infuncsetfunc) =>
% 97.31/13.17 ((
% 97.31/13.17 (ap2p) =>
% 97.31/13.17 ((
% 97.31/13.17 (funcinfuncset) =>
% 97.31/13.17 ((
% 97.31/13.17 (lamProp) =>
% 97.31/13.17 ((
% 97.31/13.17 (lamp) =>
% 97.31/13.17 ((
% 97.31/13.17 (lam2p) =>
% 97.31/13.17 ((
% 97.31/13.17 (brelnall1) =>
% 97.31/13.17 ((
% 97.31/13.17 (brelnall2) =>
% 97.31/13.17 ((
% 97.31/13.17 (ex1E2) =>
% 97.31/13.17 ((
% 97.31/13.17 (funcGraphProp1) =>
% 97.31/13.17 ((
% 97.31/13.17 (funcGraphProp3) =>
% 97.31/13.17 ((
% 97.31/13.17 (funcGraphProp2) =>
% 97.31/13.17 ((
% 97.31/13.17 (funcextLem) =>
% 97.31/13.17 ((
% 97.31/13.17 (funcGraphProp4) =>
% 97.31/13.17 ((
% 97.31/13.17 (subbreln) =>
% 97.31/13.17 ((
% 97.31/13.17 (eqbreln) =>
% 97.31/13.17 ((
% 97.31/13.17 (funcext) =>
% 97.31/13.17 ((
% 97.31/13.17 (funcext2) =>
% 97.31/13.17 ((
% 97.31/13.17 (ap2apEq1) =>
% 97.31/13.17 ((
% 97.31/13.17 (ap2apEq2) =>
% 97.31/13.17 ((
% 97.31/13.17 (beta1) =>
% 97.31/13.17 ((
% 97.31/13.17 (eta1) =>
% 97.31/13.17 ((
% 97.31/13.17 (lam2lamEq) =>
% 97.31/13.17 ((
% 97.31/13.17 (beta2) =>
% 97.31/13.17 ((
% 97.31/13.17 (eta2) =>
% 97.31/13.17 ((
% 97.31/13.17 (iffalseProp1) =>
% 97.31/13.17 ((
% 97.31/13.17 (iffalseProp2) =>
% 97.31/13.17 ((
% 97.31/13.17 (iftrueProp1) =>
% 97.31/13.17 ((
% 97.31/13.17 (iftrueProp2) =>
% 97.31/13.17 ((
% 97.31/13.17 (ifSingleton) =>
% 97.31/13.17 ((
% 97.31/13.17 (ifp) =>
% 97.31/13.17 ((
% 97.31/13.17 (theeq) =>
% 97.31/13.17 ((
% 97.31/13.17 (iftrue) =>
% 97.31/13.17 ((
% 97.31/13.17 (iffalse) =>
% 97.31/13.17 ((
% 97.31/13.17 (iftrueorfalse) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectT_lem) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionT_lem) =>
% 97.31/13.17 ((
% 97.31/13.17 (powersetT_lem) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusT_lem) =>
% 97.31/13.17 ((
% 97.31/13.17 (complementT_lem) =>
% 97.31/13.17 ((
% 97.31/13.17 (setextT) =>
% 97.31/13.17 ((
% 97.31/13.17 (subsetTI) =>
% 97.31/13.17 ((
% 97.31/13.17 (powersetTI1) =>
% 97.31/13.17 ((
% 97.31/13.17 (powersetTE1) =>
% 97.31/13.17 ((
% 97.31/13.17 (complementTI1) =>
% 97.31/13.17 ((
% 97.31/13.17 (complementTE1) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectTELcontra) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectTERcontra) =>
% 97.31/13.17 ((
% 97.31/13.17 (contrasubsetT) =>
% 97.31/13.17 ((
% 97.31/13.17 (contrasubsetT1) =>
% 97.31/13.17 ((
% 97.31/13.17 (contrasubsetT2) =>
% 97.31/13.17 ((
% 97.31/13.17 (contrasubsetT3) =>
% 97.31/13.17 ((
% 97.31/13.17 (doubleComplementI1) =>
% 97.31/13.17 ((
% 97.31/13.17 (doubleComplementE1) =>
% 97.31/13.17 ((
% 97.31/13.17 (doubleComplementSub1) =>
% 97.31/13.17 ((
% 97.31/13.17 (doubleComplementSub2) =>
% 97.31/13.17 ((
% 97.31/13.17 (doubleComplementEq) =>
% 97.31/13.17 ((
% 97.31/13.17 (complementTnotintersectT) =>
% 97.31/13.17 ((
% 97.31/13.17 (complementImpComplementIntersect) =>
% 97.31/13.17 ((
% 97.31/13.17 (complementSubsetComplementIntersect) =>
% 97.31/13.17 ((
% 97.31/13.17 (complementInPowersetComplementIntersect) =>
% 97.31/13.17 ((
% 97.31/13.17 (contraSubsetComplement) =>
% 97.31/13.17 ((
% 97.31/13.17 (complementTcontraSubset) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionTILcontra) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionTIRcontra) =>
% 97.31/13.17 ((
% 97.31/13.17 (inIntersectImpInUnion) =>
% 97.31/13.17 ((
% 97.31/13.17 (inIntersectImpInUnion2) =>
% 97.31/13.17 ((
% 97.31/13.17 (inIntersectImpInIntersectUnions) =>
% 97.31/13.17 ((
% 97.31/13.17 (intersectInPowersetIntersectUnions) =>
% 97.31/13.17 ((
% 97.31/13.17 (inComplementUnionImpNotIn1) =>
% 97.31/13.17 ((
% 97.31/13.17 (inComplementUnionImpInComplement1) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionTE) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionTEcontra) =>
% 97.31/13.17 ((
% 97.31/13.17 (demorgan2a1) =>
% 97.31/13.17 ((
% 97.31/13.17 (complementUnionInPowersetComplement) =>
% 97.31/13.17 ((
% 97.31/13.17 (demorgan2a2) =>
% 97.31/13.17 ((
% 97.31/13.17 (demorgan1a) =>
% 97.31/13.17 ((
% 97.31/13.17 (demorgan1b) =>
% 97.31/13.17 ((
% 97.31/13.17 (demorgan1) =>
% 97.31/13.17 ((
% 97.31/13.17 (demorgan2a) =>
% 97.31/13.17 ((
% 97.31/13.17 (demorgan2b2) =>
% 97.31/13.17 ((
% 97.31/13.17 (demorgan2b) =>
% 97.31/13.17 ((
% 97.31/13.17 (demorgan2) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz13rule0) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz13rule1) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz13rule2) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz13rule3) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz13rule4) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz1_1) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz1_2) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz1_3) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz1_4) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz1_5) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1all2) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1SetBreln1) =>
% 97.31/13.17 ((
% 97.31/13.17 (choice2fnsingleton) =>
% 97.31/13.17 ((
% 97.31/13.17 (setOfPairsIsBReln1) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1all1) =>
% 97.31/13.17 ((
% 97.31/13.17 (subbreln1) =>
% 97.31/13.17 ((
% 97.31/13.17 (eqbreln1) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1invprop) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1invI) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1invE) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1compprop) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1compI) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1compE) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1compEex) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1unionprop) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1unionIL) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1unionIR) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1unionI) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1unionE) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1unionEcases) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1unionCommutes) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz2Ex) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz2W) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz2A) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz2B) =>
% 97.31/13.17 ((
% 97.31/13.17 (image1Ex) =>
% 97.31/13.17 ((
% 97.31/13.17 (image1Ex1) =>
% 97.31/13.17 ((
% 97.31/13.17 (image1Equiv) =>
% 97.31/13.17 ((
% 97.31/13.17 (image1E) =>
% 97.31/13.17 ((
% 97.31/13.17 (image1I) =>
% 97.31/13.17 ((
% 97.31/13.17 (injFuncInInjFuncSet) =>
% 97.31/13.17 ((
% 97.31/13.17 (injFuncSetFuncIn) =>
% 97.31/13.17 ((
% 97.31/13.17 (injFuncSetFuncInj) =>
% 97.31/13.17 ((
% 97.31/13.17 (surjFuncSetFuncIn) =>
% 97.31/13.17 ((
% 97.31/13.17 (surjFuncSetFuncSurj) =>
% 97.31/13.17 ((
% 97.31/13.17 (leftInvIsSurj) =>
% 97.31/13.17 ((
% 97.31/13.17 (surjCantorThm) =>
% 97.31/13.17 ((
% 97.31/13.17 (foundation2) =>
% 97.31/13.17 ((
% 97.31/13.17 (notinself) =>
% 97.31/13.17 ((
% 97.31/13.17 (notinself2) =>
% 97.31/13.17 ((
% 97.31/13.17 (omegaSp) =>
% 97.31/13.17 ((
% 97.31/13.17 (omegaSclos) =>
% 97.31/13.17 ((
% 97.31/13.17 (peano0notS) =>
% 97.31/13.17 ((
% 97.31/13.17 (!!) @ (
% 97.31/13.17 (('#S') @ (
% 97.31/13.17 (
% 97.31/13.17 ('#B') @ (
% 97.31/13.17 =>) @
% 97.31/13.17 (
% 97.31/13.17 (
% 97.31/13.17 ('#C') @ in @
% 97.31/13.17 omega)))) @
% 97.31/13.17 (
% 97.31/13.17 (
% 97.31/13.17 ('#B') @ (
% 97.31/13.17 !!) @
% 97.31/13.17 (
% 97.31/13.17 (
% 97.31/13.17 ('#B') @ (
% 97.31/13.17 (
% 97.31/13.17 ('#S') @ (
% 97.31/13.17 (
% 97.31/13.17 ('#B') @ (
% 97.31/13.17 =>) @
% 97.31/13.17 (
% 97.31/13.17 (
% 97.31/13.17 ('#C') @ in @
% 97.31/13.17 omega)))))) @
% 97.31/13.17 (
% 97.31/13.17 (
% 97.31/13.17 ('#S') @ (
% 97.31/13.17 (
% 97.31/13.17 ('#B') @ (
% 97.31/13.17 '#S') @
% 97.31/13.17 (
% 97.31/13.17 (
% 97.31/13.17 ('#B') @ (
% 97.31/13.17 (
% 97.31/13.17 ('#B') @ (
% 97.31/13.17 =>))) @
% 97.31/13.17 (
% 97.31/13.17 (
% 97.31/13.17 ('#C') @ (
% 97.31/13.17 (
% 97.31/13.17 ('#B') @ (
% 97.31/13.17 '#B') @
% 97.31/13.17 (
% 97.31/13.17 (
% 97.31/13.17 ('#B') @ (
% 97.31/13.17 =) @
% 97.31/13.17 omegaS)))) @
% 97.31/13.17 omegaS)))))) @
% 97.31/13.17 (
% 97.31/13.17 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.31/13.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl355])).
% 97.31/13.17 thf(zip_derived_cl369, plain,
% 97.31/13.17 (~ (((powersetI) =>
% 97.31/13.17 (((emptyinPowerset) =>
% 97.31/13.17 (((emptyInPowerset) =>
% 97.31/13.17 (((powersetE) =>
% 97.31/13.17 (((setunionI) =>
% 97.31/13.17 (((setunionE) =>
% 97.31/13.17 (((subPowSU) =>
% 97.31/13.17 (((exuE2) =>
% 97.31/13.17 (((nonemptyImpWitness) =>
% 97.31/13.17 (((uniqinunit) =>
% 97.31/13.17 (((notinsingleton) =>
% 97.31/13.17 (((eqinunit) =>
% 97.31/13.17 (((singletonsswitch) =>
% 97.31/13.17 (((upairsetE) =>
% 97.31/13.17 (((upairsetIL) =>
% 97.31/13.17 (((upairsetIR) =>
% 97.31/13.17 (((emptyE1) =>
% 97.31/13.17 (((vacuousDall) =>
% 97.31/13.17 (((quantDeMorgan1) =>
% 97.31/13.17 (((quantDeMorgan2) =>
% 97.31/13.17 (((quantDeMorgan3) =>
% 97.31/13.17 (((quantDeMorgan4) =>
% 97.31/13.17 (((prop2setI) =>
% 97.31/13.17 (((prop2set2propI) =>
% 97.31/13.17 (((notdexE) =>
% 97.31/13.17 (((notdallE) =>
% 97.31/13.17 (((exuI1) =>
% 97.31/13.17 (((exuI3) =>
% 97.31/13.17 (((exuI2) =>
% 97.31/13.17 (((inCongP) =>
% 97.31/13.17 ((
% 97.31/13.17 (in__Cong) =>
% 97.31/13.17 ((
% 97.31/13.17 (exuE3u) =>
% 97.31/13.17 ((
% 97.31/13.17 (exu__Cong) =>
% 97.31/13.17 ((
% 97.31/13.17 (setadjoin__Cong) =>
% 97.31/13.17 ((
% 97.31/13.17 (powerset__Cong) =>
% 97.31/13.17 ((
% 97.31/13.17 (setunion__Cong) =>
% 97.31/13.17 ((
% 97.31/13.17 (exuEu) =>
% 97.31/13.17 ((
% 97.31/13.17 (descr__Cong) =>
% 97.31/13.17 ((
% 97.31/13.17 (dsetconstr__Cong) =>
% 97.31/13.17 ((
% 97.31/13.17 (subsetI1) =>
% 97.31/13.17 ((
% 97.31/13.17 (eqimpsubset2) =>
% 97.31/13.17 ((
% 97.31/13.17 (eqimpsubset1) =>
% 97.31/13.17 ((
% 97.31/13.17 (subsetI2) =>
% 97.31/13.17 ((
% 97.31/13.17 (emptysetsubset) =>
% 97.31/13.17 ((
% 97.31/13.17 (subsetE) =>
% 97.31/13.17 ((
% 97.31/13.17 (subsetE2) =>
% 97.31/13.17 ((
% 97.31/13.17 (notsubsetI) =>
% 97.31/13.17 ((
% 97.31/13.17 (notequalI1) =>
% 97.31/13.17 ((
% 97.31/13.17 (notequalI2) =>
% 97.31/13.17 ((
% 97.31/13.17 (subsetRefl) =>
% 97.31/13.17 ((
% 97.31/13.17 (subsetTrans) =>
% 97.31/13.17 ((
% 97.31/13.17 (setadjoinSub) =>
% 97.31/13.17 ((
% 97.31/13.17 (setadjoinSub2) =>
% 97.31/13.17 ((
% 97.31/13.17 (subset2powerset) =>
% 97.31/13.17 ((
% 97.31/13.17 (setextsub) =>
% 97.31/13.17 ((
% 97.31/13.17 (subsetemptysetimpeq) =>
% 97.31/13.17 ((
% 97.31/13.17 (powersetI1) =>
% 97.31/13.17 ((
% 97.31/13.17 (powersetE1) =>
% 97.31/13.17 ((
% 97.31/13.17 (inPowerset) =>
% 97.31/13.17 ((
% 97.31/13.17 (powersetsubset) =>
% 97.31/13.17 ((
% 97.31/13.17 (sepInPowerset) =>
% 97.31/13.17 ((
% 97.31/13.17 (sepSubset) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionIL) =>
% 97.31/13.17 ((
% 97.31/13.17 (upairset2IR) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionIR) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionEcases) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionE) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionLsub) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionRsub) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectI) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectSubset5) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectEL) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectLsub) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectSubset2) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectSubset3) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectER) =>
% 97.31/13.17 ((
% 97.31/13.17 (disjointsetsI1) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectRsub) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectSubset4) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectSubset1) =>
% 97.31/13.17 ((
% 97.31/13.17 (bs114d) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusI) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusEL) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusER) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusSubset2) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusERneg) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusELneg) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusILneg) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusIRneg) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusLsub) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusSubset1) =>
% 97.31/13.17 ((
% 97.31/13.17 (symdiffE) =>
% 97.31/13.17 ((
% 97.31/13.17 (symdiffI1) =>
% 97.31/13.17 ((
% 97.31/13.17 (symdiffI2) =>
% 97.31/13.17 ((
% 97.31/13.17 (symdiffIneg1) =>
% 97.31/13.17 ((
% 97.31/13.17 (symdiffIneg2) =>
% 97.31/13.17 ((
% 97.31/13.17 (secondinupair) =>
% 97.31/13.17 ((
% 97.31/13.17 (setukpairIL) =>
% 97.31/13.17 ((
% 97.31/13.17 (setukpairIR) =>
% 97.31/13.17 ((
% 97.31/13.17 (kpairiskpair) =>
% 97.31/13.17 ((
% 97.31/13.17 (kpairp) =>
% 97.31/13.17 ((
% 97.31/13.17 (singletonsubset) =>
% 97.31/13.17 ((
% 97.31/13.17 (singletoninpowerset) =>
% 97.31/13.17 ((
% 97.31/13.17 (singletoninpowunion) =>
% 97.31/13.17 ((
% 97.31/13.17 (upairset2E) =>
% 97.31/13.17 ((
% 97.31/13.17 (upairsubunion) =>
% 97.31/13.17 ((
% 97.31/13.17 (upairinpowunion) =>
% 97.31/13.17 ((
% 97.31/13.17 (ubforcartprodlem1) =>
% 97.31/13.17 ((
% 97.31/13.17 (ubforcartprodlem2) =>
% 97.31/13.17 ((
% 97.31/13.17 (ubforcartprodlem3) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodpairin) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodmempair1) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodmempair) =>
% 97.31/13.17 ((
% 97.31/13.17 (setunionE2) =>
% 97.31/13.17 ((
% 97.31/13.17 (setunionsingleton1) =>
% 97.31/13.17 ((
% 97.31/13.17 (setunionsingleton2) =>
% 97.31/13.17 ((
% 97.31/13.17 (setunionsingleton) =>
% 97.31/13.17 ((
% 97.31/13.17 (singletonprop) =>
% 97.31/13.17 ((
% 97.31/13.17 (ex1E1) =>
% 97.31/13.17 ((
% 97.31/13.17 (ex1I) =>
% 97.31/13.17 ((
% 97.31/13.17 (ex1I2) =>
% 97.31/13.17 ((
% 97.31/13.17 (singletonsuniq) =>
% 97.31/13.17 ((
% 97.31/13.17 (setukpairinjL1) =>
% 97.31/13.17 ((
% 97.31/13.17 (kfstsingleton) =>
% 97.31/13.17 ((
% 97.31/13.17 (theprop) =>
% 97.31/13.17 ((
% 97.31/13.17 (kfstpairEq) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodfstin) =>
% 97.31/13.17 ((
% 97.31/13.17 (setukpairinjL2) =>
% 97.31/13.17 ((
% 97.31/13.17 (setukpairinjL) =>
% 97.31/13.17 ((
% 97.31/13.17 (setukpairinjR11) =>
% 97.31/13.17 ((
% 97.31/13.17 (setukpairinjR12) =>
% 97.31/13.17 ((
% 97.31/13.17 (setukpairinjR1) =>
% 97.31/13.17 ((
% 97.31/13.17 (upairequniteq) =>
% 97.31/13.17 ((
% 97.31/13.17 (setukpairinjR2) =>
% 97.31/13.17 ((
% 97.31/13.17 (setukpairinjR) =>
% 97.31/13.17 ((
% 97.31/13.17 (ksndsingleton) =>
% 97.31/13.17 ((
% 97.31/13.17 (ksndpairEq) =>
% 97.31/13.17 ((
% 97.31/13.17 (kpairsurjEq) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodsndin) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodpairmemEL) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodpairmemER) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodmempaircEq) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodfstpairEq) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodsndpairEq) =>
% 97.31/13.17 ((
% 97.31/13.17 (cartprodpairsurjEq) =>
% 97.31/13.17 ((
% 97.31/13.17 (dpsetconstrI) =>
% 97.31/13.17 ((
% 97.31/13.17 (dpsetconstrSub) =>
% 97.31/13.17 ((
% 97.31/13.17 (setOfPairsIsBReln) =>
% 97.31/13.17 ((
% 97.31/13.17 (dpsetconstrERa) =>
% 97.31/13.17 ((
% 97.31/13.17 (dpsetconstrEL1) =>
% 97.31/13.17 ((
% 97.31/13.17 (dpsetconstrEL2) =>
% 97.31/13.17 ((
% 97.31/13.17 (dpsetconstrER) =>
% 97.31/13.17 ((
% 97.31/13.17 (funcImageSingleton) =>
% 97.31/13.17 ((
% 97.31/13.17 (apProp) =>
% 97.31/13.17 ((
% 97.31/13.17 (app) =>
% 97.31/13.17 ((
% 97.31/13.17 (infuncsetfunc) =>
% 97.31/13.17 ((
% 97.31/13.17 (ap2p) =>
% 97.31/13.17 ((
% 97.31/13.17 (funcinfuncset) =>
% 97.31/13.17 ((
% 97.31/13.17 (lamProp) =>
% 97.31/13.17 ((
% 97.31/13.17 (lamp) =>
% 97.31/13.17 ((
% 97.31/13.17 (lam2p) =>
% 97.31/13.17 ((
% 97.31/13.17 (brelnall1) =>
% 97.31/13.17 ((
% 97.31/13.17 (brelnall2) =>
% 97.31/13.17 ((
% 97.31/13.17 (ex1E2) =>
% 97.31/13.17 ((
% 97.31/13.17 (funcGraphProp1) =>
% 97.31/13.17 ((
% 97.31/13.17 (funcGraphProp3) =>
% 97.31/13.17 ((
% 97.31/13.17 (funcGraphProp2) =>
% 97.31/13.17 ((
% 97.31/13.17 (funcextLem) =>
% 97.31/13.17 ((
% 97.31/13.17 (funcGraphProp4) =>
% 97.31/13.17 ((
% 97.31/13.17 (subbreln) =>
% 97.31/13.17 ((
% 97.31/13.17 (eqbreln) =>
% 97.31/13.17 ((
% 97.31/13.17 (funcext) =>
% 97.31/13.17 ((
% 97.31/13.17 (funcext2) =>
% 97.31/13.17 ((
% 97.31/13.17 (ap2apEq1) =>
% 97.31/13.17 ((
% 97.31/13.17 (ap2apEq2) =>
% 97.31/13.17 ((
% 97.31/13.17 (beta1) =>
% 97.31/13.17 ((
% 97.31/13.17 (eta1) =>
% 97.31/13.17 ((
% 97.31/13.17 (lam2lamEq) =>
% 97.31/13.17 ((
% 97.31/13.17 (beta2) =>
% 97.31/13.17 ((
% 97.31/13.17 (eta2) =>
% 97.31/13.17 ((
% 97.31/13.17 (iffalseProp1) =>
% 97.31/13.17 ((
% 97.31/13.17 (iffalseProp2) =>
% 97.31/13.17 ((
% 97.31/13.17 (iftrueProp1) =>
% 97.31/13.17 ((
% 97.31/13.17 (iftrueProp2) =>
% 97.31/13.17 ((
% 97.31/13.17 (ifSingleton) =>
% 97.31/13.17 ((
% 97.31/13.17 (ifp) =>
% 97.31/13.17 ((
% 97.31/13.17 (theeq) =>
% 97.31/13.17 ((
% 97.31/13.17 (iftrue) =>
% 97.31/13.17 ((
% 97.31/13.17 (iffalse) =>
% 97.31/13.17 ((
% 97.31/13.17 (iftrueorfalse) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectT_lem) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionT_lem) =>
% 97.31/13.17 ((
% 97.31/13.17 (powersetT_lem) =>
% 97.31/13.17 ((
% 97.31/13.17 (setminusT_lem) =>
% 97.31/13.17 ((
% 97.31/13.17 (complementT_lem) =>
% 97.31/13.17 ((
% 97.31/13.17 (setextT) =>
% 97.31/13.17 ((
% 97.31/13.17 (subsetTI) =>
% 97.31/13.17 ((
% 97.31/13.17 (powersetTI1) =>
% 97.31/13.17 ((
% 97.31/13.17 (powersetTE1) =>
% 97.31/13.17 ((
% 97.31/13.17 (complementTI1) =>
% 97.31/13.17 ((
% 97.31/13.17 (complementTE1) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectTELcontra) =>
% 97.31/13.17 ((
% 97.31/13.17 (binintersectTERcontra) =>
% 97.31/13.17 ((
% 97.31/13.17 (contrasubsetT) =>
% 97.31/13.17 ((
% 97.31/13.17 (contrasubsetT1) =>
% 97.31/13.17 ((
% 97.31/13.17 (contrasubsetT2) =>
% 97.31/13.17 ((
% 97.31/13.17 (contrasubsetT3) =>
% 97.31/13.17 ((
% 97.31/13.17 (doubleComplementI1) =>
% 97.31/13.17 ((
% 97.31/13.17 (doubleComplementE1) =>
% 97.31/13.17 ((
% 97.31/13.17 (doubleComplementSub1) =>
% 97.31/13.17 ((
% 97.31/13.17 (doubleComplementSub2) =>
% 97.31/13.17 ((
% 97.31/13.17 (doubleComplementEq) =>
% 97.31/13.17 ((
% 97.31/13.17 (complementTnotintersectT) =>
% 97.31/13.17 ((
% 97.31/13.17 (complementImpComplementIntersect) =>
% 97.31/13.17 ((
% 97.31/13.17 (complementSubsetComplementIntersect) =>
% 97.31/13.17 ((
% 97.31/13.17 (complementInPowersetComplementIntersect) =>
% 97.31/13.17 ((
% 97.31/13.17 (contraSubsetComplement) =>
% 97.31/13.17 ((
% 97.31/13.17 (complementTcontraSubset) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionTILcontra) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionTIRcontra) =>
% 97.31/13.17 ((
% 97.31/13.17 (inIntersectImpInUnion) =>
% 97.31/13.17 ((
% 97.31/13.17 (inIntersectImpInUnion2) =>
% 97.31/13.17 ((
% 97.31/13.17 (inIntersectImpInIntersectUnions) =>
% 97.31/13.17 ((
% 97.31/13.17 (intersectInPowersetIntersectUnions) =>
% 97.31/13.17 ((
% 97.31/13.17 (inComplementUnionImpNotIn1) =>
% 97.31/13.17 ((
% 97.31/13.17 (inComplementUnionImpInComplement1) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionTE) =>
% 97.31/13.17 ((
% 97.31/13.17 (binunionTEcontra) =>
% 97.31/13.17 ((
% 97.31/13.17 (demorgan2a1) =>
% 97.31/13.17 ((
% 97.31/13.17 (complementUnionInPowersetComplement) =>
% 97.31/13.17 ((
% 97.31/13.17 (demorgan2a2) =>
% 97.31/13.17 ((
% 97.31/13.17 (demorgan1a) =>
% 97.31/13.17 ((
% 97.31/13.17 (demorgan1b) =>
% 97.31/13.17 ((
% 97.31/13.17 (demorgan1) =>
% 97.31/13.17 ((
% 97.31/13.17 (demorgan2a) =>
% 97.31/13.17 ((
% 97.31/13.17 (demorgan2b2) =>
% 97.31/13.17 ((
% 97.31/13.17 (demorgan2b) =>
% 97.31/13.17 ((
% 97.31/13.17 (demorgan2) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz13rule0) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz13rule1) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz13rule2) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz13rule3) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz13rule4) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz1_1) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz1_2) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz1_3) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz1_4) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz1_5) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1all2) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1SetBreln1) =>
% 97.31/13.17 ((
% 97.31/13.17 (choice2fnsingleton) =>
% 97.31/13.17 ((
% 97.31/13.17 (setOfPairsIsBReln1) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1all1) =>
% 97.31/13.17 ((
% 97.31/13.17 (subbreln1) =>
% 97.31/13.17 ((
% 97.31/13.17 (eqbreln1) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1invprop) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1invI) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1invE) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1compprop) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1compI) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1compE) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1compEex) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1unionprop) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1unionIL) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1unionIR) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1unionI) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1unionE) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1unionEcases) =>
% 97.31/13.17 ((
% 97.31/13.17 (breln1unionCommutes) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz2Ex) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz2W) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz2A) =>
% 97.31/13.17 ((
% 97.31/13.17 (woz2B) =>
% 97.31/13.17 ((
% 97.31/13.17 (image1Ex) =>
% 97.31/13.17 ((
% 97.31/13.17 (image1Ex1) =>
% 97.31/13.17 ((
% 97.31/13.17 (image1Equiv) =>
% 97.31/13.17 ((
% 97.31/13.17 (image1E) =>
% 97.31/13.17 ((
% 97.31/13.17 (image1I) =>
% 97.31/13.17 ((
% 97.31/13.17 (injFuncInInjFuncSet) =>
% 97.31/13.17 ((
% 97.31/13.17 (injFuncSetFuncIn) =>
% 97.31/13.17 ((
% 97.31/13.17 (injFuncSetFuncInj) =>
% 97.31/13.17 ((
% 97.31/13.17 (surjFuncSetFuncIn) =>
% 97.31/13.17 ((
% 97.31/13.17 (surjFuncSetFuncSurj) =>
% 97.31/13.17 ((
% 97.31/13.17 (leftInvIsSurj) =>
% 97.31/13.17 ((
% 97.31/13.17 (surjCantorThm) =>
% 97.31/13.17 ((
% 97.31/13.17 (foundation2) =>
% 97.31/13.17 ((
% 97.31/13.17 (notinself) =>
% 97.31/13.17 ((
% 97.31/13.17 (notinself2) =>
% 97.31/13.17 ((
% 97.31/13.17 (omegaSp) =>
% 97.31/13.17 ((
% 97.31/13.17 (omegaSclos) =>
% 97.31/13.17 ((
% 97.31/13.17 (peano0notS) =>
% 97.31/13.17 ((
% 97.31/13.17 (!!) @ (
% 97.31/13.17 (('#S') @ (
% 97.31/13.17 (
% 97.31/13.17 ('#B') @ (
% 97.31/13.17 =>) @
% 97.31/13.17 (
% 97.31/13.17 (
% 97.31/13.17 ('#C') @ in @
% 97.31/13.17 omega)))) @
% 97.31/13.17 (
% 97.31/13.17 (
% 97.31/13.17 ('#B') @ (
% 97.31/13.17 !!) @
% 97.31/13.17 (
% 97.31/13.17 (
% 97.31/13.17 ('#B') @ (
% 97.31/13.17 (
% 97.31/13.17 ('#S') @ (
% 97.31/13.17 (
% 97.31/13.17 ('#B') @ (
% 97.31/13.17 =>) @
% 97.31/13.17 (
% 97.31/13.17 (
% 97.31/13.17 ('#C') @ in @
% 97.31/13.17 omega)))))) @
% 97.31/13.17 (
% 97.31/13.17 (
% 97.31/13.17 ('#S') @ (
% 97.31/13.17 (
% 97.31/13.17 ('#B') @ (
% 97.31/13.17 '#S') @
% 97.31/13.17 (
% 97.31/13.17 (
% 97.31/13.17 ('#B') @ (
% 97.31/13.17 (
% 97.31/13.17 ('#B') @ (
% 97.31/13.17 =>))) @
% 97.31/13.17 (
% 97.31/13.17 (
% 97.31/13.17 ('#C') @ (
% 97.31/13.17 (
% 97.31/13.17 ('#B') @ (
% 97.31/13.17 '#B') @
% 97.31/13.17 (
% 97.31/13.17 (
% 97.31/13.17 ('#B') @ (
% 97.31/13.17 =) @
% 97.31/13.17 omegaS)))) @
% 97.31/13.17 omegaS)))))) @
% 97.31/13.17 (
% 97.31/13.17 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.31/13.17 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl362])).
% 97.31/13.17 thf(zip_derived_cl376, plain,
% 97.31/13.17 (~ (((emptyinPowerset) =>
% 97.31/13.17 (((emptyInPowerset) =>
% 97.31/13.17 (((powersetE) =>
% 97.31/13.17 (((setunionI) =>
% 97.31/13.17 (((setunionE) =>
% 97.31/13.17 (((subPowSU) =>
% 97.31/13.17 (((exuE2) =>
% 97.31/13.17 (((nonemptyImpWitness) =>
% 97.31/13.17 (((uniqinunit) =>
% 97.31/13.17 (((notinsingleton) =>
% 97.31/13.17 (((eqinunit) =>
% 97.31/13.17 (((singletonsswitch) =>
% 97.31/13.17 (((upairsetE) =>
% 97.31/13.17 (((upairsetIL) =>
% 97.31/13.17 (((upairsetIR) =>
% 97.31/13.17 (((emptyE1) =>
% 97.31/13.17 (((vacuousDall) =>
% 97.31/13.17 (((quantDeMorgan1) =>
% 97.31/13.17 (((quantDeMorgan2) =>
% 97.31/13.17 (((quantDeMorgan3) =>
% 97.31/13.17 (((quantDeMorgan4) =>
% 97.31/13.17 (((prop2setI) =>
% 97.31/13.17 (((prop2set2propI) =>
% 97.31/13.17 (((notdexE) =>
% 97.31/13.17 (((notdallE) =>
% 97.31/13.17 (((exuI1) =>
% 97.31/13.17 (((exuI3) =>
% 97.31/13.17 (((exuI2) =>
% 97.31/13.17 (((inCongP) =>
% 97.31/13.17 (((in__Cong) =>
% 97.31/13.17 ((
% 97.31/13.17 (exuE3u) =>
% 97.31/13.17 ((
% 97.31/13.17 (exu__Cong) =>
% 97.31/13.17 ((
% 97.31/13.17 (setadjoin__Cong) =>
% 97.31/13.17 ((
% 97.31/13.17 (powerset__Cong) =>
% 97.31/13.17 ((
% 97.31/13.17 (setunion__Cong) =>
% 97.31/13.17 ((
% 97.31/13.17 (exuEu) =>
% 97.31/13.17 ((
% 97.31/13.17 (descr__Cong) =>
% 97.31/13.17 ((
% 97.31/13.17 (dsetconstr__Cong) =>
% 97.31/13.17 ((
% 97.31/13.17 (subsetI1) =>
% 97.31/13.17 ((
% 97.31/13.17 (eqimpsubset2) =>
% 97.31/13.17 ((
% 97.31/13.17 (eqimpsubset1) =>
% 97.31/13.17 ((
% 97.31/13.17 (subsetI2) =>
% 97.31/13.17 ((
% 97.31/13.17 (emptysetsubset) =>
% 97.31/13.17 ((
% 97.31/13.17 (subsetE) =>
% 97.31/13.17 ((
% 97.31/13.17 (subsetE2) =>
% 97.31/13.17 ((
% 97.31/13.17 (notsubsetI) =>
% 97.31/13.17 ((
% 97.31/13.17 (notequalI1) =>
% 97.31/13.17 ((
% 97.31/13.17 (notequalI2) =>
% 97.31/13.17 ((
% 97.31/13.17 (subsetRefl) =>
% 97.31/13.17 ((
% 97.31/13.17 (subsetTrans) =>
% 97.31/13.17 ((
% 97.31/13.17 (setadjoinSub) =>
% 97.31/13.17 ((
% 97.31/13.17 (setadjoinSub2) =>
% 97.31/13.17 ((
% 97.31/13.18 (subset2powerset) =>
% 97.31/13.18 ((
% 97.31/13.18 (setextsub) =>
% 97.31/13.18 ((
% 97.31/13.18 (subsetemptysetimpeq) =>
% 97.31/13.18 ((
% 97.31/13.18 (powersetI1) =>
% 97.31/13.18 ((
% 97.31/13.18 (powersetE1) =>
% 97.31/13.18 ((
% 97.31/13.18 (inPowerset) =>
% 97.31/13.18 ((
% 97.31/13.18 (powersetsubset) =>
% 97.31/13.18 ((
% 97.31/13.18 (sepInPowerset) =>
% 97.31/13.18 ((
% 97.31/13.18 (sepSubset) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionIL) =>
% 97.31/13.18 ((
% 97.31/13.18 (upairset2IR) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionIR) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionEcases) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionE) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionLsub) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionRsub) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectI) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectSubset5) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectEL) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectLsub) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectSubset2) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectSubset3) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectER) =>
% 97.31/13.18 ((
% 97.31/13.18 (disjointsetsI1) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectRsub) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectSubset4) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectSubset1) =>
% 97.31/13.18 ((
% 97.31/13.18 (bs114d) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusI) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusEL) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusER) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusSubset2) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusERneg) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusELneg) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusILneg) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusIRneg) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusLsub) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusSubset1) =>
% 97.31/13.18 ((
% 97.31/13.18 (symdiffE) =>
% 97.31/13.18 ((
% 97.31/13.18 (symdiffI1) =>
% 97.31/13.18 ((
% 97.31/13.18 (symdiffI2) =>
% 97.31/13.18 ((
% 97.31/13.18 (symdiffIneg1) =>
% 97.31/13.18 ((
% 97.31/13.18 (symdiffIneg2) =>
% 97.31/13.18 ((
% 97.31/13.18 (secondinupair) =>
% 97.31/13.18 ((
% 97.31/13.18 (setukpairIL) =>
% 97.31/13.18 ((
% 97.31/13.18 (setukpairIR) =>
% 97.31/13.18 ((
% 97.31/13.18 (kpairiskpair) =>
% 97.31/13.18 ((
% 97.31/13.18 (kpairp) =>
% 97.31/13.18 ((
% 97.31/13.18 (singletonsubset) =>
% 97.31/13.18 ((
% 97.31/13.18 (singletoninpowerset) =>
% 97.31/13.18 ((
% 97.31/13.18 (singletoninpowunion) =>
% 97.31/13.18 ((
% 97.31/13.18 (upairset2E) =>
% 97.31/13.18 ((
% 97.31/13.18 (upairsubunion) =>
% 97.31/13.18 ((
% 97.31/13.18 (upairinpowunion) =>
% 97.31/13.18 ((
% 97.31/13.18 (ubforcartprodlem1) =>
% 97.31/13.18 ((
% 97.31/13.18 (ubforcartprodlem2) =>
% 97.31/13.18 ((
% 97.31/13.18 (ubforcartprodlem3) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodpairin) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodmempair1) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodmempair) =>
% 97.31/13.18 ((
% 97.31/13.18 (setunionE2) =>
% 97.31/13.18 ((
% 97.31/13.18 (setunionsingleton1) =>
% 97.31/13.18 ((
% 97.31/13.18 (setunionsingleton2) =>
% 97.31/13.18 ((
% 97.31/13.18 (setunionsingleton) =>
% 97.31/13.18 ((
% 97.31/13.18 (singletonprop) =>
% 97.31/13.18 ((
% 97.31/13.18 (ex1E1) =>
% 97.31/13.18 ((
% 97.31/13.18 (ex1I) =>
% 97.31/13.18 ((
% 97.31/13.18 (ex1I2) =>
% 97.31/13.18 ((
% 97.31/13.18 (singletonsuniq) =>
% 97.31/13.18 ((
% 97.31/13.18 (setukpairinjL1) =>
% 97.31/13.18 ((
% 97.31/13.18 (kfstsingleton) =>
% 97.31/13.18 ((
% 97.31/13.18 (theprop) =>
% 97.31/13.18 ((
% 97.31/13.18 (kfstpairEq) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodfstin) =>
% 97.31/13.18 ((
% 97.31/13.18 (setukpairinjL2) =>
% 97.31/13.18 ((
% 97.31/13.18 (setukpairinjL) =>
% 97.31/13.18 ((
% 97.31/13.18 (setukpairinjR11) =>
% 97.31/13.18 ((
% 97.31/13.18 (setukpairinjR12) =>
% 97.31/13.18 ((
% 97.31/13.18 (setukpairinjR1) =>
% 97.31/13.18 ((
% 97.31/13.18 (upairequniteq) =>
% 97.31/13.18 ((
% 97.31/13.18 (setukpairinjR2) =>
% 97.31/13.18 ((
% 97.31/13.18 (setukpairinjR) =>
% 97.31/13.18 ((
% 97.31/13.18 (ksndsingleton) =>
% 97.31/13.18 ((
% 97.31/13.18 (ksndpairEq) =>
% 97.31/13.18 ((
% 97.31/13.18 (kpairsurjEq) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodsndin) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodpairmemEL) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodpairmemER) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodmempaircEq) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodfstpairEq) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodsndpairEq) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodpairsurjEq) =>
% 97.31/13.18 ((
% 97.31/13.18 (dpsetconstrI) =>
% 97.31/13.18 ((
% 97.31/13.18 (dpsetconstrSub) =>
% 97.31/13.18 ((
% 97.31/13.18 (setOfPairsIsBReln) =>
% 97.31/13.18 ((
% 97.31/13.18 (dpsetconstrERa) =>
% 97.31/13.18 ((
% 97.31/13.18 (dpsetconstrEL1) =>
% 97.31/13.18 ((
% 97.31/13.18 (dpsetconstrEL2) =>
% 97.31/13.18 ((
% 97.31/13.18 (dpsetconstrER) =>
% 97.31/13.18 ((
% 97.31/13.18 (funcImageSingleton) =>
% 97.31/13.18 ((
% 97.31/13.18 (apProp) =>
% 97.31/13.18 ((
% 97.31/13.18 (app) =>
% 97.31/13.18 ((
% 97.31/13.18 (infuncsetfunc) =>
% 97.31/13.18 ((
% 97.31/13.18 (ap2p) =>
% 97.31/13.18 ((
% 97.31/13.18 (funcinfuncset) =>
% 97.31/13.18 ((
% 97.31/13.18 (lamProp) =>
% 97.31/13.18 ((
% 97.31/13.18 (lamp) =>
% 97.31/13.18 ((
% 97.31/13.18 (lam2p) =>
% 97.31/13.18 ((
% 97.31/13.18 (brelnall1) =>
% 97.31/13.18 ((
% 97.31/13.18 (brelnall2) =>
% 97.31/13.18 ((
% 97.31/13.18 (ex1E2) =>
% 97.31/13.18 ((
% 97.31/13.18 (funcGraphProp1) =>
% 97.31/13.18 ((
% 97.31/13.18 (funcGraphProp3) =>
% 97.31/13.18 ((
% 97.31/13.18 (funcGraphProp2) =>
% 97.31/13.18 ((
% 97.31/13.18 (funcextLem) =>
% 97.31/13.18 ((
% 97.31/13.18 (funcGraphProp4) =>
% 97.31/13.18 ((
% 97.31/13.18 (subbreln) =>
% 97.31/13.18 ((
% 97.31/13.18 (eqbreln) =>
% 97.31/13.18 ((
% 97.31/13.18 (funcext) =>
% 97.31/13.18 ((
% 97.31/13.18 (funcext2) =>
% 97.31/13.18 ((
% 97.31/13.18 (ap2apEq1) =>
% 97.31/13.18 ((
% 97.31/13.18 (ap2apEq2) =>
% 97.31/13.18 ((
% 97.31/13.18 (beta1) =>
% 97.31/13.18 ((
% 97.31/13.18 (eta1) =>
% 97.31/13.18 ((
% 97.31/13.18 (lam2lamEq) =>
% 97.31/13.18 ((
% 97.31/13.18 (beta2) =>
% 97.31/13.18 ((
% 97.31/13.18 (eta2) =>
% 97.31/13.18 ((
% 97.31/13.18 (iffalseProp1) =>
% 97.31/13.18 ((
% 97.31/13.18 (iffalseProp2) =>
% 97.31/13.18 ((
% 97.31/13.18 (iftrueProp1) =>
% 97.31/13.18 ((
% 97.31/13.18 (iftrueProp2) =>
% 97.31/13.18 ((
% 97.31/13.18 (ifSingleton) =>
% 97.31/13.18 ((
% 97.31/13.18 (ifp) =>
% 97.31/13.18 ((
% 97.31/13.18 (theeq) =>
% 97.31/13.18 ((
% 97.31/13.18 (iftrue) =>
% 97.31/13.18 ((
% 97.31/13.18 (iffalse) =>
% 97.31/13.18 ((
% 97.31/13.18 (iftrueorfalse) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectT_lem) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionT_lem) =>
% 97.31/13.18 ((
% 97.31/13.18 (powersetT_lem) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusT_lem) =>
% 97.31/13.18 ((
% 97.31/13.18 (complementT_lem) =>
% 97.31/13.18 ((
% 97.31/13.18 (setextT) =>
% 97.31/13.18 ((
% 97.31/13.18 (subsetTI) =>
% 97.31/13.18 ((
% 97.31/13.18 (powersetTI1) =>
% 97.31/13.18 ((
% 97.31/13.18 (powersetTE1) =>
% 97.31/13.18 ((
% 97.31/13.18 (complementTI1) =>
% 97.31/13.18 ((
% 97.31/13.18 (complementTE1) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectTELcontra) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectTERcontra) =>
% 97.31/13.18 ((
% 97.31/13.18 (contrasubsetT) =>
% 97.31/13.18 ((
% 97.31/13.18 (contrasubsetT1) =>
% 97.31/13.18 ((
% 97.31/13.18 (contrasubsetT2) =>
% 97.31/13.18 ((
% 97.31/13.18 (contrasubsetT3) =>
% 97.31/13.18 ((
% 97.31/13.18 (doubleComplementI1) =>
% 97.31/13.18 ((
% 97.31/13.18 (doubleComplementE1) =>
% 97.31/13.18 ((
% 97.31/13.18 (doubleComplementSub1) =>
% 97.31/13.18 ((
% 97.31/13.18 (doubleComplementSub2) =>
% 97.31/13.18 ((
% 97.31/13.18 (doubleComplementEq) =>
% 97.31/13.18 ((
% 97.31/13.18 (complementTnotintersectT) =>
% 97.31/13.18 ((
% 97.31/13.18 (complementImpComplementIntersect) =>
% 97.31/13.18 ((
% 97.31/13.18 (complementSubsetComplementIntersect) =>
% 97.31/13.18 ((
% 97.31/13.18 (complementInPowersetComplementIntersect) =>
% 97.31/13.18 ((
% 97.31/13.18 (contraSubsetComplement) =>
% 97.31/13.18 ((
% 97.31/13.18 (complementTcontraSubset) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionTILcontra) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionTIRcontra) =>
% 97.31/13.18 ((
% 97.31/13.18 (inIntersectImpInUnion) =>
% 97.31/13.18 ((
% 97.31/13.18 (inIntersectImpInUnion2) =>
% 97.31/13.18 ((
% 97.31/13.18 (inIntersectImpInIntersectUnions) =>
% 97.31/13.18 ((
% 97.31/13.18 (intersectInPowersetIntersectUnions) =>
% 97.31/13.18 ((
% 97.31/13.18 (inComplementUnionImpNotIn1) =>
% 97.31/13.18 ((
% 97.31/13.18 (inComplementUnionImpInComplement1) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionTE) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionTEcontra) =>
% 97.31/13.18 ((
% 97.31/13.18 (demorgan2a1) =>
% 97.31/13.18 ((
% 97.31/13.18 (complementUnionInPowersetComplement) =>
% 97.31/13.18 ((
% 97.31/13.18 (demorgan2a2) =>
% 97.31/13.18 ((
% 97.31/13.18 (demorgan1a) =>
% 97.31/13.18 ((
% 97.31/13.18 (demorgan1b) =>
% 97.31/13.18 ((
% 97.31/13.18 (demorgan1) =>
% 97.31/13.18 ((
% 97.31/13.18 (demorgan2a) =>
% 97.31/13.18 ((
% 97.31/13.18 (demorgan2b2) =>
% 97.31/13.18 ((
% 97.31/13.18 (demorgan2b) =>
% 97.31/13.18 ((
% 97.31/13.18 (demorgan2) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz13rule0) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz13rule1) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz13rule2) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz13rule3) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz13rule4) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz1_1) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz1_2) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz1_3) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz1_4) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz1_5) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1all2) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1SetBreln1) =>
% 97.31/13.18 ((
% 97.31/13.18 (choice2fnsingleton) =>
% 97.31/13.18 ((
% 97.31/13.18 (setOfPairsIsBReln1) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1all1) =>
% 97.31/13.18 ((
% 97.31/13.18 (subbreln1) =>
% 97.31/13.18 ((
% 97.31/13.18 (eqbreln1) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1invprop) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1invI) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1invE) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1compprop) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1compI) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1compE) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1compEex) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1unionprop) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1unionIL) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1unionIR) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1unionI) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1unionE) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1unionEcases) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1unionCommutes) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz2Ex) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz2W) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz2A) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz2B) =>
% 97.31/13.18 ((
% 97.31/13.18 (image1Ex) =>
% 97.31/13.18 ((
% 97.31/13.18 (image1Ex1) =>
% 97.31/13.18 ((
% 97.31/13.18 (image1Equiv) =>
% 97.31/13.18 ((
% 97.31/13.18 (image1E) =>
% 97.31/13.18 ((
% 97.31/13.18 (image1I) =>
% 97.31/13.18 ((
% 97.31/13.18 (injFuncInInjFuncSet) =>
% 97.31/13.18 ((
% 97.31/13.18 (injFuncSetFuncIn) =>
% 97.31/13.18 ((
% 97.31/13.18 (injFuncSetFuncInj) =>
% 97.31/13.18 ((
% 97.31/13.18 (surjFuncSetFuncIn) =>
% 97.31/13.18 ((
% 97.31/13.18 (surjFuncSetFuncSurj) =>
% 97.31/13.18 ((
% 97.31/13.18 (leftInvIsSurj) =>
% 97.31/13.18 ((
% 97.31/13.18 (surjCantorThm) =>
% 97.31/13.18 ((
% 97.31/13.18 (foundation2) =>
% 97.31/13.18 ((
% 97.31/13.18 (notinself) =>
% 97.31/13.18 ((
% 97.31/13.18 (notinself2) =>
% 97.31/13.18 ((
% 97.31/13.18 (omegaSp) =>
% 97.31/13.18 ((
% 97.31/13.18 (omegaSclos) =>
% 97.31/13.18 ((
% 97.31/13.18 (peano0notS) =>
% 97.31/13.18 ((
% 97.31/13.18 (!!) @ (
% 97.31/13.18 (('#S') @ (
% 97.31/13.18 (
% 97.31/13.18 ('#B') @ (
% 97.31/13.18 =>) @
% 97.31/13.18 (
% 97.31/13.18 (
% 97.31/13.18 ('#C') @ in @
% 97.31/13.18 omega)))) @
% 97.31/13.18 (
% 97.31/13.18 (
% 97.31/13.18 ('#B') @ (
% 97.31/13.18 !!) @
% 97.31/13.18 (
% 97.31/13.18 (
% 97.31/13.18 ('#B') @ (
% 97.31/13.18 (
% 97.31/13.18 ('#S') @ (
% 97.31/13.18 (
% 97.31/13.18 ('#B') @ (
% 97.31/13.18 =>) @
% 97.31/13.18 (
% 97.31/13.18 (
% 97.31/13.18 ('#C') @ in @
% 97.31/13.18 omega)))))) @
% 97.31/13.18 (
% 97.31/13.18 (
% 97.31/13.18 ('#S') @ (
% 97.31/13.18 (
% 97.31/13.18 ('#B') @ (
% 97.31/13.18 '#S') @
% 97.31/13.18 (
% 97.31/13.18 (
% 97.31/13.18 ('#B') @ (
% 97.31/13.18 (
% 97.31/13.18 ('#B') @ (
% 97.31/13.18 =>))) @
% 97.31/13.18 (
% 97.31/13.18 (
% 97.31/13.18 ('#C') @ (
% 97.31/13.18 (
% 97.31/13.18 ('#B') @ (
% 97.31/13.18 '#B') @
% 97.31/13.18 (
% 97.31/13.18 (
% 97.31/13.18 ('#B') @ (
% 97.31/13.18 =) @
% 97.31/13.18 omegaS)))) @
% 97.31/13.18 omegaS)))))) @
% 97.31/13.18 (
% 97.31/13.18 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.31/13.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl369])).
% 97.31/13.18 thf(zip_derived_cl384, plain,
% 97.31/13.18 (~ (((emptyInPowerset) =>
% 97.31/13.18 (((powersetE) =>
% 97.31/13.18 (((setunionI) =>
% 97.31/13.18 (((setunionE) =>
% 97.31/13.18 (((subPowSU) =>
% 97.31/13.18 (((exuE2) =>
% 97.31/13.18 (((nonemptyImpWitness) =>
% 97.31/13.18 (((uniqinunit) =>
% 97.31/13.18 (((notinsingleton) =>
% 97.31/13.18 (((eqinunit) =>
% 97.31/13.18 (((singletonsswitch) =>
% 97.31/13.18 (((upairsetE) =>
% 97.31/13.18 (((upairsetIL) =>
% 97.31/13.18 (((upairsetIR) =>
% 97.31/13.18 (((emptyE1) =>
% 97.31/13.18 (((vacuousDall) =>
% 97.31/13.18 (((quantDeMorgan1) =>
% 97.31/13.18 (((quantDeMorgan2) =>
% 97.31/13.18 (((quantDeMorgan3) =>
% 97.31/13.18 (((quantDeMorgan4) =>
% 97.31/13.18 (((prop2setI) =>
% 97.31/13.18 (((prop2set2propI) =>
% 97.31/13.18 (((notdexE) =>
% 97.31/13.18 (((notdallE) =>
% 97.31/13.18 (((exuI1) =>
% 97.31/13.18 (((exuI3) =>
% 97.31/13.18 (((exuI2) =>
% 97.31/13.18 (((inCongP) =>
% 97.31/13.18 (((in__Cong) =>
% 97.31/13.18 (((exuE3u) =>
% 97.31/13.18 ((
% 97.31/13.18 (exu__Cong) =>
% 97.31/13.18 ((
% 97.31/13.18 (setadjoin__Cong) =>
% 97.31/13.18 ((
% 97.31/13.18 (powerset__Cong) =>
% 97.31/13.18 ((
% 97.31/13.18 (setunion__Cong) =>
% 97.31/13.18 ((
% 97.31/13.18 (exuEu) =>
% 97.31/13.18 ((
% 97.31/13.18 (descr__Cong) =>
% 97.31/13.18 ((
% 97.31/13.18 (dsetconstr__Cong) =>
% 97.31/13.18 ((
% 97.31/13.18 (subsetI1) =>
% 97.31/13.18 ((
% 97.31/13.18 (eqimpsubset2) =>
% 97.31/13.18 ((
% 97.31/13.18 (eqimpsubset1) =>
% 97.31/13.18 ((
% 97.31/13.18 (subsetI2) =>
% 97.31/13.18 ((
% 97.31/13.18 (emptysetsubset) =>
% 97.31/13.18 ((
% 97.31/13.18 (subsetE) =>
% 97.31/13.18 ((
% 97.31/13.18 (subsetE2) =>
% 97.31/13.18 ((
% 97.31/13.18 (notsubsetI) =>
% 97.31/13.18 ((
% 97.31/13.18 (notequalI1) =>
% 97.31/13.18 ((
% 97.31/13.18 (notequalI2) =>
% 97.31/13.18 ((
% 97.31/13.18 (subsetRefl) =>
% 97.31/13.18 ((
% 97.31/13.18 (subsetTrans) =>
% 97.31/13.18 ((
% 97.31/13.18 (setadjoinSub) =>
% 97.31/13.18 ((
% 97.31/13.18 (setadjoinSub2) =>
% 97.31/13.18 ((
% 97.31/13.18 (subset2powerset) =>
% 97.31/13.18 ((
% 97.31/13.18 (setextsub) =>
% 97.31/13.18 ((
% 97.31/13.18 (subsetemptysetimpeq) =>
% 97.31/13.18 ((
% 97.31/13.18 (powersetI1) =>
% 97.31/13.18 ((
% 97.31/13.18 (powersetE1) =>
% 97.31/13.18 ((
% 97.31/13.18 (inPowerset) =>
% 97.31/13.18 ((
% 97.31/13.18 (powersetsubset) =>
% 97.31/13.18 ((
% 97.31/13.18 (sepInPowerset) =>
% 97.31/13.18 ((
% 97.31/13.18 (sepSubset) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionIL) =>
% 97.31/13.18 ((
% 97.31/13.18 (upairset2IR) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionIR) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionEcases) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionE) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionLsub) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionRsub) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectI) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectSubset5) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectEL) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectLsub) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectSubset2) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectSubset3) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectER) =>
% 97.31/13.18 ((
% 97.31/13.18 (disjointsetsI1) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectRsub) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectSubset4) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectSubset1) =>
% 97.31/13.18 ((
% 97.31/13.18 (bs114d) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusI) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusEL) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusER) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusSubset2) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusERneg) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusELneg) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusILneg) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusIRneg) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusLsub) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusSubset1) =>
% 97.31/13.18 ((
% 97.31/13.18 (symdiffE) =>
% 97.31/13.18 ((
% 97.31/13.18 (symdiffI1) =>
% 97.31/13.18 ((
% 97.31/13.18 (symdiffI2) =>
% 97.31/13.18 ((
% 97.31/13.18 (symdiffIneg1) =>
% 97.31/13.18 ((
% 97.31/13.18 (symdiffIneg2) =>
% 97.31/13.18 ((
% 97.31/13.18 (secondinupair) =>
% 97.31/13.18 ((
% 97.31/13.18 (setukpairIL) =>
% 97.31/13.18 ((
% 97.31/13.18 (setukpairIR) =>
% 97.31/13.18 ((
% 97.31/13.18 (kpairiskpair) =>
% 97.31/13.18 ((
% 97.31/13.18 (kpairp) =>
% 97.31/13.18 ((
% 97.31/13.18 (singletonsubset) =>
% 97.31/13.18 ((
% 97.31/13.18 (singletoninpowerset) =>
% 97.31/13.18 ((
% 97.31/13.18 (singletoninpowunion) =>
% 97.31/13.18 ((
% 97.31/13.18 (upairset2E) =>
% 97.31/13.18 ((
% 97.31/13.18 (upairsubunion) =>
% 97.31/13.18 ((
% 97.31/13.18 (upairinpowunion) =>
% 97.31/13.18 ((
% 97.31/13.18 (ubforcartprodlem1) =>
% 97.31/13.18 ((
% 97.31/13.18 (ubforcartprodlem2) =>
% 97.31/13.18 ((
% 97.31/13.18 (ubforcartprodlem3) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodpairin) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodmempair1) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodmempair) =>
% 97.31/13.18 ((
% 97.31/13.18 (setunionE2) =>
% 97.31/13.18 ((
% 97.31/13.18 (setunionsingleton1) =>
% 97.31/13.18 ((
% 97.31/13.18 (setunionsingleton2) =>
% 97.31/13.18 ((
% 97.31/13.18 (setunionsingleton) =>
% 97.31/13.18 ((
% 97.31/13.18 (singletonprop) =>
% 97.31/13.18 ((
% 97.31/13.18 (ex1E1) =>
% 97.31/13.18 ((
% 97.31/13.18 (ex1I) =>
% 97.31/13.18 ((
% 97.31/13.18 (ex1I2) =>
% 97.31/13.18 ((
% 97.31/13.18 (singletonsuniq) =>
% 97.31/13.18 ((
% 97.31/13.18 (setukpairinjL1) =>
% 97.31/13.18 ((
% 97.31/13.18 (kfstsingleton) =>
% 97.31/13.18 ((
% 97.31/13.18 (theprop) =>
% 97.31/13.18 ((
% 97.31/13.18 (kfstpairEq) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodfstin) =>
% 97.31/13.18 ((
% 97.31/13.18 (setukpairinjL2) =>
% 97.31/13.18 ((
% 97.31/13.18 (setukpairinjL) =>
% 97.31/13.18 ((
% 97.31/13.18 (setukpairinjR11) =>
% 97.31/13.18 ((
% 97.31/13.18 (setukpairinjR12) =>
% 97.31/13.18 ((
% 97.31/13.18 (setukpairinjR1) =>
% 97.31/13.18 ((
% 97.31/13.18 (upairequniteq) =>
% 97.31/13.18 ((
% 97.31/13.18 (setukpairinjR2) =>
% 97.31/13.18 ((
% 97.31/13.18 (setukpairinjR) =>
% 97.31/13.18 ((
% 97.31/13.18 (ksndsingleton) =>
% 97.31/13.18 ((
% 97.31/13.18 (ksndpairEq) =>
% 97.31/13.18 ((
% 97.31/13.18 (kpairsurjEq) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodsndin) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodpairmemEL) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodpairmemER) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodmempaircEq) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodfstpairEq) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodsndpairEq) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodpairsurjEq) =>
% 97.31/13.18 ((
% 97.31/13.18 (dpsetconstrI) =>
% 97.31/13.18 ((
% 97.31/13.18 (dpsetconstrSub) =>
% 97.31/13.18 ((
% 97.31/13.18 (setOfPairsIsBReln) =>
% 97.31/13.18 ((
% 97.31/13.18 (dpsetconstrERa) =>
% 97.31/13.18 ((
% 97.31/13.18 (dpsetconstrEL1) =>
% 97.31/13.18 ((
% 97.31/13.18 (dpsetconstrEL2) =>
% 97.31/13.18 ((
% 97.31/13.18 (dpsetconstrER) =>
% 97.31/13.18 ((
% 97.31/13.18 (funcImageSingleton) =>
% 97.31/13.18 ((
% 97.31/13.18 (apProp) =>
% 97.31/13.18 ((
% 97.31/13.18 (app) =>
% 97.31/13.18 ((
% 97.31/13.18 (infuncsetfunc) =>
% 97.31/13.18 ((
% 97.31/13.18 (ap2p) =>
% 97.31/13.18 ((
% 97.31/13.18 (funcinfuncset) =>
% 97.31/13.18 ((
% 97.31/13.18 (lamProp) =>
% 97.31/13.18 ((
% 97.31/13.18 (lamp) =>
% 97.31/13.18 ((
% 97.31/13.18 (lam2p) =>
% 97.31/13.18 ((
% 97.31/13.18 (brelnall1) =>
% 97.31/13.18 ((
% 97.31/13.18 (brelnall2) =>
% 97.31/13.18 ((
% 97.31/13.18 (ex1E2) =>
% 97.31/13.18 ((
% 97.31/13.18 (funcGraphProp1) =>
% 97.31/13.18 ((
% 97.31/13.18 (funcGraphProp3) =>
% 97.31/13.18 ((
% 97.31/13.18 (funcGraphProp2) =>
% 97.31/13.18 ((
% 97.31/13.18 (funcextLem) =>
% 97.31/13.18 ((
% 97.31/13.18 (funcGraphProp4) =>
% 97.31/13.18 ((
% 97.31/13.18 (subbreln) =>
% 97.31/13.18 ((
% 97.31/13.18 (eqbreln) =>
% 97.31/13.18 ((
% 97.31/13.18 (funcext) =>
% 97.31/13.18 ((
% 97.31/13.18 (funcext2) =>
% 97.31/13.18 ((
% 97.31/13.18 (ap2apEq1) =>
% 97.31/13.18 ((
% 97.31/13.18 (ap2apEq2) =>
% 97.31/13.18 ((
% 97.31/13.18 (beta1) =>
% 97.31/13.18 ((
% 97.31/13.18 (eta1) =>
% 97.31/13.18 ((
% 97.31/13.18 (lam2lamEq) =>
% 97.31/13.18 ((
% 97.31/13.18 (beta2) =>
% 97.31/13.18 ((
% 97.31/13.18 (eta2) =>
% 97.31/13.18 ((
% 97.31/13.18 (iffalseProp1) =>
% 97.31/13.18 ((
% 97.31/13.18 (iffalseProp2) =>
% 97.31/13.18 ((
% 97.31/13.18 (iftrueProp1) =>
% 97.31/13.18 ((
% 97.31/13.18 (iftrueProp2) =>
% 97.31/13.18 ((
% 97.31/13.18 (ifSingleton) =>
% 97.31/13.18 ((
% 97.31/13.18 (ifp) =>
% 97.31/13.18 ((
% 97.31/13.18 (theeq) =>
% 97.31/13.18 ((
% 97.31/13.18 (iftrue) =>
% 97.31/13.18 ((
% 97.31/13.18 (iffalse) =>
% 97.31/13.18 ((
% 97.31/13.18 (iftrueorfalse) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectT_lem) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionT_lem) =>
% 97.31/13.18 ((
% 97.31/13.18 (powersetT_lem) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusT_lem) =>
% 97.31/13.18 ((
% 97.31/13.18 (complementT_lem) =>
% 97.31/13.18 ((
% 97.31/13.18 (setextT) =>
% 97.31/13.18 ((
% 97.31/13.18 (subsetTI) =>
% 97.31/13.18 ((
% 97.31/13.18 (powersetTI1) =>
% 97.31/13.18 ((
% 97.31/13.18 (powersetTE1) =>
% 97.31/13.18 ((
% 97.31/13.18 (complementTI1) =>
% 97.31/13.18 ((
% 97.31/13.18 (complementTE1) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectTELcontra) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectTERcontra) =>
% 97.31/13.18 ((
% 97.31/13.18 (contrasubsetT) =>
% 97.31/13.18 ((
% 97.31/13.18 (contrasubsetT1) =>
% 97.31/13.18 ((
% 97.31/13.18 (contrasubsetT2) =>
% 97.31/13.18 ((
% 97.31/13.18 (contrasubsetT3) =>
% 97.31/13.18 ((
% 97.31/13.18 (doubleComplementI1) =>
% 97.31/13.18 ((
% 97.31/13.18 (doubleComplementE1) =>
% 97.31/13.18 ((
% 97.31/13.18 (doubleComplementSub1) =>
% 97.31/13.18 ((
% 97.31/13.18 (doubleComplementSub2) =>
% 97.31/13.18 ((
% 97.31/13.18 (doubleComplementEq) =>
% 97.31/13.18 ((
% 97.31/13.18 (complementTnotintersectT) =>
% 97.31/13.18 ((
% 97.31/13.18 (complementImpComplementIntersect) =>
% 97.31/13.18 ((
% 97.31/13.18 (complementSubsetComplementIntersect) =>
% 97.31/13.18 ((
% 97.31/13.18 (complementInPowersetComplementIntersect) =>
% 97.31/13.18 ((
% 97.31/13.18 (contraSubsetComplement) =>
% 97.31/13.18 ((
% 97.31/13.18 (complementTcontraSubset) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionTILcontra) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionTIRcontra) =>
% 97.31/13.18 ((
% 97.31/13.18 (inIntersectImpInUnion) =>
% 97.31/13.18 ((
% 97.31/13.18 (inIntersectImpInUnion2) =>
% 97.31/13.18 ((
% 97.31/13.18 (inIntersectImpInIntersectUnions) =>
% 97.31/13.18 ((
% 97.31/13.18 (intersectInPowersetIntersectUnions) =>
% 97.31/13.18 ((
% 97.31/13.18 (inComplementUnionImpNotIn1) =>
% 97.31/13.18 ((
% 97.31/13.18 (inComplementUnionImpInComplement1) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionTE) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionTEcontra) =>
% 97.31/13.18 ((
% 97.31/13.18 (demorgan2a1) =>
% 97.31/13.18 ((
% 97.31/13.18 (complementUnionInPowersetComplement) =>
% 97.31/13.18 ((
% 97.31/13.18 (demorgan2a2) =>
% 97.31/13.18 ((
% 97.31/13.18 (demorgan1a) =>
% 97.31/13.18 ((
% 97.31/13.18 (demorgan1b) =>
% 97.31/13.18 ((
% 97.31/13.18 (demorgan1) =>
% 97.31/13.18 ((
% 97.31/13.18 (demorgan2a) =>
% 97.31/13.18 ((
% 97.31/13.18 (demorgan2b2) =>
% 97.31/13.18 ((
% 97.31/13.18 (demorgan2b) =>
% 97.31/13.18 ((
% 97.31/13.18 (demorgan2) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz13rule0) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz13rule1) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz13rule2) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz13rule3) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz13rule4) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz1_1) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz1_2) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz1_3) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz1_4) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz1_5) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1all2) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1SetBreln1) =>
% 97.31/13.18 ((
% 97.31/13.18 (choice2fnsingleton) =>
% 97.31/13.18 ((
% 97.31/13.18 (setOfPairsIsBReln1) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1all1) =>
% 97.31/13.18 ((
% 97.31/13.18 (subbreln1) =>
% 97.31/13.18 ((
% 97.31/13.18 (eqbreln1) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1invprop) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1invI) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1invE) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1compprop) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1compI) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1compE) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1compEex) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1unionprop) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1unionIL) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1unionIR) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1unionI) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1unionE) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1unionEcases) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1unionCommutes) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz2Ex) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz2W) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz2A) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz2B) =>
% 97.31/13.18 ((
% 97.31/13.18 (image1Ex) =>
% 97.31/13.18 ((
% 97.31/13.18 (image1Ex1) =>
% 97.31/13.18 ((
% 97.31/13.18 (image1Equiv) =>
% 97.31/13.18 ((
% 97.31/13.18 (image1E) =>
% 97.31/13.18 ((
% 97.31/13.18 (image1I) =>
% 97.31/13.18 ((
% 97.31/13.18 (injFuncInInjFuncSet) =>
% 97.31/13.18 ((
% 97.31/13.18 (injFuncSetFuncIn) =>
% 97.31/13.18 ((
% 97.31/13.18 (injFuncSetFuncInj) =>
% 97.31/13.18 ((
% 97.31/13.18 (surjFuncSetFuncIn) =>
% 97.31/13.18 ((
% 97.31/13.18 (surjFuncSetFuncSurj) =>
% 97.31/13.18 ((
% 97.31/13.18 (leftInvIsSurj) =>
% 97.31/13.18 ((
% 97.31/13.18 (surjCantorThm) =>
% 97.31/13.18 ((
% 97.31/13.18 (foundation2) =>
% 97.31/13.18 ((
% 97.31/13.18 (notinself) =>
% 97.31/13.18 ((
% 97.31/13.18 (notinself2) =>
% 97.31/13.18 ((
% 97.31/13.18 (omegaSp) =>
% 97.31/13.18 ((
% 97.31/13.18 (omegaSclos) =>
% 97.31/13.18 ((
% 97.31/13.18 (peano0notS) =>
% 97.31/13.18 ((
% 97.31/13.18 (!!) @ (
% 97.31/13.18 (('#S') @ (
% 97.31/13.18 (
% 97.31/13.18 ('#B') @ (
% 97.31/13.18 =>) @
% 97.31/13.18 (
% 97.31/13.18 (
% 97.31/13.18 ('#C') @ in @
% 97.31/13.18 omega)))) @
% 97.31/13.18 (
% 97.31/13.18 (
% 97.31/13.18 ('#B') @ (
% 97.31/13.18 !!) @
% 97.31/13.18 (
% 97.31/13.18 (
% 97.31/13.18 ('#B') @ (
% 97.31/13.18 (
% 97.31/13.18 ('#S') @ (
% 97.31/13.18 (
% 97.31/13.18 ('#B') @ (
% 97.31/13.18 =>) @
% 97.31/13.18 (
% 97.31/13.18 (
% 97.31/13.18 ('#C') @ in @
% 97.31/13.18 omega)))))) @
% 97.31/13.18 (
% 97.31/13.18 (
% 97.31/13.18 ('#S') @ (
% 97.31/13.18 (
% 97.31/13.18 ('#B') @ (
% 97.31/13.18 '#S') @
% 97.31/13.18 (
% 97.31/13.18 (
% 97.31/13.18 ('#B') @ (
% 97.31/13.18 (
% 97.31/13.18 ('#B') @ (
% 97.31/13.18 =>))) @
% 97.31/13.18 (
% 97.31/13.18 (
% 97.31/13.18 ('#C') @ (
% 97.31/13.18 (
% 97.31/13.18 ('#B') @ (
% 97.31/13.18 '#B') @
% 97.31/13.18 (
% 97.31/13.18 (
% 97.31/13.18 ('#B') @ (
% 97.31/13.18 =) @
% 97.31/13.18 omegaS)))) @
% 97.31/13.18 omegaS)))))) @
% 97.31/13.18 (
% 97.31/13.18 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.31/13.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl376])).
% 97.31/13.18 thf(zip_derived_cl392, plain,
% 97.31/13.18 (~ (((powersetE) =>
% 97.31/13.18 (((setunionI) =>
% 97.31/13.18 (((setunionE) =>
% 97.31/13.18 (((subPowSU) =>
% 97.31/13.18 (((exuE2) =>
% 97.31/13.18 (((nonemptyImpWitness) =>
% 97.31/13.18 (((uniqinunit) =>
% 97.31/13.18 (((notinsingleton) =>
% 97.31/13.18 (((eqinunit) =>
% 97.31/13.18 (((singletonsswitch) =>
% 97.31/13.18 (((upairsetE) =>
% 97.31/13.18 (((upairsetIL) =>
% 97.31/13.18 (((upairsetIR) =>
% 97.31/13.18 (((emptyE1) =>
% 97.31/13.18 (((vacuousDall) =>
% 97.31/13.18 (((quantDeMorgan1) =>
% 97.31/13.18 (((quantDeMorgan2) =>
% 97.31/13.18 (((quantDeMorgan3) =>
% 97.31/13.18 (((quantDeMorgan4) =>
% 97.31/13.18 (((prop2setI) =>
% 97.31/13.18 (((prop2set2propI) =>
% 97.31/13.18 (((notdexE) =>
% 97.31/13.18 (((notdallE) =>
% 97.31/13.18 (((exuI1) =>
% 97.31/13.18 (((exuI3) =>
% 97.31/13.18 (((exuI2) =>
% 97.31/13.18 (((inCongP) =>
% 97.31/13.18 (((in__Cong) =>
% 97.31/13.18 (((exuE3u) =>
% 97.31/13.18 (((exu__Cong) =>
% 97.31/13.18 ((
% 97.31/13.18 (setadjoin__Cong) =>
% 97.31/13.18 ((
% 97.31/13.18 (powerset__Cong) =>
% 97.31/13.18 ((
% 97.31/13.18 (setunion__Cong) =>
% 97.31/13.18 ((
% 97.31/13.18 (exuEu) =>
% 97.31/13.18 ((
% 97.31/13.18 (descr__Cong) =>
% 97.31/13.18 ((
% 97.31/13.18 (dsetconstr__Cong) =>
% 97.31/13.18 ((
% 97.31/13.18 (subsetI1) =>
% 97.31/13.18 ((
% 97.31/13.18 (eqimpsubset2) =>
% 97.31/13.18 ((
% 97.31/13.18 (eqimpsubset1) =>
% 97.31/13.18 ((
% 97.31/13.18 (subsetI2) =>
% 97.31/13.18 ((
% 97.31/13.18 (emptysetsubset) =>
% 97.31/13.18 ((
% 97.31/13.18 (subsetE) =>
% 97.31/13.18 ((
% 97.31/13.18 (subsetE2) =>
% 97.31/13.18 ((
% 97.31/13.18 (notsubsetI) =>
% 97.31/13.18 ((
% 97.31/13.18 (notequalI1) =>
% 97.31/13.18 ((
% 97.31/13.18 (notequalI2) =>
% 97.31/13.18 ((
% 97.31/13.18 (subsetRefl) =>
% 97.31/13.18 ((
% 97.31/13.18 (subsetTrans) =>
% 97.31/13.18 ((
% 97.31/13.18 (setadjoinSub) =>
% 97.31/13.18 ((
% 97.31/13.18 (setadjoinSub2) =>
% 97.31/13.18 ((
% 97.31/13.18 (subset2powerset) =>
% 97.31/13.18 ((
% 97.31/13.18 (setextsub) =>
% 97.31/13.18 ((
% 97.31/13.18 (subsetemptysetimpeq) =>
% 97.31/13.18 ((
% 97.31/13.18 (powersetI1) =>
% 97.31/13.18 ((
% 97.31/13.18 (powersetE1) =>
% 97.31/13.18 ((
% 97.31/13.18 (inPowerset) =>
% 97.31/13.18 ((
% 97.31/13.18 (powersetsubset) =>
% 97.31/13.18 ((
% 97.31/13.18 (sepInPowerset) =>
% 97.31/13.18 ((
% 97.31/13.18 (sepSubset) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionIL) =>
% 97.31/13.18 ((
% 97.31/13.18 (upairset2IR) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionIR) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionEcases) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionE) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionLsub) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionRsub) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectI) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectSubset5) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectEL) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectLsub) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectSubset2) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectSubset3) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectER) =>
% 97.31/13.18 ((
% 97.31/13.18 (disjointsetsI1) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectRsub) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectSubset4) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectSubset1) =>
% 97.31/13.18 ((
% 97.31/13.18 (bs114d) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusI) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusEL) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusER) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusSubset2) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusERneg) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusELneg) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusILneg) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusIRneg) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusLsub) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusSubset1) =>
% 97.31/13.18 ((
% 97.31/13.18 (symdiffE) =>
% 97.31/13.18 ((
% 97.31/13.18 (symdiffI1) =>
% 97.31/13.18 ((
% 97.31/13.18 (symdiffI2) =>
% 97.31/13.18 ((
% 97.31/13.18 (symdiffIneg1) =>
% 97.31/13.18 ((
% 97.31/13.18 (symdiffIneg2) =>
% 97.31/13.18 ((
% 97.31/13.18 (secondinupair) =>
% 97.31/13.18 ((
% 97.31/13.18 (setukpairIL) =>
% 97.31/13.18 ((
% 97.31/13.18 (setukpairIR) =>
% 97.31/13.18 ((
% 97.31/13.18 (kpairiskpair) =>
% 97.31/13.18 ((
% 97.31/13.18 (kpairp) =>
% 97.31/13.18 ((
% 97.31/13.18 (singletonsubset) =>
% 97.31/13.18 ((
% 97.31/13.18 (singletoninpowerset) =>
% 97.31/13.18 ((
% 97.31/13.18 (singletoninpowunion) =>
% 97.31/13.18 ((
% 97.31/13.18 (upairset2E) =>
% 97.31/13.18 ((
% 97.31/13.18 (upairsubunion) =>
% 97.31/13.18 ((
% 97.31/13.18 (upairinpowunion) =>
% 97.31/13.18 ((
% 97.31/13.18 (ubforcartprodlem1) =>
% 97.31/13.18 ((
% 97.31/13.18 (ubforcartprodlem2) =>
% 97.31/13.18 ((
% 97.31/13.18 (ubforcartprodlem3) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodpairin) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodmempair1) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodmempair) =>
% 97.31/13.18 ((
% 97.31/13.18 (setunionE2) =>
% 97.31/13.18 ((
% 97.31/13.18 (setunionsingleton1) =>
% 97.31/13.18 ((
% 97.31/13.18 (setunionsingleton2) =>
% 97.31/13.18 ((
% 97.31/13.18 (setunionsingleton) =>
% 97.31/13.18 ((
% 97.31/13.18 (singletonprop) =>
% 97.31/13.18 ((
% 97.31/13.18 (ex1E1) =>
% 97.31/13.18 ((
% 97.31/13.18 (ex1I) =>
% 97.31/13.18 ((
% 97.31/13.18 (ex1I2) =>
% 97.31/13.18 ((
% 97.31/13.18 (singletonsuniq) =>
% 97.31/13.18 ((
% 97.31/13.18 (setukpairinjL1) =>
% 97.31/13.18 ((
% 97.31/13.18 (kfstsingleton) =>
% 97.31/13.18 ((
% 97.31/13.18 (theprop) =>
% 97.31/13.18 ((
% 97.31/13.18 (kfstpairEq) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodfstin) =>
% 97.31/13.18 ((
% 97.31/13.18 (setukpairinjL2) =>
% 97.31/13.18 ((
% 97.31/13.18 (setukpairinjL) =>
% 97.31/13.18 ((
% 97.31/13.18 (setukpairinjR11) =>
% 97.31/13.18 ((
% 97.31/13.18 (setukpairinjR12) =>
% 97.31/13.18 ((
% 97.31/13.18 (setukpairinjR1) =>
% 97.31/13.18 ((
% 97.31/13.18 (upairequniteq) =>
% 97.31/13.18 ((
% 97.31/13.18 (setukpairinjR2) =>
% 97.31/13.18 ((
% 97.31/13.18 (setukpairinjR) =>
% 97.31/13.18 ((
% 97.31/13.18 (ksndsingleton) =>
% 97.31/13.18 ((
% 97.31/13.18 (ksndpairEq) =>
% 97.31/13.18 ((
% 97.31/13.18 (kpairsurjEq) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodsndin) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodpairmemEL) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodpairmemER) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodmempaircEq) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodfstpairEq) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodsndpairEq) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodpairsurjEq) =>
% 97.31/13.18 ((
% 97.31/13.18 (dpsetconstrI) =>
% 97.31/13.18 ((
% 97.31/13.18 (dpsetconstrSub) =>
% 97.31/13.18 ((
% 97.31/13.18 (setOfPairsIsBReln) =>
% 97.31/13.18 ((
% 97.31/13.18 (dpsetconstrERa) =>
% 97.31/13.18 ((
% 97.31/13.18 (dpsetconstrEL1) =>
% 97.31/13.18 ((
% 97.31/13.18 (dpsetconstrEL2) =>
% 97.31/13.18 ((
% 97.31/13.18 (dpsetconstrER) =>
% 97.31/13.18 ((
% 97.31/13.18 (funcImageSingleton) =>
% 97.31/13.18 ((
% 97.31/13.18 (apProp) =>
% 97.31/13.18 ((
% 97.31/13.18 (app) =>
% 97.31/13.18 ((
% 97.31/13.18 (infuncsetfunc) =>
% 97.31/13.18 ((
% 97.31/13.18 (ap2p) =>
% 97.31/13.18 ((
% 97.31/13.18 (funcinfuncset) =>
% 97.31/13.18 ((
% 97.31/13.18 (lamProp) =>
% 97.31/13.18 ((
% 97.31/13.18 (lamp) =>
% 97.31/13.18 ((
% 97.31/13.18 (lam2p) =>
% 97.31/13.18 ((
% 97.31/13.18 (brelnall1) =>
% 97.31/13.18 ((
% 97.31/13.18 (brelnall2) =>
% 97.31/13.18 ((
% 97.31/13.18 (ex1E2) =>
% 97.31/13.18 ((
% 97.31/13.18 (funcGraphProp1) =>
% 97.31/13.18 ((
% 97.31/13.18 (funcGraphProp3) =>
% 97.31/13.18 ((
% 97.31/13.18 (funcGraphProp2) =>
% 97.31/13.18 ((
% 97.31/13.18 (funcextLem) =>
% 97.31/13.18 ((
% 97.31/13.18 (funcGraphProp4) =>
% 97.31/13.18 ((
% 97.31/13.18 (subbreln) =>
% 97.31/13.18 ((
% 97.31/13.18 (eqbreln) =>
% 97.31/13.18 ((
% 97.31/13.18 (funcext) =>
% 97.31/13.18 ((
% 97.31/13.18 (funcext2) =>
% 97.31/13.18 ((
% 97.31/13.18 (ap2apEq1) =>
% 97.31/13.18 ((
% 97.31/13.18 (ap2apEq2) =>
% 97.31/13.18 ((
% 97.31/13.18 (beta1) =>
% 97.31/13.18 ((
% 97.31/13.18 (eta1) =>
% 97.31/13.18 ((
% 97.31/13.18 (lam2lamEq) =>
% 97.31/13.18 ((
% 97.31/13.18 (beta2) =>
% 97.31/13.18 ((
% 97.31/13.18 (eta2) =>
% 97.31/13.18 ((
% 97.31/13.18 (iffalseProp1) =>
% 97.31/13.18 ((
% 97.31/13.18 (iffalseProp2) =>
% 97.31/13.18 ((
% 97.31/13.18 (iftrueProp1) =>
% 97.31/13.18 ((
% 97.31/13.18 (iftrueProp2) =>
% 97.31/13.18 ((
% 97.31/13.18 (ifSingleton) =>
% 97.31/13.18 ((
% 97.31/13.18 (ifp) =>
% 97.31/13.18 ((
% 97.31/13.18 (theeq) =>
% 97.31/13.18 ((
% 97.31/13.18 (iftrue) =>
% 97.31/13.18 ((
% 97.31/13.18 (iffalse) =>
% 97.31/13.18 ((
% 97.31/13.18 (iftrueorfalse) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectT_lem) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionT_lem) =>
% 97.31/13.18 ((
% 97.31/13.18 (powersetT_lem) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusT_lem) =>
% 97.31/13.18 ((
% 97.31/13.18 (complementT_lem) =>
% 97.31/13.18 ((
% 97.31/13.18 (setextT) =>
% 97.31/13.18 ((
% 97.31/13.18 (subsetTI) =>
% 97.31/13.18 ((
% 97.31/13.18 (powersetTI1) =>
% 97.31/13.18 ((
% 97.31/13.18 (powersetTE1) =>
% 97.31/13.18 ((
% 97.31/13.18 (complementTI1) =>
% 97.31/13.18 ((
% 97.31/13.18 (complementTE1) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectTELcontra) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectTERcontra) =>
% 97.31/13.18 ((
% 97.31/13.18 (contrasubsetT) =>
% 97.31/13.18 ((
% 97.31/13.18 (contrasubsetT1) =>
% 97.31/13.18 ((
% 97.31/13.18 (contrasubsetT2) =>
% 97.31/13.18 ((
% 97.31/13.18 (contrasubsetT3) =>
% 97.31/13.18 ((
% 97.31/13.18 (doubleComplementI1) =>
% 97.31/13.18 ((
% 97.31/13.18 (doubleComplementE1) =>
% 97.31/13.18 ((
% 97.31/13.18 (doubleComplementSub1) =>
% 97.31/13.18 ((
% 97.31/13.18 (doubleComplementSub2) =>
% 97.31/13.18 ((
% 97.31/13.18 (doubleComplementEq) =>
% 97.31/13.18 ((
% 97.31/13.18 (complementTnotintersectT) =>
% 97.31/13.18 ((
% 97.31/13.18 (complementImpComplementIntersect) =>
% 97.31/13.18 ((
% 97.31/13.18 (complementSubsetComplementIntersect) =>
% 97.31/13.18 ((
% 97.31/13.18 (complementInPowersetComplementIntersect) =>
% 97.31/13.18 ((
% 97.31/13.18 (contraSubsetComplement) =>
% 97.31/13.18 ((
% 97.31/13.18 (complementTcontraSubset) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionTILcontra) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionTIRcontra) =>
% 97.31/13.18 ((
% 97.31/13.18 (inIntersectImpInUnion) =>
% 97.31/13.18 ((
% 97.31/13.18 (inIntersectImpInUnion2) =>
% 97.31/13.18 ((
% 97.31/13.18 (inIntersectImpInIntersectUnions) =>
% 97.31/13.18 ((
% 97.31/13.18 (intersectInPowersetIntersectUnions) =>
% 97.31/13.18 ((
% 97.31/13.18 (inComplementUnionImpNotIn1) =>
% 97.31/13.18 ((
% 97.31/13.18 (inComplementUnionImpInComplement1) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionTE) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionTEcontra) =>
% 97.31/13.18 ((
% 97.31/13.18 (demorgan2a1) =>
% 97.31/13.18 ((
% 97.31/13.18 (complementUnionInPowersetComplement) =>
% 97.31/13.18 ((
% 97.31/13.18 (demorgan2a2) =>
% 97.31/13.18 ((
% 97.31/13.18 (demorgan1a) =>
% 97.31/13.18 ((
% 97.31/13.18 (demorgan1b) =>
% 97.31/13.18 ((
% 97.31/13.18 (demorgan1) =>
% 97.31/13.18 ((
% 97.31/13.18 (demorgan2a) =>
% 97.31/13.18 ((
% 97.31/13.18 (demorgan2b2) =>
% 97.31/13.18 ((
% 97.31/13.18 (demorgan2b) =>
% 97.31/13.18 ((
% 97.31/13.18 (demorgan2) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz13rule0) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz13rule1) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz13rule2) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz13rule3) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz13rule4) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz1_1) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz1_2) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz1_3) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz1_4) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz1_5) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1all2) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1SetBreln1) =>
% 97.31/13.18 ((
% 97.31/13.18 (choice2fnsingleton) =>
% 97.31/13.18 ((
% 97.31/13.18 (setOfPairsIsBReln1) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1all1) =>
% 97.31/13.18 ((
% 97.31/13.18 (subbreln1) =>
% 97.31/13.18 ((
% 97.31/13.18 (eqbreln1) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1invprop) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1invI) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1invE) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1compprop) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1compI) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1compE) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1compEex) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1unionprop) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1unionIL) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1unionIR) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1unionI) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1unionE) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1unionEcases) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1unionCommutes) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz2Ex) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz2W) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz2A) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz2B) =>
% 97.31/13.18 ((
% 97.31/13.18 (image1Ex) =>
% 97.31/13.18 ((
% 97.31/13.18 (image1Ex1) =>
% 97.31/13.18 ((
% 97.31/13.18 (image1Equiv) =>
% 97.31/13.18 ((
% 97.31/13.18 (image1E) =>
% 97.31/13.18 ((
% 97.31/13.18 (image1I) =>
% 97.31/13.18 ((
% 97.31/13.18 (injFuncInInjFuncSet) =>
% 97.31/13.18 ((
% 97.31/13.18 (injFuncSetFuncIn) =>
% 97.31/13.18 ((
% 97.31/13.18 (injFuncSetFuncInj) =>
% 97.31/13.18 ((
% 97.31/13.18 (surjFuncSetFuncIn) =>
% 97.31/13.18 ((
% 97.31/13.18 (surjFuncSetFuncSurj) =>
% 97.31/13.18 ((
% 97.31/13.18 (leftInvIsSurj) =>
% 97.31/13.18 ((
% 97.31/13.18 (surjCantorThm) =>
% 97.31/13.18 ((
% 97.31/13.18 (foundation2) =>
% 97.31/13.18 ((
% 97.31/13.18 (notinself) =>
% 97.31/13.18 ((
% 97.31/13.18 (notinself2) =>
% 97.31/13.18 ((
% 97.31/13.18 (omegaSp) =>
% 97.31/13.18 ((
% 97.31/13.18 (omegaSclos) =>
% 97.31/13.18 ((
% 97.31/13.18 (peano0notS) =>
% 97.31/13.18 ((
% 97.31/13.18 (!!) @ (
% 97.31/13.18 (('#S') @ (
% 97.31/13.18 (
% 97.31/13.18 ('#B') @ (
% 97.31/13.18 =>) @
% 97.31/13.18 (
% 97.31/13.18 (
% 97.31/13.18 ('#C') @ in @
% 97.31/13.18 omega)))) @
% 97.31/13.18 (
% 97.31/13.18 (
% 97.31/13.18 ('#B') @ (
% 97.31/13.18 !!) @
% 97.31/13.18 (
% 97.31/13.18 (
% 97.31/13.18 ('#B') @ (
% 97.31/13.18 (
% 97.31/13.18 ('#S') @ (
% 97.31/13.18 (
% 97.31/13.18 ('#B') @ (
% 97.31/13.18 =>) @
% 97.31/13.18 (
% 97.31/13.18 (
% 97.31/13.18 ('#C') @ in @
% 97.31/13.18 omega)))))) @
% 97.31/13.18 (
% 97.31/13.18 (
% 97.31/13.18 ('#S') @ (
% 97.31/13.18 (
% 97.31/13.18 ('#B') @ (
% 97.31/13.18 '#S') @
% 97.31/13.18 (
% 97.31/13.18 (
% 97.31/13.18 ('#B') @ (
% 97.31/13.18 (
% 97.31/13.18 ('#B') @ (
% 97.31/13.18 =>))) @
% 97.31/13.18 (
% 97.31/13.18 (
% 97.31/13.18 ('#C') @ (
% 97.31/13.18 (
% 97.31/13.18 ('#B') @ (
% 97.31/13.18 '#B') @
% 97.31/13.18 (
% 97.31/13.18 (
% 97.31/13.18 ('#B') @ (
% 97.31/13.18 =) @
% 97.31/13.18 omegaS)))) @
% 97.31/13.18 omegaS)))))) @
% 97.31/13.18 (
% 97.31/13.18 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.31/13.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl384])).
% 97.31/13.18 thf(zip_derived_cl400, plain,
% 97.31/13.18 (~ (((setunionI) =>
% 97.31/13.18 (((setunionE) =>
% 97.31/13.18 (((subPowSU) =>
% 97.31/13.18 (((exuE2) =>
% 97.31/13.18 (((nonemptyImpWitness) =>
% 97.31/13.18 (((uniqinunit) =>
% 97.31/13.18 (((notinsingleton) =>
% 97.31/13.18 (((eqinunit) =>
% 97.31/13.18 (((singletonsswitch) =>
% 97.31/13.18 (((upairsetE) =>
% 97.31/13.18 (((upairsetIL) =>
% 97.31/13.18 (((upairsetIR) =>
% 97.31/13.18 (((emptyE1) =>
% 97.31/13.18 (((vacuousDall) =>
% 97.31/13.18 (((quantDeMorgan1) =>
% 97.31/13.18 (((quantDeMorgan2) =>
% 97.31/13.18 (((quantDeMorgan3) =>
% 97.31/13.18 (((quantDeMorgan4) =>
% 97.31/13.18 (((prop2setI) =>
% 97.31/13.18 (((prop2set2propI) =>
% 97.31/13.18 (((notdexE) =>
% 97.31/13.18 (((notdallE) =>
% 97.31/13.18 (((exuI1) =>
% 97.31/13.18 (((exuI3) =>
% 97.31/13.18 (((exuI2) =>
% 97.31/13.18 (((inCongP) =>
% 97.31/13.18 (((in__Cong) =>
% 97.31/13.18 (((exuE3u) =>
% 97.31/13.18 (((exu__Cong) =>
% 97.31/13.18 (((setadjoin__Cong) =>
% 97.31/13.18 ((
% 97.31/13.18 (powerset__Cong) =>
% 97.31/13.18 ((
% 97.31/13.18 (setunion__Cong) =>
% 97.31/13.18 ((
% 97.31/13.18 (exuEu) =>
% 97.31/13.18 ((
% 97.31/13.18 (descr__Cong) =>
% 97.31/13.18 ((
% 97.31/13.18 (dsetconstr__Cong) =>
% 97.31/13.18 ((
% 97.31/13.18 (subsetI1) =>
% 97.31/13.18 ((
% 97.31/13.18 (eqimpsubset2) =>
% 97.31/13.18 ((
% 97.31/13.18 (eqimpsubset1) =>
% 97.31/13.18 ((
% 97.31/13.18 (subsetI2) =>
% 97.31/13.18 ((
% 97.31/13.18 (emptysetsubset) =>
% 97.31/13.18 ((
% 97.31/13.18 (subsetE) =>
% 97.31/13.18 ((
% 97.31/13.18 (subsetE2) =>
% 97.31/13.18 ((
% 97.31/13.18 (notsubsetI) =>
% 97.31/13.18 ((
% 97.31/13.18 (notequalI1) =>
% 97.31/13.18 ((
% 97.31/13.18 (notequalI2) =>
% 97.31/13.18 ((
% 97.31/13.18 (subsetRefl) =>
% 97.31/13.18 ((
% 97.31/13.18 (subsetTrans) =>
% 97.31/13.18 ((
% 97.31/13.18 (setadjoinSub) =>
% 97.31/13.18 ((
% 97.31/13.18 (setadjoinSub2) =>
% 97.31/13.18 ((
% 97.31/13.18 (subset2powerset) =>
% 97.31/13.18 ((
% 97.31/13.18 (setextsub) =>
% 97.31/13.18 ((
% 97.31/13.18 (subsetemptysetimpeq) =>
% 97.31/13.18 ((
% 97.31/13.18 (powersetI1) =>
% 97.31/13.18 ((
% 97.31/13.18 (powersetE1) =>
% 97.31/13.18 ((
% 97.31/13.18 (inPowerset) =>
% 97.31/13.18 ((
% 97.31/13.18 (powersetsubset) =>
% 97.31/13.18 ((
% 97.31/13.18 (sepInPowerset) =>
% 97.31/13.18 ((
% 97.31/13.18 (sepSubset) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionIL) =>
% 97.31/13.18 ((
% 97.31/13.18 (upairset2IR) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionIR) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionEcases) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionE) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionLsub) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionRsub) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectI) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectSubset5) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectEL) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectLsub) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectSubset2) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectSubset3) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectER) =>
% 97.31/13.18 ((
% 97.31/13.18 (disjointsetsI1) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectRsub) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectSubset4) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectSubset1) =>
% 97.31/13.18 ((
% 97.31/13.18 (bs114d) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusI) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusEL) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusER) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusSubset2) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusERneg) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusELneg) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusILneg) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusIRneg) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusLsub) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusSubset1) =>
% 97.31/13.18 ((
% 97.31/13.18 (symdiffE) =>
% 97.31/13.18 ((
% 97.31/13.18 (symdiffI1) =>
% 97.31/13.18 ((
% 97.31/13.18 (symdiffI2) =>
% 97.31/13.18 ((
% 97.31/13.18 (symdiffIneg1) =>
% 97.31/13.18 ((
% 97.31/13.18 (symdiffIneg2) =>
% 97.31/13.18 ((
% 97.31/13.18 (secondinupair) =>
% 97.31/13.18 ((
% 97.31/13.18 (setukpairIL) =>
% 97.31/13.18 ((
% 97.31/13.18 (setukpairIR) =>
% 97.31/13.18 ((
% 97.31/13.18 (kpairiskpair) =>
% 97.31/13.18 ((
% 97.31/13.18 (kpairp) =>
% 97.31/13.18 ((
% 97.31/13.18 (singletonsubset) =>
% 97.31/13.18 ((
% 97.31/13.18 (singletoninpowerset) =>
% 97.31/13.18 ((
% 97.31/13.18 (singletoninpowunion) =>
% 97.31/13.18 ((
% 97.31/13.18 (upairset2E) =>
% 97.31/13.18 ((
% 97.31/13.18 (upairsubunion) =>
% 97.31/13.18 ((
% 97.31/13.18 (upairinpowunion) =>
% 97.31/13.18 ((
% 97.31/13.18 (ubforcartprodlem1) =>
% 97.31/13.18 ((
% 97.31/13.18 (ubforcartprodlem2) =>
% 97.31/13.18 ((
% 97.31/13.18 (ubforcartprodlem3) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodpairin) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodmempair1) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodmempair) =>
% 97.31/13.18 ((
% 97.31/13.18 (setunionE2) =>
% 97.31/13.18 ((
% 97.31/13.18 (setunionsingleton1) =>
% 97.31/13.18 ((
% 97.31/13.18 (setunionsingleton2) =>
% 97.31/13.18 ((
% 97.31/13.18 (setunionsingleton) =>
% 97.31/13.18 ((
% 97.31/13.18 (singletonprop) =>
% 97.31/13.18 ((
% 97.31/13.18 (ex1E1) =>
% 97.31/13.18 ((
% 97.31/13.18 (ex1I) =>
% 97.31/13.18 ((
% 97.31/13.18 (ex1I2) =>
% 97.31/13.18 ((
% 97.31/13.18 (singletonsuniq) =>
% 97.31/13.18 ((
% 97.31/13.18 (setukpairinjL1) =>
% 97.31/13.18 ((
% 97.31/13.18 (kfstsingleton) =>
% 97.31/13.18 ((
% 97.31/13.18 (theprop) =>
% 97.31/13.18 ((
% 97.31/13.18 (kfstpairEq) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodfstin) =>
% 97.31/13.18 ((
% 97.31/13.18 (setukpairinjL2) =>
% 97.31/13.18 ((
% 97.31/13.18 (setukpairinjL) =>
% 97.31/13.18 ((
% 97.31/13.18 (setukpairinjR11) =>
% 97.31/13.18 ((
% 97.31/13.18 (setukpairinjR12) =>
% 97.31/13.18 ((
% 97.31/13.18 (setukpairinjR1) =>
% 97.31/13.18 ((
% 97.31/13.18 (upairequniteq) =>
% 97.31/13.18 ((
% 97.31/13.18 (setukpairinjR2) =>
% 97.31/13.18 ((
% 97.31/13.18 (setukpairinjR) =>
% 97.31/13.18 ((
% 97.31/13.18 (ksndsingleton) =>
% 97.31/13.18 ((
% 97.31/13.18 (ksndpairEq) =>
% 97.31/13.18 ((
% 97.31/13.18 (kpairsurjEq) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodsndin) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodpairmemEL) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodpairmemER) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodmempaircEq) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodfstpairEq) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodsndpairEq) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodpairsurjEq) =>
% 97.31/13.18 ((
% 97.31/13.18 (dpsetconstrI) =>
% 97.31/13.18 ((
% 97.31/13.18 (dpsetconstrSub) =>
% 97.31/13.18 ((
% 97.31/13.18 (setOfPairsIsBReln) =>
% 97.31/13.18 ((
% 97.31/13.18 (dpsetconstrERa) =>
% 97.31/13.18 ((
% 97.31/13.18 (dpsetconstrEL1) =>
% 97.31/13.18 ((
% 97.31/13.18 (dpsetconstrEL2) =>
% 97.31/13.18 ((
% 97.31/13.18 (dpsetconstrER) =>
% 97.31/13.18 ((
% 97.31/13.18 (funcImageSingleton) =>
% 97.31/13.18 ((
% 97.31/13.18 (apProp) =>
% 97.31/13.18 ((
% 97.31/13.18 (app) =>
% 97.31/13.18 ((
% 97.31/13.18 (infuncsetfunc) =>
% 97.31/13.18 ((
% 97.31/13.18 (ap2p) =>
% 97.31/13.18 ((
% 97.31/13.18 (funcinfuncset) =>
% 97.31/13.18 ((
% 97.31/13.18 (lamProp) =>
% 97.31/13.18 ((
% 97.31/13.18 (lamp) =>
% 97.31/13.18 ((
% 97.31/13.18 (lam2p) =>
% 97.31/13.18 ((
% 97.31/13.18 (brelnall1) =>
% 97.31/13.18 ((
% 97.31/13.18 (brelnall2) =>
% 97.31/13.18 ((
% 97.31/13.18 (ex1E2) =>
% 97.31/13.18 ((
% 97.31/13.18 (funcGraphProp1) =>
% 97.31/13.18 ((
% 97.31/13.18 (funcGraphProp3) =>
% 97.31/13.18 ((
% 97.31/13.18 (funcGraphProp2) =>
% 97.31/13.18 ((
% 97.31/13.18 (funcextLem) =>
% 97.31/13.18 ((
% 97.31/13.18 (funcGraphProp4) =>
% 97.31/13.18 ((
% 97.31/13.18 (subbreln) =>
% 97.31/13.18 ((
% 97.31/13.18 (eqbreln) =>
% 97.31/13.18 ((
% 97.31/13.18 (funcext) =>
% 97.31/13.18 ((
% 97.31/13.18 (funcext2) =>
% 97.31/13.18 ((
% 97.31/13.18 (ap2apEq1) =>
% 97.31/13.18 ((
% 97.31/13.18 (ap2apEq2) =>
% 97.31/13.18 ((
% 97.31/13.18 (beta1) =>
% 97.31/13.18 ((
% 97.31/13.18 (eta1) =>
% 97.31/13.18 ((
% 97.31/13.18 (lam2lamEq) =>
% 97.31/13.18 ((
% 97.31/13.18 (beta2) =>
% 97.31/13.18 ((
% 97.31/13.18 (eta2) =>
% 97.31/13.18 ((
% 97.31/13.18 (iffalseProp1) =>
% 97.31/13.18 ((
% 97.31/13.18 (iffalseProp2) =>
% 97.31/13.18 ((
% 97.31/13.18 (iftrueProp1) =>
% 97.31/13.18 ((
% 97.31/13.18 (iftrueProp2) =>
% 97.31/13.18 ((
% 97.31/13.18 (ifSingleton) =>
% 97.31/13.18 ((
% 97.31/13.18 (ifp) =>
% 97.31/13.18 ((
% 97.31/13.18 (theeq) =>
% 97.31/13.18 ((
% 97.31/13.18 (iftrue) =>
% 97.31/13.18 ((
% 97.31/13.18 (iffalse) =>
% 97.31/13.18 ((
% 97.31/13.18 (iftrueorfalse) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectT_lem) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionT_lem) =>
% 97.31/13.18 ((
% 97.31/13.18 (powersetT_lem) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusT_lem) =>
% 97.31/13.18 ((
% 97.31/13.18 (complementT_lem) =>
% 97.31/13.18 ((
% 97.31/13.18 (setextT) =>
% 97.31/13.18 ((
% 97.31/13.18 (subsetTI) =>
% 97.31/13.18 ((
% 97.31/13.18 (powersetTI1) =>
% 97.31/13.18 ((
% 97.31/13.18 (powersetTE1) =>
% 97.31/13.18 ((
% 97.31/13.18 (complementTI1) =>
% 97.31/13.18 ((
% 97.31/13.18 (complementTE1) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectTELcontra) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectTERcontra) =>
% 97.31/13.18 ((
% 97.31/13.18 (contrasubsetT) =>
% 97.31/13.18 ((
% 97.31/13.18 (contrasubsetT1) =>
% 97.31/13.18 ((
% 97.31/13.18 (contrasubsetT2) =>
% 97.31/13.18 ((
% 97.31/13.18 (contrasubsetT3) =>
% 97.31/13.18 ((
% 97.31/13.18 (doubleComplementI1) =>
% 97.31/13.18 ((
% 97.31/13.18 (doubleComplementE1) =>
% 97.31/13.18 ((
% 97.31/13.18 (doubleComplementSub1) =>
% 97.31/13.18 ((
% 97.31/13.18 (doubleComplementSub2) =>
% 97.31/13.18 ((
% 97.31/13.18 (doubleComplementEq) =>
% 97.31/13.18 ((
% 97.31/13.18 (complementTnotintersectT) =>
% 97.31/13.18 ((
% 97.31/13.18 (complementImpComplementIntersect) =>
% 97.31/13.18 ((
% 97.31/13.18 (complementSubsetComplementIntersect) =>
% 97.31/13.18 ((
% 97.31/13.18 (complementInPowersetComplementIntersect) =>
% 97.31/13.18 ((
% 97.31/13.18 (contraSubsetComplement) =>
% 97.31/13.18 ((
% 97.31/13.18 (complementTcontraSubset) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionTILcontra) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionTIRcontra) =>
% 97.31/13.18 ((
% 97.31/13.18 (inIntersectImpInUnion) =>
% 97.31/13.18 ((
% 97.31/13.18 (inIntersectImpInUnion2) =>
% 97.31/13.18 ((
% 97.31/13.18 (inIntersectImpInIntersectUnions) =>
% 97.31/13.18 ((
% 97.31/13.18 (intersectInPowersetIntersectUnions) =>
% 97.31/13.18 ((
% 97.31/13.18 (inComplementUnionImpNotIn1) =>
% 97.31/13.18 ((
% 97.31/13.18 (inComplementUnionImpInComplement1) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionTE) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionTEcontra) =>
% 97.31/13.18 ((
% 97.31/13.18 (demorgan2a1) =>
% 97.31/13.18 ((
% 97.31/13.18 (complementUnionInPowersetComplement) =>
% 97.31/13.18 ((
% 97.31/13.18 (demorgan2a2) =>
% 97.31/13.18 ((
% 97.31/13.18 (demorgan1a) =>
% 97.31/13.18 ((
% 97.31/13.18 (demorgan1b) =>
% 97.31/13.18 ((
% 97.31/13.18 (demorgan1) =>
% 97.31/13.18 ((
% 97.31/13.18 (demorgan2a) =>
% 97.31/13.18 ((
% 97.31/13.18 (demorgan2b2) =>
% 97.31/13.18 ((
% 97.31/13.18 (demorgan2b) =>
% 97.31/13.18 ((
% 97.31/13.18 (demorgan2) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz13rule0) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz13rule1) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz13rule2) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz13rule3) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz13rule4) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz1_1) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz1_2) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz1_3) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz1_4) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz1_5) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1all2) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1SetBreln1) =>
% 97.31/13.18 ((
% 97.31/13.18 (choice2fnsingleton) =>
% 97.31/13.18 ((
% 97.31/13.18 (setOfPairsIsBReln1) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1all1) =>
% 97.31/13.18 ((
% 97.31/13.18 (subbreln1) =>
% 97.31/13.18 ((
% 97.31/13.18 (eqbreln1) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1invprop) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1invI) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1invE) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1compprop) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1compI) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1compE) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1compEex) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1unionprop) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1unionIL) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1unionIR) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1unionI) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1unionE) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1unionEcases) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1unionCommutes) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz2Ex) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz2W) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz2A) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz2B) =>
% 97.31/13.18 ((
% 97.31/13.18 (image1Ex) =>
% 97.31/13.18 ((
% 97.31/13.18 (image1Ex1) =>
% 97.31/13.18 ((
% 97.31/13.18 (image1Equiv) =>
% 97.31/13.18 ((
% 97.31/13.18 (image1E) =>
% 97.31/13.18 ((
% 97.31/13.18 (image1I) =>
% 97.31/13.18 ((
% 97.31/13.18 (injFuncInInjFuncSet) =>
% 97.31/13.18 ((
% 97.31/13.18 (injFuncSetFuncIn) =>
% 97.31/13.18 ((
% 97.31/13.18 (injFuncSetFuncInj) =>
% 97.31/13.18 ((
% 97.31/13.18 (surjFuncSetFuncIn) =>
% 97.31/13.18 ((
% 97.31/13.18 (surjFuncSetFuncSurj) =>
% 97.31/13.18 ((
% 97.31/13.18 (leftInvIsSurj) =>
% 97.31/13.18 ((
% 97.31/13.18 (surjCantorThm) =>
% 97.31/13.18 ((
% 97.31/13.18 (foundation2) =>
% 97.31/13.18 ((
% 97.31/13.18 (notinself) =>
% 97.31/13.18 ((
% 97.31/13.18 (notinself2) =>
% 97.31/13.18 ((
% 97.31/13.18 (omegaSp) =>
% 97.31/13.18 ((
% 97.31/13.18 (omegaSclos) =>
% 97.31/13.18 ((
% 97.31/13.18 (peano0notS) =>
% 97.31/13.18 ((
% 97.31/13.18 (!!) @ (
% 97.31/13.18 (('#S') @ (
% 97.31/13.18 (
% 97.31/13.18 ('#B') @ (
% 97.31/13.18 =>) @
% 97.31/13.18 (
% 97.31/13.18 (
% 97.31/13.18 ('#C') @ in @
% 97.31/13.18 omega)))) @
% 97.31/13.18 (
% 97.31/13.18 (
% 97.31/13.18 ('#B') @ (
% 97.31/13.18 !!) @
% 97.31/13.18 (
% 97.31/13.18 (
% 97.31/13.18 ('#B') @ (
% 97.31/13.18 (
% 97.31/13.18 ('#S') @ (
% 97.31/13.18 (
% 97.31/13.18 ('#B') @ (
% 97.31/13.18 =>) @
% 97.31/13.18 (
% 97.31/13.18 (
% 97.31/13.18 ('#C') @ in @
% 97.31/13.18 omega)))))) @
% 97.31/13.18 (
% 97.31/13.18 (
% 97.31/13.18 ('#S') @ (
% 97.31/13.18 (
% 97.31/13.18 ('#B') @ (
% 97.31/13.18 '#S') @
% 97.31/13.18 (
% 97.31/13.18 (
% 97.31/13.18 ('#B') @ (
% 97.31/13.18 (
% 97.31/13.18 ('#B') @ (
% 97.31/13.18 =>))) @
% 97.31/13.18 (
% 97.31/13.18 (
% 97.31/13.18 ('#C') @ (
% 97.31/13.18 (
% 97.31/13.18 ('#B') @ (
% 97.31/13.18 '#B') @
% 97.31/13.18 (
% 97.31/13.18 (
% 97.31/13.18 ('#B') @ (
% 97.31/13.18 =) @
% 97.31/13.18 omegaS)))) @
% 97.31/13.18 omegaS)))))) @
% 97.31/13.18 (
% 97.31/13.18 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.31/13.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl392])).
% 97.31/13.18 thf(zip_derived_cl408, plain,
% 97.31/13.18 (~ (((setunionE) =>
% 97.31/13.18 (((subPowSU) =>
% 97.31/13.18 (((exuE2) =>
% 97.31/13.18 (((nonemptyImpWitness) =>
% 97.31/13.18 (((uniqinunit) =>
% 97.31/13.18 (((notinsingleton) =>
% 97.31/13.18 (((eqinunit) =>
% 97.31/13.18 (((singletonsswitch) =>
% 97.31/13.18 (((upairsetE) =>
% 97.31/13.18 (((upairsetIL) =>
% 97.31/13.18 (((upairsetIR) =>
% 97.31/13.18 (((emptyE1) =>
% 97.31/13.18 (((vacuousDall) =>
% 97.31/13.18 (((quantDeMorgan1) =>
% 97.31/13.18 (((quantDeMorgan2) =>
% 97.31/13.18 (((quantDeMorgan3) =>
% 97.31/13.18 (((quantDeMorgan4) =>
% 97.31/13.18 (((prop2setI) =>
% 97.31/13.18 (((prop2set2propI) =>
% 97.31/13.18 (((notdexE) =>
% 97.31/13.18 (((notdallE) =>
% 97.31/13.18 (((exuI1) =>
% 97.31/13.18 (((exuI3) =>
% 97.31/13.18 (((exuI2) =>
% 97.31/13.18 (((inCongP) =>
% 97.31/13.18 (((in__Cong) =>
% 97.31/13.18 (((exuE3u) =>
% 97.31/13.18 (((exu__Cong) =>
% 97.31/13.18 (((setadjoin__Cong) =>
% 97.31/13.18 (((powerset__Cong) =>
% 97.31/13.18 ((
% 97.31/13.18 (setunion__Cong) =>
% 97.31/13.18 ((
% 97.31/13.18 (exuEu) =>
% 97.31/13.18 ((
% 97.31/13.18 (descr__Cong) =>
% 97.31/13.18 ((
% 97.31/13.18 (dsetconstr__Cong) =>
% 97.31/13.18 ((
% 97.31/13.18 (subsetI1) =>
% 97.31/13.18 ((
% 97.31/13.18 (eqimpsubset2) =>
% 97.31/13.18 ((
% 97.31/13.18 (eqimpsubset1) =>
% 97.31/13.18 ((
% 97.31/13.18 (subsetI2) =>
% 97.31/13.18 ((
% 97.31/13.18 (emptysetsubset) =>
% 97.31/13.18 ((
% 97.31/13.18 (subsetE) =>
% 97.31/13.18 ((
% 97.31/13.18 (subsetE2) =>
% 97.31/13.18 ((
% 97.31/13.18 (notsubsetI) =>
% 97.31/13.18 ((
% 97.31/13.18 (notequalI1) =>
% 97.31/13.18 ((
% 97.31/13.18 (notequalI2) =>
% 97.31/13.18 ((
% 97.31/13.18 (subsetRefl) =>
% 97.31/13.18 ((
% 97.31/13.18 (subsetTrans) =>
% 97.31/13.18 ((
% 97.31/13.18 (setadjoinSub) =>
% 97.31/13.18 ((
% 97.31/13.18 (setadjoinSub2) =>
% 97.31/13.18 ((
% 97.31/13.18 (subset2powerset) =>
% 97.31/13.18 ((
% 97.31/13.18 (setextsub) =>
% 97.31/13.18 ((
% 97.31/13.18 (subsetemptysetimpeq) =>
% 97.31/13.18 ((
% 97.31/13.18 (powersetI1) =>
% 97.31/13.18 ((
% 97.31/13.18 (powersetE1) =>
% 97.31/13.18 ((
% 97.31/13.18 (inPowerset) =>
% 97.31/13.18 ((
% 97.31/13.18 (powersetsubset) =>
% 97.31/13.18 ((
% 97.31/13.18 (sepInPowerset) =>
% 97.31/13.18 ((
% 97.31/13.18 (sepSubset) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionIL) =>
% 97.31/13.18 ((
% 97.31/13.18 (upairset2IR) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionIR) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionEcases) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionE) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionLsub) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionRsub) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectI) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectSubset5) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectEL) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectLsub) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectSubset2) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectSubset3) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectER) =>
% 97.31/13.18 ((
% 97.31/13.18 (disjointsetsI1) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectRsub) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectSubset4) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectSubset1) =>
% 97.31/13.18 ((
% 97.31/13.18 (bs114d) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusI) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusEL) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusER) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusSubset2) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusERneg) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusELneg) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusILneg) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusIRneg) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusLsub) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusSubset1) =>
% 97.31/13.18 ((
% 97.31/13.18 (symdiffE) =>
% 97.31/13.18 ((
% 97.31/13.18 (symdiffI1) =>
% 97.31/13.18 ((
% 97.31/13.18 (symdiffI2) =>
% 97.31/13.18 ((
% 97.31/13.18 (symdiffIneg1) =>
% 97.31/13.18 ((
% 97.31/13.18 (symdiffIneg2) =>
% 97.31/13.18 ((
% 97.31/13.18 (secondinupair) =>
% 97.31/13.18 ((
% 97.31/13.18 (setukpairIL) =>
% 97.31/13.18 ((
% 97.31/13.18 (setukpairIR) =>
% 97.31/13.18 ((
% 97.31/13.18 (kpairiskpair) =>
% 97.31/13.18 ((
% 97.31/13.18 (kpairp) =>
% 97.31/13.18 ((
% 97.31/13.18 (singletonsubset) =>
% 97.31/13.18 ((
% 97.31/13.18 (singletoninpowerset) =>
% 97.31/13.18 ((
% 97.31/13.18 (singletoninpowunion) =>
% 97.31/13.18 ((
% 97.31/13.18 (upairset2E) =>
% 97.31/13.18 ((
% 97.31/13.18 (upairsubunion) =>
% 97.31/13.18 ((
% 97.31/13.18 (upairinpowunion) =>
% 97.31/13.18 ((
% 97.31/13.18 (ubforcartprodlem1) =>
% 97.31/13.18 ((
% 97.31/13.18 (ubforcartprodlem2) =>
% 97.31/13.18 ((
% 97.31/13.18 (ubforcartprodlem3) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodpairin) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodmempair1) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodmempair) =>
% 97.31/13.18 ((
% 97.31/13.18 (setunionE2) =>
% 97.31/13.18 ((
% 97.31/13.18 (setunionsingleton1) =>
% 97.31/13.18 ((
% 97.31/13.18 (setunionsingleton2) =>
% 97.31/13.18 ((
% 97.31/13.18 (setunionsingleton) =>
% 97.31/13.18 ((
% 97.31/13.18 (singletonprop) =>
% 97.31/13.18 ((
% 97.31/13.18 (ex1E1) =>
% 97.31/13.18 ((
% 97.31/13.18 (ex1I) =>
% 97.31/13.18 ((
% 97.31/13.18 (ex1I2) =>
% 97.31/13.18 ((
% 97.31/13.18 (singletonsuniq) =>
% 97.31/13.18 ((
% 97.31/13.18 (setukpairinjL1) =>
% 97.31/13.18 ((
% 97.31/13.18 (kfstsingleton) =>
% 97.31/13.18 ((
% 97.31/13.18 (theprop) =>
% 97.31/13.18 ((
% 97.31/13.18 (kfstpairEq) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodfstin) =>
% 97.31/13.18 ((
% 97.31/13.18 (setukpairinjL2) =>
% 97.31/13.18 ((
% 97.31/13.18 (setukpairinjL) =>
% 97.31/13.18 ((
% 97.31/13.18 (setukpairinjR11) =>
% 97.31/13.18 ((
% 97.31/13.18 (setukpairinjR12) =>
% 97.31/13.18 ((
% 97.31/13.18 (setukpairinjR1) =>
% 97.31/13.18 ((
% 97.31/13.18 (upairequniteq) =>
% 97.31/13.18 ((
% 97.31/13.18 (setukpairinjR2) =>
% 97.31/13.18 ((
% 97.31/13.18 (setukpairinjR) =>
% 97.31/13.18 ((
% 97.31/13.18 (ksndsingleton) =>
% 97.31/13.18 ((
% 97.31/13.18 (ksndpairEq) =>
% 97.31/13.18 ((
% 97.31/13.18 (kpairsurjEq) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodsndin) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodpairmemEL) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodpairmemER) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodmempaircEq) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodfstpairEq) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodsndpairEq) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodpairsurjEq) =>
% 97.31/13.18 ((
% 97.31/13.18 (dpsetconstrI) =>
% 97.31/13.18 ((
% 97.31/13.18 (dpsetconstrSub) =>
% 97.31/13.18 ((
% 97.31/13.18 (setOfPairsIsBReln) =>
% 97.31/13.18 ((
% 97.31/13.18 (dpsetconstrERa) =>
% 97.31/13.18 ((
% 97.31/13.18 (dpsetconstrEL1) =>
% 97.31/13.18 ((
% 97.31/13.18 (dpsetconstrEL2) =>
% 97.31/13.18 ((
% 97.31/13.18 (dpsetconstrER) =>
% 97.31/13.18 ((
% 97.31/13.18 (funcImageSingleton) =>
% 97.31/13.18 ((
% 97.31/13.18 (apProp) =>
% 97.31/13.18 ((
% 97.31/13.18 (app) =>
% 97.31/13.18 ((
% 97.31/13.18 (infuncsetfunc) =>
% 97.31/13.18 ((
% 97.31/13.18 (ap2p) =>
% 97.31/13.18 ((
% 97.31/13.18 (funcinfuncset) =>
% 97.31/13.18 ((
% 97.31/13.18 (lamProp) =>
% 97.31/13.18 ((
% 97.31/13.18 (lamp) =>
% 97.31/13.18 ((
% 97.31/13.18 (lam2p) =>
% 97.31/13.18 ((
% 97.31/13.18 (brelnall1) =>
% 97.31/13.18 ((
% 97.31/13.18 (brelnall2) =>
% 97.31/13.18 ((
% 97.31/13.18 (ex1E2) =>
% 97.31/13.18 ((
% 97.31/13.18 (funcGraphProp1) =>
% 97.31/13.18 ((
% 97.31/13.18 (funcGraphProp3) =>
% 97.31/13.18 ((
% 97.31/13.18 (funcGraphProp2) =>
% 97.31/13.18 ((
% 97.31/13.18 (funcextLem) =>
% 97.31/13.18 ((
% 97.31/13.18 (funcGraphProp4) =>
% 97.31/13.18 ((
% 97.31/13.18 (subbreln) =>
% 97.31/13.18 ((
% 97.31/13.18 (eqbreln) =>
% 97.31/13.18 ((
% 97.31/13.18 (funcext) =>
% 97.31/13.18 ((
% 97.31/13.18 (funcext2) =>
% 97.31/13.18 ((
% 97.31/13.18 (ap2apEq1) =>
% 97.31/13.18 ((
% 97.31/13.18 (ap2apEq2) =>
% 97.31/13.18 ((
% 97.31/13.18 (beta1) =>
% 97.31/13.18 ((
% 97.31/13.18 (eta1) =>
% 97.31/13.18 ((
% 97.31/13.18 (lam2lamEq) =>
% 97.31/13.18 ((
% 97.31/13.18 (beta2) =>
% 97.31/13.18 ((
% 97.31/13.18 (eta2) =>
% 97.31/13.18 ((
% 97.31/13.18 (iffalseProp1) =>
% 97.31/13.18 ((
% 97.31/13.18 (iffalseProp2) =>
% 97.31/13.18 ((
% 97.31/13.18 (iftrueProp1) =>
% 97.31/13.18 ((
% 97.31/13.18 (iftrueProp2) =>
% 97.31/13.18 ((
% 97.31/13.18 (ifSingleton) =>
% 97.31/13.18 ((
% 97.31/13.18 (ifp) =>
% 97.31/13.18 ((
% 97.31/13.18 (theeq) =>
% 97.31/13.18 ((
% 97.31/13.18 (iftrue) =>
% 97.31/13.18 ((
% 97.31/13.18 (iffalse) =>
% 97.31/13.18 ((
% 97.31/13.18 (iftrueorfalse) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectT_lem) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionT_lem) =>
% 97.31/13.18 ((
% 97.31/13.18 (powersetT_lem) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusT_lem) =>
% 97.31/13.18 ((
% 97.31/13.18 (complementT_lem) =>
% 97.31/13.18 ((
% 97.31/13.18 (setextT) =>
% 97.31/13.18 ((
% 97.31/13.18 (subsetTI) =>
% 97.31/13.18 ((
% 97.31/13.18 (powersetTI1) =>
% 97.31/13.18 ((
% 97.31/13.18 (powersetTE1) =>
% 97.31/13.18 ((
% 97.31/13.18 (complementTI1) =>
% 97.31/13.18 ((
% 97.31/13.18 (complementTE1) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectTELcontra) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectTERcontra) =>
% 97.31/13.18 ((
% 97.31/13.18 (contrasubsetT) =>
% 97.31/13.18 ((
% 97.31/13.18 (contrasubsetT1) =>
% 97.31/13.18 ((
% 97.31/13.18 (contrasubsetT2) =>
% 97.31/13.18 ((
% 97.31/13.18 (contrasubsetT3) =>
% 97.31/13.18 ((
% 97.31/13.18 (doubleComplementI1) =>
% 97.31/13.18 ((
% 97.31/13.18 (doubleComplementE1) =>
% 97.31/13.18 ((
% 97.31/13.18 (doubleComplementSub1) =>
% 97.31/13.18 ((
% 97.31/13.18 (doubleComplementSub2) =>
% 97.31/13.18 ((
% 97.31/13.18 (doubleComplementEq) =>
% 97.31/13.18 ((
% 97.31/13.18 (complementTnotintersectT) =>
% 97.31/13.18 ((
% 97.31/13.18 (complementImpComplementIntersect) =>
% 97.31/13.18 ((
% 97.31/13.18 (complementSubsetComplementIntersect) =>
% 97.31/13.18 ((
% 97.31/13.18 (complementInPowersetComplementIntersect) =>
% 97.31/13.18 ((
% 97.31/13.18 (contraSubsetComplement) =>
% 97.31/13.18 ((
% 97.31/13.18 (complementTcontraSubset) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionTILcontra) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionTIRcontra) =>
% 97.31/13.18 ((
% 97.31/13.18 (inIntersectImpInUnion) =>
% 97.31/13.18 ((
% 97.31/13.18 (inIntersectImpInUnion2) =>
% 97.31/13.18 ((
% 97.31/13.18 (inIntersectImpInIntersectUnions) =>
% 97.31/13.18 ((
% 97.31/13.18 (intersectInPowersetIntersectUnions) =>
% 97.31/13.18 ((
% 97.31/13.18 (inComplementUnionImpNotIn1) =>
% 97.31/13.18 ((
% 97.31/13.18 (inComplementUnionImpInComplement1) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionTE) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionTEcontra) =>
% 97.31/13.18 ((
% 97.31/13.18 (demorgan2a1) =>
% 97.31/13.18 ((
% 97.31/13.18 (complementUnionInPowersetComplement) =>
% 97.31/13.18 ((
% 97.31/13.18 (demorgan2a2) =>
% 97.31/13.18 ((
% 97.31/13.18 (demorgan1a) =>
% 97.31/13.18 ((
% 97.31/13.18 (demorgan1b) =>
% 97.31/13.18 ((
% 97.31/13.18 (demorgan1) =>
% 97.31/13.18 ((
% 97.31/13.18 (demorgan2a) =>
% 97.31/13.18 ((
% 97.31/13.18 (demorgan2b2) =>
% 97.31/13.18 ((
% 97.31/13.18 (demorgan2b) =>
% 97.31/13.18 ((
% 97.31/13.18 (demorgan2) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz13rule0) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz13rule1) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz13rule2) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz13rule3) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz13rule4) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz1_1) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz1_2) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz1_3) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz1_4) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz1_5) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1all2) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1SetBreln1) =>
% 97.31/13.18 ((
% 97.31/13.18 (choice2fnsingleton) =>
% 97.31/13.18 ((
% 97.31/13.18 (setOfPairsIsBReln1) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1all1) =>
% 97.31/13.18 ((
% 97.31/13.18 (subbreln1) =>
% 97.31/13.18 ((
% 97.31/13.18 (eqbreln1) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1invprop) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1invI) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1invE) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1compprop) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1compI) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1compE) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1compEex) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1unionprop) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1unionIL) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1unionIR) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1unionI) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1unionE) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1unionEcases) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1unionCommutes) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz2Ex) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz2W) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz2A) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz2B) =>
% 97.31/13.18 ((
% 97.31/13.18 (image1Ex) =>
% 97.31/13.18 ((
% 97.31/13.18 (image1Ex1) =>
% 97.31/13.18 ((
% 97.31/13.18 (image1Equiv) =>
% 97.31/13.18 ((
% 97.31/13.18 (image1E) =>
% 97.31/13.18 ((
% 97.31/13.18 (image1I) =>
% 97.31/13.18 ((
% 97.31/13.18 (injFuncInInjFuncSet) =>
% 97.31/13.18 ((
% 97.31/13.18 (injFuncSetFuncIn) =>
% 97.31/13.18 ((
% 97.31/13.18 (injFuncSetFuncInj) =>
% 97.31/13.18 ((
% 97.31/13.18 (surjFuncSetFuncIn) =>
% 97.31/13.18 ((
% 97.31/13.18 (surjFuncSetFuncSurj) =>
% 97.31/13.18 ((
% 97.31/13.18 (leftInvIsSurj) =>
% 97.31/13.18 ((
% 97.31/13.18 (surjCantorThm) =>
% 97.31/13.18 ((
% 97.31/13.18 (foundation2) =>
% 97.31/13.18 ((
% 97.31/13.18 (notinself) =>
% 97.31/13.18 ((
% 97.31/13.18 (notinself2) =>
% 97.31/13.18 ((
% 97.31/13.18 (omegaSp) =>
% 97.31/13.18 ((
% 97.31/13.18 (omegaSclos) =>
% 97.31/13.18 ((
% 97.31/13.18 (peano0notS) =>
% 97.31/13.18 ((
% 97.31/13.18 (!!) @ (
% 97.31/13.18 (('#S') @ (
% 97.31/13.18 (
% 97.31/13.18 ('#B') @ (
% 97.31/13.18 =>) @
% 97.31/13.18 (
% 97.31/13.18 (
% 97.31/13.18 ('#C') @ in @
% 97.31/13.18 omega)))) @
% 97.31/13.18 (
% 97.31/13.18 (
% 97.31/13.18 ('#B') @ (
% 97.31/13.18 !!) @
% 97.31/13.18 (
% 97.31/13.18 (
% 97.31/13.18 ('#B') @ (
% 97.31/13.18 (
% 97.31/13.18 ('#S') @ (
% 97.31/13.18 (
% 97.31/13.18 ('#B') @ (
% 97.31/13.18 =>) @
% 97.31/13.18 (
% 97.31/13.18 (
% 97.31/13.18 ('#C') @ in @
% 97.31/13.18 omega)))))) @
% 97.31/13.18 (
% 97.31/13.18 (
% 97.31/13.18 ('#S') @ (
% 97.31/13.18 (
% 97.31/13.18 ('#B') @ (
% 97.31/13.18 '#S') @
% 97.31/13.18 (
% 97.31/13.18 (
% 97.31/13.18 ('#B') @ (
% 97.31/13.18 (
% 97.31/13.18 ('#B') @ (
% 97.31/13.18 =>))) @
% 97.31/13.18 (
% 97.31/13.18 (
% 97.31/13.18 ('#C') @ (
% 97.31/13.18 (
% 97.31/13.18 ('#B') @ (
% 97.31/13.18 '#B') @
% 97.31/13.18 (
% 97.31/13.18 (
% 97.31/13.18 ('#B') @ (
% 97.31/13.18 =) @
% 97.31/13.18 omegaS)))) @
% 97.31/13.18 omegaS)))))) @
% 97.31/13.18 (
% 97.31/13.18 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.31/13.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl400])).
% 97.31/13.18 thf(zip_derived_cl417, plain,
% 97.31/13.18 (~ (((subPowSU) =>
% 97.31/13.18 (((exuE2) =>
% 97.31/13.18 (((nonemptyImpWitness) =>
% 97.31/13.18 (((uniqinunit) =>
% 97.31/13.18 (((notinsingleton) =>
% 97.31/13.18 (((eqinunit) =>
% 97.31/13.18 (((singletonsswitch) =>
% 97.31/13.18 (((upairsetE) =>
% 97.31/13.18 (((upairsetIL) =>
% 97.31/13.18 (((upairsetIR) =>
% 97.31/13.18 (((emptyE1) =>
% 97.31/13.18 (((vacuousDall) =>
% 97.31/13.18 (((quantDeMorgan1) =>
% 97.31/13.18 (((quantDeMorgan2) =>
% 97.31/13.18 (((quantDeMorgan3) =>
% 97.31/13.18 (((quantDeMorgan4) =>
% 97.31/13.18 (((prop2setI) =>
% 97.31/13.18 (((prop2set2propI) =>
% 97.31/13.18 (((notdexE) =>
% 97.31/13.18 (((notdallE) =>
% 97.31/13.18 (((exuI1) =>
% 97.31/13.18 (((exuI3) =>
% 97.31/13.18 (((exuI2) =>
% 97.31/13.18 (((inCongP) =>
% 97.31/13.18 (((in__Cong) =>
% 97.31/13.18 (((exuE3u) =>
% 97.31/13.18 (((exu__Cong) =>
% 97.31/13.18 (((setadjoin__Cong) =>
% 97.31/13.18 (((powerset__Cong) =>
% 97.31/13.18 (((setunion__Cong) =>
% 97.31/13.18 ((
% 97.31/13.18 (exuEu) =>
% 97.31/13.18 ((
% 97.31/13.18 (descr__Cong) =>
% 97.31/13.18 ((
% 97.31/13.18 (dsetconstr__Cong) =>
% 97.31/13.18 ((
% 97.31/13.18 (subsetI1) =>
% 97.31/13.18 ((
% 97.31/13.18 (eqimpsubset2) =>
% 97.31/13.18 ((
% 97.31/13.18 (eqimpsubset1) =>
% 97.31/13.18 ((
% 97.31/13.18 (subsetI2) =>
% 97.31/13.18 ((
% 97.31/13.18 (emptysetsubset) =>
% 97.31/13.18 ((
% 97.31/13.18 (subsetE) =>
% 97.31/13.18 ((
% 97.31/13.18 (subsetE2) =>
% 97.31/13.18 ((
% 97.31/13.18 (notsubsetI) =>
% 97.31/13.18 ((
% 97.31/13.18 (notequalI1) =>
% 97.31/13.18 ((
% 97.31/13.18 (notequalI2) =>
% 97.31/13.18 ((
% 97.31/13.18 (subsetRefl) =>
% 97.31/13.18 ((
% 97.31/13.18 (subsetTrans) =>
% 97.31/13.18 ((
% 97.31/13.18 (setadjoinSub) =>
% 97.31/13.18 ((
% 97.31/13.18 (setadjoinSub2) =>
% 97.31/13.18 ((
% 97.31/13.18 (subset2powerset) =>
% 97.31/13.18 ((
% 97.31/13.18 (setextsub) =>
% 97.31/13.18 ((
% 97.31/13.18 (subsetemptysetimpeq) =>
% 97.31/13.18 ((
% 97.31/13.18 (powersetI1) =>
% 97.31/13.18 ((
% 97.31/13.18 (powersetE1) =>
% 97.31/13.18 ((
% 97.31/13.18 (inPowerset) =>
% 97.31/13.18 ((
% 97.31/13.18 (powersetsubset) =>
% 97.31/13.18 ((
% 97.31/13.18 (sepInPowerset) =>
% 97.31/13.18 ((
% 97.31/13.18 (sepSubset) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionIL) =>
% 97.31/13.18 ((
% 97.31/13.18 (upairset2IR) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionIR) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionEcases) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionE) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionLsub) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionRsub) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectI) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectSubset5) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectEL) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectLsub) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectSubset2) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectSubset3) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectER) =>
% 97.31/13.18 ((
% 97.31/13.18 (disjointsetsI1) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectRsub) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectSubset4) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectSubset1) =>
% 97.31/13.18 ((
% 97.31/13.18 (bs114d) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusI) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusEL) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusER) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusSubset2) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusERneg) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusELneg) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusILneg) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusIRneg) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusLsub) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusSubset1) =>
% 97.31/13.18 ((
% 97.31/13.18 (symdiffE) =>
% 97.31/13.18 ((
% 97.31/13.18 (symdiffI1) =>
% 97.31/13.18 ((
% 97.31/13.18 (symdiffI2) =>
% 97.31/13.18 ((
% 97.31/13.18 (symdiffIneg1) =>
% 97.31/13.18 ((
% 97.31/13.18 (symdiffIneg2) =>
% 97.31/13.18 ((
% 97.31/13.18 (secondinupair) =>
% 97.31/13.18 ((
% 97.31/13.18 (setukpairIL) =>
% 97.31/13.18 ((
% 97.31/13.18 (setukpairIR) =>
% 97.31/13.18 ((
% 97.31/13.18 (kpairiskpair) =>
% 97.31/13.18 ((
% 97.31/13.18 (kpairp) =>
% 97.31/13.18 ((
% 97.31/13.18 (singletonsubset) =>
% 97.31/13.18 ((
% 97.31/13.18 (singletoninpowerset) =>
% 97.31/13.18 ((
% 97.31/13.18 (singletoninpowunion) =>
% 97.31/13.18 ((
% 97.31/13.18 (upairset2E) =>
% 97.31/13.18 ((
% 97.31/13.18 (upairsubunion) =>
% 97.31/13.18 ((
% 97.31/13.18 (upairinpowunion) =>
% 97.31/13.18 ((
% 97.31/13.18 (ubforcartprodlem1) =>
% 97.31/13.18 ((
% 97.31/13.18 (ubforcartprodlem2) =>
% 97.31/13.18 ((
% 97.31/13.18 (ubforcartprodlem3) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodpairin) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodmempair1) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodmempair) =>
% 97.31/13.18 ((
% 97.31/13.18 (setunionE2) =>
% 97.31/13.18 ((
% 97.31/13.18 (setunionsingleton1) =>
% 97.31/13.18 ((
% 97.31/13.18 (setunionsingleton2) =>
% 97.31/13.18 ((
% 97.31/13.18 (setunionsingleton) =>
% 97.31/13.18 ((
% 97.31/13.18 (singletonprop) =>
% 97.31/13.18 ((
% 97.31/13.18 (ex1E1) =>
% 97.31/13.18 ((
% 97.31/13.18 (ex1I) =>
% 97.31/13.18 ((
% 97.31/13.18 (ex1I2) =>
% 97.31/13.18 ((
% 97.31/13.18 (singletonsuniq) =>
% 97.31/13.18 ((
% 97.31/13.18 (setukpairinjL1) =>
% 97.31/13.18 ((
% 97.31/13.18 (kfstsingleton) =>
% 97.31/13.18 ((
% 97.31/13.18 (theprop) =>
% 97.31/13.18 ((
% 97.31/13.18 (kfstpairEq) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodfstin) =>
% 97.31/13.18 ((
% 97.31/13.18 (setukpairinjL2) =>
% 97.31/13.18 ((
% 97.31/13.18 (setukpairinjL) =>
% 97.31/13.18 ((
% 97.31/13.18 (setukpairinjR11) =>
% 97.31/13.18 ((
% 97.31/13.18 (setukpairinjR12) =>
% 97.31/13.18 ((
% 97.31/13.18 (setukpairinjR1) =>
% 97.31/13.18 ((
% 97.31/13.18 (upairequniteq) =>
% 97.31/13.18 ((
% 97.31/13.18 (setukpairinjR2) =>
% 97.31/13.18 ((
% 97.31/13.18 (setukpairinjR) =>
% 97.31/13.18 ((
% 97.31/13.18 (ksndsingleton) =>
% 97.31/13.18 ((
% 97.31/13.18 (ksndpairEq) =>
% 97.31/13.18 ((
% 97.31/13.18 (kpairsurjEq) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodsndin) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodpairmemEL) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodpairmemER) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodmempaircEq) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodfstpairEq) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodsndpairEq) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodpairsurjEq) =>
% 97.31/13.18 ((
% 97.31/13.18 (dpsetconstrI) =>
% 97.31/13.18 ((
% 97.31/13.18 (dpsetconstrSub) =>
% 97.31/13.18 ((
% 97.31/13.18 (setOfPairsIsBReln) =>
% 97.31/13.18 ((
% 97.31/13.18 (dpsetconstrERa) =>
% 97.31/13.18 ((
% 97.31/13.18 (dpsetconstrEL1) =>
% 97.31/13.18 ((
% 97.31/13.18 (dpsetconstrEL2) =>
% 97.31/13.18 ((
% 97.31/13.18 (dpsetconstrER) =>
% 97.31/13.18 ((
% 97.31/13.18 (funcImageSingleton) =>
% 97.31/13.18 ((
% 97.31/13.18 (apProp) =>
% 97.31/13.18 ((
% 97.31/13.18 (app) =>
% 97.31/13.18 ((
% 97.31/13.18 (infuncsetfunc) =>
% 97.31/13.18 ((
% 97.31/13.18 (ap2p) =>
% 97.31/13.18 ((
% 97.31/13.18 (funcinfuncset) =>
% 97.31/13.18 ((
% 97.31/13.18 (lamProp) =>
% 97.31/13.18 ((
% 97.31/13.18 (lamp) =>
% 97.31/13.18 ((
% 97.31/13.18 (lam2p) =>
% 97.31/13.18 ((
% 97.31/13.18 (brelnall1) =>
% 97.31/13.18 ((
% 97.31/13.18 (brelnall2) =>
% 97.31/13.18 ((
% 97.31/13.18 (ex1E2) =>
% 97.31/13.18 ((
% 97.31/13.18 (funcGraphProp1) =>
% 97.31/13.18 ((
% 97.31/13.18 (funcGraphProp3) =>
% 97.31/13.18 ((
% 97.31/13.18 (funcGraphProp2) =>
% 97.31/13.18 ((
% 97.31/13.18 (funcextLem) =>
% 97.31/13.18 ((
% 97.31/13.18 (funcGraphProp4) =>
% 97.31/13.18 ((
% 97.31/13.18 (subbreln) =>
% 97.31/13.18 ((
% 97.31/13.18 (eqbreln) =>
% 97.31/13.18 ((
% 97.31/13.18 (funcext) =>
% 97.31/13.18 ((
% 97.31/13.18 (funcext2) =>
% 97.31/13.18 ((
% 97.31/13.18 (ap2apEq1) =>
% 97.31/13.18 ((
% 97.31/13.18 (ap2apEq2) =>
% 97.31/13.18 ((
% 97.31/13.18 (beta1) =>
% 97.31/13.18 ((
% 97.31/13.18 (eta1) =>
% 97.31/13.18 ((
% 97.31/13.18 (lam2lamEq) =>
% 97.31/13.18 ((
% 97.31/13.18 (beta2) =>
% 97.31/13.18 ((
% 97.31/13.18 (eta2) =>
% 97.31/13.18 ((
% 97.31/13.18 (iffalseProp1) =>
% 97.31/13.18 ((
% 97.31/13.18 (iffalseProp2) =>
% 97.31/13.18 ((
% 97.31/13.18 (iftrueProp1) =>
% 97.31/13.18 ((
% 97.31/13.18 (iftrueProp2) =>
% 97.31/13.18 ((
% 97.31/13.18 (ifSingleton) =>
% 97.31/13.18 ((
% 97.31/13.18 (ifp) =>
% 97.31/13.18 ((
% 97.31/13.18 (theeq) =>
% 97.31/13.18 ((
% 97.31/13.18 (iftrue) =>
% 97.31/13.18 ((
% 97.31/13.18 (iffalse) =>
% 97.31/13.18 ((
% 97.31/13.18 (iftrueorfalse) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectT_lem) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionT_lem) =>
% 97.31/13.18 ((
% 97.31/13.18 (powersetT_lem) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusT_lem) =>
% 97.31/13.18 ((
% 97.31/13.18 (complementT_lem) =>
% 97.31/13.18 ((
% 97.31/13.18 (setextT) =>
% 97.31/13.18 ((
% 97.31/13.18 (subsetTI) =>
% 97.31/13.18 ((
% 97.31/13.18 (powersetTI1) =>
% 97.31/13.18 ((
% 97.31/13.18 (powersetTE1) =>
% 97.31/13.18 ((
% 97.31/13.18 (complementTI1) =>
% 97.31/13.18 ((
% 97.31/13.18 (complementTE1) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectTELcontra) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectTERcontra) =>
% 97.31/13.18 ((
% 97.31/13.18 (contrasubsetT) =>
% 97.31/13.18 ((
% 97.31/13.18 (contrasubsetT1) =>
% 97.31/13.18 ((
% 97.31/13.18 (contrasubsetT2) =>
% 97.31/13.18 ((
% 97.31/13.18 (contrasubsetT3) =>
% 97.31/13.18 ((
% 97.31/13.18 (doubleComplementI1) =>
% 97.31/13.18 ((
% 97.31/13.18 (doubleComplementE1) =>
% 97.31/13.18 ((
% 97.31/13.18 (doubleComplementSub1) =>
% 97.31/13.18 ((
% 97.31/13.18 (doubleComplementSub2) =>
% 97.31/13.18 ((
% 97.31/13.18 (doubleComplementEq) =>
% 97.31/13.18 ((
% 97.31/13.18 (complementTnotintersectT) =>
% 97.31/13.18 ((
% 97.31/13.18 (complementImpComplementIntersect) =>
% 97.31/13.18 ((
% 97.31/13.18 (complementSubsetComplementIntersect) =>
% 97.31/13.18 ((
% 97.31/13.18 (complementInPowersetComplementIntersect) =>
% 97.31/13.18 ((
% 97.31/13.18 (contraSubsetComplement) =>
% 97.31/13.18 ((
% 97.31/13.18 (complementTcontraSubset) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionTILcontra) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionTIRcontra) =>
% 97.31/13.18 ((
% 97.31/13.18 (inIntersectImpInUnion) =>
% 97.31/13.18 ((
% 97.31/13.18 (inIntersectImpInUnion2) =>
% 97.31/13.18 ((
% 97.31/13.18 (inIntersectImpInIntersectUnions) =>
% 97.31/13.18 ((
% 97.31/13.18 (intersectInPowersetIntersectUnions) =>
% 97.31/13.18 ((
% 97.31/13.18 (inComplementUnionImpNotIn1) =>
% 97.31/13.18 ((
% 97.31/13.18 (inComplementUnionImpInComplement1) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionTE) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionTEcontra) =>
% 97.31/13.18 ((
% 97.31/13.18 (demorgan2a1) =>
% 97.31/13.18 ((
% 97.31/13.18 (complementUnionInPowersetComplement) =>
% 97.31/13.18 ((
% 97.31/13.18 (demorgan2a2) =>
% 97.31/13.18 ((
% 97.31/13.18 (demorgan1a) =>
% 97.31/13.18 ((
% 97.31/13.18 (demorgan1b) =>
% 97.31/13.18 ((
% 97.31/13.18 (demorgan1) =>
% 97.31/13.18 ((
% 97.31/13.18 (demorgan2a) =>
% 97.31/13.18 ((
% 97.31/13.18 (demorgan2b2) =>
% 97.31/13.18 ((
% 97.31/13.18 (demorgan2b) =>
% 97.31/13.18 ((
% 97.31/13.18 (demorgan2) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz13rule0) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz13rule1) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz13rule2) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz13rule3) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz13rule4) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz1_1) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz1_2) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz1_3) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz1_4) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz1_5) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1all2) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1SetBreln1) =>
% 97.31/13.18 ((
% 97.31/13.18 (choice2fnsingleton) =>
% 97.31/13.18 ((
% 97.31/13.18 (setOfPairsIsBReln1) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1all1) =>
% 97.31/13.18 ((
% 97.31/13.18 (subbreln1) =>
% 97.31/13.18 ((
% 97.31/13.18 (eqbreln1) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1invprop) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1invI) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1invE) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1compprop) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1compI) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1compE) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1compEex) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1unionprop) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1unionIL) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1unionIR) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1unionI) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1unionE) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1unionEcases) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1unionCommutes) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz2Ex) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz2W) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz2A) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz2B) =>
% 97.31/13.18 ((
% 97.31/13.18 (image1Ex) =>
% 97.31/13.18 ((
% 97.31/13.18 (image1Ex1) =>
% 97.31/13.18 ((
% 97.31/13.18 (image1Equiv) =>
% 97.31/13.18 ((
% 97.31/13.18 (image1E) =>
% 97.31/13.18 ((
% 97.31/13.18 (image1I) =>
% 97.31/13.18 ((
% 97.31/13.18 (injFuncInInjFuncSet) =>
% 97.31/13.18 ((
% 97.31/13.18 (injFuncSetFuncIn) =>
% 97.31/13.18 ((
% 97.31/13.18 (injFuncSetFuncInj) =>
% 97.31/13.18 ((
% 97.31/13.18 (surjFuncSetFuncIn) =>
% 97.31/13.18 ((
% 97.31/13.18 (surjFuncSetFuncSurj) =>
% 97.31/13.18 ((
% 97.31/13.18 (leftInvIsSurj) =>
% 97.31/13.18 ((
% 97.31/13.18 (surjCantorThm) =>
% 97.31/13.18 ((
% 97.31/13.18 (foundation2) =>
% 97.31/13.18 ((
% 97.31/13.18 (notinself) =>
% 97.31/13.18 ((
% 97.31/13.18 (notinself2) =>
% 97.31/13.18 ((
% 97.31/13.18 (omegaSp) =>
% 97.31/13.18 ((
% 97.31/13.18 (omegaSclos) =>
% 97.31/13.18 ((
% 97.31/13.18 (peano0notS) =>
% 97.31/13.18 ((
% 97.31/13.18 (!!) @ (
% 97.31/13.18 (('#S') @ (
% 97.31/13.18 (
% 97.31/13.18 ('#B') @ (
% 97.31/13.18 =>) @
% 97.31/13.18 (
% 97.31/13.18 (
% 97.31/13.18 ('#C') @ in @
% 97.31/13.18 omega)))) @
% 97.31/13.18 (
% 97.31/13.18 (
% 97.31/13.18 ('#B') @ (
% 97.31/13.18 !!) @
% 97.31/13.18 (
% 97.31/13.18 (
% 97.31/13.18 ('#B') @ (
% 97.31/13.18 (
% 97.31/13.18 ('#S') @ (
% 97.31/13.18 (
% 97.31/13.18 ('#B') @ (
% 97.31/13.18 =>) @
% 97.31/13.18 (
% 97.31/13.18 (
% 97.31/13.18 ('#C') @ in @
% 97.31/13.18 omega)))))) @
% 97.31/13.18 (
% 97.31/13.18 (
% 97.31/13.18 ('#S') @ (
% 97.31/13.18 (
% 97.31/13.18 ('#B') @ (
% 97.31/13.18 '#S') @
% 97.31/13.18 (
% 97.31/13.18 (
% 97.31/13.18 ('#B') @ (
% 97.31/13.18 (
% 97.31/13.18 ('#B') @ (
% 97.31/13.18 =>))) @
% 97.31/13.18 (
% 97.31/13.18 (
% 97.31/13.18 ('#C') @ (
% 97.31/13.18 (
% 97.31/13.18 ('#B') @ (
% 97.31/13.18 '#B') @
% 97.31/13.18 (
% 97.31/13.18 (
% 97.31/13.18 ('#B') @ (
% 97.31/13.18 =) @
% 97.31/13.18 omegaS)))) @
% 97.31/13.18 omegaS)))))) @
% 97.31/13.18 (
% 97.31/13.18 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.31/13.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl408])).
% 97.31/13.18 thf(zip_derived_cl428, plain,
% 97.31/13.18 (~ (((exuE2) =>
% 97.31/13.18 (((nonemptyImpWitness) =>
% 97.31/13.18 (((uniqinunit) =>
% 97.31/13.18 (((notinsingleton) =>
% 97.31/13.18 (((eqinunit) =>
% 97.31/13.18 (((singletonsswitch) =>
% 97.31/13.18 (((upairsetE) =>
% 97.31/13.18 (((upairsetIL) =>
% 97.31/13.18 (((upairsetIR) =>
% 97.31/13.18 (((emptyE1) =>
% 97.31/13.18 (((vacuousDall) =>
% 97.31/13.18 (((quantDeMorgan1) =>
% 97.31/13.18 (((quantDeMorgan2) =>
% 97.31/13.18 (((quantDeMorgan3) =>
% 97.31/13.18 (((quantDeMorgan4) =>
% 97.31/13.18 (((prop2setI) =>
% 97.31/13.18 (((prop2set2propI) =>
% 97.31/13.18 (((notdexE) =>
% 97.31/13.18 (((notdallE) =>
% 97.31/13.18 (((exuI1) =>
% 97.31/13.18 (((exuI3) =>
% 97.31/13.18 (((exuI2) =>
% 97.31/13.18 (((inCongP) =>
% 97.31/13.18 (((in__Cong) =>
% 97.31/13.18 (((exuE3u) =>
% 97.31/13.18 (((exu__Cong) =>
% 97.31/13.18 (((setadjoin__Cong) =>
% 97.31/13.18 (((powerset__Cong) =>
% 97.31/13.18 (((setunion__Cong) =>
% 97.31/13.18 (((exuEu) =>
% 97.31/13.18 ((
% 97.31/13.18 (descr__Cong) =>
% 97.31/13.18 ((
% 97.31/13.18 (dsetconstr__Cong) =>
% 97.31/13.18 ((
% 97.31/13.18 (subsetI1) =>
% 97.31/13.18 ((
% 97.31/13.18 (eqimpsubset2) =>
% 97.31/13.18 ((
% 97.31/13.18 (eqimpsubset1) =>
% 97.31/13.18 ((
% 97.31/13.18 (subsetI2) =>
% 97.31/13.18 ((
% 97.31/13.18 (emptysetsubset) =>
% 97.31/13.18 ((
% 97.31/13.18 (subsetE) =>
% 97.31/13.18 ((
% 97.31/13.18 (subsetE2) =>
% 97.31/13.18 ((
% 97.31/13.18 (notsubsetI) =>
% 97.31/13.18 ((
% 97.31/13.18 (notequalI1) =>
% 97.31/13.18 ((
% 97.31/13.18 (notequalI2) =>
% 97.31/13.18 ((
% 97.31/13.18 (subsetRefl) =>
% 97.31/13.18 ((
% 97.31/13.18 (subsetTrans) =>
% 97.31/13.18 ((
% 97.31/13.18 (setadjoinSub) =>
% 97.31/13.18 ((
% 97.31/13.18 (setadjoinSub2) =>
% 97.31/13.18 ((
% 97.31/13.18 (subset2powerset) =>
% 97.31/13.18 ((
% 97.31/13.18 (setextsub) =>
% 97.31/13.18 ((
% 97.31/13.18 (subsetemptysetimpeq) =>
% 97.31/13.18 ((
% 97.31/13.18 (powersetI1) =>
% 97.31/13.18 ((
% 97.31/13.18 (powersetE1) =>
% 97.31/13.18 ((
% 97.31/13.18 (inPowerset) =>
% 97.31/13.18 ((
% 97.31/13.18 (powersetsubset) =>
% 97.31/13.18 ((
% 97.31/13.18 (sepInPowerset) =>
% 97.31/13.18 ((
% 97.31/13.18 (sepSubset) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionIL) =>
% 97.31/13.18 ((
% 97.31/13.18 (upairset2IR) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionIR) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionEcases) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionE) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionLsub) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionRsub) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectI) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectSubset5) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectEL) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectLsub) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectSubset2) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectSubset3) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectER) =>
% 97.31/13.18 ((
% 97.31/13.18 (disjointsetsI1) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectRsub) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectSubset4) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectSubset1) =>
% 97.31/13.18 ((
% 97.31/13.18 (bs114d) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusI) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusEL) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusER) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusSubset2) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusERneg) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusELneg) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusILneg) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusIRneg) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusLsub) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusSubset1) =>
% 97.31/13.18 ((
% 97.31/13.18 (symdiffE) =>
% 97.31/13.18 ((
% 97.31/13.18 (symdiffI1) =>
% 97.31/13.18 ((
% 97.31/13.18 (symdiffI2) =>
% 97.31/13.18 ((
% 97.31/13.18 (symdiffIneg1) =>
% 97.31/13.18 ((
% 97.31/13.18 (symdiffIneg2) =>
% 97.31/13.18 ((
% 97.31/13.18 (secondinupair) =>
% 97.31/13.18 ((
% 97.31/13.18 (setukpairIL) =>
% 97.31/13.18 ((
% 97.31/13.18 (setukpairIR) =>
% 97.31/13.18 ((
% 97.31/13.18 (kpairiskpair) =>
% 97.31/13.18 ((
% 97.31/13.18 (kpairp) =>
% 97.31/13.18 ((
% 97.31/13.18 (singletonsubset) =>
% 97.31/13.18 ((
% 97.31/13.18 (singletoninpowerset) =>
% 97.31/13.18 ((
% 97.31/13.18 (singletoninpowunion) =>
% 97.31/13.18 ((
% 97.31/13.18 (upairset2E) =>
% 97.31/13.18 ((
% 97.31/13.18 (upairsubunion) =>
% 97.31/13.18 ((
% 97.31/13.18 (upairinpowunion) =>
% 97.31/13.18 ((
% 97.31/13.18 (ubforcartprodlem1) =>
% 97.31/13.18 ((
% 97.31/13.18 (ubforcartprodlem2) =>
% 97.31/13.18 ((
% 97.31/13.18 (ubforcartprodlem3) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodpairin) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodmempair1) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodmempair) =>
% 97.31/13.18 ((
% 97.31/13.18 (setunionE2) =>
% 97.31/13.18 ((
% 97.31/13.18 (setunionsingleton1) =>
% 97.31/13.18 ((
% 97.31/13.18 (setunionsingleton2) =>
% 97.31/13.18 ((
% 97.31/13.18 (setunionsingleton) =>
% 97.31/13.18 ((
% 97.31/13.18 (singletonprop) =>
% 97.31/13.18 ((
% 97.31/13.18 (ex1E1) =>
% 97.31/13.18 ((
% 97.31/13.18 (ex1I) =>
% 97.31/13.18 ((
% 97.31/13.18 (ex1I2) =>
% 97.31/13.18 ((
% 97.31/13.18 (singletonsuniq) =>
% 97.31/13.18 ((
% 97.31/13.18 (setukpairinjL1) =>
% 97.31/13.18 ((
% 97.31/13.18 (kfstsingleton) =>
% 97.31/13.18 ((
% 97.31/13.18 (theprop) =>
% 97.31/13.18 ((
% 97.31/13.18 (kfstpairEq) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodfstin) =>
% 97.31/13.18 ((
% 97.31/13.18 (setukpairinjL2) =>
% 97.31/13.18 ((
% 97.31/13.18 (setukpairinjL) =>
% 97.31/13.18 ((
% 97.31/13.18 (setukpairinjR11) =>
% 97.31/13.18 ((
% 97.31/13.18 (setukpairinjR12) =>
% 97.31/13.18 ((
% 97.31/13.18 (setukpairinjR1) =>
% 97.31/13.18 ((
% 97.31/13.18 (upairequniteq) =>
% 97.31/13.18 ((
% 97.31/13.18 (setukpairinjR2) =>
% 97.31/13.18 ((
% 97.31/13.18 (setukpairinjR) =>
% 97.31/13.18 ((
% 97.31/13.18 (ksndsingleton) =>
% 97.31/13.18 ((
% 97.31/13.18 (ksndpairEq) =>
% 97.31/13.18 ((
% 97.31/13.18 (kpairsurjEq) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodsndin) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodpairmemEL) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodpairmemER) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodmempaircEq) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodfstpairEq) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodsndpairEq) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodpairsurjEq) =>
% 97.31/13.18 ((
% 97.31/13.18 (dpsetconstrI) =>
% 97.31/13.18 ((
% 97.31/13.18 (dpsetconstrSub) =>
% 97.31/13.18 ((
% 97.31/13.18 (setOfPairsIsBReln) =>
% 97.31/13.18 ((
% 97.31/13.18 (dpsetconstrERa) =>
% 97.31/13.18 ((
% 97.31/13.18 (dpsetconstrEL1) =>
% 97.31/13.18 ((
% 97.31/13.18 (dpsetconstrEL2) =>
% 97.31/13.18 ((
% 97.31/13.18 (dpsetconstrER) =>
% 97.31/13.18 ((
% 97.31/13.18 (funcImageSingleton) =>
% 97.31/13.18 ((
% 97.31/13.18 (apProp) =>
% 97.31/13.18 ((
% 97.31/13.18 (app) =>
% 97.31/13.18 ((
% 97.31/13.18 (infuncsetfunc) =>
% 97.31/13.18 ((
% 97.31/13.18 (ap2p) =>
% 97.31/13.18 ((
% 97.31/13.18 (funcinfuncset) =>
% 97.31/13.18 ((
% 97.31/13.18 (lamProp) =>
% 97.31/13.18 ((
% 97.31/13.18 (lamp) =>
% 97.31/13.18 ((
% 97.31/13.18 (lam2p) =>
% 97.31/13.18 ((
% 97.31/13.18 (brelnall1) =>
% 97.31/13.18 ((
% 97.31/13.18 (brelnall2) =>
% 97.31/13.18 ((
% 97.31/13.18 (ex1E2) =>
% 97.31/13.18 ((
% 97.31/13.18 (funcGraphProp1) =>
% 97.31/13.18 ((
% 97.31/13.18 (funcGraphProp3) =>
% 97.31/13.18 ((
% 97.31/13.18 (funcGraphProp2) =>
% 97.31/13.18 ((
% 97.31/13.18 (funcextLem) =>
% 97.31/13.18 ((
% 97.31/13.18 (funcGraphProp4) =>
% 97.31/13.18 ((
% 97.31/13.18 (subbreln) =>
% 97.31/13.18 ((
% 97.31/13.18 (eqbreln) =>
% 97.31/13.18 ((
% 97.31/13.18 (funcext) =>
% 97.31/13.18 ((
% 97.31/13.18 (funcext2) =>
% 97.31/13.18 ((
% 97.31/13.18 (ap2apEq1) =>
% 97.31/13.18 ((
% 97.31/13.18 (ap2apEq2) =>
% 97.31/13.18 ((
% 97.31/13.18 (beta1) =>
% 97.31/13.18 ((
% 97.31/13.18 (eta1) =>
% 97.31/13.18 ((
% 97.31/13.18 (lam2lamEq) =>
% 97.31/13.18 ((
% 97.31/13.18 (beta2) =>
% 97.31/13.18 ((
% 97.31/13.18 (eta2) =>
% 97.31/13.18 ((
% 97.31/13.18 (iffalseProp1) =>
% 97.31/13.18 ((
% 97.31/13.18 (iffalseProp2) =>
% 97.31/13.18 ((
% 97.31/13.18 (iftrueProp1) =>
% 97.31/13.18 ((
% 97.31/13.18 (iftrueProp2) =>
% 97.31/13.18 ((
% 97.31/13.18 (ifSingleton) =>
% 97.31/13.18 ((
% 97.31/13.18 (ifp) =>
% 97.31/13.18 ((
% 97.31/13.18 (theeq) =>
% 97.31/13.18 ((
% 97.31/13.18 (iftrue) =>
% 97.31/13.18 ((
% 97.31/13.18 (iffalse) =>
% 97.31/13.18 ((
% 97.31/13.18 (iftrueorfalse) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectT_lem) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionT_lem) =>
% 97.31/13.18 ((
% 97.31/13.18 (powersetT_lem) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusT_lem) =>
% 97.31/13.18 ((
% 97.31/13.18 (complementT_lem) =>
% 97.31/13.18 ((
% 97.31/13.18 (setextT) =>
% 97.31/13.18 ((
% 97.31/13.18 (subsetTI) =>
% 97.31/13.18 ((
% 97.31/13.18 (powersetTI1) =>
% 97.31/13.18 ((
% 97.31/13.18 (powersetTE1) =>
% 97.31/13.18 ((
% 97.31/13.18 (complementTI1) =>
% 97.31/13.18 ((
% 97.31/13.18 (complementTE1) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectTELcontra) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectTERcontra) =>
% 97.31/13.18 ((
% 97.31/13.18 (contrasubsetT) =>
% 97.31/13.18 ((
% 97.31/13.18 (contrasubsetT1) =>
% 97.31/13.18 ((
% 97.31/13.18 (contrasubsetT2) =>
% 97.31/13.18 ((
% 97.31/13.18 (contrasubsetT3) =>
% 97.31/13.18 ((
% 97.31/13.18 (doubleComplementI1) =>
% 97.31/13.18 ((
% 97.31/13.18 (doubleComplementE1) =>
% 97.31/13.18 ((
% 97.31/13.18 (doubleComplementSub1) =>
% 97.31/13.18 ((
% 97.31/13.18 (doubleComplementSub2) =>
% 97.31/13.18 ((
% 97.31/13.18 (doubleComplementEq) =>
% 97.31/13.18 ((
% 97.31/13.18 (complementTnotintersectT) =>
% 97.31/13.18 ((
% 97.31/13.18 (complementImpComplementIntersect) =>
% 97.31/13.18 ((
% 97.31/13.18 (complementSubsetComplementIntersect) =>
% 97.31/13.18 ((
% 97.31/13.18 (complementInPowersetComplementIntersect) =>
% 97.31/13.18 ((
% 97.31/13.18 (contraSubsetComplement) =>
% 97.31/13.18 ((
% 97.31/13.18 (complementTcontraSubset) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionTILcontra) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionTIRcontra) =>
% 97.31/13.18 ((
% 97.31/13.18 (inIntersectImpInUnion) =>
% 97.31/13.18 ((
% 97.31/13.18 (inIntersectImpInUnion2) =>
% 97.31/13.18 ((
% 97.31/13.18 (inIntersectImpInIntersectUnions) =>
% 97.31/13.18 ((
% 97.31/13.18 (intersectInPowersetIntersectUnions) =>
% 97.31/13.18 ((
% 97.31/13.18 (inComplementUnionImpNotIn1) =>
% 97.31/13.18 ((
% 97.31/13.18 (inComplementUnionImpInComplement1) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionTE) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionTEcontra) =>
% 97.31/13.18 ((
% 97.31/13.18 (demorgan2a1) =>
% 97.31/13.18 ((
% 97.31/13.18 (complementUnionInPowersetComplement) =>
% 97.31/13.18 ((
% 97.31/13.18 (demorgan2a2) =>
% 97.31/13.18 ((
% 97.31/13.18 (demorgan1a) =>
% 97.31/13.18 ((
% 97.31/13.18 (demorgan1b) =>
% 97.31/13.18 ((
% 97.31/13.18 (demorgan1) =>
% 97.31/13.18 ((
% 97.31/13.18 (demorgan2a) =>
% 97.31/13.18 ((
% 97.31/13.18 (demorgan2b2) =>
% 97.31/13.18 ((
% 97.31/13.18 (demorgan2b) =>
% 97.31/13.18 ((
% 97.31/13.18 (demorgan2) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz13rule0) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz13rule1) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz13rule2) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz13rule3) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz13rule4) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz1_1) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz1_2) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz1_3) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz1_4) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz1_5) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1all2) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1SetBreln1) =>
% 97.31/13.18 ((
% 97.31/13.18 (choice2fnsingleton) =>
% 97.31/13.18 ((
% 97.31/13.18 (setOfPairsIsBReln1) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1all1) =>
% 97.31/13.18 ((
% 97.31/13.18 (subbreln1) =>
% 97.31/13.18 ((
% 97.31/13.18 (eqbreln1) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1invprop) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1invI) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1invE) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1compprop) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1compI) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1compE) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1compEex) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1unionprop) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1unionIL) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1unionIR) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1unionI) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1unionE) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1unionEcases) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1unionCommutes) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz2Ex) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz2W) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz2A) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz2B) =>
% 97.31/13.18 ((
% 97.31/13.18 (image1Ex) =>
% 97.31/13.18 ((
% 97.31/13.18 (image1Ex1) =>
% 97.31/13.18 ((
% 97.31/13.18 (image1Equiv) =>
% 97.31/13.18 ((
% 97.31/13.18 (image1E) =>
% 97.31/13.18 ((
% 97.31/13.18 (image1I) =>
% 97.31/13.18 ((
% 97.31/13.18 (injFuncInInjFuncSet) =>
% 97.31/13.18 ((
% 97.31/13.18 (injFuncSetFuncIn) =>
% 97.31/13.18 ((
% 97.31/13.18 (injFuncSetFuncInj) =>
% 97.31/13.18 ((
% 97.31/13.18 (surjFuncSetFuncIn) =>
% 97.31/13.18 ((
% 97.31/13.18 (surjFuncSetFuncSurj) =>
% 97.31/13.18 ((
% 97.31/13.18 (leftInvIsSurj) =>
% 97.31/13.18 ((
% 97.31/13.18 (surjCantorThm) =>
% 97.31/13.18 ((
% 97.31/13.18 (foundation2) =>
% 97.31/13.18 ((
% 97.31/13.18 (notinself) =>
% 97.31/13.18 ((
% 97.31/13.18 (notinself2) =>
% 97.31/13.18 ((
% 97.31/13.18 (omegaSp) =>
% 97.31/13.18 ((
% 97.31/13.18 (omegaSclos) =>
% 97.31/13.18 ((
% 97.31/13.18 (peano0notS) =>
% 97.31/13.18 ((
% 97.31/13.18 (!!) @ (
% 97.31/13.18 (('#S') @ (
% 97.31/13.18 (
% 97.31/13.18 ('#B') @ (
% 97.31/13.18 =>) @
% 97.31/13.18 (
% 97.31/13.18 (
% 97.31/13.18 ('#C') @ in @
% 97.31/13.18 omega)))) @
% 97.31/13.18 (
% 97.31/13.18 (
% 97.31/13.18 ('#B') @ (
% 97.31/13.18 !!) @
% 97.31/13.18 (
% 97.31/13.18 (
% 97.31/13.18 ('#B') @ (
% 97.31/13.18 (
% 97.31/13.18 ('#S') @ (
% 97.31/13.18 (
% 97.31/13.18 ('#B') @ (
% 97.31/13.18 =>) @
% 97.31/13.18 (
% 97.31/13.18 (
% 97.31/13.18 ('#C') @ in @
% 97.31/13.18 omega)))))) @
% 97.31/13.18 (
% 97.31/13.18 (
% 97.31/13.18 ('#S') @ (
% 97.31/13.18 (
% 97.31/13.18 ('#B') @ (
% 97.31/13.18 '#S') @
% 97.31/13.18 (
% 97.31/13.18 (
% 97.31/13.18 ('#B') @ (
% 97.31/13.18 (
% 97.31/13.18 ('#B') @ (
% 97.31/13.18 =>))) @
% 97.31/13.18 (
% 97.31/13.18 (
% 97.31/13.18 ('#C') @ (
% 97.31/13.18 (
% 97.31/13.18 ('#B') @ (
% 97.31/13.18 '#B') @
% 97.31/13.18 (
% 97.31/13.18 (
% 97.31/13.18 ('#B') @ (
% 97.31/13.18 =) @
% 97.31/13.18 omegaS)))) @
% 97.31/13.18 omegaS)))))) @
% 97.31/13.18 (
% 97.31/13.18 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.31/13.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl417])).
% 97.31/13.18 thf(zip_derived_cl439, plain,
% 97.31/13.18 (~ (((nonemptyImpWitness) =>
% 97.31/13.18 (((uniqinunit) =>
% 97.31/13.18 (((notinsingleton) =>
% 97.31/13.18 (((eqinunit) =>
% 97.31/13.18 (((singletonsswitch) =>
% 97.31/13.18 (((upairsetE) =>
% 97.31/13.18 (((upairsetIL) =>
% 97.31/13.18 (((upairsetIR) =>
% 97.31/13.18 (((emptyE1) =>
% 97.31/13.18 (((vacuousDall) =>
% 97.31/13.18 (((quantDeMorgan1) =>
% 97.31/13.18 (((quantDeMorgan2) =>
% 97.31/13.18 (((quantDeMorgan3) =>
% 97.31/13.18 (((quantDeMorgan4) =>
% 97.31/13.18 (((prop2setI) =>
% 97.31/13.18 (((prop2set2propI) =>
% 97.31/13.18 (((notdexE) =>
% 97.31/13.18 (((notdallE) =>
% 97.31/13.18 (((exuI1) =>
% 97.31/13.18 (((exuI3) =>
% 97.31/13.18 (((exuI2) =>
% 97.31/13.18 (((inCongP) =>
% 97.31/13.18 (((in__Cong) =>
% 97.31/13.18 (((exuE3u) =>
% 97.31/13.18 (((exu__Cong) =>
% 97.31/13.18 (((setadjoin__Cong) =>
% 97.31/13.18 (((powerset__Cong) =>
% 97.31/13.18 (((setunion__Cong) =>
% 97.31/13.18 (((exuEu) =>
% 97.31/13.18 (((descr__Cong) =>
% 97.31/13.18 ((
% 97.31/13.18 (dsetconstr__Cong) =>
% 97.31/13.18 ((
% 97.31/13.18 (subsetI1) =>
% 97.31/13.18 ((
% 97.31/13.18 (eqimpsubset2) =>
% 97.31/13.18 ((
% 97.31/13.18 (eqimpsubset1) =>
% 97.31/13.18 ((
% 97.31/13.18 (subsetI2) =>
% 97.31/13.18 ((
% 97.31/13.18 (emptysetsubset) =>
% 97.31/13.18 ((
% 97.31/13.18 (subsetE) =>
% 97.31/13.18 ((
% 97.31/13.18 (subsetE2) =>
% 97.31/13.18 ((
% 97.31/13.18 (notsubsetI) =>
% 97.31/13.18 ((
% 97.31/13.18 (notequalI1) =>
% 97.31/13.18 ((
% 97.31/13.18 (notequalI2) =>
% 97.31/13.18 ((
% 97.31/13.18 (subsetRefl) =>
% 97.31/13.18 ((
% 97.31/13.18 (subsetTrans) =>
% 97.31/13.18 ((
% 97.31/13.18 (setadjoinSub) =>
% 97.31/13.18 ((
% 97.31/13.18 (setadjoinSub2) =>
% 97.31/13.18 ((
% 97.31/13.18 (subset2powerset) =>
% 97.31/13.18 ((
% 97.31/13.18 (setextsub) =>
% 97.31/13.18 ((
% 97.31/13.18 (subsetemptysetimpeq) =>
% 97.31/13.18 ((
% 97.31/13.18 (powersetI1) =>
% 97.31/13.18 ((
% 97.31/13.18 (powersetE1) =>
% 97.31/13.18 ((
% 97.31/13.18 (inPowerset) =>
% 97.31/13.18 ((
% 97.31/13.18 (powersetsubset) =>
% 97.31/13.18 ((
% 97.31/13.18 (sepInPowerset) =>
% 97.31/13.18 ((
% 97.31/13.18 (sepSubset) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionIL) =>
% 97.31/13.18 ((
% 97.31/13.18 (upairset2IR) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionIR) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionEcases) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionE) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionLsub) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionRsub) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectI) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectSubset5) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectEL) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectLsub) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectSubset2) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectSubset3) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectER) =>
% 97.31/13.18 ((
% 97.31/13.18 (disjointsetsI1) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectRsub) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectSubset4) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectSubset1) =>
% 97.31/13.18 ((
% 97.31/13.18 (bs114d) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusI) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusEL) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusER) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusSubset2) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusERneg) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusELneg) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusILneg) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusIRneg) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusLsub) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusSubset1) =>
% 97.31/13.18 ((
% 97.31/13.18 (symdiffE) =>
% 97.31/13.18 ((
% 97.31/13.18 (symdiffI1) =>
% 97.31/13.18 ((
% 97.31/13.18 (symdiffI2) =>
% 97.31/13.18 ((
% 97.31/13.18 (symdiffIneg1) =>
% 97.31/13.18 ((
% 97.31/13.18 (symdiffIneg2) =>
% 97.31/13.18 ((
% 97.31/13.18 (secondinupair) =>
% 97.31/13.18 ((
% 97.31/13.18 (setukpairIL) =>
% 97.31/13.18 ((
% 97.31/13.18 (setukpairIR) =>
% 97.31/13.18 ((
% 97.31/13.18 (kpairiskpair) =>
% 97.31/13.18 ((
% 97.31/13.18 (kpairp) =>
% 97.31/13.18 ((
% 97.31/13.18 (singletonsubset) =>
% 97.31/13.18 ((
% 97.31/13.18 (singletoninpowerset) =>
% 97.31/13.18 ((
% 97.31/13.18 (singletoninpowunion) =>
% 97.31/13.18 ((
% 97.31/13.18 (upairset2E) =>
% 97.31/13.18 ((
% 97.31/13.18 (upairsubunion) =>
% 97.31/13.18 ((
% 97.31/13.18 (upairinpowunion) =>
% 97.31/13.18 ((
% 97.31/13.18 (ubforcartprodlem1) =>
% 97.31/13.18 ((
% 97.31/13.18 (ubforcartprodlem2) =>
% 97.31/13.18 ((
% 97.31/13.18 (ubforcartprodlem3) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodpairin) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodmempair1) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodmempair) =>
% 97.31/13.18 ((
% 97.31/13.18 (setunionE2) =>
% 97.31/13.18 ((
% 97.31/13.18 (setunionsingleton1) =>
% 97.31/13.18 ((
% 97.31/13.18 (setunionsingleton2) =>
% 97.31/13.18 ((
% 97.31/13.18 (setunionsingleton) =>
% 97.31/13.18 ((
% 97.31/13.18 (singletonprop) =>
% 97.31/13.18 ((
% 97.31/13.18 (ex1E1) =>
% 97.31/13.18 ((
% 97.31/13.18 (ex1I) =>
% 97.31/13.18 ((
% 97.31/13.18 (ex1I2) =>
% 97.31/13.18 ((
% 97.31/13.18 (singletonsuniq) =>
% 97.31/13.18 ((
% 97.31/13.18 (setukpairinjL1) =>
% 97.31/13.18 ((
% 97.31/13.18 (kfstsingleton) =>
% 97.31/13.18 ((
% 97.31/13.18 (theprop) =>
% 97.31/13.18 ((
% 97.31/13.18 (kfstpairEq) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodfstin) =>
% 97.31/13.18 ((
% 97.31/13.18 (setukpairinjL2) =>
% 97.31/13.18 ((
% 97.31/13.18 (setukpairinjL) =>
% 97.31/13.18 ((
% 97.31/13.18 (setukpairinjR11) =>
% 97.31/13.18 ((
% 97.31/13.18 (setukpairinjR12) =>
% 97.31/13.18 ((
% 97.31/13.18 (setukpairinjR1) =>
% 97.31/13.18 ((
% 97.31/13.18 (upairequniteq) =>
% 97.31/13.18 ((
% 97.31/13.18 (setukpairinjR2) =>
% 97.31/13.18 ((
% 97.31/13.18 (setukpairinjR) =>
% 97.31/13.18 ((
% 97.31/13.18 (ksndsingleton) =>
% 97.31/13.18 ((
% 97.31/13.18 (ksndpairEq) =>
% 97.31/13.18 ((
% 97.31/13.18 (kpairsurjEq) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodsndin) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodpairmemEL) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodpairmemER) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodmempaircEq) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodfstpairEq) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodsndpairEq) =>
% 97.31/13.18 ((
% 97.31/13.18 (cartprodpairsurjEq) =>
% 97.31/13.18 ((
% 97.31/13.18 (dpsetconstrI) =>
% 97.31/13.18 ((
% 97.31/13.18 (dpsetconstrSub) =>
% 97.31/13.18 ((
% 97.31/13.18 (setOfPairsIsBReln) =>
% 97.31/13.18 ((
% 97.31/13.18 (dpsetconstrERa) =>
% 97.31/13.18 ((
% 97.31/13.18 (dpsetconstrEL1) =>
% 97.31/13.18 ((
% 97.31/13.18 (dpsetconstrEL2) =>
% 97.31/13.18 ((
% 97.31/13.18 (dpsetconstrER) =>
% 97.31/13.18 ((
% 97.31/13.18 (funcImageSingleton) =>
% 97.31/13.18 ((
% 97.31/13.18 (apProp) =>
% 97.31/13.18 ((
% 97.31/13.18 (app) =>
% 97.31/13.18 ((
% 97.31/13.18 (infuncsetfunc) =>
% 97.31/13.18 ((
% 97.31/13.18 (ap2p) =>
% 97.31/13.18 ((
% 97.31/13.18 (funcinfuncset) =>
% 97.31/13.18 ((
% 97.31/13.18 (lamProp) =>
% 97.31/13.18 ((
% 97.31/13.18 (lamp) =>
% 97.31/13.18 ((
% 97.31/13.18 (lam2p) =>
% 97.31/13.18 ((
% 97.31/13.18 (brelnall1) =>
% 97.31/13.18 ((
% 97.31/13.18 (brelnall2) =>
% 97.31/13.18 ((
% 97.31/13.18 (ex1E2) =>
% 97.31/13.18 ((
% 97.31/13.18 (funcGraphProp1) =>
% 97.31/13.18 ((
% 97.31/13.18 (funcGraphProp3) =>
% 97.31/13.18 ((
% 97.31/13.18 (funcGraphProp2) =>
% 97.31/13.18 ((
% 97.31/13.18 (funcextLem) =>
% 97.31/13.18 ((
% 97.31/13.18 (funcGraphProp4) =>
% 97.31/13.18 ((
% 97.31/13.18 (subbreln) =>
% 97.31/13.18 ((
% 97.31/13.18 (eqbreln) =>
% 97.31/13.18 ((
% 97.31/13.18 (funcext) =>
% 97.31/13.18 ((
% 97.31/13.18 (funcext2) =>
% 97.31/13.18 ((
% 97.31/13.18 (ap2apEq1) =>
% 97.31/13.18 ((
% 97.31/13.18 (ap2apEq2) =>
% 97.31/13.18 ((
% 97.31/13.18 (beta1) =>
% 97.31/13.18 ((
% 97.31/13.18 (eta1) =>
% 97.31/13.18 ((
% 97.31/13.18 (lam2lamEq) =>
% 97.31/13.18 ((
% 97.31/13.18 (beta2) =>
% 97.31/13.18 ((
% 97.31/13.18 (eta2) =>
% 97.31/13.18 ((
% 97.31/13.18 (iffalseProp1) =>
% 97.31/13.18 ((
% 97.31/13.18 (iffalseProp2) =>
% 97.31/13.18 ((
% 97.31/13.18 (iftrueProp1) =>
% 97.31/13.18 ((
% 97.31/13.18 (iftrueProp2) =>
% 97.31/13.18 ((
% 97.31/13.18 (ifSingleton) =>
% 97.31/13.18 ((
% 97.31/13.18 (ifp) =>
% 97.31/13.18 ((
% 97.31/13.18 (theeq) =>
% 97.31/13.18 ((
% 97.31/13.18 (iftrue) =>
% 97.31/13.18 ((
% 97.31/13.18 (iffalse) =>
% 97.31/13.18 ((
% 97.31/13.18 (iftrueorfalse) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectT_lem) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionT_lem) =>
% 97.31/13.18 ((
% 97.31/13.18 (powersetT_lem) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusT_lem) =>
% 97.31/13.18 ((
% 97.31/13.18 (complementT_lem) =>
% 97.31/13.18 ((
% 97.31/13.18 (setextT) =>
% 97.31/13.18 ((
% 97.31/13.18 (subsetTI) =>
% 97.31/13.18 ((
% 97.31/13.18 (powersetTI1) =>
% 97.31/13.18 ((
% 97.31/13.18 (powersetTE1) =>
% 97.31/13.18 ((
% 97.31/13.18 (complementTI1) =>
% 97.31/13.18 ((
% 97.31/13.18 (complementTE1) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectTELcontra) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectTERcontra) =>
% 97.31/13.18 ((
% 97.31/13.18 (contrasubsetT) =>
% 97.31/13.18 ((
% 97.31/13.18 (contrasubsetT1) =>
% 97.31/13.18 ((
% 97.31/13.18 (contrasubsetT2) =>
% 97.31/13.18 ((
% 97.31/13.18 (contrasubsetT3) =>
% 97.31/13.18 ((
% 97.31/13.18 (doubleComplementI1) =>
% 97.31/13.18 ((
% 97.31/13.18 (doubleComplementE1) =>
% 97.31/13.18 ((
% 97.31/13.18 (doubleComplementSub1) =>
% 97.31/13.18 ((
% 97.31/13.18 (doubleComplementSub2) =>
% 97.31/13.18 ((
% 97.31/13.18 (doubleComplementEq) =>
% 97.31/13.18 ((
% 97.31/13.18 (complementTnotintersectT) =>
% 97.31/13.18 ((
% 97.31/13.18 (complementImpComplementIntersect) =>
% 97.31/13.18 ((
% 97.31/13.18 (complementSubsetComplementIntersect) =>
% 97.31/13.18 ((
% 97.31/13.18 (complementInPowersetComplementIntersect) =>
% 97.31/13.18 ((
% 97.31/13.18 (contraSubsetComplement) =>
% 97.31/13.18 ((
% 97.31/13.18 (complementTcontraSubset) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionTILcontra) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionTIRcontra) =>
% 97.31/13.18 ((
% 97.31/13.18 (inIntersectImpInUnion) =>
% 97.31/13.18 ((
% 97.31/13.18 (inIntersectImpInUnion2) =>
% 97.31/13.18 ((
% 97.31/13.18 (inIntersectImpInIntersectUnions) =>
% 97.31/13.18 ((
% 97.31/13.18 (intersectInPowersetIntersectUnions) =>
% 97.31/13.18 ((
% 97.31/13.18 (inComplementUnionImpNotIn1) =>
% 97.31/13.18 ((
% 97.31/13.18 (inComplementUnionImpInComplement1) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionTE) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionTEcontra) =>
% 97.31/13.18 ((
% 97.31/13.18 (demorgan2a1) =>
% 97.31/13.18 ((
% 97.31/13.18 (complementUnionInPowersetComplement) =>
% 97.31/13.18 ((
% 97.31/13.18 (demorgan2a2) =>
% 97.31/13.18 ((
% 97.31/13.18 (demorgan1a) =>
% 97.31/13.18 ((
% 97.31/13.18 (demorgan1b) =>
% 97.31/13.18 ((
% 97.31/13.18 (demorgan1) =>
% 97.31/13.18 ((
% 97.31/13.18 (demorgan2a) =>
% 97.31/13.18 ((
% 97.31/13.18 (demorgan2b2) =>
% 97.31/13.18 ((
% 97.31/13.18 (demorgan2b) =>
% 97.31/13.18 ((
% 97.31/13.18 (demorgan2) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz13rule0) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz13rule1) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz13rule2) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz13rule3) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz13rule4) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz1_1) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz1_2) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz1_3) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz1_4) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz1_5) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1all2) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1SetBreln1) =>
% 97.31/13.18 ((
% 97.31/13.18 (choice2fnsingleton) =>
% 97.31/13.18 ((
% 97.31/13.18 (setOfPairsIsBReln1) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1all1) =>
% 97.31/13.18 ((
% 97.31/13.18 (subbreln1) =>
% 97.31/13.18 ((
% 97.31/13.18 (eqbreln1) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1invprop) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1invI) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1invE) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1compprop) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1compI) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1compE) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1compEex) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1unionprop) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1unionIL) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1unionIR) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1unionI) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1unionE) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1unionEcases) =>
% 97.31/13.18 ((
% 97.31/13.18 (breln1unionCommutes) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz2Ex) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz2W) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz2A) =>
% 97.31/13.18 ((
% 97.31/13.18 (woz2B) =>
% 97.31/13.18 ((
% 97.31/13.18 (image1Ex) =>
% 97.31/13.18 ((
% 97.31/13.18 (image1Ex1) =>
% 97.31/13.18 ((
% 97.31/13.18 (image1Equiv) =>
% 97.31/13.18 ((
% 97.31/13.18 (image1E) =>
% 97.31/13.18 ((
% 97.31/13.18 (image1I) =>
% 97.31/13.18 ((
% 97.31/13.18 (injFuncInInjFuncSet) =>
% 97.31/13.18 ((
% 97.31/13.18 (injFuncSetFuncIn) =>
% 97.31/13.18 ((
% 97.31/13.18 (injFuncSetFuncInj) =>
% 97.31/13.18 ((
% 97.31/13.18 (surjFuncSetFuncIn) =>
% 97.31/13.18 ((
% 97.31/13.18 (surjFuncSetFuncSurj) =>
% 97.31/13.18 ((
% 97.31/13.18 (leftInvIsSurj) =>
% 97.31/13.18 ((
% 97.31/13.18 (surjCantorThm) =>
% 97.31/13.18 ((
% 97.31/13.18 (foundation2) =>
% 97.31/13.18 ((
% 97.31/13.18 (notinself) =>
% 97.31/13.18 ((
% 97.31/13.18 (notinself2) =>
% 97.31/13.18 ((
% 97.31/13.18 (omegaSp) =>
% 97.31/13.18 ((
% 97.31/13.18 (omegaSclos) =>
% 97.31/13.18 ((
% 97.31/13.18 (peano0notS) =>
% 97.31/13.18 ((
% 97.31/13.18 (!!) @ (
% 97.31/13.18 (('#S') @ (
% 97.31/13.18 (
% 97.31/13.18 ('#B') @ (
% 97.31/13.18 =>) @
% 97.31/13.18 (
% 97.31/13.18 (
% 97.31/13.18 ('#C') @ in @
% 97.31/13.18 omega)))) @
% 97.31/13.18 (
% 97.31/13.18 (
% 97.31/13.18 ('#B') @ (
% 97.31/13.18 !!) @
% 97.31/13.18 (
% 97.31/13.18 (
% 97.31/13.18 ('#B') @ (
% 97.31/13.18 (
% 97.31/13.18 ('#S') @ (
% 97.31/13.18 (
% 97.31/13.18 ('#B') @ (
% 97.31/13.18 =>) @
% 97.31/13.18 (
% 97.31/13.18 (
% 97.31/13.18 ('#C') @ in @
% 97.31/13.18 omega)))))) @
% 97.31/13.18 (
% 97.31/13.18 (
% 97.31/13.18 ('#S') @ (
% 97.31/13.18 (
% 97.31/13.18 ('#B') @ (
% 97.31/13.18 '#S') @
% 97.31/13.18 (
% 97.31/13.18 (
% 97.31/13.18 ('#B') @ (
% 97.31/13.18 (
% 97.31/13.18 ('#B') @ (
% 97.31/13.18 =>))) @
% 97.31/13.18 (
% 97.31/13.18 (
% 97.31/13.18 ('#C') @ (
% 97.31/13.18 (
% 97.31/13.18 ('#B') @ (
% 97.31/13.18 '#B') @
% 97.31/13.18 (
% 97.31/13.18 (
% 97.31/13.18 ('#B') @ (
% 97.31/13.18 =) @
% 97.31/13.18 omegaS)))) @
% 97.31/13.18 omegaS)))))) @
% 97.31/13.18 (
% 97.31/13.18 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.31/13.18 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl428])).
% 97.31/13.18 thf(zip_derived_cl449, plain,
% 97.31/13.18 (~ (((uniqinunit) =>
% 97.31/13.18 (((notinsingleton) =>
% 97.31/13.18 (((eqinunit) =>
% 97.31/13.18 (((singletonsswitch) =>
% 97.31/13.18 (((upairsetE) =>
% 97.31/13.18 (((upairsetIL) =>
% 97.31/13.18 (((upairsetIR) =>
% 97.31/13.18 (((emptyE1) =>
% 97.31/13.18 (((vacuousDall) =>
% 97.31/13.18 (((quantDeMorgan1) =>
% 97.31/13.18 (((quantDeMorgan2) =>
% 97.31/13.18 (((quantDeMorgan3) =>
% 97.31/13.18 (((quantDeMorgan4) =>
% 97.31/13.18 (((prop2setI) =>
% 97.31/13.18 (((prop2set2propI) =>
% 97.31/13.18 (((notdexE) =>
% 97.31/13.18 (((notdallE) =>
% 97.31/13.18 (((exuI1) =>
% 97.31/13.18 (((exuI3) =>
% 97.31/13.18 (((exuI2) =>
% 97.31/13.18 (((inCongP) =>
% 97.31/13.18 (((in__Cong) =>
% 97.31/13.18 (((exuE3u) =>
% 97.31/13.18 (((exu__Cong) =>
% 97.31/13.18 (((setadjoin__Cong) =>
% 97.31/13.18 (((powerset__Cong) =>
% 97.31/13.18 (((setunion__Cong) =>
% 97.31/13.18 (((exuEu) =>
% 97.31/13.18 (((descr__Cong) =>
% 97.31/13.18 (((dsetconstr__Cong) =>
% 97.31/13.18 ((
% 97.31/13.18 (subsetI1) =>
% 97.31/13.18 ((
% 97.31/13.18 (eqimpsubset2) =>
% 97.31/13.18 ((
% 97.31/13.18 (eqimpsubset1) =>
% 97.31/13.18 ((
% 97.31/13.18 (subsetI2) =>
% 97.31/13.18 ((
% 97.31/13.18 (emptysetsubset) =>
% 97.31/13.18 ((
% 97.31/13.18 (subsetE) =>
% 97.31/13.18 ((
% 97.31/13.18 (subsetE2) =>
% 97.31/13.18 ((
% 97.31/13.18 (notsubsetI) =>
% 97.31/13.18 ((
% 97.31/13.18 (notequalI1) =>
% 97.31/13.18 ((
% 97.31/13.18 (notequalI2) =>
% 97.31/13.18 ((
% 97.31/13.18 (subsetRefl) =>
% 97.31/13.18 ((
% 97.31/13.18 (subsetTrans) =>
% 97.31/13.18 ((
% 97.31/13.18 (setadjoinSub) =>
% 97.31/13.18 ((
% 97.31/13.18 (setadjoinSub2) =>
% 97.31/13.18 ((
% 97.31/13.18 (subset2powerset) =>
% 97.31/13.18 ((
% 97.31/13.18 (setextsub) =>
% 97.31/13.18 ((
% 97.31/13.18 (subsetemptysetimpeq) =>
% 97.31/13.18 ((
% 97.31/13.18 (powersetI1) =>
% 97.31/13.18 ((
% 97.31/13.18 (powersetE1) =>
% 97.31/13.18 ((
% 97.31/13.18 (inPowerset) =>
% 97.31/13.18 ((
% 97.31/13.18 (powersetsubset) =>
% 97.31/13.18 ((
% 97.31/13.18 (sepInPowerset) =>
% 97.31/13.18 ((
% 97.31/13.18 (sepSubset) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionIL) =>
% 97.31/13.18 ((
% 97.31/13.18 (upairset2IR) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionIR) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionEcases) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionE) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionLsub) =>
% 97.31/13.18 ((
% 97.31/13.18 (binunionRsub) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectI) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectSubset5) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectEL) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectLsub) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectSubset2) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectSubset3) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectER) =>
% 97.31/13.18 ((
% 97.31/13.18 (disjointsetsI1) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectRsub) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectSubset4) =>
% 97.31/13.18 ((
% 97.31/13.18 (binintersectSubset1) =>
% 97.31/13.18 ((
% 97.31/13.18 (bs114d) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusI) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusEL) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusER) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusSubset2) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusERneg) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusELneg) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusILneg) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusIRneg) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusLsub) =>
% 97.31/13.18 ((
% 97.31/13.18 (setminusSubset1) =>
% 97.31/13.18 ((
% 97.31/13.19 (symdiffE) =>
% 97.31/13.19 ((
% 97.31/13.19 (symdiffI1) =>
% 97.31/13.19 ((
% 97.31/13.19 (symdiffI2) =>
% 97.31/13.19 ((
% 97.31/13.19 (symdiffIneg1) =>
% 97.31/13.19 ((
% 97.31/13.19 (symdiffIneg2) =>
% 97.31/13.19 ((
% 97.31/13.19 (secondinupair) =>
% 97.31/13.19 ((
% 97.31/13.19 (setukpairIL) =>
% 97.31/13.19 ((
% 97.31/13.19 (setukpairIR) =>
% 97.31/13.19 ((
% 97.31/13.19 (kpairiskpair) =>
% 97.31/13.19 ((
% 97.31/13.19 (kpairp) =>
% 97.31/13.19 ((
% 97.31/13.19 (singletonsubset) =>
% 97.31/13.19 ((
% 97.31/13.19 (singletoninpowerset) =>
% 97.31/13.19 ((
% 97.31/13.19 (singletoninpowunion) =>
% 97.31/13.19 ((
% 97.31/13.19 (upairset2E) =>
% 97.31/13.19 ((
% 97.31/13.19 (upairsubunion) =>
% 97.31/13.19 ((
% 97.31/13.19 (upairinpowunion) =>
% 97.31/13.19 ((
% 97.31/13.19 (ubforcartprodlem1) =>
% 97.31/13.19 ((
% 97.31/13.19 (ubforcartprodlem2) =>
% 97.31/13.19 ((
% 97.31/13.19 (ubforcartprodlem3) =>
% 97.31/13.19 ((
% 97.31/13.19 (cartprodpairin) =>
% 97.31/13.19 ((
% 97.31/13.19 (cartprodmempair1) =>
% 97.31/13.19 ((
% 97.31/13.19 (cartprodmempair) =>
% 97.31/13.19 ((
% 97.31/13.19 (setunionE2) =>
% 97.31/13.19 ((
% 97.31/13.19 (setunionsingleton1) =>
% 97.31/13.19 ((
% 97.31/13.19 (setunionsingleton2) =>
% 97.31/13.19 ((
% 97.31/13.19 (setunionsingleton) =>
% 97.31/13.19 ((
% 97.31/13.19 (singletonprop) =>
% 97.31/13.19 ((
% 97.31/13.19 (ex1E1) =>
% 97.31/13.19 ((
% 97.31/13.19 (ex1I) =>
% 97.31/13.19 ((
% 97.31/13.19 (ex1I2) =>
% 97.31/13.19 ((
% 97.31/13.19 (singletonsuniq) =>
% 97.31/13.19 ((
% 97.31/13.19 (setukpairinjL1) =>
% 97.31/13.19 ((
% 97.31/13.19 (kfstsingleton) =>
% 97.31/13.19 ((
% 97.31/13.19 (theprop) =>
% 97.31/13.19 ((
% 97.31/13.19 (kfstpairEq) =>
% 97.31/13.19 ((
% 97.31/13.19 (cartprodfstin) =>
% 97.31/13.19 ((
% 97.31/13.19 (setukpairinjL2) =>
% 97.31/13.19 ((
% 97.31/13.19 (setukpairinjL) =>
% 97.31/13.19 ((
% 97.31/13.19 (setukpairinjR11) =>
% 97.31/13.19 ((
% 97.31/13.19 (setukpairinjR12) =>
% 97.31/13.19 ((
% 97.31/13.19 (setukpairinjR1) =>
% 97.31/13.19 ((
% 97.31/13.19 (upairequniteq) =>
% 97.31/13.19 ((
% 97.31/13.19 (setukpairinjR2) =>
% 97.31/13.19 ((
% 97.31/13.19 (setukpairinjR) =>
% 97.31/13.19 ((
% 97.31/13.19 (ksndsingleton) =>
% 97.31/13.19 ((
% 97.31/13.19 (ksndpairEq) =>
% 97.31/13.19 ((
% 97.31/13.19 (kpairsurjEq) =>
% 97.31/13.19 ((
% 97.31/13.19 (cartprodsndin) =>
% 97.31/13.19 ((
% 97.31/13.19 (cartprodpairmemEL) =>
% 97.31/13.19 ((
% 97.31/13.19 (cartprodpairmemER) =>
% 97.31/13.19 ((
% 97.31/13.19 (cartprodmempaircEq) =>
% 97.31/13.19 ((
% 97.31/13.19 (cartprodfstpairEq) =>
% 97.31/13.19 ((
% 97.31/13.19 (cartprodsndpairEq) =>
% 97.31/13.19 ((
% 97.31/13.19 (cartprodpairsurjEq) =>
% 97.31/13.19 ((
% 97.31/13.19 (dpsetconstrI) =>
% 97.31/13.19 ((
% 97.31/13.19 (dpsetconstrSub) =>
% 97.31/13.19 ((
% 97.31/13.19 (setOfPairsIsBReln) =>
% 97.31/13.19 ((
% 97.31/13.19 (dpsetconstrERa) =>
% 97.31/13.19 ((
% 97.31/13.19 (dpsetconstrEL1) =>
% 97.31/13.19 ((
% 97.31/13.19 (dpsetconstrEL2) =>
% 97.31/13.19 ((
% 97.31/13.19 (dpsetconstrER) =>
% 97.31/13.19 ((
% 97.31/13.19 (funcImageSingleton) =>
% 97.31/13.19 ((
% 97.31/13.19 (apProp) =>
% 97.31/13.19 ((
% 97.31/13.19 (app) =>
% 97.31/13.19 ((
% 97.31/13.19 (infuncsetfunc) =>
% 97.31/13.19 ((
% 97.31/13.19 (ap2p) =>
% 97.31/13.19 ((
% 97.31/13.19 (funcinfuncset) =>
% 97.31/13.19 ((
% 97.31/13.19 (lamProp) =>
% 97.31/13.19 ((
% 97.31/13.19 (lamp) =>
% 97.31/13.19 ((
% 97.31/13.19 (lam2p) =>
% 97.31/13.19 ((
% 97.31/13.19 (brelnall1) =>
% 97.31/13.19 ((
% 97.31/13.19 (brelnall2) =>
% 97.31/13.19 ((
% 97.31/13.19 (ex1E2) =>
% 97.31/13.19 ((
% 97.31/13.19 (funcGraphProp1) =>
% 97.31/13.19 ((
% 97.31/13.19 (funcGraphProp3) =>
% 97.31/13.19 ((
% 97.31/13.19 (funcGraphProp2) =>
% 97.31/13.19 ((
% 97.31/13.19 (funcextLem) =>
% 97.31/13.19 ((
% 97.31/13.19 (funcGraphProp4) =>
% 97.31/13.19 ((
% 97.31/13.19 (subbreln) =>
% 97.31/13.19 ((
% 97.31/13.19 (eqbreln) =>
% 97.31/13.19 ((
% 97.31/13.19 (funcext) =>
% 97.31/13.19 ((
% 97.31/13.19 (funcext2) =>
% 97.31/13.19 ((
% 97.31/13.19 (ap2apEq1) =>
% 97.31/13.19 ((
% 97.31/13.19 (ap2apEq2) =>
% 97.31/13.19 ((
% 97.31/13.19 (beta1) =>
% 97.31/13.19 ((
% 97.31/13.19 (eta1) =>
% 97.31/13.19 ((
% 97.31/13.19 (lam2lamEq) =>
% 97.31/13.19 ((
% 97.31/13.19 (beta2) =>
% 97.31/13.19 ((
% 97.31/13.19 (eta2) =>
% 97.31/13.19 ((
% 97.31/13.19 (iffalseProp1) =>
% 97.31/13.19 ((
% 97.31/13.19 (iffalseProp2) =>
% 97.31/13.19 ((
% 97.31/13.19 (iftrueProp1) =>
% 97.31/13.19 ((
% 97.31/13.19 (iftrueProp2) =>
% 97.31/13.19 ((
% 97.31/13.19 (ifSingleton) =>
% 97.31/13.19 ((
% 97.31/13.19 (ifp) =>
% 97.31/13.19 ((
% 97.31/13.19 (theeq) =>
% 97.31/13.19 ((
% 97.31/13.19 (iftrue) =>
% 97.31/13.19 ((
% 97.31/13.19 (iffalse) =>
% 97.31/13.19 ((
% 97.31/13.19 (iftrueorfalse) =>
% 97.31/13.19 ((
% 97.31/13.19 (binintersectT_lem) =>
% 97.31/13.19 ((
% 97.31/13.19 (binunionT_lem) =>
% 97.31/13.19 ((
% 97.31/13.19 (powersetT_lem) =>
% 97.31/13.19 ((
% 97.31/13.19 (setminusT_lem) =>
% 97.31/13.19 ((
% 97.31/13.19 (complementT_lem) =>
% 97.31/13.19 ((
% 97.31/13.19 (setextT) =>
% 97.31/13.19 ((
% 97.31/13.19 (subsetTI) =>
% 97.31/13.19 ((
% 97.31/13.19 (powersetTI1) =>
% 97.31/13.19 ((
% 97.31/13.19 (powersetTE1) =>
% 97.31/13.19 ((
% 97.31/13.19 (complementTI1) =>
% 97.31/13.19 ((
% 97.31/13.19 (complementTE1) =>
% 97.31/13.19 ((
% 97.31/13.19 (binintersectTELcontra) =>
% 97.31/13.19 ((
% 97.31/13.19 (binintersectTERcontra) =>
% 97.31/13.19 ((
% 97.31/13.19 (contrasubsetT) =>
% 97.31/13.19 ((
% 97.31/13.19 (contrasubsetT1) =>
% 97.31/13.19 ((
% 97.31/13.19 (contrasubsetT2) =>
% 97.31/13.19 ((
% 97.31/13.19 (contrasubsetT3) =>
% 97.31/13.19 ((
% 97.31/13.19 (doubleComplementI1) =>
% 97.31/13.19 ((
% 97.31/13.19 (doubleComplementE1) =>
% 97.31/13.19 ((
% 97.31/13.19 (doubleComplementSub1) =>
% 97.31/13.19 ((
% 97.31/13.19 (doubleComplementSub2) =>
% 97.31/13.19 ((
% 97.31/13.19 (doubleComplementEq) =>
% 97.31/13.19 ((
% 97.31/13.19 (complementTnotintersectT) =>
% 97.31/13.19 ((
% 97.31/13.19 (complementImpComplementIntersect) =>
% 97.31/13.19 ((
% 97.31/13.19 (complementSubsetComplementIntersect) =>
% 97.31/13.19 ((
% 97.31/13.19 (complementInPowersetComplementIntersect) =>
% 97.31/13.19 ((
% 97.31/13.19 (contraSubsetComplement) =>
% 97.31/13.19 ((
% 97.31/13.19 (complementTcontraSubset) =>
% 97.31/13.19 ((
% 97.31/13.19 (binunionTILcontra) =>
% 97.31/13.19 ((
% 97.31/13.19 (binunionTIRcontra) =>
% 97.31/13.19 ((
% 97.31/13.19 (inIntersectImpInUnion) =>
% 97.31/13.19 ((
% 97.31/13.19 (inIntersectImpInUnion2) =>
% 97.31/13.19 ((
% 97.31/13.19 (inIntersectImpInIntersectUnions) =>
% 97.31/13.19 ((
% 97.31/13.19 (intersectInPowersetIntersectUnions) =>
% 97.31/13.19 ((
% 97.31/13.19 (inComplementUnionImpNotIn1) =>
% 97.31/13.19 ((
% 97.31/13.19 (inComplementUnionImpInComplement1) =>
% 97.31/13.19 ((
% 97.31/13.19 (binunionTE) =>
% 97.31/13.19 ((
% 97.31/13.19 (binunionTEcontra) =>
% 97.31/13.19 ((
% 97.31/13.19 (demorgan2a1) =>
% 97.31/13.19 ((
% 97.31/13.19 (complementUnionInPowersetComplement) =>
% 97.31/13.19 ((
% 97.31/13.19 (demorgan2a2) =>
% 97.31/13.19 ((
% 97.31/13.19 (demorgan1a) =>
% 97.31/13.19 ((
% 97.31/13.19 (demorgan1b) =>
% 97.31/13.19 ((
% 97.31/13.19 (demorgan1) =>
% 97.31/13.19 ((
% 97.31/13.19 (demorgan2a) =>
% 97.31/13.19 ((
% 97.31/13.19 (demorgan2b2) =>
% 97.31/13.19 ((
% 97.31/13.19 (demorgan2b) =>
% 97.31/13.19 ((
% 97.31/13.19 (demorgan2) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz13rule0) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz13rule1) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz13rule2) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz13rule3) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz13rule4) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz1_1) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz1_2) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz1_3) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz1_4) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz1_5) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1all2) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1SetBreln1) =>
% 97.31/13.19 ((
% 97.31/13.19 (choice2fnsingleton) =>
% 97.31/13.19 ((
% 97.31/13.19 (setOfPairsIsBReln1) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1all1) =>
% 97.31/13.19 ((
% 97.31/13.19 (subbreln1) =>
% 97.31/13.19 ((
% 97.31/13.19 (eqbreln1) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1invprop) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1invI) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1invE) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1compprop) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1compI) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1compE) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1compEex) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1unionprop) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1unionIL) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1unionIR) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1unionI) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1unionE) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1unionEcases) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1unionCommutes) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz2Ex) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz2W) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz2A) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz2B) =>
% 97.31/13.19 ((
% 97.31/13.19 (image1Ex) =>
% 97.31/13.19 ((
% 97.31/13.19 (image1Ex1) =>
% 97.31/13.19 ((
% 97.31/13.19 (image1Equiv) =>
% 97.31/13.19 ((
% 97.31/13.19 (image1E) =>
% 97.31/13.19 ((
% 97.31/13.19 (image1I) =>
% 97.31/13.19 ((
% 97.31/13.19 (injFuncInInjFuncSet) =>
% 97.31/13.19 ((
% 97.31/13.19 (injFuncSetFuncIn) =>
% 97.31/13.19 ((
% 97.31/13.19 (injFuncSetFuncInj) =>
% 97.31/13.19 ((
% 97.31/13.19 (surjFuncSetFuncIn) =>
% 97.31/13.19 ((
% 97.31/13.19 (surjFuncSetFuncSurj) =>
% 97.31/13.19 ((
% 97.31/13.19 (leftInvIsSurj) =>
% 97.31/13.19 ((
% 97.31/13.19 (surjCantorThm) =>
% 97.31/13.19 ((
% 97.31/13.19 (foundation2) =>
% 97.31/13.19 ((
% 97.31/13.19 (notinself) =>
% 97.31/13.19 ((
% 97.31/13.19 (notinself2) =>
% 97.31/13.19 ((
% 97.31/13.19 (omegaSp) =>
% 97.31/13.19 ((
% 97.31/13.19 (omegaSclos) =>
% 97.31/13.19 ((
% 97.31/13.19 (peano0notS) =>
% 97.31/13.19 ((
% 97.31/13.19 (!!) @ (
% 97.31/13.19 (('#S') @ (
% 97.31/13.19 (
% 97.31/13.19 ('#B') @ (
% 97.31/13.19 =>) @
% 97.31/13.19 (
% 97.31/13.19 (
% 97.31/13.19 ('#C') @ in @
% 97.31/13.19 omega)))) @
% 97.31/13.19 (
% 97.31/13.19 (
% 97.31/13.19 ('#B') @ (
% 97.31/13.19 !!) @
% 97.31/13.19 (
% 97.31/13.19 (
% 97.31/13.19 ('#B') @ (
% 97.31/13.19 (
% 97.31/13.19 ('#S') @ (
% 97.31/13.19 (
% 97.31/13.19 ('#B') @ (
% 97.31/13.19 =>) @
% 97.31/13.19 (
% 97.31/13.19 (
% 97.31/13.19 ('#C') @ in @
% 97.31/13.19 omega)))))) @
% 97.31/13.19 (
% 97.31/13.19 (
% 97.31/13.19 ('#S') @ (
% 97.31/13.19 (
% 97.31/13.19 ('#B') @ (
% 97.31/13.19 '#S') @
% 97.31/13.19 (
% 97.31/13.19 (
% 97.31/13.19 ('#B') @ (
% 97.31/13.19 (
% 97.31/13.19 ('#B') @ (
% 97.31/13.19 =>))) @
% 97.31/13.19 (
% 97.31/13.19 (
% 97.31/13.19 ('#C') @ (
% 97.31/13.19 (
% 97.31/13.19 ('#B') @ (
% 97.31/13.19 '#B') @
% 97.31/13.19 (
% 97.31/13.19 (
% 97.31/13.19 ('#B') @ (
% 97.31/13.19 =) @
% 97.31/13.19 omegaS)))) @
% 97.31/13.19 omegaS)))))) @
% 97.31/13.19 (
% 97.31/13.19 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.31/13.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl439])).
% 97.31/13.19 thf(zip_derived_cl458, plain,
% 97.31/13.19 (~ (((notinsingleton) =>
% 97.31/13.19 (((eqinunit) =>
% 97.31/13.19 (((singletonsswitch) =>
% 97.31/13.19 (((upairsetE) =>
% 97.31/13.19 (((upairsetIL) =>
% 97.31/13.19 (((upairsetIR) =>
% 97.31/13.19 (((emptyE1) =>
% 97.31/13.19 (((vacuousDall) =>
% 97.31/13.19 (((quantDeMorgan1) =>
% 97.31/13.19 (((quantDeMorgan2) =>
% 97.31/13.19 (((quantDeMorgan3) =>
% 97.31/13.19 (((quantDeMorgan4) =>
% 97.31/13.19 (((prop2setI) =>
% 97.31/13.19 (((prop2set2propI) =>
% 97.31/13.19 (((notdexE) =>
% 97.31/13.19 (((notdallE) =>
% 97.31/13.19 (((exuI1) =>
% 97.31/13.19 (((exuI3) =>
% 97.31/13.19 (((exuI2) =>
% 97.31/13.19 (((inCongP) =>
% 97.31/13.19 (((in__Cong) =>
% 97.31/13.19 (((exuE3u) =>
% 97.31/13.19 (((exu__Cong) =>
% 97.31/13.19 (((setadjoin__Cong) =>
% 97.31/13.19 (((powerset__Cong) =>
% 97.31/13.19 (((setunion__Cong) =>
% 97.31/13.19 (((exuEu) =>
% 97.31/13.19 (((descr__Cong) =>
% 97.31/13.19 (((dsetconstr__Cong) =>
% 97.31/13.19 (((subsetI1) =>
% 97.31/13.19 ((
% 97.31/13.19 (eqimpsubset2) =>
% 97.31/13.19 ((
% 97.31/13.19 (eqimpsubset1) =>
% 97.31/13.19 ((
% 97.31/13.19 (subsetI2) =>
% 97.31/13.19 ((
% 97.31/13.19 (emptysetsubset) =>
% 97.31/13.19 ((
% 97.31/13.19 (subsetE) =>
% 97.31/13.19 ((
% 97.31/13.19 (subsetE2) =>
% 97.31/13.19 ((
% 97.31/13.19 (notsubsetI) =>
% 97.31/13.19 ((
% 97.31/13.19 (notequalI1) =>
% 97.31/13.19 ((
% 97.31/13.19 (notequalI2) =>
% 97.31/13.19 ((
% 97.31/13.19 (subsetRefl) =>
% 97.31/13.19 ((
% 97.31/13.19 (subsetTrans) =>
% 97.31/13.19 ((
% 97.31/13.19 (setadjoinSub) =>
% 97.31/13.19 ((
% 97.31/13.19 (setadjoinSub2) =>
% 97.31/13.19 ((
% 97.31/13.19 (subset2powerset) =>
% 97.31/13.19 ((
% 97.31/13.19 (setextsub) =>
% 97.31/13.19 ((
% 97.31/13.19 (subsetemptysetimpeq) =>
% 97.31/13.19 ((
% 97.31/13.19 (powersetI1) =>
% 97.31/13.19 ((
% 97.31/13.19 (powersetE1) =>
% 97.31/13.19 ((
% 97.31/13.19 (inPowerset) =>
% 97.31/13.19 ((
% 97.31/13.19 (powersetsubset) =>
% 97.31/13.19 ((
% 97.31/13.19 (sepInPowerset) =>
% 97.31/13.19 ((
% 97.31/13.19 (sepSubset) =>
% 97.31/13.19 ((
% 97.31/13.19 (binunionIL) =>
% 97.31/13.19 ((
% 97.31/13.19 (upairset2IR) =>
% 97.31/13.19 ((
% 97.31/13.19 (binunionIR) =>
% 97.31/13.19 ((
% 97.31/13.19 (binunionEcases) =>
% 97.31/13.19 ((
% 97.31/13.19 (binunionE) =>
% 97.31/13.19 ((
% 97.31/13.19 (binunionLsub) =>
% 97.31/13.19 ((
% 97.31/13.19 (binunionRsub) =>
% 97.31/13.19 ((
% 97.31/13.19 (binintersectI) =>
% 97.31/13.19 ((
% 97.31/13.19 (binintersectSubset5) =>
% 97.31/13.19 ((
% 97.31/13.19 (binintersectEL) =>
% 97.31/13.19 ((
% 97.31/13.19 (binintersectLsub) =>
% 97.31/13.19 ((
% 97.31/13.19 (binintersectSubset2) =>
% 97.31/13.19 ((
% 97.31/13.19 (binintersectSubset3) =>
% 97.31/13.19 ((
% 97.31/13.19 (binintersectER) =>
% 97.31/13.19 ((
% 97.31/13.19 (disjointsetsI1) =>
% 97.31/13.19 ((
% 97.31/13.19 (binintersectRsub) =>
% 97.31/13.19 ((
% 97.31/13.19 (binintersectSubset4) =>
% 97.31/13.19 ((
% 97.31/13.19 (binintersectSubset1) =>
% 97.31/13.19 ((
% 97.31/13.19 (bs114d) =>
% 97.31/13.19 ((
% 97.31/13.19 (setminusI) =>
% 97.31/13.19 ((
% 97.31/13.19 (setminusEL) =>
% 97.31/13.19 ((
% 97.31/13.19 (setminusER) =>
% 97.31/13.19 ((
% 97.31/13.19 (setminusSubset2) =>
% 97.31/13.19 ((
% 97.31/13.19 (setminusERneg) =>
% 97.31/13.19 ((
% 97.31/13.19 (setminusELneg) =>
% 97.31/13.19 ((
% 97.31/13.19 (setminusILneg) =>
% 97.31/13.19 ((
% 97.31/13.19 (setminusIRneg) =>
% 97.31/13.19 ((
% 97.31/13.19 (setminusLsub) =>
% 97.31/13.19 ((
% 97.31/13.19 (setminusSubset1) =>
% 97.31/13.19 ((
% 97.31/13.19 (symdiffE) =>
% 97.31/13.19 ((
% 97.31/13.19 (symdiffI1) =>
% 97.31/13.19 ((
% 97.31/13.19 (symdiffI2) =>
% 97.31/13.19 ((
% 97.31/13.19 (symdiffIneg1) =>
% 97.31/13.19 ((
% 97.31/13.19 (symdiffIneg2) =>
% 97.31/13.19 ((
% 97.31/13.19 (secondinupair) =>
% 97.31/13.19 ((
% 97.31/13.19 (setukpairIL) =>
% 97.31/13.19 ((
% 97.31/13.19 (setukpairIR) =>
% 97.31/13.19 ((
% 97.31/13.19 (kpairiskpair) =>
% 97.31/13.19 ((
% 97.31/13.19 (kpairp) =>
% 97.31/13.19 ((
% 97.31/13.19 (singletonsubset) =>
% 97.31/13.19 ((
% 97.31/13.19 (singletoninpowerset) =>
% 97.31/13.19 ((
% 97.31/13.19 (singletoninpowunion) =>
% 97.31/13.19 ((
% 97.31/13.19 (upairset2E) =>
% 97.31/13.19 ((
% 97.31/13.19 (upairsubunion) =>
% 97.31/13.19 ((
% 97.31/13.19 (upairinpowunion) =>
% 97.31/13.19 ((
% 97.31/13.19 (ubforcartprodlem1) =>
% 97.31/13.19 ((
% 97.31/13.19 (ubforcartprodlem2) =>
% 97.31/13.19 ((
% 97.31/13.19 (ubforcartprodlem3) =>
% 97.31/13.19 ((
% 97.31/13.19 (cartprodpairin) =>
% 97.31/13.19 ((
% 97.31/13.19 (cartprodmempair1) =>
% 97.31/13.19 ((
% 97.31/13.19 (cartprodmempair) =>
% 97.31/13.19 ((
% 97.31/13.19 (setunionE2) =>
% 97.31/13.19 ((
% 97.31/13.19 (setunionsingleton1) =>
% 97.31/13.19 ((
% 97.31/13.19 (setunionsingleton2) =>
% 97.31/13.19 ((
% 97.31/13.19 (setunionsingleton) =>
% 97.31/13.19 ((
% 97.31/13.19 (singletonprop) =>
% 97.31/13.19 ((
% 97.31/13.19 (ex1E1) =>
% 97.31/13.19 ((
% 97.31/13.19 (ex1I) =>
% 97.31/13.19 ((
% 97.31/13.19 (ex1I2) =>
% 97.31/13.19 ((
% 97.31/13.19 (singletonsuniq) =>
% 97.31/13.19 ((
% 97.31/13.19 (setukpairinjL1) =>
% 97.31/13.19 ((
% 97.31/13.19 (kfstsingleton) =>
% 97.31/13.19 ((
% 97.31/13.19 (theprop) =>
% 97.31/13.19 ((
% 97.31/13.19 (kfstpairEq) =>
% 97.31/13.19 ((
% 97.31/13.19 (cartprodfstin) =>
% 97.31/13.19 ((
% 97.31/13.19 (setukpairinjL2) =>
% 97.31/13.19 ((
% 97.31/13.19 (setukpairinjL) =>
% 97.31/13.19 ((
% 97.31/13.19 (setukpairinjR11) =>
% 97.31/13.19 ((
% 97.31/13.19 (setukpairinjR12) =>
% 97.31/13.19 ((
% 97.31/13.19 (setukpairinjR1) =>
% 97.31/13.19 ((
% 97.31/13.19 (upairequniteq) =>
% 97.31/13.19 ((
% 97.31/13.19 (setukpairinjR2) =>
% 97.31/13.19 ((
% 97.31/13.19 (setukpairinjR) =>
% 97.31/13.19 ((
% 97.31/13.19 (ksndsingleton) =>
% 97.31/13.19 ((
% 97.31/13.19 (ksndpairEq) =>
% 97.31/13.19 ((
% 97.31/13.19 (kpairsurjEq) =>
% 97.31/13.19 ((
% 97.31/13.19 (cartprodsndin) =>
% 97.31/13.19 ((
% 97.31/13.19 (cartprodpairmemEL) =>
% 97.31/13.19 ((
% 97.31/13.19 (cartprodpairmemER) =>
% 97.31/13.19 ((
% 97.31/13.19 (cartprodmempaircEq) =>
% 97.31/13.19 ((
% 97.31/13.19 (cartprodfstpairEq) =>
% 97.31/13.19 ((
% 97.31/13.19 (cartprodsndpairEq) =>
% 97.31/13.19 ((
% 97.31/13.19 (cartprodpairsurjEq) =>
% 97.31/13.19 ((
% 97.31/13.19 (dpsetconstrI) =>
% 97.31/13.19 ((
% 97.31/13.19 (dpsetconstrSub) =>
% 97.31/13.19 ((
% 97.31/13.19 (setOfPairsIsBReln) =>
% 97.31/13.19 ((
% 97.31/13.19 (dpsetconstrERa) =>
% 97.31/13.19 ((
% 97.31/13.19 (dpsetconstrEL1) =>
% 97.31/13.19 ((
% 97.31/13.19 (dpsetconstrEL2) =>
% 97.31/13.19 ((
% 97.31/13.19 (dpsetconstrER) =>
% 97.31/13.19 ((
% 97.31/13.19 (funcImageSingleton) =>
% 97.31/13.19 ((
% 97.31/13.19 (apProp) =>
% 97.31/13.19 ((
% 97.31/13.19 (app) =>
% 97.31/13.19 ((
% 97.31/13.19 (infuncsetfunc) =>
% 97.31/13.19 ((
% 97.31/13.19 (ap2p) =>
% 97.31/13.19 ((
% 97.31/13.19 (funcinfuncset) =>
% 97.31/13.19 ((
% 97.31/13.19 (lamProp) =>
% 97.31/13.19 ((
% 97.31/13.19 (lamp) =>
% 97.31/13.19 ((
% 97.31/13.19 (lam2p) =>
% 97.31/13.19 ((
% 97.31/13.19 (brelnall1) =>
% 97.31/13.19 ((
% 97.31/13.19 (brelnall2) =>
% 97.31/13.19 ((
% 97.31/13.19 (ex1E2) =>
% 97.31/13.19 ((
% 97.31/13.19 (funcGraphProp1) =>
% 97.31/13.19 ((
% 97.31/13.19 (funcGraphProp3) =>
% 97.31/13.19 ((
% 97.31/13.19 (funcGraphProp2) =>
% 97.31/13.19 ((
% 97.31/13.19 (funcextLem) =>
% 97.31/13.19 ((
% 97.31/13.19 (funcGraphProp4) =>
% 97.31/13.19 ((
% 97.31/13.19 (subbreln) =>
% 97.31/13.19 ((
% 97.31/13.19 (eqbreln) =>
% 97.31/13.19 ((
% 97.31/13.19 (funcext) =>
% 97.31/13.19 ((
% 97.31/13.19 (funcext2) =>
% 97.31/13.19 ((
% 97.31/13.19 (ap2apEq1) =>
% 97.31/13.19 ((
% 97.31/13.19 (ap2apEq2) =>
% 97.31/13.19 ((
% 97.31/13.19 (beta1) =>
% 97.31/13.19 ((
% 97.31/13.19 (eta1) =>
% 97.31/13.19 ((
% 97.31/13.19 (lam2lamEq) =>
% 97.31/13.19 ((
% 97.31/13.19 (beta2) =>
% 97.31/13.19 ((
% 97.31/13.19 (eta2) =>
% 97.31/13.19 ((
% 97.31/13.19 (iffalseProp1) =>
% 97.31/13.19 ((
% 97.31/13.19 (iffalseProp2) =>
% 97.31/13.19 ((
% 97.31/13.19 (iftrueProp1) =>
% 97.31/13.19 ((
% 97.31/13.19 (iftrueProp2) =>
% 97.31/13.19 ((
% 97.31/13.19 (ifSingleton) =>
% 97.31/13.19 ((
% 97.31/13.19 (ifp) =>
% 97.31/13.19 ((
% 97.31/13.19 (theeq) =>
% 97.31/13.19 ((
% 97.31/13.19 (iftrue) =>
% 97.31/13.19 ((
% 97.31/13.19 (iffalse) =>
% 97.31/13.19 ((
% 97.31/13.19 (iftrueorfalse) =>
% 97.31/13.19 ((
% 97.31/13.19 (binintersectT_lem) =>
% 97.31/13.19 ((
% 97.31/13.19 (binunionT_lem) =>
% 97.31/13.19 ((
% 97.31/13.19 (powersetT_lem) =>
% 97.31/13.19 ((
% 97.31/13.19 (setminusT_lem) =>
% 97.31/13.19 ((
% 97.31/13.19 (complementT_lem) =>
% 97.31/13.19 ((
% 97.31/13.19 (setextT) =>
% 97.31/13.19 ((
% 97.31/13.19 (subsetTI) =>
% 97.31/13.19 ((
% 97.31/13.19 (powersetTI1) =>
% 97.31/13.19 ((
% 97.31/13.19 (powersetTE1) =>
% 97.31/13.19 ((
% 97.31/13.19 (complementTI1) =>
% 97.31/13.19 ((
% 97.31/13.19 (complementTE1) =>
% 97.31/13.19 ((
% 97.31/13.19 (binintersectTELcontra) =>
% 97.31/13.19 ((
% 97.31/13.19 (binintersectTERcontra) =>
% 97.31/13.19 ((
% 97.31/13.19 (contrasubsetT) =>
% 97.31/13.19 ((
% 97.31/13.19 (contrasubsetT1) =>
% 97.31/13.19 ((
% 97.31/13.19 (contrasubsetT2) =>
% 97.31/13.19 ((
% 97.31/13.19 (contrasubsetT3) =>
% 97.31/13.19 ((
% 97.31/13.19 (doubleComplementI1) =>
% 97.31/13.19 ((
% 97.31/13.19 (doubleComplementE1) =>
% 97.31/13.19 ((
% 97.31/13.19 (doubleComplementSub1) =>
% 97.31/13.19 ((
% 97.31/13.19 (doubleComplementSub2) =>
% 97.31/13.19 ((
% 97.31/13.19 (doubleComplementEq) =>
% 97.31/13.19 ((
% 97.31/13.19 (complementTnotintersectT) =>
% 97.31/13.19 ((
% 97.31/13.19 (complementImpComplementIntersect) =>
% 97.31/13.19 ((
% 97.31/13.19 (complementSubsetComplementIntersect) =>
% 97.31/13.19 ((
% 97.31/13.19 (complementInPowersetComplementIntersect) =>
% 97.31/13.19 ((
% 97.31/13.19 (contraSubsetComplement) =>
% 97.31/13.19 ((
% 97.31/13.19 (complementTcontraSubset) =>
% 97.31/13.19 ((
% 97.31/13.19 (binunionTILcontra) =>
% 97.31/13.19 ((
% 97.31/13.19 (binunionTIRcontra) =>
% 97.31/13.19 ((
% 97.31/13.19 (inIntersectImpInUnion) =>
% 97.31/13.19 ((
% 97.31/13.19 (inIntersectImpInUnion2) =>
% 97.31/13.19 ((
% 97.31/13.19 (inIntersectImpInIntersectUnions) =>
% 97.31/13.19 ((
% 97.31/13.19 (intersectInPowersetIntersectUnions) =>
% 97.31/13.19 ((
% 97.31/13.19 (inComplementUnionImpNotIn1) =>
% 97.31/13.19 ((
% 97.31/13.19 (inComplementUnionImpInComplement1) =>
% 97.31/13.19 ((
% 97.31/13.19 (binunionTE) =>
% 97.31/13.19 ((
% 97.31/13.19 (binunionTEcontra) =>
% 97.31/13.19 ((
% 97.31/13.19 (demorgan2a1) =>
% 97.31/13.19 ((
% 97.31/13.19 (complementUnionInPowersetComplement) =>
% 97.31/13.19 ((
% 97.31/13.19 (demorgan2a2) =>
% 97.31/13.19 ((
% 97.31/13.19 (demorgan1a) =>
% 97.31/13.19 ((
% 97.31/13.19 (demorgan1b) =>
% 97.31/13.19 ((
% 97.31/13.19 (demorgan1) =>
% 97.31/13.19 ((
% 97.31/13.19 (demorgan2a) =>
% 97.31/13.19 ((
% 97.31/13.19 (demorgan2b2) =>
% 97.31/13.19 ((
% 97.31/13.19 (demorgan2b) =>
% 97.31/13.19 ((
% 97.31/13.19 (demorgan2) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz13rule0) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz13rule1) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz13rule2) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz13rule3) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz13rule4) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz1_1) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz1_2) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz1_3) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz1_4) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz1_5) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1all2) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1SetBreln1) =>
% 97.31/13.19 ((
% 97.31/13.19 (choice2fnsingleton) =>
% 97.31/13.19 ((
% 97.31/13.19 (setOfPairsIsBReln1) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1all1) =>
% 97.31/13.19 ((
% 97.31/13.19 (subbreln1) =>
% 97.31/13.19 ((
% 97.31/13.19 (eqbreln1) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1invprop) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1invI) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1invE) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1compprop) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1compI) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1compE) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1compEex) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1unionprop) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1unionIL) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1unionIR) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1unionI) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1unionE) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1unionEcases) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1unionCommutes) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz2Ex) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz2W) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz2A) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz2B) =>
% 97.31/13.19 ((
% 97.31/13.19 (image1Ex) =>
% 97.31/13.19 ((
% 97.31/13.19 (image1Ex1) =>
% 97.31/13.19 ((
% 97.31/13.19 (image1Equiv) =>
% 97.31/13.19 ((
% 97.31/13.19 (image1E) =>
% 97.31/13.19 ((
% 97.31/13.19 (image1I) =>
% 97.31/13.19 ((
% 97.31/13.19 (injFuncInInjFuncSet) =>
% 97.31/13.19 ((
% 97.31/13.19 (injFuncSetFuncIn) =>
% 97.31/13.19 ((
% 97.31/13.19 (injFuncSetFuncInj) =>
% 97.31/13.19 ((
% 97.31/13.19 (surjFuncSetFuncIn) =>
% 97.31/13.19 ((
% 97.31/13.19 (surjFuncSetFuncSurj) =>
% 97.31/13.19 ((
% 97.31/13.19 (leftInvIsSurj) =>
% 97.31/13.19 ((
% 97.31/13.19 (surjCantorThm) =>
% 97.31/13.19 ((
% 97.31/13.19 (foundation2) =>
% 97.31/13.19 ((
% 97.31/13.19 (notinself) =>
% 97.31/13.19 ((
% 97.31/13.19 (notinself2) =>
% 97.31/13.19 ((
% 97.31/13.19 (omegaSp) =>
% 97.31/13.19 ((
% 97.31/13.19 (omegaSclos) =>
% 97.31/13.19 ((
% 97.31/13.19 (peano0notS) =>
% 97.31/13.19 ((
% 97.31/13.19 (!!) @ (
% 97.31/13.19 (('#S') @ (
% 97.31/13.19 (
% 97.31/13.19 ('#B') @ (
% 97.31/13.19 =>) @
% 97.31/13.19 (
% 97.31/13.19 (
% 97.31/13.19 ('#C') @ in @
% 97.31/13.19 omega)))) @
% 97.31/13.19 (
% 97.31/13.19 (
% 97.31/13.19 ('#B') @ (
% 97.31/13.19 !!) @
% 97.31/13.19 (
% 97.31/13.19 (
% 97.31/13.19 ('#B') @ (
% 97.31/13.19 (
% 97.31/13.19 ('#S') @ (
% 97.31/13.19 (
% 97.31/13.19 ('#B') @ (
% 97.31/13.19 =>) @
% 97.31/13.19 (
% 97.31/13.19 (
% 97.31/13.19 ('#C') @ in @
% 97.31/13.19 omega)))))) @
% 97.31/13.19 (
% 97.31/13.19 (
% 97.31/13.19 ('#S') @ (
% 97.31/13.19 (
% 97.31/13.19 ('#B') @ (
% 97.31/13.19 '#S') @
% 97.31/13.19 (
% 97.31/13.19 (
% 97.31/13.19 ('#B') @ (
% 97.31/13.19 (
% 97.31/13.19 ('#B') @ (
% 97.31/13.19 =>))) @
% 97.31/13.19 (
% 97.31/13.19 (
% 97.31/13.19 ('#C') @ (
% 97.31/13.19 (
% 97.31/13.19 ('#B') @ (
% 97.31/13.19 '#B') @
% 97.31/13.19 (
% 97.31/13.19 (
% 97.31/13.19 ('#B') @ (
% 97.31/13.19 =) @
% 97.31/13.19 omegaS)))) @
% 97.31/13.19 omegaS)))))) @
% 97.31/13.19 (
% 97.31/13.19 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.31/13.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl449])).
% 97.31/13.19 thf(zip_derived_cl467, plain,
% 97.31/13.19 (~ (((eqinunit) =>
% 97.31/13.19 (((singletonsswitch) =>
% 97.31/13.19 (((upairsetE) =>
% 97.31/13.19 (((upairsetIL) =>
% 97.31/13.19 (((upairsetIR) =>
% 97.31/13.19 (((emptyE1) =>
% 97.31/13.19 (((vacuousDall) =>
% 97.31/13.19 (((quantDeMorgan1) =>
% 97.31/13.19 (((quantDeMorgan2) =>
% 97.31/13.19 (((quantDeMorgan3) =>
% 97.31/13.19 (((quantDeMorgan4) =>
% 97.31/13.19 (((prop2setI) =>
% 97.31/13.19 (((prop2set2propI) =>
% 97.31/13.19 (((notdexE) =>
% 97.31/13.19 (((notdallE) =>
% 97.31/13.19 (((exuI1) =>
% 97.31/13.19 (((exuI3) =>
% 97.31/13.19 (((exuI2) =>
% 97.31/13.19 (((inCongP) =>
% 97.31/13.19 (((in__Cong) =>
% 97.31/13.19 (((exuE3u) =>
% 97.31/13.19 (((exu__Cong) =>
% 97.31/13.19 (((setadjoin__Cong) =>
% 97.31/13.19 (((powerset__Cong) =>
% 97.31/13.19 (((setunion__Cong) =>
% 97.31/13.19 (((exuEu) =>
% 97.31/13.19 (((descr__Cong) =>
% 97.31/13.19 (((dsetconstr__Cong) =>
% 97.31/13.19 (((subsetI1) =>
% 97.31/13.19 (((eqimpsubset2) =>
% 97.31/13.19 ((
% 97.31/13.19 (eqimpsubset1) =>
% 97.31/13.19 ((
% 97.31/13.19 (subsetI2) =>
% 97.31/13.19 ((
% 97.31/13.19 (emptysetsubset) =>
% 97.31/13.19 ((
% 97.31/13.19 (subsetE) =>
% 97.31/13.19 ((
% 97.31/13.19 (subsetE2) =>
% 97.31/13.19 ((
% 97.31/13.19 (notsubsetI) =>
% 97.31/13.19 ((
% 97.31/13.19 (notequalI1) =>
% 97.31/13.19 ((
% 97.31/13.19 (notequalI2) =>
% 97.31/13.19 ((
% 97.31/13.19 (subsetRefl) =>
% 97.31/13.19 ((
% 97.31/13.19 (subsetTrans) =>
% 97.31/13.19 ((
% 97.31/13.19 (setadjoinSub) =>
% 97.31/13.19 ((
% 97.31/13.19 (setadjoinSub2) =>
% 97.31/13.19 ((
% 97.31/13.19 (subset2powerset) =>
% 97.31/13.19 ((
% 97.31/13.19 (setextsub) =>
% 97.31/13.19 ((
% 97.31/13.19 (subsetemptysetimpeq) =>
% 97.31/13.19 ((
% 97.31/13.19 (powersetI1) =>
% 97.31/13.19 ((
% 97.31/13.19 (powersetE1) =>
% 97.31/13.19 ((
% 97.31/13.19 (inPowerset) =>
% 97.31/13.19 ((
% 97.31/13.19 (powersetsubset) =>
% 97.31/13.19 ((
% 97.31/13.19 (sepInPowerset) =>
% 97.31/13.19 ((
% 97.31/13.19 (sepSubset) =>
% 97.31/13.19 ((
% 97.31/13.19 (binunionIL) =>
% 97.31/13.19 ((
% 97.31/13.19 (upairset2IR) =>
% 97.31/13.19 ((
% 97.31/13.19 (binunionIR) =>
% 97.31/13.19 ((
% 97.31/13.19 (binunionEcases) =>
% 97.31/13.19 ((
% 97.31/13.19 (binunionE) =>
% 97.31/13.19 ((
% 97.31/13.19 (binunionLsub) =>
% 97.31/13.19 ((
% 97.31/13.19 (binunionRsub) =>
% 97.31/13.19 ((
% 97.31/13.19 (binintersectI) =>
% 97.31/13.19 ((
% 97.31/13.19 (binintersectSubset5) =>
% 97.31/13.19 ((
% 97.31/13.19 (binintersectEL) =>
% 97.31/13.19 ((
% 97.31/13.19 (binintersectLsub) =>
% 97.31/13.19 ((
% 97.31/13.19 (binintersectSubset2) =>
% 97.31/13.19 ((
% 97.31/13.19 (binintersectSubset3) =>
% 97.31/13.19 ((
% 97.31/13.19 (binintersectER) =>
% 97.31/13.19 ((
% 97.31/13.19 (disjointsetsI1) =>
% 97.31/13.19 ((
% 97.31/13.19 (binintersectRsub) =>
% 97.31/13.19 ((
% 97.31/13.19 (binintersectSubset4) =>
% 97.31/13.19 ((
% 97.31/13.19 (binintersectSubset1) =>
% 97.31/13.19 ((
% 97.31/13.19 (bs114d) =>
% 97.31/13.19 ((
% 97.31/13.19 (setminusI) =>
% 97.31/13.19 ((
% 97.31/13.19 (setminusEL) =>
% 97.31/13.19 ((
% 97.31/13.19 (setminusER) =>
% 97.31/13.19 ((
% 97.31/13.19 (setminusSubset2) =>
% 97.31/13.19 ((
% 97.31/13.19 (setminusERneg) =>
% 97.31/13.19 ((
% 97.31/13.19 (setminusELneg) =>
% 97.31/13.19 ((
% 97.31/13.19 (setminusILneg) =>
% 97.31/13.19 ((
% 97.31/13.19 (setminusIRneg) =>
% 97.31/13.19 ((
% 97.31/13.19 (setminusLsub) =>
% 97.31/13.19 ((
% 97.31/13.19 (setminusSubset1) =>
% 97.31/13.19 ((
% 97.31/13.19 (symdiffE) =>
% 97.31/13.19 ((
% 97.31/13.19 (symdiffI1) =>
% 97.31/13.19 ((
% 97.31/13.19 (symdiffI2) =>
% 97.31/13.19 ((
% 97.31/13.19 (symdiffIneg1) =>
% 97.31/13.19 ((
% 97.31/13.19 (symdiffIneg2) =>
% 97.31/13.19 ((
% 97.31/13.19 (secondinupair) =>
% 97.31/13.19 ((
% 97.31/13.19 (setukpairIL) =>
% 97.31/13.19 ((
% 97.31/13.19 (setukpairIR) =>
% 97.31/13.19 ((
% 97.31/13.19 (kpairiskpair) =>
% 97.31/13.19 ((
% 97.31/13.19 (kpairp) =>
% 97.31/13.19 ((
% 97.31/13.19 (singletonsubset) =>
% 97.31/13.19 ((
% 97.31/13.19 (singletoninpowerset) =>
% 97.31/13.19 ((
% 97.31/13.19 (singletoninpowunion) =>
% 97.31/13.19 ((
% 97.31/13.19 (upairset2E) =>
% 97.31/13.19 ((
% 97.31/13.19 (upairsubunion) =>
% 97.31/13.19 ((
% 97.31/13.19 (upairinpowunion) =>
% 97.31/13.19 ((
% 97.31/13.19 (ubforcartprodlem1) =>
% 97.31/13.19 ((
% 97.31/13.19 (ubforcartprodlem2) =>
% 97.31/13.19 ((
% 97.31/13.19 (ubforcartprodlem3) =>
% 97.31/13.19 ((
% 97.31/13.19 (cartprodpairin) =>
% 97.31/13.19 ((
% 97.31/13.19 (cartprodmempair1) =>
% 97.31/13.19 ((
% 97.31/13.19 (cartprodmempair) =>
% 97.31/13.19 ((
% 97.31/13.19 (setunionE2) =>
% 97.31/13.19 ((
% 97.31/13.19 (setunionsingleton1) =>
% 97.31/13.19 ((
% 97.31/13.19 (setunionsingleton2) =>
% 97.31/13.19 ((
% 97.31/13.19 (setunionsingleton) =>
% 97.31/13.19 ((
% 97.31/13.19 (singletonprop) =>
% 97.31/13.19 ((
% 97.31/13.19 (ex1E1) =>
% 97.31/13.19 ((
% 97.31/13.19 (ex1I) =>
% 97.31/13.19 ((
% 97.31/13.19 (ex1I2) =>
% 97.31/13.19 ((
% 97.31/13.19 (singletonsuniq) =>
% 97.31/13.19 ((
% 97.31/13.19 (setukpairinjL1) =>
% 97.31/13.19 ((
% 97.31/13.19 (kfstsingleton) =>
% 97.31/13.19 ((
% 97.31/13.19 (theprop) =>
% 97.31/13.19 ((
% 97.31/13.19 (kfstpairEq) =>
% 97.31/13.19 ((
% 97.31/13.19 (cartprodfstin) =>
% 97.31/13.19 ((
% 97.31/13.19 (setukpairinjL2) =>
% 97.31/13.19 ((
% 97.31/13.19 (setukpairinjL) =>
% 97.31/13.19 ((
% 97.31/13.19 (setukpairinjR11) =>
% 97.31/13.19 ((
% 97.31/13.19 (setukpairinjR12) =>
% 97.31/13.19 ((
% 97.31/13.19 (setukpairinjR1) =>
% 97.31/13.19 ((
% 97.31/13.19 (upairequniteq) =>
% 97.31/13.19 ((
% 97.31/13.19 (setukpairinjR2) =>
% 97.31/13.19 ((
% 97.31/13.19 (setukpairinjR) =>
% 97.31/13.19 ((
% 97.31/13.19 (ksndsingleton) =>
% 97.31/13.19 ((
% 97.31/13.19 (ksndpairEq) =>
% 97.31/13.19 ((
% 97.31/13.19 (kpairsurjEq) =>
% 97.31/13.19 ((
% 97.31/13.19 (cartprodsndin) =>
% 97.31/13.19 ((
% 97.31/13.19 (cartprodpairmemEL) =>
% 97.31/13.19 ((
% 97.31/13.19 (cartprodpairmemER) =>
% 97.31/13.19 ((
% 97.31/13.19 (cartprodmempaircEq) =>
% 97.31/13.19 ((
% 97.31/13.19 (cartprodfstpairEq) =>
% 97.31/13.19 ((
% 97.31/13.19 (cartprodsndpairEq) =>
% 97.31/13.19 ((
% 97.31/13.19 (cartprodpairsurjEq) =>
% 97.31/13.19 ((
% 97.31/13.19 (dpsetconstrI) =>
% 97.31/13.19 ((
% 97.31/13.19 (dpsetconstrSub) =>
% 97.31/13.19 ((
% 97.31/13.19 (setOfPairsIsBReln) =>
% 97.31/13.19 ((
% 97.31/13.19 (dpsetconstrERa) =>
% 97.31/13.19 ((
% 97.31/13.19 (dpsetconstrEL1) =>
% 97.31/13.19 ((
% 97.31/13.19 (dpsetconstrEL2) =>
% 97.31/13.19 ((
% 97.31/13.19 (dpsetconstrER) =>
% 97.31/13.19 ((
% 97.31/13.19 (funcImageSingleton) =>
% 97.31/13.19 ((
% 97.31/13.19 (apProp) =>
% 97.31/13.19 ((
% 97.31/13.19 (app) =>
% 97.31/13.19 ((
% 97.31/13.19 (infuncsetfunc) =>
% 97.31/13.19 ((
% 97.31/13.19 (ap2p) =>
% 97.31/13.19 ((
% 97.31/13.19 (funcinfuncset) =>
% 97.31/13.19 ((
% 97.31/13.19 (lamProp) =>
% 97.31/13.19 ((
% 97.31/13.19 (lamp) =>
% 97.31/13.19 ((
% 97.31/13.19 (lam2p) =>
% 97.31/13.19 ((
% 97.31/13.19 (brelnall1) =>
% 97.31/13.19 ((
% 97.31/13.19 (brelnall2) =>
% 97.31/13.19 ((
% 97.31/13.19 (ex1E2) =>
% 97.31/13.19 ((
% 97.31/13.19 (funcGraphProp1) =>
% 97.31/13.19 ((
% 97.31/13.19 (funcGraphProp3) =>
% 97.31/13.19 ((
% 97.31/13.19 (funcGraphProp2) =>
% 97.31/13.19 ((
% 97.31/13.19 (funcextLem) =>
% 97.31/13.19 ((
% 97.31/13.19 (funcGraphProp4) =>
% 97.31/13.19 ((
% 97.31/13.19 (subbreln) =>
% 97.31/13.19 ((
% 97.31/13.19 (eqbreln) =>
% 97.31/13.19 ((
% 97.31/13.19 (funcext) =>
% 97.31/13.19 ((
% 97.31/13.19 (funcext2) =>
% 97.31/13.19 ((
% 97.31/13.19 (ap2apEq1) =>
% 97.31/13.19 ((
% 97.31/13.19 (ap2apEq2) =>
% 97.31/13.19 ((
% 97.31/13.19 (beta1) =>
% 97.31/13.19 ((
% 97.31/13.19 (eta1) =>
% 97.31/13.19 ((
% 97.31/13.19 (lam2lamEq) =>
% 97.31/13.19 ((
% 97.31/13.19 (beta2) =>
% 97.31/13.19 ((
% 97.31/13.19 (eta2) =>
% 97.31/13.19 ((
% 97.31/13.19 (iffalseProp1) =>
% 97.31/13.19 ((
% 97.31/13.19 (iffalseProp2) =>
% 97.31/13.19 ((
% 97.31/13.19 (iftrueProp1) =>
% 97.31/13.19 ((
% 97.31/13.19 (iftrueProp2) =>
% 97.31/13.19 ((
% 97.31/13.19 (ifSingleton) =>
% 97.31/13.19 ((
% 97.31/13.19 (ifp) =>
% 97.31/13.19 ((
% 97.31/13.19 (theeq) =>
% 97.31/13.19 ((
% 97.31/13.19 (iftrue) =>
% 97.31/13.19 ((
% 97.31/13.19 (iffalse) =>
% 97.31/13.19 ((
% 97.31/13.19 (iftrueorfalse) =>
% 97.31/13.19 ((
% 97.31/13.19 (binintersectT_lem) =>
% 97.31/13.19 ((
% 97.31/13.19 (binunionT_lem) =>
% 97.31/13.19 ((
% 97.31/13.19 (powersetT_lem) =>
% 97.31/13.19 ((
% 97.31/13.19 (setminusT_lem) =>
% 97.31/13.19 ((
% 97.31/13.19 (complementT_lem) =>
% 97.31/13.19 ((
% 97.31/13.19 (setextT) =>
% 97.31/13.19 ((
% 97.31/13.19 (subsetTI) =>
% 97.31/13.19 ((
% 97.31/13.19 (powersetTI1) =>
% 97.31/13.19 ((
% 97.31/13.19 (powersetTE1) =>
% 97.31/13.19 ((
% 97.31/13.19 (complementTI1) =>
% 97.31/13.19 ((
% 97.31/13.19 (complementTE1) =>
% 97.31/13.19 ((
% 97.31/13.19 (binintersectTELcontra) =>
% 97.31/13.19 ((
% 97.31/13.19 (binintersectTERcontra) =>
% 97.31/13.19 ((
% 97.31/13.19 (contrasubsetT) =>
% 97.31/13.19 ((
% 97.31/13.19 (contrasubsetT1) =>
% 97.31/13.19 ((
% 97.31/13.19 (contrasubsetT2) =>
% 97.31/13.19 ((
% 97.31/13.19 (contrasubsetT3) =>
% 97.31/13.19 ((
% 97.31/13.19 (doubleComplementI1) =>
% 97.31/13.19 ((
% 97.31/13.19 (doubleComplementE1) =>
% 97.31/13.19 ((
% 97.31/13.19 (doubleComplementSub1) =>
% 97.31/13.19 ((
% 97.31/13.19 (doubleComplementSub2) =>
% 97.31/13.19 ((
% 97.31/13.19 (doubleComplementEq) =>
% 97.31/13.19 ((
% 97.31/13.19 (complementTnotintersectT) =>
% 97.31/13.19 ((
% 97.31/13.19 (complementImpComplementIntersect) =>
% 97.31/13.19 ((
% 97.31/13.19 (complementSubsetComplementIntersect) =>
% 97.31/13.19 ((
% 97.31/13.19 (complementInPowersetComplementIntersect) =>
% 97.31/13.19 ((
% 97.31/13.19 (contraSubsetComplement) =>
% 97.31/13.19 ((
% 97.31/13.19 (complementTcontraSubset) =>
% 97.31/13.19 ((
% 97.31/13.19 (binunionTILcontra) =>
% 97.31/13.19 ((
% 97.31/13.19 (binunionTIRcontra) =>
% 97.31/13.19 ((
% 97.31/13.19 (inIntersectImpInUnion) =>
% 97.31/13.19 ((
% 97.31/13.19 (inIntersectImpInUnion2) =>
% 97.31/13.19 ((
% 97.31/13.19 (inIntersectImpInIntersectUnions) =>
% 97.31/13.19 ((
% 97.31/13.19 (intersectInPowersetIntersectUnions) =>
% 97.31/13.19 ((
% 97.31/13.19 (inComplementUnionImpNotIn1) =>
% 97.31/13.19 ((
% 97.31/13.19 (inComplementUnionImpInComplement1) =>
% 97.31/13.19 ((
% 97.31/13.19 (binunionTE) =>
% 97.31/13.19 ((
% 97.31/13.19 (binunionTEcontra) =>
% 97.31/13.19 ((
% 97.31/13.19 (demorgan2a1) =>
% 97.31/13.19 ((
% 97.31/13.19 (complementUnionInPowersetComplement) =>
% 97.31/13.19 ((
% 97.31/13.19 (demorgan2a2) =>
% 97.31/13.19 ((
% 97.31/13.19 (demorgan1a) =>
% 97.31/13.19 ((
% 97.31/13.19 (demorgan1b) =>
% 97.31/13.19 ((
% 97.31/13.19 (demorgan1) =>
% 97.31/13.19 ((
% 97.31/13.19 (demorgan2a) =>
% 97.31/13.19 ((
% 97.31/13.19 (demorgan2b2) =>
% 97.31/13.19 ((
% 97.31/13.19 (demorgan2b) =>
% 97.31/13.19 ((
% 97.31/13.19 (demorgan2) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz13rule0) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz13rule1) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz13rule2) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz13rule3) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz13rule4) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz1_1) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz1_2) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz1_3) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz1_4) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz1_5) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1all2) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1SetBreln1) =>
% 97.31/13.19 ((
% 97.31/13.19 (choice2fnsingleton) =>
% 97.31/13.19 ((
% 97.31/13.19 (setOfPairsIsBReln1) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1all1) =>
% 97.31/13.19 ((
% 97.31/13.19 (subbreln1) =>
% 97.31/13.19 ((
% 97.31/13.19 (eqbreln1) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1invprop) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1invI) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1invE) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1compprop) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1compI) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1compE) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1compEex) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1unionprop) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1unionIL) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1unionIR) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1unionI) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1unionE) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1unionEcases) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1unionCommutes) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz2Ex) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz2W) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz2A) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz2B) =>
% 97.31/13.19 ((
% 97.31/13.19 (image1Ex) =>
% 97.31/13.19 ((
% 97.31/13.19 (image1Ex1) =>
% 97.31/13.19 ((
% 97.31/13.19 (image1Equiv) =>
% 97.31/13.19 ((
% 97.31/13.19 (image1E) =>
% 97.31/13.19 ((
% 97.31/13.19 (image1I) =>
% 97.31/13.19 ((
% 97.31/13.19 (injFuncInInjFuncSet) =>
% 97.31/13.19 ((
% 97.31/13.19 (injFuncSetFuncIn) =>
% 97.31/13.19 ((
% 97.31/13.19 (injFuncSetFuncInj) =>
% 97.31/13.19 ((
% 97.31/13.19 (surjFuncSetFuncIn) =>
% 97.31/13.19 ((
% 97.31/13.19 (surjFuncSetFuncSurj) =>
% 97.31/13.19 ((
% 97.31/13.19 (leftInvIsSurj) =>
% 97.31/13.19 ((
% 97.31/13.19 (surjCantorThm) =>
% 97.31/13.19 ((
% 97.31/13.19 (foundation2) =>
% 97.31/13.19 ((
% 97.31/13.19 (notinself) =>
% 97.31/13.19 ((
% 97.31/13.19 (notinself2) =>
% 97.31/13.19 ((
% 97.31/13.19 (omegaSp) =>
% 97.31/13.19 ((
% 97.31/13.19 (omegaSclos) =>
% 97.31/13.19 ((
% 97.31/13.19 (peano0notS) =>
% 97.31/13.19 ((
% 97.31/13.19 (!!) @ (
% 97.31/13.19 (('#S') @ (
% 97.31/13.19 (
% 97.31/13.19 ('#B') @ (
% 97.31/13.19 =>) @
% 97.31/13.19 (
% 97.31/13.19 (
% 97.31/13.19 ('#C') @ in @
% 97.31/13.19 omega)))) @
% 97.31/13.19 (
% 97.31/13.19 (
% 97.31/13.19 ('#B') @ (
% 97.31/13.19 !!) @
% 97.31/13.19 (
% 97.31/13.19 (
% 97.31/13.19 ('#B') @ (
% 97.31/13.19 (
% 97.31/13.19 ('#S') @ (
% 97.31/13.19 (
% 97.31/13.19 ('#B') @ (
% 97.31/13.19 =>) @
% 97.31/13.19 (
% 97.31/13.19 (
% 97.31/13.19 ('#C') @ in @
% 97.31/13.19 omega)))))) @
% 97.31/13.19 (
% 97.31/13.19 (
% 97.31/13.19 ('#S') @ (
% 97.31/13.19 (
% 97.31/13.19 ('#B') @ (
% 97.31/13.19 '#S') @
% 97.31/13.19 (
% 97.31/13.19 (
% 97.31/13.19 ('#B') @ (
% 97.31/13.19 (
% 97.31/13.19 ('#B') @ (
% 97.31/13.19 =>))) @
% 97.31/13.19 (
% 97.31/13.19 (
% 97.31/13.19 ('#C') @ (
% 97.31/13.19 (
% 97.31/13.19 ('#B') @ (
% 97.31/13.19 '#B') @
% 97.31/13.19 (
% 97.31/13.19 (
% 97.31/13.19 ('#B') @ (
% 97.31/13.19 =) @
% 97.31/13.19 omegaS)))) @
% 97.31/13.19 omegaS)))))) @
% 97.31/13.19 (
% 97.31/13.19 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.31/13.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl458])).
% 97.31/13.19 thf(zip_derived_cl475, plain,
% 97.31/13.19 (~ (((singletonsswitch) =>
% 97.31/13.19 (((upairsetE) =>
% 97.31/13.19 (((upairsetIL) =>
% 97.31/13.19 (((upairsetIR) =>
% 97.31/13.19 (((emptyE1) =>
% 97.31/13.19 (((vacuousDall) =>
% 97.31/13.19 (((quantDeMorgan1) =>
% 97.31/13.19 (((quantDeMorgan2) =>
% 97.31/13.19 (((quantDeMorgan3) =>
% 97.31/13.19 (((quantDeMorgan4) =>
% 97.31/13.19 (((prop2setI) =>
% 97.31/13.19 (((prop2set2propI) =>
% 97.31/13.19 (((notdexE) =>
% 97.31/13.19 (((notdallE) =>
% 97.31/13.19 (((exuI1) =>
% 97.31/13.19 (((exuI3) =>
% 97.31/13.19 (((exuI2) =>
% 97.31/13.19 (((inCongP) =>
% 97.31/13.19 (((in__Cong) =>
% 97.31/13.19 (((exuE3u) =>
% 97.31/13.19 (((exu__Cong) =>
% 97.31/13.19 (((setadjoin__Cong) =>
% 97.31/13.19 (((powerset__Cong) =>
% 97.31/13.19 (((setunion__Cong) =>
% 97.31/13.19 (((exuEu) =>
% 97.31/13.19 (((descr__Cong) =>
% 97.31/13.19 (((dsetconstr__Cong) =>
% 97.31/13.19 (((subsetI1) =>
% 97.31/13.19 (((eqimpsubset2) =>
% 97.31/13.19 (((eqimpsubset1) =>
% 97.31/13.19 ((
% 97.31/13.19 (subsetI2) =>
% 97.31/13.19 ((
% 97.31/13.19 (emptysetsubset) =>
% 97.31/13.19 ((
% 97.31/13.19 (subsetE) =>
% 97.31/13.19 ((
% 97.31/13.19 (subsetE2) =>
% 97.31/13.19 ((
% 97.31/13.19 (notsubsetI) =>
% 97.31/13.19 ((
% 97.31/13.19 (notequalI1) =>
% 97.31/13.19 ((
% 97.31/13.19 (notequalI2) =>
% 97.31/13.19 ((
% 97.31/13.19 (subsetRefl) =>
% 97.31/13.19 ((
% 97.31/13.19 (subsetTrans) =>
% 97.31/13.19 ((
% 97.31/13.19 (setadjoinSub) =>
% 97.31/13.19 ((
% 97.31/13.19 (setadjoinSub2) =>
% 97.31/13.19 ((
% 97.31/13.19 (subset2powerset) =>
% 97.31/13.19 ((
% 97.31/13.19 (setextsub) =>
% 97.31/13.19 ((
% 97.31/13.19 (subsetemptysetimpeq) =>
% 97.31/13.19 ((
% 97.31/13.19 (powersetI1) =>
% 97.31/13.19 ((
% 97.31/13.19 (powersetE1) =>
% 97.31/13.19 ((
% 97.31/13.19 (inPowerset) =>
% 97.31/13.19 ((
% 97.31/13.19 (powersetsubset) =>
% 97.31/13.19 ((
% 97.31/13.19 (sepInPowerset) =>
% 97.31/13.19 ((
% 97.31/13.19 (sepSubset) =>
% 97.31/13.19 ((
% 97.31/13.19 (binunionIL) =>
% 97.31/13.19 ((
% 97.31/13.19 (upairset2IR) =>
% 97.31/13.19 ((
% 97.31/13.19 (binunionIR) =>
% 97.31/13.19 ((
% 97.31/13.19 (binunionEcases) =>
% 97.31/13.19 ((
% 97.31/13.19 (binunionE) =>
% 97.31/13.19 ((
% 97.31/13.19 (binunionLsub) =>
% 97.31/13.19 ((
% 97.31/13.19 (binunionRsub) =>
% 97.31/13.19 ((
% 97.31/13.19 (binintersectI) =>
% 97.31/13.19 ((
% 97.31/13.19 (binintersectSubset5) =>
% 97.31/13.19 ((
% 97.31/13.19 (binintersectEL) =>
% 97.31/13.19 ((
% 97.31/13.19 (binintersectLsub) =>
% 97.31/13.19 ((
% 97.31/13.19 (binintersectSubset2) =>
% 97.31/13.19 ((
% 97.31/13.19 (binintersectSubset3) =>
% 97.31/13.19 ((
% 97.31/13.19 (binintersectER) =>
% 97.31/13.19 ((
% 97.31/13.19 (disjointsetsI1) =>
% 97.31/13.19 ((
% 97.31/13.19 (binintersectRsub) =>
% 97.31/13.19 ((
% 97.31/13.19 (binintersectSubset4) =>
% 97.31/13.19 ((
% 97.31/13.19 (binintersectSubset1) =>
% 97.31/13.19 ((
% 97.31/13.19 (bs114d) =>
% 97.31/13.19 ((
% 97.31/13.19 (setminusI) =>
% 97.31/13.19 ((
% 97.31/13.19 (setminusEL) =>
% 97.31/13.19 ((
% 97.31/13.19 (setminusER) =>
% 97.31/13.19 ((
% 97.31/13.19 (setminusSubset2) =>
% 97.31/13.19 ((
% 97.31/13.19 (setminusERneg) =>
% 97.31/13.19 ((
% 97.31/13.19 (setminusELneg) =>
% 97.31/13.19 ((
% 97.31/13.19 (setminusILneg) =>
% 97.31/13.19 ((
% 97.31/13.19 (setminusIRneg) =>
% 97.31/13.19 ((
% 97.31/13.19 (setminusLsub) =>
% 97.31/13.19 ((
% 97.31/13.19 (setminusSubset1) =>
% 97.31/13.19 ((
% 97.31/13.19 (symdiffE) =>
% 97.31/13.19 ((
% 97.31/13.19 (symdiffI1) =>
% 97.31/13.19 ((
% 97.31/13.19 (symdiffI2) =>
% 97.31/13.19 ((
% 97.31/13.19 (symdiffIneg1) =>
% 97.31/13.19 ((
% 97.31/13.19 (symdiffIneg2) =>
% 97.31/13.19 ((
% 97.31/13.19 (secondinupair) =>
% 97.31/13.19 ((
% 97.31/13.19 (setukpairIL) =>
% 97.31/13.19 ((
% 97.31/13.19 (setukpairIR) =>
% 97.31/13.19 ((
% 97.31/13.19 (kpairiskpair) =>
% 97.31/13.19 ((
% 97.31/13.19 (kpairp) =>
% 97.31/13.19 ((
% 97.31/13.19 (singletonsubset) =>
% 97.31/13.19 ((
% 97.31/13.19 (singletoninpowerset) =>
% 97.31/13.19 ((
% 97.31/13.19 (singletoninpowunion) =>
% 97.31/13.19 ((
% 97.31/13.19 (upairset2E) =>
% 97.31/13.19 ((
% 97.31/13.19 (upairsubunion) =>
% 97.31/13.19 ((
% 97.31/13.19 (upairinpowunion) =>
% 97.31/13.19 ((
% 97.31/13.19 (ubforcartprodlem1) =>
% 97.31/13.19 ((
% 97.31/13.19 (ubforcartprodlem2) =>
% 97.31/13.19 ((
% 97.31/13.19 (ubforcartprodlem3) =>
% 97.31/13.19 ((
% 97.31/13.19 (cartprodpairin) =>
% 97.31/13.19 ((
% 97.31/13.19 (cartprodmempair1) =>
% 97.31/13.19 ((
% 97.31/13.19 (cartprodmempair) =>
% 97.31/13.19 ((
% 97.31/13.19 (setunionE2) =>
% 97.31/13.19 ((
% 97.31/13.19 (setunionsingleton1) =>
% 97.31/13.19 ((
% 97.31/13.19 (setunionsingleton2) =>
% 97.31/13.19 ((
% 97.31/13.19 (setunionsingleton) =>
% 97.31/13.19 ((
% 97.31/13.19 (singletonprop) =>
% 97.31/13.19 ((
% 97.31/13.19 (ex1E1) =>
% 97.31/13.19 ((
% 97.31/13.19 (ex1I) =>
% 97.31/13.19 ((
% 97.31/13.19 (ex1I2) =>
% 97.31/13.19 ((
% 97.31/13.19 (singletonsuniq) =>
% 97.31/13.19 ((
% 97.31/13.19 (setukpairinjL1) =>
% 97.31/13.19 ((
% 97.31/13.19 (kfstsingleton) =>
% 97.31/13.19 ((
% 97.31/13.19 (theprop) =>
% 97.31/13.19 ((
% 97.31/13.19 (kfstpairEq) =>
% 97.31/13.19 ((
% 97.31/13.19 (cartprodfstin) =>
% 97.31/13.19 ((
% 97.31/13.19 (setukpairinjL2) =>
% 97.31/13.19 ((
% 97.31/13.19 (setukpairinjL) =>
% 97.31/13.19 ((
% 97.31/13.19 (setukpairinjR11) =>
% 97.31/13.19 ((
% 97.31/13.19 (setukpairinjR12) =>
% 97.31/13.19 ((
% 97.31/13.19 (setukpairinjR1) =>
% 97.31/13.19 ((
% 97.31/13.19 (upairequniteq) =>
% 97.31/13.19 ((
% 97.31/13.19 (setukpairinjR2) =>
% 97.31/13.19 ((
% 97.31/13.19 (setukpairinjR) =>
% 97.31/13.19 ((
% 97.31/13.19 (ksndsingleton) =>
% 97.31/13.19 ((
% 97.31/13.19 (ksndpairEq) =>
% 97.31/13.19 ((
% 97.31/13.19 (kpairsurjEq) =>
% 97.31/13.19 ((
% 97.31/13.19 (cartprodsndin) =>
% 97.31/13.19 ((
% 97.31/13.19 (cartprodpairmemEL) =>
% 97.31/13.19 ((
% 97.31/13.19 (cartprodpairmemER) =>
% 97.31/13.19 ((
% 97.31/13.19 (cartprodmempaircEq) =>
% 97.31/13.19 ((
% 97.31/13.19 (cartprodfstpairEq) =>
% 97.31/13.19 ((
% 97.31/13.19 (cartprodsndpairEq) =>
% 97.31/13.19 ((
% 97.31/13.19 (cartprodpairsurjEq) =>
% 97.31/13.19 ((
% 97.31/13.19 (dpsetconstrI) =>
% 97.31/13.19 ((
% 97.31/13.19 (dpsetconstrSub) =>
% 97.31/13.19 ((
% 97.31/13.19 (setOfPairsIsBReln) =>
% 97.31/13.19 ((
% 97.31/13.19 (dpsetconstrERa) =>
% 97.31/13.19 ((
% 97.31/13.19 (dpsetconstrEL1) =>
% 97.31/13.19 ((
% 97.31/13.19 (dpsetconstrEL2) =>
% 97.31/13.19 ((
% 97.31/13.19 (dpsetconstrER) =>
% 97.31/13.19 ((
% 97.31/13.19 (funcImageSingleton) =>
% 97.31/13.19 ((
% 97.31/13.19 (apProp) =>
% 97.31/13.19 ((
% 97.31/13.19 (app) =>
% 97.31/13.19 ((
% 97.31/13.19 (infuncsetfunc) =>
% 97.31/13.19 ((
% 97.31/13.19 (ap2p) =>
% 97.31/13.19 ((
% 97.31/13.19 (funcinfuncset) =>
% 97.31/13.19 ((
% 97.31/13.19 (lamProp) =>
% 97.31/13.19 ((
% 97.31/13.19 (lamp) =>
% 97.31/13.19 ((
% 97.31/13.19 (lam2p) =>
% 97.31/13.19 ((
% 97.31/13.19 (brelnall1) =>
% 97.31/13.19 ((
% 97.31/13.19 (brelnall2) =>
% 97.31/13.19 ((
% 97.31/13.19 (ex1E2) =>
% 97.31/13.19 ((
% 97.31/13.19 (funcGraphProp1) =>
% 97.31/13.19 ((
% 97.31/13.19 (funcGraphProp3) =>
% 97.31/13.19 ((
% 97.31/13.19 (funcGraphProp2) =>
% 97.31/13.19 ((
% 97.31/13.19 (funcextLem) =>
% 97.31/13.19 ((
% 97.31/13.19 (funcGraphProp4) =>
% 97.31/13.19 ((
% 97.31/13.19 (subbreln) =>
% 97.31/13.19 ((
% 97.31/13.19 (eqbreln) =>
% 97.31/13.19 ((
% 97.31/13.19 (funcext) =>
% 97.31/13.19 ((
% 97.31/13.19 (funcext2) =>
% 97.31/13.19 ((
% 97.31/13.19 (ap2apEq1) =>
% 97.31/13.19 ((
% 97.31/13.19 (ap2apEq2) =>
% 97.31/13.19 ((
% 97.31/13.19 (beta1) =>
% 97.31/13.19 ((
% 97.31/13.19 (eta1) =>
% 97.31/13.19 ((
% 97.31/13.19 (lam2lamEq) =>
% 97.31/13.19 ((
% 97.31/13.19 (beta2) =>
% 97.31/13.19 ((
% 97.31/13.19 (eta2) =>
% 97.31/13.19 ((
% 97.31/13.19 (iffalseProp1) =>
% 97.31/13.19 ((
% 97.31/13.19 (iffalseProp2) =>
% 97.31/13.19 ((
% 97.31/13.19 (iftrueProp1) =>
% 97.31/13.19 ((
% 97.31/13.19 (iftrueProp2) =>
% 97.31/13.19 ((
% 97.31/13.19 (ifSingleton) =>
% 97.31/13.19 ((
% 97.31/13.19 (ifp) =>
% 97.31/13.19 ((
% 97.31/13.19 (theeq) =>
% 97.31/13.19 ((
% 97.31/13.19 (iftrue) =>
% 97.31/13.19 ((
% 97.31/13.19 (iffalse) =>
% 97.31/13.19 ((
% 97.31/13.19 (iftrueorfalse) =>
% 97.31/13.19 ((
% 97.31/13.19 (binintersectT_lem) =>
% 97.31/13.19 ((
% 97.31/13.19 (binunionT_lem) =>
% 97.31/13.19 ((
% 97.31/13.19 (powersetT_lem) =>
% 97.31/13.19 ((
% 97.31/13.19 (setminusT_lem) =>
% 97.31/13.19 ((
% 97.31/13.19 (complementT_lem) =>
% 97.31/13.19 ((
% 97.31/13.19 (setextT) =>
% 97.31/13.19 ((
% 97.31/13.19 (subsetTI) =>
% 97.31/13.19 ((
% 97.31/13.19 (powersetTI1) =>
% 97.31/13.19 ((
% 97.31/13.19 (powersetTE1) =>
% 97.31/13.19 ((
% 97.31/13.19 (complementTI1) =>
% 97.31/13.19 ((
% 97.31/13.19 (complementTE1) =>
% 97.31/13.19 ((
% 97.31/13.19 (binintersectTELcontra) =>
% 97.31/13.19 ((
% 97.31/13.19 (binintersectTERcontra) =>
% 97.31/13.19 ((
% 97.31/13.19 (contrasubsetT) =>
% 97.31/13.19 ((
% 97.31/13.19 (contrasubsetT1) =>
% 97.31/13.19 ((
% 97.31/13.19 (contrasubsetT2) =>
% 97.31/13.19 ((
% 97.31/13.19 (contrasubsetT3) =>
% 97.31/13.19 ((
% 97.31/13.19 (doubleComplementI1) =>
% 97.31/13.19 ((
% 97.31/13.19 (doubleComplementE1) =>
% 97.31/13.19 ((
% 97.31/13.19 (doubleComplementSub1) =>
% 97.31/13.19 ((
% 97.31/13.19 (doubleComplementSub2) =>
% 97.31/13.19 ((
% 97.31/13.19 (doubleComplementEq) =>
% 97.31/13.19 ((
% 97.31/13.19 (complementTnotintersectT) =>
% 97.31/13.19 ((
% 97.31/13.19 (complementImpComplementIntersect) =>
% 97.31/13.19 ((
% 97.31/13.19 (complementSubsetComplementIntersect) =>
% 97.31/13.19 ((
% 97.31/13.19 (complementInPowersetComplementIntersect) =>
% 97.31/13.19 ((
% 97.31/13.19 (contraSubsetComplement) =>
% 97.31/13.19 ((
% 97.31/13.19 (complementTcontraSubset) =>
% 97.31/13.19 ((
% 97.31/13.19 (binunionTILcontra) =>
% 97.31/13.19 ((
% 97.31/13.19 (binunionTIRcontra) =>
% 97.31/13.19 ((
% 97.31/13.19 (inIntersectImpInUnion) =>
% 97.31/13.19 ((
% 97.31/13.19 (inIntersectImpInUnion2) =>
% 97.31/13.19 ((
% 97.31/13.19 (inIntersectImpInIntersectUnions) =>
% 97.31/13.19 ((
% 97.31/13.19 (intersectInPowersetIntersectUnions) =>
% 97.31/13.19 ((
% 97.31/13.19 (inComplementUnionImpNotIn1) =>
% 97.31/13.19 ((
% 97.31/13.19 (inComplementUnionImpInComplement1) =>
% 97.31/13.19 ((
% 97.31/13.19 (binunionTE) =>
% 97.31/13.19 ((
% 97.31/13.19 (binunionTEcontra) =>
% 97.31/13.19 ((
% 97.31/13.19 (demorgan2a1) =>
% 97.31/13.19 ((
% 97.31/13.19 (complementUnionInPowersetComplement) =>
% 97.31/13.19 ((
% 97.31/13.19 (demorgan2a2) =>
% 97.31/13.19 ((
% 97.31/13.19 (demorgan1a) =>
% 97.31/13.19 ((
% 97.31/13.19 (demorgan1b) =>
% 97.31/13.19 ((
% 97.31/13.19 (demorgan1) =>
% 97.31/13.19 ((
% 97.31/13.19 (demorgan2a) =>
% 97.31/13.19 ((
% 97.31/13.19 (demorgan2b2) =>
% 97.31/13.19 ((
% 97.31/13.19 (demorgan2b) =>
% 97.31/13.19 ((
% 97.31/13.19 (demorgan2) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz13rule0) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz13rule1) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz13rule2) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz13rule3) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz13rule4) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz1_1) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz1_2) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz1_3) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz1_4) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz1_5) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1all2) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1SetBreln1) =>
% 97.31/13.19 ((
% 97.31/13.19 (choice2fnsingleton) =>
% 97.31/13.19 ((
% 97.31/13.19 (setOfPairsIsBReln1) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1all1) =>
% 97.31/13.19 ((
% 97.31/13.19 (subbreln1) =>
% 97.31/13.19 ((
% 97.31/13.19 (eqbreln1) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1invprop) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1invI) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1invE) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1compprop) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1compI) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1compE) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1compEex) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1unionprop) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1unionIL) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1unionIR) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1unionI) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1unionE) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1unionEcases) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1unionCommutes) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz2Ex) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz2W) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz2A) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz2B) =>
% 97.31/13.19 ((
% 97.31/13.19 (image1Ex) =>
% 97.31/13.19 ((
% 97.31/13.19 (image1Ex1) =>
% 97.31/13.19 ((
% 97.31/13.19 (image1Equiv) =>
% 97.31/13.19 ((
% 97.31/13.19 (image1E) =>
% 97.31/13.19 ((
% 97.31/13.19 (image1I) =>
% 97.31/13.19 ((
% 97.31/13.19 (injFuncInInjFuncSet) =>
% 97.31/13.19 ((
% 97.31/13.19 (injFuncSetFuncIn) =>
% 97.31/13.19 ((
% 97.31/13.19 (injFuncSetFuncInj) =>
% 97.31/13.19 ((
% 97.31/13.19 (surjFuncSetFuncIn) =>
% 97.31/13.19 ((
% 97.31/13.19 (surjFuncSetFuncSurj) =>
% 97.31/13.19 ((
% 97.31/13.19 (leftInvIsSurj) =>
% 97.31/13.19 ((
% 97.31/13.19 (surjCantorThm) =>
% 97.31/13.19 ((
% 97.31/13.19 (foundation2) =>
% 97.31/13.19 ((
% 97.31/13.19 (notinself) =>
% 97.31/13.19 ((
% 97.31/13.19 (notinself2) =>
% 97.31/13.19 ((
% 97.31/13.19 (omegaSp) =>
% 97.31/13.19 ((
% 97.31/13.19 (omegaSclos) =>
% 97.31/13.19 ((
% 97.31/13.19 (peano0notS) =>
% 97.31/13.19 ((
% 97.31/13.19 (!!) @ (
% 97.31/13.19 (('#S') @ (
% 97.31/13.19 (
% 97.31/13.19 ('#B') @ (
% 97.31/13.19 =>) @
% 97.31/13.19 (
% 97.31/13.19 (
% 97.31/13.19 ('#C') @ in @
% 97.31/13.19 omega)))) @
% 97.31/13.19 (
% 97.31/13.19 (
% 97.31/13.19 ('#B') @ (
% 97.31/13.19 !!) @
% 97.31/13.19 (
% 97.31/13.19 (
% 97.31/13.19 ('#B') @ (
% 97.31/13.19 (
% 97.31/13.19 ('#S') @ (
% 97.31/13.19 (
% 97.31/13.19 ('#B') @ (
% 97.31/13.19 =>) @
% 97.31/13.19 (
% 97.31/13.19 (
% 97.31/13.19 ('#C') @ in @
% 97.31/13.19 omega)))))) @
% 97.31/13.19 (
% 97.31/13.19 (
% 97.31/13.19 ('#S') @ (
% 97.31/13.19 (
% 97.31/13.19 ('#B') @ (
% 97.31/13.19 '#S') @
% 97.31/13.19 (
% 97.31/13.19 (
% 97.31/13.19 ('#B') @ (
% 97.31/13.19 (
% 97.31/13.19 ('#B') @ (
% 97.31/13.19 =>))) @
% 97.31/13.19 (
% 97.31/13.19 (
% 97.31/13.19 ('#C') @ (
% 97.31/13.19 (
% 97.31/13.19 ('#B') @ (
% 97.31/13.19 '#B') @
% 97.31/13.19 (
% 97.31/13.19 (
% 97.31/13.19 ('#B') @ (
% 97.31/13.19 =) @
% 97.31/13.19 omegaS)))) @
% 97.31/13.19 omegaS)))))) @
% 97.31/13.19 (
% 97.31/13.19 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.31/13.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl467])).
% 97.31/13.19 thf(zip_derived_cl485, plain,
% 97.31/13.19 (~ (((upairsetE) =>
% 97.31/13.19 (((upairsetIL) =>
% 97.31/13.19 (((upairsetIR) =>
% 97.31/13.19 (((emptyE1) =>
% 97.31/13.19 (((vacuousDall) =>
% 97.31/13.19 (((quantDeMorgan1) =>
% 97.31/13.19 (((quantDeMorgan2) =>
% 97.31/13.19 (((quantDeMorgan3) =>
% 97.31/13.19 (((quantDeMorgan4) =>
% 97.31/13.19 (((prop2setI) =>
% 97.31/13.19 (((prop2set2propI) =>
% 97.31/13.19 (((notdexE) =>
% 97.31/13.19 (((notdallE) =>
% 97.31/13.19 (((exuI1) =>
% 97.31/13.19 (((exuI3) =>
% 97.31/13.19 (((exuI2) =>
% 97.31/13.19 (((inCongP) =>
% 97.31/13.19 (((in__Cong) =>
% 97.31/13.19 (((exuE3u) =>
% 97.31/13.19 (((exu__Cong) =>
% 97.31/13.19 (((setadjoin__Cong) =>
% 97.31/13.19 (((powerset__Cong) =>
% 97.31/13.19 (((setunion__Cong) =>
% 97.31/13.19 (((exuEu) =>
% 97.31/13.19 (((descr__Cong) =>
% 97.31/13.19 (((dsetconstr__Cong) =>
% 97.31/13.19 (((subsetI1) =>
% 97.31/13.19 (((eqimpsubset2) =>
% 97.31/13.19 (((eqimpsubset1) =>
% 97.31/13.19 (((subsetI2) =>
% 97.31/13.19 ((
% 97.31/13.19 (emptysetsubset) =>
% 97.31/13.19 ((
% 97.31/13.19 (subsetE) =>
% 97.31/13.19 ((
% 97.31/13.19 (subsetE2) =>
% 97.31/13.19 ((
% 97.31/13.19 (notsubsetI) =>
% 97.31/13.19 ((
% 97.31/13.19 (notequalI1) =>
% 97.31/13.19 ((
% 97.31/13.19 (notequalI2) =>
% 97.31/13.19 ((
% 97.31/13.19 (subsetRefl) =>
% 97.31/13.19 ((
% 97.31/13.19 (subsetTrans) =>
% 97.31/13.19 ((
% 97.31/13.19 (setadjoinSub) =>
% 97.31/13.19 ((
% 97.31/13.19 (setadjoinSub2) =>
% 97.31/13.19 ((
% 97.31/13.19 (subset2powerset) =>
% 97.31/13.19 ((
% 97.31/13.19 (setextsub) =>
% 97.31/13.19 ((
% 97.31/13.19 (subsetemptysetimpeq) =>
% 97.31/13.19 ((
% 97.31/13.19 (powersetI1) =>
% 97.31/13.19 ((
% 97.31/13.19 (powersetE1) =>
% 97.31/13.19 ((
% 97.31/13.19 (inPowerset) =>
% 97.31/13.19 ((
% 97.31/13.19 (powersetsubset) =>
% 97.31/13.19 ((
% 97.31/13.19 (sepInPowerset) =>
% 97.31/13.19 ((
% 97.31/13.19 (sepSubset) =>
% 97.31/13.19 ((
% 97.31/13.19 (binunionIL) =>
% 97.31/13.19 ((
% 97.31/13.19 (upairset2IR) =>
% 97.31/13.19 ((
% 97.31/13.19 (binunionIR) =>
% 97.31/13.19 ((
% 97.31/13.19 (binunionEcases) =>
% 97.31/13.19 ((
% 97.31/13.19 (binunionE) =>
% 97.31/13.19 ((
% 97.31/13.19 (binunionLsub) =>
% 97.31/13.19 ((
% 97.31/13.19 (binunionRsub) =>
% 97.31/13.19 ((
% 97.31/13.19 (binintersectI) =>
% 97.31/13.19 ((
% 97.31/13.19 (binintersectSubset5) =>
% 97.31/13.19 ((
% 97.31/13.19 (binintersectEL) =>
% 97.31/13.19 ((
% 97.31/13.19 (binintersectLsub) =>
% 97.31/13.19 ((
% 97.31/13.19 (binintersectSubset2) =>
% 97.31/13.19 ((
% 97.31/13.19 (binintersectSubset3) =>
% 97.31/13.19 ((
% 97.31/13.19 (binintersectER) =>
% 97.31/13.19 ((
% 97.31/13.19 (disjointsetsI1) =>
% 97.31/13.19 ((
% 97.31/13.19 (binintersectRsub) =>
% 97.31/13.19 ((
% 97.31/13.19 (binintersectSubset4) =>
% 97.31/13.19 ((
% 97.31/13.19 (binintersectSubset1) =>
% 97.31/13.19 ((
% 97.31/13.19 (bs114d) =>
% 97.31/13.19 ((
% 97.31/13.19 (setminusI) =>
% 97.31/13.19 ((
% 97.31/13.19 (setminusEL) =>
% 97.31/13.19 ((
% 97.31/13.19 (setminusER) =>
% 97.31/13.19 ((
% 97.31/13.19 (setminusSubset2) =>
% 97.31/13.19 ((
% 97.31/13.19 (setminusERneg) =>
% 97.31/13.19 ((
% 97.31/13.19 (setminusELneg) =>
% 97.31/13.19 ((
% 97.31/13.19 (setminusILneg) =>
% 97.31/13.19 ((
% 97.31/13.19 (setminusIRneg) =>
% 97.31/13.19 ((
% 97.31/13.19 (setminusLsub) =>
% 97.31/13.19 ((
% 97.31/13.19 (setminusSubset1) =>
% 97.31/13.19 ((
% 97.31/13.19 (symdiffE) =>
% 97.31/13.19 ((
% 97.31/13.19 (symdiffI1) =>
% 97.31/13.19 ((
% 97.31/13.19 (symdiffI2) =>
% 97.31/13.19 ((
% 97.31/13.19 (symdiffIneg1) =>
% 97.31/13.19 ((
% 97.31/13.19 (symdiffIneg2) =>
% 97.31/13.19 ((
% 97.31/13.19 (secondinupair) =>
% 97.31/13.19 ((
% 97.31/13.19 (setukpairIL) =>
% 97.31/13.19 ((
% 97.31/13.19 (setukpairIR) =>
% 97.31/13.19 ((
% 97.31/13.19 (kpairiskpair) =>
% 97.31/13.19 ((
% 97.31/13.19 (kpairp) =>
% 97.31/13.19 ((
% 97.31/13.19 (singletonsubset) =>
% 97.31/13.19 ((
% 97.31/13.19 (singletoninpowerset) =>
% 97.31/13.19 ((
% 97.31/13.19 (singletoninpowunion) =>
% 97.31/13.19 ((
% 97.31/13.19 (upairset2E) =>
% 97.31/13.19 ((
% 97.31/13.19 (upairsubunion) =>
% 97.31/13.19 ((
% 97.31/13.19 (upairinpowunion) =>
% 97.31/13.19 ((
% 97.31/13.19 (ubforcartprodlem1) =>
% 97.31/13.19 ((
% 97.31/13.19 (ubforcartprodlem2) =>
% 97.31/13.19 ((
% 97.31/13.19 (ubforcartprodlem3) =>
% 97.31/13.19 ((
% 97.31/13.19 (cartprodpairin) =>
% 97.31/13.19 ((
% 97.31/13.19 (cartprodmempair1) =>
% 97.31/13.19 ((
% 97.31/13.19 (cartprodmempair) =>
% 97.31/13.19 ((
% 97.31/13.19 (setunionE2) =>
% 97.31/13.19 ((
% 97.31/13.19 (setunionsingleton1) =>
% 97.31/13.19 ((
% 97.31/13.19 (setunionsingleton2) =>
% 97.31/13.19 ((
% 97.31/13.19 (setunionsingleton) =>
% 97.31/13.19 ((
% 97.31/13.19 (singletonprop) =>
% 97.31/13.19 ((
% 97.31/13.19 (ex1E1) =>
% 97.31/13.19 ((
% 97.31/13.19 (ex1I) =>
% 97.31/13.19 ((
% 97.31/13.19 (ex1I2) =>
% 97.31/13.19 ((
% 97.31/13.19 (singletonsuniq) =>
% 97.31/13.19 ((
% 97.31/13.19 (setukpairinjL1) =>
% 97.31/13.19 ((
% 97.31/13.19 (kfstsingleton) =>
% 97.31/13.19 ((
% 97.31/13.19 (theprop) =>
% 97.31/13.19 ((
% 97.31/13.19 (kfstpairEq) =>
% 97.31/13.19 ((
% 97.31/13.19 (cartprodfstin) =>
% 97.31/13.19 ((
% 97.31/13.19 (setukpairinjL2) =>
% 97.31/13.19 ((
% 97.31/13.19 (setukpairinjL) =>
% 97.31/13.19 ((
% 97.31/13.19 (setukpairinjR11) =>
% 97.31/13.19 ((
% 97.31/13.19 (setukpairinjR12) =>
% 97.31/13.19 ((
% 97.31/13.19 (setukpairinjR1) =>
% 97.31/13.19 ((
% 97.31/13.19 (upairequniteq) =>
% 97.31/13.19 ((
% 97.31/13.19 (setukpairinjR2) =>
% 97.31/13.19 ((
% 97.31/13.19 (setukpairinjR) =>
% 97.31/13.19 ((
% 97.31/13.19 (ksndsingleton) =>
% 97.31/13.19 ((
% 97.31/13.19 (ksndpairEq) =>
% 97.31/13.19 ((
% 97.31/13.19 (kpairsurjEq) =>
% 97.31/13.19 ((
% 97.31/13.19 (cartprodsndin) =>
% 97.31/13.19 ((
% 97.31/13.19 (cartprodpairmemEL) =>
% 97.31/13.19 ((
% 97.31/13.19 (cartprodpairmemER) =>
% 97.31/13.19 ((
% 97.31/13.19 (cartprodmempaircEq) =>
% 97.31/13.19 ((
% 97.31/13.19 (cartprodfstpairEq) =>
% 97.31/13.19 ((
% 97.31/13.19 (cartprodsndpairEq) =>
% 97.31/13.19 ((
% 97.31/13.19 (cartprodpairsurjEq) =>
% 97.31/13.19 ((
% 97.31/13.19 (dpsetconstrI) =>
% 97.31/13.19 ((
% 97.31/13.19 (dpsetconstrSub) =>
% 97.31/13.19 ((
% 97.31/13.19 (setOfPairsIsBReln) =>
% 97.31/13.19 ((
% 97.31/13.19 (dpsetconstrERa) =>
% 97.31/13.19 ((
% 97.31/13.19 (dpsetconstrEL1) =>
% 97.31/13.19 ((
% 97.31/13.19 (dpsetconstrEL2) =>
% 97.31/13.19 ((
% 97.31/13.19 (dpsetconstrER) =>
% 97.31/13.19 ((
% 97.31/13.19 (funcImageSingleton) =>
% 97.31/13.19 ((
% 97.31/13.19 (apProp) =>
% 97.31/13.19 ((
% 97.31/13.19 (app) =>
% 97.31/13.19 ((
% 97.31/13.19 (infuncsetfunc) =>
% 97.31/13.19 ((
% 97.31/13.19 (ap2p) =>
% 97.31/13.19 ((
% 97.31/13.19 (funcinfuncset) =>
% 97.31/13.19 ((
% 97.31/13.19 (lamProp) =>
% 97.31/13.19 ((
% 97.31/13.19 (lamp) =>
% 97.31/13.19 ((
% 97.31/13.19 (lam2p) =>
% 97.31/13.19 ((
% 97.31/13.19 (brelnall1) =>
% 97.31/13.19 ((
% 97.31/13.19 (brelnall2) =>
% 97.31/13.19 ((
% 97.31/13.19 (ex1E2) =>
% 97.31/13.19 ((
% 97.31/13.19 (funcGraphProp1) =>
% 97.31/13.19 ((
% 97.31/13.19 (funcGraphProp3) =>
% 97.31/13.19 ((
% 97.31/13.19 (funcGraphProp2) =>
% 97.31/13.19 ((
% 97.31/13.19 (funcextLem) =>
% 97.31/13.19 ((
% 97.31/13.19 (funcGraphProp4) =>
% 97.31/13.19 ((
% 97.31/13.19 (subbreln) =>
% 97.31/13.19 ((
% 97.31/13.19 (eqbreln) =>
% 97.31/13.19 ((
% 97.31/13.19 (funcext) =>
% 97.31/13.19 ((
% 97.31/13.19 (funcext2) =>
% 97.31/13.19 ((
% 97.31/13.19 (ap2apEq1) =>
% 97.31/13.19 ((
% 97.31/13.19 (ap2apEq2) =>
% 97.31/13.19 ((
% 97.31/13.19 (beta1) =>
% 97.31/13.19 ((
% 97.31/13.19 (eta1) =>
% 97.31/13.19 ((
% 97.31/13.19 (lam2lamEq) =>
% 97.31/13.19 ((
% 97.31/13.19 (beta2) =>
% 97.31/13.19 ((
% 97.31/13.19 (eta2) =>
% 97.31/13.19 ((
% 97.31/13.19 (iffalseProp1) =>
% 97.31/13.19 ((
% 97.31/13.19 (iffalseProp2) =>
% 97.31/13.19 ((
% 97.31/13.19 (iftrueProp1) =>
% 97.31/13.19 ((
% 97.31/13.19 (iftrueProp2) =>
% 97.31/13.19 ((
% 97.31/13.19 (ifSingleton) =>
% 97.31/13.19 ((
% 97.31/13.19 (ifp) =>
% 97.31/13.19 ((
% 97.31/13.19 (theeq) =>
% 97.31/13.19 ((
% 97.31/13.19 (iftrue) =>
% 97.31/13.19 ((
% 97.31/13.19 (iffalse) =>
% 97.31/13.19 ((
% 97.31/13.19 (iftrueorfalse) =>
% 97.31/13.19 ((
% 97.31/13.19 (binintersectT_lem) =>
% 97.31/13.19 ((
% 97.31/13.19 (binunionT_lem) =>
% 97.31/13.19 ((
% 97.31/13.19 (powersetT_lem) =>
% 97.31/13.19 ((
% 97.31/13.19 (setminusT_lem) =>
% 97.31/13.19 ((
% 97.31/13.19 (complementT_lem) =>
% 97.31/13.19 ((
% 97.31/13.19 (setextT) =>
% 97.31/13.19 ((
% 97.31/13.19 (subsetTI) =>
% 97.31/13.19 ((
% 97.31/13.19 (powersetTI1) =>
% 97.31/13.19 ((
% 97.31/13.19 (powersetTE1) =>
% 97.31/13.19 ((
% 97.31/13.19 (complementTI1) =>
% 97.31/13.19 ((
% 97.31/13.19 (complementTE1) =>
% 97.31/13.19 ((
% 97.31/13.19 (binintersectTELcontra) =>
% 97.31/13.19 ((
% 97.31/13.19 (binintersectTERcontra) =>
% 97.31/13.19 ((
% 97.31/13.19 (contrasubsetT) =>
% 97.31/13.19 ((
% 97.31/13.19 (contrasubsetT1) =>
% 97.31/13.19 ((
% 97.31/13.19 (contrasubsetT2) =>
% 97.31/13.19 ((
% 97.31/13.19 (contrasubsetT3) =>
% 97.31/13.19 ((
% 97.31/13.19 (doubleComplementI1) =>
% 97.31/13.19 ((
% 97.31/13.19 (doubleComplementE1) =>
% 97.31/13.19 ((
% 97.31/13.19 (doubleComplementSub1) =>
% 97.31/13.19 ((
% 97.31/13.19 (doubleComplementSub2) =>
% 97.31/13.19 ((
% 97.31/13.19 (doubleComplementEq) =>
% 97.31/13.19 ((
% 97.31/13.19 (complementTnotintersectT) =>
% 97.31/13.19 ((
% 97.31/13.19 (complementImpComplementIntersect) =>
% 97.31/13.19 ((
% 97.31/13.19 (complementSubsetComplementIntersect) =>
% 97.31/13.19 ((
% 97.31/13.19 (complementInPowersetComplementIntersect) =>
% 97.31/13.19 ((
% 97.31/13.19 (contraSubsetComplement) =>
% 97.31/13.19 ((
% 97.31/13.19 (complementTcontraSubset) =>
% 97.31/13.19 ((
% 97.31/13.19 (binunionTILcontra) =>
% 97.31/13.19 ((
% 97.31/13.19 (binunionTIRcontra) =>
% 97.31/13.19 ((
% 97.31/13.19 (inIntersectImpInUnion) =>
% 97.31/13.19 ((
% 97.31/13.19 (inIntersectImpInUnion2) =>
% 97.31/13.19 ((
% 97.31/13.19 (inIntersectImpInIntersectUnions) =>
% 97.31/13.19 ((
% 97.31/13.19 (intersectInPowersetIntersectUnions) =>
% 97.31/13.19 ((
% 97.31/13.19 (inComplementUnionImpNotIn1) =>
% 97.31/13.19 ((
% 97.31/13.19 (inComplementUnionImpInComplement1) =>
% 97.31/13.19 ((
% 97.31/13.19 (binunionTE) =>
% 97.31/13.19 ((
% 97.31/13.19 (binunionTEcontra) =>
% 97.31/13.19 ((
% 97.31/13.19 (demorgan2a1) =>
% 97.31/13.19 ((
% 97.31/13.19 (complementUnionInPowersetComplement) =>
% 97.31/13.19 ((
% 97.31/13.19 (demorgan2a2) =>
% 97.31/13.19 ((
% 97.31/13.19 (demorgan1a) =>
% 97.31/13.19 ((
% 97.31/13.19 (demorgan1b) =>
% 97.31/13.19 ((
% 97.31/13.19 (demorgan1) =>
% 97.31/13.19 ((
% 97.31/13.19 (demorgan2a) =>
% 97.31/13.19 ((
% 97.31/13.19 (demorgan2b2) =>
% 97.31/13.19 ((
% 97.31/13.19 (demorgan2b) =>
% 97.31/13.19 ((
% 97.31/13.19 (demorgan2) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz13rule0) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz13rule1) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz13rule2) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz13rule3) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz13rule4) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz1_1) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz1_2) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz1_3) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz1_4) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz1_5) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1all2) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1SetBreln1) =>
% 97.31/13.19 ((
% 97.31/13.19 (choice2fnsingleton) =>
% 97.31/13.19 ((
% 97.31/13.19 (setOfPairsIsBReln1) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1all1) =>
% 97.31/13.19 ((
% 97.31/13.19 (subbreln1) =>
% 97.31/13.19 ((
% 97.31/13.19 (eqbreln1) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1invprop) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1invI) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1invE) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1compprop) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1compI) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1compE) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1compEex) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1unionprop) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1unionIL) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1unionIR) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1unionI) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1unionE) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1unionEcases) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1unionCommutes) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz2Ex) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz2W) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz2A) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz2B) =>
% 97.31/13.19 ((
% 97.31/13.19 (image1Ex) =>
% 97.31/13.19 ((
% 97.31/13.19 (image1Ex1) =>
% 97.31/13.19 ((
% 97.31/13.19 (image1Equiv) =>
% 97.31/13.19 ((
% 97.31/13.19 (image1E) =>
% 97.31/13.19 ((
% 97.31/13.19 (image1I) =>
% 97.31/13.19 ((
% 97.31/13.19 (injFuncInInjFuncSet) =>
% 97.31/13.19 ((
% 97.31/13.19 (injFuncSetFuncIn) =>
% 97.31/13.19 ((
% 97.31/13.19 (injFuncSetFuncInj) =>
% 97.31/13.19 ((
% 97.31/13.19 (surjFuncSetFuncIn) =>
% 97.31/13.19 ((
% 97.31/13.19 (surjFuncSetFuncSurj) =>
% 97.31/13.19 ((
% 97.31/13.19 (leftInvIsSurj) =>
% 97.31/13.19 ((
% 97.31/13.19 (surjCantorThm) =>
% 97.31/13.19 ((
% 97.31/13.19 (foundation2) =>
% 97.31/13.19 ((
% 97.31/13.19 (notinself) =>
% 97.31/13.19 ((
% 97.31/13.19 (notinself2) =>
% 97.31/13.19 ((
% 97.31/13.19 (omegaSp) =>
% 97.31/13.19 ((
% 97.31/13.19 (omegaSclos) =>
% 97.31/13.19 ((
% 97.31/13.19 (peano0notS) =>
% 97.31/13.19 ((
% 97.31/13.19 (!!) @ (
% 97.31/13.19 (('#S') @ (
% 97.31/13.19 (
% 97.31/13.19 ('#B') @ (
% 97.31/13.19 =>) @
% 97.31/13.19 (
% 97.31/13.19 (
% 97.31/13.19 ('#C') @ in @
% 97.31/13.19 omega)))) @
% 97.31/13.19 (
% 97.31/13.19 (
% 97.31/13.19 ('#B') @ (
% 97.31/13.19 !!) @
% 97.31/13.19 (
% 97.31/13.19 (
% 97.31/13.19 ('#B') @ (
% 97.31/13.19 (
% 97.31/13.19 ('#S') @ (
% 97.31/13.19 (
% 97.31/13.19 ('#B') @ (
% 97.31/13.19 =>) @
% 97.31/13.19 (
% 97.31/13.19 (
% 97.31/13.19 ('#C') @ in @
% 97.31/13.19 omega)))))) @
% 97.31/13.19 (
% 97.31/13.19 (
% 97.31/13.19 ('#S') @ (
% 97.31/13.19 (
% 97.31/13.19 ('#B') @ (
% 97.31/13.19 '#S') @
% 97.31/13.19 (
% 97.31/13.19 (
% 97.31/13.19 ('#B') @ (
% 97.31/13.19 (
% 97.31/13.19 ('#B') @ (
% 97.31/13.19 =>))) @
% 97.31/13.19 (
% 97.31/13.19 (
% 97.31/13.19 ('#C') @ (
% 97.31/13.19 (
% 97.31/13.19 ('#B') @ (
% 97.31/13.19 '#B') @
% 97.31/13.19 (
% 97.31/13.19 (
% 97.31/13.19 ('#B') @ (
% 97.31/13.19 =) @
% 97.31/13.19 omegaS)))) @
% 97.31/13.19 omegaS)))))) @
% 97.31/13.19 (
% 97.31/13.19 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.31/13.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl475])).
% 97.31/13.19 thf(zip_derived_cl496, plain,
% 97.31/13.19 (~ (((upairsetIL) =>
% 97.31/13.19 (((upairsetIR) =>
% 97.31/13.19 (((emptyE1) =>
% 97.31/13.19 (((vacuousDall) =>
% 97.31/13.19 (((quantDeMorgan1) =>
% 97.31/13.19 (((quantDeMorgan2) =>
% 97.31/13.19 (((quantDeMorgan3) =>
% 97.31/13.19 (((quantDeMorgan4) =>
% 97.31/13.19 (((prop2setI) =>
% 97.31/13.19 (((prop2set2propI) =>
% 97.31/13.19 (((notdexE) =>
% 97.31/13.19 (((notdallE) =>
% 97.31/13.19 (((exuI1) =>
% 97.31/13.19 (((exuI3) =>
% 97.31/13.19 (((exuI2) =>
% 97.31/13.19 (((inCongP) =>
% 97.31/13.19 (((in__Cong) =>
% 97.31/13.19 (((exuE3u) =>
% 97.31/13.19 (((exu__Cong) =>
% 97.31/13.19 (((setadjoin__Cong) =>
% 97.31/13.19 (((powerset__Cong) =>
% 97.31/13.19 (((setunion__Cong) =>
% 97.31/13.19 (((exuEu) =>
% 97.31/13.19 (((descr__Cong) =>
% 97.31/13.19 (((dsetconstr__Cong) =>
% 97.31/13.19 (((subsetI1) =>
% 97.31/13.19 (((eqimpsubset2) =>
% 97.31/13.19 (((eqimpsubset1) =>
% 97.31/13.19 (((subsetI2) =>
% 97.31/13.19 (((emptysetsubset) =>
% 97.31/13.19 ((
% 97.31/13.19 (subsetE) =>
% 97.31/13.19 ((
% 97.31/13.19 (subsetE2) =>
% 97.31/13.19 ((
% 97.31/13.19 (notsubsetI) =>
% 97.31/13.19 ((
% 97.31/13.19 (notequalI1) =>
% 97.31/13.19 ((
% 97.31/13.19 (notequalI2) =>
% 97.31/13.19 ((
% 97.31/13.19 (subsetRefl) =>
% 97.31/13.19 ((
% 97.31/13.19 (subsetTrans) =>
% 97.31/13.19 ((
% 97.31/13.19 (setadjoinSub) =>
% 97.31/13.19 ((
% 97.31/13.19 (setadjoinSub2) =>
% 97.31/13.19 ((
% 97.31/13.19 (subset2powerset) =>
% 97.31/13.19 ((
% 97.31/13.19 (setextsub) =>
% 97.31/13.19 ((
% 97.31/13.19 (subsetemptysetimpeq) =>
% 97.31/13.19 ((
% 97.31/13.19 (powersetI1) =>
% 97.31/13.19 ((
% 97.31/13.19 (powersetE1) =>
% 97.31/13.19 ((
% 97.31/13.19 (inPowerset) =>
% 97.31/13.19 ((
% 97.31/13.19 (powersetsubset) =>
% 97.31/13.19 ((
% 97.31/13.19 (sepInPowerset) =>
% 97.31/13.19 ((
% 97.31/13.19 (sepSubset) =>
% 97.31/13.19 ((
% 97.31/13.19 (binunionIL) =>
% 97.31/13.19 ((
% 97.31/13.19 (upairset2IR) =>
% 97.31/13.19 ((
% 97.31/13.19 (binunionIR) =>
% 97.31/13.19 ((
% 97.31/13.19 (binunionEcases) =>
% 97.31/13.19 ((
% 97.31/13.19 (binunionE) =>
% 97.31/13.19 ((
% 97.31/13.19 (binunionLsub) =>
% 97.31/13.19 ((
% 97.31/13.19 (binunionRsub) =>
% 97.31/13.19 ((
% 97.31/13.19 (binintersectI) =>
% 97.31/13.19 ((
% 97.31/13.19 (binintersectSubset5) =>
% 97.31/13.19 ((
% 97.31/13.19 (binintersectEL) =>
% 97.31/13.19 ((
% 97.31/13.19 (binintersectLsub) =>
% 97.31/13.19 ((
% 97.31/13.19 (binintersectSubset2) =>
% 97.31/13.19 ((
% 97.31/13.19 (binintersectSubset3) =>
% 97.31/13.19 ((
% 97.31/13.19 (binintersectER) =>
% 97.31/13.19 ((
% 97.31/13.19 (disjointsetsI1) =>
% 97.31/13.19 ((
% 97.31/13.19 (binintersectRsub) =>
% 97.31/13.19 ((
% 97.31/13.19 (binintersectSubset4) =>
% 97.31/13.19 ((
% 97.31/13.19 (binintersectSubset1) =>
% 97.31/13.19 ((
% 97.31/13.19 (bs114d) =>
% 97.31/13.19 ((
% 97.31/13.19 (setminusI) =>
% 97.31/13.19 ((
% 97.31/13.19 (setminusEL) =>
% 97.31/13.19 ((
% 97.31/13.19 (setminusER) =>
% 97.31/13.19 ((
% 97.31/13.19 (setminusSubset2) =>
% 97.31/13.19 ((
% 97.31/13.19 (setminusERneg) =>
% 97.31/13.19 ((
% 97.31/13.19 (setminusELneg) =>
% 97.31/13.19 ((
% 97.31/13.19 (setminusILneg) =>
% 97.31/13.19 ((
% 97.31/13.19 (setminusIRneg) =>
% 97.31/13.19 ((
% 97.31/13.19 (setminusLsub) =>
% 97.31/13.19 ((
% 97.31/13.19 (setminusSubset1) =>
% 97.31/13.19 ((
% 97.31/13.19 (symdiffE) =>
% 97.31/13.19 ((
% 97.31/13.19 (symdiffI1) =>
% 97.31/13.19 ((
% 97.31/13.19 (symdiffI2) =>
% 97.31/13.19 ((
% 97.31/13.19 (symdiffIneg1) =>
% 97.31/13.19 ((
% 97.31/13.19 (symdiffIneg2) =>
% 97.31/13.19 ((
% 97.31/13.19 (secondinupair) =>
% 97.31/13.19 ((
% 97.31/13.19 (setukpairIL) =>
% 97.31/13.19 ((
% 97.31/13.19 (setukpairIR) =>
% 97.31/13.19 ((
% 97.31/13.19 (kpairiskpair) =>
% 97.31/13.19 ((
% 97.31/13.19 (kpairp) =>
% 97.31/13.19 ((
% 97.31/13.19 (singletonsubset) =>
% 97.31/13.19 ((
% 97.31/13.19 (singletoninpowerset) =>
% 97.31/13.19 ((
% 97.31/13.19 (singletoninpowunion) =>
% 97.31/13.19 ((
% 97.31/13.19 (upairset2E) =>
% 97.31/13.19 ((
% 97.31/13.19 (upairsubunion) =>
% 97.31/13.19 ((
% 97.31/13.19 (upairinpowunion) =>
% 97.31/13.19 ((
% 97.31/13.19 (ubforcartprodlem1) =>
% 97.31/13.19 ((
% 97.31/13.19 (ubforcartprodlem2) =>
% 97.31/13.19 ((
% 97.31/13.19 (ubforcartprodlem3) =>
% 97.31/13.19 ((
% 97.31/13.19 (cartprodpairin) =>
% 97.31/13.19 ((
% 97.31/13.19 (cartprodmempair1) =>
% 97.31/13.19 ((
% 97.31/13.19 (cartprodmempair) =>
% 97.31/13.19 ((
% 97.31/13.19 (setunionE2) =>
% 97.31/13.19 ((
% 97.31/13.19 (setunionsingleton1) =>
% 97.31/13.19 ((
% 97.31/13.19 (setunionsingleton2) =>
% 97.31/13.19 ((
% 97.31/13.19 (setunionsingleton) =>
% 97.31/13.19 ((
% 97.31/13.19 (singletonprop) =>
% 97.31/13.19 ((
% 97.31/13.19 (ex1E1) =>
% 97.31/13.19 ((
% 97.31/13.19 (ex1I) =>
% 97.31/13.19 ((
% 97.31/13.19 (ex1I2) =>
% 97.31/13.19 ((
% 97.31/13.19 (singletonsuniq) =>
% 97.31/13.19 ((
% 97.31/13.19 (setukpairinjL1) =>
% 97.31/13.19 ((
% 97.31/13.19 (kfstsingleton) =>
% 97.31/13.19 ((
% 97.31/13.19 (theprop) =>
% 97.31/13.19 ((
% 97.31/13.19 (kfstpairEq) =>
% 97.31/13.19 ((
% 97.31/13.19 (cartprodfstin) =>
% 97.31/13.19 ((
% 97.31/13.19 (setukpairinjL2) =>
% 97.31/13.19 ((
% 97.31/13.19 (setukpairinjL) =>
% 97.31/13.19 ((
% 97.31/13.19 (setukpairinjR11) =>
% 97.31/13.19 ((
% 97.31/13.19 (setukpairinjR12) =>
% 97.31/13.19 ((
% 97.31/13.19 (setukpairinjR1) =>
% 97.31/13.19 ((
% 97.31/13.19 (upairequniteq) =>
% 97.31/13.19 ((
% 97.31/13.19 (setukpairinjR2) =>
% 97.31/13.19 ((
% 97.31/13.19 (setukpairinjR) =>
% 97.31/13.19 ((
% 97.31/13.19 (ksndsingleton) =>
% 97.31/13.19 ((
% 97.31/13.19 (ksndpairEq) =>
% 97.31/13.19 ((
% 97.31/13.19 (kpairsurjEq) =>
% 97.31/13.19 ((
% 97.31/13.19 (cartprodsndin) =>
% 97.31/13.19 ((
% 97.31/13.19 (cartprodpairmemEL) =>
% 97.31/13.19 ((
% 97.31/13.19 (cartprodpairmemER) =>
% 97.31/13.19 ((
% 97.31/13.19 (cartprodmempaircEq) =>
% 97.31/13.19 ((
% 97.31/13.19 (cartprodfstpairEq) =>
% 97.31/13.19 ((
% 97.31/13.19 (cartprodsndpairEq) =>
% 97.31/13.19 ((
% 97.31/13.19 (cartprodpairsurjEq) =>
% 97.31/13.19 ((
% 97.31/13.19 (dpsetconstrI) =>
% 97.31/13.19 ((
% 97.31/13.19 (dpsetconstrSub) =>
% 97.31/13.19 ((
% 97.31/13.19 (setOfPairsIsBReln) =>
% 97.31/13.19 ((
% 97.31/13.19 (dpsetconstrERa) =>
% 97.31/13.19 ((
% 97.31/13.19 (dpsetconstrEL1) =>
% 97.31/13.19 ((
% 97.31/13.19 (dpsetconstrEL2) =>
% 97.31/13.19 ((
% 97.31/13.19 (dpsetconstrER) =>
% 97.31/13.19 ((
% 97.31/13.19 (funcImageSingleton) =>
% 97.31/13.19 ((
% 97.31/13.19 (apProp) =>
% 97.31/13.19 ((
% 97.31/13.19 (app) =>
% 97.31/13.19 ((
% 97.31/13.19 (infuncsetfunc) =>
% 97.31/13.19 ((
% 97.31/13.19 (ap2p) =>
% 97.31/13.19 ((
% 97.31/13.19 (funcinfuncset) =>
% 97.31/13.19 ((
% 97.31/13.19 (lamProp) =>
% 97.31/13.19 ((
% 97.31/13.19 (lamp) =>
% 97.31/13.19 ((
% 97.31/13.19 (lam2p) =>
% 97.31/13.19 ((
% 97.31/13.19 (brelnall1) =>
% 97.31/13.19 ((
% 97.31/13.19 (brelnall2) =>
% 97.31/13.19 ((
% 97.31/13.19 (ex1E2) =>
% 97.31/13.19 ((
% 97.31/13.19 (funcGraphProp1) =>
% 97.31/13.19 ((
% 97.31/13.19 (funcGraphProp3) =>
% 97.31/13.19 ((
% 97.31/13.19 (funcGraphProp2) =>
% 97.31/13.19 ((
% 97.31/13.19 (funcextLem) =>
% 97.31/13.19 ((
% 97.31/13.19 (funcGraphProp4) =>
% 97.31/13.19 ((
% 97.31/13.19 (subbreln) =>
% 97.31/13.19 ((
% 97.31/13.19 (eqbreln) =>
% 97.31/13.19 ((
% 97.31/13.19 (funcext) =>
% 97.31/13.19 ((
% 97.31/13.19 (funcext2) =>
% 97.31/13.19 ((
% 97.31/13.19 (ap2apEq1) =>
% 97.31/13.19 ((
% 97.31/13.19 (ap2apEq2) =>
% 97.31/13.19 ((
% 97.31/13.19 (beta1) =>
% 97.31/13.19 ((
% 97.31/13.19 (eta1) =>
% 97.31/13.19 ((
% 97.31/13.19 (lam2lamEq) =>
% 97.31/13.19 ((
% 97.31/13.19 (beta2) =>
% 97.31/13.19 ((
% 97.31/13.19 (eta2) =>
% 97.31/13.19 ((
% 97.31/13.19 (iffalseProp1) =>
% 97.31/13.19 ((
% 97.31/13.19 (iffalseProp2) =>
% 97.31/13.19 ((
% 97.31/13.19 (iftrueProp1) =>
% 97.31/13.19 ((
% 97.31/13.19 (iftrueProp2) =>
% 97.31/13.19 ((
% 97.31/13.19 (ifSingleton) =>
% 97.31/13.19 ((
% 97.31/13.19 (ifp) =>
% 97.31/13.19 ((
% 97.31/13.19 (theeq) =>
% 97.31/13.19 ((
% 97.31/13.19 (iftrue) =>
% 97.31/13.19 ((
% 97.31/13.19 (iffalse) =>
% 97.31/13.19 ((
% 97.31/13.19 (iftrueorfalse) =>
% 97.31/13.19 ((
% 97.31/13.19 (binintersectT_lem) =>
% 97.31/13.19 ((
% 97.31/13.19 (binunionT_lem) =>
% 97.31/13.19 ((
% 97.31/13.19 (powersetT_lem) =>
% 97.31/13.19 ((
% 97.31/13.19 (setminusT_lem) =>
% 97.31/13.19 ((
% 97.31/13.19 (complementT_lem) =>
% 97.31/13.19 ((
% 97.31/13.19 (setextT) =>
% 97.31/13.19 ((
% 97.31/13.19 (subsetTI) =>
% 97.31/13.19 ((
% 97.31/13.19 (powersetTI1) =>
% 97.31/13.19 ((
% 97.31/13.19 (powersetTE1) =>
% 97.31/13.19 ((
% 97.31/13.19 (complementTI1) =>
% 97.31/13.19 ((
% 97.31/13.19 (complementTE1) =>
% 97.31/13.19 ((
% 97.31/13.19 (binintersectTELcontra) =>
% 97.31/13.19 ((
% 97.31/13.19 (binintersectTERcontra) =>
% 97.31/13.19 ((
% 97.31/13.19 (contrasubsetT) =>
% 97.31/13.19 ((
% 97.31/13.19 (contrasubsetT1) =>
% 97.31/13.19 ((
% 97.31/13.19 (contrasubsetT2) =>
% 97.31/13.19 ((
% 97.31/13.19 (contrasubsetT3) =>
% 97.31/13.19 ((
% 97.31/13.19 (doubleComplementI1) =>
% 97.31/13.19 ((
% 97.31/13.19 (doubleComplementE1) =>
% 97.31/13.19 ((
% 97.31/13.19 (doubleComplementSub1) =>
% 97.31/13.19 ((
% 97.31/13.19 (doubleComplementSub2) =>
% 97.31/13.19 ((
% 97.31/13.19 (doubleComplementEq) =>
% 97.31/13.19 ((
% 97.31/13.19 (complementTnotintersectT) =>
% 97.31/13.19 ((
% 97.31/13.19 (complementImpComplementIntersect) =>
% 97.31/13.19 ((
% 97.31/13.19 (complementSubsetComplementIntersect) =>
% 97.31/13.19 ((
% 97.31/13.19 (complementInPowersetComplementIntersect) =>
% 97.31/13.19 ((
% 97.31/13.19 (contraSubsetComplement) =>
% 97.31/13.19 ((
% 97.31/13.19 (complementTcontraSubset) =>
% 97.31/13.19 ((
% 97.31/13.19 (binunionTILcontra) =>
% 97.31/13.19 ((
% 97.31/13.19 (binunionTIRcontra) =>
% 97.31/13.19 ((
% 97.31/13.19 (inIntersectImpInUnion) =>
% 97.31/13.19 ((
% 97.31/13.19 (inIntersectImpInUnion2) =>
% 97.31/13.19 ((
% 97.31/13.19 (inIntersectImpInIntersectUnions) =>
% 97.31/13.19 ((
% 97.31/13.19 (intersectInPowersetIntersectUnions) =>
% 97.31/13.19 ((
% 97.31/13.19 (inComplementUnionImpNotIn1) =>
% 97.31/13.19 ((
% 97.31/13.19 (inComplementUnionImpInComplement1) =>
% 97.31/13.19 ((
% 97.31/13.19 (binunionTE) =>
% 97.31/13.19 ((
% 97.31/13.19 (binunionTEcontra) =>
% 97.31/13.19 ((
% 97.31/13.19 (demorgan2a1) =>
% 97.31/13.19 ((
% 97.31/13.19 (complementUnionInPowersetComplement) =>
% 97.31/13.19 ((
% 97.31/13.19 (demorgan2a2) =>
% 97.31/13.19 ((
% 97.31/13.19 (demorgan1a) =>
% 97.31/13.19 ((
% 97.31/13.19 (demorgan1b) =>
% 97.31/13.19 ((
% 97.31/13.19 (demorgan1) =>
% 97.31/13.19 ((
% 97.31/13.19 (demorgan2a) =>
% 97.31/13.19 ((
% 97.31/13.19 (demorgan2b2) =>
% 97.31/13.19 ((
% 97.31/13.19 (demorgan2b) =>
% 97.31/13.19 ((
% 97.31/13.19 (demorgan2) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz13rule0) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz13rule1) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz13rule2) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz13rule3) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz13rule4) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz1_1) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz1_2) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz1_3) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz1_4) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz1_5) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1all2) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1SetBreln1) =>
% 97.31/13.19 ((
% 97.31/13.19 (choice2fnsingleton) =>
% 97.31/13.19 ((
% 97.31/13.19 (setOfPairsIsBReln1) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1all1) =>
% 97.31/13.19 ((
% 97.31/13.19 (subbreln1) =>
% 97.31/13.19 ((
% 97.31/13.19 (eqbreln1) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1invprop) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1invI) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1invE) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1compprop) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1compI) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1compE) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1compEex) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1unionprop) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1unionIL) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1unionIR) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1unionI) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1unionE) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1unionEcases) =>
% 97.31/13.19 ((
% 97.31/13.19 (breln1unionCommutes) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz2Ex) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz2W) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz2A) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz2B) =>
% 97.31/13.19 ((
% 97.31/13.19 (image1Ex) =>
% 97.31/13.19 ((
% 97.31/13.19 (image1Ex1) =>
% 97.31/13.19 ((
% 97.31/13.19 (image1Equiv) =>
% 97.31/13.19 ((
% 97.31/13.19 (image1E) =>
% 97.31/13.19 ((
% 97.31/13.19 (image1I) =>
% 97.31/13.19 ((
% 97.31/13.19 (injFuncInInjFuncSet) =>
% 97.31/13.19 ((
% 97.31/13.19 (injFuncSetFuncIn) =>
% 97.31/13.19 ((
% 97.31/13.19 (injFuncSetFuncInj) =>
% 97.31/13.19 ((
% 97.31/13.19 (surjFuncSetFuncIn) =>
% 97.31/13.19 ((
% 97.31/13.19 (surjFuncSetFuncSurj) =>
% 97.31/13.19 ((
% 97.31/13.19 (leftInvIsSurj) =>
% 97.31/13.19 ((
% 97.31/13.19 (surjCantorThm) =>
% 97.31/13.19 ((
% 97.31/13.19 (foundation2) =>
% 97.31/13.19 ((
% 97.31/13.19 (notinself) =>
% 97.31/13.19 ((
% 97.31/13.19 (notinself2) =>
% 97.31/13.19 ((
% 97.31/13.19 (omegaSp) =>
% 97.31/13.19 ((
% 97.31/13.19 (omegaSclos) =>
% 97.31/13.19 ((
% 97.31/13.19 (peano0notS) =>
% 97.31/13.19 ((
% 97.31/13.19 (!!) @ (
% 97.31/13.19 (('#S') @ (
% 97.31/13.19 (
% 97.31/13.19 ('#B') @ (
% 97.31/13.19 =>) @
% 97.31/13.19 (
% 97.31/13.19 (
% 97.31/13.19 ('#C') @ in @
% 97.31/13.19 omega)))) @
% 97.31/13.19 (
% 97.31/13.19 (
% 97.31/13.19 ('#B') @ (
% 97.31/13.19 !!) @
% 97.31/13.19 (
% 97.31/13.19 (
% 97.31/13.19 ('#B') @ (
% 97.31/13.19 (
% 97.31/13.19 ('#S') @ (
% 97.31/13.19 (
% 97.31/13.19 ('#B') @ (
% 97.31/13.19 =>) @
% 97.31/13.19 (
% 97.31/13.19 (
% 97.31/13.19 ('#C') @ in @
% 97.31/13.19 omega)))))) @
% 97.31/13.19 (
% 97.31/13.19 (
% 97.31/13.19 ('#S') @ (
% 97.31/13.19 (
% 97.31/13.19 ('#B') @ (
% 97.31/13.19 '#S') @
% 97.31/13.19 (
% 97.31/13.19 (
% 97.31/13.19 ('#B') @ (
% 97.31/13.19 (
% 97.31/13.19 ('#B') @ (
% 97.31/13.19 =>))) @
% 97.31/13.19 (
% 97.31/13.19 (
% 97.31/13.19 ('#C') @ (
% 97.31/13.19 (
% 97.31/13.19 ('#B') @ (
% 97.31/13.19 '#B') @
% 97.31/13.19 (
% 97.31/13.19 (
% 97.31/13.19 ('#B') @ (
% 97.31/13.19 =) @
% 97.31/13.19 omegaS)))) @
% 97.31/13.19 omegaS)))))) @
% 97.31/13.19 (
% 97.31/13.19 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.31/13.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl485])).
% 97.31/13.19 thf(zip_derived_cl507, plain,
% 97.31/13.19 (~ (((upairsetIR) =>
% 97.31/13.19 (((emptyE1) =>
% 97.31/13.19 (((vacuousDall) =>
% 97.31/13.19 (((quantDeMorgan1) =>
% 97.31/13.19 (((quantDeMorgan2) =>
% 97.31/13.19 (((quantDeMorgan3) =>
% 97.31/13.19 (((quantDeMorgan4) =>
% 97.31/13.19 (((prop2setI) =>
% 97.31/13.19 (((prop2set2propI) =>
% 97.31/13.19 (((notdexE) =>
% 97.31/13.19 (((notdallE) =>
% 97.31/13.19 (((exuI1) =>
% 97.31/13.19 (((exuI3) =>
% 97.31/13.19 (((exuI2) =>
% 97.31/13.19 (((inCongP) =>
% 97.31/13.19 (((in__Cong) =>
% 97.31/13.19 (((exuE3u) =>
% 97.31/13.19 (((exu__Cong) =>
% 97.31/13.19 (((setadjoin__Cong) =>
% 97.31/13.19 (((powerset__Cong) =>
% 97.31/13.19 (((setunion__Cong) =>
% 97.31/13.19 (((exuEu) =>
% 97.31/13.19 (((descr__Cong) =>
% 97.31/13.19 (((dsetconstr__Cong) =>
% 97.31/13.19 (((subsetI1) =>
% 97.31/13.19 (((eqimpsubset2) =>
% 97.31/13.19 (((eqimpsubset1) =>
% 97.31/13.19 (((subsetI2) =>
% 97.31/13.19 (((emptysetsubset) =>
% 97.31/13.19 (((subsetE) =>
% 97.31/13.19 ((
% 97.31/13.19 (subsetE2) =>
% 97.31/13.19 ((
% 97.31/13.19 (notsubsetI) =>
% 97.31/13.19 ((
% 97.31/13.19 (notequalI1) =>
% 97.31/13.19 ((
% 97.31/13.19 (notequalI2) =>
% 97.31/13.19 ((
% 97.31/13.19 (subsetRefl) =>
% 97.31/13.19 ((
% 97.31/13.19 (subsetTrans) =>
% 97.31/13.19 ((
% 97.31/13.19 (setadjoinSub) =>
% 97.31/13.19 ((
% 97.31/13.19 (setadjoinSub2) =>
% 97.31/13.19 ((
% 97.31/13.19 (subset2powerset) =>
% 97.31/13.19 ((
% 97.31/13.19 (setextsub) =>
% 97.31/13.19 ((
% 97.31/13.19 (subsetemptysetimpeq) =>
% 97.31/13.19 ((
% 97.31/13.19 (powersetI1) =>
% 97.31/13.19 ((
% 97.31/13.19 (powersetE1) =>
% 97.31/13.19 ((
% 97.31/13.19 (inPowerset) =>
% 97.31/13.19 ((
% 97.31/13.19 (powersetsubset) =>
% 97.31/13.19 ((
% 97.31/13.19 (sepInPowerset) =>
% 97.31/13.19 ((
% 97.31/13.19 (sepSubset) =>
% 97.31/13.19 ((
% 97.31/13.19 (binunionIL) =>
% 97.31/13.19 ((
% 97.31/13.19 (upairset2IR) =>
% 97.31/13.19 ((
% 97.31/13.19 (binunionIR) =>
% 97.31/13.19 ((
% 97.31/13.19 (binunionEcases) =>
% 97.31/13.19 ((
% 97.31/13.19 (binunionE) =>
% 97.31/13.19 ((
% 97.31/13.19 (binunionLsub) =>
% 97.31/13.19 ((
% 97.31/13.19 (binunionRsub) =>
% 97.31/13.19 ((
% 97.31/13.19 (binintersectI) =>
% 97.31/13.19 ((
% 97.31/13.19 (binintersectSubset5) =>
% 97.31/13.19 ((
% 97.31/13.19 (binintersectEL) =>
% 97.31/13.19 ((
% 97.31/13.19 (binintersectLsub) =>
% 97.31/13.19 ((
% 97.31/13.19 (binintersectSubset2) =>
% 97.31/13.19 ((
% 97.31/13.19 (binintersectSubset3) =>
% 97.31/13.19 ((
% 97.31/13.19 (binintersectER) =>
% 97.31/13.19 ((
% 97.31/13.19 (disjointsetsI1) =>
% 97.31/13.19 ((
% 97.31/13.19 (binintersectRsub) =>
% 97.31/13.19 ((
% 97.31/13.19 (binintersectSubset4) =>
% 97.31/13.19 ((
% 97.31/13.19 (binintersectSubset1) =>
% 97.31/13.19 ((
% 97.31/13.19 (bs114d) =>
% 97.31/13.19 ((
% 97.31/13.19 (setminusI) =>
% 97.31/13.19 ((
% 97.31/13.19 (setminusEL) =>
% 97.31/13.19 ((
% 97.31/13.19 (setminusER) =>
% 97.31/13.19 ((
% 97.31/13.19 (setminusSubset2) =>
% 97.31/13.19 ((
% 97.31/13.19 (setminusERneg) =>
% 97.31/13.19 ((
% 97.31/13.19 (setminusELneg) =>
% 97.31/13.19 ((
% 97.31/13.19 (setminusILneg) =>
% 97.31/13.19 ((
% 97.31/13.19 (setminusIRneg) =>
% 97.31/13.19 ((
% 97.31/13.19 (setminusLsub) =>
% 97.31/13.19 ((
% 97.31/13.19 (setminusSubset1) =>
% 97.31/13.19 ((
% 97.31/13.19 (symdiffE) =>
% 97.31/13.19 ((
% 97.31/13.19 (symdiffI1) =>
% 97.31/13.19 ((
% 97.31/13.19 (symdiffI2) =>
% 97.31/13.19 ((
% 97.31/13.19 (symdiffIneg1) =>
% 97.31/13.19 ((
% 97.31/13.19 (symdiffIneg2) =>
% 97.31/13.19 ((
% 97.31/13.19 (secondinupair) =>
% 97.31/13.19 ((
% 97.31/13.19 (setukpairIL) =>
% 97.31/13.19 ((
% 97.31/13.19 (setukpairIR) =>
% 97.31/13.19 ((
% 97.31/13.19 (kpairiskpair) =>
% 97.31/13.19 ((
% 97.31/13.19 (kpairp) =>
% 97.31/13.19 ((
% 97.31/13.19 (singletonsubset) =>
% 97.31/13.19 ((
% 97.31/13.19 (singletoninpowerset) =>
% 97.31/13.19 ((
% 97.31/13.19 (singletoninpowunion) =>
% 97.31/13.19 ((
% 97.31/13.19 (upairset2E) =>
% 97.31/13.19 ((
% 97.31/13.19 (upairsubunion) =>
% 97.31/13.19 ((
% 97.31/13.19 (upairinpowunion) =>
% 97.31/13.19 ((
% 97.31/13.19 (ubforcartprodlem1) =>
% 97.31/13.19 ((
% 97.31/13.19 (ubforcartprodlem2) =>
% 97.31/13.19 ((
% 97.31/13.19 (ubforcartprodlem3) =>
% 97.31/13.19 ((
% 97.31/13.19 (cartprodpairin) =>
% 97.31/13.19 ((
% 97.31/13.19 (cartprodmempair1) =>
% 97.31/13.19 ((
% 97.31/13.19 (cartprodmempair) =>
% 97.31/13.19 ((
% 97.31/13.19 (setunionE2) =>
% 97.31/13.19 ((
% 97.31/13.19 (setunionsingleton1) =>
% 97.31/13.19 ((
% 97.31/13.19 (setunionsingleton2) =>
% 97.31/13.19 ((
% 97.31/13.19 (setunionsingleton) =>
% 97.31/13.19 ((
% 97.31/13.19 (singletonprop) =>
% 97.31/13.19 ((
% 97.31/13.19 (ex1E1) =>
% 97.31/13.19 ((
% 97.31/13.19 (ex1I) =>
% 97.31/13.19 ((
% 97.31/13.19 (ex1I2) =>
% 97.31/13.19 ((
% 97.31/13.19 (singletonsuniq) =>
% 97.31/13.19 ((
% 97.31/13.19 (setukpairinjL1) =>
% 97.31/13.19 ((
% 97.31/13.19 (kfstsingleton) =>
% 97.31/13.19 ((
% 97.31/13.19 (theprop) =>
% 97.31/13.19 ((
% 97.31/13.19 (kfstpairEq) =>
% 97.31/13.19 ((
% 97.31/13.19 (cartprodfstin) =>
% 97.31/13.19 ((
% 97.31/13.19 (setukpairinjL2) =>
% 97.31/13.19 ((
% 97.31/13.19 (setukpairinjL) =>
% 97.31/13.19 ((
% 97.31/13.19 (setukpairinjR11) =>
% 97.31/13.19 ((
% 97.31/13.19 (setukpairinjR12) =>
% 97.31/13.19 ((
% 97.31/13.19 (setukpairinjR1) =>
% 97.31/13.19 ((
% 97.31/13.19 (upairequniteq) =>
% 97.31/13.19 ((
% 97.31/13.19 (setukpairinjR2) =>
% 97.31/13.19 ((
% 97.31/13.19 (setukpairinjR) =>
% 97.31/13.19 ((
% 97.31/13.19 (ksndsingleton) =>
% 97.31/13.19 ((
% 97.31/13.19 (ksndpairEq) =>
% 97.31/13.19 ((
% 97.31/13.19 (kpairsurjEq) =>
% 97.31/13.19 ((
% 97.31/13.19 (cartprodsndin) =>
% 97.31/13.19 ((
% 97.31/13.19 (cartprodpairmemEL) =>
% 97.31/13.19 ((
% 97.31/13.19 (cartprodpairmemER) =>
% 97.31/13.19 ((
% 97.31/13.19 (cartprodmempaircEq) =>
% 97.31/13.19 ((
% 97.31/13.19 (cartprodfstpairEq) =>
% 97.31/13.19 ((
% 97.31/13.19 (cartprodsndpairEq) =>
% 97.31/13.19 ((
% 97.31/13.19 (cartprodpairsurjEq) =>
% 97.31/13.19 ((
% 97.31/13.19 (dpsetconstrI) =>
% 97.31/13.19 ((
% 97.31/13.19 (dpsetconstrSub) =>
% 97.31/13.19 ((
% 97.31/13.19 (setOfPairsIsBReln) =>
% 97.31/13.19 ((
% 97.31/13.19 (dpsetconstrERa) =>
% 97.31/13.19 ((
% 97.31/13.19 (dpsetconstrEL1) =>
% 97.31/13.19 ((
% 97.31/13.19 (dpsetconstrEL2) =>
% 97.31/13.19 ((
% 97.31/13.19 (dpsetconstrER) =>
% 97.31/13.19 ((
% 97.31/13.19 (funcImageSingleton) =>
% 97.31/13.19 ((
% 97.31/13.19 (apProp) =>
% 97.31/13.19 ((
% 97.31/13.19 (app) =>
% 97.31/13.19 ((
% 97.31/13.19 (infuncsetfunc) =>
% 97.31/13.19 ((
% 97.31/13.19 (ap2p) =>
% 97.31/13.19 ((
% 97.31/13.19 (funcinfuncset) =>
% 97.31/13.19 ((
% 97.31/13.19 (lamProp) =>
% 97.31/13.19 ((
% 97.31/13.19 (lamp) =>
% 97.31/13.19 ((
% 97.31/13.19 (lam2p) =>
% 97.31/13.19 ((
% 97.31/13.19 (brelnall1) =>
% 97.31/13.19 ((
% 97.31/13.19 (brelnall2) =>
% 97.31/13.19 ((
% 97.31/13.19 (ex1E2) =>
% 97.31/13.19 ((
% 97.31/13.19 (funcGraphProp1) =>
% 97.31/13.19 ((
% 97.31/13.19 (funcGraphProp3) =>
% 97.31/13.19 ((
% 97.31/13.19 (funcGraphProp2) =>
% 97.31/13.19 ((
% 97.31/13.19 (funcextLem) =>
% 97.31/13.19 ((
% 97.31/13.19 (funcGraphProp4) =>
% 97.31/13.19 ((
% 97.31/13.19 (subbreln) =>
% 97.31/13.19 ((
% 97.31/13.19 (eqbreln) =>
% 97.31/13.19 ((
% 97.31/13.19 (funcext) =>
% 97.31/13.19 ((
% 97.31/13.19 (funcext2) =>
% 97.31/13.19 ((
% 97.31/13.19 (ap2apEq1) =>
% 97.31/13.19 ((
% 97.31/13.19 (ap2apEq2) =>
% 97.31/13.19 ((
% 97.31/13.19 (beta1) =>
% 97.31/13.19 ((
% 97.31/13.19 (eta1) =>
% 97.31/13.19 ((
% 97.31/13.19 (lam2lamEq) =>
% 97.31/13.19 ((
% 97.31/13.19 (beta2) =>
% 97.31/13.19 ((
% 97.31/13.19 (eta2) =>
% 97.31/13.19 ((
% 97.31/13.19 (iffalseProp1) =>
% 97.31/13.19 ((
% 97.31/13.19 (iffalseProp2) =>
% 97.31/13.19 ((
% 97.31/13.19 (iftrueProp1) =>
% 97.31/13.19 ((
% 97.31/13.19 (iftrueProp2) =>
% 97.31/13.19 ((
% 97.31/13.19 (ifSingleton) =>
% 97.31/13.19 ((
% 97.31/13.19 (ifp) =>
% 97.31/13.19 ((
% 97.31/13.19 (theeq) =>
% 97.31/13.19 ((
% 97.31/13.19 (iftrue) =>
% 97.31/13.19 ((
% 97.31/13.19 (iffalse) =>
% 97.31/13.19 ((
% 97.31/13.19 (iftrueorfalse) =>
% 97.31/13.19 ((
% 97.31/13.19 (binintersectT_lem) =>
% 97.31/13.19 ((
% 97.31/13.19 (binunionT_lem) =>
% 97.31/13.19 ((
% 97.31/13.19 (powersetT_lem) =>
% 97.31/13.19 ((
% 97.31/13.19 (setminusT_lem) =>
% 97.31/13.19 ((
% 97.31/13.19 (complementT_lem) =>
% 97.31/13.19 ((
% 97.31/13.19 (setextT) =>
% 97.31/13.19 ((
% 97.31/13.19 (subsetTI) =>
% 97.31/13.19 ((
% 97.31/13.19 (powersetTI1) =>
% 97.31/13.19 ((
% 97.31/13.19 (powersetTE1) =>
% 97.31/13.19 ((
% 97.31/13.19 (complementTI1) =>
% 97.31/13.19 ((
% 97.31/13.19 (complementTE1) =>
% 97.31/13.19 ((
% 97.31/13.19 (binintersectTELcontra) =>
% 97.31/13.19 ((
% 97.31/13.19 (binintersectTERcontra) =>
% 97.31/13.19 ((
% 97.31/13.19 (contrasubsetT) =>
% 97.31/13.19 ((
% 97.31/13.19 (contrasubsetT1) =>
% 97.31/13.19 ((
% 97.31/13.19 (contrasubsetT2) =>
% 97.31/13.19 ((
% 97.31/13.19 (contrasubsetT3) =>
% 97.31/13.19 ((
% 97.31/13.19 (doubleComplementI1) =>
% 97.31/13.19 ((
% 97.31/13.19 (doubleComplementE1) =>
% 97.31/13.19 ((
% 97.31/13.19 (doubleComplementSub1) =>
% 97.31/13.19 ((
% 97.31/13.19 (doubleComplementSub2) =>
% 97.31/13.19 ((
% 97.31/13.19 (doubleComplementEq) =>
% 97.31/13.19 ((
% 97.31/13.19 (complementTnotintersectT) =>
% 97.31/13.19 ((
% 97.31/13.19 (complementImpComplementIntersect) =>
% 97.31/13.19 ((
% 97.31/13.19 (complementSubsetComplementIntersect) =>
% 97.31/13.19 ((
% 97.31/13.19 (complementInPowersetComplementIntersect) =>
% 97.31/13.19 ((
% 97.31/13.19 (contraSubsetComplement) =>
% 97.31/13.19 ((
% 97.31/13.19 (complementTcontraSubset) =>
% 97.31/13.19 ((
% 97.31/13.19 (binunionTILcontra) =>
% 97.31/13.19 ((
% 97.31/13.19 (binunionTIRcontra) =>
% 97.31/13.19 ((
% 97.31/13.19 (inIntersectImpInUnion) =>
% 97.31/13.19 ((
% 97.31/13.19 (inIntersectImpInUnion2) =>
% 97.31/13.19 ((
% 97.31/13.19 (inIntersectImpInIntersectUnions) =>
% 97.31/13.19 ((
% 97.31/13.19 (intersectInPowersetIntersectUnions) =>
% 97.31/13.19 ((
% 97.31/13.19 (inComplementUnionImpNotIn1) =>
% 97.31/13.19 ((
% 97.31/13.19 (inComplementUnionImpInComplement1) =>
% 97.31/13.19 ((
% 97.31/13.19 (binunionTE) =>
% 97.31/13.19 ((
% 97.31/13.19 (binunionTEcontra) =>
% 97.31/13.19 ((
% 97.31/13.19 (demorgan2a1) =>
% 97.31/13.19 ((
% 97.31/13.19 (complementUnionInPowersetComplement) =>
% 97.31/13.19 ((
% 97.31/13.19 (demorgan2a2) =>
% 97.31/13.19 ((
% 97.31/13.19 (demorgan1a) =>
% 97.31/13.19 ((
% 97.31/13.19 (demorgan1b) =>
% 97.31/13.19 ((
% 97.31/13.19 (demorgan1) =>
% 97.31/13.19 ((
% 97.31/13.19 (demorgan2a) =>
% 97.31/13.19 ((
% 97.31/13.19 (demorgan2b2) =>
% 97.31/13.19 ((
% 97.31/13.19 (demorgan2b) =>
% 97.31/13.19 ((
% 97.31/13.19 (demorgan2) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz13rule0) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz13rule1) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz13rule2) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz13rule3) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz13rule4) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz1_1) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz1_2) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz1_3) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz1_4) =>
% 97.31/13.19 ((
% 97.31/13.19 (woz1_5) =>
% 97.31/13.19 ((
% 97.60/13.19 (breln1all2) =>
% 97.60/13.19 ((
% 97.60/13.19 (breln1SetBreln1) =>
% 97.60/13.19 ((
% 97.60/13.19 (choice2fnsingleton) =>
% 97.60/13.19 ((
% 97.60/13.19 (setOfPairsIsBReln1) =>
% 97.60/13.19 ((
% 97.60/13.19 (breln1all1) =>
% 97.60/13.19 ((
% 97.60/13.19 (subbreln1) =>
% 97.60/13.19 ((
% 97.60/13.19 (eqbreln1) =>
% 97.60/13.19 ((
% 97.60/13.19 (breln1invprop) =>
% 97.60/13.19 ((
% 97.60/13.19 (breln1invI) =>
% 97.60/13.19 ((
% 97.60/13.19 (breln1invE) =>
% 97.60/13.19 ((
% 97.60/13.19 (breln1compprop) =>
% 97.60/13.19 ((
% 97.60/13.19 (breln1compI) =>
% 97.60/13.19 ((
% 97.60/13.19 (breln1compE) =>
% 97.60/13.19 ((
% 97.60/13.19 (breln1compEex) =>
% 97.60/13.19 ((
% 97.60/13.19 (breln1unionprop) =>
% 97.60/13.19 ((
% 97.60/13.19 (breln1unionIL) =>
% 97.60/13.19 ((
% 97.60/13.19 (breln1unionIR) =>
% 97.60/13.19 ((
% 97.60/13.19 (breln1unionI) =>
% 97.60/13.19 ((
% 97.60/13.19 (breln1unionE) =>
% 97.60/13.19 ((
% 97.60/13.19 (breln1unionEcases) =>
% 97.60/13.19 ((
% 97.60/13.19 (breln1unionCommutes) =>
% 97.60/13.19 ((
% 97.60/13.19 (woz2Ex) =>
% 97.60/13.19 ((
% 97.60/13.19 (woz2W) =>
% 97.60/13.19 ((
% 97.60/13.19 (woz2A) =>
% 97.60/13.19 ((
% 97.60/13.19 (woz2B) =>
% 97.60/13.19 ((
% 97.60/13.19 (image1Ex) =>
% 97.60/13.19 ((
% 97.60/13.19 (image1Ex1) =>
% 97.60/13.19 ((
% 97.60/13.19 (image1Equiv) =>
% 97.60/13.19 ((
% 97.60/13.19 (image1E) =>
% 97.60/13.19 ((
% 97.60/13.19 (image1I) =>
% 97.60/13.19 ((
% 97.60/13.19 (injFuncInInjFuncSet) =>
% 97.60/13.19 ((
% 97.60/13.19 (injFuncSetFuncIn) =>
% 97.60/13.19 ((
% 97.60/13.19 (injFuncSetFuncInj) =>
% 97.60/13.19 ((
% 97.60/13.19 (surjFuncSetFuncIn) =>
% 97.60/13.19 ((
% 97.60/13.19 (surjFuncSetFuncSurj) =>
% 97.60/13.19 ((
% 97.60/13.19 (leftInvIsSurj) =>
% 97.60/13.19 ((
% 97.60/13.19 (surjCantorThm) =>
% 97.60/13.19 ((
% 97.60/13.19 (foundation2) =>
% 97.60/13.19 ((
% 97.60/13.19 (notinself) =>
% 97.60/13.19 ((
% 97.60/13.19 (notinself2) =>
% 97.60/13.19 ((
% 97.60/13.19 (omegaSp) =>
% 97.60/13.19 ((
% 97.60/13.19 (omegaSclos) =>
% 97.60/13.19 ((
% 97.60/13.19 (peano0notS) =>
% 97.60/13.19 ((
% 97.60/13.19 (!!) @ (
% 97.60/13.19 (('#S') @ (
% 97.60/13.19 (
% 97.60/13.19 ('#B') @ (
% 97.60/13.19 =>) @
% 97.60/13.19 (
% 97.60/13.19 (
% 97.60/13.19 ('#C') @ in @
% 97.60/13.19 omega)))) @
% 97.60/13.19 (
% 97.60/13.19 (
% 97.60/13.19 ('#B') @ (
% 97.60/13.19 !!) @
% 97.60/13.19 (
% 97.60/13.19 (
% 97.60/13.19 ('#B') @ (
% 97.60/13.19 (
% 97.60/13.19 ('#S') @ (
% 97.60/13.19 (
% 97.60/13.19 ('#B') @ (
% 97.60/13.19 =>) @
% 97.60/13.19 (
% 97.60/13.19 (
% 97.60/13.19 ('#C') @ in @
% 97.60/13.19 omega)))))) @
% 97.60/13.19 (
% 97.60/13.19 (
% 97.60/13.19 ('#S') @ (
% 97.60/13.19 (
% 97.60/13.19 ('#B') @ (
% 97.60/13.19 '#S') @
% 97.60/13.19 (
% 97.60/13.19 (
% 97.60/13.19 ('#B') @ (
% 97.60/13.19 (
% 97.60/13.19 ('#B') @ (
% 97.60/13.19 =>))) @
% 97.60/13.19 (
% 97.60/13.19 (
% 97.60/13.19 ('#C') @ (
% 97.60/13.19 (
% 97.60/13.19 ('#B') @ (
% 97.60/13.19 '#B') @
% 97.60/13.19 (
% 97.60/13.19 (
% 97.60/13.19 ('#B') @ (
% 97.60/13.19 =) @
% 97.60/13.19 omegaS)))) @
% 97.60/13.19 omegaS)))))) @
% 97.60/13.19 (
% 97.60/13.19 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.60/13.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl496])).
% 97.60/13.19 thf(zip_derived_cl517, plain,
% 97.60/13.19 (~ (((emptyE1) =>
% 97.60/13.19 (((vacuousDall) =>
% 97.60/13.19 (((quantDeMorgan1) =>
% 97.60/13.19 (((quantDeMorgan2) =>
% 97.60/13.19 (((quantDeMorgan3) =>
% 97.60/13.19 (((quantDeMorgan4) =>
% 97.60/13.19 (((prop2setI) =>
% 97.60/13.19 (((prop2set2propI) =>
% 97.60/13.19 (((notdexE) =>
% 97.60/13.19 (((notdallE) =>
% 97.60/13.19 (((exuI1) =>
% 97.60/13.19 (((exuI3) =>
% 97.60/13.19 (((exuI2) =>
% 97.60/13.19 (((inCongP) =>
% 97.60/13.19 (((in__Cong) =>
% 97.60/13.19 (((exuE3u) =>
% 97.60/13.19 (((exu__Cong) =>
% 97.60/13.19 (((setadjoin__Cong) =>
% 97.60/13.19 (((powerset__Cong) =>
% 97.60/13.19 (((setunion__Cong) =>
% 97.60/13.19 (((exuEu) =>
% 97.60/13.19 (((descr__Cong) =>
% 97.60/13.19 (((dsetconstr__Cong) =>
% 97.60/13.19 (((subsetI1) =>
% 97.60/13.19 (((eqimpsubset2) =>
% 97.60/13.19 (((eqimpsubset1) =>
% 97.60/13.19 (((subsetI2) =>
% 97.60/13.19 (((emptysetsubset) =>
% 97.60/13.19 (((subsetE) =>
% 97.60/13.19 (((subsetE2) =>
% 97.60/13.19 ((
% 97.60/13.19 (notsubsetI) =>
% 97.60/13.19 ((
% 97.60/13.19 (notequalI1) =>
% 97.60/13.19 ((
% 97.60/13.19 (notequalI2) =>
% 97.60/13.19 ((
% 97.60/13.19 (subsetRefl) =>
% 97.60/13.19 ((
% 97.60/13.19 (subsetTrans) =>
% 97.60/13.19 ((
% 97.60/13.19 (setadjoinSub) =>
% 97.60/13.19 ((
% 97.60/13.19 (setadjoinSub2) =>
% 97.60/13.19 ((
% 97.60/13.19 (subset2powerset) =>
% 97.60/13.19 ((
% 97.60/13.19 (setextsub) =>
% 97.60/13.19 ((
% 97.60/13.19 (subsetemptysetimpeq) =>
% 97.60/13.19 ((
% 97.60/13.19 (powersetI1) =>
% 97.60/13.19 ((
% 97.60/13.19 (powersetE1) =>
% 97.60/13.19 ((
% 97.60/13.19 (inPowerset) =>
% 97.60/13.19 ((
% 97.60/13.19 (powersetsubset) =>
% 97.60/13.19 ((
% 97.60/13.19 (sepInPowerset) =>
% 97.60/13.19 ((
% 97.60/13.19 (sepSubset) =>
% 97.60/13.19 ((
% 97.60/13.19 (binunionIL) =>
% 97.60/13.19 ((
% 97.60/13.19 (upairset2IR) =>
% 97.60/13.19 ((
% 97.60/13.19 (binunionIR) =>
% 97.60/13.19 ((
% 97.60/13.19 (binunionEcases) =>
% 97.60/13.19 ((
% 97.60/13.19 (binunionE) =>
% 97.60/13.19 ((
% 97.60/13.19 (binunionLsub) =>
% 97.60/13.19 ((
% 97.60/13.19 (binunionRsub) =>
% 97.60/13.19 ((
% 97.60/13.19 (binintersectI) =>
% 97.60/13.19 ((
% 97.60/13.19 (binintersectSubset5) =>
% 97.60/13.19 ((
% 97.60/13.19 (binintersectEL) =>
% 97.60/13.19 ((
% 97.60/13.19 (binintersectLsub) =>
% 97.60/13.19 ((
% 97.60/13.19 (binintersectSubset2) =>
% 97.60/13.19 ((
% 97.60/13.19 (binintersectSubset3) =>
% 97.60/13.19 ((
% 97.60/13.19 (binintersectER) =>
% 97.60/13.19 ((
% 97.60/13.19 (disjointsetsI1) =>
% 97.60/13.19 ((
% 97.60/13.19 (binintersectRsub) =>
% 97.60/13.19 ((
% 97.60/13.19 (binintersectSubset4) =>
% 97.60/13.19 ((
% 97.60/13.19 (binintersectSubset1) =>
% 97.60/13.19 ((
% 97.60/13.19 (bs114d) =>
% 97.60/13.19 ((
% 97.60/13.19 (setminusI) =>
% 97.60/13.19 ((
% 97.60/13.19 (setminusEL) =>
% 97.60/13.19 ((
% 97.60/13.19 (setminusER) =>
% 97.60/13.19 ((
% 97.60/13.19 (setminusSubset2) =>
% 97.60/13.19 ((
% 97.60/13.19 (setminusERneg) =>
% 97.60/13.19 ((
% 97.60/13.19 (setminusELneg) =>
% 97.60/13.19 ((
% 97.60/13.19 (setminusILneg) =>
% 97.60/13.19 ((
% 97.60/13.19 (setminusIRneg) =>
% 97.60/13.19 ((
% 97.60/13.19 (setminusLsub) =>
% 97.60/13.19 ((
% 97.60/13.19 (setminusSubset1) =>
% 97.60/13.19 ((
% 97.60/13.19 (symdiffE) =>
% 97.60/13.19 ((
% 97.60/13.19 (symdiffI1) =>
% 97.60/13.19 ((
% 97.60/13.19 (symdiffI2) =>
% 97.60/13.19 ((
% 97.60/13.19 (symdiffIneg1) =>
% 97.60/13.19 ((
% 97.60/13.19 (symdiffIneg2) =>
% 97.60/13.19 ((
% 97.60/13.19 (secondinupair) =>
% 97.60/13.19 ((
% 97.60/13.19 (setukpairIL) =>
% 97.60/13.19 ((
% 97.60/13.19 (setukpairIR) =>
% 97.60/13.19 ((
% 97.60/13.19 (kpairiskpair) =>
% 97.60/13.19 ((
% 97.60/13.19 (kpairp) =>
% 97.60/13.19 ((
% 97.60/13.19 (singletonsubset) =>
% 97.60/13.19 ((
% 97.60/13.19 (singletoninpowerset) =>
% 97.60/13.19 ((
% 97.60/13.19 (singletoninpowunion) =>
% 97.60/13.19 ((
% 97.60/13.19 (upairset2E) =>
% 97.60/13.19 ((
% 97.60/13.19 (upairsubunion) =>
% 97.60/13.19 ((
% 97.60/13.19 (upairinpowunion) =>
% 97.60/13.19 ((
% 97.60/13.19 (ubforcartprodlem1) =>
% 97.60/13.19 ((
% 97.60/13.19 (ubforcartprodlem2) =>
% 97.60/13.19 ((
% 97.60/13.19 (ubforcartprodlem3) =>
% 97.60/13.19 ((
% 97.60/13.19 (cartprodpairin) =>
% 97.60/13.19 ((
% 97.60/13.19 (cartprodmempair1) =>
% 97.60/13.19 ((
% 97.60/13.19 (cartprodmempair) =>
% 97.60/13.19 ((
% 97.60/13.19 (setunionE2) =>
% 97.60/13.19 ((
% 97.60/13.19 (setunionsingleton1) =>
% 97.60/13.19 ((
% 97.60/13.19 (setunionsingleton2) =>
% 97.60/13.19 ((
% 97.60/13.19 (setunionsingleton) =>
% 97.60/13.19 ((
% 97.60/13.19 (singletonprop) =>
% 97.60/13.19 ((
% 97.60/13.19 (ex1E1) =>
% 97.60/13.19 ((
% 97.60/13.19 (ex1I) =>
% 97.60/13.19 ((
% 97.60/13.19 (ex1I2) =>
% 97.60/13.19 ((
% 97.60/13.19 (singletonsuniq) =>
% 97.60/13.19 ((
% 97.60/13.19 (setukpairinjL1) =>
% 97.60/13.19 ((
% 97.60/13.19 (kfstsingleton) =>
% 97.60/13.19 ((
% 97.60/13.19 (theprop) =>
% 97.60/13.19 ((
% 97.60/13.19 (kfstpairEq) =>
% 97.60/13.19 ((
% 97.60/13.19 (cartprodfstin) =>
% 97.60/13.19 ((
% 97.60/13.19 (setukpairinjL2) =>
% 97.60/13.19 ((
% 97.60/13.19 (setukpairinjL) =>
% 97.60/13.19 ((
% 97.60/13.19 (setukpairinjR11) =>
% 97.60/13.19 ((
% 97.60/13.19 (setukpairinjR12) =>
% 97.60/13.19 ((
% 97.60/13.19 (setukpairinjR1) =>
% 97.60/13.19 ((
% 97.60/13.19 (upairequniteq) =>
% 97.60/13.19 ((
% 97.60/13.19 (setukpairinjR2) =>
% 97.60/13.19 ((
% 97.60/13.19 (setukpairinjR) =>
% 97.60/13.19 ((
% 97.60/13.19 (ksndsingleton) =>
% 97.60/13.19 ((
% 97.60/13.19 (ksndpairEq) =>
% 97.60/13.19 ((
% 97.60/13.19 (kpairsurjEq) =>
% 97.60/13.19 ((
% 97.60/13.19 (cartprodsndin) =>
% 97.60/13.19 ((
% 97.60/13.19 (cartprodpairmemEL) =>
% 97.60/13.19 ((
% 97.60/13.19 (cartprodpairmemER) =>
% 97.60/13.19 ((
% 97.60/13.19 (cartprodmempaircEq) =>
% 97.60/13.19 ((
% 97.60/13.19 (cartprodfstpairEq) =>
% 97.60/13.19 ((
% 97.60/13.19 (cartprodsndpairEq) =>
% 97.60/13.19 ((
% 97.60/13.19 (cartprodpairsurjEq) =>
% 97.60/13.19 ((
% 97.60/13.19 (dpsetconstrI) =>
% 97.60/13.19 ((
% 97.60/13.19 (dpsetconstrSub) =>
% 97.60/13.19 ((
% 97.60/13.19 (setOfPairsIsBReln) =>
% 97.60/13.19 ((
% 97.60/13.19 (dpsetconstrERa) =>
% 97.60/13.19 ((
% 97.60/13.19 (dpsetconstrEL1) =>
% 97.60/13.19 ((
% 97.60/13.19 (dpsetconstrEL2) =>
% 97.60/13.19 ((
% 97.60/13.19 (dpsetconstrER) =>
% 97.60/13.19 ((
% 97.60/13.19 (funcImageSingleton) =>
% 97.60/13.19 ((
% 97.60/13.19 (apProp) =>
% 97.60/13.19 ((
% 97.60/13.19 (app) =>
% 97.60/13.19 ((
% 97.60/13.19 (infuncsetfunc) =>
% 97.60/13.19 ((
% 97.60/13.19 (ap2p) =>
% 97.60/13.19 ((
% 97.60/13.19 (funcinfuncset) =>
% 97.60/13.19 ((
% 97.60/13.19 (lamProp) =>
% 97.60/13.19 ((
% 97.60/13.19 (lamp) =>
% 97.60/13.19 ((
% 97.60/13.19 (lam2p) =>
% 97.60/13.19 ((
% 97.60/13.19 (brelnall1) =>
% 97.60/13.19 ((
% 97.60/13.19 (brelnall2) =>
% 97.60/13.19 ((
% 97.60/13.19 (ex1E2) =>
% 97.60/13.19 ((
% 97.60/13.19 (funcGraphProp1) =>
% 97.60/13.19 ((
% 97.60/13.19 (funcGraphProp3) =>
% 97.60/13.19 ((
% 97.60/13.19 (funcGraphProp2) =>
% 97.60/13.19 ((
% 97.60/13.19 (funcextLem) =>
% 97.60/13.19 ((
% 97.60/13.19 (funcGraphProp4) =>
% 97.60/13.19 ((
% 97.60/13.19 (subbreln) =>
% 97.60/13.19 ((
% 97.60/13.19 (eqbreln) =>
% 97.60/13.19 ((
% 97.60/13.19 (funcext) =>
% 97.60/13.19 ((
% 97.60/13.19 (funcext2) =>
% 97.60/13.19 ((
% 97.60/13.19 (ap2apEq1) =>
% 97.60/13.19 ((
% 97.60/13.19 (ap2apEq2) =>
% 97.60/13.19 ((
% 97.60/13.19 (beta1) =>
% 97.60/13.19 ((
% 97.60/13.19 (eta1) =>
% 97.60/13.19 ((
% 97.60/13.19 (lam2lamEq) =>
% 97.60/13.19 ((
% 97.60/13.19 (beta2) =>
% 97.60/13.19 ((
% 97.60/13.19 (eta2) =>
% 97.60/13.19 ((
% 97.60/13.19 (iffalseProp1) =>
% 97.60/13.19 ((
% 97.60/13.19 (iffalseProp2) =>
% 97.60/13.19 ((
% 97.60/13.19 (iftrueProp1) =>
% 97.60/13.19 ((
% 97.60/13.19 (iftrueProp2) =>
% 97.60/13.19 ((
% 97.60/13.19 (ifSingleton) =>
% 97.60/13.19 ((
% 97.60/13.19 (ifp) =>
% 97.60/13.19 ((
% 97.60/13.19 (theeq) =>
% 97.60/13.19 ((
% 97.60/13.19 (iftrue) =>
% 97.60/13.19 ((
% 97.60/13.19 (iffalse) =>
% 97.60/13.19 ((
% 97.60/13.19 (iftrueorfalse) =>
% 97.60/13.19 ((
% 97.60/13.19 (binintersectT_lem) =>
% 97.60/13.19 ((
% 97.60/13.19 (binunionT_lem) =>
% 97.60/13.19 ((
% 97.60/13.19 (powersetT_lem) =>
% 97.60/13.19 ((
% 97.60/13.19 (setminusT_lem) =>
% 97.60/13.19 ((
% 97.60/13.19 (complementT_lem) =>
% 97.60/13.19 ((
% 97.60/13.19 (setextT) =>
% 97.60/13.19 ((
% 97.60/13.19 (subsetTI) =>
% 97.60/13.19 ((
% 97.60/13.19 (powersetTI1) =>
% 97.60/13.19 ((
% 97.60/13.19 (powersetTE1) =>
% 97.60/13.19 ((
% 97.60/13.19 (complementTI1) =>
% 97.60/13.19 ((
% 97.60/13.19 (complementTE1) =>
% 97.60/13.19 ((
% 97.60/13.19 (binintersectTELcontra) =>
% 97.60/13.19 ((
% 97.60/13.19 (binintersectTERcontra) =>
% 97.60/13.19 ((
% 97.60/13.19 (contrasubsetT) =>
% 97.60/13.19 ((
% 97.60/13.19 (contrasubsetT1) =>
% 97.60/13.19 ((
% 97.60/13.19 (contrasubsetT2) =>
% 97.60/13.19 ((
% 97.60/13.19 (contrasubsetT3) =>
% 97.60/13.19 ((
% 97.60/13.19 (doubleComplementI1) =>
% 97.60/13.19 ((
% 97.60/13.19 (doubleComplementE1) =>
% 97.60/13.19 ((
% 97.60/13.19 (doubleComplementSub1) =>
% 97.60/13.19 ((
% 97.60/13.19 (doubleComplementSub2) =>
% 97.60/13.19 ((
% 97.60/13.19 (doubleComplementEq) =>
% 97.60/13.19 ((
% 97.60/13.19 (complementTnotintersectT) =>
% 97.60/13.19 ((
% 97.60/13.19 (complementImpComplementIntersect) =>
% 97.60/13.19 ((
% 97.60/13.19 (complementSubsetComplementIntersect) =>
% 97.60/13.19 ((
% 97.60/13.19 (complementInPowersetComplementIntersect) =>
% 97.60/13.19 ((
% 97.60/13.19 (contraSubsetComplement) =>
% 97.60/13.19 ((
% 97.60/13.19 (complementTcontraSubset) =>
% 97.60/13.19 ((
% 97.60/13.19 (binunionTILcontra) =>
% 97.60/13.19 ((
% 97.60/13.19 (binunionTIRcontra) =>
% 97.60/13.19 ((
% 97.60/13.19 (inIntersectImpInUnion) =>
% 97.60/13.19 ((
% 97.60/13.19 (inIntersectImpInUnion2) =>
% 97.60/13.19 ((
% 97.60/13.19 (inIntersectImpInIntersectUnions) =>
% 97.60/13.19 ((
% 97.60/13.19 (intersectInPowersetIntersectUnions) =>
% 97.60/13.19 ((
% 97.60/13.19 (inComplementUnionImpNotIn1) =>
% 97.60/13.19 ((
% 97.60/13.19 (inComplementUnionImpInComplement1) =>
% 97.60/13.19 ((
% 97.60/13.19 (binunionTE) =>
% 97.60/13.19 ((
% 97.60/13.19 (binunionTEcontra) =>
% 97.60/13.19 ((
% 97.60/13.19 (demorgan2a1) =>
% 97.60/13.19 ((
% 97.60/13.19 (complementUnionInPowersetComplement) =>
% 97.60/13.19 ((
% 97.60/13.19 (demorgan2a2) =>
% 97.60/13.19 ((
% 97.60/13.19 (demorgan1a) =>
% 97.60/13.19 ((
% 97.60/13.19 (demorgan1b) =>
% 97.60/13.19 ((
% 97.60/13.19 (demorgan1) =>
% 97.60/13.19 ((
% 97.60/13.19 (demorgan2a) =>
% 97.60/13.19 ((
% 97.60/13.19 (demorgan2b2) =>
% 97.60/13.19 ((
% 97.60/13.19 (demorgan2b) =>
% 97.60/13.19 ((
% 97.60/13.19 (demorgan2) =>
% 97.60/13.19 ((
% 97.60/13.19 (woz13rule0) =>
% 97.60/13.19 ((
% 97.60/13.19 (woz13rule1) =>
% 97.60/13.19 ((
% 97.60/13.19 (woz13rule2) =>
% 97.60/13.19 ((
% 97.60/13.19 (woz13rule3) =>
% 97.60/13.19 ((
% 97.60/13.19 (woz13rule4) =>
% 97.60/13.19 ((
% 97.60/13.19 (woz1_1) =>
% 97.60/13.19 ((
% 97.60/13.19 (woz1_2) =>
% 97.60/13.19 ((
% 97.60/13.19 (woz1_3) =>
% 97.60/13.19 ((
% 97.60/13.19 (woz1_4) =>
% 97.60/13.19 ((
% 97.60/13.19 (woz1_5) =>
% 97.60/13.19 ((
% 97.60/13.19 (breln1all2) =>
% 97.60/13.19 ((
% 97.60/13.19 (breln1SetBreln1) =>
% 97.60/13.19 ((
% 97.60/13.19 (choice2fnsingleton) =>
% 97.60/13.19 ((
% 97.60/13.19 (setOfPairsIsBReln1) =>
% 97.60/13.19 ((
% 97.60/13.19 (breln1all1) =>
% 97.60/13.19 ((
% 97.60/13.19 (subbreln1) =>
% 97.60/13.19 ((
% 97.60/13.19 (eqbreln1) =>
% 97.60/13.19 ((
% 97.60/13.19 (breln1invprop) =>
% 97.60/13.19 ((
% 97.60/13.19 (breln1invI) =>
% 97.60/13.19 ((
% 97.60/13.19 (breln1invE) =>
% 97.60/13.19 ((
% 97.60/13.19 (breln1compprop) =>
% 97.60/13.19 ((
% 97.60/13.19 (breln1compI) =>
% 97.60/13.19 ((
% 97.60/13.19 (breln1compE) =>
% 97.60/13.19 ((
% 97.60/13.19 (breln1compEex) =>
% 97.60/13.19 ((
% 97.60/13.19 (breln1unionprop) =>
% 97.60/13.19 ((
% 97.60/13.19 (breln1unionIL) =>
% 97.60/13.19 ((
% 97.60/13.19 (breln1unionIR) =>
% 97.60/13.19 ((
% 97.60/13.19 (breln1unionI) =>
% 97.60/13.19 ((
% 97.60/13.19 (breln1unionE) =>
% 97.60/13.19 ((
% 97.60/13.19 (breln1unionEcases) =>
% 97.60/13.19 ((
% 97.60/13.19 (breln1unionCommutes) =>
% 97.60/13.19 ((
% 97.60/13.19 (woz2Ex) =>
% 97.60/13.19 ((
% 97.60/13.19 (woz2W) =>
% 97.60/13.19 ((
% 97.60/13.19 (woz2A) =>
% 97.60/13.19 ((
% 97.60/13.19 (woz2B) =>
% 97.60/13.19 ((
% 97.60/13.19 (image1Ex) =>
% 97.60/13.19 ((
% 97.60/13.19 (image1Ex1) =>
% 97.60/13.19 ((
% 97.60/13.19 (image1Equiv) =>
% 97.60/13.19 ((
% 97.60/13.19 (image1E) =>
% 97.60/13.19 ((
% 97.60/13.19 (image1I) =>
% 97.60/13.19 ((
% 97.60/13.19 (injFuncInInjFuncSet) =>
% 97.60/13.19 ((
% 97.60/13.19 (injFuncSetFuncIn) =>
% 97.60/13.19 ((
% 97.60/13.19 (injFuncSetFuncInj) =>
% 97.60/13.19 ((
% 97.60/13.19 (surjFuncSetFuncIn) =>
% 97.60/13.19 ((
% 97.60/13.19 (surjFuncSetFuncSurj) =>
% 97.60/13.19 ((
% 97.60/13.19 (leftInvIsSurj) =>
% 97.60/13.19 ((
% 97.60/13.19 (surjCantorThm) =>
% 97.60/13.19 ((
% 97.60/13.19 (foundation2) =>
% 97.60/13.19 ((
% 97.60/13.19 (notinself) =>
% 97.60/13.19 ((
% 97.60/13.19 (notinself2) =>
% 97.60/13.19 ((
% 97.60/13.19 (omegaSp) =>
% 97.60/13.19 ((
% 97.60/13.19 (omegaSclos) =>
% 97.60/13.19 ((
% 97.60/13.19 (peano0notS) =>
% 97.60/13.19 ((
% 97.60/13.19 (!!) @ (
% 97.60/13.19 (('#S') @ (
% 97.60/13.19 (
% 97.60/13.19 ('#B') @ (
% 97.60/13.19 =>) @
% 97.60/13.19 (
% 97.60/13.19 (
% 97.60/13.19 ('#C') @ in @
% 97.60/13.19 omega)))) @
% 97.60/13.19 (
% 97.60/13.19 (
% 97.60/13.19 ('#B') @ (
% 97.60/13.19 !!) @
% 97.60/13.19 (
% 97.60/13.19 (
% 97.60/13.19 ('#B') @ (
% 97.60/13.19 (
% 97.60/13.19 ('#S') @ (
% 97.60/13.19 (
% 97.60/13.19 ('#B') @ (
% 97.60/13.19 =>) @
% 97.60/13.19 (
% 97.60/13.19 (
% 97.60/13.19 ('#C') @ in @
% 97.60/13.19 omega)))))) @
% 97.60/13.19 (
% 97.60/13.19 (
% 97.60/13.19 ('#S') @ (
% 97.60/13.19 (
% 97.60/13.19 ('#B') @ (
% 97.60/13.19 '#S') @
% 97.60/13.19 (
% 97.60/13.19 (
% 97.60/13.19 ('#B') @ (
% 97.60/13.19 (
% 97.60/13.19 ('#B') @ (
% 97.60/13.19 =>))) @
% 97.60/13.19 (
% 97.60/13.19 (
% 97.60/13.19 ('#C') @ (
% 97.60/13.19 (
% 97.60/13.19 ('#B') @ (
% 97.60/13.19 '#B') @
% 97.60/13.19 (
% 97.60/13.19 (
% 97.60/13.19 ('#B') @ (
% 97.60/13.19 =) @
% 97.60/13.19 omegaS)))) @
% 97.60/13.19 omegaS)))))) @
% 97.60/13.19 (
% 97.60/13.19 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.60/13.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl507])).
% 97.60/13.19 thf(zip_derived_cl528, plain,
% 97.60/13.19 (~ (((vacuousDall) =>
% 97.60/13.19 (((quantDeMorgan1) =>
% 97.60/13.19 (((quantDeMorgan2) =>
% 97.60/13.19 (((quantDeMorgan3) =>
% 97.60/13.19 (((quantDeMorgan4) =>
% 97.60/13.19 (((prop2setI) =>
% 97.60/13.19 (((prop2set2propI) =>
% 97.60/13.19 (((notdexE) =>
% 97.60/13.19 (((notdallE) =>
% 97.60/13.19 (((exuI1) =>
% 97.60/13.19 (((exuI3) =>
% 97.60/13.19 (((exuI2) =>
% 97.60/13.19 (((inCongP) =>
% 97.60/13.19 (((in__Cong) =>
% 97.60/13.19 (((exuE3u) =>
% 97.60/13.19 (((exu__Cong) =>
% 97.60/13.19 (((setadjoin__Cong) =>
% 97.60/13.19 (((powerset__Cong) =>
% 97.60/13.19 (((setunion__Cong) =>
% 97.60/13.19 (((exuEu) =>
% 97.60/13.19 (((descr__Cong) =>
% 97.60/13.19 (((dsetconstr__Cong) =>
% 97.60/13.19 (((subsetI1) =>
% 97.60/13.19 (((eqimpsubset2) =>
% 97.60/13.19 (((eqimpsubset1) =>
% 97.60/13.19 (((subsetI2) =>
% 97.60/13.19 (((emptysetsubset) =>
% 97.60/13.19 (((subsetE) =>
% 97.60/13.19 (((subsetE2) =>
% 97.60/13.19 (((notsubsetI) =>
% 97.60/13.19 ((
% 97.60/13.19 (notequalI1) =>
% 97.60/13.19 ((
% 97.60/13.19 (notequalI2) =>
% 97.60/13.19 ((
% 97.60/13.19 (subsetRefl) =>
% 97.60/13.19 ((
% 97.60/13.19 (subsetTrans) =>
% 97.60/13.19 ((
% 97.60/13.19 (setadjoinSub) =>
% 97.60/13.19 ((
% 97.60/13.19 (setadjoinSub2) =>
% 97.60/13.19 ((
% 97.60/13.19 (subset2powerset) =>
% 97.60/13.19 ((
% 97.60/13.19 (setextsub) =>
% 97.60/13.19 ((
% 97.60/13.19 (subsetemptysetimpeq) =>
% 97.60/13.19 ((
% 97.60/13.19 (powersetI1) =>
% 97.60/13.19 ((
% 97.60/13.19 (powersetE1) =>
% 97.60/13.19 ((
% 97.60/13.19 (inPowerset) =>
% 97.60/13.19 ((
% 97.60/13.19 (powersetsubset) =>
% 97.60/13.19 ((
% 97.60/13.19 (sepInPowerset) =>
% 97.60/13.19 ((
% 97.60/13.19 (sepSubset) =>
% 97.60/13.19 ((
% 97.60/13.19 (binunionIL) =>
% 97.60/13.19 ((
% 97.60/13.19 (upairset2IR) =>
% 97.60/13.19 ((
% 97.60/13.19 (binunionIR) =>
% 97.60/13.19 ((
% 97.60/13.19 (binunionEcases) =>
% 97.60/13.19 ((
% 97.60/13.19 (binunionE) =>
% 97.60/13.19 ((
% 97.60/13.19 (binunionLsub) =>
% 97.60/13.19 ((
% 97.60/13.19 (binunionRsub) =>
% 97.60/13.19 ((
% 97.60/13.19 (binintersectI) =>
% 97.60/13.19 ((
% 97.60/13.19 (binintersectSubset5) =>
% 97.60/13.19 ((
% 97.60/13.19 (binintersectEL) =>
% 97.60/13.19 ((
% 97.60/13.19 (binintersectLsub) =>
% 97.60/13.19 ((
% 97.60/13.19 (binintersectSubset2) =>
% 97.60/13.19 ((
% 97.60/13.19 (binintersectSubset3) =>
% 97.60/13.19 ((
% 97.60/13.19 (binintersectER) =>
% 97.60/13.19 ((
% 97.60/13.19 (disjointsetsI1) =>
% 97.60/13.19 ((
% 97.60/13.19 (binintersectRsub) =>
% 97.60/13.19 ((
% 97.60/13.19 (binintersectSubset4) =>
% 97.60/13.19 ((
% 97.60/13.19 (binintersectSubset1) =>
% 97.60/13.19 ((
% 97.60/13.19 (bs114d) =>
% 97.60/13.19 ((
% 97.60/13.19 (setminusI) =>
% 97.60/13.19 ((
% 97.60/13.19 (setminusEL) =>
% 97.60/13.19 ((
% 97.60/13.19 (setminusER) =>
% 97.60/13.19 ((
% 97.60/13.19 (setminusSubset2) =>
% 97.60/13.19 ((
% 97.60/13.19 (setminusERneg) =>
% 97.60/13.19 ((
% 97.60/13.19 (setminusELneg) =>
% 97.60/13.19 ((
% 97.60/13.19 (setminusILneg) =>
% 97.60/13.19 ((
% 97.60/13.19 (setminusIRneg) =>
% 97.60/13.19 ((
% 97.60/13.19 (setminusLsub) =>
% 97.60/13.19 ((
% 97.60/13.19 (setminusSubset1) =>
% 97.60/13.19 ((
% 97.60/13.19 (symdiffE) =>
% 97.60/13.19 ((
% 97.60/13.19 (symdiffI1) =>
% 97.60/13.19 ((
% 97.60/13.19 (symdiffI2) =>
% 97.60/13.19 ((
% 97.60/13.19 (symdiffIneg1) =>
% 97.60/13.19 ((
% 97.60/13.19 (symdiffIneg2) =>
% 97.60/13.19 ((
% 97.60/13.19 (secondinupair) =>
% 97.60/13.19 ((
% 97.60/13.19 (setukpairIL) =>
% 97.60/13.19 ((
% 97.60/13.19 (setukpairIR) =>
% 97.60/13.19 ((
% 97.60/13.19 (kpairiskpair) =>
% 97.60/13.19 ((
% 97.60/13.19 (kpairp) =>
% 97.60/13.19 ((
% 97.60/13.19 (singletonsubset) =>
% 97.60/13.19 ((
% 97.60/13.19 (singletoninpowerset) =>
% 97.60/13.19 ((
% 97.60/13.19 (singletoninpowunion) =>
% 97.60/13.19 ((
% 97.60/13.19 (upairset2E) =>
% 97.60/13.19 ((
% 97.60/13.19 (upairsubunion) =>
% 97.60/13.19 ((
% 97.60/13.19 (upairinpowunion) =>
% 97.60/13.19 ((
% 97.60/13.19 (ubforcartprodlem1) =>
% 97.60/13.19 ((
% 97.60/13.19 (ubforcartprodlem2) =>
% 97.60/13.19 ((
% 97.60/13.19 (ubforcartprodlem3) =>
% 97.60/13.19 ((
% 97.60/13.19 (cartprodpairin) =>
% 97.60/13.19 ((
% 97.60/13.19 (cartprodmempair1) =>
% 97.60/13.19 ((
% 97.60/13.19 (cartprodmempair) =>
% 97.60/13.19 ((
% 97.60/13.19 (setunionE2) =>
% 97.60/13.19 ((
% 97.60/13.19 (setunionsingleton1) =>
% 97.60/13.19 ((
% 97.60/13.19 (setunionsingleton2) =>
% 97.60/13.19 ((
% 97.60/13.19 (setunionsingleton) =>
% 97.60/13.19 ((
% 97.60/13.19 (singletonprop) =>
% 97.60/13.19 ((
% 97.60/13.19 (ex1E1) =>
% 97.60/13.19 ((
% 97.60/13.19 (ex1I) =>
% 97.60/13.19 ((
% 97.60/13.19 (ex1I2) =>
% 97.60/13.19 ((
% 97.60/13.19 (singletonsuniq) =>
% 97.60/13.19 ((
% 97.60/13.19 (setukpairinjL1) =>
% 97.60/13.19 ((
% 97.60/13.19 (kfstsingleton) =>
% 97.60/13.19 ((
% 97.60/13.19 (theprop) =>
% 97.60/13.19 ((
% 97.60/13.19 (kfstpairEq) =>
% 97.60/13.19 ((
% 97.60/13.19 (cartprodfstin) =>
% 97.60/13.19 ((
% 97.60/13.19 (setukpairinjL2) =>
% 97.60/13.19 ((
% 97.60/13.19 (setukpairinjL) =>
% 97.60/13.19 ((
% 97.60/13.19 (setukpairinjR11) =>
% 97.60/13.19 ((
% 97.60/13.19 (setukpairinjR12) =>
% 97.60/13.19 ((
% 97.60/13.19 (setukpairinjR1) =>
% 97.60/13.19 ((
% 97.60/13.19 (upairequniteq) =>
% 97.60/13.19 ((
% 97.60/13.19 (setukpairinjR2) =>
% 97.60/13.19 ((
% 97.60/13.19 (setukpairinjR) =>
% 97.60/13.19 ((
% 97.60/13.19 (ksndsingleton) =>
% 97.60/13.19 ((
% 97.60/13.19 (ksndpairEq) =>
% 97.60/13.19 ((
% 97.60/13.19 (kpairsurjEq) =>
% 97.60/13.19 ((
% 97.60/13.19 (cartprodsndin) =>
% 97.60/13.19 ((
% 97.60/13.19 (cartprodpairmemEL) =>
% 97.60/13.19 ((
% 97.60/13.19 (cartprodpairmemER) =>
% 97.60/13.19 ((
% 97.60/13.19 (cartprodmempaircEq) =>
% 97.60/13.19 ((
% 97.60/13.19 (cartprodfstpairEq) =>
% 97.60/13.19 ((
% 97.60/13.19 (cartprodsndpairEq) =>
% 97.60/13.19 ((
% 97.60/13.19 (cartprodpairsurjEq) =>
% 97.60/13.19 ((
% 97.60/13.19 (dpsetconstrI) =>
% 97.60/13.19 ((
% 97.60/13.19 (dpsetconstrSub) =>
% 97.60/13.19 ((
% 97.60/13.19 (setOfPairsIsBReln) =>
% 97.60/13.19 ((
% 97.60/13.19 (dpsetconstrERa) =>
% 97.60/13.19 ((
% 97.60/13.19 (dpsetconstrEL1) =>
% 97.60/13.19 ((
% 97.60/13.19 (dpsetconstrEL2) =>
% 97.60/13.19 ((
% 97.60/13.19 (dpsetconstrER) =>
% 97.60/13.19 ((
% 97.60/13.19 (funcImageSingleton) =>
% 97.60/13.19 ((
% 97.60/13.19 (apProp) =>
% 97.60/13.19 ((
% 97.60/13.19 (app) =>
% 97.60/13.19 ((
% 97.60/13.19 (infuncsetfunc) =>
% 97.60/13.19 ((
% 97.60/13.19 (ap2p) =>
% 97.60/13.19 ((
% 97.60/13.19 (funcinfuncset) =>
% 97.60/13.19 ((
% 97.60/13.19 (lamProp) =>
% 97.60/13.19 ((
% 97.60/13.19 (lamp) =>
% 97.60/13.19 ((
% 97.60/13.19 (lam2p) =>
% 97.60/13.19 ((
% 97.60/13.19 (brelnall1) =>
% 97.60/13.19 ((
% 97.60/13.19 (brelnall2) =>
% 97.60/13.19 ((
% 97.60/13.19 (ex1E2) =>
% 97.60/13.19 ((
% 97.60/13.19 (funcGraphProp1) =>
% 97.60/13.19 ((
% 97.60/13.19 (funcGraphProp3) =>
% 97.60/13.19 ((
% 97.60/13.19 (funcGraphProp2) =>
% 97.60/13.19 ((
% 97.60/13.19 (funcextLem) =>
% 97.60/13.19 ((
% 97.60/13.19 (funcGraphProp4) =>
% 97.60/13.19 ((
% 97.60/13.19 (subbreln) =>
% 97.60/13.19 ((
% 97.60/13.19 (eqbreln) =>
% 97.60/13.19 ((
% 97.60/13.19 (funcext) =>
% 97.60/13.19 ((
% 97.60/13.19 (funcext2) =>
% 97.60/13.19 ((
% 97.60/13.19 (ap2apEq1) =>
% 97.60/13.19 ((
% 97.60/13.19 (ap2apEq2) =>
% 97.60/13.19 ((
% 97.60/13.19 (beta1) =>
% 97.60/13.19 ((
% 97.60/13.19 (eta1) =>
% 97.60/13.19 ((
% 97.60/13.19 (lam2lamEq) =>
% 97.60/13.19 ((
% 97.60/13.19 (beta2) =>
% 97.60/13.19 ((
% 97.60/13.19 (eta2) =>
% 97.60/13.19 ((
% 97.60/13.19 (iffalseProp1) =>
% 97.60/13.19 ((
% 97.60/13.19 (iffalseProp2) =>
% 97.60/13.19 ((
% 97.60/13.19 (iftrueProp1) =>
% 97.60/13.19 ((
% 97.60/13.19 (iftrueProp2) =>
% 97.60/13.19 ((
% 97.60/13.19 (ifSingleton) =>
% 97.60/13.19 ((
% 97.60/13.19 (ifp) =>
% 97.60/13.19 ((
% 97.60/13.19 (theeq) =>
% 97.60/13.19 ((
% 97.60/13.19 (iftrue) =>
% 97.60/13.19 ((
% 97.60/13.19 (iffalse) =>
% 97.60/13.19 ((
% 97.60/13.19 (iftrueorfalse) =>
% 97.60/13.19 ((
% 97.60/13.19 (binintersectT_lem) =>
% 97.60/13.19 ((
% 97.60/13.19 (binunionT_lem) =>
% 97.60/13.19 ((
% 97.60/13.19 (powersetT_lem) =>
% 97.60/13.19 ((
% 97.60/13.19 (setminusT_lem) =>
% 97.60/13.19 ((
% 97.60/13.19 (complementT_lem) =>
% 97.60/13.19 ((
% 97.60/13.19 (setextT) =>
% 97.60/13.19 ((
% 97.60/13.19 (subsetTI) =>
% 97.60/13.19 ((
% 97.60/13.19 (powersetTI1) =>
% 97.60/13.19 ((
% 97.60/13.19 (powersetTE1) =>
% 97.60/13.19 ((
% 97.60/13.19 (complementTI1) =>
% 97.60/13.19 ((
% 97.60/13.19 (complementTE1) =>
% 97.60/13.19 ((
% 97.60/13.19 (binintersectTELcontra) =>
% 97.60/13.19 ((
% 97.60/13.19 (binintersectTERcontra) =>
% 97.60/13.19 ((
% 97.60/13.19 (contrasubsetT) =>
% 97.60/13.19 ((
% 97.60/13.19 (contrasubsetT1) =>
% 97.60/13.19 ((
% 97.60/13.19 (contrasubsetT2) =>
% 97.60/13.19 ((
% 97.60/13.19 (contrasubsetT3) =>
% 97.60/13.19 ((
% 97.60/13.19 (doubleComplementI1) =>
% 97.60/13.19 ((
% 97.60/13.19 (doubleComplementE1) =>
% 97.60/13.19 ((
% 97.60/13.19 (doubleComplementSub1) =>
% 97.60/13.19 ((
% 97.60/13.19 (doubleComplementSub2) =>
% 97.60/13.19 ((
% 97.60/13.19 (doubleComplementEq) =>
% 97.60/13.19 ((
% 97.60/13.19 (complementTnotintersectT) =>
% 97.60/13.19 ((
% 97.60/13.19 (complementImpComplementIntersect) =>
% 97.60/13.19 ((
% 97.60/13.19 (complementSubsetComplementIntersect) =>
% 97.60/13.19 ((
% 97.60/13.19 (complementInPowersetComplementIntersect) =>
% 97.60/13.19 ((
% 97.60/13.19 (contraSubsetComplement) =>
% 97.60/13.19 ((
% 97.60/13.19 (complementTcontraSubset) =>
% 97.60/13.19 ((
% 97.60/13.19 (binunionTILcontra) =>
% 97.60/13.19 ((
% 97.60/13.19 (binunionTIRcontra) =>
% 97.60/13.19 ((
% 97.60/13.19 (inIntersectImpInUnion) =>
% 97.60/13.19 ((
% 97.60/13.19 (inIntersectImpInUnion2) =>
% 97.60/13.19 ((
% 97.60/13.19 (inIntersectImpInIntersectUnions) =>
% 97.60/13.19 ((
% 97.60/13.19 (intersectInPowersetIntersectUnions) =>
% 97.60/13.19 ((
% 97.60/13.19 (inComplementUnionImpNotIn1) =>
% 97.60/13.19 ((
% 97.60/13.19 (inComplementUnionImpInComplement1) =>
% 97.60/13.19 ((
% 97.60/13.19 (binunionTE) =>
% 97.60/13.19 ((
% 97.60/13.19 (binunionTEcontra) =>
% 97.60/13.19 ((
% 97.60/13.19 (demorgan2a1) =>
% 97.60/13.19 ((
% 97.60/13.19 (complementUnionInPowersetComplement) =>
% 97.60/13.19 ((
% 97.60/13.19 (demorgan2a2) =>
% 97.60/13.19 ((
% 97.60/13.19 (demorgan1a) =>
% 97.60/13.19 ((
% 97.60/13.19 (demorgan1b) =>
% 97.60/13.19 ((
% 97.60/13.19 (demorgan1) =>
% 97.60/13.19 ((
% 97.60/13.19 (demorgan2a) =>
% 97.60/13.19 ((
% 97.60/13.19 (demorgan2b2) =>
% 97.60/13.19 ((
% 97.60/13.19 (demorgan2b) =>
% 97.60/13.19 ((
% 97.60/13.19 (demorgan2) =>
% 97.60/13.19 ((
% 97.60/13.19 (woz13rule0) =>
% 97.60/13.19 ((
% 97.60/13.19 (woz13rule1) =>
% 97.60/13.19 ((
% 97.60/13.19 (woz13rule2) =>
% 97.60/13.19 ((
% 97.60/13.19 (woz13rule3) =>
% 97.60/13.19 ((
% 97.60/13.19 (woz13rule4) =>
% 97.60/13.19 ((
% 97.60/13.19 (woz1_1) =>
% 97.60/13.19 ((
% 97.60/13.19 (woz1_2) =>
% 97.60/13.19 ((
% 97.60/13.19 (woz1_3) =>
% 97.60/13.19 ((
% 97.60/13.19 (woz1_4) =>
% 97.60/13.19 ((
% 97.60/13.19 (woz1_5) =>
% 97.60/13.19 ((
% 97.60/13.19 (breln1all2) =>
% 97.60/13.19 ((
% 97.60/13.19 (breln1SetBreln1) =>
% 97.60/13.19 ((
% 97.60/13.19 (choice2fnsingleton) =>
% 97.60/13.19 ((
% 97.60/13.19 (setOfPairsIsBReln1) =>
% 97.60/13.19 ((
% 97.60/13.19 (breln1all1) =>
% 97.60/13.19 ((
% 97.60/13.19 (subbreln1) =>
% 97.60/13.19 ((
% 97.60/13.19 (eqbreln1) =>
% 97.60/13.19 ((
% 97.60/13.19 (breln1invprop) =>
% 97.60/13.19 ((
% 97.60/13.19 (breln1invI) =>
% 97.60/13.19 ((
% 97.60/13.19 (breln1invE) =>
% 97.60/13.19 ((
% 97.60/13.19 (breln1compprop) =>
% 97.60/13.19 ((
% 97.60/13.19 (breln1compI) =>
% 97.60/13.19 ((
% 97.60/13.19 (breln1compE) =>
% 97.60/13.19 ((
% 97.60/13.19 (breln1compEex) =>
% 97.60/13.19 ((
% 97.60/13.19 (breln1unionprop) =>
% 97.60/13.19 ((
% 97.60/13.19 (breln1unionIL) =>
% 97.60/13.19 ((
% 97.60/13.19 (breln1unionIR) =>
% 97.60/13.19 ((
% 97.60/13.19 (breln1unionI) =>
% 97.60/13.19 ((
% 97.60/13.19 (breln1unionE) =>
% 97.60/13.19 ((
% 97.60/13.19 (breln1unionEcases) =>
% 97.60/13.19 ((
% 97.60/13.19 (breln1unionCommutes) =>
% 97.60/13.19 ((
% 97.60/13.19 (woz2Ex) =>
% 97.60/13.19 ((
% 97.60/13.19 (woz2W) =>
% 97.60/13.19 ((
% 97.60/13.19 (woz2A) =>
% 97.60/13.19 ((
% 97.60/13.19 (woz2B) =>
% 97.60/13.19 ((
% 97.60/13.19 (image1Ex) =>
% 97.60/13.19 ((
% 97.60/13.19 (image1Ex1) =>
% 97.60/13.19 ((
% 97.60/13.19 (image1Equiv) =>
% 97.60/13.19 ((
% 97.60/13.19 (image1E) =>
% 97.60/13.19 ((
% 97.60/13.19 (image1I) =>
% 97.60/13.19 ((
% 97.60/13.19 (injFuncInInjFuncSet) =>
% 97.60/13.19 ((
% 97.60/13.19 (injFuncSetFuncIn) =>
% 97.60/13.19 ((
% 97.60/13.19 (injFuncSetFuncInj) =>
% 97.60/13.19 ((
% 97.60/13.19 (surjFuncSetFuncIn) =>
% 97.60/13.19 ((
% 97.60/13.19 (surjFuncSetFuncSurj) =>
% 97.60/13.19 ((
% 97.60/13.19 (leftInvIsSurj) =>
% 97.60/13.19 ((
% 97.60/13.19 (surjCantorThm) =>
% 97.60/13.19 ((
% 97.60/13.19 (foundation2) =>
% 97.60/13.19 ((
% 97.60/13.19 (notinself) =>
% 97.60/13.19 ((
% 97.60/13.19 (notinself2) =>
% 97.60/13.19 ((
% 97.60/13.19 (omegaSp) =>
% 97.60/13.19 ((
% 97.60/13.19 (omegaSclos) =>
% 97.60/13.19 ((
% 97.60/13.19 (peano0notS) =>
% 97.60/13.19 ((
% 97.60/13.19 (!!) @ (
% 97.60/13.19 (('#S') @ (
% 97.60/13.19 (
% 97.60/13.19 ('#B') @ (
% 97.60/13.19 =>) @
% 97.60/13.19 (
% 97.60/13.19 (
% 97.60/13.19 ('#C') @ in @
% 97.60/13.19 omega)))) @
% 97.60/13.19 (
% 97.60/13.19 (
% 97.60/13.19 ('#B') @ (
% 97.60/13.19 !!) @
% 97.60/13.19 (
% 97.60/13.19 (
% 97.60/13.19 ('#B') @ (
% 97.60/13.19 (
% 97.60/13.19 ('#S') @ (
% 97.60/13.19 (
% 97.60/13.19 ('#B') @ (
% 97.60/13.19 =>) @
% 97.60/13.19 (
% 97.60/13.19 (
% 97.60/13.19 ('#C') @ in @
% 97.60/13.19 omega)))))) @
% 97.60/13.19 (
% 97.60/13.19 (
% 97.60/13.19 ('#S') @ (
% 97.60/13.19 (
% 97.60/13.19 ('#B') @ (
% 97.60/13.19 '#S') @
% 97.60/13.19 (
% 97.60/13.19 (
% 97.60/13.19 ('#B') @ (
% 97.60/13.19 (
% 97.60/13.19 ('#B') @ (
% 97.60/13.19 =>))) @
% 97.60/13.19 (
% 97.60/13.19 (
% 97.60/13.19 ('#C') @ (
% 97.60/13.19 (
% 97.60/13.19 ('#B') @ (
% 97.60/13.19 '#B') @
% 97.60/13.19 (
% 97.60/13.19 (
% 97.60/13.19 ('#B') @ (
% 97.60/13.19 =) @
% 97.60/13.19 omegaS)))) @
% 97.60/13.19 omegaS)))))) @
% 97.60/13.19 (
% 97.60/13.19 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.60/13.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl517])).
% 97.60/13.19 thf(zip_derived_cl537, plain,
% 97.60/13.19 (~ (((quantDeMorgan1) =>
% 97.60/13.19 (((quantDeMorgan2) =>
% 97.60/13.19 (((quantDeMorgan3) =>
% 97.60/13.19 (((quantDeMorgan4) =>
% 97.60/13.19 (((prop2setI) =>
% 97.60/13.19 (((prop2set2propI) =>
% 97.60/13.19 (((notdexE) =>
% 97.60/13.19 (((notdallE) =>
% 97.60/13.19 (((exuI1) =>
% 97.60/13.19 (((exuI3) =>
% 97.60/13.19 (((exuI2) =>
% 97.60/13.19 (((inCongP) =>
% 97.60/13.19 (((in__Cong) =>
% 97.60/13.19 (((exuE3u) =>
% 97.60/13.19 (((exu__Cong) =>
% 97.60/13.19 (((setadjoin__Cong) =>
% 97.60/13.19 (((powerset__Cong) =>
% 97.60/13.19 (((setunion__Cong) =>
% 97.60/13.19 (((exuEu) =>
% 97.60/13.19 (((descr__Cong) =>
% 97.60/13.19 (((dsetconstr__Cong) =>
% 97.60/13.19 (((subsetI1) =>
% 97.60/13.19 (((eqimpsubset2) =>
% 97.60/13.19 (((eqimpsubset1) =>
% 97.60/13.19 (((subsetI2) =>
% 97.60/13.19 (((emptysetsubset) =>
% 97.60/13.19 (((subsetE) =>
% 97.60/13.19 (((subsetE2) =>
% 97.60/13.19 (((notsubsetI) =>
% 97.60/13.19 (((notequalI1) =>
% 97.60/13.19 ((
% 97.60/13.19 (notequalI2) =>
% 97.60/13.19 ((
% 97.60/13.19 (subsetRefl) =>
% 97.60/13.19 ((
% 97.60/13.19 (subsetTrans) =>
% 97.60/13.19 ((
% 97.60/13.19 (setadjoinSub) =>
% 97.60/13.19 ((
% 97.60/13.19 (setadjoinSub2) =>
% 97.60/13.19 ((
% 97.60/13.19 (subset2powerset) =>
% 97.60/13.19 ((
% 97.60/13.19 (setextsub) =>
% 97.60/13.19 ((
% 97.60/13.19 (subsetemptysetimpeq) =>
% 97.60/13.19 ((
% 97.60/13.19 (powersetI1) =>
% 97.60/13.19 ((
% 97.60/13.19 (powersetE1) =>
% 97.60/13.19 ((
% 97.60/13.19 (inPowerset) =>
% 97.60/13.19 ((
% 97.60/13.19 (powersetsubset) =>
% 97.60/13.19 ((
% 97.60/13.19 (sepInPowerset) =>
% 97.60/13.19 ((
% 97.60/13.19 (sepSubset) =>
% 97.60/13.19 ((
% 97.60/13.19 (binunionIL) =>
% 97.60/13.19 ((
% 97.60/13.19 (upairset2IR) =>
% 97.60/13.19 ((
% 97.60/13.19 (binunionIR) =>
% 97.60/13.19 ((
% 97.60/13.19 (binunionEcases) =>
% 97.60/13.19 ((
% 97.60/13.19 (binunionE) =>
% 97.60/13.19 ((
% 97.60/13.19 (binunionLsub) =>
% 97.60/13.19 ((
% 97.60/13.19 (binunionRsub) =>
% 97.60/13.19 ((
% 97.60/13.19 (binintersectI) =>
% 97.60/13.19 ((
% 97.60/13.19 (binintersectSubset5) =>
% 97.60/13.19 ((
% 97.60/13.19 (binintersectEL) =>
% 97.60/13.19 ((
% 97.60/13.19 (binintersectLsub) =>
% 97.60/13.19 ((
% 97.60/13.19 (binintersectSubset2) =>
% 97.60/13.19 ((
% 97.60/13.19 (binintersectSubset3) =>
% 97.60/13.19 ((
% 97.60/13.19 (binintersectER) =>
% 97.60/13.19 ((
% 97.60/13.19 (disjointsetsI1) =>
% 97.60/13.19 ((
% 97.60/13.19 (binintersectRsub) =>
% 97.60/13.19 ((
% 97.60/13.19 (binintersectSubset4) =>
% 97.60/13.19 ((
% 97.60/13.19 (binintersectSubset1) =>
% 97.60/13.19 ((
% 97.60/13.19 (bs114d) =>
% 97.60/13.19 ((
% 97.60/13.19 (setminusI) =>
% 97.60/13.19 ((
% 97.60/13.19 (setminusEL) =>
% 97.60/13.19 ((
% 97.60/13.19 (setminusER) =>
% 97.60/13.19 ((
% 97.60/13.19 (setminusSubset2) =>
% 97.60/13.19 ((
% 97.60/13.19 (setminusERneg) =>
% 97.60/13.19 ((
% 97.60/13.19 (setminusELneg) =>
% 97.60/13.19 ((
% 97.60/13.19 (setminusILneg) =>
% 97.60/13.19 ((
% 97.60/13.19 (setminusIRneg) =>
% 97.60/13.19 ((
% 97.60/13.19 (setminusLsub) =>
% 97.60/13.19 ((
% 97.60/13.19 (setminusSubset1) =>
% 97.60/13.19 ((
% 97.60/13.19 (symdiffE) =>
% 97.60/13.19 ((
% 97.60/13.19 (symdiffI1) =>
% 97.60/13.19 ((
% 97.60/13.19 (symdiffI2) =>
% 97.60/13.19 ((
% 97.60/13.19 (symdiffIneg1) =>
% 97.60/13.19 ((
% 97.60/13.19 (symdiffIneg2) =>
% 97.60/13.19 ((
% 97.60/13.19 (secondinupair) =>
% 97.60/13.19 ((
% 97.60/13.19 (setukpairIL) =>
% 97.60/13.19 ((
% 97.60/13.19 (setukpairIR) =>
% 97.60/13.19 ((
% 97.60/13.19 (kpairiskpair) =>
% 97.60/13.19 ((
% 97.60/13.19 (kpairp) =>
% 97.60/13.20 ((
% 97.60/13.20 (singletonsubset) =>
% 97.60/13.20 ((
% 97.60/13.20 (singletoninpowerset) =>
% 97.60/13.20 ((
% 97.60/13.20 (singletoninpowunion) =>
% 97.60/13.20 ((
% 97.60/13.20 (upairset2E) =>
% 97.60/13.20 ((
% 97.60/13.20 (upairsubunion) =>
% 97.60/13.20 ((
% 97.60/13.20 (upairinpowunion) =>
% 97.60/13.20 ((
% 97.60/13.20 (ubforcartprodlem1) =>
% 97.60/13.20 ((
% 97.60/13.20 (ubforcartprodlem2) =>
% 97.60/13.20 ((
% 97.60/13.20 (ubforcartprodlem3) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodpairin) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodmempair1) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodmempair) =>
% 97.60/13.20 ((
% 97.60/13.20 (setunionE2) =>
% 97.60/13.20 ((
% 97.60/13.20 (setunionsingleton1) =>
% 97.60/13.20 ((
% 97.60/13.20 (setunionsingleton2) =>
% 97.60/13.20 ((
% 97.60/13.20 (setunionsingleton) =>
% 97.60/13.20 ((
% 97.60/13.20 (singletonprop) =>
% 97.60/13.20 ((
% 97.60/13.20 (ex1E1) =>
% 97.60/13.20 ((
% 97.60/13.20 (ex1I) =>
% 97.60/13.20 ((
% 97.60/13.20 (ex1I2) =>
% 97.60/13.20 ((
% 97.60/13.20 (singletonsuniq) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairinjL1) =>
% 97.60/13.20 ((
% 97.60/13.20 (kfstsingleton) =>
% 97.60/13.20 ((
% 97.60/13.20 (theprop) =>
% 97.60/13.20 ((
% 97.60/13.20 (kfstpairEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodfstin) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairinjL2) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairinjL) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairinjR11) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairinjR12) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairinjR1) =>
% 97.60/13.20 ((
% 97.60/13.20 (upairequniteq) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairinjR2) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairinjR) =>
% 97.60/13.20 ((
% 97.60/13.20 (ksndsingleton) =>
% 97.60/13.20 ((
% 97.60/13.20 (ksndpairEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (kpairsurjEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodsndin) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodpairmemEL) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodpairmemER) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodmempaircEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodfstpairEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodsndpairEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodpairsurjEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (dpsetconstrI) =>
% 97.60/13.20 ((
% 97.60/13.20 (dpsetconstrSub) =>
% 97.60/13.20 ((
% 97.60/13.20 (setOfPairsIsBReln) =>
% 97.60/13.20 ((
% 97.60/13.20 (dpsetconstrERa) =>
% 97.60/13.20 ((
% 97.60/13.20 (dpsetconstrEL1) =>
% 97.60/13.20 ((
% 97.60/13.20 (dpsetconstrEL2) =>
% 97.60/13.20 ((
% 97.60/13.20 (dpsetconstrER) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcImageSingleton) =>
% 97.60/13.20 ((
% 97.60/13.20 (apProp) =>
% 97.60/13.20 ((
% 97.60/13.20 (app) =>
% 97.60/13.20 ((
% 97.60/13.20 (infuncsetfunc) =>
% 97.60/13.20 ((
% 97.60/13.20 (ap2p) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcinfuncset) =>
% 97.60/13.20 ((
% 97.60/13.20 (lamProp) =>
% 97.60/13.20 ((
% 97.60/13.20 (lamp) =>
% 97.60/13.20 ((
% 97.60/13.20 (lam2p) =>
% 97.60/13.20 ((
% 97.60/13.20 (brelnall1) =>
% 97.60/13.20 ((
% 97.60/13.20 (brelnall2) =>
% 97.60/13.20 ((
% 97.60/13.20 (ex1E2) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcGraphProp1) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcGraphProp3) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcGraphProp2) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcextLem) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcGraphProp4) =>
% 97.60/13.20 ((
% 97.60/13.20 (subbreln) =>
% 97.60/13.20 ((
% 97.60/13.20 (eqbreln) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcext) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcext2) =>
% 97.60/13.20 ((
% 97.60/13.20 (ap2apEq1) =>
% 97.60/13.20 ((
% 97.60/13.20 (ap2apEq2) =>
% 97.60/13.20 ((
% 97.60/13.20 (beta1) =>
% 97.60/13.20 ((
% 97.60/13.20 (eta1) =>
% 97.60/13.20 ((
% 97.60/13.20 (lam2lamEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (beta2) =>
% 97.60/13.20 ((
% 97.60/13.20 (eta2) =>
% 97.60/13.20 ((
% 97.60/13.20 (iffalseProp1) =>
% 97.60/13.20 ((
% 97.60/13.20 (iffalseProp2) =>
% 97.60/13.20 ((
% 97.60/13.20 (iftrueProp1) =>
% 97.60/13.20 ((
% 97.60/13.20 (iftrueProp2) =>
% 97.60/13.20 ((
% 97.60/13.20 (ifSingleton) =>
% 97.60/13.20 ((
% 97.60/13.20 (ifp) =>
% 97.60/13.20 ((
% 97.60/13.20 (theeq) =>
% 97.60/13.20 ((
% 97.60/13.20 (iftrue) =>
% 97.60/13.20 ((
% 97.60/13.20 (iffalse) =>
% 97.60/13.20 ((
% 97.60/13.20 (iftrueorfalse) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectT_lem) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionT_lem) =>
% 97.60/13.20 ((
% 97.60/13.20 (powersetT_lem) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusT_lem) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementT_lem) =>
% 97.60/13.20 ((
% 97.60/13.20 (setextT) =>
% 97.60/13.20 ((
% 97.60/13.20 (subsetTI) =>
% 97.60/13.20 ((
% 97.60/13.20 (powersetTI1) =>
% 97.60/13.20 ((
% 97.60/13.20 (powersetTE1) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementTI1) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementTE1) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectTELcontra) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectTERcontra) =>
% 97.60/13.20 ((
% 97.60/13.20 (contrasubsetT) =>
% 97.60/13.20 ((
% 97.60/13.20 (contrasubsetT1) =>
% 97.60/13.20 ((
% 97.60/13.20 (contrasubsetT2) =>
% 97.60/13.20 ((
% 97.60/13.20 (contrasubsetT3) =>
% 97.60/13.20 ((
% 97.60/13.20 (doubleComplementI1) =>
% 97.60/13.20 ((
% 97.60/13.20 (doubleComplementE1) =>
% 97.60/13.20 ((
% 97.60/13.20 (doubleComplementSub1) =>
% 97.60/13.20 ((
% 97.60/13.20 (doubleComplementSub2) =>
% 97.60/13.20 ((
% 97.60/13.20 (doubleComplementEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementTnotintersectT) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementImpComplementIntersect) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementSubsetComplementIntersect) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementInPowersetComplementIntersect) =>
% 97.60/13.20 ((
% 97.60/13.20 (contraSubsetComplement) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementTcontraSubset) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionTILcontra) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionTIRcontra) =>
% 97.60/13.20 ((
% 97.60/13.20 (inIntersectImpInUnion) =>
% 97.60/13.20 ((
% 97.60/13.20 (inIntersectImpInUnion2) =>
% 97.60/13.20 ((
% 97.60/13.20 (inIntersectImpInIntersectUnions) =>
% 97.60/13.20 ((
% 97.60/13.20 (intersectInPowersetIntersectUnions) =>
% 97.60/13.20 ((
% 97.60/13.20 (inComplementUnionImpNotIn1) =>
% 97.60/13.20 ((
% 97.60/13.20 (inComplementUnionImpInComplement1) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionTE) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionTEcontra) =>
% 97.60/13.20 ((
% 97.60/13.20 (demorgan2a1) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementUnionInPowersetComplement) =>
% 97.60/13.20 ((
% 97.60/13.20 (demorgan2a2) =>
% 97.60/13.20 ((
% 97.60/13.20 (demorgan1a) =>
% 97.60/13.20 ((
% 97.60/13.20 (demorgan1b) =>
% 97.60/13.20 ((
% 97.60/13.20 (demorgan1) =>
% 97.60/13.20 ((
% 97.60/13.20 (demorgan2a) =>
% 97.60/13.20 ((
% 97.60/13.20 (demorgan2b2) =>
% 97.60/13.20 ((
% 97.60/13.20 (demorgan2b) =>
% 97.60/13.20 ((
% 97.60/13.20 (demorgan2) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz13rule0) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz13rule1) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz13rule2) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz13rule3) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz13rule4) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz1_1) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz1_2) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz1_3) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz1_4) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz1_5) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1all2) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1SetBreln1) =>
% 97.60/13.20 ((
% 97.60/13.20 (choice2fnsingleton) =>
% 97.60/13.20 ((
% 97.60/13.20 (setOfPairsIsBReln1) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1all1) =>
% 97.60/13.20 ((
% 97.60/13.20 (subbreln1) =>
% 97.60/13.20 ((
% 97.60/13.20 (eqbreln1) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1invprop) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1invI) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1invE) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1compprop) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1compI) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1compE) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1compEex) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1unionprop) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1unionIL) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1unionIR) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1unionI) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1unionE) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1unionEcases) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1unionCommutes) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz2Ex) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz2W) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz2A) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz2B) =>
% 97.60/13.20 ((
% 97.60/13.20 (image1Ex) =>
% 97.60/13.20 ((
% 97.60/13.20 (image1Ex1) =>
% 97.60/13.20 ((
% 97.60/13.20 (image1Equiv) =>
% 97.60/13.20 ((
% 97.60/13.20 (image1E) =>
% 97.60/13.20 ((
% 97.60/13.20 (image1I) =>
% 97.60/13.20 ((
% 97.60/13.20 (injFuncInInjFuncSet) =>
% 97.60/13.20 ((
% 97.60/13.20 (injFuncSetFuncIn) =>
% 97.60/13.20 ((
% 97.60/13.20 (injFuncSetFuncInj) =>
% 97.60/13.20 ((
% 97.60/13.20 (surjFuncSetFuncIn) =>
% 97.60/13.20 ((
% 97.60/13.20 (surjFuncSetFuncSurj) =>
% 97.60/13.20 ((
% 97.60/13.20 (leftInvIsSurj) =>
% 97.60/13.20 ((
% 97.60/13.20 (surjCantorThm) =>
% 97.60/13.20 ((
% 97.60/13.20 (foundation2) =>
% 97.60/13.20 ((
% 97.60/13.20 (notinself) =>
% 97.60/13.20 ((
% 97.60/13.20 (notinself2) =>
% 97.60/13.20 ((
% 97.60/13.20 (omegaSp) =>
% 97.60/13.20 ((
% 97.60/13.20 (omegaSclos) =>
% 97.60/13.20 ((
% 97.60/13.20 (peano0notS) =>
% 97.60/13.20 ((
% 97.60/13.20 (!!) @ (
% 97.60/13.20 (('#S') @ (
% 97.60/13.20 (
% 97.60/13.20 ('#B') @ (
% 97.60/13.20 =>) @
% 97.60/13.20 (
% 97.60/13.20 (
% 97.60/13.20 ('#C') @ in @
% 97.60/13.20 omega)))) @
% 97.60/13.20 (
% 97.60/13.20 (
% 97.60/13.20 ('#B') @ (
% 97.60/13.20 !!) @
% 97.60/13.20 (
% 97.60/13.20 (
% 97.60/13.20 ('#B') @ (
% 97.60/13.20 (
% 97.60/13.20 ('#S') @ (
% 97.60/13.20 (
% 97.60/13.20 ('#B') @ (
% 97.60/13.20 =>) @
% 97.60/13.20 (
% 97.60/13.20 (
% 97.60/13.20 ('#C') @ in @
% 97.60/13.20 omega)))))) @
% 97.60/13.20 (
% 97.60/13.20 (
% 97.60/13.20 ('#S') @ (
% 97.60/13.20 (
% 97.60/13.20 ('#B') @ (
% 97.60/13.20 '#S') @
% 97.60/13.20 (
% 97.60/13.20 (
% 97.60/13.20 ('#B') @ (
% 97.60/13.20 (
% 97.60/13.20 ('#B') @ (
% 97.60/13.20 =>))) @
% 97.60/13.20 (
% 97.60/13.20 (
% 97.60/13.20 ('#C') @ (
% 97.60/13.20 (
% 97.60/13.20 ('#B') @ (
% 97.60/13.20 '#B') @
% 97.60/13.20 (
% 97.60/13.20 (
% 97.60/13.20 ('#B') @ (
% 97.60/13.20 =) @
% 97.60/13.20 omegaS)))) @
% 97.60/13.20 omegaS)))))) @
% 97.60/13.20 (
% 97.60/13.20 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.60/13.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl528])).
% 97.60/13.20 thf(zip_derived_cl546, plain,
% 97.60/13.20 (~ (((quantDeMorgan2) =>
% 97.60/13.20 (((quantDeMorgan3) =>
% 97.60/13.20 (((quantDeMorgan4) =>
% 97.60/13.20 (((prop2setI) =>
% 97.60/13.20 (((prop2set2propI) =>
% 97.60/13.20 (((notdexE) =>
% 97.60/13.20 (((notdallE) =>
% 97.60/13.20 (((exuI1) =>
% 97.60/13.20 (((exuI3) =>
% 97.60/13.20 (((exuI2) =>
% 97.60/13.20 (((inCongP) =>
% 97.60/13.20 (((in__Cong) =>
% 97.60/13.20 (((exuE3u) =>
% 97.60/13.20 (((exu__Cong) =>
% 97.60/13.20 (((setadjoin__Cong) =>
% 97.60/13.20 (((powerset__Cong) =>
% 97.60/13.20 (((setunion__Cong) =>
% 97.60/13.20 (((exuEu) =>
% 97.60/13.20 (((descr__Cong) =>
% 97.60/13.20 (((dsetconstr__Cong) =>
% 97.60/13.20 (((subsetI1) =>
% 97.60/13.20 (((eqimpsubset2) =>
% 97.60/13.20 (((eqimpsubset1) =>
% 97.60/13.20 (((subsetI2) =>
% 97.60/13.20 (((emptysetsubset) =>
% 97.60/13.20 (((subsetE) =>
% 97.60/13.20 (((subsetE2) =>
% 97.60/13.20 (((notsubsetI) =>
% 97.60/13.20 (((notequalI1) =>
% 97.60/13.20 (((notequalI2) =>
% 97.60/13.20 ((
% 97.60/13.20 (subsetRefl) =>
% 97.60/13.20 ((
% 97.60/13.20 (subsetTrans) =>
% 97.60/13.20 ((
% 97.60/13.20 (setadjoinSub) =>
% 97.60/13.20 ((
% 97.60/13.20 (setadjoinSub2) =>
% 97.60/13.20 ((
% 97.60/13.20 (subset2powerset) =>
% 97.60/13.20 ((
% 97.60/13.20 (setextsub) =>
% 97.60/13.20 ((
% 97.60/13.20 (subsetemptysetimpeq) =>
% 97.60/13.20 ((
% 97.60/13.20 (powersetI1) =>
% 97.60/13.20 ((
% 97.60/13.20 (powersetE1) =>
% 97.60/13.20 ((
% 97.60/13.20 (inPowerset) =>
% 97.60/13.20 ((
% 97.60/13.20 (powersetsubset) =>
% 97.60/13.20 ((
% 97.60/13.20 (sepInPowerset) =>
% 97.60/13.20 ((
% 97.60/13.20 (sepSubset) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionIL) =>
% 97.60/13.20 ((
% 97.60/13.20 (upairset2IR) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionIR) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionEcases) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionE) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionLsub) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionRsub) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectI) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectSubset5) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectEL) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectLsub) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectSubset2) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectSubset3) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectER) =>
% 97.60/13.20 ((
% 97.60/13.20 (disjointsetsI1) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectRsub) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectSubset4) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectSubset1) =>
% 97.60/13.20 ((
% 97.60/13.20 (bs114d) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusI) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusEL) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusER) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusSubset2) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusERneg) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusELneg) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusILneg) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusIRneg) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusLsub) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusSubset1) =>
% 97.60/13.20 ((
% 97.60/13.20 (symdiffE) =>
% 97.60/13.20 ((
% 97.60/13.20 (symdiffI1) =>
% 97.60/13.20 ((
% 97.60/13.20 (symdiffI2) =>
% 97.60/13.20 ((
% 97.60/13.20 (symdiffIneg1) =>
% 97.60/13.20 ((
% 97.60/13.20 (symdiffIneg2) =>
% 97.60/13.20 ((
% 97.60/13.20 (secondinupair) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairIL) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairIR) =>
% 97.60/13.20 ((
% 97.60/13.20 (kpairiskpair) =>
% 97.60/13.20 ((
% 97.60/13.20 (kpairp) =>
% 97.60/13.20 ((
% 97.60/13.20 (singletonsubset) =>
% 97.60/13.20 ((
% 97.60/13.20 (singletoninpowerset) =>
% 97.60/13.20 ((
% 97.60/13.20 (singletoninpowunion) =>
% 97.60/13.20 ((
% 97.60/13.20 (upairset2E) =>
% 97.60/13.20 ((
% 97.60/13.20 (upairsubunion) =>
% 97.60/13.20 ((
% 97.60/13.20 (upairinpowunion) =>
% 97.60/13.20 ((
% 97.60/13.20 (ubforcartprodlem1) =>
% 97.60/13.20 ((
% 97.60/13.20 (ubforcartprodlem2) =>
% 97.60/13.20 ((
% 97.60/13.20 (ubforcartprodlem3) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodpairin) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodmempair1) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodmempair) =>
% 97.60/13.20 ((
% 97.60/13.20 (setunionE2) =>
% 97.60/13.20 ((
% 97.60/13.20 (setunionsingleton1) =>
% 97.60/13.20 ((
% 97.60/13.20 (setunionsingleton2) =>
% 97.60/13.20 ((
% 97.60/13.20 (setunionsingleton) =>
% 97.60/13.20 ((
% 97.60/13.20 (singletonprop) =>
% 97.60/13.20 ((
% 97.60/13.20 (ex1E1) =>
% 97.60/13.20 ((
% 97.60/13.20 (ex1I) =>
% 97.60/13.20 ((
% 97.60/13.20 (ex1I2) =>
% 97.60/13.20 ((
% 97.60/13.20 (singletonsuniq) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairinjL1) =>
% 97.60/13.20 ((
% 97.60/13.20 (kfstsingleton) =>
% 97.60/13.20 ((
% 97.60/13.20 (theprop) =>
% 97.60/13.20 ((
% 97.60/13.20 (kfstpairEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodfstin) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairinjL2) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairinjL) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairinjR11) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairinjR12) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairinjR1) =>
% 97.60/13.20 ((
% 97.60/13.20 (upairequniteq) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairinjR2) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairinjR) =>
% 97.60/13.20 ((
% 97.60/13.20 (ksndsingleton) =>
% 97.60/13.20 ((
% 97.60/13.20 (ksndpairEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (kpairsurjEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodsndin) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodpairmemEL) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodpairmemER) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodmempaircEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodfstpairEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodsndpairEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodpairsurjEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (dpsetconstrI) =>
% 97.60/13.20 ((
% 97.60/13.20 (dpsetconstrSub) =>
% 97.60/13.20 ((
% 97.60/13.20 (setOfPairsIsBReln) =>
% 97.60/13.20 ((
% 97.60/13.20 (dpsetconstrERa) =>
% 97.60/13.20 ((
% 97.60/13.20 (dpsetconstrEL1) =>
% 97.60/13.20 ((
% 97.60/13.20 (dpsetconstrEL2) =>
% 97.60/13.20 ((
% 97.60/13.20 (dpsetconstrER) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcImageSingleton) =>
% 97.60/13.20 ((
% 97.60/13.20 (apProp) =>
% 97.60/13.20 ((
% 97.60/13.20 (app) =>
% 97.60/13.20 ((
% 97.60/13.20 (infuncsetfunc) =>
% 97.60/13.20 ((
% 97.60/13.20 (ap2p) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcinfuncset) =>
% 97.60/13.20 ((
% 97.60/13.20 (lamProp) =>
% 97.60/13.20 ((
% 97.60/13.20 (lamp) =>
% 97.60/13.20 ((
% 97.60/13.20 (lam2p) =>
% 97.60/13.20 ((
% 97.60/13.20 (brelnall1) =>
% 97.60/13.20 ((
% 97.60/13.20 (brelnall2) =>
% 97.60/13.20 ((
% 97.60/13.20 (ex1E2) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcGraphProp1) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcGraphProp3) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcGraphProp2) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcextLem) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcGraphProp4) =>
% 97.60/13.20 ((
% 97.60/13.20 (subbreln) =>
% 97.60/13.20 ((
% 97.60/13.20 (eqbreln) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcext) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcext2) =>
% 97.60/13.20 ((
% 97.60/13.20 (ap2apEq1) =>
% 97.60/13.20 ((
% 97.60/13.20 (ap2apEq2) =>
% 97.60/13.20 ((
% 97.60/13.20 (beta1) =>
% 97.60/13.20 ((
% 97.60/13.20 (eta1) =>
% 97.60/13.20 ((
% 97.60/13.20 (lam2lamEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (beta2) =>
% 97.60/13.20 ((
% 97.60/13.20 (eta2) =>
% 97.60/13.20 ((
% 97.60/13.20 (iffalseProp1) =>
% 97.60/13.20 ((
% 97.60/13.20 (iffalseProp2) =>
% 97.60/13.20 ((
% 97.60/13.20 (iftrueProp1) =>
% 97.60/13.20 ((
% 97.60/13.20 (iftrueProp2) =>
% 97.60/13.20 ((
% 97.60/13.20 (ifSingleton) =>
% 97.60/13.20 ((
% 97.60/13.20 (ifp) =>
% 97.60/13.20 ((
% 97.60/13.20 (theeq) =>
% 97.60/13.20 ((
% 97.60/13.20 (iftrue) =>
% 97.60/13.20 ((
% 97.60/13.20 (iffalse) =>
% 97.60/13.20 ((
% 97.60/13.20 (iftrueorfalse) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectT_lem) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionT_lem) =>
% 97.60/13.20 ((
% 97.60/13.20 (powersetT_lem) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusT_lem) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementT_lem) =>
% 97.60/13.20 ((
% 97.60/13.20 (setextT) =>
% 97.60/13.20 ((
% 97.60/13.20 (subsetTI) =>
% 97.60/13.20 ((
% 97.60/13.20 (powersetTI1) =>
% 97.60/13.20 ((
% 97.60/13.20 (powersetTE1) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementTI1) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementTE1) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectTELcontra) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectTERcontra) =>
% 97.60/13.20 ((
% 97.60/13.20 (contrasubsetT) =>
% 97.60/13.20 ((
% 97.60/13.20 (contrasubsetT1) =>
% 97.60/13.20 ((
% 97.60/13.20 (contrasubsetT2) =>
% 97.60/13.20 ((
% 97.60/13.20 (contrasubsetT3) =>
% 97.60/13.20 ((
% 97.60/13.20 (doubleComplementI1) =>
% 97.60/13.20 ((
% 97.60/13.20 (doubleComplementE1) =>
% 97.60/13.20 ((
% 97.60/13.20 (doubleComplementSub1) =>
% 97.60/13.20 ((
% 97.60/13.20 (doubleComplementSub2) =>
% 97.60/13.20 ((
% 97.60/13.20 (doubleComplementEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementTnotintersectT) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementImpComplementIntersect) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementSubsetComplementIntersect) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementInPowersetComplementIntersect) =>
% 97.60/13.20 ((
% 97.60/13.20 (contraSubsetComplement) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementTcontraSubset) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionTILcontra) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionTIRcontra) =>
% 97.60/13.20 ((
% 97.60/13.20 (inIntersectImpInUnion) =>
% 97.60/13.20 ((
% 97.60/13.20 (inIntersectImpInUnion2) =>
% 97.60/13.20 ((
% 97.60/13.20 (inIntersectImpInIntersectUnions) =>
% 97.60/13.20 ((
% 97.60/13.20 (intersectInPowersetIntersectUnions) =>
% 97.60/13.20 ((
% 97.60/13.20 (inComplementUnionImpNotIn1) =>
% 97.60/13.20 ((
% 97.60/13.20 (inComplementUnionImpInComplement1) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionTE) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionTEcontra) =>
% 97.60/13.20 ((
% 97.60/13.20 (demorgan2a1) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementUnionInPowersetComplement) =>
% 97.60/13.20 ((
% 97.60/13.20 (demorgan2a2) =>
% 97.60/13.20 ((
% 97.60/13.20 (demorgan1a) =>
% 97.60/13.20 ((
% 97.60/13.20 (demorgan1b) =>
% 97.60/13.20 ((
% 97.60/13.20 (demorgan1) =>
% 97.60/13.20 ((
% 97.60/13.20 (demorgan2a) =>
% 97.60/13.20 ((
% 97.60/13.20 (demorgan2b2) =>
% 97.60/13.20 ((
% 97.60/13.20 (demorgan2b) =>
% 97.60/13.20 ((
% 97.60/13.20 (demorgan2) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz13rule0) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz13rule1) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz13rule2) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz13rule3) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz13rule4) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz1_1) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz1_2) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz1_3) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz1_4) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz1_5) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1all2) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1SetBreln1) =>
% 97.60/13.20 ((
% 97.60/13.20 (choice2fnsingleton) =>
% 97.60/13.20 ((
% 97.60/13.20 (setOfPairsIsBReln1) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1all1) =>
% 97.60/13.20 ((
% 97.60/13.20 (subbreln1) =>
% 97.60/13.20 ((
% 97.60/13.20 (eqbreln1) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1invprop) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1invI) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1invE) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1compprop) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1compI) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1compE) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1compEex) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1unionprop) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1unionIL) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1unionIR) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1unionI) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1unionE) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1unionEcases) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1unionCommutes) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz2Ex) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz2W) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz2A) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz2B) =>
% 97.60/13.20 ((
% 97.60/13.20 (image1Ex) =>
% 97.60/13.20 ((
% 97.60/13.20 (image1Ex1) =>
% 97.60/13.20 ((
% 97.60/13.20 (image1Equiv) =>
% 97.60/13.20 ((
% 97.60/13.20 (image1E) =>
% 97.60/13.20 ((
% 97.60/13.20 (image1I) =>
% 97.60/13.20 ((
% 97.60/13.20 (injFuncInInjFuncSet) =>
% 97.60/13.20 ((
% 97.60/13.20 (injFuncSetFuncIn) =>
% 97.60/13.20 ((
% 97.60/13.20 (injFuncSetFuncInj) =>
% 97.60/13.20 ((
% 97.60/13.20 (surjFuncSetFuncIn) =>
% 97.60/13.20 ((
% 97.60/13.20 (surjFuncSetFuncSurj) =>
% 97.60/13.20 ((
% 97.60/13.20 (leftInvIsSurj) =>
% 97.60/13.20 ((
% 97.60/13.20 (surjCantorThm) =>
% 97.60/13.20 ((
% 97.60/13.20 (foundation2) =>
% 97.60/13.20 ((
% 97.60/13.20 (notinself) =>
% 97.60/13.20 ((
% 97.60/13.20 (notinself2) =>
% 97.60/13.20 ((
% 97.60/13.20 (omegaSp) =>
% 97.60/13.20 ((
% 97.60/13.20 (omegaSclos) =>
% 97.60/13.20 ((
% 97.60/13.20 (peano0notS) =>
% 97.60/13.20 ((
% 97.60/13.20 (!!) @ (
% 97.60/13.20 (('#S') @ (
% 97.60/13.20 (
% 97.60/13.20 ('#B') @ (
% 97.60/13.20 =>) @
% 97.60/13.20 (
% 97.60/13.20 (
% 97.60/13.20 ('#C') @ in @
% 97.60/13.20 omega)))) @
% 97.60/13.20 (
% 97.60/13.20 (
% 97.60/13.20 ('#B') @ (
% 97.60/13.20 !!) @
% 97.60/13.20 (
% 97.60/13.20 (
% 97.60/13.20 ('#B') @ (
% 97.60/13.20 (
% 97.60/13.20 ('#S') @ (
% 97.60/13.20 (
% 97.60/13.20 ('#B') @ (
% 97.60/13.20 =>) @
% 97.60/13.20 (
% 97.60/13.20 (
% 97.60/13.20 ('#C') @ in @
% 97.60/13.20 omega)))))) @
% 97.60/13.20 (
% 97.60/13.20 (
% 97.60/13.20 ('#S') @ (
% 97.60/13.20 (
% 97.60/13.20 ('#B') @ (
% 97.60/13.20 '#S') @
% 97.60/13.20 (
% 97.60/13.20 (
% 97.60/13.20 ('#B') @ (
% 97.60/13.20 (
% 97.60/13.20 ('#B') @ (
% 97.60/13.20 =>))) @
% 97.60/13.20 (
% 97.60/13.20 (
% 97.60/13.20 ('#C') @ (
% 97.60/13.20 (
% 97.60/13.20 ('#B') @ (
% 97.60/13.20 '#B') @
% 97.60/13.20 (
% 97.60/13.20 (
% 97.60/13.20 ('#B') @ (
% 97.60/13.20 =) @
% 97.60/13.20 omegaS)))) @
% 97.60/13.20 omegaS)))))) @
% 97.60/13.20 (
% 97.60/13.20 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.60/13.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl537])).
% 97.60/13.20 thf(zip_derived_cl553, plain,
% 97.60/13.20 (~ (((quantDeMorgan3) =>
% 97.60/13.20 (((quantDeMorgan4) =>
% 97.60/13.20 (((prop2setI) =>
% 97.60/13.20 (((prop2set2propI) =>
% 97.60/13.20 (((notdexE) =>
% 97.60/13.20 (((notdallE) =>
% 97.60/13.20 (((exuI1) =>
% 97.60/13.20 (((exuI3) =>
% 97.60/13.20 (((exuI2) =>
% 97.60/13.20 (((inCongP) =>
% 97.60/13.20 (((in__Cong) =>
% 97.60/13.20 (((exuE3u) =>
% 97.60/13.20 (((exu__Cong) =>
% 97.60/13.20 (((setadjoin__Cong) =>
% 97.60/13.20 (((powerset__Cong) =>
% 97.60/13.20 (((setunion__Cong) =>
% 97.60/13.20 (((exuEu) =>
% 97.60/13.20 (((descr__Cong) =>
% 97.60/13.20 (((dsetconstr__Cong) =>
% 97.60/13.20 (((subsetI1) =>
% 97.60/13.20 (((eqimpsubset2) =>
% 97.60/13.20 (((eqimpsubset1) =>
% 97.60/13.20 (((subsetI2) =>
% 97.60/13.20 (((emptysetsubset) =>
% 97.60/13.20 (((subsetE) =>
% 97.60/13.20 (((subsetE2) =>
% 97.60/13.20 (((notsubsetI) =>
% 97.60/13.20 (((notequalI1) =>
% 97.60/13.20 (((notequalI2) =>
% 97.60/13.20 (((subsetRefl) =>
% 97.60/13.20 ((
% 97.60/13.20 (subsetTrans) =>
% 97.60/13.20 ((
% 97.60/13.20 (setadjoinSub) =>
% 97.60/13.20 ((
% 97.60/13.20 (setadjoinSub2) =>
% 97.60/13.20 ((
% 97.60/13.20 (subset2powerset) =>
% 97.60/13.20 ((
% 97.60/13.20 (setextsub) =>
% 97.60/13.20 ((
% 97.60/13.20 (subsetemptysetimpeq) =>
% 97.60/13.20 ((
% 97.60/13.20 (powersetI1) =>
% 97.60/13.20 ((
% 97.60/13.20 (powersetE1) =>
% 97.60/13.20 ((
% 97.60/13.20 (inPowerset) =>
% 97.60/13.20 ((
% 97.60/13.20 (powersetsubset) =>
% 97.60/13.20 ((
% 97.60/13.20 (sepInPowerset) =>
% 97.60/13.20 ((
% 97.60/13.20 (sepSubset) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionIL) =>
% 97.60/13.20 ((
% 97.60/13.20 (upairset2IR) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionIR) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionEcases) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionE) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionLsub) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionRsub) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectI) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectSubset5) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectEL) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectLsub) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectSubset2) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectSubset3) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectER) =>
% 97.60/13.20 ((
% 97.60/13.20 (disjointsetsI1) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectRsub) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectSubset4) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectSubset1) =>
% 97.60/13.20 ((
% 97.60/13.20 (bs114d) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusI) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusEL) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusER) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusSubset2) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusERneg) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusELneg) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusILneg) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusIRneg) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusLsub) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusSubset1) =>
% 97.60/13.20 ((
% 97.60/13.20 (symdiffE) =>
% 97.60/13.20 ((
% 97.60/13.20 (symdiffI1) =>
% 97.60/13.20 ((
% 97.60/13.20 (symdiffI2) =>
% 97.60/13.20 ((
% 97.60/13.20 (symdiffIneg1) =>
% 97.60/13.20 ((
% 97.60/13.20 (symdiffIneg2) =>
% 97.60/13.20 ((
% 97.60/13.20 (secondinupair) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairIL) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairIR) =>
% 97.60/13.20 ((
% 97.60/13.20 (kpairiskpair) =>
% 97.60/13.20 ((
% 97.60/13.20 (kpairp) =>
% 97.60/13.20 ((
% 97.60/13.20 (singletonsubset) =>
% 97.60/13.20 ((
% 97.60/13.20 (singletoninpowerset) =>
% 97.60/13.20 ((
% 97.60/13.20 (singletoninpowunion) =>
% 97.60/13.20 ((
% 97.60/13.20 (upairset2E) =>
% 97.60/13.20 ((
% 97.60/13.20 (upairsubunion) =>
% 97.60/13.20 ((
% 97.60/13.20 (upairinpowunion) =>
% 97.60/13.20 ((
% 97.60/13.20 (ubforcartprodlem1) =>
% 97.60/13.20 ((
% 97.60/13.20 (ubforcartprodlem2) =>
% 97.60/13.20 ((
% 97.60/13.20 (ubforcartprodlem3) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodpairin) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodmempair1) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodmempair) =>
% 97.60/13.20 ((
% 97.60/13.20 (setunionE2) =>
% 97.60/13.20 ((
% 97.60/13.20 (setunionsingleton1) =>
% 97.60/13.20 ((
% 97.60/13.20 (setunionsingleton2) =>
% 97.60/13.20 ((
% 97.60/13.20 (setunionsingleton) =>
% 97.60/13.20 ((
% 97.60/13.20 (singletonprop) =>
% 97.60/13.20 ((
% 97.60/13.20 (ex1E1) =>
% 97.60/13.20 ((
% 97.60/13.20 (ex1I) =>
% 97.60/13.20 ((
% 97.60/13.20 (ex1I2) =>
% 97.60/13.20 ((
% 97.60/13.20 (singletonsuniq) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairinjL1) =>
% 97.60/13.20 ((
% 97.60/13.20 (kfstsingleton) =>
% 97.60/13.20 ((
% 97.60/13.20 (theprop) =>
% 97.60/13.20 ((
% 97.60/13.20 (kfstpairEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodfstin) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairinjL2) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairinjL) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairinjR11) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairinjR12) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairinjR1) =>
% 97.60/13.20 ((
% 97.60/13.20 (upairequniteq) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairinjR2) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairinjR) =>
% 97.60/13.20 ((
% 97.60/13.20 (ksndsingleton) =>
% 97.60/13.20 ((
% 97.60/13.20 (ksndpairEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (kpairsurjEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodsndin) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodpairmemEL) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodpairmemER) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodmempaircEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodfstpairEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodsndpairEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodpairsurjEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (dpsetconstrI) =>
% 97.60/13.20 ((
% 97.60/13.20 (dpsetconstrSub) =>
% 97.60/13.20 ((
% 97.60/13.20 (setOfPairsIsBReln) =>
% 97.60/13.20 ((
% 97.60/13.20 (dpsetconstrERa) =>
% 97.60/13.20 ((
% 97.60/13.20 (dpsetconstrEL1) =>
% 97.60/13.20 ((
% 97.60/13.20 (dpsetconstrEL2) =>
% 97.60/13.20 ((
% 97.60/13.20 (dpsetconstrER) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcImageSingleton) =>
% 97.60/13.20 ((
% 97.60/13.20 (apProp) =>
% 97.60/13.20 ((
% 97.60/13.20 (app) =>
% 97.60/13.20 ((
% 97.60/13.20 (infuncsetfunc) =>
% 97.60/13.20 ((
% 97.60/13.20 (ap2p) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcinfuncset) =>
% 97.60/13.20 ((
% 97.60/13.20 (lamProp) =>
% 97.60/13.20 ((
% 97.60/13.20 (lamp) =>
% 97.60/13.20 ((
% 97.60/13.20 (lam2p) =>
% 97.60/13.20 ((
% 97.60/13.20 (brelnall1) =>
% 97.60/13.20 ((
% 97.60/13.20 (brelnall2) =>
% 97.60/13.20 ((
% 97.60/13.20 (ex1E2) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcGraphProp1) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcGraphProp3) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcGraphProp2) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcextLem) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcGraphProp4) =>
% 97.60/13.20 ((
% 97.60/13.20 (subbreln) =>
% 97.60/13.20 ((
% 97.60/13.20 (eqbreln) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcext) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcext2) =>
% 97.60/13.20 ((
% 97.60/13.20 (ap2apEq1) =>
% 97.60/13.20 ((
% 97.60/13.20 (ap2apEq2) =>
% 97.60/13.20 ((
% 97.60/13.20 (beta1) =>
% 97.60/13.20 ((
% 97.60/13.20 (eta1) =>
% 97.60/13.20 ((
% 97.60/13.20 (lam2lamEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (beta2) =>
% 97.60/13.20 ((
% 97.60/13.20 (eta2) =>
% 97.60/13.20 ((
% 97.60/13.20 (iffalseProp1) =>
% 97.60/13.20 ((
% 97.60/13.20 (iffalseProp2) =>
% 97.60/13.20 ((
% 97.60/13.20 (iftrueProp1) =>
% 97.60/13.20 ((
% 97.60/13.20 (iftrueProp2) =>
% 97.60/13.20 ((
% 97.60/13.20 (ifSingleton) =>
% 97.60/13.20 ((
% 97.60/13.20 (ifp) =>
% 97.60/13.20 ((
% 97.60/13.20 (theeq) =>
% 97.60/13.20 ((
% 97.60/13.20 (iftrue) =>
% 97.60/13.20 ((
% 97.60/13.20 (iffalse) =>
% 97.60/13.20 ((
% 97.60/13.20 (iftrueorfalse) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectT_lem) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionT_lem) =>
% 97.60/13.20 ((
% 97.60/13.20 (powersetT_lem) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusT_lem) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementT_lem) =>
% 97.60/13.20 ((
% 97.60/13.20 (setextT) =>
% 97.60/13.20 ((
% 97.60/13.20 (subsetTI) =>
% 97.60/13.20 ((
% 97.60/13.20 (powersetTI1) =>
% 97.60/13.20 ((
% 97.60/13.20 (powersetTE1) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementTI1) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementTE1) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectTELcontra) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectTERcontra) =>
% 97.60/13.20 ((
% 97.60/13.20 (contrasubsetT) =>
% 97.60/13.20 ((
% 97.60/13.20 (contrasubsetT1) =>
% 97.60/13.20 ((
% 97.60/13.20 (contrasubsetT2) =>
% 97.60/13.20 ((
% 97.60/13.20 (contrasubsetT3) =>
% 97.60/13.20 ((
% 97.60/13.20 (doubleComplementI1) =>
% 97.60/13.20 ((
% 97.60/13.20 (doubleComplementE1) =>
% 97.60/13.20 ((
% 97.60/13.20 (doubleComplementSub1) =>
% 97.60/13.20 ((
% 97.60/13.20 (doubleComplementSub2) =>
% 97.60/13.20 ((
% 97.60/13.20 (doubleComplementEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementTnotintersectT) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementImpComplementIntersect) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementSubsetComplementIntersect) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementInPowersetComplementIntersect) =>
% 97.60/13.20 ((
% 97.60/13.20 (contraSubsetComplement) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementTcontraSubset) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionTILcontra) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionTIRcontra) =>
% 97.60/13.20 ((
% 97.60/13.20 (inIntersectImpInUnion) =>
% 97.60/13.20 ((
% 97.60/13.20 (inIntersectImpInUnion2) =>
% 97.60/13.20 ((
% 97.60/13.20 (inIntersectImpInIntersectUnions) =>
% 97.60/13.20 ((
% 97.60/13.20 (intersectInPowersetIntersectUnions) =>
% 97.60/13.20 ((
% 97.60/13.20 (inComplementUnionImpNotIn1) =>
% 97.60/13.20 ((
% 97.60/13.20 (inComplementUnionImpInComplement1) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionTE) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionTEcontra) =>
% 97.60/13.20 ((
% 97.60/13.20 (demorgan2a1) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementUnionInPowersetComplement) =>
% 97.60/13.20 ((
% 97.60/13.20 (demorgan2a2) =>
% 97.60/13.20 ((
% 97.60/13.20 (demorgan1a) =>
% 97.60/13.20 ((
% 97.60/13.20 (demorgan1b) =>
% 97.60/13.20 ((
% 97.60/13.20 (demorgan1) =>
% 97.60/13.20 ((
% 97.60/13.20 (demorgan2a) =>
% 97.60/13.20 ((
% 97.60/13.20 (demorgan2b2) =>
% 97.60/13.20 ((
% 97.60/13.20 (demorgan2b) =>
% 97.60/13.20 ((
% 97.60/13.20 (demorgan2) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz13rule0) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz13rule1) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz13rule2) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz13rule3) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz13rule4) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz1_1) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz1_2) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz1_3) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz1_4) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz1_5) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1all2) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1SetBreln1) =>
% 97.60/13.20 ((
% 97.60/13.20 (choice2fnsingleton) =>
% 97.60/13.20 ((
% 97.60/13.20 (setOfPairsIsBReln1) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1all1) =>
% 97.60/13.20 ((
% 97.60/13.20 (subbreln1) =>
% 97.60/13.20 ((
% 97.60/13.20 (eqbreln1) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1invprop) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1invI) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1invE) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1compprop) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1compI) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1compE) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1compEex) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1unionprop) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1unionIL) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1unionIR) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1unionI) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1unionE) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1unionEcases) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1unionCommutes) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz2Ex) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz2W) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz2A) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz2B) =>
% 97.60/13.20 ((
% 97.60/13.20 (image1Ex) =>
% 97.60/13.20 ((
% 97.60/13.20 (image1Ex1) =>
% 97.60/13.20 ((
% 97.60/13.20 (image1Equiv) =>
% 97.60/13.20 ((
% 97.60/13.20 (image1E) =>
% 97.60/13.20 ((
% 97.60/13.20 (image1I) =>
% 97.60/13.20 ((
% 97.60/13.20 (injFuncInInjFuncSet) =>
% 97.60/13.20 ((
% 97.60/13.20 (injFuncSetFuncIn) =>
% 97.60/13.20 ((
% 97.60/13.20 (injFuncSetFuncInj) =>
% 97.60/13.20 ((
% 97.60/13.20 (surjFuncSetFuncIn) =>
% 97.60/13.20 ((
% 97.60/13.20 (surjFuncSetFuncSurj) =>
% 97.60/13.20 ((
% 97.60/13.20 (leftInvIsSurj) =>
% 97.60/13.20 ((
% 97.60/13.20 (surjCantorThm) =>
% 97.60/13.20 ((
% 97.60/13.20 (foundation2) =>
% 97.60/13.20 ((
% 97.60/13.20 (notinself) =>
% 97.60/13.20 ((
% 97.60/13.20 (notinself2) =>
% 97.60/13.20 ((
% 97.60/13.20 (omegaSp) =>
% 97.60/13.20 ((
% 97.60/13.20 (omegaSclos) =>
% 97.60/13.20 ((
% 97.60/13.20 (peano0notS) =>
% 97.60/13.20 ((
% 97.60/13.20 (!!) @ (
% 97.60/13.20 (('#S') @ (
% 97.60/13.20 (
% 97.60/13.20 ('#B') @ (
% 97.60/13.20 =>) @
% 97.60/13.20 (
% 97.60/13.20 (
% 97.60/13.20 ('#C') @ in @
% 97.60/13.20 omega)))) @
% 97.60/13.20 (
% 97.60/13.20 (
% 97.60/13.20 ('#B') @ (
% 97.60/13.20 !!) @
% 97.60/13.20 (
% 97.60/13.20 (
% 97.60/13.20 ('#B') @ (
% 97.60/13.20 (
% 97.60/13.20 ('#S') @ (
% 97.60/13.20 (
% 97.60/13.20 ('#B') @ (
% 97.60/13.20 =>) @
% 97.60/13.20 (
% 97.60/13.20 (
% 97.60/13.20 ('#C') @ in @
% 97.60/13.20 omega)))))) @
% 97.60/13.20 (
% 97.60/13.20 (
% 97.60/13.20 ('#S') @ (
% 97.60/13.20 (
% 97.60/13.20 ('#B') @ (
% 97.60/13.20 '#S') @
% 97.60/13.20 (
% 97.60/13.20 (
% 97.60/13.20 ('#B') @ (
% 97.60/13.20 (
% 97.60/13.20 ('#B') @ (
% 97.60/13.20 =>))) @
% 97.60/13.20 (
% 97.60/13.20 (
% 97.60/13.20 ('#C') @ (
% 97.60/13.20 (
% 97.60/13.20 ('#B') @ (
% 97.60/13.20 '#B') @
% 97.60/13.20 (
% 97.60/13.20 (
% 97.60/13.20 ('#B') @ (
% 97.60/13.20 =) @
% 97.60/13.20 omegaS)))) @
% 97.60/13.20 omegaS)))))) @
% 97.60/13.20 (
% 97.60/13.20 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.60/13.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl546])).
% 97.60/13.20 thf(zip_derived_cl561, plain,
% 97.60/13.20 (~ (((quantDeMorgan4) =>
% 97.60/13.20 (((prop2setI) =>
% 97.60/13.20 (((prop2set2propI) =>
% 97.60/13.20 (((notdexE) =>
% 97.60/13.20 (((notdallE) =>
% 97.60/13.20 (((exuI1) =>
% 97.60/13.20 (((exuI3) =>
% 97.60/13.20 (((exuI2) =>
% 97.60/13.20 (((inCongP) =>
% 97.60/13.20 (((in__Cong) =>
% 97.60/13.20 (((exuE3u) =>
% 97.60/13.20 (((exu__Cong) =>
% 97.60/13.20 (((setadjoin__Cong) =>
% 97.60/13.20 (((powerset__Cong) =>
% 97.60/13.20 (((setunion__Cong) =>
% 97.60/13.20 (((exuEu) =>
% 97.60/13.20 (((descr__Cong) =>
% 97.60/13.20 (((dsetconstr__Cong) =>
% 97.60/13.20 (((subsetI1) =>
% 97.60/13.20 (((eqimpsubset2) =>
% 97.60/13.20 (((eqimpsubset1) =>
% 97.60/13.20 (((subsetI2) =>
% 97.60/13.20 (((emptysetsubset) =>
% 97.60/13.20 (((subsetE) =>
% 97.60/13.20 (((subsetE2) =>
% 97.60/13.20 (((notsubsetI) =>
% 97.60/13.20 (((notequalI1) =>
% 97.60/13.20 (((notequalI2) =>
% 97.60/13.20 (((subsetRefl) =>
% 97.60/13.20 (((subsetTrans) =>
% 97.60/13.20 ((
% 97.60/13.20 (setadjoinSub) =>
% 97.60/13.20 ((
% 97.60/13.20 (setadjoinSub2) =>
% 97.60/13.20 ((
% 97.60/13.20 (subset2powerset) =>
% 97.60/13.20 ((
% 97.60/13.20 (setextsub) =>
% 97.60/13.20 ((
% 97.60/13.20 (subsetemptysetimpeq) =>
% 97.60/13.20 ((
% 97.60/13.20 (powersetI1) =>
% 97.60/13.20 ((
% 97.60/13.20 (powersetE1) =>
% 97.60/13.20 ((
% 97.60/13.20 (inPowerset) =>
% 97.60/13.20 ((
% 97.60/13.20 (powersetsubset) =>
% 97.60/13.20 ((
% 97.60/13.20 (sepInPowerset) =>
% 97.60/13.20 ((
% 97.60/13.20 (sepSubset) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionIL) =>
% 97.60/13.20 ((
% 97.60/13.20 (upairset2IR) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionIR) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionEcases) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionE) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionLsub) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionRsub) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectI) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectSubset5) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectEL) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectLsub) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectSubset2) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectSubset3) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectER) =>
% 97.60/13.20 ((
% 97.60/13.20 (disjointsetsI1) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectRsub) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectSubset4) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectSubset1) =>
% 97.60/13.20 ((
% 97.60/13.20 (bs114d) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusI) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusEL) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusER) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusSubset2) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusERneg) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusELneg) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusILneg) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusIRneg) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusLsub) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusSubset1) =>
% 97.60/13.20 ((
% 97.60/13.20 (symdiffE) =>
% 97.60/13.20 ((
% 97.60/13.20 (symdiffI1) =>
% 97.60/13.20 ((
% 97.60/13.20 (symdiffI2) =>
% 97.60/13.20 ((
% 97.60/13.20 (symdiffIneg1) =>
% 97.60/13.20 ((
% 97.60/13.20 (symdiffIneg2) =>
% 97.60/13.20 ((
% 97.60/13.20 (secondinupair) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairIL) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairIR) =>
% 97.60/13.20 ((
% 97.60/13.20 (kpairiskpair) =>
% 97.60/13.20 ((
% 97.60/13.20 (kpairp) =>
% 97.60/13.20 ((
% 97.60/13.20 (singletonsubset) =>
% 97.60/13.20 ((
% 97.60/13.20 (singletoninpowerset) =>
% 97.60/13.20 ((
% 97.60/13.20 (singletoninpowunion) =>
% 97.60/13.20 ((
% 97.60/13.20 (upairset2E) =>
% 97.60/13.20 ((
% 97.60/13.20 (upairsubunion) =>
% 97.60/13.20 ((
% 97.60/13.20 (upairinpowunion) =>
% 97.60/13.20 ((
% 97.60/13.20 (ubforcartprodlem1) =>
% 97.60/13.20 ((
% 97.60/13.20 (ubforcartprodlem2) =>
% 97.60/13.20 ((
% 97.60/13.20 (ubforcartprodlem3) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodpairin) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodmempair1) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodmempair) =>
% 97.60/13.20 ((
% 97.60/13.20 (setunionE2) =>
% 97.60/13.20 ((
% 97.60/13.20 (setunionsingleton1) =>
% 97.60/13.20 ((
% 97.60/13.20 (setunionsingleton2) =>
% 97.60/13.20 ((
% 97.60/13.20 (setunionsingleton) =>
% 97.60/13.20 ((
% 97.60/13.20 (singletonprop) =>
% 97.60/13.20 ((
% 97.60/13.20 (ex1E1) =>
% 97.60/13.20 ((
% 97.60/13.20 (ex1I) =>
% 97.60/13.20 ((
% 97.60/13.20 (ex1I2) =>
% 97.60/13.20 ((
% 97.60/13.20 (singletonsuniq) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairinjL1) =>
% 97.60/13.20 ((
% 97.60/13.20 (kfstsingleton) =>
% 97.60/13.20 ((
% 97.60/13.20 (theprop) =>
% 97.60/13.20 ((
% 97.60/13.20 (kfstpairEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodfstin) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairinjL2) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairinjL) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairinjR11) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairinjR12) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairinjR1) =>
% 97.60/13.20 ((
% 97.60/13.20 (upairequniteq) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairinjR2) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairinjR) =>
% 97.60/13.20 ((
% 97.60/13.20 (ksndsingleton) =>
% 97.60/13.20 ((
% 97.60/13.20 (ksndpairEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (kpairsurjEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodsndin) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodpairmemEL) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodpairmemER) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodmempaircEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodfstpairEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodsndpairEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodpairsurjEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (dpsetconstrI) =>
% 97.60/13.20 ((
% 97.60/13.20 (dpsetconstrSub) =>
% 97.60/13.20 ((
% 97.60/13.20 (setOfPairsIsBReln) =>
% 97.60/13.20 ((
% 97.60/13.20 (dpsetconstrERa) =>
% 97.60/13.20 ((
% 97.60/13.20 (dpsetconstrEL1) =>
% 97.60/13.20 ((
% 97.60/13.20 (dpsetconstrEL2) =>
% 97.60/13.20 ((
% 97.60/13.20 (dpsetconstrER) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcImageSingleton) =>
% 97.60/13.20 ((
% 97.60/13.20 (apProp) =>
% 97.60/13.20 ((
% 97.60/13.20 (app) =>
% 97.60/13.20 ((
% 97.60/13.20 (infuncsetfunc) =>
% 97.60/13.20 ((
% 97.60/13.20 (ap2p) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcinfuncset) =>
% 97.60/13.20 ((
% 97.60/13.20 (lamProp) =>
% 97.60/13.20 ((
% 97.60/13.20 (lamp) =>
% 97.60/13.20 ((
% 97.60/13.20 (lam2p) =>
% 97.60/13.20 ((
% 97.60/13.20 (brelnall1) =>
% 97.60/13.20 ((
% 97.60/13.20 (brelnall2) =>
% 97.60/13.20 ((
% 97.60/13.20 (ex1E2) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcGraphProp1) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcGraphProp3) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcGraphProp2) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcextLem) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcGraphProp4) =>
% 97.60/13.20 ((
% 97.60/13.20 (subbreln) =>
% 97.60/13.20 ((
% 97.60/13.20 (eqbreln) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcext) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcext2) =>
% 97.60/13.20 ((
% 97.60/13.20 (ap2apEq1) =>
% 97.60/13.20 ((
% 97.60/13.20 (ap2apEq2) =>
% 97.60/13.20 ((
% 97.60/13.20 (beta1) =>
% 97.60/13.20 ((
% 97.60/13.20 (eta1) =>
% 97.60/13.20 ((
% 97.60/13.20 (lam2lamEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (beta2) =>
% 97.60/13.20 ((
% 97.60/13.20 (eta2) =>
% 97.60/13.20 ((
% 97.60/13.20 (iffalseProp1) =>
% 97.60/13.20 ((
% 97.60/13.20 (iffalseProp2) =>
% 97.60/13.20 ((
% 97.60/13.20 (iftrueProp1) =>
% 97.60/13.20 ((
% 97.60/13.20 (iftrueProp2) =>
% 97.60/13.20 ((
% 97.60/13.20 (ifSingleton) =>
% 97.60/13.20 ((
% 97.60/13.20 (ifp) =>
% 97.60/13.20 ((
% 97.60/13.20 (theeq) =>
% 97.60/13.20 ((
% 97.60/13.20 (iftrue) =>
% 97.60/13.20 ((
% 97.60/13.20 (iffalse) =>
% 97.60/13.20 ((
% 97.60/13.20 (iftrueorfalse) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectT_lem) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionT_lem) =>
% 97.60/13.20 ((
% 97.60/13.20 (powersetT_lem) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusT_lem) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementT_lem) =>
% 97.60/13.20 ((
% 97.60/13.20 (setextT) =>
% 97.60/13.20 ((
% 97.60/13.20 (subsetTI) =>
% 97.60/13.20 ((
% 97.60/13.20 (powersetTI1) =>
% 97.60/13.20 ((
% 97.60/13.20 (powersetTE1) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementTI1) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementTE1) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectTELcontra) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectTERcontra) =>
% 97.60/13.20 ((
% 97.60/13.20 (contrasubsetT) =>
% 97.60/13.20 ((
% 97.60/13.20 (contrasubsetT1) =>
% 97.60/13.20 ((
% 97.60/13.20 (contrasubsetT2) =>
% 97.60/13.20 ((
% 97.60/13.20 (contrasubsetT3) =>
% 97.60/13.20 ((
% 97.60/13.20 (doubleComplementI1) =>
% 97.60/13.20 ((
% 97.60/13.20 (doubleComplementE1) =>
% 97.60/13.20 ((
% 97.60/13.20 (doubleComplementSub1) =>
% 97.60/13.20 ((
% 97.60/13.20 (doubleComplementSub2) =>
% 97.60/13.20 ((
% 97.60/13.20 (doubleComplementEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementTnotintersectT) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementImpComplementIntersect) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementSubsetComplementIntersect) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementInPowersetComplementIntersect) =>
% 97.60/13.20 ((
% 97.60/13.20 (contraSubsetComplement) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementTcontraSubset) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionTILcontra) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionTIRcontra) =>
% 97.60/13.20 ((
% 97.60/13.20 (inIntersectImpInUnion) =>
% 97.60/13.20 ((
% 97.60/13.20 (inIntersectImpInUnion2) =>
% 97.60/13.20 ((
% 97.60/13.20 (inIntersectImpInIntersectUnions) =>
% 97.60/13.20 ((
% 97.60/13.20 (intersectInPowersetIntersectUnions) =>
% 97.60/13.20 ((
% 97.60/13.20 (inComplementUnionImpNotIn1) =>
% 97.60/13.20 ((
% 97.60/13.20 (inComplementUnionImpInComplement1) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionTE) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionTEcontra) =>
% 97.60/13.20 ((
% 97.60/13.20 (demorgan2a1) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementUnionInPowersetComplement) =>
% 97.60/13.20 ((
% 97.60/13.20 (demorgan2a2) =>
% 97.60/13.20 ((
% 97.60/13.20 (demorgan1a) =>
% 97.60/13.20 ((
% 97.60/13.20 (demorgan1b) =>
% 97.60/13.20 ((
% 97.60/13.20 (demorgan1) =>
% 97.60/13.20 ((
% 97.60/13.20 (demorgan2a) =>
% 97.60/13.20 ((
% 97.60/13.20 (demorgan2b2) =>
% 97.60/13.20 ((
% 97.60/13.20 (demorgan2b) =>
% 97.60/13.20 ((
% 97.60/13.20 (demorgan2) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz13rule0) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz13rule1) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz13rule2) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz13rule3) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz13rule4) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz1_1) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz1_2) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz1_3) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz1_4) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz1_5) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1all2) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1SetBreln1) =>
% 97.60/13.20 ((
% 97.60/13.20 (choice2fnsingleton) =>
% 97.60/13.20 ((
% 97.60/13.20 (setOfPairsIsBReln1) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1all1) =>
% 97.60/13.20 ((
% 97.60/13.20 (subbreln1) =>
% 97.60/13.20 ((
% 97.60/13.20 (eqbreln1) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1invprop) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1invI) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1invE) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1compprop) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1compI) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1compE) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1compEex) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1unionprop) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1unionIL) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1unionIR) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1unionI) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1unionE) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1unionEcases) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1unionCommutes) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz2Ex) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz2W) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz2A) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz2B) =>
% 97.60/13.20 ((
% 97.60/13.20 (image1Ex) =>
% 97.60/13.20 ((
% 97.60/13.20 (image1Ex1) =>
% 97.60/13.20 ((
% 97.60/13.20 (image1Equiv) =>
% 97.60/13.20 ((
% 97.60/13.20 (image1E) =>
% 97.60/13.20 ((
% 97.60/13.20 (image1I) =>
% 97.60/13.20 ((
% 97.60/13.20 (injFuncInInjFuncSet) =>
% 97.60/13.20 ((
% 97.60/13.20 (injFuncSetFuncIn) =>
% 97.60/13.20 ((
% 97.60/13.20 (injFuncSetFuncInj) =>
% 97.60/13.20 ((
% 97.60/13.20 (surjFuncSetFuncIn) =>
% 97.60/13.20 ((
% 97.60/13.20 (surjFuncSetFuncSurj) =>
% 97.60/13.20 ((
% 97.60/13.20 (leftInvIsSurj) =>
% 97.60/13.20 ((
% 97.60/13.20 (surjCantorThm) =>
% 97.60/13.20 ((
% 97.60/13.20 (foundation2) =>
% 97.60/13.20 ((
% 97.60/13.20 (notinself) =>
% 97.60/13.20 ((
% 97.60/13.20 (notinself2) =>
% 97.60/13.20 ((
% 97.60/13.20 (omegaSp) =>
% 97.60/13.20 ((
% 97.60/13.20 (omegaSclos) =>
% 97.60/13.20 ((
% 97.60/13.20 (peano0notS) =>
% 97.60/13.20 ((
% 97.60/13.20 (!!) @ (
% 97.60/13.20 (('#S') @ (
% 97.60/13.20 (
% 97.60/13.20 ('#B') @ (
% 97.60/13.20 =>) @
% 97.60/13.20 (
% 97.60/13.20 (
% 97.60/13.20 ('#C') @ in @
% 97.60/13.20 omega)))) @
% 97.60/13.20 (
% 97.60/13.20 (
% 97.60/13.20 ('#B') @ (
% 97.60/13.20 !!) @
% 97.60/13.20 (
% 97.60/13.20 (
% 97.60/13.20 ('#B') @ (
% 97.60/13.20 (
% 97.60/13.20 ('#S') @ (
% 97.60/13.20 (
% 97.60/13.20 ('#B') @ (
% 97.60/13.20 =>) @
% 97.60/13.20 (
% 97.60/13.20 (
% 97.60/13.20 ('#C') @ in @
% 97.60/13.20 omega)))))) @
% 97.60/13.20 (
% 97.60/13.20 (
% 97.60/13.20 ('#S') @ (
% 97.60/13.20 (
% 97.60/13.20 ('#B') @ (
% 97.60/13.20 '#S') @
% 97.60/13.20 (
% 97.60/13.20 (
% 97.60/13.20 ('#B') @ (
% 97.60/13.20 (
% 97.60/13.20 ('#B') @ (
% 97.60/13.20 =>))) @
% 97.60/13.20 (
% 97.60/13.20 (
% 97.60/13.20 ('#C') @ (
% 97.60/13.20 (
% 97.60/13.20 ('#B') @ (
% 97.60/13.20 '#B') @
% 97.60/13.20 (
% 97.60/13.20 (
% 97.60/13.20 ('#B') @ (
% 97.60/13.20 =) @
% 97.60/13.20 omegaS)))) @
% 97.60/13.20 omegaS)))))) @
% 97.60/13.20 (
% 97.60/13.20 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.60/13.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl553])).
% 97.60/13.20 thf(zip_derived_cl570, plain,
% 97.60/13.20 (~ (((prop2setI) =>
% 97.60/13.20 (((prop2set2propI) =>
% 97.60/13.20 (((notdexE) =>
% 97.60/13.20 (((notdallE) =>
% 97.60/13.20 (((exuI1) =>
% 97.60/13.20 (((exuI3) =>
% 97.60/13.20 (((exuI2) =>
% 97.60/13.20 (((inCongP) =>
% 97.60/13.20 (((in__Cong) =>
% 97.60/13.20 (((exuE3u) =>
% 97.60/13.20 (((exu__Cong) =>
% 97.60/13.20 (((setadjoin__Cong) =>
% 97.60/13.20 (((powerset__Cong) =>
% 97.60/13.20 (((setunion__Cong) =>
% 97.60/13.20 (((exuEu) =>
% 97.60/13.20 (((descr__Cong) =>
% 97.60/13.20 (((dsetconstr__Cong) =>
% 97.60/13.20 (((subsetI1) =>
% 97.60/13.20 (((eqimpsubset2) =>
% 97.60/13.20 (((eqimpsubset1) =>
% 97.60/13.20 (((subsetI2) =>
% 97.60/13.20 (((emptysetsubset) =>
% 97.60/13.20 (((subsetE) =>
% 97.60/13.20 (((subsetE2) =>
% 97.60/13.20 (((notsubsetI) =>
% 97.60/13.20 (((notequalI1) =>
% 97.60/13.20 (((notequalI2) =>
% 97.60/13.20 (((subsetRefl) =>
% 97.60/13.20 (((subsetTrans) =>
% 97.60/13.20 (((setadjoinSub) =>
% 97.60/13.20 ((
% 97.60/13.20 (setadjoinSub2) =>
% 97.60/13.20 ((
% 97.60/13.20 (subset2powerset) =>
% 97.60/13.20 ((
% 97.60/13.20 (setextsub) =>
% 97.60/13.20 ((
% 97.60/13.20 (subsetemptysetimpeq) =>
% 97.60/13.20 ((
% 97.60/13.20 (powersetI1) =>
% 97.60/13.20 ((
% 97.60/13.20 (powersetE1) =>
% 97.60/13.20 ((
% 97.60/13.20 (inPowerset) =>
% 97.60/13.20 ((
% 97.60/13.20 (powersetsubset) =>
% 97.60/13.20 ((
% 97.60/13.20 (sepInPowerset) =>
% 97.60/13.20 ((
% 97.60/13.20 (sepSubset) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionIL) =>
% 97.60/13.20 ((
% 97.60/13.20 (upairset2IR) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionIR) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionEcases) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionE) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionLsub) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionRsub) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectI) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectSubset5) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectEL) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectLsub) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectSubset2) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectSubset3) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectER) =>
% 97.60/13.20 ((
% 97.60/13.20 (disjointsetsI1) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectRsub) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectSubset4) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectSubset1) =>
% 97.60/13.20 ((
% 97.60/13.20 (bs114d) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusI) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusEL) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusER) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusSubset2) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusERneg) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusELneg) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusILneg) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusIRneg) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusLsub) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusSubset1) =>
% 97.60/13.20 ((
% 97.60/13.20 (symdiffE) =>
% 97.60/13.20 ((
% 97.60/13.20 (symdiffI1) =>
% 97.60/13.20 ((
% 97.60/13.20 (symdiffI2) =>
% 97.60/13.20 ((
% 97.60/13.20 (symdiffIneg1) =>
% 97.60/13.20 ((
% 97.60/13.20 (symdiffIneg2) =>
% 97.60/13.20 ((
% 97.60/13.20 (secondinupair) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairIL) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairIR) =>
% 97.60/13.20 ((
% 97.60/13.20 (kpairiskpair) =>
% 97.60/13.20 ((
% 97.60/13.20 (kpairp) =>
% 97.60/13.20 ((
% 97.60/13.20 (singletonsubset) =>
% 97.60/13.20 ((
% 97.60/13.20 (singletoninpowerset) =>
% 97.60/13.20 ((
% 97.60/13.20 (singletoninpowunion) =>
% 97.60/13.20 ((
% 97.60/13.20 (upairset2E) =>
% 97.60/13.20 ((
% 97.60/13.20 (upairsubunion) =>
% 97.60/13.20 ((
% 97.60/13.20 (upairinpowunion) =>
% 97.60/13.20 ((
% 97.60/13.20 (ubforcartprodlem1) =>
% 97.60/13.20 ((
% 97.60/13.20 (ubforcartprodlem2) =>
% 97.60/13.20 ((
% 97.60/13.20 (ubforcartprodlem3) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodpairin) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodmempair1) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodmempair) =>
% 97.60/13.20 ((
% 97.60/13.20 (setunionE2) =>
% 97.60/13.20 ((
% 97.60/13.20 (setunionsingleton1) =>
% 97.60/13.20 ((
% 97.60/13.20 (setunionsingleton2) =>
% 97.60/13.20 ((
% 97.60/13.20 (setunionsingleton) =>
% 97.60/13.20 ((
% 97.60/13.20 (singletonprop) =>
% 97.60/13.20 ((
% 97.60/13.20 (ex1E1) =>
% 97.60/13.20 ((
% 97.60/13.20 (ex1I) =>
% 97.60/13.20 ((
% 97.60/13.20 (ex1I2) =>
% 97.60/13.20 ((
% 97.60/13.20 (singletonsuniq) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairinjL1) =>
% 97.60/13.20 ((
% 97.60/13.20 (kfstsingleton) =>
% 97.60/13.20 ((
% 97.60/13.20 (theprop) =>
% 97.60/13.20 ((
% 97.60/13.20 (kfstpairEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodfstin) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairinjL2) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairinjL) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairinjR11) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairinjR12) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairinjR1) =>
% 97.60/13.20 ((
% 97.60/13.20 (upairequniteq) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairinjR2) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairinjR) =>
% 97.60/13.20 ((
% 97.60/13.20 (ksndsingleton) =>
% 97.60/13.20 ((
% 97.60/13.20 (ksndpairEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (kpairsurjEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodsndin) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodpairmemEL) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodpairmemER) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodmempaircEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodfstpairEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodsndpairEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodpairsurjEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (dpsetconstrI) =>
% 97.60/13.20 ((
% 97.60/13.20 (dpsetconstrSub) =>
% 97.60/13.20 ((
% 97.60/13.20 (setOfPairsIsBReln) =>
% 97.60/13.20 ((
% 97.60/13.20 (dpsetconstrERa) =>
% 97.60/13.20 ((
% 97.60/13.20 (dpsetconstrEL1) =>
% 97.60/13.20 ((
% 97.60/13.20 (dpsetconstrEL2) =>
% 97.60/13.20 ((
% 97.60/13.20 (dpsetconstrER) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcImageSingleton) =>
% 97.60/13.20 ((
% 97.60/13.20 (apProp) =>
% 97.60/13.20 ((
% 97.60/13.20 (app) =>
% 97.60/13.20 ((
% 97.60/13.20 (infuncsetfunc) =>
% 97.60/13.20 ((
% 97.60/13.20 (ap2p) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcinfuncset) =>
% 97.60/13.20 ((
% 97.60/13.20 (lamProp) =>
% 97.60/13.20 ((
% 97.60/13.20 (lamp) =>
% 97.60/13.20 ((
% 97.60/13.20 (lam2p) =>
% 97.60/13.20 ((
% 97.60/13.20 (brelnall1) =>
% 97.60/13.20 ((
% 97.60/13.20 (brelnall2) =>
% 97.60/13.20 ((
% 97.60/13.20 (ex1E2) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcGraphProp1) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcGraphProp3) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcGraphProp2) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcextLem) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcGraphProp4) =>
% 97.60/13.20 ((
% 97.60/13.20 (subbreln) =>
% 97.60/13.20 ((
% 97.60/13.20 (eqbreln) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcext) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcext2) =>
% 97.60/13.20 ((
% 97.60/13.20 (ap2apEq1) =>
% 97.60/13.20 ((
% 97.60/13.20 (ap2apEq2) =>
% 97.60/13.20 ((
% 97.60/13.20 (beta1) =>
% 97.60/13.20 ((
% 97.60/13.20 (eta1) =>
% 97.60/13.20 ((
% 97.60/13.20 (lam2lamEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (beta2) =>
% 97.60/13.20 ((
% 97.60/13.20 (eta2) =>
% 97.60/13.20 ((
% 97.60/13.20 (iffalseProp1) =>
% 97.60/13.20 ((
% 97.60/13.20 (iffalseProp2) =>
% 97.60/13.20 ((
% 97.60/13.20 (iftrueProp1) =>
% 97.60/13.20 ((
% 97.60/13.20 (iftrueProp2) =>
% 97.60/13.20 ((
% 97.60/13.20 (ifSingleton) =>
% 97.60/13.20 ((
% 97.60/13.20 (ifp) =>
% 97.60/13.20 ((
% 97.60/13.20 (theeq) =>
% 97.60/13.20 ((
% 97.60/13.20 (iftrue) =>
% 97.60/13.20 ((
% 97.60/13.20 (iffalse) =>
% 97.60/13.20 ((
% 97.60/13.20 (iftrueorfalse) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectT_lem) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionT_lem) =>
% 97.60/13.20 ((
% 97.60/13.20 (powersetT_lem) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusT_lem) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementT_lem) =>
% 97.60/13.20 ((
% 97.60/13.20 (setextT) =>
% 97.60/13.20 ((
% 97.60/13.20 (subsetTI) =>
% 97.60/13.20 ((
% 97.60/13.20 (powersetTI1) =>
% 97.60/13.20 ((
% 97.60/13.20 (powersetTE1) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementTI1) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementTE1) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectTELcontra) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectTERcontra) =>
% 97.60/13.20 ((
% 97.60/13.20 (contrasubsetT) =>
% 97.60/13.20 ((
% 97.60/13.20 (contrasubsetT1) =>
% 97.60/13.20 ((
% 97.60/13.20 (contrasubsetT2) =>
% 97.60/13.20 ((
% 97.60/13.20 (contrasubsetT3) =>
% 97.60/13.20 ((
% 97.60/13.20 (doubleComplementI1) =>
% 97.60/13.20 ((
% 97.60/13.20 (doubleComplementE1) =>
% 97.60/13.20 ((
% 97.60/13.20 (doubleComplementSub1) =>
% 97.60/13.20 ((
% 97.60/13.20 (doubleComplementSub2) =>
% 97.60/13.20 ((
% 97.60/13.20 (doubleComplementEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementTnotintersectT) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementImpComplementIntersect) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementSubsetComplementIntersect) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementInPowersetComplementIntersect) =>
% 97.60/13.20 ((
% 97.60/13.20 (contraSubsetComplement) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementTcontraSubset) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionTILcontra) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionTIRcontra) =>
% 97.60/13.20 ((
% 97.60/13.20 (inIntersectImpInUnion) =>
% 97.60/13.20 ((
% 97.60/13.20 (inIntersectImpInUnion2) =>
% 97.60/13.20 ((
% 97.60/13.20 (inIntersectImpInIntersectUnions) =>
% 97.60/13.20 ((
% 97.60/13.20 (intersectInPowersetIntersectUnions) =>
% 97.60/13.20 ((
% 97.60/13.20 (inComplementUnionImpNotIn1) =>
% 97.60/13.20 ((
% 97.60/13.20 (inComplementUnionImpInComplement1) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionTE) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionTEcontra) =>
% 97.60/13.20 ((
% 97.60/13.20 (demorgan2a1) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementUnionInPowersetComplement) =>
% 97.60/13.20 ((
% 97.60/13.20 (demorgan2a2) =>
% 97.60/13.20 ((
% 97.60/13.20 (demorgan1a) =>
% 97.60/13.20 ((
% 97.60/13.20 (demorgan1b) =>
% 97.60/13.20 ((
% 97.60/13.20 (demorgan1) =>
% 97.60/13.20 ((
% 97.60/13.20 (demorgan2a) =>
% 97.60/13.20 ((
% 97.60/13.20 (demorgan2b2) =>
% 97.60/13.20 ((
% 97.60/13.20 (demorgan2b) =>
% 97.60/13.20 ((
% 97.60/13.20 (demorgan2) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz13rule0) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz13rule1) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz13rule2) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz13rule3) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz13rule4) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz1_1) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz1_2) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz1_3) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz1_4) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz1_5) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1all2) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1SetBreln1) =>
% 97.60/13.20 ((
% 97.60/13.20 (choice2fnsingleton) =>
% 97.60/13.20 ((
% 97.60/13.20 (setOfPairsIsBReln1) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1all1) =>
% 97.60/13.20 ((
% 97.60/13.20 (subbreln1) =>
% 97.60/13.20 ((
% 97.60/13.20 (eqbreln1) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1invprop) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1invI) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1invE) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1compprop) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1compI) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1compE) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1compEex) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1unionprop) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1unionIL) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1unionIR) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1unionI) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1unionE) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1unionEcases) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1unionCommutes) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz2Ex) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz2W) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz2A) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz2B) =>
% 97.60/13.20 ((
% 97.60/13.20 (image1Ex) =>
% 97.60/13.20 ((
% 97.60/13.20 (image1Ex1) =>
% 97.60/13.20 ((
% 97.60/13.20 (image1Equiv) =>
% 97.60/13.20 ((
% 97.60/13.20 (image1E) =>
% 97.60/13.20 ((
% 97.60/13.20 (image1I) =>
% 97.60/13.20 ((
% 97.60/13.20 (injFuncInInjFuncSet) =>
% 97.60/13.20 ((
% 97.60/13.20 (injFuncSetFuncIn) =>
% 97.60/13.20 ((
% 97.60/13.20 (injFuncSetFuncInj) =>
% 97.60/13.20 ((
% 97.60/13.20 (surjFuncSetFuncIn) =>
% 97.60/13.20 ((
% 97.60/13.20 (surjFuncSetFuncSurj) =>
% 97.60/13.20 ((
% 97.60/13.20 (leftInvIsSurj) =>
% 97.60/13.20 ((
% 97.60/13.20 (surjCantorThm) =>
% 97.60/13.20 ((
% 97.60/13.20 (foundation2) =>
% 97.60/13.20 ((
% 97.60/13.20 (notinself) =>
% 97.60/13.20 ((
% 97.60/13.20 (notinself2) =>
% 97.60/13.20 ((
% 97.60/13.20 (omegaSp) =>
% 97.60/13.20 ((
% 97.60/13.20 (omegaSclos) =>
% 97.60/13.20 ((
% 97.60/13.20 (peano0notS) =>
% 97.60/13.20 ((
% 97.60/13.20 (!!) @ (
% 97.60/13.20 (('#S') @ (
% 97.60/13.20 (
% 97.60/13.20 ('#B') @ (
% 97.60/13.20 =>) @
% 97.60/13.20 (
% 97.60/13.20 (
% 97.60/13.20 ('#C') @ in @
% 97.60/13.20 omega)))) @
% 97.60/13.20 (
% 97.60/13.20 (
% 97.60/13.20 ('#B') @ (
% 97.60/13.20 !!) @
% 97.60/13.20 (
% 97.60/13.20 (
% 97.60/13.20 ('#B') @ (
% 97.60/13.20 (
% 97.60/13.20 ('#S') @ (
% 97.60/13.20 (
% 97.60/13.20 ('#B') @ (
% 97.60/13.20 =>) @
% 97.60/13.20 (
% 97.60/13.20 (
% 97.60/13.20 ('#C') @ in @
% 97.60/13.20 omega)))))) @
% 97.60/13.20 (
% 97.60/13.20 (
% 97.60/13.20 ('#S') @ (
% 97.60/13.20 (
% 97.60/13.20 ('#B') @ (
% 97.60/13.20 '#S') @
% 97.60/13.20 (
% 97.60/13.20 (
% 97.60/13.20 ('#B') @ (
% 97.60/13.20 (
% 97.60/13.20 ('#B') @ (
% 97.60/13.20 =>))) @
% 97.60/13.20 (
% 97.60/13.20 (
% 97.60/13.20 ('#C') @ (
% 97.60/13.20 (
% 97.60/13.20 ('#B') @ (
% 97.60/13.20 '#B') @
% 97.60/13.20 (
% 97.60/13.20 (
% 97.60/13.20 ('#B') @ (
% 97.60/13.20 =) @
% 97.60/13.20 omegaS)))) @
% 97.60/13.20 omegaS)))))) @
% 97.60/13.20 (
% 97.60/13.20 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.60/13.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl561])).
% 97.60/13.20 thf(zip_derived_cl578, plain,
% 97.60/13.20 (~ (((prop2set2propI) =>
% 97.60/13.20 (((notdexE) =>
% 97.60/13.20 (((notdallE) =>
% 97.60/13.20 (((exuI1) =>
% 97.60/13.20 (((exuI3) =>
% 97.60/13.20 (((exuI2) =>
% 97.60/13.20 (((inCongP) =>
% 97.60/13.20 (((in__Cong) =>
% 97.60/13.20 (((exuE3u) =>
% 97.60/13.20 (((exu__Cong) =>
% 97.60/13.20 (((setadjoin__Cong) =>
% 97.60/13.20 (((powerset__Cong) =>
% 97.60/13.20 (((setunion__Cong) =>
% 97.60/13.20 (((exuEu) =>
% 97.60/13.20 (((descr__Cong) =>
% 97.60/13.20 (((dsetconstr__Cong) =>
% 97.60/13.20 (((subsetI1) =>
% 97.60/13.20 (((eqimpsubset2) =>
% 97.60/13.20 (((eqimpsubset1) =>
% 97.60/13.20 (((subsetI2) =>
% 97.60/13.20 (((emptysetsubset) =>
% 97.60/13.20 (((subsetE) =>
% 97.60/13.20 (((subsetE2) =>
% 97.60/13.20 (((notsubsetI) =>
% 97.60/13.20 (((notequalI1) =>
% 97.60/13.20 (((notequalI2) =>
% 97.60/13.20 (((subsetRefl) =>
% 97.60/13.20 (((subsetTrans) =>
% 97.60/13.20 (((setadjoinSub) =>
% 97.60/13.20 (((setadjoinSub2) =>
% 97.60/13.20 ((
% 97.60/13.20 (subset2powerset) =>
% 97.60/13.20 ((
% 97.60/13.20 (setextsub) =>
% 97.60/13.20 ((
% 97.60/13.20 (subsetemptysetimpeq) =>
% 97.60/13.20 ((
% 97.60/13.20 (powersetI1) =>
% 97.60/13.20 ((
% 97.60/13.20 (powersetE1) =>
% 97.60/13.20 ((
% 97.60/13.20 (inPowerset) =>
% 97.60/13.20 ((
% 97.60/13.20 (powersetsubset) =>
% 97.60/13.20 ((
% 97.60/13.20 (sepInPowerset) =>
% 97.60/13.20 ((
% 97.60/13.20 (sepSubset) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionIL) =>
% 97.60/13.20 ((
% 97.60/13.20 (upairset2IR) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionIR) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionEcases) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionE) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionLsub) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionRsub) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectI) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectSubset5) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectEL) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectLsub) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectSubset2) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectSubset3) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectER) =>
% 97.60/13.20 ((
% 97.60/13.20 (disjointsetsI1) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectRsub) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectSubset4) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectSubset1) =>
% 97.60/13.20 ((
% 97.60/13.20 (bs114d) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusI) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusEL) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusER) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusSubset2) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusERneg) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusELneg) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusILneg) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusIRneg) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusLsub) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusSubset1) =>
% 97.60/13.20 ((
% 97.60/13.20 (symdiffE) =>
% 97.60/13.20 ((
% 97.60/13.20 (symdiffI1) =>
% 97.60/13.20 ((
% 97.60/13.20 (symdiffI2) =>
% 97.60/13.20 ((
% 97.60/13.20 (symdiffIneg1) =>
% 97.60/13.20 ((
% 97.60/13.20 (symdiffIneg2) =>
% 97.60/13.20 ((
% 97.60/13.20 (secondinupair) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairIL) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairIR) =>
% 97.60/13.20 ((
% 97.60/13.20 (kpairiskpair) =>
% 97.60/13.20 ((
% 97.60/13.20 (kpairp) =>
% 97.60/13.20 ((
% 97.60/13.20 (singletonsubset) =>
% 97.60/13.20 ((
% 97.60/13.20 (singletoninpowerset) =>
% 97.60/13.20 ((
% 97.60/13.20 (singletoninpowunion) =>
% 97.60/13.20 ((
% 97.60/13.20 (upairset2E) =>
% 97.60/13.20 ((
% 97.60/13.20 (upairsubunion) =>
% 97.60/13.20 ((
% 97.60/13.20 (upairinpowunion) =>
% 97.60/13.20 ((
% 97.60/13.20 (ubforcartprodlem1) =>
% 97.60/13.20 ((
% 97.60/13.20 (ubforcartprodlem2) =>
% 97.60/13.20 ((
% 97.60/13.20 (ubforcartprodlem3) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodpairin) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodmempair1) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodmempair) =>
% 97.60/13.20 ((
% 97.60/13.20 (setunionE2) =>
% 97.60/13.20 ((
% 97.60/13.20 (setunionsingleton1) =>
% 97.60/13.20 ((
% 97.60/13.20 (setunionsingleton2) =>
% 97.60/13.20 ((
% 97.60/13.20 (setunionsingleton) =>
% 97.60/13.20 ((
% 97.60/13.20 (singletonprop) =>
% 97.60/13.20 ((
% 97.60/13.20 (ex1E1) =>
% 97.60/13.20 ((
% 97.60/13.20 (ex1I) =>
% 97.60/13.20 ((
% 97.60/13.20 (ex1I2) =>
% 97.60/13.20 ((
% 97.60/13.20 (singletonsuniq) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairinjL1) =>
% 97.60/13.20 ((
% 97.60/13.20 (kfstsingleton) =>
% 97.60/13.20 ((
% 97.60/13.20 (theprop) =>
% 97.60/13.20 ((
% 97.60/13.20 (kfstpairEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodfstin) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairinjL2) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairinjL) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairinjR11) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairinjR12) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairinjR1) =>
% 97.60/13.20 ((
% 97.60/13.20 (upairequniteq) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairinjR2) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairinjR) =>
% 97.60/13.20 ((
% 97.60/13.20 (ksndsingleton) =>
% 97.60/13.20 ((
% 97.60/13.20 (ksndpairEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (kpairsurjEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodsndin) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodpairmemEL) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodpairmemER) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodmempaircEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodfstpairEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodsndpairEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodpairsurjEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (dpsetconstrI) =>
% 97.60/13.20 ((
% 97.60/13.20 (dpsetconstrSub) =>
% 97.60/13.20 ((
% 97.60/13.20 (setOfPairsIsBReln) =>
% 97.60/13.20 ((
% 97.60/13.20 (dpsetconstrERa) =>
% 97.60/13.20 ((
% 97.60/13.20 (dpsetconstrEL1) =>
% 97.60/13.20 ((
% 97.60/13.20 (dpsetconstrEL2) =>
% 97.60/13.20 ((
% 97.60/13.20 (dpsetconstrER) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcImageSingleton) =>
% 97.60/13.20 ((
% 97.60/13.20 (apProp) =>
% 97.60/13.20 ((
% 97.60/13.20 (app) =>
% 97.60/13.20 ((
% 97.60/13.20 (infuncsetfunc) =>
% 97.60/13.20 ((
% 97.60/13.20 (ap2p) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcinfuncset) =>
% 97.60/13.20 ((
% 97.60/13.20 (lamProp) =>
% 97.60/13.20 ((
% 97.60/13.20 (lamp) =>
% 97.60/13.20 ((
% 97.60/13.20 (lam2p) =>
% 97.60/13.20 ((
% 97.60/13.20 (brelnall1) =>
% 97.60/13.20 ((
% 97.60/13.20 (brelnall2) =>
% 97.60/13.20 ((
% 97.60/13.20 (ex1E2) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcGraphProp1) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcGraphProp3) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcGraphProp2) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcextLem) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcGraphProp4) =>
% 97.60/13.20 ((
% 97.60/13.20 (subbreln) =>
% 97.60/13.20 ((
% 97.60/13.20 (eqbreln) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcext) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcext2) =>
% 97.60/13.20 ((
% 97.60/13.20 (ap2apEq1) =>
% 97.60/13.20 ((
% 97.60/13.20 (ap2apEq2) =>
% 97.60/13.20 ((
% 97.60/13.20 (beta1) =>
% 97.60/13.20 ((
% 97.60/13.20 (eta1) =>
% 97.60/13.20 ((
% 97.60/13.20 (lam2lamEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (beta2) =>
% 97.60/13.20 ((
% 97.60/13.20 (eta2) =>
% 97.60/13.20 ((
% 97.60/13.20 (iffalseProp1) =>
% 97.60/13.20 ((
% 97.60/13.20 (iffalseProp2) =>
% 97.60/13.20 ((
% 97.60/13.20 (iftrueProp1) =>
% 97.60/13.20 ((
% 97.60/13.20 (iftrueProp2) =>
% 97.60/13.20 ((
% 97.60/13.20 (ifSingleton) =>
% 97.60/13.20 ((
% 97.60/13.20 (ifp) =>
% 97.60/13.20 ((
% 97.60/13.20 (theeq) =>
% 97.60/13.20 ((
% 97.60/13.20 (iftrue) =>
% 97.60/13.20 ((
% 97.60/13.20 (iffalse) =>
% 97.60/13.20 ((
% 97.60/13.20 (iftrueorfalse) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectT_lem) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionT_lem) =>
% 97.60/13.20 ((
% 97.60/13.20 (powersetT_lem) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusT_lem) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementT_lem) =>
% 97.60/13.20 ((
% 97.60/13.20 (setextT) =>
% 97.60/13.20 ((
% 97.60/13.20 (subsetTI) =>
% 97.60/13.20 ((
% 97.60/13.20 (powersetTI1) =>
% 97.60/13.20 ((
% 97.60/13.20 (powersetTE1) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementTI1) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementTE1) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectTELcontra) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectTERcontra) =>
% 97.60/13.20 ((
% 97.60/13.20 (contrasubsetT) =>
% 97.60/13.20 ((
% 97.60/13.20 (contrasubsetT1) =>
% 97.60/13.20 ((
% 97.60/13.20 (contrasubsetT2) =>
% 97.60/13.20 ((
% 97.60/13.20 (contrasubsetT3) =>
% 97.60/13.20 ((
% 97.60/13.20 (doubleComplementI1) =>
% 97.60/13.20 ((
% 97.60/13.20 (doubleComplementE1) =>
% 97.60/13.20 ((
% 97.60/13.20 (doubleComplementSub1) =>
% 97.60/13.20 ((
% 97.60/13.20 (doubleComplementSub2) =>
% 97.60/13.20 ((
% 97.60/13.20 (doubleComplementEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementTnotintersectT) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementImpComplementIntersect) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementSubsetComplementIntersect) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementInPowersetComplementIntersect) =>
% 97.60/13.20 ((
% 97.60/13.20 (contraSubsetComplement) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementTcontraSubset) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionTILcontra) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionTIRcontra) =>
% 97.60/13.20 ((
% 97.60/13.20 (inIntersectImpInUnion) =>
% 97.60/13.20 ((
% 97.60/13.20 (inIntersectImpInUnion2) =>
% 97.60/13.20 ((
% 97.60/13.20 (inIntersectImpInIntersectUnions) =>
% 97.60/13.20 ((
% 97.60/13.20 (intersectInPowersetIntersectUnions) =>
% 97.60/13.20 ((
% 97.60/13.20 (inComplementUnionImpNotIn1) =>
% 97.60/13.20 ((
% 97.60/13.20 (inComplementUnionImpInComplement1) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionTE) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionTEcontra) =>
% 97.60/13.20 ((
% 97.60/13.20 (demorgan2a1) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementUnionInPowersetComplement) =>
% 97.60/13.20 ((
% 97.60/13.20 (demorgan2a2) =>
% 97.60/13.20 ((
% 97.60/13.20 (demorgan1a) =>
% 97.60/13.20 ((
% 97.60/13.20 (demorgan1b) =>
% 97.60/13.20 ((
% 97.60/13.20 (demorgan1) =>
% 97.60/13.20 ((
% 97.60/13.20 (demorgan2a) =>
% 97.60/13.20 ((
% 97.60/13.20 (demorgan2b2) =>
% 97.60/13.20 ((
% 97.60/13.20 (demorgan2b) =>
% 97.60/13.20 ((
% 97.60/13.20 (demorgan2) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz13rule0) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz13rule1) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz13rule2) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz13rule3) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz13rule4) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz1_1) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz1_2) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz1_3) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz1_4) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz1_5) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1all2) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1SetBreln1) =>
% 97.60/13.20 ((
% 97.60/13.20 (choice2fnsingleton) =>
% 97.60/13.20 ((
% 97.60/13.20 (setOfPairsIsBReln1) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1all1) =>
% 97.60/13.20 ((
% 97.60/13.20 (subbreln1) =>
% 97.60/13.20 ((
% 97.60/13.20 (eqbreln1) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1invprop) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1invI) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1invE) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1compprop) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1compI) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1compE) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1compEex) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1unionprop) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1unionIL) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1unionIR) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1unionI) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1unionE) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1unionEcases) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1unionCommutes) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz2Ex) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz2W) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz2A) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz2B) =>
% 97.60/13.20 ((
% 97.60/13.20 (image1Ex) =>
% 97.60/13.20 ((
% 97.60/13.20 (image1Ex1) =>
% 97.60/13.20 ((
% 97.60/13.20 (image1Equiv) =>
% 97.60/13.20 ((
% 97.60/13.20 (image1E) =>
% 97.60/13.20 ((
% 97.60/13.20 (image1I) =>
% 97.60/13.20 ((
% 97.60/13.20 (injFuncInInjFuncSet) =>
% 97.60/13.20 ((
% 97.60/13.20 (injFuncSetFuncIn) =>
% 97.60/13.20 ((
% 97.60/13.20 (injFuncSetFuncInj) =>
% 97.60/13.20 ((
% 97.60/13.20 (surjFuncSetFuncIn) =>
% 97.60/13.20 ((
% 97.60/13.20 (surjFuncSetFuncSurj) =>
% 97.60/13.20 ((
% 97.60/13.20 (leftInvIsSurj) =>
% 97.60/13.20 ((
% 97.60/13.20 (surjCantorThm) =>
% 97.60/13.20 ((
% 97.60/13.20 (foundation2) =>
% 97.60/13.20 ((
% 97.60/13.20 (notinself) =>
% 97.60/13.20 ((
% 97.60/13.20 (notinself2) =>
% 97.60/13.20 ((
% 97.60/13.20 (omegaSp) =>
% 97.60/13.20 ((
% 97.60/13.20 (omegaSclos) =>
% 97.60/13.20 ((
% 97.60/13.20 (peano0notS) =>
% 97.60/13.20 ((
% 97.60/13.20 (!!) @ (
% 97.60/13.20 (('#S') @ (
% 97.60/13.20 (
% 97.60/13.20 ('#B') @ (
% 97.60/13.20 =>) @
% 97.60/13.20 (
% 97.60/13.20 (
% 97.60/13.20 ('#C') @ in @
% 97.60/13.20 omega)))) @
% 97.60/13.20 (
% 97.60/13.20 (
% 97.60/13.20 ('#B') @ (
% 97.60/13.20 !!) @
% 97.60/13.20 (
% 97.60/13.20 (
% 97.60/13.20 ('#B') @ (
% 97.60/13.20 (
% 97.60/13.20 ('#S') @ (
% 97.60/13.20 (
% 97.60/13.20 ('#B') @ (
% 97.60/13.20 =>) @
% 97.60/13.20 (
% 97.60/13.20 (
% 97.60/13.20 ('#C') @ in @
% 97.60/13.20 omega)))))) @
% 97.60/13.20 (
% 97.60/13.20 (
% 97.60/13.20 ('#S') @ (
% 97.60/13.20 (
% 97.60/13.20 ('#B') @ (
% 97.60/13.20 '#S') @
% 97.60/13.20 (
% 97.60/13.20 (
% 97.60/13.20 ('#B') @ (
% 97.60/13.20 (
% 97.60/13.20 ('#B') @ (
% 97.60/13.20 =>))) @
% 97.60/13.20 (
% 97.60/13.20 (
% 97.60/13.20 ('#C') @ (
% 97.60/13.20 (
% 97.60/13.20 ('#B') @ (
% 97.60/13.20 '#B') @
% 97.60/13.20 (
% 97.60/13.20 (
% 97.60/13.20 ('#B') @ (
% 97.60/13.20 =) @
% 97.60/13.20 omegaS)))) @
% 97.60/13.20 omegaS)))))) @
% 97.60/13.20 (
% 97.60/13.20 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.60/13.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl570])).
% 97.60/13.20 thf(zip_derived_cl586, plain,
% 97.60/13.20 (~ (((notdexE) =>
% 97.60/13.20 (((notdallE) =>
% 97.60/13.20 (((exuI1) =>
% 97.60/13.20 (((exuI3) =>
% 97.60/13.20 (((exuI2) =>
% 97.60/13.20 (((inCongP) =>
% 97.60/13.20 (((in__Cong) =>
% 97.60/13.20 (((exuE3u) =>
% 97.60/13.20 (((exu__Cong) =>
% 97.60/13.20 (((setadjoin__Cong) =>
% 97.60/13.20 (((powerset__Cong) =>
% 97.60/13.20 (((setunion__Cong) =>
% 97.60/13.20 (((exuEu) =>
% 97.60/13.20 (((descr__Cong) =>
% 97.60/13.20 (((dsetconstr__Cong) =>
% 97.60/13.20 (((subsetI1) =>
% 97.60/13.20 (((eqimpsubset2) =>
% 97.60/13.20 (((eqimpsubset1) =>
% 97.60/13.20 (((subsetI2) =>
% 97.60/13.20 (((emptysetsubset) =>
% 97.60/13.20 (((subsetE) =>
% 97.60/13.20 (((subsetE2) =>
% 97.60/13.20 (((notsubsetI) =>
% 97.60/13.20 (((notequalI1) =>
% 97.60/13.20 (((notequalI2) =>
% 97.60/13.20 (((subsetRefl) =>
% 97.60/13.20 (((subsetTrans) =>
% 97.60/13.20 (((setadjoinSub) =>
% 97.60/13.20 (((setadjoinSub2) =>
% 97.60/13.20 (((subset2powerset) =>
% 97.60/13.20 ((
% 97.60/13.20 (setextsub) =>
% 97.60/13.20 ((
% 97.60/13.20 (subsetemptysetimpeq) =>
% 97.60/13.20 ((
% 97.60/13.20 (powersetI1) =>
% 97.60/13.20 ((
% 97.60/13.20 (powersetE1) =>
% 97.60/13.20 ((
% 97.60/13.20 (inPowerset) =>
% 97.60/13.20 ((
% 97.60/13.20 (powersetsubset) =>
% 97.60/13.20 ((
% 97.60/13.20 (sepInPowerset) =>
% 97.60/13.20 ((
% 97.60/13.20 (sepSubset) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionIL) =>
% 97.60/13.20 ((
% 97.60/13.20 (upairset2IR) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionIR) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionEcases) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionE) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionLsub) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionRsub) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectI) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectSubset5) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectEL) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectLsub) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectSubset2) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectSubset3) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectER) =>
% 97.60/13.20 ((
% 97.60/13.20 (disjointsetsI1) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectRsub) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectSubset4) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectSubset1) =>
% 97.60/13.20 ((
% 97.60/13.20 (bs114d) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusI) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusEL) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusER) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusSubset2) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusERneg) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusELneg) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusILneg) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusIRneg) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusLsub) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusSubset1) =>
% 97.60/13.20 ((
% 97.60/13.20 (symdiffE) =>
% 97.60/13.20 ((
% 97.60/13.20 (symdiffI1) =>
% 97.60/13.20 ((
% 97.60/13.20 (symdiffI2) =>
% 97.60/13.20 ((
% 97.60/13.20 (symdiffIneg1) =>
% 97.60/13.20 ((
% 97.60/13.20 (symdiffIneg2) =>
% 97.60/13.20 ((
% 97.60/13.20 (secondinupair) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairIL) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairIR) =>
% 97.60/13.20 ((
% 97.60/13.20 (kpairiskpair) =>
% 97.60/13.20 ((
% 97.60/13.20 (kpairp) =>
% 97.60/13.20 ((
% 97.60/13.20 (singletonsubset) =>
% 97.60/13.20 ((
% 97.60/13.20 (singletoninpowerset) =>
% 97.60/13.20 ((
% 97.60/13.20 (singletoninpowunion) =>
% 97.60/13.20 ((
% 97.60/13.20 (upairset2E) =>
% 97.60/13.20 ((
% 97.60/13.20 (upairsubunion) =>
% 97.60/13.20 ((
% 97.60/13.20 (upairinpowunion) =>
% 97.60/13.20 ((
% 97.60/13.20 (ubforcartprodlem1) =>
% 97.60/13.20 ((
% 97.60/13.20 (ubforcartprodlem2) =>
% 97.60/13.20 ((
% 97.60/13.20 (ubforcartprodlem3) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodpairin) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodmempair1) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodmempair) =>
% 97.60/13.20 ((
% 97.60/13.20 (setunionE2) =>
% 97.60/13.20 ((
% 97.60/13.20 (setunionsingleton1) =>
% 97.60/13.20 ((
% 97.60/13.20 (setunionsingleton2) =>
% 97.60/13.20 ((
% 97.60/13.20 (setunionsingleton) =>
% 97.60/13.20 ((
% 97.60/13.20 (singletonprop) =>
% 97.60/13.20 ((
% 97.60/13.20 (ex1E1) =>
% 97.60/13.20 ((
% 97.60/13.20 (ex1I) =>
% 97.60/13.20 ((
% 97.60/13.20 (ex1I2) =>
% 97.60/13.20 ((
% 97.60/13.20 (singletonsuniq) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairinjL1) =>
% 97.60/13.20 ((
% 97.60/13.20 (kfstsingleton) =>
% 97.60/13.20 ((
% 97.60/13.20 (theprop) =>
% 97.60/13.20 ((
% 97.60/13.20 (kfstpairEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodfstin) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairinjL2) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairinjL) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairinjR11) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairinjR12) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairinjR1) =>
% 97.60/13.20 ((
% 97.60/13.20 (upairequniteq) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairinjR2) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairinjR) =>
% 97.60/13.20 ((
% 97.60/13.20 (ksndsingleton) =>
% 97.60/13.20 ((
% 97.60/13.20 (ksndpairEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (kpairsurjEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodsndin) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodpairmemEL) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodpairmemER) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodmempaircEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodfstpairEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodsndpairEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodpairsurjEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (dpsetconstrI) =>
% 97.60/13.20 ((
% 97.60/13.20 (dpsetconstrSub) =>
% 97.60/13.20 ((
% 97.60/13.20 (setOfPairsIsBReln) =>
% 97.60/13.20 ((
% 97.60/13.20 (dpsetconstrERa) =>
% 97.60/13.20 ((
% 97.60/13.20 (dpsetconstrEL1) =>
% 97.60/13.20 ((
% 97.60/13.20 (dpsetconstrEL2) =>
% 97.60/13.20 ((
% 97.60/13.20 (dpsetconstrER) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcImageSingleton) =>
% 97.60/13.20 ((
% 97.60/13.20 (apProp) =>
% 97.60/13.20 ((
% 97.60/13.20 (app) =>
% 97.60/13.20 ((
% 97.60/13.20 (infuncsetfunc) =>
% 97.60/13.20 ((
% 97.60/13.20 (ap2p) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcinfuncset) =>
% 97.60/13.20 ((
% 97.60/13.20 (lamProp) =>
% 97.60/13.20 ((
% 97.60/13.20 (lamp) =>
% 97.60/13.20 ((
% 97.60/13.20 (lam2p) =>
% 97.60/13.20 ((
% 97.60/13.20 (brelnall1) =>
% 97.60/13.20 ((
% 97.60/13.20 (brelnall2) =>
% 97.60/13.20 ((
% 97.60/13.20 (ex1E2) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcGraphProp1) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcGraphProp3) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcGraphProp2) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcextLem) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcGraphProp4) =>
% 97.60/13.20 ((
% 97.60/13.20 (subbreln) =>
% 97.60/13.20 ((
% 97.60/13.20 (eqbreln) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcext) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcext2) =>
% 97.60/13.20 ((
% 97.60/13.20 (ap2apEq1) =>
% 97.60/13.20 ((
% 97.60/13.20 (ap2apEq2) =>
% 97.60/13.20 ((
% 97.60/13.20 (beta1) =>
% 97.60/13.20 ((
% 97.60/13.20 (eta1) =>
% 97.60/13.20 ((
% 97.60/13.20 (lam2lamEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (beta2) =>
% 97.60/13.20 ((
% 97.60/13.20 (eta2) =>
% 97.60/13.20 ((
% 97.60/13.20 (iffalseProp1) =>
% 97.60/13.20 ((
% 97.60/13.20 (iffalseProp2) =>
% 97.60/13.20 ((
% 97.60/13.20 (iftrueProp1) =>
% 97.60/13.20 ((
% 97.60/13.20 (iftrueProp2) =>
% 97.60/13.20 ((
% 97.60/13.20 (ifSingleton) =>
% 97.60/13.20 ((
% 97.60/13.20 (ifp) =>
% 97.60/13.20 ((
% 97.60/13.20 (theeq) =>
% 97.60/13.20 ((
% 97.60/13.20 (iftrue) =>
% 97.60/13.20 ((
% 97.60/13.20 (iffalse) =>
% 97.60/13.20 ((
% 97.60/13.20 (iftrueorfalse) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectT_lem) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionT_lem) =>
% 97.60/13.20 ((
% 97.60/13.20 (powersetT_lem) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusT_lem) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementT_lem) =>
% 97.60/13.20 ((
% 97.60/13.20 (setextT) =>
% 97.60/13.20 ((
% 97.60/13.20 (subsetTI) =>
% 97.60/13.20 ((
% 97.60/13.20 (powersetTI1) =>
% 97.60/13.20 ((
% 97.60/13.20 (powersetTE1) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementTI1) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementTE1) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectTELcontra) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectTERcontra) =>
% 97.60/13.20 ((
% 97.60/13.20 (contrasubsetT) =>
% 97.60/13.20 ((
% 97.60/13.20 (contrasubsetT1) =>
% 97.60/13.20 ((
% 97.60/13.20 (contrasubsetT2) =>
% 97.60/13.20 ((
% 97.60/13.20 (contrasubsetT3) =>
% 97.60/13.20 ((
% 97.60/13.20 (doubleComplementI1) =>
% 97.60/13.20 ((
% 97.60/13.20 (doubleComplementE1) =>
% 97.60/13.20 ((
% 97.60/13.20 (doubleComplementSub1) =>
% 97.60/13.20 ((
% 97.60/13.20 (doubleComplementSub2) =>
% 97.60/13.20 ((
% 97.60/13.20 (doubleComplementEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementTnotintersectT) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementImpComplementIntersect) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementSubsetComplementIntersect) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementInPowersetComplementIntersect) =>
% 97.60/13.20 ((
% 97.60/13.20 (contraSubsetComplement) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementTcontraSubset) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionTILcontra) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionTIRcontra) =>
% 97.60/13.20 ((
% 97.60/13.20 (inIntersectImpInUnion) =>
% 97.60/13.20 ((
% 97.60/13.20 (inIntersectImpInUnion2) =>
% 97.60/13.20 ((
% 97.60/13.20 (inIntersectImpInIntersectUnions) =>
% 97.60/13.20 ((
% 97.60/13.20 (intersectInPowersetIntersectUnions) =>
% 97.60/13.20 ((
% 97.60/13.20 (inComplementUnionImpNotIn1) =>
% 97.60/13.20 ((
% 97.60/13.20 (inComplementUnionImpInComplement1) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionTE) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionTEcontra) =>
% 97.60/13.20 ((
% 97.60/13.20 (demorgan2a1) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementUnionInPowersetComplement) =>
% 97.60/13.20 ((
% 97.60/13.20 (demorgan2a2) =>
% 97.60/13.20 ((
% 97.60/13.20 (demorgan1a) =>
% 97.60/13.20 ((
% 97.60/13.20 (demorgan1b) =>
% 97.60/13.20 ((
% 97.60/13.20 (demorgan1) =>
% 97.60/13.20 ((
% 97.60/13.20 (demorgan2a) =>
% 97.60/13.20 ((
% 97.60/13.20 (demorgan2b2) =>
% 97.60/13.20 ((
% 97.60/13.20 (demorgan2b) =>
% 97.60/13.20 ((
% 97.60/13.20 (demorgan2) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz13rule0) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz13rule1) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz13rule2) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz13rule3) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz13rule4) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz1_1) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz1_2) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz1_3) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz1_4) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz1_5) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1all2) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1SetBreln1) =>
% 97.60/13.20 ((
% 97.60/13.20 (choice2fnsingleton) =>
% 97.60/13.20 ((
% 97.60/13.20 (setOfPairsIsBReln1) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1all1) =>
% 97.60/13.20 ((
% 97.60/13.20 (subbreln1) =>
% 97.60/13.20 ((
% 97.60/13.20 (eqbreln1) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1invprop) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1invI) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1invE) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1compprop) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1compI) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1compE) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1compEex) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1unionprop) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1unionIL) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1unionIR) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1unionI) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1unionE) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1unionEcases) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1unionCommutes) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz2Ex) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz2W) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz2A) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz2B) =>
% 97.60/13.20 ((
% 97.60/13.20 (image1Ex) =>
% 97.60/13.20 ((
% 97.60/13.20 (image1Ex1) =>
% 97.60/13.20 ((
% 97.60/13.20 (image1Equiv) =>
% 97.60/13.20 ((
% 97.60/13.20 (image1E) =>
% 97.60/13.20 ((
% 97.60/13.20 (image1I) =>
% 97.60/13.20 ((
% 97.60/13.20 (injFuncInInjFuncSet) =>
% 97.60/13.20 ((
% 97.60/13.20 (injFuncSetFuncIn) =>
% 97.60/13.20 ((
% 97.60/13.20 (injFuncSetFuncInj) =>
% 97.60/13.20 ((
% 97.60/13.20 (surjFuncSetFuncIn) =>
% 97.60/13.20 ((
% 97.60/13.20 (surjFuncSetFuncSurj) =>
% 97.60/13.20 ((
% 97.60/13.20 (leftInvIsSurj) =>
% 97.60/13.20 ((
% 97.60/13.20 (surjCantorThm) =>
% 97.60/13.20 ((
% 97.60/13.20 (foundation2) =>
% 97.60/13.20 ((
% 97.60/13.20 (notinself) =>
% 97.60/13.20 ((
% 97.60/13.20 (notinself2) =>
% 97.60/13.20 ((
% 97.60/13.20 (omegaSp) =>
% 97.60/13.20 ((
% 97.60/13.20 (omegaSclos) =>
% 97.60/13.20 ((
% 97.60/13.20 (peano0notS) =>
% 97.60/13.20 ((
% 97.60/13.20 (!!) @ (
% 97.60/13.20 (('#S') @ (
% 97.60/13.20 (
% 97.60/13.20 ('#B') @ (
% 97.60/13.20 =>) @
% 97.60/13.20 (
% 97.60/13.20 (
% 97.60/13.20 ('#C') @ in @
% 97.60/13.20 omega)))) @
% 97.60/13.20 (
% 97.60/13.20 (
% 97.60/13.20 ('#B') @ (
% 97.60/13.20 !!) @
% 97.60/13.20 (
% 97.60/13.20 (
% 97.60/13.20 ('#B') @ (
% 97.60/13.20 (
% 97.60/13.20 ('#S') @ (
% 97.60/13.20 (
% 97.60/13.20 ('#B') @ (
% 97.60/13.20 =>) @
% 97.60/13.20 (
% 97.60/13.20 (
% 97.60/13.20 ('#C') @ in @
% 97.60/13.20 omega)))))) @
% 97.60/13.20 (
% 97.60/13.20 (
% 97.60/13.20 ('#S') @ (
% 97.60/13.20 (
% 97.60/13.20 ('#B') @ (
% 97.60/13.20 '#S') @
% 97.60/13.20 (
% 97.60/13.20 (
% 97.60/13.20 ('#B') @ (
% 97.60/13.20 (
% 97.60/13.20 ('#B') @ (
% 97.60/13.20 =>))) @
% 97.60/13.20 (
% 97.60/13.20 (
% 97.60/13.20 ('#C') @ (
% 97.60/13.20 (
% 97.60/13.20 ('#B') @ (
% 97.60/13.20 '#B') @
% 97.60/13.20 (
% 97.60/13.20 (
% 97.60/13.20 ('#B') @ (
% 97.60/13.20 =) @
% 97.60/13.20 omegaS)))) @
% 97.60/13.20 omegaS)))))) @
% 97.60/13.20 (
% 97.60/13.20 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.60/13.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl578])).
% 97.60/13.20 thf(zip_derived_cl595, plain,
% 97.60/13.20 (~ (((notdallE) =>
% 97.60/13.20 (((exuI1) =>
% 97.60/13.20 (((exuI3) =>
% 97.60/13.20 (((exuI2) =>
% 97.60/13.20 (((inCongP) =>
% 97.60/13.20 (((in__Cong) =>
% 97.60/13.20 (((exuE3u) =>
% 97.60/13.20 (((exu__Cong) =>
% 97.60/13.20 (((setadjoin__Cong) =>
% 97.60/13.20 (((powerset__Cong) =>
% 97.60/13.20 (((setunion__Cong) =>
% 97.60/13.20 (((exuEu) =>
% 97.60/13.20 (((descr__Cong) =>
% 97.60/13.20 (((dsetconstr__Cong) =>
% 97.60/13.20 (((subsetI1) =>
% 97.60/13.20 (((eqimpsubset2) =>
% 97.60/13.20 (((eqimpsubset1) =>
% 97.60/13.20 (((subsetI2) =>
% 97.60/13.20 (((emptysetsubset) =>
% 97.60/13.20 (((subsetE) =>
% 97.60/13.20 (((subsetE2) =>
% 97.60/13.20 (((notsubsetI) =>
% 97.60/13.20 (((notequalI1) =>
% 97.60/13.20 (((notequalI2) =>
% 97.60/13.20 (((subsetRefl) =>
% 97.60/13.20 (((subsetTrans) =>
% 97.60/13.20 (((setadjoinSub) =>
% 97.60/13.20 (((setadjoinSub2) =>
% 97.60/13.20 (((subset2powerset) =>
% 97.60/13.20 (((setextsub) =>
% 97.60/13.20 ((
% 97.60/13.20 (subsetemptysetimpeq) =>
% 97.60/13.20 ((
% 97.60/13.20 (powersetI1) =>
% 97.60/13.20 ((
% 97.60/13.20 (powersetE1) =>
% 97.60/13.20 ((
% 97.60/13.20 (inPowerset) =>
% 97.60/13.20 ((
% 97.60/13.20 (powersetsubset) =>
% 97.60/13.20 ((
% 97.60/13.20 (sepInPowerset) =>
% 97.60/13.20 ((
% 97.60/13.20 (sepSubset) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionIL) =>
% 97.60/13.20 ((
% 97.60/13.20 (upairset2IR) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionIR) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionEcases) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionE) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionLsub) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionRsub) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectI) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectSubset5) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectEL) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectLsub) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectSubset2) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectSubset3) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectER) =>
% 97.60/13.20 ((
% 97.60/13.20 (disjointsetsI1) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectRsub) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectSubset4) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectSubset1) =>
% 97.60/13.20 ((
% 97.60/13.20 (bs114d) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusI) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusEL) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusER) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusSubset2) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusERneg) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusELneg) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusILneg) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusIRneg) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusLsub) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusSubset1) =>
% 97.60/13.20 ((
% 97.60/13.20 (symdiffE) =>
% 97.60/13.20 ((
% 97.60/13.20 (symdiffI1) =>
% 97.60/13.20 ((
% 97.60/13.20 (symdiffI2) =>
% 97.60/13.20 ((
% 97.60/13.20 (symdiffIneg1) =>
% 97.60/13.20 ((
% 97.60/13.20 (symdiffIneg2) =>
% 97.60/13.20 ((
% 97.60/13.20 (secondinupair) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairIL) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairIR) =>
% 97.60/13.20 ((
% 97.60/13.20 (kpairiskpair) =>
% 97.60/13.20 ((
% 97.60/13.20 (kpairp) =>
% 97.60/13.20 ((
% 97.60/13.20 (singletonsubset) =>
% 97.60/13.20 ((
% 97.60/13.20 (singletoninpowerset) =>
% 97.60/13.20 ((
% 97.60/13.20 (singletoninpowunion) =>
% 97.60/13.20 ((
% 97.60/13.20 (upairset2E) =>
% 97.60/13.20 ((
% 97.60/13.20 (upairsubunion) =>
% 97.60/13.20 ((
% 97.60/13.20 (upairinpowunion) =>
% 97.60/13.20 ((
% 97.60/13.20 (ubforcartprodlem1) =>
% 97.60/13.20 ((
% 97.60/13.20 (ubforcartprodlem2) =>
% 97.60/13.20 ((
% 97.60/13.20 (ubforcartprodlem3) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodpairin) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodmempair1) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodmempair) =>
% 97.60/13.20 ((
% 97.60/13.20 (setunionE2) =>
% 97.60/13.20 ((
% 97.60/13.20 (setunionsingleton1) =>
% 97.60/13.20 ((
% 97.60/13.20 (setunionsingleton2) =>
% 97.60/13.20 ((
% 97.60/13.20 (setunionsingleton) =>
% 97.60/13.20 ((
% 97.60/13.20 (singletonprop) =>
% 97.60/13.20 ((
% 97.60/13.20 (ex1E1) =>
% 97.60/13.20 ((
% 97.60/13.20 (ex1I) =>
% 97.60/13.20 ((
% 97.60/13.20 (ex1I2) =>
% 97.60/13.20 ((
% 97.60/13.20 (singletonsuniq) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairinjL1) =>
% 97.60/13.20 ((
% 97.60/13.20 (kfstsingleton) =>
% 97.60/13.20 ((
% 97.60/13.20 (theprop) =>
% 97.60/13.20 ((
% 97.60/13.20 (kfstpairEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodfstin) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairinjL2) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairinjL) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairinjR11) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairinjR12) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairinjR1) =>
% 97.60/13.20 ((
% 97.60/13.20 (upairequniteq) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairinjR2) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairinjR) =>
% 97.60/13.20 ((
% 97.60/13.20 (ksndsingleton) =>
% 97.60/13.20 ((
% 97.60/13.20 (ksndpairEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (kpairsurjEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodsndin) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodpairmemEL) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodpairmemER) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodmempaircEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodfstpairEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodsndpairEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodpairsurjEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (dpsetconstrI) =>
% 97.60/13.20 ((
% 97.60/13.20 (dpsetconstrSub) =>
% 97.60/13.20 ((
% 97.60/13.20 (setOfPairsIsBReln) =>
% 97.60/13.20 ((
% 97.60/13.20 (dpsetconstrERa) =>
% 97.60/13.20 ((
% 97.60/13.20 (dpsetconstrEL1) =>
% 97.60/13.20 ((
% 97.60/13.20 (dpsetconstrEL2) =>
% 97.60/13.20 ((
% 97.60/13.20 (dpsetconstrER) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcImageSingleton) =>
% 97.60/13.20 ((
% 97.60/13.20 (apProp) =>
% 97.60/13.20 ((
% 97.60/13.20 (app) =>
% 97.60/13.20 ((
% 97.60/13.20 (infuncsetfunc) =>
% 97.60/13.20 ((
% 97.60/13.20 (ap2p) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcinfuncset) =>
% 97.60/13.20 ((
% 97.60/13.20 (lamProp) =>
% 97.60/13.20 ((
% 97.60/13.20 (lamp) =>
% 97.60/13.20 ((
% 97.60/13.20 (lam2p) =>
% 97.60/13.20 ((
% 97.60/13.20 (brelnall1) =>
% 97.60/13.20 ((
% 97.60/13.20 (brelnall2) =>
% 97.60/13.20 ((
% 97.60/13.20 (ex1E2) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcGraphProp1) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcGraphProp3) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcGraphProp2) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcextLem) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcGraphProp4) =>
% 97.60/13.20 ((
% 97.60/13.20 (subbreln) =>
% 97.60/13.20 ((
% 97.60/13.20 (eqbreln) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcext) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcext2) =>
% 97.60/13.20 ((
% 97.60/13.20 (ap2apEq1) =>
% 97.60/13.20 ((
% 97.60/13.20 (ap2apEq2) =>
% 97.60/13.20 ((
% 97.60/13.20 (beta1) =>
% 97.60/13.20 ((
% 97.60/13.20 (eta1) =>
% 97.60/13.20 ((
% 97.60/13.20 (lam2lamEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (beta2) =>
% 97.60/13.20 ((
% 97.60/13.20 (eta2) =>
% 97.60/13.20 ((
% 97.60/13.20 (iffalseProp1) =>
% 97.60/13.20 ((
% 97.60/13.20 (iffalseProp2) =>
% 97.60/13.20 ((
% 97.60/13.20 (iftrueProp1) =>
% 97.60/13.20 ((
% 97.60/13.20 (iftrueProp2) =>
% 97.60/13.20 ((
% 97.60/13.20 (ifSingleton) =>
% 97.60/13.20 ((
% 97.60/13.20 (ifp) =>
% 97.60/13.20 ((
% 97.60/13.20 (theeq) =>
% 97.60/13.20 ((
% 97.60/13.20 (iftrue) =>
% 97.60/13.20 ((
% 97.60/13.20 (iffalse) =>
% 97.60/13.20 ((
% 97.60/13.20 (iftrueorfalse) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectT_lem) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionT_lem) =>
% 97.60/13.20 ((
% 97.60/13.20 (powersetT_lem) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusT_lem) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementT_lem) =>
% 97.60/13.20 ((
% 97.60/13.20 (setextT) =>
% 97.60/13.20 ((
% 97.60/13.20 (subsetTI) =>
% 97.60/13.20 ((
% 97.60/13.20 (powersetTI1) =>
% 97.60/13.20 ((
% 97.60/13.20 (powersetTE1) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementTI1) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementTE1) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectTELcontra) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectTERcontra) =>
% 97.60/13.20 ((
% 97.60/13.20 (contrasubsetT) =>
% 97.60/13.20 ((
% 97.60/13.20 (contrasubsetT1) =>
% 97.60/13.20 ((
% 97.60/13.20 (contrasubsetT2) =>
% 97.60/13.20 ((
% 97.60/13.20 (contrasubsetT3) =>
% 97.60/13.20 ((
% 97.60/13.20 (doubleComplementI1) =>
% 97.60/13.20 ((
% 97.60/13.20 (doubleComplementE1) =>
% 97.60/13.20 ((
% 97.60/13.20 (doubleComplementSub1) =>
% 97.60/13.20 ((
% 97.60/13.20 (doubleComplementSub2) =>
% 97.60/13.20 ((
% 97.60/13.20 (doubleComplementEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementTnotintersectT) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementImpComplementIntersect) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementSubsetComplementIntersect) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementInPowersetComplementIntersect) =>
% 97.60/13.20 ((
% 97.60/13.20 (contraSubsetComplement) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementTcontraSubset) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionTILcontra) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionTIRcontra) =>
% 97.60/13.20 ((
% 97.60/13.20 (inIntersectImpInUnion) =>
% 97.60/13.20 ((
% 97.60/13.20 (inIntersectImpInUnion2) =>
% 97.60/13.20 ((
% 97.60/13.20 (inIntersectImpInIntersectUnions) =>
% 97.60/13.20 ((
% 97.60/13.20 (intersectInPowersetIntersectUnions) =>
% 97.60/13.20 ((
% 97.60/13.20 (inComplementUnionImpNotIn1) =>
% 97.60/13.20 ((
% 97.60/13.20 (inComplementUnionImpInComplement1) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionTE) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionTEcontra) =>
% 97.60/13.20 ((
% 97.60/13.20 (demorgan2a1) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementUnionInPowersetComplement) =>
% 97.60/13.20 ((
% 97.60/13.20 (demorgan2a2) =>
% 97.60/13.20 ((
% 97.60/13.20 (demorgan1a) =>
% 97.60/13.20 ((
% 97.60/13.20 (demorgan1b) =>
% 97.60/13.20 ((
% 97.60/13.20 (demorgan1) =>
% 97.60/13.20 ((
% 97.60/13.20 (demorgan2a) =>
% 97.60/13.20 ((
% 97.60/13.20 (demorgan2b2) =>
% 97.60/13.20 ((
% 97.60/13.20 (demorgan2b) =>
% 97.60/13.20 ((
% 97.60/13.20 (demorgan2) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz13rule0) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz13rule1) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz13rule2) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz13rule3) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz13rule4) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz1_1) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz1_2) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz1_3) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz1_4) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz1_5) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1all2) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1SetBreln1) =>
% 97.60/13.20 ((
% 97.60/13.20 (choice2fnsingleton) =>
% 97.60/13.20 ((
% 97.60/13.20 (setOfPairsIsBReln1) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1all1) =>
% 97.60/13.20 ((
% 97.60/13.20 (subbreln1) =>
% 97.60/13.20 ((
% 97.60/13.20 (eqbreln1) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1invprop) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1invI) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1invE) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1compprop) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1compI) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1compE) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1compEex) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1unionprop) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1unionIL) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1unionIR) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1unionI) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1unionE) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1unionEcases) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1unionCommutes) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz2Ex) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz2W) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz2A) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz2B) =>
% 97.60/13.20 ((
% 97.60/13.20 (image1Ex) =>
% 97.60/13.20 ((
% 97.60/13.20 (image1Ex1) =>
% 97.60/13.20 ((
% 97.60/13.20 (image1Equiv) =>
% 97.60/13.20 ((
% 97.60/13.20 (image1E) =>
% 97.60/13.20 ((
% 97.60/13.20 (image1I) =>
% 97.60/13.20 ((
% 97.60/13.20 (injFuncInInjFuncSet) =>
% 97.60/13.20 ((
% 97.60/13.20 (injFuncSetFuncIn) =>
% 97.60/13.20 ((
% 97.60/13.20 (injFuncSetFuncInj) =>
% 97.60/13.20 ((
% 97.60/13.20 (surjFuncSetFuncIn) =>
% 97.60/13.20 ((
% 97.60/13.20 (surjFuncSetFuncSurj) =>
% 97.60/13.20 ((
% 97.60/13.20 (leftInvIsSurj) =>
% 97.60/13.20 ((
% 97.60/13.20 (surjCantorThm) =>
% 97.60/13.20 ((
% 97.60/13.20 (foundation2) =>
% 97.60/13.20 ((
% 97.60/13.20 (notinself) =>
% 97.60/13.20 ((
% 97.60/13.20 (notinself2) =>
% 97.60/13.20 ((
% 97.60/13.20 (omegaSp) =>
% 97.60/13.20 ((
% 97.60/13.20 (omegaSclos) =>
% 97.60/13.20 ((
% 97.60/13.20 (peano0notS) =>
% 97.60/13.20 ((
% 97.60/13.20 (!!) @ (
% 97.60/13.20 (('#S') @ (
% 97.60/13.20 (
% 97.60/13.20 ('#B') @ (
% 97.60/13.20 =>) @
% 97.60/13.20 (
% 97.60/13.20 (
% 97.60/13.20 ('#C') @ in @
% 97.60/13.20 omega)))) @
% 97.60/13.20 (
% 97.60/13.20 (
% 97.60/13.20 ('#B') @ (
% 97.60/13.20 !!) @
% 97.60/13.20 (
% 97.60/13.20 (
% 97.60/13.20 ('#B') @ (
% 97.60/13.20 (
% 97.60/13.20 ('#S') @ (
% 97.60/13.20 (
% 97.60/13.20 ('#B') @ (
% 97.60/13.20 =>) @
% 97.60/13.20 (
% 97.60/13.20 (
% 97.60/13.20 ('#C') @ in @
% 97.60/13.20 omega)))))) @
% 97.60/13.20 (
% 97.60/13.20 (
% 97.60/13.20 ('#S') @ (
% 97.60/13.20 (
% 97.60/13.20 ('#B') @ (
% 97.60/13.20 '#S') @
% 97.60/13.20 (
% 97.60/13.20 (
% 97.60/13.20 ('#B') @ (
% 97.60/13.20 (
% 97.60/13.20 ('#B') @ (
% 97.60/13.20 =>))) @
% 97.60/13.20 (
% 97.60/13.20 (
% 97.60/13.20 ('#C') @ (
% 97.60/13.20 (
% 97.60/13.20 ('#B') @ (
% 97.60/13.20 '#B') @
% 97.60/13.20 (
% 97.60/13.20 (
% 97.60/13.20 ('#B') @ (
% 97.60/13.20 =) @
% 97.60/13.20 omegaS)))) @
% 97.60/13.20 omegaS)))))) @
% 97.60/13.20 (
% 97.60/13.20 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.60/13.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl586])).
% 97.60/13.20 thf(zip_derived_cl606, plain,
% 97.60/13.20 (~ (((exuI1) =>
% 97.60/13.20 (((exuI3) =>
% 97.60/13.20 (((exuI2) =>
% 97.60/13.20 (((inCongP) =>
% 97.60/13.20 (((in__Cong) =>
% 97.60/13.20 (((exuE3u) =>
% 97.60/13.20 (((exu__Cong) =>
% 97.60/13.20 (((setadjoin__Cong) =>
% 97.60/13.20 (((powerset__Cong) =>
% 97.60/13.20 (((setunion__Cong) =>
% 97.60/13.20 (((exuEu) =>
% 97.60/13.20 (((descr__Cong) =>
% 97.60/13.20 (((dsetconstr__Cong) =>
% 97.60/13.20 (((subsetI1) =>
% 97.60/13.20 (((eqimpsubset2) =>
% 97.60/13.20 (((eqimpsubset1) =>
% 97.60/13.20 (((subsetI2) =>
% 97.60/13.20 (((emptysetsubset) =>
% 97.60/13.20 (((subsetE) =>
% 97.60/13.20 (((subsetE2) =>
% 97.60/13.20 (((notsubsetI) =>
% 97.60/13.20 (((notequalI1) =>
% 97.60/13.20 (((notequalI2) =>
% 97.60/13.20 (((subsetRefl) =>
% 97.60/13.20 (((subsetTrans) =>
% 97.60/13.20 (((setadjoinSub) =>
% 97.60/13.20 (((setadjoinSub2) =>
% 97.60/13.20 (((subset2powerset) =>
% 97.60/13.20 (((setextsub) =>
% 97.60/13.20 (((subsetemptysetimpeq) =>
% 97.60/13.20 ((
% 97.60/13.20 (powersetI1) =>
% 97.60/13.20 ((
% 97.60/13.20 (powersetE1) =>
% 97.60/13.20 ((
% 97.60/13.20 (inPowerset) =>
% 97.60/13.20 ((
% 97.60/13.20 (powersetsubset) =>
% 97.60/13.20 ((
% 97.60/13.20 (sepInPowerset) =>
% 97.60/13.20 ((
% 97.60/13.20 (sepSubset) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionIL) =>
% 97.60/13.20 ((
% 97.60/13.20 (upairset2IR) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionIR) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionEcases) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionE) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionLsub) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionRsub) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectI) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectSubset5) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectEL) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectLsub) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectSubset2) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectSubset3) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectER) =>
% 97.60/13.20 ((
% 97.60/13.20 (disjointsetsI1) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectRsub) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectSubset4) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectSubset1) =>
% 97.60/13.20 ((
% 97.60/13.20 (bs114d) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusI) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusEL) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusER) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusSubset2) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusERneg) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusELneg) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusILneg) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusIRneg) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusLsub) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusSubset1) =>
% 97.60/13.20 ((
% 97.60/13.20 (symdiffE) =>
% 97.60/13.20 ((
% 97.60/13.20 (symdiffI1) =>
% 97.60/13.20 ((
% 97.60/13.20 (symdiffI2) =>
% 97.60/13.20 ((
% 97.60/13.20 (symdiffIneg1) =>
% 97.60/13.20 ((
% 97.60/13.20 (symdiffIneg2) =>
% 97.60/13.20 ((
% 97.60/13.20 (secondinupair) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairIL) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairIR) =>
% 97.60/13.20 ((
% 97.60/13.20 (kpairiskpair) =>
% 97.60/13.20 ((
% 97.60/13.20 (kpairp) =>
% 97.60/13.20 ((
% 97.60/13.20 (singletonsubset) =>
% 97.60/13.20 ((
% 97.60/13.20 (singletoninpowerset) =>
% 97.60/13.20 ((
% 97.60/13.20 (singletoninpowunion) =>
% 97.60/13.20 ((
% 97.60/13.20 (upairset2E) =>
% 97.60/13.20 ((
% 97.60/13.20 (upairsubunion) =>
% 97.60/13.20 ((
% 97.60/13.20 (upairinpowunion) =>
% 97.60/13.20 ((
% 97.60/13.20 (ubforcartprodlem1) =>
% 97.60/13.20 ((
% 97.60/13.20 (ubforcartprodlem2) =>
% 97.60/13.20 ((
% 97.60/13.20 (ubforcartprodlem3) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodpairin) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodmempair1) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodmempair) =>
% 97.60/13.20 ((
% 97.60/13.20 (setunionE2) =>
% 97.60/13.20 ((
% 97.60/13.20 (setunionsingleton1) =>
% 97.60/13.20 ((
% 97.60/13.20 (setunionsingleton2) =>
% 97.60/13.20 ((
% 97.60/13.20 (setunionsingleton) =>
% 97.60/13.20 ((
% 97.60/13.20 (singletonprop) =>
% 97.60/13.20 ((
% 97.60/13.20 (ex1E1) =>
% 97.60/13.20 ((
% 97.60/13.20 (ex1I) =>
% 97.60/13.20 ((
% 97.60/13.20 (ex1I2) =>
% 97.60/13.20 ((
% 97.60/13.20 (singletonsuniq) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairinjL1) =>
% 97.60/13.20 ((
% 97.60/13.20 (kfstsingleton) =>
% 97.60/13.20 ((
% 97.60/13.20 (theprop) =>
% 97.60/13.20 ((
% 97.60/13.20 (kfstpairEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodfstin) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairinjL2) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairinjL) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairinjR11) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairinjR12) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairinjR1) =>
% 97.60/13.20 ((
% 97.60/13.20 (upairequniteq) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairinjR2) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairinjR) =>
% 97.60/13.20 ((
% 97.60/13.20 (ksndsingleton) =>
% 97.60/13.20 ((
% 97.60/13.20 (ksndpairEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (kpairsurjEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodsndin) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodpairmemEL) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodpairmemER) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodmempaircEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodfstpairEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodsndpairEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodpairsurjEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (dpsetconstrI) =>
% 97.60/13.20 ((
% 97.60/13.20 (dpsetconstrSub) =>
% 97.60/13.20 ((
% 97.60/13.20 (setOfPairsIsBReln) =>
% 97.60/13.20 ((
% 97.60/13.20 (dpsetconstrERa) =>
% 97.60/13.20 ((
% 97.60/13.20 (dpsetconstrEL1) =>
% 97.60/13.20 ((
% 97.60/13.20 (dpsetconstrEL2) =>
% 97.60/13.20 ((
% 97.60/13.20 (dpsetconstrER) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcImageSingleton) =>
% 97.60/13.20 ((
% 97.60/13.20 (apProp) =>
% 97.60/13.20 ((
% 97.60/13.20 (app) =>
% 97.60/13.20 ((
% 97.60/13.20 (infuncsetfunc) =>
% 97.60/13.20 ((
% 97.60/13.20 (ap2p) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcinfuncset) =>
% 97.60/13.20 ((
% 97.60/13.20 (lamProp) =>
% 97.60/13.20 ((
% 97.60/13.20 (lamp) =>
% 97.60/13.20 ((
% 97.60/13.20 (lam2p) =>
% 97.60/13.20 ((
% 97.60/13.20 (brelnall1) =>
% 97.60/13.20 ((
% 97.60/13.20 (brelnall2) =>
% 97.60/13.20 ((
% 97.60/13.20 (ex1E2) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcGraphProp1) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcGraphProp3) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcGraphProp2) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcextLem) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcGraphProp4) =>
% 97.60/13.20 ((
% 97.60/13.20 (subbreln) =>
% 97.60/13.20 ((
% 97.60/13.20 (eqbreln) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcext) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcext2) =>
% 97.60/13.20 ((
% 97.60/13.20 (ap2apEq1) =>
% 97.60/13.20 ((
% 97.60/13.20 (ap2apEq2) =>
% 97.60/13.20 ((
% 97.60/13.20 (beta1) =>
% 97.60/13.20 ((
% 97.60/13.20 (eta1) =>
% 97.60/13.20 ((
% 97.60/13.20 (lam2lamEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (beta2) =>
% 97.60/13.20 ((
% 97.60/13.20 (eta2) =>
% 97.60/13.20 ((
% 97.60/13.20 (iffalseProp1) =>
% 97.60/13.20 ((
% 97.60/13.20 (iffalseProp2) =>
% 97.60/13.20 ((
% 97.60/13.20 (iftrueProp1) =>
% 97.60/13.20 ((
% 97.60/13.20 (iftrueProp2) =>
% 97.60/13.20 ((
% 97.60/13.20 (ifSingleton) =>
% 97.60/13.20 ((
% 97.60/13.20 (ifp) =>
% 97.60/13.20 ((
% 97.60/13.20 (theeq) =>
% 97.60/13.20 ((
% 97.60/13.20 (iftrue) =>
% 97.60/13.20 ((
% 97.60/13.20 (iffalse) =>
% 97.60/13.20 ((
% 97.60/13.20 (iftrueorfalse) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectT_lem) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionT_lem) =>
% 97.60/13.20 ((
% 97.60/13.20 (powersetT_lem) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusT_lem) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementT_lem) =>
% 97.60/13.20 ((
% 97.60/13.20 (setextT) =>
% 97.60/13.20 ((
% 97.60/13.20 (subsetTI) =>
% 97.60/13.20 ((
% 97.60/13.20 (powersetTI1) =>
% 97.60/13.20 ((
% 97.60/13.20 (powersetTE1) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementTI1) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementTE1) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectTELcontra) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectTERcontra) =>
% 97.60/13.20 ((
% 97.60/13.20 (contrasubsetT) =>
% 97.60/13.20 ((
% 97.60/13.20 (contrasubsetT1) =>
% 97.60/13.20 ((
% 97.60/13.20 (contrasubsetT2) =>
% 97.60/13.20 ((
% 97.60/13.20 (contrasubsetT3) =>
% 97.60/13.20 ((
% 97.60/13.20 (doubleComplementI1) =>
% 97.60/13.20 ((
% 97.60/13.20 (doubleComplementE1) =>
% 97.60/13.20 ((
% 97.60/13.20 (doubleComplementSub1) =>
% 97.60/13.20 ((
% 97.60/13.20 (doubleComplementSub2) =>
% 97.60/13.20 ((
% 97.60/13.20 (doubleComplementEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementTnotintersectT) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementImpComplementIntersect) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementSubsetComplementIntersect) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementInPowersetComplementIntersect) =>
% 97.60/13.20 ((
% 97.60/13.20 (contraSubsetComplement) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementTcontraSubset) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionTILcontra) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionTIRcontra) =>
% 97.60/13.20 ((
% 97.60/13.20 (inIntersectImpInUnion) =>
% 97.60/13.20 ((
% 97.60/13.20 (inIntersectImpInUnion2) =>
% 97.60/13.20 ((
% 97.60/13.20 (inIntersectImpInIntersectUnions) =>
% 97.60/13.20 ((
% 97.60/13.20 (intersectInPowersetIntersectUnions) =>
% 97.60/13.20 ((
% 97.60/13.20 (inComplementUnionImpNotIn1) =>
% 97.60/13.20 ((
% 97.60/13.20 (inComplementUnionImpInComplement1) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionTE) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionTEcontra) =>
% 97.60/13.20 ((
% 97.60/13.20 (demorgan2a1) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementUnionInPowersetComplement) =>
% 97.60/13.20 ((
% 97.60/13.20 (demorgan2a2) =>
% 97.60/13.20 ((
% 97.60/13.20 (demorgan1a) =>
% 97.60/13.20 ((
% 97.60/13.20 (demorgan1b) =>
% 97.60/13.20 ((
% 97.60/13.20 (demorgan1) =>
% 97.60/13.20 ((
% 97.60/13.20 (demorgan2a) =>
% 97.60/13.20 ((
% 97.60/13.20 (demorgan2b2) =>
% 97.60/13.20 ((
% 97.60/13.20 (demorgan2b) =>
% 97.60/13.20 ((
% 97.60/13.20 (demorgan2) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz13rule0) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz13rule1) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz13rule2) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz13rule3) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz13rule4) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz1_1) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz1_2) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz1_3) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz1_4) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz1_5) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1all2) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1SetBreln1) =>
% 97.60/13.20 ((
% 97.60/13.20 (choice2fnsingleton) =>
% 97.60/13.20 ((
% 97.60/13.20 (setOfPairsIsBReln1) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1all1) =>
% 97.60/13.20 ((
% 97.60/13.20 (subbreln1) =>
% 97.60/13.20 ((
% 97.60/13.20 (eqbreln1) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1invprop) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1invI) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1invE) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1compprop) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1compI) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1compE) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1compEex) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1unionprop) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1unionIL) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1unionIR) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1unionI) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1unionE) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1unionEcases) =>
% 97.60/13.20 ((
% 97.60/13.20 (breln1unionCommutes) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz2Ex) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz2W) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz2A) =>
% 97.60/13.20 ((
% 97.60/13.20 (woz2B) =>
% 97.60/13.20 ((
% 97.60/13.20 (image1Ex) =>
% 97.60/13.20 ((
% 97.60/13.20 (image1Ex1) =>
% 97.60/13.20 ((
% 97.60/13.20 (image1Equiv) =>
% 97.60/13.20 ((
% 97.60/13.20 (image1E) =>
% 97.60/13.20 ((
% 97.60/13.20 (image1I) =>
% 97.60/13.20 ((
% 97.60/13.20 (injFuncInInjFuncSet) =>
% 97.60/13.20 ((
% 97.60/13.20 (injFuncSetFuncIn) =>
% 97.60/13.20 ((
% 97.60/13.20 (injFuncSetFuncInj) =>
% 97.60/13.20 ((
% 97.60/13.20 (surjFuncSetFuncIn) =>
% 97.60/13.20 ((
% 97.60/13.20 (surjFuncSetFuncSurj) =>
% 97.60/13.20 ((
% 97.60/13.20 (leftInvIsSurj) =>
% 97.60/13.20 ((
% 97.60/13.20 (surjCantorThm) =>
% 97.60/13.20 ((
% 97.60/13.20 (foundation2) =>
% 97.60/13.20 ((
% 97.60/13.20 (notinself) =>
% 97.60/13.20 ((
% 97.60/13.20 (notinself2) =>
% 97.60/13.20 ((
% 97.60/13.20 (omegaSp) =>
% 97.60/13.20 ((
% 97.60/13.20 (omegaSclos) =>
% 97.60/13.20 ((
% 97.60/13.20 (peano0notS) =>
% 97.60/13.20 ((
% 97.60/13.20 (!!) @ (
% 97.60/13.20 (('#S') @ (
% 97.60/13.20 (
% 97.60/13.20 ('#B') @ (
% 97.60/13.20 =>) @
% 97.60/13.20 (
% 97.60/13.20 (
% 97.60/13.20 ('#C') @ in @
% 97.60/13.20 omega)))) @
% 97.60/13.20 (
% 97.60/13.20 (
% 97.60/13.20 ('#B') @ (
% 97.60/13.20 !!) @
% 97.60/13.20 (
% 97.60/13.20 (
% 97.60/13.20 ('#B') @ (
% 97.60/13.20 (
% 97.60/13.20 ('#S') @ (
% 97.60/13.20 (
% 97.60/13.20 ('#B') @ (
% 97.60/13.20 =>) @
% 97.60/13.20 (
% 97.60/13.20 (
% 97.60/13.20 ('#C') @ in @
% 97.60/13.20 omega)))))) @
% 97.60/13.20 (
% 97.60/13.20 (
% 97.60/13.20 ('#S') @ (
% 97.60/13.20 (
% 97.60/13.20 ('#B') @ (
% 97.60/13.20 '#S') @
% 97.60/13.20 (
% 97.60/13.20 (
% 97.60/13.20 ('#B') @ (
% 97.60/13.20 (
% 97.60/13.20 ('#B') @ (
% 97.60/13.20 =>))) @
% 97.60/13.20 (
% 97.60/13.20 (
% 97.60/13.20 ('#C') @ (
% 97.60/13.20 (
% 97.60/13.20 ('#B') @ (
% 97.60/13.20 '#B') @
% 97.60/13.20 (
% 97.60/13.20 (
% 97.60/13.20 ('#B') @ (
% 97.60/13.20 =) @
% 97.60/13.20 omegaS)))) @
% 97.60/13.20 omegaS)))))) @
% 97.60/13.20 (
% 97.60/13.20 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.60/13.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl595])).
% 97.60/13.20 thf(zip_derived_cl619, plain,
% 97.60/13.20 (~ (((exuI3) =>
% 97.60/13.20 (((exuI2) =>
% 97.60/13.20 (((inCongP) =>
% 97.60/13.20 (((in__Cong) =>
% 97.60/13.20 (((exuE3u) =>
% 97.60/13.20 (((exu__Cong) =>
% 97.60/13.20 (((setadjoin__Cong) =>
% 97.60/13.20 (((powerset__Cong) =>
% 97.60/13.20 (((setunion__Cong) =>
% 97.60/13.20 (((exuEu) =>
% 97.60/13.20 (((descr__Cong) =>
% 97.60/13.20 (((dsetconstr__Cong) =>
% 97.60/13.20 (((subsetI1) =>
% 97.60/13.20 (((eqimpsubset2) =>
% 97.60/13.20 (((eqimpsubset1) =>
% 97.60/13.20 (((subsetI2) =>
% 97.60/13.20 (((emptysetsubset) =>
% 97.60/13.20 (((subsetE) =>
% 97.60/13.20 (((subsetE2) =>
% 97.60/13.20 (((notsubsetI) =>
% 97.60/13.20 (((notequalI1) =>
% 97.60/13.20 (((notequalI2) =>
% 97.60/13.20 (((subsetRefl) =>
% 97.60/13.20 (((subsetTrans) =>
% 97.60/13.20 (((setadjoinSub) =>
% 97.60/13.20 (((setadjoinSub2) =>
% 97.60/13.20 (((subset2powerset) =>
% 97.60/13.20 (((setextsub) =>
% 97.60/13.20 (((subsetemptysetimpeq) =>
% 97.60/13.20 (((powersetI1) =>
% 97.60/13.20 ((
% 97.60/13.20 (powersetE1) =>
% 97.60/13.20 ((
% 97.60/13.20 (inPowerset) =>
% 97.60/13.20 ((
% 97.60/13.20 (powersetsubset) =>
% 97.60/13.20 ((
% 97.60/13.20 (sepInPowerset) =>
% 97.60/13.20 ((
% 97.60/13.20 (sepSubset) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionIL) =>
% 97.60/13.20 ((
% 97.60/13.20 (upairset2IR) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionIR) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionEcases) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionE) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionLsub) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionRsub) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectI) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectSubset5) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectEL) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectLsub) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectSubset2) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectSubset3) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectER) =>
% 97.60/13.20 ((
% 97.60/13.20 (disjointsetsI1) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectRsub) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectSubset4) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectSubset1) =>
% 97.60/13.20 ((
% 97.60/13.20 (bs114d) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusI) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusEL) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusER) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusSubset2) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusERneg) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusELneg) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusILneg) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusIRneg) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusLsub) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusSubset1) =>
% 97.60/13.20 ((
% 97.60/13.20 (symdiffE) =>
% 97.60/13.20 ((
% 97.60/13.20 (symdiffI1) =>
% 97.60/13.20 ((
% 97.60/13.20 (symdiffI2) =>
% 97.60/13.20 ((
% 97.60/13.20 (symdiffIneg1) =>
% 97.60/13.20 ((
% 97.60/13.20 (symdiffIneg2) =>
% 97.60/13.20 ((
% 97.60/13.20 (secondinupair) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairIL) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairIR) =>
% 97.60/13.20 ((
% 97.60/13.20 (kpairiskpair) =>
% 97.60/13.20 ((
% 97.60/13.20 (kpairp) =>
% 97.60/13.20 ((
% 97.60/13.20 (singletonsubset) =>
% 97.60/13.20 ((
% 97.60/13.20 (singletoninpowerset) =>
% 97.60/13.20 ((
% 97.60/13.20 (singletoninpowunion) =>
% 97.60/13.20 ((
% 97.60/13.20 (upairset2E) =>
% 97.60/13.20 ((
% 97.60/13.20 (upairsubunion) =>
% 97.60/13.20 ((
% 97.60/13.20 (upairinpowunion) =>
% 97.60/13.20 ((
% 97.60/13.20 (ubforcartprodlem1) =>
% 97.60/13.20 ((
% 97.60/13.20 (ubforcartprodlem2) =>
% 97.60/13.20 ((
% 97.60/13.20 (ubforcartprodlem3) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodpairin) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodmempair1) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodmempair) =>
% 97.60/13.20 ((
% 97.60/13.20 (setunionE2) =>
% 97.60/13.20 ((
% 97.60/13.20 (setunionsingleton1) =>
% 97.60/13.20 ((
% 97.60/13.20 (setunionsingleton2) =>
% 97.60/13.20 ((
% 97.60/13.20 (setunionsingleton) =>
% 97.60/13.20 ((
% 97.60/13.20 (singletonprop) =>
% 97.60/13.20 ((
% 97.60/13.20 (ex1E1) =>
% 97.60/13.20 ((
% 97.60/13.20 (ex1I) =>
% 97.60/13.20 ((
% 97.60/13.20 (ex1I2) =>
% 97.60/13.20 ((
% 97.60/13.20 (singletonsuniq) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairinjL1) =>
% 97.60/13.20 ((
% 97.60/13.20 (kfstsingleton) =>
% 97.60/13.20 ((
% 97.60/13.20 (theprop) =>
% 97.60/13.20 ((
% 97.60/13.20 (kfstpairEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodfstin) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairinjL2) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairinjL) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairinjR11) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairinjR12) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairinjR1) =>
% 97.60/13.20 ((
% 97.60/13.20 (upairequniteq) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairinjR2) =>
% 97.60/13.20 ((
% 97.60/13.20 (setukpairinjR) =>
% 97.60/13.20 ((
% 97.60/13.20 (ksndsingleton) =>
% 97.60/13.20 ((
% 97.60/13.20 (ksndpairEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (kpairsurjEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodsndin) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodpairmemEL) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodpairmemER) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodmempaircEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodfstpairEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodsndpairEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (cartprodpairsurjEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (dpsetconstrI) =>
% 97.60/13.20 ((
% 97.60/13.20 (dpsetconstrSub) =>
% 97.60/13.20 ((
% 97.60/13.20 (setOfPairsIsBReln) =>
% 97.60/13.20 ((
% 97.60/13.20 (dpsetconstrERa) =>
% 97.60/13.20 ((
% 97.60/13.20 (dpsetconstrEL1) =>
% 97.60/13.20 ((
% 97.60/13.20 (dpsetconstrEL2) =>
% 97.60/13.20 ((
% 97.60/13.20 (dpsetconstrER) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcImageSingleton) =>
% 97.60/13.20 ((
% 97.60/13.20 (apProp) =>
% 97.60/13.20 ((
% 97.60/13.20 (app) =>
% 97.60/13.20 ((
% 97.60/13.20 (infuncsetfunc) =>
% 97.60/13.20 ((
% 97.60/13.20 (ap2p) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcinfuncset) =>
% 97.60/13.20 ((
% 97.60/13.20 (lamProp) =>
% 97.60/13.20 ((
% 97.60/13.20 (lamp) =>
% 97.60/13.20 ((
% 97.60/13.20 (lam2p) =>
% 97.60/13.20 ((
% 97.60/13.20 (brelnall1) =>
% 97.60/13.20 ((
% 97.60/13.20 (brelnall2) =>
% 97.60/13.20 ((
% 97.60/13.20 (ex1E2) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcGraphProp1) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcGraphProp3) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcGraphProp2) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcextLem) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcGraphProp4) =>
% 97.60/13.20 ((
% 97.60/13.20 (subbreln) =>
% 97.60/13.20 ((
% 97.60/13.20 (eqbreln) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcext) =>
% 97.60/13.20 ((
% 97.60/13.20 (funcext2) =>
% 97.60/13.20 ((
% 97.60/13.20 (ap2apEq1) =>
% 97.60/13.20 ((
% 97.60/13.20 (ap2apEq2) =>
% 97.60/13.20 ((
% 97.60/13.20 (beta1) =>
% 97.60/13.20 ((
% 97.60/13.20 (eta1) =>
% 97.60/13.20 ((
% 97.60/13.20 (lam2lamEq) =>
% 97.60/13.20 ((
% 97.60/13.20 (beta2) =>
% 97.60/13.20 ((
% 97.60/13.20 (eta2) =>
% 97.60/13.20 ((
% 97.60/13.20 (iffalseProp1) =>
% 97.60/13.20 ((
% 97.60/13.20 (iffalseProp2) =>
% 97.60/13.20 ((
% 97.60/13.20 (iftrueProp1) =>
% 97.60/13.20 ((
% 97.60/13.20 (iftrueProp2) =>
% 97.60/13.20 ((
% 97.60/13.20 (ifSingleton) =>
% 97.60/13.20 ((
% 97.60/13.20 (ifp) =>
% 97.60/13.20 ((
% 97.60/13.20 (theeq) =>
% 97.60/13.20 ((
% 97.60/13.20 (iftrue) =>
% 97.60/13.20 ((
% 97.60/13.20 (iffalse) =>
% 97.60/13.20 ((
% 97.60/13.20 (iftrueorfalse) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectT_lem) =>
% 97.60/13.20 ((
% 97.60/13.20 (binunionT_lem) =>
% 97.60/13.20 ((
% 97.60/13.20 (powersetT_lem) =>
% 97.60/13.20 ((
% 97.60/13.20 (setminusT_lem) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementT_lem) =>
% 97.60/13.20 ((
% 97.60/13.20 (setextT) =>
% 97.60/13.20 ((
% 97.60/13.20 (subsetTI) =>
% 97.60/13.20 ((
% 97.60/13.20 (powersetTI1) =>
% 97.60/13.20 ((
% 97.60/13.20 (powersetTE1) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementTI1) =>
% 97.60/13.20 ((
% 97.60/13.20 (complementTE1) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectTELcontra) =>
% 97.60/13.20 ((
% 97.60/13.20 (binintersectTERcontra) =>
% 97.60/13.20 ((
% 97.60/13.20 (contrasubsetT) =>
% 97.60/13.20 ((
% 97.60/13.20 (contrasubsetT1) =>
% 97.60/13.20 ((
% 97.60/13.20 (contrasubsetT2) =>
% 97.60/13.20 ((
% 97.60/13.20 (contrasubsetT3) =>
% 97.60/13.20 ((
% 97.60/13.20 (doubleComplementI1) =>
% 97.60/13.20 ((
% 97.60/13.20 (doubleComplementE1) =>
% 97.60/13.20 ((
% 97.60/13.20 (doubleComplementSub1) =>
% 97.60/13.20 ((
% 97.60/13.20 (doubleComplementSub2) =>
% 97.60/13.20 ((
% 97.60/13.20 (doubleComplementEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementTnotintersectT) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementImpComplementIntersect) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementSubsetComplementIntersect) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementInPowersetComplementIntersect) =>
% 97.60/13.21 ((
% 97.60/13.21 (contraSubsetComplement) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementTcontraSubset) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionTILcontra) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionTIRcontra) =>
% 97.60/13.21 ((
% 97.60/13.21 (inIntersectImpInUnion) =>
% 97.60/13.21 ((
% 97.60/13.21 (inIntersectImpInUnion2) =>
% 97.60/13.21 ((
% 97.60/13.21 (inIntersectImpInIntersectUnions) =>
% 97.60/13.21 ((
% 97.60/13.21 (intersectInPowersetIntersectUnions) =>
% 97.60/13.21 ((
% 97.60/13.21 (inComplementUnionImpNotIn1) =>
% 97.60/13.21 ((
% 97.60/13.21 (inComplementUnionImpInComplement1) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionTE) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionTEcontra) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan2a1) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementUnionInPowersetComplement) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan2a2) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan1a) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan1b) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan1) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan2a) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan2b2) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan2b) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan2) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz13rule0) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz13rule1) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz13rule2) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz13rule3) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz13rule4) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz1_1) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz1_2) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz1_3) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz1_4) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz1_5) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1all2) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1SetBreln1) =>
% 97.60/13.21 ((
% 97.60/13.21 (choice2fnsingleton) =>
% 97.60/13.21 ((
% 97.60/13.21 (setOfPairsIsBReln1) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1all1) =>
% 97.60/13.21 ((
% 97.60/13.21 (subbreln1) =>
% 97.60/13.21 ((
% 97.60/13.21 (eqbreln1) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1invprop) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1invI) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1invE) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1compprop) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1compI) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1compE) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1compEex) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1unionprop) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1unionIL) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1unionIR) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1unionI) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1unionE) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1unionEcases) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1unionCommutes) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz2Ex) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz2W) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz2A) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz2B) =>
% 97.60/13.21 ((
% 97.60/13.21 (image1Ex) =>
% 97.60/13.21 ((
% 97.60/13.21 (image1Ex1) =>
% 97.60/13.21 ((
% 97.60/13.21 (image1Equiv) =>
% 97.60/13.21 ((
% 97.60/13.21 (image1E) =>
% 97.60/13.21 ((
% 97.60/13.21 (image1I) =>
% 97.60/13.21 ((
% 97.60/13.21 (injFuncInInjFuncSet) =>
% 97.60/13.21 ((
% 97.60/13.21 (injFuncSetFuncIn) =>
% 97.60/13.21 ((
% 97.60/13.21 (injFuncSetFuncInj) =>
% 97.60/13.21 ((
% 97.60/13.21 (surjFuncSetFuncIn) =>
% 97.60/13.21 ((
% 97.60/13.21 (surjFuncSetFuncSurj) =>
% 97.60/13.21 ((
% 97.60/13.21 (leftInvIsSurj) =>
% 97.60/13.21 ((
% 97.60/13.21 (surjCantorThm) =>
% 97.60/13.21 ((
% 97.60/13.21 (foundation2) =>
% 97.60/13.21 ((
% 97.60/13.21 (notinself) =>
% 97.60/13.21 ((
% 97.60/13.21 (notinself2) =>
% 97.60/13.21 ((
% 97.60/13.21 (omegaSp) =>
% 97.60/13.21 ((
% 97.60/13.21 (omegaSclos) =>
% 97.60/13.21 ((
% 97.60/13.21 (peano0notS) =>
% 97.60/13.21 ((
% 97.60/13.21 (!!) @ (
% 97.60/13.21 (('#S') @ (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 =>) @
% 97.60/13.21 (
% 97.60/13.21 (
% 97.60/13.21 ('#C') @ in @
% 97.60/13.21 omega)))) @
% 97.60/13.21 (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 !!) @
% 97.60/13.21 (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 (
% 97.60/13.21 ('#S') @ (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 =>) @
% 97.60/13.21 (
% 97.60/13.21 (
% 97.60/13.21 ('#C') @ in @
% 97.60/13.21 omega)))))) @
% 97.60/13.21 (
% 97.60/13.21 (
% 97.60/13.21 ('#S') @ (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 '#S') @
% 97.60/13.21 (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 =>))) @
% 97.60/13.21 (
% 97.60/13.21 (
% 97.60/13.21 ('#C') @ (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 '#B') @
% 97.60/13.21 (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 =) @
% 97.60/13.21 omegaS)))) @
% 97.60/13.21 omegaS)))))) @
% 97.60/13.21 (
% 97.60/13.21 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.60/13.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl606])).
% 97.60/13.21 thf(zip_derived_cl630, plain,
% 97.60/13.21 (~ (((exuI2) =>
% 97.60/13.21 (((inCongP) =>
% 97.60/13.21 (((in__Cong) =>
% 97.60/13.21 (((exuE3u) =>
% 97.60/13.21 (((exu__Cong) =>
% 97.60/13.21 (((setadjoin__Cong) =>
% 97.60/13.21 (((powerset__Cong) =>
% 97.60/13.21 (((setunion__Cong) =>
% 97.60/13.21 (((exuEu) =>
% 97.60/13.21 (((descr__Cong) =>
% 97.60/13.21 (((dsetconstr__Cong) =>
% 97.60/13.21 (((subsetI1) =>
% 97.60/13.21 (((eqimpsubset2) =>
% 97.60/13.21 (((eqimpsubset1) =>
% 97.60/13.21 (((subsetI2) =>
% 97.60/13.21 (((emptysetsubset) =>
% 97.60/13.21 (((subsetE) =>
% 97.60/13.21 (((subsetE2) =>
% 97.60/13.21 (((notsubsetI) =>
% 97.60/13.21 (((notequalI1) =>
% 97.60/13.21 (((notequalI2) =>
% 97.60/13.21 (((subsetRefl) =>
% 97.60/13.21 (((subsetTrans) =>
% 97.60/13.21 (((setadjoinSub) =>
% 97.60/13.21 (((setadjoinSub2) =>
% 97.60/13.21 (((subset2powerset) =>
% 97.60/13.21 (((setextsub) =>
% 97.60/13.21 (((subsetemptysetimpeq) =>
% 97.60/13.21 (((powersetI1) =>
% 97.60/13.21 (((powersetE1) =>
% 97.60/13.21 ((
% 97.60/13.21 (inPowerset) =>
% 97.60/13.21 ((
% 97.60/13.21 (powersetsubset) =>
% 97.60/13.21 ((
% 97.60/13.21 (sepInPowerset) =>
% 97.60/13.21 ((
% 97.60/13.21 (sepSubset) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionIL) =>
% 97.60/13.21 ((
% 97.60/13.21 (upairset2IR) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionIR) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionEcases) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionE) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionLsub) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionRsub) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectI) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectSubset5) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectEL) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectLsub) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectSubset2) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectSubset3) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectER) =>
% 97.60/13.21 ((
% 97.60/13.21 (disjointsetsI1) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectRsub) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectSubset4) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectSubset1) =>
% 97.60/13.21 ((
% 97.60/13.21 (bs114d) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusI) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusEL) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusER) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusSubset2) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusERneg) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusELneg) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusILneg) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusIRneg) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusLsub) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusSubset1) =>
% 97.60/13.21 ((
% 97.60/13.21 (symdiffE) =>
% 97.60/13.21 ((
% 97.60/13.21 (symdiffI1) =>
% 97.60/13.21 ((
% 97.60/13.21 (symdiffI2) =>
% 97.60/13.21 ((
% 97.60/13.21 (symdiffIneg1) =>
% 97.60/13.21 ((
% 97.60/13.21 (symdiffIneg2) =>
% 97.60/13.21 ((
% 97.60/13.21 (secondinupair) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairIL) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairIR) =>
% 97.60/13.21 ((
% 97.60/13.21 (kpairiskpair) =>
% 97.60/13.21 ((
% 97.60/13.21 (kpairp) =>
% 97.60/13.21 ((
% 97.60/13.21 (singletonsubset) =>
% 97.60/13.21 ((
% 97.60/13.21 (singletoninpowerset) =>
% 97.60/13.21 ((
% 97.60/13.21 (singletoninpowunion) =>
% 97.60/13.21 ((
% 97.60/13.21 (upairset2E) =>
% 97.60/13.21 ((
% 97.60/13.21 (upairsubunion) =>
% 97.60/13.21 ((
% 97.60/13.21 (upairinpowunion) =>
% 97.60/13.21 ((
% 97.60/13.21 (ubforcartprodlem1) =>
% 97.60/13.21 ((
% 97.60/13.21 (ubforcartprodlem2) =>
% 97.60/13.21 ((
% 97.60/13.21 (ubforcartprodlem3) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodpairin) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodmempair1) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodmempair) =>
% 97.60/13.21 ((
% 97.60/13.21 (setunionE2) =>
% 97.60/13.21 ((
% 97.60/13.21 (setunionsingleton1) =>
% 97.60/13.21 ((
% 97.60/13.21 (setunionsingleton2) =>
% 97.60/13.21 ((
% 97.60/13.21 (setunionsingleton) =>
% 97.60/13.21 ((
% 97.60/13.21 (singletonprop) =>
% 97.60/13.21 ((
% 97.60/13.21 (ex1E1) =>
% 97.60/13.21 ((
% 97.60/13.21 (ex1I) =>
% 97.60/13.21 ((
% 97.60/13.21 (ex1I2) =>
% 97.60/13.21 ((
% 97.60/13.21 (singletonsuniq) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairinjL1) =>
% 97.60/13.21 ((
% 97.60/13.21 (kfstsingleton) =>
% 97.60/13.21 ((
% 97.60/13.21 (theprop) =>
% 97.60/13.21 ((
% 97.60/13.21 (kfstpairEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodfstin) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairinjL2) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairinjL) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairinjR11) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairinjR12) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairinjR1) =>
% 97.60/13.21 ((
% 97.60/13.21 (upairequniteq) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairinjR2) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairinjR) =>
% 97.60/13.21 ((
% 97.60/13.21 (ksndsingleton) =>
% 97.60/13.21 ((
% 97.60/13.21 (ksndpairEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (kpairsurjEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodsndin) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodpairmemEL) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodpairmemER) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodmempaircEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodfstpairEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodsndpairEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodpairsurjEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (dpsetconstrI) =>
% 97.60/13.21 ((
% 97.60/13.21 (dpsetconstrSub) =>
% 97.60/13.21 ((
% 97.60/13.21 (setOfPairsIsBReln) =>
% 97.60/13.21 ((
% 97.60/13.21 (dpsetconstrERa) =>
% 97.60/13.21 ((
% 97.60/13.21 (dpsetconstrEL1) =>
% 97.60/13.21 ((
% 97.60/13.21 (dpsetconstrEL2) =>
% 97.60/13.21 ((
% 97.60/13.21 (dpsetconstrER) =>
% 97.60/13.21 ((
% 97.60/13.21 (funcImageSingleton) =>
% 97.60/13.21 ((
% 97.60/13.21 (apProp) =>
% 97.60/13.21 ((
% 97.60/13.21 (app) =>
% 97.60/13.21 ((
% 97.60/13.21 (infuncsetfunc) =>
% 97.60/13.21 ((
% 97.60/13.21 (ap2p) =>
% 97.60/13.21 ((
% 97.60/13.21 (funcinfuncset) =>
% 97.60/13.21 ((
% 97.60/13.21 (lamProp) =>
% 97.60/13.21 ((
% 97.60/13.21 (lamp) =>
% 97.60/13.21 ((
% 97.60/13.21 (lam2p) =>
% 97.60/13.21 ((
% 97.60/13.21 (brelnall1) =>
% 97.60/13.21 ((
% 97.60/13.21 (brelnall2) =>
% 97.60/13.21 ((
% 97.60/13.21 (ex1E2) =>
% 97.60/13.21 ((
% 97.60/13.21 (funcGraphProp1) =>
% 97.60/13.21 ((
% 97.60/13.21 (funcGraphProp3) =>
% 97.60/13.21 ((
% 97.60/13.21 (funcGraphProp2) =>
% 97.60/13.21 ((
% 97.60/13.21 (funcextLem) =>
% 97.60/13.21 ((
% 97.60/13.21 (funcGraphProp4) =>
% 97.60/13.21 ((
% 97.60/13.21 (subbreln) =>
% 97.60/13.21 ((
% 97.60/13.21 (eqbreln) =>
% 97.60/13.21 ((
% 97.60/13.21 (funcext) =>
% 97.60/13.21 ((
% 97.60/13.21 (funcext2) =>
% 97.60/13.21 ((
% 97.60/13.21 (ap2apEq1) =>
% 97.60/13.21 ((
% 97.60/13.21 (ap2apEq2) =>
% 97.60/13.21 ((
% 97.60/13.21 (beta1) =>
% 97.60/13.21 ((
% 97.60/13.21 (eta1) =>
% 97.60/13.21 ((
% 97.60/13.21 (lam2lamEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (beta2) =>
% 97.60/13.21 ((
% 97.60/13.21 (eta2) =>
% 97.60/13.21 ((
% 97.60/13.21 (iffalseProp1) =>
% 97.60/13.21 ((
% 97.60/13.21 (iffalseProp2) =>
% 97.60/13.21 ((
% 97.60/13.21 (iftrueProp1) =>
% 97.60/13.21 ((
% 97.60/13.21 (iftrueProp2) =>
% 97.60/13.21 ((
% 97.60/13.21 (ifSingleton) =>
% 97.60/13.21 ((
% 97.60/13.21 (ifp) =>
% 97.60/13.21 ((
% 97.60/13.21 (theeq) =>
% 97.60/13.21 ((
% 97.60/13.21 (iftrue) =>
% 97.60/13.21 ((
% 97.60/13.21 (iffalse) =>
% 97.60/13.21 ((
% 97.60/13.21 (iftrueorfalse) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectT_lem) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionT_lem) =>
% 97.60/13.21 ((
% 97.60/13.21 (powersetT_lem) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusT_lem) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementT_lem) =>
% 97.60/13.21 ((
% 97.60/13.21 (setextT) =>
% 97.60/13.21 ((
% 97.60/13.21 (subsetTI) =>
% 97.60/13.21 ((
% 97.60/13.21 (powersetTI1) =>
% 97.60/13.21 ((
% 97.60/13.21 (powersetTE1) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementTI1) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementTE1) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectTELcontra) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectTERcontra) =>
% 97.60/13.21 ((
% 97.60/13.21 (contrasubsetT) =>
% 97.60/13.21 ((
% 97.60/13.21 (contrasubsetT1) =>
% 97.60/13.21 ((
% 97.60/13.21 (contrasubsetT2) =>
% 97.60/13.21 ((
% 97.60/13.21 (contrasubsetT3) =>
% 97.60/13.21 ((
% 97.60/13.21 (doubleComplementI1) =>
% 97.60/13.21 ((
% 97.60/13.21 (doubleComplementE1) =>
% 97.60/13.21 ((
% 97.60/13.21 (doubleComplementSub1) =>
% 97.60/13.21 ((
% 97.60/13.21 (doubleComplementSub2) =>
% 97.60/13.21 ((
% 97.60/13.21 (doubleComplementEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementTnotintersectT) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementImpComplementIntersect) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementSubsetComplementIntersect) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementInPowersetComplementIntersect) =>
% 97.60/13.21 ((
% 97.60/13.21 (contraSubsetComplement) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementTcontraSubset) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionTILcontra) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionTIRcontra) =>
% 97.60/13.21 ((
% 97.60/13.21 (inIntersectImpInUnion) =>
% 97.60/13.21 ((
% 97.60/13.21 (inIntersectImpInUnion2) =>
% 97.60/13.21 ((
% 97.60/13.21 (inIntersectImpInIntersectUnions) =>
% 97.60/13.21 ((
% 97.60/13.21 (intersectInPowersetIntersectUnions) =>
% 97.60/13.21 ((
% 97.60/13.21 (inComplementUnionImpNotIn1) =>
% 97.60/13.21 ((
% 97.60/13.21 (inComplementUnionImpInComplement1) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionTE) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionTEcontra) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan2a1) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementUnionInPowersetComplement) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan2a2) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan1a) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan1b) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan1) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan2a) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan2b2) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan2b) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan2) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz13rule0) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz13rule1) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz13rule2) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz13rule3) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz13rule4) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz1_1) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz1_2) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz1_3) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz1_4) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz1_5) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1all2) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1SetBreln1) =>
% 97.60/13.21 ((
% 97.60/13.21 (choice2fnsingleton) =>
% 97.60/13.21 ((
% 97.60/13.21 (setOfPairsIsBReln1) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1all1) =>
% 97.60/13.21 ((
% 97.60/13.21 (subbreln1) =>
% 97.60/13.21 ((
% 97.60/13.21 (eqbreln1) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1invprop) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1invI) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1invE) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1compprop) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1compI) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1compE) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1compEex) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1unionprop) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1unionIL) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1unionIR) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1unionI) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1unionE) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1unionEcases) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1unionCommutes) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz2Ex) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz2W) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz2A) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz2B) =>
% 97.60/13.21 ((
% 97.60/13.21 (image1Ex) =>
% 97.60/13.21 ((
% 97.60/13.21 (image1Ex1) =>
% 97.60/13.21 ((
% 97.60/13.21 (image1Equiv) =>
% 97.60/13.21 ((
% 97.60/13.21 (image1E) =>
% 97.60/13.21 ((
% 97.60/13.21 (image1I) =>
% 97.60/13.21 ((
% 97.60/13.21 (injFuncInInjFuncSet) =>
% 97.60/13.21 ((
% 97.60/13.21 (injFuncSetFuncIn) =>
% 97.60/13.21 ((
% 97.60/13.21 (injFuncSetFuncInj) =>
% 97.60/13.21 ((
% 97.60/13.21 (surjFuncSetFuncIn) =>
% 97.60/13.21 ((
% 97.60/13.21 (surjFuncSetFuncSurj) =>
% 97.60/13.21 ((
% 97.60/13.21 (leftInvIsSurj) =>
% 97.60/13.21 ((
% 97.60/13.21 (surjCantorThm) =>
% 97.60/13.21 ((
% 97.60/13.21 (foundation2) =>
% 97.60/13.21 ((
% 97.60/13.21 (notinself) =>
% 97.60/13.21 ((
% 97.60/13.21 (notinself2) =>
% 97.60/13.21 ((
% 97.60/13.21 (omegaSp) =>
% 97.60/13.21 ((
% 97.60/13.21 (omegaSclos) =>
% 97.60/13.21 ((
% 97.60/13.21 (peano0notS) =>
% 97.60/13.21 ((
% 97.60/13.21 (!!) @ (
% 97.60/13.21 (('#S') @ (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 =>) @
% 97.60/13.21 (
% 97.60/13.21 (
% 97.60/13.21 ('#C') @ in @
% 97.60/13.21 omega)))) @
% 97.60/13.21 (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 !!) @
% 97.60/13.21 (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 (
% 97.60/13.21 ('#S') @ (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 =>) @
% 97.60/13.21 (
% 97.60/13.21 (
% 97.60/13.21 ('#C') @ in @
% 97.60/13.21 omega)))))) @
% 97.60/13.21 (
% 97.60/13.21 (
% 97.60/13.21 ('#S') @ (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 '#S') @
% 97.60/13.21 (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 =>))) @
% 97.60/13.21 (
% 97.60/13.21 (
% 97.60/13.21 ('#C') @ (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 '#B') @
% 97.60/13.21 (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 =) @
% 97.60/13.21 omegaS)))) @
% 97.60/13.21 omegaS)))))) @
% 97.60/13.21 (
% 97.60/13.21 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.60/13.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl619])).
% 97.60/13.21 thf(zip_derived_cl640, plain,
% 97.60/13.21 (~ (((inCongP) =>
% 97.60/13.21 (((in__Cong) =>
% 97.60/13.21 (((exuE3u) =>
% 97.60/13.21 (((exu__Cong) =>
% 97.60/13.21 (((setadjoin__Cong) =>
% 97.60/13.21 (((powerset__Cong) =>
% 97.60/13.21 (((setunion__Cong) =>
% 97.60/13.21 (((exuEu) =>
% 97.60/13.21 (((descr__Cong) =>
% 97.60/13.21 (((dsetconstr__Cong) =>
% 97.60/13.21 (((subsetI1) =>
% 97.60/13.21 (((eqimpsubset2) =>
% 97.60/13.21 (((eqimpsubset1) =>
% 97.60/13.21 (((subsetI2) =>
% 97.60/13.21 (((emptysetsubset) =>
% 97.60/13.21 (((subsetE) =>
% 97.60/13.21 (((subsetE2) =>
% 97.60/13.21 (((notsubsetI) =>
% 97.60/13.21 (((notequalI1) =>
% 97.60/13.21 (((notequalI2) =>
% 97.60/13.21 (((subsetRefl) =>
% 97.60/13.21 (((subsetTrans) =>
% 97.60/13.21 (((setadjoinSub) =>
% 97.60/13.21 (((setadjoinSub2) =>
% 97.60/13.21 (((subset2powerset) =>
% 97.60/13.21 (((setextsub) =>
% 97.60/13.21 (((subsetemptysetimpeq) =>
% 97.60/13.21 (((powersetI1) =>
% 97.60/13.21 (((powersetE1) =>
% 97.60/13.21 (((inPowerset) =>
% 97.60/13.21 ((
% 97.60/13.21 (powersetsubset) =>
% 97.60/13.21 ((
% 97.60/13.21 (sepInPowerset) =>
% 97.60/13.21 ((
% 97.60/13.21 (sepSubset) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionIL) =>
% 97.60/13.21 ((
% 97.60/13.21 (upairset2IR) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionIR) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionEcases) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionE) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionLsub) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionRsub) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectI) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectSubset5) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectEL) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectLsub) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectSubset2) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectSubset3) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectER) =>
% 97.60/13.21 ((
% 97.60/13.21 (disjointsetsI1) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectRsub) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectSubset4) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectSubset1) =>
% 97.60/13.21 ((
% 97.60/13.21 (bs114d) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusI) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusEL) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusER) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusSubset2) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusERneg) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusELneg) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusILneg) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusIRneg) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusLsub) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusSubset1) =>
% 97.60/13.21 ((
% 97.60/13.21 (symdiffE) =>
% 97.60/13.21 ((
% 97.60/13.21 (symdiffI1) =>
% 97.60/13.21 ((
% 97.60/13.21 (symdiffI2) =>
% 97.60/13.21 ((
% 97.60/13.21 (symdiffIneg1) =>
% 97.60/13.21 ((
% 97.60/13.21 (symdiffIneg2) =>
% 97.60/13.21 ((
% 97.60/13.21 (secondinupair) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairIL) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairIR) =>
% 97.60/13.21 ((
% 97.60/13.21 (kpairiskpair) =>
% 97.60/13.21 ((
% 97.60/13.21 (kpairp) =>
% 97.60/13.21 ((
% 97.60/13.21 (singletonsubset) =>
% 97.60/13.21 ((
% 97.60/13.21 (singletoninpowerset) =>
% 97.60/13.21 ((
% 97.60/13.21 (singletoninpowunion) =>
% 97.60/13.21 ((
% 97.60/13.21 (upairset2E) =>
% 97.60/13.21 ((
% 97.60/13.21 (upairsubunion) =>
% 97.60/13.21 ((
% 97.60/13.21 (upairinpowunion) =>
% 97.60/13.21 ((
% 97.60/13.21 (ubforcartprodlem1) =>
% 97.60/13.21 ((
% 97.60/13.21 (ubforcartprodlem2) =>
% 97.60/13.21 ((
% 97.60/13.21 (ubforcartprodlem3) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodpairin) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodmempair1) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodmempair) =>
% 97.60/13.21 ((
% 97.60/13.21 (setunionE2) =>
% 97.60/13.21 ((
% 97.60/13.21 (setunionsingleton1) =>
% 97.60/13.21 ((
% 97.60/13.21 (setunionsingleton2) =>
% 97.60/13.21 ((
% 97.60/13.21 (setunionsingleton) =>
% 97.60/13.21 ((
% 97.60/13.21 (singletonprop) =>
% 97.60/13.21 ((
% 97.60/13.21 (ex1E1) =>
% 97.60/13.21 ((
% 97.60/13.21 (ex1I) =>
% 97.60/13.21 ((
% 97.60/13.21 (ex1I2) =>
% 97.60/13.21 ((
% 97.60/13.21 (singletonsuniq) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairinjL1) =>
% 97.60/13.21 ((
% 97.60/13.21 (kfstsingleton) =>
% 97.60/13.21 ((
% 97.60/13.21 (theprop) =>
% 97.60/13.21 ((
% 97.60/13.21 (kfstpairEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodfstin) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairinjL2) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairinjL) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairinjR11) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairinjR12) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairinjR1) =>
% 97.60/13.21 ((
% 97.60/13.21 (upairequniteq) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairinjR2) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairinjR) =>
% 97.60/13.21 ((
% 97.60/13.21 (ksndsingleton) =>
% 97.60/13.21 ((
% 97.60/13.21 (ksndpairEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (kpairsurjEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodsndin) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodpairmemEL) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodpairmemER) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodmempaircEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodfstpairEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodsndpairEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodpairsurjEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (dpsetconstrI) =>
% 97.60/13.21 ((
% 97.60/13.21 (dpsetconstrSub) =>
% 97.60/13.21 ((
% 97.60/13.21 (setOfPairsIsBReln) =>
% 97.60/13.21 ((
% 97.60/13.21 (dpsetconstrERa) =>
% 97.60/13.21 ((
% 97.60/13.21 (dpsetconstrEL1) =>
% 97.60/13.21 ((
% 97.60/13.21 (dpsetconstrEL2) =>
% 97.60/13.21 ((
% 97.60/13.21 (dpsetconstrER) =>
% 97.60/13.21 ((
% 97.60/13.21 (funcImageSingleton) =>
% 97.60/13.21 ((
% 97.60/13.21 (apProp) =>
% 97.60/13.21 ((
% 97.60/13.21 (app) =>
% 97.60/13.21 ((
% 97.60/13.21 (infuncsetfunc) =>
% 97.60/13.21 ((
% 97.60/13.21 (ap2p) =>
% 97.60/13.21 ((
% 97.60/13.21 (funcinfuncset) =>
% 97.60/13.21 ((
% 97.60/13.21 (lamProp) =>
% 97.60/13.21 ((
% 97.60/13.21 (lamp) =>
% 97.60/13.21 ((
% 97.60/13.21 (lam2p) =>
% 97.60/13.21 ((
% 97.60/13.21 (brelnall1) =>
% 97.60/13.21 ((
% 97.60/13.21 (brelnall2) =>
% 97.60/13.21 ((
% 97.60/13.21 (ex1E2) =>
% 97.60/13.21 ((
% 97.60/13.21 (funcGraphProp1) =>
% 97.60/13.21 ((
% 97.60/13.21 (funcGraphProp3) =>
% 97.60/13.21 ((
% 97.60/13.21 (funcGraphProp2) =>
% 97.60/13.21 ((
% 97.60/13.21 (funcextLem) =>
% 97.60/13.21 ((
% 97.60/13.21 (funcGraphProp4) =>
% 97.60/13.21 ((
% 97.60/13.21 (subbreln) =>
% 97.60/13.21 ((
% 97.60/13.21 (eqbreln) =>
% 97.60/13.21 ((
% 97.60/13.21 (funcext) =>
% 97.60/13.21 ((
% 97.60/13.21 (funcext2) =>
% 97.60/13.21 ((
% 97.60/13.21 (ap2apEq1) =>
% 97.60/13.21 ((
% 97.60/13.21 (ap2apEq2) =>
% 97.60/13.21 ((
% 97.60/13.21 (beta1) =>
% 97.60/13.21 ((
% 97.60/13.21 (eta1) =>
% 97.60/13.21 ((
% 97.60/13.21 (lam2lamEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (beta2) =>
% 97.60/13.21 ((
% 97.60/13.21 (eta2) =>
% 97.60/13.21 ((
% 97.60/13.21 (iffalseProp1) =>
% 97.60/13.21 ((
% 97.60/13.21 (iffalseProp2) =>
% 97.60/13.21 ((
% 97.60/13.21 (iftrueProp1) =>
% 97.60/13.21 ((
% 97.60/13.21 (iftrueProp2) =>
% 97.60/13.21 ((
% 97.60/13.21 (ifSingleton) =>
% 97.60/13.21 ((
% 97.60/13.21 (ifp) =>
% 97.60/13.21 ((
% 97.60/13.21 (theeq) =>
% 97.60/13.21 ((
% 97.60/13.21 (iftrue) =>
% 97.60/13.21 ((
% 97.60/13.21 (iffalse) =>
% 97.60/13.21 ((
% 97.60/13.21 (iftrueorfalse) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectT_lem) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionT_lem) =>
% 97.60/13.21 ((
% 97.60/13.21 (powersetT_lem) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusT_lem) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementT_lem) =>
% 97.60/13.21 ((
% 97.60/13.21 (setextT) =>
% 97.60/13.21 ((
% 97.60/13.21 (subsetTI) =>
% 97.60/13.21 ((
% 97.60/13.21 (powersetTI1) =>
% 97.60/13.21 ((
% 97.60/13.21 (powersetTE1) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementTI1) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementTE1) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectTELcontra) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectTERcontra) =>
% 97.60/13.21 ((
% 97.60/13.21 (contrasubsetT) =>
% 97.60/13.21 ((
% 97.60/13.21 (contrasubsetT1) =>
% 97.60/13.21 ((
% 97.60/13.21 (contrasubsetT2) =>
% 97.60/13.21 ((
% 97.60/13.21 (contrasubsetT3) =>
% 97.60/13.21 ((
% 97.60/13.21 (doubleComplementI1) =>
% 97.60/13.21 ((
% 97.60/13.21 (doubleComplementE1) =>
% 97.60/13.21 ((
% 97.60/13.21 (doubleComplementSub1) =>
% 97.60/13.21 ((
% 97.60/13.21 (doubleComplementSub2) =>
% 97.60/13.21 ((
% 97.60/13.21 (doubleComplementEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementTnotintersectT) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementImpComplementIntersect) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementSubsetComplementIntersect) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementInPowersetComplementIntersect) =>
% 97.60/13.21 ((
% 97.60/13.21 (contraSubsetComplement) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementTcontraSubset) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionTILcontra) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionTIRcontra) =>
% 97.60/13.21 ((
% 97.60/13.21 (inIntersectImpInUnion) =>
% 97.60/13.21 ((
% 97.60/13.21 (inIntersectImpInUnion2) =>
% 97.60/13.21 ((
% 97.60/13.21 (inIntersectImpInIntersectUnions) =>
% 97.60/13.21 ((
% 97.60/13.21 (intersectInPowersetIntersectUnions) =>
% 97.60/13.21 ((
% 97.60/13.21 (inComplementUnionImpNotIn1) =>
% 97.60/13.21 ((
% 97.60/13.21 (inComplementUnionImpInComplement1) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionTE) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionTEcontra) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan2a1) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementUnionInPowersetComplement) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan2a2) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan1a) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan1b) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan1) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan2a) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan2b2) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan2b) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan2) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz13rule0) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz13rule1) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz13rule2) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz13rule3) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz13rule4) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz1_1) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz1_2) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz1_3) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz1_4) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz1_5) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1all2) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1SetBreln1) =>
% 97.60/13.21 ((
% 97.60/13.21 (choice2fnsingleton) =>
% 97.60/13.21 ((
% 97.60/13.21 (setOfPairsIsBReln1) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1all1) =>
% 97.60/13.21 ((
% 97.60/13.21 (subbreln1) =>
% 97.60/13.21 ((
% 97.60/13.21 (eqbreln1) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1invprop) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1invI) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1invE) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1compprop) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1compI) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1compE) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1compEex) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1unionprop) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1unionIL) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1unionIR) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1unionI) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1unionE) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1unionEcases) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1unionCommutes) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz2Ex) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz2W) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz2A) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz2B) =>
% 97.60/13.21 ((
% 97.60/13.21 (image1Ex) =>
% 97.60/13.21 ((
% 97.60/13.21 (image1Ex1) =>
% 97.60/13.21 ((
% 97.60/13.21 (image1Equiv) =>
% 97.60/13.21 ((
% 97.60/13.21 (image1E) =>
% 97.60/13.21 ((
% 97.60/13.21 (image1I) =>
% 97.60/13.21 ((
% 97.60/13.21 (injFuncInInjFuncSet) =>
% 97.60/13.21 ((
% 97.60/13.21 (injFuncSetFuncIn) =>
% 97.60/13.21 ((
% 97.60/13.21 (injFuncSetFuncInj) =>
% 97.60/13.21 ((
% 97.60/13.21 (surjFuncSetFuncIn) =>
% 97.60/13.21 ((
% 97.60/13.21 (surjFuncSetFuncSurj) =>
% 97.60/13.21 ((
% 97.60/13.21 (leftInvIsSurj) =>
% 97.60/13.21 ((
% 97.60/13.21 (surjCantorThm) =>
% 97.60/13.21 ((
% 97.60/13.21 (foundation2) =>
% 97.60/13.21 ((
% 97.60/13.21 (notinself) =>
% 97.60/13.21 ((
% 97.60/13.21 (notinself2) =>
% 97.60/13.21 ((
% 97.60/13.21 (omegaSp) =>
% 97.60/13.21 ((
% 97.60/13.21 (omegaSclos) =>
% 97.60/13.21 ((
% 97.60/13.21 (peano0notS) =>
% 97.60/13.21 ((
% 97.60/13.21 (!!) @ (
% 97.60/13.21 (('#S') @ (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 =>) @
% 97.60/13.21 (
% 97.60/13.21 (
% 97.60/13.21 ('#C') @ in @
% 97.60/13.21 omega)))) @
% 97.60/13.21 (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 !!) @
% 97.60/13.21 (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 (
% 97.60/13.21 ('#S') @ (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 =>) @
% 97.60/13.21 (
% 97.60/13.21 (
% 97.60/13.21 ('#C') @ in @
% 97.60/13.21 omega)))))) @
% 97.60/13.21 (
% 97.60/13.21 (
% 97.60/13.21 ('#S') @ (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 '#S') @
% 97.60/13.21 (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 =>))) @
% 97.60/13.21 (
% 97.60/13.21 (
% 97.60/13.21 ('#C') @ (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 '#B') @
% 97.60/13.21 (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 =) @
% 97.60/13.21 omegaS)))) @
% 97.60/13.21 omegaS)))))) @
% 97.60/13.21 (
% 97.60/13.21 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.60/13.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl630])).
% 97.60/13.21 thf(zip_derived_cl650, plain,
% 97.60/13.21 (~ (((in__Cong) =>
% 97.60/13.21 (((exuE3u) =>
% 97.60/13.21 (((exu__Cong) =>
% 97.60/13.21 (((setadjoin__Cong) =>
% 97.60/13.21 (((powerset__Cong) =>
% 97.60/13.21 (((setunion__Cong) =>
% 97.60/13.21 (((exuEu) =>
% 97.60/13.21 (((descr__Cong) =>
% 97.60/13.21 (((dsetconstr__Cong) =>
% 97.60/13.21 (((subsetI1) =>
% 97.60/13.21 (((eqimpsubset2) =>
% 97.60/13.21 (((eqimpsubset1) =>
% 97.60/13.21 (((subsetI2) =>
% 97.60/13.21 (((emptysetsubset) =>
% 97.60/13.21 (((subsetE) =>
% 97.60/13.21 (((subsetE2) =>
% 97.60/13.21 (((notsubsetI) =>
% 97.60/13.21 (((notequalI1) =>
% 97.60/13.21 (((notequalI2) =>
% 97.60/13.21 (((subsetRefl) =>
% 97.60/13.21 (((subsetTrans) =>
% 97.60/13.21 (((setadjoinSub) =>
% 97.60/13.21 (((setadjoinSub2) =>
% 97.60/13.21 (((subset2powerset) =>
% 97.60/13.21 (((setextsub) =>
% 97.60/13.21 (((subsetemptysetimpeq) =>
% 97.60/13.21 (((powersetI1) =>
% 97.60/13.21 (((powersetE1) =>
% 97.60/13.21 (((inPowerset) =>
% 97.60/13.21 (((powersetsubset) =>
% 97.60/13.21 ((
% 97.60/13.21 (sepInPowerset) =>
% 97.60/13.21 ((
% 97.60/13.21 (sepSubset) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionIL) =>
% 97.60/13.21 ((
% 97.60/13.21 (upairset2IR) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionIR) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionEcases) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionE) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionLsub) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionRsub) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectI) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectSubset5) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectEL) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectLsub) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectSubset2) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectSubset3) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectER) =>
% 97.60/13.21 ((
% 97.60/13.21 (disjointsetsI1) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectRsub) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectSubset4) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectSubset1) =>
% 97.60/13.21 ((
% 97.60/13.21 (bs114d) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusI) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusEL) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusER) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusSubset2) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusERneg) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusELneg) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusILneg) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusIRneg) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusLsub) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusSubset1) =>
% 97.60/13.21 ((
% 97.60/13.21 (symdiffE) =>
% 97.60/13.21 ((
% 97.60/13.21 (symdiffI1) =>
% 97.60/13.21 ((
% 97.60/13.21 (symdiffI2) =>
% 97.60/13.21 ((
% 97.60/13.21 (symdiffIneg1) =>
% 97.60/13.21 ((
% 97.60/13.21 (symdiffIneg2) =>
% 97.60/13.21 ((
% 97.60/13.21 (secondinupair) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairIL) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairIR) =>
% 97.60/13.21 ((
% 97.60/13.21 (kpairiskpair) =>
% 97.60/13.21 ((
% 97.60/13.21 (kpairp) =>
% 97.60/13.21 ((
% 97.60/13.21 (singletonsubset) =>
% 97.60/13.21 ((
% 97.60/13.21 (singletoninpowerset) =>
% 97.60/13.21 ((
% 97.60/13.21 (singletoninpowunion) =>
% 97.60/13.21 ((
% 97.60/13.21 (upairset2E) =>
% 97.60/13.21 ((
% 97.60/13.21 (upairsubunion) =>
% 97.60/13.21 ((
% 97.60/13.21 (upairinpowunion) =>
% 97.60/13.21 ((
% 97.60/13.21 (ubforcartprodlem1) =>
% 97.60/13.21 ((
% 97.60/13.21 (ubforcartprodlem2) =>
% 97.60/13.21 ((
% 97.60/13.21 (ubforcartprodlem3) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodpairin) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodmempair1) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodmempair) =>
% 97.60/13.21 ((
% 97.60/13.21 (setunionE2) =>
% 97.60/13.21 ((
% 97.60/13.21 (setunionsingleton1) =>
% 97.60/13.21 ((
% 97.60/13.21 (setunionsingleton2) =>
% 97.60/13.21 ((
% 97.60/13.21 (setunionsingleton) =>
% 97.60/13.21 ((
% 97.60/13.21 (singletonprop) =>
% 97.60/13.21 ((
% 97.60/13.21 (ex1E1) =>
% 97.60/13.21 ((
% 97.60/13.21 (ex1I) =>
% 97.60/13.21 ((
% 97.60/13.21 (ex1I2) =>
% 97.60/13.21 ((
% 97.60/13.21 (singletonsuniq) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairinjL1) =>
% 97.60/13.21 ((
% 97.60/13.21 (kfstsingleton) =>
% 97.60/13.21 ((
% 97.60/13.21 (theprop) =>
% 97.60/13.21 ((
% 97.60/13.21 (kfstpairEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodfstin) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairinjL2) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairinjL) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairinjR11) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairinjR12) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairinjR1) =>
% 97.60/13.21 ((
% 97.60/13.21 (upairequniteq) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairinjR2) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairinjR) =>
% 97.60/13.21 ((
% 97.60/13.21 (ksndsingleton) =>
% 97.60/13.21 ((
% 97.60/13.21 (ksndpairEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (kpairsurjEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodsndin) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodpairmemEL) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodpairmemER) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodmempaircEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodfstpairEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodsndpairEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodpairsurjEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (dpsetconstrI) =>
% 97.60/13.21 ((
% 97.60/13.21 (dpsetconstrSub) =>
% 97.60/13.21 ((
% 97.60/13.21 (setOfPairsIsBReln) =>
% 97.60/13.21 ((
% 97.60/13.21 (dpsetconstrERa) =>
% 97.60/13.21 ((
% 97.60/13.21 (dpsetconstrEL1) =>
% 97.60/13.21 ((
% 97.60/13.21 (dpsetconstrEL2) =>
% 97.60/13.21 ((
% 97.60/13.21 (dpsetconstrER) =>
% 97.60/13.21 ((
% 97.60/13.21 (funcImageSingleton) =>
% 97.60/13.21 ((
% 97.60/13.21 (apProp) =>
% 97.60/13.21 ((
% 97.60/13.21 (app) =>
% 97.60/13.21 ((
% 97.60/13.21 (infuncsetfunc) =>
% 97.60/13.21 ((
% 97.60/13.21 (ap2p) =>
% 97.60/13.21 ((
% 97.60/13.21 (funcinfuncset) =>
% 97.60/13.21 ((
% 97.60/13.21 (lamProp) =>
% 97.60/13.21 ((
% 97.60/13.21 (lamp) =>
% 97.60/13.21 ((
% 97.60/13.21 (lam2p) =>
% 97.60/13.21 ((
% 97.60/13.21 (brelnall1) =>
% 97.60/13.21 ((
% 97.60/13.21 (brelnall2) =>
% 97.60/13.21 ((
% 97.60/13.21 (ex1E2) =>
% 97.60/13.21 ((
% 97.60/13.21 (funcGraphProp1) =>
% 97.60/13.21 ((
% 97.60/13.21 (funcGraphProp3) =>
% 97.60/13.21 ((
% 97.60/13.21 (funcGraphProp2) =>
% 97.60/13.21 ((
% 97.60/13.21 (funcextLem) =>
% 97.60/13.21 ((
% 97.60/13.21 (funcGraphProp4) =>
% 97.60/13.21 ((
% 97.60/13.21 (subbreln) =>
% 97.60/13.21 ((
% 97.60/13.21 (eqbreln) =>
% 97.60/13.21 ((
% 97.60/13.21 (funcext) =>
% 97.60/13.21 ((
% 97.60/13.21 (funcext2) =>
% 97.60/13.21 ((
% 97.60/13.21 (ap2apEq1) =>
% 97.60/13.21 ((
% 97.60/13.21 (ap2apEq2) =>
% 97.60/13.21 ((
% 97.60/13.21 (beta1) =>
% 97.60/13.21 ((
% 97.60/13.21 (eta1) =>
% 97.60/13.21 ((
% 97.60/13.21 (lam2lamEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (beta2) =>
% 97.60/13.21 ((
% 97.60/13.21 (eta2) =>
% 97.60/13.21 ((
% 97.60/13.21 (iffalseProp1) =>
% 97.60/13.21 ((
% 97.60/13.21 (iffalseProp2) =>
% 97.60/13.21 ((
% 97.60/13.21 (iftrueProp1) =>
% 97.60/13.21 ((
% 97.60/13.21 (iftrueProp2) =>
% 97.60/13.21 ((
% 97.60/13.21 (ifSingleton) =>
% 97.60/13.21 ((
% 97.60/13.21 (ifp) =>
% 97.60/13.21 ((
% 97.60/13.21 (theeq) =>
% 97.60/13.21 ((
% 97.60/13.21 (iftrue) =>
% 97.60/13.21 ((
% 97.60/13.21 (iffalse) =>
% 97.60/13.21 ((
% 97.60/13.21 (iftrueorfalse) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectT_lem) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionT_lem) =>
% 97.60/13.21 ((
% 97.60/13.21 (powersetT_lem) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusT_lem) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementT_lem) =>
% 97.60/13.21 ((
% 97.60/13.21 (setextT) =>
% 97.60/13.21 ((
% 97.60/13.21 (subsetTI) =>
% 97.60/13.21 ((
% 97.60/13.21 (powersetTI1) =>
% 97.60/13.21 ((
% 97.60/13.21 (powersetTE1) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementTI1) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementTE1) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectTELcontra) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectTERcontra) =>
% 97.60/13.21 ((
% 97.60/13.21 (contrasubsetT) =>
% 97.60/13.21 ((
% 97.60/13.21 (contrasubsetT1) =>
% 97.60/13.21 ((
% 97.60/13.21 (contrasubsetT2) =>
% 97.60/13.21 ((
% 97.60/13.21 (contrasubsetT3) =>
% 97.60/13.21 ((
% 97.60/13.21 (doubleComplementI1) =>
% 97.60/13.21 ((
% 97.60/13.21 (doubleComplementE1) =>
% 97.60/13.21 ((
% 97.60/13.21 (doubleComplementSub1) =>
% 97.60/13.21 ((
% 97.60/13.21 (doubleComplementSub2) =>
% 97.60/13.21 ((
% 97.60/13.21 (doubleComplementEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementTnotintersectT) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementImpComplementIntersect) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementSubsetComplementIntersect) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementInPowersetComplementIntersect) =>
% 97.60/13.21 ((
% 97.60/13.21 (contraSubsetComplement) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementTcontraSubset) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionTILcontra) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionTIRcontra) =>
% 97.60/13.21 ((
% 97.60/13.21 (inIntersectImpInUnion) =>
% 97.60/13.21 ((
% 97.60/13.21 (inIntersectImpInUnion2) =>
% 97.60/13.21 ((
% 97.60/13.21 (inIntersectImpInIntersectUnions) =>
% 97.60/13.21 ((
% 97.60/13.21 (intersectInPowersetIntersectUnions) =>
% 97.60/13.21 ((
% 97.60/13.21 (inComplementUnionImpNotIn1) =>
% 97.60/13.21 ((
% 97.60/13.21 (inComplementUnionImpInComplement1) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionTE) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionTEcontra) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan2a1) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementUnionInPowersetComplement) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan2a2) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan1a) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan1b) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan1) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan2a) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan2b2) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan2b) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan2) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz13rule0) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz13rule1) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz13rule2) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz13rule3) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz13rule4) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz1_1) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz1_2) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz1_3) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz1_4) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz1_5) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1all2) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1SetBreln1) =>
% 97.60/13.21 ((
% 97.60/13.21 (choice2fnsingleton) =>
% 97.60/13.21 ((
% 97.60/13.21 (setOfPairsIsBReln1) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1all1) =>
% 97.60/13.21 ((
% 97.60/13.21 (subbreln1) =>
% 97.60/13.21 ((
% 97.60/13.21 (eqbreln1) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1invprop) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1invI) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1invE) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1compprop) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1compI) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1compE) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1compEex) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1unionprop) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1unionIL) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1unionIR) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1unionI) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1unionE) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1unionEcases) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1unionCommutes) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz2Ex) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz2W) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz2A) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz2B) =>
% 97.60/13.21 ((
% 97.60/13.21 (image1Ex) =>
% 97.60/13.21 ((
% 97.60/13.21 (image1Ex1) =>
% 97.60/13.21 ((
% 97.60/13.21 (image1Equiv) =>
% 97.60/13.21 ((
% 97.60/13.21 (image1E) =>
% 97.60/13.21 ((
% 97.60/13.21 (image1I) =>
% 97.60/13.21 ((
% 97.60/13.21 (injFuncInInjFuncSet) =>
% 97.60/13.21 ((
% 97.60/13.21 (injFuncSetFuncIn) =>
% 97.60/13.21 ((
% 97.60/13.21 (injFuncSetFuncInj) =>
% 97.60/13.21 ((
% 97.60/13.21 (surjFuncSetFuncIn) =>
% 97.60/13.21 ((
% 97.60/13.21 (surjFuncSetFuncSurj) =>
% 97.60/13.21 ((
% 97.60/13.21 (leftInvIsSurj) =>
% 97.60/13.21 ((
% 97.60/13.21 (surjCantorThm) =>
% 97.60/13.21 ((
% 97.60/13.21 (foundation2) =>
% 97.60/13.21 ((
% 97.60/13.21 (notinself) =>
% 97.60/13.21 ((
% 97.60/13.21 (notinself2) =>
% 97.60/13.21 ((
% 97.60/13.21 (omegaSp) =>
% 97.60/13.21 ((
% 97.60/13.21 (omegaSclos) =>
% 97.60/13.21 ((
% 97.60/13.21 (peano0notS) =>
% 97.60/13.21 ((
% 97.60/13.21 (!!) @ (
% 97.60/13.21 (('#S') @ (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 =>) @
% 97.60/13.21 (
% 97.60/13.21 (
% 97.60/13.21 ('#C') @ in @
% 97.60/13.21 omega)))) @
% 97.60/13.21 (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 !!) @
% 97.60/13.21 (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 (
% 97.60/13.21 ('#S') @ (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 =>) @
% 97.60/13.21 (
% 97.60/13.21 (
% 97.60/13.21 ('#C') @ in @
% 97.60/13.21 omega)))))) @
% 97.60/13.21 (
% 97.60/13.21 (
% 97.60/13.21 ('#S') @ (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 '#S') @
% 97.60/13.21 (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 =>))) @
% 97.60/13.21 (
% 97.60/13.21 (
% 97.60/13.21 ('#C') @ (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 '#B') @
% 97.60/13.21 (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 =) @
% 97.60/13.21 omegaS)))) @
% 97.60/13.21 omegaS)))))) @
% 97.60/13.21 (
% 97.60/13.21 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.60/13.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl640])).
% 97.60/13.21 thf(zip_derived_cl660, plain,
% 97.60/13.21 (~ (((exuE3u) =>
% 97.60/13.21 (((exu__Cong) =>
% 97.60/13.21 (((setadjoin__Cong) =>
% 97.60/13.21 (((powerset__Cong) =>
% 97.60/13.21 (((setunion__Cong) =>
% 97.60/13.21 (((exuEu) =>
% 97.60/13.21 (((descr__Cong) =>
% 97.60/13.21 (((dsetconstr__Cong) =>
% 97.60/13.21 (((subsetI1) =>
% 97.60/13.21 (((eqimpsubset2) =>
% 97.60/13.21 (((eqimpsubset1) =>
% 97.60/13.21 (((subsetI2) =>
% 97.60/13.21 (((emptysetsubset) =>
% 97.60/13.21 (((subsetE) =>
% 97.60/13.21 (((subsetE2) =>
% 97.60/13.21 (((notsubsetI) =>
% 97.60/13.21 (((notequalI1) =>
% 97.60/13.21 (((notequalI2) =>
% 97.60/13.21 (((subsetRefl) =>
% 97.60/13.21 (((subsetTrans) =>
% 97.60/13.21 (((setadjoinSub) =>
% 97.60/13.21 (((setadjoinSub2) =>
% 97.60/13.21 (((subset2powerset) =>
% 97.60/13.21 (((setextsub) =>
% 97.60/13.21 (((subsetemptysetimpeq) =>
% 97.60/13.21 (((powersetI1) =>
% 97.60/13.21 (((powersetE1) =>
% 97.60/13.21 (((inPowerset) =>
% 97.60/13.21 (((powersetsubset) =>
% 97.60/13.21 (((sepInPowerset) =>
% 97.60/13.21 ((
% 97.60/13.21 (sepSubset) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionIL) =>
% 97.60/13.21 ((
% 97.60/13.21 (upairset2IR) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionIR) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionEcases) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionE) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionLsub) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionRsub) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectI) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectSubset5) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectEL) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectLsub) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectSubset2) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectSubset3) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectER) =>
% 97.60/13.21 ((
% 97.60/13.21 (disjointsetsI1) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectRsub) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectSubset4) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectSubset1) =>
% 97.60/13.21 ((
% 97.60/13.21 (bs114d) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusI) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusEL) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusER) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusSubset2) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusERneg) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusELneg) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusILneg) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusIRneg) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusLsub) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusSubset1) =>
% 97.60/13.21 ((
% 97.60/13.21 (symdiffE) =>
% 97.60/13.21 ((
% 97.60/13.21 (symdiffI1) =>
% 97.60/13.21 ((
% 97.60/13.21 (symdiffI2) =>
% 97.60/13.21 ((
% 97.60/13.21 (symdiffIneg1) =>
% 97.60/13.21 ((
% 97.60/13.21 (symdiffIneg2) =>
% 97.60/13.21 ((
% 97.60/13.21 (secondinupair) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairIL) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairIR) =>
% 97.60/13.21 ((
% 97.60/13.21 (kpairiskpair) =>
% 97.60/13.21 ((
% 97.60/13.21 (kpairp) =>
% 97.60/13.21 ((
% 97.60/13.21 (singletonsubset) =>
% 97.60/13.21 ((
% 97.60/13.21 (singletoninpowerset) =>
% 97.60/13.21 ((
% 97.60/13.21 (singletoninpowunion) =>
% 97.60/13.21 ((
% 97.60/13.21 (upairset2E) =>
% 97.60/13.21 ((
% 97.60/13.21 (upairsubunion) =>
% 97.60/13.21 ((
% 97.60/13.21 (upairinpowunion) =>
% 97.60/13.21 ((
% 97.60/13.21 (ubforcartprodlem1) =>
% 97.60/13.21 ((
% 97.60/13.21 (ubforcartprodlem2) =>
% 97.60/13.21 ((
% 97.60/13.21 (ubforcartprodlem3) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodpairin) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodmempair1) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodmempair) =>
% 97.60/13.21 ((
% 97.60/13.21 (setunionE2) =>
% 97.60/13.21 ((
% 97.60/13.21 (setunionsingleton1) =>
% 97.60/13.21 ((
% 97.60/13.21 (setunionsingleton2) =>
% 97.60/13.21 ((
% 97.60/13.21 (setunionsingleton) =>
% 97.60/13.21 ((
% 97.60/13.21 (singletonprop) =>
% 97.60/13.21 ((
% 97.60/13.21 (ex1E1) =>
% 97.60/13.21 ((
% 97.60/13.21 (ex1I) =>
% 97.60/13.21 ((
% 97.60/13.21 (ex1I2) =>
% 97.60/13.21 ((
% 97.60/13.21 (singletonsuniq) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairinjL1) =>
% 97.60/13.21 ((
% 97.60/13.21 (kfstsingleton) =>
% 97.60/13.21 ((
% 97.60/13.21 (theprop) =>
% 97.60/13.21 ((
% 97.60/13.21 (kfstpairEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodfstin) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairinjL2) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairinjL) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairinjR11) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairinjR12) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairinjR1) =>
% 97.60/13.21 ((
% 97.60/13.21 (upairequniteq) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairinjR2) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairinjR) =>
% 97.60/13.21 ((
% 97.60/13.21 (ksndsingleton) =>
% 97.60/13.21 ((
% 97.60/13.21 (ksndpairEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (kpairsurjEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodsndin) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodpairmemEL) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodpairmemER) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodmempaircEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodfstpairEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodsndpairEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodpairsurjEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (dpsetconstrI) =>
% 97.60/13.21 ((
% 97.60/13.21 (dpsetconstrSub) =>
% 97.60/13.21 ((
% 97.60/13.21 (setOfPairsIsBReln) =>
% 97.60/13.21 ((
% 97.60/13.21 (dpsetconstrERa) =>
% 97.60/13.21 ((
% 97.60/13.21 (dpsetconstrEL1) =>
% 97.60/13.21 ((
% 97.60/13.21 (dpsetconstrEL2) =>
% 97.60/13.21 ((
% 97.60/13.21 (dpsetconstrER) =>
% 97.60/13.21 ((
% 97.60/13.21 (funcImageSingleton) =>
% 97.60/13.21 ((
% 97.60/13.21 (apProp) =>
% 97.60/13.21 ((
% 97.60/13.21 (app) =>
% 97.60/13.21 ((
% 97.60/13.21 (infuncsetfunc) =>
% 97.60/13.21 ((
% 97.60/13.21 (ap2p) =>
% 97.60/13.21 ((
% 97.60/13.21 (funcinfuncset) =>
% 97.60/13.21 ((
% 97.60/13.21 (lamProp) =>
% 97.60/13.21 ((
% 97.60/13.21 (lamp) =>
% 97.60/13.21 ((
% 97.60/13.21 (lam2p) =>
% 97.60/13.21 ((
% 97.60/13.21 (brelnall1) =>
% 97.60/13.21 ((
% 97.60/13.21 (brelnall2) =>
% 97.60/13.21 ((
% 97.60/13.21 (ex1E2) =>
% 97.60/13.21 ((
% 97.60/13.21 (funcGraphProp1) =>
% 97.60/13.21 ((
% 97.60/13.21 (funcGraphProp3) =>
% 97.60/13.21 ((
% 97.60/13.21 (funcGraphProp2) =>
% 97.60/13.21 ((
% 97.60/13.21 (funcextLem) =>
% 97.60/13.21 ((
% 97.60/13.21 (funcGraphProp4) =>
% 97.60/13.21 ((
% 97.60/13.21 (subbreln) =>
% 97.60/13.21 ((
% 97.60/13.21 (eqbreln) =>
% 97.60/13.21 ((
% 97.60/13.21 (funcext) =>
% 97.60/13.21 ((
% 97.60/13.21 (funcext2) =>
% 97.60/13.21 ((
% 97.60/13.21 (ap2apEq1) =>
% 97.60/13.21 ((
% 97.60/13.21 (ap2apEq2) =>
% 97.60/13.21 ((
% 97.60/13.21 (beta1) =>
% 97.60/13.21 ((
% 97.60/13.21 (eta1) =>
% 97.60/13.21 ((
% 97.60/13.21 (lam2lamEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (beta2) =>
% 97.60/13.21 ((
% 97.60/13.21 (eta2) =>
% 97.60/13.21 ((
% 97.60/13.21 (iffalseProp1) =>
% 97.60/13.21 ((
% 97.60/13.21 (iffalseProp2) =>
% 97.60/13.21 ((
% 97.60/13.21 (iftrueProp1) =>
% 97.60/13.21 ((
% 97.60/13.21 (iftrueProp2) =>
% 97.60/13.21 ((
% 97.60/13.21 (ifSingleton) =>
% 97.60/13.21 ((
% 97.60/13.21 (ifp) =>
% 97.60/13.21 ((
% 97.60/13.21 (theeq) =>
% 97.60/13.21 ((
% 97.60/13.21 (iftrue) =>
% 97.60/13.21 ((
% 97.60/13.21 (iffalse) =>
% 97.60/13.21 ((
% 97.60/13.21 (iftrueorfalse) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectT_lem) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionT_lem) =>
% 97.60/13.21 ((
% 97.60/13.21 (powersetT_lem) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusT_lem) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementT_lem) =>
% 97.60/13.21 ((
% 97.60/13.21 (setextT) =>
% 97.60/13.21 ((
% 97.60/13.21 (subsetTI) =>
% 97.60/13.21 ((
% 97.60/13.21 (powersetTI1) =>
% 97.60/13.21 ((
% 97.60/13.21 (powersetTE1) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementTI1) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementTE1) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectTELcontra) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectTERcontra) =>
% 97.60/13.21 ((
% 97.60/13.21 (contrasubsetT) =>
% 97.60/13.21 ((
% 97.60/13.21 (contrasubsetT1) =>
% 97.60/13.21 ((
% 97.60/13.21 (contrasubsetT2) =>
% 97.60/13.21 ((
% 97.60/13.21 (contrasubsetT3) =>
% 97.60/13.21 ((
% 97.60/13.21 (doubleComplementI1) =>
% 97.60/13.21 ((
% 97.60/13.21 (doubleComplementE1) =>
% 97.60/13.21 ((
% 97.60/13.21 (doubleComplementSub1) =>
% 97.60/13.21 ((
% 97.60/13.21 (doubleComplementSub2) =>
% 97.60/13.21 ((
% 97.60/13.21 (doubleComplementEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementTnotintersectT) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementImpComplementIntersect) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementSubsetComplementIntersect) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementInPowersetComplementIntersect) =>
% 97.60/13.21 ((
% 97.60/13.21 (contraSubsetComplement) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementTcontraSubset) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionTILcontra) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionTIRcontra) =>
% 97.60/13.21 ((
% 97.60/13.21 (inIntersectImpInUnion) =>
% 97.60/13.21 ((
% 97.60/13.21 (inIntersectImpInUnion2) =>
% 97.60/13.21 ((
% 97.60/13.21 (inIntersectImpInIntersectUnions) =>
% 97.60/13.21 ((
% 97.60/13.21 (intersectInPowersetIntersectUnions) =>
% 97.60/13.21 ((
% 97.60/13.21 (inComplementUnionImpNotIn1) =>
% 97.60/13.21 ((
% 97.60/13.21 (inComplementUnionImpInComplement1) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionTE) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionTEcontra) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan2a1) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementUnionInPowersetComplement) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan2a2) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan1a) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan1b) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan1) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan2a) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan2b2) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan2b) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan2) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz13rule0) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz13rule1) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz13rule2) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz13rule3) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz13rule4) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz1_1) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz1_2) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz1_3) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz1_4) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz1_5) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1all2) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1SetBreln1) =>
% 97.60/13.21 ((
% 97.60/13.21 (choice2fnsingleton) =>
% 97.60/13.21 ((
% 97.60/13.21 (setOfPairsIsBReln1) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1all1) =>
% 97.60/13.21 ((
% 97.60/13.21 (subbreln1) =>
% 97.60/13.21 ((
% 97.60/13.21 (eqbreln1) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1invprop) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1invI) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1invE) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1compprop) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1compI) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1compE) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1compEex) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1unionprop) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1unionIL) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1unionIR) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1unionI) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1unionE) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1unionEcases) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1unionCommutes) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz2Ex) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz2W) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz2A) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz2B) =>
% 97.60/13.21 ((
% 97.60/13.21 (image1Ex) =>
% 97.60/13.21 ((
% 97.60/13.21 (image1Ex1) =>
% 97.60/13.21 ((
% 97.60/13.21 (image1Equiv) =>
% 97.60/13.21 ((
% 97.60/13.21 (image1E) =>
% 97.60/13.21 ((
% 97.60/13.21 (image1I) =>
% 97.60/13.21 ((
% 97.60/13.21 (injFuncInInjFuncSet) =>
% 97.60/13.21 ((
% 97.60/13.21 (injFuncSetFuncIn) =>
% 97.60/13.21 ((
% 97.60/13.21 (injFuncSetFuncInj) =>
% 97.60/13.21 ((
% 97.60/13.21 (surjFuncSetFuncIn) =>
% 97.60/13.21 ((
% 97.60/13.21 (surjFuncSetFuncSurj) =>
% 97.60/13.21 ((
% 97.60/13.21 (leftInvIsSurj) =>
% 97.60/13.21 ((
% 97.60/13.21 (surjCantorThm) =>
% 97.60/13.21 ((
% 97.60/13.21 (foundation2) =>
% 97.60/13.21 ((
% 97.60/13.21 (notinself) =>
% 97.60/13.21 ((
% 97.60/13.21 (notinself2) =>
% 97.60/13.21 ((
% 97.60/13.21 (omegaSp) =>
% 97.60/13.21 ((
% 97.60/13.21 (omegaSclos) =>
% 97.60/13.21 ((
% 97.60/13.21 (peano0notS) =>
% 97.60/13.21 ((
% 97.60/13.21 (!!) @ (
% 97.60/13.21 (('#S') @ (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 =>) @
% 97.60/13.21 (
% 97.60/13.21 (
% 97.60/13.21 ('#C') @ in @
% 97.60/13.21 omega)))) @
% 97.60/13.21 (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 !!) @
% 97.60/13.21 (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 (
% 97.60/13.21 ('#S') @ (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 =>) @
% 97.60/13.21 (
% 97.60/13.21 (
% 97.60/13.21 ('#C') @ in @
% 97.60/13.21 omega)))))) @
% 97.60/13.21 (
% 97.60/13.21 (
% 97.60/13.21 ('#S') @ (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 '#S') @
% 97.60/13.21 (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 =>))) @
% 97.60/13.21 (
% 97.60/13.21 (
% 97.60/13.21 ('#C') @ (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 '#B') @
% 97.60/13.21 (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 =) @
% 97.60/13.21 omegaS)))) @
% 97.60/13.21 omegaS)))))) @
% 97.60/13.21 (
% 97.60/13.21 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.60/13.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl650])).
% 97.60/13.21 thf(zip_derived_cl672, plain,
% 97.60/13.21 (~ (((exu__Cong) =>
% 97.60/13.21 (((setadjoin__Cong) =>
% 97.60/13.21 (((powerset__Cong) =>
% 97.60/13.21 (((setunion__Cong) =>
% 97.60/13.21 (((exuEu) =>
% 97.60/13.21 (((descr__Cong) =>
% 97.60/13.21 (((dsetconstr__Cong) =>
% 97.60/13.21 (((subsetI1) =>
% 97.60/13.21 (((eqimpsubset2) =>
% 97.60/13.21 (((eqimpsubset1) =>
% 97.60/13.21 (((subsetI2) =>
% 97.60/13.21 (((emptysetsubset) =>
% 97.60/13.21 (((subsetE) =>
% 97.60/13.21 (((subsetE2) =>
% 97.60/13.21 (((notsubsetI) =>
% 97.60/13.21 (((notequalI1) =>
% 97.60/13.21 (((notequalI2) =>
% 97.60/13.21 (((subsetRefl) =>
% 97.60/13.21 (((subsetTrans) =>
% 97.60/13.21 (((setadjoinSub) =>
% 97.60/13.21 (((setadjoinSub2) =>
% 97.60/13.21 (((subset2powerset) =>
% 97.60/13.21 (((setextsub) =>
% 97.60/13.21 (((subsetemptysetimpeq) =>
% 97.60/13.21 (((powersetI1) =>
% 97.60/13.21 (((powersetE1) =>
% 97.60/13.21 (((inPowerset) =>
% 97.60/13.21 (((powersetsubset) =>
% 97.60/13.21 (((sepInPowerset) =>
% 97.60/13.21 (((sepSubset) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionIL) =>
% 97.60/13.21 ((
% 97.60/13.21 (upairset2IR) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionIR) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionEcases) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionE) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionLsub) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionRsub) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectI) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectSubset5) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectEL) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectLsub) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectSubset2) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectSubset3) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectER) =>
% 97.60/13.21 ((
% 97.60/13.21 (disjointsetsI1) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectRsub) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectSubset4) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectSubset1) =>
% 97.60/13.21 ((
% 97.60/13.21 (bs114d) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusI) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusEL) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusER) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusSubset2) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusERneg) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusELneg) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusILneg) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusIRneg) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusLsub) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusSubset1) =>
% 97.60/13.21 ((
% 97.60/13.21 (symdiffE) =>
% 97.60/13.21 ((
% 97.60/13.21 (symdiffI1) =>
% 97.60/13.21 ((
% 97.60/13.21 (symdiffI2) =>
% 97.60/13.21 ((
% 97.60/13.21 (symdiffIneg1) =>
% 97.60/13.21 ((
% 97.60/13.21 (symdiffIneg2) =>
% 97.60/13.21 ((
% 97.60/13.21 (secondinupair) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairIL) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairIR) =>
% 97.60/13.21 ((
% 97.60/13.21 (kpairiskpair) =>
% 97.60/13.21 ((
% 97.60/13.21 (kpairp) =>
% 97.60/13.21 ((
% 97.60/13.21 (singletonsubset) =>
% 97.60/13.21 ((
% 97.60/13.21 (singletoninpowerset) =>
% 97.60/13.21 ((
% 97.60/13.21 (singletoninpowunion) =>
% 97.60/13.21 ((
% 97.60/13.21 (upairset2E) =>
% 97.60/13.21 ((
% 97.60/13.21 (upairsubunion) =>
% 97.60/13.21 ((
% 97.60/13.21 (upairinpowunion) =>
% 97.60/13.21 ((
% 97.60/13.21 (ubforcartprodlem1) =>
% 97.60/13.21 ((
% 97.60/13.21 (ubforcartprodlem2) =>
% 97.60/13.21 ((
% 97.60/13.21 (ubforcartprodlem3) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodpairin) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodmempair1) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodmempair) =>
% 97.60/13.21 ((
% 97.60/13.21 (setunionE2) =>
% 97.60/13.21 ((
% 97.60/13.21 (setunionsingleton1) =>
% 97.60/13.21 ((
% 97.60/13.21 (setunionsingleton2) =>
% 97.60/13.21 ((
% 97.60/13.21 (setunionsingleton) =>
% 97.60/13.21 ((
% 97.60/13.21 (singletonprop) =>
% 97.60/13.21 ((
% 97.60/13.21 (ex1E1) =>
% 97.60/13.21 ((
% 97.60/13.21 (ex1I) =>
% 97.60/13.21 ((
% 97.60/13.21 (ex1I2) =>
% 97.60/13.21 ((
% 97.60/13.21 (singletonsuniq) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairinjL1) =>
% 97.60/13.21 ((
% 97.60/13.21 (kfstsingleton) =>
% 97.60/13.21 ((
% 97.60/13.21 (theprop) =>
% 97.60/13.21 ((
% 97.60/13.21 (kfstpairEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodfstin) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairinjL2) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairinjL) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairinjR11) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairinjR12) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairinjR1) =>
% 97.60/13.21 ((
% 97.60/13.21 (upairequniteq) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairinjR2) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairinjR) =>
% 97.60/13.21 ((
% 97.60/13.21 (ksndsingleton) =>
% 97.60/13.21 ((
% 97.60/13.21 (ksndpairEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (kpairsurjEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodsndin) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodpairmemEL) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodpairmemER) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodmempaircEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodfstpairEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodsndpairEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodpairsurjEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (dpsetconstrI) =>
% 97.60/13.21 ((
% 97.60/13.21 (dpsetconstrSub) =>
% 97.60/13.21 ((
% 97.60/13.21 (setOfPairsIsBReln) =>
% 97.60/13.21 ((
% 97.60/13.21 (dpsetconstrERa) =>
% 97.60/13.21 ((
% 97.60/13.21 (dpsetconstrEL1) =>
% 97.60/13.21 ((
% 97.60/13.21 (dpsetconstrEL2) =>
% 97.60/13.21 ((
% 97.60/13.21 (dpsetconstrER) =>
% 97.60/13.21 ((
% 97.60/13.21 (funcImageSingleton) =>
% 97.60/13.21 ((
% 97.60/13.21 (apProp) =>
% 97.60/13.21 ((
% 97.60/13.21 (app) =>
% 97.60/13.21 ((
% 97.60/13.21 (infuncsetfunc) =>
% 97.60/13.21 ((
% 97.60/13.21 (ap2p) =>
% 97.60/13.21 ((
% 97.60/13.21 (funcinfuncset) =>
% 97.60/13.21 ((
% 97.60/13.21 (lamProp) =>
% 97.60/13.21 ((
% 97.60/13.21 (lamp) =>
% 97.60/13.21 ((
% 97.60/13.21 (lam2p) =>
% 97.60/13.21 ((
% 97.60/13.21 (brelnall1) =>
% 97.60/13.21 ((
% 97.60/13.21 (brelnall2) =>
% 97.60/13.21 ((
% 97.60/13.21 (ex1E2) =>
% 97.60/13.21 ((
% 97.60/13.21 (funcGraphProp1) =>
% 97.60/13.21 ((
% 97.60/13.21 (funcGraphProp3) =>
% 97.60/13.21 ((
% 97.60/13.21 (funcGraphProp2) =>
% 97.60/13.21 ((
% 97.60/13.21 (funcextLem) =>
% 97.60/13.21 ((
% 97.60/13.21 (funcGraphProp4) =>
% 97.60/13.21 ((
% 97.60/13.21 (subbreln) =>
% 97.60/13.21 ((
% 97.60/13.21 (eqbreln) =>
% 97.60/13.21 ((
% 97.60/13.21 (funcext) =>
% 97.60/13.21 ((
% 97.60/13.21 (funcext2) =>
% 97.60/13.21 ((
% 97.60/13.21 (ap2apEq1) =>
% 97.60/13.21 ((
% 97.60/13.21 (ap2apEq2) =>
% 97.60/13.21 ((
% 97.60/13.21 (beta1) =>
% 97.60/13.21 ((
% 97.60/13.21 (eta1) =>
% 97.60/13.21 ((
% 97.60/13.21 (lam2lamEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (beta2) =>
% 97.60/13.21 ((
% 97.60/13.21 (eta2) =>
% 97.60/13.21 ((
% 97.60/13.21 (iffalseProp1) =>
% 97.60/13.21 ((
% 97.60/13.21 (iffalseProp2) =>
% 97.60/13.21 ((
% 97.60/13.21 (iftrueProp1) =>
% 97.60/13.21 ((
% 97.60/13.21 (iftrueProp2) =>
% 97.60/13.21 ((
% 97.60/13.21 (ifSingleton) =>
% 97.60/13.21 ((
% 97.60/13.21 (ifp) =>
% 97.60/13.21 ((
% 97.60/13.21 (theeq) =>
% 97.60/13.21 ((
% 97.60/13.21 (iftrue) =>
% 97.60/13.21 ((
% 97.60/13.21 (iffalse) =>
% 97.60/13.21 ((
% 97.60/13.21 (iftrueorfalse) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectT_lem) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionT_lem) =>
% 97.60/13.21 ((
% 97.60/13.21 (powersetT_lem) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusT_lem) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementT_lem) =>
% 97.60/13.21 ((
% 97.60/13.21 (setextT) =>
% 97.60/13.21 ((
% 97.60/13.21 (subsetTI) =>
% 97.60/13.21 ((
% 97.60/13.21 (powersetTI1) =>
% 97.60/13.21 ((
% 97.60/13.21 (powersetTE1) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementTI1) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementTE1) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectTELcontra) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectTERcontra) =>
% 97.60/13.21 ((
% 97.60/13.21 (contrasubsetT) =>
% 97.60/13.21 ((
% 97.60/13.21 (contrasubsetT1) =>
% 97.60/13.21 ((
% 97.60/13.21 (contrasubsetT2) =>
% 97.60/13.21 ((
% 97.60/13.21 (contrasubsetT3) =>
% 97.60/13.21 ((
% 97.60/13.21 (doubleComplementI1) =>
% 97.60/13.21 ((
% 97.60/13.21 (doubleComplementE1) =>
% 97.60/13.21 ((
% 97.60/13.21 (doubleComplementSub1) =>
% 97.60/13.21 ((
% 97.60/13.21 (doubleComplementSub2) =>
% 97.60/13.21 ((
% 97.60/13.21 (doubleComplementEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementTnotintersectT) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementImpComplementIntersect) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementSubsetComplementIntersect) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementInPowersetComplementIntersect) =>
% 97.60/13.21 ((
% 97.60/13.21 (contraSubsetComplement) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementTcontraSubset) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionTILcontra) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionTIRcontra) =>
% 97.60/13.21 ((
% 97.60/13.21 (inIntersectImpInUnion) =>
% 97.60/13.21 ((
% 97.60/13.21 (inIntersectImpInUnion2) =>
% 97.60/13.21 ((
% 97.60/13.21 (inIntersectImpInIntersectUnions) =>
% 97.60/13.21 ((
% 97.60/13.21 (intersectInPowersetIntersectUnions) =>
% 97.60/13.21 ((
% 97.60/13.21 (inComplementUnionImpNotIn1) =>
% 97.60/13.21 ((
% 97.60/13.21 (inComplementUnionImpInComplement1) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionTE) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionTEcontra) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan2a1) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementUnionInPowersetComplement) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan2a2) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan1a) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan1b) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan1) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan2a) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan2b2) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan2b) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan2) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz13rule0) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz13rule1) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz13rule2) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz13rule3) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz13rule4) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz1_1) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz1_2) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz1_3) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz1_4) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz1_5) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1all2) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1SetBreln1) =>
% 97.60/13.21 ((
% 97.60/13.21 (choice2fnsingleton) =>
% 97.60/13.21 ((
% 97.60/13.21 (setOfPairsIsBReln1) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1all1) =>
% 97.60/13.21 ((
% 97.60/13.21 (subbreln1) =>
% 97.60/13.21 ((
% 97.60/13.21 (eqbreln1) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1invprop) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1invI) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1invE) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1compprop) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1compI) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1compE) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1compEex) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1unionprop) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1unionIL) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1unionIR) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1unionI) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1unionE) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1unionEcases) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1unionCommutes) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz2Ex) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz2W) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz2A) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz2B) =>
% 97.60/13.21 ((
% 97.60/13.21 (image1Ex) =>
% 97.60/13.21 ((
% 97.60/13.21 (image1Ex1) =>
% 97.60/13.21 ((
% 97.60/13.21 (image1Equiv) =>
% 97.60/13.21 ((
% 97.60/13.21 (image1E) =>
% 97.60/13.21 ((
% 97.60/13.21 (image1I) =>
% 97.60/13.21 ((
% 97.60/13.21 (injFuncInInjFuncSet) =>
% 97.60/13.21 ((
% 97.60/13.21 (injFuncSetFuncIn) =>
% 97.60/13.21 ((
% 97.60/13.21 (injFuncSetFuncInj) =>
% 97.60/13.21 ((
% 97.60/13.21 (surjFuncSetFuncIn) =>
% 97.60/13.21 ((
% 97.60/13.21 (surjFuncSetFuncSurj) =>
% 97.60/13.21 ((
% 97.60/13.21 (leftInvIsSurj) =>
% 97.60/13.21 ((
% 97.60/13.21 (surjCantorThm) =>
% 97.60/13.21 ((
% 97.60/13.21 (foundation2) =>
% 97.60/13.21 ((
% 97.60/13.21 (notinself) =>
% 97.60/13.21 ((
% 97.60/13.21 (notinself2) =>
% 97.60/13.21 ((
% 97.60/13.21 (omegaSp) =>
% 97.60/13.21 ((
% 97.60/13.21 (omegaSclos) =>
% 97.60/13.21 ((
% 97.60/13.21 (peano0notS) =>
% 97.60/13.21 ((
% 97.60/13.21 (!!) @ (
% 97.60/13.21 (('#S') @ (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 =>) @
% 97.60/13.21 (
% 97.60/13.21 (
% 97.60/13.21 ('#C') @ in @
% 97.60/13.21 omega)))) @
% 97.60/13.21 (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 !!) @
% 97.60/13.21 (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 (
% 97.60/13.21 ('#S') @ (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 =>) @
% 97.60/13.21 (
% 97.60/13.21 (
% 97.60/13.21 ('#C') @ in @
% 97.60/13.21 omega)))))) @
% 97.60/13.21 (
% 97.60/13.21 (
% 97.60/13.21 ('#S') @ (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 '#S') @
% 97.60/13.21 (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 =>))) @
% 97.60/13.21 (
% 97.60/13.21 (
% 97.60/13.21 ('#C') @ (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 '#B') @
% 97.60/13.21 (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 =) @
% 97.60/13.21 omegaS)))) @
% 97.60/13.21 omegaS)))))) @
% 97.60/13.21 (
% 97.60/13.21 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.60/13.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl660])).
% 97.60/13.21 thf(zip_derived_cl685, plain,
% 97.60/13.21 (~ (((setadjoin__Cong) =>
% 97.60/13.21 (((powerset__Cong) =>
% 97.60/13.21 (((setunion__Cong) =>
% 97.60/13.21 (((exuEu) =>
% 97.60/13.21 (((descr__Cong) =>
% 97.60/13.21 (((dsetconstr__Cong) =>
% 97.60/13.21 (((subsetI1) =>
% 97.60/13.21 (((eqimpsubset2) =>
% 97.60/13.21 (((eqimpsubset1) =>
% 97.60/13.21 (((subsetI2) =>
% 97.60/13.21 (((emptysetsubset) =>
% 97.60/13.21 (((subsetE) =>
% 97.60/13.21 (((subsetE2) =>
% 97.60/13.21 (((notsubsetI) =>
% 97.60/13.21 (((notequalI1) =>
% 97.60/13.21 (((notequalI2) =>
% 97.60/13.21 (((subsetRefl) =>
% 97.60/13.21 (((subsetTrans) =>
% 97.60/13.21 (((setadjoinSub) =>
% 97.60/13.21 (((setadjoinSub2) =>
% 97.60/13.21 (((subset2powerset) =>
% 97.60/13.21 (((setextsub) =>
% 97.60/13.21 (((subsetemptysetimpeq) =>
% 97.60/13.21 (((powersetI1) =>
% 97.60/13.21 (((powersetE1) =>
% 97.60/13.21 (((inPowerset) =>
% 97.60/13.21 (((powersetsubset) =>
% 97.60/13.21 (((sepInPowerset) =>
% 97.60/13.21 (((sepSubset) =>
% 97.60/13.21 (((binunionIL) =>
% 97.60/13.21 ((
% 97.60/13.21 (upairset2IR) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionIR) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionEcases) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionE) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionLsub) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionRsub) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectI) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectSubset5) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectEL) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectLsub) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectSubset2) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectSubset3) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectER) =>
% 97.60/13.21 ((
% 97.60/13.21 (disjointsetsI1) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectRsub) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectSubset4) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectSubset1) =>
% 97.60/13.21 ((
% 97.60/13.21 (bs114d) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusI) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusEL) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusER) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusSubset2) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusERneg) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusELneg) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusILneg) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusIRneg) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusLsub) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusSubset1) =>
% 97.60/13.21 ((
% 97.60/13.21 (symdiffE) =>
% 97.60/13.21 ((
% 97.60/13.21 (symdiffI1) =>
% 97.60/13.21 ((
% 97.60/13.21 (symdiffI2) =>
% 97.60/13.21 ((
% 97.60/13.21 (symdiffIneg1) =>
% 97.60/13.21 ((
% 97.60/13.21 (symdiffIneg2) =>
% 97.60/13.21 ((
% 97.60/13.21 (secondinupair) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairIL) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairIR) =>
% 97.60/13.21 ((
% 97.60/13.21 (kpairiskpair) =>
% 97.60/13.21 ((
% 97.60/13.21 (kpairp) =>
% 97.60/13.21 ((
% 97.60/13.21 (singletonsubset) =>
% 97.60/13.21 ((
% 97.60/13.21 (singletoninpowerset) =>
% 97.60/13.21 ((
% 97.60/13.21 (singletoninpowunion) =>
% 97.60/13.21 ((
% 97.60/13.21 (upairset2E) =>
% 97.60/13.21 ((
% 97.60/13.21 (upairsubunion) =>
% 97.60/13.21 ((
% 97.60/13.21 (upairinpowunion) =>
% 97.60/13.21 ((
% 97.60/13.21 (ubforcartprodlem1) =>
% 97.60/13.21 ((
% 97.60/13.21 (ubforcartprodlem2) =>
% 97.60/13.21 ((
% 97.60/13.21 (ubforcartprodlem3) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodpairin) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodmempair1) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodmempair) =>
% 97.60/13.21 ((
% 97.60/13.21 (setunionE2) =>
% 97.60/13.21 ((
% 97.60/13.21 (setunionsingleton1) =>
% 97.60/13.21 ((
% 97.60/13.21 (setunionsingleton2) =>
% 97.60/13.21 ((
% 97.60/13.21 (setunionsingleton) =>
% 97.60/13.21 ((
% 97.60/13.21 (singletonprop) =>
% 97.60/13.21 ((
% 97.60/13.21 (ex1E1) =>
% 97.60/13.21 ((
% 97.60/13.21 (ex1I) =>
% 97.60/13.21 ((
% 97.60/13.21 (ex1I2) =>
% 97.60/13.21 ((
% 97.60/13.21 (singletonsuniq) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairinjL1) =>
% 97.60/13.21 ((
% 97.60/13.21 (kfstsingleton) =>
% 97.60/13.21 ((
% 97.60/13.21 (theprop) =>
% 97.60/13.21 ((
% 97.60/13.21 (kfstpairEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodfstin) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairinjL2) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairinjL) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairinjR11) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairinjR12) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairinjR1) =>
% 97.60/13.21 ((
% 97.60/13.21 (upairequniteq) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairinjR2) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairinjR) =>
% 97.60/13.21 ((
% 97.60/13.21 (ksndsingleton) =>
% 97.60/13.21 ((
% 97.60/13.21 (ksndpairEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (kpairsurjEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodsndin) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodpairmemEL) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodpairmemER) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodmempaircEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodfstpairEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodsndpairEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodpairsurjEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (dpsetconstrI) =>
% 97.60/13.21 ((
% 97.60/13.21 (dpsetconstrSub) =>
% 97.60/13.21 ((
% 97.60/13.21 (setOfPairsIsBReln) =>
% 97.60/13.21 ((
% 97.60/13.21 (dpsetconstrERa) =>
% 97.60/13.21 ((
% 97.60/13.21 (dpsetconstrEL1) =>
% 97.60/13.21 ((
% 97.60/13.21 (dpsetconstrEL2) =>
% 97.60/13.21 ((
% 97.60/13.21 (dpsetconstrER) =>
% 97.60/13.21 ((
% 97.60/13.21 (funcImageSingleton) =>
% 97.60/13.21 ((
% 97.60/13.21 (apProp) =>
% 97.60/13.21 ((
% 97.60/13.21 (app) =>
% 97.60/13.21 ((
% 97.60/13.21 (infuncsetfunc) =>
% 97.60/13.21 ((
% 97.60/13.21 (ap2p) =>
% 97.60/13.21 ((
% 97.60/13.21 (funcinfuncset) =>
% 97.60/13.21 ((
% 97.60/13.21 (lamProp) =>
% 97.60/13.21 ((
% 97.60/13.21 (lamp) =>
% 97.60/13.21 ((
% 97.60/13.21 (lam2p) =>
% 97.60/13.21 ((
% 97.60/13.21 (brelnall1) =>
% 97.60/13.21 ((
% 97.60/13.21 (brelnall2) =>
% 97.60/13.21 ((
% 97.60/13.21 (ex1E2) =>
% 97.60/13.21 ((
% 97.60/13.21 (funcGraphProp1) =>
% 97.60/13.21 ((
% 97.60/13.21 (funcGraphProp3) =>
% 97.60/13.21 ((
% 97.60/13.21 (funcGraphProp2) =>
% 97.60/13.21 ((
% 97.60/13.21 (funcextLem) =>
% 97.60/13.21 ((
% 97.60/13.21 (funcGraphProp4) =>
% 97.60/13.21 ((
% 97.60/13.21 (subbreln) =>
% 97.60/13.21 ((
% 97.60/13.21 (eqbreln) =>
% 97.60/13.21 ((
% 97.60/13.21 (funcext) =>
% 97.60/13.21 ((
% 97.60/13.21 (funcext2) =>
% 97.60/13.21 ((
% 97.60/13.21 (ap2apEq1) =>
% 97.60/13.21 ((
% 97.60/13.21 (ap2apEq2) =>
% 97.60/13.21 ((
% 97.60/13.21 (beta1) =>
% 97.60/13.21 ((
% 97.60/13.21 (eta1) =>
% 97.60/13.21 ((
% 97.60/13.21 (lam2lamEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (beta2) =>
% 97.60/13.21 ((
% 97.60/13.21 (eta2) =>
% 97.60/13.21 ((
% 97.60/13.21 (iffalseProp1) =>
% 97.60/13.21 ((
% 97.60/13.21 (iffalseProp2) =>
% 97.60/13.21 ((
% 97.60/13.21 (iftrueProp1) =>
% 97.60/13.21 ((
% 97.60/13.21 (iftrueProp2) =>
% 97.60/13.21 ((
% 97.60/13.21 (ifSingleton) =>
% 97.60/13.21 ((
% 97.60/13.21 (ifp) =>
% 97.60/13.21 ((
% 97.60/13.21 (theeq) =>
% 97.60/13.21 ((
% 97.60/13.21 (iftrue) =>
% 97.60/13.21 ((
% 97.60/13.21 (iffalse) =>
% 97.60/13.21 ((
% 97.60/13.21 (iftrueorfalse) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectT_lem) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionT_lem) =>
% 97.60/13.21 ((
% 97.60/13.21 (powersetT_lem) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusT_lem) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementT_lem) =>
% 97.60/13.21 ((
% 97.60/13.21 (setextT) =>
% 97.60/13.21 ((
% 97.60/13.21 (subsetTI) =>
% 97.60/13.21 ((
% 97.60/13.21 (powersetTI1) =>
% 97.60/13.21 ((
% 97.60/13.21 (powersetTE1) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementTI1) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementTE1) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectTELcontra) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectTERcontra) =>
% 97.60/13.21 ((
% 97.60/13.21 (contrasubsetT) =>
% 97.60/13.21 ((
% 97.60/13.21 (contrasubsetT1) =>
% 97.60/13.21 ((
% 97.60/13.21 (contrasubsetT2) =>
% 97.60/13.21 ((
% 97.60/13.21 (contrasubsetT3) =>
% 97.60/13.21 ((
% 97.60/13.21 (doubleComplementI1) =>
% 97.60/13.21 ((
% 97.60/13.21 (doubleComplementE1) =>
% 97.60/13.21 ((
% 97.60/13.21 (doubleComplementSub1) =>
% 97.60/13.21 ((
% 97.60/13.21 (doubleComplementSub2) =>
% 97.60/13.21 ((
% 97.60/13.21 (doubleComplementEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementTnotintersectT) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementImpComplementIntersect) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementSubsetComplementIntersect) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementInPowersetComplementIntersect) =>
% 97.60/13.21 ((
% 97.60/13.21 (contraSubsetComplement) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementTcontraSubset) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionTILcontra) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionTIRcontra) =>
% 97.60/13.21 ((
% 97.60/13.21 (inIntersectImpInUnion) =>
% 97.60/13.21 ((
% 97.60/13.21 (inIntersectImpInUnion2) =>
% 97.60/13.21 ((
% 97.60/13.21 (inIntersectImpInIntersectUnions) =>
% 97.60/13.21 ((
% 97.60/13.21 (intersectInPowersetIntersectUnions) =>
% 97.60/13.21 ((
% 97.60/13.21 (inComplementUnionImpNotIn1) =>
% 97.60/13.21 ((
% 97.60/13.21 (inComplementUnionImpInComplement1) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionTE) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionTEcontra) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan2a1) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementUnionInPowersetComplement) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan2a2) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan1a) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan1b) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan1) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan2a) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan2b2) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan2b) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan2) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz13rule0) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz13rule1) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz13rule2) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz13rule3) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz13rule4) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz1_1) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz1_2) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz1_3) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz1_4) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz1_5) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1all2) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1SetBreln1) =>
% 97.60/13.21 ((
% 97.60/13.21 (choice2fnsingleton) =>
% 97.60/13.21 ((
% 97.60/13.21 (setOfPairsIsBReln1) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1all1) =>
% 97.60/13.21 ((
% 97.60/13.21 (subbreln1) =>
% 97.60/13.21 ((
% 97.60/13.21 (eqbreln1) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1invprop) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1invI) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1invE) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1compprop) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1compI) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1compE) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1compEex) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1unionprop) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1unionIL) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1unionIR) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1unionI) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1unionE) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1unionEcases) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1unionCommutes) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz2Ex) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz2W) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz2A) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz2B) =>
% 97.60/13.21 ((
% 97.60/13.21 (image1Ex) =>
% 97.60/13.21 ((
% 97.60/13.21 (image1Ex1) =>
% 97.60/13.21 ((
% 97.60/13.21 (image1Equiv) =>
% 97.60/13.21 ((
% 97.60/13.21 (image1E) =>
% 97.60/13.21 ((
% 97.60/13.21 (image1I) =>
% 97.60/13.21 ((
% 97.60/13.21 (injFuncInInjFuncSet) =>
% 97.60/13.21 ((
% 97.60/13.21 (injFuncSetFuncIn) =>
% 97.60/13.21 ((
% 97.60/13.21 (injFuncSetFuncInj) =>
% 97.60/13.21 ((
% 97.60/13.21 (surjFuncSetFuncIn) =>
% 97.60/13.21 ((
% 97.60/13.21 (surjFuncSetFuncSurj) =>
% 97.60/13.21 ((
% 97.60/13.21 (leftInvIsSurj) =>
% 97.60/13.21 ((
% 97.60/13.21 (surjCantorThm) =>
% 97.60/13.21 ((
% 97.60/13.21 (foundation2) =>
% 97.60/13.21 ((
% 97.60/13.21 (notinself) =>
% 97.60/13.21 ((
% 97.60/13.21 (notinself2) =>
% 97.60/13.21 ((
% 97.60/13.21 (omegaSp) =>
% 97.60/13.21 ((
% 97.60/13.21 (omegaSclos) =>
% 97.60/13.21 ((
% 97.60/13.21 (peano0notS) =>
% 97.60/13.21 ((
% 97.60/13.21 (!!) @ (
% 97.60/13.21 (('#S') @ (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 =>) @
% 97.60/13.21 (
% 97.60/13.21 (
% 97.60/13.21 ('#C') @ in @
% 97.60/13.21 omega)))) @
% 97.60/13.21 (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 !!) @
% 97.60/13.21 (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 (
% 97.60/13.21 ('#S') @ (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 =>) @
% 97.60/13.21 (
% 97.60/13.21 (
% 97.60/13.21 ('#C') @ in @
% 97.60/13.21 omega)))))) @
% 97.60/13.21 (
% 97.60/13.21 (
% 97.60/13.21 ('#S') @ (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 '#S') @
% 97.60/13.21 (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 =>))) @
% 97.60/13.21 (
% 97.60/13.21 (
% 97.60/13.21 ('#C') @ (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 '#B') @
% 97.60/13.21 (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 =) @
% 97.60/13.21 omegaS)))) @
% 97.60/13.21 omegaS)))))) @
% 97.60/13.21 (
% 97.60/13.21 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.60/13.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl672])).
% 97.60/13.21 thf(zip_derived_cl699, plain,
% 97.60/13.21 (~ (((powerset__Cong) =>
% 97.60/13.21 (((setunion__Cong) =>
% 97.60/13.21 (((exuEu) =>
% 97.60/13.21 (((descr__Cong) =>
% 97.60/13.21 (((dsetconstr__Cong) =>
% 97.60/13.21 (((subsetI1) =>
% 97.60/13.21 (((eqimpsubset2) =>
% 97.60/13.21 (((eqimpsubset1) =>
% 97.60/13.21 (((subsetI2) =>
% 97.60/13.21 (((emptysetsubset) =>
% 97.60/13.21 (((subsetE) =>
% 97.60/13.21 (((subsetE2) =>
% 97.60/13.21 (((notsubsetI) =>
% 97.60/13.21 (((notequalI1) =>
% 97.60/13.21 (((notequalI2) =>
% 97.60/13.21 (((subsetRefl) =>
% 97.60/13.21 (((subsetTrans) =>
% 97.60/13.21 (((setadjoinSub) =>
% 97.60/13.21 (((setadjoinSub2) =>
% 97.60/13.21 (((subset2powerset) =>
% 97.60/13.21 (((setextsub) =>
% 97.60/13.21 (((subsetemptysetimpeq) =>
% 97.60/13.21 (((powersetI1) =>
% 97.60/13.21 (((powersetE1) =>
% 97.60/13.21 (((inPowerset) =>
% 97.60/13.21 (((powersetsubset) =>
% 97.60/13.21 (((sepInPowerset) =>
% 97.60/13.21 (((sepSubset) =>
% 97.60/13.21 (((binunionIL) =>
% 97.60/13.21 (((upairset2IR) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionIR) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionEcases) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionE) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionLsub) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionRsub) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectI) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectSubset5) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectEL) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectLsub) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectSubset2) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectSubset3) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectER) =>
% 97.60/13.21 ((
% 97.60/13.21 (disjointsetsI1) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectRsub) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectSubset4) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectSubset1) =>
% 97.60/13.21 ((
% 97.60/13.21 (bs114d) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusI) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusEL) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusER) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusSubset2) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusERneg) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusELneg) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusILneg) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusIRneg) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusLsub) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusSubset1) =>
% 97.60/13.21 ((
% 97.60/13.21 (symdiffE) =>
% 97.60/13.21 ((
% 97.60/13.21 (symdiffI1) =>
% 97.60/13.21 ((
% 97.60/13.21 (symdiffI2) =>
% 97.60/13.21 ((
% 97.60/13.21 (symdiffIneg1) =>
% 97.60/13.21 ((
% 97.60/13.21 (symdiffIneg2) =>
% 97.60/13.21 ((
% 97.60/13.21 (secondinupair) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairIL) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairIR) =>
% 97.60/13.21 ((
% 97.60/13.21 (kpairiskpair) =>
% 97.60/13.21 ((
% 97.60/13.21 (kpairp) =>
% 97.60/13.21 ((
% 97.60/13.21 (singletonsubset) =>
% 97.60/13.21 ((
% 97.60/13.21 (singletoninpowerset) =>
% 97.60/13.21 ((
% 97.60/13.21 (singletoninpowunion) =>
% 97.60/13.21 ((
% 97.60/13.21 (upairset2E) =>
% 97.60/13.21 ((
% 97.60/13.21 (upairsubunion) =>
% 97.60/13.21 ((
% 97.60/13.21 (upairinpowunion) =>
% 97.60/13.21 ((
% 97.60/13.21 (ubforcartprodlem1) =>
% 97.60/13.21 ((
% 97.60/13.21 (ubforcartprodlem2) =>
% 97.60/13.21 ((
% 97.60/13.21 (ubforcartprodlem3) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodpairin) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodmempair1) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodmempair) =>
% 97.60/13.21 ((
% 97.60/13.21 (setunionE2) =>
% 97.60/13.21 ((
% 97.60/13.21 (setunionsingleton1) =>
% 97.60/13.21 ((
% 97.60/13.21 (setunionsingleton2) =>
% 97.60/13.21 ((
% 97.60/13.21 (setunionsingleton) =>
% 97.60/13.21 ((
% 97.60/13.21 (singletonprop) =>
% 97.60/13.21 ((
% 97.60/13.21 (ex1E1) =>
% 97.60/13.21 ((
% 97.60/13.21 (ex1I) =>
% 97.60/13.21 ((
% 97.60/13.21 (ex1I2) =>
% 97.60/13.21 ((
% 97.60/13.21 (singletonsuniq) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairinjL1) =>
% 97.60/13.21 ((
% 97.60/13.21 (kfstsingleton) =>
% 97.60/13.21 ((
% 97.60/13.21 (theprop) =>
% 97.60/13.21 ((
% 97.60/13.21 (kfstpairEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodfstin) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairinjL2) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairinjL) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairinjR11) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairinjR12) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairinjR1) =>
% 97.60/13.21 ((
% 97.60/13.21 (upairequniteq) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairinjR2) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairinjR) =>
% 97.60/13.21 ((
% 97.60/13.21 (ksndsingleton) =>
% 97.60/13.21 ((
% 97.60/13.21 (ksndpairEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (kpairsurjEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodsndin) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodpairmemEL) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodpairmemER) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodmempaircEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodfstpairEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodsndpairEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodpairsurjEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (dpsetconstrI) =>
% 97.60/13.21 ((
% 97.60/13.21 (dpsetconstrSub) =>
% 97.60/13.21 ((
% 97.60/13.21 (setOfPairsIsBReln) =>
% 97.60/13.21 ((
% 97.60/13.21 (dpsetconstrERa) =>
% 97.60/13.21 ((
% 97.60/13.21 (dpsetconstrEL1) =>
% 97.60/13.21 ((
% 97.60/13.21 (dpsetconstrEL2) =>
% 97.60/13.21 ((
% 97.60/13.21 (dpsetconstrER) =>
% 97.60/13.21 ((
% 97.60/13.21 (funcImageSingleton) =>
% 97.60/13.21 ((
% 97.60/13.21 (apProp) =>
% 97.60/13.21 ((
% 97.60/13.21 (app) =>
% 97.60/13.21 ((
% 97.60/13.21 (infuncsetfunc) =>
% 97.60/13.21 ((
% 97.60/13.21 (ap2p) =>
% 97.60/13.21 ((
% 97.60/13.21 (funcinfuncset) =>
% 97.60/13.21 ((
% 97.60/13.21 (lamProp) =>
% 97.60/13.21 ((
% 97.60/13.21 (lamp) =>
% 97.60/13.21 ((
% 97.60/13.21 (lam2p) =>
% 97.60/13.21 ((
% 97.60/13.21 (brelnall1) =>
% 97.60/13.21 ((
% 97.60/13.21 (brelnall2) =>
% 97.60/13.21 ((
% 97.60/13.21 (ex1E2) =>
% 97.60/13.21 ((
% 97.60/13.21 (funcGraphProp1) =>
% 97.60/13.21 ((
% 97.60/13.21 (funcGraphProp3) =>
% 97.60/13.21 ((
% 97.60/13.21 (funcGraphProp2) =>
% 97.60/13.21 ((
% 97.60/13.21 (funcextLem) =>
% 97.60/13.21 ((
% 97.60/13.21 (funcGraphProp4) =>
% 97.60/13.21 ((
% 97.60/13.21 (subbreln) =>
% 97.60/13.21 ((
% 97.60/13.21 (eqbreln) =>
% 97.60/13.21 ((
% 97.60/13.21 (funcext) =>
% 97.60/13.21 ((
% 97.60/13.21 (funcext2) =>
% 97.60/13.21 ((
% 97.60/13.21 (ap2apEq1) =>
% 97.60/13.21 ((
% 97.60/13.21 (ap2apEq2) =>
% 97.60/13.21 ((
% 97.60/13.21 (beta1) =>
% 97.60/13.21 ((
% 97.60/13.21 (eta1) =>
% 97.60/13.21 ((
% 97.60/13.21 (lam2lamEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (beta2) =>
% 97.60/13.21 ((
% 97.60/13.21 (eta2) =>
% 97.60/13.21 ((
% 97.60/13.21 (iffalseProp1) =>
% 97.60/13.21 ((
% 97.60/13.21 (iffalseProp2) =>
% 97.60/13.21 ((
% 97.60/13.21 (iftrueProp1) =>
% 97.60/13.21 ((
% 97.60/13.21 (iftrueProp2) =>
% 97.60/13.21 ((
% 97.60/13.21 (ifSingleton) =>
% 97.60/13.21 ((
% 97.60/13.21 (ifp) =>
% 97.60/13.21 ((
% 97.60/13.21 (theeq) =>
% 97.60/13.21 ((
% 97.60/13.21 (iftrue) =>
% 97.60/13.21 ((
% 97.60/13.21 (iffalse) =>
% 97.60/13.21 ((
% 97.60/13.21 (iftrueorfalse) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectT_lem) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionT_lem) =>
% 97.60/13.21 ((
% 97.60/13.21 (powersetT_lem) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusT_lem) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementT_lem) =>
% 97.60/13.21 ((
% 97.60/13.21 (setextT) =>
% 97.60/13.21 ((
% 97.60/13.21 (subsetTI) =>
% 97.60/13.21 ((
% 97.60/13.21 (powersetTI1) =>
% 97.60/13.21 ((
% 97.60/13.21 (powersetTE1) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementTI1) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementTE1) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectTELcontra) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectTERcontra) =>
% 97.60/13.21 ((
% 97.60/13.21 (contrasubsetT) =>
% 97.60/13.21 ((
% 97.60/13.21 (contrasubsetT1) =>
% 97.60/13.21 ((
% 97.60/13.21 (contrasubsetT2) =>
% 97.60/13.21 ((
% 97.60/13.21 (contrasubsetT3) =>
% 97.60/13.21 ((
% 97.60/13.21 (doubleComplementI1) =>
% 97.60/13.21 ((
% 97.60/13.21 (doubleComplementE1) =>
% 97.60/13.21 ((
% 97.60/13.21 (doubleComplementSub1) =>
% 97.60/13.21 ((
% 97.60/13.21 (doubleComplementSub2) =>
% 97.60/13.21 ((
% 97.60/13.21 (doubleComplementEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementTnotintersectT) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementImpComplementIntersect) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementSubsetComplementIntersect) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementInPowersetComplementIntersect) =>
% 97.60/13.21 ((
% 97.60/13.21 (contraSubsetComplement) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementTcontraSubset) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionTILcontra) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionTIRcontra) =>
% 97.60/13.21 ((
% 97.60/13.21 (inIntersectImpInUnion) =>
% 97.60/13.21 ((
% 97.60/13.21 (inIntersectImpInUnion2) =>
% 97.60/13.21 ((
% 97.60/13.21 (inIntersectImpInIntersectUnions) =>
% 97.60/13.21 ((
% 97.60/13.21 (intersectInPowersetIntersectUnions) =>
% 97.60/13.21 ((
% 97.60/13.21 (inComplementUnionImpNotIn1) =>
% 97.60/13.21 ((
% 97.60/13.21 (inComplementUnionImpInComplement1) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionTE) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionTEcontra) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan2a1) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementUnionInPowersetComplement) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan2a2) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan1a) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan1b) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan1) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan2a) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan2b2) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan2b) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan2) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz13rule0) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz13rule1) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz13rule2) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz13rule3) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz13rule4) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz1_1) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz1_2) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz1_3) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz1_4) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz1_5) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1all2) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1SetBreln1) =>
% 97.60/13.21 ((
% 97.60/13.21 (choice2fnsingleton) =>
% 97.60/13.21 ((
% 97.60/13.21 (setOfPairsIsBReln1) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1all1) =>
% 97.60/13.21 ((
% 97.60/13.21 (subbreln1) =>
% 97.60/13.21 ((
% 97.60/13.21 (eqbreln1) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1invprop) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1invI) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1invE) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1compprop) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1compI) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1compE) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1compEex) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1unionprop) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1unionIL) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1unionIR) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1unionI) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1unionE) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1unionEcases) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1unionCommutes) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz2Ex) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz2W) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz2A) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz2B) =>
% 97.60/13.21 ((
% 97.60/13.21 (image1Ex) =>
% 97.60/13.21 ((
% 97.60/13.21 (image1Ex1) =>
% 97.60/13.21 ((
% 97.60/13.21 (image1Equiv) =>
% 97.60/13.21 ((
% 97.60/13.21 (image1E) =>
% 97.60/13.21 ((
% 97.60/13.21 (image1I) =>
% 97.60/13.21 ((
% 97.60/13.21 (injFuncInInjFuncSet) =>
% 97.60/13.21 ((
% 97.60/13.21 (injFuncSetFuncIn) =>
% 97.60/13.21 ((
% 97.60/13.21 (injFuncSetFuncInj) =>
% 97.60/13.21 ((
% 97.60/13.21 (surjFuncSetFuncIn) =>
% 97.60/13.21 ((
% 97.60/13.21 (surjFuncSetFuncSurj) =>
% 97.60/13.21 ((
% 97.60/13.21 (leftInvIsSurj) =>
% 97.60/13.21 ((
% 97.60/13.21 (surjCantorThm) =>
% 97.60/13.21 ((
% 97.60/13.21 (foundation2) =>
% 97.60/13.21 ((
% 97.60/13.21 (notinself) =>
% 97.60/13.21 ((
% 97.60/13.21 (notinself2) =>
% 97.60/13.21 ((
% 97.60/13.21 (omegaSp) =>
% 97.60/13.21 ((
% 97.60/13.21 (omegaSclos) =>
% 97.60/13.21 ((
% 97.60/13.21 (peano0notS) =>
% 97.60/13.21 ((
% 97.60/13.21 (!!) @ (
% 97.60/13.21 (('#S') @ (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 =>) @
% 97.60/13.21 (
% 97.60/13.21 (
% 97.60/13.21 ('#C') @ in @
% 97.60/13.21 omega)))) @
% 97.60/13.21 (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 !!) @
% 97.60/13.21 (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 (
% 97.60/13.21 ('#S') @ (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 =>) @
% 97.60/13.21 (
% 97.60/13.21 (
% 97.60/13.21 ('#C') @ in @
% 97.60/13.21 omega)))))) @
% 97.60/13.21 (
% 97.60/13.21 (
% 97.60/13.21 ('#S') @ (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 '#S') @
% 97.60/13.21 (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 =>))) @
% 97.60/13.21 (
% 97.60/13.21 (
% 97.60/13.21 ('#C') @ (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 '#B') @
% 97.60/13.21 (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 =) @
% 97.60/13.21 omegaS)))) @
% 97.60/13.21 omegaS)))))) @
% 97.60/13.21 (
% 97.60/13.21 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.60/13.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl685])).
% 97.60/13.21 thf(zip_derived_cl714, plain,
% 97.60/13.21 (~ (((setunion__Cong) =>
% 97.60/13.21 (((exuEu) =>
% 97.60/13.21 (((descr__Cong) =>
% 97.60/13.21 (((dsetconstr__Cong) =>
% 97.60/13.21 (((subsetI1) =>
% 97.60/13.21 (((eqimpsubset2) =>
% 97.60/13.21 (((eqimpsubset1) =>
% 97.60/13.21 (((subsetI2) =>
% 97.60/13.21 (((emptysetsubset) =>
% 97.60/13.21 (((subsetE) =>
% 97.60/13.21 (((subsetE2) =>
% 97.60/13.21 (((notsubsetI) =>
% 97.60/13.21 (((notequalI1) =>
% 97.60/13.21 (((notequalI2) =>
% 97.60/13.21 (((subsetRefl) =>
% 97.60/13.21 (((subsetTrans) =>
% 97.60/13.21 (((setadjoinSub) =>
% 97.60/13.21 (((setadjoinSub2) =>
% 97.60/13.21 (((subset2powerset) =>
% 97.60/13.21 (((setextsub) =>
% 97.60/13.21 (((subsetemptysetimpeq) =>
% 97.60/13.21 (((powersetI1) =>
% 97.60/13.21 (((powersetE1) =>
% 97.60/13.21 (((inPowerset) =>
% 97.60/13.21 (((powersetsubset) =>
% 97.60/13.21 (((sepInPowerset) =>
% 97.60/13.21 (((sepSubset) =>
% 97.60/13.21 (((binunionIL) =>
% 97.60/13.21 (((upairset2IR) =>
% 97.60/13.21 (((binunionIR) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionEcases) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionE) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionLsub) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionRsub) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectI) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectSubset5) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectEL) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectLsub) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectSubset2) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectSubset3) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectER) =>
% 97.60/13.21 ((
% 97.60/13.21 (disjointsetsI1) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectRsub) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectSubset4) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectSubset1) =>
% 97.60/13.21 ((
% 97.60/13.21 (bs114d) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusI) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusEL) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusER) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusSubset2) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusERneg) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusELneg) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusILneg) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusIRneg) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusLsub) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusSubset1) =>
% 97.60/13.21 ((
% 97.60/13.21 (symdiffE) =>
% 97.60/13.21 ((
% 97.60/13.21 (symdiffI1) =>
% 97.60/13.21 ((
% 97.60/13.21 (symdiffI2) =>
% 97.60/13.21 ((
% 97.60/13.21 (symdiffIneg1) =>
% 97.60/13.21 ((
% 97.60/13.21 (symdiffIneg2) =>
% 97.60/13.21 ((
% 97.60/13.21 (secondinupair) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairIL) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairIR) =>
% 97.60/13.21 ((
% 97.60/13.21 (kpairiskpair) =>
% 97.60/13.21 ((
% 97.60/13.21 (kpairp) =>
% 97.60/13.21 ((
% 97.60/13.21 (singletonsubset) =>
% 97.60/13.21 ((
% 97.60/13.21 (singletoninpowerset) =>
% 97.60/13.21 ((
% 97.60/13.21 (singletoninpowunion) =>
% 97.60/13.21 ((
% 97.60/13.21 (upairset2E) =>
% 97.60/13.21 ((
% 97.60/13.21 (upairsubunion) =>
% 97.60/13.21 ((
% 97.60/13.21 (upairinpowunion) =>
% 97.60/13.21 ((
% 97.60/13.21 (ubforcartprodlem1) =>
% 97.60/13.21 ((
% 97.60/13.21 (ubforcartprodlem2) =>
% 97.60/13.21 ((
% 97.60/13.21 (ubforcartprodlem3) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodpairin) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodmempair1) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodmempair) =>
% 97.60/13.21 ((
% 97.60/13.21 (setunionE2) =>
% 97.60/13.21 ((
% 97.60/13.21 (setunionsingleton1) =>
% 97.60/13.21 ((
% 97.60/13.21 (setunionsingleton2) =>
% 97.60/13.21 ((
% 97.60/13.21 (setunionsingleton) =>
% 97.60/13.21 ((
% 97.60/13.21 (singletonprop) =>
% 97.60/13.21 ((
% 97.60/13.21 (ex1E1) =>
% 97.60/13.21 ((
% 97.60/13.21 (ex1I) =>
% 97.60/13.21 ((
% 97.60/13.21 (ex1I2) =>
% 97.60/13.21 ((
% 97.60/13.21 (singletonsuniq) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairinjL1) =>
% 97.60/13.21 ((
% 97.60/13.21 (kfstsingleton) =>
% 97.60/13.21 ((
% 97.60/13.21 (theprop) =>
% 97.60/13.21 ((
% 97.60/13.21 (kfstpairEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodfstin) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairinjL2) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairinjL) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairinjR11) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairinjR12) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairinjR1) =>
% 97.60/13.21 ((
% 97.60/13.21 (upairequniteq) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairinjR2) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairinjR) =>
% 97.60/13.21 ((
% 97.60/13.21 (ksndsingleton) =>
% 97.60/13.21 ((
% 97.60/13.21 (ksndpairEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (kpairsurjEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodsndin) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodpairmemEL) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodpairmemER) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodmempaircEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodfstpairEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodsndpairEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodpairsurjEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (dpsetconstrI) =>
% 97.60/13.21 ((
% 97.60/13.21 (dpsetconstrSub) =>
% 97.60/13.21 ((
% 97.60/13.21 (setOfPairsIsBReln) =>
% 97.60/13.21 ((
% 97.60/13.21 (dpsetconstrERa) =>
% 97.60/13.21 ((
% 97.60/13.21 (dpsetconstrEL1) =>
% 97.60/13.21 ((
% 97.60/13.21 (dpsetconstrEL2) =>
% 97.60/13.21 ((
% 97.60/13.21 (dpsetconstrER) =>
% 97.60/13.21 ((
% 97.60/13.21 (funcImageSingleton) =>
% 97.60/13.21 ((
% 97.60/13.21 (apProp) =>
% 97.60/13.21 ((
% 97.60/13.21 (app) =>
% 97.60/13.21 ((
% 97.60/13.21 (infuncsetfunc) =>
% 97.60/13.21 ((
% 97.60/13.21 (ap2p) =>
% 97.60/13.21 ((
% 97.60/13.21 (funcinfuncset) =>
% 97.60/13.21 ((
% 97.60/13.21 (lamProp) =>
% 97.60/13.21 ((
% 97.60/13.21 (lamp) =>
% 97.60/13.21 ((
% 97.60/13.21 (lam2p) =>
% 97.60/13.21 ((
% 97.60/13.21 (brelnall1) =>
% 97.60/13.21 ((
% 97.60/13.21 (brelnall2) =>
% 97.60/13.21 ((
% 97.60/13.21 (ex1E2) =>
% 97.60/13.21 ((
% 97.60/13.21 (funcGraphProp1) =>
% 97.60/13.21 ((
% 97.60/13.21 (funcGraphProp3) =>
% 97.60/13.21 ((
% 97.60/13.21 (funcGraphProp2) =>
% 97.60/13.21 ((
% 97.60/13.21 (funcextLem) =>
% 97.60/13.21 ((
% 97.60/13.21 (funcGraphProp4) =>
% 97.60/13.21 ((
% 97.60/13.21 (subbreln) =>
% 97.60/13.21 ((
% 97.60/13.21 (eqbreln) =>
% 97.60/13.21 ((
% 97.60/13.21 (funcext) =>
% 97.60/13.21 ((
% 97.60/13.21 (funcext2) =>
% 97.60/13.21 ((
% 97.60/13.21 (ap2apEq1) =>
% 97.60/13.21 ((
% 97.60/13.21 (ap2apEq2) =>
% 97.60/13.21 ((
% 97.60/13.21 (beta1) =>
% 97.60/13.21 ((
% 97.60/13.21 (eta1) =>
% 97.60/13.21 ((
% 97.60/13.21 (lam2lamEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (beta2) =>
% 97.60/13.21 ((
% 97.60/13.21 (eta2) =>
% 97.60/13.21 ((
% 97.60/13.21 (iffalseProp1) =>
% 97.60/13.21 ((
% 97.60/13.21 (iffalseProp2) =>
% 97.60/13.21 ((
% 97.60/13.21 (iftrueProp1) =>
% 97.60/13.21 ((
% 97.60/13.21 (iftrueProp2) =>
% 97.60/13.21 ((
% 97.60/13.21 (ifSingleton) =>
% 97.60/13.21 ((
% 97.60/13.21 (ifp) =>
% 97.60/13.21 ((
% 97.60/13.21 (theeq) =>
% 97.60/13.21 ((
% 97.60/13.21 (iftrue) =>
% 97.60/13.21 ((
% 97.60/13.21 (iffalse) =>
% 97.60/13.21 ((
% 97.60/13.21 (iftrueorfalse) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectT_lem) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionT_lem) =>
% 97.60/13.21 ((
% 97.60/13.21 (powersetT_lem) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusT_lem) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementT_lem) =>
% 97.60/13.21 ((
% 97.60/13.21 (setextT) =>
% 97.60/13.21 ((
% 97.60/13.21 (subsetTI) =>
% 97.60/13.21 ((
% 97.60/13.21 (powersetTI1) =>
% 97.60/13.21 ((
% 97.60/13.21 (powersetTE1) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementTI1) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementTE1) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectTELcontra) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectTERcontra) =>
% 97.60/13.21 ((
% 97.60/13.21 (contrasubsetT) =>
% 97.60/13.21 ((
% 97.60/13.21 (contrasubsetT1) =>
% 97.60/13.21 ((
% 97.60/13.21 (contrasubsetT2) =>
% 97.60/13.21 ((
% 97.60/13.21 (contrasubsetT3) =>
% 97.60/13.21 ((
% 97.60/13.21 (doubleComplementI1) =>
% 97.60/13.21 ((
% 97.60/13.21 (doubleComplementE1) =>
% 97.60/13.21 ((
% 97.60/13.21 (doubleComplementSub1) =>
% 97.60/13.21 ((
% 97.60/13.21 (doubleComplementSub2) =>
% 97.60/13.21 ((
% 97.60/13.21 (doubleComplementEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementTnotintersectT) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementImpComplementIntersect) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementSubsetComplementIntersect) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementInPowersetComplementIntersect) =>
% 97.60/13.21 ((
% 97.60/13.21 (contraSubsetComplement) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementTcontraSubset) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionTILcontra) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionTIRcontra) =>
% 97.60/13.21 ((
% 97.60/13.21 (inIntersectImpInUnion) =>
% 97.60/13.21 ((
% 97.60/13.21 (inIntersectImpInUnion2) =>
% 97.60/13.21 ((
% 97.60/13.21 (inIntersectImpInIntersectUnions) =>
% 97.60/13.21 ((
% 97.60/13.21 (intersectInPowersetIntersectUnions) =>
% 97.60/13.21 ((
% 97.60/13.21 (inComplementUnionImpNotIn1) =>
% 97.60/13.21 ((
% 97.60/13.21 (inComplementUnionImpInComplement1) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionTE) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionTEcontra) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan2a1) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementUnionInPowersetComplement) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan2a2) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan1a) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan1b) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan1) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan2a) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan2b2) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan2b) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan2) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz13rule0) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz13rule1) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz13rule2) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz13rule3) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz13rule4) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz1_1) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz1_2) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz1_3) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz1_4) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz1_5) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1all2) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1SetBreln1) =>
% 97.60/13.21 ((
% 97.60/13.21 (choice2fnsingleton) =>
% 97.60/13.21 ((
% 97.60/13.21 (setOfPairsIsBReln1) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1all1) =>
% 97.60/13.21 ((
% 97.60/13.21 (subbreln1) =>
% 97.60/13.21 ((
% 97.60/13.21 (eqbreln1) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1invprop) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1invI) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1invE) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1compprop) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1compI) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1compE) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1compEex) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1unionprop) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1unionIL) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1unionIR) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1unionI) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1unionE) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1unionEcases) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1unionCommutes) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz2Ex) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz2W) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz2A) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz2B) =>
% 97.60/13.21 ((
% 97.60/13.21 (image1Ex) =>
% 97.60/13.21 ((
% 97.60/13.21 (image1Ex1) =>
% 97.60/13.21 ((
% 97.60/13.21 (image1Equiv) =>
% 97.60/13.21 ((
% 97.60/13.21 (image1E) =>
% 97.60/13.21 ((
% 97.60/13.21 (image1I) =>
% 97.60/13.21 ((
% 97.60/13.21 (injFuncInInjFuncSet) =>
% 97.60/13.21 ((
% 97.60/13.21 (injFuncSetFuncIn) =>
% 97.60/13.21 ((
% 97.60/13.21 (injFuncSetFuncInj) =>
% 97.60/13.21 ((
% 97.60/13.21 (surjFuncSetFuncIn) =>
% 97.60/13.21 ((
% 97.60/13.21 (surjFuncSetFuncSurj) =>
% 97.60/13.21 ((
% 97.60/13.21 (leftInvIsSurj) =>
% 97.60/13.21 ((
% 97.60/13.21 (surjCantorThm) =>
% 97.60/13.21 ((
% 97.60/13.21 (foundation2) =>
% 97.60/13.21 ((
% 97.60/13.21 (notinself) =>
% 97.60/13.21 ((
% 97.60/13.21 (notinself2) =>
% 97.60/13.21 ((
% 97.60/13.21 (omegaSp) =>
% 97.60/13.21 ((
% 97.60/13.21 (omegaSclos) =>
% 97.60/13.21 ((
% 97.60/13.21 (peano0notS) =>
% 97.60/13.21 ((
% 97.60/13.21 (!!) @ (
% 97.60/13.21 (('#S') @ (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 =>) @
% 97.60/13.21 (
% 97.60/13.21 (
% 97.60/13.21 ('#C') @ in @
% 97.60/13.21 omega)))) @
% 97.60/13.21 (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 !!) @
% 97.60/13.21 (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 (
% 97.60/13.21 ('#S') @ (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 =>) @
% 97.60/13.21 (
% 97.60/13.21 (
% 97.60/13.21 ('#C') @ in @
% 97.60/13.21 omega)))))) @
% 97.60/13.21 (
% 97.60/13.21 (
% 97.60/13.21 ('#S') @ (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 '#S') @
% 97.60/13.21 (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 =>))) @
% 97.60/13.21 (
% 97.60/13.21 (
% 97.60/13.21 ('#C') @ (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 '#B') @
% 97.60/13.21 (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 =) @
% 97.60/13.21 omegaS)))) @
% 97.60/13.21 omegaS)))))) @
% 97.60/13.21 (
% 97.60/13.21 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.60/13.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl699])).
% 97.60/13.21 thf(zip_derived_cl731, plain,
% 97.60/13.21 (~ (((exuEu) =>
% 97.60/13.21 (((descr__Cong) =>
% 97.60/13.21 (((dsetconstr__Cong) =>
% 97.60/13.21 (((subsetI1) =>
% 97.60/13.21 (((eqimpsubset2) =>
% 97.60/13.21 (((eqimpsubset1) =>
% 97.60/13.21 (((subsetI2) =>
% 97.60/13.21 (((emptysetsubset) =>
% 97.60/13.21 (((subsetE) =>
% 97.60/13.21 (((subsetE2) =>
% 97.60/13.21 (((notsubsetI) =>
% 97.60/13.21 (((notequalI1) =>
% 97.60/13.21 (((notequalI2) =>
% 97.60/13.21 (((subsetRefl) =>
% 97.60/13.21 (((subsetTrans) =>
% 97.60/13.21 (((setadjoinSub) =>
% 97.60/13.21 (((setadjoinSub2) =>
% 97.60/13.21 (((subset2powerset) =>
% 97.60/13.21 (((setextsub) =>
% 97.60/13.21 (((subsetemptysetimpeq) =>
% 97.60/13.21 (((powersetI1) =>
% 97.60/13.21 (((powersetE1) =>
% 97.60/13.21 (((inPowerset) =>
% 97.60/13.21 (((powersetsubset) =>
% 97.60/13.21 (((sepInPowerset) =>
% 97.60/13.21 (((sepSubset) =>
% 97.60/13.21 (((binunionIL) =>
% 97.60/13.21 (((upairset2IR) =>
% 97.60/13.21 (((binunionIR) =>
% 97.60/13.21 (((binunionEcases) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionE) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionLsub) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionRsub) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectI) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectSubset5) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectEL) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectLsub) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectSubset2) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectSubset3) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectER) =>
% 97.60/13.21 ((
% 97.60/13.21 (disjointsetsI1) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectRsub) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectSubset4) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectSubset1) =>
% 97.60/13.21 ((
% 97.60/13.21 (bs114d) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusI) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusEL) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusER) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusSubset2) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusERneg) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusELneg) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusILneg) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusIRneg) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusLsub) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusSubset1) =>
% 97.60/13.21 ((
% 97.60/13.21 (symdiffE) =>
% 97.60/13.21 ((
% 97.60/13.21 (symdiffI1) =>
% 97.60/13.21 ((
% 97.60/13.21 (symdiffI2) =>
% 97.60/13.21 ((
% 97.60/13.21 (symdiffIneg1) =>
% 97.60/13.21 ((
% 97.60/13.21 (symdiffIneg2) =>
% 97.60/13.21 ((
% 97.60/13.21 (secondinupair) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairIL) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairIR) =>
% 97.60/13.21 ((
% 97.60/13.21 (kpairiskpair) =>
% 97.60/13.21 ((
% 97.60/13.21 (kpairp) =>
% 97.60/13.21 ((
% 97.60/13.21 (singletonsubset) =>
% 97.60/13.21 ((
% 97.60/13.21 (singletoninpowerset) =>
% 97.60/13.21 ((
% 97.60/13.21 (singletoninpowunion) =>
% 97.60/13.21 ((
% 97.60/13.21 (upairset2E) =>
% 97.60/13.21 ((
% 97.60/13.21 (upairsubunion) =>
% 97.60/13.21 ((
% 97.60/13.21 (upairinpowunion) =>
% 97.60/13.21 ((
% 97.60/13.21 (ubforcartprodlem1) =>
% 97.60/13.21 ((
% 97.60/13.21 (ubforcartprodlem2) =>
% 97.60/13.21 ((
% 97.60/13.21 (ubforcartprodlem3) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodpairin) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodmempair1) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodmempair) =>
% 97.60/13.21 ((
% 97.60/13.21 (setunionE2) =>
% 97.60/13.21 ((
% 97.60/13.21 (setunionsingleton1) =>
% 97.60/13.21 ((
% 97.60/13.21 (setunionsingleton2) =>
% 97.60/13.21 ((
% 97.60/13.21 (setunionsingleton) =>
% 97.60/13.21 ((
% 97.60/13.21 (singletonprop) =>
% 97.60/13.21 ((
% 97.60/13.21 (ex1E1) =>
% 97.60/13.21 ((
% 97.60/13.21 (ex1I) =>
% 97.60/13.21 ((
% 97.60/13.21 (ex1I2) =>
% 97.60/13.21 ((
% 97.60/13.21 (singletonsuniq) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairinjL1) =>
% 97.60/13.21 ((
% 97.60/13.21 (kfstsingleton) =>
% 97.60/13.21 ((
% 97.60/13.21 (theprop) =>
% 97.60/13.21 ((
% 97.60/13.21 (kfstpairEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodfstin) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairinjL2) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairinjL) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairinjR11) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairinjR12) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairinjR1) =>
% 97.60/13.21 ((
% 97.60/13.21 (upairequniteq) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairinjR2) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairinjR) =>
% 97.60/13.21 ((
% 97.60/13.21 (ksndsingleton) =>
% 97.60/13.21 ((
% 97.60/13.21 (ksndpairEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (kpairsurjEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodsndin) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodpairmemEL) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodpairmemER) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodmempaircEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodfstpairEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodsndpairEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodpairsurjEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (dpsetconstrI) =>
% 97.60/13.21 ((
% 97.60/13.21 (dpsetconstrSub) =>
% 97.60/13.21 ((
% 97.60/13.21 (setOfPairsIsBReln) =>
% 97.60/13.21 ((
% 97.60/13.21 (dpsetconstrERa) =>
% 97.60/13.21 ((
% 97.60/13.21 (dpsetconstrEL1) =>
% 97.60/13.21 ((
% 97.60/13.21 (dpsetconstrEL2) =>
% 97.60/13.21 ((
% 97.60/13.21 (dpsetconstrER) =>
% 97.60/13.21 ((
% 97.60/13.21 (funcImageSingleton) =>
% 97.60/13.21 ((
% 97.60/13.21 (apProp) =>
% 97.60/13.21 ((
% 97.60/13.21 (app) =>
% 97.60/13.21 ((
% 97.60/13.21 (infuncsetfunc) =>
% 97.60/13.21 ((
% 97.60/13.21 (ap2p) =>
% 97.60/13.21 ((
% 97.60/13.21 (funcinfuncset) =>
% 97.60/13.21 ((
% 97.60/13.21 (lamProp) =>
% 97.60/13.21 ((
% 97.60/13.21 (lamp) =>
% 97.60/13.21 ((
% 97.60/13.21 (lam2p) =>
% 97.60/13.21 ((
% 97.60/13.21 (brelnall1) =>
% 97.60/13.21 ((
% 97.60/13.21 (brelnall2) =>
% 97.60/13.21 ((
% 97.60/13.21 (ex1E2) =>
% 97.60/13.21 ((
% 97.60/13.21 (funcGraphProp1) =>
% 97.60/13.21 ((
% 97.60/13.21 (funcGraphProp3) =>
% 97.60/13.21 ((
% 97.60/13.21 (funcGraphProp2) =>
% 97.60/13.21 ((
% 97.60/13.21 (funcextLem) =>
% 97.60/13.21 ((
% 97.60/13.21 (funcGraphProp4) =>
% 97.60/13.21 ((
% 97.60/13.21 (subbreln) =>
% 97.60/13.21 ((
% 97.60/13.21 (eqbreln) =>
% 97.60/13.21 ((
% 97.60/13.21 (funcext) =>
% 97.60/13.21 ((
% 97.60/13.21 (funcext2) =>
% 97.60/13.21 ((
% 97.60/13.21 (ap2apEq1) =>
% 97.60/13.21 ((
% 97.60/13.21 (ap2apEq2) =>
% 97.60/13.21 ((
% 97.60/13.21 (beta1) =>
% 97.60/13.21 ((
% 97.60/13.21 (eta1) =>
% 97.60/13.21 ((
% 97.60/13.21 (lam2lamEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (beta2) =>
% 97.60/13.21 ((
% 97.60/13.21 (eta2) =>
% 97.60/13.21 ((
% 97.60/13.21 (iffalseProp1) =>
% 97.60/13.21 ((
% 97.60/13.21 (iffalseProp2) =>
% 97.60/13.21 ((
% 97.60/13.21 (iftrueProp1) =>
% 97.60/13.21 ((
% 97.60/13.21 (iftrueProp2) =>
% 97.60/13.21 ((
% 97.60/13.21 (ifSingleton) =>
% 97.60/13.21 ((
% 97.60/13.21 (ifp) =>
% 97.60/13.21 ((
% 97.60/13.21 (theeq) =>
% 97.60/13.21 ((
% 97.60/13.21 (iftrue) =>
% 97.60/13.21 ((
% 97.60/13.21 (iffalse) =>
% 97.60/13.21 ((
% 97.60/13.21 (iftrueorfalse) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectT_lem) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionT_lem) =>
% 97.60/13.21 ((
% 97.60/13.21 (powersetT_lem) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusT_lem) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementT_lem) =>
% 97.60/13.21 ((
% 97.60/13.21 (setextT) =>
% 97.60/13.21 ((
% 97.60/13.21 (subsetTI) =>
% 97.60/13.21 ((
% 97.60/13.21 (powersetTI1) =>
% 97.60/13.21 ((
% 97.60/13.21 (powersetTE1) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementTI1) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementTE1) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectTELcontra) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectTERcontra) =>
% 97.60/13.21 ((
% 97.60/13.21 (contrasubsetT) =>
% 97.60/13.21 ((
% 97.60/13.21 (contrasubsetT1) =>
% 97.60/13.21 ((
% 97.60/13.21 (contrasubsetT2) =>
% 97.60/13.21 ((
% 97.60/13.21 (contrasubsetT3) =>
% 97.60/13.21 ((
% 97.60/13.21 (doubleComplementI1) =>
% 97.60/13.21 ((
% 97.60/13.21 (doubleComplementE1) =>
% 97.60/13.21 ((
% 97.60/13.21 (doubleComplementSub1) =>
% 97.60/13.21 ((
% 97.60/13.21 (doubleComplementSub2) =>
% 97.60/13.21 ((
% 97.60/13.21 (doubleComplementEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementTnotintersectT) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementImpComplementIntersect) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementSubsetComplementIntersect) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementInPowersetComplementIntersect) =>
% 97.60/13.21 ((
% 97.60/13.21 (contraSubsetComplement) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementTcontraSubset) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionTILcontra) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionTIRcontra) =>
% 97.60/13.21 ((
% 97.60/13.21 (inIntersectImpInUnion) =>
% 97.60/13.21 ((
% 97.60/13.21 (inIntersectImpInUnion2) =>
% 97.60/13.21 ((
% 97.60/13.21 (inIntersectImpInIntersectUnions) =>
% 97.60/13.21 ((
% 97.60/13.21 (intersectInPowersetIntersectUnions) =>
% 97.60/13.21 ((
% 97.60/13.21 (inComplementUnionImpNotIn1) =>
% 97.60/13.21 ((
% 97.60/13.21 (inComplementUnionImpInComplement1) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionTE) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionTEcontra) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan2a1) =>
% 97.60/13.21 ((
% 97.60/13.21 (complementUnionInPowersetComplement) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan2a2) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan1a) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan1b) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan1) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan2a) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan2b2) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan2b) =>
% 97.60/13.21 ((
% 97.60/13.21 (demorgan2) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz13rule0) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz13rule1) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz13rule2) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz13rule3) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz13rule4) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz1_1) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz1_2) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz1_3) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz1_4) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz1_5) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1all2) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1SetBreln1) =>
% 97.60/13.21 ((
% 97.60/13.21 (choice2fnsingleton) =>
% 97.60/13.21 ((
% 97.60/13.21 (setOfPairsIsBReln1) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1all1) =>
% 97.60/13.21 ((
% 97.60/13.21 (subbreln1) =>
% 97.60/13.21 ((
% 97.60/13.21 (eqbreln1) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1invprop) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1invI) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1invE) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1compprop) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1compI) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1compE) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1compEex) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1unionprop) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1unionIL) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1unionIR) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1unionI) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1unionE) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1unionEcases) =>
% 97.60/13.21 ((
% 97.60/13.21 (breln1unionCommutes) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz2Ex) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz2W) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz2A) =>
% 97.60/13.21 ((
% 97.60/13.21 (woz2B) =>
% 97.60/13.21 ((
% 97.60/13.21 (image1Ex) =>
% 97.60/13.21 ((
% 97.60/13.21 (image1Ex1) =>
% 97.60/13.21 ((
% 97.60/13.21 (image1Equiv) =>
% 97.60/13.21 ((
% 97.60/13.21 (image1E) =>
% 97.60/13.21 ((
% 97.60/13.21 (image1I) =>
% 97.60/13.21 ((
% 97.60/13.21 (injFuncInInjFuncSet) =>
% 97.60/13.21 ((
% 97.60/13.21 (injFuncSetFuncIn) =>
% 97.60/13.21 ((
% 97.60/13.21 (injFuncSetFuncInj) =>
% 97.60/13.21 ((
% 97.60/13.21 (surjFuncSetFuncIn) =>
% 97.60/13.21 ((
% 97.60/13.21 (surjFuncSetFuncSurj) =>
% 97.60/13.21 ((
% 97.60/13.21 (leftInvIsSurj) =>
% 97.60/13.21 ((
% 97.60/13.21 (surjCantorThm) =>
% 97.60/13.21 ((
% 97.60/13.21 (foundation2) =>
% 97.60/13.21 ((
% 97.60/13.21 (notinself) =>
% 97.60/13.21 ((
% 97.60/13.21 (notinself2) =>
% 97.60/13.21 ((
% 97.60/13.21 (omegaSp) =>
% 97.60/13.21 ((
% 97.60/13.21 (omegaSclos) =>
% 97.60/13.21 ((
% 97.60/13.21 (peano0notS) =>
% 97.60/13.21 ((
% 97.60/13.21 (!!) @ (
% 97.60/13.21 (('#S') @ (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 =>) @
% 97.60/13.21 (
% 97.60/13.21 (
% 97.60/13.21 ('#C') @ in @
% 97.60/13.21 omega)))) @
% 97.60/13.21 (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 !!) @
% 97.60/13.21 (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 (
% 97.60/13.21 ('#S') @ (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 =>) @
% 97.60/13.21 (
% 97.60/13.21 (
% 97.60/13.21 ('#C') @ in @
% 97.60/13.21 omega)))))) @
% 97.60/13.21 (
% 97.60/13.21 (
% 97.60/13.21 ('#S') @ (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 '#S') @
% 97.60/13.21 (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 =>))) @
% 97.60/13.21 (
% 97.60/13.21 (
% 97.60/13.21 ('#C') @ (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 '#B') @
% 97.60/13.21 (
% 97.60/13.21 (
% 97.60/13.21 ('#B') @ (
% 97.60/13.21 =) @
% 97.60/13.21 omegaS)))) @
% 97.60/13.21 omegaS)))))) @
% 97.60/13.21 (
% 97.60/13.21 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.60/13.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl714])).
% 97.60/13.21 thf(zip_derived_cl749, plain,
% 97.60/13.21 (~ (((descr__Cong) =>
% 97.60/13.21 (((dsetconstr__Cong) =>
% 97.60/13.21 (((subsetI1) =>
% 97.60/13.21 (((eqimpsubset2) =>
% 97.60/13.21 (((eqimpsubset1) =>
% 97.60/13.21 (((subsetI2) =>
% 97.60/13.21 (((emptysetsubset) =>
% 97.60/13.21 (((subsetE) =>
% 97.60/13.21 (((subsetE2) =>
% 97.60/13.21 (((notsubsetI) =>
% 97.60/13.21 (((notequalI1) =>
% 97.60/13.21 (((notequalI2) =>
% 97.60/13.21 (((subsetRefl) =>
% 97.60/13.21 (((subsetTrans) =>
% 97.60/13.21 (((setadjoinSub) =>
% 97.60/13.21 (((setadjoinSub2) =>
% 97.60/13.21 (((subset2powerset) =>
% 97.60/13.21 (((setextsub) =>
% 97.60/13.21 (((subsetemptysetimpeq) =>
% 97.60/13.21 (((powersetI1) =>
% 97.60/13.21 (((powersetE1) =>
% 97.60/13.21 (((inPowerset) =>
% 97.60/13.21 (((powersetsubset) =>
% 97.60/13.21 (((sepInPowerset) =>
% 97.60/13.21 (((sepSubset) =>
% 97.60/13.21 (((binunionIL) =>
% 97.60/13.21 (((upairset2IR) =>
% 97.60/13.21 (((binunionIR) =>
% 97.60/13.21 (((binunionEcases) =>
% 97.60/13.21 (((binunionE) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionLsub) =>
% 97.60/13.21 ((
% 97.60/13.21 (binunionRsub) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectI) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectSubset5) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectEL) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectLsub) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectSubset2) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectSubset3) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectER) =>
% 97.60/13.21 ((
% 97.60/13.21 (disjointsetsI1) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectRsub) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectSubset4) =>
% 97.60/13.21 ((
% 97.60/13.21 (binintersectSubset1) =>
% 97.60/13.21 ((
% 97.60/13.21 (bs114d) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusI) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusEL) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusER) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusSubset2) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusERneg) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusELneg) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusILneg) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusIRneg) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusLsub) =>
% 97.60/13.21 ((
% 97.60/13.21 (setminusSubset1) =>
% 97.60/13.21 ((
% 97.60/13.21 (symdiffE) =>
% 97.60/13.21 ((
% 97.60/13.21 (symdiffI1) =>
% 97.60/13.21 ((
% 97.60/13.21 (symdiffI2) =>
% 97.60/13.21 ((
% 97.60/13.21 (symdiffIneg1) =>
% 97.60/13.21 ((
% 97.60/13.21 (symdiffIneg2) =>
% 97.60/13.21 ((
% 97.60/13.21 (secondinupair) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairIL) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairIR) =>
% 97.60/13.21 ((
% 97.60/13.21 (kpairiskpair) =>
% 97.60/13.21 ((
% 97.60/13.21 (kpairp) =>
% 97.60/13.21 ((
% 97.60/13.21 (singletonsubset) =>
% 97.60/13.21 ((
% 97.60/13.21 (singletoninpowerset) =>
% 97.60/13.21 ((
% 97.60/13.21 (singletoninpowunion) =>
% 97.60/13.21 ((
% 97.60/13.21 (upairset2E) =>
% 97.60/13.21 ((
% 97.60/13.21 (upairsubunion) =>
% 97.60/13.21 ((
% 97.60/13.21 (upairinpowunion) =>
% 97.60/13.21 ((
% 97.60/13.21 (ubforcartprodlem1) =>
% 97.60/13.21 ((
% 97.60/13.21 (ubforcartprodlem2) =>
% 97.60/13.21 ((
% 97.60/13.21 (ubforcartprodlem3) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodpairin) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodmempair1) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodmempair) =>
% 97.60/13.21 ((
% 97.60/13.21 (setunionE2) =>
% 97.60/13.21 ((
% 97.60/13.21 (setunionsingleton1) =>
% 97.60/13.21 ((
% 97.60/13.21 (setunionsingleton2) =>
% 97.60/13.21 ((
% 97.60/13.21 (setunionsingleton) =>
% 97.60/13.21 ((
% 97.60/13.21 (singletonprop) =>
% 97.60/13.21 ((
% 97.60/13.21 (ex1E1) =>
% 97.60/13.21 ((
% 97.60/13.21 (ex1I) =>
% 97.60/13.21 ((
% 97.60/13.21 (ex1I2) =>
% 97.60/13.21 ((
% 97.60/13.21 (singletonsuniq) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairinjL1) =>
% 97.60/13.21 ((
% 97.60/13.21 (kfstsingleton) =>
% 97.60/13.21 ((
% 97.60/13.21 (theprop) =>
% 97.60/13.21 ((
% 97.60/13.21 (kfstpairEq) =>
% 97.60/13.21 ((
% 97.60/13.21 (cartprodfstin) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairinjL2) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairinjL) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairinjR11) =>
% 97.60/13.21 ((
% 97.60/13.21 (setukpairinjR12) =>
% 97.60/13.21 ((
% 97.60/13.22 (setukpairinjR1) =>
% 97.60/13.22 ((
% 97.60/13.22 (upairequniteq) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjR2) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjR) =>
% 97.60/13.22 ((
% 97.60/13.22 (ksndsingleton) =>
% 97.60/13.22 ((
% 97.60/13.22 (ksndpairEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (kpairsurjEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodsndin) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodpairmemEL) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodpairmemER) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodmempaircEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodfstpairEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodsndpairEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodpairsurjEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (dpsetconstrI) =>
% 97.60/13.22 ((
% 97.60/13.22 (dpsetconstrSub) =>
% 97.60/13.22 ((
% 97.60/13.22 (setOfPairsIsBReln) =>
% 97.60/13.22 ((
% 97.60/13.22 (dpsetconstrERa) =>
% 97.60/13.22 ((
% 97.60/13.22 (dpsetconstrEL1) =>
% 97.60/13.22 ((
% 97.60/13.22 (dpsetconstrEL2) =>
% 97.60/13.22 ((
% 97.60/13.22 (dpsetconstrER) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcImageSingleton) =>
% 97.60/13.22 ((
% 97.60/13.22 (apProp) =>
% 97.60/13.22 ((
% 97.60/13.22 (app) =>
% 97.60/13.22 ((
% 97.60/13.22 (infuncsetfunc) =>
% 97.60/13.22 ((
% 97.60/13.22 (ap2p) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcinfuncset) =>
% 97.60/13.22 ((
% 97.60/13.22 (lamProp) =>
% 97.60/13.22 ((
% 97.60/13.22 (lamp) =>
% 97.60/13.22 ((
% 97.60/13.22 (lam2p) =>
% 97.60/13.22 ((
% 97.60/13.22 (brelnall1) =>
% 97.60/13.22 ((
% 97.60/13.22 (brelnall2) =>
% 97.60/13.22 ((
% 97.60/13.22 (ex1E2) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcGraphProp1) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcGraphProp3) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcGraphProp2) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcextLem) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcGraphProp4) =>
% 97.60/13.22 ((
% 97.60/13.22 (subbreln) =>
% 97.60/13.22 ((
% 97.60/13.22 (eqbreln) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcext) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcext2) =>
% 97.60/13.22 ((
% 97.60/13.22 (ap2apEq1) =>
% 97.60/13.22 ((
% 97.60/13.22 (ap2apEq2) =>
% 97.60/13.22 ((
% 97.60/13.22 (beta1) =>
% 97.60/13.22 ((
% 97.60/13.22 (eta1) =>
% 97.60/13.22 ((
% 97.60/13.22 (lam2lamEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (beta2) =>
% 97.60/13.22 ((
% 97.60/13.22 (eta2) =>
% 97.60/13.22 ((
% 97.60/13.22 (iffalseProp1) =>
% 97.60/13.22 ((
% 97.60/13.22 (iffalseProp2) =>
% 97.60/13.22 ((
% 97.60/13.22 (iftrueProp1) =>
% 97.60/13.22 ((
% 97.60/13.22 (iftrueProp2) =>
% 97.60/13.22 ((
% 97.60/13.22 (ifSingleton) =>
% 97.60/13.22 ((
% 97.60/13.22 (ifp) =>
% 97.60/13.22 ((
% 97.60/13.22 (theeq) =>
% 97.60/13.22 ((
% 97.60/13.22 (iftrue) =>
% 97.60/13.22 ((
% 97.60/13.22 (iffalse) =>
% 97.60/13.22 ((
% 97.60/13.22 (iftrueorfalse) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectT_lem) =>
% 97.60/13.22 ((
% 97.60/13.22 (binunionT_lem) =>
% 97.60/13.22 ((
% 97.60/13.22 (powersetT_lem) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusT_lem) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementT_lem) =>
% 97.60/13.22 ((
% 97.60/13.22 (setextT) =>
% 97.60/13.22 ((
% 97.60/13.22 (subsetTI) =>
% 97.60/13.22 ((
% 97.60/13.22 (powersetTI1) =>
% 97.60/13.22 ((
% 97.60/13.22 (powersetTE1) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementTI1) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementTE1) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectTELcontra) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectTERcontra) =>
% 97.60/13.22 ((
% 97.60/13.22 (contrasubsetT) =>
% 97.60/13.22 ((
% 97.60/13.22 (contrasubsetT1) =>
% 97.60/13.22 ((
% 97.60/13.22 (contrasubsetT2) =>
% 97.60/13.22 ((
% 97.60/13.22 (contrasubsetT3) =>
% 97.60/13.22 ((
% 97.60/13.22 (doubleComplementI1) =>
% 97.60/13.22 ((
% 97.60/13.22 (doubleComplementE1) =>
% 97.60/13.22 ((
% 97.60/13.22 (doubleComplementSub1) =>
% 97.60/13.22 ((
% 97.60/13.22 (doubleComplementSub2) =>
% 97.60/13.22 ((
% 97.60/13.22 (doubleComplementEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementTnotintersectT) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementImpComplementIntersect) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementSubsetComplementIntersect) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementInPowersetComplementIntersect) =>
% 97.60/13.22 ((
% 97.60/13.22 (contraSubsetComplement) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementTcontraSubset) =>
% 97.60/13.22 ((
% 97.60/13.22 (binunionTILcontra) =>
% 97.60/13.22 ((
% 97.60/13.22 (binunionTIRcontra) =>
% 97.60/13.22 ((
% 97.60/13.22 (inIntersectImpInUnion) =>
% 97.60/13.22 ((
% 97.60/13.22 (inIntersectImpInUnion2) =>
% 97.60/13.22 ((
% 97.60/13.22 (inIntersectImpInIntersectUnions) =>
% 97.60/13.22 ((
% 97.60/13.22 (intersectInPowersetIntersectUnions) =>
% 97.60/13.22 ((
% 97.60/13.22 (inComplementUnionImpNotIn1) =>
% 97.60/13.22 ((
% 97.60/13.22 (inComplementUnionImpInComplement1) =>
% 97.60/13.22 ((
% 97.60/13.22 (binunionTE) =>
% 97.60/13.22 ((
% 97.60/13.22 (binunionTEcontra) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan2a1) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementUnionInPowersetComplement) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan2a2) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan1a) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan1b) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan1) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan2a) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan2b2) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan2b) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan2) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz13rule0) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz13rule1) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz13rule2) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz13rule3) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz13rule4) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz1_1) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz1_2) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz1_3) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz1_4) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz1_5) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1all2) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1SetBreln1) =>
% 97.60/13.22 ((
% 97.60/13.22 (choice2fnsingleton) =>
% 97.60/13.22 ((
% 97.60/13.22 (setOfPairsIsBReln1) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1all1) =>
% 97.60/13.22 ((
% 97.60/13.22 (subbreln1) =>
% 97.60/13.22 ((
% 97.60/13.22 (eqbreln1) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1invprop) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1invI) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1invE) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1compprop) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1compI) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1compE) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1compEex) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1unionprop) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1unionIL) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1unionIR) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1unionI) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1unionE) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1unionEcases) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1unionCommutes) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz2Ex) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz2W) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz2A) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz2B) =>
% 97.60/13.22 ((
% 97.60/13.22 (image1Ex) =>
% 97.60/13.22 ((
% 97.60/13.22 (image1Ex1) =>
% 97.60/13.22 ((
% 97.60/13.22 (image1Equiv) =>
% 97.60/13.22 ((
% 97.60/13.22 (image1E) =>
% 97.60/13.22 ((
% 97.60/13.22 (image1I) =>
% 97.60/13.22 ((
% 97.60/13.22 (injFuncInInjFuncSet) =>
% 97.60/13.22 ((
% 97.60/13.22 (injFuncSetFuncIn) =>
% 97.60/13.22 ((
% 97.60/13.22 (injFuncSetFuncInj) =>
% 97.60/13.22 ((
% 97.60/13.22 (surjFuncSetFuncIn) =>
% 97.60/13.22 ((
% 97.60/13.22 (surjFuncSetFuncSurj) =>
% 97.60/13.22 ((
% 97.60/13.22 (leftInvIsSurj) =>
% 97.60/13.22 ((
% 97.60/13.22 (surjCantorThm) =>
% 97.60/13.22 ((
% 97.60/13.22 (foundation2) =>
% 97.60/13.22 ((
% 97.60/13.22 (notinself) =>
% 97.60/13.22 ((
% 97.60/13.22 (notinself2) =>
% 97.60/13.22 ((
% 97.60/13.22 (omegaSp) =>
% 97.60/13.22 ((
% 97.60/13.22 (omegaSclos) =>
% 97.60/13.22 ((
% 97.60/13.22 (peano0notS) =>
% 97.60/13.22 ((
% 97.60/13.22 (!!) @ (
% 97.60/13.22 (('#S') @ (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 =>) @
% 97.60/13.22 (
% 97.60/13.22 (
% 97.60/13.22 ('#C') @ in @
% 97.60/13.22 omega)))) @
% 97.60/13.22 (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 !!) @
% 97.60/13.22 (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 (
% 97.60/13.22 ('#S') @ (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 =>) @
% 97.60/13.22 (
% 97.60/13.22 (
% 97.60/13.22 ('#C') @ in @
% 97.60/13.22 omega)))))) @
% 97.60/13.22 (
% 97.60/13.22 (
% 97.60/13.22 ('#S') @ (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 '#S') @
% 97.60/13.22 (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 =>))) @
% 97.60/13.22 (
% 97.60/13.22 (
% 97.60/13.22 ('#C') @ (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 '#B') @
% 97.60/13.22 (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 =) @
% 97.60/13.22 omegaS)))) @
% 97.60/13.22 omegaS)))))) @
% 97.60/13.22 (
% 97.60/13.22 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.60/13.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl731])).
% 97.60/13.22 thf(zip_derived_cl769, plain,
% 97.60/13.22 (~ (((dsetconstr__Cong) =>
% 97.60/13.22 (((subsetI1) =>
% 97.60/13.22 (((eqimpsubset2) =>
% 97.60/13.22 (((eqimpsubset1) =>
% 97.60/13.22 (((subsetI2) =>
% 97.60/13.22 (((emptysetsubset) =>
% 97.60/13.22 (((subsetE) =>
% 97.60/13.22 (((subsetE2) =>
% 97.60/13.22 (((notsubsetI) =>
% 97.60/13.22 (((notequalI1) =>
% 97.60/13.22 (((notequalI2) =>
% 97.60/13.22 (((subsetRefl) =>
% 97.60/13.22 (((subsetTrans) =>
% 97.60/13.22 (((setadjoinSub) =>
% 97.60/13.22 (((setadjoinSub2) =>
% 97.60/13.22 (((subset2powerset) =>
% 97.60/13.22 (((setextsub) =>
% 97.60/13.22 (((subsetemptysetimpeq) =>
% 97.60/13.22 (((powersetI1) =>
% 97.60/13.22 (((powersetE1) =>
% 97.60/13.22 (((inPowerset) =>
% 97.60/13.22 (((powersetsubset) =>
% 97.60/13.22 (((sepInPowerset) =>
% 97.60/13.22 (((sepSubset) =>
% 97.60/13.22 (((binunionIL) =>
% 97.60/13.22 (((upairset2IR) =>
% 97.60/13.22 (((binunionIR) =>
% 97.60/13.22 (((binunionEcases) =>
% 97.60/13.22 (((binunionE) =>
% 97.60/13.22 (((binunionLsub) =>
% 97.60/13.22 ((
% 97.60/13.22 (binunionRsub) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectI) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectSubset5) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectEL) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectLsub) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectSubset2) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectSubset3) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectER) =>
% 97.60/13.22 ((
% 97.60/13.22 (disjointsetsI1) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectRsub) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectSubset4) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectSubset1) =>
% 97.60/13.22 ((
% 97.60/13.22 (bs114d) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusI) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusEL) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusER) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusSubset2) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusERneg) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusELneg) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusILneg) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusIRneg) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusLsub) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusSubset1) =>
% 97.60/13.22 ((
% 97.60/13.22 (symdiffE) =>
% 97.60/13.22 ((
% 97.60/13.22 (symdiffI1) =>
% 97.60/13.22 ((
% 97.60/13.22 (symdiffI2) =>
% 97.60/13.22 ((
% 97.60/13.22 (symdiffIneg1) =>
% 97.60/13.22 ((
% 97.60/13.22 (symdiffIneg2) =>
% 97.60/13.22 ((
% 97.60/13.22 (secondinupair) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairIL) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairIR) =>
% 97.60/13.22 ((
% 97.60/13.22 (kpairiskpair) =>
% 97.60/13.22 ((
% 97.60/13.22 (kpairp) =>
% 97.60/13.22 ((
% 97.60/13.22 (singletonsubset) =>
% 97.60/13.22 ((
% 97.60/13.22 (singletoninpowerset) =>
% 97.60/13.22 ((
% 97.60/13.22 (singletoninpowunion) =>
% 97.60/13.22 ((
% 97.60/13.22 (upairset2E) =>
% 97.60/13.22 ((
% 97.60/13.22 (upairsubunion) =>
% 97.60/13.22 ((
% 97.60/13.22 (upairinpowunion) =>
% 97.60/13.22 ((
% 97.60/13.22 (ubforcartprodlem1) =>
% 97.60/13.22 ((
% 97.60/13.22 (ubforcartprodlem2) =>
% 97.60/13.22 ((
% 97.60/13.22 (ubforcartprodlem3) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodpairin) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodmempair1) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodmempair) =>
% 97.60/13.22 ((
% 97.60/13.22 (setunionE2) =>
% 97.60/13.22 ((
% 97.60/13.22 (setunionsingleton1) =>
% 97.60/13.22 ((
% 97.60/13.22 (setunionsingleton2) =>
% 97.60/13.22 ((
% 97.60/13.22 (setunionsingleton) =>
% 97.60/13.22 ((
% 97.60/13.22 (singletonprop) =>
% 97.60/13.22 ((
% 97.60/13.22 (ex1E1) =>
% 97.60/13.22 ((
% 97.60/13.22 (ex1I) =>
% 97.60/13.22 ((
% 97.60/13.22 (ex1I2) =>
% 97.60/13.22 ((
% 97.60/13.22 (singletonsuniq) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjL1) =>
% 97.60/13.22 ((
% 97.60/13.22 (kfstsingleton) =>
% 97.60/13.22 ((
% 97.60/13.22 (theprop) =>
% 97.60/13.22 ((
% 97.60/13.22 (kfstpairEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodfstin) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjL2) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjL) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjR11) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjR12) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjR1) =>
% 97.60/13.22 ((
% 97.60/13.22 (upairequniteq) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjR2) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjR) =>
% 97.60/13.22 ((
% 97.60/13.22 (ksndsingleton) =>
% 97.60/13.22 ((
% 97.60/13.22 (ksndpairEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (kpairsurjEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodsndin) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodpairmemEL) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodpairmemER) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodmempaircEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodfstpairEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodsndpairEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodpairsurjEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (dpsetconstrI) =>
% 97.60/13.22 ((
% 97.60/13.22 (dpsetconstrSub) =>
% 97.60/13.22 ((
% 97.60/13.22 (setOfPairsIsBReln) =>
% 97.60/13.22 ((
% 97.60/13.22 (dpsetconstrERa) =>
% 97.60/13.22 ((
% 97.60/13.22 (dpsetconstrEL1) =>
% 97.60/13.22 ((
% 97.60/13.22 (dpsetconstrEL2) =>
% 97.60/13.22 ((
% 97.60/13.22 (dpsetconstrER) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcImageSingleton) =>
% 97.60/13.22 ((
% 97.60/13.22 (apProp) =>
% 97.60/13.22 ((
% 97.60/13.22 (app) =>
% 97.60/13.22 ((
% 97.60/13.22 (infuncsetfunc) =>
% 97.60/13.22 ((
% 97.60/13.22 (ap2p) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcinfuncset) =>
% 97.60/13.22 ((
% 97.60/13.22 (lamProp) =>
% 97.60/13.22 ((
% 97.60/13.22 (lamp) =>
% 97.60/13.22 ((
% 97.60/13.22 (lam2p) =>
% 97.60/13.22 ((
% 97.60/13.22 (brelnall1) =>
% 97.60/13.22 ((
% 97.60/13.22 (brelnall2) =>
% 97.60/13.22 ((
% 97.60/13.22 (ex1E2) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcGraphProp1) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcGraphProp3) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcGraphProp2) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcextLem) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcGraphProp4) =>
% 97.60/13.22 ((
% 97.60/13.22 (subbreln) =>
% 97.60/13.22 ((
% 97.60/13.22 (eqbreln) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcext) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcext2) =>
% 97.60/13.22 ((
% 97.60/13.22 (ap2apEq1) =>
% 97.60/13.22 ((
% 97.60/13.22 (ap2apEq2) =>
% 97.60/13.22 ((
% 97.60/13.22 (beta1) =>
% 97.60/13.22 ((
% 97.60/13.22 (eta1) =>
% 97.60/13.22 ((
% 97.60/13.22 (lam2lamEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (beta2) =>
% 97.60/13.22 ((
% 97.60/13.22 (eta2) =>
% 97.60/13.22 ((
% 97.60/13.22 (iffalseProp1) =>
% 97.60/13.22 ((
% 97.60/13.22 (iffalseProp2) =>
% 97.60/13.22 ((
% 97.60/13.22 (iftrueProp1) =>
% 97.60/13.22 ((
% 97.60/13.22 (iftrueProp2) =>
% 97.60/13.22 ((
% 97.60/13.22 (ifSingleton) =>
% 97.60/13.22 ((
% 97.60/13.22 (ifp) =>
% 97.60/13.22 ((
% 97.60/13.22 (theeq) =>
% 97.60/13.22 ((
% 97.60/13.22 (iftrue) =>
% 97.60/13.22 ((
% 97.60/13.22 (iffalse) =>
% 97.60/13.22 ((
% 97.60/13.22 (iftrueorfalse) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectT_lem) =>
% 97.60/13.22 ((
% 97.60/13.22 (binunionT_lem) =>
% 97.60/13.22 ((
% 97.60/13.22 (powersetT_lem) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusT_lem) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementT_lem) =>
% 97.60/13.22 ((
% 97.60/13.22 (setextT) =>
% 97.60/13.22 ((
% 97.60/13.22 (subsetTI) =>
% 97.60/13.22 ((
% 97.60/13.22 (powersetTI1) =>
% 97.60/13.22 ((
% 97.60/13.22 (powersetTE1) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementTI1) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementTE1) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectTELcontra) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectTERcontra) =>
% 97.60/13.22 ((
% 97.60/13.22 (contrasubsetT) =>
% 97.60/13.22 ((
% 97.60/13.22 (contrasubsetT1) =>
% 97.60/13.22 ((
% 97.60/13.22 (contrasubsetT2) =>
% 97.60/13.22 ((
% 97.60/13.22 (contrasubsetT3) =>
% 97.60/13.22 ((
% 97.60/13.22 (doubleComplementI1) =>
% 97.60/13.22 ((
% 97.60/13.22 (doubleComplementE1) =>
% 97.60/13.22 ((
% 97.60/13.22 (doubleComplementSub1) =>
% 97.60/13.22 ((
% 97.60/13.22 (doubleComplementSub2) =>
% 97.60/13.22 ((
% 97.60/13.22 (doubleComplementEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementTnotintersectT) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementImpComplementIntersect) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementSubsetComplementIntersect) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementInPowersetComplementIntersect) =>
% 97.60/13.22 ((
% 97.60/13.22 (contraSubsetComplement) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementTcontraSubset) =>
% 97.60/13.22 ((
% 97.60/13.22 (binunionTILcontra) =>
% 97.60/13.22 ((
% 97.60/13.22 (binunionTIRcontra) =>
% 97.60/13.22 ((
% 97.60/13.22 (inIntersectImpInUnion) =>
% 97.60/13.22 ((
% 97.60/13.22 (inIntersectImpInUnion2) =>
% 97.60/13.22 ((
% 97.60/13.22 (inIntersectImpInIntersectUnions) =>
% 97.60/13.22 ((
% 97.60/13.22 (intersectInPowersetIntersectUnions) =>
% 97.60/13.22 ((
% 97.60/13.22 (inComplementUnionImpNotIn1) =>
% 97.60/13.22 ((
% 97.60/13.22 (inComplementUnionImpInComplement1) =>
% 97.60/13.22 ((
% 97.60/13.22 (binunionTE) =>
% 97.60/13.22 ((
% 97.60/13.22 (binunionTEcontra) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan2a1) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementUnionInPowersetComplement) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan2a2) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan1a) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan1b) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan1) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan2a) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan2b2) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan2b) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan2) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz13rule0) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz13rule1) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz13rule2) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz13rule3) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz13rule4) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz1_1) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz1_2) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz1_3) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz1_4) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz1_5) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1all2) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1SetBreln1) =>
% 97.60/13.22 ((
% 97.60/13.22 (choice2fnsingleton) =>
% 97.60/13.22 ((
% 97.60/13.22 (setOfPairsIsBReln1) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1all1) =>
% 97.60/13.22 ((
% 97.60/13.22 (subbreln1) =>
% 97.60/13.22 ((
% 97.60/13.22 (eqbreln1) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1invprop) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1invI) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1invE) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1compprop) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1compI) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1compE) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1compEex) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1unionprop) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1unionIL) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1unionIR) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1unionI) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1unionE) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1unionEcases) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1unionCommutes) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz2Ex) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz2W) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz2A) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz2B) =>
% 97.60/13.22 ((
% 97.60/13.22 (image1Ex) =>
% 97.60/13.22 ((
% 97.60/13.22 (image1Ex1) =>
% 97.60/13.22 ((
% 97.60/13.22 (image1Equiv) =>
% 97.60/13.22 ((
% 97.60/13.22 (image1E) =>
% 97.60/13.22 ((
% 97.60/13.22 (image1I) =>
% 97.60/13.22 ((
% 97.60/13.22 (injFuncInInjFuncSet) =>
% 97.60/13.22 ((
% 97.60/13.22 (injFuncSetFuncIn) =>
% 97.60/13.22 ((
% 97.60/13.22 (injFuncSetFuncInj) =>
% 97.60/13.22 ((
% 97.60/13.22 (surjFuncSetFuncIn) =>
% 97.60/13.22 ((
% 97.60/13.22 (surjFuncSetFuncSurj) =>
% 97.60/13.22 ((
% 97.60/13.22 (leftInvIsSurj) =>
% 97.60/13.22 ((
% 97.60/13.22 (surjCantorThm) =>
% 97.60/13.22 ((
% 97.60/13.22 (foundation2) =>
% 97.60/13.22 ((
% 97.60/13.22 (notinself) =>
% 97.60/13.22 ((
% 97.60/13.22 (notinself2) =>
% 97.60/13.22 ((
% 97.60/13.22 (omegaSp) =>
% 97.60/13.22 ((
% 97.60/13.22 (omegaSclos) =>
% 97.60/13.22 ((
% 97.60/13.22 (peano0notS) =>
% 97.60/13.22 ((
% 97.60/13.22 (!!) @ (
% 97.60/13.22 (('#S') @ (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 =>) @
% 97.60/13.22 (
% 97.60/13.22 (
% 97.60/13.22 ('#C') @ in @
% 97.60/13.22 omega)))) @
% 97.60/13.22 (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 !!) @
% 97.60/13.22 (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 (
% 97.60/13.22 ('#S') @ (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 =>) @
% 97.60/13.22 (
% 97.60/13.22 (
% 97.60/13.22 ('#C') @ in @
% 97.60/13.22 omega)))))) @
% 97.60/13.22 (
% 97.60/13.22 (
% 97.60/13.22 ('#S') @ (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 '#S') @
% 97.60/13.22 (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 =>))) @
% 97.60/13.22 (
% 97.60/13.22 (
% 97.60/13.22 ('#C') @ (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 '#B') @
% 97.60/13.22 (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 =) @
% 97.60/13.22 omegaS)))) @
% 97.60/13.22 omegaS)))))) @
% 97.60/13.22 (
% 97.60/13.22 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.60/13.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl749])).
% 97.60/13.22 thf(zip_derived_cl789, plain,
% 97.60/13.22 (~ (((subsetI1) =>
% 97.60/13.22 (((eqimpsubset2) =>
% 97.60/13.22 (((eqimpsubset1) =>
% 97.60/13.22 (((subsetI2) =>
% 97.60/13.22 (((emptysetsubset) =>
% 97.60/13.22 (((subsetE) =>
% 97.60/13.22 (((subsetE2) =>
% 97.60/13.22 (((notsubsetI) =>
% 97.60/13.22 (((notequalI1) =>
% 97.60/13.22 (((notequalI2) =>
% 97.60/13.22 (((subsetRefl) =>
% 97.60/13.22 (((subsetTrans) =>
% 97.60/13.22 (((setadjoinSub) =>
% 97.60/13.22 (((setadjoinSub2) =>
% 97.60/13.22 (((subset2powerset) =>
% 97.60/13.22 (((setextsub) =>
% 97.60/13.22 (((subsetemptysetimpeq) =>
% 97.60/13.22 (((powersetI1) =>
% 97.60/13.22 (((powersetE1) =>
% 97.60/13.22 (((inPowerset) =>
% 97.60/13.22 (((powersetsubset) =>
% 97.60/13.22 (((sepInPowerset) =>
% 97.60/13.22 (((sepSubset) =>
% 97.60/13.22 (((binunionIL) =>
% 97.60/13.22 (((upairset2IR) =>
% 97.60/13.22 (((binunionIR) =>
% 97.60/13.22 (((binunionEcases) =>
% 97.60/13.22 (((binunionE) =>
% 97.60/13.22 (((binunionLsub) =>
% 97.60/13.22 (((binunionRsub) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectI) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectSubset5) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectEL) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectLsub) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectSubset2) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectSubset3) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectER) =>
% 97.60/13.22 ((
% 97.60/13.22 (disjointsetsI1) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectRsub) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectSubset4) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectSubset1) =>
% 97.60/13.22 ((
% 97.60/13.22 (bs114d) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusI) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusEL) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusER) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusSubset2) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusERneg) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusELneg) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusILneg) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusIRneg) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusLsub) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusSubset1) =>
% 97.60/13.22 ((
% 97.60/13.22 (symdiffE) =>
% 97.60/13.22 ((
% 97.60/13.22 (symdiffI1) =>
% 97.60/13.22 ((
% 97.60/13.22 (symdiffI2) =>
% 97.60/13.22 ((
% 97.60/13.22 (symdiffIneg1) =>
% 97.60/13.22 ((
% 97.60/13.22 (symdiffIneg2) =>
% 97.60/13.22 ((
% 97.60/13.22 (secondinupair) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairIL) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairIR) =>
% 97.60/13.22 ((
% 97.60/13.22 (kpairiskpair) =>
% 97.60/13.22 ((
% 97.60/13.22 (kpairp) =>
% 97.60/13.22 ((
% 97.60/13.22 (singletonsubset) =>
% 97.60/13.22 ((
% 97.60/13.22 (singletoninpowerset) =>
% 97.60/13.22 ((
% 97.60/13.22 (singletoninpowunion) =>
% 97.60/13.22 ((
% 97.60/13.22 (upairset2E) =>
% 97.60/13.22 ((
% 97.60/13.22 (upairsubunion) =>
% 97.60/13.22 ((
% 97.60/13.22 (upairinpowunion) =>
% 97.60/13.22 ((
% 97.60/13.22 (ubforcartprodlem1) =>
% 97.60/13.22 ((
% 97.60/13.22 (ubforcartprodlem2) =>
% 97.60/13.22 ((
% 97.60/13.22 (ubforcartprodlem3) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodpairin) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodmempair1) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodmempair) =>
% 97.60/13.22 ((
% 97.60/13.22 (setunionE2) =>
% 97.60/13.22 ((
% 97.60/13.22 (setunionsingleton1) =>
% 97.60/13.22 ((
% 97.60/13.22 (setunionsingleton2) =>
% 97.60/13.22 ((
% 97.60/13.22 (setunionsingleton) =>
% 97.60/13.22 ((
% 97.60/13.22 (singletonprop) =>
% 97.60/13.22 ((
% 97.60/13.22 (ex1E1) =>
% 97.60/13.22 ((
% 97.60/13.22 (ex1I) =>
% 97.60/13.22 ((
% 97.60/13.22 (ex1I2) =>
% 97.60/13.22 ((
% 97.60/13.22 (singletonsuniq) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjL1) =>
% 97.60/13.22 ((
% 97.60/13.22 (kfstsingleton) =>
% 97.60/13.22 ((
% 97.60/13.22 (theprop) =>
% 97.60/13.22 ((
% 97.60/13.22 (kfstpairEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodfstin) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjL2) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjL) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjR11) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjR12) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjR1) =>
% 97.60/13.22 ((
% 97.60/13.22 (upairequniteq) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjR2) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjR) =>
% 97.60/13.22 ((
% 97.60/13.22 (ksndsingleton) =>
% 97.60/13.22 ((
% 97.60/13.22 (ksndpairEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (kpairsurjEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodsndin) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodpairmemEL) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodpairmemER) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodmempaircEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodfstpairEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodsndpairEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodpairsurjEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (dpsetconstrI) =>
% 97.60/13.22 ((
% 97.60/13.22 (dpsetconstrSub) =>
% 97.60/13.22 ((
% 97.60/13.22 (setOfPairsIsBReln) =>
% 97.60/13.22 ((
% 97.60/13.22 (dpsetconstrERa) =>
% 97.60/13.22 ((
% 97.60/13.22 (dpsetconstrEL1) =>
% 97.60/13.22 ((
% 97.60/13.22 (dpsetconstrEL2) =>
% 97.60/13.22 ((
% 97.60/13.22 (dpsetconstrER) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcImageSingleton) =>
% 97.60/13.22 ((
% 97.60/13.22 (apProp) =>
% 97.60/13.22 ((
% 97.60/13.22 (app) =>
% 97.60/13.22 ((
% 97.60/13.22 (infuncsetfunc) =>
% 97.60/13.22 ((
% 97.60/13.22 (ap2p) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcinfuncset) =>
% 97.60/13.22 ((
% 97.60/13.22 (lamProp) =>
% 97.60/13.22 ((
% 97.60/13.22 (lamp) =>
% 97.60/13.22 ((
% 97.60/13.22 (lam2p) =>
% 97.60/13.22 ((
% 97.60/13.22 (brelnall1) =>
% 97.60/13.22 ((
% 97.60/13.22 (brelnall2) =>
% 97.60/13.22 ((
% 97.60/13.22 (ex1E2) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcGraphProp1) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcGraphProp3) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcGraphProp2) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcextLem) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcGraphProp4) =>
% 97.60/13.22 ((
% 97.60/13.22 (subbreln) =>
% 97.60/13.22 ((
% 97.60/13.22 (eqbreln) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcext) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcext2) =>
% 97.60/13.22 ((
% 97.60/13.22 (ap2apEq1) =>
% 97.60/13.22 ((
% 97.60/13.22 (ap2apEq2) =>
% 97.60/13.22 ((
% 97.60/13.22 (beta1) =>
% 97.60/13.22 ((
% 97.60/13.22 (eta1) =>
% 97.60/13.22 ((
% 97.60/13.22 (lam2lamEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (beta2) =>
% 97.60/13.22 ((
% 97.60/13.22 (eta2) =>
% 97.60/13.22 ((
% 97.60/13.22 (iffalseProp1) =>
% 97.60/13.22 ((
% 97.60/13.22 (iffalseProp2) =>
% 97.60/13.22 ((
% 97.60/13.22 (iftrueProp1) =>
% 97.60/13.22 ((
% 97.60/13.22 (iftrueProp2) =>
% 97.60/13.22 ((
% 97.60/13.22 (ifSingleton) =>
% 97.60/13.22 ((
% 97.60/13.22 (ifp) =>
% 97.60/13.22 ((
% 97.60/13.22 (theeq) =>
% 97.60/13.22 ((
% 97.60/13.22 (iftrue) =>
% 97.60/13.22 ((
% 97.60/13.22 (iffalse) =>
% 97.60/13.22 ((
% 97.60/13.22 (iftrueorfalse) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectT_lem) =>
% 97.60/13.22 ((
% 97.60/13.22 (binunionT_lem) =>
% 97.60/13.22 ((
% 97.60/13.22 (powersetT_lem) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusT_lem) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementT_lem) =>
% 97.60/13.22 ((
% 97.60/13.22 (setextT) =>
% 97.60/13.22 ((
% 97.60/13.22 (subsetTI) =>
% 97.60/13.22 ((
% 97.60/13.22 (powersetTI1) =>
% 97.60/13.22 ((
% 97.60/13.22 (powersetTE1) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementTI1) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementTE1) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectTELcontra) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectTERcontra) =>
% 97.60/13.22 ((
% 97.60/13.22 (contrasubsetT) =>
% 97.60/13.22 ((
% 97.60/13.22 (contrasubsetT1) =>
% 97.60/13.22 ((
% 97.60/13.22 (contrasubsetT2) =>
% 97.60/13.22 ((
% 97.60/13.22 (contrasubsetT3) =>
% 97.60/13.22 ((
% 97.60/13.22 (doubleComplementI1) =>
% 97.60/13.22 ((
% 97.60/13.22 (doubleComplementE1) =>
% 97.60/13.22 ((
% 97.60/13.22 (doubleComplementSub1) =>
% 97.60/13.22 ((
% 97.60/13.22 (doubleComplementSub2) =>
% 97.60/13.22 ((
% 97.60/13.22 (doubleComplementEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementTnotintersectT) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementImpComplementIntersect) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementSubsetComplementIntersect) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementInPowersetComplementIntersect) =>
% 97.60/13.22 ((
% 97.60/13.22 (contraSubsetComplement) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementTcontraSubset) =>
% 97.60/13.22 ((
% 97.60/13.22 (binunionTILcontra) =>
% 97.60/13.22 ((
% 97.60/13.22 (binunionTIRcontra) =>
% 97.60/13.22 ((
% 97.60/13.22 (inIntersectImpInUnion) =>
% 97.60/13.22 ((
% 97.60/13.22 (inIntersectImpInUnion2) =>
% 97.60/13.22 ((
% 97.60/13.22 (inIntersectImpInIntersectUnions) =>
% 97.60/13.22 ((
% 97.60/13.22 (intersectInPowersetIntersectUnions) =>
% 97.60/13.22 ((
% 97.60/13.22 (inComplementUnionImpNotIn1) =>
% 97.60/13.22 ((
% 97.60/13.22 (inComplementUnionImpInComplement1) =>
% 97.60/13.22 ((
% 97.60/13.22 (binunionTE) =>
% 97.60/13.22 ((
% 97.60/13.22 (binunionTEcontra) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan2a1) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementUnionInPowersetComplement) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan2a2) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan1a) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan1b) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan1) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan2a) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan2b2) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan2b) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan2) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz13rule0) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz13rule1) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz13rule2) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz13rule3) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz13rule4) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz1_1) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz1_2) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz1_3) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz1_4) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz1_5) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1all2) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1SetBreln1) =>
% 97.60/13.22 ((
% 97.60/13.22 (choice2fnsingleton) =>
% 97.60/13.22 ((
% 97.60/13.22 (setOfPairsIsBReln1) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1all1) =>
% 97.60/13.22 ((
% 97.60/13.22 (subbreln1) =>
% 97.60/13.22 ((
% 97.60/13.22 (eqbreln1) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1invprop) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1invI) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1invE) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1compprop) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1compI) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1compE) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1compEex) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1unionprop) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1unionIL) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1unionIR) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1unionI) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1unionE) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1unionEcases) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1unionCommutes) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz2Ex) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz2W) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz2A) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz2B) =>
% 97.60/13.22 ((
% 97.60/13.22 (image1Ex) =>
% 97.60/13.22 ((
% 97.60/13.22 (image1Ex1) =>
% 97.60/13.22 ((
% 97.60/13.22 (image1Equiv) =>
% 97.60/13.22 ((
% 97.60/13.22 (image1E) =>
% 97.60/13.22 ((
% 97.60/13.22 (image1I) =>
% 97.60/13.22 ((
% 97.60/13.22 (injFuncInInjFuncSet) =>
% 97.60/13.22 ((
% 97.60/13.22 (injFuncSetFuncIn) =>
% 97.60/13.22 ((
% 97.60/13.22 (injFuncSetFuncInj) =>
% 97.60/13.22 ((
% 97.60/13.22 (surjFuncSetFuncIn) =>
% 97.60/13.22 ((
% 97.60/13.22 (surjFuncSetFuncSurj) =>
% 97.60/13.22 ((
% 97.60/13.22 (leftInvIsSurj) =>
% 97.60/13.22 ((
% 97.60/13.22 (surjCantorThm) =>
% 97.60/13.22 ((
% 97.60/13.22 (foundation2) =>
% 97.60/13.22 ((
% 97.60/13.22 (notinself) =>
% 97.60/13.22 ((
% 97.60/13.22 (notinself2) =>
% 97.60/13.22 ((
% 97.60/13.22 (omegaSp) =>
% 97.60/13.22 ((
% 97.60/13.22 (omegaSclos) =>
% 97.60/13.22 ((
% 97.60/13.22 (peano0notS) =>
% 97.60/13.22 ((
% 97.60/13.22 (!!) @ (
% 97.60/13.22 (('#S') @ (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 =>) @
% 97.60/13.22 (
% 97.60/13.22 (
% 97.60/13.22 ('#C') @ in @
% 97.60/13.22 omega)))) @
% 97.60/13.22 (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 !!) @
% 97.60/13.22 (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 (
% 97.60/13.22 ('#S') @ (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 =>) @
% 97.60/13.22 (
% 97.60/13.22 (
% 97.60/13.22 ('#C') @ in @
% 97.60/13.22 omega)))))) @
% 97.60/13.22 (
% 97.60/13.22 (
% 97.60/13.22 ('#S') @ (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 '#S') @
% 97.60/13.22 (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 =>))) @
% 97.60/13.22 (
% 97.60/13.22 (
% 97.60/13.22 ('#C') @ (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 '#B') @
% 97.60/13.22 (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 =) @
% 97.60/13.22 omegaS)))) @
% 97.60/13.22 omegaS)))))) @
% 97.60/13.22 (
% 97.60/13.22 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.60/13.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl769])).
% 97.60/13.22 thf(zip_derived_cl807, plain,
% 97.60/13.22 (~ (((eqimpsubset2) =>
% 97.60/13.22 (((eqimpsubset1) =>
% 97.60/13.22 (((subsetI2) =>
% 97.60/13.22 (((emptysetsubset) =>
% 97.60/13.22 (((subsetE) =>
% 97.60/13.22 (((subsetE2) =>
% 97.60/13.22 (((notsubsetI) =>
% 97.60/13.22 (((notequalI1) =>
% 97.60/13.22 (((notequalI2) =>
% 97.60/13.22 (((subsetRefl) =>
% 97.60/13.22 (((subsetTrans) =>
% 97.60/13.22 (((setadjoinSub) =>
% 97.60/13.22 (((setadjoinSub2) =>
% 97.60/13.22 (((subset2powerset) =>
% 97.60/13.22 (((setextsub) =>
% 97.60/13.22 (((subsetemptysetimpeq) =>
% 97.60/13.22 (((powersetI1) =>
% 97.60/13.22 (((powersetE1) =>
% 97.60/13.22 (((inPowerset) =>
% 97.60/13.22 (((powersetsubset) =>
% 97.60/13.22 (((sepInPowerset) =>
% 97.60/13.22 (((sepSubset) =>
% 97.60/13.22 (((binunionIL) =>
% 97.60/13.22 (((upairset2IR) =>
% 97.60/13.22 (((binunionIR) =>
% 97.60/13.22 (((binunionEcases) =>
% 97.60/13.22 (((binunionE) =>
% 97.60/13.22 (((binunionLsub) =>
% 97.60/13.22 (((binunionRsub) =>
% 97.60/13.22 (((binintersectI) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectSubset5) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectEL) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectLsub) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectSubset2) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectSubset3) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectER) =>
% 97.60/13.22 ((
% 97.60/13.22 (disjointsetsI1) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectRsub) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectSubset4) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectSubset1) =>
% 97.60/13.22 ((
% 97.60/13.22 (bs114d) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusI) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusEL) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusER) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusSubset2) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusERneg) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusELneg) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusILneg) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusIRneg) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusLsub) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusSubset1) =>
% 97.60/13.22 ((
% 97.60/13.22 (symdiffE) =>
% 97.60/13.22 ((
% 97.60/13.22 (symdiffI1) =>
% 97.60/13.22 ((
% 97.60/13.22 (symdiffI2) =>
% 97.60/13.22 ((
% 97.60/13.22 (symdiffIneg1) =>
% 97.60/13.22 ((
% 97.60/13.22 (symdiffIneg2) =>
% 97.60/13.22 ((
% 97.60/13.22 (secondinupair) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairIL) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairIR) =>
% 97.60/13.22 ((
% 97.60/13.22 (kpairiskpair) =>
% 97.60/13.22 ((
% 97.60/13.22 (kpairp) =>
% 97.60/13.22 ((
% 97.60/13.22 (singletonsubset) =>
% 97.60/13.22 ((
% 97.60/13.22 (singletoninpowerset) =>
% 97.60/13.22 ((
% 97.60/13.22 (singletoninpowunion) =>
% 97.60/13.22 ((
% 97.60/13.22 (upairset2E) =>
% 97.60/13.22 ((
% 97.60/13.22 (upairsubunion) =>
% 97.60/13.22 ((
% 97.60/13.22 (upairinpowunion) =>
% 97.60/13.22 ((
% 97.60/13.22 (ubforcartprodlem1) =>
% 97.60/13.22 ((
% 97.60/13.22 (ubforcartprodlem2) =>
% 97.60/13.22 ((
% 97.60/13.22 (ubforcartprodlem3) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodpairin) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodmempair1) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodmempair) =>
% 97.60/13.22 ((
% 97.60/13.22 (setunionE2) =>
% 97.60/13.22 ((
% 97.60/13.22 (setunionsingleton1) =>
% 97.60/13.22 ((
% 97.60/13.22 (setunionsingleton2) =>
% 97.60/13.22 ((
% 97.60/13.22 (setunionsingleton) =>
% 97.60/13.22 ((
% 97.60/13.22 (singletonprop) =>
% 97.60/13.22 ((
% 97.60/13.22 (ex1E1) =>
% 97.60/13.22 ((
% 97.60/13.22 (ex1I) =>
% 97.60/13.22 ((
% 97.60/13.22 (ex1I2) =>
% 97.60/13.22 ((
% 97.60/13.22 (singletonsuniq) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjL1) =>
% 97.60/13.22 ((
% 97.60/13.22 (kfstsingleton) =>
% 97.60/13.22 ((
% 97.60/13.22 (theprop) =>
% 97.60/13.22 ((
% 97.60/13.22 (kfstpairEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodfstin) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjL2) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjL) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjR11) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjR12) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjR1) =>
% 97.60/13.22 ((
% 97.60/13.22 (upairequniteq) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjR2) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjR) =>
% 97.60/13.22 ((
% 97.60/13.22 (ksndsingleton) =>
% 97.60/13.22 ((
% 97.60/13.22 (ksndpairEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (kpairsurjEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodsndin) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodpairmemEL) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodpairmemER) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodmempaircEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodfstpairEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodsndpairEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodpairsurjEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (dpsetconstrI) =>
% 97.60/13.22 ((
% 97.60/13.22 (dpsetconstrSub) =>
% 97.60/13.22 ((
% 97.60/13.22 (setOfPairsIsBReln) =>
% 97.60/13.22 ((
% 97.60/13.22 (dpsetconstrERa) =>
% 97.60/13.22 ((
% 97.60/13.22 (dpsetconstrEL1) =>
% 97.60/13.22 ((
% 97.60/13.22 (dpsetconstrEL2) =>
% 97.60/13.22 ((
% 97.60/13.22 (dpsetconstrER) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcImageSingleton) =>
% 97.60/13.22 ((
% 97.60/13.22 (apProp) =>
% 97.60/13.22 ((
% 97.60/13.22 (app) =>
% 97.60/13.22 ((
% 97.60/13.22 (infuncsetfunc) =>
% 97.60/13.22 ((
% 97.60/13.22 (ap2p) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcinfuncset) =>
% 97.60/13.22 ((
% 97.60/13.22 (lamProp) =>
% 97.60/13.22 ((
% 97.60/13.22 (lamp) =>
% 97.60/13.22 ((
% 97.60/13.22 (lam2p) =>
% 97.60/13.22 ((
% 97.60/13.22 (brelnall1) =>
% 97.60/13.22 ((
% 97.60/13.22 (brelnall2) =>
% 97.60/13.22 ((
% 97.60/13.22 (ex1E2) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcGraphProp1) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcGraphProp3) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcGraphProp2) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcextLem) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcGraphProp4) =>
% 97.60/13.22 ((
% 97.60/13.22 (subbreln) =>
% 97.60/13.22 ((
% 97.60/13.22 (eqbreln) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcext) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcext2) =>
% 97.60/13.22 ((
% 97.60/13.22 (ap2apEq1) =>
% 97.60/13.22 ((
% 97.60/13.22 (ap2apEq2) =>
% 97.60/13.22 ((
% 97.60/13.22 (beta1) =>
% 97.60/13.22 ((
% 97.60/13.22 (eta1) =>
% 97.60/13.22 ((
% 97.60/13.22 (lam2lamEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (beta2) =>
% 97.60/13.22 ((
% 97.60/13.22 (eta2) =>
% 97.60/13.22 ((
% 97.60/13.22 (iffalseProp1) =>
% 97.60/13.22 ((
% 97.60/13.22 (iffalseProp2) =>
% 97.60/13.22 ((
% 97.60/13.22 (iftrueProp1) =>
% 97.60/13.22 ((
% 97.60/13.22 (iftrueProp2) =>
% 97.60/13.22 ((
% 97.60/13.22 (ifSingleton) =>
% 97.60/13.22 ((
% 97.60/13.22 (ifp) =>
% 97.60/13.22 ((
% 97.60/13.22 (theeq) =>
% 97.60/13.22 ((
% 97.60/13.22 (iftrue) =>
% 97.60/13.22 ((
% 97.60/13.22 (iffalse) =>
% 97.60/13.22 ((
% 97.60/13.22 (iftrueorfalse) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectT_lem) =>
% 97.60/13.22 ((
% 97.60/13.22 (binunionT_lem) =>
% 97.60/13.22 ((
% 97.60/13.22 (powersetT_lem) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusT_lem) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementT_lem) =>
% 97.60/13.22 ((
% 97.60/13.22 (setextT) =>
% 97.60/13.22 ((
% 97.60/13.22 (subsetTI) =>
% 97.60/13.22 ((
% 97.60/13.22 (powersetTI1) =>
% 97.60/13.22 ((
% 97.60/13.22 (powersetTE1) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementTI1) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementTE1) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectTELcontra) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectTERcontra) =>
% 97.60/13.22 ((
% 97.60/13.22 (contrasubsetT) =>
% 97.60/13.22 ((
% 97.60/13.22 (contrasubsetT1) =>
% 97.60/13.22 ((
% 97.60/13.22 (contrasubsetT2) =>
% 97.60/13.22 ((
% 97.60/13.22 (contrasubsetT3) =>
% 97.60/13.22 ((
% 97.60/13.22 (doubleComplementI1) =>
% 97.60/13.22 ((
% 97.60/13.22 (doubleComplementE1) =>
% 97.60/13.22 ((
% 97.60/13.22 (doubleComplementSub1) =>
% 97.60/13.22 ((
% 97.60/13.22 (doubleComplementSub2) =>
% 97.60/13.22 ((
% 97.60/13.22 (doubleComplementEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementTnotintersectT) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementImpComplementIntersect) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementSubsetComplementIntersect) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementInPowersetComplementIntersect) =>
% 97.60/13.22 ((
% 97.60/13.22 (contraSubsetComplement) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementTcontraSubset) =>
% 97.60/13.22 ((
% 97.60/13.22 (binunionTILcontra) =>
% 97.60/13.22 ((
% 97.60/13.22 (binunionTIRcontra) =>
% 97.60/13.22 ((
% 97.60/13.22 (inIntersectImpInUnion) =>
% 97.60/13.22 ((
% 97.60/13.22 (inIntersectImpInUnion2) =>
% 97.60/13.22 ((
% 97.60/13.22 (inIntersectImpInIntersectUnions) =>
% 97.60/13.22 ((
% 97.60/13.22 (intersectInPowersetIntersectUnions) =>
% 97.60/13.22 ((
% 97.60/13.22 (inComplementUnionImpNotIn1) =>
% 97.60/13.22 ((
% 97.60/13.22 (inComplementUnionImpInComplement1) =>
% 97.60/13.22 ((
% 97.60/13.22 (binunionTE) =>
% 97.60/13.22 ((
% 97.60/13.22 (binunionTEcontra) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan2a1) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementUnionInPowersetComplement) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan2a2) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan1a) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan1b) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan1) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan2a) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan2b2) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan2b) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan2) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz13rule0) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz13rule1) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz13rule2) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz13rule3) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz13rule4) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz1_1) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz1_2) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz1_3) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz1_4) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz1_5) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1all2) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1SetBreln1) =>
% 97.60/13.22 ((
% 97.60/13.22 (choice2fnsingleton) =>
% 97.60/13.22 ((
% 97.60/13.22 (setOfPairsIsBReln1) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1all1) =>
% 97.60/13.22 ((
% 97.60/13.22 (subbreln1) =>
% 97.60/13.22 ((
% 97.60/13.22 (eqbreln1) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1invprop) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1invI) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1invE) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1compprop) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1compI) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1compE) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1compEex) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1unionprop) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1unionIL) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1unionIR) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1unionI) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1unionE) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1unionEcases) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1unionCommutes) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz2Ex) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz2W) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz2A) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz2B) =>
% 97.60/13.22 ((
% 97.60/13.22 (image1Ex) =>
% 97.60/13.22 ((
% 97.60/13.22 (image1Ex1) =>
% 97.60/13.22 ((
% 97.60/13.22 (image1Equiv) =>
% 97.60/13.22 ((
% 97.60/13.22 (image1E) =>
% 97.60/13.22 ((
% 97.60/13.22 (image1I) =>
% 97.60/13.22 ((
% 97.60/13.22 (injFuncInInjFuncSet) =>
% 97.60/13.22 ((
% 97.60/13.22 (injFuncSetFuncIn) =>
% 97.60/13.22 ((
% 97.60/13.22 (injFuncSetFuncInj) =>
% 97.60/13.22 ((
% 97.60/13.22 (surjFuncSetFuncIn) =>
% 97.60/13.22 ((
% 97.60/13.22 (surjFuncSetFuncSurj) =>
% 97.60/13.22 ((
% 97.60/13.22 (leftInvIsSurj) =>
% 97.60/13.22 ((
% 97.60/13.22 (surjCantorThm) =>
% 97.60/13.22 ((
% 97.60/13.22 (foundation2) =>
% 97.60/13.22 ((
% 97.60/13.22 (notinself) =>
% 97.60/13.22 ((
% 97.60/13.22 (notinself2) =>
% 97.60/13.22 ((
% 97.60/13.22 (omegaSp) =>
% 97.60/13.22 ((
% 97.60/13.22 (omegaSclos) =>
% 97.60/13.22 ((
% 97.60/13.22 (peano0notS) =>
% 97.60/13.22 ((
% 97.60/13.22 (!!) @ (
% 97.60/13.22 (('#S') @ (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 =>) @
% 97.60/13.22 (
% 97.60/13.22 (
% 97.60/13.22 ('#C') @ in @
% 97.60/13.22 omega)))) @
% 97.60/13.22 (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 !!) @
% 97.60/13.22 (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 (
% 97.60/13.22 ('#S') @ (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 =>) @
% 97.60/13.22 (
% 97.60/13.22 (
% 97.60/13.22 ('#C') @ in @
% 97.60/13.22 omega)))))) @
% 97.60/13.22 (
% 97.60/13.22 (
% 97.60/13.22 ('#S') @ (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 '#S') @
% 97.60/13.22 (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 =>))) @
% 97.60/13.22 (
% 97.60/13.22 (
% 97.60/13.22 ('#C') @ (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 '#B') @
% 97.60/13.22 (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 =) @
% 97.60/13.22 omegaS)))) @
% 97.60/13.22 omegaS)))))) @
% 97.60/13.22 (
% 97.60/13.22 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.60/13.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl789])).
% 97.60/13.22 thf(zip_derived_cl824, plain,
% 97.60/13.22 (~ (((eqimpsubset1) =>
% 97.60/13.22 (((subsetI2) =>
% 97.60/13.22 (((emptysetsubset) =>
% 97.60/13.22 (((subsetE) =>
% 97.60/13.22 (((subsetE2) =>
% 97.60/13.22 (((notsubsetI) =>
% 97.60/13.22 (((notequalI1) =>
% 97.60/13.22 (((notequalI2) =>
% 97.60/13.22 (((subsetRefl) =>
% 97.60/13.22 (((subsetTrans) =>
% 97.60/13.22 (((setadjoinSub) =>
% 97.60/13.22 (((setadjoinSub2) =>
% 97.60/13.22 (((subset2powerset) =>
% 97.60/13.22 (((setextsub) =>
% 97.60/13.22 (((subsetemptysetimpeq) =>
% 97.60/13.22 (((powersetI1) =>
% 97.60/13.22 (((powersetE1) =>
% 97.60/13.22 (((inPowerset) =>
% 97.60/13.22 (((powersetsubset) =>
% 97.60/13.22 (((sepInPowerset) =>
% 97.60/13.22 (((sepSubset) =>
% 97.60/13.22 (((binunionIL) =>
% 97.60/13.22 (((upairset2IR) =>
% 97.60/13.22 (((binunionIR) =>
% 97.60/13.22 (((binunionEcases) =>
% 97.60/13.22 (((binunionE) =>
% 97.60/13.22 (((binunionLsub) =>
% 97.60/13.22 (((binunionRsub) =>
% 97.60/13.22 (((binintersectI) =>
% 97.60/13.22 (((binintersectSubset5) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectEL) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectLsub) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectSubset2) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectSubset3) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectER) =>
% 97.60/13.22 ((
% 97.60/13.22 (disjointsetsI1) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectRsub) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectSubset4) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectSubset1) =>
% 97.60/13.22 ((
% 97.60/13.22 (bs114d) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusI) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusEL) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusER) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusSubset2) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusERneg) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusELneg) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusILneg) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusIRneg) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusLsub) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusSubset1) =>
% 97.60/13.22 ((
% 97.60/13.22 (symdiffE) =>
% 97.60/13.22 ((
% 97.60/13.22 (symdiffI1) =>
% 97.60/13.22 ((
% 97.60/13.22 (symdiffI2) =>
% 97.60/13.22 ((
% 97.60/13.22 (symdiffIneg1) =>
% 97.60/13.22 ((
% 97.60/13.22 (symdiffIneg2) =>
% 97.60/13.22 ((
% 97.60/13.22 (secondinupair) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairIL) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairIR) =>
% 97.60/13.22 ((
% 97.60/13.22 (kpairiskpair) =>
% 97.60/13.22 ((
% 97.60/13.22 (kpairp) =>
% 97.60/13.22 ((
% 97.60/13.22 (singletonsubset) =>
% 97.60/13.22 ((
% 97.60/13.22 (singletoninpowerset) =>
% 97.60/13.22 ((
% 97.60/13.22 (singletoninpowunion) =>
% 97.60/13.22 ((
% 97.60/13.22 (upairset2E) =>
% 97.60/13.22 ((
% 97.60/13.22 (upairsubunion) =>
% 97.60/13.22 ((
% 97.60/13.22 (upairinpowunion) =>
% 97.60/13.22 ((
% 97.60/13.22 (ubforcartprodlem1) =>
% 97.60/13.22 ((
% 97.60/13.22 (ubforcartprodlem2) =>
% 97.60/13.22 ((
% 97.60/13.22 (ubforcartprodlem3) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodpairin) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodmempair1) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodmempair) =>
% 97.60/13.22 ((
% 97.60/13.22 (setunionE2) =>
% 97.60/13.22 ((
% 97.60/13.22 (setunionsingleton1) =>
% 97.60/13.22 ((
% 97.60/13.22 (setunionsingleton2) =>
% 97.60/13.22 ((
% 97.60/13.22 (setunionsingleton) =>
% 97.60/13.22 ((
% 97.60/13.22 (singletonprop) =>
% 97.60/13.22 ((
% 97.60/13.22 (ex1E1) =>
% 97.60/13.22 ((
% 97.60/13.22 (ex1I) =>
% 97.60/13.22 ((
% 97.60/13.22 (ex1I2) =>
% 97.60/13.22 ((
% 97.60/13.22 (singletonsuniq) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjL1) =>
% 97.60/13.22 ((
% 97.60/13.22 (kfstsingleton) =>
% 97.60/13.22 ((
% 97.60/13.22 (theprop) =>
% 97.60/13.22 ((
% 97.60/13.22 (kfstpairEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodfstin) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjL2) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjL) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjR11) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjR12) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjR1) =>
% 97.60/13.22 ((
% 97.60/13.22 (upairequniteq) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjR2) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjR) =>
% 97.60/13.22 ((
% 97.60/13.22 (ksndsingleton) =>
% 97.60/13.22 ((
% 97.60/13.22 (ksndpairEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (kpairsurjEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodsndin) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodpairmemEL) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodpairmemER) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodmempaircEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodfstpairEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodsndpairEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodpairsurjEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (dpsetconstrI) =>
% 97.60/13.22 ((
% 97.60/13.22 (dpsetconstrSub) =>
% 97.60/13.22 ((
% 97.60/13.22 (setOfPairsIsBReln) =>
% 97.60/13.22 ((
% 97.60/13.22 (dpsetconstrERa) =>
% 97.60/13.22 ((
% 97.60/13.22 (dpsetconstrEL1) =>
% 97.60/13.22 ((
% 97.60/13.22 (dpsetconstrEL2) =>
% 97.60/13.22 ((
% 97.60/13.22 (dpsetconstrER) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcImageSingleton) =>
% 97.60/13.22 ((
% 97.60/13.22 (apProp) =>
% 97.60/13.22 ((
% 97.60/13.22 (app) =>
% 97.60/13.22 ((
% 97.60/13.22 (infuncsetfunc) =>
% 97.60/13.22 ((
% 97.60/13.22 (ap2p) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcinfuncset) =>
% 97.60/13.22 ((
% 97.60/13.22 (lamProp) =>
% 97.60/13.22 ((
% 97.60/13.22 (lamp) =>
% 97.60/13.22 ((
% 97.60/13.22 (lam2p) =>
% 97.60/13.22 ((
% 97.60/13.22 (brelnall1) =>
% 97.60/13.22 ((
% 97.60/13.22 (brelnall2) =>
% 97.60/13.22 ((
% 97.60/13.22 (ex1E2) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcGraphProp1) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcGraphProp3) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcGraphProp2) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcextLem) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcGraphProp4) =>
% 97.60/13.22 ((
% 97.60/13.22 (subbreln) =>
% 97.60/13.22 ((
% 97.60/13.22 (eqbreln) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcext) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcext2) =>
% 97.60/13.22 ((
% 97.60/13.22 (ap2apEq1) =>
% 97.60/13.22 ((
% 97.60/13.22 (ap2apEq2) =>
% 97.60/13.22 ((
% 97.60/13.22 (beta1) =>
% 97.60/13.22 ((
% 97.60/13.22 (eta1) =>
% 97.60/13.22 ((
% 97.60/13.22 (lam2lamEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (beta2) =>
% 97.60/13.22 ((
% 97.60/13.22 (eta2) =>
% 97.60/13.22 ((
% 97.60/13.22 (iffalseProp1) =>
% 97.60/13.22 ((
% 97.60/13.22 (iffalseProp2) =>
% 97.60/13.22 ((
% 97.60/13.22 (iftrueProp1) =>
% 97.60/13.22 ((
% 97.60/13.22 (iftrueProp2) =>
% 97.60/13.22 ((
% 97.60/13.22 (ifSingleton) =>
% 97.60/13.22 ((
% 97.60/13.22 (ifp) =>
% 97.60/13.22 ((
% 97.60/13.22 (theeq) =>
% 97.60/13.22 ((
% 97.60/13.22 (iftrue) =>
% 97.60/13.22 ((
% 97.60/13.22 (iffalse) =>
% 97.60/13.22 ((
% 97.60/13.22 (iftrueorfalse) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectT_lem) =>
% 97.60/13.22 ((
% 97.60/13.22 (binunionT_lem) =>
% 97.60/13.22 ((
% 97.60/13.22 (powersetT_lem) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusT_lem) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementT_lem) =>
% 97.60/13.22 ((
% 97.60/13.22 (setextT) =>
% 97.60/13.22 ((
% 97.60/13.22 (subsetTI) =>
% 97.60/13.22 ((
% 97.60/13.22 (powersetTI1) =>
% 97.60/13.22 ((
% 97.60/13.22 (powersetTE1) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementTI1) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementTE1) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectTELcontra) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectTERcontra) =>
% 97.60/13.22 ((
% 97.60/13.22 (contrasubsetT) =>
% 97.60/13.22 ((
% 97.60/13.22 (contrasubsetT1) =>
% 97.60/13.22 ((
% 97.60/13.22 (contrasubsetT2) =>
% 97.60/13.22 ((
% 97.60/13.22 (contrasubsetT3) =>
% 97.60/13.22 ((
% 97.60/13.22 (doubleComplementI1) =>
% 97.60/13.22 ((
% 97.60/13.22 (doubleComplementE1) =>
% 97.60/13.22 ((
% 97.60/13.22 (doubleComplementSub1) =>
% 97.60/13.22 ((
% 97.60/13.22 (doubleComplementSub2) =>
% 97.60/13.22 ((
% 97.60/13.22 (doubleComplementEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementTnotintersectT) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementImpComplementIntersect) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementSubsetComplementIntersect) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementInPowersetComplementIntersect) =>
% 97.60/13.22 ((
% 97.60/13.22 (contraSubsetComplement) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementTcontraSubset) =>
% 97.60/13.22 ((
% 97.60/13.22 (binunionTILcontra) =>
% 97.60/13.22 ((
% 97.60/13.22 (binunionTIRcontra) =>
% 97.60/13.22 ((
% 97.60/13.22 (inIntersectImpInUnion) =>
% 97.60/13.22 ((
% 97.60/13.22 (inIntersectImpInUnion2) =>
% 97.60/13.22 ((
% 97.60/13.22 (inIntersectImpInIntersectUnions) =>
% 97.60/13.22 ((
% 97.60/13.22 (intersectInPowersetIntersectUnions) =>
% 97.60/13.22 ((
% 97.60/13.22 (inComplementUnionImpNotIn1) =>
% 97.60/13.22 ((
% 97.60/13.22 (inComplementUnionImpInComplement1) =>
% 97.60/13.22 ((
% 97.60/13.22 (binunionTE) =>
% 97.60/13.22 ((
% 97.60/13.22 (binunionTEcontra) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan2a1) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementUnionInPowersetComplement) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan2a2) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan1a) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan1b) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan1) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan2a) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan2b2) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan2b) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan2) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz13rule0) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz13rule1) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz13rule2) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz13rule3) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz13rule4) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz1_1) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz1_2) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz1_3) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz1_4) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz1_5) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1all2) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1SetBreln1) =>
% 97.60/13.22 ((
% 97.60/13.22 (choice2fnsingleton) =>
% 97.60/13.22 ((
% 97.60/13.22 (setOfPairsIsBReln1) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1all1) =>
% 97.60/13.22 ((
% 97.60/13.22 (subbreln1) =>
% 97.60/13.22 ((
% 97.60/13.22 (eqbreln1) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1invprop) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1invI) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1invE) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1compprop) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1compI) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1compE) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1compEex) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1unionprop) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1unionIL) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1unionIR) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1unionI) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1unionE) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1unionEcases) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1unionCommutes) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz2Ex) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz2W) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz2A) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz2B) =>
% 97.60/13.22 ((
% 97.60/13.22 (image1Ex) =>
% 97.60/13.22 ((
% 97.60/13.22 (image1Ex1) =>
% 97.60/13.22 ((
% 97.60/13.22 (image1Equiv) =>
% 97.60/13.22 ((
% 97.60/13.22 (image1E) =>
% 97.60/13.22 ((
% 97.60/13.22 (image1I) =>
% 97.60/13.22 ((
% 97.60/13.22 (injFuncInInjFuncSet) =>
% 97.60/13.22 ((
% 97.60/13.22 (injFuncSetFuncIn) =>
% 97.60/13.22 ((
% 97.60/13.22 (injFuncSetFuncInj) =>
% 97.60/13.22 ((
% 97.60/13.22 (surjFuncSetFuncIn) =>
% 97.60/13.22 ((
% 97.60/13.22 (surjFuncSetFuncSurj) =>
% 97.60/13.22 ((
% 97.60/13.22 (leftInvIsSurj) =>
% 97.60/13.22 ((
% 97.60/13.22 (surjCantorThm) =>
% 97.60/13.22 ((
% 97.60/13.22 (foundation2) =>
% 97.60/13.22 ((
% 97.60/13.22 (notinself) =>
% 97.60/13.22 ((
% 97.60/13.22 (notinself2) =>
% 97.60/13.22 ((
% 97.60/13.22 (omegaSp) =>
% 97.60/13.22 ((
% 97.60/13.22 (omegaSclos) =>
% 97.60/13.22 ((
% 97.60/13.22 (peano0notS) =>
% 97.60/13.22 ((
% 97.60/13.22 (!!) @ (
% 97.60/13.22 (('#S') @ (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 =>) @
% 97.60/13.22 (
% 97.60/13.22 (
% 97.60/13.22 ('#C') @ in @
% 97.60/13.22 omega)))) @
% 97.60/13.22 (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 !!) @
% 97.60/13.22 (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 (
% 97.60/13.22 ('#S') @ (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 =>) @
% 97.60/13.22 (
% 97.60/13.22 (
% 97.60/13.22 ('#C') @ in @
% 97.60/13.22 omega)))))) @
% 97.60/13.22 (
% 97.60/13.22 (
% 97.60/13.22 ('#S') @ (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 '#S') @
% 97.60/13.22 (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 =>))) @
% 97.60/13.22 (
% 97.60/13.22 (
% 97.60/13.22 ('#C') @ (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 '#B') @
% 97.60/13.22 (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 =) @
% 97.60/13.22 omegaS)))) @
% 97.60/13.22 omegaS)))))) @
% 97.60/13.22 (
% 97.60/13.22 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.60/13.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl807])).
% 97.60/13.22 thf(zip_derived_cl838, plain,
% 97.60/13.22 (~ (((subsetI2) =>
% 97.60/13.22 (((emptysetsubset) =>
% 97.60/13.22 (((subsetE) =>
% 97.60/13.22 (((subsetE2) =>
% 97.60/13.22 (((notsubsetI) =>
% 97.60/13.22 (((notequalI1) =>
% 97.60/13.22 (((notequalI2) =>
% 97.60/13.22 (((subsetRefl) =>
% 97.60/13.22 (((subsetTrans) =>
% 97.60/13.22 (((setadjoinSub) =>
% 97.60/13.22 (((setadjoinSub2) =>
% 97.60/13.22 (((subset2powerset) =>
% 97.60/13.22 (((setextsub) =>
% 97.60/13.22 (((subsetemptysetimpeq) =>
% 97.60/13.22 (((powersetI1) =>
% 97.60/13.22 (((powersetE1) =>
% 97.60/13.22 (((inPowerset) =>
% 97.60/13.22 (((powersetsubset) =>
% 97.60/13.22 (((sepInPowerset) =>
% 97.60/13.22 (((sepSubset) =>
% 97.60/13.22 (((binunionIL) =>
% 97.60/13.22 (((upairset2IR) =>
% 97.60/13.22 (((binunionIR) =>
% 97.60/13.22 (((binunionEcases) =>
% 97.60/13.22 (((binunionE) =>
% 97.60/13.22 (((binunionLsub) =>
% 97.60/13.22 (((binunionRsub) =>
% 97.60/13.22 (((binintersectI) =>
% 97.60/13.22 (((binintersectSubset5) =>
% 97.60/13.22 (((binintersectEL) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectLsub) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectSubset2) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectSubset3) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectER) =>
% 97.60/13.22 ((
% 97.60/13.22 (disjointsetsI1) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectRsub) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectSubset4) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectSubset1) =>
% 97.60/13.22 ((
% 97.60/13.22 (bs114d) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusI) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusEL) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusER) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusSubset2) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusERneg) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusELneg) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusILneg) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusIRneg) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusLsub) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusSubset1) =>
% 97.60/13.22 ((
% 97.60/13.22 (symdiffE) =>
% 97.60/13.22 ((
% 97.60/13.22 (symdiffI1) =>
% 97.60/13.22 ((
% 97.60/13.22 (symdiffI2) =>
% 97.60/13.22 ((
% 97.60/13.22 (symdiffIneg1) =>
% 97.60/13.22 ((
% 97.60/13.22 (symdiffIneg2) =>
% 97.60/13.22 ((
% 97.60/13.22 (secondinupair) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairIL) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairIR) =>
% 97.60/13.22 ((
% 97.60/13.22 (kpairiskpair) =>
% 97.60/13.22 ((
% 97.60/13.22 (kpairp) =>
% 97.60/13.22 ((
% 97.60/13.22 (singletonsubset) =>
% 97.60/13.22 ((
% 97.60/13.22 (singletoninpowerset) =>
% 97.60/13.22 ((
% 97.60/13.22 (singletoninpowunion) =>
% 97.60/13.22 ((
% 97.60/13.22 (upairset2E) =>
% 97.60/13.22 ((
% 97.60/13.22 (upairsubunion) =>
% 97.60/13.22 ((
% 97.60/13.22 (upairinpowunion) =>
% 97.60/13.22 ((
% 97.60/13.22 (ubforcartprodlem1) =>
% 97.60/13.22 ((
% 97.60/13.22 (ubforcartprodlem2) =>
% 97.60/13.22 ((
% 97.60/13.22 (ubforcartprodlem3) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodpairin) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodmempair1) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodmempair) =>
% 97.60/13.22 ((
% 97.60/13.22 (setunionE2) =>
% 97.60/13.22 ((
% 97.60/13.22 (setunionsingleton1) =>
% 97.60/13.22 ((
% 97.60/13.22 (setunionsingleton2) =>
% 97.60/13.22 ((
% 97.60/13.22 (setunionsingleton) =>
% 97.60/13.22 ((
% 97.60/13.22 (singletonprop) =>
% 97.60/13.22 ((
% 97.60/13.22 (ex1E1) =>
% 97.60/13.22 ((
% 97.60/13.22 (ex1I) =>
% 97.60/13.22 ((
% 97.60/13.22 (ex1I2) =>
% 97.60/13.22 ((
% 97.60/13.22 (singletonsuniq) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjL1) =>
% 97.60/13.22 ((
% 97.60/13.22 (kfstsingleton) =>
% 97.60/13.22 ((
% 97.60/13.22 (theprop) =>
% 97.60/13.22 ((
% 97.60/13.22 (kfstpairEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodfstin) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjL2) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjL) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjR11) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjR12) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjR1) =>
% 97.60/13.22 ((
% 97.60/13.22 (upairequniteq) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjR2) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjR) =>
% 97.60/13.22 ((
% 97.60/13.22 (ksndsingleton) =>
% 97.60/13.22 ((
% 97.60/13.22 (ksndpairEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (kpairsurjEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodsndin) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodpairmemEL) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodpairmemER) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodmempaircEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodfstpairEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodsndpairEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodpairsurjEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (dpsetconstrI) =>
% 97.60/13.22 ((
% 97.60/13.22 (dpsetconstrSub) =>
% 97.60/13.22 ((
% 97.60/13.22 (setOfPairsIsBReln) =>
% 97.60/13.22 ((
% 97.60/13.22 (dpsetconstrERa) =>
% 97.60/13.22 ((
% 97.60/13.22 (dpsetconstrEL1) =>
% 97.60/13.22 ((
% 97.60/13.22 (dpsetconstrEL2) =>
% 97.60/13.22 ((
% 97.60/13.22 (dpsetconstrER) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcImageSingleton) =>
% 97.60/13.22 ((
% 97.60/13.22 (apProp) =>
% 97.60/13.22 ((
% 97.60/13.22 (app) =>
% 97.60/13.22 ((
% 97.60/13.22 (infuncsetfunc) =>
% 97.60/13.22 ((
% 97.60/13.22 (ap2p) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcinfuncset) =>
% 97.60/13.22 ((
% 97.60/13.22 (lamProp) =>
% 97.60/13.22 ((
% 97.60/13.22 (lamp) =>
% 97.60/13.22 ((
% 97.60/13.22 (lam2p) =>
% 97.60/13.22 ((
% 97.60/13.22 (brelnall1) =>
% 97.60/13.22 ((
% 97.60/13.22 (brelnall2) =>
% 97.60/13.22 ((
% 97.60/13.22 (ex1E2) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcGraphProp1) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcGraphProp3) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcGraphProp2) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcextLem) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcGraphProp4) =>
% 97.60/13.22 ((
% 97.60/13.22 (subbreln) =>
% 97.60/13.22 ((
% 97.60/13.22 (eqbreln) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcext) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcext2) =>
% 97.60/13.22 ((
% 97.60/13.22 (ap2apEq1) =>
% 97.60/13.22 ((
% 97.60/13.22 (ap2apEq2) =>
% 97.60/13.22 ((
% 97.60/13.22 (beta1) =>
% 97.60/13.22 ((
% 97.60/13.22 (eta1) =>
% 97.60/13.22 ((
% 97.60/13.22 (lam2lamEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (beta2) =>
% 97.60/13.22 ((
% 97.60/13.22 (eta2) =>
% 97.60/13.22 ((
% 97.60/13.22 (iffalseProp1) =>
% 97.60/13.22 ((
% 97.60/13.22 (iffalseProp2) =>
% 97.60/13.22 ((
% 97.60/13.22 (iftrueProp1) =>
% 97.60/13.22 ((
% 97.60/13.22 (iftrueProp2) =>
% 97.60/13.22 ((
% 97.60/13.22 (ifSingleton) =>
% 97.60/13.22 ((
% 97.60/13.22 (ifp) =>
% 97.60/13.22 ((
% 97.60/13.22 (theeq) =>
% 97.60/13.22 ((
% 97.60/13.22 (iftrue) =>
% 97.60/13.22 ((
% 97.60/13.22 (iffalse) =>
% 97.60/13.22 ((
% 97.60/13.22 (iftrueorfalse) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectT_lem) =>
% 97.60/13.22 ((
% 97.60/13.22 (binunionT_lem) =>
% 97.60/13.22 ((
% 97.60/13.22 (powersetT_lem) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusT_lem) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementT_lem) =>
% 97.60/13.22 ((
% 97.60/13.22 (setextT) =>
% 97.60/13.22 ((
% 97.60/13.22 (subsetTI) =>
% 97.60/13.22 ((
% 97.60/13.22 (powersetTI1) =>
% 97.60/13.22 ((
% 97.60/13.22 (powersetTE1) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementTI1) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementTE1) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectTELcontra) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectTERcontra) =>
% 97.60/13.22 ((
% 97.60/13.22 (contrasubsetT) =>
% 97.60/13.22 ((
% 97.60/13.22 (contrasubsetT1) =>
% 97.60/13.22 ((
% 97.60/13.22 (contrasubsetT2) =>
% 97.60/13.22 ((
% 97.60/13.22 (contrasubsetT3) =>
% 97.60/13.22 ((
% 97.60/13.22 (doubleComplementI1) =>
% 97.60/13.22 ((
% 97.60/13.22 (doubleComplementE1) =>
% 97.60/13.22 ((
% 97.60/13.22 (doubleComplementSub1) =>
% 97.60/13.22 ((
% 97.60/13.22 (doubleComplementSub2) =>
% 97.60/13.22 ((
% 97.60/13.22 (doubleComplementEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementTnotintersectT) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementImpComplementIntersect) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementSubsetComplementIntersect) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementInPowersetComplementIntersect) =>
% 97.60/13.22 ((
% 97.60/13.22 (contraSubsetComplement) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementTcontraSubset) =>
% 97.60/13.22 ((
% 97.60/13.22 (binunionTILcontra) =>
% 97.60/13.22 ((
% 97.60/13.22 (binunionTIRcontra) =>
% 97.60/13.22 ((
% 97.60/13.22 (inIntersectImpInUnion) =>
% 97.60/13.22 ((
% 97.60/13.22 (inIntersectImpInUnion2) =>
% 97.60/13.22 ((
% 97.60/13.22 (inIntersectImpInIntersectUnions) =>
% 97.60/13.22 ((
% 97.60/13.22 (intersectInPowersetIntersectUnions) =>
% 97.60/13.22 ((
% 97.60/13.22 (inComplementUnionImpNotIn1) =>
% 97.60/13.22 ((
% 97.60/13.22 (inComplementUnionImpInComplement1) =>
% 97.60/13.22 ((
% 97.60/13.22 (binunionTE) =>
% 97.60/13.22 ((
% 97.60/13.22 (binunionTEcontra) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan2a1) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementUnionInPowersetComplement) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan2a2) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan1a) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan1b) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan1) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan2a) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan2b2) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan2b) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan2) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz13rule0) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz13rule1) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz13rule2) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz13rule3) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz13rule4) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz1_1) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz1_2) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz1_3) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz1_4) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz1_5) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1all2) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1SetBreln1) =>
% 97.60/13.22 ((
% 97.60/13.22 (choice2fnsingleton) =>
% 97.60/13.22 ((
% 97.60/13.22 (setOfPairsIsBReln1) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1all1) =>
% 97.60/13.22 ((
% 97.60/13.22 (subbreln1) =>
% 97.60/13.22 ((
% 97.60/13.22 (eqbreln1) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1invprop) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1invI) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1invE) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1compprop) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1compI) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1compE) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1compEex) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1unionprop) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1unionIL) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1unionIR) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1unionI) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1unionE) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1unionEcases) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1unionCommutes) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz2Ex) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz2W) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz2A) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz2B) =>
% 97.60/13.22 ((
% 97.60/13.22 (image1Ex) =>
% 97.60/13.22 ((
% 97.60/13.22 (image1Ex1) =>
% 97.60/13.22 ((
% 97.60/13.22 (image1Equiv) =>
% 97.60/13.22 ((
% 97.60/13.22 (image1E) =>
% 97.60/13.22 ((
% 97.60/13.22 (image1I) =>
% 97.60/13.22 ((
% 97.60/13.22 (injFuncInInjFuncSet) =>
% 97.60/13.22 ((
% 97.60/13.22 (injFuncSetFuncIn) =>
% 97.60/13.22 ((
% 97.60/13.22 (injFuncSetFuncInj) =>
% 97.60/13.22 ((
% 97.60/13.22 (surjFuncSetFuncIn) =>
% 97.60/13.22 ((
% 97.60/13.22 (surjFuncSetFuncSurj) =>
% 97.60/13.22 ((
% 97.60/13.22 (leftInvIsSurj) =>
% 97.60/13.22 ((
% 97.60/13.22 (surjCantorThm) =>
% 97.60/13.22 ((
% 97.60/13.22 (foundation2) =>
% 97.60/13.22 ((
% 97.60/13.22 (notinself) =>
% 97.60/13.22 ((
% 97.60/13.22 (notinself2) =>
% 97.60/13.22 ((
% 97.60/13.22 (omegaSp) =>
% 97.60/13.22 ((
% 97.60/13.22 (omegaSclos) =>
% 97.60/13.22 ((
% 97.60/13.22 (peano0notS) =>
% 97.60/13.22 ((
% 97.60/13.22 (!!) @ (
% 97.60/13.22 (('#S') @ (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 =>) @
% 97.60/13.22 (
% 97.60/13.22 (
% 97.60/13.22 ('#C') @ in @
% 97.60/13.22 omega)))) @
% 97.60/13.22 (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 !!) @
% 97.60/13.22 (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 (
% 97.60/13.22 ('#S') @ (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 =>) @
% 97.60/13.22 (
% 97.60/13.22 (
% 97.60/13.22 ('#C') @ in @
% 97.60/13.22 omega)))))) @
% 97.60/13.22 (
% 97.60/13.22 (
% 97.60/13.22 ('#S') @ (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 '#S') @
% 97.60/13.22 (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 =>))) @
% 97.60/13.22 (
% 97.60/13.22 (
% 97.60/13.22 ('#C') @ (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 '#B') @
% 97.60/13.22 (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 =) @
% 97.60/13.22 omegaS)))) @
% 97.60/13.22 omegaS)))))) @
% 97.60/13.22 (
% 97.60/13.22 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.60/13.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl824])).
% 97.60/13.22 thf(zip_derived_cl850, plain,
% 97.60/13.22 (~ (((emptysetsubset) =>
% 97.60/13.22 (((subsetE) =>
% 97.60/13.22 (((subsetE2) =>
% 97.60/13.22 (((notsubsetI) =>
% 97.60/13.22 (((notequalI1) =>
% 97.60/13.22 (((notequalI2) =>
% 97.60/13.22 (((subsetRefl) =>
% 97.60/13.22 (((subsetTrans) =>
% 97.60/13.22 (((setadjoinSub) =>
% 97.60/13.22 (((setadjoinSub2) =>
% 97.60/13.22 (((subset2powerset) =>
% 97.60/13.22 (((setextsub) =>
% 97.60/13.22 (((subsetemptysetimpeq) =>
% 97.60/13.22 (((powersetI1) =>
% 97.60/13.22 (((powersetE1) =>
% 97.60/13.22 (((inPowerset) =>
% 97.60/13.22 (((powersetsubset) =>
% 97.60/13.22 (((sepInPowerset) =>
% 97.60/13.22 (((sepSubset) =>
% 97.60/13.22 (((binunionIL) =>
% 97.60/13.22 (((upairset2IR) =>
% 97.60/13.22 (((binunionIR) =>
% 97.60/13.22 (((binunionEcases) =>
% 97.60/13.22 (((binunionE) =>
% 97.60/13.22 (((binunionLsub) =>
% 97.60/13.22 (((binunionRsub) =>
% 97.60/13.22 (((binintersectI) =>
% 97.60/13.22 (((binintersectSubset5) =>
% 97.60/13.22 (((binintersectEL) =>
% 97.60/13.22 (((binintersectLsub) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectSubset2) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectSubset3) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectER) =>
% 97.60/13.22 ((
% 97.60/13.22 (disjointsetsI1) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectRsub) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectSubset4) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectSubset1) =>
% 97.60/13.22 ((
% 97.60/13.22 (bs114d) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusI) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusEL) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusER) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusSubset2) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusERneg) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusELneg) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusILneg) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusIRneg) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusLsub) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusSubset1) =>
% 97.60/13.22 ((
% 97.60/13.22 (symdiffE) =>
% 97.60/13.22 ((
% 97.60/13.22 (symdiffI1) =>
% 97.60/13.22 ((
% 97.60/13.22 (symdiffI2) =>
% 97.60/13.22 ((
% 97.60/13.22 (symdiffIneg1) =>
% 97.60/13.22 ((
% 97.60/13.22 (symdiffIneg2) =>
% 97.60/13.22 ((
% 97.60/13.22 (secondinupair) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairIL) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairIR) =>
% 97.60/13.22 ((
% 97.60/13.22 (kpairiskpair) =>
% 97.60/13.22 ((
% 97.60/13.22 (kpairp) =>
% 97.60/13.22 ((
% 97.60/13.22 (singletonsubset) =>
% 97.60/13.22 ((
% 97.60/13.22 (singletoninpowerset) =>
% 97.60/13.22 ((
% 97.60/13.22 (singletoninpowunion) =>
% 97.60/13.22 ((
% 97.60/13.22 (upairset2E) =>
% 97.60/13.22 ((
% 97.60/13.22 (upairsubunion) =>
% 97.60/13.22 ((
% 97.60/13.22 (upairinpowunion) =>
% 97.60/13.22 ((
% 97.60/13.22 (ubforcartprodlem1) =>
% 97.60/13.22 ((
% 97.60/13.22 (ubforcartprodlem2) =>
% 97.60/13.22 ((
% 97.60/13.22 (ubforcartprodlem3) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodpairin) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodmempair1) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodmempair) =>
% 97.60/13.22 ((
% 97.60/13.22 (setunionE2) =>
% 97.60/13.22 ((
% 97.60/13.22 (setunionsingleton1) =>
% 97.60/13.22 ((
% 97.60/13.22 (setunionsingleton2) =>
% 97.60/13.22 ((
% 97.60/13.22 (setunionsingleton) =>
% 97.60/13.22 ((
% 97.60/13.22 (singletonprop) =>
% 97.60/13.22 ((
% 97.60/13.22 (ex1E1) =>
% 97.60/13.22 ((
% 97.60/13.22 (ex1I) =>
% 97.60/13.22 ((
% 97.60/13.22 (ex1I2) =>
% 97.60/13.22 ((
% 97.60/13.22 (singletonsuniq) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjL1) =>
% 97.60/13.22 ((
% 97.60/13.22 (kfstsingleton) =>
% 97.60/13.22 ((
% 97.60/13.22 (theprop) =>
% 97.60/13.22 ((
% 97.60/13.22 (kfstpairEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodfstin) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjL2) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjL) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjR11) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjR12) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjR1) =>
% 97.60/13.22 ((
% 97.60/13.22 (upairequniteq) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjR2) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjR) =>
% 97.60/13.22 ((
% 97.60/13.22 (ksndsingleton) =>
% 97.60/13.22 ((
% 97.60/13.22 (ksndpairEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (kpairsurjEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodsndin) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodpairmemEL) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodpairmemER) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodmempaircEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodfstpairEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodsndpairEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodpairsurjEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (dpsetconstrI) =>
% 97.60/13.22 ((
% 97.60/13.22 (dpsetconstrSub) =>
% 97.60/13.22 ((
% 97.60/13.22 (setOfPairsIsBReln) =>
% 97.60/13.22 ((
% 97.60/13.22 (dpsetconstrERa) =>
% 97.60/13.22 ((
% 97.60/13.22 (dpsetconstrEL1) =>
% 97.60/13.22 ((
% 97.60/13.22 (dpsetconstrEL2) =>
% 97.60/13.22 ((
% 97.60/13.22 (dpsetconstrER) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcImageSingleton) =>
% 97.60/13.22 ((
% 97.60/13.22 (apProp) =>
% 97.60/13.22 ((
% 97.60/13.22 (app) =>
% 97.60/13.22 ((
% 97.60/13.22 (infuncsetfunc) =>
% 97.60/13.22 ((
% 97.60/13.22 (ap2p) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcinfuncset) =>
% 97.60/13.22 ((
% 97.60/13.22 (lamProp) =>
% 97.60/13.22 ((
% 97.60/13.22 (lamp) =>
% 97.60/13.22 ((
% 97.60/13.22 (lam2p) =>
% 97.60/13.22 ((
% 97.60/13.22 (brelnall1) =>
% 97.60/13.22 ((
% 97.60/13.22 (brelnall2) =>
% 97.60/13.22 ((
% 97.60/13.22 (ex1E2) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcGraphProp1) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcGraphProp3) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcGraphProp2) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcextLem) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcGraphProp4) =>
% 97.60/13.22 ((
% 97.60/13.22 (subbreln) =>
% 97.60/13.22 ((
% 97.60/13.22 (eqbreln) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcext) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcext2) =>
% 97.60/13.22 ((
% 97.60/13.22 (ap2apEq1) =>
% 97.60/13.22 ((
% 97.60/13.22 (ap2apEq2) =>
% 97.60/13.22 ((
% 97.60/13.22 (beta1) =>
% 97.60/13.22 ((
% 97.60/13.22 (eta1) =>
% 97.60/13.22 ((
% 97.60/13.22 (lam2lamEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (beta2) =>
% 97.60/13.22 ((
% 97.60/13.22 (eta2) =>
% 97.60/13.22 ((
% 97.60/13.22 (iffalseProp1) =>
% 97.60/13.22 ((
% 97.60/13.22 (iffalseProp2) =>
% 97.60/13.22 ((
% 97.60/13.22 (iftrueProp1) =>
% 97.60/13.22 ((
% 97.60/13.22 (iftrueProp2) =>
% 97.60/13.22 ((
% 97.60/13.22 (ifSingleton) =>
% 97.60/13.22 ((
% 97.60/13.22 (ifp) =>
% 97.60/13.22 ((
% 97.60/13.22 (theeq) =>
% 97.60/13.22 ((
% 97.60/13.22 (iftrue) =>
% 97.60/13.22 ((
% 97.60/13.22 (iffalse) =>
% 97.60/13.22 ((
% 97.60/13.22 (iftrueorfalse) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectT_lem) =>
% 97.60/13.22 ((
% 97.60/13.22 (binunionT_lem) =>
% 97.60/13.22 ((
% 97.60/13.22 (powersetT_lem) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusT_lem) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementT_lem) =>
% 97.60/13.22 ((
% 97.60/13.22 (setextT) =>
% 97.60/13.22 ((
% 97.60/13.22 (subsetTI) =>
% 97.60/13.22 ((
% 97.60/13.22 (powersetTI1) =>
% 97.60/13.22 ((
% 97.60/13.22 (powersetTE1) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementTI1) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementTE1) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectTELcontra) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectTERcontra) =>
% 97.60/13.22 ((
% 97.60/13.22 (contrasubsetT) =>
% 97.60/13.22 ((
% 97.60/13.22 (contrasubsetT1) =>
% 97.60/13.22 ((
% 97.60/13.22 (contrasubsetT2) =>
% 97.60/13.22 ((
% 97.60/13.22 (contrasubsetT3) =>
% 97.60/13.22 ((
% 97.60/13.22 (doubleComplementI1) =>
% 97.60/13.22 ((
% 97.60/13.22 (doubleComplementE1) =>
% 97.60/13.22 ((
% 97.60/13.22 (doubleComplementSub1) =>
% 97.60/13.22 ((
% 97.60/13.22 (doubleComplementSub2) =>
% 97.60/13.22 ((
% 97.60/13.22 (doubleComplementEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementTnotintersectT) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementImpComplementIntersect) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementSubsetComplementIntersect) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementInPowersetComplementIntersect) =>
% 97.60/13.22 ((
% 97.60/13.22 (contraSubsetComplement) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementTcontraSubset) =>
% 97.60/13.22 ((
% 97.60/13.22 (binunionTILcontra) =>
% 97.60/13.22 ((
% 97.60/13.22 (binunionTIRcontra) =>
% 97.60/13.22 ((
% 97.60/13.22 (inIntersectImpInUnion) =>
% 97.60/13.22 ((
% 97.60/13.22 (inIntersectImpInUnion2) =>
% 97.60/13.22 ((
% 97.60/13.22 (inIntersectImpInIntersectUnions) =>
% 97.60/13.22 ((
% 97.60/13.22 (intersectInPowersetIntersectUnions) =>
% 97.60/13.22 ((
% 97.60/13.22 (inComplementUnionImpNotIn1) =>
% 97.60/13.22 ((
% 97.60/13.22 (inComplementUnionImpInComplement1) =>
% 97.60/13.22 ((
% 97.60/13.22 (binunionTE) =>
% 97.60/13.22 ((
% 97.60/13.22 (binunionTEcontra) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan2a1) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementUnionInPowersetComplement) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan2a2) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan1a) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan1b) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan1) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan2a) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan2b2) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan2b) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan2) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz13rule0) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz13rule1) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz13rule2) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz13rule3) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz13rule4) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz1_1) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz1_2) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz1_3) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz1_4) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz1_5) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1all2) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1SetBreln1) =>
% 97.60/13.22 ((
% 97.60/13.22 (choice2fnsingleton) =>
% 97.60/13.22 ((
% 97.60/13.22 (setOfPairsIsBReln1) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1all1) =>
% 97.60/13.22 ((
% 97.60/13.22 (subbreln1) =>
% 97.60/13.22 ((
% 97.60/13.22 (eqbreln1) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1invprop) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1invI) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1invE) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1compprop) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1compI) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1compE) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1compEex) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1unionprop) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1unionIL) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1unionIR) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1unionI) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1unionE) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1unionEcases) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1unionCommutes) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz2Ex) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz2W) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz2A) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz2B) =>
% 97.60/13.22 ((
% 97.60/13.22 (image1Ex) =>
% 97.60/13.22 ((
% 97.60/13.22 (image1Ex1) =>
% 97.60/13.22 ((
% 97.60/13.22 (image1Equiv) =>
% 97.60/13.22 ((
% 97.60/13.22 (image1E) =>
% 97.60/13.22 ((
% 97.60/13.22 (image1I) =>
% 97.60/13.22 ((
% 97.60/13.22 (injFuncInInjFuncSet) =>
% 97.60/13.22 ((
% 97.60/13.22 (injFuncSetFuncIn) =>
% 97.60/13.22 ((
% 97.60/13.22 (injFuncSetFuncInj) =>
% 97.60/13.22 ((
% 97.60/13.22 (surjFuncSetFuncIn) =>
% 97.60/13.22 ((
% 97.60/13.22 (surjFuncSetFuncSurj) =>
% 97.60/13.22 ((
% 97.60/13.22 (leftInvIsSurj) =>
% 97.60/13.22 ((
% 97.60/13.22 (surjCantorThm) =>
% 97.60/13.22 ((
% 97.60/13.22 (foundation2) =>
% 97.60/13.22 ((
% 97.60/13.22 (notinself) =>
% 97.60/13.22 ((
% 97.60/13.22 (notinself2) =>
% 97.60/13.22 ((
% 97.60/13.22 (omegaSp) =>
% 97.60/13.22 ((
% 97.60/13.22 (omegaSclos) =>
% 97.60/13.22 ((
% 97.60/13.22 (peano0notS) =>
% 97.60/13.22 ((
% 97.60/13.22 (!!) @ (
% 97.60/13.22 (('#S') @ (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 =>) @
% 97.60/13.22 (
% 97.60/13.22 (
% 97.60/13.22 ('#C') @ in @
% 97.60/13.22 omega)))) @
% 97.60/13.22 (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 !!) @
% 97.60/13.22 (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 (
% 97.60/13.22 ('#S') @ (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 =>) @
% 97.60/13.22 (
% 97.60/13.22 (
% 97.60/13.22 ('#C') @ in @
% 97.60/13.22 omega)))))) @
% 97.60/13.22 (
% 97.60/13.22 (
% 97.60/13.22 ('#S') @ (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 '#S') @
% 97.60/13.22 (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 =>))) @
% 97.60/13.22 (
% 97.60/13.22 (
% 97.60/13.22 ('#C') @ (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 '#B') @
% 97.60/13.22 (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 =) @
% 97.60/13.22 omegaS)))) @
% 97.60/13.22 omegaS)))))) @
% 97.60/13.22 (
% 97.60/13.22 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.60/13.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl838])).
% 97.60/13.22 thf(zip_derived_cl863, plain,
% 97.60/13.22 (~ (((subsetE) =>
% 97.60/13.22 (((subsetE2) =>
% 97.60/13.22 (((notsubsetI) =>
% 97.60/13.22 (((notequalI1) =>
% 97.60/13.22 (((notequalI2) =>
% 97.60/13.22 (((subsetRefl) =>
% 97.60/13.22 (((subsetTrans) =>
% 97.60/13.22 (((setadjoinSub) =>
% 97.60/13.22 (((setadjoinSub2) =>
% 97.60/13.22 (((subset2powerset) =>
% 97.60/13.22 (((setextsub) =>
% 97.60/13.22 (((subsetemptysetimpeq) =>
% 97.60/13.22 (((powersetI1) =>
% 97.60/13.22 (((powersetE1) =>
% 97.60/13.22 (((inPowerset) =>
% 97.60/13.22 (((powersetsubset) =>
% 97.60/13.22 (((sepInPowerset) =>
% 97.60/13.22 (((sepSubset) =>
% 97.60/13.22 (((binunionIL) =>
% 97.60/13.22 (((upairset2IR) =>
% 97.60/13.22 (((binunionIR) =>
% 97.60/13.22 (((binunionEcases) =>
% 97.60/13.22 (((binunionE) =>
% 97.60/13.22 (((binunionLsub) =>
% 97.60/13.22 (((binunionRsub) =>
% 97.60/13.22 (((binintersectI) =>
% 97.60/13.22 (((binintersectSubset5) =>
% 97.60/13.22 (((binintersectEL) =>
% 97.60/13.22 (((binintersectLsub) =>
% 97.60/13.22 (((binintersectSubset2) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectSubset3) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectER) =>
% 97.60/13.22 ((
% 97.60/13.22 (disjointsetsI1) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectRsub) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectSubset4) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectSubset1) =>
% 97.60/13.22 ((
% 97.60/13.22 (bs114d) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusI) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusEL) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusER) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusSubset2) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusERneg) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusELneg) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusILneg) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusIRneg) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusLsub) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusSubset1) =>
% 97.60/13.22 ((
% 97.60/13.22 (symdiffE) =>
% 97.60/13.22 ((
% 97.60/13.22 (symdiffI1) =>
% 97.60/13.22 ((
% 97.60/13.22 (symdiffI2) =>
% 97.60/13.22 ((
% 97.60/13.22 (symdiffIneg1) =>
% 97.60/13.22 ((
% 97.60/13.22 (symdiffIneg2) =>
% 97.60/13.22 ((
% 97.60/13.22 (secondinupair) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairIL) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairIR) =>
% 97.60/13.22 ((
% 97.60/13.22 (kpairiskpair) =>
% 97.60/13.22 ((
% 97.60/13.22 (kpairp) =>
% 97.60/13.22 ((
% 97.60/13.22 (singletonsubset) =>
% 97.60/13.22 ((
% 97.60/13.22 (singletoninpowerset) =>
% 97.60/13.22 ((
% 97.60/13.22 (singletoninpowunion) =>
% 97.60/13.22 ((
% 97.60/13.22 (upairset2E) =>
% 97.60/13.22 ((
% 97.60/13.22 (upairsubunion) =>
% 97.60/13.22 ((
% 97.60/13.22 (upairinpowunion) =>
% 97.60/13.22 ((
% 97.60/13.22 (ubforcartprodlem1) =>
% 97.60/13.22 ((
% 97.60/13.22 (ubforcartprodlem2) =>
% 97.60/13.22 ((
% 97.60/13.22 (ubforcartprodlem3) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodpairin) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodmempair1) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodmempair) =>
% 97.60/13.22 ((
% 97.60/13.22 (setunionE2) =>
% 97.60/13.22 ((
% 97.60/13.22 (setunionsingleton1) =>
% 97.60/13.22 ((
% 97.60/13.22 (setunionsingleton2) =>
% 97.60/13.22 ((
% 97.60/13.22 (setunionsingleton) =>
% 97.60/13.22 ((
% 97.60/13.22 (singletonprop) =>
% 97.60/13.22 ((
% 97.60/13.22 (ex1E1) =>
% 97.60/13.22 ((
% 97.60/13.22 (ex1I) =>
% 97.60/13.22 ((
% 97.60/13.22 (ex1I2) =>
% 97.60/13.22 ((
% 97.60/13.22 (singletonsuniq) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjL1) =>
% 97.60/13.22 ((
% 97.60/13.22 (kfstsingleton) =>
% 97.60/13.22 ((
% 97.60/13.22 (theprop) =>
% 97.60/13.22 ((
% 97.60/13.22 (kfstpairEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodfstin) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjL2) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjL) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjR11) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjR12) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjR1) =>
% 97.60/13.22 ((
% 97.60/13.22 (upairequniteq) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjR2) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjR) =>
% 97.60/13.22 ((
% 97.60/13.22 (ksndsingleton) =>
% 97.60/13.22 ((
% 97.60/13.22 (ksndpairEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (kpairsurjEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodsndin) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodpairmemEL) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodpairmemER) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodmempaircEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodfstpairEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodsndpairEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodpairsurjEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (dpsetconstrI) =>
% 97.60/13.22 ((
% 97.60/13.22 (dpsetconstrSub) =>
% 97.60/13.22 ((
% 97.60/13.22 (setOfPairsIsBReln) =>
% 97.60/13.22 ((
% 97.60/13.22 (dpsetconstrERa) =>
% 97.60/13.22 ((
% 97.60/13.22 (dpsetconstrEL1) =>
% 97.60/13.22 ((
% 97.60/13.22 (dpsetconstrEL2) =>
% 97.60/13.22 ((
% 97.60/13.22 (dpsetconstrER) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcImageSingleton) =>
% 97.60/13.22 ((
% 97.60/13.22 (apProp) =>
% 97.60/13.22 ((
% 97.60/13.22 (app) =>
% 97.60/13.22 ((
% 97.60/13.22 (infuncsetfunc) =>
% 97.60/13.22 ((
% 97.60/13.22 (ap2p) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcinfuncset) =>
% 97.60/13.22 ((
% 97.60/13.22 (lamProp) =>
% 97.60/13.22 ((
% 97.60/13.22 (lamp) =>
% 97.60/13.22 ((
% 97.60/13.22 (lam2p) =>
% 97.60/13.22 ((
% 97.60/13.22 (brelnall1) =>
% 97.60/13.22 ((
% 97.60/13.22 (brelnall2) =>
% 97.60/13.22 ((
% 97.60/13.22 (ex1E2) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcGraphProp1) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcGraphProp3) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcGraphProp2) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcextLem) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcGraphProp4) =>
% 97.60/13.22 ((
% 97.60/13.22 (subbreln) =>
% 97.60/13.22 ((
% 97.60/13.22 (eqbreln) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcext) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcext2) =>
% 97.60/13.22 ((
% 97.60/13.22 (ap2apEq1) =>
% 97.60/13.22 ((
% 97.60/13.22 (ap2apEq2) =>
% 97.60/13.22 ((
% 97.60/13.22 (beta1) =>
% 97.60/13.22 ((
% 97.60/13.22 (eta1) =>
% 97.60/13.22 ((
% 97.60/13.22 (lam2lamEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (beta2) =>
% 97.60/13.22 ((
% 97.60/13.22 (eta2) =>
% 97.60/13.22 ((
% 97.60/13.22 (iffalseProp1) =>
% 97.60/13.22 ((
% 97.60/13.22 (iffalseProp2) =>
% 97.60/13.22 ((
% 97.60/13.22 (iftrueProp1) =>
% 97.60/13.22 ((
% 97.60/13.22 (iftrueProp2) =>
% 97.60/13.22 ((
% 97.60/13.22 (ifSingleton) =>
% 97.60/13.22 ((
% 97.60/13.22 (ifp) =>
% 97.60/13.22 ((
% 97.60/13.22 (theeq) =>
% 97.60/13.22 ((
% 97.60/13.22 (iftrue) =>
% 97.60/13.22 ((
% 97.60/13.22 (iffalse) =>
% 97.60/13.22 ((
% 97.60/13.22 (iftrueorfalse) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectT_lem) =>
% 97.60/13.22 ((
% 97.60/13.22 (binunionT_lem) =>
% 97.60/13.22 ((
% 97.60/13.22 (powersetT_lem) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusT_lem) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementT_lem) =>
% 97.60/13.22 ((
% 97.60/13.22 (setextT) =>
% 97.60/13.22 ((
% 97.60/13.22 (subsetTI) =>
% 97.60/13.22 ((
% 97.60/13.22 (powersetTI1) =>
% 97.60/13.22 ((
% 97.60/13.22 (powersetTE1) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementTI1) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementTE1) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectTELcontra) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectTERcontra) =>
% 97.60/13.22 ((
% 97.60/13.22 (contrasubsetT) =>
% 97.60/13.22 ((
% 97.60/13.22 (contrasubsetT1) =>
% 97.60/13.22 ((
% 97.60/13.22 (contrasubsetT2) =>
% 97.60/13.22 ((
% 97.60/13.22 (contrasubsetT3) =>
% 97.60/13.22 ((
% 97.60/13.22 (doubleComplementI1) =>
% 97.60/13.22 ((
% 97.60/13.22 (doubleComplementE1) =>
% 97.60/13.22 ((
% 97.60/13.22 (doubleComplementSub1) =>
% 97.60/13.22 ((
% 97.60/13.22 (doubleComplementSub2) =>
% 97.60/13.22 ((
% 97.60/13.22 (doubleComplementEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementTnotintersectT) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementImpComplementIntersect) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementSubsetComplementIntersect) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementInPowersetComplementIntersect) =>
% 97.60/13.22 ((
% 97.60/13.22 (contraSubsetComplement) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementTcontraSubset) =>
% 97.60/13.22 ((
% 97.60/13.22 (binunionTILcontra) =>
% 97.60/13.22 ((
% 97.60/13.22 (binunionTIRcontra) =>
% 97.60/13.22 ((
% 97.60/13.22 (inIntersectImpInUnion) =>
% 97.60/13.22 ((
% 97.60/13.22 (inIntersectImpInUnion2) =>
% 97.60/13.22 ((
% 97.60/13.22 (inIntersectImpInIntersectUnions) =>
% 97.60/13.22 ((
% 97.60/13.22 (intersectInPowersetIntersectUnions) =>
% 97.60/13.22 ((
% 97.60/13.22 (inComplementUnionImpNotIn1) =>
% 97.60/13.22 ((
% 97.60/13.22 (inComplementUnionImpInComplement1) =>
% 97.60/13.22 ((
% 97.60/13.22 (binunionTE) =>
% 97.60/13.22 ((
% 97.60/13.22 (binunionTEcontra) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan2a1) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementUnionInPowersetComplement) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan2a2) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan1a) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan1b) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan1) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan2a) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan2b2) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan2b) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan2) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz13rule0) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz13rule1) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz13rule2) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz13rule3) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz13rule4) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz1_1) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz1_2) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz1_3) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz1_4) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz1_5) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1all2) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1SetBreln1) =>
% 97.60/13.22 ((
% 97.60/13.22 (choice2fnsingleton) =>
% 97.60/13.22 ((
% 97.60/13.22 (setOfPairsIsBReln1) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1all1) =>
% 97.60/13.22 ((
% 97.60/13.22 (subbreln1) =>
% 97.60/13.22 ((
% 97.60/13.22 (eqbreln1) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1invprop) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1invI) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1invE) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1compprop) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1compI) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1compE) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1compEex) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1unionprop) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1unionIL) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1unionIR) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1unionI) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1unionE) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1unionEcases) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1unionCommutes) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz2Ex) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz2W) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz2A) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz2B) =>
% 97.60/13.22 ((
% 97.60/13.22 (image1Ex) =>
% 97.60/13.22 ((
% 97.60/13.22 (image1Ex1) =>
% 97.60/13.22 ((
% 97.60/13.22 (image1Equiv) =>
% 97.60/13.22 ((
% 97.60/13.22 (image1E) =>
% 97.60/13.22 ((
% 97.60/13.22 (image1I) =>
% 97.60/13.22 ((
% 97.60/13.22 (injFuncInInjFuncSet) =>
% 97.60/13.22 ((
% 97.60/13.22 (injFuncSetFuncIn) =>
% 97.60/13.22 ((
% 97.60/13.22 (injFuncSetFuncInj) =>
% 97.60/13.22 ((
% 97.60/13.22 (surjFuncSetFuncIn) =>
% 97.60/13.22 ((
% 97.60/13.22 (surjFuncSetFuncSurj) =>
% 97.60/13.22 ((
% 97.60/13.22 (leftInvIsSurj) =>
% 97.60/13.22 ((
% 97.60/13.22 (surjCantorThm) =>
% 97.60/13.22 ((
% 97.60/13.22 (foundation2) =>
% 97.60/13.22 ((
% 97.60/13.22 (notinself) =>
% 97.60/13.22 ((
% 97.60/13.22 (notinself2) =>
% 97.60/13.22 ((
% 97.60/13.22 (omegaSp) =>
% 97.60/13.22 ((
% 97.60/13.22 (omegaSclos) =>
% 97.60/13.22 ((
% 97.60/13.22 (peano0notS) =>
% 97.60/13.22 ((
% 97.60/13.22 (!!) @ (
% 97.60/13.22 (('#S') @ (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 =>) @
% 97.60/13.22 (
% 97.60/13.22 (
% 97.60/13.22 ('#C') @ in @
% 97.60/13.22 omega)))) @
% 97.60/13.22 (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 !!) @
% 97.60/13.22 (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 (
% 97.60/13.22 ('#S') @ (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 =>) @
% 97.60/13.22 (
% 97.60/13.22 (
% 97.60/13.22 ('#C') @ in @
% 97.60/13.22 omega)))))) @
% 97.60/13.22 (
% 97.60/13.22 (
% 97.60/13.22 ('#S') @ (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 '#S') @
% 97.60/13.22 (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 =>))) @
% 97.60/13.22 (
% 97.60/13.22 (
% 97.60/13.22 ('#C') @ (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 '#B') @
% 97.60/13.22 (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 =) @
% 97.60/13.22 omegaS)))) @
% 97.60/13.22 omegaS)))))) @
% 97.60/13.22 (
% 97.60/13.22 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.60/13.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl850])).
% 97.60/13.22 thf(zip_derived_cl878, plain,
% 97.60/13.22 (~ (((subsetE2) =>
% 97.60/13.22 (((notsubsetI) =>
% 97.60/13.22 (((notequalI1) =>
% 97.60/13.22 (((notequalI2) =>
% 97.60/13.22 (((subsetRefl) =>
% 97.60/13.22 (((subsetTrans) =>
% 97.60/13.22 (((setadjoinSub) =>
% 97.60/13.22 (((setadjoinSub2) =>
% 97.60/13.22 (((subset2powerset) =>
% 97.60/13.22 (((setextsub) =>
% 97.60/13.22 (((subsetemptysetimpeq) =>
% 97.60/13.22 (((powersetI1) =>
% 97.60/13.22 (((powersetE1) =>
% 97.60/13.22 (((inPowerset) =>
% 97.60/13.22 (((powersetsubset) =>
% 97.60/13.22 (((sepInPowerset) =>
% 97.60/13.22 (((sepSubset) =>
% 97.60/13.22 (((binunionIL) =>
% 97.60/13.22 (((upairset2IR) =>
% 97.60/13.22 (((binunionIR) =>
% 97.60/13.22 (((binunionEcases) =>
% 97.60/13.22 (((binunionE) =>
% 97.60/13.22 (((binunionLsub) =>
% 97.60/13.22 (((binunionRsub) =>
% 97.60/13.22 (((binintersectI) =>
% 97.60/13.22 (((binintersectSubset5) =>
% 97.60/13.22 (((binintersectEL) =>
% 97.60/13.22 (((binintersectLsub) =>
% 97.60/13.22 (((binintersectSubset2) =>
% 97.60/13.22 (((binintersectSubset3) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectER) =>
% 97.60/13.22 ((
% 97.60/13.22 (disjointsetsI1) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectRsub) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectSubset4) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectSubset1) =>
% 97.60/13.22 ((
% 97.60/13.22 (bs114d) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusI) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusEL) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusER) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusSubset2) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusERneg) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusELneg) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusILneg) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusIRneg) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusLsub) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusSubset1) =>
% 97.60/13.22 ((
% 97.60/13.22 (symdiffE) =>
% 97.60/13.22 ((
% 97.60/13.22 (symdiffI1) =>
% 97.60/13.22 ((
% 97.60/13.22 (symdiffI2) =>
% 97.60/13.22 ((
% 97.60/13.22 (symdiffIneg1) =>
% 97.60/13.22 ((
% 97.60/13.22 (symdiffIneg2) =>
% 97.60/13.22 ((
% 97.60/13.22 (secondinupair) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairIL) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairIR) =>
% 97.60/13.22 ((
% 97.60/13.22 (kpairiskpair) =>
% 97.60/13.22 ((
% 97.60/13.22 (kpairp) =>
% 97.60/13.22 ((
% 97.60/13.22 (singletonsubset) =>
% 97.60/13.22 ((
% 97.60/13.22 (singletoninpowerset) =>
% 97.60/13.22 ((
% 97.60/13.22 (singletoninpowunion) =>
% 97.60/13.22 ((
% 97.60/13.22 (upairset2E) =>
% 97.60/13.22 ((
% 97.60/13.22 (upairsubunion) =>
% 97.60/13.22 ((
% 97.60/13.22 (upairinpowunion) =>
% 97.60/13.22 ((
% 97.60/13.22 (ubforcartprodlem1) =>
% 97.60/13.22 ((
% 97.60/13.22 (ubforcartprodlem2) =>
% 97.60/13.22 ((
% 97.60/13.22 (ubforcartprodlem3) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodpairin) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodmempair1) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodmempair) =>
% 97.60/13.22 ((
% 97.60/13.22 (setunionE2) =>
% 97.60/13.22 ((
% 97.60/13.22 (setunionsingleton1) =>
% 97.60/13.22 ((
% 97.60/13.22 (setunionsingleton2) =>
% 97.60/13.22 ((
% 97.60/13.22 (setunionsingleton) =>
% 97.60/13.22 ((
% 97.60/13.22 (singletonprop) =>
% 97.60/13.22 ((
% 97.60/13.22 (ex1E1) =>
% 97.60/13.22 ((
% 97.60/13.22 (ex1I) =>
% 97.60/13.22 ((
% 97.60/13.22 (ex1I2) =>
% 97.60/13.22 ((
% 97.60/13.22 (singletonsuniq) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjL1) =>
% 97.60/13.22 ((
% 97.60/13.22 (kfstsingleton) =>
% 97.60/13.22 ((
% 97.60/13.22 (theprop) =>
% 97.60/13.22 ((
% 97.60/13.22 (kfstpairEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodfstin) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjL2) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjL) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjR11) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjR12) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjR1) =>
% 97.60/13.22 ((
% 97.60/13.22 (upairequniteq) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjR2) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjR) =>
% 97.60/13.22 ((
% 97.60/13.22 (ksndsingleton) =>
% 97.60/13.22 ((
% 97.60/13.22 (ksndpairEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (kpairsurjEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodsndin) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodpairmemEL) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodpairmemER) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodmempaircEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodfstpairEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodsndpairEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodpairsurjEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (dpsetconstrI) =>
% 97.60/13.22 ((
% 97.60/13.22 (dpsetconstrSub) =>
% 97.60/13.22 ((
% 97.60/13.22 (setOfPairsIsBReln) =>
% 97.60/13.22 ((
% 97.60/13.22 (dpsetconstrERa) =>
% 97.60/13.22 ((
% 97.60/13.22 (dpsetconstrEL1) =>
% 97.60/13.22 ((
% 97.60/13.22 (dpsetconstrEL2) =>
% 97.60/13.22 ((
% 97.60/13.22 (dpsetconstrER) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcImageSingleton) =>
% 97.60/13.22 ((
% 97.60/13.22 (apProp) =>
% 97.60/13.22 ((
% 97.60/13.22 (app) =>
% 97.60/13.22 ((
% 97.60/13.22 (infuncsetfunc) =>
% 97.60/13.22 ((
% 97.60/13.22 (ap2p) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcinfuncset) =>
% 97.60/13.22 ((
% 97.60/13.22 (lamProp) =>
% 97.60/13.22 ((
% 97.60/13.22 (lamp) =>
% 97.60/13.22 ((
% 97.60/13.22 (lam2p) =>
% 97.60/13.22 ((
% 97.60/13.22 (brelnall1) =>
% 97.60/13.22 ((
% 97.60/13.22 (brelnall2) =>
% 97.60/13.22 ((
% 97.60/13.22 (ex1E2) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcGraphProp1) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcGraphProp3) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcGraphProp2) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcextLem) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcGraphProp4) =>
% 97.60/13.22 ((
% 97.60/13.22 (subbreln) =>
% 97.60/13.22 ((
% 97.60/13.22 (eqbreln) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcext) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcext2) =>
% 97.60/13.22 ((
% 97.60/13.22 (ap2apEq1) =>
% 97.60/13.22 ((
% 97.60/13.22 (ap2apEq2) =>
% 97.60/13.22 ((
% 97.60/13.22 (beta1) =>
% 97.60/13.22 ((
% 97.60/13.22 (eta1) =>
% 97.60/13.22 ((
% 97.60/13.22 (lam2lamEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (beta2) =>
% 97.60/13.22 ((
% 97.60/13.22 (eta2) =>
% 97.60/13.22 ((
% 97.60/13.22 (iffalseProp1) =>
% 97.60/13.22 ((
% 97.60/13.22 (iffalseProp2) =>
% 97.60/13.22 ((
% 97.60/13.22 (iftrueProp1) =>
% 97.60/13.22 ((
% 97.60/13.22 (iftrueProp2) =>
% 97.60/13.22 ((
% 97.60/13.22 (ifSingleton) =>
% 97.60/13.22 ((
% 97.60/13.22 (ifp) =>
% 97.60/13.22 ((
% 97.60/13.22 (theeq) =>
% 97.60/13.22 ((
% 97.60/13.22 (iftrue) =>
% 97.60/13.22 ((
% 97.60/13.22 (iffalse) =>
% 97.60/13.22 ((
% 97.60/13.22 (iftrueorfalse) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectT_lem) =>
% 97.60/13.22 ((
% 97.60/13.22 (binunionT_lem) =>
% 97.60/13.22 ((
% 97.60/13.22 (powersetT_lem) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusT_lem) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementT_lem) =>
% 97.60/13.22 ((
% 97.60/13.22 (setextT) =>
% 97.60/13.22 ((
% 97.60/13.22 (subsetTI) =>
% 97.60/13.22 ((
% 97.60/13.22 (powersetTI1) =>
% 97.60/13.22 ((
% 97.60/13.22 (powersetTE1) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementTI1) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementTE1) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectTELcontra) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectTERcontra) =>
% 97.60/13.22 ((
% 97.60/13.22 (contrasubsetT) =>
% 97.60/13.22 ((
% 97.60/13.22 (contrasubsetT1) =>
% 97.60/13.22 ((
% 97.60/13.22 (contrasubsetT2) =>
% 97.60/13.22 ((
% 97.60/13.22 (contrasubsetT3) =>
% 97.60/13.22 ((
% 97.60/13.22 (doubleComplementI1) =>
% 97.60/13.22 ((
% 97.60/13.22 (doubleComplementE1) =>
% 97.60/13.22 ((
% 97.60/13.22 (doubleComplementSub1) =>
% 97.60/13.22 ((
% 97.60/13.22 (doubleComplementSub2) =>
% 97.60/13.22 ((
% 97.60/13.22 (doubleComplementEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementTnotintersectT) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementImpComplementIntersect) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementSubsetComplementIntersect) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementInPowersetComplementIntersect) =>
% 97.60/13.22 ((
% 97.60/13.22 (contraSubsetComplement) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementTcontraSubset) =>
% 97.60/13.22 ((
% 97.60/13.22 (binunionTILcontra) =>
% 97.60/13.22 ((
% 97.60/13.22 (binunionTIRcontra) =>
% 97.60/13.22 ((
% 97.60/13.22 (inIntersectImpInUnion) =>
% 97.60/13.22 ((
% 97.60/13.22 (inIntersectImpInUnion2) =>
% 97.60/13.22 ((
% 97.60/13.22 (inIntersectImpInIntersectUnions) =>
% 97.60/13.22 ((
% 97.60/13.22 (intersectInPowersetIntersectUnions) =>
% 97.60/13.22 ((
% 97.60/13.22 (inComplementUnionImpNotIn1) =>
% 97.60/13.22 ((
% 97.60/13.22 (inComplementUnionImpInComplement1) =>
% 97.60/13.22 ((
% 97.60/13.22 (binunionTE) =>
% 97.60/13.22 ((
% 97.60/13.22 (binunionTEcontra) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan2a1) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementUnionInPowersetComplement) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan2a2) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan1a) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan1b) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan1) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan2a) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan2b2) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan2b) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan2) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz13rule0) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz13rule1) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz13rule2) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz13rule3) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz13rule4) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz1_1) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz1_2) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz1_3) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz1_4) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz1_5) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1all2) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1SetBreln1) =>
% 97.60/13.22 ((
% 97.60/13.22 (choice2fnsingleton) =>
% 97.60/13.22 ((
% 97.60/13.22 (setOfPairsIsBReln1) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1all1) =>
% 97.60/13.22 ((
% 97.60/13.22 (subbreln1) =>
% 97.60/13.22 ((
% 97.60/13.22 (eqbreln1) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1invprop) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1invI) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1invE) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1compprop) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1compI) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1compE) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1compEex) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1unionprop) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1unionIL) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1unionIR) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1unionI) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1unionE) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1unionEcases) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1unionCommutes) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz2Ex) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz2W) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz2A) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz2B) =>
% 97.60/13.22 ((
% 97.60/13.22 (image1Ex) =>
% 97.60/13.22 ((
% 97.60/13.22 (image1Ex1) =>
% 97.60/13.22 ((
% 97.60/13.22 (image1Equiv) =>
% 97.60/13.22 ((
% 97.60/13.22 (image1E) =>
% 97.60/13.22 ((
% 97.60/13.22 (image1I) =>
% 97.60/13.22 ((
% 97.60/13.22 (injFuncInInjFuncSet) =>
% 97.60/13.22 ((
% 97.60/13.22 (injFuncSetFuncIn) =>
% 97.60/13.22 ((
% 97.60/13.22 (injFuncSetFuncInj) =>
% 97.60/13.22 ((
% 97.60/13.22 (surjFuncSetFuncIn) =>
% 97.60/13.22 ((
% 97.60/13.22 (surjFuncSetFuncSurj) =>
% 97.60/13.22 ((
% 97.60/13.22 (leftInvIsSurj) =>
% 97.60/13.22 ((
% 97.60/13.22 (surjCantorThm) =>
% 97.60/13.22 ((
% 97.60/13.22 (foundation2) =>
% 97.60/13.22 ((
% 97.60/13.22 (notinself) =>
% 97.60/13.22 ((
% 97.60/13.22 (notinself2) =>
% 97.60/13.22 ((
% 97.60/13.22 (omegaSp) =>
% 97.60/13.22 ((
% 97.60/13.22 (omegaSclos) =>
% 97.60/13.22 ((
% 97.60/13.22 (peano0notS) =>
% 97.60/13.22 ((
% 97.60/13.22 (!!) @ (
% 97.60/13.22 (('#S') @ (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 =>) @
% 97.60/13.22 (
% 97.60/13.22 (
% 97.60/13.22 ('#C') @ in @
% 97.60/13.22 omega)))) @
% 97.60/13.22 (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 !!) @
% 97.60/13.22 (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 (
% 97.60/13.22 ('#S') @ (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 =>) @
% 97.60/13.22 (
% 97.60/13.22 (
% 97.60/13.22 ('#C') @ in @
% 97.60/13.22 omega)))))) @
% 97.60/13.22 (
% 97.60/13.22 (
% 97.60/13.22 ('#S') @ (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 '#S') @
% 97.60/13.22 (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 =>))) @
% 97.60/13.22 (
% 97.60/13.22 (
% 97.60/13.22 ('#C') @ (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 '#B') @
% 97.60/13.22 (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 =) @
% 97.60/13.22 omegaS)))) @
% 97.60/13.22 omegaS)))))) @
% 97.60/13.22 (
% 97.60/13.22 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.60/13.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl863])).
% 97.60/13.22 thf(zip_derived_cl896, plain,
% 97.60/13.22 (~ (((notsubsetI) =>
% 97.60/13.22 (((notequalI1) =>
% 97.60/13.22 (((notequalI2) =>
% 97.60/13.22 (((subsetRefl) =>
% 97.60/13.22 (((subsetTrans) =>
% 97.60/13.22 (((setadjoinSub) =>
% 97.60/13.22 (((setadjoinSub2) =>
% 97.60/13.22 (((subset2powerset) =>
% 97.60/13.22 (((setextsub) =>
% 97.60/13.22 (((subsetemptysetimpeq) =>
% 97.60/13.22 (((powersetI1) =>
% 97.60/13.22 (((powersetE1) =>
% 97.60/13.22 (((inPowerset) =>
% 97.60/13.22 (((powersetsubset) =>
% 97.60/13.22 (((sepInPowerset) =>
% 97.60/13.22 (((sepSubset) =>
% 97.60/13.22 (((binunionIL) =>
% 97.60/13.22 (((upairset2IR) =>
% 97.60/13.22 (((binunionIR) =>
% 97.60/13.22 (((binunionEcases) =>
% 97.60/13.22 (((binunionE) =>
% 97.60/13.22 (((binunionLsub) =>
% 97.60/13.22 (((binunionRsub) =>
% 97.60/13.22 (((binintersectI) =>
% 97.60/13.22 (((binintersectSubset5) =>
% 97.60/13.22 (((binintersectEL) =>
% 97.60/13.22 (((binintersectLsub) =>
% 97.60/13.22 (((binintersectSubset2) =>
% 97.60/13.22 (((binintersectSubset3) =>
% 97.60/13.22 (((binintersectER) =>
% 97.60/13.22 ((
% 97.60/13.22 (disjointsetsI1) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectRsub) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectSubset4) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectSubset1) =>
% 97.60/13.22 ((
% 97.60/13.22 (bs114d) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusI) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusEL) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusER) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusSubset2) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusERneg) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusELneg) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusILneg) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusIRneg) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusLsub) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusSubset1) =>
% 97.60/13.22 ((
% 97.60/13.22 (symdiffE) =>
% 97.60/13.22 ((
% 97.60/13.22 (symdiffI1) =>
% 97.60/13.22 ((
% 97.60/13.22 (symdiffI2) =>
% 97.60/13.22 ((
% 97.60/13.22 (symdiffIneg1) =>
% 97.60/13.22 ((
% 97.60/13.22 (symdiffIneg2) =>
% 97.60/13.22 ((
% 97.60/13.22 (secondinupair) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairIL) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairIR) =>
% 97.60/13.22 ((
% 97.60/13.22 (kpairiskpair) =>
% 97.60/13.22 ((
% 97.60/13.22 (kpairp) =>
% 97.60/13.22 ((
% 97.60/13.22 (singletonsubset) =>
% 97.60/13.22 ((
% 97.60/13.22 (singletoninpowerset) =>
% 97.60/13.22 ((
% 97.60/13.22 (singletoninpowunion) =>
% 97.60/13.22 ((
% 97.60/13.22 (upairset2E) =>
% 97.60/13.22 ((
% 97.60/13.22 (upairsubunion) =>
% 97.60/13.22 ((
% 97.60/13.22 (upairinpowunion) =>
% 97.60/13.22 ((
% 97.60/13.22 (ubforcartprodlem1) =>
% 97.60/13.22 ((
% 97.60/13.22 (ubforcartprodlem2) =>
% 97.60/13.22 ((
% 97.60/13.22 (ubforcartprodlem3) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodpairin) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodmempair1) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodmempair) =>
% 97.60/13.22 ((
% 97.60/13.22 (setunionE2) =>
% 97.60/13.22 ((
% 97.60/13.22 (setunionsingleton1) =>
% 97.60/13.22 ((
% 97.60/13.22 (setunionsingleton2) =>
% 97.60/13.22 ((
% 97.60/13.22 (setunionsingleton) =>
% 97.60/13.22 ((
% 97.60/13.22 (singletonprop) =>
% 97.60/13.22 ((
% 97.60/13.22 (ex1E1) =>
% 97.60/13.22 ((
% 97.60/13.22 (ex1I) =>
% 97.60/13.22 ((
% 97.60/13.22 (ex1I2) =>
% 97.60/13.22 ((
% 97.60/13.22 (singletonsuniq) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjL1) =>
% 97.60/13.22 ((
% 97.60/13.22 (kfstsingleton) =>
% 97.60/13.22 ((
% 97.60/13.22 (theprop) =>
% 97.60/13.22 ((
% 97.60/13.22 (kfstpairEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodfstin) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjL2) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjL) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjR11) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjR12) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjR1) =>
% 97.60/13.22 ((
% 97.60/13.22 (upairequniteq) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjR2) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjR) =>
% 97.60/13.22 ((
% 97.60/13.22 (ksndsingleton) =>
% 97.60/13.22 ((
% 97.60/13.22 (ksndpairEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (kpairsurjEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodsndin) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodpairmemEL) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodpairmemER) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodmempaircEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodfstpairEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodsndpairEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodpairsurjEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (dpsetconstrI) =>
% 97.60/13.22 ((
% 97.60/13.22 (dpsetconstrSub) =>
% 97.60/13.22 ((
% 97.60/13.22 (setOfPairsIsBReln) =>
% 97.60/13.22 ((
% 97.60/13.22 (dpsetconstrERa) =>
% 97.60/13.22 ((
% 97.60/13.22 (dpsetconstrEL1) =>
% 97.60/13.22 ((
% 97.60/13.22 (dpsetconstrEL2) =>
% 97.60/13.22 ((
% 97.60/13.22 (dpsetconstrER) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcImageSingleton) =>
% 97.60/13.22 ((
% 97.60/13.22 (apProp) =>
% 97.60/13.22 ((
% 97.60/13.22 (app) =>
% 97.60/13.22 ((
% 97.60/13.22 (infuncsetfunc) =>
% 97.60/13.22 ((
% 97.60/13.22 (ap2p) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcinfuncset) =>
% 97.60/13.22 ((
% 97.60/13.22 (lamProp) =>
% 97.60/13.22 ((
% 97.60/13.22 (lamp) =>
% 97.60/13.22 ((
% 97.60/13.22 (lam2p) =>
% 97.60/13.22 ((
% 97.60/13.22 (brelnall1) =>
% 97.60/13.22 ((
% 97.60/13.22 (brelnall2) =>
% 97.60/13.22 ((
% 97.60/13.22 (ex1E2) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcGraphProp1) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcGraphProp3) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcGraphProp2) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcextLem) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcGraphProp4) =>
% 97.60/13.22 ((
% 97.60/13.22 (subbreln) =>
% 97.60/13.22 ((
% 97.60/13.22 (eqbreln) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcext) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcext2) =>
% 97.60/13.22 ((
% 97.60/13.22 (ap2apEq1) =>
% 97.60/13.22 ((
% 97.60/13.22 (ap2apEq2) =>
% 97.60/13.22 ((
% 97.60/13.22 (beta1) =>
% 97.60/13.22 ((
% 97.60/13.22 (eta1) =>
% 97.60/13.22 ((
% 97.60/13.22 (lam2lamEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (beta2) =>
% 97.60/13.22 ((
% 97.60/13.22 (eta2) =>
% 97.60/13.22 ((
% 97.60/13.22 (iffalseProp1) =>
% 97.60/13.22 ((
% 97.60/13.22 (iffalseProp2) =>
% 97.60/13.22 ((
% 97.60/13.22 (iftrueProp1) =>
% 97.60/13.22 ((
% 97.60/13.22 (iftrueProp2) =>
% 97.60/13.22 ((
% 97.60/13.22 (ifSingleton) =>
% 97.60/13.22 ((
% 97.60/13.22 (ifp) =>
% 97.60/13.22 ((
% 97.60/13.22 (theeq) =>
% 97.60/13.22 ((
% 97.60/13.22 (iftrue) =>
% 97.60/13.22 ((
% 97.60/13.22 (iffalse) =>
% 97.60/13.22 ((
% 97.60/13.22 (iftrueorfalse) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectT_lem) =>
% 97.60/13.22 ((
% 97.60/13.22 (binunionT_lem) =>
% 97.60/13.22 ((
% 97.60/13.22 (powersetT_lem) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusT_lem) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementT_lem) =>
% 97.60/13.22 ((
% 97.60/13.22 (setextT) =>
% 97.60/13.22 ((
% 97.60/13.22 (subsetTI) =>
% 97.60/13.22 ((
% 97.60/13.22 (powersetTI1) =>
% 97.60/13.22 ((
% 97.60/13.22 (powersetTE1) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementTI1) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementTE1) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectTELcontra) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectTERcontra) =>
% 97.60/13.22 ((
% 97.60/13.22 (contrasubsetT) =>
% 97.60/13.22 ((
% 97.60/13.22 (contrasubsetT1) =>
% 97.60/13.22 ((
% 97.60/13.22 (contrasubsetT2) =>
% 97.60/13.22 ((
% 97.60/13.22 (contrasubsetT3) =>
% 97.60/13.22 ((
% 97.60/13.22 (doubleComplementI1) =>
% 97.60/13.22 ((
% 97.60/13.22 (doubleComplementE1) =>
% 97.60/13.22 ((
% 97.60/13.22 (doubleComplementSub1) =>
% 97.60/13.22 ((
% 97.60/13.22 (doubleComplementSub2) =>
% 97.60/13.22 ((
% 97.60/13.22 (doubleComplementEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementTnotintersectT) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementImpComplementIntersect) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementSubsetComplementIntersect) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementInPowersetComplementIntersect) =>
% 97.60/13.22 ((
% 97.60/13.22 (contraSubsetComplement) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementTcontraSubset) =>
% 97.60/13.22 ((
% 97.60/13.22 (binunionTILcontra) =>
% 97.60/13.22 ((
% 97.60/13.22 (binunionTIRcontra) =>
% 97.60/13.22 ((
% 97.60/13.22 (inIntersectImpInUnion) =>
% 97.60/13.22 ((
% 97.60/13.22 (inIntersectImpInUnion2) =>
% 97.60/13.22 ((
% 97.60/13.22 (inIntersectImpInIntersectUnions) =>
% 97.60/13.22 ((
% 97.60/13.22 (intersectInPowersetIntersectUnions) =>
% 97.60/13.22 ((
% 97.60/13.22 (inComplementUnionImpNotIn1) =>
% 97.60/13.22 ((
% 97.60/13.22 (inComplementUnionImpInComplement1) =>
% 97.60/13.22 ((
% 97.60/13.22 (binunionTE) =>
% 97.60/13.22 ((
% 97.60/13.22 (binunionTEcontra) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan2a1) =>
% 97.60/13.22 ((
% 97.60/13.22 (complementUnionInPowersetComplement) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan2a2) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan1a) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan1b) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan1) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan2a) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan2b2) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan2b) =>
% 97.60/13.22 ((
% 97.60/13.22 (demorgan2) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz13rule0) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz13rule1) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz13rule2) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz13rule3) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz13rule4) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz1_1) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz1_2) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz1_3) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz1_4) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz1_5) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1all2) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1SetBreln1) =>
% 97.60/13.22 ((
% 97.60/13.22 (choice2fnsingleton) =>
% 97.60/13.22 ((
% 97.60/13.22 (setOfPairsIsBReln1) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1all1) =>
% 97.60/13.22 ((
% 97.60/13.22 (subbreln1) =>
% 97.60/13.22 ((
% 97.60/13.22 (eqbreln1) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1invprop) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1invI) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1invE) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1compprop) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1compI) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1compE) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1compEex) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1unionprop) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1unionIL) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1unionIR) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1unionI) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1unionE) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1unionEcases) =>
% 97.60/13.22 ((
% 97.60/13.22 (breln1unionCommutes) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz2Ex) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz2W) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz2A) =>
% 97.60/13.22 ((
% 97.60/13.22 (woz2B) =>
% 97.60/13.22 ((
% 97.60/13.22 (image1Ex) =>
% 97.60/13.22 ((
% 97.60/13.22 (image1Ex1) =>
% 97.60/13.22 ((
% 97.60/13.22 (image1Equiv) =>
% 97.60/13.22 ((
% 97.60/13.22 (image1E) =>
% 97.60/13.22 ((
% 97.60/13.22 (image1I) =>
% 97.60/13.22 ((
% 97.60/13.22 (injFuncInInjFuncSet) =>
% 97.60/13.22 ((
% 97.60/13.22 (injFuncSetFuncIn) =>
% 97.60/13.22 ((
% 97.60/13.22 (injFuncSetFuncInj) =>
% 97.60/13.22 ((
% 97.60/13.22 (surjFuncSetFuncIn) =>
% 97.60/13.22 ((
% 97.60/13.22 (surjFuncSetFuncSurj) =>
% 97.60/13.22 ((
% 97.60/13.22 (leftInvIsSurj) =>
% 97.60/13.22 ((
% 97.60/13.22 (surjCantorThm) =>
% 97.60/13.22 ((
% 97.60/13.22 (foundation2) =>
% 97.60/13.22 ((
% 97.60/13.22 (notinself) =>
% 97.60/13.22 ((
% 97.60/13.22 (notinself2) =>
% 97.60/13.22 ((
% 97.60/13.22 (omegaSp) =>
% 97.60/13.22 ((
% 97.60/13.22 (omegaSclos) =>
% 97.60/13.22 ((
% 97.60/13.22 (peano0notS) =>
% 97.60/13.22 ((
% 97.60/13.22 (!!) @ (
% 97.60/13.22 (('#S') @ (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 =>) @
% 97.60/13.22 (
% 97.60/13.22 (
% 97.60/13.22 ('#C') @ in @
% 97.60/13.22 omega)))) @
% 97.60/13.22 (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 !!) @
% 97.60/13.22 (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 (
% 97.60/13.22 ('#S') @ (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 =>) @
% 97.60/13.22 (
% 97.60/13.22 (
% 97.60/13.22 ('#C') @ in @
% 97.60/13.22 omega)))))) @
% 97.60/13.22 (
% 97.60/13.22 (
% 97.60/13.22 ('#S') @ (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 '#S') @
% 97.60/13.22 (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 =>))) @
% 97.60/13.22 (
% 97.60/13.22 (
% 97.60/13.22 ('#C') @ (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 '#B') @
% 97.60/13.22 (
% 97.60/13.22 (
% 97.60/13.22 ('#B') @ (
% 97.60/13.22 =) @
% 97.60/13.22 omegaS)))) @
% 97.60/13.22 omegaS)))))) @
% 97.60/13.22 (
% 97.60/13.22 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.60/13.22 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl878])).
% 97.60/13.22 thf(zip_derived_cl909, plain,
% 97.60/13.22 (~ (((notequalI1) =>
% 97.60/13.22 (((notequalI2) =>
% 97.60/13.22 (((subsetRefl) =>
% 97.60/13.22 (((subsetTrans) =>
% 97.60/13.22 (((setadjoinSub) =>
% 97.60/13.22 (((setadjoinSub2) =>
% 97.60/13.22 (((subset2powerset) =>
% 97.60/13.22 (((setextsub) =>
% 97.60/13.22 (((subsetemptysetimpeq) =>
% 97.60/13.22 (((powersetI1) =>
% 97.60/13.22 (((powersetE1) =>
% 97.60/13.22 (((inPowerset) =>
% 97.60/13.22 (((powersetsubset) =>
% 97.60/13.22 (((sepInPowerset) =>
% 97.60/13.22 (((sepSubset) =>
% 97.60/13.22 (((binunionIL) =>
% 97.60/13.22 (((upairset2IR) =>
% 97.60/13.22 (((binunionIR) =>
% 97.60/13.22 (((binunionEcases) =>
% 97.60/13.22 (((binunionE) =>
% 97.60/13.22 (((binunionLsub) =>
% 97.60/13.22 (((binunionRsub) =>
% 97.60/13.22 (((binintersectI) =>
% 97.60/13.22 (((binintersectSubset5) =>
% 97.60/13.22 (((binintersectEL) =>
% 97.60/13.22 (((binintersectLsub) =>
% 97.60/13.22 (((binintersectSubset2) =>
% 97.60/13.22 (((binintersectSubset3) =>
% 97.60/13.22 (((binintersectER) =>
% 97.60/13.22 (((disjointsetsI1) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectRsub) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectSubset4) =>
% 97.60/13.22 ((
% 97.60/13.22 (binintersectSubset1) =>
% 97.60/13.22 ((
% 97.60/13.22 (bs114d) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusI) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusEL) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusER) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusSubset2) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusERneg) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusELneg) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusILneg) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusIRneg) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusLsub) =>
% 97.60/13.22 ((
% 97.60/13.22 (setminusSubset1) =>
% 97.60/13.22 ((
% 97.60/13.22 (symdiffE) =>
% 97.60/13.22 ((
% 97.60/13.22 (symdiffI1) =>
% 97.60/13.22 ((
% 97.60/13.22 (symdiffI2) =>
% 97.60/13.22 ((
% 97.60/13.22 (symdiffIneg1) =>
% 97.60/13.22 ((
% 97.60/13.22 (symdiffIneg2) =>
% 97.60/13.22 ((
% 97.60/13.22 (secondinupair) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairIL) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairIR) =>
% 97.60/13.22 ((
% 97.60/13.22 (kpairiskpair) =>
% 97.60/13.22 ((
% 97.60/13.22 (kpairp) =>
% 97.60/13.22 ((
% 97.60/13.22 (singletonsubset) =>
% 97.60/13.22 ((
% 97.60/13.22 (singletoninpowerset) =>
% 97.60/13.22 ((
% 97.60/13.22 (singletoninpowunion) =>
% 97.60/13.22 ((
% 97.60/13.22 (upairset2E) =>
% 97.60/13.22 ((
% 97.60/13.22 (upairsubunion) =>
% 97.60/13.22 ((
% 97.60/13.22 (upairinpowunion) =>
% 97.60/13.22 ((
% 97.60/13.22 (ubforcartprodlem1) =>
% 97.60/13.22 ((
% 97.60/13.22 (ubforcartprodlem2) =>
% 97.60/13.22 ((
% 97.60/13.22 (ubforcartprodlem3) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodpairin) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodmempair1) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodmempair) =>
% 97.60/13.22 ((
% 97.60/13.22 (setunionE2) =>
% 97.60/13.22 ((
% 97.60/13.22 (setunionsingleton1) =>
% 97.60/13.22 ((
% 97.60/13.22 (setunionsingleton2) =>
% 97.60/13.22 ((
% 97.60/13.22 (setunionsingleton) =>
% 97.60/13.22 ((
% 97.60/13.22 (singletonprop) =>
% 97.60/13.22 ((
% 97.60/13.22 (ex1E1) =>
% 97.60/13.22 ((
% 97.60/13.22 (ex1I) =>
% 97.60/13.22 ((
% 97.60/13.22 (ex1I2) =>
% 97.60/13.22 ((
% 97.60/13.22 (singletonsuniq) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjL1) =>
% 97.60/13.22 ((
% 97.60/13.22 (kfstsingleton) =>
% 97.60/13.22 ((
% 97.60/13.22 (theprop) =>
% 97.60/13.22 ((
% 97.60/13.22 (kfstpairEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodfstin) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjL2) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjL) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjR11) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjR12) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjR1) =>
% 97.60/13.22 ((
% 97.60/13.22 (upairequniteq) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjR2) =>
% 97.60/13.22 ((
% 97.60/13.22 (setukpairinjR) =>
% 97.60/13.22 ((
% 97.60/13.22 (ksndsingleton) =>
% 97.60/13.22 ((
% 97.60/13.22 (ksndpairEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (kpairsurjEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodsndin) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodpairmemEL) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodpairmemER) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodmempaircEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodfstpairEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodsndpairEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (cartprodpairsurjEq) =>
% 97.60/13.22 ((
% 97.60/13.22 (dpsetconstrI) =>
% 97.60/13.22 ((
% 97.60/13.22 (dpsetconstrSub) =>
% 97.60/13.22 ((
% 97.60/13.22 (setOfPairsIsBReln) =>
% 97.60/13.22 ((
% 97.60/13.22 (dpsetconstrERa) =>
% 97.60/13.22 ((
% 97.60/13.22 (dpsetconstrEL1) =>
% 97.60/13.22 ((
% 97.60/13.22 (dpsetconstrEL2) =>
% 97.60/13.22 ((
% 97.60/13.22 (dpsetconstrER) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcImageSingleton) =>
% 97.60/13.22 ((
% 97.60/13.22 (apProp) =>
% 97.60/13.22 ((
% 97.60/13.22 (app) =>
% 97.60/13.22 ((
% 97.60/13.22 (infuncsetfunc) =>
% 97.60/13.22 ((
% 97.60/13.22 (ap2p) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcinfuncset) =>
% 97.60/13.22 ((
% 97.60/13.22 (lamProp) =>
% 97.60/13.22 ((
% 97.60/13.22 (lamp) =>
% 97.60/13.22 ((
% 97.60/13.22 (lam2p) =>
% 97.60/13.22 ((
% 97.60/13.22 (brelnall1) =>
% 97.60/13.22 ((
% 97.60/13.22 (brelnall2) =>
% 97.60/13.22 ((
% 97.60/13.22 (ex1E2) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcGraphProp1) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcGraphProp3) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcGraphProp2) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcextLem) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcGraphProp4) =>
% 97.60/13.22 ((
% 97.60/13.22 (subbreln) =>
% 97.60/13.22 ((
% 97.60/13.22 (eqbreln) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcext) =>
% 97.60/13.22 ((
% 97.60/13.22 (funcext2) =>
% 97.60/13.22 ((
% 97.60/13.22 (ap2apEq1) =>
% 97.60/13.22 ((
% 97.60/13.22 (ap2apEq2) =>
% 97.60/13.22 ((
% 97.60/13.22 (beta1) =>
% 97.60/13.22 ((
% 97.60/13.22 (eta1) =>
% 97.60/13.22 ((
% 97.60/13.22 (lam2lamEq) =>
% 97.60/13.22 ((
% 97.60/13.23 (beta2) =>
% 97.60/13.23 ((
% 97.60/13.23 (eta2) =>
% 97.60/13.23 ((
% 97.60/13.23 (iffalseProp1) =>
% 97.60/13.23 ((
% 97.60/13.23 (iffalseProp2) =>
% 97.60/13.23 ((
% 97.60/13.23 (iftrueProp1) =>
% 97.60/13.23 ((
% 97.60/13.23 (iftrueProp2) =>
% 97.60/13.23 ((
% 97.60/13.23 (ifSingleton) =>
% 97.60/13.23 ((
% 97.60/13.23 (ifp) =>
% 97.60/13.23 ((
% 97.60/13.23 (theeq) =>
% 97.60/13.23 ((
% 97.60/13.23 (iftrue) =>
% 97.60/13.23 ((
% 97.60/13.23 (iffalse) =>
% 97.60/13.23 ((
% 97.60/13.23 (iftrueorfalse) =>
% 97.60/13.23 ((
% 97.60/13.23 (binintersectT_lem) =>
% 97.60/13.23 ((
% 97.60/13.23 (binunionT_lem) =>
% 97.60/13.23 ((
% 97.60/13.23 (powersetT_lem) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusT_lem) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementT_lem) =>
% 97.60/13.23 ((
% 97.60/13.23 (setextT) =>
% 97.60/13.23 ((
% 97.60/13.23 (subsetTI) =>
% 97.60/13.23 ((
% 97.60/13.23 (powersetTI1) =>
% 97.60/13.23 ((
% 97.60/13.23 (powersetTE1) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementTI1) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementTE1) =>
% 97.60/13.23 ((
% 97.60/13.23 (binintersectTELcontra) =>
% 97.60/13.23 ((
% 97.60/13.23 (binintersectTERcontra) =>
% 97.60/13.23 ((
% 97.60/13.23 (contrasubsetT) =>
% 97.60/13.23 ((
% 97.60/13.23 (contrasubsetT1) =>
% 97.60/13.23 ((
% 97.60/13.23 (contrasubsetT2) =>
% 97.60/13.23 ((
% 97.60/13.23 (contrasubsetT3) =>
% 97.60/13.23 ((
% 97.60/13.23 (doubleComplementI1) =>
% 97.60/13.23 ((
% 97.60/13.23 (doubleComplementE1) =>
% 97.60/13.23 ((
% 97.60/13.23 (doubleComplementSub1) =>
% 97.60/13.23 ((
% 97.60/13.23 (doubleComplementSub2) =>
% 97.60/13.23 ((
% 97.60/13.23 (doubleComplementEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementTnotintersectT) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementImpComplementIntersect) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementSubsetComplementIntersect) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementInPowersetComplementIntersect) =>
% 97.60/13.23 ((
% 97.60/13.23 (contraSubsetComplement) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementTcontraSubset) =>
% 97.60/13.23 ((
% 97.60/13.23 (binunionTILcontra) =>
% 97.60/13.23 ((
% 97.60/13.23 (binunionTIRcontra) =>
% 97.60/13.23 ((
% 97.60/13.23 (inIntersectImpInUnion) =>
% 97.60/13.23 ((
% 97.60/13.23 (inIntersectImpInUnion2) =>
% 97.60/13.23 ((
% 97.60/13.23 (inIntersectImpInIntersectUnions) =>
% 97.60/13.23 ((
% 97.60/13.23 (intersectInPowersetIntersectUnions) =>
% 97.60/13.23 ((
% 97.60/13.23 (inComplementUnionImpNotIn1) =>
% 97.60/13.23 ((
% 97.60/13.23 (inComplementUnionImpInComplement1) =>
% 97.60/13.23 ((
% 97.60/13.23 (binunionTE) =>
% 97.60/13.23 ((
% 97.60/13.23 (binunionTEcontra) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan2a1) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementUnionInPowersetComplement) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan2a2) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan1a) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan1b) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan1) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan2a) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan2b2) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan2b) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan2) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz13rule0) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz13rule1) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz13rule2) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz13rule3) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz13rule4) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz1_1) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz1_2) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz1_3) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz1_4) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz1_5) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1all2) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1SetBreln1) =>
% 97.60/13.23 ((
% 97.60/13.23 (choice2fnsingleton) =>
% 97.60/13.23 ((
% 97.60/13.23 (setOfPairsIsBReln1) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1all1) =>
% 97.60/13.23 ((
% 97.60/13.23 (subbreln1) =>
% 97.60/13.23 ((
% 97.60/13.23 (eqbreln1) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1invprop) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1invI) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1invE) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1compprop) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1compI) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1compE) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1compEex) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1unionprop) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1unionIL) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1unionIR) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1unionI) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1unionE) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1unionEcases) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1unionCommutes) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz2Ex) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz2W) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz2A) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz2B) =>
% 97.60/13.23 ((
% 97.60/13.23 (image1Ex) =>
% 97.60/13.23 ((
% 97.60/13.23 (image1Ex1) =>
% 97.60/13.23 ((
% 97.60/13.23 (image1Equiv) =>
% 97.60/13.23 ((
% 97.60/13.23 (image1E) =>
% 97.60/13.23 ((
% 97.60/13.23 (image1I) =>
% 97.60/13.23 ((
% 97.60/13.23 (injFuncInInjFuncSet) =>
% 97.60/13.23 ((
% 97.60/13.23 (injFuncSetFuncIn) =>
% 97.60/13.23 ((
% 97.60/13.23 (injFuncSetFuncInj) =>
% 97.60/13.23 ((
% 97.60/13.23 (surjFuncSetFuncIn) =>
% 97.60/13.23 ((
% 97.60/13.23 (surjFuncSetFuncSurj) =>
% 97.60/13.23 ((
% 97.60/13.23 (leftInvIsSurj) =>
% 97.60/13.23 ((
% 97.60/13.23 (surjCantorThm) =>
% 97.60/13.23 ((
% 97.60/13.23 (foundation2) =>
% 97.60/13.23 ((
% 97.60/13.23 (notinself) =>
% 97.60/13.23 ((
% 97.60/13.23 (notinself2) =>
% 97.60/13.23 ((
% 97.60/13.23 (omegaSp) =>
% 97.60/13.23 ((
% 97.60/13.23 (omegaSclos) =>
% 97.60/13.23 ((
% 97.60/13.23 (peano0notS) =>
% 97.60/13.23 ((
% 97.60/13.23 (!!) @ (
% 97.60/13.23 (('#S') @ (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 =>) @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#C') @ in @
% 97.60/13.23 omega)))) @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 !!) @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 (
% 97.60/13.23 ('#S') @ (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 =>) @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#C') @ in @
% 97.60/13.23 omega)))))) @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#S') @ (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 '#S') @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 =>))) @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#C') @ (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 '#B') @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 =) @
% 97.60/13.23 omegaS)))) @
% 97.60/13.23 omegaS)))))) @
% 97.60/13.23 (
% 97.60/13.23 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.60/13.23 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl896])).
% 97.60/13.23 thf(zip_derived_cl924, plain,
% 97.60/13.23 (~ (((notequalI2) =>
% 97.60/13.23 (((subsetRefl) =>
% 97.60/13.23 (((subsetTrans) =>
% 97.60/13.23 (((setadjoinSub) =>
% 97.60/13.23 (((setadjoinSub2) =>
% 97.60/13.23 (((subset2powerset) =>
% 97.60/13.23 (((setextsub) =>
% 97.60/13.23 (((subsetemptysetimpeq) =>
% 97.60/13.23 (((powersetI1) =>
% 97.60/13.23 (((powersetE1) =>
% 97.60/13.23 (((inPowerset) =>
% 97.60/13.23 (((powersetsubset) =>
% 97.60/13.23 (((sepInPowerset) =>
% 97.60/13.23 (((sepSubset) =>
% 97.60/13.23 (((binunionIL) =>
% 97.60/13.23 (((upairset2IR) =>
% 97.60/13.23 (((binunionIR) =>
% 97.60/13.23 (((binunionEcases) =>
% 97.60/13.23 (((binunionE) =>
% 97.60/13.23 (((binunionLsub) =>
% 97.60/13.23 (((binunionRsub) =>
% 97.60/13.23 (((binintersectI) =>
% 97.60/13.23 (((binintersectSubset5) =>
% 97.60/13.23 (((binintersectEL) =>
% 97.60/13.23 (((binintersectLsub) =>
% 97.60/13.23 (((binintersectSubset2) =>
% 97.60/13.23 (((binintersectSubset3) =>
% 97.60/13.23 (((binintersectER) =>
% 97.60/13.23 (((disjointsetsI1) =>
% 97.60/13.23 (((binintersectRsub) =>
% 97.60/13.23 ((
% 97.60/13.23 (binintersectSubset4) =>
% 97.60/13.23 ((
% 97.60/13.23 (binintersectSubset1) =>
% 97.60/13.23 ((
% 97.60/13.23 (bs114d) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusI) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusEL) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusER) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusSubset2) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusERneg) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusELneg) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusILneg) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusIRneg) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusLsub) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusSubset1) =>
% 97.60/13.23 ((
% 97.60/13.23 (symdiffE) =>
% 97.60/13.23 ((
% 97.60/13.23 (symdiffI1) =>
% 97.60/13.23 ((
% 97.60/13.23 (symdiffI2) =>
% 97.60/13.23 ((
% 97.60/13.23 (symdiffIneg1) =>
% 97.60/13.23 ((
% 97.60/13.23 (symdiffIneg2) =>
% 97.60/13.23 ((
% 97.60/13.23 (secondinupair) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairIL) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairIR) =>
% 97.60/13.23 ((
% 97.60/13.23 (kpairiskpair) =>
% 97.60/13.23 ((
% 97.60/13.23 (kpairp) =>
% 97.60/13.23 ((
% 97.60/13.23 (singletonsubset) =>
% 97.60/13.23 ((
% 97.60/13.23 (singletoninpowerset) =>
% 97.60/13.23 ((
% 97.60/13.23 (singletoninpowunion) =>
% 97.60/13.23 ((
% 97.60/13.23 (upairset2E) =>
% 97.60/13.23 ((
% 97.60/13.23 (upairsubunion) =>
% 97.60/13.23 ((
% 97.60/13.23 (upairinpowunion) =>
% 97.60/13.23 ((
% 97.60/13.23 (ubforcartprodlem1) =>
% 97.60/13.23 ((
% 97.60/13.23 (ubforcartprodlem2) =>
% 97.60/13.23 ((
% 97.60/13.23 (ubforcartprodlem3) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodpairin) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodmempair1) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodmempair) =>
% 97.60/13.23 ((
% 97.60/13.23 (setunionE2) =>
% 97.60/13.23 ((
% 97.60/13.23 (setunionsingleton1) =>
% 97.60/13.23 ((
% 97.60/13.23 (setunionsingleton2) =>
% 97.60/13.23 ((
% 97.60/13.23 (setunionsingleton) =>
% 97.60/13.23 ((
% 97.60/13.23 (singletonprop) =>
% 97.60/13.23 ((
% 97.60/13.23 (ex1E1) =>
% 97.60/13.23 ((
% 97.60/13.23 (ex1I) =>
% 97.60/13.23 ((
% 97.60/13.23 (ex1I2) =>
% 97.60/13.23 ((
% 97.60/13.23 (singletonsuniq) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairinjL1) =>
% 97.60/13.23 ((
% 97.60/13.23 (kfstsingleton) =>
% 97.60/13.23 ((
% 97.60/13.23 (theprop) =>
% 97.60/13.23 ((
% 97.60/13.23 (kfstpairEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodfstin) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairinjL2) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairinjL) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairinjR11) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairinjR12) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairinjR1) =>
% 97.60/13.23 ((
% 97.60/13.23 (upairequniteq) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairinjR2) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairinjR) =>
% 97.60/13.23 ((
% 97.60/13.23 (ksndsingleton) =>
% 97.60/13.23 ((
% 97.60/13.23 (ksndpairEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (kpairsurjEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodsndin) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodpairmemEL) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodpairmemER) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodmempaircEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodfstpairEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodsndpairEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodpairsurjEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (dpsetconstrI) =>
% 97.60/13.23 ((
% 97.60/13.23 (dpsetconstrSub) =>
% 97.60/13.23 ((
% 97.60/13.23 (setOfPairsIsBReln) =>
% 97.60/13.23 ((
% 97.60/13.23 (dpsetconstrERa) =>
% 97.60/13.23 ((
% 97.60/13.23 (dpsetconstrEL1) =>
% 97.60/13.23 ((
% 97.60/13.23 (dpsetconstrEL2) =>
% 97.60/13.23 ((
% 97.60/13.23 (dpsetconstrER) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcImageSingleton) =>
% 97.60/13.23 ((
% 97.60/13.23 (apProp) =>
% 97.60/13.23 ((
% 97.60/13.23 (app) =>
% 97.60/13.23 ((
% 97.60/13.23 (infuncsetfunc) =>
% 97.60/13.23 ((
% 97.60/13.23 (ap2p) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcinfuncset) =>
% 97.60/13.23 ((
% 97.60/13.23 (lamProp) =>
% 97.60/13.23 ((
% 97.60/13.23 (lamp) =>
% 97.60/13.23 ((
% 97.60/13.23 (lam2p) =>
% 97.60/13.23 ((
% 97.60/13.23 (brelnall1) =>
% 97.60/13.23 ((
% 97.60/13.23 (brelnall2) =>
% 97.60/13.23 ((
% 97.60/13.23 (ex1E2) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcGraphProp1) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcGraphProp3) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcGraphProp2) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcextLem) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcGraphProp4) =>
% 97.60/13.23 ((
% 97.60/13.23 (subbreln) =>
% 97.60/13.23 ((
% 97.60/13.23 (eqbreln) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcext) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcext2) =>
% 97.60/13.23 ((
% 97.60/13.23 (ap2apEq1) =>
% 97.60/13.23 ((
% 97.60/13.23 (ap2apEq2) =>
% 97.60/13.23 ((
% 97.60/13.23 (beta1) =>
% 97.60/13.23 ((
% 97.60/13.23 (eta1) =>
% 97.60/13.23 ((
% 97.60/13.23 (lam2lamEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (beta2) =>
% 97.60/13.23 ((
% 97.60/13.23 (eta2) =>
% 97.60/13.23 ((
% 97.60/13.23 (iffalseProp1) =>
% 97.60/13.23 ((
% 97.60/13.23 (iffalseProp2) =>
% 97.60/13.23 ((
% 97.60/13.23 (iftrueProp1) =>
% 97.60/13.23 ((
% 97.60/13.23 (iftrueProp2) =>
% 97.60/13.23 ((
% 97.60/13.23 (ifSingleton) =>
% 97.60/13.23 ((
% 97.60/13.23 (ifp) =>
% 97.60/13.23 ((
% 97.60/13.23 (theeq) =>
% 97.60/13.23 ((
% 97.60/13.23 (iftrue) =>
% 97.60/13.23 ((
% 97.60/13.23 (iffalse) =>
% 97.60/13.23 ((
% 97.60/13.23 (iftrueorfalse) =>
% 97.60/13.23 ((
% 97.60/13.23 (binintersectT_lem) =>
% 97.60/13.23 ((
% 97.60/13.23 (binunionT_lem) =>
% 97.60/13.23 ((
% 97.60/13.23 (powersetT_lem) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusT_lem) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementT_lem) =>
% 97.60/13.23 ((
% 97.60/13.23 (setextT) =>
% 97.60/13.23 ((
% 97.60/13.23 (subsetTI) =>
% 97.60/13.23 ((
% 97.60/13.23 (powersetTI1) =>
% 97.60/13.23 ((
% 97.60/13.23 (powersetTE1) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementTI1) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementTE1) =>
% 97.60/13.23 ((
% 97.60/13.23 (binintersectTELcontra) =>
% 97.60/13.23 ((
% 97.60/13.23 (binintersectTERcontra) =>
% 97.60/13.23 ((
% 97.60/13.23 (contrasubsetT) =>
% 97.60/13.23 ((
% 97.60/13.23 (contrasubsetT1) =>
% 97.60/13.23 ((
% 97.60/13.23 (contrasubsetT2) =>
% 97.60/13.23 ((
% 97.60/13.23 (contrasubsetT3) =>
% 97.60/13.23 ((
% 97.60/13.23 (doubleComplementI1) =>
% 97.60/13.23 ((
% 97.60/13.23 (doubleComplementE1) =>
% 97.60/13.23 ((
% 97.60/13.23 (doubleComplementSub1) =>
% 97.60/13.23 ((
% 97.60/13.23 (doubleComplementSub2) =>
% 97.60/13.23 ((
% 97.60/13.23 (doubleComplementEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementTnotintersectT) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementImpComplementIntersect) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementSubsetComplementIntersect) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementInPowersetComplementIntersect) =>
% 97.60/13.23 ((
% 97.60/13.23 (contraSubsetComplement) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementTcontraSubset) =>
% 97.60/13.23 ((
% 97.60/13.23 (binunionTILcontra) =>
% 97.60/13.23 ((
% 97.60/13.23 (binunionTIRcontra) =>
% 97.60/13.23 ((
% 97.60/13.23 (inIntersectImpInUnion) =>
% 97.60/13.23 ((
% 97.60/13.23 (inIntersectImpInUnion2) =>
% 97.60/13.23 ((
% 97.60/13.23 (inIntersectImpInIntersectUnions) =>
% 97.60/13.23 ((
% 97.60/13.23 (intersectInPowersetIntersectUnions) =>
% 97.60/13.23 ((
% 97.60/13.23 (inComplementUnionImpNotIn1) =>
% 97.60/13.23 ((
% 97.60/13.23 (inComplementUnionImpInComplement1) =>
% 97.60/13.23 ((
% 97.60/13.23 (binunionTE) =>
% 97.60/13.23 ((
% 97.60/13.23 (binunionTEcontra) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan2a1) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementUnionInPowersetComplement) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan2a2) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan1a) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan1b) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan1) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan2a) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan2b2) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan2b) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan2) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz13rule0) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz13rule1) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz13rule2) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz13rule3) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz13rule4) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz1_1) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz1_2) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz1_3) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz1_4) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz1_5) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1all2) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1SetBreln1) =>
% 97.60/13.23 ((
% 97.60/13.23 (choice2fnsingleton) =>
% 97.60/13.23 ((
% 97.60/13.23 (setOfPairsIsBReln1) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1all1) =>
% 97.60/13.23 ((
% 97.60/13.23 (subbreln1) =>
% 97.60/13.23 ((
% 97.60/13.23 (eqbreln1) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1invprop) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1invI) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1invE) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1compprop) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1compI) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1compE) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1compEex) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1unionprop) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1unionIL) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1unionIR) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1unionI) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1unionE) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1unionEcases) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1unionCommutes) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz2Ex) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz2W) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz2A) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz2B) =>
% 97.60/13.23 ((
% 97.60/13.23 (image1Ex) =>
% 97.60/13.23 ((
% 97.60/13.23 (image1Ex1) =>
% 97.60/13.23 ((
% 97.60/13.23 (image1Equiv) =>
% 97.60/13.23 ((
% 97.60/13.23 (image1E) =>
% 97.60/13.23 ((
% 97.60/13.23 (image1I) =>
% 97.60/13.23 ((
% 97.60/13.23 (injFuncInInjFuncSet) =>
% 97.60/13.23 ((
% 97.60/13.23 (injFuncSetFuncIn) =>
% 97.60/13.23 ((
% 97.60/13.23 (injFuncSetFuncInj) =>
% 97.60/13.23 ((
% 97.60/13.23 (surjFuncSetFuncIn) =>
% 97.60/13.23 ((
% 97.60/13.23 (surjFuncSetFuncSurj) =>
% 97.60/13.23 ((
% 97.60/13.23 (leftInvIsSurj) =>
% 97.60/13.23 ((
% 97.60/13.23 (surjCantorThm) =>
% 97.60/13.23 ((
% 97.60/13.23 (foundation2) =>
% 97.60/13.23 ((
% 97.60/13.23 (notinself) =>
% 97.60/13.23 ((
% 97.60/13.23 (notinself2) =>
% 97.60/13.23 ((
% 97.60/13.23 (omegaSp) =>
% 97.60/13.23 ((
% 97.60/13.23 (omegaSclos) =>
% 97.60/13.23 ((
% 97.60/13.23 (peano0notS) =>
% 97.60/13.23 ((
% 97.60/13.23 (!!) @ (
% 97.60/13.23 (('#S') @ (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 =>) @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#C') @ in @
% 97.60/13.23 omega)))) @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 !!) @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 (
% 97.60/13.23 ('#S') @ (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 =>) @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#C') @ in @
% 97.60/13.23 omega)))))) @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#S') @ (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 '#S') @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 =>))) @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#C') @ (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 '#B') @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 =) @
% 97.60/13.23 omegaS)))) @
% 97.60/13.23 omegaS)))))) @
% 97.60/13.23 (
% 97.60/13.23 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.60/13.23 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl909])).
% 97.60/13.23 thf(zip_derived_cl938, plain,
% 97.60/13.23 (~ (((subsetRefl) =>
% 97.60/13.23 (((subsetTrans) =>
% 97.60/13.23 (((setadjoinSub) =>
% 97.60/13.23 (((setadjoinSub2) =>
% 97.60/13.23 (((subset2powerset) =>
% 97.60/13.23 (((setextsub) =>
% 97.60/13.23 (((subsetemptysetimpeq) =>
% 97.60/13.23 (((powersetI1) =>
% 97.60/13.23 (((powersetE1) =>
% 97.60/13.23 (((inPowerset) =>
% 97.60/13.23 (((powersetsubset) =>
% 97.60/13.23 (((sepInPowerset) =>
% 97.60/13.23 (((sepSubset) =>
% 97.60/13.23 (((binunionIL) =>
% 97.60/13.23 (((upairset2IR) =>
% 97.60/13.23 (((binunionIR) =>
% 97.60/13.23 (((binunionEcases) =>
% 97.60/13.23 (((binunionE) =>
% 97.60/13.23 (((binunionLsub) =>
% 97.60/13.23 (((binunionRsub) =>
% 97.60/13.23 (((binintersectI) =>
% 97.60/13.23 (((binintersectSubset5) =>
% 97.60/13.23 (((binintersectEL) =>
% 97.60/13.23 (((binintersectLsub) =>
% 97.60/13.23 (((binintersectSubset2) =>
% 97.60/13.23 (((binintersectSubset3) =>
% 97.60/13.23 (((binintersectER) =>
% 97.60/13.23 (((disjointsetsI1) =>
% 97.60/13.23 (((binintersectRsub) =>
% 97.60/13.23 (((binintersectSubset4) =>
% 97.60/13.23 ((
% 97.60/13.23 (binintersectSubset1) =>
% 97.60/13.23 ((
% 97.60/13.23 (bs114d) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusI) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusEL) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusER) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusSubset2) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusERneg) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusELneg) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusILneg) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusIRneg) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusLsub) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusSubset1) =>
% 97.60/13.23 ((
% 97.60/13.23 (symdiffE) =>
% 97.60/13.23 ((
% 97.60/13.23 (symdiffI1) =>
% 97.60/13.23 ((
% 97.60/13.23 (symdiffI2) =>
% 97.60/13.23 ((
% 97.60/13.23 (symdiffIneg1) =>
% 97.60/13.23 ((
% 97.60/13.23 (symdiffIneg2) =>
% 97.60/13.23 ((
% 97.60/13.23 (secondinupair) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairIL) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairIR) =>
% 97.60/13.23 ((
% 97.60/13.23 (kpairiskpair) =>
% 97.60/13.23 ((
% 97.60/13.23 (kpairp) =>
% 97.60/13.23 ((
% 97.60/13.23 (singletonsubset) =>
% 97.60/13.23 ((
% 97.60/13.23 (singletoninpowerset) =>
% 97.60/13.23 ((
% 97.60/13.23 (singletoninpowunion) =>
% 97.60/13.23 ((
% 97.60/13.23 (upairset2E) =>
% 97.60/13.23 ((
% 97.60/13.23 (upairsubunion) =>
% 97.60/13.23 ((
% 97.60/13.23 (upairinpowunion) =>
% 97.60/13.23 ((
% 97.60/13.23 (ubforcartprodlem1) =>
% 97.60/13.23 ((
% 97.60/13.23 (ubforcartprodlem2) =>
% 97.60/13.23 ((
% 97.60/13.23 (ubforcartprodlem3) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodpairin) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodmempair1) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodmempair) =>
% 97.60/13.23 ((
% 97.60/13.23 (setunionE2) =>
% 97.60/13.23 ((
% 97.60/13.23 (setunionsingleton1) =>
% 97.60/13.23 ((
% 97.60/13.23 (setunionsingleton2) =>
% 97.60/13.23 ((
% 97.60/13.23 (setunionsingleton) =>
% 97.60/13.23 ((
% 97.60/13.23 (singletonprop) =>
% 97.60/13.23 ((
% 97.60/13.23 (ex1E1) =>
% 97.60/13.23 ((
% 97.60/13.23 (ex1I) =>
% 97.60/13.23 ((
% 97.60/13.23 (ex1I2) =>
% 97.60/13.23 ((
% 97.60/13.23 (singletonsuniq) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairinjL1) =>
% 97.60/13.23 ((
% 97.60/13.23 (kfstsingleton) =>
% 97.60/13.23 ((
% 97.60/13.23 (theprop) =>
% 97.60/13.23 ((
% 97.60/13.23 (kfstpairEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodfstin) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairinjL2) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairinjL) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairinjR11) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairinjR12) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairinjR1) =>
% 97.60/13.23 ((
% 97.60/13.23 (upairequniteq) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairinjR2) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairinjR) =>
% 97.60/13.23 ((
% 97.60/13.23 (ksndsingleton) =>
% 97.60/13.23 ((
% 97.60/13.23 (ksndpairEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (kpairsurjEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodsndin) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodpairmemEL) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodpairmemER) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodmempaircEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodfstpairEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodsndpairEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodpairsurjEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (dpsetconstrI) =>
% 97.60/13.23 ((
% 97.60/13.23 (dpsetconstrSub) =>
% 97.60/13.23 ((
% 97.60/13.23 (setOfPairsIsBReln) =>
% 97.60/13.23 ((
% 97.60/13.23 (dpsetconstrERa) =>
% 97.60/13.23 ((
% 97.60/13.23 (dpsetconstrEL1) =>
% 97.60/13.23 ((
% 97.60/13.23 (dpsetconstrEL2) =>
% 97.60/13.23 ((
% 97.60/13.23 (dpsetconstrER) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcImageSingleton) =>
% 97.60/13.23 ((
% 97.60/13.23 (apProp) =>
% 97.60/13.23 ((
% 97.60/13.23 (app) =>
% 97.60/13.23 ((
% 97.60/13.23 (infuncsetfunc) =>
% 97.60/13.23 ((
% 97.60/13.23 (ap2p) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcinfuncset) =>
% 97.60/13.23 ((
% 97.60/13.23 (lamProp) =>
% 97.60/13.23 ((
% 97.60/13.23 (lamp) =>
% 97.60/13.23 ((
% 97.60/13.23 (lam2p) =>
% 97.60/13.23 ((
% 97.60/13.23 (brelnall1) =>
% 97.60/13.23 ((
% 97.60/13.23 (brelnall2) =>
% 97.60/13.23 ((
% 97.60/13.23 (ex1E2) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcGraphProp1) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcGraphProp3) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcGraphProp2) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcextLem) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcGraphProp4) =>
% 97.60/13.23 ((
% 97.60/13.23 (subbreln) =>
% 97.60/13.23 ((
% 97.60/13.23 (eqbreln) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcext) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcext2) =>
% 97.60/13.23 ((
% 97.60/13.23 (ap2apEq1) =>
% 97.60/13.23 ((
% 97.60/13.23 (ap2apEq2) =>
% 97.60/13.23 ((
% 97.60/13.23 (beta1) =>
% 97.60/13.23 ((
% 97.60/13.23 (eta1) =>
% 97.60/13.23 ((
% 97.60/13.23 (lam2lamEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (beta2) =>
% 97.60/13.23 ((
% 97.60/13.23 (eta2) =>
% 97.60/13.23 ((
% 97.60/13.23 (iffalseProp1) =>
% 97.60/13.23 ((
% 97.60/13.23 (iffalseProp2) =>
% 97.60/13.23 ((
% 97.60/13.23 (iftrueProp1) =>
% 97.60/13.23 ((
% 97.60/13.23 (iftrueProp2) =>
% 97.60/13.23 ((
% 97.60/13.23 (ifSingleton) =>
% 97.60/13.23 ((
% 97.60/13.23 (ifp) =>
% 97.60/13.23 ((
% 97.60/13.23 (theeq) =>
% 97.60/13.23 ((
% 97.60/13.23 (iftrue) =>
% 97.60/13.23 ((
% 97.60/13.23 (iffalse) =>
% 97.60/13.23 ((
% 97.60/13.23 (iftrueorfalse) =>
% 97.60/13.23 ((
% 97.60/13.23 (binintersectT_lem) =>
% 97.60/13.23 ((
% 97.60/13.23 (binunionT_lem) =>
% 97.60/13.23 ((
% 97.60/13.23 (powersetT_lem) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusT_lem) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementT_lem) =>
% 97.60/13.23 ((
% 97.60/13.23 (setextT) =>
% 97.60/13.23 ((
% 97.60/13.23 (subsetTI) =>
% 97.60/13.23 ((
% 97.60/13.23 (powersetTI1) =>
% 97.60/13.23 ((
% 97.60/13.23 (powersetTE1) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementTI1) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementTE1) =>
% 97.60/13.23 ((
% 97.60/13.23 (binintersectTELcontra) =>
% 97.60/13.23 ((
% 97.60/13.23 (binintersectTERcontra) =>
% 97.60/13.23 ((
% 97.60/13.23 (contrasubsetT) =>
% 97.60/13.23 ((
% 97.60/13.23 (contrasubsetT1) =>
% 97.60/13.23 ((
% 97.60/13.23 (contrasubsetT2) =>
% 97.60/13.23 ((
% 97.60/13.23 (contrasubsetT3) =>
% 97.60/13.23 ((
% 97.60/13.23 (doubleComplementI1) =>
% 97.60/13.23 ((
% 97.60/13.23 (doubleComplementE1) =>
% 97.60/13.23 ((
% 97.60/13.23 (doubleComplementSub1) =>
% 97.60/13.23 ((
% 97.60/13.23 (doubleComplementSub2) =>
% 97.60/13.23 ((
% 97.60/13.23 (doubleComplementEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementTnotintersectT) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementImpComplementIntersect) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementSubsetComplementIntersect) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementInPowersetComplementIntersect) =>
% 97.60/13.23 ((
% 97.60/13.23 (contraSubsetComplement) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementTcontraSubset) =>
% 97.60/13.23 ((
% 97.60/13.23 (binunionTILcontra) =>
% 97.60/13.23 ((
% 97.60/13.23 (binunionTIRcontra) =>
% 97.60/13.23 ((
% 97.60/13.23 (inIntersectImpInUnion) =>
% 97.60/13.23 ((
% 97.60/13.23 (inIntersectImpInUnion2) =>
% 97.60/13.23 ((
% 97.60/13.23 (inIntersectImpInIntersectUnions) =>
% 97.60/13.23 ((
% 97.60/13.23 (intersectInPowersetIntersectUnions) =>
% 97.60/13.23 ((
% 97.60/13.23 (inComplementUnionImpNotIn1) =>
% 97.60/13.23 ((
% 97.60/13.23 (inComplementUnionImpInComplement1) =>
% 97.60/13.23 ((
% 97.60/13.23 (binunionTE) =>
% 97.60/13.23 ((
% 97.60/13.23 (binunionTEcontra) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan2a1) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementUnionInPowersetComplement) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan2a2) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan1a) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan1b) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan1) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan2a) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan2b2) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan2b) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan2) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz13rule0) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz13rule1) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz13rule2) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz13rule3) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz13rule4) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz1_1) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz1_2) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz1_3) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz1_4) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz1_5) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1all2) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1SetBreln1) =>
% 97.60/13.23 ((
% 97.60/13.23 (choice2fnsingleton) =>
% 97.60/13.23 ((
% 97.60/13.23 (setOfPairsIsBReln1) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1all1) =>
% 97.60/13.23 ((
% 97.60/13.23 (subbreln1) =>
% 97.60/13.23 ((
% 97.60/13.23 (eqbreln1) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1invprop) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1invI) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1invE) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1compprop) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1compI) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1compE) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1compEex) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1unionprop) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1unionIL) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1unionIR) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1unionI) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1unionE) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1unionEcases) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1unionCommutes) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz2Ex) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz2W) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz2A) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz2B) =>
% 97.60/13.23 ((
% 97.60/13.23 (image1Ex) =>
% 97.60/13.23 ((
% 97.60/13.23 (image1Ex1) =>
% 97.60/13.23 ((
% 97.60/13.23 (image1Equiv) =>
% 97.60/13.23 ((
% 97.60/13.23 (image1E) =>
% 97.60/13.23 ((
% 97.60/13.23 (image1I) =>
% 97.60/13.23 ((
% 97.60/13.23 (injFuncInInjFuncSet) =>
% 97.60/13.23 ((
% 97.60/13.23 (injFuncSetFuncIn) =>
% 97.60/13.23 ((
% 97.60/13.23 (injFuncSetFuncInj) =>
% 97.60/13.23 ((
% 97.60/13.23 (surjFuncSetFuncIn) =>
% 97.60/13.23 ((
% 97.60/13.23 (surjFuncSetFuncSurj) =>
% 97.60/13.23 ((
% 97.60/13.23 (leftInvIsSurj) =>
% 97.60/13.23 ((
% 97.60/13.23 (surjCantorThm) =>
% 97.60/13.23 ((
% 97.60/13.23 (foundation2) =>
% 97.60/13.23 ((
% 97.60/13.23 (notinself) =>
% 97.60/13.23 ((
% 97.60/13.23 (notinself2) =>
% 97.60/13.23 ((
% 97.60/13.23 (omegaSp) =>
% 97.60/13.23 ((
% 97.60/13.23 (omegaSclos) =>
% 97.60/13.23 ((
% 97.60/13.23 (peano0notS) =>
% 97.60/13.23 ((
% 97.60/13.23 (!!) @ (
% 97.60/13.23 (('#S') @ (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 =>) @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#C') @ in @
% 97.60/13.23 omega)))) @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 !!) @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 (
% 97.60/13.23 ('#S') @ (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 =>) @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#C') @ in @
% 97.60/13.23 omega)))))) @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#S') @ (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 '#S') @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 =>))) @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#C') @ (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 '#B') @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 =) @
% 97.60/13.23 omegaS)))) @
% 97.60/13.23 omegaS)))))) @
% 97.60/13.23 (
% 97.60/13.23 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.60/13.23 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl924])).
% 97.60/13.23 thf(zip_derived_cl952, plain,
% 97.60/13.23 (~ (((subsetTrans) =>
% 97.60/13.23 (((setadjoinSub) =>
% 97.60/13.23 (((setadjoinSub2) =>
% 97.60/13.23 (((subset2powerset) =>
% 97.60/13.23 (((setextsub) =>
% 97.60/13.23 (((subsetemptysetimpeq) =>
% 97.60/13.23 (((powersetI1) =>
% 97.60/13.23 (((powersetE1) =>
% 97.60/13.23 (((inPowerset) =>
% 97.60/13.23 (((powersetsubset) =>
% 97.60/13.23 (((sepInPowerset) =>
% 97.60/13.23 (((sepSubset) =>
% 97.60/13.23 (((binunionIL) =>
% 97.60/13.23 (((upairset2IR) =>
% 97.60/13.23 (((binunionIR) =>
% 97.60/13.23 (((binunionEcases) =>
% 97.60/13.23 (((binunionE) =>
% 97.60/13.23 (((binunionLsub) =>
% 97.60/13.23 (((binunionRsub) =>
% 97.60/13.23 (((binintersectI) =>
% 97.60/13.23 (((binintersectSubset5) =>
% 97.60/13.23 (((binintersectEL) =>
% 97.60/13.23 (((binintersectLsub) =>
% 97.60/13.23 (((binintersectSubset2) =>
% 97.60/13.23 (((binintersectSubset3) =>
% 97.60/13.23 (((binintersectER) =>
% 97.60/13.23 (((disjointsetsI1) =>
% 97.60/13.23 (((binintersectRsub) =>
% 97.60/13.23 (((binintersectSubset4) =>
% 97.60/13.23 (((binintersectSubset1) =>
% 97.60/13.23 ((
% 97.60/13.23 (bs114d) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusI) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusEL) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusER) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusSubset2) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusERneg) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusELneg) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusILneg) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusIRneg) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusLsub) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusSubset1) =>
% 97.60/13.23 ((
% 97.60/13.23 (symdiffE) =>
% 97.60/13.23 ((
% 97.60/13.23 (symdiffI1) =>
% 97.60/13.23 ((
% 97.60/13.23 (symdiffI2) =>
% 97.60/13.23 ((
% 97.60/13.23 (symdiffIneg1) =>
% 97.60/13.23 ((
% 97.60/13.23 (symdiffIneg2) =>
% 97.60/13.23 ((
% 97.60/13.23 (secondinupair) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairIL) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairIR) =>
% 97.60/13.23 ((
% 97.60/13.23 (kpairiskpair) =>
% 97.60/13.23 ((
% 97.60/13.23 (kpairp) =>
% 97.60/13.23 ((
% 97.60/13.23 (singletonsubset) =>
% 97.60/13.23 ((
% 97.60/13.23 (singletoninpowerset) =>
% 97.60/13.23 ((
% 97.60/13.23 (singletoninpowunion) =>
% 97.60/13.23 ((
% 97.60/13.23 (upairset2E) =>
% 97.60/13.23 ((
% 97.60/13.23 (upairsubunion) =>
% 97.60/13.23 ((
% 97.60/13.23 (upairinpowunion) =>
% 97.60/13.23 ((
% 97.60/13.23 (ubforcartprodlem1) =>
% 97.60/13.23 ((
% 97.60/13.23 (ubforcartprodlem2) =>
% 97.60/13.23 ((
% 97.60/13.23 (ubforcartprodlem3) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodpairin) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodmempair1) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodmempair) =>
% 97.60/13.23 ((
% 97.60/13.23 (setunionE2) =>
% 97.60/13.23 ((
% 97.60/13.23 (setunionsingleton1) =>
% 97.60/13.23 ((
% 97.60/13.23 (setunionsingleton2) =>
% 97.60/13.23 ((
% 97.60/13.23 (setunionsingleton) =>
% 97.60/13.23 ((
% 97.60/13.23 (singletonprop) =>
% 97.60/13.23 ((
% 97.60/13.23 (ex1E1) =>
% 97.60/13.23 ((
% 97.60/13.23 (ex1I) =>
% 97.60/13.23 ((
% 97.60/13.23 (ex1I2) =>
% 97.60/13.23 ((
% 97.60/13.23 (singletonsuniq) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairinjL1) =>
% 97.60/13.23 ((
% 97.60/13.23 (kfstsingleton) =>
% 97.60/13.23 ((
% 97.60/13.23 (theprop) =>
% 97.60/13.23 ((
% 97.60/13.23 (kfstpairEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodfstin) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairinjL2) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairinjL) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairinjR11) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairinjR12) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairinjR1) =>
% 97.60/13.23 ((
% 97.60/13.23 (upairequniteq) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairinjR2) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairinjR) =>
% 97.60/13.23 ((
% 97.60/13.23 (ksndsingleton) =>
% 97.60/13.23 ((
% 97.60/13.23 (ksndpairEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (kpairsurjEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodsndin) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodpairmemEL) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodpairmemER) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodmempaircEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodfstpairEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodsndpairEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodpairsurjEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (dpsetconstrI) =>
% 97.60/13.23 ((
% 97.60/13.23 (dpsetconstrSub) =>
% 97.60/13.23 ((
% 97.60/13.23 (setOfPairsIsBReln) =>
% 97.60/13.23 ((
% 97.60/13.23 (dpsetconstrERa) =>
% 97.60/13.23 ((
% 97.60/13.23 (dpsetconstrEL1) =>
% 97.60/13.23 ((
% 97.60/13.23 (dpsetconstrEL2) =>
% 97.60/13.23 ((
% 97.60/13.23 (dpsetconstrER) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcImageSingleton) =>
% 97.60/13.23 ((
% 97.60/13.23 (apProp) =>
% 97.60/13.23 ((
% 97.60/13.23 (app) =>
% 97.60/13.23 ((
% 97.60/13.23 (infuncsetfunc) =>
% 97.60/13.23 ((
% 97.60/13.23 (ap2p) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcinfuncset) =>
% 97.60/13.23 ((
% 97.60/13.23 (lamProp) =>
% 97.60/13.23 ((
% 97.60/13.23 (lamp) =>
% 97.60/13.23 ((
% 97.60/13.23 (lam2p) =>
% 97.60/13.23 ((
% 97.60/13.23 (brelnall1) =>
% 97.60/13.23 ((
% 97.60/13.23 (brelnall2) =>
% 97.60/13.23 ((
% 97.60/13.23 (ex1E2) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcGraphProp1) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcGraphProp3) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcGraphProp2) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcextLem) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcGraphProp4) =>
% 97.60/13.23 ((
% 97.60/13.23 (subbreln) =>
% 97.60/13.23 ((
% 97.60/13.23 (eqbreln) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcext) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcext2) =>
% 97.60/13.23 ((
% 97.60/13.23 (ap2apEq1) =>
% 97.60/13.23 ((
% 97.60/13.23 (ap2apEq2) =>
% 97.60/13.23 ((
% 97.60/13.23 (beta1) =>
% 97.60/13.23 ((
% 97.60/13.23 (eta1) =>
% 97.60/13.23 ((
% 97.60/13.23 (lam2lamEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (beta2) =>
% 97.60/13.23 ((
% 97.60/13.23 (eta2) =>
% 97.60/13.23 ((
% 97.60/13.23 (iffalseProp1) =>
% 97.60/13.23 ((
% 97.60/13.23 (iffalseProp2) =>
% 97.60/13.23 ((
% 97.60/13.23 (iftrueProp1) =>
% 97.60/13.23 ((
% 97.60/13.23 (iftrueProp2) =>
% 97.60/13.23 ((
% 97.60/13.23 (ifSingleton) =>
% 97.60/13.23 ((
% 97.60/13.23 (ifp) =>
% 97.60/13.23 ((
% 97.60/13.23 (theeq) =>
% 97.60/13.23 ((
% 97.60/13.23 (iftrue) =>
% 97.60/13.23 ((
% 97.60/13.23 (iffalse) =>
% 97.60/13.23 ((
% 97.60/13.23 (iftrueorfalse) =>
% 97.60/13.23 ((
% 97.60/13.23 (binintersectT_lem) =>
% 97.60/13.23 ((
% 97.60/13.23 (binunionT_lem) =>
% 97.60/13.23 ((
% 97.60/13.23 (powersetT_lem) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusT_lem) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementT_lem) =>
% 97.60/13.23 ((
% 97.60/13.23 (setextT) =>
% 97.60/13.23 ((
% 97.60/13.23 (subsetTI) =>
% 97.60/13.23 ((
% 97.60/13.23 (powersetTI1) =>
% 97.60/13.23 ((
% 97.60/13.23 (powersetTE1) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementTI1) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementTE1) =>
% 97.60/13.23 ((
% 97.60/13.23 (binintersectTELcontra) =>
% 97.60/13.23 ((
% 97.60/13.23 (binintersectTERcontra) =>
% 97.60/13.23 ((
% 97.60/13.23 (contrasubsetT) =>
% 97.60/13.23 ((
% 97.60/13.23 (contrasubsetT1) =>
% 97.60/13.23 ((
% 97.60/13.23 (contrasubsetT2) =>
% 97.60/13.23 ((
% 97.60/13.23 (contrasubsetT3) =>
% 97.60/13.23 ((
% 97.60/13.23 (doubleComplementI1) =>
% 97.60/13.23 ((
% 97.60/13.23 (doubleComplementE1) =>
% 97.60/13.23 ((
% 97.60/13.23 (doubleComplementSub1) =>
% 97.60/13.23 ((
% 97.60/13.23 (doubleComplementSub2) =>
% 97.60/13.23 ((
% 97.60/13.23 (doubleComplementEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementTnotintersectT) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementImpComplementIntersect) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementSubsetComplementIntersect) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementInPowersetComplementIntersect) =>
% 97.60/13.23 ((
% 97.60/13.23 (contraSubsetComplement) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementTcontraSubset) =>
% 97.60/13.23 ((
% 97.60/13.23 (binunionTILcontra) =>
% 97.60/13.23 ((
% 97.60/13.23 (binunionTIRcontra) =>
% 97.60/13.23 ((
% 97.60/13.23 (inIntersectImpInUnion) =>
% 97.60/13.23 ((
% 97.60/13.23 (inIntersectImpInUnion2) =>
% 97.60/13.23 ((
% 97.60/13.23 (inIntersectImpInIntersectUnions) =>
% 97.60/13.23 ((
% 97.60/13.23 (intersectInPowersetIntersectUnions) =>
% 97.60/13.23 ((
% 97.60/13.23 (inComplementUnionImpNotIn1) =>
% 97.60/13.23 ((
% 97.60/13.23 (inComplementUnionImpInComplement1) =>
% 97.60/13.23 ((
% 97.60/13.23 (binunionTE) =>
% 97.60/13.23 ((
% 97.60/13.23 (binunionTEcontra) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan2a1) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementUnionInPowersetComplement) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan2a2) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan1a) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan1b) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan1) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan2a) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan2b2) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan2b) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan2) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz13rule0) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz13rule1) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz13rule2) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz13rule3) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz13rule4) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz1_1) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz1_2) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz1_3) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz1_4) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz1_5) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1all2) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1SetBreln1) =>
% 97.60/13.23 ((
% 97.60/13.23 (choice2fnsingleton) =>
% 97.60/13.23 ((
% 97.60/13.23 (setOfPairsIsBReln1) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1all1) =>
% 97.60/13.23 ((
% 97.60/13.23 (subbreln1) =>
% 97.60/13.23 ((
% 97.60/13.23 (eqbreln1) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1invprop) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1invI) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1invE) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1compprop) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1compI) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1compE) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1compEex) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1unionprop) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1unionIL) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1unionIR) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1unionI) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1unionE) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1unionEcases) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1unionCommutes) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz2Ex) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz2W) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz2A) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz2B) =>
% 97.60/13.23 ((
% 97.60/13.23 (image1Ex) =>
% 97.60/13.23 ((
% 97.60/13.23 (image1Ex1) =>
% 97.60/13.23 ((
% 97.60/13.23 (image1Equiv) =>
% 97.60/13.23 ((
% 97.60/13.23 (image1E) =>
% 97.60/13.23 ((
% 97.60/13.23 (image1I) =>
% 97.60/13.23 ((
% 97.60/13.23 (injFuncInInjFuncSet) =>
% 97.60/13.23 ((
% 97.60/13.23 (injFuncSetFuncIn) =>
% 97.60/13.23 ((
% 97.60/13.23 (injFuncSetFuncInj) =>
% 97.60/13.23 ((
% 97.60/13.23 (surjFuncSetFuncIn) =>
% 97.60/13.23 ((
% 97.60/13.23 (surjFuncSetFuncSurj) =>
% 97.60/13.23 ((
% 97.60/13.23 (leftInvIsSurj) =>
% 97.60/13.23 ((
% 97.60/13.23 (surjCantorThm) =>
% 97.60/13.23 ((
% 97.60/13.23 (foundation2) =>
% 97.60/13.23 ((
% 97.60/13.23 (notinself) =>
% 97.60/13.23 ((
% 97.60/13.23 (notinself2) =>
% 97.60/13.23 ((
% 97.60/13.23 (omegaSp) =>
% 97.60/13.23 ((
% 97.60/13.23 (omegaSclos) =>
% 97.60/13.23 ((
% 97.60/13.23 (peano0notS) =>
% 97.60/13.23 ((
% 97.60/13.23 (!!) @ (
% 97.60/13.23 (('#S') @ (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 =>) @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#C') @ in @
% 97.60/13.23 omega)))) @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 !!) @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 (
% 97.60/13.23 ('#S') @ (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 =>) @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#C') @ in @
% 97.60/13.23 omega)))))) @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#S') @ (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 '#S') @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 =>))) @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#C') @ (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 '#B') @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 =) @
% 97.60/13.23 omegaS)))) @
% 97.60/13.23 omegaS)))))) @
% 97.60/13.23 (
% 97.60/13.23 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.60/13.23 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl938])).
% 97.60/13.23 thf(zip_derived_cl967, plain,
% 97.60/13.23 (~ (((setadjoinSub) =>
% 97.60/13.23 (((setadjoinSub2) =>
% 97.60/13.23 (((subset2powerset) =>
% 97.60/13.23 (((setextsub) =>
% 97.60/13.23 (((subsetemptysetimpeq) =>
% 97.60/13.23 (((powersetI1) =>
% 97.60/13.23 (((powersetE1) =>
% 97.60/13.23 (((inPowerset) =>
% 97.60/13.23 (((powersetsubset) =>
% 97.60/13.23 (((sepInPowerset) =>
% 97.60/13.23 (((sepSubset) =>
% 97.60/13.23 (((binunionIL) =>
% 97.60/13.23 (((upairset2IR) =>
% 97.60/13.23 (((binunionIR) =>
% 97.60/13.23 (((binunionEcases) =>
% 97.60/13.23 (((binunionE) =>
% 97.60/13.23 (((binunionLsub) =>
% 97.60/13.23 (((binunionRsub) =>
% 97.60/13.23 (((binintersectI) =>
% 97.60/13.23 (((binintersectSubset5) =>
% 97.60/13.23 (((binintersectEL) =>
% 97.60/13.23 (((binintersectLsub) =>
% 97.60/13.23 (((binintersectSubset2) =>
% 97.60/13.23 (((binintersectSubset3) =>
% 97.60/13.23 (((binintersectER) =>
% 97.60/13.23 (((disjointsetsI1) =>
% 97.60/13.23 (((binintersectRsub) =>
% 97.60/13.23 (((binintersectSubset4) =>
% 97.60/13.23 (((binintersectSubset1) =>
% 97.60/13.23 (((bs114d) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusI) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusEL) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusER) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusSubset2) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusERneg) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusELneg) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusILneg) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusIRneg) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusLsub) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusSubset1) =>
% 97.60/13.23 ((
% 97.60/13.23 (symdiffE) =>
% 97.60/13.23 ((
% 97.60/13.23 (symdiffI1) =>
% 97.60/13.23 ((
% 97.60/13.23 (symdiffI2) =>
% 97.60/13.23 ((
% 97.60/13.23 (symdiffIneg1) =>
% 97.60/13.23 ((
% 97.60/13.23 (symdiffIneg2) =>
% 97.60/13.23 ((
% 97.60/13.23 (secondinupair) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairIL) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairIR) =>
% 97.60/13.23 ((
% 97.60/13.23 (kpairiskpair) =>
% 97.60/13.23 ((
% 97.60/13.23 (kpairp) =>
% 97.60/13.23 ((
% 97.60/13.23 (singletonsubset) =>
% 97.60/13.23 ((
% 97.60/13.23 (singletoninpowerset) =>
% 97.60/13.23 ((
% 97.60/13.23 (singletoninpowunion) =>
% 97.60/13.23 ((
% 97.60/13.23 (upairset2E) =>
% 97.60/13.23 ((
% 97.60/13.23 (upairsubunion) =>
% 97.60/13.23 ((
% 97.60/13.23 (upairinpowunion) =>
% 97.60/13.23 ((
% 97.60/13.23 (ubforcartprodlem1) =>
% 97.60/13.23 ((
% 97.60/13.23 (ubforcartprodlem2) =>
% 97.60/13.23 ((
% 97.60/13.23 (ubforcartprodlem3) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodpairin) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodmempair1) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodmempair) =>
% 97.60/13.23 ((
% 97.60/13.23 (setunionE2) =>
% 97.60/13.23 ((
% 97.60/13.23 (setunionsingleton1) =>
% 97.60/13.23 ((
% 97.60/13.23 (setunionsingleton2) =>
% 97.60/13.23 ((
% 97.60/13.23 (setunionsingleton) =>
% 97.60/13.23 ((
% 97.60/13.23 (singletonprop) =>
% 97.60/13.23 ((
% 97.60/13.23 (ex1E1) =>
% 97.60/13.23 ((
% 97.60/13.23 (ex1I) =>
% 97.60/13.23 ((
% 97.60/13.23 (ex1I2) =>
% 97.60/13.23 ((
% 97.60/13.23 (singletonsuniq) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairinjL1) =>
% 97.60/13.23 ((
% 97.60/13.23 (kfstsingleton) =>
% 97.60/13.23 ((
% 97.60/13.23 (theprop) =>
% 97.60/13.23 ((
% 97.60/13.23 (kfstpairEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodfstin) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairinjL2) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairinjL) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairinjR11) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairinjR12) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairinjR1) =>
% 97.60/13.23 ((
% 97.60/13.23 (upairequniteq) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairinjR2) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairinjR) =>
% 97.60/13.23 ((
% 97.60/13.23 (ksndsingleton) =>
% 97.60/13.23 ((
% 97.60/13.23 (ksndpairEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (kpairsurjEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodsndin) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodpairmemEL) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodpairmemER) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodmempaircEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodfstpairEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodsndpairEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodpairsurjEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (dpsetconstrI) =>
% 97.60/13.23 ((
% 97.60/13.23 (dpsetconstrSub) =>
% 97.60/13.23 ((
% 97.60/13.23 (setOfPairsIsBReln) =>
% 97.60/13.23 ((
% 97.60/13.23 (dpsetconstrERa) =>
% 97.60/13.23 ((
% 97.60/13.23 (dpsetconstrEL1) =>
% 97.60/13.23 ((
% 97.60/13.23 (dpsetconstrEL2) =>
% 97.60/13.23 ((
% 97.60/13.23 (dpsetconstrER) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcImageSingleton) =>
% 97.60/13.23 ((
% 97.60/13.23 (apProp) =>
% 97.60/13.23 ((
% 97.60/13.23 (app) =>
% 97.60/13.23 ((
% 97.60/13.23 (infuncsetfunc) =>
% 97.60/13.23 ((
% 97.60/13.23 (ap2p) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcinfuncset) =>
% 97.60/13.23 ((
% 97.60/13.23 (lamProp) =>
% 97.60/13.23 ((
% 97.60/13.23 (lamp) =>
% 97.60/13.23 ((
% 97.60/13.23 (lam2p) =>
% 97.60/13.23 ((
% 97.60/13.23 (brelnall1) =>
% 97.60/13.23 ((
% 97.60/13.23 (brelnall2) =>
% 97.60/13.23 ((
% 97.60/13.23 (ex1E2) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcGraphProp1) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcGraphProp3) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcGraphProp2) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcextLem) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcGraphProp4) =>
% 97.60/13.23 ((
% 97.60/13.23 (subbreln) =>
% 97.60/13.23 ((
% 97.60/13.23 (eqbreln) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcext) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcext2) =>
% 97.60/13.23 ((
% 97.60/13.23 (ap2apEq1) =>
% 97.60/13.23 ((
% 97.60/13.23 (ap2apEq2) =>
% 97.60/13.23 ((
% 97.60/13.23 (beta1) =>
% 97.60/13.23 ((
% 97.60/13.23 (eta1) =>
% 97.60/13.23 ((
% 97.60/13.23 (lam2lamEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (beta2) =>
% 97.60/13.23 ((
% 97.60/13.23 (eta2) =>
% 97.60/13.23 ((
% 97.60/13.23 (iffalseProp1) =>
% 97.60/13.23 ((
% 97.60/13.23 (iffalseProp2) =>
% 97.60/13.23 ((
% 97.60/13.23 (iftrueProp1) =>
% 97.60/13.23 ((
% 97.60/13.23 (iftrueProp2) =>
% 97.60/13.23 ((
% 97.60/13.23 (ifSingleton) =>
% 97.60/13.23 ((
% 97.60/13.23 (ifp) =>
% 97.60/13.23 ((
% 97.60/13.23 (theeq) =>
% 97.60/13.23 ((
% 97.60/13.23 (iftrue) =>
% 97.60/13.23 ((
% 97.60/13.23 (iffalse) =>
% 97.60/13.23 ((
% 97.60/13.23 (iftrueorfalse) =>
% 97.60/13.23 ((
% 97.60/13.23 (binintersectT_lem) =>
% 97.60/13.23 ((
% 97.60/13.23 (binunionT_lem) =>
% 97.60/13.23 ((
% 97.60/13.23 (powersetT_lem) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusT_lem) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementT_lem) =>
% 97.60/13.23 ((
% 97.60/13.23 (setextT) =>
% 97.60/13.23 ((
% 97.60/13.23 (subsetTI) =>
% 97.60/13.23 ((
% 97.60/13.23 (powersetTI1) =>
% 97.60/13.23 ((
% 97.60/13.23 (powersetTE1) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementTI1) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementTE1) =>
% 97.60/13.23 ((
% 97.60/13.23 (binintersectTELcontra) =>
% 97.60/13.23 ((
% 97.60/13.23 (binintersectTERcontra) =>
% 97.60/13.23 ((
% 97.60/13.23 (contrasubsetT) =>
% 97.60/13.23 ((
% 97.60/13.23 (contrasubsetT1) =>
% 97.60/13.23 ((
% 97.60/13.23 (contrasubsetT2) =>
% 97.60/13.23 ((
% 97.60/13.23 (contrasubsetT3) =>
% 97.60/13.23 ((
% 97.60/13.23 (doubleComplementI1) =>
% 97.60/13.23 ((
% 97.60/13.23 (doubleComplementE1) =>
% 97.60/13.23 ((
% 97.60/13.23 (doubleComplementSub1) =>
% 97.60/13.23 ((
% 97.60/13.23 (doubleComplementSub2) =>
% 97.60/13.23 ((
% 97.60/13.23 (doubleComplementEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementTnotintersectT) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementImpComplementIntersect) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementSubsetComplementIntersect) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementInPowersetComplementIntersect) =>
% 97.60/13.23 ((
% 97.60/13.23 (contraSubsetComplement) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementTcontraSubset) =>
% 97.60/13.23 ((
% 97.60/13.23 (binunionTILcontra) =>
% 97.60/13.23 ((
% 97.60/13.23 (binunionTIRcontra) =>
% 97.60/13.23 ((
% 97.60/13.23 (inIntersectImpInUnion) =>
% 97.60/13.23 ((
% 97.60/13.23 (inIntersectImpInUnion2) =>
% 97.60/13.23 ((
% 97.60/13.23 (inIntersectImpInIntersectUnions) =>
% 97.60/13.23 ((
% 97.60/13.23 (intersectInPowersetIntersectUnions) =>
% 97.60/13.23 ((
% 97.60/13.23 (inComplementUnionImpNotIn1) =>
% 97.60/13.23 ((
% 97.60/13.23 (inComplementUnionImpInComplement1) =>
% 97.60/13.23 ((
% 97.60/13.23 (binunionTE) =>
% 97.60/13.23 ((
% 97.60/13.23 (binunionTEcontra) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan2a1) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementUnionInPowersetComplement) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan2a2) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan1a) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan1b) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan1) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan2a) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan2b2) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan2b) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan2) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz13rule0) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz13rule1) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz13rule2) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz13rule3) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz13rule4) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz1_1) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz1_2) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz1_3) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz1_4) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz1_5) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1all2) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1SetBreln1) =>
% 97.60/13.23 ((
% 97.60/13.23 (choice2fnsingleton) =>
% 97.60/13.23 ((
% 97.60/13.23 (setOfPairsIsBReln1) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1all1) =>
% 97.60/13.23 ((
% 97.60/13.23 (subbreln1) =>
% 97.60/13.23 ((
% 97.60/13.23 (eqbreln1) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1invprop) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1invI) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1invE) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1compprop) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1compI) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1compE) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1compEex) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1unionprop) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1unionIL) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1unionIR) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1unionI) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1unionE) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1unionEcases) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1unionCommutes) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz2Ex) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz2W) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz2A) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz2B) =>
% 97.60/13.23 ((
% 97.60/13.23 (image1Ex) =>
% 97.60/13.23 ((
% 97.60/13.23 (image1Ex1) =>
% 97.60/13.23 ((
% 97.60/13.23 (image1Equiv) =>
% 97.60/13.23 ((
% 97.60/13.23 (image1E) =>
% 97.60/13.23 ((
% 97.60/13.23 (image1I) =>
% 97.60/13.23 ((
% 97.60/13.23 (injFuncInInjFuncSet) =>
% 97.60/13.23 ((
% 97.60/13.23 (injFuncSetFuncIn) =>
% 97.60/13.23 ((
% 97.60/13.23 (injFuncSetFuncInj) =>
% 97.60/13.23 ((
% 97.60/13.23 (surjFuncSetFuncIn) =>
% 97.60/13.23 ((
% 97.60/13.23 (surjFuncSetFuncSurj) =>
% 97.60/13.23 ((
% 97.60/13.23 (leftInvIsSurj) =>
% 97.60/13.23 ((
% 97.60/13.23 (surjCantorThm) =>
% 97.60/13.23 ((
% 97.60/13.23 (foundation2) =>
% 97.60/13.23 ((
% 97.60/13.23 (notinself) =>
% 97.60/13.23 ((
% 97.60/13.23 (notinself2) =>
% 97.60/13.23 ((
% 97.60/13.23 (omegaSp) =>
% 97.60/13.23 ((
% 97.60/13.23 (omegaSclos) =>
% 97.60/13.23 ((
% 97.60/13.23 (peano0notS) =>
% 97.60/13.23 ((
% 97.60/13.23 (!!) @ (
% 97.60/13.23 (('#S') @ (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 =>) @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#C') @ in @
% 97.60/13.23 omega)))) @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 !!) @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 (
% 97.60/13.23 ('#S') @ (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 =>) @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#C') @ in @
% 97.60/13.23 omega)))))) @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#S') @ (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 '#S') @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 =>))) @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#C') @ (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 '#B') @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 =) @
% 97.60/13.23 omegaS)))) @
% 97.60/13.23 omegaS)))))) @
% 97.60/13.23 (
% 97.60/13.23 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.60/13.23 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl952])).
% 97.60/13.23 thf(zip_derived_cl984, plain,
% 97.60/13.23 (~ (((setadjoinSub2) =>
% 97.60/13.23 (((subset2powerset) =>
% 97.60/13.23 (((setextsub) =>
% 97.60/13.23 (((subsetemptysetimpeq) =>
% 97.60/13.23 (((powersetI1) =>
% 97.60/13.23 (((powersetE1) =>
% 97.60/13.23 (((inPowerset) =>
% 97.60/13.23 (((powersetsubset) =>
% 97.60/13.23 (((sepInPowerset) =>
% 97.60/13.23 (((sepSubset) =>
% 97.60/13.23 (((binunionIL) =>
% 97.60/13.23 (((upairset2IR) =>
% 97.60/13.23 (((binunionIR) =>
% 97.60/13.23 (((binunionEcases) =>
% 97.60/13.23 (((binunionE) =>
% 97.60/13.23 (((binunionLsub) =>
% 97.60/13.23 (((binunionRsub) =>
% 97.60/13.23 (((binintersectI) =>
% 97.60/13.23 (((binintersectSubset5) =>
% 97.60/13.23 (((binintersectEL) =>
% 97.60/13.23 (((binintersectLsub) =>
% 97.60/13.23 (((binintersectSubset2) =>
% 97.60/13.23 (((binintersectSubset3) =>
% 97.60/13.23 (((binintersectER) =>
% 97.60/13.23 (((disjointsetsI1) =>
% 97.60/13.23 (((binintersectRsub) =>
% 97.60/13.23 (((binintersectSubset4) =>
% 97.60/13.23 (((binintersectSubset1) =>
% 97.60/13.23 (((bs114d) =>
% 97.60/13.23 (((setminusI) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusEL) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusER) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusSubset2) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusERneg) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusELneg) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusILneg) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusIRneg) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusLsub) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusSubset1) =>
% 97.60/13.23 ((
% 97.60/13.23 (symdiffE) =>
% 97.60/13.23 ((
% 97.60/13.23 (symdiffI1) =>
% 97.60/13.23 ((
% 97.60/13.23 (symdiffI2) =>
% 97.60/13.23 ((
% 97.60/13.23 (symdiffIneg1) =>
% 97.60/13.23 ((
% 97.60/13.23 (symdiffIneg2) =>
% 97.60/13.23 ((
% 97.60/13.23 (secondinupair) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairIL) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairIR) =>
% 97.60/13.23 ((
% 97.60/13.23 (kpairiskpair) =>
% 97.60/13.23 ((
% 97.60/13.23 (kpairp) =>
% 97.60/13.23 ((
% 97.60/13.23 (singletonsubset) =>
% 97.60/13.23 ((
% 97.60/13.23 (singletoninpowerset) =>
% 97.60/13.23 ((
% 97.60/13.23 (singletoninpowunion) =>
% 97.60/13.23 ((
% 97.60/13.23 (upairset2E) =>
% 97.60/13.23 ((
% 97.60/13.23 (upairsubunion) =>
% 97.60/13.23 ((
% 97.60/13.23 (upairinpowunion) =>
% 97.60/13.23 ((
% 97.60/13.23 (ubforcartprodlem1) =>
% 97.60/13.23 ((
% 97.60/13.23 (ubforcartprodlem2) =>
% 97.60/13.23 ((
% 97.60/13.23 (ubforcartprodlem3) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodpairin) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodmempair1) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodmempair) =>
% 97.60/13.23 ((
% 97.60/13.23 (setunionE2) =>
% 97.60/13.23 ((
% 97.60/13.23 (setunionsingleton1) =>
% 97.60/13.23 ((
% 97.60/13.23 (setunionsingleton2) =>
% 97.60/13.23 ((
% 97.60/13.23 (setunionsingleton) =>
% 97.60/13.23 ((
% 97.60/13.23 (singletonprop) =>
% 97.60/13.23 ((
% 97.60/13.23 (ex1E1) =>
% 97.60/13.23 ((
% 97.60/13.23 (ex1I) =>
% 97.60/13.23 ((
% 97.60/13.23 (ex1I2) =>
% 97.60/13.23 ((
% 97.60/13.23 (singletonsuniq) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairinjL1) =>
% 97.60/13.23 ((
% 97.60/13.23 (kfstsingleton) =>
% 97.60/13.23 ((
% 97.60/13.23 (theprop) =>
% 97.60/13.23 ((
% 97.60/13.23 (kfstpairEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodfstin) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairinjL2) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairinjL) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairinjR11) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairinjR12) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairinjR1) =>
% 97.60/13.23 ((
% 97.60/13.23 (upairequniteq) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairinjR2) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairinjR) =>
% 97.60/13.23 ((
% 97.60/13.23 (ksndsingleton) =>
% 97.60/13.23 ((
% 97.60/13.23 (ksndpairEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (kpairsurjEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodsndin) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodpairmemEL) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodpairmemER) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodmempaircEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodfstpairEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodsndpairEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodpairsurjEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (dpsetconstrI) =>
% 97.60/13.23 ((
% 97.60/13.23 (dpsetconstrSub) =>
% 97.60/13.23 ((
% 97.60/13.23 (setOfPairsIsBReln) =>
% 97.60/13.23 ((
% 97.60/13.23 (dpsetconstrERa) =>
% 97.60/13.23 ((
% 97.60/13.23 (dpsetconstrEL1) =>
% 97.60/13.23 ((
% 97.60/13.23 (dpsetconstrEL2) =>
% 97.60/13.23 ((
% 97.60/13.23 (dpsetconstrER) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcImageSingleton) =>
% 97.60/13.23 ((
% 97.60/13.23 (apProp) =>
% 97.60/13.23 ((
% 97.60/13.23 (app) =>
% 97.60/13.23 ((
% 97.60/13.23 (infuncsetfunc) =>
% 97.60/13.23 ((
% 97.60/13.23 (ap2p) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcinfuncset) =>
% 97.60/13.23 ((
% 97.60/13.23 (lamProp) =>
% 97.60/13.23 ((
% 97.60/13.23 (lamp) =>
% 97.60/13.23 ((
% 97.60/13.23 (lam2p) =>
% 97.60/13.23 ((
% 97.60/13.23 (brelnall1) =>
% 97.60/13.23 ((
% 97.60/13.23 (brelnall2) =>
% 97.60/13.23 ((
% 97.60/13.23 (ex1E2) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcGraphProp1) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcGraphProp3) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcGraphProp2) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcextLem) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcGraphProp4) =>
% 97.60/13.23 ((
% 97.60/13.23 (subbreln) =>
% 97.60/13.23 ((
% 97.60/13.23 (eqbreln) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcext) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcext2) =>
% 97.60/13.23 ((
% 97.60/13.23 (ap2apEq1) =>
% 97.60/13.23 ((
% 97.60/13.23 (ap2apEq2) =>
% 97.60/13.23 ((
% 97.60/13.23 (beta1) =>
% 97.60/13.23 ((
% 97.60/13.23 (eta1) =>
% 97.60/13.23 ((
% 97.60/13.23 (lam2lamEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (beta2) =>
% 97.60/13.23 ((
% 97.60/13.23 (eta2) =>
% 97.60/13.23 ((
% 97.60/13.23 (iffalseProp1) =>
% 97.60/13.23 ((
% 97.60/13.23 (iffalseProp2) =>
% 97.60/13.23 ((
% 97.60/13.23 (iftrueProp1) =>
% 97.60/13.23 ((
% 97.60/13.23 (iftrueProp2) =>
% 97.60/13.23 ((
% 97.60/13.23 (ifSingleton) =>
% 97.60/13.23 ((
% 97.60/13.23 (ifp) =>
% 97.60/13.23 ((
% 97.60/13.23 (theeq) =>
% 97.60/13.23 ((
% 97.60/13.23 (iftrue) =>
% 97.60/13.23 ((
% 97.60/13.23 (iffalse) =>
% 97.60/13.23 ((
% 97.60/13.23 (iftrueorfalse) =>
% 97.60/13.23 ((
% 97.60/13.23 (binintersectT_lem) =>
% 97.60/13.23 ((
% 97.60/13.23 (binunionT_lem) =>
% 97.60/13.23 ((
% 97.60/13.23 (powersetT_lem) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusT_lem) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementT_lem) =>
% 97.60/13.23 ((
% 97.60/13.23 (setextT) =>
% 97.60/13.23 ((
% 97.60/13.23 (subsetTI) =>
% 97.60/13.23 ((
% 97.60/13.23 (powersetTI1) =>
% 97.60/13.23 ((
% 97.60/13.23 (powersetTE1) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementTI1) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementTE1) =>
% 97.60/13.23 ((
% 97.60/13.23 (binintersectTELcontra) =>
% 97.60/13.23 ((
% 97.60/13.23 (binintersectTERcontra) =>
% 97.60/13.23 ((
% 97.60/13.23 (contrasubsetT) =>
% 97.60/13.23 ((
% 97.60/13.23 (contrasubsetT1) =>
% 97.60/13.23 ((
% 97.60/13.23 (contrasubsetT2) =>
% 97.60/13.23 ((
% 97.60/13.23 (contrasubsetT3) =>
% 97.60/13.23 ((
% 97.60/13.23 (doubleComplementI1) =>
% 97.60/13.23 ((
% 97.60/13.23 (doubleComplementE1) =>
% 97.60/13.23 ((
% 97.60/13.23 (doubleComplementSub1) =>
% 97.60/13.23 ((
% 97.60/13.23 (doubleComplementSub2) =>
% 97.60/13.23 ((
% 97.60/13.23 (doubleComplementEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementTnotintersectT) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementImpComplementIntersect) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementSubsetComplementIntersect) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementInPowersetComplementIntersect) =>
% 97.60/13.23 ((
% 97.60/13.23 (contraSubsetComplement) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementTcontraSubset) =>
% 97.60/13.23 ((
% 97.60/13.23 (binunionTILcontra) =>
% 97.60/13.23 ((
% 97.60/13.23 (binunionTIRcontra) =>
% 97.60/13.23 ((
% 97.60/13.23 (inIntersectImpInUnion) =>
% 97.60/13.23 ((
% 97.60/13.23 (inIntersectImpInUnion2) =>
% 97.60/13.23 ((
% 97.60/13.23 (inIntersectImpInIntersectUnions) =>
% 97.60/13.23 ((
% 97.60/13.23 (intersectInPowersetIntersectUnions) =>
% 97.60/13.23 ((
% 97.60/13.23 (inComplementUnionImpNotIn1) =>
% 97.60/13.23 ((
% 97.60/13.23 (inComplementUnionImpInComplement1) =>
% 97.60/13.23 ((
% 97.60/13.23 (binunionTE) =>
% 97.60/13.23 ((
% 97.60/13.23 (binunionTEcontra) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan2a1) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementUnionInPowersetComplement) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan2a2) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan1a) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan1b) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan1) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan2a) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan2b2) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan2b) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan2) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz13rule0) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz13rule1) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz13rule2) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz13rule3) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz13rule4) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz1_1) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz1_2) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz1_3) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz1_4) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz1_5) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1all2) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1SetBreln1) =>
% 97.60/13.23 ((
% 97.60/13.23 (choice2fnsingleton) =>
% 97.60/13.23 ((
% 97.60/13.23 (setOfPairsIsBReln1) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1all1) =>
% 97.60/13.23 ((
% 97.60/13.23 (subbreln1) =>
% 97.60/13.23 ((
% 97.60/13.23 (eqbreln1) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1invprop) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1invI) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1invE) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1compprop) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1compI) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1compE) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1compEex) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1unionprop) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1unionIL) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1unionIR) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1unionI) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1unionE) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1unionEcases) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1unionCommutes) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz2Ex) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz2W) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz2A) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz2B) =>
% 97.60/13.23 ((
% 97.60/13.23 (image1Ex) =>
% 97.60/13.23 ((
% 97.60/13.23 (image1Ex1) =>
% 97.60/13.23 ((
% 97.60/13.23 (image1Equiv) =>
% 97.60/13.23 ((
% 97.60/13.23 (image1E) =>
% 97.60/13.23 ((
% 97.60/13.23 (image1I) =>
% 97.60/13.23 ((
% 97.60/13.23 (injFuncInInjFuncSet) =>
% 97.60/13.23 ((
% 97.60/13.23 (injFuncSetFuncIn) =>
% 97.60/13.23 ((
% 97.60/13.23 (injFuncSetFuncInj) =>
% 97.60/13.23 ((
% 97.60/13.23 (surjFuncSetFuncIn) =>
% 97.60/13.23 ((
% 97.60/13.23 (surjFuncSetFuncSurj) =>
% 97.60/13.23 ((
% 97.60/13.23 (leftInvIsSurj) =>
% 97.60/13.23 ((
% 97.60/13.23 (surjCantorThm) =>
% 97.60/13.23 ((
% 97.60/13.23 (foundation2) =>
% 97.60/13.23 ((
% 97.60/13.23 (notinself) =>
% 97.60/13.23 ((
% 97.60/13.23 (notinself2) =>
% 97.60/13.23 ((
% 97.60/13.23 (omegaSp) =>
% 97.60/13.23 ((
% 97.60/13.23 (omegaSclos) =>
% 97.60/13.23 ((
% 97.60/13.23 (peano0notS) =>
% 97.60/13.23 ((
% 97.60/13.23 (!!) @ (
% 97.60/13.23 (('#S') @ (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 =>) @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#C') @ in @
% 97.60/13.23 omega)))) @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 !!) @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 (
% 97.60/13.23 ('#S') @ (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 =>) @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#C') @ in @
% 97.60/13.23 omega)))))) @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#S') @ (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 '#S') @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 =>))) @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#C') @ (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 '#B') @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 =) @
% 97.60/13.23 omegaS)))) @
% 97.60/13.23 omegaS)))))) @
% 97.60/13.23 (
% 97.60/13.23 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.60/13.23 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl967])).
% 97.60/13.23 thf(zip_derived_cl1000, plain,
% 97.60/13.23 (~ (((subset2powerset) =>
% 97.60/13.23 (((setextsub) =>
% 97.60/13.23 (((subsetemptysetimpeq) =>
% 97.60/13.23 (((powersetI1) =>
% 97.60/13.23 (((powersetE1) =>
% 97.60/13.23 (((inPowerset) =>
% 97.60/13.23 (((powersetsubset) =>
% 97.60/13.23 (((sepInPowerset) =>
% 97.60/13.23 (((sepSubset) =>
% 97.60/13.23 (((binunionIL) =>
% 97.60/13.23 (((upairset2IR) =>
% 97.60/13.23 (((binunionIR) =>
% 97.60/13.23 (((binunionEcases) =>
% 97.60/13.23 (((binunionE) =>
% 97.60/13.23 (((binunionLsub) =>
% 97.60/13.23 (((binunionRsub) =>
% 97.60/13.23 (((binintersectI) =>
% 97.60/13.23 (((binintersectSubset5) =>
% 97.60/13.23 (((binintersectEL) =>
% 97.60/13.23 (((binintersectLsub) =>
% 97.60/13.23 (((binintersectSubset2) =>
% 97.60/13.23 (((binintersectSubset3) =>
% 97.60/13.23 (((binintersectER) =>
% 97.60/13.23 (((disjointsetsI1) =>
% 97.60/13.23 (((binintersectRsub) =>
% 97.60/13.23 (((binintersectSubset4) =>
% 97.60/13.23 (((binintersectSubset1) =>
% 97.60/13.23 (((bs114d) =>
% 97.60/13.23 (((setminusI) =>
% 97.60/13.23 (((setminusEL) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusER) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusSubset2) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusERneg) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusELneg) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusILneg) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusIRneg) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusLsub) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusSubset1) =>
% 97.60/13.23 ((
% 97.60/13.23 (symdiffE) =>
% 97.60/13.23 ((
% 97.60/13.23 (symdiffI1) =>
% 97.60/13.23 ((
% 97.60/13.23 (symdiffI2) =>
% 97.60/13.23 ((
% 97.60/13.23 (symdiffIneg1) =>
% 97.60/13.23 ((
% 97.60/13.23 (symdiffIneg2) =>
% 97.60/13.23 ((
% 97.60/13.23 (secondinupair) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairIL) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairIR) =>
% 97.60/13.23 ((
% 97.60/13.23 (kpairiskpair) =>
% 97.60/13.23 ((
% 97.60/13.23 (kpairp) =>
% 97.60/13.23 ((
% 97.60/13.23 (singletonsubset) =>
% 97.60/13.23 ((
% 97.60/13.23 (singletoninpowerset) =>
% 97.60/13.23 ((
% 97.60/13.23 (singletoninpowunion) =>
% 97.60/13.23 ((
% 97.60/13.23 (upairset2E) =>
% 97.60/13.23 ((
% 97.60/13.23 (upairsubunion) =>
% 97.60/13.23 ((
% 97.60/13.23 (upairinpowunion) =>
% 97.60/13.23 ((
% 97.60/13.23 (ubforcartprodlem1) =>
% 97.60/13.23 ((
% 97.60/13.23 (ubforcartprodlem2) =>
% 97.60/13.23 ((
% 97.60/13.23 (ubforcartprodlem3) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodpairin) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodmempair1) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodmempair) =>
% 97.60/13.23 ((
% 97.60/13.23 (setunionE2) =>
% 97.60/13.23 ((
% 97.60/13.23 (setunionsingleton1) =>
% 97.60/13.23 ((
% 97.60/13.23 (setunionsingleton2) =>
% 97.60/13.23 ((
% 97.60/13.23 (setunionsingleton) =>
% 97.60/13.23 ((
% 97.60/13.23 (singletonprop) =>
% 97.60/13.23 ((
% 97.60/13.23 (ex1E1) =>
% 97.60/13.23 ((
% 97.60/13.23 (ex1I) =>
% 97.60/13.23 ((
% 97.60/13.23 (ex1I2) =>
% 97.60/13.23 ((
% 97.60/13.23 (singletonsuniq) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairinjL1) =>
% 97.60/13.23 ((
% 97.60/13.23 (kfstsingleton) =>
% 97.60/13.23 ((
% 97.60/13.23 (theprop) =>
% 97.60/13.23 ((
% 97.60/13.23 (kfstpairEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodfstin) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairinjL2) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairinjL) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairinjR11) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairinjR12) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairinjR1) =>
% 97.60/13.23 ((
% 97.60/13.23 (upairequniteq) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairinjR2) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairinjR) =>
% 97.60/13.23 ((
% 97.60/13.23 (ksndsingleton) =>
% 97.60/13.23 ((
% 97.60/13.23 (ksndpairEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (kpairsurjEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodsndin) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodpairmemEL) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodpairmemER) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodmempaircEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodfstpairEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodsndpairEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodpairsurjEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (dpsetconstrI) =>
% 97.60/13.23 ((
% 97.60/13.23 (dpsetconstrSub) =>
% 97.60/13.23 ((
% 97.60/13.23 (setOfPairsIsBReln) =>
% 97.60/13.23 ((
% 97.60/13.23 (dpsetconstrERa) =>
% 97.60/13.23 ((
% 97.60/13.23 (dpsetconstrEL1) =>
% 97.60/13.23 ((
% 97.60/13.23 (dpsetconstrEL2) =>
% 97.60/13.23 ((
% 97.60/13.23 (dpsetconstrER) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcImageSingleton) =>
% 97.60/13.23 ((
% 97.60/13.23 (apProp) =>
% 97.60/13.23 ((
% 97.60/13.23 (app) =>
% 97.60/13.23 ((
% 97.60/13.23 (infuncsetfunc) =>
% 97.60/13.23 ((
% 97.60/13.23 (ap2p) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcinfuncset) =>
% 97.60/13.23 ((
% 97.60/13.23 (lamProp) =>
% 97.60/13.23 ((
% 97.60/13.23 (lamp) =>
% 97.60/13.23 ((
% 97.60/13.23 (lam2p) =>
% 97.60/13.23 ((
% 97.60/13.23 (brelnall1) =>
% 97.60/13.23 ((
% 97.60/13.23 (brelnall2) =>
% 97.60/13.23 ((
% 97.60/13.23 (ex1E2) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcGraphProp1) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcGraphProp3) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcGraphProp2) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcextLem) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcGraphProp4) =>
% 97.60/13.23 ((
% 97.60/13.23 (subbreln) =>
% 97.60/13.23 ((
% 97.60/13.23 (eqbreln) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcext) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcext2) =>
% 97.60/13.23 ((
% 97.60/13.23 (ap2apEq1) =>
% 97.60/13.23 ((
% 97.60/13.23 (ap2apEq2) =>
% 97.60/13.23 ((
% 97.60/13.23 (beta1) =>
% 97.60/13.23 ((
% 97.60/13.23 (eta1) =>
% 97.60/13.23 ((
% 97.60/13.23 (lam2lamEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (beta2) =>
% 97.60/13.23 ((
% 97.60/13.23 (eta2) =>
% 97.60/13.23 ((
% 97.60/13.23 (iffalseProp1) =>
% 97.60/13.23 ((
% 97.60/13.23 (iffalseProp2) =>
% 97.60/13.23 ((
% 97.60/13.23 (iftrueProp1) =>
% 97.60/13.23 ((
% 97.60/13.23 (iftrueProp2) =>
% 97.60/13.23 ((
% 97.60/13.23 (ifSingleton) =>
% 97.60/13.23 ((
% 97.60/13.23 (ifp) =>
% 97.60/13.23 ((
% 97.60/13.23 (theeq) =>
% 97.60/13.23 ((
% 97.60/13.23 (iftrue) =>
% 97.60/13.23 ((
% 97.60/13.23 (iffalse) =>
% 97.60/13.23 ((
% 97.60/13.23 (iftrueorfalse) =>
% 97.60/13.23 ((
% 97.60/13.23 (binintersectT_lem) =>
% 97.60/13.23 ((
% 97.60/13.23 (binunionT_lem) =>
% 97.60/13.23 ((
% 97.60/13.23 (powersetT_lem) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusT_lem) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementT_lem) =>
% 97.60/13.23 ((
% 97.60/13.23 (setextT) =>
% 97.60/13.23 ((
% 97.60/13.23 (subsetTI) =>
% 97.60/13.23 ((
% 97.60/13.23 (powersetTI1) =>
% 97.60/13.23 ((
% 97.60/13.23 (powersetTE1) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementTI1) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementTE1) =>
% 97.60/13.23 ((
% 97.60/13.23 (binintersectTELcontra) =>
% 97.60/13.23 ((
% 97.60/13.23 (binintersectTERcontra) =>
% 97.60/13.23 ((
% 97.60/13.23 (contrasubsetT) =>
% 97.60/13.23 ((
% 97.60/13.23 (contrasubsetT1) =>
% 97.60/13.23 ((
% 97.60/13.23 (contrasubsetT2) =>
% 97.60/13.23 ((
% 97.60/13.23 (contrasubsetT3) =>
% 97.60/13.23 ((
% 97.60/13.23 (doubleComplementI1) =>
% 97.60/13.23 ((
% 97.60/13.23 (doubleComplementE1) =>
% 97.60/13.23 ((
% 97.60/13.23 (doubleComplementSub1) =>
% 97.60/13.23 ((
% 97.60/13.23 (doubleComplementSub2) =>
% 97.60/13.23 ((
% 97.60/13.23 (doubleComplementEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementTnotintersectT) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementImpComplementIntersect) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementSubsetComplementIntersect) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementInPowersetComplementIntersect) =>
% 97.60/13.23 ((
% 97.60/13.23 (contraSubsetComplement) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementTcontraSubset) =>
% 97.60/13.23 ((
% 97.60/13.23 (binunionTILcontra) =>
% 97.60/13.23 ((
% 97.60/13.23 (binunionTIRcontra) =>
% 97.60/13.23 ((
% 97.60/13.23 (inIntersectImpInUnion) =>
% 97.60/13.23 ((
% 97.60/13.23 (inIntersectImpInUnion2) =>
% 97.60/13.23 ((
% 97.60/13.23 (inIntersectImpInIntersectUnions) =>
% 97.60/13.23 ((
% 97.60/13.23 (intersectInPowersetIntersectUnions) =>
% 97.60/13.23 ((
% 97.60/13.23 (inComplementUnionImpNotIn1) =>
% 97.60/13.23 ((
% 97.60/13.23 (inComplementUnionImpInComplement1) =>
% 97.60/13.23 ((
% 97.60/13.23 (binunionTE) =>
% 97.60/13.23 ((
% 97.60/13.23 (binunionTEcontra) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan2a1) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementUnionInPowersetComplement) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan2a2) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan1a) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan1b) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan1) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan2a) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan2b2) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan2b) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan2) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz13rule0) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz13rule1) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz13rule2) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz13rule3) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz13rule4) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz1_1) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz1_2) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz1_3) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz1_4) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz1_5) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1all2) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1SetBreln1) =>
% 97.60/13.23 ((
% 97.60/13.23 (choice2fnsingleton) =>
% 97.60/13.23 ((
% 97.60/13.23 (setOfPairsIsBReln1) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1all1) =>
% 97.60/13.23 ((
% 97.60/13.23 (subbreln1) =>
% 97.60/13.23 ((
% 97.60/13.23 (eqbreln1) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1invprop) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1invI) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1invE) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1compprop) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1compI) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1compE) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1compEex) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1unionprop) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1unionIL) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1unionIR) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1unionI) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1unionE) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1unionEcases) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1unionCommutes) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz2Ex) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz2W) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz2A) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz2B) =>
% 97.60/13.23 ((
% 97.60/13.23 (image1Ex) =>
% 97.60/13.23 ((
% 97.60/13.23 (image1Ex1) =>
% 97.60/13.23 ((
% 97.60/13.23 (image1Equiv) =>
% 97.60/13.23 ((
% 97.60/13.23 (image1E) =>
% 97.60/13.23 ((
% 97.60/13.23 (image1I) =>
% 97.60/13.23 ((
% 97.60/13.23 (injFuncInInjFuncSet) =>
% 97.60/13.23 ((
% 97.60/13.23 (injFuncSetFuncIn) =>
% 97.60/13.23 ((
% 97.60/13.23 (injFuncSetFuncInj) =>
% 97.60/13.23 ((
% 97.60/13.23 (surjFuncSetFuncIn) =>
% 97.60/13.23 ((
% 97.60/13.23 (surjFuncSetFuncSurj) =>
% 97.60/13.23 ((
% 97.60/13.23 (leftInvIsSurj) =>
% 97.60/13.23 ((
% 97.60/13.23 (surjCantorThm) =>
% 97.60/13.23 ((
% 97.60/13.23 (foundation2) =>
% 97.60/13.23 ((
% 97.60/13.23 (notinself) =>
% 97.60/13.23 ((
% 97.60/13.23 (notinself2) =>
% 97.60/13.23 ((
% 97.60/13.23 (omegaSp) =>
% 97.60/13.23 ((
% 97.60/13.23 (omegaSclos) =>
% 97.60/13.23 ((
% 97.60/13.23 (peano0notS) =>
% 97.60/13.23 ((
% 97.60/13.23 (!!) @ (
% 97.60/13.23 (('#S') @ (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 =>) @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#C') @ in @
% 97.60/13.23 omega)))) @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 !!) @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 (
% 97.60/13.23 ('#S') @ (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 =>) @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#C') @ in @
% 97.60/13.23 omega)))))) @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#S') @ (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 '#S') @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 =>))) @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#C') @ (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 '#B') @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 =) @
% 97.60/13.23 omegaS)))) @
% 97.60/13.23 omegaS)))))) @
% 97.60/13.23 (
% 97.60/13.23 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.60/13.23 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl984])).
% 97.60/13.23 thf(zip_derived_cl1015, plain,
% 97.60/13.23 (~ (((setextsub) =>
% 97.60/13.23 (((subsetemptysetimpeq) =>
% 97.60/13.23 (((powersetI1) =>
% 97.60/13.23 (((powersetE1) =>
% 97.60/13.23 (((inPowerset) =>
% 97.60/13.23 (((powersetsubset) =>
% 97.60/13.23 (((sepInPowerset) =>
% 97.60/13.23 (((sepSubset) =>
% 97.60/13.23 (((binunionIL) =>
% 97.60/13.23 (((upairset2IR) =>
% 97.60/13.23 (((binunionIR) =>
% 97.60/13.23 (((binunionEcases) =>
% 97.60/13.23 (((binunionE) =>
% 97.60/13.23 (((binunionLsub) =>
% 97.60/13.23 (((binunionRsub) =>
% 97.60/13.23 (((binintersectI) =>
% 97.60/13.23 (((binintersectSubset5) =>
% 97.60/13.23 (((binintersectEL) =>
% 97.60/13.23 (((binintersectLsub) =>
% 97.60/13.23 (((binintersectSubset2) =>
% 97.60/13.23 (((binintersectSubset3) =>
% 97.60/13.23 (((binintersectER) =>
% 97.60/13.23 (((disjointsetsI1) =>
% 97.60/13.23 (((binintersectRsub) =>
% 97.60/13.23 (((binintersectSubset4) =>
% 97.60/13.23 (((binintersectSubset1) =>
% 97.60/13.23 (((bs114d) =>
% 97.60/13.23 (((setminusI) =>
% 97.60/13.23 (((setminusEL) =>
% 97.60/13.23 (((setminusER) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusSubset2) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusERneg) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusELneg) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusILneg) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusIRneg) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusLsub) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusSubset1) =>
% 97.60/13.23 ((
% 97.60/13.23 (symdiffE) =>
% 97.60/13.23 ((
% 97.60/13.23 (symdiffI1) =>
% 97.60/13.23 ((
% 97.60/13.23 (symdiffI2) =>
% 97.60/13.23 ((
% 97.60/13.23 (symdiffIneg1) =>
% 97.60/13.23 ((
% 97.60/13.23 (symdiffIneg2) =>
% 97.60/13.23 ((
% 97.60/13.23 (secondinupair) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairIL) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairIR) =>
% 97.60/13.23 ((
% 97.60/13.23 (kpairiskpair) =>
% 97.60/13.23 ((
% 97.60/13.23 (kpairp) =>
% 97.60/13.23 ((
% 97.60/13.23 (singletonsubset) =>
% 97.60/13.23 ((
% 97.60/13.23 (singletoninpowerset) =>
% 97.60/13.23 ((
% 97.60/13.23 (singletoninpowunion) =>
% 97.60/13.23 ((
% 97.60/13.23 (upairset2E) =>
% 97.60/13.23 ((
% 97.60/13.23 (upairsubunion) =>
% 97.60/13.23 ((
% 97.60/13.23 (upairinpowunion) =>
% 97.60/13.23 ((
% 97.60/13.23 (ubforcartprodlem1) =>
% 97.60/13.23 ((
% 97.60/13.23 (ubforcartprodlem2) =>
% 97.60/13.23 ((
% 97.60/13.23 (ubforcartprodlem3) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodpairin) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodmempair1) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodmempair) =>
% 97.60/13.23 ((
% 97.60/13.23 (setunionE2) =>
% 97.60/13.23 ((
% 97.60/13.23 (setunionsingleton1) =>
% 97.60/13.23 ((
% 97.60/13.23 (setunionsingleton2) =>
% 97.60/13.23 ((
% 97.60/13.23 (setunionsingleton) =>
% 97.60/13.23 ((
% 97.60/13.23 (singletonprop) =>
% 97.60/13.23 ((
% 97.60/13.23 (ex1E1) =>
% 97.60/13.23 ((
% 97.60/13.23 (ex1I) =>
% 97.60/13.23 ((
% 97.60/13.23 (ex1I2) =>
% 97.60/13.23 ((
% 97.60/13.23 (singletonsuniq) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairinjL1) =>
% 97.60/13.23 ((
% 97.60/13.23 (kfstsingleton) =>
% 97.60/13.23 ((
% 97.60/13.23 (theprop) =>
% 97.60/13.23 ((
% 97.60/13.23 (kfstpairEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodfstin) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairinjL2) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairinjL) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairinjR11) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairinjR12) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairinjR1) =>
% 97.60/13.23 ((
% 97.60/13.23 (upairequniteq) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairinjR2) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairinjR) =>
% 97.60/13.23 ((
% 97.60/13.23 (ksndsingleton) =>
% 97.60/13.23 ((
% 97.60/13.23 (ksndpairEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (kpairsurjEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodsndin) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodpairmemEL) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodpairmemER) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodmempaircEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodfstpairEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodsndpairEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodpairsurjEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (dpsetconstrI) =>
% 97.60/13.23 ((
% 97.60/13.23 (dpsetconstrSub) =>
% 97.60/13.23 ((
% 97.60/13.23 (setOfPairsIsBReln) =>
% 97.60/13.23 ((
% 97.60/13.23 (dpsetconstrERa) =>
% 97.60/13.23 ((
% 97.60/13.23 (dpsetconstrEL1) =>
% 97.60/13.23 ((
% 97.60/13.23 (dpsetconstrEL2) =>
% 97.60/13.23 ((
% 97.60/13.23 (dpsetconstrER) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcImageSingleton) =>
% 97.60/13.23 ((
% 97.60/13.23 (apProp) =>
% 97.60/13.23 ((
% 97.60/13.23 (app) =>
% 97.60/13.23 ((
% 97.60/13.23 (infuncsetfunc) =>
% 97.60/13.23 ((
% 97.60/13.23 (ap2p) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcinfuncset) =>
% 97.60/13.23 ((
% 97.60/13.23 (lamProp) =>
% 97.60/13.23 ((
% 97.60/13.23 (lamp) =>
% 97.60/13.23 ((
% 97.60/13.23 (lam2p) =>
% 97.60/13.23 ((
% 97.60/13.23 (brelnall1) =>
% 97.60/13.23 ((
% 97.60/13.23 (brelnall2) =>
% 97.60/13.23 ((
% 97.60/13.23 (ex1E2) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcGraphProp1) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcGraphProp3) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcGraphProp2) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcextLem) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcGraphProp4) =>
% 97.60/13.23 ((
% 97.60/13.23 (subbreln) =>
% 97.60/13.23 ((
% 97.60/13.23 (eqbreln) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcext) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcext2) =>
% 97.60/13.23 ((
% 97.60/13.23 (ap2apEq1) =>
% 97.60/13.23 ((
% 97.60/13.23 (ap2apEq2) =>
% 97.60/13.23 ((
% 97.60/13.23 (beta1) =>
% 97.60/13.23 ((
% 97.60/13.23 (eta1) =>
% 97.60/13.23 ((
% 97.60/13.23 (lam2lamEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (beta2) =>
% 97.60/13.23 ((
% 97.60/13.23 (eta2) =>
% 97.60/13.23 ((
% 97.60/13.23 (iffalseProp1) =>
% 97.60/13.23 ((
% 97.60/13.23 (iffalseProp2) =>
% 97.60/13.23 ((
% 97.60/13.23 (iftrueProp1) =>
% 97.60/13.23 ((
% 97.60/13.23 (iftrueProp2) =>
% 97.60/13.23 ((
% 97.60/13.23 (ifSingleton) =>
% 97.60/13.23 ((
% 97.60/13.23 (ifp) =>
% 97.60/13.23 ((
% 97.60/13.23 (theeq) =>
% 97.60/13.23 ((
% 97.60/13.23 (iftrue) =>
% 97.60/13.23 ((
% 97.60/13.23 (iffalse) =>
% 97.60/13.23 ((
% 97.60/13.23 (iftrueorfalse) =>
% 97.60/13.23 ((
% 97.60/13.23 (binintersectT_lem) =>
% 97.60/13.23 ((
% 97.60/13.23 (binunionT_lem) =>
% 97.60/13.23 ((
% 97.60/13.23 (powersetT_lem) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusT_lem) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementT_lem) =>
% 97.60/13.23 ((
% 97.60/13.23 (setextT) =>
% 97.60/13.23 ((
% 97.60/13.23 (subsetTI) =>
% 97.60/13.23 ((
% 97.60/13.23 (powersetTI1) =>
% 97.60/13.23 ((
% 97.60/13.23 (powersetTE1) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementTI1) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementTE1) =>
% 97.60/13.23 ((
% 97.60/13.23 (binintersectTELcontra) =>
% 97.60/13.23 ((
% 97.60/13.23 (binintersectTERcontra) =>
% 97.60/13.23 ((
% 97.60/13.23 (contrasubsetT) =>
% 97.60/13.23 ((
% 97.60/13.23 (contrasubsetT1) =>
% 97.60/13.23 ((
% 97.60/13.23 (contrasubsetT2) =>
% 97.60/13.23 ((
% 97.60/13.23 (contrasubsetT3) =>
% 97.60/13.23 ((
% 97.60/13.23 (doubleComplementI1) =>
% 97.60/13.23 ((
% 97.60/13.23 (doubleComplementE1) =>
% 97.60/13.23 ((
% 97.60/13.23 (doubleComplementSub1) =>
% 97.60/13.23 ((
% 97.60/13.23 (doubleComplementSub2) =>
% 97.60/13.23 ((
% 97.60/13.23 (doubleComplementEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementTnotintersectT) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementImpComplementIntersect) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementSubsetComplementIntersect) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementInPowersetComplementIntersect) =>
% 97.60/13.23 ((
% 97.60/13.23 (contraSubsetComplement) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementTcontraSubset) =>
% 97.60/13.23 ((
% 97.60/13.23 (binunionTILcontra) =>
% 97.60/13.23 ((
% 97.60/13.23 (binunionTIRcontra) =>
% 97.60/13.23 ((
% 97.60/13.23 (inIntersectImpInUnion) =>
% 97.60/13.23 ((
% 97.60/13.23 (inIntersectImpInUnion2) =>
% 97.60/13.23 ((
% 97.60/13.23 (inIntersectImpInIntersectUnions) =>
% 97.60/13.23 ((
% 97.60/13.23 (intersectInPowersetIntersectUnions) =>
% 97.60/13.23 ((
% 97.60/13.23 (inComplementUnionImpNotIn1) =>
% 97.60/13.23 ((
% 97.60/13.23 (inComplementUnionImpInComplement1) =>
% 97.60/13.23 ((
% 97.60/13.23 (binunionTE) =>
% 97.60/13.23 ((
% 97.60/13.23 (binunionTEcontra) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan2a1) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementUnionInPowersetComplement) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan2a2) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan1a) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan1b) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan1) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan2a) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan2b2) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan2b) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan2) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz13rule0) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz13rule1) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz13rule2) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz13rule3) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz13rule4) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz1_1) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz1_2) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz1_3) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz1_4) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz1_5) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1all2) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1SetBreln1) =>
% 97.60/13.23 ((
% 97.60/13.23 (choice2fnsingleton) =>
% 97.60/13.23 ((
% 97.60/13.23 (setOfPairsIsBReln1) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1all1) =>
% 97.60/13.23 ((
% 97.60/13.23 (subbreln1) =>
% 97.60/13.23 ((
% 97.60/13.23 (eqbreln1) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1invprop) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1invI) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1invE) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1compprop) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1compI) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1compE) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1compEex) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1unionprop) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1unionIL) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1unionIR) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1unionI) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1unionE) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1unionEcases) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1unionCommutes) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz2Ex) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz2W) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz2A) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz2B) =>
% 97.60/13.23 ((
% 97.60/13.23 (image1Ex) =>
% 97.60/13.23 ((
% 97.60/13.23 (image1Ex1) =>
% 97.60/13.23 ((
% 97.60/13.23 (image1Equiv) =>
% 97.60/13.23 ((
% 97.60/13.23 (image1E) =>
% 97.60/13.23 ((
% 97.60/13.23 (image1I) =>
% 97.60/13.23 ((
% 97.60/13.23 (injFuncInInjFuncSet) =>
% 97.60/13.23 ((
% 97.60/13.23 (injFuncSetFuncIn) =>
% 97.60/13.23 ((
% 97.60/13.23 (injFuncSetFuncInj) =>
% 97.60/13.23 ((
% 97.60/13.23 (surjFuncSetFuncIn) =>
% 97.60/13.23 ((
% 97.60/13.23 (surjFuncSetFuncSurj) =>
% 97.60/13.23 ((
% 97.60/13.23 (leftInvIsSurj) =>
% 97.60/13.23 ((
% 97.60/13.23 (surjCantorThm) =>
% 97.60/13.23 ((
% 97.60/13.23 (foundation2) =>
% 97.60/13.23 ((
% 97.60/13.23 (notinself) =>
% 97.60/13.23 ((
% 97.60/13.23 (notinself2) =>
% 97.60/13.23 ((
% 97.60/13.23 (omegaSp) =>
% 97.60/13.23 ((
% 97.60/13.23 (omegaSclos) =>
% 97.60/13.23 ((
% 97.60/13.23 (peano0notS) =>
% 97.60/13.23 ((
% 97.60/13.23 (!!) @ (
% 97.60/13.23 (('#S') @ (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 =>) @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#C') @ in @
% 97.60/13.23 omega)))) @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 !!) @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 (
% 97.60/13.23 ('#S') @ (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 =>) @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#C') @ in @
% 97.60/13.23 omega)))))) @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#S') @ (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 '#S') @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 =>))) @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#C') @ (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 '#B') @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 =) @
% 97.60/13.23 omegaS)))) @
% 97.60/13.23 omegaS)))))) @
% 97.60/13.23 (
% 97.60/13.23 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.60/13.23 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1000])).
% 97.60/13.23 thf(zip_derived_cl1027, plain,
% 97.60/13.23 (~ (((subsetemptysetimpeq) =>
% 97.60/13.23 (((powersetI1) =>
% 97.60/13.23 (((powersetE1) =>
% 97.60/13.23 (((inPowerset) =>
% 97.60/13.23 (((powersetsubset) =>
% 97.60/13.23 (((sepInPowerset) =>
% 97.60/13.23 (((sepSubset) =>
% 97.60/13.23 (((binunionIL) =>
% 97.60/13.23 (((upairset2IR) =>
% 97.60/13.23 (((binunionIR) =>
% 97.60/13.23 (((binunionEcases) =>
% 97.60/13.23 (((binunionE) =>
% 97.60/13.23 (((binunionLsub) =>
% 97.60/13.23 (((binunionRsub) =>
% 97.60/13.23 (((binintersectI) =>
% 97.60/13.23 (((binintersectSubset5) =>
% 97.60/13.23 (((binintersectEL) =>
% 97.60/13.23 (((binintersectLsub) =>
% 97.60/13.23 (((binintersectSubset2) =>
% 97.60/13.23 (((binintersectSubset3) =>
% 97.60/13.23 (((binintersectER) =>
% 97.60/13.23 (((disjointsetsI1) =>
% 97.60/13.23 (((binintersectRsub) =>
% 97.60/13.23 (((binintersectSubset4) =>
% 97.60/13.23 (((binintersectSubset1) =>
% 97.60/13.23 (((bs114d) =>
% 97.60/13.23 (((setminusI) =>
% 97.60/13.23 (((setminusEL) =>
% 97.60/13.23 (((setminusER) =>
% 97.60/13.23 (((setminusSubset2) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusERneg) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusELneg) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusILneg) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusIRneg) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusLsub) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusSubset1) =>
% 97.60/13.23 ((
% 97.60/13.23 (symdiffE) =>
% 97.60/13.23 ((
% 97.60/13.23 (symdiffI1) =>
% 97.60/13.23 ((
% 97.60/13.23 (symdiffI2) =>
% 97.60/13.23 ((
% 97.60/13.23 (symdiffIneg1) =>
% 97.60/13.23 ((
% 97.60/13.23 (symdiffIneg2) =>
% 97.60/13.23 ((
% 97.60/13.23 (secondinupair) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairIL) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairIR) =>
% 97.60/13.23 ((
% 97.60/13.23 (kpairiskpair) =>
% 97.60/13.23 ((
% 97.60/13.23 (kpairp) =>
% 97.60/13.23 ((
% 97.60/13.23 (singletonsubset) =>
% 97.60/13.23 ((
% 97.60/13.23 (singletoninpowerset) =>
% 97.60/13.23 ((
% 97.60/13.23 (singletoninpowunion) =>
% 97.60/13.23 ((
% 97.60/13.23 (upairset2E) =>
% 97.60/13.23 ((
% 97.60/13.23 (upairsubunion) =>
% 97.60/13.23 ((
% 97.60/13.23 (upairinpowunion) =>
% 97.60/13.23 ((
% 97.60/13.23 (ubforcartprodlem1) =>
% 97.60/13.23 ((
% 97.60/13.23 (ubforcartprodlem2) =>
% 97.60/13.23 ((
% 97.60/13.23 (ubforcartprodlem3) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodpairin) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodmempair1) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodmempair) =>
% 97.60/13.23 ((
% 97.60/13.23 (setunionE2) =>
% 97.60/13.23 ((
% 97.60/13.23 (setunionsingleton1) =>
% 97.60/13.23 ((
% 97.60/13.23 (setunionsingleton2) =>
% 97.60/13.23 ((
% 97.60/13.23 (setunionsingleton) =>
% 97.60/13.23 ((
% 97.60/13.23 (singletonprop) =>
% 97.60/13.23 ((
% 97.60/13.23 (ex1E1) =>
% 97.60/13.23 ((
% 97.60/13.23 (ex1I) =>
% 97.60/13.23 ((
% 97.60/13.23 (ex1I2) =>
% 97.60/13.23 ((
% 97.60/13.23 (singletonsuniq) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairinjL1) =>
% 97.60/13.23 ((
% 97.60/13.23 (kfstsingleton) =>
% 97.60/13.23 ((
% 97.60/13.23 (theprop) =>
% 97.60/13.23 ((
% 97.60/13.23 (kfstpairEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodfstin) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairinjL2) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairinjL) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairinjR11) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairinjR12) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairinjR1) =>
% 97.60/13.23 ((
% 97.60/13.23 (upairequniteq) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairinjR2) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairinjR) =>
% 97.60/13.23 ((
% 97.60/13.23 (ksndsingleton) =>
% 97.60/13.23 ((
% 97.60/13.23 (ksndpairEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (kpairsurjEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodsndin) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodpairmemEL) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodpairmemER) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodmempaircEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodfstpairEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodsndpairEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodpairsurjEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (dpsetconstrI) =>
% 97.60/13.23 ((
% 97.60/13.23 (dpsetconstrSub) =>
% 97.60/13.23 ((
% 97.60/13.23 (setOfPairsIsBReln) =>
% 97.60/13.23 ((
% 97.60/13.23 (dpsetconstrERa) =>
% 97.60/13.23 ((
% 97.60/13.23 (dpsetconstrEL1) =>
% 97.60/13.23 ((
% 97.60/13.23 (dpsetconstrEL2) =>
% 97.60/13.23 ((
% 97.60/13.23 (dpsetconstrER) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcImageSingleton) =>
% 97.60/13.23 ((
% 97.60/13.23 (apProp) =>
% 97.60/13.23 ((
% 97.60/13.23 (app) =>
% 97.60/13.23 ((
% 97.60/13.23 (infuncsetfunc) =>
% 97.60/13.23 ((
% 97.60/13.23 (ap2p) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcinfuncset) =>
% 97.60/13.23 ((
% 97.60/13.23 (lamProp) =>
% 97.60/13.23 ((
% 97.60/13.23 (lamp) =>
% 97.60/13.23 ((
% 97.60/13.23 (lam2p) =>
% 97.60/13.23 ((
% 97.60/13.23 (brelnall1) =>
% 97.60/13.23 ((
% 97.60/13.23 (brelnall2) =>
% 97.60/13.23 ((
% 97.60/13.23 (ex1E2) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcGraphProp1) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcGraphProp3) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcGraphProp2) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcextLem) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcGraphProp4) =>
% 97.60/13.23 ((
% 97.60/13.23 (subbreln) =>
% 97.60/13.23 ((
% 97.60/13.23 (eqbreln) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcext) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcext2) =>
% 97.60/13.23 ((
% 97.60/13.23 (ap2apEq1) =>
% 97.60/13.23 ((
% 97.60/13.23 (ap2apEq2) =>
% 97.60/13.23 ((
% 97.60/13.23 (beta1) =>
% 97.60/13.23 ((
% 97.60/13.23 (eta1) =>
% 97.60/13.23 ((
% 97.60/13.23 (lam2lamEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (beta2) =>
% 97.60/13.23 ((
% 97.60/13.23 (eta2) =>
% 97.60/13.23 ((
% 97.60/13.23 (iffalseProp1) =>
% 97.60/13.23 ((
% 97.60/13.23 (iffalseProp2) =>
% 97.60/13.23 ((
% 97.60/13.23 (iftrueProp1) =>
% 97.60/13.23 ((
% 97.60/13.23 (iftrueProp2) =>
% 97.60/13.23 ((
% 97.60/13.23 (ifSingleton) =>
% 97.60/13.23 ((
% 97.60/13.23 (ifp) =>
% 97.60/13.23 ((
% 97.60/13.23 (theeq) =>
% 97.60/13.23 ((
% 97.60/13.23 (iftrue) =>
% 97.60/13.23 ((
% 97.60/13.23 (iffalse) =>
% 97.60/13.23 ((
% 97.60/13.23 (iftrueorfalse) =>
% 97.60/13.23 ((
% 97.60/13.23 (binintersectT_lem) =>
% 97.60/13.23 ((
% 97.60/13.23 (binunionT_lem) =>
% 97.60/13.23 ((
% 97.60/13.23 (powersetT_lem) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusT_lem) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementT_lem) =>
% 97.60/13.23 ((
% 97.60/13.23 (setextT) =>
% 97.60/13.23 ((
% 97.60/13.23 (subsetTI) =>
% 97.60/13.23 ((
% 97.60/13.23 (powersetTI1) =>
% 97.60/13.23 ((
% 97.60/13.23 (powersetTE1) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementTI1) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementTE1) =>
% 97.60/13.23 ((
% 97.60/13.23 (binintersectTELcontra) =>
% 97.60/13.23 ((
% 97.60/13.23 (binintersectTERcontra) =>
% 97.60/13.23 ((
% 97.60/13.23 (contrasubsetT) =>
% 97.60/13.23 ((
% 97.60/13.23 (contrasubsetT1) =>
% 97.60/13.23 ((
% 97.60/13.23 (contrasubsetT2) =>
% 97.60/13.23 ((
% 97.60/13.23 (contrasubsetT3) =>
% 97.60/13.23 ((
% 97.60/13.23 (doubleComplementI1) =>
% 97.60/13.23 ((
% 97.60/13.23 (doubleComplementE1) =>
% 97.60/13.23 ((
% 97.60/13.23 (doubleComplementSub1) =>
% 97.60/13.23 ((
% 97.60/13.23 (doubleComplementSub2) =>
% 97.60/13.23 ((
% 97.60/13.23 (doubleComplementEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementTnotintersectT) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementImpComplementIntersect) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementSubsetComplementIntersect) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementInPowersetComplementIntersect) =>
% 97.60/13.23 ((
% 97.60/13.23 (contraSubsetComplement) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementTcontraSubset) =>
% 97.60/13.23 ((
% 97.60/13.23 (binunionTILcontra) =>
% 97.60/13.23 ((
% 97.60/13.23 (binunionTIRcontra) =>
% 97.60/13.23 ((
% 97.60/13.23 (inIntersectImpInUnion) =>
% 97.60/13.23 ((
% 97.60/13.23 (inIntersectImpInUnion2) =>
% 97.60/13.23 ((
% 97.60/13.23 (inIntersectImpInIntersectUnions) =>
% 97.60/13.23 ((
% 97.60/13.23 (intersectInPowersetIntersectUnions) =>
% 97.60/13.23 ((
% 97.60/13.23 (inComplementUnionImpNotIn1) =>
% 97.60/13.23 ((
% 97.60/13.23 (inComplementUnionImpInComplement1) =>
% 97.60/13.23 ((
% 97.60/13.23 (binunionTE) =>
% 97.60/13.23 ((
% 97.60/13.23 (binunionTEcontra) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan2a1) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementUnionInPowersetComplement) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan2a2) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan1a) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan1b) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan1) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan2a) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan2b2) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan2b) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan2) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz13rule0) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz13rule1) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz13rule2) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz13rule3) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz13rule4) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz1_1) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz1_2) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz1_3) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz1_4) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz1_5) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1all2) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1SetBreln1) =>
% 97.60/13.23 ((
% 97.60/13.23 (choice2fnsingleton) =>
% 97.60/13.23 ((
% 97.60/13.23 (setOfPairsIsBReln1) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1all1) =>
% 97.60/13.23 ((
% 97.60/13.23 (subbreln1) =>
% 97.60/13.23 ((
% 97.60/13.23 (eqbreln1) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1invprop) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1invI) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1invE) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1compprop) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1compI) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1compE) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1compEex) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1unionprop) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1unionIL) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1unionIR) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1unionI) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1unionE) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1unionEcases) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1unionCommutes) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz2Ex) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz2W) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz2A) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz2B) =>
% 97.60/13.23 ((
% 97.60/13.23 (image1Ex) =>
% 97.60/13.23 ((
% 97.60/13.23 (image1Ex1) =>
% 97.60/13.23 ((
% 97.60/13.23 (image1Equiv) =>
% 97.60/13.23 ((
% 97.60/13.23 (image1E) =>
% 97.60/13.23 ((
% 97.60/13.23 (image1I) =>
% 97.60/13.23 ((
% 97.60/13.23 (injFuncInInjFuncSet) =>
% 97.60/13.23 ((
% 97.60/13.23 (injFuncSetFuncIn) =>
% 97.60/13.23 ((
% 97.60/13.23 (injFuncSetFuncInj) =>
% 97.60/13.23 ((
% 97.60/13.23 (surjFuncSetFuncIn) =>
% 97.60/13.23 ((
% 97.60/13.23 (surjFuncSetFuncSurj) =>
% 97.60/13.23 ((
% 97.60/13.23 (leftInvIsSurj) =>
% 97.60/13.23 ((
% 97.60/13.23 (surjCantorThm) =>
% 97.60/13.23 ((
% 97.60/13.23 (foundation2) =>
% 97.60/13.23 ((
% 97.60/13.23 (notinself) =>
% 97.60/13.23 ((
% 97.60/13.23 (notinself2) =>
% 97.60/13.23 ((
% 97.60/13.23 (omegaSp) =>
% 97.60/13.23 ((
% 97.60/13.23 (omegaSclos) =>
% 97.60/13.23 ((
% 97.60/13.23 (peano0notS) =>
% 97.60/13.23 ((
% 97.60/13.23 (!!) @ (
% 97.60/13.23 (('#S') @ (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 =>) @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#C') @ in @
% 97.60/13.23 omega)))) @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 !!) @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 (
% 97.60/13.23 ('#S') @ (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 =>) @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#C') @ in @
% 97.60/13.23 omega)))))) @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#S') @ (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 '#S') @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 =>))) @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#C') @ (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 '#B') @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 =) @
% 97.60/13.23 omegaS)))) @
% 97.60/13.23 omegaS)))))) @
% 97.60/13.23 (
% 97.60/13.23 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.60/13.23 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1015])).
% 97.60/13.23 thf(zip_derived_cl1039, plain,
% 97.60/13.23 (~ (((powersetI1) =>
% 97.60/13.23 (((powersetE1) =>
% 97.60/13.23 (((inPowerset) =>
% 97.60/13.23 (((powersetsubset) =>
% 97.60/13.23 (((sepInPowerset) =>
% 97.60/13.23 (((sepSubset) =>
% 97.60/13.23 (((binunionIL) =>
% 97.60/13.23 (((upairset2IR) =>
% 97.60/13.23 (((binunionIR) =>
% 97.60/13.23 (((binunionEcases) =>
% 97.60/13.23 (((binunionE) =>
% 97.60/13.23 (((binunionLsub) =>
% 97.60/13.23 (((binunionRsub) =>
% 97.60/13.23 (((binintersectI) =>
% 97.60/13.23 (((binintersectSubset5) =>
% 97.60/13.23 (((binintersectEL) =>
% 97.60/13.23 (((binintersectLsub) =>
% 97.60/13.23 (((binintersectSubset2) =>
% 97.60/13.23 (((binintersectSubset3) =>
% 97.60/13.23 (((binintersectER) =>
% 97.60/13.23 (((disjointsetsI1) =>
% 97.60/13.23 (((binintersectRsub) =>
% 97.60/13.23 (((binintersectSubset4) =>
% 97.60/13.23 (((binintersectSubset1) =>
% 97.60/13.23 (((bs114d) =>
% 97.60/13.23 (((setminusI) =>
% 97.60/13.23 (((setminusEL) =>
% 97.60/13.23 (((setminusER) =>
% 97.60/13.23 (((setminusSubset2) =>
% 97.60/13.23 (((setminusERneg) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusELneg) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusILneg) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusIRneg) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusLsub) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusSubset1) =>
% 97.60/13.23 ((
% 97.60/13.23 (symdiffE) =>
% 97.60/13.23 ((
% 97.60/13.23 (symdiffI1) =>
% 97.60/13.23 ((
% 97.60/13.23 (symdiffI2) =>
% 97.60/13.23 ((
% 97.60/13.23 (symdiffIneg1) =>
% 97.60/13.23 ((
% 97.60/13.23 (symdiffIneg2) =>
% 97.60/13.23 ((
% 97.60/13.23 (secondinupair) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairIL) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairIR) =>
% 97.60/13.23 ((
% 97.60/13.23 (kpairiskpair) =>
% 97.60/13.23 ((
% 97.60/13.23 (kpairp) =>
% 97.60/13.23 ((
% 97.60/13.23 (singletonsubset) =>
% 97.60/13.23 ((
% 97.60/13.23 (singletoninpowerset) =>
% 97.60/13.23 ((
% 97.60/13.23 (singletoninpowunion) =>
% 97.60/13.23 ((
% 97.60/13.23 (upairset2E) =>
% 97.60/13.23 ((
% 97.60/13.23 (upairsubunion) =>
% 97.60/13.23 ((
% 97.60/13.23 (upairinpowunion) =>
% 97.60/13.23 ((
% 97.60/13.23 (ubforcartprodlem1) =>
% 97.60/13.23 ((
% 97.60/13.23 (ubforcartprodlem2) =>
% 97.60/13.23 ((
% 97.60/13.23 (ubforcartprodlem3) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodpairin) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodmempair1) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodmempair) =>
% 97.60/13.23 ((
% 97.60/13.23 (setunionE2) =>
% 97.60/13.23 ((
% 97.60/13.23 (setunionsingleton1) =>
% 97.60/13.23 ((
% 97.60/13.23 (setunionsingleton2) =>
% 97.60/13.23 ((
% 97.60/13.23 (setunionsingleton) =>
% 97.60/13.23 ((
% 97.60/13.23 (singletonprop) =>
% 97.60/13.23 ((
% 97.60/13.23 (ex1E1) =>
% 97.60/13.23 ((
% 97.60/13.23 (ex1I) =>
% 97.60/13.23 ((
% 97.60/13.23 (ex1I2) =>
% 97.60/13.23 ((
% 97.60/13.23 (singletonsuniq) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairinjL1) =>
% 97.60/13.23 ((
% 97.60/13.23 (kfstsingleton) =>
% 97.60/13.23 ((
% 97.60/13.23 (theprop) =>
% 97.60/13.23 ((
% 97.60/13.23 (kfstpairEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodfstin) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairinjL2) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairinjL) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairinjR11) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairinjR12) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairinjR1) =>
% 97.60/13.23 ((
% 97.60/13.23 (upairequniteq) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairinjR2) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairinjR) =>
% 97.60/13.23 ((
% 97.60/13.23 (ksndsingleton) =>
% 97.60/13.23 ((
% 97.60/13.23 (ksndpairEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (kpairsurjEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodsndin) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodpairmemEL) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodpairmemER) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodmempaircEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodfstpairEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodsndpairEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodpairsurjEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (dpsetconstrI) =>
% 97.60/13.23 ((
% 97.60/13.23 (dpsetconstrSub) =>
% 97.60/13.23 ((
% 97.60/13.23 (setOfPairsIsBReln) =>
% 97.60/13.23 ((
% 97.60/13.23 (dpsetconstrERa) =>
% 97.60/13.23 ((
% 97.60/13.23 (dpsetconstrEL1) =>
% 97.60/13.23 ((
% 97.60/13.23 (dpsetconstrEL2) =>
% 97.60/13.23 ((
% 97.60/13.23 (dpsetconstrER) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcImageSingleton) =>
% 97.60/13.23 ((
% 97.60/13.23 (apProp) =>
% 97.60/13.23 ((
% 97.60/13.23 (app) =>
% 97.60/13.23 ((
% 97.60/13.23 (infuncsetfunc) =>
% 97.60/13.23 ((
% 97.60/13.23 (ap2p) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcinfuncset) =>
% 97.60/13.23 ((
% 97.60/13.23 (lamProp) =>
% 97.60/13.23 ((
% 97.60/13.23 (lamp) =>
% 97.60/13.23 ((
% 97.60/13.23 (lam2p) =>
% 97.60/13.23 ((
% 97.60/13.23 (brelnall1) =>
% 97.60/13.23 ((
% 97.60/13.23 (brelnall2) =>
% 97.60/13.23 ((
% 97.60/13.23 (ex1E2) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcGraphProp1) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcGraphProp3) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcGraphProp2) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcextLem) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcGraphProp4) =>
% 97.60/13.23 ((
% 97.60/13.23 (subbreln) =>
% 97.60/13.23 ((
% 97.60/13.23 (eqbreln) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcext) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcext2) =>
% 97.60/13.23 ((
% 97.60/13.23 (ap2apEq1) =>
% 97.60/13.23 ((
% 97.60/13.23 (ap2apEq2) =>
% 97.60/13.23 ((
% 97.60/13.23 (beta1) =>
% 97.60/13.23 ((
% 97.60/13.23 (eta1) =>
% 97.60/13.23 ((
% 97.60/13.23 (lam2lamEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (beta2) =>
% 97.60/13.23 ((
% 97.60/13.23 (eta2) =>
% 97.60/13.23 ((
% 97.60/13.23 (iffalseProp1) =>
% 97.60/13.23 ((
% 97.60/13.23 (iffalseProp2) =>
% 97.60/13.23 ((
% 97.60/13.23 (iftrueProp1) =>
% 97.60/13.23 ((
% 97.60/13.23 (iftrueProp2) =>
% 97.60/13.23 ((
% 97.60/13.23 (ifSingleton) =>
% 97.60/13.23 ((
% 97.60/13.23 (ifp) =>
% 97.60/13.23 ((
% 97.60/13.23 (theeq) =>
% 97.60/13.23 ((
% 97.60/13.23 (iftrue) =>
% 97.60/13.23 ((
% 97.60/13.23 (iffalse) =>
% 97.60/13.23 ((
% 97.60/13.23 (iftrueorfalse) =>
% 97.60/13.23 ((
% 97.60/13.23 (binintersectT_lem) =>
% 97.60/13.23 ((
% 97.60/13.23 (binunionT_lem) =>
% 97.60/13.23 ((
% 97.60/13.23 (powersetT_lem) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusT_lem) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementT_lem) =>
% 97.60/13.23 ((
% 97.60/13.23 (setextT) =>
% 97.60/13.23 ((
% 97.60/13.23 (subsetTI) =>
% 97.60/13.23 ((
% 97.60/13.23 (powersetTI1) =>
% 97.60/13.23 ((
% 97.60/13.23 (powersetTE1) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementTI1) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementTE1) =>
% 97.60/13.23 ((
% 97.60/13.23 (binintersectTELcontra) =>
% 97.60/13.23 ((
% 97.60/13.23 (binintersectTERcontra) =>
% 97.60/13.23 ((
% 97.60/13.23 (contrasubsetT) =>
% 97.60/13.23 ((
% 97.60/13.23 (contrasubsetT1) =>
% 97.60/13.23 ((
% 97.60/13.23 (contrasubsetT2) =>
% 97.60/13.23 ((
% 97.60/13.23 (contrasubsetT3) =>
% 97.60/13.23 ((
% 97.60/13.23 (doubleComplementI1) =>
% 97.60/13.23 ((
% 97.60/13.23 (doubleComplementE1) =>
% 97.60/13.23 ((
% 97.60/13.23 (doubleComplementSub1) =>
% 97.60/13.23 ((
% 97.60/13.23 (doubleComplementSub2) =>
% 97.60/13.23 ((
% 97.60/13.23 (doubleComplementEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementTnotintersectT) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementImpComplementIntersect) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementSubsetComplementIntersect) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementInPowersetComplementIntersect) =>
% 97.60/13.23 ((
% 97.60/13.23 (contraSubsetComplement) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementTcontraSubset) =>
% 97.60/13.23 ((
% 97.60/13.23 (binunionTILcontra) =>
% 97.60/13.23 ((
% 97.60/13.23 (binunionTIRcontra) =>
% 97.60/13.23 ((
% 97.60/13.23 (inIntersectImpInUnion) =>
% 97.60/13.23 ((
% 97.60/13.23 (inIntersectImpInUnion2) =>
% 97.60/13.23 ((
% 97.60/13.23 (inIntersectImpInIntersectUnions) =>
% 97.60/13.23 ((
% 97.60/13.23 (intersectInPowersetIntersectUnions) =>
% 97.60/13.23 ((
% 97.60/13.23 (inComplementUnionImpNotIn1) =>
% 97.60/13.23 ((
% 97.60/13.23 (inComplementUnionImpInComplement1) =>
% 97.60/13.23 ((
% 97.60/13.23 (binunionTE) =>
% 97.60/13.23 ((
% 97.60/13.23 (binunionTEcontra) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan2a1) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementUnionInPowersetComplement) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan2a2) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan1a) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan1b) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan1) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan2a) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan2b2) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan2b) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan2) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz13rule0) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz13rule1) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz13rule2) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz13rule3) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz13rule4) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz1_1) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz1_2) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz1_3) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz1_4) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz1_5) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1all2) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1SetBreln1) =>
% 97.60/13.23 ((
% 97.60/13.23 (choice2fnsingleton) =>
% 97.60/13.23 ((
% 97.60/13.23 (setOfPairsIsBReln1) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1all1) =>
% 97.60/13.23 ((
% 97.60/13.23 (subbreln1) =>
% 97.60/13.23 ((
% 97.60/13.23 (eqbreln1) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1invprop) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1invI) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1invE) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1compprop) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1compI) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1compE) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1compEex) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1unionprop) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1unionIL) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1unionIR) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1unionI) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1unionE) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1unionEcases) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1unionCommutes) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz2Ex) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz2W) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz2A) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz2B) =>
% 97.60/13.23 ((
% 97.60/13.23 (image1Ex) =>
% 97.60/13.23 ((
% 97.60/13.23 (image1Ex1) =>
% 97.60/13.23 ((
% 97.60/13.23 (image1Equiv) =>
% 97.60/13.23 ((
% 97.60/13.23 (image1E) =>
% 97.60/13.23 ((
% 97.60/13.23 (image1I) =>
% 97.60/13.23 ((
% 97.60/13.23 (injFuncInInjFuncSet) =>
% 97.60/13.23 ((
% 97.60/13.23 (injFuncSetFuncIn) =>
% 97.60/13.23 ((
% 97.60/13.23 (injFuncSetFuncInj) =>
% 97.60/13.23 ((
% 97.60/13.23 (surjFuncSetFuncIn) =>
% 97.60/13.23 ((
% 97.60/13.23 (surjFuncSetFuncSurj) =>
% 97.60/13.23 ((
% 97.60/13.23 (leftInvIsSurj) =>
% 97.60/13.23 ((
% 97.60/13.23 (surjCantorThm) =>
% 97.60/13.23 ((
% 97.60/13.23 (foundation2) =>
% 97.60/13.23 ((
% 97.60/13.23 (notinself) =>
% 97.60/13.23 ((
% 97.60/13.23 (notinself2) =>
% 97.60/13.23 ((
% 97.60/13.23 (omegaSp) =>
% 97.60/13.23 ((
% 97.60/13.23 (omegaSclos) =>
% 97.60/13.23 ((
% 97.60/13.23 (peano0notS) =>
% 97.60/13.23 ((
% 97.60/13.23 (!!) @ (
% 97.60/13.23 (('#S') @ (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 =>) @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#C') @ in @
% 97.60/13.23 omega)))) @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 !!) @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 (
% 97.60/13.23 ('#S') @ (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 =>) @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#C') @ in @
% 97.60/13.23 omega)))))) @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#S') @ (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 '#S') @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 =>))) @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#C') @ (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 '#B') @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 =) @
% 97.60/13.23 omegaS)))) @
% 97.60/13.23 omegaS)))))) @
% 97.60/13.23 (
% 97.60/13.23 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.60/13.23 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1027])).
% 97.60/13.23 thf(zip_derived_cl1055, plain,
% 97.60/13.23 (~ (((powersetE1) =>
% 97.60/13.23 (((inPowerset) =>
% 97.60/13.23 (((powersetsubset) =>
% 97.60/13.23 (((sepInPowerset) =>
% 97.60/13.23 (((sepSubset) =>
% 97.60/13.23 (((binunionIL) =>
% 97.60/13.23 (((upairset2IR) =>
% 97.60/13.23 (((binunionIR) =>
% 97.60/13.23 (((binunionEcases) =>
% 97.60/13.23 (((binunionE) =>
% 97.60/13.23 (((binunionLsub) =>
% 97.60/13.23 (((binunionRsub) =>
% 97.60/13.23 (((binintersectI) =>
% 97.60/13.23 (((binintersectSubset5) =>
% 97.60/13.23 (((binintersectEL) =>
% 97.60/13.23 (((binintersectLsub) =>
% 97.60/13.23 (((binintersectSubset2) =>
% 97.60/13.23 (((binintersectSubset3) =>
% 97.60/13.23 (((binintersectER) =>
% 97.60/13.23 (((disjointsetsI1) =>
% 97.60/13.23 (((binintersectRsub) =>
% 97.60/13.23 (((binintersectSubset4) =>
% 97.60/13.23 (((binintersectSubset1) =>
% 97.60/13.23 (((bs114d) =>
% 97.60/13.23 (((setminusI) =>
% 97.60/13.23 (((setminusEL) =>
% 97.60/13.23 (((setminusER) =>
% 97.60/13.23 (((setminusSubset2) =>
% 97.60/13.23 (((setminusERneg) =>
% 97.60/13.23 (((setminusELneg) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusILneg) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusIRneg) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusLsub) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusSubset1) =>
% 97.60/13.23 ((
% 97.60/13.23 (symdiffE) =>
% 97.60/13.23 ((
% 97.60/13.23 (symdiffI1) =>
% 97.60/13.23 ((
% 97.60/13.23 (symdiffI2) =>
% 97.60/13.23 ((
% 97.60/13.23 (symdiffIneg1) =>
% 97.60/13.23 ((
% 97.60/13.23 (symdiffIneg2) =>
% 97.60/13.23 ((
% 97.60/13.23 (secondinupair) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairIL) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairIR) =>
% 97.60/13.23 ((
% 97.60/13.23 (kpairiskpair) =>
% 97.60/13.23 ((
% 97.60/13.23 (kpairp) =>
% 97.60/13.23 ((
% 97.60/13.23 (singletonsubset) =>
% 97.60/13.23 ((
% 97.60/13.23 (singletoninpowerset) =>
% 97.60/13.23 ((
% 97.60/13.23 (singletoninpowunion) =>
% 97.60/13.23 ((
% 97.60/13.23 (upairset2E) =>
% 97.60/13.23 ((
% 97.60/13.23 (upairsubunion) =>
% 97.60/13.23 ((
% 97.60/13.23 (upairinpowunion) =>
% 97.60/13.23 ((
% 97.60/13.23 (ubforcartprodlem1) =>
% 97.60/13.23 ((
% 97.60/13.23 (ubforcartprodlem2) =>
% 97.60/13.23 ((
% 97.60/13.23 (ubforcartprodlem3) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodpairin) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodmempair1) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodmempair) =>
% 97.60/13.23 ((
% 97.60/13.23 (setunionE2) =>
% 97.60/13.23 ((
% 97.60/13.23 (setunionsingleton1) =>
% 97.60/13.23 ((
% 97.60/13.23 (setunionsingleton2) =>
% 97.60/13.23 ((
% 97.60/13.23 (setunionsingleton) =>
% 97.60/13.23 ((
% 97.60/13.23 (singletonprop) =>
% 97.60/13.23 ((
% 97.60/13.23 (ex1E1) =>
% 97.60/13.23 ((
% 97.60/13.23 (ex1I) =>
% 97.60/13.23 ((
% 97.60/13.23 (ex1I2) =>
% 97.60/13.23 ((
% 97.60/13.23 (singletonsuniq) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairinjL1) =>
% 97.60/13.23 ((
% 97.60/13.23 (kfstsingleton) =>
% 97.60/13.23 ((
% 97.60/13.23 (theprop) =>
% 97.60/13.23 ((
% 97.60/13.23 (kfstpairEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodfstin) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairinjL2) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairinjL) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairinjR11) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairinjR12) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairinjR1) =>
% 97.60/13.23 ((
% 97.60/13.23 (upairequniteq) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairinjR2) =>
% 97.60/13.23 ((
% 97.60/13.23 (setukpairinjR) =>
% 97.60/13.23 ((
% 97.60/13.23 (ksndsingleton) =>
% 97.60/13.23 ((
% 97.60/13.23 (ksndpairEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (kpairsurjEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodsndin) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodpairmemEL) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodpairmemER) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodmempaircEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodfstpairEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodsndpairEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (cartprodpairsurjEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (dpsetconstrI) =>
% 97.60/13.23 ((
% 97.60/13.23 (dpsetconstrSub) =>
% 97.60/13.23 ((
% 97.60/13.23 (setOfPairsIsBReln) =>
% 97.60/13.23 ((
% 97.60/13.23 (dpsetconstrERa) =>
% 97.60/13.23 ((
% 97.60/13.23 (dpsetconstrEL1) =>
% 97.60/13.23 ((
% 97.60/13.23 (dpsetconstrEL2) =>
% 97.60/13.23 ((
% 97.60/13.23 (dpsetconstrER) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcImageSingleton) =>
% 97.60/13.23 ((
% 97.60/13.23 (apProp) =>
% 97.60/13.23 ((
% 97.60/13.23 (app) =>
% 97.60/13.23 ((
% 97.60/13.23 (infuncsetfunc) =>
% 97.60/13.23 ((
% 97.60/13.23 (ap2p) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcinfuncset) =>
% 97.60/13.23 ((
% 97.60/13.23 (lamProp) =>
% 97.60/13.23 ((
% 97.60/13.23 (lamp) =>
% 97.60/13.23 ((
% 97.60/13.23 (lam2p) =>
% 97.60/13.23 ((
% 97.60/13.23 (brelnall1) =>
% 97.60/13.23 ((
% 97.60/13.23 (brelnall2) =>
% 97.60/13.23 ((
% 97.60/13.23 (ex1E2) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcGraphProp1) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcGraphProp3) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcGraphProp2) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcextLem) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcGraphProp4) =>
% 97.60/13.23 ((
% 97.60/13.23 (subbreln) =>
% 97.60/13.23 ((
% 97.60/13.23 (eqbreln) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcext) =>
% 97.60/13.23 ((
% 97.60/13.23 (funcext2) =>
% 97.60/13.23 ((
% 97.60/13.23 (ap2apEq1) =>
% 97.60/13.23 ((
% 97.60/13.23 (ap2apEq2) =>
% 97.60/13.23 ((
% 97.60/13.23 (beta1) =>
% 97.60/13.23 ((
% 97.60/13.23 (eta1) =>
% 97.60/13.23 ((
% 97.60/13.23 (lam2lamEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (beta2) =>
% 97.60/13.23 ((
% 97.60/13.23 (eta2) =>
% 97.60/13.23 ((
% 97.60/13.23 (iffalseProp1) =>
% 97.60/13.23 ((
% 97.60/13.23 (iffalseProp2) =>
% 97.60/13.23 ((
% 97.60/13.23 (iftrueProp1) =>
% 97.60/13.23 ((
% 97.60/13.23 (iftrueProp2) =>
% 97.60/13.23 ((
% 97.60/13.23 (ifSingleton) =>
% 97.60/13.23 ((
% 97.60/13.23 (ifp) =>
% 97.60/13.23 ((
% 97.60/13.23 (theeq) =>
% 97.60/13.23 ((
% 97.60/13.23 (iftrue) =>
% 97.60/13.23 ((
% 97.60/13.23 (iffalse) =>
% 97.60/13.23 ((
% 97.60/13.23 (iftrueorfalse) =>
% 97.60/13.23 ((
% 97.60/13.23 (binintersectT_lem) =>
% 97.60/13.23 ((
% 97.60/13.23 (binunionT_lem) =>
% 97.60/13.23 ((
% 97.60/13.23 (powersetT_lem) =>
% 97.60/13.23 ((
% 97.60/13.23 (setminusT_lem) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementT_lem) =>
% 97.60/13.23 ((
% 97.60/13.23 (setextT) =>
% 97.60/13.23 ((
% 97.60/13.23 (subsetTI) =>
% 97.60/13.23 ((
% 97.60/13.23 (powersetTI1) =>
% 97.60/13.23 ((
% 97.60/13.23 (powersetTE1) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementTI1) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementTE1) =>
% 97.60/13.23 ((
% 97.60/13.23 (binintersectTELcontra) =>
% 97.60/13.23 ((
% 97.60/13.23 (binintersectTERcontra) =>
% 97.60/13.23 ((
% 97.60/13.23 (contrasubsetT) =>
% 97.60/13.23 ((
% 97.60/13.23 (contrasubsetT1) =>
% 97.60/13.23 ((
% 97.60/13.23 (contrasubsetT2) =>
% 97.60/13.23 ((
% 97.60/13.23 (contrasubsetT3) =>
% 97.60/13.23 ((
% 97.60/13.23 (doubleComplementI1) =>
% 97.60/13.23 ((
% 97.60/13.23 (doubleComplementE1) =>
% 97.60/13.23 ((
% 97.60/13.23 (doubleComplementSub1) =>
% 97.60/13.23 ((
% 97.60/13.23 (doubleComplementSub2) =>
% 97.60/13.23 ((
% 97.60/13.23 (doubleComplementEq) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementTnotintersectT) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementImpComplementIntersect) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementSubsetComplementIntersect) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementInPowersetComplementIntersect) =>
% 97.60/13.23 ((
% 97.60/13.23 (contraSubsetComplement) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementTcontraSubset) =>
% 97.60/13.23 ((
% 97.60/13.23 (binunionTILcontra) =>
% 97.60/13.23 ((
% 97.60/13.23 (binunionTIRcontra) =>
% 97.60/13.23 ((
% 97.60/13.23 (inIntersectImpInUnion) =>
% 97.60/13.23 ((
% 97.60/13.23 (inIntersectImpInUnion2) =>
% 97.60/13.23 ((
% 97.60/13.23 (inIntersectImpInIntersectUnions) =>
% 97.60/13.23 ((
% 97.60/13.23 (intersectInPowersetIntersectUnions) =>
% 97.60/13.23 ((
% 97.60/13.23 (inComplementUnionImpNotIn1) =>
% 97.60/13.23 ((
% 97.60/13.23 (inComplementUnionImpInComplement1) =>
% 97.60/13.23 ((
% 97.60/13.23 (binunionTE) =>
% 97.60/13.23 ((
% 97.60/13.23 (binunionTEcontra) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan2a1) =>
% 97.60/13.23 ((
% 97.60/13.23 (complementUnionInPowersetComplement) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan2a2) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan1a) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan1b) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan1) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan2a) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan2b2) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan2b) =>
% 97.60/13.23 ((
% 97.60/13.23 (demorgan2) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz13rule0) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz13rule1) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz13rule2) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz13rule3) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz13rule4) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz1_1) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz1_2) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz1_3) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz1_4) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz1_5) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1all2) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1SetBreln1) =>
% 97.60/13.23 ((
% 97.60/13.23 (choice2fnsingleton) =>
% 97.60/13.23 ((
% 97.60/13.23 (setOfPairsIsBReln1) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1all1) =>
% 97.60/13.23 ((
% 97.60/13.23 (subbreln1) =>
% 97.60/13.23 ((
% 97.60/13.23 (eqbreln1) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1invprop) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1invI) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1invE) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1compprop) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1compI) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1compE) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1compEex) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1unionprop) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1unionIL) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1unionIR) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1unionI) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1unionE) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1unionEcases) =>
% 97.60/13.23 ((
% 97.60/13.23 (breln1unionCommutes) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz2Ex) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz2W) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz2A) =>
% 97.60/13.23 ((
% 97.60/13.23 (woz2B) =>
% 97.60/13.23 ((
% 97.60/13.23 (image1Ex) =>
% 97.60/13.23 ((
% 97.60/13.23 (image1Ex1) =>
% 97.60/13.23 ((
% 97.60/13.23 (image1Equiv) =>
% 97.60/13.23 ((
% 97.60/13.23 (image1E) =>
% 97.60/13.23 ((
% 97.60/13.23 (image1I) =>
% 97.60/13.23 ((
% 97.60/13.23 (injFuncInInjFuncSet) =>
% 97.60/13.23 ((
% 97.60/13.23 (injFuncSetFuncIn) =>
% 97.60/13.23 ((
% 97.60/13.23 (injFuncSetFuncInj) =>
% 97.60/13.23 ((
% 97.60/13.23 (surjFuncSetFuncIn) =>
% 97.60/13.23 ((
% 97.60/13.23 (surjFuncSetFuncSurj) =>
% 97.60/13.23 ((
% 97.60/13.23 (leftInvIsSurj) =>
% 97.60/13.23 ((
% 97.60/13.23 (surjCantorThm) =>
% 97.60/13.23 ((
% 97.60/13.23 (foundation2) =>
% 97.60/13.23 ((
% 97.60/13.23 (notinself) =>
% 97.60/13.23 ((
% 97.60/13.23 (notinself2) =>
% 97.60/13.23 ((
% 97.60/13.23 (omegaSp) =>
% 97.60/13.23 ((
% 97.60/13.23 (omegaSclos) =>
% 97.60/13.23 ((
% 97.60/13.23 (peano0notS) =>
% 97.60/13.23 ((
% 97.60/13.23 (!!) @ (
% 97.60/13.23 (('#S') @ (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 =>) @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#C') @ in @
% 97.60/13.23 omega)))) @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 !!) @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 (
% 97.60/13.23 ('#S') @ (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 =>) @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#C') @ in @
% 97.60/13.23 omega)))))) @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#S') @ (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 '#S') @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 =>))) @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#C') @ (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 '#B') @
% 97.60/13.23 (
% 97.60/13.23 (
% 97.60/13.23 ('#B') @ (
% 97.60/13.23 =) @
% 97.60/13.23 omegaS)))) @
% 97.60/13.23 omegaS)))))) @
% 97.60/13.23 (
% 97.60/13.23 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.60/13.23 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1039])).
% 97.60/13.23 thf(zip_derived_cl1067, plain,
% 97.60/13.23 (~ (((inPowerset) =>
% 97.60/13.23 (((powersetsubset) =>
% 97.60/13.23 (((sepInPowerset) =>
% 97.60/13.23 (((sepSubset) =>
% 97.60/13.23 (((binunionIL) =>
% 97.60/13.23 (((upairset2IR) =>
% 97.60/13.23 (((binunionIR) =>
% 97.60/13.23 (((binunionEcases) =>
% 97.60/13.23 (((binunionE) =>
% 97.60/13.23 (((binunionLsub) =>
% 97.60/13.23 (((binunionRsub) =>
% 97.60/13.23 (((binintersectI) =>
% 97.60/13.23 (((binintersectSubset5) =>
% 97.60/13.23 (((binintersectEL) =>
% 97.60/13.23 (((binintersectLsub) =>
% 97.60/13.24 (((binintersectSubset2) =>
% 97.60/13.24 (((binintersectSubset3) =>
% 97.60/13.24 (((binintersectER) =>
% 97.60/13.24 (((disjointsetsI1) =>
% 97.60/13.24 (((binintersectRsub) =>
% 97.60/13.24 (((binintersectSubset4) =>
% 97.60/13.24 (((binintersectSubset1) =>
% 97.60/13.24 (((bs114d) =>
% 97.60/13.24 (((setminusI) =>
% 97.60/13.24 (((setminusEL) =>
% 97.60/13.24 (((setminusER) =>
% 97.60/13.24 (((setminusSubset2) =>
% 97.60/13.24 (((setminusERneg) =>
% 97.60/13.24 (((setminusELneg) =>
% 97.60/13.24 (((setminusILneg) =>
% 97.60/13.24 ((
% 97.60/13.24 (setminusIRneg) =>
% 97.60/13.24 ((
% 97.60/13.24 (setminusLsub) =>
% 97.60/13.24 ((
% 97.60/13.24 (setminusSubset1) =>
% 97.60/13.24 ((
% 97.60/13.24 (symdiffE) =>
% 97.60/13.24 ((
% 97.60/13.24 (symdiffI1) =>
% 97.60/13.24 ((
% 97.60/13.24 (symdiffI2) =>
% 97.60/13.24 ((
% 97.60/13.24 (symdiffIneg1) =>
% 97.60/13.24 ((
% 97.60/13.24 (symdiffIneg2) =>
% 97.60/13.24 ((
% 97.60/13.24 (secondinupair) =>
% 97.60/13.24 ((
% 97.60/13.24 (setukpairIL) =>
% 97.60/13.24 ((
% 97.60/13.24 (setukpairIR) =>
% 97.60/13.24 ((
% 97.60/13.24 (kpairiskpair) =>
% 97.60/13.24 ((
% 97.60/13.24 (kpairp) =>
% 97.60/13.24 ((
% 97.60/13.24 (singletonsubset) =>
% 97.60/13.24 ((
% 97.60/13.24 (singletoninpowerset) =>
% 97.60/13.24 ((
% 97.60/13.24 (singletoninpowunion) =>
% 97.60/13.24 ((
% 97.60/13.24 (upairset2E) =>
% 97.60/13.24 ((
% 97.60/13.24 (upairsubunion) =>
% 97.60/13.24 ((
% 97.60/13.24 (upairinpowunion) =>
% 97.60/13.24 ((
% 97.60/13.24 (ubforcartprodlem1) =>
% 97.60/13.24 ((
% 97.60/13.24 (ubforcartprodlem2) =>
% 97.60/13.24 ((
% 97.60/13.24 (ubforcartprodlem3) =>
% 97.60/13.24 ((
% 97.60/13.24 (cartprodpairin) =>
% 97.60/13.24 ((
% 97.60/13.24 (cartprodmempair1) =>
% 97.60/13.24 ((
% 97.60/13.24 (cartprodmempair) =>
% 97.60/13.24 ((
% 97.60/13.24 (setunionE2) =>
% 97.60/13.24 ((
% 97.60/13.24 (setunionsingleton1) =>
% 97.60/13.24 ((
% 97.60/13.24 (setunionsingleton2) =>
% 97.60/13.24 ((
% 97.60/13.24 (setunionsingleton) =>
% 97.60/13.24 ((
% 97.60/13.24 (singletonprop) =>
% 97.60/13.24 ((
% 97.60/13.24 (ex1E1) =>
% 97.60/13.24 ((
% 97.60/13.24 (ex1I) =>
% 97.60/13.24 ((
% 97.60/13.24 (ex1I2) =>
% 97.60/13.24 ((
% 97.60/13.24 (singletonsuniq) =>
% 97.60/13.24 ((
% 97.60/13.24 (setukpairinjL1) =>
% 97.60/13.24 ((
% 97.60/13.24 (kfstsingleton) =>
% 97.60/13.24 ((
% 97.60/13.24 (theprop) =>
% 97.60/13.24 ((
% 97.60/13.24 (kfstpairEq) =>
% 97.60/13.24 ((
% 97.60/13.24 (cartprodfstin) =>
% 97.60/13.24 ((
% 97.60/13.24 (setukpairinjL2) =>
% 97.60/13.24 ((
% 97.60/13.24 (setukpairinjL) =>
% 97.60/13.24 ((
% 97.60/13.24 (setukpairinjR11) =>
% 97.60/13.24 ((
% 97.60/13.24 (setukpairinjR12) =>
% 97.60/13.24 ((
% 97.60/13.24 (setukpairinjR1) =>
% 97.60/13.24 ((
% 97.60/13.24 (upairequniteq) =>
% 97.60/13.24 ((
% 97.60/13.24 (setukpairinjR2) =>
% 97.60/13.24 ((
% 97.60/13.24 (setukpairinjR) =>
% 97.60/13.24 ((
% 97.60/13.24 (ksndsingleton) =>
% 97.60/13.24 ((
% 97.60/13.24 (ksndpairEq) =>
% 97.60/13.24 ((
% 97.60/13.24 (kpairsurjEq) =>
% 97.60/13.24 ((
% 97.60/13.24 (cartprodsndin) =>
% 97.60/13.24 ((
% 97.60/13.24 (cartprodpairmemEL) =>
% 97.60/13.24 ((
% 97.60/13.24 (cartprodpairmemER) =>
% 97.60/13.24 ((
% 97.60/13.24 (cartprodmempaircEq) =>
% 97.60/13.24 ((
% 97.60/13.24 (cartprodfstpairEq) =>
% 97.60/13.24 ((
% 97.60/13.24 (cartprodsndpairEq) =>
% 97.60/13.24 ((
% 97.60/13.24 (cartprodpairsurjEq) =>
% 97.60/13.24 ((
% 97.60/13.24 (dpsetconstrI) =>
% 97.60/13.24 ((
% 97.60/13.24 (dpsetconstrSub) =>
% 97.60/13.24 ((
% 97.60/13.24 (setOfPairsIsBReln) =>
% 97.60/13.24 ((
% 97.60/13.24 (dpsetconstrERa) =>
% 97.60/13.24 ((
% 97.60/13.24 (dpsetconstrEL1) =>
% 97.60/13.24 ((
% 97.60/13.24 (dpsetconstrEL2) =>
% 97.60/13.24 ((
% 97.60/13.24 (dpsetconstrER) =>
% 97.60/13.24 ((
% 97.60/13.24 (funcImageSingleton) =>
% 97.60/13.24 ((
% 97.60/13.24 (apProp) =>
% 97.60/13.24 ((
% 97.60/13.24 (app) =>
% 97.60/13.24 ((
% 97.60/13.24 (infuncsetfunc) =>
% 97.60/13.24 ((
% 97.60/13.24 (ap2p) =>
% 97.60/13.24 ((
% 97.60/13.24 (funcinfuncset) =>
% 97.60/13.24 ((
% 97.60/13.24 (lamProp) =>
% 97.60/13.24 ((
% 97.60/13.24 (lamp) =>
% 97.60/13.24 ((
% 97.60/13.24 (lam2p) =>
% 97.60/13.24 ((
% 97.60/13.24 (brelnall1) =>
% 97.60/13.24 ((
% 97.60/13.24 (brelnall2) =>
% 97.60/13.24 ((
% 97.60/13.24 (ex1E2) =>
% 97.60/13.24 ((
% 97.60/13.24 (funcGraphProp1) =>
% 97.60/13.24 ((
% 97.60/13.24 (funcGraphProp3) =>
% 97.60/13.24 ((
% 97.60/13.24 (funcGraphProp2) =>
% 97.60/13.24 ((
% 97.60/13.24 (funcextLem) =>
% 97.60/13.24 ((
% 97.60/13.24 (funcGraphProp4) =>
% 97.60/13.24 ((
% 97.60/13.24 (subbreln) =>
% 97.60/13.24 ((
% 97.60/13.24 (eqbreln) =>
% 97.60/13.24 ((
% 97.60/13.24 (funcext) =>
% 97.60/13.24 ((
% 97.60/13.24 (funcext2) =>
% 97.60/13.24 ((
% 97.60/13.24 (ap2apEq1) =>
% 97.60/13.24 ((
% 97.60/13.24 (ap2apEq2) =>
% 97.60/13.24 ((
% 97.60/13.24 (beta1) =>
% 97.60/13.24 ((
% 97.60/13.24 (eta1) =>
% 97.60/13.24 ((
% 97.60/13.24 (lam2lamEq) =>
% 97.60/13.24 ((
% 97.60/13.24 (beta2) =>
% 97.60/13.24 ((
% 97.60/13.24 (eta2) =>
% 97.60/13.24 ((
% 97.60/13.24 (iffalseProp1) =>
% 97.60/13.24 ((
% 97.60/13.24 (iffalseProp2) =>
% 97.60/13.24 ((
% 97.60/13.24 (iftrueProp1) =>
% 97.60/13.24 ((
% 97.60/13.24 (iftrueProp2) =>
% 97.60/13.24 ((
% 97.60/13.24 (ifSingleton) =>
% 97.60/13.24 ((
% 97.60/13.24 (ifp) =>
% 97.60/13.24 ((
% 97.60/13.24 (theeq) =>
% 97.60/13.24 ((
% 97.60/13.24 (iftrue) =>
% 97.60/13.24 ((
% 97.60/13.24 (iffalse) =>
% 97.60/13.24 ((
% 97.60/13.24 (iftrueorfalse) =>
% 97.60/13.24 ((
% 97.60/13.24 (binintersectT_lem) =>
% 97.60/13.24 ((
% 97.60/13.24 (binunionT_lem) =>
% 97.60/13.24 ((
% 97.60/13.24 (powersetT_lem) =>
% 97.60/13.24 ((
% 97.60/13.24 (setminusT_lem) =>
% 97.60/13.24 ((
% 97.60/13.24 (complementT_lem) =>
% 97.60/13.24 ((
% 97.60/13.24 (setextT) =>
% 97.60/13.24 ((
% 97.60/13.24 (subsetTI) =>
% 97.60/13.24 ((
% 97.60/13.24 (powersetTI1) =>
% 97.60/13.24 ((
% 97.60/13.24 (powersetTE1) =>
% 97.60/13.24 ((
% 97.60/13.24 (complementTI1) =>
% 97.60/13.24 ((
% 97.60/13.24 (complementTE1) =>
% 97.60/13.24 ((
% 97.60/13.24 (binintersectTELcontra) =>
% 97.60/13.24 ((
% 97.60/13.24 (binintersectTERcontra) =>
% 97.60/13.24 ((
% 97.60/13.24 (contrasubsetT) =>
% 97.60/13.24 ((
% 97.60/13.24 (contrasubsetT1) =>
% 97.60/13.24 ((
% 97.60/13.24 (contrasubsetT2) =>
% 97.60/13.24 ((
% 97.60/13.24 (contrasubsetT3) =>
% 97.60/13.24 ((
% 97.60/13.24 (doubleComplementI1) =>
% 97.60/13.24 ((
% 97.60/13.24 (doubleComplementE1) =>
% 97.60/13.24 ((
% 97.60/13.24 (doubleComplementSub1) =>
% 97.60/13.24 ((
% 97.60/13.24 (doubleComplementSub2) =>
% 97.60/13.24 ((
% 97.60/13.24 (doubleComplementEq) =>
% 97.60/13.24 ((
% 97.60/13.24 (complementTnotintersectT) =>
% 97.60/13.24 ((
% 97.60/13.24 (complementImpComplementIntersect) =>
% 97.60/13.24 ((
% 97.60/13.24 (complementSubsetComplementIntersect) =>
% 97.60/13.24 ((
% 97.60/13.24 (complementInPowersetComplementIntersect) =>
% 97.60/13.24 ((
% 97.60/13.24 (contraSubsetComplement) =>
% 97.60/13.24 ((
% 97.60/13.24 (complementTcontraSubset) =>
% 97.60/13.24 ((
% 97.60/13.24 (binunionTILcontra) =>
% 97.60/13.24 ((
% 97.60/13.24 (binunionTIRcontra) =>
% 97.60/13.24 ((
% 97.60/13.24 (inIntersectImpInUnion) =>
% 97.60/13.24 ((
% 97.60/13.24 (inIntersectImpInUnion2) =>
% 97.60/13.24 ((
% 97.60/13.24 (inIntersectImpInIntersectUnions) =>
% 97.60/13.24 ((
% 97.60/13.24 (intersectInPowersetIntersectUnions) =>
% 97.60/13.24 ((
% 97.60/13.24 (inComplementUnionImpNotIn1) =>
% 97.60/13.24 ((
% 97.60/13.24 (inComplementUnionImpInComplement1) =>
% 97.60/13.24 ((
% 97.60/13.24 (binunionTE) =>
% 97.60/13.24 ((
% 97.60/13.24 (binunionTEcontra) =>
% 97.60/13.24 ((
% 97.60/13.24 (demorgan2a1) =>
% 97.60/13.24 ((
% 97.60/13.24 (complementUnionInPowersetComplement) =>
% 97.60/13.24 ((
% 97.60/13.24 (demorgan2a2) =>
% 97.60/13.24 ((
% 97.60/13.24 (demorgan1a) =>
% 97.60/13.24 ((
% 97.60/13.24 (demorgan1b) =>
% 97.60/13.24 ((
% 97.60/13.24 (demorgan1) =>
% 97.60/13.24 ((
% 97.60/13.24 (demorgan2a) =>
% 97.60/13.24 ((
% 97.60/13.24 (demorgan2b2) =>
% 97.60/13.24 ((
% 97.60/13.24 (demorgan2b) =>
% 97.60/13.24 ((
% 97.60/13.24 (demorgan2) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz13rule0) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz13rule1) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz13rule2) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz13rule3) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz13rule4) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz1_1) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz1_2) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz1_3) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz1_4) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz1_5) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1all2) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1SetBreln1) =>
% 97.60/13.24 ((
% 97.60/13.24 (choice2fnsingleton) =>
% 97.60/13.24 ((
% 97.60/13.24 (setOfPairsIsBReln1) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1all1) =>
% 97.60/13.24 ((
% 97.60/13.24 (subbreln1) =>
% 97.60/13.24 ((
% 97.60/13.24 (eqbreln1) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1invprop) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1invI) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1invE) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1compprop) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1compI) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1compE) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1compEex) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1unionprop) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1unionIL) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1unionIR) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1unionI) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1unionE) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1unionEcases) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1unionCommutes) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz2Ex) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz2W) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz2A) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz2B) =>
% 97.60/13.24 ((
% 97.60/13.24 (image1Ex) =>
% 97.60/13.24 ((
% 97.60/13.24 (image1Ex1) =>
% 97.60/13.24 ((
% 97.60/13.24 (image1Equiv) =>
% 97.60/13.24 ((
% 97.60/13.24 (image1E) =>
% 97.60/13.24 ((
% 97.60/13.24 (image1I) =>
% 97.60/13.24 ((
% 97.60/13.24 (injFuncInInjFuncSet) =>
% 97.60/13.24 ((
% 97.60/13.24 (injFuncSetFuncIn) =>
% 97.60/13.24 ((
% 97.60/13.24 (injFuncSetFuncInj) =>
% 97.60/13.24 ((
% 97.60/13.24 (surjFuncSetFuncIn) =>
% 97.60/13.24 ((
% 97.60/13.24 (surjFuncSetFuncSurj) =>
% 97.60/13.24 ((
% 97.60/13.24 (leftInvIsSurj) =>
% 97.60/13.24 ((
% 97.60/13.24 (surjCantorThm) =>
% 97.60/13.24 ((
% 97.60/13.24 (foundation2) =>
% 97.60/13.24 ((
% 97.60/13.24 (notinself) =>
% 97.60/13.24 ((
% 97.60/13.24 (notinself2) =>
% 97.60/13.24 ((
% 97.60/13.24 (omegaSp) =>
% 97.60/13.24 ((
% 97.60/13.24 (omegaSclos) =>
% 97.60/13.24 ((
% 97.60/13.24 (peano0notS) =>
% 97.60/13.24 ((
% 97.60/13.24 (!!) @ (
% 97.60/13.24 (('#S') @ (
% 97.60/13.24 (
% 97.60/13.24 ('#B') @ (
% 97.60/13.24 =>) @
% 97.60/13.24 (
% 97.60/13.24 (
% 97.60/13.24 ('#C') @ in @
% 97.60/13.24 omega)))) @
% 97.60/13.24 (
% 97.60/13.24 (
% 97.60/13.24 ('#B') @ (
% 97.60/13.24 !!) @
% 97.60/13.24 (
% 97.60/13.24 (
% 97.60/13.24 ('#B') @ (
% 97.60/13.24 (
% 97.60/13.24 ('#S') @ (
% 97.60/13.24 (
% 97.60/13.24 ('#B') @ (
% 97.60/13.24 =>) @
% 97.60/13.24 (
% 97.60/13.24 (
% 97.60/13.24 ('#C') @ in @
% 97.60/13.24 omega)))))) @
% 97.60/13.24 (
% 97.60/13.24 (
% 97.60/13.24 ('#S') @ (
% 97.60/13.24 (
% 97.60/13.24 ('#B') @ (
% 97.60/13.24 '#S') @
% 97.60/13.24 (
% 97.60/13.24 (
% 97.60/13.24 ('#B') @ (
% 97.60/13.24 (
% 97.60/13.24 ('#B') @ (
% 97.60/13.24 =>))) @
% 97.60/13.24 (
% 97.60/13.24 (
% 97.60/13.24 ('#C') @ (
% 97.60/13.24 (
% 97.60/13.24 ('#B') @ (
% 97.60/13.24 '#B') @
% 97.60/13.24 (
% 97.60/13.24 (
% 97.60/13.24 ('#B') @ (
% 97.60/13.24 =) @
% 97.60/13.24 omegaS)))) @
% 97.60/13.24 omegaS)))))) @
% 97.60/13.24 (
% 97.60/13.24 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.60/13.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1055])).
% 97.60/13.24 thf(zip_derived_cl1074, plain,
% 97.60/13.24 (~ (((powersetsubset) =>
% 97.60/13.24 (((sepInPowerset) =>
% 97.60/13.24 (((sepSubset) =>
% 97.60/13.24 (((binunionIL) =>
% 97.60/13.24 (((upairset2IR) =>
% 97.60/13.24 (((binunionIR) =>
% 97.60/13.24 (((binunionEcases) =>
% 97.60/13.24 (((binunionE) =>
% 97.60/13.24 (((binunionLsub) =>
% 97.60/13.24 (((binunionRsub) =>
% 97.60/13.24 (((binintersectI) =>
% 97.60/13.24 (((binintersectSubset5) =>
% 97.60/13.24 (((binintersectEL) =>
% 97.60/13.24 (((binintersectLsub) =>
% 97.60/13.24 (((binintersectSubset2) =>
% 97.60/13.24 (((binintersectSubset3) =>
% 97.60/13.24 (((binintersectER) =>
% 97.60/13.24 (((disjointsetsI1) =>
% 97.60/13.24 (((binintersectRsub) =>
% 97.60/13.24 (((binintersectSubset4) =>
% 97.60/13.24 (((binintersectSubset1) =>
% 97.60/13.24 (((bs114d) =>
% 97.60/13.24 (((setminusI) =>
% 97.60/13.24 (((setminusEL) =>
% 97.60/13.24 (((setminusER) =>
% 97.60/13.24 (((setminusSubset2) =>
% 97.60/13.24 (((setminusERneg) =>
% 97.60/13.24 (((setminusELneg) =>
% 97.60/13.24 (((setminusILneg) =>
% 97.60/13.24 (((setminusIRneg) =>
% 97.60/13.24 ((
% 97.60/13.24 (setminusLsub) =>
% 97.60/13.24 ((
% 97.60/13.24 (setminusSubset1) =>
% 97.60/13.24 ((
% 97.60/13.24 (symdiffE) =>
% 97.60/13.24 ((
% 97.60/13.24 (symdiffI1) =>
% 97.60/13.24 ((
% 97.60/13.24 (symdiffI2) =>
% 97.60/13.24 ((
% 97.60/13.24 (symdiffIneg1) =>
% 97.60/13.24 ((
% 97.60/13.24 (symdiffIneg2) =>
% 97.60/13.24 ((
% 97.60/13.24 (secondinupair) =>
% 97.60/13.24 ((
% 97.60/13.24 (setukpairIL) =>
% 97.60/13.24 ((
% 97.60/13.24 (setukpairIR) =>
% 97.60/13.24 ((
% 97.60/13.24 (kpairiskpair) =>
% 97.60/13.24 ((
% 97.60/13.24 (kpairp) =>
% 97.60/13.24 ((
% 97.60/13.24 (singletonsubset) =>
% 97.60/13.24 ((
% 97.60/13.24 (singletoninpowerset) =>
% 97.60/13.24 ((
% 97.60/13.24 (singletoninpowunion) =>
% 97.60/13.24 ((
% 97.60/13.24 (upairset2E) =>
% 97.60/13.24 ((
% 97.60/13.24 (upairsubunion) =>
% 97.60/13.24 ((
% 97.60/13.24 (upairinpowunion) =>
% 97.60/13.24 ((
% 97.60/13.24 (ubforcartprodlem1) =>
% 97.60/13.24 ((
% 97.60/13.24 (ubforcartprodlem2) =>
% 97.60/13.24 ((
% 97.60/13.24 (ubforcartprodlem3) =>
% 97.60/13.24 ((
% 97.60/13.24 (cartprodpairin) =>
% 97.60/13.24 ((
% 97.60/13.24 (cartprodmempair1) =>
% 97.60/13.24 ((
% 97.60/13.24 (cartprodmempair) =>
% 97.60/13.24 ((
% 97.60/13.24 (setunionE2) =>
% 97.60/13.24 ((
% 97.60/13.24 (setunionsingleton1) =>
% 97.60/13.24 ((
% 97.60/13.24 (setunionsingleton2) =>
% 97.60/13.24 ((
% 97.60/13.24 (setunionsingleton) =>
% 97.60/13.24 ((
% 97.60/13.24 (singletonprop) =>
% 97.60/13.24 ((
% 97.60/13.24 (ex1E1) =>
% 97.60/13.24 ((
% 97.60/13.24 (ex1I) =>
% 97.60/13.24 ((
% 97.60/13.24 (ex1I2) =>
% 97.60/13.24 ((
% 97.60/13.24 (singletonsuniq) =>
% 97.60/13.24 ((
% 97.60/13.24 (setukpairinjL1) =>
% 97.60/13.24 ((
% 97.60/13.24 (kfstsingleton) =>
% 97.60/13.24 ((
% 97.60/13.24 (theprop) =>
% 97.60/13.24 ((
% 97.60/13.24 (kfstpairEq) =>
% 97.60/13.24 ((
% 97.60/13.24 (cartprodfstin) =>
% 97.60/13.24 ((
% 97.60/13.24 (setukpairinjL2) =>
% 97.60/13.24 ((
% 97.60/13.24 (setukpairinjL) =>
% 97.60/13.24 ((
% 97.60/13.24 (setukpairinjR11) =>
% 97.60/13.24 ((
% 97.60/13.24 (setukpairinjR12) =>
% 97.60/13.24 ((
% 97.60/13.24 (setukpairinjR1) =>
% 97.60/13.24 ((
% 97.60/13.24 (upairequniteq) =>
% 97.60/13.24 ((
% 97.60/13.24 (setukpairinjR2) =>
% 97.60/13.24 ((
% 97.60/13.24 (setukpairinjR) =>
% 97.60/13.24 ((
% 97.60/13.24 (ksndsingleton) =>
% 97.60/13.24 ((
% 97.60/13.24 (ksndpairEq) =>
% 97.60/13.24 ((
% 97.60/13.24 (kpairsurjEq) =>
% 97.60/13.24 ((
% 97.60/13.24 (cartprodsndin) =>
% 97.60/13.24 ((
% 97.60/13.24 (cartprodpairmemEL) =>
% 97.60/13.24 ((
% 97.60/13.24 (cartprodpairmemER) =>
% 97.60/13.24 ((
% 97.60/13.24 (cartprodmempaircEq) =>
% 97.60/13.24 ((
% 97.60/13.24 (cartprodfstpairEq) =>
% 97.60/13.24 ((
% 97.60/13.24 (cartprodsndpairEq) =>
% 97.60/13.24 ((
% 97.60/13.24 (cartprodpairsurjEq) =>
% 97.60/13.24 ((
% 97.60/13.24 (dpsetconstrI) =>
% 97.60/13.24 ((
% 97.60/13.24 (dpsetconstrSub) =>
% 97.60/13.24 ((
% 97.60/13.24 (setOfPairsIsBReln) =>
% 97.60/13.24 ((
% 97.60/13.24 (dpsetconstrERa) =>
% 97.60/13.24 ((
% 97.60/13.24 (dpsetconstrEL1) =>
% 97.60/13.24 ((
% 97.60/13.24 (dpsetconstrEL2) =>
% 97.60/13.24 ((
% 97.60/13.24 (dpsetconstrER) =>
% 97.60/13.24 ((
% 97.60/13.24 (funcImageSingleton) =>
% 97.60/13.24 ((
% 97.60/13.24 (apProp) =>
% 97.60/13.24 ((
% 97.60/13.24 (app) =>
% 97.60/13.24 ((
% 97.60/13.24 (infuncsetfunc) =>
% 97.60/13.24 ((
% 97.60/13.24 (ap2p) =>
% 97.60/13.24 ((
% 97.60/13.24 (funcinfuncset) =>
% 97.60/13.24 ((
% 97.60/13.24 (lamProp) =>
% 97.60/13.24 ((
% 97.60/13.24 (lamp) =>
% 97.60/13.24 ((
% 97.60/13.24 (lam2p) =>
% 97.60/13.24 ((
% 97.60/13.24 (brelnall1) =>
% 97.60/13.24 ((
% 97.60/13.24 (brelnall2) =>
% 97.60/13.24 ((
% 97.60/13.24 (ex1E2) =>
% 97.60/13.24 ((
% 97.60/13.24 (funcGraphProp1) =>
% 97.60/13.24 ((
% 97.60/13.24 (funcGraphProp3) =>
% 97.60/13.24 ((
% 97.60/13.24 (funcGraphProp2) =>
% 97.60/13.24 ((
% 97.60/13.24 (funcextLem) =>
% 97.60/13.24 ((
% 97.60/13.24 (funcGraphProp4) =>
% 97.60/13.24 ((
% 97.60/13.24 (subbreln) =>
% 97.60/13.24 ((
% 97.60/13.24 (eqbreln) =>
% 97.60/13.24 ((
% 97.60/13.24 (funcext) =>
% 97.60/13.24 ((
% 97.60/13.24 (funcext2) =>
% 97.60/13.24 ((
% 97.60/13.24 (ap2apEq1) =>
% 97.60/13.24 ((
% 97.60/13.24 (ap2apEq2) =>
% 97.60/13.24 ((
% 97.60/13.24 (beta1) =>
% 97.60/13.24 ((
% 97.60/13.24 (eta1) =>
% 97.60/13.24 ((
% 97.60/13.24 (lam2lamEq) =>
% 97.60/13.24 ((
% 97.60/13.24 (beta2) =>
% 97.60/13.24 ((
% 97.60/13.24 (eta2) =>
% 97.60/13.24 ((
% 97.60/13.24 (iffalseProp1) =>
% 97.60/13.24 ((
% 97.60/13.24 (iffalseProp2) =>
% 97.60/13.24 ((
% 97.60/13.24 (iftrueProp1) =>
% 97.60/13.24 ((
% 97.60/13.24 (iftrueProp2) =>
% 97.60/13.24 ((
% 97.60/13.24 (ifSingleton) =>
% 97.60/13.24 ((
% 97.60/13.24 (ifp) =>
% 97.60/13.24 ((
% 97.60/13.24 (theeq) =>
% 97.60/13.24 ((
% 97.60/13.24 (iftrue) =>
% 97.60/13.24 ((
% 97.60/13.24 (iffalse) =>
% 97.60/13.24 ((
% 97.60/13.24 (iftrueorfalse) =>
% 97.60/13.24 ((
% 97.60/13.24 (binintersectT_lem) =>
% 97.60/13.24 ((
% 97.60/13.24 (binunionT_lem) =>
% 97.60/13.24 ((
% 97.60/13.24 (powersetT_lem) =>
% 97.60/13.24 ((
% 97.60/13.24 (setminusT_lem) =>
% 97.60/13.24 ((
% 97.60/13.24 (complementT_lem) =>
% 97.60/13.24 ((
% 97.60/13.24 (setextT) =>
% 97.60/13.24 ((
% 97.60/13.24 (subsetTI) =>
% 97.60/13.24 ((
% 97.60/13.24 (powersetTI1) =>
% 97.60/13.24 ((
% 97.60/13.24 (powersetTE1) =>
% 97.60/13.24 ((
% 97.60/13.24 (complementTI1) =>
% 97.60/13.24 ((
% 97.60/13.24 (complementTE1) =>
% 97.60/13.24 ((
% 97.60/13.24 (binintersectTELcontra) =>
% 97.60/13.24 ((
% 97.60/13.24 (binintersectTERcontra) =>
% 97.60/13.24 ((
% 97.60/13.24 (contrasubsetT) =>
% 97.60/13.24 ((
% 97.60/13.24 (contrasubsetT1) =>
% 97.60/13.24 ((
% 97.60/13.24 (contrasubsetT2) =>
% 97.60/13.24 ((
% 97.60/13.24 (contrasubsetT3) =>
% 97.60/13.24 ((
% 97.60/13.24 (doubleComplementI1) =>
% 97.60/13.24 ((
% 97.60/13.24 (doubleComplementE1) =>
% 97.60/13.24 ((
% 97.60/13.24 (doubleComplementSub1) =>
% 97.60/13.24 ((
% 97.60/13.24 (doubleComplementSub2) =>
% 97.60/13.24 ((
% 97.60/13.24 (doubleComplementEq) =>
% 97.60/13.24 ((
% 97.60/13.24 (complementTnotintersectT) =>
% 97.60/13.24 ((
% 97.60/13.24 (complementImpComplementIntersect) =>
% 97.60/13.24 ((
% 97.60/13.24 (complementSubsetComplementIntersect) =>
% 97.60/13.24 ((
% 97.60/13.24 (complementInPowersetComplementIntersect) =>
% 97.60/13.24 ((
% 97.60/13.24 (contraSubsetComplement) =>
% 97.60/13.24 ((
% 97.60/13.24 (complementTcontraSubset) =>
% 97.60/13.24 ((
% 97.60/13.24 (binunionTILcontra) =>
% 97.60/13.24 ((
% 97.60/13.24 (binunionTIRcontra) =>
% 97.60/13.24 ((
% 97.60/13.24 (inIntersectImpInUnion) =>
% 97.60/13.24 ((
% 97.60/13.24 (inIntersectImpInUnion2) =>
% 97.60/13.24 ((
% 97.60/13.24 (inIntersectImpInIntersectUnions) =>
% 97.60/13.24 ((
% 97.60/13.24 (intersectInPowersetIntersectUnions) =>
% 97.60/13.24 ((
% 97.60/13.24 (inComplementUnionImpNotIn1) =>
% 97.60/13.24 ((
% 97.60/13.24 (inComplementUnionImpInComplement1) =>
% 97.60/13.24 ((
% 97.60/13.24 (binunionTE) =>
% 97.60/13.24 ((
% 97.60/13.24 (binunionTEcontra) =>
% 97.60/13.24 ((
% 97.60/13.24 (demorgan2a1) =>
% 97.60/13.24 ((
% 97.60/13.24 (complementUnionInPowersetComplement) =>
% 97.60/13.24 ((
% 97.60/13.24 (demorgan2a2) =>
% 97.60/13.24 ((
% 97.60/13.24 (demorgan1a) =>
% 97.60/13.24 ((
% 97.60/13.24 (demorgan1b) =>
% 97.60/13.24 ((
% 97.60/13.24 (demorgan1) =>
% 97.60/13.24 ((
% 97.60/13.24 (demorgan2a) =>
% 97.60/13.24 ((
% 97.60/13.24 (demorgan2b2) =>
% 97.60/13.24 ((
% 97.60/13.24 (demorgan2b) =>
% 97.60/13.24 ((
% 97.60/13.24 (demorgan2) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz13rule0) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz13rule1) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz13rule2) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz13rule3) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz13rule4) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz1_1) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz1_2) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz1_3) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz1_4) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz1_5) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1all2) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1SetBreln1) =>
% 97.60/13.24 ((
% 97.60/13.24 (choice2fnsingleton) =>
% 97.60/13.24 ((
% 97.60/13.24 (setOfPairsIsBReln1) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1all1) =>
% 97.60/13.24 ((
% 97.60/13.24 (subbreln1) =>
% 97.60/13.24 ((
% 97.60/13.24 (eqbreln1) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1invprop) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1invI) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1invE) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1compprop) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1compI) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1compE) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1compEex) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1unionprop) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1unionIL) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1unionIR) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1unionI) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1unionE) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1unionEcases) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1unionCommutes) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz2Ex) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz2W) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz2A) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz2B) =>
% 97.60/13.24 ((
% 97.60/13.24 (image1Ex) =>
% 97.60/13.24 ((
% 97.60/13.24 (image1Ex1) =>
% 97.60/13.24 ((
% 97.60/13.24 (image1Equiv) =>
% 97.60/13.24 ((
% 97.60/13.24 (image1E) =>
% 97.60/13.24 ((
% 97.60/13.24 (image1I) =>
% 97.60/13.24 ((
% 97.60/13.24 (injFuncInInjFuncSet) =>
% 97.60/13.24 ((
% 97.60/13.24 (injFuncSetFuncIn) =>
% 97.60/13.24 ((
% 97.60/13.24 (injFuncSetFuncInj) =>
% 97.60/13.24 ((
% 97.60/13.24 (surjFuncSetFuncIn) =>
% 97.60/13.24 ((
% 97.60/13.24 (surjFuncSetFuncSurj) =>
% 97.60/13.24 ((
% 97.60/13.24 (leftInvIsSurj) =>
% 97.60/13.24 ((
% 97.60/13.24 (surjCantorThm) =>
% 97.60/13.24 ((
% 97.60/13.24 (foundation2) =>
% 97.60/13.24 ((
% 97.60/13.24 (notinself) =>
% 97.60/13.24 ((
% 97.60/13.24 (notinself2) =>
% 97.60/13.24 ((
% 97.60/13.24 (omegaSp) =>
% 97.60/13.24 ((
% 97.60/13.24 (omegaSclos) =>
% 97.60/13.24 ((
% 97.60/13.24 (peano0notS) =>
% 97.60/13.24 ((
% 97.60/13.24 (!!) @ (
% 97.60/13.24 (('#S') @ (
% 97.60/13.24 (
% 97.60/13.24 ('#B') @ (
% 97.60/13.24 =>) @
% 97.60/13.24 (
% 97.60/13.24 (
% 97.60/13.24 ('#C') @ in @
% 97.60/13.24 omega)))) @
% 97.60/13.24 (
% 97.60/13.24 (
% 97.60/13.24 ('#B') @ (
% 97.60/13.24 !!) @
% 97.60/13.24 (
% 97.60/13.24 (
% 97.60/13.24 ('#B') @ (
% 97.60/13.24 (
% 97.60/13.24 ('#S') @ (
% 97.60/13.24 (
% 97.60/13.24 ('#B') @ (
% 97.60/13.24 =>) @
% 97.60/13.24 (
% 97.60/13.24 (
% 97.60/13.24 ('#C') @ in @
% 97.60/13.24 omega)))))) @
% 97.60/13.24 (
% 97.60/13.24 (
% 97.60/13.24 ('#S') @ (
% 97.60/13.24 (
% 97.60/13.24 ('#B') @ (
% 97.60/13.24 '#S') @
% 97.60/13.24 (
% 97.60/13.24 (
% 97.60/13.24 ('#B') @ (
% 97.60/13.24 (
% 97.60/13.24 ('#B') @ (
% 97.60/13.24 =>))) @
% 97.60/13.24 (
% 97.60/13.24 (
% 97.60/13.24 ('#C') @ (
% 97.60/13.24 (
% 97.60/13.24 ('#B') @ (
% 97.60/13.24 '#B') @
% 97.60/13.24 (
% 97.60/13.24 (
% 97.60/13.24 ('#B') @ (
% 97.60/13.24 =) @
% 97.60/13.24 omegaS)))) @
% 97.60/13.24 omegaS)))))) @
% 97.60/13.24 (
% 97.60/13.24 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.60/13.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1067])).
% 97.60/13.24 thf(zip_derived_cl1082, plain,
% 97.60/13.24 (~ (((sepInPowerset) =>
% 97.60/13.24 (((sepSubset) =>
% 97.60/13.24 (((binunionIL) =>
% 97.60/13.24 (((upairset2IR) =>
% 97.60/13.24 (((binunionIR) =>
% 97.60/13.24 (((binunionEcases) =>
% 97.60/13.24 (((binunionE) =>
% 97.60/13.24 (((binunionLsub) =>
% 97.60/13.24 (((binunionRsub) =>
% 97.60/13.24 (((binintersectI) =>
% 97.60/13.24 (((binintersectSubset5) =>
% 97.60/13.24 (((binintersectEL) =>
% 97.60/13.24 (((binintersectLsub) =>
% 97.60/13.24 (((binintersectSubset2) =>
% 97.60/13.24 (((binintersectSubset3) =>
% 97.60/13.24 (((binintersectER) =>
% 97.60/13.24 (((disjointsetsI1) =>
% 97.60/13.24 (((binintersectRsub) =>
% 97.60/13.24 (((binintersectSubset4) =>
% 97.60/13.24 (((binintersectSubset1) =>
% 97.60/13.24 (((bs114d) =>
% 97.60/13.24 (((setminusI) =>
% 97.60/13.24 (((setminusEL) =>
% 97.60/13.24 (((setminusER) =>
% 97.60/13.24 (((setminusSubset2) =>
% 97.60/13.24 (((setminusERneg) =>
% 97.60/13.24 (((setminusELneg) =>
% 97.60/13.24 (((setminusILneg) =>
% 97.60/13.24 (((setminusIRneg) =>
% 97.60/13.24 (((setminusLsub) =>
% 97.60/13.24 ((
% 97.60/13.24 (setminusSubset1) =>
% 97.60/13.24 ((
% 97.60/13.24 (symdiffE) =>
% 97.60/13.24 ((
% 97.60/13.24 (symdiffI1) =>
% 97.60/13.24 ((
% 97.60/13.24 (symdiffI2) =>
% 97.60/13.24 ((
% 97.60/13.24 (symdiffIneg1) =>
% 97.60/13.24 ((
% 97.60/13.24 (symdiffIneg2) =>
% 97.60/13.24 ((
% 97.60/13.24 (secondinupair) =>
% 97.60/13.24 ((
% 97.60/13.24 (setukpairIL) =>
% 97.60/13.24 ((
% 97.60/13.24 (setukpairIR) =>
% 97.60/13.24 ((
% 97.60/13.24 (kpairiskpair) =>
% 97.60/13.24 ((
% 97.60/13.24 (kpairp) =>
% 97.60/13.24 ((
% 97.60/13.24 (singletonsubset) =>
% 97.60/13.24 ((
% 97.60/13.24 (singletoninpowerset) =>
% 97.60/13.24 ((
% 97.60/13.24 (singletoninpowunion) =>
% 97.60/13.24 ((
% 97.60/13.24 (upairset2E) =>
% 97.60/13.24 ((
% 97.60/13.24 (upairsubunion) =>
% 97.60/13.24 ((
% 97.60/13.24 (upairinpowunion) =>
% 97.60/13.24 ((
% 97.60/13.24 (ubforcartprodlem1) =>
% 97.60/13.24 ((
% 97.60/13.24 (ubforcartprodlem2) =>
% 97.60/13.24 ((
% 97.60/13.24 (ubforcartprodlem3) =>
% 97.60/13.24 ((
% 97.60/13.24 (cartprodpairin) =>
% 97.60/13.24 ((
% 97.60/13.24 (cartprodmempair1) =>
% 97.60/13.24 ((
% 97.60/13.24 (cartprodmempair) =>
% 97.60/13.24 ((
% 97.60/13.24 (setunionE2) =>
% 97.60/13.24 ((
% 97.60/13.24 (setunionsingleton1) =>
% 97.60/13.24 ((
% 97.60/13.24 (setunionsingleton2) =>
% 97.60/13.24 ((
% 97.60/13.24 (setunionsingleton) =>
% 97.60/13.24 ((
% 97.60/13.24 (singletonprop) =>
% 97.60/13.24 ((
% 97.60/13.24 (ex1E1) =>
% 97.60/13.24 ((
% 97.60/13.24 (ex1I) =>
% 97.60/13.24 ((
% 97.60/13.24 (ex1I2) =>
% 97.60/13.24 ((
% 97.60/13.24 (singletonsuniq) =>
% 97.60/13.24 ((
% 97.60/13.24 (setukpairinjL1) =>
% 97.60/13.24 ((
% 97.60/13.24 (kfstsingleton) =>
% 97.60/13.24 ((
% 97.60/13.24 (theprop) =>
% 97.60/13.24 ((
% 97.60/13.24 (kfstpairEq) =>
% 97.60/13.24 ((
% 97.60/13.24 (cartprodfstin) =>
% 97.60/13.24 ((
% 97.60/13.24 (setukpairinjL2) =>
% 97.60/13.24 ((
% 97.60/13.24 (setukpairinjL) =>
% 97.60/13.24 ((
% 97.60/13.24 (setukpairinjR11) =>
% 97.60/13.24 ((
% 97.60/13.24 (setukpairinjR12) =>
% 97.60/13.24 ((
% 97.60/13.24 (setukpairinjR1) =>
% 97.60/13.24 ((
% 97.60/13.24 (upairequniteq) =>
% 97.60/13.24 ((
% 97.60/13.24 (setukpairinjR2) =>
% 97.60/13.24 ((
% 97.60/13.24 (setukpairinjR) =>
% 97.60/13.24 ((
% 97.60/13.24 (ksndsingleton) =>
% 97.60/13.24 ((
% 97.60/13.24 (ksndpairEq) =>
% 97.60/13.24 ((
% 97.60/13.24 (kpairsurjEq) =>
% 97.60/13.24 ((
% 97.60/13.24 (cartprodsndin) =>
% 97.60/13.24 ((
% 97.60/13.24 (cartprodpairmemEL) =>
% 97.60/13.24 ((
% 97.60/13.24 (cartprodpairmemER) =>
% 97.60/13.24 ((
% 97.60/13.24 (cartprodmempaircEq) =>
% 97.60/13.24 ((
% 97.60/13.24 (cartprodfstpairEq) =>
% 97.60/13.24 ((
% 97.60/13.24 (cartprodsndpairEq) =>
% 97.60/13.24 ((
% 97.60/13.24 (cartprodpairsurjEq) =>
% 97.60/13.24 ((
% 97.60/13.24 (dpsetconstrI) =>
% 97.60/13.24 ((
% 97.60/13.24 (dpsetconstrSub) =>
% 97.60/13.24 ((
% 97.60/13.24 (setOfPairsIsBReln) =>
% 97.60/13.24 ((
% 97.60/13.24 (dpsetconstrERa) =>
% 97.60/13.24 ((
% 97.60/13.24 (dpsetconstrEL1) =>
% 97.60/13.24 ((
% 97.60/13.24 (dpsetconstrEL2) =>
% 97.60/13.24 ((
% 97.60/13.24 (dpsetconstrER) =>
% 97.60/13.24 ((
% 97.60/13.24 (funcImageSingleton) =>
% 97.60/13.24 ((
% 97.60/13.24 (apProp) =>
% 97.60/13.24 ((
% 97.60/13.24 (app) =>
% 97.60/13.24 ((
% 97.60/13.24 (infuncsetfunc) =>
% 97.60/13.24 ((
% 97.60/13.24 (ap2p) =>
% 97.60/13.24 ((
% 97.60/13.24 (funcinfuncset) =>
% 97.60/13.24 ((
% 97.60/13.24 (lamProp) =>
% 97.60/13.24 ((
% 97.60/13.24 (lamp) =>
% 97.60/13.24 ((
% 97.60/13.24 (lam2p) =>
% 97.60/13.24 ((
% 97.60/13.24 (brelnall1) =>
% 97.60/13.24 ((
% 97.60/13.24 (brelnall2) =>
% 97.60/13.24 ((
% 97.60/13.24 (ex1E2) =>
% 97.60/13.24 ((
% 97.60/13.24 (funcGraphProp1) =>
% 97.60/13.24 ((
% 97.60/13.24 (funcGraphProp3) =>
% 97.60/13.24 ((
% 97.60/13.24 (funcGraphProp2) =>
% 97.60/13.24 ((
% 97.60/13.24 (funcextLem) =>
% 97.60/13.24 ((
% 97.60/13.24 (funcGraphProp4) =>
% 97.60/13.24 ((
% 97.60/13.24 (subbreln) =>
% 97.60/13.24 ((
% 97.60/13.24 (eqbreln) =>
% 97.60/13.24 ((
% 97.60/13.24 (funcext) =>
% 97.60/13.24 ((
% 97.60/13.24 (funcext2) =>
% 97.60/13.24 ((
% 97.60/13.24 (ap2apEq1) =>
% 97.60/13.24 ((
% 97.60/13.24 (ap2apEq2) =>
% 97.60/13.24 ((
% 97.60/13.24 (beta1) =>
% 97.60/13.24 ((
% 97.60/13.24 (eta1) =>
% 97.60/13.24 ((
% 97.60/13.24 (lam2lamEq) =>
% 97.60/13.24 ((
% 97.60/13.24 (beta2) =>
% 97.60/13.24 ((
% 97.60/13.24 (eta2) =>
% 97.60/13.24 ((
% 97.60/13.24 (iffalseProp1) =>
% 97.60/13.24 ((
% 97.60/13.24 (iffalseProp2) =>
% 97.60/13.24 ((
% 97.60/13.24 (iftrueProp1) =>
% 97.60/13.24 ((
% 97.60/13.24 (iftrueProp2) =>
% 97.60/13.24 ((
% 97.60/13.24 (ifSingleton) =>
% 97.60/13.24 ((
% 97.60/13.24 (ifp) =>
% 97.60/13.24 ((
% 97.60/13.24 (theeq) =>
% 97.60/13.24 ((
% 97.60/13.24 (iftrue) =>
% 97.60/13.24 ((
% 97.60/13.24 (iffalse) =>
% 97.60/13.24 ((
% 97.60/13.24 (iftrueorfalse) =>
% 97.60/13.24 ((
% 97.60/13.24 (binintersectT_lem) =>
% 97.60/13.24 ((
% 97.60/13.24 (binunionT_lem) =>
% 97.60/13.24 ((
% 97.60/13.24 (powersetT_lem) =>
% 97.60/13.24 ((
% 97.60/13.24 (setminusT_lem) =>
% 97.60/13.24 ((
% 97.60/13.24 (complementT_lem) =>
% 97.60/13.24 ((
% 97.60/13.24 (setextT) =>
% 97.60/13.24 ((
% 97.60/13.24 (subsetTI) =>
% 97.60/13.24 ((
% 97.60/13.24 (powersetTI1) =>
% 97.60/13.24 ((
% 97.60/13.24 (powersetTE1) =>
% 97.60/13.24 ((
% 97.60/13.24 (complementTI1) =>
% 97.60/13.24 ((
% 97.60/13.24 (complementTE1) =>
% 97.60/13.24 ((
% 97.60/13.24 (binintersectTELcontra) =>
% 97.60/13.24 ((
% 97.60/13.24 (binintersectTERcontra) =>
% 97.60/13.24 ((
% 97.60/13.24 (contrasubsetT) =>
% 97.60/13.24 ((
% 97.60/13.24 (contrasubsetT1) =>
% 97.60/13.24 ((
% 97.60/13.24 (contrasubsetT2) =>
% 97.60/13.24 ((
% 97.60/13.24 (contrasubsetT3) =>
% 97.60/13.24 ((
% 97.60/13.24 (doubleComplementI1) =>
% 97.60/13.24 ((
% 97.60/13.24 (doubleComplementE1) =>
% 97.60/13.24 ((
% 97.60/13.24 (doubleComplementSub1) =>
% 97.60/13.24 ((
% 97.60/13.24 (doubleComplementSub2) =>
% 97.60/13.24 ((
% 97.60/13.24 (doubleComplementEq) =>
% 97.60/13.24 ((
% 97.60/13.24 (complementTnotintersectT) =>
% 97.60/13.24 ((
% 97.60/13.24 (complementImpComplementIntersect) =>
% 97.60/13.24 ((
% 97.60/13.24 (complementSubsetComplementIntersect) =>
% 97.60/13.24 ((
% 97.60/13.24 (complementInPowersetComplementIntersect) =>
% 97.60/13.24 ((
% 97.60/13.24 (contraSubsetComplement) =>
% 97.60/13.24 ((
% 97.60/13.24 (complementTcontraSubset) =>
% 97.60/13.24 ((
% 97.60/13.24 (binunionTILcontra) =>
% 97.60/13.24 ((
% 97.60/13.24 (binunionTIRcontra) =>
% 97.60/13.24 ((
% 97.60/13.24 (inIntersectImpInUnion) =>
% 97.60/13.24 ((
% 97.60/13.24 (inIntersectImpInUnion2) =>
% 97.60/13.24 ((
% 97.60/13.24 (inIntersectImpInIntersectUnions) =>
% 97.60/13.24 ((
% 97.60/13.24 (intersectInPowersetIntersectUnions) =>
% 97.60/13.24 ((
% 97.60/13.24 (inComplementUnionImpNotIn1) =>
% 97.60/13.24 ((
% 97.60/13.24 (inComplementUnionImpInComplement1) =>
% 97.60/13.24 ((
% 97.60/13.24 (binunionTE) =>
% 97.60/13.24 ((
% 97.60/13.24 (binunionTEcontra) =>
% 97.60/13.24 ((
% 97.60/13.24 (demorgan2a1) =>
% 97.60/13.24 ((
% 97.60/13.24 (complementUnionInPowersetComplement) =>
% 97.60/13.24 ((
% 97.60/13.24 (demorgan2a2) =>
% 97.60/13.24 ((
% 97.60/13.24 (demorgan1a) =>
% 97.60/13.24 ((
% 97.60/13.24 (demorgan1b) =>
% 97.60/13.24 ((
% 97.60/13.24 (demorgan1) =>
% 97.60/13.24 ((
% 97.60/13.24 (demorgan2a) =>
% 97.60/13.24 ((
% 97.60/13.24 (demorgan2b2) =>
% 97.60/13.24 ((
% 97.60/13.24 (demorgan2b) =>
% 97.60/13.24 ((
% 97.60/13.24 (demorgan2) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz13rule0) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz13rule1) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz13rule2) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz13rule3) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz13rule4) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz1_1) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz1_2) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz1_3) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz1_4) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz1_5) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1all2) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1SetBreln1) =>
% 97.60/13.24 ((
% 97.60/13.24 (choice2fnsingleton) =>
% 97.60/13.24 ((
% 97.60/13.24 (setOfPairsIsBReln1) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1all1) =>
% 97.60/13.24 ((
% 97.60/13.24 (subbreln1) =>
% 97.60/13.24 ((
% 97.60/13.24 (eqbreln1) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1invprop) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1invI) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1invE) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1compprop) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1compI) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1compE) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1compEex) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1unionprop) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1unionIL) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1unionIR) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1unionI) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1unionE) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1unionEcases) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1unionCommutes) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz2Ex) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz2W) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz2A) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz2B) =>
% 97.60/13.24 ((
% 97.60/13.24 (image1Ex) =>
% 97.60/13.24 ((
% 97.60/13.24 (image1Ex1) =>
% 97.60/13.24 ((
% 97.60/13.24 (image1Equiv) =>
% 97.60/13.24 ((
% 97.60/13.24 (image1E) =>
% 97.60/13.24 ((
% 97.60/13.24 (image1I) =>
% 97.60/13.24 ((
% 97.60/13.24 (injFuncInInjFuncSet) =>
% 97.60/13.24 ((
% 97.60/13.24 (injFuncSetFuncIn) =>
% 97.60/13.24 ((
% 97.60/13.24 (injFuncSetFuncInj) =>
% 97.60/13.24 ((
% 97.60/13.24 (surjFuncSetFuncIn) =>
% 97.60/13.24 ((
% 97.60/13.24 (surjFuncSetFuncSurj) =>
% 97.60/13.24 ((
% 97.60/13.24 (leftInvIsSurj) =>
% 97.60/13.24 ((
% 97.60/13.24 (surjCantorThm) =>
% 97.60/13.24 ((
% 97.60/13.24 (foundation2) =>
% 97.60/13.24 ((
% 97.60/13.24 (notinself) =>
% 97.60/13.24 ((
% 97.60/13.24 (notinself2) =>
% 97.60/13.24 ((
% 97.60/13.24 (omegaSp) =>
% 97.60/13.24 ((
% 97.60/13.24 (omegaSclos) =>
% 97.60/13.24 ((
% 97.60/13.24 (peano0notS) =>
% 97.60/13.24 ((
% 97.60/13.24 (!!) @ (
% 97.60/13.24 (('#S') @ (
% 97.60/13.24 (
% 97.60/13.24 ('#B') @ (
% 97.60/13.24 =>) @
% 97.60/13.24 (
% 97.60/13.24 (
% 97.60/13.24 ('#C') @ in @
% 97.60/13.24 omega)))) @
% 97.60/13.24 (
% 97.60/13.24 (
% 97.60/13.24 ('#B') @ (
% 97.60/13.24 !!) @
% 97.60/13.24 (
% 97.60/13.24 (
% 97.60/13.24 ('#B') @ (
% 97.60/13.24 (
% 97.60/13.24 ('#S') @ (
% 97.60/13.24 (
% 97.60/13.24 ('#B') @ (
% 97.60/13.24 =>) @
% 97.60/13.24 (
% 97.60/13.24 (
% 97.60/13.24 ('#C') @ in @
% 97.60/13.24 omega)))))) @
% 97.60/13.24 (
% 97.60/13.24 (
% 97.60/13.24 ('#S') @ (
% 97.60/13.24 (
% 97.60/13.24 ('#B') @ (
% 97.60/13.24 '#S') @
% 97.60/13.24 (
% 97.60/13.24 (
% 97.60/13.24 ('#B') @ (
% 97.60/13.24 (
% 97.60/13.24 ('#B') @ (
% 97.60/13.24 =>))) @
% 97.60/13.24 (
% 97.60/13.24 (
% 97.60/13.24 ('#C') @ (
% 97.60/13.24 (
% 97.60/13.24 ('#B') @ (
% 97.60/13.24 '#B') @
% 97.60/13.24 (
% 97.60/13.24 (
% 97.60/13.24 ('#B') @ (
% 97.60/13.24 =) @
% 97.60/13.24 omegaS)))) @
% 97.60/13.24 omegaS)))))) @
% 97.60/13.24 (
% 97.60/13.24 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.60/13.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1074])).
% 97.60/13.24 thf(zip_derived_cl1090, plain,
% 97.60/13.24 (~ (((sepSubset) =>
% 97.60/13.24 (((binunionIL) =>
% 97.60/13.24 (((upairset2IR) =>
% 97.60/13.24 (((binunionIR) =>
% 97.60/13.24 (((binunionEcases) =>
% 97.60/13.24 (((binunionE) =>
% 97.60/13.24 (((binunionLsub) =>
% 97.60/13.24 (((binunionRsub) =>
% 97.60/13.24 (((binintersectI) =>
% 97.60/13.24 (((binintersectSubset5) =>
% 97.60/13.24 (((binintersectEL) =>
% 97.60/13.24 (((binintersectLsub) =>
% 97.60/13.24 (((binintersectSubset2) =>
% 97.60/13.24 (((binintersectSubset3) =>
% 97.60/13.24 (((binintersectER) =>
% 97.60/13.24 (((disjointsetsI1) =>
% 97.60/13.24 (((binintersectRsub) =>
% 97.60/13.24 (((binintersectSubset4) =>
% 97.60/13.24 (((binintersectSubset1) =>
% 97.60/13.24 (((bs114d) =>
% 97.60/13.24 (((setminusI) =>
% 97.60/13.24 (((setminusEL) =>
% 97.60/13.24 (((setminusER) =>
% 97.60/13.24 (((setminusSubset2) =>
% 97.60/13.24 (((setminusERneg) =>
% 97.60/13.24 (((setminusELneg) =>
% 97.60/13.24 (((setminusILneg) =>
% 97.60/13.24 (((setminusIRneg) =>
% 97.60/13.24 (((setminusLsub) =>
% 97.60/13.24 (((setminusSubset1) =>
% 97.60/13.24 ((
% 97.60/13.24 (symdiffE) =>
% 97.60/13.24 ((
% 97.60/13.24 (symdiffI1) =>
% 97.60/13.24 ((
% 97.60/13.24 (symdiffI2) =>
% 97.60/13.24 ((
% 97.60/13.24 (symdiffIneg1) =>
% 97.60/13.24 ((
% 97.60/13.24 (symdiffIneg2) =>
% 97.60/13.24 ((
% 97.60/13.24 (secondinupair) =>
% 97.60/13.24 ((
% 97.60/13.24 (setukpairIL) =>
% 97.60/13.24 ((
% 97.60/13.24 (setukpairIR) =>
% 97.60/13.24 ((
% 97.60/13.24 (kpairiskpair) =>
% 97.60/13.24 ((
% 97.60/13.24 (kpairp) =>
% 97.60/13.24 ((
% 97.60/13.24 (singletonsubset) =>
% 97.60/13.24 ((
% 97.60/13.24 (singletoninpowerset) =>
% 97.60/13.24 ((
% 97.60/13.24 (singletoninpowunion) =>
% 97.60/13.24 ((
% 97.60/13.24 (upairset2E) =>
% 97.60/13.24 ((
% 97.60/13.24 (upairsubunion) =>
% 97.60/13.24 ((
% 97.60/13.24 (upairinpowunion) =>
% 97.60/13.24 ((
% 97.60/13.24 (ubforcartprodlem1) =>
% 97.60/13.24 ((
% 97.60/13.24 (ubforcartprodlem2) =>
% 97.60/13.24 ((
% 97.60/13.24 (ubforcartprodlem3) =>
% 97.60/13.24 ((
% 97.60/13.24 (cartprodpairin) =>
% 97.60/13.24 ((
% 97.60/13.24 (cartprodmempair1) =>
% 97.60/13.24 ((
% 97.60/13.24 (cartprodmempair) =>
% 97.60/13.24 ((
% 97.60/13.24 (setunionE2) =>
% 97.60/13.24 ((
% 97.60/13.24 (setunionsingleton1) =>
% 97.60/13.24 ((
% 97.60/13.24 (setunionsingleton2) =>
% 97.60/13.24 ((
% 97.60/13.24 (setunionsingleton) =>
% 97.60/13.24 ((
% 97.60/13.24 (singletonprop) =>
% 97.60/13.24 ((
% 97.60/13.24 (ex1E1) =>
% 97.60/13.24 ((
% 97.60/13.24 (ex1I) =>
% 97.60/13.24 ((
% 97.60/13.24 (ex1I2) =>
% 97.60/13.24 ((
% 97.60/13.24 (singletonsuniq) =>
% 97.60/13.24 ((
% 97.60/13.24 (setukpairinjL1) =>
% 97.60/13.24 ((
% 97.60/13.24 (kfstsingleton) =>
% 97.60/13.24 ((
% 97.60/13.24 (theprop) =>
% 97.60/13.24 ((
% 97.60/13.24 (kfstpairEq) =>
% 97.60/13.24 ((
% 97.60/13.24 (cartprodfstin) =>
% 97.60/13.24 ((
% 97.60/13.24 (setukpairinjL2) =>
% 97.60/13.24 ((
% 97.60/13.24 (setukpairinjL) =>
% 97.60/13.24 ((
% 97.60/13.24 (setukpairinjR11) =>
% 97.60/13.24 ((
% 97.60/13.24 (setukpairinjR12) =>
% 97.60/13.24 ((
% 97.60/13.24 (setukpairinjR1) =>
% 97.60/13.24 ((
% 97.60/13.24 (upairequniteq) =>
% 97.60/13.24 ((
% 97.60/13.24 (setukpairinjR2) =>
% 97.60/13.24 ((
% 97.60/13.24 (setukpairinjR) =>
% 97.60/13.24 ((
% 97.60/13.24 (ksndsingleton) =>
% 97.60/13.24 ((
% 97.60/13.24 (ksndpairEq) =>
% 97.60/13.24 ((
% 97.60/13.24 (kpairsurjEq) =>
% 97.60/13.24 ((
% 97.60/13.24 (cartprodsndin) =>
% 97.60/13.24 ((
% 97.60/13.24 (cartprodpairmemEL) =>
% 97.60/13.24 ((
% 97.60/13.24 (cartprodpairmemER) =>
% 97.60/13.24 ((
% 97.60/13.24 (cartprodmempaircEq) =>
% 97.60/13.24 ((
% 97.60/13.24 (cartprodfstpairEq) =>
% 97.60/13.24 ((
% 97.60/13.24 (cartprodsndpairEq) =>
% 97.60/13.24 ((
% 97.60/13.24 (cartprodpairsurjEq) =>
% 97.60/13.24 ((
% 97.60/13.24 (dpsetconstrI) =>
% 97.60/13.24 ((
% 97.60/13.24 (dpsetconstrSub) =>
% 97.60/13.24 ((
% 97.60/13.24 (setOfPairsIsBReln) =>
% 97.60/13.24 ((
% 97.60/13.24 (dpsetconstrERa) =>
% 97.60/13.24 ((
% 97.60/13.24 (dpsetconstrEL1) =>
% 97.60/13.24 ((
% 97.60/13.24 (dpsetconstrEL2) =>
% 97.60/13.24 ((
% 97.60/13.24 (dpsetconstrER) =>
% 97.60/13.24 ((
% 97.60/13.24 (funcImageSingleton) =>
% 97.60/13.24 ((
% 97.60/13.24 (apProp) =>
% 97.60/13.24 ((
% 97.60/13.24 (app) =>
% 97.60/13.24 ((
% 97.60/13.24 (infuncsetfunc) =>
% 97.60/13.24 ((
% 97.60/13.24 (ap2p) =>
% 97.60/13.24 ((
% 97.60/13.24 (funcinfuncset) =>
% 97.60/13.24 ((
% 97.60/13.24 (lamProp) =>
% 97.60/13.24 ((
% 97.60/13.24 (lamp) =>
% 97.60/13.24 ((
% 97.60/13.24 (lam2p) =>
% 97.60/13.24 ((
% 97.60/13.24 (brelnall1) =>
% 97.60/13.24 ((
% 97.60/13.24 (brelnall2) =>
% 97.60/13.24 ((
% 97.60/13.24 (ex1E2) =>
% 97.60/13.24 ((
% 97.60/13.24 (funcGraphProp1) =>
% 97.60/13.24 ((
% 97.60/13.24 (funcGraphProp3) =>
% 97.60/13.24 ((
% 97.60/13.24 (funcGraphProp2) =>
% 97.60/13.24 ((
% 97.60/13.24 (funcextLem) =>
% 97.60/13.24 ((
% 97.60/13.24 (funcGraphProp4) =>
% 97.60/13.24 ((
% 97.60/13.24 (subbreln) =>
% 97.60/13.24 ((
% 97.60/13.24 (eqbreln) =>
% 97.60/13.24 ((
% 97.60/13.24 (funcext) =>
% 97.60/13.24 ((
% 97.60/13.24 (funcext2) =>
% 97.60/13.24 ((
% 97.60/13.24 (ap2apEq1) =>
% 97.60/13.24 ((
% 97.60/13.24 (ap2apEq2) =>
% 97.60/13.24 ((
% 97.60/13.24 (beta1) =>
% 97.60/13.24 ((
% 97.60/13.24 (eta1) =>
% 97.60/13.24 ((
% 97.60/13.24 (lam2lamEq) =>
% 97.60/13.24 ((
% 97.60/13.24 (beta2) =>
% 97.60/13.24 ((
% 97.60/13.24 (eta2) =>
% 97.60/13.24 ((
% 97.60/13.24 (iffalseProp1) =>
% 97.60/13.24 ((
% 97.60/13.24 (iffalseProp2) =>
% 97.60/13.24 ((
% 97.60/13.24 (iftrueProp1) =>
% 97.60/13.24 ((
% 97.60/13.24 (iftrueProp2) =>
% 97.60/13.24 ((
% 97.60/13.24 (ifSingleton) =>
% 97.60/13.24 ((
% 97.60/13.24 (ifp) =>
% 97.60/13.24 ((
% 97.60/13.24 (theeq) =>
% 97.60/13.24 ((
% 97.60/13.24 (iftrue) =>
% 97.60/13.24 ((
% 97.60/13.24 (iffalse) =>
% 97.60/13.24 ((
% 97.60/13.24 (iftrueorfalse) =>
% 97.60/13.24 ((
% 97.60/13.24 (binintersectT_lem) =>
% 97.60/13.24 ((
% 97.60/13.24 (binunionT_lem) =>
% 97.60/13.24 ((
% 97.60/13.24 (powersetT_lem) =>
% 97.60/13.24 ((
% 97.60/13.24 (setminusT_lem) =>
% 97.60/13.24 ((
% 97.60/13.24 (complementT_lem) =>
% 97.60/13.24 ((
% 97.60/13.24 (setextT) =>
% 97.60/13.24 ((
% 97.60/13.24 (subsetTI) =>
% 97.60/13.24 ((
% 97.60/13.24 (powersetTI1) =>
% 97.60/13.24 ((
% 97.60/13.24 (powersetTE1) =>
% 97.60/13.24 ((
% 97.60/13.24 (complementTI1) =>
% 97.60/13.24 ((
% 97.60/13.24 (complementTE1) =>
% 97.60/13.24 ((
% 97.60/13.24 (binintersectTELcontra) =>
% 97.60/13.24 ((
% 97.60/13.24 (binintersectTERcontra) =>
% 97.60/13.24 ((
% 97.60/13.24 (contrasubsetT) =>
% 97.60/13.24 ((
% 97.60/13.24 (contrasubsetT1) =>
% 97.60/13.24 ((
% 97.60/13.24 (contrasubsetT2) =>
% 97.60/13.24 ((
% 97.60/13.24 (contrasubsetT3) =>
% 97.60/13.24 ((
% 97.60/13.24 (doubleComplementI1) =>
% 97.60/13.24 ((
% 97.60/13.24 (doubleComplementE1) =>
% 97.60/13.24 ((
% 97.60/13.24 (doubleComplementSub1) =>
% 97.60/13.24 ((
% 97.60/13.24 (doubleComplementSub2) =>
% 97.60/13.24 ((
% 97.60/13.24 (doubleComplementEq) =>
% 97.60/13.24 ((
% 97.60/13.24 (complementTnotintersectT) =>
% 97.60/13.24 ((
% 97.60/13.24 (complementImpComplementIntersect) =>
% 97.60/13.24 ((
% 97.60/13.24 (complementSubsetComplementIntersect) =>
% 97.60/13.24 ((
% 97.60/13.24 (complementInPowersetComplementIntersect) =>
% 97.60/13.24 ((
% 97.60/13.24 (contraSubsetComplement) =>
% 97.60/13.24 ((
% 97.60/13.24 (complementTcontraSubset) =>
% 97.60/13.24 ((
% 97.60/13.24 (binunionTILcontra) =>
% 97.60/13.24 ((
% 97.60/13.24 (binunionTIRcontra) =>
% 97.60/13.24 ((
% 97.60/13.24 (inIntersectImpInUnion) =>
% 97.60/13.24 ((
% 97.60/13.24 (inIntersectImpInUnion2) =>
% 97.60/13.24 ((
% 97.60/13.24 (inIntersectImpInIntersectUnions) =>
% 97.60/13.24 ((
% 97.60/13.24 (intersectInPowersetIntersectUnions) =>
% 97.60/13.24 ((
% 97.60/13.24 (inComplementUnionImpNotIn1) =>
% 97.60/13.24 ((
% 97.60/13.24 (inComplementUnionImpInComplement1) =>
% 97.60/13.24 ((
% 97.60/13.24 (binunionTE) =>
% 97.60/13.24 ((
% 97.60/13.24 (binunionTEcontra) =>
% 97.60/13.24 ((
% 97.60/13.24 (demorgan2a1) =>
% 97.60/13.24 ((
% 97.60/13.24 (complementUnionInPowersetComplement) =>
% 97.60/13.24 ((
% 97.60/13.24 (demorgan2a2) =>
% 97.60/13.24 ((
% 97.60/13.24 (demorgan1a) =>
% 97.60/13.24 ((
% 97.60/13.24 (demorgan1b) =>
% 97.60/13.24 ((
% 97.60/13.24 (demorgan1) =>
% 97.60/13.24 ((
% 97.60/13.24 (demorgan2a) =>
% 97.60/13.24 ((
% 97.60/13.24 (demorgan2b2) =>
% 97.60/13.24 ((
% 97.60/13.24 (demorgan2b) =>
% 97.60/13.24 ((
% 97.60/13.24 (demorgan2) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz13rule0) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz13rule1) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz13rule2) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz13rule3) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz13rule4) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz1_1) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz1_2) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz1_3) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz1_4) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz1_5) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1all2) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1SetBreln1) =>
% 97.60/13.24 ((
% 97.60/13.24 (choice2fnsingleton) =>
% 97.60/13.24 ((
% 97.60/13.24 (setOfPairsIsBReln1) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1all1) =>
% 97.60/13.24 ((
% 97.60/13.24 (subbreln1) =>
% 97.60/13.24 ((
% 97.60/13.24 (eqbreln1) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1invprop) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1invI) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1invE) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1compprop) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1compI) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1compE) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1compEex) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1unionprop) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1unionIL) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1unionIR) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1unionI) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1unionE) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1unionEcases) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1unionCommutes) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz2Ex) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz2W) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz2A) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz2B) =>
% 97.60/13.24 ((
% 97.60/13.24 (image1Ex) =>
% 97.60/13.24 ((
% 97.60/13.24 (image1Ex1) =>
% 97.60/13.24 ((
% 97.60/13.24 (image1Equiv) =>
% 97.60/13.24 ((
% 97.60/13.24 (image1E) =>
% 97.60/13.24 ((
% 97.60/13.24 (image1I) =>
% 97.60/13.24 ((
% 97.60/13.24 (injFuncInInjFuncSet) =>
% 97.60/13.24 ((
% 97.60/13.24 (injFuncSetFuncIn) =>
% 97.60/13.24 ((
% 97.60/13.24 (injFuncSetFuncInj) =>
% 97.60/13.24 ((
% 97.60/13.24 (surjFuncSetFuncIn) =>
% 97.60/13.24 ((
% 97.60/13.24 (surjFuncSetFuncSurj) =>
% 97.60/13.24 ((
% 97.60/13.24 (leftInvIsSurj) =>
% 97.60/13.24 ((
% 97.60/13.24 (surjCantorThm) =>
% 97.60/13.24 ((
% 97.60/13.24 (foundation2) =>
% 97.60/13.24 ((
% 97.60/13.24 (notinself) =>
% 97.60/13.24 ((
% 97.60/13.24 (notinself2) =>
% 97.60/13.24 ((
% 97.60/13.24 (omegaSp) =>
% 97.60/13.24 ((
% 97.60/13.24 (omegaSclos) =>
% 97.60/13.24 ((
% 97.60/13.24 (peano0notS) =>
% 97.60/13.24 ((
% 97.60/13.24 (!!) @ (
% 97.60/13.24 (('#S') @ (
% 97.60/13.24 (
% 97.60/13.24 ('#B') @ (
% 97.60/13.24 =>) @
% 97.60/13.24 (
% 97.60/13.24 (
% 97.60/13.24 ('#C') @ in @
% 97.60/13.24 omega)))) @
% 97.60/13.24 (
% 97.60/13.24 (
% 97.60/13.24 ('#B') @ (
% 97.60/13.24 !!) @
% 97.60/13.24 (
% 97.60/13.24 (
% 97.60/13.24 ('#B') @ (
% 97.60/13.24 (
% 97.60/13.24 ('#S') @ (
% 97.60/13.24 (
% 97.60/13.24 ('#B') @ (
% 97.60/13.24 =>) @
% 97.60/13.24 (
% 97.60/13.24 (
% 97.60/13.24 ('#C') @ in @
% 97.60/13.24 omega)))))) @
% 97.60/13.24 (
% 97.60/13.24 (
% 97.60/13.24 ('#S') @ (
% 97.60/13.24 (
% 97.60/13.24 ('#B') @ (
% 97.60/13.24 '#S') @
% 97.60/13.24 (
% 97.60/13.24 (
% 97.60/13.24 ('#B') @ (
% 97.60/13.24 (
% 97.60/13.24 ('#B') @ (
% 97.60/13.24 =>))) @
% 97.60/13.24 (
% 97.60/13.24 (
% 97.60/13.24 ('#C') @ (
% 97.60/13.24 (
% 97.60/13.24 ('#B') @ (
% 97.60/13.24 '#B') @
% 97.60/13.24 (
% 97.60/13.24 (
% 97.60/13.24 ('#B') @ (
% 97.60/13.24 =) @
% 97.60/13.24 omegaS)))) @
% 97.60/13.24 omegaS)))))) @
% 97.60/13.24 (
% 97.60/13.24 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.60/13.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1082])).
% 97.60/13.24 thf(zip_derived_cl1096, plain,
% 97.60/13.24 (~ (((binunionIL) =>
% 97.60/13.24 (((upairset2IR) =>
% 97.60/13.24 (((binunionIR) =>
% 97.60/13.24 (((binunionEcases) =>
% 97.60/13.24 (((binunionE) =>
% 97.60/13.24 (((binunionLsub) =>
% 97.60/13.24 (((binunionRsub) =>
% 97.60/13.24 (((binintersectI) =>
% 97.60/13.24 (((binintersectSubset5) =>
% 97.60/13.24 (((binintersectEL) =>
% 97.60/13.24 (((binintersectLsub) =>
% 97.60/13.24 (((binintersectSubset2) =>
% 97.60/13.24 (((binintersectSubset3) =>
% 97.60/13.24 (((binintersectER) =>
% 97.60/13.24 (((disjointsetsI1) =>
% 97.60/13.24 (((binintersectRsub) =>
% 97.60/13.24 (((binintersectSubset4) =>
% 97.60/13.24 (((binintersectSubset1) =>
% 97.60/13.24 (((bs114d) =>
% 97.60/13.24 (((setminusI) =>
% 97.60/13.24 (((setminusEL) =>
% 97.60/13.24 (((setminusER) =>
% 97.60/13.24 (((setminusSubset2) =>
% 97.60/13.24 (((setminusERneg) =>
% 97.60/13.24 (((setminusELneg) =>
% 97.60/13.24 (((setminusILneg) =>
% 97.60/13.24 (((setminusIRneg) =>
% 97.60/13.24 (((setminusLsub) =>
% 97.60/13.24 (((setminusSubset1) =>
% 97.60/13.24 (((symdiffE) =>
% 97.60/13.24 ((
% 97.60/13.24 (symdiffI1) =>
% 97.60/13.24 ((
% 97.60/13.24 (symdiffI2) =>
% 97.60/13.24 ((
% 97.60/13.24 (symdiffIneg1) =>
% 97.60/13.24 ((
% 97.60/13.24 (symdiffIneg2) =>
% 97.60/13.24 ((
% 97.60/13.24 (secondinupair) =>
% 97.60/13.24 ((
% 97.60/13.24 (setukpairIL) =>
% 97.60/13.24 ((
% 97.60/13.24 (setukpairIR) =>
% 97.60/13.24 ((
% 97.60/13.24 (kpairiskpair) =>
% 97.60/13.24 ((
% 97.60/13.24 (kpairp) =>
% 97.60/13.24 ((
% 97.60/13.24 (singletonsubset) =>
% 97.60/13.24 ((
% 97.60/13.24 (singletoninpowerset) =>
% 97.60/13.24 ((
% 97.60/13.24 (singletoninpowunion) =>
% 97.60/13.24 ((
% 97.60/13.24 (upairset2E) =>
% 97.60/13.24 ((
% 97.60/13.24 (upairsubunion) =>
% 97.60/13.24 ((
% 97.60/13.24 (upairinpowunion) =>
% 97.60/13.24 ((
% 97.60/13.24 (ubforcartprodlem1) =>
% 97.60/13.24 ((
% 97.60/13.24 (ubforcartprodlem2) =>
% 97.60/13.24 ((
% 97.60/13.24 (ubforcartprodlem3) =>
% 97.60/13.24 ((
% 97.60/13.24 (cartprodpairin) =>
% 97.60/13.24 ((
% 97.60/13.24 (cartprodmempair1) =>
% 97.60/13.24 ((
% 97.60/13.24 (cartprodmempair) =>
% 97.60/13.24 ((
% 97.60/13.24 (setunionE2) =>
% 97.60/13.24 ((
% 97.60/13.24 (setunionsingleton1) =>
% 97.60/13.24 ((
% 97.60/13.24 (setunionsingleton2) =>
% 97.60/13.24 ((
% 97.60/13.24 (setunionsingleton) =>
% 97.60/13.24 ((
% 97.60/13.24 (singletonprop) =>
% 97.60/13.24 ((
% 97.60/13.24 (ex1E1) =>
% 97.60/13.24 ((
% 97.60/13.24 (ex1I) =>
% 97.60/13.24 ((
% 97.60/13.24 (ex1I2) =>
% 97.60/13.24 ((
% 97.60/13.24 (singletonsuniq) =>
% 97.60/13.24 ((
% 97.60/13.24 (setukpairinjL1) =>
% 97.60/13.24 ((
% 97.60/13.24 (kfstsingleton) =>
% 97.60/13.24 ((
% 97.60/13.24 (theprop) =>
% 97.60/13.24 ((
% 97.60/13.24 (kfstpairEq) =>
% 97.60/13.24 ((
% 97.60/13.24 (cartprodfstin) =>
% 97.60/13.24 ((
% 97.60/13.24 (setukpairinjL2) =>
% 97.60/13.24 ((
% 97.60/13.24 (setukpairinjL) =>
% 97.60/13.24 ((
% 97.60/13.24 (setukpairinjR11) =>
% 97.60/13.24 ((
% 97.60/13.24 (setukpairinjR12) =>
% 97.60/13.24 ((
% 97.60/13.24 (setukpairinjR1) =>
% 97.60/13.24 ((
% 97.60/13.24 (upairequniteq) =>
% 97.60/13.24 ((
% 97.60/13.24 (setukpairinjR2) =>
% 97.60/13.24 ((
% 97.60/13.24 (setukpairinjR) =>
% 97.60/13.24 ((
% 97.60/13.24 (ksndsingleton) =>
% 97.60/13.24 ((
% 97.60/13.24 (ksndpairEq) =>
% 97.60/13.24 ((
% 97.60/13.24 (kpairsurjEq) =>
% 97.60/13.24 ((
% 97.60/13.24 (cartprodsndin) =>
% 97.60/13.24 ((
% 97.60/13.24 (cartprodpairmemEL) =>
% 97.60/13.24 ((
% 97.60/13.24 (cartprodpairmemER) =>
% 97.60/13.24 ((
% 97.60/13.24 (cartprodmempaircEq) =>
% 97.60/13.24 ((
% 97.60/13.24 (cartprodfstpairEq) =>
% 97.60/13.24 ((
% 97.60/13.24 (cartprodsndpairEq) =>
% 97.60/13.24 ((
% 97.60/13.24 (cartprodpairsurjEq) =>
% 97.60/13.24 ((
% 97.60/13.24 (dpsetconstrI) =>
% 97.60/13.24 ((
% 97.60/13.24 (dpsetconstrSub) =>
% 97.60/13.24 ((
% 97.60/13.24 (setOfPairsIsBReln) =>
% 97.60/13.24 ((
% 97.60/13.24 (dpsetconstrERa) =>
% 97.60/13.24 ((
% 97.60/13.24 (dpsetconstrEL1) =>
% 97.60/13.24 ((
% 97.60/13.24 (dpsetconstrEL2) =>
% 97.60/13.24 ((
% 97.60/13.24 (dpsetconstrER) =>
% 97.60/13.24 ((
% 97.60/13.24 (funcImageSingleton) =>
% 97.60/13.24 ((
% 97.60/13.24 (apProp) =>
% 97.60/13.24 ((
% 97.60/13.24 (app) =>
% 97.60/13.24 ((
% 97.60/13.24 (infuncsetfunc) =>
% 97.60/13.24 ((
% 97.60/13.24 (ap2p) =>
% 97.60/13.24 ((
% 97.60/13.24 (funcinfuncset) =>
% 97.60/13.24 ((
% 97.60/13.24 (lamProp) =>
% 97.60/13.24 ((
% 97.60/13.24 (lamp) =>
% 97.60/13.24 ((
% 97.60/13.24 (lam2p) =>
% 97.60/13.24 ((
% 97.60/13.24 (brelnall1) =>
% 97.60/13.24 ((
% 97.60/13.24 (brelnall2) =>
% 97.60/13.24 ((
% 97.60/13.24 (ex1E2) =>
% 97.60/13.24 ((
% 97.60/13.24 (funcGraphProp1) =>
% 97.60/13.24 ((
% 97.60/13.24 (funcGraphProp3) =>
% 97.60/13.24 ((
% 97.60/13.24 (funcGraphProp2) =>
% 97.60/13.24 ((
% 97.60/13.24 (funcextLem) =>
% 97.60/13.24 ((
% 97.60/13.24 (funcGraphProp4) =>
% 97.60/13.24 ((
% 97.60/13.24 (subbreln) =>
% 97.60/13.24 ((
% 97.60/13.24 (eqbreln) =>
% 97.60/13.24 ((
% 97.60/13.24 (funcext) =>
% 97.60/13.24 ((
% 97.60/13.24 (funcext2) =>
% 97.60/13.24 ((
% 97.60/13.24 (ap2apEq1) =>
% 97.60/13.24 ((
% 97.60/13.24 (ap2apEq2) =>
% 97.60/13.24 ((
% 97.60/13.24 (beta1) =>
% 97.60/13.24 ((
% 97.60/13.24 (eta1) =>
% 97.60/13.24 ((
% 97.60/13.24 (lam2lamEq) =>
% 97.60/13.24 ((
% 97.60/13.24 (beta2) =>
% 97.60/13.24 ((
% 97.60/13.24 (eta2) =>
% 97.60/13.24 ((
% 97.60/13.24 (iffalseProp1) =>
% 97.60/13.24 ((
% 97.60/13.24 (iffalseProp2) =>
% 97.60/13.24 ((
% 97.60/13.24 (iftrueProp1) =>
% 97.60/13.24 ((
% 97.60/13.24 (iftrueProp2) =>
% 97.60/13.24 ((
% 97.60/13.24 (ifSingleton) =>
% 97.60/13.24 ((
% 97.60/13.24 (ifp) =>
% 97.60/13.24 ((
% 97.60/13.24 (theeq) =>
% 97.60/13.24 ((
% 97.60/13.24 (iftrue) =>
% 97.60/13.24 ((
% 97.60/13.24 (iffalse) =>
% 97.60/13.24 ((
% 97.60/13.24 (iftrueorfalse) =>
% 97.60/13.24 ((
% 97.60/13.24 (binintersectT_lem) =>
% 97.60/13.24 ((
% 97.60/13.24 (binunionT_lem) =>
% 97.60/13.24 ((
% 97.60/13.24 (powersetT_lem) =>
% 97.60/13.24 ((
% 97.60/13.24 (setminusT_lem) =>
% 97.60/13.24 ((
% 97.60/13.24 (complementT_lem) =>
% 97.60/13.24 ((
% 97.60/13.24 (setextT) =>
% 97.60/13.24 ((
% 97.60/13.24 (subsetTI) =>
% 97.60/13.24 ((
% 97.60/13.24 (powersetTI1) =>
% 97.60/13.24 ((
% 97.60/13.24 (powersetTE1) =>
% 97.60/13.24 ((
% 97.60/13.24 (complementTI1) =>
% 97.60/13.24 ((
% 97.60/13.24 (complementTE1) =>
% 97.60/13.24 ((
% 97.60/13.24 (binintersectTELcontra) =>
% 97.60/13.24 ((
% 97.60/13.24 (binintersectTERcontra) =>
% 97.60/13.24 ((
% 97.60/13.24 (contrasubsetT) =>
% 97.60/13.24 ((
% 97.60/13.24 (contrasubsetT1) =>
% 97.60/13.24 ((
% 97.60/13.24 (contrasubsetT2) =>
% 97.60/13.24 ((
% 97.60/13.24 (contrasubsetT3) =>
% 97.60/13.24 ((
% 97.60/13.24 (doubleComplementI1) =>
% 97.60/13.24 ((
% 97.60/13.24 (doubleComplementE1) =>
% 97.60/13.24 ((
% 97.60/13.24 (doubleComplementSub1) =>
% 97.60/13.24 ((
% 97.60/13.24 (doubleComplementSub2) =>
% 97.60/13.24 ((
% 97.60/13.24 (doubleComplementEq) =>
% 97.60/13.24 ((
% 97.60/13.24 (complementTnotintersectT) =>
% 97.60/13.24 ((
% 97.60/13.24 (complementImpComplementIntersect) =>
% 97.60/13.24 ((
% 97.60/13.24 (complementSubsetComplementIntersect) =>
% 97.60/13.24 ((
% 97.60/13.24 (complementInPowersetComplementIntersect) =>
% 97.60/13.24 ((
% 97.60/13.24 (contraSubsetComplement) =>
% 97.60/13.24 ((
% 97.60/13.24 (complementTcontraSubset) =>
% 97.60/13.24 ((
% 97.60/13.24 (binunionTILcontra) =>
% 97.60/13.24 ((
% 97.60/13.24 (binunionTIRcontra) =>
% 97.60/13.24 ((
% 97.60/13.24 (inIntersectImpInUnion) =>
% 97.60/13.24 ((
% 97.60/13.24 (inIntersectImpInUnion2) =>
% 97.60/13.24 ((
% 97.60/13.24 (inIntersectImpInIntersectUnions) =>
% 97.60/13.24 ((
% 97.60/13.24 (intersectInPowersetIntersectUnions) =>
% 97.60/13.24 ((
% 97.60/13.24 (inComplementUnionImpNotIn1) =>
% 97.60/13.24 ((
% 97.60/13.24 (inComplementUnionImpInComplement1) =>
% 97.60/13.24 ((
% 97.60/13.24 (binunionTE) =>
% 97.60/13.24 ((
% 97.60/13.24 (binunionTEcontra) =>
% 97.60/13.24 ((
% 97.60/13.24 (demorgan2a1) =>
% 97.60/13.24 ((
% 97.60/13.24 (complementUnionInPowersetComplement) =>
% 97.60/13.24 ((
% 97.60/13.24 (demorgan2a2) =>
% 97.60/13.24 ((
% 97.60/13.24 (demorgan1a) =>
% 97.60/13.24 ((
% 97.60/13.24 (demorgan1b) =>
% 97.60/13.24 ((
% 97.60/13.24 (demorgan1) =>
% 97.60/13.24 ((
% 97.60/13.24 (demorgan2a) =>
% 97.60/13.24 ((
% 97.60/13.24 (demorgan2b2) =>
% 97.60/13.24 ((
% 97.60/13.24 (demorgan2b) =>
% 97.60/13.24 ((
% 97.60/13.24 (demorgan2) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz13rule0) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz13rule1) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz13rule2) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz13rule3) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz13rule4) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz1_1) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz1_2) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz1_3) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz1_4) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz1_5) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1all2) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1SetBreln1) =>
% 97.60/13.24 ((
% 97.60/13.24 (choice2fnsingleton) =>
% 97.60/13.24 ((
% 97.60/13.24 (setOfPairsIsBReln1) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1all1) =>
% 97.60/13.24 ((
% 97.60/13.24 (subbreln1) =>
% 97.60/13.24 ((
% 97.60/13.24 (eqbreln1) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1invprop) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1invI) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1invE) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1compprop) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1compI) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1compE) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1compEex) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1unionprop) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1unionIL) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1unionIR) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1unionI) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1unionE) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1unionEcases) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1unionCommutes) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz2Ex) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz2W) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz2A) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz2B) =>
% 97.60/13.24 ((
% 97.60/13.24 (image1Ex) =>
% 97.60/13.24 ((
% 97.60/13.24 (image1Ex1) =>
% 97.60/13.24 ((
% 97.60/13.24 (image1Equiv) =>
% 97.60/13.24 ((
% 97.60/13.24 (image1E) =>
% 97.60/13.24 ((
% 97.60/13.24 (image1I) =>
% 97.60/13.24 ((
% 97.60/13.24 (injFuncInInjFuncSet) =>
% 97.60/13.24 ((
% 97.60/13.24 (injFuncSetFuncIn) =>
% 97.60/13.24 ((
% 97.60/13.24 (injFuncSetFuncInj) =>
% 97.60/13.24 ((
% 97.60/13.24 (surjFuncSetFuncIn) =>
% 97.60/13.24 ((
% 97.60/13.24 (surjFuncSetFuncSurj) =>
% 97.60/13.24 ((
% 97.60/13.24 (leftInvIsSurj) =>
% 97.60/13.24 ((
% 97.60/13.24 (surjCantorThm) =>
% 97.60/13.24 ((
% 97.60/13.24 (foundation2) =>
% 97.60/13.24 ((
% 97.60/13.24 (notinself) =>
% 97.60/13.24 ((
% 97.60/13.24 (notinself2) =>
% 97.60/13.24 ((
% 97.60/13.24 (omegaSp) =>
% 97.60/13.24 ((
% 97.60/13.24 (omegaSclos) =>
% 97.60/13.24 ((
% 97.60/13.24 (peano0notS) =>
% 97.60/13.24 ((
% 97.60/13.24 (!!) @ (
% 97.60/13.24 (('#S') @ (
% 97.60/13.24 (
% 97.60/13.24 ('#B') @ (
% 97.60/13.24 =>) @
% 97.60/13.24 (
% 97.60/13.24 (
% 97.60/13.24 ('#C') @ in @
% 97.60/13.24 omega)))) @
% 97.60/13.24 (
% 97.60/13.24 (
% 97.60/13.24 ('#B') @ (
% 97.60/13.24 !!) @
% 97.60/13.24 (
% 97.60/13.24 (
% 97.60/13.24 ('#B') @ (
% 97.60/13.24 (
% 97.60/13.24 ('#S') @ (
% 97.60/13.24 (
% 97.60/13.24 ('#B') @ (
% 97.60/13.24 =>) @
% 97.60/13.24 (
% 97.60/13.24 (
% 97.60/13.24 ('#C') @ in @
% 97.60/13.24 omega)))))) @
% 97.60/13.24 (
% 97.60/13.24 (
% 97.60/13.24 ('#S') @ (
% 97.60/13.24 (
% 97.60/13.24 ('#B') @ (
% 97.60/13.24 '#S') @
% 97.60/13.24 (
% 97.60/13.24 (
% 97.60/13.24 ('#B') @ (
% 97.60/13.24 (
% 97.60/13.24 ('#B') @ (
% 97.60/13.24 =>))) @
% 97.60/13.24 (
% 97.60/13.24 (
% 97.60/13.24 ('#C') @ (
% 97.60/13.24 (
% 97.60/13.24 ('#B') @ (
% 97.60/13.24 '#B') @
% 97.60/13.24 (
% 97.60/13.24 (
% 97.60/13.24 ('#B') @ (
% 97.60/13.24 =) @
% 97.60/13.24 omegaS)))) @
% 97.60/13.24 omegaS)))))) @
% 97.60/13.24 (
% 97.60/13.24 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.60/13.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1090])).
% 97.60/13.24 thf(zip_derived_cl1102, plain,
% 97.60/13.24 (~ (((upairset2IR) =>
% 97.60/13.24 (((binunionIR) =>
% 97.60/13.24 (((binunionEcases) =>
% 97.60/13.24 (((binunionE) =>
% 97.60/13.24 (((binunionLsub) =>
% 97.60/13.24 (((binunionRsub) =>
% 97.60/13.24 (((binintersectI) =>
% 97.60/13.24 (((binintersectSubset5) =>
% 97.60/13.24 (((binintersectEL) =>
% 97.60/13.24 (((binintersectLsub) =>
% 97.60/13.24 (((binintersectSubset2) =>
% 97.60/13.24 (((binintersectSubset3) =>
% 97.60/13.24 (((binintersectER) =>
% 97.60/13.24 (((disjointsetsI1) =>
% 97.60/13.24 (((binintersectRsub) =>
% 97.60/13.24 (((binintersectSubset4) =>
% 97.60/13.24 (((binintersectSubset1) =>
% 97.60/13.24 (((bs114d) =>
% 97.60/13.24 (((setminusI) =>
% 97.60/13.24 (((setminusEL) =>
% 97.60/13.24 (((setminusER) =>
% 97.60/13.24 (((setminusSubset2) =>
% 97.60/13.24 (((setminusERneg) =>
% 97.60/13.24 (((setminusELneg) =>
% 97.60/13.24 (((setminusILneg) =>
% 97.60/13.24 (((setminusIRneg) =>
% 97.60/13.24 (((setminusLsub) =>
% 97.60/13.24 (((setminusSubset1) =>
% 97.60/13.24 (((symdiffE) =>
% 97.60/13.24 (((symdiffI1) =>
% 97.60/13.24 ((
% 97.60/13.24 (symdiffI2) =>
% 97.60/13.24 ((
% 97.60/13.24 (symdiffIneg1) =>
% 97.60/13.24 ((
% 97.60/13.24 (symdiffIneg2) =>
% 97.60/13.24 ((
% 97.60/13.24 (secondinupair) =>
% 97.60/13.24 ((
% 97.60/13.24 (setukpairIL) =>
% 97.60/13.24 ((
% 97.60/13.24 (setukpairIR) =>
% 97.60/13.24 ((
% 97.60/13.24 (kpairiskpair) =>
% 97.60/13.24 ((
% 97.60/13.24 (kpairp) =>
% 97.60/13.24 ((
% 97.60/13.24 (singletonsubset) =>
% 97.60/13.24 ((
% 97.60/13.24 (singletoninpowerset) =>
% 97.60/13.24 ((
% 97.60/13.24 (singletoninpowunion) =>
% 97.60/13.24 ((
% 97.60/13.24 (upairset2E) =>
% 97.60/13.24 ((
% 97.60/13.24 (upairsubunion) =>
% 97.60/13.24 ((
% 97.60/13.24 (upairinpowunion) =>
% 97.60/13.24 ((
% 97.60/13.24 (ubforcartprodlem1) =>
% 97.60/13.24 ((
% 97.60/13.24 (ubforcartprodlem2) =>
% 97.60/13.24 ((
% 97.60/13.24 (ubforcartprodlem3) =>
% 97.60/13.24 ((
% 97.60/13.24 (cartprodpairin) =>
% 97.60/13.24 ((
% 97.60/13.24 (cartprodmempair1) =>
% 97.60/13.24 ((
% 97.60/13.24 (cartprodmempair) =>
% 97.60/13.24 ((
% 97.60/13.24 (setunionE2) =>
% 97.60/13.24 ((
% 97.60/13.24 (setunionsingleton1) =>
% 97.60/13.24 ((
% 97.60/13.24 (setunionsingleton2) =>
% 97.60/13.24 ((
% 97.60/13.24 (setunionsingleton) =>
% 97.60/13.24 ((
% 97.60/13.24 (singletonprop) =>
% 97.60/13.24 ((
% 97.60/13.24 (ex1E1) =>
% 97.60/13.24 ((
% 97.60/13.24 (ex1I) =>
% 97.60/13.24 ((
% 97.60/13.24 (ex1I2) =>
% 97.60/13.24 ((
% 97.60/13.24 (singletonsuniq) =>
% 97.60/13.24 ((
% 97.60/13.24 (setukpairinjL1) =>
% 97.60/13.24 ((
% 97.60/13.24 (kfstsingleton) =>
% 97.60/13.24 ((
% 97.60/13.24 (theprop) =>
% 97.60/13.24 ((
% 97.60/13.24 (kfstpairEq) =>
% 97.60/13.24 ((
% 97.60/13.24 (cartprodfstin) =>
% 97.60/13.24 ((
% 97.60/13.24 (setukpairinjL2) =>
% 97.60/13.24 ((
% 97.60/13.24 (setukpairinjL) =>
% 97.60/13.24 ((
% 97.60/13.24 (setukpairinjR11) =>
% 97.60/13.24 ((
% 97.60/13.24 (setukpairinjR12) =>
% 97.60/13.24 ((
% 97.60/13.24 (setukpairinjR1) =>
% 97.60/13.24 ((
% 97.60/13.24 (upairequniteq) =>
% 97.60/13.24 ((
% 97.60/13.24 (setukpairinjR2) =>
% 97.60/13.24 ((
% 97.60/13.24 (setukpairinjR) =>
% 97.60/13.24 ((
% 97.60/13.24 (ksndsingleton) =>
% 97.60/13.24 ((
% 97.60/13.24 (ksndpairEq) =>
% 97.60/13.24 ((
% 97.60/13.24 (kpairsurjEq) =>
% 97.60/13.24 ((
% 97.60/13.24 (cartprodsndin) =>
% 97.60/13.24 ((
% 97.60/13.24 (cartprodpairmemEL) =>
% 97.60/13.24 ((
% 97.60/13.24 (cartprodpairmemER) =>
% 97.60/13.24 ((
% 97.60/13.24 (cartprodmempaircEq) =>
% 97.60/13.24 ((
% 97.60/13.24 (cartprodfstpairEq) =>
% 97.60/13.24 ((
% 97.60/13.24 (cartprodsndpairEq) =>
% 97.60/13.24 ((
% 97.60/13.24 (cartprodpairsurjEq) =>
% 97.60/13.24 ((
% 97.60/13.24 (dpsetconstrI) =>
% 97.60/13.24 ((
% 97.60/13.24 (dpsetconstrSub) =>
% 97.60/13.24 ((
% 97.60/13.24 (setOfPairsIsBReln) =>
% 97.60/13.24 ((
% 97.60/13.24 (dpsetconstrERa) =>
% 97.60/13.24 ((
% 97.60/13.24 (dpsetconstrEL1) =>
% 97.60/13.24 ((
% 97.60/13.24 (dpsetconstrEL2) =>
% 97.60/13.24 ((
% 97.60/13.24 (dpsetconstrER) =>
% 97.60/13.24 ((
% 97.60/13.24 (funcImageSingleton) =>
% 97.60/13.24 ((
% 97.60/13.24 (apProp) =>
% 97.60/13.24 ((
% 97.60/13.24 (app) =>
% 97.60/13.24 ((
% 97.60/13.24 (infuncsetfunc) =>
% 97.60/13.24 ((
% 97.60/13.24 (ap2p) =>
% 97.60/13.24 ((
% 97.60/13.24 (funcinfuncset) =>
% 97.60/13.24 ((
% 97.60/13.24 (lamProp) =>
% 97.60/13.24 ((
% 97.60/13.24 (lamp) =>
% 97.60/13.24 ((
% 97.60/13.24 (lam2p) =>
% 97.60/13.24 ((
% 97.60/13.24 (brelnall1) =>
% 97.60/13.24 ((
% 97.60/13.24 (brelnall2) =>
% 97.60/13.24 ((
% 97.60/13.24 (ex1E2) =>
% 97.60/13.24 ((
% 97.60/13.24 (funcGraphProp1) =>
% 97.60/13.24 ((
% 97.60/13.24 (funcGraphProp3) =>
% 97.60/13.24 ((
% 97.60/13.24 (funcGraphProp2) =>
% 97.60/13.24 ((
% 97.60/13.24 (funcextLem) =>
% 97.60/13.24 ((
% 97.60/13.24 (funcGraphProp4) =>
% 97.60/13.24 ((
% 97.60/13.24 (subbreln) =>
% 97.60/13.24 ((
% 97.60/13.24 (eqbreln) =>
% 97.60/13.24 ((
% 97.60/13.24 (funcext) =>
% 97.60/13.24 ((
% 97.60/13.24 (funcext2) =>
% 97.60/13.24 ((
% 97.60/13.24 (ap2apEq1) =>
% 97.60/13.24 ((
% 97.60/13.24 (ap2apEq2) =>
% 97.60/13.24 ((
% 97.60/13.24 (beta1) =>
% 97.60/13.24 ((
% 97.60/13.24 (eta1) =>
% 97.60/13.24 ((
% 97.60/13.24 (lam2lamEq) =>
% 97.60/13.24 ((
% 97.60/13.24 (beta2) =>
% 97.60/13.24 ((
% 97.60/13.24 (eta2) =>
% 97.60/13.24 ((
% 97.60/13.24 (iffalseProp1) =>
% 97.60/13.24 ((
% 97.60/13.24 (iffalseProp2) =>
% 97.60/13.24 ((
% 97.60/13.24 (iftrueProp1) =>
% 97.60/13.24 ((
% 97.60/13.24 (iftrueProp2) =>
% 97.60/13.24 ((
% 97.60/13.24 (ifSingleton) =>
% 97.60/13.24 ((
% 97.60/13.24 (ifp) =>
% 97.60/13.24 ((
% 97.60/13.24 (theeq) =>
% 97.60/13.24 ((
% 97.60/13.24 (iftrue) =>
% 97.60/13.24 ((
% 97.60/13.24 (iffalse) =>
% 97.60/13.24 ((
% 97.60/13.24 (iftrueorfalse) =>
% 97.60/13.24 ((
% 97.60/13.24 (binintersectT_lem) =>
% 97.60/13.24 ((
% 97.60/13.24 (binunionT_lem) =>
% 97.60/13.24 ((
% 97.60/13.24 (powersetT_lem) =>
% 97.60/13.24 ((
% 97.60/13.24 (setminusT_lem) =>
% 97.60/13.24 ((
% 97.60/13.24 (complementT_lem) =>
% 97.60/13.24 ((
% 97.60/13.24 (setextT) =>
% 97.60/13.24 ((
% 97.60/13.24 (subsetTI) =>
% 97.60/13.24 ((
% 97.60/13.24 (powersetTI1) =>
% 97.60/13.24 ((
% 97.60/13.24 (powersetTE1) =>
% 97.60/13.24 ((
% 97.60/13.24 (complementTI1) =>
% 97.60/13.24 ((
% 97.60/13.24 (complementTE1) =>
% 97.60/13.24 ((
% 97.60/13.24 (binintersectTELcontra) =>
% 97.60/13.24 ((
% 97.60/13.24 (binintersectTERcontra) =>
% 97.60/13.24 ((
% 97.60/13.24 (contrasubsetT) =>
% 97.60/13.24 ((
% 97.60/13.24 (contrasubsetT1) =>
% 97.60/13.24 ((
% 97.60/13.24 (contrasubsetT2) =>
% 97.60/13.24 ((
% 97.60/13.24 (contrasubsetT3) =>
% 97.60/13.24 ((
% 97.60/13.24 (doubleComplementI1) =>
% 97.60/13.24 ((
% 97.60/13.24 (doubleComplementE1) =>
% 97.60/13.24 ((
% 97.60/13.24 (doubleComplementSub1) =>
% 97.60/13.24 ((
% 97.60/13.24 (doubleComplementSub2) =>
% 97.60/13.24 ((
% 97.60/13.24 (doubleComplementEq) =>
% 97.60/13.24 ((
% 97.60/13.24 (complementTnotintersectT) =>
% 97.60/13.24 ((
% 97.60/13.24 (complementImpComplementIntersect) =>
% 97.60/13.24 ((
% 97.60/13.24 (complementSubsetComplementIntersect) =>
% 97.60/13.24 ((
% 97.60/13.24 (complementInPowersetComplementIntersect) =>
% 97.60/13.24 ((
% 97.60/13.24 (contraSubsetComplement) =>
% 97.60/13.24 ((
% 97.60/13.24 (complementTcontraSubset) =>
% 97.60/13.24 ((
% 97.60/13.24 (binunionTILcontra) =>
% 97.60/13.24 ((
% 97.60/13.24 (binunionTIRcontra) =>
% 97.60/13.24 ((
% 97.60/13.24 (inIntersectImpInUnion) =>
% 97.60/13.24 ((
% 97.60/13.24 (inIntersectImpInUnion2) =>
% 97.60/13.24 ((
% 97.60/13.24 (inIntersectImpInIntersectUnions) =>
% 97.60/13.24 ((
% 97.60/13.24 (intersectInPowersetIntersectUnions) =>
% 97.60/13.24 ((
% 97.60/13.24 (inComplementUnionImpNotIn1) =>
% 97.60/13.24 ((
% 97.60/13.24 (inComplementUnionImpInComplement1) =>
% 97.60/13.24 ((
% 97.60/13.24 (binunionTE) =>
% 97.60/13.24 ((
% 97.60/13.24 (binunionTEcontra) =>
% 97.60/13.24 ((
% 97.60/13.24 (demorgan2a1) =>
% 97.60/13.24 ((
% 97.60/13.24 (complementUnionInPowersetComplement) =>
% 97.60/13.24 ((
% 97.60/13.24 (demorgan2a2) =>
% 97.60/13.24 ((
% 97.60/13.24 (demorgan1a) =>
% 97.60/13.24 ((
% 97.60/13.24 (demorgan1b) =>
% 97.60/13.24 ((
% 97.60/13.24 (demorgan1) =>
% 97.60/13.24 ((
% 97.60/13.24 (demorgan2a) =>
% 97.60/13.24 ((
% 97.60/13.24 (demorgan2b2) =>
% 97.60/13.24 ((
% 97.60/13.24 (demorgan2b) =>
% 97.60/13.24 ((
% 97.60/13.24 (demorgan2) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz13rule0) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz13rule1) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz13rule2) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz13rule3) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz13rule4) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz1_1) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz1_2) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz1_3) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz1_4) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz1_5) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1all2) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1SetBreln1) =>
% 97.60/13.24 ((
% 97.60/13.24 (choice2fnsingleton) =>
% 97.60/13.24 ((
% 97.60/13.24 (setOfPairsIsBReln1) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1all1) =>
% 97.60/13.24 ((
% 97.60/13.24 (subbreln1) =>
% 97.60/13.24 ((
% 97.60/13.24 (eqbreln1) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1invprop) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1invI) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1invE) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1compprop) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1compI) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1compE) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1compEex) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1unionprop) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1unionIL) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1unionIR) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1unionI) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1unionE) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1unionEcases) =>
% 97.60/13.24 ((
% 97.60/13.24 (breln1unionCommutes) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz2Ex) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz2W) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz2A) =>
% 97.60/13.24 ((
% 97.60/13.24 (woz2B) =>
% 97.60/13.24 ((
% 97.60/13.24 (image1Ex) =>
% 97.60/13.24 ((
% 97.60/13.24 (image1Ex1) =>
% 97.60/13.24 ((
% 97.60/13.24 (image1Equiv) =>
% 97.60/13.24 ((
% 97.60/13.24 (image1E) =>
% 97.60/13.24 ((
% 97.60/13.24 (image1I) =>
% 97.60/13.24 ((
% 97.60/13.24 (injFuncInInjFuncSet) =>
% 97.60/13.24 ((
% 97.60/13.24 (injFuncSetFuncIn) =>
% 97.60/13.24 ((
% 97.60/13.24 (injFuncSetFuncInj) =>
% 97.60/13.24 ((
% 97.60/13.24 (surjFuncSetFuncIn) =>
% 97.60/13.24 ((
% 97.60/13.24 (surjFuncSetFuncSurj) =>
% 97.60/13.24 ((
% 97.60/13.24 (leftInvIsSurj) =>
% 97.60/13.24 ((
% 97.60/13.24 (surjCantorThm) =>
% 97.60/13.24 ((
% 97.60/13.24 (foundation2) =>
% 97.60/13.24 ((
% 97.60/13.24 (notinself) =>
% 97.60/13.24 ((
% 97.60/13.24 (notinself2) =>
% 97.60/13.24 ((
% 97.60/13.24 (omegaSp) =>
% 97.60/13.24 ((
% 97.60/13.24 (omegaSclos) =>
% 97.60/13.24 ((
% 97.60/13.24 (peano0notS) =>
% 97.60/13.24 ((
% 97.60/13.24 (!!) @ (
% 97.60/13.24 (('#S') @ (
% 97.60/13.24 (
% 97.60/13.24 ('#B') @ (
% 97.60/13.24 =>) @
% 97.60/13.24 (
% 97.60/13.24 (
% 97.60/13.24 ('#C') @ in @
% 97.60/13.24 omega)))) @
% 97.60/13.24 (
% 97.60/13.24 (
% 97.60/13.24 ('#B') @ (
% 97.60/13.24 !!) @
% 97.60/13.24 (
% 97.60/13.24 (
% 97.60/13.24 ('#B') @ (
% 97.60/13.24 (
% 97.60/13.24 ('#S') @ (
% 97.60/13.24 (
% 97.60/13.24 ('#B') @ (
% 97.60/13.24 =>) @
% 97.60/13.24 (
% 97.60/13.24 (
% 97.60/13.24 ('#C') @ in @
% 97.60/13.24 omega)))))) @
% 97.60/13.24 (
% 97.60/13.24 (
% 97.60/13.24 ('#S') @ (
% 97.60/13.24 (
% 97.60/13.24 ('#B') @ (
% 97.60/13.24 '#S') @
% 97.60/13.24 (
% 97.60/13.24 (
% 97.60/13.24 ('#B') @ (
% 97.60/13.24 (
% 97.60/13.24 ('#B') @ (
% 97.60/13.24 =>))) @
% 97.60/13.24 (
% 97.60/13.24 (
% 97.60/13.24 ('#C') @ (
% 97.60/13.24 (
% 97.60/13.24 ('#B') @ (
% 97.60/13.24 '#B') @
% 97.60/13.24 (
% 97.60/13.24 (
% 97.60/13.24 ('#B') @ (
% 97.60/13.24 =) @
% 97.60/13.24 omegaS)))) @
% 97.60/13.24 omegaS)))))) @
% 97.60/13.24 (
% 97.60/13.24 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.60/13.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1096])).
% 97.60/13.24 thf(zip_derived_cl1109, plain,
% 97.60/13.24 (~ (((binunionIR) =>
% 97.60/13.24 (((binunionEcases) =>
% 97.60/13.24 (((binunionE) =>
% 97.60/13.24 (((binunionLsub) =>
% 97.60/13.24 (((binunionRsub) =>
% 97.60/13.24 (((binintersectI) =>
% 97.60/13.24 (((binintersectSubset5) =>
% 97.60/13.24 (((binintersectEL) =>
% 97.60/13.24 (((binintersectLsub) =>
% 97.60/13.24 (((binintersectSubset2) =>
% 97.60/13.24 (((binintersectSubset3) =>
% 97.60/13.24 (((binintersectER) =>
% 97.60/13.24 (((disjointsetsI1) =>
% 97.60/13.24 (((binintersectRsub) =>
% 97.60/13.24 (((binintersectSubset4) =>
% 97.60/13.24 (((binintersectSubset1) =>
% 97.60/13.24 (((bs114d) =>
% 97.60/13.24 (((setminusI) =>
% 97.60/13.24 (((setminusEL) =>
% 97.60/13.24 (((setminusER) =>
% 97.60/13.24 (((setminusSubset2) =>
% 97.60/13.24 (((setminusERneg) =>
% 97.60/13.24 (((setminusELneg) =>
% 97.60/13.24 (((setminusILneg) =>
% 97.60/13.24 (((setminusIRneg) =>
% 97.60/13.24 (((setminusLsub) =>
% 97.60/13.24 (((setminusSubset1) =>
% 97.60/13.24 (((symdiffE) =>
% 97.60/13.24 (((symdiffI1) =>
% 97.60/13.24 (((symdiffI2) =>
% 97.60/13.24 ((
% 97.60/13.24 (symdiffIneg1) =>
% 97.60/13.24 ((
% 97.60/13.24 (symdiffIneg2) =>
% 97.60/13.24 ((
% 97.60/13.24 (secondinupair) =>
% 97.60/13.24 ((
% 97.60/13.24 (setukpairIL) =>
% 97.60/13.24 ((
% 97.60/13.24 (setukpairIR) =>
% 97.60/13.24 ((
% 97.60/13.24 (kpairiskpair) =>
% 97.60/13.24 ((
% 97.60/13.24 (kpairp) =>
% 97.60/13.24 ((
% 97.60/13.24 (singletonsubset) =>
% 97.60/13.24 ((
% 97.60/13.24 (singletoninpowerset) =>
% 97.60/13.24 ((
% 97.60/13.24 (singletoninpowunion) =>
% 97.60/13.24 ((
% 97.60/13.24 (upairset2E) =>
% 97.60/13.24 ((
% 97.60/13.24 (upairsubunion) =>
% 97.60/13.24 ((
% 97.60/13.24 (upairinpowunion) =>
% 97.60/13.24 ((
% 97.60/13.24 (ubforcartprodlem1) =>
% 97.60/13.24 ((
% 97.60/13.24 (ubforcartprodlem2) =>
% 97.60/13.24 ((
% 97.60/13.24 (ubforcartprodlem3) =>
% 97.60/13.24 ((
% 97.60/13.24 (cartprodpairin) =>
% 97.60/13.24 ((
% 97.60/13.24 (cartprodmempair1) =>
% 97.60/13.24 ((
% 97.60/13.24 (cartprodmempair) =>
% 97.60/13.24 ((
% 97.60/13.24 (setunionE2) =>
% 97.60/13.24 ((
% 97.60/13.24 (setunionsingleton1) =>
% 97.60/13.24 ((
% 97.60/13.24 (setunionsingleton2) =>
% 97.60/13.24 ((
% 97.60/13.24 (setunionsingleton) =>
% 97.60/13.24 ((
% 97.60/13.24 (singletonprop) =>
% 97.60/13.24 ((
% 97.60/13.24 (ex1E1) =>
% 97.60/13.24 ((
% 97.60/13.24 (ex1I) =>
% 97.60/13.24 ((
% 97.60/13.24 (ex1I2) =>
% 97.60/13.24 ((
% 97.60/13.24 (singletonsuniq) =>
% 97.60/13.24 ((
% 97.60/13.24 (setukpairinjL1) =>
% 97.60/13.24 ((
% 97.60/13.24 (kfstsingleton) =>
% 97.60/13.24 ((
% 97.60/13.24 (theprop) =>
% 97.60/13.24 ((
% 97.60/13.24 (kfstpairEq) =>
% 97.60/13.24 ((
% 97.60/13.24 (cartprodfstin) =>
% 97.60/13.24 ((
% 97.60/13.24 (setukpairinjL2) =>
% 97.60/13.24 ((
% 97.60/13.24 (setukpairinjL) =>
% 97.60/13.24 ((
% 97.60/13.24 (setukpairinjR11) =>
% 97.60/13.24 ((
% 97.60/13.24 (setukpairinjR12) =>
% 97.60/13.24 ((
% 97.60/13.24 (setukpairinjR1) =>
% 97.60/13.24 ((
% 97.60/13.24 (upairequniteq) =>
% 97.60/13.24 ((
% 97.60/13.24 (setukpairinjR2) =>
% 97.60/13.24 ((
% 97.60/13.24 (setukpairinjR) =>
% 97.60/13.24 ((
% 97.60/13.24 (ksndsingleton) =>
% 97.60/13.24 ((
% 97.60/13.24 (ksndpairEq) =>
% 97.60/13.24 ((
% 97.60/13.24 (kpairsurjEq) =>
% 97.60/13.24 ((
% 97.60/13.24 (cartprodsndin) =>
% 97.60/13.24 ((
% 97.60/13.24 (cartprodpairmemEL) =>
% 97.60/13.24 ((
% 97.60/13.24 (cartprodpairmemER) =>
% 97.60/13.24 ((
% 97.60/13.24 (cartprodmempaircEq) =>
% 97.60/13.24 ((
% 97.60/13.24 (cartprodfstpairEq) =>
% 97.60/13.24 ((
% 97.60/13.24 (cartprodsndpairEq) =>
% 97.60/13.24 ((
% 97.60/13.24 (cartprodpairsurjEq) =>
% 97.60/13.24 ((
% 97.60/13.24 (dpsetconstrI) =>
% 97.60/13.24 ((
% 97.60/13.24 (dpsetconstrSub) =>
% 97.60/13.24 ((
% 97.60/13.24 (setOfPairsIsBReln) =>
% 97.60/13.24 ((
% 97.60/13.24 (dpsetconstrERa) =>
% 97.60/13.24 ((
% 97.60/13.24 (dpsetconstrEL1) =>
% 97.60/13.24 ((
% 97.60/13.24 (dpsetconstrEL2) =>
% 97.60/13.24 ((
% 97.60/13.24 (dpsetconstrER) =>
% 97.60/13.24 ((
% 97.60/13.24 (funcImageSingleton) =>
% 97.60/13.24 ((
% 97.60/13.24 (apProp) =>
% 97.60/13.24 ((
% 97.60/13.24 (app) =>
% 97.60/13.24 ((
% 97.60/13.24 (infuncsetfunc) =>
% 97.60/13.24 ((
% 97.60/13.24 (ap2p) =>
% 97.60/13.24 ((
% 97.60/13.24 (funcinfuncset) =>
% 97.60/13.24 ((
% 97.60/13.24 (lamProp) =>
% 97.60/13.24 ((
% 97.60/13.24 (lamp) =>
% 97.60/13.24 ((
% 97.60/13.24 (lam2p) =>
% 97.60/13.24 ((
% 97.60/13.24 (brelnall1) =>
% 97.60/13.24 ((
% 97.60/13.24 (brelnall2) =>
% 97.60/13.24 ((
% 97.60/13.24 (ex1E2) =>
% 97.60/13.24 ((
% 97.60/13.24 (funcGraphProp1) =>
% 97.60/13.24 ((
% 97.60/13.24 (funcGraphProp3) =>
% 97.60/13.24 ((
% 97.60/13.24 (funcGraphProp2) =>
% 97.60/13.24 ((
% 97.60/13.24 (funcextLem) =>
% 97.60/13.24 ((
% 97.60/13.24 (funcGraphProp4) =>
% 97.60/13.24 ((
% 97.60/13.24 (subbreln) =>
% 97.60/13.24 ((
% 97.60/13.24 (eqbreln) =>
% 97.60/13.24 ((
% 97.60/13.24 (funcext) =>
% 97.60/13.24 ((
% 97.60/13.24 (funcext2) =>
% 97.60/13.24 ((
% 97.60/13.24 (ap2apEq1) =>
% 97.60/13.24 ((
% 97.60/13.24 (ap2apEq2) =>
% 97.60/13.24 ((
% 97.60/13.24 (beta1) =>
% 97.60/13.24 ((
% 97.60/13.24 (eta1) =>
% 97.60/13.24 ((
% 97.60/13.24 (lam2lamEq) =>
% 97.60/13.24 ((
% 97.60/13.24 (beta2) =>
% 97.60/13.24 ((
% 97.60/13.24 (eta2) =>
% 97.60/13.24 ((
% 97.60/13.24 (iffalseProp1) =>
% 97.60/13.24 ((
% 97.60/13.24 (iffalseProp2) =>
% 97.60/13.24 ((
% 97.60/13.24 (iftrueProp1) =>
% 97.60/13.24 ((
% 97.60/13.24 (iftrueProp2) =>
% 97.60/13.24 ((
% 97.60/13.24 (ifSingleton) =>
% 97.60/13.24 ((
% 97.60/13.24 (ifp) =>
% 97.60/13.24 ((
% 97.60/13.24 (theeq) =>
% 97.60/13.24 ((
% 97.60/13.24 (iftrue) =>
% 97.60/13.24 ((
% 97.60/13.24 (iffalse) =>
% 97.60/13.24 ((
% 97.60/13.24 (iftrueorfalse) =>
% 97.60/13.24 ((
% 97.60/13.24 (binintersectT_lem) =>
% 97.60/13.24 ((
% 97.60/13.24 (binunionT_lem) =>
% 97.60/13.24 ((
% 97.60/13.24 (powersetT_lem) =>
% 97.60/13.24 ((
% 97.60/13.24 (setminusT_lem) =>
% 97.60/13.24 ((
% 97.60/13.24 (complementT_lem) =>
% 97.60/13.24 ((
% 97.60/13.24 (setextT) =>
% 97.60/13.24 ((
% 97.60/13.24 (subsetTI) =>
% 97.60/13.24 ((
% 97.60/13.24 (powersetTI1) =>
% 97.60/13.24 ((
% 97.60/13.24 (powersetTE1) =>
% 97.60/13.24 ((
% 97.60/13.24 (complementTI1) =>
% 97.60/13.24 ((
% 97.60/13.24 (complementTE1) =>
% 97.60/13.24 ((
% 97.60/13.24 (binintersectTELcontra) =>
% 97.60/13.24 ((
% 97.60/13.24 (binintersectTERcontra) =>
% 97.60/13.24 ((
% 97.60/13.24 (contrasubsetT) =>
% 97.60/13.24 ((
% 97.60/13.24 (contrasubsetT1) =>
% 97.60/13.24 ((
% 97.60/13.24 (contrasubsetT2) =>
% 97.60/13.24 ((
% 97.60/13.24 (contrasubsetT3) =>
% 97.60/13.24 ((
% 97.60/13.24 (doubleComplementI1) =>
% 97.60/13.24 ((
% 97.60/13.24 (doubleComplementE1) =>
% 97.60/13.24 ((
% 97.60/13.24 (doubleComplementSub1) =>
% 97.60/13.24 ((
% 97.60/13.24 (doubleComplementSub2) =>
% 97.60/13.24 ((
% 97.60/13.24 (doubleComplementEq) =>
% 97.60/13.24 ((
% 97.60/13.24 (complementTnotintersectT) =>
% 97.60/13.24 ((
% 97.60/13.24 (complementImpComplementIntersect) =>
% 97.60/13.24 ((
% 97.60/13.24 (complementSubsetComplementIntersect) =>
% 97.60/13.24 ((
% 97.60/13.24 (complementInPowersetComplementIntersect) =>
% 97.60/13.24 ((
% 97.60/13.24 (contraSubsetComplement) =>
% 97.60/13.24 ((
% 97.60/13.24 (complementTcontraSubset) =>
% 97.60/13.24 ((
% 97.60/13.24 (binunionTILcontra) =>
% 97.60/13.24 ((
% 97.60/13.24 (binunionTIRcontra) =>
% 97.60/13.24 ((
% 97.60/13.24 (inIntersectImpInUnion) =>
% 97.60/13.24 ((
% 97.60/13.24 (inIntersectImpInUnion2) =>
% 97.60/13.24 ((
% 97.60/13.24 (inIntersectImpInIntersectUnions) =>
% 97.60/13.24 ((
% 97.60/13.24 (intersectInPowersetIntersectUnions) =>
% 97.60/13.24 ((
% 97.60/13.24 (inComplementUnionImpNotIn1) =>
% 97.60/13.24 ((
% 97.60/13.24 (inComplementUnionImpInComplement1) =>
% 97.60/13.24 ((
% 97.60/13.24 (binunionTE) =>
% 97.60/13.24 ((
% 97.60/13.24 (binunionTEcontra) =>
% 97.60/13.24 ((
% 97.60/13.24 (demorgan2a1) =>
% 97.60/13.24 ((
% 97.60/13.24 (complementUnionInPowersetComplement) =>
% 97.60/13.24 ((
% 97.60/13.24 (demorgan2a2) =>
% 97.60/13.24 ((
% 97.60/13.24 (demorgan1a) =>
% 97.60/13.24 ((
% 97.60/13.24 (demorgan1b) =>
% 97.60/13.24 ((
% 97.60/13.24 (demorgan1) =>
% 97.60/13.24 ((
% 97.60/13.24 (demorgan2a) =>
% 97.60/13.24 ((
% 97.95/13.24 (demorgan2b2) =>
% 97.95/13.24 ((
% 97.95/13.24 (demorgan2b) =>
% 97.95/13.24 ((
% 97.95/13.24 (demorgan2) =>
% 97.95/13.24 ((
% 97.95/13.24 (woz13rule0) =>
% 97.95/13.24 ((
% 97.95/13.24 (woz13rule1) =>
% 97.95/13.24 ((
% 97.95/13.24 (woz13rule2) =>
% 97.95/13.24 ((
% 97.95/13.24 (woz13rule3) =>
% 97.95/13.24 ((
% 97.95/13.24 (woz13rule4) =>
% 97.95/13.24 ((
% 97.95/13.24 (woz1_1) =>
% 97.95/13.24 ((
% 97.95/13.24 (woz1_2) =>
% 97.95/13.24 ((
% 97.95/13.24 (woz1_3) =>
% 97.95/13.24 ((
% 97.95/13.24 (woz1_4) =>
% 97.95/13.24 ((
% 97.95/13.24 (woz1_5) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1all2) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1SetBreln1) =>
% 97.95/13.24 ((
% 97.95/13.24 (choice2fnsingleton) =>
% 97.95/13.24 ((
% 97.95/13.24 (setOfPairsIsBReln1) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1all1) =>
% 97.95/13.24 ((
% 97.95/13.24 (subbreln1) =>
% 97.95/13.24 ((
% 97.95/13.24 (eqbreln1) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1invprop) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1invI) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1invE) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1compprop) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1compI) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1compE) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1compEex) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1unionprop) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1unionIL) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1unionIR) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1unionI) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1unionE) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1unionEcases) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1unionCommutes) =>
% 97.95/13.24 ((
% 97.95/13.24 (woz2Ex) =>
% 97.95/13.24 ((
% 97.95/13.24 (woz2W) =>
% 97.95/13.24 ((
% 97.95/13.24 (woz2A) =>
% 97.95/13.24 ((
% 97.95/13.24 (woz2B) =>
% 97.95/13.24 ((
% 97.95/13.24 (image1Ex) =>
% 97.95/13.24 ((
% 97.95/13.24 (image1Ex1) =>
% 97.95/13.24 ((
% 97.95/13.24 (image1Equiv) =>
% 97.95/13.24 ((
% 97.95/13.24 (image1E) =>
% 97.95/13.24 ((
% 97.95/13.24 (image1I) =>
% 97.95/13.24 ((
% 97.95/13.24 (injFuncInInjFuncSet) =>
% 97.95/13.24 ((
% 97.95/13.24 (injFuncSetFuncIn) =>
% 97.95/13.24 ((
% 97.95/13.24 (injFuncSetFuncInj) =>
% 97.95/13.24 ((
% 97.95/13.24 (surjFuncSetFuncIn) =>
% 97.95/13.24 ((
% 97.95/13.24 (surjFuncSetFuncSurj) =>
% 97.95/13.24 ((
% 97.95/13.24 (leftInvIsSurj) =>
% 97.95/13.24 ((
% 97.95/13.24 (surjCantorThm) =>
% 97.95/13.24 ((
% 97.95/13.24 (foundation2) =>
% 97.95/13.24 ((
% 97.95/13.24 (notinself) =>
% 97.95/13.24 ((
% 97.95/13.24 (notinself2) =>
% 97.95/13.24 ((
% 97.95/13.24 (omegaSp) =>
% 97.95/13.24 ((
% 97.95/13.24 (omegaSclos) =>
% 97.95/13.24 ((
% 97.95/13.24 (peano0notS) =>
% 97.95/13.24 ((
% 97.95/13.24 (!!) @ (
% 97.95/13.24 (('#S') @ (
% 97.95/13.24 (
% 97.95/13.24 ('#B') @ (
% 97.95/13.24 =>) @
% 97.95/13.24 (
% 97.95/13.24 (
% 97.95/13.24 ('#C') @ in @
% 97.95/13.24 omega)))) @
% 97.95/13.24 (
% 97.95/13.24 (
% 97.95/13.24 ('#B') @ (
% 97.95/13.24 !!) @
% 97.95/13.24 (
% 97.95/13.24 (
% 97.95/13.24 ('#B') @ (
% 97.95/13.24 (
% 97.95/13.24 ('#S') @ (
% 97.95/13.24 (
% 97.95/13.24 ('#B') @ (
% 97.95/13.24 =>) @
% 97.95/13.24 (
% 97.95/13.24 (
% 97.95/13.24 ('#C') @ in @
% 97.95/13.24 omega)))))) @
% 97.95/13.24 (
% 97.95/13.24 (
% 97.95/13.24 ('#S') @ (
% 97.95/13.24 (
% 97.95/13.24 ('#B') @ (
% 97.95/13.24 '#S') @
% 97.95/13.24 (
% 97.95/13.24 (
% 97.95/13.24 ('#B') @ (
% 97.95/13.24 (
% 97.95/13.24 ('#B') @ (
% 97.95/13.24 =>))) @
% 97.95/13.24 (
% 97.95/13.24 (
% 97.95/13.24 ('#C') @ (
% 97.95/13.24 (
% 97.95/13.24 ('#B') @ (
% 97.95/13.24 '#B') @
% 97.95/13.24 (
% 97.95/13.24 (
% 97.95/13.24 ('#B') @ (
% 97.95/13.24 =) @
% 97.95/13.24 omegaS)))) @
% 97.95/13.24 omegaS)))))) @
% 97.95/13.24 (
% 97.95/13.24 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.95/13.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1102])).
% 97.95/13.24 thf(zip_derived_cl1115, plain,
% 97.95/13.24 (~ (((binunionEcases) =>
% 97.95/13.24 (((binunionE) =>
% 97.95/13.24 (((binunionLsub) =>
% 97.95/13.24 (((binunionRsub) =>
% 97.95/13.24 (((binintersectI) =>
% 97.95/13.24 (((binintersectSubset5) =>
% 97.95/13.24 (((binintersectEL) =>
% 97.95/13.24 (((binintersectLsub) =>
% 97.95/13.24 (((binintersectSubset2) =>
% 97.95/13.24 (((binintersectSubset3) =>
% 97.95/13.24 (((binintersectER) =>
% 97.95/13.24 (((disjointsetsI1) =>
% 97.95/13.24 (((binintersectRsub) =>
% 97.95/13.24 (((binintersectSubset4) =>
% 97.95/13.24 (((binintersectSubset1) =>
% 97.95/13.24 (((bs114d) =>
% 97.95/13.24 (((setminusI) =>
% 97.95/13.24 (((setminusEL) =>
% 97.95/13.24 (((setminusER) =>
% 97.95/13.24 (((setminusSubset2) =>
% 97.95/13.24 (((setminusERneg) =>
% 97.95/13.24 (((setminusELneg) =>
% 97.95/13.24 (((setminusILneg) =>
% 97.95/13.24 (((setminusIRneg) =>
% 97.95/13.24 (((setminusLsub) =>
% 97.95/13.24 (((setminusSubset1) =>
% 97.95/13.24 (((symdiffE) =>
% 97.95/13.24 (((symdiffI1) =>
% 97.95/13.24 (((symdiffI2) =>
% 97.95/13.24 (((symdiffIneg1) =>
% 97.95/13.24 ((
% 97.95/13.24 (symdiffIneg2) =>
% 97.95/13.24 ((
% 97.95/13.24 (secondinupair) =>
% 97.95/13.24 ((
% 97.95/13.24 (setukpairIL) =>
% 97.95/13.24 ((
% 97.95/13.24 (setukpairIR) =>
% 97.95/13.24 ((
% 97.95/13.24 (kpairiskpair) =>
% 97.95/13.24 ((
% 97.95/13.24 (kpairp) =>
% 97.95/13.24 ((
% 97.95/13.24 (singletonsubset) =>
% 97.95/13.24 ((
% 97.95/13.24 (singletoninpowerset) =>
% 97.95/13.24 ((
% 97.95/13.24 (singletoninpowunion) =>
% 97.95/13.24 ((
% 97.95/13.24 (upairset2E) =>
% 97.95/13.24 ((
% 97.95/13.24 (upairsubunion) =>
% 97.95/13.24 ((
% 97.95/13.24 (upairinpowunion) =>
% 97.95/13.24 ((
% 97.95/13.24 (ubforcartprodlem1) =>
% 97.95/13.24 ((
% 97.95/13.24 (ubforcartprodlem2) =>
% 97.95/13.24 ((
% 97.95/13.24 (ubforcartprodlem3) =>
% 97.95/13.24 ((
% 97.95/13.24 (cartprodpairin) =>
% 97.95/13.24 ((
% 97.95/13.24 (cartprodmempair1) =>
% 97.95/13.24 ((
% 97.95/13.24 (cartprodmempair) =>
% 97.95/13.24 ((
% 97.95/13.24 (setunionE2) =>
% 97.95/13.24 ((
% 97.95/13.24 (setunionsingleton1) =>
% 97.95/13.24 ((
% 97.95/13.24 (setunionsingleton2) =>
% 97.95/13.24 ((
% 97.95/13.24 (setunionsingleton) =>
% 97.95/13.24 ((
% 97.95/13.24 (singletonprop) =>
% 97.95/13.24 ((
% 97.95/13.24 (ex1E1) =>
% 97.95/13.24 ((
% 97.95/13.24 (ex1I) =>
% 97.95/13.24 ((
% 97.95/13.24 (ex1I2) =>
% 97.95/13.24 ((
% 97.95/13.24 (singletonsuniq) =>
% 97.95/13.24 ((
% 97.95/13.24 (setukpairinjL1) =>
% 97.95/13.24 ((
% 97.95/13.24 (kfstsingleton) =>
% 97.95/13.24 ((
% 97.95/13.24 (theprop) =>
% 97.95/13.24 ((
% 97.95/13.24 (kfstpairEq) =>
% 97.95/13.24 ((
% 97.95/13.24 (cartprodfstin) =>
% 97.95/13.24 ((
% 97.95/13.24 (setukpairinjL2) =>
% 97.95/13.24 ((
% 97.95/13.24 (setukpairinjL) =>
% 97.95/13.24 ((
% 97.95/13.24 (setukpairinjR11) =>
% 97.95/13.24 ((
% 97.95/13.24 (setukpairinjR12) =>
% 97.95/13.24 ((
% 97.95/13.24 (setukpairinjR1) =>
% 97.95/13.24 ((
% 97.95/13.24 (upairequniteq) =>
% 97.95/13.24 ((
% 97.95/13.24 (setukpairinjR2) =>
% 97.95/13.24 ((
% 97.95/13.24 (setukpairinjR) =>
% 97.95/13.24 ((
% 97.95/13.24 (ksndsingleton) =>
% 97.95/13.24 ((
% 97.95/13.24 (ksndpairEq) =>
% 97.95/13.24 ((
% 97.95/13.24 (kpairsurjEq) =>
% 97.95/13.24 ((
% 97.95/13.24 (cartprodsndin) =>
% 97.95/13.24 ((
% 97.95/13.24 (cartprodpairmemEL) =>
% 97.95/13.24 ((
% 97.95/13.24 (cartprodpairmemER) =>
% 97.95/13.24 ((
% 97.95/13.24 (cartprodmempaircEq) =>
% 97.95/13.24 ((
% 97.95/13.24 (cartprodfstpairEq) =>
% 97.95/13.24 ((
% 97.95/13.24 (cartprodsndpairEq) =>
% 97.95/13.24 ((
% 97.95/13.24 (cartprodpairsurjEq) =>
% 97.95/13.24 ((
% 97.95/13.24 (dpsetconstrI) =>
% 97.95/13.24 ((
% 97.95/13.24 (dpsetconstrSub) =>
% 97.95/13.24 ((
% 97.95/13.24 (setOfPairsIsBReln) =>
% 97.95/13.24 ((
% 97.95/13.24 (dpsetconstrERa) =>
% 97.95/13.24 ((
% 97.95/13.24 (dpsetconstrEL1) =>
% 97.95/13.24 ((
% 97.95/13.24 (dpsetconstrEL2) =>
% 97.95/13.24 ((
% 97.95/13.24 (dpsetconstrER) =>
% 97.95/13.24 ((
% 97.95/13.24 (funcImageSingleton) =>
% 97.95/13.24 ((
% 97.95/13.24 (apProp) =>
% 97.95/13.24 ((
% 97.95/13.24 (app) =>
% 97.95/13.24 ((
% 97.95/13.24 (infuncsetfunc) =>
% 97.95/13.24 ((
% 97.95/13.24 (ap2p) =>
% 97.95/13.24 ((
% 97.95/13.24 (funcinfuncset) =>
% 97.95/13.24 ((
% 97.95/13.24 (lamProp) =>
% 97.95/13.24 ((
% 97.95/13.24 (lamp) =>
% 97.95/13.24 ((
% 97.95/13.24 (lam2p) =>
% 97.95/13.24 ((
% 97.95/13.24 (brelnall1) =>
% 97.95/13.24 ((
% 97.95/13.24 (brelnall2) =>
% 97.95/13.24 ((
% 97.95/13.24 (ex1E2) =>
% 97.95/13.24 ((
% 97.95/13.24 (funcGraphProp1) =>
% 97.95/13.24 ((
% 97.95/13.24 (funcGraphProp3) =>
% 97.95/13.24 ((
% 97.95/13.24 (funcGraphProp2) =>
% 97.95/13.24 ((
% 97.95/13.24 (funcextLem) =>
% 97.95/13.24 ((
% 97.95/13.24 (funcGraphProp4) =>
% 97.95/13.24 ((
% 97.95/13.24 (subbreln) =>
% 97.95/13.24 ((
% 97.95/13.24 (eqbreln) =>
% 97.95/13.24 ((
% 97.95/13.24 (funcext) =>
% 97.95/13.24 ((
% 97.95/13.24 (funcext2) =>
% 97.95/13.24 ((
% 97.95/13.24 (ap2apEq1) =>
% 97.95/13.24 ((
% 97.95/13.24 (ap2apEq2) =>
% 97.95/13.24 ((
% 97.95/13.24 (beta1) =>
% 97.95/13.24 ((
% 97.95/13.24 (eta1) =>
% 97.95/13.24 ((
% 97.95/13.24 (lam2lamEq) =>
% 97.95/13.24 ((
% 97.95/13.24 (beta2) =>
% 97.95/13.24 ((
% 97.95/13.24 (eta2) =>
% 97.95/13.24 ((
% 97.95/13.24 (iffalseProp1) =>
% 97.95/13.24 ((
% 97.95/13.24 (iffalseProp2) =>
% 97.95/13.24 ((
% 97.95/13.24 (iftrueProp1) =>
% 97.95/13.24 ((
% 97.95/13.24 (iftrueProp2) =>
% 97.95/13.24 ((
% 97.95/13.24 (ifSingleton) =>
% 97.95/13.24 ((
% 97.95/13.24 (ifp) =>
% 97.95/13.24 ((
% 97.95/13.24 (theeq) =>
% 97.95/13.24 ((
% 97.95/13.24 (iftrue) =>
% 97.95/13.24 ((
% 97.95/13.24 (iffalse) =>
% 97.95/13.24 ((
% 97.95/13.24 (iftrueorfalse) =>
% 97.95/13.24 ((
% 97.95/13.24 (binintersectT_lem) =>
% 97.95/13.24 ((
% 97.95/13.24 (binunionT_lem) =>
% 97.95/13.24 ((
% 97.95/13.24 (powersetT_lem) =>
% 97.95/13.24 ((
% 97.95/13.24 (setminusT_lem) =>
% 97.95/13.24 ((
% 97.95/13.24 (complementT_lem) =>
% 97.95/13.24 ((
% 97.95/13.24 (setextT) =>
% 97.95/13.24 ((
% 97.95/13.24 (subsetTI) =>
% 97.95/13.24 ((
% 97.95/13.24 (powersetTI1) =>
% 97.95/13.24 ((
% 97.95/13.24 (powersetTE1) =>
% 97.95/13.24 ((
% 97.95/13.24 (complementTI1) =>
% 97.95/13.24 ((
% 97.95/13.24 (complementTE1) =>
% 97.95/13.24 ((
% 97.95/13.24 (binintersectTELcontra) =>
% 97.95/13.24 ((
% 97.95/13.24 (binintersectTERcontra) =>
% 97.95/13.24 ((
% 97.95/13.24 (contrasubsetT) =>
% 97.95/13.24 ((
% 97.95/13.24 (contrasubsetT1) =>
% 97.95/13.24 ((
% 97.95/13.24 (contrasubsetT2) =>
% 97.95/13.24 ((
% 97.95/13.24 (contrasubsetT3) =>
% 97.95/13.24 ((
% 97.95/13.24 (doubleComplementI1) =>
% 97.95/13.24 ((
% 97.95/13.24 (doubleComplementE1) =>
% 97.95/13.24 ((
% 97.95/13.24 (doubleComplementSub1) =>
% 97.95/13.24 ((
% 97.95/13.24 (doubleComplementSub2) =>
% 97.95/13.24 ((
% 97.95/13.24 (doubleComplementEq) =>
% 97.95/13.24 ((
% 97.95/13.24 (complementTnotintersectT) =>
% 97.95/13.24 ((
% 97.95/13.24 (complementImpComplementIntersect) =>
% 97.95/13.24 ((
% 97.95/13.24 (complementSubsetComplementIntersect) =>
% 97.95/13.24 ((
% 97.95/13.24 (complementInPowersetComplementIntersect) =>
% 97.95/13.24 ((
% 97.95/13.24 (contraSubsetComplement) =>
% 97.95/13.24 ((
% 97.95/13.24 (complementTcontraSubset) =>
% 97.95/13.24 ((
% 97.95/13.24 (binunionTILcontra) =>
% 97.95/13.24 ((
% 97.95/13.24 (binunionTIRcontra) =>
% 97.95/13.24 ((
% 97.95/13.24 (inIntersectImpInUnion) =>
% 97.95/13.24 ((
% 97.95/13.24 (inIntersectImpInUnion2) =>
% 97.95/13.24 ((
% 97.95/13.24 (inIntersectImpInIntersectUnions) =>
% 97.95/13.24 ((
% 97.95/13.24 (intersectInPowersetIntersectUnions) =>
% 97.95/13.24 ((
% 97.95/13.24 (inComplementUnionImpNotIn1) =>
% 97.95/13.24 ((
% 97.95/13.24 (inComplementUnionImpInComplement1) =>
% 97.95/13.24 ((
% 97.95/13.24 (binunionTE) =>
% 97.95/13.24 ((
% 97.95/13.24 (binunionTEcontra) =>
% 97.95/13.24 ((
% 97.95/13.24 (demorgan2a1) =>
% 97.95/13.24 ((
% 97.95/13.24 (complementUnionInPowersetComplement) =>
% 97.95/13.24 ((
% 97.95/13.24 (demorgan2a2) =>
% 97.95/13.24 ((
% 97.95/13.24 (demorgan1a) =>
% 97.95/13.24 ((
% 97.95/13.24 (demorgan1b) =>
% 97.95/13.24 ((
% 97.95/13.24 (demorgan1) =>
% 97.95/13.24 ((
% 97.95/13.24 (demorgan2a) =>
% 97.95/13.24 ((
% 97.95/13.24 (demorgan2b2) =>
% 97.95/13.24 ((
% 97.95/13.24 (demorgan2b) =>
% 97.95/13.24 ((
% 97.95/13.24 (demorgan2) =>
% 97.95/13.24 ((
% 97.95/13.24 (woz13rule0) =>
% 97.95/13.24 ((
% 97.95/13.24 (woz13rule1) =>
% 97.95/13.24 ((
% 97.95/13.24 (woz13rule2) =>
% 97.95/13.24 ((
% 97.95/13.24 (woz13rule3) =>
% 97.95/13.24 ((
% 97.95/13.24 (woz13rule4) =>
% 97.95/13.24 ((
% 97.95/13.24 (woz1_1) =>
% 97.95/13.24 ((
% 97.95/13.24 (woz1_2) =>
% 97.95/13.24 ((
% 97.95/13.24 (woz1_3) =>
% 97.95/13.24 ((
% 97.95/13.24 (woz1_4) =>
% 97.95/13.24 ((
% 97.95/13.24 (woz1_5) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1all2) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1SetBreln1) =>
% 97.95/13.24 ((
% 97.95/13.24 (choice2fnsingleton) =>
% 97.95/13.24 ((
% 97.95/13.24 (setOfPairsIsBReln1) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1all1) =>
% 97.95/13.24 ((
% 97.95/13.24 (subbreln1) =>
% 97.95/13.24 ((
% 97.95/13.24 (eqbreln1) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1invprop) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1invI) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1invE) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1compprop) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1compI) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1compE) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1compEex) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1unionprop) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1unionIL) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1unionIR) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1unionI) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1unionE) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1unionEcases) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1unionCommutes) =>
% 97.95/13.24 ((
% 97.95/13.24 (woz2Ex) =>
% 97.95/13.24 ((
% 97.95/13.24 (woz2W) =>
% 97.95/13.24 ((
% 97.95/13.24 (woz2A) =>
% 97.95/13.24 ((
% 97.95/13.24 (woz2B) =>
% 97.95/13.24 ((
% 97.95/13.24 (image1Ex) =>
% 97.95/13.24 ((
% 97.95/13.24 (image1Ex1) =>
% 97.95/13.24 ((
% 97.95/13.24 (image1Equiv) =>
% 97.95/13.24 ((
% 97.95/13.24 (image1E) =>
% 97.95/13.24 ((
% 97.95/13.24 (image1I) =>
% 97.95/13.24 ((
% 97.95/13.24 (injFuncInInjFuncSet) =>
% 97.95/13.24 ((
% 97.95/13.24 (injFuncSetFuncIn) =>
% 97.95/13.24 ((
% 97.95/13.24 (injFuncSetFuncInj) =>
% 97.95/13.24 ((
% 97.95/13.24 (surjFuncSetFuncIn) =>
% 97.95/13.24 ((
% 97.95/13.24 (surjFuncSetFuncSurj) =>
% 97.95/13.24 ((
% 97.95/13.24 (leftInvIsSurj) =>
% 97.95/13.24 ((
% 97.95/13.24 (surjCantorThm) =>
% 97.95/13.24 ((
% 97.95/13.24 (foundation2) =>
% 97.95/13.24 ((
% 97.95/13.24 (notinself) =>
% 97.95/13.24 ((
% 97.95/13.24 (notinself2) =>
% 97.95/13.24 ((
% 97.95/13.24 (omegaSp) =>
% 97.95/13.24 ((
% 97.95/13.24 (omegaSclos) =>
% 97.95/13.24 ((
% 97.95/13.24 (peano0notS) =>
% 97.95/13.24 ((
% 97.95/13.24 (!!) @ (
% 97.95/13.24 (('#S') @ (
% 97.95/13.24 (
% 97.95/13.24 ('#B') @ (
% 97.95/13.24 =>) @
% 97.95/13.24 (
% 97.95/13.24 (
% 97.95/13.24 ('#C') @ in @
% 97.95/13.24 omega)))) @
% 97.95/13.24 (
% 97.95/13.24 (
% 97.95/13.24 ('#B') @ (
% 97.95/13.24 !!) @
% 97.95/13.24 (
% 97.95/13.24 (
% 97.95/13.24 ('#B') @ (
% 97.95/13.24 (
% 97.95/13.24 ('#S') @ (
% 97.95/13.24 (
% 97.95/13.24 ('#B') @ (
% 97.95/13.24 =>) @
% 97.95/13.24 (
% 97.95/13.24 (
% 97.95/13.24 ('#C') @ in @
% 97.95/13.24 omega)))))) @
% 97.95/13.24 (
% 97.95/13.24 (
% 97.95/13.24 ('#S') @ (
% 97.95/13.24 (
% 97.95/13.24 ('#B') @ (
% 97.95/13.24 '#S') @
% 97.95/13.24 (
% 97.95/13.24 (
% 97.95/13.24 ('#B') @ (
% 97.95/13.24 (
% 97.95/13.24 ('#B') @ (
% 97.95/13.24 =>))) @
% 97.95/13.24 (
% 97.95/13.24 (
% 97.95/13.24 ('#C') @ (
% 97.95/13.24 (
% 97.95/13.24 ('#B') @ (
% 97.95/13.24 '#B') @
% 97.95/13.24 (
% 97.95/13.24 (
% 97.95/13.24 ('#B') @ (
% 97.95/13.24 =) @
% 97.95/13.24 omegaS)))) @
% 97.95/13.24 omegaS)))))) @
% 97.95/13.24 (
% 97.95/13.24 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.95/13.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1109])).
% 97.95/13.24 thf(zip_derived_cl1121, plain,
% 97.95/13.24 (~ (((binunionE) =>
% 97.95/13.24 (((binunionLsub) =>
% 97.95/13.24 (((binunionRsub) =>
% 97.95/13.24 (((binintersectI) =>
% 97.95/13.24 (((binintersectSubset5) =>
% 97.95/13.24 (((binintersectEL) =>
% 97.95/13.24 (((binintersectLsub) =>
% 97.95/13.24 (((binintersectSubset2) =>
% 97.95/13.24 (((binintersectSubset3) =>
% 97.95/13.24 (((binintersectER) =>
% 97.95/13.24 (((disjointsetsI1) =>
% 97.95/13.24 (((binintersectRsub) =>
% 97.95/13.24 (((binintersectSubset4) =>
% 97.95/13.24 (((binintersectSubset1) =>
% 97.95/13.24 (((bs114d) =>
% 97.95/13.24 (((setminusI) =>
% 97.95/13.24 (((setminusEL) =>
% 97.95/13.24 (((setminusER) =>
% 97.95/13.24 (((setminusSubset2) =>
% 97.95/13.24 (((setminusERneg) =>
% 97.95/13.24 (((setminusELneg) =>
% 97.95/13.24 (((setminusILneg) =>
% 97.95/13.24 (((setminusIRneg) =>
% 97.95/13.24 (((setminusLsub) =>
% 97.95/13.24 (((setminusSubset1) =>
% 97.95/13.24 (((symdiffE) =>
% 97.95/13.24 (((symdiffI1) =>
% 97.95/13.24 (((symdiffI2) =>
% 97.95/13.24 (((symdiffIneg1) =>
% 97.95/13.24 (((symdiffIneg2) =>
% 97.95/13.24 ((
% 97.95/13.24 (secondinupair) =>
% 97.95/13.24 ((
% 97.95/13.24 (setukpairIL) =>
% 97.95/13.24 ((
% 97.95/13.24 (setukpairIR) =>
% 97.95/13.24 ((
% 97.95/13.24 (kpairiskpair) =>
% 97.95/13.24 ((
% 97.95/13.24 (kpairp) =>
% 97.95/13.24 ((
% 97.95/13.24 (singletonsubset) =>
% 97.95/13.24 ((
% 97.95/13.24 (singletoninpowerset) =>
% 97.95/13.24 ((
% 97.95/13.24 (singletoninpowunion) =>
% 97.95/13.24 ((
% 97.95/13.24 (upairset2E) =>
% 97.95/13.24 ((
% 97.95/13.24 (upairsubunion) =>
% 97.95/13.24 ((
% 97.95/13.24 (upairinpowunion) =>
% 97.95/13.24 ((
% 97.95/13.24 (ubforcartprodlem1) =>
% 97.95/13.24 ((
% 97.95/13.24 (ubforcartprodlem2) =>
% 97.95/13.24 ((
% 97.95/13.24 (ubforcartprodlem3) =>
% 97.95/13.24 ((
% 97.95/13.24 (cartprodpairin) =>
% 97.95/13.24 ((
% 97.95/13.24 (cartprodmempair1) =>
% 97.95/13.24 ((
% 97.95/13.24 (cartprodmempair) =>
% 97.95/13.24 ((
% 97.95/13.24 (setunionE2) =>
% 97.95/13.24 ((
% 97.95/13.24 (setunionsingleton1) =>
% 97.95/13.24 ((
% 97.95/13.24 (setunionsingleton2) =>
% 97.95/13.24 ((
% 97.95/13.24 (setunionsingleton) =>
% 97.95/13.24 ((
% 97.95/13.24 (singletonprop) =>
% 97.95/13.24 ((
% 97.95/13.24 (ex1E1) =>
% 97.95/13.24 ((
% 97.95/13.24 (ex1I) =>
% 97.95/13.24 ((
% 97.95/13.24 (ex1I2) =>
% 97.95/13.24 ((
% 97.95/13.24 (singletonsuniq) =>
% 97.95/13.24 ((
% 97.95/13.24 (setukpairinjL1) =>
% 97.95/13.24 ((
% 97.95/13.24 (kfstsingleton) =>
% 97.95/13.24 ((
% 97.95/13.24 (theprop) =>
% 97.95/13.24 ((
% 97.95/13.24 (kfstpairEq) =>
% 97.95/13.24 ((
% 97.95/13.24 (cartprodfstin) =>
% 97.95/13.24 ((
% 97.95/13.24 (setukpairinjL2) =>
% 97.95/13.24 ((
% 97.95/13.24 (setukpairinjL) =>
% 97.95/13.24 ((
% 97.95/13.24 (setukpairinjR11) =>
% 97.95/13.24 ((
% 97.95/13.24 (setukpairinjR12) =>
% 97.95/13.24 ((
% 97.95/13.24 (setukpairinjR1) =>
% 97.95/13.24 ((
% 97.95/13.24 (upairequniteq) =>
% 97.95/13.24 ((
% 97.95/13.24 (setukpairinjR2) =>
% 97.95/13.24 ((
% 97.95/13.24 (setukpairinjR) =>
% 97.95/13.24 ((
% 97.95/13.24 (ksndsingleton) =>
% 97.95/13.24 ((
% 97.95/13.24 (ksndpairEq) =>
% 97.95/13.24 ((
% 97.95/13.24 (kpairsurjEq) =>
% 97.95/13.24 ((
% 97.95/13.24 (cartprodsndin) =>
% 97.95/13.24 ((
% 97.95/13.24 (cartprodpairmemEL) =>
% 97.95/13.24 ((
% 97.95/13.24 (cartprodpairmemER) =>
% 97.95/13.24 ((
% 97.95/13.24 (cartprodmempaircEq) =>
% 97.95/13.24 ((
% 97.95/13.24 (cartprodfstpairEq) =>
% 97.95/13.24 ((
% 97.95/13.24 (cartprodsndpairEq) =>
% 97.95/13.24 ((
% 97.95/13.24 (cartprodpairsurjEq) =>
% 97.95/13.24 ((
% 97.95/13.24 (dpsetconstrI) =>
% 97.95/13.24 ((
% 97.95/13.24 (dpsetconstrSub) =>
% 97.95/13.24 ((
% 97.95/13.24 (setOfPairsIsBReln) =>
% 97.95/13.24 ((
% 97.95/13.24 (dpsetconstrERa) =>
% 97.95/13.24 ((
% 97.95/13.24 (dpsetconstrEL1) =>
% 97.95/13.24 ((
% 97.95/13.24 (dpsetconstrEL2) =>
% 97.95/13.24 ((
% 97.95/13.24 (dpsetconstrER) =>
% 97.95/13.24 ((
% 97.95/13.24 (funcImageSingleton) =>
% 97.95/13.24 ((
% 97.95/13.24 (apProp) =>
% 97.95/13.24 ((
% 97.95/13.24 (app) =>
% 97.95/13.24 ((
% 97.95/13.24 (infuncsetfunc) =>
% 97.95/13.24 ((
% 97.95/13.24 (ap2p) =>
% 97.95/13.24 ((
% 97.95/13.24 (funcinfuncset) =>
% 97.95/13.24 ((
% 97.95/13.24 (lamProp) =>
% 97.95/13.24 ((
% 97.95/13.24 (lamp) =>
% 97.95/13.24 ((
% 97.95/13.24 (lam2p) =>
% 97.95/13.24 ((
% 97.95/13.24 (brelnall1) =>
% 97.95/13.24 ((
% 97.95/13.24 (brelnall2) =>
% 97.95/13.24 ((
% 97.95/13.24 (ex1E2) =>
% 97.95/13.24 ((
% 97.95/13.24 (funcGraphProp1) =>
% 97.95/13.24 ((
% 97.95/13.24 (funcGraphProp3) =>
% 97.95/13.24 ((
% 97.95/13.24 (funcGraphProp2) =>
% 97.95/13.24 ((
% 97.95/13.24 (funcextLem) =>
% 97.95/13.24 ((
% 97.95/13.24 (funcGraphProp4) =>
% 97.95/13.24 ((
% 97.95/13.24 (subbreln) =>
% 97.95/13.24 ((
% 97.95/13.24 (eqbreln) =>
% 97.95/13.24 ((
% 97.95/13.24 (funcext) =>
% 97.95/13.24 ((
% 97.95/13.24 (funcext2) =>
% 97.95/13.24 ((
% 97.95/13.24 (ap2apEq1) =>
% 97.95/13.24 ((
% 97.95/13.24 (ap2apEq2) =>
% 97.95/13.24 ((
% 97.95/13.24 (beta1) =>
% 97.95/13.24 ((
% 97.95/13.24 (eta1) =>
% 97.95/13.24 ((
% 97.95/13.24 (lam2lamEq) =>
% 97.95/13.24 ((
% 97.95/13.24 (beta2) =>
% 97.95/13.24 ((
% 97.95/13.24 (eta2) =>
% 97.95/13.24 ((
% 97.95/13.24 (iffalseProp1) =>
% 97.95/13.24 ((
% 97.95/13.24 (iffalseProp2) =>
% 97.95/13.24 ((
% 97.95/13.24 (iftrueProp1) =>
% 97.95/13.24 ((
% 97.95/13.24 (iftrueProp2) =>
% 97.95/13.24 ((
% 97.95/13.24 (ifSingleton) =>
% 97.95/13.24 ((
% 97.95/13.24 (ifp) =>
% 97.95/13.24 ((
% 97.95/13.24 (theeq) =>
% 97.95/13.24 ((
% 97.95/13.24 (iftrue) =>
% 97.95/13.24 ((
% 97.95/13.24 (iffalse) =>
% 97.95/13.24 ((
% 97.95/13.24 (iftrueorfalse) =>
% 97.95/13.24 ((
% 97.95/13.24 (binintersectT_lem) =>
% 97.95/13.24 ((
% 97.95/13.24 (binunionT_lem) =>
% 97.95/13.24 ((
% 97.95/13.24 (powersetT_lem) =>
% 97.95/13.24 ((
% 97.95/13.24 (setminusT_lem) =>
% 97.95/13.24 ((
% 97.95/13.24 (complementT_lem) =>
% 97.95/13.24 ((
% 97.95/13.24 (setextT) =>
% 97.95/13.24 ((
% 97.95/13.24 (subsetTI) =>
% 97.95/13.24 ((
% 97.95/13.24 (powersetTI1) =>
% 97.95/13.24 ((
% 97.95/13.24 (powersetTE1) =>
% 97.95/13.24 ((
% 97.95/13.24 (complementTI1) =>
% 97.95/13.24 ((
% 97.95/13.24 (complementTE1) =>
% 97.95/13.24 ((
% 97.95/13.24 (binintersectTELcontra) =>
% 97.95/13.24 ((
% 97.95/13.24 (binintersectTERcontra) =>
% 97.95/13.24 ((
% 97.95/13.24 (contrasubsetT) =>
% 97.95/13.24 ((
% 97.95/13.24 (contrasubsetT1) =>
% 97.95/13.24 ((
% 97.95/13.24 (contrasubsetT2) =>
% 97.95/13.24 ((
% 97.95/13.24 (contrasubsetT3) =>
% 97.95/13.24 ((
% 97.95/13.24 (doubleComplementI1) =>
% 97.95/13.24 ((
% 97.95/13.24 (doubleComplementE1) =>
% 97.95/13.24 ((
% 97.95/13.24 (doubleComplementSub1) =>
% 97.95/13.24 ((
% 97.95/13.24 (doubleComplementSub2) =>
% 97.95/13.24 ((
% 97.95/13.24 (doubleComplementEq) =>
% 97.95/13.24 ((
% 97.95/13.24 (complementTnotintersectT) =>
% 97.95/13.24 ((
% 97.95/13.24 (complementImpComplementIntersect) =>
% 97.95/13.24 ((
% 97.95/13.24 (complementSubsetComplementIntersect) =>
% 97.95/13.24 ((
% 97.95/13.24 (complementInPowersetComplementIntersect) =>
% 97.95/13.24 ((
% 97.95/13.24 (contraSubsetComplement) =>
% 97.95/13.24 ((
% 97.95/13.24 (complementTcontraSubset) =>
% 97.95/13.24 ((
% 97.95/13.24 (binunionTILcontra) =>
% 97.95/13.24 ((
% 97.95/13.24 (binunionTIRcontra) =>
% 97.95/13.24 ((
% 97.95/13.24 (inIntersectImpInUnion) =>
% 97.95/13.24 ((
% 97.95/13.24 (inIntersectImpInUnion2) =>
% 97.95/13.24 ((
% 97.95/13.24 (inIntersectImpInIntersectUnions) =>
% 97.95/13.24 ((
% 97.95/13.24 (intersectInPowersetIntersectUnions) =>
% 97.95/13.24 ((
% 97.95/13.24 (inComplementUnionImpNotIn1) =>
% 97.95/13.24 ((
% 97.95/13.24 (inComplementUnionImpInComplement1) =>
% 97.95/13.24 ((
% 97.95/13.24 (binunionTE) =>
% 97.95/13.24 ((
% 97.95/13.24 (binunionTEcontra) =>
% 97.95/13.24 ((
% 97.95/13.24 (demorgan2a1) =>
% 97.95/13.24 ((
% 97.95/13.24 (complementUnionInPowersetComplement) =>
% 97.95/13.24 ((
% 97.95/13.24 (demorgan2a2) =>
% 97.95/13.24 ((
% 97.95/13.24 (demorgan1a) =>
% 97.95/13.24 ((
% 97.95/13.24 (demorgan1b) =>
% 97.95/13.24 ((
% 97.95/13.24 (demorgan1) =>
% 97.95/13.24 ((
% 97.95/13.24 (demorgan2a) =>
% 97.95/13.24 ((
% 97.95/13.24 (demorgan2b2) =>
% 97.95/13.24 ((
% 97.95/13.24 (demorgan2b) =>
% 97.95/13.24 ((
% 97.95/13.24 (demorgan2) =>
% 97.95/13.24 ((
% 97.95/13.24 (woz13rule0) =>
% 97.95/13.24 ((
% 97.95/13.24 (woz13rule1) =>
% 97.95/13.24 ((
% 97.95/13.24 (woz13rule2) =>
% 97.95/13.24 ((
% 97.95/13.24 (woz13rule3) =>
% 97.95/13.24 ((
% 97.95/13.24 (woz13rule4) =>
% 97.95/13.24 ((
% 97.95/13.24 (woz1_1) =>
% 97.95/13.24 ((
% 97.95/13.24 (woz1_2) =>
% 97.95/13.24 ((
% 97.95/13.24 (woz1_3) =>
% 97.95/13.24 ((
% 97.95/13.24 (woz1_4) =>
% 97.95/13.24 ((
% 97.95/13.24 (woz1_5) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1all2) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1SetBreln1) =>
% 97.95/13.24 ((
% 97.95/13.24 (choice2fnsingleton) =>
% 97.95/13.24 ((
% 97.95/13.24 (setOfPairsIsBReln1) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1all1) =>
% 97.95/13.24 ((
% 97.95/13.24 (subbreln1) =>
% 97.95/13.24 ((
% 97.95/13.24 (eqbreln1) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1invprop) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1invI) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1invE) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1compprop) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1compI) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1compE) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1compEex) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1unionprop) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1unionIL) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1unionIR) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1unionI) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1unionE) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1unionEcases) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1unionCommutes) =>
% 97.95/13.24 ((
% 97.95/13.24 (woz2Ex) =>
% 97.95/13.24 ((
% 97.95/13.24 (woz2W) =>
% 97.95/13.24 ((
% 97.95/13.24 (woz2A) =>
% 97.95/13.24 ((
% 97.95/13.24 (woz2B) =>
% 97.95/13.24 ((
% 97.95/13.24 (image1Ex) =>
% 97.95/13.24 ((
% 97.95/13.24 (image1Ex1) =>
% 97.95/13.24 ((
% 97.95/13.24 (image1Equiv) =>
% 97.95/13.24 ((
% 97.95/13.24 (image1E) =>
% 97.95/13.24 ((
% 97.95/13.24 (image1I) =>
% 97.95/13.24 ((
% 97.95/13.24 (injFuncInInjFuncSet) =>
% 97.95/13.24 ((
% 97.95/13.24 (injFuncSetFuncIn) =>
% 97.95/13.24 ((
% 97.95/13.24 (injFuncSetFuncInj) =>
% 97.95/13.24 ((
% 97.95/13.24 (surjFuncSetFuncIn) =>
% 97.95/13.24 ((
% 97.95/13.24 (surjFuncSetFuncSurj) =>
% 97.95/13.24 ((
% 97.95/13.24 (leftInvIsSurj) =>
% 97.95/13.24 ((
% 97.95/13.24 (surjCantorThm) =>
% 97.95/13.24 ((
% 97.95/13.24 (foundation2) =>
% 97.95/13.24 ((
% 97.95/13.24 (notinself) =>
% 97.95/13.24 ((
% 97.95/13.24 (notinself2) =>
% 97.95/13.24 ((
% 97.95/13.24 (omegaSp) =>
% 97.95/13.24 ((
% 97.95/13.24 (omegaSclos) =>
% 97.95/13.24 ((
% 97.95/13.24 (peano0notS) =>
% 97.95/13.24 ((
% 97.95/13.24 (!!) @ (
% 97.95/13.24 (('#S') @ (
% 97.95/13.24 (
% 97.95/13.24 ('#B') @ (
% 97.95/13.24 =>) @
% 97.95/13.24 (
% 97.95/13.24 (
% 97.95/13.24 ('#C') @ in @
% 97.95/13.24 omega)))) @
% 97.95/13.24 (
% 97.95/13.24 (
% 97.95/13.24 ('#B') @ (
% 97.95/13.24 !!) @
% 97.95/13.24 (
% 97.95/13.24 (
% 97.95/13.24 ('#B') @ (
% 97.95/13.24 (
% 97.95/13.24 ('#S') @ (
% 97.95/13.24 (
% 97.95/13.24 ('#B') @ (
% 97.95/13.24 =>) @
% 97.95/13.24 (
% 97.95/13.24 (
% 97.95/13.24 ('#C') @ in @
% 97.95/13.24 omega)))))) @
% 97.95/13.24 (
% 97.95/13.24 (
% 97.95/13.24 ('#S') @ (
% 97.95/13.24 (
% 97.95/13.24 ('#B') @ (
% 97.95/13.24 '#S') @
% 97.95/13.24 (
% 97.95/13.24 (
% 97.95/13.24 ('#B') @ (
% 97.95/13.24 (
% 97.95/13.24 ('#B') @ (
% 97.95/13.24 =>))) @
% 97.95/13.24 (
% 97.95/13.24 (
% 97.95/13.24 ('#C') @ (
% 97.95/13.24 (
% 97.95/13.24 ('#B') @ (
% 97.95/13.24 '#B') @
% 97.95/13.24 (
% 97.95/13.24 (
% 97.95/13.24 ('#B') @ (
% 97.95/13.24 =) @
% 97.95/13.24 omegaS)))) @
% 97.95/13.24 omegaS)))))) @
% 97.95/13.24 (
% 97.95/13.24 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.95/13.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1115])).
% 97.95/13.24 thf(zip_derived_cl1128, plain,
% 97.95/13.24 (~ (((binunionLsub) =>
% 97.95/13.24 (((binunionRsub) =>
% 97.95/13.24 (((binintersectI) =>
% 97.95/13.24 (((binintersectSubset5) =>
% 97.95/13.24 (((binintersectEL) =>
% 97.95/13.24 (((binintersectLsub) =>
% 97.95/13.24 (((binintersectSubset2) =>
% 97.95/13.24 (((binintersectSubset3) =>
% 97.95/13.24 (((binintersectER) =>
% 97.95/13.24 (((disjointsetsI1) =>
% 97.95/13.24 (((binintersectRsub) =>
% 97.95/13.24 (((binintersectSubset4) =>
% 97.95/13.24 (((binintersectSubset1) =>
% 97.95/13.24 (((bs114d) =>
% 97.95/13.24 (((setminusI) =>
% 97.95/13.24 (((setminusEL) =>
% 97.95/13.24 (((setminusER) =>
% 97.95/13.24 (((setminusSubset2) =>
% 97.95/13.24 (((setminusERneg) =>
% 97.95/13.24 (((setminusELneg) =>
% 97.95/13.24 (((setminusILneg) =>
% 97.95/13.24 (((setminusIRneg) =>
% 97.95/13.24 (((setminusLsub) =>
% 97.95/13.24 (((setminusSubset1) =>
% 97.95/13.24 (((symdiffE) =>
% 97.95/13.24 (((symdiffI1) =>
% 97.95/13.24 (((symdiffI2) =>
% 97.95/13.24 (((symdiffIneg1) =>
% 97.95/13.24 (((symdiffIneg2) =>
% 97.95/13.24 (((secondinupair) =>
% 97.95/13.24 ((
% 97.95/13.24 (setukpairIL) =>
% 97.95/13.24 ((
% 97.95/13.24 (setukpairIR) =>
% 97.95/13.24 ((
% 97.95/13.24 (kpairiskpair) =>
% 97.95/13.24 ((
% 97.95/13.24 (kpairp) =>
% 97.95/13.24 ((
% 97.95/13.24 (singletonsubset) =>
% 97.95/13.24 ((
% 97.95/13.24 (singletoninpowerset) =>
% 97.95/13.24 ((
% 97.95/13.24 (singletoninpowunion) =>
% 97.95/13.24 ((
% 97.95/13.24 (upairset2E) =>
% 97.95/13.24 ((
% 97.95/13.24 (upairsubunion) =>
% 97.95/13.24 ((
% 97.95/13.24 (upairinpowunion) =>
% 97.95/13.24 ((
% 97.95/13.24 (ubforcartprodlem1) =>
% 97.95/13.24 ((
% 97.95/13.24 (ubforcartprodlem2) =>
% 97.95/13.24 ((
% 97.95/13.24 (ubforcartprodlem3) =>
% 97.95/13.24 ((
% 97.95/13.24 (cartprodpairin) =>
% 97.95/13.24 ((
% 97.95/13.24 (cartprodmempair1) =>
% 97.95/13.24 ((
% 97.95/13.24 (cartprodmempair) =>
% 97.95/13.24 ((
% 97.95/13.24 (setunionE2) =>
% 97.95/13.24 ((
% 97.95/13.24 (setunionsingleton1) =>
% 97.95/13.24 ((
% 97.95/13.24 (setunionsingleton2) =>
% 97.95/13.24 ((
% 97.95/13.24 (setunionsingleton) =>
% 97.95/13.24 ((
% 97.95/13.24 (singletonprop) =>
% 97.95/13.24 ((
% 97.95/13.24 (ex1E1) =>
% 97.95/13.24 ((
% 97.95/13.24 (ex1I) =>
% 97.95/13.24 ((
% 97.95/13.24 (ex1I2) =>
% 97.95/13.24 ((
% 97.95/13.24 (singletonsuniq) =>
% 97.95/13.24 ((
% 97.95/13.24 (setukpairinjL1) =>
% 97.95/13.24 ((
% 97.95/13.24 (kfstsingleton) =>
% 97.95/13.24 ((
% 97.95/13.24 (theprop) =>
% 97.95/13.24 ((
% 97.95/13.24 (kfstpairEq) =>
% 97.95/13.24 ((
% 97.95/13.24 (cartprodfstin) =>
% 97.95/13.24 ((
% 97.95/13.24 (setukpairinjL2) =>
% 97.95/13.24 ((
% 97.95/13.24 (setukpairinjL) =>
% 97.95/13.24 ((
% 97.95/13.24 (setukpairinjR11) =>
% 97.95/13.24 ((
% 97.95/13.24 (setukpairinjR12) =>
% 97.95/13.24 ((
% 97.95/13.24 (setukpairinjR1) =>
% 97.95/13.24 ((
% 97.95/13.24 (upairequniteq) =>
% 97.95/13.24 ((
% 97.95/13.24 (setukpairinjR2) =>
% 97.95/13.24 ((
% 97.95/13.24 (setukpairinjR) =>
% 97.95/13.24 ((
% 97.95/13.24 (ksndsingleton) =>
% 97.95/13.24 ((
% 97.95/13.24 (ksndpairEq) =>
% 97.95/13.24 ((
% 97.95/13.24 (kpairsurjEq) =>
% 97.95/13.24 ((
% 97.95/13.24 (cartprodsndin) =>
% 97.95/13.24 ((
% 97.95/13.24 (cartprodpairmemEL) =>
% 97.95/13.24 ((
% 97.95/13.24 (cartprodpairmemER) =>
% 97.95/13.24 ((
% 97.95/13.24 (cartprodmempaircEq) =>
% 97.95/13.24 ((
% 97.95/13.24 (cartprodfstpairEq) =>
% 97.95/13.24 ((
% 97.95/13.24 (cartprodsndpairEq) =>
% 97.95/13.24 ((
% 97.95/13.24 (cartprodpairsurjEq) =>
% 97.95/13.24 ((
% 97.95/13.24 (dpsetconstrI) =>
% 97.95/13.24 ((
% 97.95/13.24 (dpsetconstrSub) =>
% 97.95/13.24 ((
% 97.95/13.24 (setOfPairsIsBReln) =>
% 97.95/13.24 ((
% 97.95/13.24 (dpsetconstrERa) =>
% 97.95/13.24 ((
% 97.95/13.24 (dpsetconstrEL1) =>
% 97.95/13.24 ((
% 97.95/13.24 (dpsetconstrEL2) =>
% 97.95/13.24 ((
% 97.95/13.24 (dpsetconstrER) =>
% 97.95/13.24 ((
% 97.95/13.24 (funcImageSingleton) =>
% 97.95/13.24 ((
% 97.95/13.24 (apProp) =>
% 97.95/13.24 ((
% 97.95/13.24 (app) =>
% 97.95/13.24 ((
% 97.95/13.24 (infuncsetfunc) =>
% 97.95/13.24 ((
% 97.95/13.24 (ap2p) =>
% 97.95/13.24 ((
% 97.95/13.24 (funcinfuncset) =>
% 97.95/13.24 ((
% 97.95/13.24 (lamProp) =>
% 97.95/13.24 ((
% 97.95/13.24 (lamp) =>
% 97.95/13.24 ((
% 97.95/13.24 (lam2p) =>
% 97.95/13.24 ((
% 97.95/13.24 (brelnall1) =>
% 97.95/13.24 ((
% 97.95/13.24 (brelnall2) =>
% 97.95/13.24 ((
% 97.95/13.24 (ex1E2) =>
% 97.95/13.24 ((
% 97.95/13.24 (funcGraphProp1) =>
% 97.95/13.24 ((
% 97.95/13.24 (funcGraphProp3) =>
% 97.95/13.24 ((
% 97.95/13.24 (funcGraphProp2) =>
% 97.95/13.24 ((
% 97.95/13.24 (funcextLem) =>
% 97.95/13.24 ((
% 97.95/13.24 (funcGraphProp4) =>
% 97.95/13.24 ((
% 97.95/13.24 (subbreln) =>
% 97.95/13.24 ((
% 97.95/13.24 (eqbreln) =>
% 97.95/13.24 ((
% 97.95/13.24 (funcext) =>
% 97.95/13.24 ((
% 97.95/13.24 (funcext2) =>
% 97.95/13.24 ((
% 97.95/13.24 (ap2apEq1) =>
% 97.95/13.24 ((
% 97.95/13.24 (ap2apEq2) =>
% 97.95/13.24 ((
% 97.95/13.24 (beta1) =>
% 97.95/13.24 ((
% 97.95/13.24 (eta1) =>
% 97.95/13.24 ((
% 97.95/13.24 (lam2lamEq) =>
% 97.95/13.24 ((
% 97.95/13.24 (beta2) =>
% 97.95/13.24 ((
% 97.95/13.24 (eta2) =>
% 97.95/13.24 ((
% 97.95/13.24 (iffalseProp1) =>
% 97.95/13.24 ((
% 97.95/13.24 (iffalseProp2) =>
% 97.95/13.24 ((
% 97.95/13.24 (iftrueProp1) =>
% 97.95/13.24 ((
% 97.95/13.24 (iftrueProp2) =>
% 97.95/13.24 ((
% 97.95/13.24 (ifSingleton) =>
% 97.95/13.24 ((
% 97.95/13.24 (ifp) =>
% 97.95/13.24 ((
% 97.95/13.24 (theeq) =>
% 97.95/13.24 ((
% 97.95/13.24 (iftrue) =>
% 97.95/13.24 ((
% 97.95/13.24 (iffalse) =>
% 97.95/13.24 ((
% 97.95/13.24 (iftrueorfalse) =>
% 97.95/13.24 ((
% 97.95/13.24 (binintersectT_lem) =>
% 97.95/13.24 ((
% 97.95/13.24 (binunionT_lem) =>
% 97.95/13.24 ((
% 97.95/13.24 (powersetT_lem) =>
% 97.95/13.24 ((
% 97.95/13.24 (setminusT_lem) =>
% 97.95/13.24 ((
% 97.95/13.24 (complementT_lem) =>
% 97.95/13.24 ((
% 97.95/13.24 (setextT) =>
% 97.95/13.24 ((
% 97.95/13.24 (subsetTI) =>
% 97.95/13.24 ((
% 97.95/13.24 (powersetTI1) =>
% 97.95/13.24 ((
% 97.95/13.24 (powersetTE1) =>
% 97.95/13.24 ((
% 97.95/13.24 (complementTI1) =>
% 97.95/13.24 ((
% 97.95/13.24 (complementTE1) =>
% 97.95/13.24 ((
% 97.95/13.24 (binintersectTELcontra) =>
% 97.95/13.24 ((
% 97.95/13.24 (binintersectTERcontra) =>
% 97.95/13.24 ((
% 97.95/13.24 (contrasubsetT) =>
% 97.95/13.24 ((
% 97.95/13.24 (contrasubsetT1) =>
% 97.95/13.24 ((
% 97.95/13.24 (contrasubsetT2) =>
% 97.95/13.24 ((
% 97.95/13.24 (contrasubsetT3) =>
% 97.95/13.24 ((
% 97.95/13.24 (doubleComplementI1) =>
% 97.95/13.24 ((
% 97.95/13.24 (doubleComplementE1) =>
% 97.95/13.24 ((
% 97.95/13.24 (doubleComplementSub1) =>
% 97.95/13.24 ((
% 97.95/13.24 (doubleComplementSub2) =>
% 97.95/13.24 ((
% 97.95/13.24 (doubleComplementEq) =>
% 97.95/13.24 ((
% 97.95/13.24 (complementTnotintersectT) =>
% 97.95/13.24 ((
% 97.95/13.24 (complementImpComplementIntersect) =>
% 97.95/13.24 ((
% 97.95/13.24 (complementSubsetComplementIntersect) =>
% 97.95/13.24 ((
% 97.95/13.24 (complementInPowersetComplementIntersect) =>
% 97.95/13.24 ((
% 97.95/13.24 (contraSubsetComplement) =>
% 97.95/13.24 ((
% 97.95/13.24 (complementTcontraSubset) =>
% 97.95/13.24 ((
% 97.95/13.24 (binunionTILcontra) =>
% 97.95/13.24 ((
% 97.95/13.24 (binunionTIRcontra) =>
% 97.95/13.24 ((
% 97.95/13.24 (inIntersectImpInUnion) =>
% 97.95/13.24 ((
% 97.95/13.24 (inIntersectImpInUnion2) =>
% 97.95/13.24 ((
% 97.95/13.24 (inIntersectImpInIntersectUnions) =>
% 97.95/13.24 ((
% 97.95/13.24 (intersectInPowersetIntersectUnions) =>
% 97.95/13.24 ((
% 97.95/13.24 (inComplementUnionImpNotIn1) =>
% 97.95/13.24 ((
% 97.95/13.24 (inComplementUnionImpInComplement1) =>
% 97.95/13.24 ((
% 97.95/13.24 (binunionTE) =>
% 97.95/13.24 ((
% 97.95/13.24 (binunionTEcontra) =>
% 97.95/13.24 ((
% 97.95/13.24 (demorgan2a1) =>
% 97.95/13.24 ((
% 97.95/13.24 (complementUnionInPowersetComplement) =>
% 97.95/13.24 ((
% 97.95/13.24 (demorgan2a2) =>
% 97.95/13.24 ((
% 97.95/13.24 (demorgan1a) =>
% 97.95/13.24 ((
% 97.95/13.24 (demorgan1b) =>
% 97.95/13.24 ((
% 97.95/13.24 (demorgan1) =>
% 97.95/13.24 ((
% 97.95/13.24 (demorgan2a) =>
% 97.95/13.24 ((
% 97.95/13.24 (demorgan2b2) =>
% 97.95/13.24 ((
% 97.95/13.24 (demorgan2b) =>
% 97.95/13.24 ((
% 97.95/13.24 (demorgan2) =>
% 97.95/13.24 ((
% 97.95/13.24 (woz13rule0) =>
% 97.95/13.24 ((
% 97.95/13.24 (woz13rule1) =>
% 97.95/13.24 ((
% 97.95/13.24 (woz13rule2) =>
% 97.95/13.24 ((
% 97.95/13.24 (woz13rule3) =>
% 97.95/13.24 ((
% 97.95/13.24 (woz13rule4) =>
% 97.95/13.24 ((
% 97.95/13.24 (woz1_1) =>
% 97.95/13.24 ((
% 97.95/13.24 (woz1_2) =>
% 97.95/13.24 ((
% 97.95/13.24 (woz1_3) =>
% 97.95/13.24 ((
% 97.95/13.24 (woz1_4) =>
% 97.95/13.24 ((
% 97.95/13.24 (woz1_5) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1all2) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1SetBreln1) =>
% 97.95/13.24 ((
% 97.95/13.24 (choice2fnsingleton) =>
% 97.95/13.24 ((
% 97.95/13.24 (setOfPairsIsBReln1) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1all1) =>
% 97.95/13.24 ((
% 97.95/13.24 (subbreln1) =>
% 97.95/13.24 ((
% 97.95/13.24 (eqbreln1) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1invprop) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1invI) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1invE) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1compprop) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1compI) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1compE) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1compEex) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1unionprop) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1unionIL) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1unionIR) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1unionI) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1unionE) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1unionEcases) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1unionCommutes) =>
% 97.95/13.24 ((
% 97.95/13.24 (woz2Ex) =>
% 97.95/13.24 ((
% 97.95/13.24 (woz2W) =>
% 97.95/13.24 ((
% 97.95/13.24 (woz2A) =>
% 97.95/13.24 ((
% 97.95/13.24 (woz2B) =>
% 97.95/13.24 ((
% 97.95/13.24 (image1Ex) =>
% 97.95/13.24 ((
% 97.95/13.24 (image1Ex1) =>
% 97.95/13.24 ((
% 97.95/13.24 (image1Equiv) =>
% 97.95/13.24 ((
% 97.95/13.24 (image1E) =>
% 97.95/13.24 ((
% 97.95/13.24 (image1I) =>
% 97.95/13.24 ((
% 97.95/13.24 (injFuncInInjFuncSet) =>
% 97.95/13.24 ((
% 97.95/13.24 (injFuncSetFuncIn) =>
% 97.95/13.24 ((
% 97.95/13.24 (injFuncSetFuncInj) =>
% 97.95/13.24 ((
% 97.95/13.24 (surjFuncSetFuncIn) =>
% 97.95/13.24 ((
% 97.95/13.24 (surjFuncSetFuncSurj) =>
% 97.95/13.24 ((
% 97.95/13.24 (leftInvIsSurj) =>
% 97.95/13.24 ((
% 97.95/13.24 (surjCantorThm) =>
% 97.95/13.24 ((
% 97.95/13.24 (foundation2) =>
% 97.95/13.24 ((
% 97.95/13.24 (notinself) =>
% 97.95/13.24 ((
% 97.95/13.24 (notinself2) =>
% 97.95/13.24 ((
% 97.95/13.24 (omegaSp) =>
% 97.95/13.24 ((
% 97.95/13.24 (omegaSclos) =>
% 97.95/13.24 ((
% 97.95/13.24 (peano0notS) =>
% 97.95/13.24 ((
% 97.95/13.24 (!!) @ (
% 97.95/13.24 (('#S') @ (
% 97.95/13.24 (
% 97.95/13.24 ('#B') @ (
% 97.95/13.24 =>) @
% 97.95/13.24 (
% 97.95/13.24 (
% 97.95/13.24 ('#C') @ in @
% 97.95/13.24 omega)))) @
% 97.95/13.24 (
% 97.95/13.24 (
% 97.95/13.24 ('#B') @ (
% 97.95/13.24 !!) @
% 97.95/13.24 (
% 97.95/13.24 (
% 97.95/13.24 ('#B') @ (
% 97.95/13.24 (
% 97.95/13.24 ('#S') @ (
% 97.95/13.24 (
% 97.95/13.24 ('#B') @ (
% 97.95/13.24 =>) @
% 97.95/13.24 (
% 97.95/13.24 (
% 97.95/13.24 ('#C') @ in @
% 97.95/13.24 omega)))))) @
% 97.95/13.24 (
% 97.95/13.24 (
% 97.95/13.24 ('#S') @ (
% 97.95/13.24 (
% 97.95/13.24 ('#B') @ (
% 97.95/13.24 '#S') @
% 97.95/13.24 (
% 97.95/13.24 (
% 97.95/13.24 ('#B') @ (
% 97.95/13.24 (
% 97.95/13.24 ('#B') @ (
% 97.95/13.24 =>))) @
% 97.95/13.24 (
% 97.95/13.24 (
% 97.95/13.24 ('#C') @ (
% 97.95/13.24 (
% 97.95/13.24 ('#B') @ (
% 97.95/13.24 '#B') @
% 97.95/13.24 (
% 97.95/13.24 (
% 97.95/13.24 ('#B') @ (
% 97.95/13.24 =) @
% 97.95/13.24 omegaS)))) @
% 97.95/13.24 omegaS)))))) @
% 97.95/13.24 (
% 97.95/13.24 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.95/13.24 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1121])).
% 97.95/13.24 thf(zip_derived_cl1135, plain,
% 97.95/13.24 (~ (((binunionRsub) =>
% 97.95/13.24 (((binintersectI) =>
% 97.95/13.24 (((binintersectSubset5) =>
% 97.95/13.24 (((binintersectEL) =>
% 97.95/13.24 (((binintersectLsub) =>
% 97.95/13.24 (((binintersectSubset2) =>
% 97.95/13.24 (((binintersectSubset3) =>
% 97.95/13.24 (((binintersectER) =>
% 97.95/13.24 (((disjointsetsI1) =>
% 97.95/13.24 (((binintersectRsub) =>
% 97.95/13.24 (((binintersectSubset4) =>
% 97.95/13.24 (((binintersectSubset1) =>
% 97.95/13.24 (((bs114d) =>
% 97.95/13.24 (((setminusI) =>
% 97.95/13.24 (((setminusEL) =>
% 97.95/13.24 (((setminusER) =>
% 97.95/13.24 (((setminusSubset2) =>
% 97.95/13.24 (((setminusERneg) =>
% 97.95/13.24 (((setminusELneg) =>
% 97.95/13.24 (((setminusILneg) =>
% 97.95/13.24 (((setminusIRneg) =>
% 97.95/13.24 (((setminusLsub) =>
% 97.95/13.24 (((setminusSubset1) =>
% 97.95/13.24 (((symdiffE) =>
% 97.95/13.24 (((symdiffI1) =>
% 97.95/13.24 (((symdiffI2) =>
% 97.95/13.24 (((symdiffIneg1) =>
% 97.95/13.24 (((symdiffIneg2) =>
% 97.95/13.24 (((secondinupair) =>
% 97.95/13.24 (((setukpairIL) =>
% 97.95/13.24 ((
% 97.95/13.24 (setukpairIR) =>
% 97.95/13.24 ((
% 97.95/13.24 (kpairiskpair) =>
% 97.95/13.24 ((
% 97.95/13.24 (kpairp) =>
% 97.95/13.24 ((
% 97.95/13.24 (singletonsubset) =>
% 97.95/13.24 ((
% 97.95/13.24 (singletoninpowerset) =>
% 97.95/13.24 ((
% 97.95/13.24 (singletoninpowunion) =>
% 97.95/13.24 ((
% 97.95/13.24 (upairset2E) =>
% 97.95/13.24 ((
% 97.95/13.24 (upairsubunion) =>
% 97.95/13.24 ((
% 97.95/13.24 (upairinpowunion) =>
% 97.95/13.24 ((
% 97.95/13.24 (ubforcartprodlem1) =>
% 97.95/13.24 ((
% 97.95/13.24 (ubforcartprodlem2) =>
% 97.95/13.24 ((
% 97.95/13.24 (ubforcartprodlem3) =>
% 97.95/13.24 ((
% 97.95/13.24 (cartprodpairin) =>
% 97.95/13.24 ((
% 97.95/13.24 (cartprodmempair1) =>
% 97.95/13.24 ((
% 97.95/13.24 (cartprodmempair) =>
% 97.95/13.24 ((
% 97.95/13.24 (setunionE2) =>
% 97.95/13.24 ((
% 97.95/13.24 (setunionsingleton1) =>
% 97.95/13.24 ((
% 97.95/13.24 (setunionsingleton2) =>
% 97.95/13.24 ((
% 97.95/13.24 (setunionsingleton) =>
% 97.95/13.24 ((
% 97.95/13.24 (singletonprop) =>
% 97.95/13.24 ((
% 97.95/13.24 (ex1E1) =>
% 97.95/13.24 ((
% 97.95/13.24 (ex1I) =>
% 97.95/13.24 ((
% 97.95/13.24 (ex1I2) =>
% 97.95/13.24 ((
% 97.95/13.24 (singletonsuniq) =>
% 97.95/13.24 ((
% 97.95/13.24 (setukpairinjL1) =>
% 97.95/13.24 ((
% 97.95/13.24 (kfstsingleton) =>
% 97.95/13.24 ((
% 97.95/13.24 (theprop) =>
% 97.95/13.24 ((
% 97.95/13.24 (kfstpairEq) =>
% 97.95/13.24 ((
% 97.95/13.24 (cartprodfstin) =>
% 97.95/13.24 ((
% 97.95/13.24 (setukpairinjL2) =>
% 97.95/13.24 ((
% 97.95/13.24 (setukpairinjL) =>
% 97.95/13.24 ((
% 97.95/13.24 (setukpairinjR11) =>
% 97.95/13.24 ((
% 97.95/13.24 (setukpairinjR12) =>
% 97.95/13.24 ((
% 97.95/13.24 (setukpairinjR1) =>
% 97.95/13.24 ((
% 97.95/13.24 (upairequniteq) =>
% 97.95/13.24 ((
% 97.95/13.24 (setukpairinjR2) =>
% 97.95/13.24 ((
% 97.95/13.24 (setukpairinjR) =>
% 97.95/13.24 ((
% 97.95/13.24 (ksndsingleton) =>
% 97.95/13.24 ((
% 97.95/13.24 (ksndpairEq) =>
% 97.95/13.24 ((
% 97.95/13.24 (kpairsurjEq) =>
% 97.95/13.24 ((
% 97.95/13.24 (cartprodsndin) =>
% 97.95/13.24 ((
% 97.95/13.24 (cartprodpairmemEL) =>
% 97.95/13.24 ((
% 97.95/13.24 (cartprodpairmemER) =>
% 97.95/13.24 ((
% 97.95/13.24 (cartprodmempaircEq) =>
% 97.95/13.24 ((
% 97.95/13.24 (cartprodfstpairEq) =>
% 97.95/13.24 ((
% 97.95/13.24 (cartprodsndpairEq) =>
% 97.95/13.24 ((
% 97.95/13.24 (cartprodpairsurjEq) =>
% 97.95/13.24 ((
% 97.95/13.24 (dpsetconstrI) =>
% 97.95/13.24 ((
% 97.95/13.24 (dpsetconstrSub) =>
% 97.95/13.24 ((
% 97.95/13.24 (setOfPairsIsBReln) =>
% 97.95/13.24 ((
% 97.95/13.24 (dpsetconstrERa) =>
% 97.95/13.24 ((
% 97.95/13.24 (dpsetconstrEL1) =>
% 97.95/13.24 ((
% 97.95/13.24 (dpsetconstrEL2) =>
% 97.95/13.24 ((
% 97.95/13.24 (dpsetconstrER) =>
% 97.95/13.24 ((
% 97.95/13.24 (funcImageSingleton) =>
% 97.95/13.24 ((
% 97.95/13.24 (apProp) =>
% 97.95/13.24 ((
% 97.95/13.24 (app) =>
% 97.95/13.24 ((
% 97.95/13.24 (infuncsetfunc) =>
% 97.95/13.24 ((
% 97.95/13.24 (ap2p) =>
% 97.95/13.24 ((
% 97.95/13.24 (funcinfuncset) =>
% 97.95/13.24 ((
% 97.95/13.24 (lamProp) =>
% 97.95/13.24 ((
% 97.95/13.24 (lamp) =>
% 97.95/13.24 ((
% 97.95/13.24 (lam2p) =>
% 97.95/13.24 ((
% 97.95/13.24 (brelnall1) =>
% 97.95/13.24 ((
% 97.95/13.24 (brelnall2) =>
% 97.95/13.24 ((
% 97.95/13.24 (ex1E2) =>
% 97.95/13.24 ((
% 97.95/13.24 (funcGraphProp1) =>
% 97.95/13.24 ((
% 97.95/13.24 (funcGraphProp3) =>
% 97.95/13.24 ((
% 97.95/13.24 (funcGraphProp2) =>
% 97.95/13.24 ((
% 97.95/13.24 (funcextLem) =>
% 97.95/13.24 ((
% 97.95/13.24 (funcGraphProp4) =>
% 97.95/13.24 ((
% 97.95/13.24 (subbreln) =>
% 97.95/13.24 ((
% 97.95/13.24 (eqbreln) =>
% 97.95/13.24 ((
% 97.95/13.24 (funcext) =>
% 97.95/13.24 ((
% 97.95/13.24 (funcext2) =>
% 97.95/13.24 ((
% 97.95/13.24 (ap2apEq1) =>
% 97.95/13.24 ((
% 97.95/13.24 (ap2apEq2) =>
% 97.95/13.24 ((
% 97.95/13.24 (beta1) =>
% 97.95/13.24 ((
% 97.95/13.24 (eta1) =>
% 97.95/13.24 ((
% 97.95/13.24 (lam2lamEq) =>
% 97.95/13.24 ((
% 97.95/13.24 (beta2) =>
% 97.95/13.24 ((
% 97.95/13.24 (eta2) =>
% 97.95/13.24 ((
% 97.95/13.24 (iffalseProp1) =>
% 97.95/13.24 ((
% 97.95/13.24 (iffalseProp2) =>
% 97.95/13.24 ((
% 97.95/13.24 (iftrueProp1) =>
% 97.95/13.24 ((
% 97.95/13.24 (iftrueProp2) =>
% 97.95/13.24 ((
% 97.95/13.24 (ifSingleton) =>
% 97.95/13.24 ((
% 97.95/13.24 (ifp) =>
% 97.95/13.24 ((
% 97.95/13.24 (theeq) =>
% 97.95/13.24 ((
% 97.95/13.24 (iftrue) =>
% 97.95/13.24 ((
% 97.95/13.24 (iffalse) =>
% 97.95/13.24 ((
% 97.95/13.24 (iftrueorfalse) =>
% 97.95/13.24 ((
% 97.95/13.24 (binintersectT_lem) =>
% 97.95/13.24 ((
% 97.95/13.24 (binunionT_lem) =>
% 97.95/13.24 ((
% 97.95/13.24 (powersetT_lem) =>
% 97.95/13.24 ((
% 97.95/13.24 (setminusT_lem) =>
% 97.95/13.24 ((
% 97.95/13.24 (complementT_lem) =>
% 97.95/13.24 ((
% 97.95/13.24 (setextT) =>
% 97.95/13.24 ((
% 97.95/13.24 (subsetTI) =>
% 97.95/13.24 ((
% 97.95/13.24 (powersetTI1) =>
% 97.95/13.24 ((
% 97.95/13.24 (powersetTE1) =>
% 97.95/13.24 ((
% 97.95/13.24 (complementTI1) =>
% 97.95/13.24 ((
% 97.95/13.24 (complementTE1) =>
% 97.95/13.24 ((
% 97.95/13.24 (binintersectTELcontra) =>
% 97.95/13.24 ((
% 97.95/13.24 (binintersectTERcontra) =>
% 97.95/13.24 ((
% 97.95/13.24 (contrasubsetT) =>
% 97.95/13.24 ((
% 97.95/13.24 (contrasubsetT1) =>
% 97.95/13.24 ((
% 97.95/13.24 (contrasubsetT2) =>
% 97.95/13.24 ((
% 97.95/13.24 (contrasubsetT3) =>
% 97.95/13.24 ((
% 97.95/13.24 (doubleComplementI1) =>
% 97.95/13.24 ((
% 97.95/13.24 (doubleComplementE1) =>
% 97.95/13.24 ((
% 97.95/13.24 (doubleComplementSub1) =>
% 97.95/13.24 ((
% 97.95/13.24 (doubleComplementSub2) =>
% 97.95/13.24 ((
% 97.95/13.24 (doubleComplementEq) =>
% 97.95/13.24 ((
% 97.95/13.24 (complementTnotintersectT) =>
% 97.95/13.24 ((
% 97.95/13.24 (complementImpComplementIntersect) =>
% 97.95/13.24 ((
% 97.95/13.24 (complementSubsetComplementIntersect) =>
% 97.95/13.24 ((
% 97.95/13.24 (complementInPowersetComplementIntersect) =>
% 97.95/13.24 ((
% 97.95/13.24 (contraSubsetComplement) =>
% 97.95/13.24 ((
% 97.95/13.24 (complementTcontraSubset) =>
% 97.95/13.24 ((
% 97.95/13.24 (binunionTILcontra) =>
% 97.95/13.24 ((
% 97.95/13.24 (binunionTIRcontra) =>
% 97.95/13.24 ((
% 97.95/13.24 (inIntersectImpInUnion) =>
% 97.95/13.24 ((
% 97.95/13.24 (inIntersectImpInUnion2) =>
% 97.95/13.24 ((
% 97.95/13.24 (inIntersectImpInIntersectUnions) =>
% 97.95/13.24 ((
% 97.95/13.24 (intersectInPowersetIntersectUnions) =>
% 97.95/13.24 ((
% 97.95/13.24 (inComplementUnionImpNotIn1) =>
% 97.95/13.24 ((
% 97.95/13.24 (inComplementUnionImpInComplement1) =>
% 97.95/13.24 ((
% 97.95/13.24 (binunionTE) =>
% 97.95/13.24 ((
% 97.95/13.24 (binunionTEcontra) =>
% 97.95/13.24 ((
% 97.95/13.24 (demorgan2a1) =>
% 97.95/13.24 ((
% 97.95/13.24 (complementUnionInPowersetComplement) =>
% 97.95/13.24 ((
% 97.95/13.24 (demorgan2a2) =>
% 97.95/13.24 ((
% 97.95/13.24 (demorgan1a) =>
% 97.95/13.24 ((
% 97.95/13.24 (demorgan1b) =>
% 97.95/13.24 ((
% 97.95/13.24 (demorgan1) =>
% 97.95/13.24 ((
% 97.95/13.24 (demorgan2a) =>
% 97.95/13.24 ((
% 97.95/13.24 (demorgan2b2) =>
% 97.95/13.24 ((
% 97.95/13.24 (demorgan2b) =>
% 97.95/13.24 ((
% 97.95/13.24 (demorgan2) =>
% 97.95/13.24 ((
% 97.95/13.24 (woz13rule0) =>
% 97.95/13.24 ((
% 97.95/13.24 (woz13rule1) =>
% 97.95/13.24 ((
% 97.95/13.24 (woz13rule2) =>
% 97.95/13.24 ((
% 97.95/13.24 (woz13rule3) =>
% 97.95/13.24 ((
% 97.95/13.24 (woz13rule4) =>
% 97.95/13.24 ((
% 97.95/13.24 (woz1_1) =>
% 97.95/13.24 ((
% 97.95/13.24 (woz1_2) =>
% 97.95/13.24 ((
% 97.95/13.24 (woz1_3) =>
% 97.95/13.24 ((
% 97.95/13.24 (woz1_4) =>
% 97.95/13.24 ((
% 97.95/13.24 (woz1_5) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1all2) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1SetBreln1) =>
% 97.95/13.24 ((
% 97.95/13.24 (choice2fnsingleton) =>
% 97.95/13.24 ((
% 97.95/13.24 (setOfPairsIsBReln1) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1all1) =>
% 97.95/13.24 ((
% 97.95/13.24 (subbreln1) =>
% 97.95/13.24 ((
% 97.95/13.24 (eqbreln1) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1invprop) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1invI) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1invE) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1compprop) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1compI) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1compE) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1compEex) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1unionprop) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1unionIL) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1unionIR) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1unionI) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1unionE) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1unionEcases) =>
% 97.95/13.24 ((
% 97.95/13.24 (breln1unionCommutes) =>
% 97.95/13.24 ((
% 97.95/13.24 (woz2Ex) =>
% 97.95/13.24 ((
% 97.95/13.24 (woz2W) =>
% 97.95/13.24 ((
% 97.95/13.24 (woz2A) =>
% 97.95/13.24 ((
% 97.95/13.24 (woz2B) =>
% 97.95/13.24 ((
% 97.95/13.24 (image1Ex) =>
% 97.95/13.24 ((
% 97.95/13.24 (image1Ex1) =>
% 97.95/13.24 ((
% 97.95/13.24 (image1Equiv) =>
% 97.95/13.24 ((
% 97.95/13.24 (image1E) =>
% 97.95/13.24 ((
% 97.95/13.24 (image1I) =>
% 97.95/13.24 ((
% 97.95/13.24 (injFuncInInjFuncSet) =>
% 97.95/13.24 ((
% 97.95/13.24 (injFuncSetFuncIn) =>
% 97.95/13.24 ((
% 97.95/13.24 (injFuncSetFuncInj) =>
% 97.95/13.24 ((
% 97.95/13.24 (surjFuncSetFuncIn) =>
% 97.95/13.24 ((
% 97.95/13.24 (surjFuncSetFuncSurj) =>
% 97.95/13.24 ((
% 97.95/13.24 (leftInvIsSurj) =>
% 97.95/13.24 ((
% 97.95/13.24 (surjCantorThm) =>
% 97.95/13.24 ((
% 97.95/13.24 (foundation2) =>
% 97.95/13.24 ((
% 97.95/13.24 (notinself) =>
% 97.95/13.24 ((
% 97.95/13.24 (notinself2) =>
% 97.95/13.24 ((
% 97.95/13.24 (omegaSp) =>
% 97.95/13.24 ((
% 97.95/13.24 (omegaSclos) =>
% 97.95/13.24 ((
% 97.95/13.24 (peano0notS) =>
% 97.95/13.24 ((
% 97.95/13.24 (!!) @ (
% 97.95/13.24 (('#S') @ (
% 97.95/13.24 (
% 97.95/13.24 ('#B') @ (
% 97.95/13.24 =>) @
% 97.95/13.24 (
% 97.95/13.24 (
% 97.95/13.24 ('#C') @ in @
% 97.95/13.24 omega)))) @
% 97.95/13.24 (
% 97.95/13.24 (
% 97.95/13.24 ('#B') @ (
% 97.95/13.24 !!) @
% 97.95/13.24 (
% 97.95/13.24 (
% 97.95/13.24 ('#B') @ (
% 97.95/13.24 (
% 97.95/13.24 ('#S') @ (
% 97.95/13.24 (
% 97.95/13.24 ('#B') @ (
% 97.95/13.24 =>) @
% 97.95/13.24 (
% 97.95/13.24 (
% 97.95/13.24 ('#C') @ in @
% 97.95/13.24 omega)))))) @
% 97.95/13.24 (
% 97.95/13.24 (
% 97.95/13.24 ('#S') @ (
% 97.95/13.24 (
% 97.95/13.24 ('#B') @ (
% 97.95/13.24 '#S') @
% 97.95/13.24 (
% 97.95/13.24 (
% 97.95/13.24 ('#B') @ (
% 97.95/13.24 (
% 97.95/13.24 ('#B') @ (
% 97.95/13.24 =>))) @
% 97.95/13.24 (
% 97.95/13.24 (
% 97.95/13.24 ('#C') @ (
% 97.95/13.24 (
% 97.95/13.24 ('#B') @ (
% 97.95/13.25 '#B') @
% 97.95/13.25 (
% 97.95/13.25 (
% 97.95/13.25 ('#B') @ (
% 97.95/13.25 =) @
% 97.95/13.25 omegaS)))) @
% 97.95/13.25 omegaS)))))) @
% 97.95/13.25 (
% 97.95/13.25 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.95/13.25 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1128])).
% 97.95/13.25 thf(zip_derived_cl1142, plain,
% 97.95/13.25 (~ (((binintersectI) =>
% 97.95/13.25 (((binintersectSubset5) =>
% 97.95/13.25 (((binintersectEL) =>
% 97.95/13.25 (((binintersectLsub) =>
% 97.95/13.25 (((binintersectSubset2) =>
% 97.95/13.25 (((binintersectSubset3) =>
% 97.95/13.25 (((binintersectER) =>
% 97.95/13.25 (((disjointsetsI1) =>
% 97.95/13.25 (((binintersectRsub) =>
% 97.95/13.25 (((binintersectSubset4) =>
% 97.95/13.25 (((binintersectSubset1) =>
% 97.95/13.25 (((bs114d) =>
% 97.95/13.25 (((setminusI) =>
% 97.95/13.25 (((setminusEL) =>
% 97.95/13.25 (((setminusER) =>
% 97.95/13.25 (((setminusSubset2) =>
% 97.95/13.25 (((setminusERneg) =>
% 97.95/13.25 (((setminusELneg) =>
% 97.95/13.25 (((setminusILneg) =>
% 97.95/13.25 (((setminusIRneg) =>
% 97.95/13.25 (((setminusLsub) =>
% 97.95/13.25 (((setminusSubset1) =>
% 97.95/13.25 (((symdiffE) =>
% 97.95/13.25 (((symdiffI1) =>
% 97.95/13.25 (((symdiffI2) =>
% 97.95/13.25 (((symdiffIneg1) =>
% 97.95/13.25 (((symdiffIneg2) =>
% 97.95/13.25 (((secondinupair) =>
% 97.95/13.25 (((setukpairIL) =>
% 97.95/13.25 (((setukpairIR) =>
% 97.95/13.25 ((
% 97.95/13.25 (kpairiskpair) =>
% 97.95/13.25 ((
% 97.95/13.25 (kpairp) =>
% 97.95/13.25 ((
% 97.95/13.25 (singletonsubset) =>
% 97.95/13.25 ((
% 97.95/13.25 (singletoninpowerset) =>
% 97.95/13.25 ((
% 97.95/13.25 (singletoninpowunion) =>
% 97.95/13.25 ((
% 97.95/13.25 (upairset2E) =>
% 97.95/13.25 ((
% 97.95/13.25 (upairsubunion) =>
% 97.95/13.25 ((
% 97.95/13.25 (upairinpowunion) =>
% 97.95/13.25 ((
% 97.95/13.25 (ubforcartprodlem1) =>
% 97.95/13.25 ((
% 97.95/13.25 (ubforcartprodlem2) =>
% 97.95/13.25 ((
% 97.95/13.25 (ubforcartprodlem3) =>
% 97.95/13.25 ((
% 97.95/13.25 (cartprodpairin) =>
% 97.95/13.25 ((
% 97.95/13.25 (cartprodmempair1) =>
% 97.95/13.25 ((
% 97.95/13.25 (cartprodmempair) =>
% 97.95/13.25 ((
% 97.95/13.25 (setunionE2) =>
% 97.95/13.25 ((
% 97.95/13.25 (setunionsingleton1) =>
% 97.95/13.25 ((
% 97.95/13.25 (setunionsingleton2) =>
% 97.95/13.25 ((
% 97.95/13.25 (setunionsingleton) =>
% 97.95/13.25 ((
% 97.95/13.25 (singletonprop) =>
% 97.95/13.25 ((
% 97.95/13.25 (ex1E1) =>
% 97.95/13.25 ((
% 97.95/13.25 (ex1I) =>
% 97.95/13.25 ((
% 97.95/13.25 (ex1I2) =>
% 97.95/13.25 ((
% 97.95/13.25 (singletonsuniq) =>
% 97.95/13.25 ((
% 97.95/13.25 (setukpairinjL1) =>
% 97.95/13.25 ((
% 97.95/13.25 (kfstsingleton) =>
% 97.95/13.25 ((
% 97.95/13.25 (theprop) =>
% 97.95/13.25 ((
% 97.95/13.25 (kfstpairEq) =>
% 97.95/13.25 ((
% 97.95/13.25 (cartprodfstin) =>
% 97.95/13.25 ((
% 97.95/13.25 (setukpairinjL2) =>
% 97.95/13.25 ((
% 97.95/13.25 (setukpairinjL) =>
% 97.95/13.25 ((
% 97.95/13.25 (setukpairinjR11) =>
% 97.95/13.25 ((
% 97.95/13.25 (setukpairinjR12) =>
% 97.95/13.25 ((
% 97.95/13.25 (setukpairinjR1) =>
% 97.95/13.25 ((
% 97.95/13.25 (upairequniteq) =>
% 97.95/13.25 ((
% 97.95/13.25 (setukpairinjR2) =>
% 97.95/13.25 ((
% 97.95/13.25 (setukpairinjR) =>
% 97.95/13.25 ((
% 97.95/13.25 (ksndsingleton) =>
% 97.95/13.25 ((
% 97.95/13.25 (ksndpairEq) =>
% 97.95/13.25 ((
% 97.95/13.25 (kpairsurjEq) =>
% 97.95/13.25 ((
% 97.95/13.25 (cartprodsndin) =>
% 97.95/13.25 ((
% 97.95/13.25 (cartprodpairmemEL) =>
% 97.95/13.25 ((
% 97.95/13.25 (cartprodpairmemER) =>
% 97.95/13.25 ((
% 97.95/13.25 (cartprodmempaircEq) =>
% 97.95/13.25 ((
% 97.95/13.25 (cartprodfstpairEq) =>
% 97.95/13.25 ((
% 97.95/13.25 (cartprodsndpairEq) =>
% 97.95/13.25 ((
% 97.95/13.25 (cartprodpairsurjEq) =>
% 97.95/13.25 ((
% 97.95/13.25 (dpsetconstrI) =>
% 97.95/13.25 ((
% 97.95/13.25 (dpsetconstrSub) =>
% 97.95/13.25 ((
% 97.95/13.25 (setOfPairsIsBReln) =>
% 97.95/13.25 ((
% 97.95/13.25 (dpsetconstrERa) =>
% 97.95/13.25 ((
% 97.95/13.25 (dpsetconstrEL1) =>
% 97.95/13.25 ((
% 97.95/13.25 (dpsetconstrEL2) =>
% 97.95/13.25 ((
% 97.95/13.25 (dpsetconstrER) =>
% 97.95/13.25 ((
% 97.95/13.25 (funcImageSingleton) =>
% 97.95/13.25 ((
% 97.95/13.25 (apProp) =>
% 97.95/13.25 ((
% 97.95/13.25 (app) =>
% 97.95/13.25 ((
% 97.95/13.25 (infuncsetfunc) =>
% 97.95/13.25 ((
% 97.95/13.25 (ap2p) =>
% 97.95/13.25 ((
% 97.95/13.25 (funcinfuncset) =>
% 97.95/13.25 ((
% 97.95/13.25 (lamProp) =>
% 97.95/13.25 ((
% 97.95/13.25 (lamp) =>
% 97.95/13.25 ((
% 97.95/13.25 (lam2p) =>
% 97.95/13.25 ((
% 97.95/13.25 (brelnall1) =>
% 97.95/13.25 ((
% 97.95/13.25 (brelnall2) =>
% 97.95/13.25 ((
% 97.95/13.25 (ex1E2) =>
% 97.95/13.25 ((
% 97.95/13.25 (funcGraphProp1) =>
% 97.95/13.25 ((
% 97.95/13.25 (funcGraphProp3) =>
% 97.95/13.25 ((
% 97.95/13.25 (funcGraphProp2) =>
% 97.95/13.25 ((
% 97.95/13.25 (funcextLem) =>
% 97.95/13.25 ((
% 97.95/13.25 (funcGraphProp4) =>
% 97.95/13.25 ((
% 97.95/13.25 (subbreln) =>
% 97.95/13.25 ((
% 97.95/13.25 (eqbreln) =>
% 97.95/13.25 ((
% 97.95/13.25 (funcext) =>
% 97.95/13.25 ((
% 97.95/13.25 (funcext2) =>
% 97.95/13.25 ((
% 97.95/13.25 (ap2apEq1) =>
% 97.95/13.25 ((
% 97.95/13.25 (ap2apEq2) =>
% 97.95/13.25 ((
% 97.95/13.25 (beta1) =>
% 97.95/13.25 ((
% 97.95/13.25 (eta1) =>
% 97.95/13.25 ((
% 97.95/13.25 (lam2lamEq) =>
% 97.95/13.25 ((
% 97.95/13.25 (beta2) =>
% 97.95/13.25 ((
% 97.95/13.25 (eta2) =>
% 97.95/13.25 ((
% 97.95/13.25 (iffalseProp1) =>
% 97.95/13.25 ((
% 97.95/13.25 (iffalseProp2) =>
% 97.95/13.25 ((
% 97.95/13.25 (iftrueProp1) =>
% 97.95/13.25 ((
% 97.95/13.25 (iftrueProp2) =>
% 97.95/13.25 ((
% 97.95/13.25 (ifSingleton) =>
% 97.95/13.25 ((
% 97.95/13.25 (ifp) =>
% 97.95/13.25 ((
% 97.95/13.25 (theeq) =>
% 97.95/13.25 ((
% 97.95/13.25 (iftrue) =>
% 97.95/13.25 ((
% 97.95/13.25 (iffalse) =>
% 97.95/13.25 ((
% 97.95/13.25 (iftrueorfalse) =>
% 97.95/13.25 ((
% 97.95/13.25 (binintersectT_lem) =>
% 97.95/13.25 ((
% 97.95/13.25 (binunionT_lem) =>
% 97.95/13.25 ((
% 97.95/13.25 (powersetT_lem) =>
% 97.95/13.25 ((
% 97.95/13.25 (setminusT_lem) =>
% 97.95/13.25 ((
% 97.95/13.25 (complementT_lem) =>
% 97.95/13.25 ((
% 97.95/13.25 (setextT) =>
% 97.95/13.25 ((
% 97.95/13.25 (subsetTI) =>
% 97.95/13.25 ((
% 97.95/13.25 (powersetTI1) =>
% 97.95/13.25 ((
% 97.95/13.25 (powersetTE1) =>
% 97.95/13.25 ((
% 97.95/13.25 (complementTI1) =>
% 97.95/13.25 ((
% 97.95/13.25 (complementTE1) =>
% 97.95/13.25 ((
% 97.95/13.25 (binintersectTELcontra) =>
% 97.95/13.25 ((
% 97.95/13.25 (binintersectTERcontra) =>
% 97.95/13.25 ((
% 97.95/13.25 (contrasubsetT) =>
% 97.95/13.25 ((
% 97.95/13.25 (contrasubsetT1) =>
% 97.95/13.25 ((
% 97.95/13.25 (contrasubsetT2) =>
% 97.95/13.25 ((
% 97.95/13.25 (contrasubsetT3) =>
% 97.95/13.25 ((
% 97.95/13.25 (doubleComplementI1) =>
% 97.95/13.25 ((
% 97.95/13.25 (doubleComplementE1) =>
% 97.95/13.25 ((
% 97.95/13.25 (doubleComplementSub1) =>
% 97.95/13.25 ((
% 97.95/13.25 (doubleComplementSub2) =>
% 97.95/13.25 ((
% 97.95/13.25 (doubleComplementEq) =>
% 97.95/13.25 ((
% 97.95/13.25 (complementTnotintersectT) =>
% 97.95/13.25 ((
% 97.95/13.25 (complementImpComplementIntersect) =>
% 97.95/13.25 ((
% 97.95/13.25 (complementSubsetComplementIntersect) =>
% 97.95/13.25 ((
% 97.95/13.25 (complementInPowersetComplementIntersect) =>
% 97.95/13.25 ((
% 97.95/13.25 (contraSubsetComplement) =>
% 97.95/13.25 ((
% 97.95/13.25 (complementTcontraSubset) =>
% 97.95/13.25 ((
% 97.95/13.25 (binunionTILcontra) =>
% 97.95/13.25 ((
% 97.95/13.25 (binunionTIRcontra) =>
% 97.95/13.25 ((
% 97.95/13.25 (inIntersectImpInUnion) =>
% 97.95/13.25 ((
% 97.95/13.25 (inIntersectImpInUnion2) =>
% 97.95/13.25 ((
% 97.95/13.25 (inIntersectImpInIntersectUnions) =>
% 97.95/13.25 ((
% 97.95/13.25 (intersectInPowersetIntersectUnions) =>
% 97.95/13.25 ((
% 97.95/13.25 (inComplementUnionImpNotIn1) =>
% 97.95/13.25 ((
% 97.95/13.25 (inComplementUnionImpInComplement1) =>
% 97.95/13.25 ((
% 97.95/13.25 (binunionTE) =>
% 97.95/13.25 ((
% 97.95/13.25 (binunionTEcontra) =>
% 97.95/13.25 ((
% 97.95/13.25 (demorgan2a1) =>
% 97.95/13.25 ((
% 97.95/13.25 (complementUnionInPowersetComplement) =>
% 97.95/13.25 ((
% 97.95/13.25 (demorgan2a2) =>
% 97.95/13.25 ((
% 97.95/13.25 (demorgan1a) =>
% 97.95/13.25 ((
% 97.95/13.25 (demorgan1b) =>
% 97.95/13.25 ((
% 97.95/13.25 (demorgan1) =>
% 97.95/13.25 ((
% 97.95/13.25 (demorgan2a) =>
% 97.95/13.25 ((
% 97.95/13.25 (demorgan2b2) =>
% 97.95/13.25 ((
% 97.95/13.25 (demorgan2b) =>
% 97.95/13.25 ((
% 97.95/13.25 (demorgan2) =>
% 97.95/13.25 ((
% 97.95/13.25 (woz13rule0) =>
% 97.95/13.25 ((
% 97.95/13.25 (woz13rule1) =>
% 97.95/13.25 ((
% 97.95/13.25 (woz13rule2) =>
% 97.95/13.25 ((
% 97.95/13.25 (woz13rule3) =>
% 97.95/13.25 ((
% 97.95/13.25 (woz13rule4) =>
% 97.95/13.25 ((
% 97.95/13.25 (woz1_1) =>
% 97.95/13.25 ((
% 97.95/13.25 (woz1_2) =>
% 97.95/13.25 ((
% 97.95/13.25 (woz1_3) =>
% 97.95/13.25 ((
% 97.95/13.25 (woz1_4) =>
% 97.95/13.25 ((
% 97.95/13.25 (woz1_5) =>
% 97.95/13.25 ((
% 97.95/13.25 (breln1all2) =>
% 97.95/13.25 ((
% 97.95/13.25 (breln1SetBreln1) =>
% 97.95/13.25 ((
% 97.95/13.25 (choice2fnsingleton) =>
% 97.95/13.25 ((
% 97.95/13.25 (setOfPairsIsBReln1) =>
% 97.95/13.25 ((
% 97.95/13.25 (breln1all1) =>
% 97.95/13.25 ((
% 97.95/13.25 (subbreln1) =>
% 97.95/13.25 ((
% 97.95/13.25 (eqbreln1) =>
% 97.95/13.25 ((
% 97.95/13.25 (breln1invprop) =>
% 97.95/13.25 ((
% 97.95/13.25 (breln1invI) =>
% 97.95/13.25 ((
% 97.95/13.25 (breln1invE) =>
% 97.95/13.25 ((
% 97.95/13.25 (breln1compprop) =>
% 97.95/13.25 ((
% 97.95/13.25 (breln1compI) =>
% 97.95/13.25 ((
% 97.95/13.25 (breln1compE) =>
% 97.95/13.25 ((
% 97.95/13.25 (breln1compEex) =>
% 97.95/13.25 ((
% 97.95/13.25 (breln1unionprop) =>
% 97.95/13.25 ((
% 97.95/13.25 (breln1unionIL) =>
% 97.95/13.25 ((
% 97.95/13.25 (breln1unionIR) =>
% 97.95/13.25 ((
% 97.95/13.25 (breln1unionI) =>
% 97.95/13.25 ((
% 97.95/13.25 (breln1unionE) =>
% 97.95/13.25 ((
% 97.95/13.25 (breln1unionEcases) =>
% 97.95/13.25 ((
% 97.95/13.25 (breln1unionCommutes) =>
% 97.95/13.25 ((
% 97.95/13.25 (woz2Ex) =>
% 97.95/13.25 ((
% 97.95/13.25 (woz2W) =>
% 97.95/13.25 ((
% 97.95/13.25 (woz2A) =>
% 97.95/13.25 ((
% 97.95/13.25 (woz2B) =>
% 97.95/13.25 ((
% 97.95/13.25 (image1Ex) =>
% 97.95/13.25 ((
% 97.95/13.25 (image1Ex1) =>
% 97.95/13.25 ((
% 97.95/13.25 (image1Equiv) =>
% 97.95/13.25 ((
% 97.95/13.25 (image1E) =>
% 97.95/13.25 ((
% 97.95/13.25 (image1I) =>
% 97.95/13.25 ((
% 97.95/13.25 (injFuncInInjFuncSet) =>
% 97.95/13.25 ((
% 97.95/13.25 (injFuncSetFuncIn) =>
% 97.95/13.25 ((
% 97.95/13.25 (injFuncSetFuncInj) =>
% 97.95/13.25 ((
% 97.95/13.25 (surjFuncSetFuncIn) =>
% 97.95/13.25 ((
% 97.95/13.25 (surjFuncSetFuncSurj) =>
% 97.95/13.25 ((
% 97.95/13.25 (leftInvIsSurj) =>
% 97.95/13.25 ((
% 97.95/13.25 (surjCantorThm) =>
% 97.95/13.25 ((
% 97.95/13.25 (foundation2) =>
% 97.95/13.25 ((
% 97.95/13.25 (notinself) =>
% 97.95/13.25 ((
% 97.95/13.25 (notinself2) =>
% 97.95/13.25 ((
% 97.95/13.25 (omegaSp) =>
% 97.95/13.25 ((
% 97.95/13.25 (omegaSclos) =>
% 97.95/13.25 ((
% 97.95/13.25 (peano0notS) =>
% 97.95/13.25 ((
% 97.95/13.25 (!!) @ (
% 97.95/13.25 (('#S') @ (
% 97.95/13.25 (
% 97.95/13.25 ('#B') @ (
% 97.95/13.25 =>) @
% 97.95/13.25 (
% 97.95/13.25 (
% 97.95/13.25 ('#C') @ in @
% 97.95/13.25 omega)))) @
% 97.95/13.25 (
% 97.95/13.25 (
% 97.95/13.25 ('#B') @ (
% 97.95/13.25 !!) @
% 97.95/13.25 (
% 97.95/13.25 (
% 97.95/13.25 ('#B') @ (
% 97.95/13.25 (
% 97.95/13.25 ('#S') @ (
% 97.95/13.25 (
% 97.95/13.25 ('#B') @ (
% 97.95/13.25 =>) @
% 97.95/13.25 (
% 97.95/13.25 (
% 97.95/13.25 ('#C') @ in @
% 97.95/13.25 omega)))))) @
% 97.95/13.25 (
% 97.95/13.25 (
% 97.95/13.25 ('#S') @ (
% 97.95/13.25 (
% 97.95/13.25 ('#B') @ (
% 97.95/13.25 '#S') @
% 97.95/13.25 (
% 97.95/13.25 (
% 97.95/13.25 ('#B') @ (
% 97.95/13.25 (
% 97.95/13.25 ('#B') @ (
% 97.95/13.25 =>))) @
% 97.95/13.25 (
% 97.95/13.25 (
% 97.95/13.25 ('#C') @ (
% 97.95/13.25 (
% 97.95/13.25 ('#B') @ (
% 97.95/13.25 '#B') @
% 97.95/13.25 (
% 97.95/13.25 (
% 97.95/13.25 ('#B') @ (
% 97.95/13.25 =) @
% 97.95/13.25 omegaS)))) @
% 97.95/13.25 omegaS)))))) @
% 97.95/13.25 (
% 97.95/13.25 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.95/13.25 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1135])).
% 97.95/13.25 thf(zip_derived_cl1150, plain,
% 97.95/13.25 (~ (((binintersectSubset5) =>
% 97.95/13.25 (((binintersectEL) =>
% 97.95/13.25 (((binintersectLsub) =>
% 97.95/13.25 (((binintersectSubset2) =>
% 97.95/13.25 (((binintersectSubset3) =>
% 97.95/13.25 (((binintersectER) =>
% 97.95/13.25 (((disjointsetsI1) =>
% 97.95/13.25 (((binintersectRsub) =>
% 97.95/13.25 (((binintersectSubset4) =>
% 97.95/13.25 (((binintersectSubset1) =>
% 97.95/13.25 (((bs114d) =>
% 97.95/13.25 (((setminusI) =>
% 97.95/13.25 (((setminusEL) =>
% 97.95/13.25 (((setminusER) =>
% 97.95/13.25 (((setminusSubset2) =>
% 97.95/13.25 (((setminusERneg) =>
% 97.95/13.25 (((setminusELneg) =>
% 97.95/13.25 (((setminusILneg) =>
% 97.95/13.25 (((setminusIRneg) =>
% 97.95/13.25 (((setminusLsub) =>
% 97.95/13.25 (((setminusSubset1) =>
% 97.95/13.25 (((symdiffE) =>
% 97.95/13.25 (((symdiffI1) =>
% 97.95/13.25 (((symdiffI2) =>
% 97.95/13.25 (((symdiffIneg1) =>
% 97.95/13.25 (((symdiffIneg2) =>
% 97.95/13.25 (((secondinupair) =>
% 97.95/13.25 (((setukpairIL) =>
% 97.95/13.25 (((setukpairIR) =>
% 97.95/13.25 (((kpairiskpair) =>
% 97.95/13.25 ((
% 97.95/13.25 (kpairp) =>
% 97.95/13.25 ((
% 97.95/13.25 (singletonsubset) =>
% 97.95/13.25 ((
% 97.95/13.25 (singletoninpowerset) =>
% 97.95/13.25 ((
% 97.95/13.25 (singletoninpowunion) =>
% 97.95/13.25 ((
% 97.95/13.25 (upairset2E) =>
% 97.95/13.25 ((
% 97.95/13.25 (upairsubunion) =>
% 97.95/13.25 ((
% 97.95/13.25 (upairinpowunion) =>
% 97.95/13.25 ((
% 97.95/13.25 (ubforcartprodlem1) =>
% 97.95/13.25 ((
% 97.95/13.25 (ubforcartprodlem2) =>
% 97.95/13.25 ((
% 97.95/13.25 (ubforcartprodlem3) =>
% 97.95/13.25 ((
% 97.95/13.25 (cartprodpairin) =>
% 97.95/13.25 ((
% 97.95/13.25 (cartprodmempair1) =>
% 97.95/13.25 ((
% 97.95/13.25 (cartprodmempair) =>
% 97.95/13.25 ((
% 97.95/13.25 (setunionE2) =>
% 97.95/13.25 ((
% 97.95/13.25 (setunionsingleton1) =>
% 97.95/13.25 ((
% 97.95/13.25 (setunionsingleton2) =>
% 97.95/13.25 ((
% 97.95/13.25 (setunionsingleton) =>
% 97.95/13.25 ((
% 97.95/13.25 (singletonprop) =>
% 97.95/13.25 ((
% 97.95/13.25 (ex1E1) =>
% 97.95/13.25 ((
% 97.95/13.25 (ex1I) =>
% 97.95/13.25 ((
% 97.95/13.25 (ex1I2) =>
% 97.95/13.25 ((
% 97.95/13.25 (singletonsuniq) =>
% 97.95/13.25 ((
% 97.95/13.25 (setukpairinjL1) =>
% 97.95/13.25 ((
% 97.95/13.25 (kfstsingleton) =>
% 97.95/13.25 ((
% 97.95/13.25 (theprop) =>
% 97.95/13.25 ((
% 97.95/13.25 (kfstpairEq) =>
% 97.95/13.25 ((
% 97.95/13.25 (cartprodfstin) =>
% 97.95/13.25 ((
% 97.95/13.25 (setukpairinjL2) =>
% 97.95/13.25 ((
% 97.95/13.25 (setukpairinjL) =>
% 97.95/13.25 ((
% 97.95/13.25 (setukpairinjR11) =>
% 97.95/13.25 ((
% 97.95/13.25 (setukpairinjR12) =>
% 97.95/13.25 ((
% 97.95/13.25 (setukpairinjR1) =>
% 97.95/13.25 ((
% 97.95/13.25 (upairequniteq) =>
% 97.95/13.25 ((
% 97.95/13.25 (setukpairinjR2) =>
% 97.95/13.25 ((
% 97.95/13.25 (setukpairinjR) =>
% 97.95/13.25 ((
% 97.95/13.25 (ksndsingleton) =>
% 97.95/13.25 ((
% 97.95/13.25 (ksndpairEq) =>
% 97.95/13.25 ((
% 97.95/13.25 (kpairsurjEq) =>
% 97.95/13.25 ((
% 97.95/13.25 (cartprodsndin) =>
% 97.95/13.25 ((
% 97.95/13.25 (cartprodpairmemEL) =>
% 97.95/13.25 ((
% 97.95/13.25 (cartprodpairmemER) =>
% 97.95/13.25 ((
% 97.95/13.25 (cartprodmempaircEq) =>
% 97.95/13.25 ((
% 97.95/13.25 (cartprodfstpairEq) =>
% 97.95/13.25 ((
% 97.95/13.25 (cartprodsndpairEq) =>
% 97.95/13.25 ((
% 97.95/13.25 (cartprodpairsurjEq) =>
% 97.95/13.25 ((
% 97.95/13.25 (dpsetconstrI) =>
% 97.95/13.25 ((
% 97.95/13.25 (dpsetconstrSub) =>
% 97.95/13.25 ((
% 97.95/13.25 (setOfPairsIsBReln) =>
% 97.95/13.25 ((
% 97.95/13.25 (dpsetconstrERa) =>
% 97.95/13.25 ((
% 97.95/13.25 (dpsetconstrEL1) =>
% 97.95/13.25 ((
% 97.95/13.25 (dpsetconstrEL2) =>
% 97.95/13.25 ((
% 97.95/13.25 (dpsetconstrER) =>
% 97.95/13.25 ((
% 97.95/13.25 (funcImageSingleton) =>
% 97.95/13.25 ((
% 97.95/13.25 (apProp) =>
% 97.95/13.25 ((
% 97.95/13.25 (app) =>
% 97.95/13.25 ((
% 97.95/13.25 (infuncsetfunc) =>
% 97.95/13.25 ((
% 97.95/13.25 (ap2p) =>
% 97.95/13.25 ((
% 97.95/13.25 (funcinfuncset) =>
% 97.95/13.25 ((
% 97.95/13.25 (lamProp) =>
% 97.95/13.25 ((
% 97.95/13.25 (lamp) =>
% 97.95/13.25 ((
% 97.95/13.25 (lam2p) =>
% 97.95/13.25 ((
% 97.95/13.25 (brelnall1) =>
% 97.95/13.25 ((
% 97.95/13.25 (brelnall2) =>
% 97.95/13.25 ((
% 97.95/13.25 (ex1E2) =>
% 97.95/13.25 ((
% 97.95/13.25 (funcGraphProp1) =>
% 97.95/13.25 ((
% 97.95/13.25 (funcGraphProp3) =>
% 97.95/13.25 ((
% 97.95/13.25 (funcGraphProp2) =>
% 97.95/13.25 ((
% 97.95/13.25 (funcextLem) =>
% 97.95/13.25 ((
% 97.95/13.25 (funcGraphProp4) =>
% 97.95/13.25 ((
% 97.95/13.25 (subbreln) =>
% 97.95/13.25 ((
% 97.95/13.25 (eqbreln) =>
% 97.95/13.25 ((
% 97.99/13.25 (funcext) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcext2) =>
% 97.99/13.25 ((
% 97.99/13.25 (ap2apEq1) =>
% 97.99/13.25 ((
% 97.99/13.25 (ap2apEq2) =>
% 97.99/13.25 ((
% 97.99/13.25 (beta1) =>
% 97.99/13.25 ((
% 97.99/13.25 (eta1) =>
% 97.99/13.25 ((
% 97.99/13.25 (lam2lamEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (beta2) =>
% 97.99/13.25 ((
% 97.99/13.25 (eta2) =>
% 97.99/13.25 ((
% 97.99/13.25 (iffalseProp1) =>
% 97.99/13.25 ((
% 97.99/13.25 (iffalseProp2) =>
% 97.99/13.25 ((
% 97.99/13.25 (iftrueProp1) =>
% 97.99/13.25 ((
% 97.99/13.25 (iftrueProp2) =>
% 97.99/13.25 ((
% 97.99/13.25 (ifSingleton) =>
% 97.99/13.25 ((
% 97.99/13.25 (ifp) =>
% 97.99/13.25 ((
% 97.99/13.25 (theeq) =>
% 97.99/13.25 ((
% 97.99/13.25 (iftrue) =>
% 97.99/13.25 ((
% 97.99/13.25 (iffalse) =>
% 97.99/13.25 ((
% 97.99/13.25 (iftrueorfalse) =>
% 97.99/13.25 ((
% 97.99/13.25 (binintersectT_lem) =>
% 97.99/13.25 ((
% 97.99/13.25 (binunionT_lem) =>
% 97.99/13.25 ((
% 97.99/13.25 (powersetT_lem) =>
% 97.99/13.25 ((
% 97.99/13.25 (setminusT_lem) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementT_lem) =>
% 97.99/13.25 ((
% 97.99/13.25 (setextT) =>
% 97.99/13.25 ((
% 97.99/13.25 (subsetTI) =>
% 97.99/13.25 ((
% 97.99/13.25 (powersetTI1) =>
% 97.99/13.25 ((
% 97.99/13.25 (powersetTE1) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementTI1) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementTE1) =>
% 97.99/13.25 ((
% 97.99/13.25 (binintersectTELcontra) =>
% 97.99/13.25 ((
% 97.99/13.25 (binintersectTERcontra) =>
% 97.99/13.25 ((
% 97.99/13.25 (contrasubsetT) =>
% 97.99/13.25 ((
% 97.99/13.25 (contrasubsetT1) =>
% 97.99/13.25 ((
% 97.99/13.25 (contrasubsetT2) =>
% 97.99/13.25 ((
% 97.99/13.25 (contrasubsetT3) =>
% 97.99/13.25 ((
% 97.99/13.25 (doubleComplementI1) =>
% 97.99/13.25 ((
% 97.99/13.25 (doubleComplementE1) =>
% 97.99/13.25 ((
% 97.99/13.25 (doubleComplementSub1) =>
% 97.99/13.25 ((
% 97.99/13.25 (doubleComplementSub2) =>
% 97.99/13.25 ((
% 97.99/13.25 (doubleComplementEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementTnotintersectT) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementImpComplementIntersect) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementSubsetComplementIntersect) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementInPowersetComplementIntersect) =>
% 97.99/13.25 ((
% 97.99/13.25 (contraSubsetComplement) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementTcontraSubset) =>
% 97.99/13.25 ((
% 97.99/13.25 (binunionTILcontra) =>
% 97.99/13.25 ((
% 97.99/13.25 (binunionTIRcontra) =>
% 97.99/13.25 ((
% 97.99/13.25 (inIntersectImpInUnion) =>
% 97.99/13.25 ((
% 97.99/13.25 (inIntersectImpInUnion2) =>
% 97.99/13.25 ((
% 97.99/13.25 (inIntersectImpInIntersectUnions) =>
% 97.99/13.25 ((
% 97.99/13.25 (intersectInPowersetIntersectUnions) =>
% 97.99/13.25 ((
% 97.99/13.25 (inComplementUnionImpNotIn1) =>
% 97.99/13.25 ((
% 97.99/13.25 (inComplementUnionImpInComplement1) =>
% 97.99/13.25 ((
% 97.99/13.25 (binunionTE) =>
% 97.99/13.25 ((
% 97.99/13.25 (binunionTEcontra) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan2a1) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementUnionInPowersetComplement) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan2a2) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan1a) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan1b) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan1) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan2a) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan2b2) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan2b) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan2) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz13rule0) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz13rule1) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz13rule2) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz13rule3) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz13rule4) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz1_1) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz1_2) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz1_3) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz1_4) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz1_5) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1all2) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1SetBreln1) =>
% 97.99/13.25 ((
% 97.99/13.25 (choice2fnsingleton) =>
% 97.99/13.25 ((
% 97.99/13.25 (setOfPairsIsBReln1) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1all1) =>
% 97.99/13.25 ((
% 97.99/13.25 (subbreln1) =>
% 97.99/13.25 ((
% 97.99/13.25 (eqbreln1) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1invprop) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1invI) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1invE) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1compprop) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1compI) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1compE) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1compEex) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1unionprop) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1unionIL) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1unionIR) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1unionI) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1unionE) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1unionEcases) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1unionCommutes) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz2Ex) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz2W) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz2A) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz2B) =>
% 97.99/13.25 ((
% 97.99/13.25 (image1Ex) =>
% 97.99/13.25 ((
% 97.99/13.25 (image1Ex1) =>
% 97.99/13.25 ((
% 97.99/13.25 (image1Equiv) =>
% 97.99/13.25 ((
% 97.99/13.25 (image1E) =>
% 97.99/13.25 ((
% 97.99/13.25 (image1I) =>
% 97.99/13.25 ((
% 97.99/13.25 (injFuncInInjFuncSet) =>
% 97.99/13.25 ((
% 97.99/13.25 (injFuncSetFuncIn) =>
% 97.99/13.25 ((
% 97.99/13.25 (injFuncSetFuncInj) =>
% 97.99/13.25 ((
% 97.99/13.25 (surjFuncSetFuncIn) =>
% 97.99/13.25 ((
% 97.99/13.25 (surjFuncSetFuncSurj) =>
% 97.99/13.25 ((
% 97.99/13.25 (leftInvIsSurj) =>
% 97.99/13.25 ((
% 97.99/13.25 (surjCantorThm) =>
% 97.99/13.25 ((
% 97.99/13.25 (foundation2) =>
% 97.99/13.25 ((
% 97.99/13.25 (notinself) =>
% 97.99/13.25 ((
% 97.99/13.25 (notinself2) =>
% 97.99/13.25 ((
% 97.99/13.25 (omegaSp) =>
% 97.99/13.25 ((
% 97.99/13.25 (omegaSclos) =>
% 97.99/13.25 ((
% 97.99/13.25 (peano0notS) =>
% 97.99/13.25 ((
% 97.99/13.25 (!!) @ (
% 97.99/13.25 (('#S') @ (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 =>) @
% 97.99/13.25 (
% 97.99/13.25 (
% 97.99/13.25 ('#C') @ in @
% 97.99/13.25 omega)))) @
% 97.99/13.25 (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 !!) @
% 97.99/13.25 (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 (
% 97.99/13.25 ('#S') @ (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 =>) @
% 97.99/13.25 (
% 97.99/13.25 (
% 97.99/13.25 ('#C') @ in @
% 97.99/13.25 omega)))))) @
% 97.99/13.25 (
% 97.99/13.25 (
% 97.99/13.25 ('#S') @ (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 '#S') @
% 97.99/13.25 (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 =>))) @
% 97.99/13.25 (
% 97.99/13.25 (
% 97.99/13.25 ('#C') @ (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 '#B') @
% 97.99/13.25 (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 =) @
% 97.99/13.25 omegaS)))) @
% 97.99/13.25 omegaS)))))) @
% 97.99/13.25 (
% 97.99/13.25 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.99/13.25 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1142])).
% 97.99/13.25 thf(zip_derived_cl1158, plain,
% 97.99/13.25 (~ (((binintersectEL) =>
% 97.99/13.25 (((binintersectLsub) =>
% 97.99/13.25 (((binintersectSubset2) =>
% 97.99/13.25 (((binintersectSubset3) =>
% 97.99/13.25 (((binintersectER) =>
% 97.99/13.25 (((disjointsetsI1) =>
% 97.99/13.25 (((binintersectRsub) =>
% 97.99/13.25 (((binintersectSubset4) =>
% 97.99/13.25 (((binintersectSubset1) =>
% 97.99/13.25 (((bs114d) =>
% 97.99/13.25 (((setminusI) =>
% 97.99/13.25 (((setminusEL) =>
% 97.99/13.25 (((setminusER) =>
% 97.99/13.25 (((setminusSubset2) =>
% 97.99/13.25 (((setminusERneg) =>
% 97.99/13.25 (((setminusELneg) =>
% 97.99/13.25 (((setminusILneg) =>
% 97.99/13.25 (((setminusIRneg) =>
% 97.99/13.25 (((setminusLsub) =>
% 97.99/13.25 (((setminusSubset1) =>
% 97.99/13.25 (((symdiffE) =>
% 97.99/13.25 (((symdiffI1) =>
% 97.99/13.25 (((symdiffI2) =>
% 97.99/13.25 (((symdiffIneg1) =>
% 97.99/13.25 (((symdiffIneg2) =>
% 97.99/13.25 (((secondinupair) =>
% 97.99/13.25 (((setukpairIL) =>
% 97.99/13.25 (((setukpairIR) =>
% 97.99/13.25 (((kpairiskpair) =>
% 97.99/13.25 (((kpairp) =>
% 97.99/13.25 ((
% 97.99/13.25 (singletonsubset) =>
% 97.99/13.25 ((
% 97.99/13.25 (singletoninpowerset) =>
% 97.99/13.25 ((
% 97.99/13.25 (singletoninpowunion) =>
% 97.99/13.25 ((
% 97.99/13.25 (upairset2E) =>
% 97.99/13.25 ((
% 97.99/13.25 (upairsubunion) =>
% 97.99/13.25 ((
% 97.99/13.25 (upairinpowunion) =>
% 97.99/13.25 ((
% 97.99/13.25 (ubforcartprodlem1) =>
% 97.99/13.25 ((
% 97.99/13.25 (ubforcartprodlem2) =>
% 97.99/13.25 ((
% 97.99/13.25 (ubforcartprodlem3) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodpairin) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodmempair1) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodmempair) =>
% 97.99/13.25 ((
% 97.99/13.25 (setunionE2) =>
% 97.99/13.25 ((
% 97.99/13.25 (setunionsingleton1) =>
% 97.99/13.25 ((
% 97.99/13.25 (setunionsingleton2) =>
% 97.99/13.25 ((
% 97.99/13.25 (setunionsingleton) =>
% 97.99/13.25 ((
% 97.99/13.25 (singletonprop) =>
% 97.99/13.25 ((
% 97.99/13.25 (ex1E1) =>
% 97.99/13.25 ((
% 97.99/13.25 (ex1I) =>
% 97.99/13.25 ((
% 97.99/13.25 (ex1I2) =>
% 97.99/13.25 ((
% 97.99/13.25 (singletonsuniq) =>
% 97.99/13.25 ((
% 97.99/13.25 (setukpairinjL1) =>
% 97.99/13.25 ((
% 97.99/13.25 (kfstsingleton) =>
% 97.99/13.25 ((
% 97.99/13.25 (theprop) =>
% 97.99/13.25 ((
% 97.99/13.25 (kfstpairEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodfstin) =>
% 97.99/13.25 ((
% 97.99/13.25 (setukpairinjL2) =>
% 97.99/13.25 ((
% 97.99/13.25 (setukpairinjL) =>
% 97.99/13.25 ((
% 97.99/13.25 (setukpairinjR11) =>
% 97.99/13.25 ((
% 97.99/13.25 (setukpairinjR12) =>
% 97.99/13.25 ((
% 97.99/13.25 (setukpairinjR1) =>
% 97.99/13.25 ((
% 97.99/13.25 (upairequniteq) =>
% 97.99/13.25 ((
% 97.99/13.25 (setukpairinjR2) =>
% 97.99/13.25 ((
% 97.99/13.25 (setukpairinjR) =>
% 97.99/13.25 ((
% 97.99/13.25 (ksndsingleton) =>
% 97.99/13.25 ((
% 97.99/13.25 (ksndpairEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (kpairsurjEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodsndin) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodpairmemEL) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodpairmemER) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodmempaircEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodfstpairEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodsndpairEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodpairsurjEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (dpsetconstrI) =>
% 97.99/13.25 ((
% 97.99/13.25 (dpsetconstrSub) =>
% 97.99/13.25 ((
% 97.99/13.25 (setOfPairsIsBReln) =>
% 97.99/13.25 ((
% 97.99/13.25 (dpsetconstrERa) =>
% 97.99/13.25 ((
% 97.99/13.25 (dpsetconstrEL1) =>
% 97.99/13.25 ((
% 97.99/13.25 (dpsetconstrEL2) =>
% 97.99/13.25 ((
% 97.99/13.25 (dpsetconstrER) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcImageSingleton) =>
% 97.99/13.25 ((
% 97.99/13.25 (apProp) =>
% 97.99/13.25 ((
% 97.99/13.25 (app) =>
% 97.99/13.25 ((
% 97.99/13.25 (infuncsetfunc) =>
% 97.99/13.25 ((
% 97.99/13.25 (ap2p) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcinfuncset) =>
% 97.99/13.25 ((
% 97.99/13.25 (lamProp) =>
% 97.99/13.25 ((
% 97.99/13.25 (lamp) =>
% 97.99/13.25 ((
% 97.99/13.25 (lam2p) =>
% 97.99/13.25 ((
% 97.99/13.25 (brelnall1) =>
% 97.99/13.25 ((
% 97.99/13.25 (brelnall2) =>
% 97.99/13.25 ((
% 97.99/13.25 (ex1E2) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcGraphProp1) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcGraphProp3) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcGraphProp2) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcextLem) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcGraphProp4) =>
% 97.99/13.25 ((
% 97.99/13.25 (subbreln) =>
% 97.99/13.25 ((
% 97.99/13.25 (eqbreln) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcext) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcext2) =>
% 97.99/13.25 ((
% 97.99/13.25 (ap2apEq1) =>
% 97.99/13.25 ((
% 97.99/13.25 (ap2apEq2) =>
% 97.99/13.25 ((
% 97.99/13.25 (beta1) =>
% 97.99/13.25 ((
% 97.99/13.25 (eta1) =>
% 97.99/13.25 ((
% 97.99/13.25 (lam2lamEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (beta2) =>
% 97.99/13.25 ((
% 97.99/13.25 (eta2) =>
% 97.99/13.25 ((
% 97.99/13.25 (iffalseProp1) =>
% 97.99/13.25 ((
% 97.99/13.25 (iffalseProp2) =>
% 97.99/13.25 ((
% 97.99/13.25 (iftrueProp1) =>
% 97.99/13.25 ((
% 97.99/13.25 (iftrueProp2) =>
% 97.99/13.25 ((
% 97.99/13.25 (ifSingleton) =>
% 97.99/13.25 ((
% 97.99/13.25 (ifp) =>
% 97.99/13.25 ((
% 97.99/13.25 (theeq) =>
% 97.99/13.25 ((
% 97.99/13.25 (iftrue) =>
% 97.99/13.25 ((
% 97.99/13.25 (iffalse) =>
% 97.99/13.25 ((
% 97.99/13.25 (iftrueorfalse) =>
% 97.99/13.25 ((
% 97.99/13.25 (binintersectT_lem) =>
% 97.99/13.25 ((
% 97.99/13.25 (binunionT_lem) =>
% 97.99/13.25 ((
% 97.99/13.25 (powersetT_lem) =>
% 97.99/13.25 ((
% 97.99/13.25 (setminusT_lem) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementT_lem) =>
% 97.99/13.25 ((
% 97.99/13.25 (setextT) =>
% 97.99/13.25 ((
% 97.99/13.25 (subsetTI) =>
% 97.99/13.25 ((
% 97.99/13.25 (powersetTI1) =>
% 97.99/13.25 ((
% 97.99/13.25 (powersetTE1) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementTI1) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementTE1) =>
% 97.99/13.25 ((
% 97.99/13.25 (binintersectTELcontra) =>
% 97.99/13.25 ((
% 97.99/13.25 (binintersectTERcontra) =>
% 97.99/13.25 ((
% 97.99/13.25 (contrasubsetT) =>
% 97.99/13.25 ((
% 97.99/13.25 (contrasubsetT1) =>
% 97.99/13.25 ((
% 97.99/13.25 (contrasubsetT2) =>
% 97.99/13.25 ((
% 97.99/13.25 (contrasubsetT3) =>
% 97.99/13.25 ((
% 97.99/13.25 (doubleComplementI1) =>
% 97.99/13.25 ((
% 97.99/13.25 (doubleComplementE1) =>
% 97.99/13.25 ((
% 97.99/13.25 (doubleComplementSub1) =>
% 97.99/13.25 ((
% 97.99/13.25 (doubleComplementSub2) =>
% 97.99/13.25 ((
% 97.99/13.25 (doubleComplementEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementTnotintersectT) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementImpComplementIntersect) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementSubsetComplementIntersect) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementInPowersetComplementIntersect) =>
% 97.99/13.25 ((
% 97.99/13.25 (contraSubsetComplement) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementTcontraSubset) =>
% 97.99/13.25 ((
% 97.99/13.25 (binunionTILcontra) =>
% 97.99/13.25 ((
% 97.99/13.25 (binunionTIRcontra) =>
% 97.99/13.25 ((
% 97.99/13.25 (inIntersectImpInUnion) =>
% 97.99/13.25 ((
% 97.99/13.25 (inIntersectImpInUnion2) =>
% 97.99/13.25 ((
% 97.99/13.25 (inIntersectImpInIntersectUnions) =>
% 97.99/13.25 ((
% 97.99/13.25 (intersectInPowersetIntersectUnions) =>
% 97.99/13.25 ((
% 97.99/13.25 (inComplementUnionImpNotIn1) =>
% 97.99/13.25 ((
% 97.99/13.25 (inComplementUnionImpInComplement1) =>
% 97.99/13.25 ((
% 97.99/13.25 (binunionTE) =>
% 97.99/13.25 ((
% 97.99/13.25 (binunionTEcontra) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan2a1) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementUnionInPowersetComplement) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan2a2) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan1a) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan1b) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan1) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan2a) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan2b2) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan2b) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan2) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz13rule0) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz13rule1) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz13rule2) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz13rule3) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz13rule4) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz1_1) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz1_2) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz1_3) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz1_4) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz1_5) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1all2) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1SetBreln1) =>
% 97.99/13.25 ((
% 97.99/13.25 (choice2fnsingleton) =>
% 97.99/13.25 ((
% 97.99/13.25 (setOfPairsIsBReln1) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1all1) =>
% 97.99/13.25 ((
% 97.99/13.25 (subbreln1) =>
% 97.99/13.25 ((
% 97.99/13.25 (eqbreln1) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1invprop) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1invI) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1invE) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1compprop) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1compI) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1compE) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1compEex) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1unionprop) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1unionIL) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1unionIR) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1unionI) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1unionE) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1unionEcases) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1unionCommutes) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz2Ex) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz2W) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz2A) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz2B) =>
% 97.99/13.25 ((
% 97.99/13.25 (image1Ex) =>
% 97.99/13.25 ((
% 97.99/13.25 (image1Ex1) =>
% 97.99/13.25 ((
% 97.99/13.25 (image1Equiv) =>
% 97.99/13.25 ((
% 97.99/13.25 (image1E) =>
% 97.99/13.25 ((
% 97.99/13.25 (image1I) =>
% 97.99/13.25 ((
% 97.99/13.25 (injFuncInInjFuncSet) =>
% 97.99/13.25 ((
% 97.99/13.25 (injFuncSetFuncIn) =>
% 97.99/13.25 ((
% 97.99/13.25 (injFuncSetFuncInj) =>
% 97.99/13.25 ((
% 97.99/13.25 (surjFuncSetFuncIn) =>
% 97.99/13.25 ((
% 97.99/13.25 (surjFuncSetFuncSurj) =>
% 97.99/13.25 ((
% 97.99/13.25 (leftInvIsSurj) =>
% 97.99/13.25 ((
% 97.99/13.25 (surjCantorThm) =>
% 97.99/13.25 ((
% 97.99/13.25 (foundation2) =>
% 97.99/13.25 ((
% 97.99/13.25 (notinself) =>
% 97.99/13.25 ((
% 97.99/13.25 (notinself2) =>
% 97.99/13.25 ((
% 97.99/13.25 (omegaSp) =>
% 97.99/13.25 ((
% 97.99/13.25 (omegaSclos) =>
% 97.99/13.25 ((
% 97.99/13.25 (peano0notS) =>
% 97.99/13.25 ((
% 97.99/13.25 (!!) @ (
% 97.99/13.25 (('#S') @ (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 =>) @
% 97.99/13.25 (
% 97.99/13.25 (
% 97.99/13.25 ('#C') @ in @
% 97.99/13.25 omega)))) @
% 97.99/13.25 (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 !!) @
% 97.99/13.25 (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 (
% 97.99/13.25 ('#S') @ (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 =>) @
% 97.99/13.25 (
% 97.99/13.25 (
% 97.99/13.25 ('#C') @ in @
% 97.99/13.25 omega)))))) @
% 97.99/13.25 (
% 97.99/13.25 (
% 97.99/13.25 ('#S') @ (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 '#S') @
% 97.99/13.25 (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 =>))) @
% 97.99/13.25 (
% 97.99/13.25 (
% 97.99/13.25 ('#C') @ (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 '#B') @
% 97.99/13.25 (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 =) @
% 97.99/13.25 omegaS)))) @
% 97.99/13.25 omegaS)))))) @
% 97.99/13.25 (
% 97.99/13.25 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.99/13.25 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1150])).
% 97.99/13.25 thf(zip_derived_cl1166, plain,
% 97.99/13.25 (~ (((binintersectLsub) =>
% 97.99/13.25 (((binintersectSubset2) =>
% 97.99/13.25 (((binintersectSubset3) =>
% 97.99/13.25 (((binintersectER) =>
% 97.99/13.25 (((disjointsetsI1) =>
% 97.99/13.25 (((binintersectRsub) =>
% 97.99/13.25 (((binintersectSubset4) =>
% 97.99/13.25 (((binintersectSubset1) =>
% 97.99/13.25 (((bs114d) =>
% 97.99/13.25 (((setminusI) =>
% 97.99/13.25 (((setminusEL) =>
% 97.99/13.25 (((setminusER) =>
% 97.99/13.25 (((setminusSubset2) =>
% 97.99/13.25 (((setminusERneg) =>
% 97.99/13.25 (((setminusELneg) =>
% 97.99/13.25 (((setminusILneg) =>
% 97.99/13.25 (((setminusIRneg) =>
% 97.99/13.25 (((setminusLsub) =>
% 97.99/13.25 (((setminusSubset1) =>
% 97.99/13.25 (((symdiffE) =>
% 97.99/13.25 (((symdiffI1) =>
% 97.99/13.25 (((symdiffI2) =>
% 97.99/13.25 (((symdiffIneg1) =>
% 97.99/13.25 (((symdiffIneg2) =>
% 97.99/13.25 (((secondinupair) =>
% 97.99/13.25 (((setukpairIL) =>
% 97.99/13.25 (((setukpairIR) =>
% 97.99/13.25 (((kpairiskpair) =>
% 97.99/13.25 (((kpairp) =>
% 97.99/13.25 (((singletonsubset) =>
% 97.99/13.25 ((
% 97.99/13.25 (singletoninpowerset) =>
% 97.99/13.25 ((
% 97.99/13.25 (singletoninpowunion) =>
% 97.99/13.25 ((
% 97.99/13.25 (upairset2E) =>
% 97.99/13.25 ((
% 97.99/13.25 (upairsubunion) =>
% 97.99/13.25 ((
% 97.99/13.25 (upairinpowunion) =>
% 97.99/13.25 ((
% 97.99/13.25 (ubforcartprodlem1) =>
% 97.99/13.25 ((
% 97.99/13.25 (ubforcartprodlem2) =>
% 97.99/13.25 ((
% 97.99/13.25 (ubforcartprodlem3) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodpairin) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodmempair1) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodmempair) =>
% 97.99/13.25 ((
% 97.99/13.25 (setunionE2) =>
% 97.99/13.25 ((
% 97.99/13.25 (setunionsingleton1) =>
% 97.99/13.25 ((
% 97.99/13.25 (setunionsingleton2) =>
% 97.99/13.25 ((
% 97.99/13.25 (setunionsingleton) =>
% 97.99/13.25 ((
% 97.99/13.25 (singletonprop) =>
% 97.99/13.25 ((
% 97.99/13.25 (ex1E1) =>
% 97.99/13.25 ((
% 97.99/13.25 (ex1I) =>
% 97.99/13.25 ((
% 97.99/13.25 (ex1I2) =>
% 97.99/13.25 ((
% 97.99/13.25 (singletonsuniq) =>
% 97.99/13.25 ((
% 97.99/13.25 (setukpairinjL1) =>
% 97.99/13.25 ((
% 97.99/13.25 (kfstsingleton) =>
% 97.99/13.25 ((
% 97.99/13.25 (theprop) =>
% 97.99/13.25 ((
% 97.99/13.25 (kfstpairEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodfstin) =>
% 97.99/13.25 ((
% 97.99/13.25 (setukpairinjL2) =>
% 97.99/13.25 ((
% 97.99/13.25 (setukpairinjL) =>
% 97.99/13.25 ((
% 97.99/13.25 (setukpairinjR11) =>
% 97.99/13.25 ((
% 97.99/13.25 (setukpairinjR12) =>
% 97.99/13.25 ((
% 97.99/13.25 (setukpairinjR1) =>
% 97.99/13.25 ((
% 97.99/13.25 (upairequniteq) =>
% 97.99/13.25 ((
% 97.99/13.25 (setukpairinjR2) =>
% 97.99/13.25 ((
% 97.99/13.25 (setukpairinjR) =>
% 97.99/13.25 ((
% 97.99/13.25 (ksndsingleton) =>
% 97.99/13.25 ((
% 97.99/13.25 (ksndpairEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (kpairsurjEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodsndin) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodpairmemEL) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodpairmemER) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodmempaircEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodfstpairEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodsndpairEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodpairsurjEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (dpsetconstrI) =>
% 97.99/13.25 ((
% 97.99/13.25 (dpsetconstrSub) =>
% 97.99/13.25 ((
% 97.99/13.25 (setOfPairsIsBReln) =>
% 97.99/13.25 ((
% 97.99/13.25 (dpsetconstrERa) =>
% 97.99/13.25 ((
% 97.99/13.25 (dpsetconstrEL1) =>
% 97.99/13.25 ((
% 97.99/13.25 (dpsetconstrEL2) =>
% 97.99/13.25 ((
% 97.99/13.25 (dpsetconstrER) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcImageSingleton) =>
% 97.99/13.25 ((
% 97.99/13.25 (apProp) =>
% 97.99/13.25 ((
% 97.99/13.25 (app) =>
% 97.99/13.25 ((
% 97.99/13.25 (infuncsetfunc) =>
% 97.99/13.25 ((
% 97.99/13.25 (ap2p) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcinfuncset) =>
% 97.99/13.25 ((
% 97.99/13.25 (lamProp) =>
% 97.99/13.25 ((
% 97.99/13.25 (lamp) =>
% 97.99/13.25 ((
% 97.99/13.25 (lam2p) =>
% 97.99/13.25 ((
% 97.99/13.25 (brelnall1) =>
% 97.99/13.25 ((
% 97.99/13.25 (brelnall2) =>
% 97.99/13.25 ((
% 97.99/13.25 (ex1E2) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcGraphProp1) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcGraphProp3) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcGraphProp2) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcextLem) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcGraphProp4) =>
% 97.99/13.25 ((
% 97.99/13.25 (subbreln) =>
% 97.99/13.25 ((
% 97.99/13.25 (eqbreln) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcext) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcext2) =>
% 97.99/13.25 ((
% 97.99/13.25 (ap2apEq1) =>
% 97.99/13.25 ((
% 97.99/13.25 (ap2apEq2) =>
% 97.99/13.25 ((
% 97.99/13.25 (beta1) =>
% 97.99/13.25 ((
% 97.99/13.25 (eta1) =>
% 97.99/13.25 ((
% 97.99/13.25 (lam2lamEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (beta2) =>
% 97.99/13.25 ((
% 97.99/13.25 (eta2) =>
% 97.99/13.25 ((
% 97.99/13.25 (iffalseProp1) =>
% 97.99/13.25 ((
% 97.99/13.25 (iffalseProp2) =>
% 97.99/13.25 ((
% 97.99/13.25 (iftrueProp1) =>
% 97.99/13.25 ((
% 97.99/13.25 (iftrueProp2) =>
% 97.99/13.25 ((
% 97.99/13.25 (ifSingleton) =>
% 97.99/13.25 ((
% 97.99/13.25 (ifp) =>
% 97.99/13.25 ((
% 97.99/13.25 (theeq) =>
% 97.99/13.25 ((
% 97.99/13.25 (iftrue) =>
% 97.99/13.25 ((
% 97.99/13.25 (iffalse) =>
% 97.99/13.25 ((
% 97.99/13.25 (iftrueorfalse) =>
% 97.99/13.25 ((
% 97.99/13.25 (binintersectT_lem) =>
% 97.99/13.25 ((
% 97.99/13.25 (binunionT_lem) =>
% 97.99/13.25 ((
% 97.99/13.25 (powersetT_lem) =>
% 97.99/13.25 ((
% 97.99/13.25 (setminusT_lem) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementT_lem) =>
% 97.99/13.25 ((
% 97.99/13.25 (setextT) =>
% 97.99/13.25 ((
% 97.99/13.25 (subsetTI) =>
% 97.99/13.25 ((
% 97.99/13.25 (powersetTI1) =>
% 97.99/13.25 ((
% 97.99/13.25 (powersetTE1) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementTI1) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementTE1) =>
% 97.99/13.25 ((
% 97.99/13.25 (binintersectTELcontra) =>
% 97.99/13.25 ((
% 97.99/13.25 (binintersectTERcontra) =>
% 97.99/13.25 ((
% 97.99/13.25 (contrasubsetT) =>
% 97.99/13.25 ((
% 97.99/13.25 (contrasubsetT1) =>
% 97.99/13.25 ((
% 97.99/13.25 (contrasubsetT2) =>
% 97.99/13.25 ((
% 97.99/13.25 (contrasubsetT3) =>
% 97.99/13.25 ((
% 97.99/13.25 (doubleComplementI1) =>
% 97.99/13.25 ((
% 97.99/13.25 (doubleComplementE1) =>
% 97.99/13.25 ((
% 97.99/13.25 (doubleComplementSub1) =>
% 97.99/13.25 ((
% 97.99/13.25 (doubleComplementSub2) =>
% 97.99/13.25 ((
% 97.99/13.25 (doubleComplementEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementTnotintersectT) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementImpComplementIntersect) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementSubsetComplementIntersect) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementInPowersetComplementIntersect) =>
% 97.99/13.25 ((
% 97.99/13.25 (contraSubsetComplement) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementTcontraSubset) =>
% 97.99/13.25 ((
% 97.99/13.25 (binunionTILcontra) =>
% 97.99/13.25 ((
% 97.99/13.25 (binunionTIRcontra) =>
% 97.99/13.25 ((
% 97.99/13.25 (inIntersectImpInUnion) =>
% 97.99/13.25 ((
% 97.99/13.25 (inIntersectImpInUnion2) =>
% 97.99/13.25 ((
% 97.99/13.25 (inIntersectImpInIntersectUnions) =>
% 97.99/13.25 ((
% 97.99/13.25 (intersectInPowersetIntersectUnions) =>
% 97.99/13.25 ((
% 97.99/13.25 (inComplementUnionImpNotIn1) =>
% 97.99/13.25 ((
% 97.99/13.25 (inComplementUnionImpInComplement1) =>
% 97.99/13.25 ((
% 97.99/13.25 (binunionTE) =>
% 97.99/13.25 ((
% 97.99/13.25 (binunionTEcontra) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan2a1) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementUnionInPowersetComplement) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan2a2) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan1a) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan1b) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan1) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan2a) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan2b2) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan2b) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan2) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz13rule0) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz13rule1) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz13rule2) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz13rule3) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz13rule4) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz1_1) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz1_2) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz1_3) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz1_4) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz1_5) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1all2) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1SetBreln1) =>
% 97.99/13.25 ((
% 97.99/13.25 (choice2fnsingleton) =>
% 97.99/13.25 ((
% 97.99/13.25 (setOfPairsIsBReln1) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1all1) =>
% 97.99/13.25 ((
% 97.99/13.25 (subbreln1) =>
% 97.99/13.25 ((
% 97.99/13.25 (eqbreln1) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1invprop) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1invI) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1invE) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1compprop) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1compI) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1compE) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1compEex) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1unionprop) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1unionIL) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1unionIR) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1unionI) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1unionE) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1unionEcases) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1unionCommutes) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz2Ex) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz2W) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz2A) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz2B) =>
% 97.99/13.25 ((
% 97.99/13.25 (image1Ex) =>
% 97.99/13.25 ((
% 97.99/13.25 (image1Ex1) =>
% 97.99/13.25 ((
% 97.99/13.25 (image1Equiv) =>
% 97.99/13.25 ((
% 97.99/13.25 (image1E) =>
% 97.99/13.25 ((
% 97.99/13.25 (image1I) =>
% 97.99/13.25 ((
% 97.99/13.25 (injFuncInInjFuncSet) =>
% 97.99/13.25 ((
% 97.99/13.25 (injFuncSetFuncIn) =>
% 97.99/13.25 ((
% 97.99/13.25 (injFuncSetFuncInj) =>
% 97.99/13.25 ((
% 97.99/13.25 (surjFuncSetFuncIn) =>
% 97.99/13.25 ((
% 97.99/13.25 (surjFuncSetFuncSurj) =>
% 97.99/13.25 ((
% 97.99/13.25 (leftInvIsSurj) =>
% 97.99/13.25 ((
% 97.99/13.25 (surjCantorThm) =>
% 97.99/13.25 ((
% 97.99/13.25 (foundation2) =>
% 97.99/13.25 ((
% 97.99/13.25 (notinself) =>
% 97.99/13.25 ((
% 97.99/13.25 (notinself2) =>
% 97.99/13.25 ((
% 97.99/13.25 (omegaSp) =>
% 97.99/13.25 ((
% 97.99/13.25 (omegaSclos) =>
% 97.99/13.25 ((
% 97.99/13.25 (peano0notS) =>
% 97.99/13.25 ((
% 97.99/13.25 (!!) @ (
% 97.99/13.25 (('#S') @ (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 =>) @
% 97.99/13.25 (
% 97.99/13.25 (
% 97.99/13.25 ('#C') @ in @
% 97.99/13.25 omega)))) @
% 97.99/13.25 (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 !!) @
% 97.99/13.25 (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 (
% 97.99/13.25 ('#S') @ (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 =>) @
% 97.99/13.25 (
% 97.99/13.25 (
% 97.99/13.25 ('#C') @ in @
% 97.99/13.25 omega)))))) @
% 97.99/13.25 (
% 97.99/13.25 (
% 97.99/13.25 ('#S') @ (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 '#S') @
% 97.99/13.25 (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 =>))) @
% 97.99/13.25 (
% 97.99/13.25 (
% 97.99/13.25 ('#C') @ (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 '#B') @
% 97.99/13.25 (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 =) @
% 97.99/13.25 omegaS)))) @
% 97.99/13.25 omegaS)))))) @
% 97.99/13.25 (
% 97.99/13.25 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.99/13.25 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1158])).
% 97.99/13.25 thf(zip_derived_cl1174, plain,
% 97.99/13.25 (~ (((binintersectSubset2) =>
% 97.99/13.25 (((binintersectSubset3) =>
% 97.99/13.25 (((binintersectER) =>
% 97.99/13.25 (((disjointsetsI1) =>
% 97.99/13.25 (((binintersectRsub) =>
% 97.99/13.25 (((binintersectSubset4) =>
% 97.99/13.25 (((binintersectSubset1) =>
% 97.99/13.25 (((bs114d) =>
% 97.99/13.25 (((setminusI) =>
% 97.99/13.25 (((setminusEL) =>
% 97.99/13.25 (((setminusER) =>
% 97.99/13.25 (((setminusSubset2) =>
% 97.99/13.25 (((setminusERneg) =>
% 97.99/13.25 (((setminusELneg) =>
% 97.99/13.25 (((setminusILneg) =>
% 97.99/13.25 (((setminusIRneg) =>
% 97.99/13.25 (((setminusLsub) =>
% 97.99/13.25 (((setminusSubset1) =>
% 97.99/13.25 (((symdiffE) =>
% 97.99/13.25 (((symdiffI1) =>
% 97.99/13.25 (((symdiffI2) =>
% 97.99/13.25 (((symdiffIneg1) =>
% 97.99/13.25 (((symdiffIneg2) =>
% 97.99/13.25 (((secondinupair) =>
% 97.99/13.25 (((setukpairIL) =>
% 97.99/13.25 (((setukpairIR) =>
% 97.99/13.25 (((kpairiskpair) =>
% 97.99/13.25 (((kpairp) =>
% 97.99/13.25 (((singletonsubset) =>
% 97.99/13.25 (((singletoninpowerset) =>
% 97.99/13.25 ((
% 97.99/13.25 (singletoninpowunion) =>
% 97.99/13.25 ((
% 97.99/13.25 (upairset2E) =>
% 97.99/13.25 ((
% 97.99/13.25 (upairsubunion) =>
% 97.99/13.25 ((
% 97.99/13.25 (upairinpowunion) =>
% 97.99/13.25 ((
% 97.99/13.25 (ubforcartprodlem1) =>
% 97.99/13.25 ((
% 97.99/13.25 (ubforcartprodlem2) =>
% 97.99/13.25 ((
% 97.99/13.25 (ubforcartprodlem3) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodpairin) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodmempair1) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodmempair) =>
% 97.99/13.25 ((
% 97.99/13.25 (setunionE2) =>
% 97.99/13.25 ((
% 97.99/13.25 (setunionsingleton1) =>
% 97.99/13.25 ((
% 97.99/13.25 (setunionsingleton2) =>
% 97.99/13.25 ((
% 97.99/13.25 (setunionsingleton) =>
% 97.99/13.25 ((
% 97.99/13.25 (singletonprop) =>
% 97.99/13.25 ((
% 97.99/13.25 (ex1E1) =>
% 97.99/13.25 ((
% 97.99/13.25 (ex1I) =>
% 97.99/13.25 ((
% 97.99/13.25 (ex1I2) =>
% 97.99/13.25 ((
% 97.99/13.25 (singletonsuniq) =>
% 97.99/13.25 ((
% 97.99/13.25 (setukpairinjL1) =>
% 97.99/13.25 ((
% 97.99/13.25 (kfstsingleton) =>
% 97.99/13.25 ((
% 97.99/13.25 (theprop) =>
% 97.99/13.25 ((
% 97.99/13.25 (kfstpairEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodfstin) =>
% 97.99/13.25 ((
% 97.99/13.25 (setukpairinjL2) =>
% 97.99/13.25 ((
% 97.99/13.25 (setukpairinjL) =>
% 97.99/13.25 ((
% 97.99/13.25 (setukpairinjR11) =>
% 97.99/13.25 ((
% 97.99/13.25 (setukpairinjR12) =>
% 97.99/13.25 ((
% 97.99/13.25 (setukpairinjR1) =>
% 97.99/13.25 ((
% 97.99/13.25 (upairequniteq) =>
% 97.99/13.25 ((
% 97.99/13.25 (setukpairinjR2) =>
% 97.99/13.25 ((
% 97.99/13.25 (setukpairinjR) =>
% 97.99/13.25 ((
% 97.99/13.25 (ksndsingleton) =>
% 97.99/13.25 ((
% 97.99/13.25 (ksndpairEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (kpairsurjEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodsndin) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodpairmemEL) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodpairmemER) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodmempaircEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodfstpairEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodsndpairEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodpairsurjEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (dpsetconstrI) =>
% 97.99/13.25 ((
% 97.99/13.25 (dpsetconstrSub) =>
% 97.99/13.25 ((
% 97.99/13.25 (setOfPairsIsBReln) =>
% 97.99/13.25 ((
% 97.99/13.25 (dpsetconstrERa) =>
% 97.99/13.25 ((
% 97.99/13.25 (dpsetconstrEL1) =>
% 97.99/13.25 ((
% 97.99/13.25 (dpsetconstrEL2) =>
% 97.99/13.25 ((
% 97.99/13.25 (dpsetconstrER) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcImageSingleton) =>
% 97.99/13.25 ((
% 97.99/13.25 (apProp) =>
% 97.99/13.25 ((
% 97.99/13.25 (app) =>
% 97.99/13.25 ((
% 97.99/13.25 (infuncsetfunc) =>
% 97.99/13.25 ((
% 97.99/13.25 (ap2p) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcinfuncset) =>
% 97.99/13.25 ((
% 97.99/13.25 (lamProp) =>
% 97.99/13.25 ((
% 97.99/13.25 (lamp) =>
% 97.99/13.25 ((
% 97.99/13.25 (lam2p) =>
% 97.99/13.25 ((
% 97.99/13.25 (brelnall1) =>
% 97.99/13.25 ((
% 97.99/13.25 (brelnall2) =>
% 97.99/13.25 ((
% 97.99/13.25 (ex1E2) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcGraphProp1) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcGraphProp3) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcGraphProp2) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcextLem) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcGraphProp4) =>
% 97.99/13.25 ((
% 97.99/13.25 (subbreln) =>
% 97.99/13.25 ((
% 97.99/13.25 (eqbreln) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcext) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcext2) =>
% 97.99/13.25 ((
% 97.99/13.25 (ap2apEq1) =>
% 97.99/13.25 ((
% 97.99/13.25 (ap2apEq2) =>
% 97.99/13.25 ((
% 97.99/13.25 (beta1) =>
% 97.99/13.25 ((
% 97.99/13.25 (eta1) =>
% 97.99/13.25 ((
% 97.99/13.25 (lam2lamEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (beta2) =>
% 97.99/13.25 ((
% 97.99/13.25 (eta2) =>
% 97.99/13.25 ((
% 97.99/13.25 (iffalseProp1) =>
% 97.99/13.25 ((
% 97.99/13.25 (iffalseProp2) =>
% 97.99/13.25 ((
% 97.99/13.25 (iftrueProp1) =>
% 97.99/13.25 ((
% 97.99/13.25 (iftrueProp2) =>
% 97.99/13.25 ((
% 97.99/13.25 (ifSingleton) =>
% 97.99/13.25 ((
% 97.99/13.25 (ifp) =>
% 97.99/13.25 ((
% 97.99/13.25 (theeq) =>
% 97.99/13.25 ((
% 97.99/13.25 (iftrue) =>
% 97.99/13.25 ((
% 97.99/13.25 (iffalse) =>
% 97.99/13.25 ((
% 97.99/13.25 (iftrueorfalse) =>
% 97.99/13.25 ((
% 97.99/13.25 (binintersectT_lem) =>
% 97.99/13.25 ((
% 97.99/13.25 (binunionT_lem) =>
% 97.99/13.25 ((
% 97.99/13.25 (powersetT_lem) =>
% 97.99/13.25 ((
% 97.99/13.25 (setminusT_lem) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementT_lem) =>
% 97.99/13.25 ((
% 97.99/13.25 (setextT) =>
% 97.99/13.25 ((
% 97.99/13.25 (subsetTI) =>
% 97.99/13.25 ((
% 97.99/13.25 (powersetTI1) =>
% 97.99/13.25 ((
% 97.99/13.25 (powersetTE1) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementTI1) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementTE1) =>
% 97.99/13.25 ((
% 97.99/13.25 (binintersectTELcontra) =>
% 97.99/13.25 ((
% 97.99/13.25 (binintersectTERcontra) =>
% 97.99/13.25 ((
% 97.99/13.25 (contrasubsetT) =>
% 97.99/13.25 ((
% 97.99/13.25 (contrasubsetT1) =>
% 97.99/13.25 ((
% 97.99/13.25 (contrasubsetT2) =>
% 97.99/13.25 ((
% 97.99/13.25 (contrasubsetT3) =>
% 97.99/13.25 ((
% 97.99/13.25 (doubleComplementI1) =>
% 97.99/13.25 ((
% 97.99/13.25 (doubleComplementE1) =>
% 97.99/13.25 ((
% 97.99/13.25 (doubleComplementSub1) =>
% 97.99/13.25 ((
% 97.99/13.25 (doubleComplementSub2) =>
% 97.99/13.25 ((
% 97.99/13.25 (doubleComplementEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementTnotintersectT) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementImpComplementIntersect) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementSubsetComplementIntersect) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementInPowersetComplementIntersect) =>
% 97.99/13.25 ((
% 97.99/13.25 (contraSubsetComplement) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementTcontraSubset) =>
% 97.99/13.25 ((
% 97.99/13.25 (binunionTILcontra) =>
% 97.99/13.25 ((
% 97.99/13.25 (binunionTIRcontra) =>
% 97.99/13.25 ((
% 97.99/13.25 (inIntersectImpInUnion) =>
% 97.99/13.25 ((
% 97.99/13.25 (inIntersectImpInUnion2) =>
% 97.99/13.25 ((
% 97.99/13.25 (inIntersectImpInIntersectUnions) =>
% 97.99/13.25 ((
% 97.99/13.25 (intersectInPowersetIntersectUnions) =>
% 97.99/13.25 ((
% 97.99/13.25 (inComplementUnionImpNotIn1) =>
% 97.99/13.25 ((
% 97.99/13.25 (inComplementUnionImpInComplement1) =>
% 97.99/13.25 ((
% 97.99/13.25 (binunionTE) =>
% 97.99/13.25 ((
% 97.99/13.25 (binunionTEcontra) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan2a1) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementUnionInPowersetComplement) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan2a2) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan1a) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan1b) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan1) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan2a) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan2b2) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan2b) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan2) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz13rule0) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz13rule1) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz13rule2) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz13rule3) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz13rule4) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz1_1) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz1_2) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz1_3) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz1_4) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz1_5) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1all2) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1SetBreln1) =>
% 97.99/13.25 ((
% 97.99/13.25 (choice2fnsingleton) =>
% 97.99/13.25 ((
% 97.99/13.25 (setOfPairsIsBReln1) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1all1) =>
% 97.99/13.25 ((
% 97.99/13.25 (subbreln1) =>
% 97.99/13.25 ((
% 97.99/13.25 (eqbreln1) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1invprop) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1invI) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1invE) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1compprop) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1compI) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1compE) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1compEex) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1unionprop) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1unionIL) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1unionIR) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1unionI) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1unionE) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1unionEcases) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1unionCommutes) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz2Ex) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz2W) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz2A) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz2B) =>
% 97.99/13.25 ((
% 97.99/13.25 (image1Ex) =>
% 97.99/13.25 ((
% 97.99/13.25 (image1Ex1) =>
% 97.99/13.25 ((
% 97.99/13.25 (image1Equiv) =>
% 97.99/13.25 ((
% 97.99/13.25 (image1E) =>
% 97.99/13.25 ((
% 97.99/13.25 (image1I) =>
% 97.99/13.25 ((
% 97.99/13.25 (injFuncInInjFuncSet) =>
% 97.99/13.25 ((
% 97.99/13.25 (injFuncSetFuncIn) =>
% 97.99/13.25 ((
% 97.99/13.25 (injFuncSetFuncInj) =>
% 97.99/13.25 ((
% 97.99/13.25 (surjFuncSetFuncIn) =>
% 97.99/13.25 ((
% 97.99/13.25 (surjFuncSetFuncSurj) =>
% 97.99/13.25 ((
% 97.99/13.25 (leftInvIsSurj) =>
% 97.99/13.25 ((
% 97.99/13.25 (surjCantorThm) =>
% 97.99/13.25 ((
% 97.99/13.25 (foundation2) =>
% 97.99/13.25 ((
% 97.99/13.25 (notinself) =>
% 97.99/13.25 ((
% 97.99/13.25 (notinself2) =>
% 97.99/13.25 ((
% 97.99/13.25 (omegaSp) =>
% 97.99/13.25 ((
% 97.99/13.25 (omegaSclos) =>
% 97.99/13.25 ((
% 97.99/13.25 (peano0notS) =>
% 97.99/13.25 ((
% 97.99/13.25 (!!) @ (
% 97.99/13.25 (('#S') @ (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 =>) @
% 97.99/13.25 (
% 97.99/13.25 (
% 97.99/13.25 ('#C') @ in @
% 97.99/13.25 omega)))) @
% 97.99/13.25 (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 !!) @
% 97.99/13.25 (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 (
% 97.99/13.25 ('#S') @ (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 =>) @
% 97.99/13.25 (
% 97.99/13.25 (
% 97.99/13.25 ('#C') @ in @
% 97.99/13.25 omega)))))) @
% 97.99/13.25 (
% 97.99/13.25 (
% 97.99/13.25 ('#S') @ (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 '#S') @
% 97.99/13.25 (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 =>))) @
% 97.99/13.25 (
% 97.99/13.25 (
% 97.99/13.25 ('#C') @ (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 '#B') @
% 97.99/13.25 (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 =) @
% 97.99/13.25 omegaS)))) @
% 97.99/13.25 omegaS)))))) @
% 97.99/13.25 (
% 97.99/13.25 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.99/13.25 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1166])).
% 97.99/13.25 thf(zip_derived_cl1183, plain,
% 97.99/13.25 (~ (((binintersectSubset3) =>
% 97.99/13.25 (((binintersectER) =>
% 97.99/13.25 (((disjointsetsI1) =>
% 97.99/13.25 (((binintersectRsub) =>
% 97.99/13.25 (((binintersectSubset4) =>
% 97.99/13.25 (((binintersectSubset1) =>
% 97.99/13.25 (((bs114d) =>
% 97.99/13.25 (((setminusI) =>
% 97.99/13.25 (((setminusEL) =>
% 97.99/13.25 (((setminusER) =>
% 97.99/13.25 (((setminusSubset2) =>
% 97.99/13.25 (((setminusERneg) =>
% 97.99/13.25 (((setminusELneg) =>
% 97.99/13.25 (((setminusILneg) =>
% 97.99/13.25 (((setminusIRneg) =>
% 97.99/13.25 (((setminusLsub) =>
% 97.99/13.25 (((setminusSubset1) =>
% 97.99/13.25 (((symdiffE) =>
% 97.99/13.25 (((symdiffI1) =>
% 97.99/13.25 (((symdiffI2) =>
% 97.99/13.25 (((symdiffIneg1) =>
% 97.99/13.25 (((symdiffIneg2) =>
% 97.99/13.25 (((secondinupair) =>
% 97.99/13.25 (((setukpairIL) =>
% 97.99/13.25 (((setukpairIR) =>
% 97.99/13.25 (((kpairiskpair) =>
% 97.99/13.25 (((kpairp) =>
% 97.99/13.25 (((singletonsubset) =>
% 97.99/13.25 (((singletoninpowerset) =>
% 97.99/13.25 (((singletoninpowunion) =>
% 97.99/13.25 ((
% 97.99/13.25 (upairset2E) =>
% 97.99/13.25 ((
% 97.99/13.25 (upairsubunion) =>
% 97.99/13.25 ((
% 97.99/13.25 (upairinpowunion) =>
% 97.99/13.25 ((
% 97.99/13.25 (ubforcartprodlem1) =>
% 97.99/13.25 ((
% 97.99/13.25 (ubforcartprodlem2) =>
% 97.99/13.25 ((
% 97.99/13.25 (ubforcartprodlem3) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodpairin) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodmempair1) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodmempair) =>
% 97.99/13.25 ((
% 97.99/13.25 (setunionE2) =>
% 97.99/13.25 ((
% 97.99/13.25 (setunionsingleton1) =>
% 97.99/13.25 ((
% 97.99/13.25 (setunionsingleton2) =>
% 97.99/13.25 ((
% 97.99/13.25 (setunionsingleton) =>
% 97.99/13.25 ((
% 97.99/13.25 (singletonprop) =>
% 97.99/13.25 ((
% 97.99/13.25 (ex1E1) =>
% 97.99/13.25 ((
% 97.99/13.25 (ex1I) =>
% 97.99/13.25 ((
% 97.99/13.25 (ex1I2) =>
% 97.99/13.25 ((
% 97.99/13.25 (singletonsuniq) =>
% 97.99/13.25 ((
% 97.99/13.25 (setukpairinjL1) =>
% 97.99/13.25 ((
% 97.99/13.25 (kfstsingleton) =>
% 97.99/13.25 ((
% 97.99/13.25 (theprop) =>
% 97.99/13.25 ((
% 97.99/13.25 (kfstpairEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodfstin) =>
% 97.99/13.25 ((
% 97.99/13.25 (setukpairinjL2) =>
% 97.99/13.25 ((
% 97.99/13.25 (setukpairinjL) =>
% 97.99/13.25 ((
% 97.99/13.25 (setukpairinjR11) =>
% 97.99/13.25 ((
% 97.99/13.25 (setukpairinjR12) =>
% 97.99/13.25 ((
% 97.99/13.25 (setukpairinjR1) =>
% 97.99/13.25 ((
% 97.99/13.25 (upairequniteq) =>
% 97.99/13.25 ((
% 97.99/13.25 (setukpairinjR2) =>
% 97.99/13.25 ((
% 97.99/13.25 (setukpairinjR) =>
% 97.99/13.25 ((
% 97.99/13.25 (ksndsingleton) =>
% 97.99/13.25 ((
% 97.99/13.25 (ksndpairEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (kpairsurjEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodsndin) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodpairmemEL) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodpairmemER) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodmempaircEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodfstpairEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodsndpairEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodpairsurjEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (dpsetconstrI) =>
% 97.99/13.25 ((
% 97.99/13.25 (dpsetconstrSub) =>
% 97.99/13.25 ((
% 97.99/13.25 (setOfPairsIsBReln) =>
% 97.99/13.25 ((
% 97.99/13.25 (dpsetconstrERa) =>
% 97.99/13.25 ((
% 97.99/13.25 (dpsetconstrEL1) =>
% 97.99/13.25 ((
% 97.99/13.25 (dpsetconstrEL2) =>
% 97.99/13.25 ((
% 97.99/13.25 (dpsetconstrER) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcImageSingleton) =>
% 97.99/13.25 ((
% 97.99/13.25 (apProp) =>
% 97.99/13.25 ((
% 97.99/13.25 (app) =>
% 97.99/13.25 ((
% 97.99/13.25 (infuncsetfunc) =>
% 97.99/13.25 ((
% 97.99/13.25 (ap2p) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcinfuncset) =>
% 97.99/13.25 ((
% 97.99/13.25 (lamProp) =>
% 97.99/13.25 ((
% 97.99/13.25 (lamp) =>
% 97.99/13.25 ((
% 97.99/13.25 (lam2p) =>
% 97.99/13.25 ((
% 97.99/13.25 (brelnall1) =>
% 97.99/13.25 ((
% 97.99/13.25 (brelnall2) =>
% 97.99/13.25 ((
% 97.99/13.25 (ex1E2) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcGraphProp1) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcGraphProp3) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcGraphProp2) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcextLem) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcGraphProp4) =>
% 97.99/13.25 ((
% 97.99/13.25 (subbreln) =>
% 97.99/13.25 ((
% 97.99/13.25 (eqbreln) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcext) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcext2) =>
% 97.99/13.25 ((
% 97.99/13.25 (ap2apEq1) =>
% 97.99/13.25 ((
% 97.99/13.25 (ap2apEq2) =>
% 97.99/13.25 ((
% 97.99/13.25 (beta1) =>
% 97.99/13.25 ((
% 97.99/13.25 (eta1) =>
% 97.99/13.25 ((
% 97.99/13.25 (lam2lamEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (beta2) =>
% 97.99/13.25 ((
% 97.99/13.25 (eta2) =>
% 97.99/13.25 ((
% 97.99/13.25 (iffalseProp1) =>
% 97.99/13.25 ((
% 97.99/13.25 (iffalseProp2) =>
% 97.99/13.25 ((
% 97.99/13.25 (iftrueProp1) =>
% 97.99/13.25 ((
% 97.99/13.25 (iftrueProp2) =>
% 97.99/13.25 ((
% 97.99/13.25 (ifSingleton) =>
% 97.99/13.25 ((
% 97.99/13.25 (ifp) =>
% 97.99/13.25 ((
% 97.99/13.25 (theeq) =>
% 97.99/13.25 ((
% 97.99/13.25 (iftrue) =>
% 97.99/13.25 ((
% 97.99/13.25 (iffalse) =>
% 97.99/13.25 ((
% 97.99/13.25 (iftrueorfalse) =>
% 97.99/13.25 ((
% 97.99/13.25 (binintersectT_lem) =>
% 97.99/13.25 ((
% 97.99/13.25 (binunionT_lem) =>
% 97.99/13.25 ((
% 97.99/13.25 (powersetT_lem) =>
% 97.99/13.25 ((
% 97.99/13.25 (setminusT_lem) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementT_lem) =>
% 97.99/13.25 ((
% 97.99/13.25 (setextT) =>
% 97.99/13.25 ((
% 97.99/13.25 (subsetTI) =>
% 97.99/13.25 ((
% 97.99/13.25 (powersetTI1) =>
% 97.99/13.25 ((
% 97.99/13.25 (powersetTE1) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementTI1) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementTE1) =>
% 97.99/13.25 ((
% 97.99/13.25 (binintersectTELcontra) =>
% 97.99/13.25 ((
% 97.99/13.25 (binintersectTERcontra) =>
% 97.99/13.25 ((
% 97.99/13.25 (contrasubsetT) =>
% 97.99/13.25 ((
% 97.99/13.25 (contrasubsetT1) =>
% 97.99/13.25 ((
% 97.99/13.25 (contrasubsetT2) =>
% 97.99/13.25 ((
% 97.99/13.25 (contrasubsetT3) =>
% 97.99/13.25 ((
% 97.99/13.25 (doubleComplementI1) =>
% 97.99/13.25 ((
% 97.99/13.25 (doubleComplementE1) =>
% 97.99/13.25 ((
% 97.99/13.25 (doubleComplementSub1) =>
% 97.99/13.25 ((
% 97.99/13.25 (doubleComplementSub2) =>
% 97.99/13.25 ((
% 97.99/13.25 (doubleComplementEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementTnotintersectT) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementImpComplementIntersect) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementSubsetComplementIntersect) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementInPowersetComplementIntersect) =>
% 97.99/13.25 ((
% 97.99/13.25 (contraSubsetComplement) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementTcontraSubset) =>
% 97.99/13.25 ((
% 97.99/13.25 (binunionTILcontra) =>
% 97.99/13.25 ((
% 97.99/13.25 (binunionTIRcontra) =>
% 97.99/13.25 ((
% 97.99/13.25 (inIntersectImpInUnion) =>
% 97.99/13.25 ((
% 97.99/13.25 (inIntersectImpInUnion2) =>
% 97.99/13.25 ((
% 97.99/13.25 (inIntersectImpInIntersectUnions) =>
% 97.99/13.25 ((
% 97.99/13.25 (intersectInPowersetIntersectUnions) =>
% 97.99/13.25 ((
% 97.99/13.25 (inComplementUnionImpNotIn1) =>
% 97.99/13.25 ((
% 97.99/13.25 (inComplementUnionImpInComplement1) =>
% 97.99/13.25 ((
% 97.99/13.25 (binunionTE) =>
% 97.99/13.25 ((
% 97.99/13.25 (binunionTEcontra) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan2a1) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementUnionInPowersetComplement) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan2a2) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan1a) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan1b) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan1) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan2a) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan2b2) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan2b) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan2) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz13rule0) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz13rule1) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz13rule2) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz13rule3) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz13rule4) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz1_1) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz1_2) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz1_3) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz1_4) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz1_5) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1all2) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1SetBreln1) =>
% 97.99/13.25 ((
% 97.99/13.25 (choice2fnsingleton) =>
% 97.99/13.25 ((
% 97.99/13.25 (setOfPairsIsBReln1) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1all1) =>
% 97.99/13.25 ((
% 97.99/13.25 (subbreln1) =>
% 97.99/13.25 ((
% 97.99/13.25 (eqbreln1) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1invprop) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1invI) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1invE) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1compprop) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1compI) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1compE) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1compEex) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1unionprop) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1unionIL) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1unionIR) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1unionI) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1unionE) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1unionEcases) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1unionCommutes) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz2Ex) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz2W) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz2A) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz2B) =>
% 97.99/13.25 ((
% 97.99/13.25 (image1Ex) =>
% 97.99/13.25 ((
% 97.99/13.25 (image1Ex1) =>
% 97.99/13.25 ((
% 97.99/13.25 (image1Equiv) =>
% 97.99/13.25 ((
% 97.99/13.25 (image1E) =>
% 97.99/13.25 ((
% 97.99/13.25 (image1I) =>
% 97.99/13.25 ((
% 97.99/13.25 (injFuncInInjFuncSet) =>
% 97.99/13.25 ((
% 97.99/13.25 (injFuncSetFuncIn) =>
% 97.99/13.25 ((
% 97.99/13.25 (injFuncSetFuncInj) =>
% 97.99/13.25 ((
% 97.99/13.25 (surjFuncSetFuncIn) =>
% 97.99/13.25 ((
% 97.99/13.25 (surjFuncSetFuncSurj) =>
% 97.99/13.25 ((
% 97.99/13.25 (leftInvIsSurj) =>
% 97.99/13.25 ((
% 97.99/13.25 (surjCantorThm) =>
% 97.99/13.25 ((
% 97.99/13.25 (foundation2) =>
% 97.99/13.25 ((
% 97.99/13.25 (notinself) =>
% 97.99/13.25 ((
% 97.99/13.25 (notinself2) =>
% 97.99/13.25 ((
% 97.99/13.25 (omegaSp) =>
% 97.99/13.25 ((
% 97.99/13.25 (omegaSclos) =>
% 97.99/13.25 ((
% 97.99/13.25 (peano0notS) =>
% 97.99/13.25 ((
% 97.99/13.25 (!!) @ (
% 97.99/13.25 (('#S') @ (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 =>) @
% 97.99/13.25 (
% 97.99/13.25 (
% 97.99/13.25 ('#C') @ in @
% 97.99/13.25 omega)))) @
% 97.99/13.25 (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 !!) @
% 97.99/13.25 (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 (
% 97.99/13.25 ('#S') @ (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 =>) @
% 97.99/13.25 (
% 97.99/13.25 (
% 97.99/13.25 ('#C') @ in @
% 97.99/13.25 omega)))))) @
% 97.99/13.25 (
% 97.99/13.25 (
% 97.99/13.25 ('#S') @ (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 '#S') @
% 97.99/13.25 (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 =>))) @
% 97.99/13.25 (
% 97.99/13.25 (
% 97.99/13.25 ('#C') @ (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 '#B') @
% 97.99/13.25 (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 =) @
% 97.99/13.25 omegaS)))) @
% 97.99/13.25 omegaS)))))) @
% 97.99/13.25 (
% 97.99/13.25 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.99/13.25 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1174])).
% 97.99/13.25 thf(zip_derived_cl1193, plain,
% 97.99/13.25 (~ (((binintersectER) =>
% 97.99/13.25 (((disjointsetsI1) =>
% 97.99/13.25 (((binintersectRsub) =>
% 97.99/13.25 (((binintersectSubset4) =>
% 97.99/13.25 (((binintersectSubset1) =>
% 97.99/13.25 (((bs114d) =>
% 97.99/13.25 (((setminusI) =>
% 97.99/13.25 (((setminusEL) =>
% 97.99/13.25 (((setminusER) =>
% 97.99/13.25 (((setminusSubset2) =>
% 97.99/13.25 (((setminusERneg) =>
% 97.99/13.25 (((setminusELneg) =>
% 97.99/13.25 (((setminusILneg) =>
% 97.99/13.25 (((setminusIRneg) =>
% 97.99/13.25 (((setminusLsub) =>
% 97.99/13.25 (((setminusSubset1) =>
% 97.99/13.25 (((symdiffE) =>
% 97.99/13.25 (((symdiffI1) =>
% 97.99/13.25 (((symdiffI2) =>
% 97.99/13.25 (((symdiffIneg1) =>
% 97.99/13.25 (((symdiffIneg2) =>
% 97.99/13.25 (((secondinupair) =>
% 97.99/13.25 (((setukpairIL) =>
% 97.99/13.25 (((setukpairIR) =>
% 97.99/13.25 (((kpairiskpair) =>
% 97.99/13.25 (((kpairp) =>
% 97.99/13.25 (((singletonsubset) =>
% 97.99/13.25 (((singletoninpowerset) =>
% 97.99/13.25 (((singletoninpowunion) =>
% 97.99/13.25 (((upairset2E) =>
% 97.99/13.25 ((
% 97.99/13.25 (upairsubunion) =>
% 97.99/13.25 ((
% 97.99/13.25 (upairinpowunion) =>
% 97.99/13.25 ((
% 97.99/13.25 (ubforcartprodlem1) =>
% 97.99/13.25 ((
% 97.99/13.25 (ubforcartprodlem2) =>
% 97.99/13.25 ((
% 97.99/13.25 (ubforcartprodlem3) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodpairin) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodmempair1) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodmempair) =>
% 97.99/13.25 ((
% 97.99/13.25 (setunionE2) =>
% 97.99/13.25 ((
% 97.99/13.25 (setunionsingleton1) =>
% 97.99/13.25 ((
% 97.99/13.25 (setunionsingleton2) =>
% 97.99/13.25 ((
% 97.99/13.25 (setunionsingleton) =>
% 97.99/13.25 ((
% 97.99/13.25 (singletonprop) =>
% 97.99/13.25 ((
% 97.99/13.25 (ex1E1) =>
% 97.99/13.25 ((
% 97.99/13.25 (ex1I) =>
% 97.99/13.25 ((
% 97.99/13.25 (ex1I2) =>
% 97.99/13.25 ((
% 97.99/13.25 (singletonsuniq) =>
% 97.99/13.25 ((
% 97.99/13.25 (setukpairinjL1) =>
% 97.99/13.25 ((
% 97.99/13.25 (kfstsingleton) =>
% 97.99/13.25 ((
% 97.99/13.25 (theprop) =>
% 97.99/13.25 ((
% 97.99/13.25 (kfstpairEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodfstin) =>
% 97.99/13.25 ((
% 97.99/13.25 (setukpairinjL2) =>
% 97.99/13.25 ((
% 97.99/13.25 (setukpairinjL) =>
% 97.99/13.25 ((
% 97.99/13.25 (setukpairinjR11) =>
% 97.99/13.25 ((
% 97.99/13.25 (setukpairinjR12) =>
% 97.99/13.25 ((
% 97.99/13.25 (setukpairinjR1) =>
% 97.99/13.25 ((
% 97.99/13.25 (upairequniteq) =>
% 97.99/13.25 ((
% 97.99/13.25 (setukpairinjR2) =>
% 97.99/13.25 ((
% 97.99/13.25 (setukpairinjR) =>
% 97.99/13.25 ((
% 97.99/13.25 (ksndsingleton) =>
% 97.99/13.25 ((
% 97.99/13.25 (ksndpairEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (kpairsurjEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodsndin) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodpairmemEL) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodpairmemER) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodmempaircEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodfstpairEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodsndpairEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodpairsurjEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (dpsetconstrI) =>
% 97.99/13.25 ((
% 97.99/13.25 (dpsetconstrSub) =>
% 97.99/13.25 ((
% 97.99/13.25 (setOfPairsIsBReln) =>
% 97.99/13.25 ((
% 97.99/13.25 (dpsetconstrERa) =>
% 97.99/13.25 ((
% 97.99/13.25 (dpsetconstrEL1) =>
% 97.99/13.25 ((
% 97.99/13.25 (dpsetconstrEL2) =>
% 97.99/13.25 ((
% 97.99/13.25 (dpsetconstrER) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcImageSingleton) =>
% 97.99/13.25 ((
% 97.99/13.25 (apProp) =>
% 97.99/13.25 ((
% 97.99/13.25 (app) =>
% 97.99/13.25 ((
% 97.99/13.25 (infuncsetfunc) =>
% 97.99/13.25 ((
% 97.99/13.25 (ap2p) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcinfuncset) =>
% 97.99/13.25 ((
% 97.99/13.25 (lamProp) =>
% 97.99/13.25 ((
% 97.99/13.25 (lamp) =>
% 97.99/13.25 ((
% 97.99/13.25 (lam2p) =>
% 97.99/13.25 ((
% 97.99/13.25 (brelnall1) =>
% 97.99/13.25 ((
% 97.99/13.25 (brelnall2) =>
% 97.99/13.25 ((
% 97.99/13.25 (ex1E2) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcGraphProp1) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcGraphProp3) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcGraphProp2) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcextLem) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcGraphProp4) =>
% 97.99/13.25 ((
% 97.99/13.25 (subbreln) =>
% 97.99/13.25 ((
% 97.99/13.25 (eqbreln) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcext) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcext2) =>
% 97.99/13.25 ((
% 97.99/13.25 (ap2apEq1) =>
% 97.99/13.25 ((
% 97.99/13.25 (ap2apEq2) =>
% 97.99/13.25 ((
% 97.99/13.25 (beta1) =>
% 97.99/13.25 ((
% 97.99/13.25 (eta1) =>
% 97.99/13.25 ((
% 97.99/13.25 (lam2lamEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (beta2) =>
% 97.99/13.25 ((
% 97.99/13.25 (eta2) =>
% 97.99/13.25 ((
% 97.99/13.25 (iffalseProp1) =>
% 97.99/13.25 ((
% 97.99/13.25 (iffalseProp2) =>
% 97.99/13.25 ((
% 97.99/13.25 (iftrueProp1) =>
% 97.99/13.25 ((
% 97.99/13.25 (iftrueProp2) =>
% 97.99/13.25 ((
% 97.99/13.25 (ifSingleton) =>
% 97.99/13.25 ((
% 97.99/13.25 (ifp) =>
% 97.99/13.25 ((
% 97.99/13.25 (theeq) =>
% 97.99/13.25 ((
% 97.99/13.25 (iftrue) =>
% 97.99/13.25 ((
% 97.99/13.25 (iffalse) =>
% 97.99/13.25 ((
% 97.99/13.25 (iftrueorfalse) =>
% 97.99/13.25 ((
% 97.99/13.25 (binintersectT_lem) =>
% 97.99/13.25 ((
% 97.99/13.25 (binunionT_lem) =>
% 97.99/13.25 ((
% 97.99/13.25 (powersetT_lem) =>
% 97.99/13.25 ((
% 97.99/13.25 (setminusT_lem) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementT_lem) =>
% 97.99/13.25 ((
% 97.99/13.25 (setextT) =>
% 97.99/13.25 ((
% 97.99/13.25 (subsetTI) =>
% 97.99/13.25 ((
% 97.99/13.25 (powersetTI1) =>
% 97.99/13.25 ((
% 97.99/13.25 (powersetTE1) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementTI1) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementTE1) =>
% 97.99/13.25 ((
% 97.99/13.25 (binintersectTELcontra) =>
% 97.99/13.25 ((
% 97.99/13.25 (binintersectTERcontra) =>
% 97.99/13.25 ((
% 97.99/13.25 (contrasubsetT) =>
% 97.99/13.25 ((
% 97.99/13.25 (contrasubsetT1) =>
% 97.99/13.25 ((
% 97.99/13.25 (contrasubsetT2) =>
% 97.99/13.25 ((
% 97.99/13.25 (contrasubsetT3) =>
% 97.99/13.25 ((
% 97.99/13.25 (doubleComplementI1) =>
% 97.99/13.25 ((
% 97.99/13.25 (doubleComplementE1) =>
% 97.99/13.25 ((
% 97.99/13.25 (doubleComplementSub1) =>
% 97.99/13.25 ((
% 97.99/13.25 (doubleComplementSub2) =>
% 97.99/13.25 ((
% 97.99/13.25 (doubleComplementEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementTnotintersectT) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementImpComplementIntersect) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementSubsetComplementIntersect) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementInPowersetComplementIntersect) =>
% 97.99/13.25 ((
% 97.99/13.25 (contraSubsetComplement) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementTcontraSubset) =>
% 97.99/13.25 ((
% 97.99/13.25 (binunionTILcontra) =>
% 97.99/13.25 ((
% 97.99/13.25 (binunionTIRcontra) =>
% 97.99/13.25 ((
% 97.99/13.25 (inIntersectImpInUnion) =>
% 97.99/13.25 ((
% 97.99/13.25 (inIntersectImpInUnion2) =>
% 97.99/13.25 ((
% 97.99/13.25 (inIntersectImpInIntersectUnions) =>
% 97.99/13.25 ((
% 97.99/13.25 (intersectInPowersetIntersectUnions) =>
% 97.99/13.25 ((
% 97.99/13.25 (inComplementUnionImpNotIn1) =>
% 97.99/13.25 ((
% 97.99/13.25 (inComplementUnionImpInComplement1) =>
% 97.99/13.25 ((
% 97.99/13.25 (binunionTE) =>
% 97.99/13.25 ((
% 97.99/13.25 (binunionTEcontra) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan2a1) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementUnionInPowersetComplement) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan2a2) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan1a) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan1b) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan1) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan2a) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan2b2) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan2b) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan2) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz13rule0) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz13rule1) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz13rule2) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz13rule3) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz13rule4) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz1_1) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz1_2) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz1_3) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz1_4) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz1_5) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1all2) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1SetBreln1) =>
% 97.99/13.25 ((
% 97.99/13.25 (choice2fnsingleton) =>
% 97.99/13.25 ((
% 97.99/13.25 (setOfPairsIsBReln1) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1all1) =>
% 97.99/13.25 ((
% 97.99/13.25 (subbreln1) =>
% 97.99/13.25 ((
% 97.99/13.25 (eqbreln1) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1invprop) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1invI) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1invE) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1compprop) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1compI) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1compE) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1compEex) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1unionprop) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1unionIL) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1unionIR) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1unionI) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1unionE) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1unionEcases) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1unionCommutes) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz2Ex) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz2W) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz2A) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz2B) =>
% 97.99/13.25 ((
% 97.99/13.25 (image1Ex) =>
% 97.99/13.25 ((
% 97.99/13.25 (image1Ex1) =>
% 97.99/13.25 ((
% 97.99/13.25 (image1Equiv) =>
% 97.99/13.25 ((
% 97.99/13.25 (image1E) =>
% 97.99/13.25 ((
% 97.99/13.25 (image1I) =>
% 97.99/13.25 ((
% 97.99/13.25 (injFuncInInjFuncSet) =>
% 97.99/13.25 ((
% 97.99/13.25 (injFuncSetFuncIn) =>
% 97.99/13.25 ((
% 97.99/13.25 (injFuncSetFuncInj) =>
% 97.99/13.25 ((
% 97.99/13.25 (surjFuncSetFuncIn) =>
% 97.99/13.25 ((
% 97.99/13.25 (surjFuncSetFuncSurj) =>
% 97.99/13.25 ((
% 97.99/13.25 (leftInvIsSurj) =>
% 97.99/13.25 ((
% 97.99/13.25 (surjCantorThm) =>
% 97.99/13.25 ((
% 97.99/13.25 (foundation2) =>
% 97.99/13.25 ((
% 97.99/13.25 (notinself) =>
% 97.99/13.25 ((
% 97.99/13.25 (notinself2) =>
% 97.99/13.25 ((
% 97.99/13.25 (omegaSp) =>
% 97.99/13.25 ((
% 97.99/13.25 (omegaSclos) =>
% 97.99/13.25 ((
% 97.99/13.25 (peano0notS) =>
% 97.99/13.25 ((
% 97.99/13.25 (!!) @ (
% 97.99/13.25 (('#S') @ (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 =>) @
% 97.99/13.25 (
% 97.99/13.25 (
% 97.99/13.25 ('#C') @ in @
% 97.99/13.25 omega)))) @
% 97.99/13.25 (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 !!) @
% 97.99/13.25 (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 (
% 97.99/13.25 ('#S') @ (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 =>) @
% 97.99/13.25 (
% 97.99/13.25 (
% 97.99/13.25 ('#C') @ in @
% 97.99/13.25 omega)))))) @
% 97.99/13.25 (
% 97.99/13.25 (
% 97.99/13.25 ('#S') @ (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 '#S') @
% 97.99/13.25 (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 =>))) @
% 97.99/13.25 (
% 97.99/13.25 (
% 97.99/13.25 ('#C') @ (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 '#B') @
% 97.99/13.25 (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 =) @
% 97.99/13.25 omegaS)))) @
% 97.99/13.25 omegaS)))))) @
% 97.99/13.25 (
% 97.99/13.25 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.99/13.25 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1183])).
% 97.99/13.25 thf(zip_derived_cl1206, plain,
% 97.99/13.25 (~ (((disjointsetsI1) =>
% 97.99/13.25 (((binintersectRsub) =>
% 97.99/13.25 (((binintersectSubset4) =>
% 97.99/13.25 (((binintersectSubset1) =>
% 97.99/13.25 (((bs114d) =>
% 97.99/13.25 (((setminusI) =>
% 97.99/13.25 (((setminusEL) =>
% 97.99/13.25 (((setminusER) =>
% 97.99/13.25 (((setminusSubset2) =>
% 97.99/13.25 (((setminusERneg) =>
% 97.99/13.25 (((setminusELneg) =>
% 97.99/13.25 (((setminusILneg) =>
% 97.99/13.25 (((setminusIRneg) =>
% 97.99/13.25 (((setminusLsub) =>
% 97.99/13.25 (((setminusSubset1) =>
% 97.99/13.25 (((symdiffE) =>
% 97.99/13.25 (((symdiffI1) =>
% 97.99/13.25 (((symdiffI2) =>
% 97.99/13.25 (((symdiffIneg1) =>
% 97.99/13.25 (((symdiffIneg2) =>
% 97.99/13.25 (((secondinupair) =>
% 97.99/13.25 (((setukpairIL) =>
% 97.99/13.25 (((setukpairIR) =>
% 97.99/13.25 (((kpairiskpair) =>
% 97.99/13.25 (((kpairp) =>
% 97.99/13.25 (((singletonsubset) =>
% 97.99/13.25 (((singletoninpowerset) =>
% 97.99/13.25 (((singletoninpowunion) =>
% 97.99/13.25 (((upairset2E) =>
% 97.99/13.25 (((upairsubunion) =>
% 97.99/13.25 ((
% 97.99/13.25 (upairinpowunion) =>
% 97.99/13.25 ((
% 97.99/13.25 (ubforcartprodlem1) =>
% 97.99/13.25 ((
% 97.99/13.25 (ubforcartprodlem2) =>
% 97.99/13.25 ((
% 97.99/13.25 (ubforcartprodlem3) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodpairin) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodmempair1) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodmempair) =>
% 97.99/13.25 ((
% 97.99/13.25 (setunionE2) =>
% 97.99/13.25 ((
% 97.99/13.25 (setunionsingleton1) =>
% 97.99/13.25 ((
% 97.99/13.25 (setunionsingleton2) =>
% 97.99/13.25 ((
% 97.99/13.25 (setunionsingleton) =>
% 97.99/13.25 ((
% 97.99/13.25 (singletonprop) =>
% 97.99/13.25 ((
% 97.99/13.25 (ex1E1) =>
% 97.99/13.25 ((
% 97.99/13.25 (ex1I) =>
% 97.99/13.25 ((
% 97.99/13.25 (ex1I2) =>
% 97.99/13.25 ((
% 97.99/13.25 (singletonsuniq) =>
% 97.99/13.25 ((
% 97.99/13.25 (setukpairinjL1) =>
% 97.99/13.25 ((
% 97.99/13.25 (kfstsingleton) =>
% 97.99/13.25 ((
% 97.99/13.25 (theprop) =>
% 97.99/13.25 ((
% 97.99/13.25 (kfstpairEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodfstin) =>
% 97.99/13.25 ((
% 97.99/13.25 (setukpairinjL2) =>
% 97.99/13.25 ((
% 97.99/13.25 (setukpairinjL) =>
% 97.99/13.25 ((
% 97.99/13.25 (setukpairinjR11) =>
% 97.99/13.25 ((
% 97.99/13.25 (setukpairinjR12) =>
% 97.99/13.25 ((
% 97.99/13.25 (setukpairinjR1) =>
% 97.99/13.25 ((
% 97.99/13.25 (upairequniteq) =>
% 97.99/13.25 ((
% 97.99/13.25 (setukpairinjR2) =>
% 97.99/13.25 ((
% 97.99/13.25 (setukpairinjR) =>
% 97.99/13.25 ((
% 97.99/13.25 (ksndsingleton) =>
% 97.99/13.25 ((
% 97.99/13.25 (ksndpairEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (kpairsurjEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodsndin) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodpairmemEL) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodpairmemER) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodmempaircEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodfstpairEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodsndpairEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodpairsurjEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (dpsetconstrI) =>
% 97.99/13.25 ((
% 97.99/13.25 (dpsetconstrSub) =>
% 97.99/13.25 ((
% 97.99/13.25 (setOfPairsIsBReln) =>
% 97.99/13.25 ((
% 97.99/13.25 (dpsetconstrERa) =>
% 97.99/13.25 ((
% 97.99/13.25 (dpsetconstrEL1) =>
% 97.99/13.25 ((
% 97.99/13.25 (dpsetconstrEL2) =>
% 97.99/13.25 ((
% 97.99/13.25 (dpsetconstrER) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcImageSingleton) =>
% 97.99/13.25 ((
% 97.99/13.25 (apProp) =>
% 97.99/13.25 ((
% 97.99/13.25 (app) =>
% 97.99/13.25 ((
% 97.99/13.25 (infuncsetfunc) =>
% 97.99/13.25 ((
% 97.99/13.25 (ap2p) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcinfuncset) =>
% 97.99/13.25 ((
% 97.99/13.25 (lamProp) =>
% 97.99/13.25 ((
% 97.99/13.25 (lamp) =>
% 97.99/13.25 ((
% 97.99/13.25 (lam2p) =>
% 97.99/13.25 ((
% 97.99/13.25 (brelnall1) =>
% 97.99/13.25 ((
% 97.99/13.25 (brelnall2) =>
% 97.99/13.25 ((
% 97.99/13.25 (ex1E2) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcGraphProp1) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcGraphProp3) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcGraphProp2) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcextLem) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcGraphProp4) =>
% 97.99/13.25 ((
% 97.99/13.25 (subbreln) =>
% 97.99/13.25 ((
% 97.99/13.25 (eqbreln) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcext) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcext2) =>
% 97.99/13.25 ((
% 97.99/13.25 (ap2apEq1) =>
% 97.99/13.25 ((
% 97.99/13.25 (ap2apEq2) =>
% 97.99/13.25 ((
% 97.99/13.25 (beta1) =>
% 97.99/13.25 ((
% 97.99/13.25 (eta1) =>
% 97.99/13.25 ((
% 97.99/13.25 (lam2lamEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (beta2) =>
% 97.99/13.25 ((
% 97.99/13.25 (eta2) =>
% 97.99/13.25 ((
% 97.99/13.25 (iffalseProp1) =>
% 97.99/13.25 ((
% 97.99/13.25 (iffalseProp2) =>
% 97.99/13.25 ((
% 97.99/13.25 (iftrueProp1) =>
% 97.99/13.25 ((
% 97.99/13.25 (iftrueProp2) =>
% 97.99/13.25 ((
% 97.99/13.25 (ifSingleton) =>
% 97.99/13.25 ((
% 97.99/13.25 (ifp) =>
% 97.99/13.25 ((
% 97.99/13.25 (theeq) =>
% 97.99/13.25 ((
% 97.99/13.25 (iftrue) =>
% 97.99/13.25 ((
% 97.99/13.25 (iffalse) =>
% 97.99/13.25 ((
% 97.99/13.25 (iftrueorfalse) =>
% 97.99/13.25 ((
% 97.99/13.25 (binintersectT_lem) =>
% 97.99/13.25 ((
% 97.99/13.25 (binunionT_lem) =>
% 97.99/13.25 ((
% 97.99/13.25 (powersetT_lem) =>
% 97.99/13.25 ((
% 97.99/13.25 (setminusT_lem) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementT_lem) =>
% 97.99/13.25 ((
% 97.99/13.25 (setextT) =>
% 97.99/13.25 ((
% 97.99/13.25 (subsetTI) =>
% 97.99/13.25 ((
% 97.99/13.25 (powersetTI1) =>
% 97.99/13.25 ((
% 97.99/13.25 (powersetTE1) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementTI1) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementTE1) =>
% 97.99/13.25 ((
% 97.99/13.25 (binintersectTELcontra) =>
% 97.99/13.25 ((
% 97.99/13.25 (binintersectTERcontra) =>
% 97.99/13.25 ((
% 97.99/13.25 (contrasubsetT) =>
% 97.99/13.25 ((
% 97.99/13.25 (contrasubsetT1) =>
% 97.99/13.25 ((
% 97.99/13.25 (contrasubsetT2) =>
% 97.99/13.25 ((
% 97.99/13.25 (contrasubsetT3) =>
% 97.99/13.25 ((
% 97.99/13.25 (doubleComplementI1) =>
% 97.99/13.25 ((
% 97.99/13.25 (doubleComplementE1) =>
% 97.99/13.25 ((
% 97.99/13.25 (doubleComplementSub1) =>
% 97.99/13.25 ((
% 97.99/13.25 (doubleComplementSub2) =>
% 97.99/13.25 ((
% 97.99/13.25 (doubleComplementEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementTnotintersectT) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementImpComplementIntersect) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementSubsetComplementIntersect) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementInPowersetComplementIntersect) =>
% 97.99/13.25 ((
% 97.99/13.25 (contraSubsetComplement) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementTcontraSubset) =>
% 97.99/13.25 ((
% 97.99/13.25 (binunionTILcontra) =>
% 97.99/13.25 ((
% 97.99/13.25 (binunionTIRcontra) =>
% 97.99/13.25 ((
% 97.99/13.25 (inIntersectImpInUnion) =>
% 97.99/13.25 ((
% 97.99/13.25 (inIntersectImpInUnion2) =>
% 97.99/13.25 ((
% 97.99/13.25 (inIntersectImpInIntersectUnions) =>
% 97.99/13.25 ((
% 97.99/13.25 (intersectInPowersetIntersectUnions) =>
% 97.99/13.25 ((
% 97.99/13.25 (inComplementUnionImpNotIn1) =>
% 97.99/13.25 ((
% 97.99/13.25 (inComplementUnionImpInComplement1) =>
% 97.99/13.25 ((
% 97.99/13.25 (binunionTE) =>
% 97.99/13.25 ((
% 97.99/13.25 (binunionTEcontra) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan2a1) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementUnionInPowersetComplement) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan2a2) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan1a) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan1b) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan1) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan2a) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan2b2) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan2b) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan2) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz13rule0) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz13rule1) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz13rule2) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz13rule3) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz13rule4) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz1_1) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz1_2) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz1_3) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz1_4) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz1_5) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1all2) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1SetBreln1) =>
% 97.99/13.25 ((
% 97.99/13.25 (choice2fnsingleton) =>
% 97.99/13.25 ((
% 97.99/13.25 (setOfPairsIsBReln1) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1all1) =>
% 97.99/13.25 ((
% 97.99/13.25 (subbreln1) =>
% 97.99/13.25 ((
% 97.99/13.25 (eqbreln1) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1invprop) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1invI) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1invE) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1compprop) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1compI) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1compE) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1compEex) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1unionprop) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1unionIL) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1unionIR) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1unionI) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1unionE) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1unionEcases) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1unionCommutes) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz2Ex) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz2W) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz2A) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz2B) =>
% 97.99/13.25 ((
% 97.99/13.25 (image1Ex) =>
% 97.99/13.25 ((
% 97.99/13.25 (image1Ex1) =>
% 97.99/13.25 ((
% 97.99/13.25 (image1Equiv) =>
% 97.99/13.25 ((
% 97.99/13.25 (image1E) =>
% 97.99/13.25 ((
% 97.99/13.25 (image1I) =>
% 97.99/13.25 ((
% 97.99/13.25 (injFuncInInjFuncSet) =>
% 97.99/13.25 ((
% 97.99/13.25 (injFuncSetFuncIn) =>
% 97.99/13.25 ((
% 97.99/13.25 (injFuncSetFuncInj) =>
% 97.99/13.25 ((
% 97.99/13.25 (surjFuncSetFuncIn) =>
% 97.99/13.25 ((
% 97.99/13.25 (surjFuncSetFuncSurj) =>
% 97.99/13.25 ((
% 97.99/13.25 (leftInvIsSurj) =>
% 97.99/13.25 ((
% 97.99/13.25 (surjCantorThm) =>
% 97.99/13.25 ((
% 97.99/13.25 (foundation2) =>
% 97.99/13.25 ((
% 97.99/13.25 (notinself) =>
% 97.99/13.25 ((
% 97.99/13.25 (notinself2) =>
% 97.99/13.25 ((
% 97.99/13.25 (omegaSp) =>
% 97.99/13.25 ((
% 97.99/13.25 (omegaSclos) =>
% 97.99/13.25 ((
% 97.99/13.25 (peano0notS) =>
% 97.99/13.25 ((
% 97.99/13.25 (!!) @ (
% 97.99/13.25 (('#S') @ (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 =>) @
% 97.99/13.25 (
% 97.99/13.25 (
% 97.99/13.25 ('#C') @ in @
% 97.99/13.25 omega)))) @
% 97.99/13.25 (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 !!) @
% 97.99/13.25 (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 (
% 97.99/13.25 ('#S') @ (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 =>) @
% 97.99/13.25 (
% 97.99/13.25 (
% 97.99/13.25 ('#C') @ in @
% 97.99/13.25 omega)))))) @
% 97.99/13.25 (
% 97.99/13.25 (
% 97.99/13.25 ('#S') @ (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 '#S') @
% 97.99/13.25 (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 =>))) @
% 97.99/13.25 (
% 97.99/13.25 (
% 97.99/13.25 ('#C') @ (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 '#B') @
% 97.99/13.25 (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 =) @
% 97.99/13.25 omegaS)))) @
% 97.99/13.25 omegaS)))))) @
% 97.99/13.25 (
% 97.99/13.25 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.99/13.25 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1193])).
% 97.99/13.25 thf(zip_derived_cl1216, plain,
% 97.99/13.25 (~ (((binintersectRsub) =>
% 97.99/13.25 (((binintersectSubset4) =>
% 97.99/13.25 (((binintersectSubset1) =>
% 97.99/13.25 (((bs114d) =>
% 97.99/13.25 (((setminusI) =>
% 97.99/13.25 (((setminusEL) =>
% 97.99/13.25 (((setminusER) =>
% 97.99/13.25 (((setminusSubset2) =>
% 97.99/13.25 (((setminusERneg) =>
% 97.99/13.25 (((setminusELneg) =>
% 97.99/13.25 (((setminusILneg) =>
% 97.99/13.25 (((setminusIRneg) =>
% 97.99/13.25 (((setminusLsub) =>
% 97.99/13.25 (((setminusSubset1) =>
% 97.99/13.25 (((symdiffE) =>
% 97.99/13.25 (((symdiffI1) =>
% 97.99/13.25 (((symdiffI2) =>
% 97.99/13.25 (((symdiffIneg1) =>
% 97.99/13.25 (((symdiffIneg2) =>
% 97.99/13.25 (((secondinupair) =>
% 97.99/13.25 (((setukpairIL) =>
% 97.99/13.25 (((setukpairIR) =>
% 97.99/13.25 (((kpairiskpair) =>
% 97.99/13.25 (((kpairp) =>
% 97.99/13.25 (((singletonsubset) =>
% 97.99/13.25 (((singletoninpowerset) =>
% 97.99/13.25 (((singletoninpowunion) =>
% 97.99/13.25 (((upairset2E) =>
% 97.99/13.25 (((upairsubunion) =>
% 97.99/13.25 (((upairinpowunion) =>
% 97.99/13.25 ((
% 97.99/13.25 (ubforcartprodlem1) =>
% 97.99/13.25 ((
% 97.99/13.25 (ubforcartprodlem2) =>
% 97.99/13.25 ((
% 97.99/13.25 (ubforcartprodlem3) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodpairin) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodmempair1) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodmempair) =>
% 97.99/13.25 ((
% 97.99/13.25 (setunionE2) =>
% 97.99/13.25 ((
% 97.99/13.25 (setunionsingleton1) =>
% 97.99/13.25 ((
% 97.99/13.25 (setunionsingleton2) =>
% 97.99/13.25 ((
% 97.99/13.25 (setunionsingleton) =>
% 97.99/13.25 ((
% 97.99/13.25 (singletonprop) =>
% 97.99/13.25 ((
% 97.99/13.25 (ex1E1) =>
% 97.99/13.25 ((
% 97.99/13.25 (ex1I) =>
% 97.99/13.25 ((
% 97.99/13.25 (ex1I2) =>
% 97.99/13.25 ((
% 97.99/13.25 (singletonsuniq) =>
% 97.99/13.25 ((
% 97.99/13.25 (setukpairinjL1) =>
% 97.99/13.25 ((
% 97.99/13.25 (kfstsingleton) =>
% 97.99/13.25 ((
% 97.99/13.25 (theprop) =>
% 97.99/13.25 ((
% 97.99/13.25 (kfstpairEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodfstin) =>
% 97.99/13.25 ((
% 97.99/13.25 (setukpairinjL2) =>
% 97.99/13.25 ((
% 97.99/13.25 (setukpairinjL) =>
% 97.99/13.25 ((
% 97.99/13.25 (setukpairinjR11) =>
% 97.99/13.25 ((
% 97.99/13.25 (setukpairinjR12) =>
% 97.99/13.25 ((
% 97.99/13.25 (setukpairinjR1) =>
% 97.99/13.25 ((
% 97.99/13.25 (upairequniteq) =>
% 97.99/13.25 ((
% 97.99/13.25 (setukpairinjR2) =>
% 97.99/13.25 ((
% 97.99/13.25 (setukpairinjR) =>
% 97.99/13.25 ((
% 97.99/13.25 (ksndsingleton) =>
% 97.99/13.25 ((
% 97.99/13.25 (ksndpairEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (kpairsurjEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodsndin) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodpairmemEL) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodpairmemER) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodmempaircEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodfstpairEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodsndpairEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodpairsurjEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (dpsetconstrI) =>
% 97.99/13.25 ((
% 97.99/13.25 (dpsetconstrSub) =>
% 97.99/13.25 ((
% 97.99/13.25 (setOfPairsIsBReln) =>
% 97.99/13.25 ((
% 97.99/13.25 (dpsetconstrERa) =>
% 97.99/13.25 ((
% 97.99/13.25 (dpsetconstrEL1) =>
% 97.99/13.25 ((
% 97.99/13.25 (dpsetconstrEL2) =>
% 97.99/13.25 ((
% 97.99/13.25 (dpsetconstrER) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcImageSingleton) =>
% 97.99/13.25 ((
% 97.99/13.25 (apProp) =>
% 97.99/13.25 ((
% 97.99/13.25 (app) =>
% 97.99/13.25 ((
% 97.99/13.25 (infuncsetfunc) =>
% 97.99/13.25 ((
% 97.99/13.25 (ap2p) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcinfuncset) =>
% 97.99/13.25 ((
% 97.99/13.25 (lamProp) =>
% 97.99/13.25 ((
% 97.99/13.25 (lamp) =>
% 97.99/13.25 ((
% 97.99/13.25 (lam2p) =>
% 97.99/13.25 ((
% 97.99/13.25 (brelnall1) =>
% 97.99/13.25 ((
% 97.99/13.25 (brelnall2) =>
% 97.99/13.25 ((
% 97.99/13.25 (ex1E2) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcGraphProp1) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcGraphProp3) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcGraphProp2) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcextLem) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcGraphProp4) =>
% 97.99/13.25 ((
% 97.99/13.25 (subbreln) =>
% 97.99/13.25 ((
% 97.99/13.25 (eqbreln) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcext) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcext2) =>
% 97.99/13.25 ((
% 97.99/13.25 (ap2apEq1) =>
% 97.99/13.25 ((
% 97.99/13.25 (ap2apEq2) =>
% 97.99/13.25 ((
% 97.99/13.25 (beta1) =>
% 97.99/13.25 ((
% 97.99/13.25 (eta1) =>
% 97.99/13.25 ((
% 97.99/13.25 (lam2lamEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (beta2) =>
% 97.99/13.25 ((
% 97.99/13.25 (eta2) =>
% 97.99/13.25 ((
% 97.99/13.25 (iffalseProp1) =>
% 97.99/13.25 ((
% 97.99/13.25 (iffalseProp2) =>
% 97.99/13.25 ((
% 97.99/13.25 (iftrueProp1) =>
% 97.99/13.25 ((
% 97.99/13.25 (iftrueProp2) =>
% 97.99/13.25 ((
% 97.99/13.25 (ifSingleton) =>
% 97.99/13.25 ((
% 97.99/13.25 (ifp) =>
% 97.99/13.25 ((
% 97.99/13.25 (theeq) =>
% 97.99/13.25 ((
% 97.99/13.25 (iftrue) =>
% 97.99/13.25 ((
% 97.99/13.25 (iffalse) =>
% 97.99/13.25 ((
% 97.99/13.25 (iftrueorfalse) =>
% 97.99/13.25 ((
% 97.99/13.25 (binintersectT_lem) =>
% 97.99/13.25 ((
% 97.99/13.25 (binunionT_lem) =>
% 97.99/13.25 ((
% 97.99/13.25 (powersetT_lem) =>
% 97.99/13.25 ((
% 97.99/13.25 (setminusT_lem) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementT_lem) =>
% 97.99/13.25 ((
% 97.99/13.25 (setextT) =>
% 97.99/13.25 ((
% 97.99/13.25 (subsetTI) =>
% 97.99/13.25 ((
% 97.99/13.25 (powersetTI1) =>
% 97.99/13.25 ((
% 97.99/13.25 (powersetTE1) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementTI1) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementTE1) =>
% 97.99/13.25 ((
% 97.99/13.25 (binintersectTELcontra) =>
% 97.99/13.25 ((
% 97.99/13.25 (binintersectTERcontra) =>
% 97.99/13.25 ((
% 97.99/13.25 (contrasubsetT) =>
% 97.99/13.25 ((
% 97.99/13.25 (contrasubsetT1) =>
% 97.99/13.25 ((
% 97.99/13.25 (contrasubsetT2) =>
% 97.99/13.25 ((
% 97.99/13.25 (contrasubsetT3) =>
% 97.99/13.25 ((
% 97.99/13.25 (doubleComplementI1) =>
% 97.99/13.25 ((
% 97.99/13.25 (doubleComplementE1) =>
% 97.99/13.25 ((
% 97.99/13.25 (doubleComplementSub1) =>
% 97.99/13.25 ((
% 97.99/13.25 (doubleComplementSub2) =>
% 97.99/13.25 ((
% 97.99/13.25 (doubleComplementEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementTnotintersectT) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementImpComplementIntersect) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementSubsetComplementIntersect) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementInPowersetComplementIntersect) =>
% 97.99/13.25 ((
% 97.99/13.25 (contraSubsetComplement) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementTcontraSubset) =>
% 97.99/13.25 ((
% 97.99/13.25 (binunionTILcontra) =>
% 97.99/13.25 ((
% 97.99/13.25 (binunionTIRcontra) =>
% 97.99/13.25 ((
% 97.99/13.25 (inIntersectImpInUnion) =>
% 97.99/13.25 ((
% 97.99/13.25 (inIntersectImpInUnion2) =>
% 97.99/13.25 ((
% 97.99/13.25 (inIntersectImpInIntersectUnions) =>
% 97.99/13.25 ((
% 97.99/13.25 (intersectInPowersetIntersectUnions) =>
% 97.99/13.25 ((
% 97.99/13.25 (inComplementUnionImpNotIn1) =>
% 97.99/13.25 ((
% 97.99/13.25 (inComplementUnionImpInComplement1) =>
% 97.99/13.25 ((
% 97.99/13.25 (binunionTE) =>
% 97.99/13.25 ((
% 97.99/13.25 (binunionTEcontra) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan2a1) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementUnionInPowersetComplement) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan2a2) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan1a) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan1b) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan1) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan2a) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan2b2) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan2b) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan2) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz13rule0) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz13rule1) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz13rule2) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz13rule3) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz13rule4) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz1_1) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz1_2) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz1_3) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz1_4) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz1_5) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1all2) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1SetBreln1) =>
% 97.99/13.25 ((
% 97.99/13.25 (choice2fnsingleton) =>
% 97.99/13.25 ((
% 97.99/13.25 (setOfPairsIsBReln1) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1all1) =>
% 97.99/13.25 ((
% 97.99/13.25 (subbreln1) =>
% 97.99/13.25 ((
% 97.99/13.25 (eqbreln1) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1invprop) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1invI) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1invE) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1compprop) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1compI) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1compE) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1compEex) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1unionprop) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1unionIL) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1unionIR) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1unionI) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1unionE) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1unionEcases) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1unionCommutes) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz2Ex) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz2W) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz2A) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz2B) =>
% 97.99/13.25 ((
% 97.99/13.25 (image1Ex) =>
% 97.99/13.25 ((
% 97.99/13.25 (image1Ex1) =>
% 97.99/13.25 ((
% 97.99/13.25 (image1Equiv) =>
% 97.99/13.25 ((
% 97.99/13.25 (image1E) =>
% 97.99/13.25 ((
% 97.99/13.25 (image1I) =>
% 97.99/13.25 ((
% 97.99/13.25 (injFuncInInjFuncSet) =>
% 97.99/13.25 ((
% 97.99/13.25 (injFuncSetFuncIn) =>
% 97.99/13.25 ((
% 97.99/13.25 (injFuncSetFuncInj) =>
% 97.99/13.25 ((
% 97.99/13.25 (surjFuncSetFuncIn) =>
% 97.99/13.25 ((
% 97.99/13.25 (surjFuncSetFuncSurj) =>
% 97.99/13.25 ((
% 97.99/13.25 (leftInvIsSurj) =>
% 97.99/13.25 ((
% 97.99/13.25 (surjCantorThm) =>
% 97.99/13.25 ((
% 97.99/13.25 (foundation2) =>
% 97.99/13.25 ((
% 97.99/13.25 (notinself) =>
% 97.99/13.25 ((
% 97.99/13.25 (notinself2) =>
% 97.99/13.25 ((
% 97.99/13.25 (omegaSp) =>
% 97.99/13.25 ((
% 97.99/13.25 (omegaSclos) =>
% 97.99/13.25 ((
% 97.99/13.25 (peano0notS) =>
% 97.99/13.25 ((
% 97.99/13.25 (!!) @ (
% 97.99/13.25 (('#S') @ (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 =>) @
% 97.99/13.25 (
% 97.99/13.25 (
% 97.99/13.25 ('#C') @ in @
% 97.99/13.25 omega)))) @
% 97.99/13.25 (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 !!) @
% 97.99/13.25 (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 (
% 97.99/13.25 ('#S') @ (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 =>) @
% 97.99/13.25 (
% 97.99/13.25 (
% 97.99/13.25 ('#C') @ in @
% 97.99/13.25 omega)))))) @
% 97.99/13.25 (
% 97.99/13.25 (
% 97.99/13.25 ('#S') @ (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 '#S') @
% 97.99/13.25 (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 =>))) @
% 97.99/13.25 (
% 97.99/13.25 (
% 97.99/13.25 ('#C') @ (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 '#B') @
% 97.99/13.25 (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 =) @
% 97.99/13.25 omegaS)))) @
% 97.99/13.25 omegaS)))))) @
% 97.99/13.25 (
% 97.99/13.25 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.99/13.25 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1206])).
% 97.99/13.25 thf(zip_derived_cl1223, plain,
% 97.99/13.25 (~ (((binintersectSubset4) =>
% 97.99/13.25 (((binintersectSubset1) =>
% 97.99/13.25 (((bs114d) =>
% 97.99/13.25 (((setminusI) =>
% 97.99/13.25 (((setminusEL) =>
% 97.99/13.25 (((setminusER) =>
% 97.99/13.25 (((setminusSubset2) =>
% 97.99/13.25 (((setminusERneg) =>
% 97.99/13.25 (((setminusELneg) =>
% 97.99/13.25 (((setminusILneg) =>
% 97.99/13.25 (((setminusIRneg) =>
% 97.99/13.25 (((setminusLsub) =>
% 97.99/13.25 (((setminusSubset1) =>
% 97.99/13.25 (((symdiffE) =>
% 97.99/13.25 (((symdiffI1) =>
% 97.99/13.25 (((symdiffI2) =>
% 97.99/13.25 (((symdiffIneg1) =>
% 97.99/13.25 (((symdiffIneg2) =>
% 97.99/13.25 (((secondinupair) =>
% 97.99/13.25 (((setukpairIL) =>
% 97.99/13.25 (((setukpairIR) =>
% 97.99/13.25 (((kpairiskpair) =>
% 97.99/13.25 (((kpairp) =>
% 97.99/13.25 (((singletonsubset) =>
% 97.99/13.25 (((singletoninpowerset) =>
% 97.99/13.25 (((singletoninpowunion) =>
% 97.99/13.25 (((upairset2E) =>
% 97.99/13.25 (((upairsubunion) =>
% 97.99/13.25 (((upairinpowunion) =>
% 97.99/13.25 (((ubforcartprodlem1) =>
% 97.99/13.25 ((
% 97.99/13.25 (ubforcartprodlem2) =>
% 97.99/13.25 ((
% 97.99/13.25 (ubforcartprodlem3) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodpairin) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodmempair1) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodmempair) =>
% 97.99/13.25 ((
% 97.99/13.25 (setunionE2) =>
% 97.99/13.25 ((
% 97.99/13.25 (setunionsingleton1) =>
% 97.99/13.25 ((
% 97.99/13.25 (setunionsingleton2) =>
% 97.99/13.25 ((
% 97.99/13.25 (setunionsingleton) =>
% 97.99/13.25 ((
% 97.99/13.25 (singletonprop) =>
% 97.99/13.25 ((
% 97.99/13.25 (ex1E1) =>
% 97.99/13.25 ((
% 97.99/13.25 (ex1I) =>
% 97.99/13.25 ((
% 97.99/13.25 (ex1I2) =>
% 97.99/13.25 ((
% 97.99/13.25 (singletonsuniq) =>
% 97.99/13.25 ((
% 97.99/13.25 (setukpairinjL1) =>
% 97.99/13.25 ((
% 97.99/13.25 (kfstsingleton) =>
% 97.99/13.25 ((
% 97.99/13.25 (theprop) =>
% 97.99/13.25 ((
% 97.99/13.25 (kfstpairEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodfstin) =>
% 97.99/13.25 ((
% 97.99/13.25 (setukpairinjL2) =>
% 97.99/13.25 ((
% 97.99/13.25 (setukpairinjL) =>
% 97.99/13.25 ((
% 97.99/13.25 (setukpairinjR11) =>
% 97.99/13.25 ((
% 97.99/13.25 (setukpairinjR12) =>
% 97.99/13.25 ((
% 97.99/13.25 (setukpairinjR1) =>
% 97.99/13.25 ((
% 97.99/13.25 (upairequniteq) =>
% 97.99/13.25 ((
% 97.99/13.25 (setukpairinjR2) =>
% 97.99/13.25 ((
% 97.99/13.25 (setukpairinjR) =>
% 97.99/13.25 ((
% 97.99/13.25 (ksndsingleton) =>
% 97.99/13.25 ((
% 97.99/13.25 (ksndpairEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (kpairsurjEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodsndin) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodpairmemEL) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodpairmemER) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodmempaircEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodfstpairEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodsndpairEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodpairsurjEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (dpsetconstrI) =>
% 97.99/13.25 ((
% 97.99/13.25 (dpsetconstrSub) =>
% 97.99/13.25 ((
% 97.99/13.25 (setOfPairsIsBReln) =>
% 97.99/13.25 ((
% 97.99/13.25 (dpsetconstrERa) =>
% 97.99/13.25 ((
% 97.99/13.25 (dpsetconstrEL1) =>
% 97.99/13.25 ((
% 97.99/13.25 (dpsetconstrEL2) =>
% 97.99/13.25 ((
% 97.99/13.25 (dpsetconstrER) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcImageSingleton) =>
% 97.99/13.25 ((
% 97.99/13.25 (apProp) =>
% 97.99/13.25 ((
% 97.99/13.25 (app) =>
% 97.99/13.25 ((
% 97.99/13.25 (infuncsetfunc) =>
% 97.99/13.25 ((
% 97.99/13.25 (ap2p) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcinfuncset) =>
% 97.99/13.25 ((
% 97.99/13.25 (lamProp) =>
% 97.99/13.25 ((
% 97.99/13.25 (lamp) =>
% 97.99/13.25 ((
% 97.99/13.25 (lam2p) =>
% 97.99/13.25 ((
% 97.99/13.25 (brelnall1) =>
% 97.99/13.25 ((
% 97.99/13.25 (brelnall2) =>
% 97.99/13.25 ((
% 97.99/13.25 (ex1E2) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcGraphProp1) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcGraphProp3) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcGraphProp2) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcextLem) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcGraphProp4) =>
% 97.99/13.25 ((
% 97.99/13.25 (subbreln) =>
% 97.99/13.25 ((
% 97.99/13.25 (eqbreln) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcext) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcext2) =>
% 97.99/13.25 ((
% 97.99/13.25 (ap2apEq1) =>
% 97.99/13.25 ((
% 97.99/13.25 (ap2apEq2) =>
% 97.99/13.25 ((
% 97.99/13.25 (beta1) =>
% 97.99/13.25 ((
% 97.99/13.25 (eta1) =>
% 97.99/13.25 ((
% 97.99/13.25 (lam2lamEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (beta2) =>
% 97.99/13.25 ((
% 97.99/13.25 (eta2) =>
% 97.99/13.25 ((
% 97.99/13.25 (iffalseProp1) =>
% 97.99/13.25 ((
% 97.99/13.25 (iffalseProp2) =>
% 97.99/13.25 ((
% 97.99/13.25 (iftrueProp1) =>
% 97.99/13.25 ((
% 97.99/13.25 (iftrueProp2) =>
% 97.99/13.25 ((
% 97.99/13.25 (ifSingleton) =>
% 97.99/13.25 ((
% 97.99/13.25 (ifp) =>
% 97.99/13.25 ((
% 97.99/13.25 (theeq) =>
% 97.99/13.25 ((
% 97.99/13.25 (iftrue) =>
% 97.99/13.25 ((
% 97.99/13.25 (iffalse) =>
% 97.99/13.25 ((
% 97.99/13.25 (iftrueorfalse) =>
% 97.99/13.25 ((
% 97.99/13.25 (binintersectT_lem) =>
% 97.99/13.25 ((
% 97.99/13.25 (binunionT_lem) =>
% 97.99/13.25 ((
% 97.99/13.25 (powersetT_lem) =>
% 97.99/13.25 ((
% 97.99/13.25 (setminusT_lem) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementT_lem) =>
% 97.99/13.25 ((
% 97.99/13.25 (setextT) =>
% 97.99/13.25 ((
% 97.99/13.25 (subsetTI) =>
% 97.99/13.25 ((
% 97.99/13.25 (powersetTI1) =>
% 97.99/13.25 ((
% 97.99/13.25 (powersetTE1) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementTI1) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementTE1) =>
% 97.99/13.25 ((
% 97.99/13.25 (binintersectTELcontra) =>
% 97.99/13.25 ((
% 97.99/13.25 (binintersectTERcontra) =>
% 97.99/13.25 ((
% 97.99/13.25 (contrasubsetT) =>
% 97.99/13.25 ((
% 97.99/13.25 (contrasubsetT1) =>
% 97.99/13.25 ((
% 97.99/13.25 (contrasubsetT2) =>
% 97.99/13.25 ((
% 97.99/13.25 (contrasubsetT3) =>
% 97.99/13.25 ((
% 97.99/13.25 (doubleComplementI1) =>
% 97.99/13.25 ((
% 97.99/13.25 (doubleComplementE1) =>
% 97.99/13.25 ((
% 97.99/13.25 (doubleComplementSub1) =>
% 97.99/13.25 ((
% 97.99/13.25 (doubleComplementSub2) =>
% 97.99/13.25 ((
% 97.99/13.25 (doubleComplementEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementTnotintersectT) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementImpComplementIntersect) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementSubsetComplementIntersect) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementInPowersetComplementIntersect) =>
% 97.99/13.25 ((
% 97.99/13.25 (contraSubsetComplement) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementTcontraSubset) =>
% 97.99/13.25 ((
% 97.99/13.25 (binunionTILcontra) =>
% 97.99/13.25 ((
% 97.99/13.25 (binunionTIRcontra) =>
% 97.99/13.25 ((
% 97.99/13.25 (inIntersectImpInUnion) =>
% 97.99/13.25 ((
% 97.99/13.25 (inIntersectImpInUnion2) =>
% 97.99/13.25 ((
% 97.99/13.25 (inIntersectImpInIntersectUnions) =>
% 97.99/13.25 ((
% 97.99/13.25 (intersectInPowersetIntersectUnions) =>
% 97.99/13.25 ((
% 97.99/13.25 (inComplementUnionImpNotIn1) =>
% 97.99/13.25 ((
% 97.99/13.25 (inComplementUnionImpInComplement1) =>
% 97.99/13.25 ((
% 97.99/13.25 (binunionTE) =>
% 97.99/13.25 ((
% 97.99/13.25 (binunionTEcontra) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan2a1) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementUnionInPowersetComplement) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan2a2) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan1a) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan1b) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan1) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan2a) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan2b2) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan2b) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan2) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz13rule0) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz13rule1) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz13rule2) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz13rule3) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz13rule4) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz1_1) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz1_2) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz1_3) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz1_4) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz1_5) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1all2) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1SetBreln1) =>
% 97.99/13.25 ((
% 97.99/13.25 (choice2fnsingleton) =>
% 97.99/13.25 ((
% 97.99/13.25 (setOfPairsIsBReln1) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1all1) =>
% 97.99/13.25 ((
% 97.99/13.25 (subbreln1) =>
% 97.99/13.25 ((
% 97.99/13.25 (eqbreln1) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1invprop) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1invI) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1invE) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1compprop) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1compI) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1compE) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1compEex) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1unionprop) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1unionIL) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1unionIR) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1unionI) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1unionE) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1unionEcases) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1unionCommutes) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz2Ex) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz2W) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz2A) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz2B) =>
% 97.99/13.25 ((
% 97.99/13.25 (image1Ex) =>
% 97.99/13.25 ((
% 97.99/13.25 (image1Ex1) =>
% 97.99/13.25 ((
% 97.99/13.25 (image1Equiv) =>
% 97.99/13.25 ((
% 97.99/13.25 (image1E) =>
% 97.99/13.25 ((
% 97.99/13.25 (image1I) =>
% 97.99/13.25 ((
% 97.99/13.25 (injFuncInInjFuncSet) =>
% 97.99/13.25 ((
% 97.99/13.25 (injFuncSetFuncIn) =>
% 97.99/13.25 ((
% 97.99/13.25 (injFuncSetFuncInj) =>
% 97.99/13.25 ((
% 97.99/13.25 (surjFuncSetFuncIn) =>
% 97.99/13.25 ((
% 97.99/13.25 (surjFuncSetFuncSurj) =>
% 97.99/13.25 ((
% 97.99/13.25 (leftInvIsSurj) =>
% 97.99/13.25 ((
% 97.99/13.25 (surjCantorThm) =>
% 97.99/13.25 ((
% 97.99/13.25 (foundation2) =>
% 97.99/13.25 ((
% 97.99/13.25 (notinself) =>
% 97.99/13.25 ((
% 97.99/13.25 (notinself2) =>
% 97.99/13.25 ((
% 97.99/13.25 (omegaSp) =>
% 97.99/13.25 ((
% 97.99/13.25 (omegaSclos) =>
% 97.99/13.25 ((
% 97.99/13.25 (peano0notS) =>
% 97.99/13.25 ((
% 97.99/13.25 (!!) @ (
% 97.99/13.25 (('#S') @ (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 =>) @
% 97.99/13.25 (
% 97.99/13.25 (
% 97.99/13.25 ('#C') @ in @
% 97.99/13.25 omega)))) @
% 97.99/13.25 (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 !!) @
% 97.99/13.25 (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 (
% 97.99/13.25 ('#S') @ (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 =>) @
% 97.99/13.25 (
% 97.99/13.25 (
% 97.99/13.25 ('#C') @ in @
% 97.99/13.25 omega)))))) @
% 97.99/13.25 (
% 97.99/13.25 (
% 97.99/13.25 ('#S') @ (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 '#S') @
% 97.99/13.25 (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 =>))) @
% 97.99/13.25 (
% 97.99/13.25 (
% 97.99/13.25 ('#C') @ (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 '#B') @
% 97.99/13.25 (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 =) @
% 97.99/13.25 omegaS)))) @
% 97.99/13.25 omegaS)))))) @
% 97.99/13.25 (
% 97.99/13.25 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.99/13.25 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1216])).
% 97.99/13.25 thf(zip_derived_cl1231, plain,
% 97.99/13.25 (~ (((binintersectSubset1) =>
% 97.99/13.25 (((bs114d) =>
% 97.99/13.25 (((setminusI) =>
% 97.99/13.25 (((setminusEL) =>
% 97.99/13.25 (((setminusER) =>
% 97.99/13.25 (((setminusSubset2) =>
% 97.99/13.25 (((setminusERneg) =>
% 97.99/13.25 (((setminusELneg) =>
% 97.99/13.25 (((setminusILneg) =>
% 97.99/13.25 (((setminusIRneg) =>
% 97.99/13.25 (((setminusLsub) =>
% 97.99/13.25 (((setminusSubset1) =>
% 97.99/13.25 (((symdiffE) =>
% 97.99/13.25 (((symdiffI1) =>
% 97.99/13.25 (((symdiffI2) =>
% 97.99/13.25 (((symdiffIneg1) =>
% 97.99/13.25 (((symdiffIneg2) =>
% 97.99/13.25 (((secondinupair) =>
% 97.99/13.25 (((setukpairIL) =>
% 97.99/13.25 (((setukpairIR) =>
% 97.99/13.25 (((kpairiskpair) =>
% 97.99/13.25 (((kpairp) =>
% 97.99/13.25 (((singletonsubset) =>
% 97.99/13.25 (((singletoninpowerset) =>
% 97.99/13.25 (((singletoninpowunion) =>
% 97.99/13.25 (((upairset2E) =>
% 97.99/13.25 (((upairsubunion) =>
% 97.99/13.25 (((upairinpowunion) =>
% 97.99/13.25 (((ubforcartprodlem1) =>
% 97.99/13.25 (((ubforcartprodlem2) =>
% 97.99/13.25 ((
% 97.99/13.25 (ubforcartprodlem3) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodpairin) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodmempair1) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodmempair) =>
% 97.99/13.25 ((
% 97.99/13.25 (setunionE2) =>
% 97.99/13.25 ((
% 97.99/13.25 (setunionsingleton1) =>
% 97.99/13.25 ((
% 97.99/13.25 (setunionsingleton2) =>
% 97.99/13.25 ((
% 97.99/13.25 (setunionsingleton) =>
% 97.99/13.25 ((
% 97.99/13.25 (singletonprop) =>
% 97.99/13.25 ((
% 97.99/13.25 (ex1E1) =>
% 97.99/13.25 ((
% 97.99/13.25 (ex1I) =>
% 97.99/13.25 ((
% 97.99/13.25 (ex1I2) =>
% 97.99/13.25 ((
% 97.99/13.25 (singletonsuniq) =>
% 97.99/13.25 ((
% 97.99/13.25 (setukpairinjL1) =>
% 97.99/13.25 ((
% 97.99/13.25 (kfstsingleton) =>
% 97.99/13.25 ((
% 97.99/13.25 (theprop) =>
% 97.99/13.25 ((
% 97.99/13.25 (kfstpairEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodfstin) =>
% 97.99/13.25 ((
% 97.99/13.25 (setukpairinjL2) =>
% 97.99/13.25 ((
% 97.99/13.25 (setukpairinjL) =>
% 97.99/13.25 ((
% 97.99/13.25 (setukpairinjR11) =>
% 97.99/13.25 ((
% 97.99/13.25 (setukpairinjR12) =>
% 97.99/13.25 ((
% 97.99/13.25 (setukpairinjR1) =>
% 97.99/13.25 ((
% 97.99/13.25 (upairequniteq) =>
% 97.99/13.25 ((
% 97.99/13.25 (setukpairinjR2) =>
% 97.99/13.25 ((
% 97.99/13.25 (setukpairinjR) =>
% 97.99/13.25 ((
% 97.99/13.25 (ksndsingleton) =>
% 97.99/13.25 ((
% 97.99/13.25 (ksndpairEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (kpairsurjEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodsndin) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodpairmemEL) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodpairmemER) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodmempaircEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodfstpairEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodsndpairEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodpairsurjEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (dpsetconstrI) =>
% 97.99/13.25 ((
% 97.99/13.25 (dpsetconstrSub) =>
% 97.99/13.25 ((
% 97.99/13.25 (setOfPairsIsBReln) =>
% 97.99/13.25 ((
% 97.99/13.25 (dpsetconstrERa) =>
% 97.99/13.25 ((
% 97.99/13.25 (dpsetconstrEL1) =>
% 97.99/13.25 ((
% 97.99/13.25 (dpsetconstrEL2) =>
% 97.99/13.25 ((
% 97.99/13.25 (dpsetconstrER) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcImageSingleton) =>
% 97.99/13.25 ((
% 97.99/13.25 (apProp) =>
% 97.99/13.25 ((
% 97.99/13.25 (app) =>
% 97.99/13.25 ((
% 97.99/13.25 (infuncsetfunc) =>
% 97.99/13.25 ((
% 97.99/13.25 (ap2p) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcinfuncset) =>
% 97.99/13.25 ((
% 97.99/13.25 (lamProp) =>
% 97.99/13.25 ((
% 97.99/13.25 (lamp) =>
% 97.99/13.25 ((
% 97.99/13.25 (lam2p) =>
% 97.99/13.25 ((
% 97.99/13.25 (brelnall1) =>
% 97.99/13.25 ((
% 97.99/13.25 (brelnall2) =>
% 97.99/13.25 ((
% 97.99/13.25 (ex1E2) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcGraphProp1) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcGraphProp3) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcGraphProp2) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcextLem) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcGraphProp4) =>
% 97.99/13.25 ((
% 97.99/13.25 (subbreln) =>
% 97.99/13.25 ((
% 97.99/13.25 (eqbreln) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcext) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcext2) =>
% 97.99/13.25 ((
% 97.99/13.25 (ap2apEq1) =>
% 97.99/13.25 ((
% 97.99/13.25 (ap2apEq2) =>
% 97.99/13.25 ((
% 97.99/13.25 (beta1) =>
% 97.99/13.25 ((
% 97.99/13.25 (eta1) =>
% 97.99/13.25 ((
% 97.99/13.25 (lam2lamEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (beta2) =>
% 97.99/13.25 ((
% 97.99/13.25 (eta2) =>
% 97.99/13.25 ((
% 97.99/13.25 (iffalseProp1) =>
% 97.99/13.25 ((
% 97.99/13.25 (iffalseProp2) =>
% 97.99/13.25 ((
% 97.99/13.25 (iftrueProp1) =>
% 97.99/13.25 ((
% 97.99/13.25 (iftrueProp2) =>
% 97.99/13.25 ((
% 97.99/13.25 (ifSingleton) =>
% 97.99/13.25 ((
% 97.99/13.25 (ifp) =>
% 97.99/13.25 ((
% 97.99/13.25 (theeq) =>
% 97.99/13.25 ((
% 97.99/13.25 (iftrue) =>
% 97.99/13.25 ((
% 97.99/13.25 (iffalse) =>
% 97.99/13.25 ((
% 97.99/13.25 (iftrueorfalse) =>
% 97.99/13.25 ((
% 97.99/13.25 (binintersectT_lem) =>
% 97.99/13.25 ((
% 97.99/13.25 (binunionT_lem) =>
% 97.99/13.25 ((
% 97.99/13.25 (powersetT_lem) =>
% 97.99/13.25 ((
% 97.99/13.25 (setminusT_lem) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementT_lem) =>
% 97.99/13.25 ((
% 97.99/13.25 (setextT) =>
% 97.99/13.25 ((
% 97.99/13.25 (subsetTI) =>
% 97.99/13.25 ((
% 97.99/13.25 (powersetTI1) =>
% 97.99/13.25 ((
% 97.99/13.25 (powersetTE1) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementTI1) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementTE1) =>
% 97.99/13.25 ((
% 97.99/13.25 (binintersectTELcontra) =>
% 97.99/13.25 ((
% 97.99/13.25 (binintersectTERcontra) =>
% 97.99/13.25 ((
% 97.99/13.25 (contrasubsetT) =>
% 97.99/13.25 ((
% 97.99/13.25 (contrasubsetT1) =>
% 97.99/13.25 ((
% 97.99/13.25 (contrasubsetT2) =>
% 97.99/13.25 ((
% 97.99/13.25 (contrasubsetT3) =>
% 97.99/13.25 ((
% 97.99/13.25 (doubleComplementI1) =>
% 97.99/13.25 ((
% 97.99/13.25 (doubleComplementE1) =>
% 97.99/13.25 ((
% 97.99/13.25 (doubleComplementSub1) =>
% 97.99/13.25 ((
% 97.99/13.25 (doubleComplementSub2) =>
% 97.99/13.25 ((
% 97.99/13.25 (doubleComplementEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementTnotintersectT) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementImpComplementIntersect) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementSubsetComplementIntersect) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementInPowersetComplementIntersect) =>
% 97.99/13.25 ((
% 97.99/13.25 (contraSubsetComplement) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementTcontraSubset) =>
% 97.99/13.25 ((
% 97.99/13.25 (binunionTILcontra) =>
% 97.99/13.25 ((
% 97.99/13.25 (binunionTIRcontra) =>
% 97.99/13.25 ((
% 97.99/13.25 (inIntersectImpInUnion) =>
% 97.99/13.25 ((
% 97.99/13.25 (inIntersectImpInUnion2) =>
% 97.99/13.25 ((
% 97.99/13.25 (inIntersectImpInIntersectUnions) =>
% 97.99/13.25 ((
% 97.99/13.25 (intersectInPowersetIntersectUnions) =>
% 97.99/13.25 ((
% 97.99/13.25 (inComplementUnionImpNotIn1) =>
% 97.99/13.25 ((
% 97.99/13.25 (inComplementUnionImpInComplement1) =>
% 97.99/13.25 ((
% 97.99/13.25 (binunionTE) =>
% 97.99/13.25 ((
% 97.99/13.25 (binunionTEcontra) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan2a1) =>
% 97.99/13.25 ((
% 97.99/13.25 (complementUnionInPowersetComplement) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan2a2) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan1a) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan1b) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan1) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan2a) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan2b2) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan2b) =>
% 97.99/13.25 ((
% 97.99/13.25 (demorgan2) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz13rule0) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz13rule1) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz13rule2) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz13rule3) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz13rule4) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz1_1) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz1_2) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz1_3) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz1_4) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz1_5) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1all2) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1SetBreln1) =>
% 97.99/13.25 ((
% 97.99/13.25 (choice2fnsingleton) =>
% 97.99/13.25 ((
% 97.99/13.25 (setOfPairsIsBReln1) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1all1) =>
% 97.99/13.25 ((
% 97.99/13.25 (subbreln1) =>
% 97.99/13.25 ((
% 97.99/13.25 (eqbreln1) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1invprop) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1invI) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1invE) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1compprop) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1compI) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1compE) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1compEex) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1unionprop) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1unionIL) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1unionIR) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1unionI) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1unionE) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1unionEcases) =>
% 97.99/13.25 ((
% 97.99/13.25 (breln1unionCommutes) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz2Ex) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz2W) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz2A) =>
% 97.99/13.25 ((
% 97.99/13.25 (woz2B) =>
% 97.99/13.25 ((
% 97.99/13.25 (image1Ex) =>
% 97.99/13.25 ((
% 97.99/13.25 (image1Ex1) =>
% 97.99/13.25 ((
% 97.99/13.25 (image1Equiv) =>
% 97.99/13.25 ((
% 97.99/13.25 (image1E) =>
% 97.99/13.25 ((
% 97.99/13.25 (image1I) =>
% 97.99/13.25 ((
% 97.99/13.25 (injFuncInInjFuncSet) =>
% 97.99/13.25 ((
% 97.99/13.25 (injFuncSetFuncIn) =>
% 97.99/13.25 ((
% 97.99/13.25 (injFuncSetFuncInj) =>
% 97.99/13.25 ((
% 97.99/13.25 (surjFuncSetFuncIn) =>
% 97.99/13.25 ((
% 97.99/13.25 (surjFuncSetFuncSurj) =>
% 97.99/13.25 ((
% 97.99/13.25 (leftInvIsSurj) =>
% 97.99/13.25 ((
% 97.99/13.25 (surjCantorThm) =>
% 97.99/13.25 ((
% 97.99/13.25 (foundation2) =>
% 97.99/13.25 ((
% 97.99/13.25 (notinself) =>
% 97.99/13.25 ((
% 97.99/13.25 (notinself2) =>
% 97.99/13.25 ((
% 97.99/13.25 (omegaSp) =>
% 97.99/13.25 ((
% 97.99/13.25 (omegaSclos) =>
% 97.99/13.25 ((
% 97.99/13.25 (peano0notS) =>
% 97.99/13.25 ((
% 97.99/13.25 (!!) @ (
% 97.99/13.25 (('#S') @ (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 =>) @
% 97.99/13.25 (
% 97.99/13.25 (
% 97.99/13.25 ('#C') @ in @
% 97.99/13.25 omega)))) @
% 97.99/13.25 (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 !!) @
% 97.99/13.25 (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 (
% 97.99/13.25 ('#S') @ (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 =>) @
% 97.99/13.25 (
% 97.99/13.25 (
% 97.99/13.25 ('#C') @ in @
% 97.99/13.25 omega)))))) @
% 97.99/13.25 (
% 97.99/13.25 (
% 97.99/13.25 ('#S') @ (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 '#S') @
% 97.99/13.25 (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 =>))) @
% 97.99/13.25 (
% 97.99/13.25 (
% 97.99/13.25 ('#C') @ (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 '#B') @
% 97.99/13.25 (
% 97.99/13.25 (
% 97.99/13.25 ('#B') @ (
% 97.99/13.25 =) @
% 97.99/13.25 omegaS)))) @
% 97.99/13.25 omegaS)))))) @
% 97.99/13.25 (
% 97.99/13.25 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.99/13.25 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1223])).
% 97.99/13.25 thf(zip_derived_cl1239, plain,
% 97.99/13.25 (~ (((bs114d) =>
% 97.99/13.25 (((setminusI) =>
% 97.99/13.25 (((setminusEL) =>
% 97.99/13.25 (((setminusER) =>
% 97.99/13.25 (((setminusSubset2) =>
% 97.99/13.25 (((setminusERneg) =>
% 97.99/13.25 (((setminusELneg) =>
% 97.99/13.25 (((setminusILneg) =>
% 97.99/13.25 (((setminusIRneg) =>
% 97.99/13.25 (((setminusLsub) =>
% 97.99/13.25 (((setminusSubset1) =>
% 97.99/13.25 (((symdiffE) =>
% 97.99/13.25 (((symdiffI1) =>
% 97.99/13.25 (((symdiffI2) =>
% 97.99/13.25 (((symdiffIneg1) =>
% 97.99/13.25 (((symdiffIneg2) =>
% 97.99/13.25 (((secondinupair) =>
% 97.99/13.25 (((setukpairIL) =>
% 97.99/13.25 (((setukpairIR) =>
% 97.99/13.25 (((kpairiskpair) =>
% 97.99/13.25 (((kpairp) =>
% 97.99/13.25 (((singletonsubset) =>
% 97.99/13.25 (((singletoninpowerset) =>
% 97.99/13.25 (((singletoninpowunion) =>
% 97.99/13.25 (((upairset2E) =>
% 97.99/13.25 (((upairsubunion) =>
% 97.99/13.25 (((upairinpowunion) =>
% 97.99/13.25 (((ubforcartprodlem1) =>
% 97.99/13.25 (((ubforcartprodlem2) =>
% 97.99/13.25 (((ubforcartprodlem3) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodpairin) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodmempair1) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodmempair) =>
% 97.99/13.25 ((
% 97.99/13.25 (setunionE2) =>
% 97.99/13.25 ((
% 97.99/13.25 (setunionsingleton1) =>
% 97.99/13.25 ((
% 97.99/13.25 (setunionsingleton2) =>
% 97.99/13.25 ((
% 97.99/13.25 (setunionsingleton) =>
% 97.99/13.25 ((
% 97.99/13.25 (singletonprop) =>
% 97.99/13.25 ((
% 97.99/13.25 (ex1E1) =>
% 97.99/13.25 ((
% 97.99/13.25 (ex1I) =>
% 97.99/13.25 ((
% 97.99/13.25 (ex1I2) =>
% 97.99/13.25 ((
% 97.99/13.25 (singletonsuniq) =>
% 97.99/13.25 ((
% 97.99/13.25 (setukpairinjL1) =>
% 97.99/13.25 ((
% 97.99/13.25 (kfstsingleton) =>
% 97.99/13.25 ((
% 97.99/13.25 (theprop) =>
% 97.99/13.25 ((
% 97.99/13.25 (kfstpairEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodfstin) =>
% 97.99/13.25 ((
% 97.99/13.25 (setukpairinjL2) =>
% 97.99/13.25 ((
% 97.99/13.25 (setukpairinjL) =>
% 97.99/13.25 ((
% 97.99/13.25 (setukpairinjR11) =>
% 97.99/13.25 ((
% 97.99/13.25 (setukpairinjR12) =>
% 97.99/13.25 ((
% 97.99/13.25 (setukpairinjR1) =>
% 97.99/13.25 ((
% 97.99/13.25 (upairequniteq) =>
% 97.99/13.25 ((
% 97.99/13.25 (setukpairinjR2) =>
% 97.99/13.25 ((
% 97.99/13.25 (setukpairinjR) =>
% 97.99/13.25 ((
% 97.99/13.25 (ksndsingleton) =>
% 97.99/13.25 ((
% 97.99/13.25 (ksndpairEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (kpairsurjEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodsndin) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodpairmemEL) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodpairmemER) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodmempaircEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodfstpairEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodsndpairEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (cartprodpairsurjEq) =>
% 97.99/13.25 ((
% 97.99/13.25 (dpsetconstrI) =>
% 97.99/13.25 ((
% 97.99/13.25 (dpsetconstrSub) =>
% 97.99/13.25 ((
% 97.99/13.25 (setOfPairsIsBReln) =>
% 97.99/13.25 ((
% 97.99/13.25 (dpsetconstrERa) =>
% 97.99/13.25 ((
% 97.99/13.25 (dpsetconstrEL1) =>
% 97.99/13.25 ((
% 97.99/13.25 (dpsetconstrEL2) =>
% 97.99/13.25 ((
% 97.99/13.25 (dpsetconstrER) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcImageSingleton) =>
% 97.99/13.25 ((
% 97.99/13.25 (apProp) =>
% 97.99/13.25 ((
% 97.99/13.25 (app) =>
% 97.99/13.25 ((
% 97.99/13.25 (infuncsetfunc) =>
% 97.99/13.25 ((
% 97.99/13.25 (ap2p) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcinfuncset) =>
% 97.99/13.25 ((
% 97.99/13.25 (lamProp) =>
% 97.99/13.25 ((
% 97.99/13.25 (lamp) =>
% 97.99/13.25 ((
% 97.99/13.25 (lam2p) =>
% 97.99/13.25 ((
% 97.99/13.25 (brelnall1) =>
% 97.99/13.25 ((
% 97.99/13.25 (brelnall2) =>
% 97.99/13.25 ((
% 97.99/13.25 (ex1E2) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcGraphProp1) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcGraphProp3) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcGraphProp2) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcextLem) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcGraphProp4) =>
% 97.99/13.25 ((
% 97.99/13.25 (subbreln) =>
% 97.99/13.25 ((
% 97.99/13.25 (eqbreln) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcext) =>
% 97.99/13.25 ((
% 97.99/13.25 (funcext2) =>
% 97.99/13.25 ((
% 97.99/13.25 (ap2apEq1) =>
% 97.99/13.25 ((
% 97.99/13.25 (ap2apEq2) =>
% 97.99/13.25 ((
% 97.99/13.25 (beta1) =>
% 97.99/13.26 ((
% 97.99/13.26 (eta1) =>
% 97.99/13.26 ((
% 97.99/13.26 (lam2lamEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (beta2) =>
% 97.99/13.26 ((
% 97.99/13.26 (eta2) =>
% 97.99/13.26 ((
% 97.99/13.26 (iffalseProp1) =>
% 97.99/13.26 ((
% 97.99/13.26 (iffalseProp2) =>
% 97.99/13.26 ((
% 97.99/13.26 (iftrueProp1) =>
% 97.99/13.26 ((
% 97.99/13.26 (iftrueProp2) =>
% 97.99/13.26 ((
% 97.99/13.26 (ifSingleton) =>
% 97.99/13.26 ((
% 97.99/13.26 (ifp) =>
% 97.99/13.26 ((
% 97.99/13.26 (theeq) =>
% 97.99/13.26 ((
% 97.99/13.26 (iftrue) =>
% 97.99/13.26 ((
% 97.99/13.26 (iffalse) =>
% 97.99/13.26 ((
% 97.99/13.26 (iftrueorfalse) =>
% 97.99/13.26 ((
% 97.99/13.26 (binintersectT_lem) =>
% 97.99/13.26 ((
% 97.99/13.26 (binunionT_lem) =>
% 97.99/13.26 ((
% 97.99/13.26 (powersetT_lem) =>
% 97.99/13.26 ((
% 97.99/13.26 (setminusT_lem) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementT_lem) =>
% 97.99/13.26 ((
% 97.99/13.26 (setextT) =>
% 97.99/13.26 ((
% 97.99/13.26 (subsetTI) =>
% 97.99/13.26 ((
% 97.99/13.26 (powersetTI1) =>
% 97.99/13.26 ((
% 97.99/13.26 (powersetTE1) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementTI1) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementTE1) =>
% 97.99/13.26 ((
% 97.99/13.26 (binintersectTELcontra) =>
% 97.99/13.26 ((
% 97.99/13.26 (binintersectTERcontra) =>
% 97.99/13.26 ((
% 97.99/13.26 (contrasubsetT) =>
% 97.99/13.26 ((
% 97.99/13.26 (contrasubsetT1) =>
% 97.99/13.26 ((
% 97.99/13.26 (contrasubsetT2) =>
% 97.99/13.26 ((
% 97.99/13.26 (contrasubsetT3) =>
% 97.99/13.26 ((
% 97.99/13.26 (doubleComplementI1) =>
% 97.99/13.26 ((
% 97.99/13.26 (doubleComplementE1) =>
% 97.99/13.26 ((
% 97.99/13.26 (doubleComplementSub1) =>
% 97.99/13.26 ((
% 97.99/13.26 (doubleComplementSub2) =>
% 97.99/13.26 ((
% 97.99/13.26 (doubleComplementEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementTnotintersectT) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementImpComplementIntersect) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementSubsetComplementIntersect) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementInPowersetComplementIntersect) =>
% 97.99/13.26 ((
% 97.99/13.26 (contraSubsetComplement) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementTcontraSubset) =>
% 97.99/13.26 ((
% 97.99/13.26 (binunionTILcontra) =>
% 97.99/13.26 ((
% 97.99/13.26 (binunionTIRcontra) =>
% 97.99/13.26 ((
% 97.99/13.26 (inIntersectImpInUnion) =>
% 97.99/13.26 ((
% 97.99/13.26 (inIntersectImpInUnion2) =>
% 97.99/13.26 ((
% 97.99/13.26 (inIntersectImpInIntersectUnions) =>
% 97.99/13.26 ((
% 97.99/13.26 (intersectInPowersetIntersectUnions) =>
% 97.99/13.26 ((
% 97.99/13.26 (inComplementUnionImpNotIn1) =>
% 97.99/13.26 ((
% 97.99/13.26 (inComplementUnionImpInComplement1) =>
% 97.99/13.26 ((
% 97.99/13.26 (binunionTE) =>
% 97.99/13.26 ((
% 97.99/13.26 (binunionTEcontra) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan2a1) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementUnionInPowersetComplement) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan2a2) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan1a) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan1b) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan1) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan2a) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan2b2) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan2b) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan2) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz13rule0) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz13rule1) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz13rule2) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz13rule3) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz13rule4) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz1_1) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz1_2) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz1_3) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz1_4) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz1_5) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1all2) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1SetBreln1) =>
% 97.99/13.26 ((
% 97.99/13.26 (choice2fnsingleton) =>
% 97.99/13.26 ((
% 97.99/13.26 (setOfPairsIsBReln1) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1all1) =>
% 97.99/13.26 ((
% 97.99/13.26 (subbreln1) =>
% 97.99/13.26 ((
% 97.99/13.26 (eqbreln1) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1invprop) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1invI) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1invE) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1compprop) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1compI) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1compE) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1compEex) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionprop) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionIL) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionIR) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionI) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionE) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionEcases) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionCommutes) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz2Ex) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz2W) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz2A) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz2B) =>
% 97.99/13.26 ((
% 97.99/13.26 (image1Ex) =>
% 97.99/13.26 ((
% 97.99/13.26 (image1Ex1) =>
% 97.99/13.26 ((
% 97.99/13.26 (image1Equiv) =>
% 97.99/13.26 ((
% 97.99/13.26 (image1E) =>
% 97.99/13.26 ((
% 97.99/13.26 (image1I) =>
% 97.99/13.26 ((
% 97.99/13.26 (injFuncInInjFuncSet) =>
% 97.99/13.26 ((
% 97.99/13.26 (injFuncSetFuncIn) =>
% 97.99/13.26 ((
% 97.99/13.26 (injFuncSetFuncInj) =>
% 97.99/13.26 ((
% 97.99/13.26 (surjFuncSetFuncIn) =>
% 97.99/13.26 ((
% 97.99/13.26 (surjFuncSetFuncSurj) =>
% 97.99/13.26 ((
% 97.99/13.26 (leftInvIsSurj) =>
% 97.99/13.26 ((
% 97.99/13.26 (surjCantorThm) =>
% 97.99/13.26 ((
% 97.99/13.26 (foundation2) =>
% 97.99/13.26 ((
% 97.99/13.26 (notinself) =>
% 97.99/13.26 ((
% 97.99/13.26 (notinself2) =>
% 97.99/13.26 ((
% 97.99/13.26 (omegaSp) =>
% 97.99/13.26 ((
% 97.99/13.26 (omegaSclos) =>
% 97.99/13.26 ((
% 97.99/13.26 (peano0notS) =>
% 97.99/13.26 ((
% 97.99/13.26 (!!) @ (
% 97.99/13.26 (('#S') @ (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 =>) @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#C') @ in @
% 97.99/13.26 omega)))) @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 !!) @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 (
% 97.99/13.26 ('#S') @ (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 =>) @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#C') @ in @
% 97.99/13.26 omega)))))) @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#S') @ (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 '#S') @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 =>))) @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#C') @ (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 '#B') @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 =) @
% 97.99/13.26 omegaS)))) @
% 97.99/13.26 omegaS)))))) @
% 97.99/13.26 (
% 97.99/13.26 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.99/13.26 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1231])).
% 97.99/13.26 thf(zip_derived_cl1247, plain,
% 97.99/13.26 (~ (((setminusI) =>
% 97.99/13.26 (((setminusEL) =>
% 97.99/13.26 (((setminusER) =>
% 97.99/13.26 (((setminusSubset2) =>
% 97.99/13.26 (((setminusERneg) =>
% 97.99/13.26 (((setminusELneg) =>
% 97.99/13.26 (((setminusILneg) =>
% 97.99/13.26 (((setminusIRneg) =>
% 97.99/13.26 (((setminusLsub) =>
% 97.99/13.26 (((setminusSubset1) =>
% 97.99/13.26 (((symdiffE) =>
% 97.99/13.26 (((symdiffI1) =>
% 97.99/13.26 (((symdiffI2) =>
% 97.99/13.26 (((symdiffIneg1) =>
% 97.99/13.26 (((symdiffIneg2) =>
% 97.99/13.26 (((secondinupair) =>
% 97.99/13.26 (((setukpairIL) =>
% 97.99/13.26 (((setukpairIR) =>
% 97.99/13.26 (((kpairiskpair) =>
% 97.99/13.26 (((kpairp) =>
% 97.99/13.26 (((singletonsubset) =>
% 97.99/13.26 (((singletoninpowerset) =>
% 97.99/13.26 (((singletoninpowunion) =>
% 97.99/13.26 (((upairset2E) =>
% 97.99/13.26 (((upairsubunion) =>
% 97.99/13.26 (((upairinpowunion) =>
% 97.99/13.26 (((ubforcartprodlem1) =>
% 97.99/13.26 (((ubforcartprodlem2) =>
% 97.99/13.26 (((ubforcartprodlem3) =>
% 97.99/13.26 (((cartprodpairin) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodmempair1) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodmempair) =>
% 97.99/13.26 ((
% 97.99/13.26 (setunionE2) =>
% 97.99/13.26 ((
% 97.99/13.26 (setunionsingleton1) =>
% 97.99/13.26 ((
% 97.99/13.26 (setunionsingleton2) =>
% 97.99/13.26 ((
% 97.99/13.26 (setunionsingleton) =>
% 97.99/13.26 ((
% 97.99/13.26 (singletonprop) =>
% 97.99/13.26 ((
% 97.99/13.26 (ex1E1) =>
% 97.99/13.26 ((
% 97.99/13.26 (ex1I) =>
% 97.99/13.26 ((
% 97.99/13.26 (ex1I2) =>
% 97.99/13.26 ((
% 97.99/13.26 (singletonsuniq) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjL1) =>
% 97.99/13.26 ((
% 97.99/13.26 (kfstsingleton) =>
% 97.99/13.26 ((
% 97.99/13.26 (theprop) =>
% 97.99/13.26 ((
% 97.99/13.26 (kfstpairEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodfstin) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjL2) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjL) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjR11) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjR12) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjR1) =>
% 97.99/13.26 ((
% 97.99/13.26 (upairequniteq) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjR2) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjR) =>
% 97.99/13.26 ((
% 97.99/13.26 (ksndsingleton) =>
% 97.99/13.26 ((
% 97.99/13.26 (ksndpairEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (kpairsurjEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodsndin) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodpairmemEL) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodpairmemER) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodmempaircEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodfstpairEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodsndpairEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodpairsurjEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (dpsetconstrI) =>
% 97.99/13.26 ((
% 97.99/13.26 (dpsetconstrSub) =>
% 97.99/13.26 ((
% 97.99/13.26 (setOfPairsIsBReln) =>
% 97.99/13.26 ((
% 97.99/13.26 (dpsetconstrERa) =>
% 97.99/13.26 ((
% 97.99/13.26 (dpsetconstrEL1) =>
% 97.99/13.26 ((
% 97.99/13.26 (dpsetconstrEL2) =>
% 97.99/13.26 ((
% 97.99/13.26 (dpsetconstrER) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcImageSingleton) =>
% 97.99/13.26 ((
% 97.99/13.26 (apProp) =>
% 97.99/13.26 ((
% 97.99/13.26 (app) =>
% 97.99/13.26 ((
% 97.99/13.26 (infuncsetfunc) =>
% 97.99/13.26 ((
% 97.99/13.26 (ap2p) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcinfuncset) =>
% 97.99/13.26 ((
% 97.99/13.26 (lamProp) =>
% 97.99/13.26 ((
% 97.99/13.26 (lamp) =>
% 97.99/13.26 ((
% 97.99/13.26 (lam2p) =>
% 97.99/13.26 ((
% 97.99/13.26 (brelnall1) =>
% 97.99/13.26 ((
% 97.99/13.26 (brelnall2) =>
% 97.99/13.26 ((
% 97.99/13.26 (ex1E2) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcGraphProp1) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcGraphProp3) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcGraphProp2) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcextLem) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcGraphProp4) =>
% 97.99/13.26 ((
% 97.99/13.26 (subbreln) =>
% 97.99/13.26 ((
% 97.99/13.26 (eqbreln) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcext) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcext2) =>
% 97.99/13.26 ((
% 97.99/13.26 (ap2apEq1) =>
% 97.99/13.26 ((
% 97.99/13.26 (ap2apEq2) =>
% 97.99/13.26 ((
% 97.99/13.26 (beta1) =>
% 97.99/13.26 ((
% 97.99/13.26 (eta1) =>
% 97.99/13.26 ((
% 97.99/13.26 (lam2lamEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (beta2) =>
% 97.99/13.26 ((
% 97.99/13.26 (eta2) =>
% 97.99/13.26 ((
% 97.99/13.26 (iffalseProp1) =>
% 97.99/13.26 ((
% 97.99/13.26 (iffalseProp2) =>
% 97.99/13.26 ((
% 97.99/13.26 (iftrueProp1) =>
% 97.99/13.26 ((
% 97.99/13.26 (iftrueProp2) =>
% 97.99/13.26 ((
% 97.99/13.26 (ifSingleton) =>
% 97.99/13.26 ((
% 97.99/13.26 (ifp) =>
% 97.99/13.26 ((
% 97.99/13.26 (theeq) =>
% 97.99/13.26 ((
% 97.99/13.26 (iftrue) =>
% 97.99/13.26 ((
% 97.99/13.26 (iffalse) =>
% 97.99/13.26 ((
% 97.99/13.26 (iftrueorfalse) =>
% 97.99/13.26 ((
% 97.99/13.26 (binintersectT_lem) =>
% 97.99/13.26 ((
% 97.99/13.26 (binunionT_lem) =>
% 97.99/13.26 ((
% 97.99/13.26 (powersetT_lem) =>
% 97.99/13.26 ((
% 97.99/13.26 (setminusT_lem) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementT_lem) =>
% 97.99/13.26 ((
% 97.99/13.26 (setextT) =>
% 97.99/13.26 ((
% 97.99/13.26 (subsetTI) =>
% 97.99/13.26 ((
% 97.99/13.26 (powersetTI1) =>
% 97.99/13.26 ((
% 97.99/13.26 (powersetTE1) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementTI1) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementTE1) =>
% 97.99/13.26 ((
% 97.99/13.26 (binintersectTELcontra) =>
% 97.99/13.26 ((
% 97.99/13.26 (binintersectTERcontra) =>
% 97.99/13.26 ((
% 97.99/13.26 (contrasubsetT) =>
% 97.99/13.26 ((
% 97.99/13.26 (contrasubsetT1) =>
% 97.99/13.26 ((
% 97.99/13.26 (contrasubsetT2) =>
% 97.99/13.26 ((
% 97.99/13.26 (contrasubsetT3) =>
% 97.99/13.26 ((
% 97.99/13.26 (doubleComplementI1) =>
% 97.99/13.26 ((
% 97.99/13.26 (doubleComplementE1) =>
% 97.99/13.26 ((
% 97.99/13.26 (doubleComplementSub1) =>
% 97.99/13.26 ((
% 97.99/13.26 (doubleComplementSub2) =>
% 97.99/13.26 ((
% 97.99/13.26 (doubleComplementEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementTnotintersectT) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementImpComplementIntersect) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementSubsetComplementIntersect) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementInPowersetComplementIntersect) =>
% 97.99/13.26 ((
% 97.99/13.26 (contraSubsetComplement) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementTcontraSubset) =>
% 97.99/13.26 ((
% 97.99/13.26 (binunionTILcontra) =>
% 97.99/13.26 ((
% 97.99/13.26 (binunionTIRcontra) =>
% 97.99/13.26 ((
% 97.99/13.26 (inIntersectImpInUnion) =>
% 97.99/13.26 ((
% 97.99/13.26 (inIntersectImpInUnion2) =>
% 97.99/13.26 ((
% 97.99/13.26 (inIntersectImpInIntersectUnions) =>
% 97.99/13.26 ((
% 97.99/13.26 (intersectInPowersetIntersectUnions) =>
% 97.99/13.26 ((
% 97.99/13.26 (inComplementUnionImpNotIn1) =>
% 97.99/13.26 ((
% 97.99/13.26 (inComplementUnionImpInComplement1) =>
% 97.99/13.26 ((
% 97.99/13.26 (binunionTE) =>
% 97.99/13.26 ((
% 97.99/13.26 (binunionTEcontra) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan2a1) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementUnionInPowersetComplement) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan2a2) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan1a) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan1b) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan1) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan2a) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan2b2) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan2b) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan2) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz13rule0) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz13rule1) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz13rule2) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz13rule3) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz13rule4) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz1_1) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz1_2) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz1_3) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz1_4) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz1_5) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1all2) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1SetBreln1) =>
% 97.99/13.26 ((
% 97.99/13.26 (choice2fnsingleton) =>
% 97.99/13.26 ((
% 97.99/13.26 (setOfPairsIsBReln1) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1all1) =>
% 97.99/13.26 ((
% 97.99/13.26 (subbreln1) =>
% 97.99/13.26 ((
% 97.99/13.26 (eqbreln1) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1invprop) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1invI) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1invE) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1compprop) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1compI) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1compE) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1compEex) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionprop) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionIL) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionIR) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionI) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionE) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionEcases) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionCommutes) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz2Ex) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz2W) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz2A) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz2B) =>
% 97.99/13.26 ((
% 97.99/13.26 (image1Ex) =>
% 97.99/13.26 ((
% 97.99/13.26 (image1Ex1) =>
% 97.99/13.26 ((
% 97.99/13.26 (image1Equiv) =>
% 97.99/13.26 ((
% 97.99/13.26 (image1E) =>
% 97.99/13.26 ((
% 97.99/13.26 (image1I) =>
% 97.99/13.26 ((
% 97.99/13.26 (injFuncInInjFuncSet) =>
% 97.99/13.26 ((
% 97.99/13.26 (injFuncSetFuncIn) =>
% 97.99/13.26 ((
% 97.99/13.26 (injFuncSetFuncInj) =>
% 97.99/13.26 ((
% 97.99/13.26 (surjFuncSetFuncIn) =>
% 97.99/13.26 ((
% 97.99/13.26 (surjFuncSetFuncSurj) =>
% 97.99/13.26 ((
% 97.99/13.26 (leftInvIsSurj) =>
% 97.99/13.26 ((
% 97.99/13.26 (surjCantorThm) =>
% 97.99/13.26 ((
% 97.99/13.26 (foundation2) =>
% 97.99/13.26 ((
% 97.99/13.26 (notinself) =>
% 97.99/13.26 ((
% 97.99/13.26 (notinself2) =>
% 97.99/13.26 ((
% 97.99/13.26 (omegaSp) =>
% 97.99/13.26 ((
% 97.99/13.26 (omegaSclos) =>
% 97.99/13.26 ((
% 97.99/13.26 (peano0notS) =>
% 97.99/13.26 ((
% 97.99/13.26 (!!) @ (
% 97.99/13.26 (('#S') @ (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 =>) @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#C') @ in @
% 97.99/13.26 omega)))) @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 !!) @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 (
% 97.99/13.26 ('#S') @ (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 =>) @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#C') @ in @
% 97.99/13.26 omega)))))) @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#S') @ (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 '#S') @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 =>))) @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#C') @ (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 '#B') @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 =) @
% 97.99/13.26 omegaS)))) @
% 97.99/13.26 omegaS)))))) @
% 97.99/13.26 (
% 97.99/13.26 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.99/13.26 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1239])).
% 97.99/13.26 thf(zip_derived_cl1255, plain,
% 97.99/13.26 (~ (((setminusEL) =>
% 97.99/13.26 (((setminusER) =>
% 97.99/13.26 (((setminusSubset2) =>
% 97.99/13.26 (((setminusERneg) =>
% 97.99/13.26 (((setminusELneg) =>
% 97.99/13.26 (((setminusILneg) =>
% 97.99/13.26 (((setminusIRneg) =>
% 97.99/13.26 (((setminusLsub) =>
% 97.99/13.26 (((setminusSubset1) =>
% 97.99/13.26 (((symdiffE) =>
% 97.99/13.26 (((symdiffI1) =>
% 97.99/13.26 (((symdiffI2) =>
% 97.99/13.26 (((symdiffIneg1) =>
% 97.99/13.26 (((symdiffIneg2) =>
% 97.99/13.26 (((secondinupair) =>
% 97.99/13.26 (((setukpairIL) =>
% 97.99/13.26 (((setukpairIR) =>
% 97.99/13.26 (((kpairiskpair) =>
% 97.99/13.26 (((kpairp) =>
% 97.99/13.26 (((singletonsubset) =>
% 97.99/13.26 (((singletoninpowerset) =>
% 97.99/13.26 (((singletoninpowunion) =>
% 97.99/13.26 (((upairset2E) =>
% 97.99/13.26 (((upairsubunion) =>
% 97.99/13.26 (((upairinpowunion) =>
% 97.99/13.26 (((ubforcartprodlem1) =>
% 97.99/13.26 (((ubforcartprodlem2) =>
% 97.99/13.26 (((ubforcartprodlem3) =>
% 97.99/13.26 (((cartprodpairin) =>
% 97.99/13.26 (((cartprodmempair1) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodmempair) =>
% 97.99/13.26 ((
% 97.99/13.26 (setunionE2) =>
% 97.99/13.26 ((
% 97.99/13.26 (setunionsingleton1) =>
% 97.99/13.26 ((
% 97.99/13.26 (setunionsingleton2) =>
% 97.99/13.26 ((
% 97.99/13.26 (setunionsingleton) =>
% 97.99/13.26 ((
% 97.99/13.26 (singletonprop) =>
% 97.99/13.26 ((
% 97.99/13.26 (ex1E1) =>
% 97.99/13.26 ((
% 97.99/13.26 (ex1I) =>
% 97.99/13.26 ((
% 97.99/13.26 (ex1I2) =>
% 97.99/13.26 ((
% 97.99/13.26 (singletonsuniq) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjL1) =>
% 97.99/13.26 ((
% 97.99/13.26 (kfstsingleton) =>
% 97.99/13.26 ((
% 97.99/13.26 (theprop) =>
% 97.99/13.26 ((
% 97.99/13.26 (kfstpairEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodfstin) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjL2) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjL) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjR11) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjR12) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjR1) =>
% 97.99/13.26 ((
% 97.99/13.26 (upairequniteq) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjR2) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjR) =>
% 97.99/13.26 ((
% 97.99/13.26 (ksndsingleton) =>
% 97.99/13.26 ((
% 97.99/13.26 (ksndpairEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (kpairsurjEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodsndin) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodpairmemEL) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodpairmemER) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodmempaircEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodfstpairEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodsndpairEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodpairsurjEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (dpsetconstrI) =>
% 97.99/13.26 ((
% 97.99/13.26 (dpsetconstrSub) =>
% 97.99/13.26 ((
% 97.99/13.26 (setOfPairsIsBReln) =>
% 97.99/13.26 ((
% 97.99/13.26 (dpsetconstrERa) =>
% 97.99/13.26 ((
% 97.99/13.26 (dpsetconstrEL1) =>
% 97.99/13.26 ((
% 97.99/13.26 (dpsetconstrEL2) =>
% 97.99/13.26 ((
% 97.99/13.26 (dpsetconstrER) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcImageSingleton) =>
% 97.99/13.26 ((
% 97.99/13.26 (apProp) =>
% 97.99/13.26 ((
% 97.99/13.26 (app) =>
% 97.99/13.26 ((
% 97.99/13.26 (infuncsetfunc) =>
% 97.99/13.26 ((
% 97.99/13.26 (ap2p) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcinfuncset) =>
% 97.99/13.26 ((
% 97.99/13.26 (lamProp) =>
% 97.99/13.26 ((
% 97.99/13.26 (lamp) =>
% 97.99/13.26 ((
% 97.99/13.26 (lam2p) =>
% 97.99/13.26 ((
% 97.99/13.26 (brelnall1) =>
% 97.99/13.26 ((
% 97.99/13.26 (brelnall2) =>
% 97.99/13.26 ((
% 97.99/13.26 (ex1E2) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcGraphProp1) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcGraphProp3) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcGraphProp2) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcextLem) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcGraphProp4) =>
% 97.99/13.26 ((
% 97.99/13.26 (subbreln) =>
% 97.99/13.26 ((
% 97.99/13.26 (eqbreln) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcext) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcext2) =>
% 97.99/13.26 ((
% 97.99/13.26 (ap2apEq1) =>
% 97.99/13.26 ((
% 97.99/13.26 (ap2apEq2) =>
% 97.99/13.26 ((
% 97.99/13.26 (beta1) =>
% 97.99/13.26 ((
% 97.99/13.26 (eta1) =>
% 97.99/13.26 ((
% 97.99/13.26 (lam2lamEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (beta2) =>
% 97.99/13.26 ((
% 97.99/13.26 (eta2) =>
% 97.99/13.26 ((
% 97.99/13.26 (iffalseProp1) =>
% 97.99/13.26 ((
% 97.99/13.26 (iffalseProp2) =>
% 97.99/13.26 ((
% 97.99/13.26 (iftrueProp1) =>
% 97.99/13.26 ((
% 97.99/13.26 (iftrueProp2) =>
% 97.99/13.26 ((
% 97.99/13.26 (ifSingleton) =>
% 97.99/13.26 ((
% 97.99/13.26 (ifp) =>
% 97.99/13.26 ((
% 97.99/13.26 (theeq) =>
% 97.99/13.26 ((
% 97.99/13.26 (iftrue) =>
% 97.99/13.26 ((
% 97.99/13.26 (iffalse) =>
% 97.99/13.26 ((
% 97.99/13.26 (iftrueorfalse) =>
% 97.99/13.26 ((
% 97.99/13.26 (binintersectT_lem) =>
% 97.99/13.26 ((
% 97.99/13.26 (binunionT_lem) =>
% 97.99/13.26 ((
% 97.99/13.26 (powersetT_lem) =>
% 97.99/13.26 ((
% 97.99/13.26 (setminusT_lem) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementT_lem) =>
% 97.99/13.26 ((
% 97.99/13.26 (setextT) =>
% 97.99/13.26 ((
% 97.99/13.26 (subsetTI) =>
% 97.99/13.26 ((
% 97.99/13.26 (powersetTI1) =>
% 97.99/13.26 ((
% 97.99/13.26 (powersetTE1) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementTI1) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementTE1) =>
% 97.99/13.26 ((
% 97.99/13.26 (binintersectTELcontra) =>
% 97.99/13.26 ((
% 97.99/13.26 (binintersectTERcontra) =>
% 97.99/13.26 ((
% 97.99/13.26 (contrasubsetT) =>
% 97.99/13.26 ((
% 97.99/13.26 (contrasubsetT1) =>
% 97.99/13.26 ((
% 97.99/13.26 (contrasubsetT2) =>
% 97.99/13.26 ((
% 97.99/13.26 (contrasubsetT3) =>
% 97.99/13.26 ((
% 97.99/13.26 (doubleComplementI1) =>
% 97.99/13.26 ((
% 97.99/13.26 (doubleComplementE1) =>
% 97.99/13.26 ((
% 97.99/13.26 (doubleComplementSub1) =>
% 97.99/13.26 ((
% 97.99/13.26 (doubleComplementSub2) =>
% 97.99/13.26 ((
% 97.99/13.26 (doubleComplementEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementTnotintersectT) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementImpComplementIntersect) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementSubsetComplementIntersect) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementInPowersetComplementIntersect) =>
% 97.99/13.26 ((
% 97.99/13.26 (contraSubsetComplement) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementTcontraSubset) =>
% 97.99/13.26 ((
% 97.99/13.26 (binunionTILcontra) =>
% 97.99/13.26 ((
% 97.99/13.26 (binunionTIRcontra) =>
% 97.99/13.26 ((
% 97.99/13.26 (inIntersectImpInUnion) =>
% 97.99/13.26 ((
% 97.99/13.26 (inIntersectImpInUnion2) =>
% 97.99/13.26 ((
% 97.99/13.26 (inIntersectImpInIntersectUnions) =>
% 97.99/13.26 ((
% 97.99/13.26 (intersectInPowersetIntersectUnions) =>
% 97.99/13.26 ((
% 97.99/13.26 (inComplementUnionImpNotIn1) =>
% 97.99/13.26 ((
% 97.99/13.26 (inComplementUnionImpInComplement1) =>
% 97.99/13.26 ((
% 97.99/13.26 (binunionTE) =>
% 97.99/13.26 ((
% 97.99/13.26 (binunionTEcontra) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan2a1) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementUnionInPowersetComplement) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan2a2) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan1a) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan1b) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan1) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan2a) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan2b2) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan2b) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan2) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz13rule0) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz13rule1) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz13rule2) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz13rule3) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz13rule4) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz1_1) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz1_2) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz1_3) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz1_4) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz1_5) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1all2) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1SetBreln1) =>
% 97.99/13.26 ((
% 97.99/13.26 (choice2fnsingleton) =>
% 97.99/13.26 ((
% 97.99/13.26 (setOfPairsIsBReln1) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1all1) =>
% 97.99/13.26 ((
% 97.99/13.26 (subbreln1) =>
% 97.99/13.26 ((
% 97.99/13.26 (eqbreln1) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1invprop) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1invI) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1invE) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1compprop) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1compI) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1compE) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1compEex) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionprop) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionIL) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionIR) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionI) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionE) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionEcases) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionCommutes) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz2Ex) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz2W) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz2A) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz2B) =>
% 97.99/13.26 ((
% 97.99/13.26 (image1Ex) =>
% 97.99/13.26 ((
% 97.99/13.26 (image1Ex1) =>
% 97.99/13.26 ((
% 97.99/13.26 (image1Equiv) =>
% 97.99/13.26 ((
% 97.99/13.26 (image1E) =>
% 97.99/13.26 ((
% 97.99/13.26 (image1I) =>
% 97.99/13.26 ((
% 97.99/13.26 (injFuncInInjFuncSet) =>
% 97.99/13.26 ((
% 97.99/13.26 (injFuncSetFuncIn) =>
% 97.99/13.26 ((
% 97.99/13.26 (injFuncSetFuncInj) =>
% 97.99/13.26 ((
% 97.99/13.26 (surjFuncSetFuncIn) =>
% 97.99/13.26 ((
% 97.99/13.26 (surjFuncSetFuncSurj) =>
% 97.99/13.26 ((
% 97.99/13.26 (leftInvIsSurj) =>
% 97.99/13.26 ((
% 97.99/13.26 (surjCantorThm) =>
% 97.99/13.26 ((
% 97.99/13.26 (foundation2) =>
% 97.99/13.26 ((
% 97.99/13.26 (notinself) =>
% 97.99/13.26 ((
% 97.99/13.26 (notinself2) =>
% 97.99/13.26 ((
% 97.99/13.26 (omegaSp) =>
% 97.99/13.26 ((
% 97.99/13.26 (omegaSclos) =>
% 97.99/13.26 ((
% 97.99/13.26 (peano0notS) =>
% 97.99/13.26 ((
% 97.99/13.26 (!!) @ (
% 97.99/13.26 (('#S') @ (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 =>) @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#C') @ in @
% 97.99/13.26 omega)))) @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 !!) @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 (
% 97.99/13.26 ('#S') @ (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 =>) @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#C') @ in @
% 97.99/13.26 omega)))))) @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#S') @ (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 '#S') @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 =>))) @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#C') @ (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 '#B') @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 =) @
% 97.99/13.26 omegaS)))) @
% 97.99/13.26 omegaS)))))) @
% 97.99/13.26 (
% 97.99/13.26 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.99/13.26 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1247])).
% 97.99/13.26 thf(zip_derived_cl1264, plain,
% 97.99/13.26 (~ (((setminusER) =>
% 97.99/13.26 (((setminusSubset2) =>
% 97.99/13.26 (((setminusERneg) =>
% 97.99/13.26 (((setminusELneg) =>
% 97.99/13.26 (((setminusILneg) =>
% 97.99/13.26 (((setminusIRneg) =>
% 97.99/13.26 (((setminusLsub) =>
% 97.99/13.26 (((setminusSubset1) =>
% 97.99/13.26 (((symdiffE) =>
% 97.99/13.26 (((symdiffI1) =>
% 97.99/13.26 (((symdiffI2) =>
% 97.99/13.26 (((symdiffIneg1) =>
% 97.99/13.26 (((symdiffIneg2) =>
% 97.99/13.26 (((secondinupair) =>
% 97.99/13.26 (((setukpairIL) =>
% 97.99/13.26 (((setukpairIR) =>
% 97.99/13.26 (((kpairiskpair) =>
% 97.99/13.26 (((kpairp) =>
% 97.99/13.26 (((singletonsubset) =>
% 97.99/13.26 (((singletoninpowerset) =>
% 97.99/13.26 (((singletoninpowunion) =>
% 97.99/13.26 (((upairset2E) =>
% 97.99/13.26 (((upairsubunion) =>
% 97.99/13.26 (((upairinpowunion) =>
% 97.99/13.26 (((ubforcartprodlem1) =>
% 97.99/13.26 (((ubforcartprodlem2) =>
% 97.99/13.26 (((ubforcartprodlem3) =>
% 97.99/13.26 (((cartprodpairin) =>
% 97.99/13.26 (((cartprodmempair1) =>
% 97.99/13.26 (((cartprodmempair) =>
% 97.99/13.26 ((
% 97.99/13.26 (setunionE2) =>
% 97.99/13.26 ((
% 97.99/13.26 (setunionsingleton1) =>
% 97.99/13.26 ((
% 97.99/13.26 (setunionsingleton2) =>
% 97.99/13.26 ((
% 97.99/13.26 (setunionsingleton) =>
% 97.99/13.26 ((
% 97.99/13.26 (singletonprop) =>
% 97.99/13.26 ((
% 97.99/13.26 (ex1E1) =>
% 97.99/13.26 ((
% 97.99/13.26 (ex1I) =>
% 97.99/13.26 ((
% 97.99/13.26 (ex1I2) =>
% 97.99/13.26 ((
% 97.99/13.26 (singletonsuniq) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjL1) =>
% 97.99/13.26 ((
% 97.99/13.26 (kfstsingleton) =>
% 97.99/13.26 ((
% 97.99/13.26 (theprop) =>
% 97.99/13.26 ((
% 97.99/13.26 (kfstpairEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodfstin) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjL2) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjL) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjR11) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjR12) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjR1) =>
% 97.99/13.26 ((
% 97.99/13.26 (upairequniteq) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjR2) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjR) =>
% 97.99/13.26 ((
% 97.99/13.26 (ksndsingleton) =>
% 97.99/13.26 ((
% 97.99/13.26 (ksndpairEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (kpairsurjEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodsndin) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodpairmemEL) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodpairmemER) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodmempaircEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodfstpairEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodsndpairEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodpairsurjEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (dpsetconstrI) =>
% 97.99/13.26 ((
% 97.99/13.26 (dpsetconstrSub) =>
% 97.99/13.26 ((
% 97.99/13.26 (setOfPairsIsBReln) =>
% 97.99/13.26 ((
% 97.99/13.26 (dpsetconstrERa) =>
% 97.99/13.26 ((
% 97.99/13.26 (dpsetconstrEL1) =>
% 97.99/13.26 ((
% 97.99/13.26 (dpsetconstrEL2) =>
% 97.99/13.26 ((
% 97.99/13.26 (dpsetconstrER) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcImageSingleton) =>
% 97.99/13.26 ((
% 97.99/13.26 (apProp) =>
% 97.99/13.26 ((
% 97.99/13.26 (app) =>
% 97.99/13.26 ((
% 97.99/13.26 (infuncsetfunc) =>
% 97.99/13.26 ((
% 97.99/13.26 (ap2p) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcinfuncset) =>
% 97.99/13.26 ((
% 97.99/13.26 (lamProp) =>
% 97.99/13.26 ((
% 97.99/13.26 (lamp) =>
% 97.99/13.26 ((
% 97.99/13.26 (lam2p) =>
% 97.99/13.26 ((
% 97.99/13.26 (brelnall1) =>
% 97.99/13.26 ((
% 97.99/13.26 (brelnall2) =>
% 97.99/13.26 ((
% 97.99/13.26 (ex1E2) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcGraphProp1) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcGraphProp3) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcGraphProp2) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcextLem) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcGraphProp4) =>
% 97.99/13.26 ((
% 97.99/13.26 (subbreln) =>
% 97.99/13.26 ((
% 97.99/13.26 (eqbreln) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcext) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcext2) =>
% 97.99/13.26 ((
% 97.99/13.26 (ap2apEq1) =>
% 97.99/13.26 ((
% 97.99/13.26 (ap2apEq2) =>
% 97.99/13.26 ((
% 97.99/13.26 (beta1) =>
% 97.99/13.26 ((
% 97.99/13.26 (eta1) =>
% 97.99/13.26 ((
% 97.99/13.26 (lam2lamEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (beta2) =>
% 97.99/13.26 ((
% 97.99/13.26 (eta2) =>
% 97.99/13.26 ((
% 97.99/13.26 (iffalseProp1) =>
% 97.99/13.26 ((
% 97.99/13.26 (iffalseProp2) =>
% 97.99/13.26 ((
% 97.99/13.26 (iftrueProp1) =>
% 97.99/13.26 ((
% 97.99/13.26 (iftrueProp2) =>
% 97.99/13.26 ((
% 97.99/13.26 (ifSingleton) =>
% 97.99/13.26 ((
% 97.99/13.26 (ifp) =>
% 97.99/13.26 ((
% 97.99/13.26 (theeq) =>
% 97.99/13.26 ((
% 97.99/13.26 (iftrue) =>
% 97.99/13.26 ((
% 97.99/13.26 (iffalse) =>
% 97.99/13.26 ((
% 97.99/13.26 (iftrueorfalse) =>
% 97.99/13.26 ((
% 97.99/13.26 (binintersectT_lem) =>
% 97.99/13.26 ((
% 97.99/13.26 (binunionT_lem) =>
% 97.99/13.26 ((
% 97.99/13.26 (powersetT_lem) =>
% 97.99/13.26 ((
% 97.99/13.26 (setminusT_lem) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementT_lem) =>
% 97.99/13.26 ((
% 97.99/13.26 (setextT) =>
% 97.99/13.26 ((
% 97.99/13.26 (subsetTI) =>
% 97.99/13.26 ((
% 97.99/13.26 (powersetTI1) =>
% 97.99/13.26 ((
% 97.99/13.26 (powersetTE1) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementTI1) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementTE1) =>
% 97.99/13.26 ((
% 97.99/13.26 (binintersectTELcontra) =>
% 97.99/13.26 ((
% 97.99/13.26 (binintersectTERcontra) =>
% 97.99/13.26 ((
% 97.99/13.26 (contrasubsetT) =>
% 97.99/13.26 ((
% 97.99/13.26 (contrasubsetT1) =>
% 97.99/13.26 ((
% 97.99/13.26 (contrasubsetT2) =>
% 97.99/13.26 ((
% 97.99/13.26 (contrasubsetT3) =>
% 97.99/13.26 ((
% 97.99/13.26 (doubleComplementI1) =>
% 97.99/13.26 ((
% 97.99/13.26 (doubleComplementE1) =>
% 97.99/13.26 ((
% 97.99/13.26 (doubleComplementSub1) =>
% 97.99/13.26 ((
% 97.99/13.26 (doubleComplementSub2) =>
% 97.99/13.26 ((
% 97.99/13.26 (doubleComplementEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementTnotintersectT) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementImpComplementIntersect) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementSubsetComplementIntersect) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementInPowersetComplementIntersect) =>
% 97.99/13.26 ((
% 97.99/13.26 (contraSubsetComplement) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementTcontraSubset) =>
% 97.99/13.26 ((
% 97.99/13.26 (binunionTILcontra) =>
% 97.99/13.26 ((
% 97.99/13.26 (binunionTIRcontra) =>
% 97.99/13.26 ((
% 97.99/13.26 (inIntersectImpInUnion) =>
% 97.99/13.26 ((
% 97.99/13.26 (inIntersectImpInUnion2) =>
% 97.99/13.26 ((
% 97.99/13.26 (inIntersectImpInIntersectUnions) =>
% 97.99/13.26 ((
% 97.99/13.26 (intersectInPowersetIntersectUnions) =>
% 97.99/13.26 ((
% 97.99/13.26 (inComplementUnionImpNotIn1) =>
% 97.99/13.26 ((
% 97.99/13.26 (inComplementUnionImpInComplement1) =>
% 97.99/13.26 ((
% 97.99/13.26 (binunionTE) =>
% 97.99/13.26 ((
% 97.99/13.26 (binunionTEcontra) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan2a1) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementUnionInPowersetComplement) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan2a2) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan1a) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan1b) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan1) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan2a) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan2b2) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan2b) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan2) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz13rule0) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz13rule1) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz13rule2) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz13rule3) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz13rule4) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz1_1) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz1_2) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz1_3) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz1_4) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz1_5) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1all2) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1SetBreln1) =>
% 97.99/13.26 ((
% 97.99/13.26 (choice2fnsingleton) =>
% 97.99/13.26 ((
% 97.99/13.26 (setOfPairsIsBReln1) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1all1) =>
% 97.99/13.26 ((
% 97.99/13.26 (subbreln1) =>
% 97.99/13.26 ((
% 97.99/13.26 (eqbreln1) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1invprop) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1invI) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1invE) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1compprop) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1compI) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1compE) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1compEex) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionprop) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionIL) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionIR) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionI) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionE) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionEcases) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionCommutes) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz2Ex) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz2W) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz2A) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz2B) =>
% 97.99/13.26 ((
% 97.99/13.26 (image1Ex) =>
% 97.99/13.26 ((
% 97.99/13.26 (image1Ex1) =>
% 97.99/13.26 ((
% 97.99/13.26 (image1Equiv) =>
% 97.99/13.26 ((
% 97.99/13.26 (image1E) =>
% 97.99/13.26 ((
% 97.99/13.26 (image1I) =>
% 97.99/13.26 ((
% 97.99/13.26 (injFuncInInjFuncSet) =>
% 97.99/13.26 ((
% 97.99/13.26 (injFuncSetFuncIn) =>
% 97.99/13.26 ((
% 97.99/13.26 (injFuncSetFuncInj) =>
% 97.99/13.26 ((
% 97.99/13.26 (surjFuncSetFuncIn) =>
% 97.99/13.26 ((
% 97.99/13.26 (surjFuncSetFuncSurj) =>
% 97.99/13.26 ((
% 97.99/13.26 (leftInvIsSurj) =>
% 97.99/13.26 ((
% 97.99/13.26 (surjCantorThm) =>
% 97.99/13.26 ((
% 97.99/13.26 (foundation2) =>
% 97.99/13.26 ((
% 97.99/13.26 (notinself) =>
% 97.99/13.26 ((
% 97.99/13.26 (notinself2) =>
% 97.99/13.26 ((
% 97.99/13.26 (omegaSp) =>
% 97.99/13.26 ((
% 97.99/13.26 (omegaSclos) =>
% 97.99/13.26 ((
% 97.99/13.26 (peano0notS) =>
% 97.99/13.26 ((
% 97.99/13.26 (!!) @ (
% 97.99/13.26 (('#S') @ (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 =>) @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#C') @ in @
% 97.99/13.26 omega)))) @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 !!) @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 (
% 97.99/13.26 ('#S') @ (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 =>) @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#C') @ in @
% 97.99/13.26 omega)))))) @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#S') @ (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 '#S') @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 =>))) @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#C') @ (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 '#B') @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 =) @
% 97.99/13.26 omegaS)))) @
% 97.99/13.26 omegaS)))))) @
% 97.99/13.26 (
% 97.99/13.26 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.99/13.26 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1255])).
% 97.99/13.26 thf(zip_derived_cl1272, plain,
% 97.99/13.26 (~ (((setminusSubset2) =>
% 97.99/13.26 (((setminusERneg) =>
% 97.99/13.26 (((setminusELneg) =>
% 97.99/13.26 (((setminusILneg) =>
% 97.99/13.26 (((setminusIRneg) =>
% 97.99/13.26 (((setminusLsub) =>
% 97.99/13.26 (((setminusSubset1) =>
% 97.99/13.26 (((symdiffE) =>
% 97.99/13.26 (((symdiffI1) =>
% 97.99/13.26 (((symdiffI2) =>
% 97.99/13.26 (((symdiffIneg1) =>
% 97.99/13.26 (((symdiffIneg2) =>
% 97.99/13.26 (((secondinupair) =>
% 97.99/13.26 (((setukpairIL) =>
% 97.99/13.26 (((setukpairIR) =>
% 97.99/13.26 (((kpairiskpair) =>
% 97.99/13.26 (((kpairp) =>
% 97.99/13.26 (((singletonsubset) =>
% 97.99/13.26 (((singletoninpowerset) =>
% 97.99/13.26 (((singletoninpowunion) =>
% 97.99/13.26 (((upairset2E) =>
% 97.99/13.26 (((upairsubunion) =>
% 97.99/13.26 (((upairinpowunion) =>
% 97.99/13.26 (((ubforcartprodlem1) =>
% 97.99/13.26 (((ubforcartprodlem2) =>
% 97.99/13.26 (((ubforcartprodlem3) =>
% 97.99/13.26 (((cartprodpairin) =>
% 97.99/13.26 (((cartprodmempair1) =>
% 97.99/13.26 (((cartprodmempair) =>
% 97.99/13.26 (((setunionE2) =>
% 97.99/13.26 ((
% 97.99/13.26 (setunionsingleton1) =>
% 97.99/13.26 ((
% 97.99/13.26 (setunionsingleton2) =>
% 97.99/13.26 ((
% 97.99/13.26 (setunionsingleton) =>
% 97.99/13.26 ((
% 97.99/13.26 (singletonprop) =>
% 97.99/13.26 ((
% 97.99/13.26 (ex1E1) =>
% 97.99/13.26 ((
% 97.99/13.26 (ex1I) =>
% 97.99/13.26 ((
% 97.99/13.26 (ex1I2) =>
% 97.99/13.26 ((
% 97.99/13.26 (singletonsuniq) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjL1) =>
% 97.99/13.26 ((
% 97.99/13.26 (kfstsingleton) =>
% 97.99/13.26 ((
% 97.99/13.26 (theprop) =>
% 97.99/13.26 ((
% 97.99/13.26 (kfstpairEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodfstin) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjL2) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjL) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjR11) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjR12) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjR1) =>
% 97.99/13.26 ((
% 97.99/13.26 (upairequniteq) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjR2) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjR) =>
% 97.99/13.26 ((
% 97.99/13.26 (ksndsingleton) =>
% 97.99/13.26 ((
% 97.99/13.26 (ksndpairEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (kpairsurjEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodsndin) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodpairmemEL) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodpairmemER) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodmempaircEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodfstpairEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodsndpairEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodpairsurjEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (dpsetconstrI) =>
% 97.99/13.26 ((
% 97.99/13.26 (dpsetconstrSub) =>
% 97.99/13.26 ((
% 97.99/13.26 (setOfPairsIsBReln) =>
% 97.99/13.26 ((
% 97.99/13.26 (dpsetconstrERa) =>
% 97.99/13.26 ((
% 97.99/13.26 (dpsetconstrEL1) =>
% 97.99/13.26 ((
% 97.99/13.26 (dpsetconstrEL2) =>
% 97.99/13.26 ((
% 97.99/13.26 (dpsetconstrER) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcImageSingleton) =>
% 97.99/13.26 ((
% 97.99/13.26 (apProp) =>
% 97.99/13.26 ((
% 97.99/13.26 (app) =>
% 97.99/13.26 ((
% 97.99/13.26 (infuncsetfunc) =>
% 97.99/13.26 ((
% 97.99/13.26 (ap2p) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcinfuncset) =>
% 97.99/13.26 ((
% 97.99/13.26 (lamProp) =>
% 97.99/13.26 ((
% 97.99/13.26 (lamp) =>
% 97.99/13.26 ((
% 97.99/13.26 (lam2p) =>
% 97.99/13.26 ((
% 97.99/13.26 (brelnall1) =>
% 97.99/13.26 ((
% 97.99/13.26 (brelnall2) =>
% 97.99/13.26 ((
% 97.99/13.26 (ex1E2) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcGraphProp1) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcGraphProp3) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcGraphProp2) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcextLem) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcGraphProp4) =>
% 97.99/13.26 ((
% 97.99/13.26 (subbreln) =>
% 97.99/13.26 ((
% 97.99/13.26 (eqbreln) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcext) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcext2) =>
% 97.99/13.26 ((
% 97.99/13.26 (ap2apEq1) =>
% 97.99/13.26 ((
% 97.99/13.26 (ap2apEq2) =>
% 97.99/13.26 ((
% 97.99/13.26 (beta1) =>
% 97.99/13.26 ((
% 97.99/13.26 (eta1) =>
% 97.99/13.26 ((
% 97.99/13.26 (lam2lamEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (beta2) =>
% 97.99/13.26 ((
% 97.99/13.26 (eta2) =>
% 97.99/13.26 ((
% 97.99/13.26 (iffalseProp1) =>
% 97.99/13.26 ((
% 97.99/13.26 (iffalseProp2) =>
% 97.99/13.26 ((
% 97.99/13.26 (iftrueProp1) =>
% 97.99/13.26 ((
% 97.99/13.26 (iftrueProp2) =>
% 97.99/13.26 ((
% 97.99/13.26 (ifSingleton) =>
% 97.99/13.26 ((
% 97.99/13.26 (ifp) =>
% 97.99/13.26 ((
% 97.99/13.26 (theeq) =>
% 97.99/13.26 ((
% 97.99/13.26 (iftrue) =>
% 97.99/13.26 ((
% 97.99/13.26 (iffalse) =>
% 97.99/13.26 ((
% 97.99/13.26 (iftrueorfalse) =>
% 97.99/13.26 ((
% 97.99/13.26 (binintersectT_lem) =>
% 97.99/13.26 ((
% 97.99/13.26 (binunionT_lem) =>
% 97.99/13.26 ((
% 97.99/13.26 (powersetT_lem) =>
% 97.99/13.26 ((
% 97.99/13.26 (setminusT_lem) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementT_lem) =>
% 97.99/13.26 ((
% 97.99/13.26 (setextT) =>
% 97.99/13.26 ((
% 97.99/13.26 (subsetTI) =>
% 97.99/13.26 ((
% 97.99/13.26 (powersetTI1) =>
% 97.99/13.26 ((
% 97.99/13.26 (powersetTE1) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementTI1) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementTE1) =>
% 97.99/13.26 ((
% 97.99/13.26 (binintersectTELcontra) =>
% 97.99/13.26 ((
% 97.99/13.26 (binintersectTERcontra) =>
% 97.99/13.26 ((
% 97.99/13.26 (contrasubsetT) =>
% 97.99/13.26 ((
% 97.99/13.26 (contrasubsetT1) =>
% 97.99/13.26 ((
% 97.99/13.26 (contrasubsetT2) =>
% 97.99/13.26 ((
% 97.99/13.26 (contrasubsetT3) =>
% 97.99/13.26 ((
% 97.99/13.26 (doubleComplementI1) =>
% 97.99/13.26 ((
% 97.99/13.26 (doubleComplementE1) =>
% 97.99/13.26 ((
% 97.99/13.26 (doubleComplementSub1) =>
% 97.99/13.26 ((
% 97.99/13.26 (doubleComplementSub2) =>
% 97.99/13.26 ((
% 97.99/13.26 (doubleComplementEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementTnotintersectT) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementImpComplementIntersect) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementSubsetComplementIntersect) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementInPowersetComplementIntersect) =>
% 97.99/13.26 ((
% 97.99/13.26 (contraSubsetComplement) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementTcontraSubset) =>
% 97.99/13.26 ((
% 97.99/13.26 (binunionTILcontra) =>
% 97.99/13.26 ((
% 97.99/13.26 (binunionTIRcontra) =>
% 97.99/13.26 ((
% 97.99/13.26 (inIntersectImpInUnion) =>
% 97.99/13.26 ((
% 97.99/13.26 (inIntersectImpInUnion2) =>
% 97.99/13.26 ((
% 97.99/13.26 (inIntersectImpInIntersectUnions) =>
% 97.99/13.26 ((
% 97.99/13.26 (intersectInPowersetIntersectUnions) =>
% 97.99/13.26 ((
% 97.99/13.26 (inComplementUnionImpNotIn1) =>
% 97.99/13.26 ((
% 97.99/13.26 (inComplementUnionImpInComplement1) =>
% 97.99/13.26 ((
% 97.99/13.26 (binunionTE) =>
% 97.99/13.26 ((
% 97.99/13.26 (binunionTEcontra) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan2a1) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementUnionInPowersetComplement) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan2a2) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan1a) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan1b) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan1) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan2a) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan2b2) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan2b) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan2) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz13rule0) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz13rule1) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz13rule2) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz13rule3) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz13rule4) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz1_1) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz1_2) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz1_3) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz1_4) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz1_5) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1all2) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1SetBreln1) =>
% 97.99/13.26 ((
% 97.99/13.26 (choice2fnsingleton) =>
% 97.99/13.26 ((
% 97.99/13.26 (setOfPairsIsBReln1) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1all1) =>
% 97.99/13.26 ((
% 97.99/13.26 (subbreln1) =>
% 97.99/13.26 ((
% 97.99/13.26 (eqbreln1) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1invprop) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1invI) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1invE) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1compprop) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1compI) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1compE) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1compEex) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionprop) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionIL) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionIR) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionI) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionE) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionEcases) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionCommutes) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz2Ex) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz2W) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz2A) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz2B) =>
% 97.99/13.26 ((
% 97.99/13.26 (image1Ex) =>
% 97.99/13.26 ((
% 97.99/13.26 (image1Ex1) =>
% 97.99/13.26 ((
% 97.99/13.26 (image1Equiv) =>
% 97.99/13.26 ((
% 97.99/13.26 (image1E) =>
% 97.99/13.26 ((
% 97.99/13.26 (image1I) =>
% 97.99/13.26 ((
% 97.99/13.26 (injFuncInInjFuncSet) =>
% 97.99/13.26 ((
% 97.99/13.26 (injFuncSetFuncIn) =>
% 97.99/13.26 ((
% 97.99/13.26 (injFuncSetFuncInj) =>
% 97.99/13.26 ((
% 97.99/13.26 (surjFuncSetFuncIn) =>
% 97.99/13.26 ((
% 97.99/13.26 (surjFuncSetFuncSurj) =>
% 97.99/13.26 ((
% 97.99/13.26 (leftInvIsSurj) =>
% 97.99/13.26 ((
% 97.99/13.26 (surjCantorThm) =>
% 97.99/13.26 ((
% 97.99/13.26 (foundation2) =>
% 97.99/13.26 ((
% 97.99/13.26 (notinself) =>
% 97.99/13.26 ((
% 97.99/13.26 (notinself2) =>
% 97.99/13.26 ((
% 97.99/13.26 (omegaSp) =>
% 97.99/13.26 ((
% 97.99/13.26 (omegaSclos) =>
% 97.99/13.26 ((
% 97.99/13.26 (peano0notS) =>
% 97.99/13.26 ((
% 97.99/13.26 (!!) @ (
% 97.99/13.26 (('#S') @ (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 =>) @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#C') @ in @
% 97.99/13.26 omega)))) @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 !!) @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 (
% 97.99/13.26 ('#S') @ (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 =>) @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#C') @ in @
% 97.99/13.26 omega)))))) @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#S') @ (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 '#S') @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 =>))) @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#C') @ (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 '#B') @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 =) @
% 97.99/13.26 omegaS)))) @
% 97.99/13.26 omegaS)))))) @
% 97.99/13.26 (
% 97.99/13.26 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.99/13.26 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1264])).
% 97.99/13.26 thf(zip_derived_cl1280, plain,
% 97.99/13.26 (~ (((setminusERneg) =>
% 97.99/13.26 (((setminusELneg) =>
% 97.99/13.26 (((setminusILneg) =>
% 97.99/13.26 (((setminusIRneg) =>
% 97.99/13.26 (((setminusLsub) =>
% 97.99/13.26 (((setminusSubset1) =>
% 97.99/13.26 (((symdiffE) =>
% 97.99/13.26 (((symdiffI1) =>
% 97.99/13.26 (((symdiffI2) =>
% 97.99/13.26 (((symdiffIneg1) =>
% 97.99/13.26 (((symdiffIneg2) =>
% 97.99/13.26 (((secondinupair) =>
% 97.99/13.26 (((setukpairIL) =>
% 97.99/13.26 (((setukpairIR) =>
% 97.99/13.26 (((kpairiskpair) =>
% 97.99/13.26 (((kpairp) =>
% 97.99/13.26 (((singletonsubset) =>
% 97.99/13.26 (((singletoninpowerset) =>
% 97.99/13.26 (((singletoninpowunion) =>
% 97.99/13.26 (((upairset2E) =>
% 97.99/13.26 (((upairsubunion) =>
% 97.99/13.26 (((upairinpowunion) =>
% 97.99/13.26 (((ubforcartprodlem1) =>
% 97.99/13.26 (((ubforcartprodlem2) =>
% 97.99/13.26 (((ubforcartprodlem3) =>
% 97.99/13.26 (((cartprodpairin) =>
% 97.99/13.26 (((cartprodmempair1) =>
% 97.99/13.26 (((cartprodmempair) =>
% 97.99/13.26 (((setunionE2) =>
% 97.99/13.26 (((setunionsingleton1) =>
% 97.99/13.26 ((
% 97.99/13.26 (setunionsingleton2) =>
% 97.99/13.26 ((
% 97.99/13.26 (setunionsingleton) =>
% 97.99/13.26 ((
% 97.99/13.26 (singletonprop) =>
% 97.99/13.26 ((
% 97.99/13.26 (ex1E1) =>
% 97.99/13.26 ((
% 97.99/13.26 (ex1I) =>
% 97.99/13.26 ((
% 97.99/13.26 (ex1I2) =>
% 97.99/13.26 ((
% 97.99/13.26 (singletonsuniq) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjL1) =>
% 97.99/13.26 ((
% 97.99/13.26 (kfstsingleton) =>
% 97.99/13.26 ((
% 97.99/13.26 (theprop) =>
% 97.99/13.26 ((
% 97.99/13.26 (kfstpairEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodfstin) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjL2) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjL) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjR11) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjR12) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjR1) =>
% 97.99/13.26 ((
% 97.99/13.26 (upairequniteq) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjR2) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjR) =>
% 97.99/13.26 ((
% 97.99/13.26 (ksndsingleton) =>
% 97.99/13.26 ((
% 97.99/13.26 (ksndpairEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (kpairsurjEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodsndin) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodpairmemEL) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodpairmemER) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodmempaircEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodfstpairEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodsndpairEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodpairsurjEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (dpsetconstrI) =>
% 97.99/13.26 ((
% 97.99/13.26 (dpsetconstrSub) =>
% 97.99/13.26 ((
% 97.99/13.26 (setOfPairsIsBReln) =>
% 97.99/13.26 ((
% 97.99/13.26 (dpsetconstrERa) =>
% 97.99/13.26 ((
% 97.99/13.26 (dpsetconstrEL1) =>
% 97.99/13.26 ((
% 97.99/13.26 (dpsetconstrEL2) =>
% 97.99/13.26 ((
% 97.99/13.26 (dpsetconstrER) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcImageSingleton) =>
% 97.99/13.26 ((
% 97.99/13.26 (apProp) =>
% 97.99/13.26 ((
% 97.99/13.26 (app) =>
% 97.99/13.26 ((
% 97.99/13.26 (infuncsetfunc) =>
% 97.99/13.26 ((
% 97.99/13.26 (ap2p) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcinfuncset) =>
% 97.99/13.26 ((
% 97.99/13.26 (lamProp) =>
% 97.99/13.26 ((
% 97.99/13.26 (lamp) =>
% 97.99/13.26 ((
% 97.99/13.26 (lam2p) =>
% 97.99/13.26 ((
% 97.99/13.26 (brelnall1) =>
% 97.99/13.26 ((
% 97.99/13.26 (brelnall2) =>
% 97.99/13.26 ((
% 97.99/13.26 (ex1E2) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcGraphProp1) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcGraphProp3) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcGraphProp2) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcextLem) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcGraphProp4) =>
% 97.99/13.26 ((
% 97.99/13.26 (subbreln) =>
% 97.99/13.26 ((
% 97.99/13.26 (eqbreln) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcext) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcext2) =>
% 97.99/13.26 ((
% 97.99/13.26 (ap2apEq1) =>
% 97.99/13.26 ((
% 97.99/13.26 (ap2apEq2) =>
% 97.99/13.26 ((
% 97.99/13.26 (beta1) =>
% 97.99/13.26 ((
% 97.99/13.26 (eta1) =>
% 97.99/13.26 ((
% 97.99/13.26 (lam2lamEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (beta2) =>
% 97.99/13.26 ((
% 97.99/13.26 (eta2) =>
% 97.99/13.26 ((
% 97.99/13.26 (iffalseProp1) =>
% 97.99/13.26 ((
% 97.99/13.26 (iffalseProp2) =>
% 97.99/13.26 ((
% 97.99/13.26 (iftrueProp1) =>
% 97.99/13.26 ((
% 97.99/13.26 (iftrueProp2) =>
% 97.99/13.26 ((
% 97.99/13.26 (ifSingleton) =>
% 97.99/13.26 ((
% 97.99/13.26 (ifp) =>
% 97.99/13.26 ((
% 97.99/13.26 (theeq) =>
% 97.99/13.26 ((
% 97.99/13.26 (iftrue) =>
% 97.99/13.26 ((
% 97.99/13.26 (iffalse) =>
% 97.99/13.26 ((
% 97.99/13.26 (iftrueorfalse) =>
% 97.99/13.26 ((
% 97.99/13.26 (binintersectT_lem) =>
% 97.99/13.26 ((
% 97.99/13.26 (binunionT_lem) =>
% 97.99/13.26 ((
% 97.99/13.26 (powersetT_lem) =>
% 97.99/13.26 ((
% 97.99/13.26 (setminusT_lem) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementT_lem) =>
% 97.99/13.26 ((
% 97.99/13.26 (setextT) =>
% 97.99/13.26 ((
% 97.99/13.26 (subsetTI) =>
% 97.99/13.26 ((
% 97.99/13.26 (powersetTI1) =>
% 97.99/13.26 ((
% 97.99/13.26 (powersetTE1) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementTI1) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementTE1) =>
% 97.99/13.26 ((
% 97.99/13.26 (binintersectTELcontra) =>
% 97.99/13.26 ((
% 97.99/13.26 (binintersectTERcontra) =>
% 97.99/13.26 ((
% 97.99/13.26 (contrasubsetT) =>
% 97.99/13.26 ((
% 97.99/13.26 (contrasubsetT1) =>
% 97.99/13.26 ((
% 97.99/13.26 (contrasubsetT2) =>
% 97.99/13.26 ((
% 97.99/13.26 (contrasubsetT3) =>
% 97.99/13.26 ((
% 97.99/13.26 (doubleComplementI1) =>
% 97.99/13.26 ((
% 97.99/13.26 (doubleComplementE1) =>
% 97.99/13.26 ((
% 97.99/13.26 (doubleComplementSub1) =>
% 97.99/13.26 ((
% 97.99/13.26 (doubleComplementSub2) =>
% 97.99/13.26 ((
% 97.99/13.26 (doubleComplementEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementTnotintersectT) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementImpComplementIntersect) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementSubsetComplementIntersect) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementInPowersetComplementIntersect) =>
% 97.99/13.26 ((
% 97.99/13.26 (contraSubsetComplement) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementTcontraSubset) =>
% 97.99/13.26 ((
% 97.99/13.26 (binunionTILcontra) =>
% 97.99/13.26 ((
% 97.99/13.26 (binunionTIRcontra) =>
% 97.99/13.26 ((
% 97.99/13.26 (inIntersectImpInUnion) =>
% 97.99/13.26 ((
% 97.99/13.26 (inIntersectImpInUnion2) =>
% 97.99/13.26 ((
% 97.99/13.26 (inIntersectImpInIntersectUnions) =>
% 97.99/13.26 ((
% 97.99/13.26 (intersectInPowersetIntersectUnions) =>
% 97.99/13.26 ((
% 97.99/13.26 (inComplementUnionImpNotIn1) =>
% 97.99/13.26 ((
% 97.99/13.26 (inComplementUnionImpInComplement1) =>
% 97.99/13.26 ((
% 97.99/13.26 (binunionTE) =>
% 97.99/13.26 ((
% 97.99/13.26 (binunionTEcontra) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan2a1) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementUnionInPowersetComplement) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan2a2) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan1a) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan1b) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan1) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan2a) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan2b2) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan2b) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan2) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz13rule0) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz13rule1) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz13rule2) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz13rule3) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz13rule4) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz1_1) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz1_2) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz1_3) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz1_4) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz1_5) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1all2) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1SetBreln1) =>
% 97.99/13.26 ((
% 97.99/13.26 (choice2fnsingleton) =>
% 97.99/13.26 ((
% 97.99/13.26 (setOfPairsIsBReln1) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1all1) =>
% 97.99/13.26 ((
% 97.99/13.26 (subbreln1) =>
% 97.99/13.26 ((
% 97.99/13.26 (eqbreln1) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1invprop) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1invI) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1invE) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1compprop) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1compI) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1compE) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1compEex) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionprop) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionIL) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionIR) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionI) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionE) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionEcases) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionCommutes) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz2Ex) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz2W) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz2A) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz2B) =>
% 97.99/13.26 ((
% 97.99/13.26 (image1Ex) =>
% 97.99/13.26 ((
% 97.99/13.26 (image1Ex1) =>
% 97.99/13.26 ((
% 97.99/13.26 (image1Equiv) =>
% 97.99/13.26 ((
% 97.99/13.26 (image1E) =>
% 97.99/13.26 ((
% 97.99/13.26 (image1I) =>
% 97.99/13.26 ((
% 97.99/13.26 (injFuncInInjFuncSet) =>
% 97.99/13.26 ((
% 97.99/13.26 (injFuncSetFuncIn) =>
% 97.99/13.26 ((
% 97.99/13.26 (injFuncSetFuncInj) =>
% 97.99/13.26 ((
% 97.99/13.26 (surjFuncSetFuncIn) =>
% 97.99/13.26 ((
% 97.99/13.26 (surjFuncSetFuncSurj) =>
% 97.99/13.26 ((
% 97.99/13.26 (leftInvIsSurj) =>
% 97.99/13.26 ((
% 97.99/13.26 (surjCantorThm) =>
% 97.99/13.26 ((
% 97.99/13.26 (foundation2) =>
% 97.99/13.26 ((
% 97.99/13.26 (notinself) =>
% 97.99/13.26 ((
% 97.99/13.26 (notinself2) =>
% 97.99/13.26 ((
% 97.99/13.26 (omegaSp) =>
% 97.99/13.26 ((
% 97.99/13.26 (omegaSclos) =>
% 97.99/13.26 ((
% 97.99/13.26 (peano0notS) =>
% 97.99/13.26 ((
% 97.99/13.26 (!!) @ (
% 97.99/13.26 (('#S') @ (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 =>) @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#C') @ in @
% 97.99/13.26 omega)))) @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 !!) @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 (
% 97.99/13.26 ('#S') @ (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 =>) @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#C') @ in @
% 97.99/13.26 omega)))))) @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#S') @ (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 '#S') @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 =>))) @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#C') @ (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 '#B') @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 =) @
% 97.99/13.26 omegaS)))) @
% 97.99/13.26 omegaS)))))) @
% 97.99/13.26 (
% 97.99/13.26 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.99/13.26 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1272])).
% 97.99/13.26 thf(zip_derived_cl1288, plain,
% 97.99/13.26 (~ (((setminusELneg) =>
% 97.99/13.26 (((setminusILneg) =>
% 97.99/13.26 (((setminusIRneg) =>
% 97.99/13.26 (((setminusLsub) =>
% 97.99/13.26 (((setminusSubset1) =>
% 97.99/13.26 (((symdiffE) =>
% 97.99/13.26 (((symdiffI1) =>
% 97.99/13.26 (((symdiffI2) =>
% 97.99/13.26 (((symdiffIneg1) =>
% 97.99/13.26 (((symdiffIneg2) =>
% 97.99/13.26 (((secondinupair) =>
% 97.99/13.26 (((setukpairIL) =>
% 97.99/13.26 (((setukpairIR) =>
% 97.99/13.26 (((kpairiskpair) =>
% 97.99/13.26 (((kpairp) =>
% 97.99/13.26 (((singletonsubset) =>
% 97.99/13.26 (((singletoninpowerset) =>
% 97.99/13.26 (((singletoninpowunion) =>
% 97.99/13.26 (((upairset2E) =>
% 97.99/13.26 (((upairsubunion) =>
% 97.99/13.26 (((upairinpowunion) =>
% 97.99/13.26 (((ubforcartprodlem1) =>
% 97.99/13.26 (((ubforcartprodlem2) =>
% 97.99/13.26 (((ubforcartprodlem3) =>
% 97.99/13.26 (((cartprodpairin) =>
% 97.99/13.26 (((cartprodmempair1) =>
% 97.99/13.26 (((cartprodmempair) =>
% 97.99/13.26 (((setunionE2) =>
% 97.99/13.26 (((setunionsingleton1) =>
% 97.99/13.26 (((setunionsingleton2) =>
% 97.99/13.26 ((
% 97.99/13.26 (setunionsingleton) =>
% 97.99/13.26 ((
% 97.99/13.26 (singletonprop) =>
% 97.99/13.26 ((
% 97.99/13.26 (ex1E1) =>
% 97.99/13.26 ((
% 97.99/13.26 (ex1I) =>
% 97.99/13.26 ((
% 97.99/13.26 (ex1I2) =>
% 97.99/13.26 ((
% 97.99/13.26 (singletonsuniq) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjL1) =>
% 97.99/13.26 ((
% 97.99/13.26 (kfstsingleton) =>
% 97.99/13.26 ((
% 97.99/13.26 (theprop) =>
% 97.99/13.26 ((
% 97.99/13.26 (kfstpairEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodfstin) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjL2) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjL) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjR11) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjR12) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjR1) =>
% 97.99/13.26 ((
% 97.99/13.26 (upairequniteq) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjR2) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjR) =>
% 97.99/13.26 ((
% 97.99/13.26 (ksndsingleton) =>
% 97.99/13.26 ((
% 97.99/13.26 (ksndpairEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (kpairsurjEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodsndin) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodpairmemEL) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodpairmemER) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodmempaircEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodfstpairEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodsndpairEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodpairsurjEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (dpsetconstrI) =>
% 97.99/13.26 ((
% 97.99/13.26 (dpsetconstrSub) =>
% 97.99/13.26 ((
% 97.99/13.26 (setOfPairsIsBReln) =>
% 97.99/13.26 ((
% 97.99/13.26 (dpsetconstrERa) =>
% 97.99/13.26 ((
% 97.99/13.26 (dpsetconstrEL1) =>
% 97.99/13.26 ((
% 97.99/13.26 (dpsetconstrEL2) =>
% 97.99/13.26 ((
% 97.99/13.26 (dpsetconstrER) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcImageSingleton) =>
% 97.99/13.26 ((
% 97.99/13.26 (apProp) =>
% 97.99/13.26 ((
% 97.99/13.26 (app) =>
% 97.99/13.26 ((
% 97.99/13.26 (infuncsetfunc) =>
% 97.99/13.26 ((
% 97.99/13.26 (ap2p) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcinfuncset) =>
% 97.99/13.26 ((
% 97.99/13.26 (lamProp) =>
% 97.99/13.26 ((
% 97.99/13.26 (lamp) =>
% 97.99/13.26 ((
% 97.99/13.26 (lam2p) =>
% 97.99/13.26 ((
% 97.99/13.26 (brelnall1) =>
% 97.99/13.26 ((
% 97.99/13.26 (brelnall2) =>
% 97.99/13.26 ((
% 97.99/13.26 (ex1E2) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcGraphProp1) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcGraphProp3) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcGraphProp2) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcextLem) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcGraphProp4) =>
% 97.99/13.26 ((
% 97.99/13.26 (subbreln) =>
% 97.99/13.26 ((
% 97.99/13.26 (eqbreln) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcext) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcext2) =>
% 97.99/13.26 ((
% 97.99/13.26 (ap2apEq1) =>
% 97.99/13.26 ((
% 97.99/13.26 (ap2apEq2) =>
% 97.99/13.26 ((
% 97.99/13.26 (beta1) =>
% 97.99/13.26 ((
% 97.99/13.26 (eta1) =>
% 97.99/13.26 ((
% 97.99/13.26 (lam2lamEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (beta2) =>
% 97.99/13.26 ((
% 97.99/13.26 (eta2) =>
% 97.99/13.26 ((
% 97.99/13.26 (iffalseProp1) =>
% 97.99/13.26 ((
% 97.99/13.26 (iffalseProp2) =>
% 97.99/13.26 ((
% 97.99/13.26 (iftrueProp1) =>
% 97.99/13.26 ((
% 97.99/13.26 (iftrueProp2) =>
% 97.99/13.26 ((
% 97.99/13.26 (ifSingleton) =>
% 97.99/13.26 ((
% 97.99/13.26 (ifp) =>
% 97.99/13.26 ((
% 97.99/13.26 (theeq) =>
% 97.99/13.26 ((
% 97.99/13.26 (iftrue) =>
% 97.99/13.26 ((
% 97.99/13.26 (iffalse) =>
% 97.99/13.26 ((
% 97.99/13.26 (iftrueorfalse) =>
% 97.99/13.26 ((
% 97.99/13.26 (binintersectT_lem) =>
% 97.99/13.26 ((
% 97.99/13.26 (binunionT_lem) =>
% 97.99/13.26 ((
% 97.99/13.26 (powersetT_lem) =>
% 97.99/13.26 ((
% 97.99/13.26 (setminusT_lem) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementT_lem) =>
% 97.99/13.26 ((
% 97.99/13.26 (setextT) =>
% 97.99/13.26 ((
% 97.99/13.26 (subsetTI) =>
% 97.99/13.26 ((
% 97.99/13.26 (powersetTI1) =>
% 97.99/13.26 ((
% 97.99/13.26 (powersetTE1) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementTI1) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementTE1) =>
% 97.99/13.26 ((
% 97.99/13.26 (binintersectTELcontra) =>
% 97.99/13.26 ((
% 97.99/13.26 (binintersectTERcontra) =>
% 97.99/13.26 ((
% 97.99/13.26 (contrasubsetT) =>
% 97.99/13.26 ((
% 97.99/13.26 (contrasubsetT1) =>
% 97.99/13.26 ((
% 97.99/13.26 (contrasubsetT2) =>
% 97.99/13.26 ((
% 97.99/13.26 (contrasubsetT3) =>
% 97.99/13.26 ((
% 97.99/13.26 (doubleComplementI1) =>
% 97.99/13.26 ((
% 97.99/13.26 (doubleComplementE1) =>
% 97.99/13.26 ((
% 97.99/13.26 (doubleComplementSub1) =>
% 97.99/13.26 ((
% 97.99/13.26 (doubleComplementSub2) =>
% 97.99/13.26 ((
% 97.99/13.26 (doubleComplementEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementTnotintersectT) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementImpComplementIntersect) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementSubsetComplementIntersect) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementInPowersetComplementIntersect) =>
% 97.99/13.26 ((
% 97.99/13.26 (contraSubsetComplement) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementTcontraSubset) =>
% 97.99/13.26 ((
% 97.99/13.26 (binunionTILcontra) =>
% 97.99/13.26 ((
% 97.99/13.26 (binunionTIRcontra) =>
% 97.99/13.26 ((
% 97.99/13.26 (inIntersectImpInUnion) =>
% 97.99/13.26 ((
% 97.99/13.26 (inIntersectImpInUnion2) =>
% 97.99/13.26 ((
% 97.99/13.26 (inIntersectImpInIntersectUnions) =>
% 97.99/13.26 ((
% 97.99/13.26 (intersectInPowersetIntersectUnions) =>
% 97.99/13.26 ((
% 97.99/13.26 (inComplementUnionImpNotIn1) =>
% 97.99/13.26 ((
% 97.99/13.26 (inComplementUnionImpInComplement1) =>
% 97.99/13.26 ((
% 97.99/13.26 (binunionTE) =>
% 97.99/13.26 ((
% 97.99/13.26 (binunionTEcontra) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan2a1) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementUnionInPowersetComplement) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan2a2) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan1a) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan1b) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan1) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan2a) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan2b2) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan2b) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan2) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz13rule0) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz13rule1) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz13rule2) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz13rule3) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz13rule4) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz1_1) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz1_2) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz1_3) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz1_4) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz1_5) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1all2) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1SetBreln1) =>
% 97.99/13.26 ((
% 97.99/13.26 (choice2fnsingleton) =>
% 97.99/13.26 ((
% 97.99/13.26 (setOfPairsIsBReln1) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1all1) =>
% 97.99/13.26 ((
% 97.99/13.26 (subbreln1) =>
% 97.99/13.26 ((
% 97.99/13.26 (eqbreln1) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1invprop) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1invI) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1invE) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1compprop) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1compI) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1compE) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1compEex) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionprop) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionIL) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionIR) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionI) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionE) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionEcases) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionCommutes) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz2Ex) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz2W) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz2A) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz2B) =>
% 97.99/13.26 ((
% 97.99/13.26 (image1Ex) =>
% 97.99/13.26 ((
% 97.99/13.26 (image1Ex1) =>
% 97.99/13.26 ((
% 97.99/13.26 (image1Equiv) =>
% 97.99/13.26 ((
% 97.99/13.26 (image1E) =>
% 97.99/13.26 ((
% 97.99/13.26 (image1I) =>
% 97.99/13.26 ((
% 97.99/13.26 (injFuncInInjFuncSet) =>
% 97.99/13.26 ((
% 97.99/13.26 (injFuncSetFuncIn) =>
% 97.99/13.26 ((
% 97.99/13.26 (injFuncSetFuncInj) =>
% 97.99/13.26 ((
% 97.99/13.26 (surjFuncSetFuncIn) =>
% 97.99/13.26 ((
% 97.99/13.26 (surjFuncSetFuncSurj) =>
% 97.99/13.26 ((
% 97.99/13.26 (leftInvIsSurj) =>
% 97.99/13.26 ((
% 97.99/13.26 (surjCantorThm) =>
% 97.99/13.26 ((
% 97.99/13.26 (foundation2) =>
% 97.99/13.26 ((
% 97.99/13.26 (notinself) =>
% 97.99/13.26 ((
% 97.99/13.26 (notinself2) =>
% 97.99/13.26 ((
% 97.99/13.26 (omegaSp) =>
% 97.99/13.26 ((
% 97.99/13.26 (omegaSclos) =>
% 97.99/13.26 ((
% 97.99/13.26 (peano0notS) =>
% 97.99/13.26 ((
% 97.99/13.26 (!!) @ (
% 97.99/13.26 (('#S') @ (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 =>) @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#C') @ in @
% 97.99/13.26 omega)))) @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 !!) @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 (
% 97.99/13.26 ('#S') @ (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 =>) @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#C') @ in @
% 97.99/13.26 omega)))))) @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#S') @ (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 '#S') @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 =>))) @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#C') @ (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 '#B') @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 =) @
% 97.99/13.26 omegaS)))) @
% 97.99/13.26 omegaS)))))) @
% 97.99/13.26 (
% 97.99/13.26 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.99/13.26 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1280])).
% 97.99/13.26 thf(zip_derived_cl1296, plain,
% 97.99/13.26 (~ (((setminusILneg) =>
% 97.99/13.26 (((setminusIRneg) =>
% 97.99/13.26 (((setminusLsub) =>
% 97.99/13.26 (((setminusSubset1) =>
% 97.99/13.26 (((symdiffE) =>
% 97.99/13.26 (((symdiffI1) =>
% 97.99/13.26 (((symdiffI2) =>
% 97.99/13.26 (((symdiffIneg1) =>
% 97.99/13.26 (((symdiffIneg2) =>
% 97.99/13.26 (((secondinupair) =>
% 97.99/13.26 (((setukpairIL) =>
% 97.99/13.26 (((setukpairIR) =>
% 97.99/13.26 (((kpairiskpair) =>
% 97.99/13.26 (((kpairp) =>
% 97.99/13.26 (((singletonsubset) =>
% 97.99/13.26 (((singletoninpowerset) =>
% 97.99/13.26 (((singletoninpowunion) =>
% 97.99/13.26 (((upairset2E) =>
% 97.99/13.26 (((upairsubunion) =>
% 97.99/13.26 (((upairinpowunion) =>
% 97.99/13.26 (((ubforcartprodlem1) =>
% 97.99/13.26 (((ubforcartprodlem2) =>
% 97.99/13.26 (((ubforcartprodlem3) =>
% 97.99/13.26 (((cartprodpairin) =>
% 97.99/13.26 (((cartprodmempair1) =>
% 97.99/13.26 (((cartprodmempair) =>
% 97.99/13.26 (((setunionE2) =>
% 97.99/13.26 (((setunionsingleton1) =>
% 97.99/13.26 (((setunionsingleton2) =>
% 97.99/13.26 (((setunionsingleton) =>
% 97.99/13.26 ((
% 97.99/13.26 (singletonprop) =>
% 97.99/13.26 ((
% 97.99/13.26 (ex1E1) =>
% 97.99/13.26 ((
% 97.99/13.26 (ex1I) =>
% 97.99/13.26 ((
% 97.99/13.26 (ex1I2) =>
% 97.99/13.26 ((
% 97.99/13.26 (singletonsuniq) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjL1) =>
% 97.99/13.26 ((
% 97.99/13.26 (kfstsingleton) =>
% 97.99/13.26 ((
% 97.99/13.26 (theprop) =>
% 97.99/13.26 ((
% 97.99/13.26 (kfstpairEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodfstin) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjL2) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjL) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjR11) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjR12) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjR1) =>
% 97.99/13.26 ((
% 97.99/13.26 (upairequniteq) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjR2) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjR) =>
% 97.99/13.26 ((
% 97.99/13.26 (ksndsingleton) =>
% 97.99/13.26 ((
% 97.99/13.26 (ksndpairEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (kpairsurjEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodsndin) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodpairmemEL) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodpairmemER) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodmempaircEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodfstpairEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodsndpairEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodpairsurjEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (dpsetconstrI) =>
% 97.99/13.26 ((
% 97.99/13.26 (dpsetconstrSub) =>
% 97.99/13.26 ((
% 97.99/13.26 (setOfPairsIsBReln) =>
% 97.99/13.26 ((
% 97.99/13.26 (dpsetconstrERa) =>
% 97.99/13.26 ((
% 97.99/13.26 (dpsetconstrEL1) =>
% 97.99/13.26 ((
% 97.99/13.26 (dpsetconstrEL2) =>
% 97.99/13.26 ((
% 97.99/13.26 (dpsetconstrER) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcImageSingleton) =>
% 97.99/13.26 ((
% 97.99/13.26 (apProp) =>
% 97.99/13.26 ((
% 97.99/13.26 (app) =>
% 97.99/13.26 ((
% 97.99/13.26 (infuncsetfunc) =>
% 97.99/13.26 ((
% 97.99/13.26 (ap2p) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcinfuncset) =>
% 97.99/13.26 ((
% 97.99/13.26 (lamProp) =>
% 97.99/13.26 ((
% 97.99/13.26 (lamp) =>
% 97.99/13.26 ((
% 97.99/13.26 (lam2p) =>
% 97.99/13.26 ((
% 97.99/13.26 (brelnall1) =>
% 97.99/13.26 ((
% 97.99/13.26 (brelnall2) =>
% 97.99/13.26 ((
% 97.99/13.26 (ex1E2) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcGraphProp1) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcGraphProp3) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcGraphProp2) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcextLem) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcGraphProp4) =>
% 97.99/13.26 ((
% 97.99/13.26 (subbreln) =>
% 97.99/13.26 ((
% 97.99/13.26 (eqbreln) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcext) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcext2) =>
% 97.99/13.26 ((
% 97.99/13.26 (ap2apEq1) =>
% 97.99/13.26 ((
% 97.99/13.26 (ap2apEq2) =>
% 97.99/13.26 ((
% 97.99/13.26 (beta1) =>
% 97.99/13.26 ((
% 97.99/13.26 (eta1) =>
% 97.99/13.26 ((
% 97.99/13.26 (lam2lamEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (beta2) =>
% 97.99/13.26 ((
% 97.99/13.26 (eta2) =>
% 97.99/13.26 ((
% 97.99/13.26 (iffalseProp1) =>
% 97.99/13.26 ((
% 97.99/13.26 (iffalseProp2) =>
% 97.99/13.26 ((
% 97.99/13.26 (iftrueProp1) =>
% 97.99/13.26 ((
% 97.99/13.26 (iftrueProp2) =>
% 97.99/13.26 ((
% 97.99/13.26 (ifSingleton) =>
% 97.99/13.26 ((
% 97.99/13.26 (ifp) =>
% 97.99/13.26 ((
% 97.99/13.26 (theeq) =>
% 97.99/13.26 ((
% 97.99/13.26 (iftrue) =>
% 97.99/13.26 ((
% 97.99/13.26 (iffalse) =>
% 97.99/13.26 ((
% 97.99/13.26 (iftrueorfalse) =>
% 97.99/13.26 ((
% 97.99/13.26 (binintersectT_lem) =>
% 97.99/13.26 ((
% 97.99/13.26 (binunionT_lem) =>
% 97.99/13.26 ((
% 97.99/13.26 (powersetT_lem) =>
% 97.99/13.26 ((
% 97.99/13.26 (setminusT_lem) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementT_lem) =>
% 97.99/13.26 ((
% 97.99/13.26 (setextT) =>
% 97.99/13.26 ((
% 97.99/13.26 (subsetTI) =>
% 97.99/13.26 ((
% 97.99/13.26 (powersetTI1) =>
% 97.99/13.26 ((
% 97.99/13.26 (powersetTE1) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementTI1) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementTE1) =>
% 97.99/13.26 ((
% 97.99/13.26 (binintersectTELcontra) =>
% 97.99/13.26 ((
% 97.99/13.26 (binintersectTERcontra) =>
% 97.99/13.26 ((
% 97.99/13.26 (contrasubsetT) =>
% 97.99/13.26 ((
% 97.99/13.26 (contrasubsetT1) =>
% 97.99/13.26 ((
% 97.99/13.26 (contrasubsetT2) =>
% 97.99/13.26 ((
% 97.99/13.26 (contrasubsetT3) =>
% 97.99/13.26 ((
% 97.99/13.26 (doubleComplementI1) =>
% 97.99/13.26 ((
% 97.99/13.26 (doubleComplementE1) =>
% 97.99/13.26 ((
% 97.99/13.26 (doubleComplementSub1) =>
% 97.99/13.26 ((
% 97.99/13.26 (doubleComplementSub2) =>
% 97.99/13.26 ((
% 97.99/13.26 (doubleComplementEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementTnotintersectT) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementImpComplementIntersect) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementSubsetComplementIntersect) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementInPowersetComplementIntersect) =>
% 97.99/13.26 ((
% 97.99/13.26 (contraSubsetComplement) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementTcontraSubset) =>
% 97.99/13.26 ((
% 97.99/13.26 (binunionTILcontra) =>
% 97.99/13.26 ((
% 97.99/13.26 (binunionTIRcontra) =>
% 97.99/13.26 ((
% 97.99/13.26 (inIntersectImpInUnion) =>
% 97.99/13.26 ((
% 97.99/13.26 (inIntersectImpInUnion2) =>
% 97.99/13.26 ((
% 97.99/13.26 (inIntersectImpInIntersectUnions) =>
% 97.99/13.26 ((
% 97.99/13.26 (intersectInPowersetIntersectUnions) =>
% 97.99/13.26 ((
% 97.99/13.26 (inComplementUnionImpNotIn1) =>
% 97.99/13.26 ((
% 97.99/13.26 (inComplementUnionImpInComplement1) =>
% 97.99/13.26 ((
% 97.99/13.26 (binunionTE) =>
% 97.99/13.26 ((
% 97.99/13.26 (binunionTEcontra) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan2a1) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementUnionInPowersetComplement) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan2a2) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan1a) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan1b) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan1) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan2a) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan2b2) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan2b) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan2) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz13rule0) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz13rule1) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz13rule2) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz13rule3) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz13rule4) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz1_1) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz1_2) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz1_3) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz1_4) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz1_5) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1all2) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1SetBreln1) =>
% 97.99/13.26 ((
% 97.99/13.26 (choice2fnsingleton) =>
% 97.99/13.26 ((
% 97.99/13.26 (setOfPairsIsBReln1) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1all1) =>
% 97.99/13.26 ((
% 97.99/13.26 (subbreln1) =>
% 97.99/13.26 ((
% 97.99/13.26 (eqbreln1) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1invprop) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1invI) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1invE) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1compprop) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1compI) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1compE) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1compEex) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionprop) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionIL) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionIR) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionI) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionE) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionEcases) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionCommutes) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz2Ex) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz2W) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz2A) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz2B) =>
% 97.99/13.26 ((
% 97.99/13.26 (image1Ex) =>
% 97.99/13.26 ((
% 97.99/13.26 (image1Ex1) =>
% 97.99/13.26 ((
% 97.99/13.26 (image1Equiv) =>
% 97.99/13.26 ((
% 97.99/13.26 (image1E) =>
% 97.99/13.26 ((
% 97.99/13.26 (image1I) =>
% 97.99/13.26 ((
% 97.99/13.26 (injFuncInInjFuncSet) =>
% 97.99/13.26 ((
% 97.99/13.26 (injFuncSetFuncIn) =>
% 97.99/13.26 ((
% 97.99/13.26 (injFuncSetFuncInj) =>
% 97.99/13.26 ((
% 97.99/13.26 (surjFuncSetFuncIn) =>
% 97.99/13.26 ((
% 97.99/13.26 (surjFuncSetFuncSurj) =>
% 97.99/13.26 ((
% 97.99/13.26 (leftInvIsSurj) =>
% 97.99/13.26 ((
% 97.99/13.26 (surjCantorThm) =>
% 97.99/13.26 ((
% 97.99/13.26 (foundation2) =>
% 97.99/13.26 ((
% 97.99/13.26 (notinself) =>
% 97.99/13.26 ((
% 97.99/13.26 (notinself2) =>
% 97.99/13.26 ((
% 97.99/13.26 (omegaSp) =>
% 97.99/13.26 ((
% 97.99/13.26 (omegaSclos) =>
% 97.99/13.26 ((
% 97.99/13.26 (peano0notS) =>
% 97.99/13.26 ((
% 97.99/13.26 (!!) @ (
% 97.99/13.26 (('#S') @ (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 =>) @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#C') @ in @
% 97.99/13.26 omega)))) @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 !!) @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 (
% 97.99/13.26 ('#S') @ (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 =>) @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#C') @ in @
% 97.99/13.26 omega)))))) @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#S') @ (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 '#S') @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 =>))) @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#C') @ (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 '#B') @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 =) @
% 97.99/13.26 omegaS)))) @
% 97.99/13.26 omegaS)))))) @
% 97.99/13.26 (
% 97.99/13.26 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.99/13.26 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1288])).
% 97.99/13.26 thf(zip_derived_cl1305, plain,
% 97.99/13.26 (~ (((setminusIRneg) =>
% 97.99/13.26 (((setminusLsub) =>
% 97.99/13.26 (((setminusSubset1) =>
% 97.99/13.26 (((symdiffE) =>
% 97.99/13.26 (((symdiffI1) =>
% 97.99/13.26 (((symdiffI2) =>
% 97.99/13.26 (((symdiffIneg1) =>
% 97.99/13.26 (((symdiffIneg2) =>
% 97.99/13.26 (((secondinupair) =>
% 97.99/13.26 (((setukpairIL) =>
% 97.99/13.26 (((setukpairIR) =>
% 97.99/13.26 (((kpairiskpair) =>
% 97.99/13.26 (((kpairp) =>
% 97.99/13.26 (((singletonsubset) =>
% 97.99/13.26 (((singletoninpowerset) =>
% 97.99/13.26 (((singletoninpowunion) =>
% 97.99/13.26 (((upairset2E) =>
% 97.99/13.26 (((upairsubunion) =>
% 97.99/13.26 (((upairinpowunion) =>
% 97.99/13.26 (((ubforcartprodlem1) =>
% 97.99/13.26 (((ubforcartprodlem2) =>
% 97.99/13.26 (((ubforcartprodlem3) =>
% 97.99/13.26 (((cartprodpairin) =>
% 97.99/13.26 (((cartprodmempair1) =>
% 97.99/13.26 (((cartprodmempair) =>
% 97.99/13.26 (((setunionE2) =>
% 97.99/13.26 (((setunionsingleton1) =>
% 97.99/13.26 (((setunionsingleton2) =>
% 97.99/13.26 (((setunionsingleton) =>
% 97.99/13.26 (((singletonprop) =>
% 97.99/13.26 ((
% 97.99/13.26 (ex1E1) =>
% 97.99/13.26 ((
% 97.99/13.26 (ex1I) =>
% 97.99/13.26 ((
% 97.99/13.26 (ex1I2) =>
% 97.99/13.26 ((
% 97.99/13.26 (singletonsuniq) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjL1) =>
% 97.99/13.26 ((
% 97.99/13.26 (kfstsingleton) =>
% 97.99/13.26 ((
% 97.99/13.26 (theprop) =>
% 97.99/13.26 ((
% 97.99/13.26 (kfstpairEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodfstin) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjL2) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjL) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjR11) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjR12) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjR1) =>
% 97.99/13.26 ((
% 97.99/13.26 (upairequniteq) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjR2) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjR) =>
% 97.99/13.26 ((
% 97.99/13.26 (ksndsingleton) =>
% 97.99/13.26 ((
% 97.99/13.26 (ksndpairEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (kpairsurjEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodsndin) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodpairmemEL) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodpairmemER) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodmempaircEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodfstpairEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodsndpairEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodpairsurjEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (dpsetconstrI) =>
% 97.99/13.26 ((
% 97.99/13.26 (dpsetconstrSub) =>
% 97.99/13.26 ((
% 97.99/13.26 (setOfPairsIsBReln) =>
% 97.99/13.26 ((
% 97.99/13.26 (dpsetconstrERa) =>
% 97.99/13.26 ((
% 97.99/13.26 (dpsetconstrEL1) =>
% 97.99/13.26 ((
% 97.99/13.26 (dpsetconstrEL2) =>
% 97.99/13.26 ((
% 97.99/13.26 (dpsetconstrER) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcImageSingleton) =>
% 97.99/13.26 ((
% 97.99/13.26 (apProp) =>
% 97.99/13.26 ((
% 97.99/13.26 (app) =>
% 97.99/13.26 ((
% 97.99/13.26 (infuncsetfunc) =>
% 97.99/13.26 ((
% 97.99/13.26 (ap2p) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcinfuncset) =>
% 97.99/13.26 ((
% 97.99/13.26 (lamProp) =>
% 97.99/13.26 ((
% 97.99/13.26 (lamp) =>
% 97.99/13.26 ((
% 97.99/13.26 (lam2p) =>
% 97.99/13.26 ((
% 97.99/13.26 (brelnall1) =>
% 97.99/13.26 ((
% 97.99/13.26 (brelnall2) =>
% 97.99/13.26 ((
% 97.99/13.26 (ex1E2) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcGraphProp1) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcGraphProp3) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcGraphProp2) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcextLem) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcGraphProp4) =>
% 97.99/13.26 ((
% 97.99/13.26 (subbreln) =>
% 97.99/13.26 ((
% 97.99/13.26 (eqbreln) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcext) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcext2) =>
% 97.99/13.26 ((
% 97.99/13.26 (ap2apEq1) =>
% 97.99/13.26 ((
% 97.99/13.26 (ap2apEq2) =>
% 97.99/13.26 ((
% 97.99/13.26 (beta1) =>
% 97.99/13.26 ((
% 97.99/13.26 (eta1) =>
% 97.99/13.26 ((
% 97.99/13.26 (lam2lamEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (beta2) =>
% 97.99/13.26 ((
% 97.99/13.26 (eta2) =>
% 97.99/13.26 ((
% 97.99/13.26 (iffalseProp1) =>
% 97.99/13.26 ((
% 97.99/13.26 (iffalseProp2) =>
% 97.99/13.26 ((
% 97.99/13.26 (iftrueProp1) =>
% 97.99/13.26 ((
% 97.99/13.26 (iftrueProp2) =>
% 97.99/13.26 ((
% 97.99/13.26 (ifSingleton) =>
% 97.99/13.26 ((
% 97.99/13.26 (ifp) =>
% 97.99/13.26 ((
% 97.99/13.26 (theeq) =>
% 97.99/13.26 ((
% 97.99/13.26 (iftrue) =>
% 97.99/13.26 ((
% 97.99/13.26 (iffalse) =>
% 97.99/13.26 ((
% 97.99/13.26 (iftrueorfalse) =>
% 97.99/13.26 ((
% 97.99/13.26 (binintersectT_lem) =>
% 97.99/13.26 ((
% 97.99/13.26 (binunionT_lem) =>
% 97.99/13.26 ((
% 97.99/13.26 (powersetT_lem) =>
% 97.99/13.26 ((
% 97.99/13.26 (setminusT_lem) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementT_lem) =>
% 97.99/13.26 ((
% 97.99/13.26 (setextT) =>
% 97.99/13.26 ((
% 97.99/13.26 (subsetTI) =>
% 97.99/13.26 ((
% 97.99/13.26 (powersetTI1) =>
% 97.99/13.26 ((
% 97.99/13.26 (powersetTE1) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementTI1) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementTE1) =>
% 97.99/13.26 ((
% 97.99/13.26 (binintersectTELcontra) =>
% 97.99/13.26 ((
% 97.99/13.26 (binintersectTERcontra) =>
% 97.99/13.26 ((
% 97.99/13.26 (contrasubsetT) =>
% 97.99/13.26 ((
% 97.99/13.26 (contrasubsetT1) =>
% 97.99/13.26 ((
% 97.99/13.26 (contrasubsetT2) =>
% 97.99/13.26 ((
% 97.99/13.26 (contrasubsetT3) =>
% 97.99/13.26 ((
% 97.99/13.26 (doubleComplementI1) =>
% 97.99/13.26 ((
% 97.99/13.26 (doubleComplementE1) =>
% 97.99/13.26 ((
% 97.99/13.26 (doubleComplementSub1) =>
% 97.99/13.26 ((
% 97.99/13.26 (doubleComplementSub2) =>
% 97.99/13.26 ((
% 97.99/13.26 (doubleComplementEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementTnotintersectT) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementImpComplementIntersect) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementSubsetComplementIntersect) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementInPowersetComplementIntersect) =>
% 97.99/13.26 ((
% 97.99/13.26 (contraSubsetComplement) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementTcontraSubset) =>
% 97.99/13.26 ((
% 97.99/13.26 (binunionTILcontra) =>
% 97.99/13.26 ((
% 97.99/13.26 (binunionTIRcontra) =>
% 97.99/13.26 ((
% 97.99/13.26 (inIntersectImpInUnion) =>
% 97.99/13.26 ((
% 97.99/13.26 (inIntersectImpInUnion2) =>
% 97.99/13.26 ((
% 97.99/13.26 (inIntersectImpInIntersectUnions) =>
% 97.99/13.26 ((
% 97.99/13.26 (intersectInPowersetIntersectUnions) =>
% 97.99/13.26 ((
% 97.99/13.26 (inComplementUnionImpNotIn1) =>
% 97.99/13.26 ((
% 97.99/13.26 (inComplementUnionImpInComplement1) =>
% 97.99/13.26 ((
% 97.99/13.26 (binunionTE) =>
% 97.99/13.26 ((
% 97.99/13.26 (binunionTEcontra) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan2a1) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementUnionInPowersetComplement) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan2a2) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan1a) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan1b) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan1) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan2a) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan2b2) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan2b) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan2) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz13rule0) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz13rule1) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz13rule2) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz13rule3) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz13rule4) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz1_1) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz1_2) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz1_3) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz1_4) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz1_5) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1all2) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1SetBreln1) =>
% 97.99/13.26 ((
% 97.99/13.26 (choice2fnsingleton) =>
% 97.99/13.26 ((
% 97.99/13.26 (setOfPairsIsBReln1) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1all1) =>
% 97.99/13.26 ((
% 97.99/13.26 (subbreln1) =>
% 97.99/13.26 ((
% 97.99/13.26 (eqbreln1) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1invprop) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1invI) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1invE) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1compprop) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1compI) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1compE) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1compEex) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionprop) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionIL) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionIR) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionI) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionE) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionEcases) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionCommutes) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz2Ex) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz2W) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz2A) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz2B) =>
% 97.99/13.26 ((
% 97.99/13.26 (image1Ex) =>
% 97.99/13.26 ((
% 97.99/13.26 (image1Ex1) =>
% 97.99/13.26 ((
% 97.99/13.26 (image1Equiv) =>
% 97.99/13.26 ((
% 97.99/13.26 (image1E) =>
% 97.99/13.26 ((
% 97.99/13.26 (image1I) =>
% 97.99/13.26 ((
% 97.99/13.26 (injFuncInInjFuncSet) =>
% 97.99/13.26 ((
% 97.99/13.26 (injFuncSetFuncIn) =>
% 97.99/13.26 ((
% 97.99/13.26 (injFuncSetFuncInj) =>
% 97.99/13.26 ((
% 97.99/13.26 (surjFuncSetFuncIn) =>
% 97.99/13.26 ((
% 97.99/13.26 (surjFuncSetFuncSurj) =>
% 97.99/13.26 ((
% 97.99/13.26 (leftInvIsSurj) =>
% 97.99/13.26 ((
% 97.99/13.26 (surjCantorThm) =>
% 97.99/13.26 ((
% 97.99/13.26 (foundation2) =>
% 97.99/13.26 ((
% 97.99/13.26 (notinself) =>
% 97.99/13.26 ((
% 97.99/13.26 (notinself2) =>
% 97.99/13.26 ((
% 97.99/13.26 (omegaSp) =>
% 97.99/13.26 ((
% 97.99/13.26 (omegaSclos) =>
% 97.99/13.26 ((
% 97.99/13.26 (peano0notS) =>
% 97.99/13.26 ((
% 97.99/13.26 (!!) @ (
% 97.99/13.26 (('#S') @ (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 =>) @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#C') @ in @
% 97.99/13.26 omega)))) @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 !!) @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 (
% 97.99/13.26 ('#S') @ (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 =>) @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#C') @ in @
% 97.99/13.26 omega)))))) @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#S') @ (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 '#S') @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 =>))) @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#C') @ (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 '#B') @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 =) @
% 97.99/13.26 omegaS)))) @
% 97.99/13.26 omegaS)))))) @
% 97.99/13.26 (
% 97.99/13.26 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.99/13.26 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1296])).
% 97.99/13.26 thf(zip_derived_cl1313, plain,
% 97.99/13.26 (~ (((setminusLsub) =>
% 97.99/13.26 (((setminusSubset1) =>
% 97.99/13.26 (((symdiffE) =>
% 97.99/13.26 (((symdiffI1) =>
% 97.99/13.26 (((symdiffI2) =>
% 97.99/13.26 (((symdiffIneg1) =>
% 97.99/13.26 (((symdiffIneg2) =>
% 97.99/13.26 (((secondinupair) =>
% 97.99/13.26 (((setukpairIL) =>
% 97.99/13.26 (((setukpairIR) =>
% 97.99/13.26 (((kpairiskpair) =>
% 97.99/13.26 (((kpairp) =>
% 97.99/13.26 (((singletonsubset) =>
% 97.99/13.26 (((singletoninpowerset) =>
% 97.99/13.26 (((singletoninpowunion) =>
% 97.99/13.26 (((upairset2E) =>
% 97.99/13.26 (((upairsubunion) =>
% 97.99/13.26 (((upairinpowunion) =>
% 97.99/13.26 (((ubforcartprodlem1) =>
% 97.99/13.26 (((ubforcartprodlem2) =>
% 97.99/13.26 (((ubforcartprodlem3) =>
% 97.99/13.26 (((cartprodpairin) =>
% 97.99/13.26 (((cartprodmempair1) =>
% 97.99/13.26 (((cartprodmempair) =>
% 97.99/13.26 (((setunionE2) =>
% 97.99/13.26 (((setunionsingleton1) =>
% 97.99/13.26 (((setunionsingleton2) =>
% 97.99/13.26 (((setunionsingleton) =>
% 97.99/13.26 (((singletonprop) =>
% 97.99/13.26 (((ex1E1) =>
% 97.99/13.26 ((
% 97.99/13.26 (ex1I) =>
% 97.99/13.26 ((
% 97.99/13.26 (ex1I2) =>
% 97.99/13.26 ((
% 97.99/13.26 (singletonsuniq) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjL1) =>
% 97.99/13.26 ((
% 97.99/13.26 (kfstsingleton) =>
% 97.99/13.26 ((
% 97.99/13.26 (theprop) =>
% 97.99/13.26 ((
% 97.99/13.26 (kfstpairEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodfstin) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjL2) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjL) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjR11) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjR12) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjR1) =>
% 97.99/13.26 ((
% 97.99/13.26 (upairequniteq) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjR2) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjR) =>
% 97.99/13.26 ((
% 97.99/13.26 (ksndsingleton) =>
% 97.99/13.26 ((
% 97.99/13.26 (ksndpairEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (kpairsurjEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodsndin) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodpairmemEL) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodpairmemER) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodmempaircEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodfstpairEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodsndpairEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodpairsurjEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (dpsetconstrI) =>
% 97.99/13.26 ((
% 97.99/13.26 (dpsetconstrSub) =>
% 97.99/13.26 ((
% 97.99/13.26 (setOfPairsIsBReln) =>
% 97.99/13.26 ((
% 97.99/13.26 (dpsetconstrERa) =>
% 97.99/13.26 ((
% 97.99/13.26 (dpsetconstrEL1) =>
% 97.99/13.26 ((
% 97.99/13.26 (dpsetconstrEL2) =>
% 97.99/13.26 ((
% 97.99/13.26 (dpsetconstrER) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcImageSingleton) =>
% 97.99/13.26 ((
% 97.99/13.26 (apProp) =>
% 97.99/13.26 ((
% 97.99/13.26 (app) =>
% 97.99/13.26 ((
% 97.99/13.26 (infuncsetfunc) =>
% 97.99/13.26 ((
% 97.99/13.26 (ap2p) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcinfuncset) =>
% 97.99/13.26 ((
% 97.99/13.26 (lamProp) =>
% 97.99/13.26 ((
% 97.99/13.26 (lamp) =>
% 97.99/13.26 ((
% 97.99/13.26 (lam2p) =>
% 97.99/13.26 ((
% 97.99/13.26 (brelnall1) =>
% 97.99/13.26 ((
% 97.99/13.26 (brelnall2) =>
% 97.99/13.26 ((
% 97.99/13.26 (ex1E2) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcGraphProp1) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcGraphProp3) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcGraphProp2) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcextLem) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcGraphProp4) =>
% 97.99/13.26 ((
% 97.99/13.26 (subbreln) =>
% 97.99/13.26 ((
% 97.99/13.26 (eqbreln) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcext) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcext2) =>
% 97.99/13.26 ((
% 97.99/13.26 (ap2apEq1) =>
% 97.99/13.26 ((
% 97.99/13.26 (ap2apEq2) =>
% 97.99/13.26 ((
% 97.99/13.26 (beta1) =>
% 97.99/13.26 ((
% 97.99/13.26 (eta1) =>
% 97.99/13.26 ((
% 97.99/13.26 (lam2lamEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (beta2) =>
% 97.99/13.26 ((
% 97.99/13.26 (eta2) =>
% 97.99/13.26 ((
% 97.99/13.26 (iffalseProp1) =>
% 97.99/13.26 ((
% 97.99/13.26 (iffalseProp2) =>
% 97.99/13.26 ((
% 97.99/13.26 (iftrueProp1) =>
% 97.99/13.26 ((
% 97.99/13.26 (iftrueProp2) =>
% 97.99/13.26 ((
% 97.99/13.26 (ifSingleton) =>
% 97.99/13.26 ((
% 97.99/13.26 (ifp) =>
% 97.99/13.26 ((
% 97.99/13.26 (theeq) =>
% 97.99/13.26 ((
% 97.99/13.26 (iftrue) =>
% 97.99/13.26 ((
% 97.99/13.26 (iffalse) =>
% 97.99/13.26 ((
% 97.99/13.26 (iftrueorfalse) =>
% 97.99/13.26 ((
% 97.99/13.26 (binintersectT_lem) =>
% 97.99/13.26 ((
% 97.99/13.26 (binunionT_lem) =>
% 97.99/13.26 ((
% 97.99/13.26 (powersetT_lem) =>
% 97.99/13.26 ((
% 97.99/13.26 (setminusT_lem) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementT_lem) =>
% 97.99/13.26 ((
% 97.99/13.26 (setextT) =>
% 97.99/13.26 ((
% 97.99/13.26 (subsetTI) =>
% 97.99/13.26 ((
% 97.99/13.26 (powersetTI1) =>
% 97.99/13.26 ((
% 97.99/13.26 (powersetTE1) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementTI1) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementTE1) =>
% 97.99/13.26 ((
% 97.99/13.26 (binintersectTELcontra) =>
% 97.99/13.26 ((
% 97.99/13.26 (binintersectTERcontra) =>
% 97.99/13.26 ((
% 97.99/13.26 (contrasubsetT) =>
% 97.99/13.26 ((
% 97.99/13.26 (contrasubsetT1) =>
% 97.99/13.26 ((
% 97.99/13.26 (contrasubsetT2) =>
% 97.99/13.26 ((
% 97.99/13.26 (contrasubsetT3) =>
% 97.99/13.26 ((
% 97.99/13.26 (doubleComplementI1) =>
% 97.99/13.26 ((
% 97.99/13.26 (doubleComplementE1) =>
% 97.99/13.26 ((
% 97.99/13.26 (doubleComplementSub1) =>
% 97.99/13.26 ((
% 97.99/13.26 (doubleComplementSub2) =>
% 97.99/13.26 ((
% 97.99/13.26 (doubleComplementEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementTnotintersectT) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementImpComplementIntersect) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementSubsetComplementIntersect) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementInPowersetComplementIntersect) =>
% 97.99/13.26 ((
% 97.99/13.26 (contraSubsetComplement) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementTcontraSubset) =>
% 97.99/13.26 ((
% 97.99/13.26 (binunionTILcontra) =>
% 97.99/13.26 ((
% 97.99/13.26 (binunionTIRcontra) =>
% 97.99/13.26 ((
% 97.99/13.26 (inIntersectImpInUnion) =>
% 97.99/13.26 ((
% 97.99/13.26 (inIntersectImpInUnion2) =>
% 97.99/13.26 ((
% 97.99/13.26 (inIntersectImpInIntersectUnions) =>
% 97.99/13.26 ((
% 97.99/13.26 (intersectInPowersetIntersectUnions) =>
% 97.99/13.26 ((
% 97.99/13.26 (inComplementUnionImpNotIn1) =>
% 97.99/13.26 ((
% 97.99/13.26 (inComplementUnionImpInComplement1) =>
% 97.99/13.26 ((
% 97.99/13.26 (binunionTE) =>
% 97.99/13.26 ((
% 97.99/13.26 (binunionTEcontra) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan2a1) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementUnionInPowersetComplement) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan2a2) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan1a) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan1b) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan1) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan2a) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan2b2) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan2b) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan2) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz13rule0) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz13rule1) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz13rule2) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz13rule3) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz13rule4) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz1_1) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz1_2) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz1_3) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz1_4) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz1_5) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1all2) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1SetBreln1) =>
% 97.99/13.26 ((
% 97.99/13.26 (choice2fnsingleton) =>
% 97.99/13.26 ((
% 97.99/13.26 (setOfPairsIsBReln1) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1all1) =>
% 97.99/13.26 ((
% 97.99/13.26 (subbreln1) =>
% 97.99/13.26 ((
% 97.99/13.26 (eqbreln1) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1invprop) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1invI) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1invE) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1compprop) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1compI) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1compE) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1compEex) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionprop) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionIL) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionIR) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionI) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionE) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionEcases) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionCommutes) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz2Ex) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz2W) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz2A) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz2B) =>
% 97.99/13.26 ((
% 97.99/13.26 (image1Ex) =>
% 97.99/13.26 ((
% 97.99/13.26 (image1Ex1) =>
% 97.99/13.26 ((
% 97.99/13.26 (image1Equiv) =>
% 97.99/13.26 ((
% 97.99/13.26 (image1E) =>
% 97.99/13.26 ((
% 97.99/13.26 (image1I) =>
% 97.99/13.26 ((
% 97.99/13.26 (injFuncInInjFuncSet) =>
% 97.99/13.26 ((
% 97.99/13.26 (injFuncSetFuncIn) =>
% 97.99/13.26 ((
% 97.99/13.26 (injFuncSetFuncInj) =>
% 97.99/13.26 ((
% 97.99/13.26 (surjFuncSetFuncIn) =>
% 97.99/13.26 ((
% 97.99/13.26 (surjFuncSetFuncSurj) =>
% 97.99/13.26 ((
% 97.99/13.26 (leftInvIsSurj) =>
% 97.99/13.26 ((
% 97.99/13.26 (surjCantorThm) =>
% 97.99/13.26 ((
% 97.99/13.26 (foundation2) =>
% 97.99/13.26 ((
% 97.99/13.26 (notinself) =>
% 97.99/13.26 ((
% 97.99/13.26 (notinself2) =>
% 97.99/13.26 ((
% 97.99/13.26 (omegaSp) =>
% 97.99/13.26 ((
% 97.99/13.26 (omegaSclos) =>
% 97.99/13.26 ((
% 97.99/13.26 (peano0notS) =>
% 97.99/13.26 ((
% 97.99/13.26 (!!) @ (
% 97.99/13.26 (('#S') @ (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 =>) @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#C') @ in @
% 97.99/13.26 omega)))) @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 !!) @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 (
% 97.99/13.26 ('#S') @ (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 =>) @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#C') @ in @
% 97.99/13.26 omega)))))) @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#S') @ (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 '#S') @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 =>))) @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#C') @ (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 '#B') @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 =) @
% 97.99/13.26 omegaS)))) @
% 97.99/13.26 omegaS)))))) @
% 97.99/13.26 (
% 97.99/13.26 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.99/13.26 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1305])).
% 97.99/13.26 thf(zip_derived_cl1321, plain,
% 97.99/13.26 (~ (((setminusSubset1) =>
% 97.99/13.26 (((symdiffE) =>
% 97.99/13.26 (((symdiffI1) =>
% 97.99/13.26 (((symdiffI2) =>
% 97.99/13.26 (((symdiffIneg1) =>
% 97.99/13.26 (((symdiffIneg2) =>
% 97.99/13.26 (((secondinupair) =>
% 97.99/13.26 (((setukpairIL) =>
% 97.99/13.26 (((setukpairIR) =>
% 97.99/13.26 (((kpairiskpair) =>
% 97.99/13.26 (((kpairp) =>
% 97.99/13.26 (((singletonsubset) =>
% 97.99/13.26 (((singletoninpowerset) =>
% 97.99/13.26 (((singletoninpowunion) =>
% 97.99/13.26 (((upairset2E) =>
% 97.99/13.26 (((upairsubunion) =>
% 97.99/13.26 (((upairinpowunion) =>
% 97.99/13.26 (((ubforcartprodlem1) =>
% 97.99/13.26 (((ubforcartprodlem2) =>
% 97.99/13.26 (((ubforcartprodlem3) =>
% 97.99/13.26 (((cartprodpairin) =>
% 97.99/13.26 (((cartprodmempair1) =>
% 97.99/13.26 (((cartprodmempair) =>
% 97.99/13.26 (((setunionE2) =>
% 97.99/13.26 (((setunionsingleton1) =>
% 97.99/13.26 (((setunionsingleton2) =>
% 97.99/13.26 (((setunionsingleton) =>
% 97.99/13.26 (((singletonprop) =>
% 97.99/13.26 (((ex1E1) =>
% 97.99/13.26 (((ex1I) =>
% 97.99/13.26 ((
% 97.99/13.26 (ex1I2) =>
% 97.99/13.26 ((
% 97.99/13.26 (singletonsuniq) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjL1) =>
% 97.99/13.26 ((
% 97.99/13.26 (kfstsingleton) =>
% 97.99/13.26 ((
% 97.99/13.26 (theprop) =>
% 97.99/13.26 ((
% 97.99/13.26 (kfstpairEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodfstin) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjL2) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjL) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjR11) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjR12) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjR1) =>
% 97.99/13.26 ((
% 97.99/13.26 (upairequniteq) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjR2) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjR) =>
% 97.99/13.26 ((
% 97.99/13.26 (ksndsingleton) =>
% 97.99/13.26 ((
% 97.99/13.26 (ksndpairEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (kpairsurjEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodsndin) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodpairmemEL) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodpairmemER) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodmempaircEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodfstpairEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodsndpairEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodpairsurjEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (dpsetconstrI) =>
% 97.99/13.26 ((
% 97.99/13.26 (dpsetconstrSub) =>
% 97.99/13.26 ((
% 97.99/13.26 (setOfPairsIsBReln) =>
% 97.99/13.26 ((
% 97.99/13.26 (dpsetconstrERa) =>
% 97.99/13.26 ((
% 97.99/13.26 (dpsetconstrEL1) =>
% 97.99/13.26 ((
% 97.99/13.26 (dpsetconstrEL2) =>
% 97.99/13.26 ((
% 97.99/13.26 (dpsetconstrER) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcImageSingleton) =>
% 97.99/13.26 ((
% 97.99/13.26 (apProp) =>
% 97.99/13.26 ((
% 97.99/13.26 (app) =>
% 97.99/13.26 ((
% 97.99/13.26 (infuncsetfunc) =>
% 97.99/13.26 ((
% 97.99/13.26 (ap2p) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcinfuncset) =>
% 97.99/13.26 ((
% 97.99/13.26 (lamProp) =>
% 97.99/13.26 ((
% 97.99/13.26 (lamp) =>
% 97.99/13.26 ((
% 97.99/13.26 (lam2p) =>
% 97.99/13.26 ((
% 97.99/13.26 (brelnall1) =>
% 97.99/13.26 ((
% 97.99/13.26 (brelnall2) =>
% 97.99/13.26 ((
% 97.99/13.26 (ex1E2) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcGraphProp1) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcGraphProp3) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcGraphProp2) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcextLem) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcGraphProp4) =>
% 97.99/13.26 ((
% 97.99/13.26 (subbreln) =>
% 97.99/13.26 ((
% 97.99/13.26 (eqbreln) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcext) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcext2) =>
% 97.99/13.26 ((
% 97.99/13.26 (ap2apEq1) =>
% 97.99/13.26 ((
% 97.99/13.26 (ap2apEq2) =>
% 97.99/13.26 ((
% 97.99/13.26 (beta1) =>
% 97.99/13.26 ((
% 97.99/13.26 (eta1) =>
% 97.99/13.26 ((
% 97.99/13.26 (lam2lamEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (beta2) =>
% 97.99/13.26 ((
% 97.99/13.26 (eta2) =>
% 97.99/13.26 ((
% 97.99/13.26 (iffalseProp1) =>
% 97.99/13.26 ((
% 97.99/13.26 (iffalseProp2) =>
% 97.99/13.26 ((
% 97.99/13.26 (iftrueProp1) =>
% 97.99/13.26 ((
% 97.99/13.26 (iftrueProp2) =>
% 97.99/13.26 ((
% 97.99/13.26 (ifSingleton) =>
% 97.99/13.26 ((
% 97.99/13.26 (ifp) =>
% 97.99/13.26 ((
% 97.99/13.26 (theeq) =>
% 97.99/13.26 ((
% 97.99/13.26 (iftrue) =>
% 97.99/13.26 ((
% 97.99/13.26 (iffalse) =>
% 97.99/13.26 ((
% 97.99/13.26 (iftrueorfalse) =>
% 97.99/13.26 ((
% 97.99/13.26 (binintersectT_lem) =>
% 97.99/13.26 ((
% 97.99/13.26 (binunionT_lem) =>
% 97.99/13.26 ((
% 97.99/13.26 (powersetT_lem) =>
% 97.99/13.26 ((
% 97.99/13.26 (setminusT_lem) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementT_lem) =>
% 97.99/13.26 ((
% 97.99/13.26 (setextT) =>
% 97.99/13.26 ((
% 97.99/13.26 (subsetTI) =>
% 97.99/13.26 ((
% 97.99/13.26 (powersetTI1) =>
% 97.99/13.26 ((
% 97.99/13.26 (powersetTE1) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementTI1) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementTE1) =>
% 97.99/13.26 ((
% 97.99/13.26 (binintersectTELcontra) =>
% 97.99/13.26 ((
% 97.99/13.26 (binintersectTERcontra) =>
% 97.99/13.26 ((
% 97.99/13.26 (contrasubsetT) =>
% 97.99/13.26 ((
% 97.99/13.26 (contrasubsetT1) =>
% 97.99/13.26 ((
% 97.99/13.26 (contrasubsetT2) =>
% 97.99/13.26 ((
% 97.99/13.26 (contrasubsetT3) =>
% 97.99/13.26 ((
% 97.99/13.26 (doubleComplementI1) =>
% 97.99/13.26 ((
% 97.99/13.26 (doubleComplementE1) =>
% 97.99/13.26 ((
% 97.99/13.26 (doubleComplementSub1) =>
% 97.99/13.26 ((
% 97.99/13.26 (doubleComplementSub2) =>
% 97.99/13.26 ((
% 97.99/13.26 (doubleComplementEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementTnotintersectT) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementImpComplementIntersect) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementSubsetComplementIntersect) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementInPowersetComplementIntersect) =>
% 97.99/13.26 ((
% 97.99/13.26 (contraSubsetComplement) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementTcontraSubset) =>
% 97.99/13.26 ((
% 97.99/13.26 (binunionTILcontra) =>
% 97.99/13.26 ((
% 97.99/13.26 (binunionTIRcontra) =>
% 97.99/13.26 ((
% 97.99/13.26 (inIntersectImpInUnion) =>
% 97.99/13.26 ((
% 97.99/13.26 (inIntersectImpInUnion2) =>
% 97.99/13.26 ((
% 97.99/13.26 (inIntersectImpInIntersectUnions) =>
% 97.99/13.26 ((
% 97.99/13.26 (intersectInPowersetIntersectUnions) =>
% 97.99/13.26 ((
% 97.99/13.26 (inComplementUnionImpNotIn1) =>
% 97.99/13.26 ((
% 97.99/13.26 (inComplementUnionImpInComplement1) =>
% 97.99/13.26 ((
% 97.99/13.26 (binunionTE) =>
% 97.99/13.26 ((
% 97.99/13.26 (binunionTEcontra) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan2a1) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementUnionInPowersetComplement) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan2a2) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan1a) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan1b) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan1) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan2a) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan2b2) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan2b) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan2) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz13rule0) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz13rule1) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz13rule2) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz13rule3) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz13rule4) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz1_1) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz1_2) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz1_3) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz1_4) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz1_5) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1all2) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1SetBreln1) =>
% 97.99/13.26 ((
% 97.99/13.26 (choice2fnsingleton) =>
% 97.99/13.26 ((
% 97.99/13.26 (setOfPairsIsBReln1) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1all1) =>
% 97.99/13.26 ((
% 97.99/13.26 (subbreln1) =>
% 97.99/13.26 ((
% 97.99/13.26 (eqbreln1) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1invprop) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1invI) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1invE) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1compprop) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1compI) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1compE) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1compEex) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionprop) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionIL) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionIR) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionI) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionE) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionEcases) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionCommutes) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz2Ex) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz2W) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz2A) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz2B) =>
% 97.99/13.26 ((
% 97.99/13.26 (image1Ex) =>
% 97.99/13.26 ((
% 97.99/13.26 (image1Ex1) =>
% 97.99/13.26 ((
% 97.99/13.26 (image1Equiv) =>
% 97.99/13.26 ((
% 97.99/13.26 (image1E) =>
% 97.99/13.26 ((
% 97.99/13.26 (image1I) =>
% 97.99/13.26 ((
% 97.99/13.26 (injFuncInInjFuncSet) =>
% 97.99/13.26 ((
% 97.99/13.26 (injFuncSetFuncIn) =>
% 97.99/13.26 ((
% 97.99/13.26 (injFuncSetFuncInj) =>
% 97.99/13.26 ((
% 97.99/13.26 (surjFuncSetFuncIn) =>
% 97.99/13.26 ((
% 97.99/13.26 (surjFuncSetFuncSurj) =>
% 97.99/13.26 ((
% 97.99/13.26 (leftInvIsSurj) =>
% 97.99/13.26 ((
% 97.99/13.26 (surjCantorThm) =>
% 97.99/13.26 ((
% 97.99/13.26 (foundation2) =>
% 97.99/13.26 ((
% 97.99/13.26 (notinself) =>
% 97.99/13.26 ((
% 97.99/13.26 (notinself2) =>
% 97.99/13.26 ((
% 97.99/13.26 (omegaSp) =>
% 97.99/13.26 ((
% 97.99/13.26 (omegaSclos) =>
% 97.99/13.26 ((
% 97.99/13.26 (peano0notS) =>
% 97.99/13.26 ((
% 97.99/13.26 (!!) @ (
% 97.99/13.26 (('#S') @ (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 =>) @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#C') @ in @
% 97.99/13.26 omega)))) @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 !!) @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 (
% 97.99/13.26 ('#S') @ (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 =>) @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#C') @ in @
% 97.99/13.26 omega)))))) @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#S') @ (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 '#S') @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 =>))) @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#C') @ (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 '#B') @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 =) @
% 97.99/13.26 omegaS)))) @
% 97.99/13.26 omegaS)))))) @
% 97.99/13.26 (
% 97.99/13.26 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.99/13.26 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1313])).
% 97.99/13.26 thf(zip_derived_cl1329, plain,
% 97.99/13.26 (~ (((symdiffE) =>
% 97.99/13.26 (((symdiffI1) =>
% 97.99/13.26 (((symdiffI2) =>
% 97.99/13.26 (((symdiffIneg1) =>
% 97.99/13.26 (((symdiffIneg2) =>
% 97.99/13.26 (((secondinupair) =>
% 97.99/13.26 (((setukpairIL) =>
% 97.99/13.26 (((setukpairIR) =>
% 97.99/13.26 (((kpairiskpair) =>
% 97.99/13.26 (((kpairp) =>
% 97.99/13.26 (((singletonsubset) =>
% 97.99/13.26 (((singletoninpowerset) =>
% 97.99/13.26 (((singletoninpowunion) =>
% 97.99/13.26 (((upairset2E) =>
% 97.99/13.26 (((upairsubunion) =>
% 97.99/13.26 (((upairinpowunion) =>
% 97.99/13.26 (((ubforcartprodlem1) =>
% 97.99/13.26 (((ubforcartprodlem2) =>
% 97.99/13.26 (((ubforcartprodlem3) =>
% 97.99/13.26 (((cartprodpairin) =>
% 97.99/13.26 (((cartprodmempair1) =>
% 97.99/13.26 (((cartprodmempair) =>
% 97.99/13.26 (((setunionE2) =>
% 97.99/13.26 (((setunionsingleton1) =>
% 97.99/13.26 (((setunionsingleton2) =>
% 97.99/13.26 (((setunionsingleton) =>
% 97.99/13.26 (((singletonprop) =>
% 97.99/13.26 (((ex1E1) =>
% 97.99/13.26 (((ex1I) =>
% 97.99/13.26 (((ex1I2) =>
% 97.99/13.26 ((
% 97.99/13.26 (singletonsuniq) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjL1) =>
% 97.99/13.26 ((
% 97.99/13.26 (kfstsingleton) =>
% 97.99/13.26 ((
% 97.99/13.26 (theprop) =>
% 97.99/13.26 ((
% 97.99/13.26 (kfstpairEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodfstin) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjL2) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjL) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjR11) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjR12) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjR1) =>
% 97.99/13.26 ((
% 97.99/13.26 (upairequniteq) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjR2) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjR) =>
% 97.99/13.26 ((
% 97.99/13.26 (ksndsingleton) =>
% 97.99/13.26 ((
% 97.99/13.26 (ksndpairEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (kpairsurjEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodsndin) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodpairmemEL) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodpairmemER) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodmempaircEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodfstpairEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodsndpairEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodpairsurjEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (dpsetconstrI) =>
% 97.99/13.26 ((
% 97.99/13.26 (dpsetconstrSub) =>
% 97.99/13.26 ((
% 97.99/13.26 (setOfPairsIsBReln) =>
% 97.99/13.26 ((
% 97.99/13.26 (dpsetconstrERa) =>
% 97.99/13.26 ((
% 97.99/13.26 (dpsetconstrEL1) =>
% 97.99/13.26 ((
% 97.99/13.26 (dpsetconstrEL2) =>
% 97.99/13.26 ((
% 97.99/13.26 (dpsetconstrER) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcImageSingleton) =>
% 97.99/13.26 ((
% 97.99/13.26 (apProp) =>
% 97.99/13.26 ((
% 97.99/13.26 (app) =>
% 97.99/13.26 ((
% 97.99/13.26 (infuncsetfunc) =>
% 97.99/13.26 ((
% 97.99/13.26 (ap2p) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcinfuncset) =>
% 97.99/13.26 ((
% 97.99/13.26 (lamProp) =>
% 97.99/13.26 ((
% 97.99/13.26 (lamp) =>
% 97.99/13.26 ((
% 97.99/13.26 (lam2p) =>
% 97.99/13.26 ((
% 97.99/13.26 (brelnall1) =>
% 97.99/13.26 ((
% 97.99/13.26 (brelnall2) =>
% 97.99/13.26 ((
% 97.99/13.26 (ex1E2) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcGraphProp1) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcGraphProp3) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcGraphProp2) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcextLem) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcGraphProp4) =>
% 97.99/13.26 ((
% 97.99/13.26 (subbreln) =>
% 97.99/13.26 ((
% 97.99/13.26 (eqbreln) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcext) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcext2) =>
% 97.99/13.26 ((
% 97.99/13.26 (ap2apEq1) =>
% 97.99/13.26 ((
% 97.99/13.26 (ap2apEq2) =>
% 97.99/13.26 ((
% 97.99/13.26 (beta1) =>
% 97.99/13.26 ((
% 97.99/13.26 (eta1) =>
% 97.99/13.26 ((
% 97.99/13.26 (lam2lamEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (beta2) =>
% 97.99/13.26 ((
% 97.99/13.26 (eta2) =>
% 97.99/13.26 ((
% 97.99/13.26 (iffalseProp1) =>
% 97.99/13.26 ((
% 97.99/13.26 (iffalseProp2) =>
% 97.99/13.26 ((
% 97.99/13.26 (iftrueProp1) =>
% 97.99/13.26 ((
% 97.99/13.26 (iftrueProp2) =>
% 97.99/13.26 ((
% 97.99/13.26 (ifSingleton) =>
% 97.99/13.26 ((
% 97.99/13.26 (ifp) =>
% 97.99/13.26 ((
% 97.99/13.26 (theeq) =>
% 97.99/13.26 ((
% 97.99/13.26 (iftrue) =>
% 97.99/13.26 ((
% 97.99/13.26 (iffalse) =>
% 97.99/13.26 ((
% 97.99/13.26 (iftrueorfalse) =>
% 97.99/13.26 ((
% 97.99/13.26 (binintersectT_lem) =>
% 97.99/13.26 ((
% 97.99/13.26 (binunionT_lem) =>
% 97.99/13.26 ((
% 97.99/13.26 (powersetT_lem) =>
% 97.99/13.26 ((
% 97.99/13.26 (setminusT_lem) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementT_lem) =>
% 97.99/13.26 ((
% 97.99/13.26 (setextT) =>
% 97.99/13.26 ((
% 97.99/13.26 (subsetTI) =>
% 97.99/13.26 ((
% 97.99/13.26 (powersetTI1) =>
% 97.99/13.26 ((
% 97.99/13.26 (powersetTE1) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementTI1) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementTE1) =>
% 97.99/13.26 ((
% 97.99/13.26 (binintersectTELcontra) =>
% 97.99/13.26 ((
% 97.99/13.26 (binintersectTERcontra) =>
% 97.99/13.26 ((
% 97.99/13.26 (contrasubsetT) =>
% 97.99/13.26 ((
% 97.99/13.26 (contrasubsetT1) =>
% 97.99/13.26 ((
% 97.99/13.26 (contrasubsetT2) =>
% 97.99/13.26 ((
% 97.99/13.26 (contrasubsetT3) =>
% 97.99/13.26 ((
% 97.99/13.26 (doubleComplementI1) =>
% 97.99/13.26 ((
% 97.99/13.26 (doubleComplementE1) =>
% 97.99/13.26 ((
% 97.99/13.26 (doubleComplementSub1) =>
% 97.99/13.26 ((
% 97.99/13.26 (doubleComplementSub2) =>
% 97.99/13.26 ((
% 97.99/13.26 (doubleComplementEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementTnotintersectT) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementImpComplementIntersect) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementSubsetComplementIntersect) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementInPowersetComplementIntersect) =>
% 97.99/13.26 ((
% 97.99/13.26 (contraSubsetComplement) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementTcontraSubset) =>
% 97.99/13.26 ((
% 97.99/13.26 (binunionTILcontra) =>
% 97.99/13.26 ((
% 97.99/13.26 (binunionTIRcontra) =>
% 97.99/13.26 ((
% 97.99/13.26 (inIntersectImpInUnion) =>
% 97.99/13.26 ((
% 97.99/13.26 (inIntersectImpInUnion2) =>
% 97.99/13.26 ((
% 97.99/13.26 (inIntersectImpInIntersectUnions) =>
% 97.99/13.26 ((
% 97.99/13.26 (intersectInPowersetIntersectUnions) =>
% 97.99/13.26 ((
% 97.99/13.26 (inComplementUnionImpNotIn1) =>
% 97.99/13.26 ((
% 97.99/13.26 (inComplementUnionImpInComplement1) =>
% 97.99/13.26 ((
% 97.99/13.26 (binunionTE) =>
% 97.99/13.26 ((
% 97.99/13.26 (binunionTEcontra) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan2a1) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementUnionInPowersetComplement) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan2a2) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan1a) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan1b) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan1) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan2a) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan2b2) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan2b) =>
% 97.99/13.26 ((
% 97.99/13.26 (demorgan2) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz13rule0) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz13rule1) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz13rule2) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz13rule3) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz13rule4) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz1_1) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz1_2) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz1_3) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz1_4) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz1_5) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1all2) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1SetBreln1) =>
% 97.99/13.26 ((
% 97.99/13.26 (choice2fnsingleton) =>
% 97.99/13.26 ((
% 97.99/13.26 (setOfPairsIsBReln1) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1all1) =>
% 97.99/13.26 ((
% 97.99/13.26 (subbreln1) =>
% 97.99/13.26 ((
% 97.99/13.26 (eqbreln1) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1invprop) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1invI) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1invE) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1compprop) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1compI) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1compE) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1compEex) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionprop) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionIL) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionIR) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionI) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionE) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionEcases) =>
% 97.99/13.26 ((
% 97.99/13.26 (breln1unionCommutes) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz2Ex) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz2W) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz2A) =>
% 97.99/13.26 ((
% 97.99/13.26 (woz2B) =>
% 97.99/13.26 ((
% 97.99/13.26 (image1Ex) =>
% 97.99/13.26 ((
% 97.99/13.26 (image1Ex1) =>
% 97.99/13.26 ((
% 97.99/13.26 (image1Equiv) =>
% 97.99/13.26 ((
% 97.99/13.26 (image1E) =>
% 97.99/13.26 ((
% 97.99/13.26 (image1I) =>
% 97.99/13.26 ((
% 97.99/13.26 (injFuncInInjFuncSet) =>
% 97.99/13.26 ((
% 97.99/13.26 (injFuncSetFuncIn) =>
% 97.99/13.26 ((
% 97.99/13.26 (injFuncSetFuncInj) =>
% 97.99/13.26 ((
% 97.99/13.26 (surjFuncSetFuncIn) =>
% 97.99/13.26 ((
% 97.99/13.26 (surjFuncSetFuncSurj) =>
% 97.99/13.26 ((
% 97.99/13.26 (leftInvIsSurj) =>
% 97.99/13.26 ((
% 97.99/13.26 (surjCantorThm) =>
% 97.99/13.26 ((
% 97.99/13.26 (foundation2) =>
% 97.99/13.26 ((
% 97.99/13.26 (notinself) =>
% 97.99/13.26 ((
% 97.99/13.26 (notinself2) =>
% 97.99/13.26 ((
% 97.99/13.26 (omegaSp) =>
% 97.99/13.26 ((
% 97.99/13.26 (omegaSclos) =>
% 97.99/13.26 ((
% 97.99/13.26 (peano0notS) =>
% 97.99/13.26 ((
% 97.99/13.26 (!!) @ (
% 97.99/13.26 (('#S') @ (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 =>) @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#C') @ in @
% 97.99/13.26 omega)))) @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 !!) @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 (
% 97.99/13.26 ('#S') @ (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 =>) @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#C') @ in @
% 97.99/13.26 omega)))))) @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#S') @ (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 '#S') @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 =>))) @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#C') @ (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 '#B') @
% 97.99/13.26 (
% 97.99/13.26 (
% 97.99/13.26 ('#B') @ (
% 97.99/13.26 =) @
% 97.99/13.26 omegaS)))) @
% 97.99/13.26 omegaS)))))) @
% 97.99/13.26 (
% 97.99/13.26 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.99/13.26 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1321])).
% 97.99/13.26 thf(zip_derived_cl1338, plain,
% 97.99/13.26 (~ (((symdiffI1) =>
% 97.99/13.26 (((symdiffI2) =>
% 97.99/13.26 (((symdiffIneg1) =>
% 97.99/13.26 (((symdiffIneg2) =>
% 97.99/13.26 (((secondinupair) =>
% 97.99/13.26 (((setukpairIL) =>
% 97.99/13.26 (((setukpairIR) =>
% 97.99/13.26 (((kpairiskpair) =>
% 97.99/13.26 (((kpairp) =>
% 97.99/13.26 (((singletonsubset) =>
% 97.99/13.26 (((singletoninpowerset) =>
% 97.99/13.26 (((singletoninpowunion) =>
% 97.99/13.26 (((upairset2E) =>
% 97.99/13.26 (((upairsubunion) =>
% 97.99/13.26 (((upairinpowunion) =>
% 97.99/13.26 (((ubforcartprodlem1) =>
% 97.99/13.26 (((ubforcartprodlem2) =>
% 97.99/13.26 (((ubforcartprodlem3) =>
% 97.99/13.26 (((cartprodpairin) =>
% 97.99/13.26 (((cartprodmempair1) =>
% 97.99/13.26 (((cartprodmempair) =>
% 97.99/13.26 (((setunionE2) =>
% 97.99/13.26 (((setunionsingleton1) =>
% 97.99/13.26 (((setunionsingleton2) =>
% 97.99/13.26 (((setunionsingleton) =>
% 97.99/13.26 (((singletonprop) =>
% 97.99/13.26 (((ex1E1) =>
% 97.99/13.26 (((ex1I) =>
% 97.99/13.26 (((ex1I2) =>
% 97.99/13.26 (((singletonsuniq) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjL1) =>
% 97.99/13.26 ((
% 97.99/13.26 (kfstsingleton) =>
% 97.99/13.26 ((
% 97.99/13.26 (theprop) =>
% 97.99/13.26 ((
% 97.99/13.26 (kfstpairEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodfstin) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjL2) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjL) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjR11) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjR12) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjR1) =>
% 97.99/13.26 ((
% 97.99/13.26 (upairequniteq) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjR2) =>
% 97.99/13.26 ((
% 97.99/13.26 (setukpairinjR) =>
% 97.99/13.26 ((
% 97.99/13.26 (ksndsingleton) =>
% 97.99/13.26 ((
% 97.99/13.26 (ksndpairEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (kpairsurjEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodsndin) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodpairmemEL) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodpairmemER) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodmempaircEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodfstpairEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodsndpairEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (cartprodpairsurjEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (dpsetconstrI) =>
% 97.99/13.26 ((
% 97.99/13.26 (dpsetconstrSub) =>
% 97.99/13.26 ((
% 97.99/13.26 (setOfPairsIsBReln) =>
% 97.99/13.26 ((
% 97.99/13.26 (dpsetconstrERa) =>
% 97.99/13.26 ((
% 97.99/13.26 (dpsetconstrEL1) =>
% 97.99/13.26 ((
% 97.99/13.26 (dpsetconstrEL2) =>
% 97.99/13.26 ((
% 97.99/13.26 (dpsetconstrER) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcImageSingleton) =>
% 97.99/13.26 ((
% 97.99/13.26 (apProp) =>
% 97.99/13.26 ((
% 97.99/13.26 (app) =>
% 97.99/13.26 ((
% 97.99/13.26 (infuncsetfunc) =>
% 97.99/13.26 ((
% 97.99/13.26 (ap2p) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcinfuncset) =>
% 97.99/13.26 ((
% 97.99/13.26 (lamProp) =>
% 97.99/13.26 ((
% 97.99/13.26 (lamp) =>
% 97.99/13.26 ((
% 97.99/13.26 (lam2p) =>
% 97.99/13.26 ((
% 97.99/13.26 (brelnall1) =>
% 97.99/13.26 ((
% 97.99/13.26 (brelnall2) =>
% 97.99/13.26 ((
% 97.99/13.26 (ex1E2) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcGraphProp1) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcGraphProp3) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcGraphProp2) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcextLem) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcGraphProp4) =>
% 97.99/13.26 ((
% 97.99/13.26 (subbreln) =>
% 97.99/13.26 ((
% 97.99/13.26 (eqbreln) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcext) =>
% 97.99/13.26 ((
% 97.99/13.26 (funcext2) =>
% 97.99/13.26 ((
% 97.99/13.26 (ap2apEq1) =>
% 97.99/13.26 ((
% 97.99/13.26 (ap2apEq2) =>
% 97.99/13.26 ((
% 97.99/13.26 (beta1) =>
% 97.99/13.26 ((
% 97.99/13.26 (eta1) =>
% 97.99/13.26 ((
% 97.99/13.26 (lam2lamEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (beta2) =>
% 97.99/13.26 ((
% 97.99/13.26 (eta2) =>
% 97.99/13.26 ((
% 97.99/13.26 (iffalseProp1) =>
% 97.99/13.26 ((
% 97.99/13.26 (iffalseProp2) =>
% 97.99/13.26 ((
% 97.99/13.26 (iftrueProp1) =>
% 97.99/13.26 ((
% 97.99/13.26 (iftrueProp2) =>
% 97.99/13.26 ((
% 97.99/13.26 (ifSingleton) =>
% 97.99/13.26 ((
% 97.99/13.26 (ifp) =>
% 97.99/13.26 ((
% 97.99/13.26 (theeq) =>
% 97.99/13.26 ((
% 97.99/13.26 (iftrue) =>
% 97.99/13.26 ((
% 97.99/13.26 (iffalse) =>
% 97.99/13.26 ((
% 97.99/13.26 (iftrueorfalse) =>
% 97.99/13.26 ((
% 97.99/13.26 (binintersectT_lem) =>
% 97.99/13.26 ((
% 97.99/13.26 (binunionT_lem) =>
% 97.99/13.26 ((
% 97.99/13.26 (powersetT_lem) =>
% 97.99/13.26 ((
% 97.99/13.26 (setminusT_lem) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementT_lem) =>
% 97.99/13.26 ((
% 97.99/13.26 (setextT) =>
% 97.99/13.26 ((
% 97.99/13.26 (subsetTI) =>
% 97.99/13.26 ((
% 97.99/13.26 (powersetTI1) =>
% 97.99/13.26 ((
% 97.99/13.26 (powersetTE1) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementTI1) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementTE1) =>
% 97.99/13.26 ((
% 97.99/13.26 (binintersectTELcontra) =>
% 97.99/13.26 ((
% 97.99/13.26 (binintersectTERcontra) =>
% 97.99/13.26 ((
% 97.99/13.26 (contrasubsetT) =>
% 97.99/13.26 ((
% 97.99/13.26 (contrasubsetT1) =>
% 97.99/13.26 ((
% 97.99/13.26 (contrasubsetT2) =>
% 97.99/13.26 ((
% 97.99/13.26 (contrasubsetT3) =>
% 97.99/13.26 ((
% 97.99/13.26 (doubleComplementI1) =>
% 97.99/13.26 ((
% 97.99/13.26 (doubleComplementE1) =>
% 97.99/13.26 ((
% 97.99/13.26 (doubleComplementSub1) =>
% 97.99/13.26 ((
% 97.99/13.26 (doubleComplementSub2) =>
% 97.99/13.26 ((
% 97.99/13.26 (doubleComplementEq) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementTnotintersectT) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementImpComplementIntersect) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementSubsetComplementIntersect) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementInPowersetComplementIntersect) =>
% 97.99/13.26 ((
% 97.99/13.26 (contraSubsetComplement) =>
% 97.99/13.26 ((
% 97.99/13.26 (complementTcontraSubset) =>
% 97.99/13.26 ((
% 97.99/13.26 (binunionTILcontra) =>
% 97.99/13.27 ((
% 97.99/13.27 (binunionTIRcontra) =>
% 97.99/13.27 ((
% 97.99/13.27 (inIntersectImpInUnion) =>
% 97.99/13.27 ((
% 97.99/13.27 (inIntersectImpInUnion2) =>
% 97.99/13.27 ((
% 97.99/13.27 (inIntersectImpInIntersectUnions) =>
% 97.99/13.27 ((
% 97.99/13.27 (intersectInPowersetIntersectUnions) =>
% 97.99/13.27 ((
% 97.99/13.27 (inComplementUnionImpNotIn1) =>
% 97.99/13.27 ((
% 97.99/13.27 (inComplementUnionImpInComplement1) =>
% 97.99/13.27 ((
% 97.99/13.27 (binunionTE) =>
% 97.99/13.27 ((
% 97.99/13.27 (binunionTEcontra) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan2a1) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementUnionInPowersetComplement) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan2a2) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan1a) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan1b) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan1) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan2a) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan2b2) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan2b) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan2) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz13rule0) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz13rule1) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz13rule2) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz13rule3) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz13rule4) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz1_1) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz1_2) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz1_3) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz1_4) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz1_5) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1all2) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1SetBreln1) =>
% 97.99/13.27 ((
% 97.99/13.27 (choice2fnsingleton) =>
% 97.99/13.27 ((
% 97.99/13.27 (setOfPairsIsBReln1) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1all1) =>
% 97.99/13.27 ((
% 97.99/13.27 (subbreln1) =>
% 97.99/13.27 ((
% 97.99/13.27 (eqbreln1) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1invprop) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1invI) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1invE) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1compprop) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1compI) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1compE) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1compEex) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionprop) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionIL) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionIR) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionI) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionE) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionEcases) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionCommutes) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz2Ex) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz2W) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz2A) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz2B) =>
% 97.99/13.27 ((
% 97.99/13.27 (image1Ex) =>
% 97.99/13.27 ((
% 97.99/13.27 (image1Ex1) =>
% 97.99/13.27 ((
% 97.99/13.27 (image1Equiv) =>
% 97.99/13.27 ((
% 97.99/13.27 (image1E) =>
% 97.99/13.27 ((
% 97.99/13.27 (image1I) =>
% 97.99/13.27 ((
% 97.99/13.27 (injFuncInInjFuncSet) =>
% 97.99/13.27 ((
% 97.99/13.27 (injFuncSetFuncIn) =>
% 97.99/13.27 ((
% 97.99/13.27 (injFuncSetFuncInj) =>
% 97.99/13.27 ((
% 97.99/13.27 (surjFuncSetFuncIn) =>
% 97.99/13.27 ((
% 97.99/13.27 (surjFuncSetFuncSurj) =>
% 97.99/13.27 ((
% 97.99/13.27 (leftInvIsSurj) =>
% 97.99/13.27 ((
% 97.99/13.27 (surjCantorThm) =>
% 97.99/13.27 ((
% 97.99/13.27 (foundation2) =>
% 97.99/13.27 ((
% 97.99/13.27 (notinself) =>
% 97.99/13.27 ((
% 97.99/13.27 (notinself2) =>
% 97.99/13.27 ((
% 97.99/13.27 (omegaSp) =>
% 97.99/13.27 ((
% 97.99/13.27 (omegaSclos) =>
% 97.99/13.27 ((
% 97.99/13.27 (peano0notS) =>
% 97.99/13.27 ((
% 97.99/13.27 (!!) @ (
% 97.99/13.27 (('#S') @ (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 =>) @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#C') @ in @
% 97.99/13.27 omega)))) @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 !!) @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 (
% 97.99/13.27 ('#S') @ (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 =>) @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#C') @ in @
% 97.99/13.27 omega)))))) @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#S') @ (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 '#S') @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 =>))) @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#C') @ (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 '#B') @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 =) @
% 97.99/13.27 omegaS)))) @
% 97.99/13.27 omegaS)))))) @
% 97.99/13.27 (
% 97.99/13.27 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.99/13.27 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1329])).
% 97.99/13.27 thf(zip_derived_cl1347, plain,
% 97.99/13.27 (~ (((symdiffI2) =>
% 97.99/13.27 (((symdiffIneg1) =>
% 97.99/13.27 (((symdiffIneg2) =>
% 97.99/13.27 (((secondinupair) =>
% 97.99/13.27 (((setukpairIL) =>
% 97.99/13.27 (((setukpairIR) =>
% 97.99/13.27 (((kpairiskpair) =>
% 97.99/13.27 (((kpairp) =>
% 97.99/13.27 (((singletonsubset) =>
% 97.99/13.27 (((singletoninpowerset) =>
% 97.99/13.27 (((singletoninpowunion) =>
% 97.99/13.27 (((upairset2E) =>
% 97.99/13.27 (((upairsubunion) =>
% 97.99/13.27 (((upairinpowunion) =>
% 97.99/13.27 (((ubforcartprodlem1) =>
% 97.99/13.27 (((ubforcartprodlem2) =>
% 97.99/13.27 (((ubforcartprodlem3) =>
% 97.99/13.27 (((cartprodpairin) =>
% 97.99/13.27 (((cartprodmempair1) =>
% 97.99/13.27 (((cartprodmempair) =>
% 97.99/13.27 (((setunionE2) =>
% 97.99/13.27 (((setunionsingleton1) =>
% 97.99/13.27 (((setunionsingleton2) =>
% 97.99/13.27 (((setunionsingleton) =>
% 97.99/13.27 (((singletonprop) =>
% 97.99/13.27 (((ex1E1) =>
% 97.99/13.27 (((ex1I) =>
% 97.99/13.27 (((ex1I2) =>
% 97.99/13.27 (((singletonsuniq) =>
% 97.99/13.27 (((setukpairinjL1) =>
% 97.99/13.27 ((
% 97.99/13.27 (kfstsingleton) =>
% 97.99/13.27 ((
% 97.99/13.27 (theprop) =>
% 97.99/13.27 ((
% 97.99/13.27 (kfstpairEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodfstin) =>
% 97.99/13.27 ((
% 97.99/13.27 (setukpairinjL2) =>
% 97.99/13.27 ((
% 97.99/13.27 (setukpairinjL) =>
% 97.99/13.27 ((
% 97.99/13.27 (setukpairinjR11) =>
% 97.99/13.27 ((
% 97.99/13.27 (setukpairinjR12) =>
% 97.99/13.27 ((
% 97.99/13.27 (setukpairinjR1) =>
% 97.99/13.27 ((
% 97.99/13.27 (upairequniteq) =>
% 97.99/13.27 ((
% 97.99/13.27 (setukpairinjR2) =>
% 97.99/13.27 ((
% 97.99/13.27 (setukpairinjR) =>
% 97.99/13.27 ((
% 97.99/13.27 (ksndsingleton) =>
% 97.99/13.27 ((
% 97.99/13.27 (ksndpairEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (kpairsurjEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodsndin) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodpairmemEL) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodpairmemER) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodmempaircEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodfstpairEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodsndpairEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodpairsurjEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (dpsetconstrI) =>
% 97.99/13.27 ((
% 97.99/13.27 (dpsetconstrSub) =>
% 97.99/13.27 ((
% 97.99/13.27 (setOfPairsIsBReln) =>
% 97.99/13.27 ((
% 97.99/13.27 (dpsetconstrERa) =>
% 97.99/13.27 ((
% 97.99/13.27 (dpsetconstrEL1) =>
% 97.99/13.27 ((
% 97.99/13.27 (dpsetconstrEL2) =>
% 97.99/13.27 ((
% 97.99/13.27 (dpsetconstrER) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcImageSingleton) =>
% 97.99/13.27 ((
% 97.99/13.27 (apProp) =>
% 97.99/13.27 ((
% 97.99/13.27 (app) =>
% 97.99/13.27 ((
% 97.99/13.27 (infuncsetfunc) =>
% 97.99/13.27 ((
% 97.99/13.27 (ap2p) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcinfuncset) =>
% 97.99/13.27 ((
% 97.99/13.27 (lamProp) =>
% 97.99/13.27 ((
% 97.99/13.27 (lamp) =>
% 97.99/13.27 ((
% 97.99/13.27 (lam2p) =>
% 97.99/13.27 ((
% 97.99/13.27 (brelnall1) =>
% 97.99/13.27 ((
% 97.99/13.27 (brelnall2) =>
% 97.99/13.27 ((
% 97.99/13.27 (ex1E2) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcGraphProp1) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcGraphProp3) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcGraphProp2) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcextLem) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcGraphProp4) =>
% 97.99/13.27 ((
% 97.99/13.27 (subbreln) =>
% 97.99/13.27 ((
% 97.99/13.27 (eqbreln) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcext) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcext2) =>
% 97.99/13.27 ((
% 97.99/13.27 (ap2apEq1) =>
% 97.99/13.27 ((
% 97.99/13.27 (ap2apEq2) =>
% 97.99/13.27 ((
% 97.99/13.27 (beta1) =>
% 97.99/13.27 ((
% 97.99/13.27 (eta1) =>
% 97.99/13.27 ((
% 97.99/13.27 (lam2lamEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (beta2) =>
% 97.99/13.27 ((
% 97.99/13.27 (eta2) =>
% 97.99/13.27 ((
% 97.99/13.27 (iffalseProp1) =>
% 97.99/13.27 ((
% 97.99/13.27 (iffalseProp2) =>
% 97.99/13.27 ((
% 97.99/13.27 (iftrueProp1) =>
% 97.99/13.27 ((
% 97.99/13.27 (iftrueProp2) =>
% 97.99/13.27 ((
% 97.99/13.27 (ifSingleton) =>
% 97.99/13.27 ((
% 97.99/13.27 (ifp) =>
% 97.99/13.27 ((
% 97.99/13.27 (theeq) =>
% 97.99/13.27 ((
% 97.99/13.27 (iftrue) =>
% 97.99/13.27 ((
% 97.99/13.27 (iffalse) =>
% 97.99/13.27 ((
% 97.99/13.27 (iftrueorfalse) =>
% 97.99/13.27 ((
% 97.99/13.27 (binintersectT_lem) =>
% 97.99/13.27 ((
% 97.99/13.27 (binunionT_lem) =>
% 97.99/13.27 ((
% 97.99/13.27 (powersetT_lem) =>
% 97.99/13.27 ((
% 97.99/13.27 (setminusT_lem) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementT_lem) =>
% 97.99/13.27 ((
% 97.99/13.27 (setextT) =>
% 97.99/13.27 ((
% 97.99/13.27 (subsetTI) =>
% 97.99/13.27 ((
% 97.99/13.27 (powersetTI1) =>
% 97.99/13.27 ((
% 97.99/13.27 (powersetTE1) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementTI1) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementTE1) =>
% 97.99/13.27 ((
% 97.99/13.27 (binintersectTELcontra) =>
% 97.99/13.27 ((
% 97.99/13.27 (binintersectTERcontra) =>
% 97.99/13.27 ((
% 97.99/13.27 (contrasubsetT) =>
% 97.99/13.27 ((
% 97.99/13.27 (contrasubsetT1) =>
% 97.99/13.27 ((
% 97.99/13.27 (contrasubsetT2) =>
% 97.99/13.27 ((
% 97.99/13.27 (contrasubsetT3) =>
% 97.99/13.27 ((
% 97.99/13.27 (doubleComplementI1) =>
% 97.99/13.27 ((
% 97.99/13.27 (doubleComplementE1) =>
% 97.99/13.27 ((
% 97.99/13.27 (doubleComplementSub1) =>
% 97.99/13.27 ((
% 97.99/13.27 (doubleComplementSub2) =>
% 97.99/13.27 ((
% 97.99/13.27 (doubleComplementEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementTnotintersectT) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementImpComplementIntersect) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementSubsetComplementIntersect) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementInPowersetComplementIntersect) =>
% 97.99/13.27 ((
% 97.99/13.27 (contraSubsetComplement) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementTcontraSubset) =>
% 97.99/13.27 ((
% 97.99/13.27 (binunionTILcontra) =>
% 97.99/13.27 ((
% 97.99/13.27 (binunionTIRcontra) =>
% 97.99/13.27 ((
% 97.99/13.27 (inIntersectImpInUnion) =>
% 97.99/13.27 ((
% 97.99/13.27 (inIntersectImpInUnion2) =>
% 97.99/13.27 ((
% 97.99/13.27 (inIntersectImpInIntersectUnions) =>
% 97.99/13.27 ((
% 97.99/13.27 (intersectInPowersetIntersectUnions) =>
% 97.99/13.27 ((
% 97.99/13.27 (inComplementUnionImpNotIn1) =>
% 97.99/13.27 ((
% 97.99/13.27 (inComplementUnionImpInComplement1) =>
% 97.99/13.27 ((
% 97.99/13.27 (binunionTE) =>
% 97.99/13.27 ((
% 97.99/13.27 (binunionTEcontra) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan2a1) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementUnionInPowersetComplement) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan2a2) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan1a) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan1b) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan1) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan2a) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan2b2) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan2b) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan2) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz13rule0) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz13rule1) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz13rule2) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz13rule3) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz13rule4) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz1_1) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz1_2) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz1_3) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz1_4) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz1_5) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1all2) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1SetBreln1) =>
% 97.99/13.27 ((
% 97.99/13.27 (choice2fnsingleton) =>
% 97.99/13.27 ((
% 97.99/13.27 (setOfPairsIsBReln1) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1all1) =>
% 97.99/13.27 ((
% 97.99/13.27 (subbreln1) =>
% 97.99/13.27 ((
% 97.99/13.27 (eqbreln1) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1invprop) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1invI) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1invE) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1compprop) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1compI) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1compE) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1compEex) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionprop) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionIL) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionIR) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionI) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionE) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionEcases) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionCommutes) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz2Ex) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz2W) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz2A) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz2B) =>
% 97.99/13.27 ((
% 97.99/13.27 (image1Ex) =>
% 97.99/13.27 ((
% 97.99/13.27 (image1Ex1) =>
% 97.99/13.27 ((
% 97.99/13.27 (image1Equiv) =>
% 97.99/13.27 ((
% 97.99/13.27 (image1E) =>
% 97.99/13.27 ((
% 97.99/13.27 (image1I) =>
% 97.99/13.27 ((
% 97.99/13.27 (injFuncInInjFuncSet) =>
% 97.99/13.27 ((
% 97.99/13.27 (injFuncSetFuncIn) =>
% 97.99/13.27 ((
% 97.99/13.27 (injFuncSetFuncInj) =>
% 97.99/13.27 ((
% 97.99/13.27 (surjFuncSetFuncIn) =>
% 97.99/13.27 ((
% 97.99/13.27 (surjFuncSetFuncSurj) =>
% 97.99/13.27 ((
% 97.99/13.27 (leftInvIsSurj) =>
% 97.99/13.27 ((
% 97.99/13.27 (surjCantorThm) =>
% 97.99/13.27 ((
% 97.99/13.27 (foundation2) =>
% 97.99/13.27 ((
% 97.99/13.27 (notinself) =>
% 97.99/13.27 ((
% 97.99/13.27 (notinself2) =>
% 97.99/13.27 ((
% 97.99/13.27 (omegaSp) =>
% 97.99/13.27 ((
% 97.99/13.27 (omegaSclos) =>
% 97.99/13.27 ((
% 97.99/13.27 (peano0notS) =>
% 97.99/13.27 ((
% 97.99/13.27 (!!) @ (
% 97.99/13.27 (('#S') @ (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 =>) @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#C') @ in @
% 97.99/13.27 omega)))) @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 !!) @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 (
% 97.99/13.27 ('#S') @ (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 =>) @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#C') @ in @
% 97.99/13.27 omega)))))) @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#S') @ (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 '#S') @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 =>))) @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#C') @ (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 '#B') @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 =) @
% 97.99/13.27 omegaS)))) @
% 97.99/13.27 omegaS)))))) @
% 97.99/13.27 (
% 97.99/13.27 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.99/13.27 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1338])).
% 97.99/13.27 thf(zip_derived_cl1354, plain,
% 97.99/13.27 (~ (((symdiffIneg1) =>
% 97.99/13.27 (((symdiffIneg2) =>
% 97.99/13.27 (((secondinupair) =>
% 97.99/13.27 (((setukpairIL) =>
% 97.99/13.27 (((setukpairIR) =>
% 97.99/13.27 (((kpairiskpair) =>
% 97.99/13.27 (((kpairp) =>
% 97.99/13.27 (((singletonsubset) =>
% 97.99/13.27 (((singletoninpowerset) =>
% 97.99/13.27 (((singletoninpowunion) =>
% 97.99/13.27 (((upairset2E) =>
% 97.99/13.27 (((upairsubunion) =>
% 97.99/13.27 (((upairinpowunion) =>
% 97.99/13.27 (((ubforcartprodlem1) =>
% 97.99/13.27 (((ubforcartprodlem2) =>
% 97.99/13.27 (((ubforcartprodlem3) =>
% 97.99/13.27 (((cartprodpairin) =>
% 97.99/13.27 (((cartprodmempair1) =>
% 97.99/13.27 (((cartprodmempair) =>
% 97.99/13.27 (((setunionE2) =>
% 97.99/13.27 (((setunionsingleton1) =>
% 97.99/13.27 (((setunionsingleton2) =>
% 97.99/13.27 (((setunionsingleton) =>
% 97.99/13.27 (((singletonprop) =>
% 97.99/13.27 (((ex1E1) =>
% 97.99/13.27 (((ex1I) =>
% 97.99/13.27 (((ex1I2) =>
% 97.99/13.27 (((singletonsuniq) =>
% 97.99/13.27 (((setukpairinjL1) =>
% 97.99/13.27 (((kfstsingleton) =>
% 97.99/13.27 ((
% 97.99/13.27 (theprop) =>
% 97.99/13.27 ((
% 97.99/13.27 (kfstpairEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodfstin) =>
% 97.99/13.27 ((
% 97.99/13.27 (setukpairinjL2) =>
% 97.99/13.27 ((
% 97.99/13.27 (setukpairinjL) =>
% 97.99/13.27 ((
% 97.99/13.27 (setukpairinjR11) =>
% 97.99/13.27 ((
% 97.99/13.27 (setukpairinjR12) =>
% 97.99/13.27 ((
% 97.99/13.27 (setukpairinjR1) =>
% 97.99/13.27 ((
% 97.99/13.27 (upairequniteq) =>
% 97.99/13.27 ((
% 97.99/13.27 (setukpairinjR2) =>
% 97.99/13.27 ((
% 97.99/13.27 (setukpairinjR) =>
% 97.99/13.27 ((
% 97.99/13.27 (ksndsingleton) =>
% 97.99/13.27 ((
% 97.99/13.27 (ksndpairEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (kpairsurjEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodsndin) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodpairmemEL) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodpairmemER) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodmempaircEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodfstpairEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodsndpairEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodpairsurjEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (dpsetconstrI) =>
% 97.99/13.27 ((
% 97.99/13.27 (dpsetconstrSub) =>
% 97.99/13.27 ((
% 97.99/13.27 (setOfPairsIsBReln) =>
% 97.99/13.27 ((
% 97.99/13.27 (dpsetconstrERa) =>
% 97.99/13.27 ((
% 97.99/13.27 (dpsetconstrEL1) =>
% 97.99/13.27 ((
% 97.99/13.27 (dpsetconstrEL2) =>
% 97.99/13.27 ((
% 97.99/13.27 (dpsetconstrER) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcImageSingleton) =>
% 97.99/13.27 ((
% 97.99/13.27 (apProp) =>
% 97.99/13.27 ((
% 97.99/13.27 (app) =>
% 97.99/13.27 ((
% 97.99/13.27 (infuncsetfunc) =>
% 97.99/13.27 ((
% 97.99/13.27 (ap2p) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcinfuncset) =>
% 97.99/13.27 ((
% 97.99/13.27 (lamProp) =>
% 97.99/13.27 ((
% 97.99/13.27 (lamp) =>
% 97.99/13.27 ((
% 97.99/13.27 (lam2p) =>
% 97.99/13.27 ((
% 97.99/13.27 (brelnall1) =>
% 97.99/13.27 ((
% 97.99/13.27 (brelnall2) =>
% 97.99/13.27 ((
% 97.99/13.27 (ex1E2) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcGraphProp1) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcGraphProp3) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcGraphProp2) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcextLem) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcGraphProp4) =>
% 97.99/13.27 ((
% 97.99/13.27 (subbreln) =>
% 97.99/13.27 ((
% 97.99/13.27 (eqbreln) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcext) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcext2) =>
% 97.99/13.27 ((
% 97.99/13.27 (ap2apEq1) =>
% 97.99/13.27 ((
% 97.99/13.27 (ap2apEq2) =>
% 97.99/13.27 ((
% 97.99/13.27 (beta1) =>
% 97.99/13.27 ((
% 97.99/13.27 (eta1) =>
% 97.99/13.27 ((
% 97.99/13.27 (lam2lamEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (beta2) =>
% 97.99/13.27 ((
% 97.99/13.27 (eta2) =>
% 97.99/13.27 ((
% 97.99/13.27 (iffalseProp1) =>
% 97.99/13.27 ((
% 97.99/13.27 (iffalseProp2) =>
% 97.99/13.27 ((
% 97.99/13.27 (iftrueProp1) =>
% 97.99/13.27 ((
% 97.99/13.27 (iftrueProp2) =>
% 97.99/13.27 ((
% 97.99/13.27 (ifSingleton) =>
% 97.99/13.27 ((
% 97.99/13.27 (ifp) =>
% 97.99/13.27 ((
% 97.99/13.27 (theeq) =>
% 97.99/13.27 ((
% 97.99/13.27 (iftrue) =>
% 97.99/13.27 ((
% 97.99/13.27 (iffalse) =>
% 97.99/13.27 ((
% 97.99/13.27 (iftrueorfalse) =>
% 97.99/13.27 ((
% 97.99/13.27 (binintersectT_lem) =>
% 97.99/13.27 ((
% 97.99/13.27 (binunionT_lem) =>
% 97.99/13.27 ((
% 97.99/13.27 (powersetT_lem) =>
% 97.99/13.27 ((
% 97.99/13.27 (setminusT_lem) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementT_lem) =>
% 97.99/13.27 ((
% 97.99/13.27 (setextT) =>
% 97.99/13.27 ((
% 97.99/13.27 (subsetTI) =>
% 97.99/13.27 ((
% 97.99/13.27 (powersetTI1) =>
% 97.99/13.27 ((
% 97.99/13.27 (powersetTE1) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementTI1) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementTE1) =>
% 97.99/13.27 ((
% 97.99/13.27 (binintersectTELcontra) =>
% 97.99/13.27 ((
% 97.99/13.27 (binintersectTERcontra) =>
% 97.99/13.27 ((
% 97.99/13.27 (contrasubsetT) =>
% 97.99/13.27 ((
% 97.99/13.27 (contrasubsetT1) =>
% 97.99/13.27 ((
% 97.99/13.27 (contrasubsetT2) =>
% 97.99/13.27 ((
% 97.99/13.27 (contrasubsetT3) =>
% 97.99/13.27 ((
% 97.99/13.27 (doubleComplementI1) =>
% 97.99/13.27 ((
% 97.99/13.27 (doubleComplementE1) =>
% 97.99/13.27 ((
% 97.99/13.27 (doubleComplementSub1) =>
% 97.99/13.27 ((
% 97.99/13.27 (doubleComplementSub2) =>
% 97.99/13.27 ((
% 97.99/13.27 (doubleComplementEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementTnotintersectT) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementImpComplementIntersect) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementSubsetComplementIntersect) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementInPowersetComplementIntersect) =>
% 97.99/13.27 ((
% 97.99/13.27 (contraSubsetComplement) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementTcontraSubset) =>
% 97.99/13.27 ((
% 97.99/13.27 (binunionTILcontra) =>
% 97.99/13.27 ((
% 97.99/13.27 (binunionTIRcontra) =>
% 97.99/13.27 ((
% 97.99/13.27 (inIntersectImpInUnion) =>
% 97.99/13.27 ((
% 97.99/13.27 (inIntersectImpInUnion2) =>
% 97.99/13.27 ((
% 97.99/13.27 (inIntersectImpInIntersectUnions) =>
% 97.99/13.27 ((
% 97.99/13.27 (intersectInPowersetIntersectUnions) =>
% 97.99/13.27 ((
% 97.99/13.27 (inComplementUnionImpNotIn1) =>
% 97.99/13.27 ((
% 97.99/13.27 (inComplementUnionImpInComplement1) =>
% 97.99/13.27 ((
% 97.99/13.27 (binunionTE) =>
% 97.99/13.27 ((
% 97.99/13.27 (binunionTEcontra) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan2a1) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementUnionInPowersetComplement) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan2a2) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan1a) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan1b) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan1) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan2a) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan2b2) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan2b) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan2) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz13rule0) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz13rule1) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz13rule2) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz13rule3) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz13rule4) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz1_1) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz1_2) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz1_3) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz1_4) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz1_5) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1all2) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1SetBreln1) =>
% 97.99/13.27 ((
% 97.99/13.27 (choice2fnsingleton) =>
% 97.99/13.27 ((
% 97.99/13.27 (setOfPairsIsBReln1) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1all1) =>
% 97.99/13.27 ((
% 97.99/13.27 (subbreln1) =>
% 97.99/13.27 ((
% 97.99/13.27 (eqbreln1) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1invprop) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1invI) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1invE) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1compprop) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1compI) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1compE) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1compEex) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionprop) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionIL) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionIR) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionI) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionE) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionEcases) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionCommutes) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz2Ex) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz2W) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz2A) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz2B) =>
% 97.99/13.27 ((
% 97.99/13.27 (image1Ex) =>
% 97.99/13.27 ((
% 97.99/13.27 (image1Ex1) =>
% 97.99/13.27 ((
% 97.99/13.27 (image1Equiv) =>
% 97.99/13.27 ((
% 97.99/13.27 (image1E) =>
% 97.99/13.27 ((
% 97.99/13.27 (image1I) =>
% 97.99/13.27 ((
% 97.99/13.27 (injFuncInInjFuncSet) =>
% 97.99/13.27 ((
% 97.99/13.27 (injFuncSetFuncIn) =>
% 97.99/13.27 ((
% 97.99/13.27 (injFuncSetFuncInj) =>
% 97.99/13.27 ((
% 97.99/13.27 (surjFuncSetFuncIn) =>
% 97.99/13.27 ((
% 97.99/13.27 (surjFuncSetFuncSurj) =>
% 97.99/13.27 ((
% 97.99/13.27 (leftInvIsSurj) =>
% 97.99/13.27 ((
% 97.99/13.27 (surjCantorThm) =>
% 97.99/13.27 ((
% 97.99/13.27 (foundation2) =>
% 97.99/13.27 ((
% 97.99/13.27 (notinself) =>
% 97.99/13.27 ((
% 97.99/13.27 (notinself2) =>
% 97.99/13.27 ((
% 97.99/13.27 (omegaSp) =>
% 97.99/13.27 ((
% 97.99/13.27 (omegaSclos) =>
% 97.99/13.27 ((
% 97.99/13.27 (peano0notS) =>
% 97.99/13.27 ((
% 97.99/13.27 (!!) @ (
% 97.99/13.27 (('#S') @ (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 =>) @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#C') @ in @
% 97.99/13.27 omega)))) @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 !!) @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 (
% 97.99/13.27 ('#S') @ (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 =>) @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#C') @ in @
% 97.99/13.27 omega)))))) @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#S') @ (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 '#S') @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 =>))) @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#C') @ (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 '#B') @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 =) @
% 97.99/13.27 omegaS)))) @
% 97.99/13.27 omegaS)))))) @
% 97.99/13.27 (
% 97.99/13.27 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.99/13.27 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1347])).
% 97.99/13.27 thf(zip_derived_cl1361, plain,
% 97.99/13.27 (~ (((symdiffIneg2) =>
% 97.99/13.27 (((secondinupair) =>
% 97.99/13.27 (((setukpairIL) =>
% 97.99/13.27 (((setukpairIR) =>
% 97.99/13.27 (((kpairiskpair) =>
% 97.99/13.27 (((kpairp) =>
% 97.99/13.27 (((singletonsubset) =>
% 97.99/13.27 (((singletoninpowerset) =>
% 97.99/13.27 (((singletoninpowunion) =>
% 97.99/13.27 (((upairset2E) =>
% 97.99/13.27 (((upairsubunion) =>
% 97.99/13.27 (((upairinpowunion) =>
% 97.99/13.27 (((ubforcartprodlem1) =>
% 97.99/13.27 (((ubforcartprodlem2) =>
% 97.99/13.27 (((ubforcartprodlem3) =>
% 97.99/13.27 (((cartprodpairin) =>
% 97.99/13.27 (((cartprodmempair1) =>
% 97.99/13.27 (((cartprodmempair) =>
% 97.99/13.27 (((setunionE2) =>
% 97.99/13.27 (((setunionsingleton1) =>
% 97.99/13.27 (((setunionsingleton2) =>
% 97.99/13.27 (((setunionsingleton) =>
% 97.99/13.27 (((singletonprop) =>
% 97.99/13.27 (((ex1E1) =>
% 97.99/13.27 (((ex1I) =>
% 97.99/13.27 (((ex1I2) =>
% 97.99/13.27 (((singletonsuniq) =>
% 97.99/13.27 (((setukpairinjL1) =>
% 97.99/13.27 (((kfstsingleton) =>
% 97.99/13.27 (((theprop) =>
% 97.99/13.27 ((
% 97.99/13.27 (kfstpairEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodfstin) =>
% 97.99/13.27 ((
% 97.99/13.27 (setukpairinjL2) =>
% 97.99/13.27 ((
% 97.99/13.27 (setukpairinjL) =>
% 97.99/13.27 ((
% 97.99/13.27 (setukpairinjR11) =>
% 97.99/13.27 ((
% 97.99/13.27 (setukpairinjR12) =>
% 97.99/13.27 ((
% 97.99/13.27 (setukpairinjR1) =>
% 97.99/13.27 ((
% 97.99/13.27 (upairequniteq) =>
% 97.99/13.27 ((
% 97.99/13.27 (setukpairinjR2) =>
% 97.99/13.27 ((
% 97.99/13.27 (setukpairinjR) =>
% 97.99/13.27 ((
% 97.99/13.27 (ksndsingleton) =>
% 97.99/13.27 ((
% 97.99/13.27 (ksndpairEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (kpairsurjEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodsndin) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodpairmemEL) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodpairmemER) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodmempaircEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodfstpairEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodsndpairEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodpairsurjEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (dpsetconstrI) =>
% 97.99/13.27 ((
% 97.99/13.27 (dpsetconstrSub) =>
% 97.99/13.27 ((
% 97.99/13.27 (setOfPairsIsBReln) =>
% 97.99/13.27 ((
% 97.99/13.27 (dpsetconstrERa) =>
% 97.99/13.27 ((
% 97.99/13.27 (dpsetconstrEL1) =>
% 97.99/13.27 ((
% 97.99/13.27 (dpsetconstrEL2) =>
% 97.99/13.27 ((
% 97.99/13.27 (dpsetconstrER) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcImageSingleton) =>
% 97.99/13.27 ((
% 97.99/13.27 (apProp) =>
% 97.99/13.27 ((
% 97.99/13.27 (app) =>
% 97.99/13.27 ((
% 97.99/13.27 (infuncsetfunc) =>
% 97.99/13.27 ((
% 97.99/13.27 (ap2p) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcinfuncset) =>
% 97.99/13.27 ((
% 97.99/13.27 (lamProp) =>
% 97.99/13.27 ((
% 97.99/13.27 (lamp) =>
% 97.99/13.27 ((
% 97.99/13.27 (lam2p) =>
% 97.99/13.27 ((
% 97.99/13.27 (brelnall1) =>
% 97.99/13.27 ((
% 97.99/13.27 (brelnall2) =>
% 97.99/13.27 ((
% 97.99/13.27 (ex1E2) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcGraphProp1) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcGraphProp3) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcGraphProp2) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcextLem) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcGraphProp4) =>
% 97.99/13.27 ((
% 97.99/13.27 (subbreln) =>
% 97.99/13.27 ((
% 97.99/13.27 (eqbreln) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcext) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcext2) =>
% 97.99/13.27 ((
% 97.99/13.27 (ap2apEq1) =>
% 97.99/13.27 ((
% 97.99/13.27 (ap2apEq2) =>
% 97.99/13.27 ((
% 97.99/13.27 (beta1) =>
% 97.99/13.27 ((
% 97.99/13.27 (eta1) =>
% 97.99/13.27 ((
% 97.99/13.27 (lam2lamEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (beta2) =>
% 97.99/13.27 ((
% 97.99/13.27 (eta2) =>
% 97.99/13.27 ((
% 97.99/13.27 (iffalseProp1) =>
% 97.99/13.27 ((
% 97.99/13.27 (iffalseProp2) =>
% 97.99/13.27 ((
% 97.99/13.27 (iftrueProp1) =>
% 97.99/13.27 ((
% 97.99/13.27 (iftrueProp2) =>
% 97.99/13.27 ((
% 97.99/13.27 (ifSingleton) =>
% 97.99/13.27 ((
% 97.99/13.27 (ifp) =>
% 97.99/13.27 ((
% 97.99/13.27 (theeq) =>
% 97.99/13.27 ((
% 97.99/13.27 (iftrue) =>
% 97.99/13.27 ((
% 97.99/13.27 (iffalse) =>
% 97.99/13.27 ((
% 97.99/13.27 (iftrueorfalse) =>
% 97.99/13.27 ((
% 97.99/13.27 (binintersectT_lem) =>
% 97.99/13.27 ((
% 97.99/13.27 (binunionT_lem) =>
% 97.99/13.27 ((
% 97.99/13.27 (powersetT_lem) =>
% 97.99/13.27 ((
% 97.99/13.27 (setminusT_lem) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementT_lem) =>
% 97.99/13.27 ((
% 97.99/13.27 (setextT) =>
% 97.99/13.27 ((
% 97.99/13.27 (subsetTI) =>
% 97.99/13.27 ((
% 97.99/13.27 (powersetTI1) =>
% 97.99/13.27 ((
% 97.99/13.27 (powersetTE1) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementTI1) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementTE1) =>
% 97.99/13.27 ((
% 97.99/13.27 (binintersectTELcontra) =>
% 97.99/13.27 ((
% 97.99/13.27 (binintersectTERcontra) =>
% 97.99/13.27 ((
% 97.99/13.27 (contrasubsetT) =>
% 97.99/13.27 ((
% 97.99/13.27 (contrasubsetT1) =>
% 97.99/13.27 ((
% 97.99/13.27 (contrasubsetT2) =>
% 97.99/13.27 ((
% 97.99/13.27 (contrasubsetT3) =>
% 97.99/13.27 ((
% 97.99/13.27 (doubleComplementI1) =>
% 97.99/13.27 ((
% 97.99/13.27 (doubleComplementE1) =>
% 97.99/13.27 ((
% 97.99/13.27 (doubleComplementSub1) =>
% 97.99/13.27 ((
% 97.99/13.27 (doubleComplementSub2) =>
% 97.99/13.27 ((
% 97.99/13.27 (doubleComplementEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementTnotintersectT) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementImpComplementIntersect) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementSubsetComplementIntersect) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementInPowersetComplementIntersect) =>
% 97.99/13.27 ((
% 97.99/13.27 (contraSubsetComplement) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementTcontraSubset) =>
% 97.99/13.27 ((
% 97.99/13.27 (binunionTILcontra) =>
% 97.99/13.27 ((
% 97.99/13.27 (binunionTIRcontra) =>
% 97.99/13.27 ((
% 97.99/13.27 (inIntersectImpInUnion) =>
% 97.99/13.27 ((
% 97.99/13.27 (inIntersectImpInUnion2) =>
% 97.99/13.27 ((
% 97.99/13.27 (inIntersectImpInIntersectUnions) =>
% 97.99/13.27 ((
% 97.99/13.27 (intersectInPowersetIntersectUnions) =>
% 97.99/13.27 ((
% 97.99/13.27 (inComplementUnionImpNotIn1) =>
% 97.99/13.27 ((
% 97.99/13.27 (inComplementUnionImpInComplement1) =>
% 97.99/13.27 ((
% 97.99/13.27 (binunionTE) =>
% 97.99/13.27 ((
% 97.99/13.27 (binunionTEcontra) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan2a1) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementUnionInPowersetComplement) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan2a2) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan1a) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan1b) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan1) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan2a) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan2b2) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan2b) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan2) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz13rule0) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz13rule1) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz13rule2) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz13rule3) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz13rule4) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz1_1) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz1_2) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz1_3) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz1_4) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz1_5) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1all2) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1SetBreln1) =>
% 97.99/13.27 ((
% 97.99/13.27 (choice2fnsingleton) =>
% 97.99/13.27 ((
% 97.99/13.27 (setOfPairsIsBReln1) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1all1) =>
% 97.99/13.27 ((
% 97.99/13.27 (subbreln1) =>
% 97.99/13.27 ((
% 97.99/13.27 (eqbreln1) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1invprop) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1invI) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1invE) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1compprop) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1compI) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1compE) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1compEex) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionprop) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionIL) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionIR) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionI) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionE) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionEcases) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionCommutes) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz2Ex) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz2W) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz2A) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz2B) =>
% 97.99/13.27 ((
% 97.99/13.27 (image1Ex) =>
% 97.99/13.27 ((
% 97.99/13.27 (image1Ex1) =>
% 97.99/13.27 ((
% 97.99/13.27 (image1Equiv) =>
% 97.99/13.27 ((
% 97.99/13.27 (image1E) =>
% 97.99/13.27 ((
% 97.99/13.27 (image1I) =>
% 97.99/13.27 ((
% 97.99/13.27 (injFuncInInjFuncSet) =>
% 97.99/13.27 ((
% 97.99/13.27 (injFuncSetFuncIn) =>
% 97.99/13.27 ((
% 97.99/13.27 (injFuncSetFuncInj) =>
% 97.99/13.27 ((
% 97.99/13.27 (surjFuncSetFuncIn) =>
% 97.99/13.27 ((
% 97.99/13.27 (surjFuncSetFuncSurj) =>
% 97.99/13.27 ((
% 97.99/13.27 (leftInvIsSurj) =>
% 97.99/13.27 ((
% 97.99/13.27 (surjCantorThm) =>
% 97.99/13.27 ((
% 97.99/13.27 (foundation2) =>
% 97.99/13.27 ((
% 97.99/13.27 (notinself) =>
% 97.99/13.27 ((
% 97.99/13.27 (notinself2) =>
% 97.99/13.27 ((
% 97.99/13.27 (omegaSp) =>
% 97.99/13.27 ((
% 97.99/13.27 (omegaSclos) =>
% 97.99/13.27 ((
% 97.99/13.27 (peano0notS) =>
% 97.99/13.27 ((
% 97.99/13.27 (!!) @ (
% 97.99/13.27 (('#S') @ (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 =>) @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#C') @ in @
% 97.99/13.27 omega)))) @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 !!) @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 (
% 97.99/13.27 ('#S') @ (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 =>) @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#C') @ in @
% 97.99/13.27 omega)))))) @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#S') @ (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 '#S') @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 =>))) @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#C') @ (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 '#B') @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 =) @
% 97.99/13.27 omegaS)))) @
% 97.99/13.27 omegaS)))))) @
% 97.99/13.27 (
% 97.99/13.27 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.99/13.27 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1354])).
% 97.99/13.27 thf(zip_derived_cl1369, plain,
% 97.99/13.27 (~ (((secondinupair) =>
% 97.99/13.27 (((setukpairIL) =>
% 97.99/13.27 (((setukpairIR) =>
% 97.99/13.27 (((kpairiskpair) =>
% 97.99/13.27 (((kpairp) =>
% 97.99/13.27 (((singletonsubset) =>
% 97.99/13.27 (((singletoninpowerset) =>
% 97.99/13.27 (((singletoninpowunion) =>
% 97.99/13.27 (((upairset2E) =>
% 97.99/13.27 (((upairsubunion) =>
% 97.99/13.27 (((upairinpowunion) =>
% 97.99/13.27 (((ubforcartprodlem1) =>
% 97.99/13.27 (((ubforcartprodlem2) =>
% 97.99/13.27 (((ubforcartprodlem3) =>
% 97.99/13.27 (((cartprodpairin) =>
% 97.99/13.27 (((cartprodmempair1) =>
% 97.99/13.27 (((cartprodmempair) =>
% 97.99/13.27 (((setunionE2) =>
% 97.99/13.27 (((setunionsingleton1) =>
% 97.99/13.27 (((setunionsingleton2) =>
% 97.99/13.27 (((setunionsingleton) =>
% 97.99/13.27 (((singletonprop) =>
% 97.99/13.27 (((ex1E1) =>
% 97.99/13.27 (((ex1I) =>
% 97.99/13.27 (((ex1I2) =>
% 97.99/13.27 (((singletonsuniq) =>
% 97.99/13.27 (((setukpairinjL1) =>
% 97.99/13.27 (((kfstsingleton) =>
% 97.99/13.27 (((theprop) =>
% 97.99/13.27 (((kfstpairEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodfstin) =>
% 97.99/13.27 ((
% 97.99/13.27 (setukpairinjL2) =>
% 97.99/13.27 ((
% 97.99/13.27 (setukpairinjL) =>
% 97.99/13.27 ((
% 97.99/13.27 (setukpairinjR11) =>
% 97.99/13.27 ((
% 97.99/13.27 (setukpairinjR12) =>
% 97.99/13.27 ((
% 97.99/13.27 (setukpairinjR1) =>
% 97.99/13.27 ((
% 97.99/13.27 (upairequniteq) =>
% 97.99/13.27 ((
% 97.99/13.27 (setukpairinjR2) =>
% 97.99/13.27 ((
% 97.99/13.27 (setukpairinjR) =>
% 97.99/13.27 ((
% 97.99/13.27 (ksndsingleton) =>
% 97.99/13.27 ((
% 97.99/13.27 (ksndpairEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (kpairsurjEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodsndin) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodpairmemEL) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodpairmemER) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodmempaircEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodfstpairEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodsndpairEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodpairsurjEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (dpsetconstrI) =>
% 97.99/13.27 ((
% 97.99/13.27 (dpsetconstrSub) =>
% 97.99/13.27 ((
% 97.99/13.27 (setOfPairsIsBReln) =>
% 97.99/13.27 ((
% 97.99/13.27 (dpsetconstrERa) =>
% 97.99/13.27 ((
% 97.99/13.27 (dpsetconstrEL1) =>
% 97.99/13.27 ((
% 97.99/13.27 (dpsetconstrEL2) =>
% 97.99/13.27 ((
% 97.99/13.27 (dpsetconstrER) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcImageSingleton) =>
% 97.99/13.27 ((
% 97.99/13.27 (apProp) =>
% 97.99/13.27 ((
% 97.99/13.27 (app) =>
% 97.99/13.27 ((
% 97.99/13.27 (infuncsetfunc) =>
% 97.99/13.27 ((
% 97.99/13.27 (ap2p) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcinfuncset) =>
% 97.99/13.27 ((
% 97.99/13.27 (lamProp) =>
% 97.99/13.27 ((
% 97.99/13.27 (lamp) =>
% 97.99/13.27 ((
% 97.99/13.27 (lam2p) =>
% 97.99/13.27 ((
% 97.99/13.27 (brelnall1) =>
% 97.99/13.27 ((
% 97.99/13.27 (brelnall2) =>
% 97.99/13.27 ((
% 97.99/13.27 (ex1E2) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcGraphProp1) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcGraphProp3) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcGraphProp2) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcextLem) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcGraphProp4) =>
% 97.99/13.27 ((
% 97.99/13.27 (subbreln) =>
% 97.99/13.27 ((
% 97.99/13.27 (eqbreln) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcext) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcext2) =>
% 97.99/13.27 ((
% 97.99/13.27 (ap2apEq1) =>
% 97.99/13.27 ((
% 97.99/13.27 (ap2apEq2) =>
% 97.99/13.27 ((
% 97.99/13.27 (beta1) =>
% 97.99/13.27 ((
% 97.99/13.27 (eta1) =>
% 97.99/13.27 ((
% 97.99/13.27 (lam2lamEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (beta2) =>
% 97.99/13.27 ((
% 97.99/13.27 (eta2) =>
% 97.99/13.27 ((
% 97.99/13.27 (iffalseProp1) =>
% 97.99/13.27 ((
% 97.99/13.27 (iffalseProp2) =>
% 97.99/13.27 ((
% 97.99/13.27 (iftrueProp1) =>
% 97.99/13.27 ((
% 97.99/13.27 (iftrueProp2) =>
% 97.99/13.27 ((
% 97.99/13.27 (ifSingleton) =>
% 97.99/13.27 ((
% 97.99/13.27 (ifp) =>
% 97.99/13.27 ((
% 97.99/13.27 (theeq) =>
% 97.99/13.27 ((
% 97.99/13.27 (iftrue) =>
% 97.99/13.27 ((
% 97.99/13.27 (iffalse) =>
% 97.99/13.27 ((
% 97.99/13.27 (iftrueorfalse) =>
% 97.99/13.27 ((
% 97.99/13.27 (binintersectT_lem) =>
% 97.99/13.27 ((
% 97.99/13.27 (binunionT_lem) =>
% 97.99/13.27 ((
% 97.99/13.27 (powersetT_lem) =>
% 97.99/13.27 ((
% 97.99/13.27 (setminusT_lem) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementT_lem) =>
% 97.99/13.27 ((
% 97.99/13.27 (setextT) =>
% 97.99/13.27 ((
% 97.99/13.27 (subsetTI) =>
% 97.99/13.27 ((
% 97.99/13.27 (powersetTI1) =>
% 97.99/13.27 ((
% 97.99/13.27 (powersetTE1) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementTI1) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementTE1) =>
% 97.99/13.27 ((
% 97.99/13.27 (binintersectTELcontra) =>
% 97.99/13.27 ((
% 97.99/13.27 (binintersectTERcontra) =>
% 97.99/13.27 ((
% 97.99/13.27 (contrasubsetT) =>
% 97.99/13.27 ((
% 97.99/13.27 (contrasubsetT1) =>
% 97.99/13.27 ((
% 97.99/13.27 (contrasubsetT2) =>
% 97.99/13.27 ((
% 97.99/13.27 (contrasubsetT3) =>
% 97.99/13.27 ((
% 97.99/13.27 (doubleComplementI1) =>
% 97.99/13.27 ((
% 97.99/13.27 (doubleComplementE1) =>
% 97.99/13.27 ((
% 97.99/13.27 (doubleComplementSub1) =>
% 97.99/13.27 ((
% 97.99/13.27 (doubleComplementSub2) =>
% 97.99/13.27 ((
% 97.99/13.27 (doubleComplementEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementTnotintersectT) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementImpComplementIntersect) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementSubsetComplementIntersect) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementInPowersetComplementIntersect) =>
% 97.99/13.27 ((
% 97.99/13.27 (contraSubsetComplement) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementTcontraSubset) =>
% 97.99/13.27 ((
% 97.99/13.27 (binunionTILcontra) =>
% 97.99/13.27 ((
% 97.99/13.27 (binunionTIRcontra) =>
% 97.99/13.27 ((
% 97.99/13.27 (inIntersectImpInUnion) =>
% 97.99/13.27 ((
% 97.99/13.27 (inIntersectImpInUnion2) =>
% 97.99/13.27 ((
% 97.99/13.27 (inIntersectImpInIntersectUnions) =>
% 97.99/13.27 ((
% 97.99/13.27 (intersectInPowersetIntersectUnions) =>
% 97.99/13.27 ((
% 97.99/13.27 (inComplementUnionImpNotIn1) =>
% 97.99/13.27 ((
% 97.99/13.27 (inComplementUnionImpInComplement1) =>
% 97.99/13.27 ((
% 97.99/13.27 (binunionTE) =>
% 97.99/13.27 ((
% 97.99/13.27 (binunionTEcontra) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan2a1) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementUnionInPowersetComplement) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan2a2) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan1a) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan1b) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan1) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan2a) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan2b2) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan2b) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan2) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz13rule0) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz13rule1) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz13rule2) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz13rule3) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz13rule4) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz1_1) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz1_2) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz1_3) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz1_4) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz1_5) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1all2) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1SetBreln1) =>
% 97.99/13.27 ((
% 97.99/13.27 (choice2fnsingleton) =>
% 97.99/13.27 ((
% 97.99/13.27 (setOfPairsIsBReln1) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1all1) =>
% 97.99/13.27 ((
% 97.99/13.27 (subbreln1) =>
% 97.99/13.27 ((
% 97.99/13.27 (eqbreln1) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1invprop) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1invI) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1invE) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1compprop) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1compI) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1compE) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1compEex) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionprop) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionIL) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionIR) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionI) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionE) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionEcases) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionCommutes) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz2Ex) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz2W) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz2A) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz2B) =>
% 97.99/13.27 ((
% 97.99/13.27 (image1Ex) =>
% 97.99/13.27 ((
% 97.99/13.27 (image1Ex1) =>
% 97.99/13.27 ((
% 97.99/13.27 (image1Equiv) =>
% 97.99/13.27 ((
% 97.99/13.27 (image1E) =>
% 97.99/13.27 ((
% 97.99/13.27 (image1I) =>
% 97.99/13.27 ((
% 97.99/13.27 (injFuncInInjFuncSet) =>
% 97.99/13.27 ((
% 97.99/13.27 (injFuncSetFuncIn) =>
% 97.99/13.27 ((
% 97.99/13.27 (injFuncSetFuncInj) =>
% 97.99/13.27 ((
% 97.99/13.27 (surjFuncSetFuncIn) =>
% 97.99/13.27 ((
% 97.99/13.27 (surjFuncSetFuncSurj) =>
% 97.99/13.27 ((
% 97.99/13.27 (leftInvIsSurj) =>
% 97.99/13.27 ((
% 97.99/13.27 (surjCantorThm) =>
% 97.99/13.27 ((
% 97.99/13.27 (foundation2) =>
% 97.99/13.27 ((
% 97.99/13.27 (notinself) =>
% 97.99/13.27 ((
% 97.99/13.27 (notinself2) =>
% 97.99/13.27 ((
% 97.99/13.27 (omegaSp) =>
% 97.99/13.27 ((
% 97.99/13.27 (omegaSclos) =>
% 97.99/13.27 ((
% 97.99/13.27 (peano0notS) =>
% 97.99/13.27 ((
% 97.99/13.27 (!!) @ (
% 97.99/13.27 (('#S') @ (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 =>) @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#C') @ in @
% 97.99/13.27 omega)))) @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 !!) @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 (
% 97.99/13.27 ('#S') @ (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 =>) @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#C') @ in @
% 97.99/13.27 omega)))))) @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#S') @ (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 '#S') @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 =>))) @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#C') @ (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 '#B') @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 =) @
% 97.99/13.27 omegaS)))) @
% 97.99/13.27 omegaS)))))) @
% 97.99/13.27 (
% 97.99/13.27 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.99/13.27 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1361])).
% 97.99/13.27 thf(zip_derived_cl1377, plain,
% 97.99/13.27 (~ (((setukpairIL) =>
% 97.99/13.27 (((setukpairIR) =>
% 97.99/13.27 (((kpairiskpair) =>
% 97.99/13.27 (((kpairp) =>
% 97.99/13.27 (((singletonsubset) =>
% 97.99/13.27 (((singletoninpowerset) =>
% 97.99/13.27 (((singletoninpowunion) =>
% 97.99/13.27 (((upairset2E) =>
% 97.99/13.27 (((upairsubunion) =>
% 97.99/13.27 (((upairinpowunion) =>
% 97.99/13.27 (((ubforcartprodlem1) =>
% 97.99/13.27 (((ubforcartprodlem2) =>
% 97.99/13.27 (((ubforcartprodlem3) =>
% 97.99/13.27 (((cartprodpairin) =>
% 97.99/13.27 (((cartprodmempair1) =>
% 97.99/13.27 (((cartprodmempair) =>
% 97.99/13.27 (((setunionE2) =>
% 97.99/13.27 (((setunionsingleton1) =>
% 97.99/13.27 (((setunionsingleton2) =>
% 97.99/13.27 (((setunionsingleton) =>
% 97.99/13.27 (((singletonprop) =>
% 97.99/13.27 (((ex1E1) =>
% 97.99/13.27 (((ex1I) =>
% 97.99/13.27 (((ex1I2) =>
% 97.99/13.27 (((singletonsuniq) =>
% 97.99/13.27 (((setukpairinjL1) =>
% 97.99/13.27 (((kfstsingleton) =>
% 97.99/13.27 (((theprop) =>
% 97.99/13.27 (((kfstpairEq) =>
% 97.99/13.27 (((cartprodfstin) =>
% 97.99/13.27 ((
% 97.99/13.27 (setukpairinjL2) =>
% 97.99/13.27 ((
% 97.99/13.27 (setukpairinjL) =>
% 97.99/13.27 ((
% 97.99/13.27 (setukpairinjR11) =>
% 97.99/13.27 ((
% 97.99/13.27 (setukpairinjR12) =>
% 97.99/13.27 ((
% 97.99/13.27 (setukpairinjR1) =>
% 97.99/13.27 ((
% 97.99/13.27 (upairequniteq) =>
% 97.99/13.27 ((
% 97.99/13.27 (setukpairinjR2) =>
% 97.99/13.27 ((
% 97.99/13.27 (setukpairinjR) =>
% 97.99/13.27 ((
% 97.99/13.27 (ksndsingleton) =>
% 97.99/13.27 ((
% 97.99/13.27 (ksndpairEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (kpairsurjEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodsndin) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodpairmemEL) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodpairmemER) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodmempaircEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodfstpairEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodsndpairEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodpairsurjEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (dpsetconstrI) =>
% 97.99/13.27 ((
% 97.99/13.27 (dpsetconstrSub) =>
% 97.99/13.27 ((
% 97.99/13.27 (setOfPairsIsBReln) =>
% 97.99/13.27 ((
% 97.99/13.27 (dpsetconstrERa) =>
% 97.99/13.27 ((
% 97.99/13.27 (dpsetconstrEL1) =>
% 97.99/13.27 ((
% 97.99/13.27 (dpsetconstrEL2) =>
% 97.99/13.27 ((
% 97.99/13.27 (dpsetconstrER) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcImageSingleton) =>
% 97.99/13.27 ((
% 97.99/13.27 (apProp) =>
% 97.99/13.27 ((
% 97.99/13.27 (app) =>
% 97.99/13.27 ((
% 97.99/13.27 (infuncsetfunc) =>
% 97.99/13.27 ((
% 97.99/13.27 (ap2p) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcinfuncset) =>
% 97.99/13.27 ((
% 97.99/13.27 (lamProp) =>
% 97.99/13.27 ((
% 97.99/13.27 (lamp) =>
% 97.99/13.27 ((
% 97.99/13.27 (lam2p) =>
% 97.99/13.27 ((
% 97.99/13.27 (brelnall1) =>
% 97.99/13.27 ((
% 97.99/13.27 (brelnall2) =>
% 97.99/13.27 ((
% 97.99/13.27 (ex1E2) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcGraphProp1) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcGraphProp3) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcGraphProp2) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcextLem) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcGraphProp4) =>
% 97.99/13.27 ((
% 97.99/13.27 (subbreln) =>
% 97.99/13.27 ((
% 97.99/13.27 (eqbreln) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcext) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcext2) =>
% 97.99/13.27 ((
% 97.99/13.27 (ap2apEq1) =>
% 97.99/13.27 ((
% 97.99/13.27 (ap2apEq2) =>
% 97.99/13.27 ((
% 97.99/13.27 (beta1) =>
% 97.99/13.27 ((
% 97.99/13.27 (eta1) =>
% 97.99/13.27 ((
% 97.99/13.27 (lam2lamEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (beta2) =>
% 97.99/13.27 ((
% 97.99/13.27 (eta2) =>
% 97.99/13.27 ((
% 97.99/13.27 (iffalseProp1) =>
% 97.99/13.27 ((
% 97.99/13.27 (iffalseProp2) =>
% 97.99/13.27 ((
% 97.99/13.27 (iftrueProp1) =>
% 97.99/13.27 ((
% 97.99/13.27 (iftrueProp2) =>
% 97.99/13.27 ((
% 97.99/13.27 (ifSingleton) =>
% 97.99/13.27 ((
% 97.99/13.27 (ifp) =>
% 97.99/13.27 ((
% 97.99/13.27 (theeq) =>
% 97.99/13.27 ((
% 97.99/13.27 (iftrue) =>
% 97.99/13.27 ((
% 97.99/13.27 (iffalse) =>
% 97.99/13.27 ((
% 97.99/13.27 (iftrueorfalse) =>
% 97.99/13.27 ((
% 97.99/13.27 (binintersectT_lem) =>
% 97.99/13.27 ((
% 97.99/13.27 (binunionT_lem) =>
% 97.99/13.27 ((
% 97.99/13.27 (powersetT_lem) =>
% 97.99/13.27 ((
% 97.99/13.27 (setminusT_lem) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementT_lem) =>
% 97.99/13.27 ((
% 97.99/13.27 (setextT) =>
% 97.99/13.27 ((
% 97.99/13.27 (subsetTI) =>
% 97.99/13.27 ((
% 97.99/13.27 (powersetTI1) =>
% 97.99/13.27 ((
% 97.99/13.27 (powersetTE1) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementTI1) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementTE1) =>
% 97.99/13.27 ((
% 97.99/13.27 (binintersectTELcontra) =>
% 97.99/13.27 ((
% 97.99/13.27 (binintersectTERcontra) =>
% 97.99/13.27 ((
% 97.99/13.27 (contrasubsetT) =>
% 97.99/13.27 ((
% 97.99/13.27 (contrasubsetT1) =>
% 97.99/13.27 ((
% 97.99/13.27 (contrasubsetT2) =>
% 97.99/13.27 ((
% 97.99/13.27 (contrasubsetT3) =>
% 97.99/13.27 ((
% 97.99/13.27 (doubleComplementI1) =>
% 97.99/13.27 ((
% 97.99/13.27 (doubleComplementE1) =>
% 97.99/13.27 ((
% 97.99/13.27 (doubleComplementSub1) =>
% 97.99/13.27 ((
% 97.99/13.27 (doubleComplementSub2) =>
% 97.99/13.27 ((
% 97.99/13.27 (doubleComplementEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementTnotintersectT) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementImpComplementIntersect) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementSubsetComplementIntersect) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementInPowersetComplementIntersect) =>
% 97.99/13.27 ((
% 97.99/13.27 (contraSubsetComplement) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementTcontraSubset) =>
% 97.99/13.27 ((
% 97.99/13.27 (binunionTILcontra) =>
% 97.99/13.27 ((
% 97.99/13.27 (binunionTIRcontra) =>
% 97.99/13.27 ((
% 97.99/13.27 (inIntersectImpInUnion) =>
% 97.99/13.27 ((
% 97.99/13.27 (inIntersectImpInUnion2) =>
% 97.99/13.27 ((
% 97.99/13.27 (inIntersectImpInIntersectUnions) =>
% 97.99/13.27 ((
% 97.99/13.27 (intersectInPowersetIntersectUnions) =>
% 97.99/13.27 ((
% 97.99/13.27 (inComplementUnionImpNotIn1) =>
% 97.99/13.27 ((
% 97.99/13.27 (inComplementUnionImpInComplement1) =>
% 97.99/13.27 ((
% 97.99/13.27 (binunionTE) =>
% 97.99/13.27 ((
% 97.99/13.27 (binunionTEcontra) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan2a1) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementUnionInPowersetComplement) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan2a2) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan1a) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan1b) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan1) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan2a) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan2b2) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan2b) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan2) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz13rule0) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz13rule1) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz13rule2) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz13rule3) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz13rule4) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz1_1) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz1_2) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz1_3) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz1_4) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz1_5) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1all2) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1SetBreln1) =>
% 97.99/13.27 ((
% 97.99/13.27 (choice2fnsingleton) =>
% 97.99/13.27 ((
% 97.99/13.27 (setOfPairsIsBReln1) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1all1) =>
% 97.99/13.27 ((
% 97.99/13.27 (subbreln1) =>
% 97.99/13.27 ((
% 97.99/13.27 (eqbreln1) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1invprop) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1invI) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1invE) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1compprop) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1compI) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1compE) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1compEex) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionprop) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionIL) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionIR) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionI) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionE) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionEcases) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionCommutes) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz2Ex) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz2W) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz2A) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz2B) =>
% 97.99/13.27 ((
% 97.99/13.27 (image1Ex) =>
% 97.99/13.27 ((
% 97.99/13.27 (image1Ex1) =>
% 97.99/13.27 ((
% 97.99/13.27 (image1Equiv) =>
% 97.99/13.27 ((
% 97.99/13.27 (image1E) =>
% 97.99/13.27 ((
% 97.99/13.27 (image1I) =>
% 97.99/13.27 ((
% 97.99/13.27 (injFuncInInjFuncSet) =>
% 97.99/13.27 ((
% 97.99/13.27 (injFuncSetFuncIn) =>
% 97.99/13.27 ((
% 97.99/13.27 (injFuncSetFuncInj) =>
% 97.99/13.27 ((
% 97.99/13.27 (surjFuncSetFuncIn) =>
% 97.99/13.27 ((
% 97.99/13.27 (surjFuncSetFuncSurj) =>
% 97.99/13.27 ((
% 97.99/13.27 (leftInvIsSurj) =>
% 97.99/13.27 ((
% 97.99/13.27 (surjCantorThm) =>
% 97.99/13.27 ((
% 97.99/13.27 (foundation2) =>
% 97.99/13.27 ((
% 97.99/13.27 (notinself) =>
% 97.99/13.27 ((
% 97.99/13.27 (notinself2) =>
% 97.99/13.27 ((
% 97.99/13.27 (omegaSp) =>
% 97.99/13.27 ((
% 97.99/13.27 (omegaSclos) =>
% 97.99/13.27 ((
% 97.99/13.27 (peano0notS) =>
% 97.99/13.27 ((
% 97.99/13.27 (!!) @ (
% 97.99/13.27 (('#S') @ (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 =>) @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#C') @ in @
% 97.99/13.27 omega)))) @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 !!) @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 (
% 97.99/13.27 ('#S') @ (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 =>) @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#C') @ in @
% 97.99/13.27 omega)))))) @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#S') @ (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 '#S') @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 =>))) @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#C') @ (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 '#B') @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 =) @
% 97.99/13.27 omegaS)))) @
% 97.99/13.27 omegaS)))))) @
% 97.99/13.27 (
% 97.99/13.27 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.99/13.27 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1369])).
% 97.99/13.27 thf(zip_derived_cl1386, plain,
% 97.99/13.27 (~ (((setukpairIR) =>
% 97.99/13.27 (((kpairiskpair) =>
% 97.99/13.27 (((kpairp) =>
% 97.99/13.27 (((singletonsubset) =>
% 97.99/13.27 (((singletoninpowerset) =>
% 97.99/13.27 (((singletoninpowunion) =>
% 97.99/13.27 (((upairset2E) =>
% 97.99/13.27 (((upairsubunion) =>
% 97.99/13.27 (((upairinpowunion) =>
% 97.99/13.27 (((ubforcartprodlem1) =>
% 97.99/13.27 (((ubforcartprodlem2) =>
% 97.99/13.27 (((ubforcartprodlem3) =>
% 97.99/13.27 (((cartprodpairin) =>
% 97.99/13.27 (((cartprodmempair1) =>
% 97.99/13.27 (((cartprodmempair) =>
% 97.99/13.27 (((setunionE2) =>
% 97.99/13.27 (((setunionsingleton1) =>
% 97.99/13.27 (((setunionsingleton2) =>
% 97.99/13.27 (((setunionsingleton) =>
% 97.99/13.27 (((singletonprop) =>
% 97.99/13.27 (((ex1E1) =>
% 97.99/13.27 (((ex1I) =>
% 97.99/13.27 (((ex1I2) =>
% 97.99/13.27 (((singletonsuniq) =>
% 97.99/13.27 (((setukpairinjL1) =>
% 97.99/13.27 (((kfstsingleton) =>
% 97.99/13.27 (((theprop) =>
% 97.99/13.27 (((kfstpairEq) =>
% 97.99/13.27 (((cartprodfstin) =>
% 97.99/13.27 (((setukpairinjL2) =>
% 97.99/13.27 ((
% 97.99/13.27 (setukpairinjL) =>
% 97.99/13.27 ((
% 97.99/13.27 (setukpairinjR11) =>
% 97.99/13.27 ((
% 97.99/13.27 (setukpairinjR12) =>
% 97.99/13.27 ((
% 97.99/13.27 (setukpairinjR1) =>
% 97.99/13.27 ((
% 97.99/13.27 (upairequniteq) =>
% 97.99/13.27 ((
% 97.99/13.27 (setukpairinjR2) =>
% 97.99/13.27 ((
% 97.99/13.27 (setukpairinjR) =>
% 97.99/13.27 ((
% 97.99/13.27 (ksndsingleton) =>
% 97.99/13.27 ((
% 97.99/13.27 (ksndpairEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (kpairsurjEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodsndin) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodpairmemEL) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodpairmemER) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodmempaircEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodfstpairEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodsndpairEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodpairsurjEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (dpsetconstrI) =>
% 97.99/13.27 ((
% 97.99/13.27 (dpsetconstrSub) =>
% 97.99/13.27 ((
% 97.99/13.27 (setOfPairsIsBReln) =>
% 97.99/13.27 ((
% 97.99/13.27 (dpsetconstrERa) =>
% 97.99/13.27 ((
% 97.99/13.27 (dpsetconstrEL1) =>
% 97.99/13.27 ((
% 97.99/13.27 (dpsetconstrEL2) =>
% 97.99/13.27 ((
% 97.99/13.27 (dpsetconstrER) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcImageSingleton) =>
% 97.99/13.27 ((
% 97.99/13.27 (apProp) =>
% 97.99/13.27 ((
% 97.99/13.27 (app) =>
% 97.99/13.27 ((
% 97.99/13.27 (infuncsetfunc) =>
% 97.99/13.27 ((
% 97.99/13.27 (ap2p) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcinfuncset) =>
% 97.99/13.27 ((
% 97.99/13.27 (lamProp) =>
% 97.99/13.27 ((
% 97.99/13.27 (lamp) =>
% 97.99/13.27 ((
% 97.99/13.27 (lam2p) =>
% 97.99/13.27 ((
% 97.99/13.27 (brelnall1) =>
% 97.99/13.27 ((
% 97.99/13.27 (brelnall2) =>
% 97.99/13.27 ((
% 97.99/13.27 (ex1E2) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcGraphProp1) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcGraphProp3) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcGraphProp2) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcextLem) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcGraphProp4) =>
% 97.99/13.27 ((
% 97.99/13.27 (subbreln) =>
% 97.99/13.27 ((
% 97.99/13.27 (eqbreln) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcext) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcext2) =>
% 97.99/13.27 ((
% 97.99/13.27 (ap2apEq1) =>
% 97.99/13.27 ((
% 97.99/13.27 (ap2apEq2) =>
% 97.99/13.27 ((
% 97.99/13.27 (beta1) =>
% 97.99/13.27 ((
% 97.99/13.27 (eta1) =>
% 97.99/13.27 ((
% 97.99/13.27 (lam2lamEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (beta2) =>
% 97.99/13.27 ((
% 97.99/13.27 (eta2) =>
% 97.99/13.27 ((
% 97.99/13.27 (iffalseProp1) =>
% 97.99/13.27 ((
% 97.99/13.27 (iffalseProp2) =>
% 97.99/13.27 ((
% 97.99/13.27 (iftrueProp1) =>
% 97.99/13.27 ((
% 97.99/13.27 (iftrueProp2) =>
% 97.99/13.27 ((
% 97.99/13.27 (ifSingleton) =>
% 97.99/13.27 ((
% 97.99/13.27 (ifp) =>
% 97.99/13.27 ((
% 97.99/13.27 (theeq) =>
% 97.99/13.27 ((
% 97.99/13.27 (iftrue) =>
% 97.99/13.27 ((
% 97.99/13.27 (iffalse) =>
% 97.99/13.27 ((
% 97.99/13.27 (iftrueorfalse) =>
% 97.99/13.27 ((
% 97.99/13.27 (binintersectT_lem) =>
% 97.99/13.27 ((
% 97.99/13.27 (binunionT_lem) =>
% 97.99/13.27 ((
% 97.99/13.27 (powersetT_lem) =>
% 97.99/13.27 ((
% 97.99/13.27 (setminusT_lem) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementT_lem) =>
% 97.99/13.27 ((
% 97.99/13.27 (setextT) =>
% 97.99/13.27 ((
% 97.99/13.27 (subsetTI) =>
% 97.99/13.27 ((
% 97.99/13.27 (powersetTI1) =>
% 97.99/13.27 ((
% 97.99/13.27 (powersetTE1) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementTI1) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementTE1) =>
% 97.99/13.27 ((
% 97.99/13.27 (binintersectTELcontra) =>
% 97.99/13.27 ((
% 97.99/13.27 (binintersectTERcontra) =>
% 97.99/13.27 ((
% 97.99/13.27 (contrasubsetT) =>
% 97.99/13.27 ((
% 97.99/13.27 (contrasubsetT1) =>
% 97.99/13.27 ((
% 97.99/13.27 (contrasubsetT2) =>
% 97.99/13.27 ((
% 97.99/13.27 (contrasubsetT3) =>
% 97.99/13.27 ((
% 97.99/13.27 (doubleComplementI1) =>
% 97.99/13.27 ((
% 97.99/13.27 (doubleComplementE1) =>
% 97.99/13.27 ((
% 97.99/13.27 (doubleComplementSub1) =>
% 97.99/13.27 ((
% 97.99/13.27 (doubleComplementSub2) =>
% 97.99/13.27 ((
% 97.99/13.27 (doubleComplementEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementTnotintersectT) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementImpComplementIntersect) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementSubsetComplementIntersect) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementInPowersetComplementIntersect) =>
% 97.99/13.27 ((
% 97.99/13.27 (contraSubsetComplement) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementTcontraSubset) =>
% 97.99/13.27 ((
% 97.99/13.27 (binunionTILcontra) =>
% 97.99/13.27 ((
% 97.99/13.27 (binunionTIRcontra) =>
% 97.99/13.27 ((
% 97.99/13.27 (inIntersectImpInUnion) =>
% 97.99/13.27 ((
% 97.99/13.27 (inIntersectImpInUnion2) =>
% 97.99/13.27 ((
% 97.99/13.27 (inIntersectImpInIntersectUnions) =>
% 97.99/13.27 ((
% 97.99/13.27 (intersectInPowersetIntersectUnions) =>
% 97.99/13.27 ((
% 97.99/13.27 (inComplementUnionImpNotIn1) =>
% 97.99/13.27 ((
% 97.99/13.27 (inComplementUnionImpInComplement1) =>
% 97.99/13.27 ((
% 97.99/13.27 (binunionTE) =>
% 97.99/13.27 ((
% 97.99/13.27 (binunionTEcontra) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan2a1) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementUnionInPowersetComplement) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan2a2) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan1a) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan1b) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan1) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan2a) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan2b2) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan2b) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan2) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz13rule0) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz13rule1) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz13rule2) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz13rule3) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz13rule4) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz1_1) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz1_2) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz1_3) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz1_4) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz1_5) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1all2) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1SetBreln1) =>
% 97.99/13.27 ((
% 97.99/13.27 (choice2fnsingleton) =>
% 97.99/13.27 ((
% 97.99/13.27 (setOfPairsIsBReln1) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1all1) =>
% 97.99/13.27 ((
% 97.99/13.27 (subbreln1) =>
% 97.99/13.27 ((
% 97.99/13.27 (eqbreln1) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1invprop) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1invI) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1invE) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1compprop) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1compI) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1compE) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1compEex) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionprop) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionIL) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionIR) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionI) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionE) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionEcases) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionCommutes) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz2Ex) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz2W) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz2A) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz2B) =>
% 97.99/13.27 ((
% 97.99/13.27 (image1Ex) =>
% 97.99/13.27 ((
% 97.99/13.27 (image1Ex1) =>
% 97.99/13.27 ((
% 97.99/13.27 (image1Equiv) =>
% 97.99/13.27 ((
% 97.99/13.27 (image1E) =>
% 97.99/13.27 ((
% 97.99/13.27 (image1I) =>
% 97.99/13.27 ((
% 97.99/13.27 (injFuncInInjFuncSet) =>
% 97.99/13.27 ((
% 97.99/13.27 (injFuncSetFuncIn) =>
% 97.99/13.27 ((
% 97.99/13.27 (injFuncSetFuncInj) =>
% 97.99/13.27 ((
% 97.99/13.27 (surjFuncSetFuncIn) =>
% 97.99/13.27 ((
% 97.99/13.27 (surjFuncSetFuncSurj) =>
% 97.99/13.27 ((
% 97.99/13.27 (leftInvIsSurj) =>
% 97.99/13.27 ((
% 97.99/13.27 (surjCantorThm) =>
% 97.99/13.27 ((
% 97.99/13.27 (foundation2) =>
% 97.99/13.27 ((
% 97.99/13.27 (notinself) =>
% 97.99/13.27 ((
% 97.99/13.27 (notinself2) =>
% 97.99/13.27 ((
% 97.99/13.27 (omegaSp) =>
% 97.99/13.27 ((
% 97.99/13.27 (omegaSclos) =>
% 97.99/13.27 ((
% 97.99/13.27 (peano0notS) =>
% 97.99/13.27 ((
% 97.99/13.27 (!!) @ (
% 97.99/13.27 (('#S') @ (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 =>) @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#C') @ in @
% 97.99/13.27 omega)))) @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 !!) @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 (
% 97.99/13.27 ('#S') @ (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 =>) @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#C') @ in @
% 97.99/13.27 omega)))))) @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#S') @ (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 '#S') @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 =>))) @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#C') @ (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 '#B') @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 =) @
% 97.99/13.27 omegaS)))) @
% 97.99/13.27 omegaS)))))) @
% 97.99/13.27 (
% 97.99/13.27 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.99/13.27 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1377])).
% 97.99/13.27 thf(zip_derived_cl1396, plain,
% 97.99/13.27 (~ (((kpairiskpair) =>
% 97.99/13.27 (((kpairp) =>
% 97.99/13.27 (((singletonsubset) =>
% 97.99/13.27 (((singletoninpowerset) =>
% 97.99/13.27 (((singletoninpowunion) =>
% 97.99/13.27 (((upairset2E) =>
% 97.99/13.27 (((upairsubunion) =>
% 97.99/13.27 (((upairinpowunion) =>
% 97.99/13.27 (((ubforcartprodlem1) =>
% 97.99/13.27 (((ubforcartprodlem2) =>
% 97.99/13.27 (((ubforcartprodlem3) =>
% 97.99/13.27 (((cartprodpairin) =>
% 97.99/13.27 (((cartprodmempair1) =>
% 97.99/13.27 (((cartprodmempair) =>
% 97.99/13.27 (((setunionE2) =>
% 97.99/13.27 (((setunionsingleton1) =>
% 97.99/13.27 (((setunionsingleton2) =>
% 97.99/13.27 (((setunionsingleton) =>
% 97.99/13.27 (((singletonprop) =>
% 97.99/13.27 (((ex1E1) =>
% 97.99/13.27 (((ex1I) =>
% 97.99/13.27 (((ex1I2) =>
% 97.99/13.27 (((singletonsuniq) =>
% 97.99/13.27 (((setukpairinjL1) =>
% 97.99/13.27 (((kfstsingleton) =>
% 97.99/13.27 (((theprop) =>
% 97.99/13.27 (((kfstpairEq) =>
% 97.99/13.27 (((cartprodfstin) =>
% 97.99/13.27 (((setukpairinjL2) =>
% 97.99/13.27 (((setukpairinjL) =>
% 97.99/13.27 ((
% 97.99/13.27 (setukpairinjR11) =>
% 97.99/13.27 ((
% 97.99/13.27 (setukpairinjR12) =>
% 97.99/13.27 ((
% 97.99/13.27 (setukpairinjR1) =>
% 97.99/13.27 ((
% 97.99/13.27 (upairequniteq) =>
% 97.99/13.27 ((
% 97.99/13.27 (setukpairinjR2) =>
% 97.99/13.27 ((
% 97.99/13.27 (setukpairinjR) =>
% 97.99/13.27 ((
% 97.99/13.27 (ksndsingleton) =>
% 97.99/13.27 ((
% 97.99/13.27 (ksndpairEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (kpairsurjEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodsndin) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodpairmemEL) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodpairmemER) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodmempaircEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodfstpairEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodsndpairEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodpairsurjEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (dpsetconstrI) =>
% 97.99/13.27 ((
% 97.99/13.27 (dpsetconstrSub) =>
% 97.99/13.27 ((
% 97.99/13.27 (setOfPairsIsBReln) =>
% 97.99/13.27 ((
% 97.99/13.27 (dpsetconstrERa) =>
% 97.99/13.27 ((
% 97.99/13.27 (dpsetconstrEL1) =>
% 97.99/13.27 ((
% 97.99/13.27 (dpsetconstrEL2) =>
% 97.99/13.27 ((
% 97.99/13.27 (dpsetconstrER) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcImageSingleton) =>
% 97.99/13.27 ((
% 97.99/13.27 (apProp) =>
% 97.99/13.27 ((
% 97.99/13.27 (app) =>
% 97.99/13.27 ((
% 97.99/13.27 (infuncsetfunc) =>
% 97.99/13.27 ((
% 97.99/13.27 (ap2p) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcinfuncset) =>
% 97.99/13.27 ((
% 97.99/13.27 (lamProp) =>
% 97.99/13.27 ((
% 97.99/13.27 (lamp) =>
% 97.99/13.27 ((
% 97.99/13.27 (lam2p) =>
% 97.99/13.27 ((
% 97.99/13.27 (brelnall1) =>
% 97.99/13.27 ((
% 97.99/13.27 (brelnall2) =>
% 97.99/13.27 ((
% 97.99/13.27 (ex1E2) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcGraphProp1) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcGraphProp3) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcGraphProp2) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcextLem) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcGraphProp4) =>
% 97.99/13.27 ((
% 97.99/13.27 (subbreln) =>
% 97.99/13.27 ((
% 97.99/13.27 (eqbreln) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcext) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcext2) =>
% 97.99/13.27 ((
% 97.99/13.27 (ap2apEq1) =>
% 97.99/13.27 ((
% 97.99/13.27 (ap2apEq2) =>
% 97.99/13.27 ((
% 97.99/13.27 (beta1) =>
% 97.99/13.27 ((
% 97.99/13.27 (eta1) =>
% 97.99/13.27 ((
% 97.99/13.27 (lam2lamEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (beta2) =>
% 97.99/13.27 ((
% 97.99/13.27 (eta2) =>
% 97.99/13.27 ((
% 97.99/13.27 (iffalseProp1) =>
% 97.99/13.27 ((
% 97.99/13.27 (iffalseProp2) =>
% 97.99/13.27 ((
% 97.99/13.27 (iftrueProp1) =>
% 97.99/13.27 ((
% 97.99/13.27 (iftrueProp2) =>
% 97.99/13.27 ((
% 97.99/13.27 (ifSingleton) =>
% 97.99/13.27 ((
% 97.99/13.27 (ifp) =>
% 97.99/13.27 ((
% 97.99/13.27 (theeq) =>
% 97.99/13.27 ((
% 97.99/13.27 (iftrue) =>
% 97.99/13.27 ((
% 97.99/13.27 (iffalse) =>
% 97.99/13.27 ((
% 97.99/13.27 (iftrueorfalse) =>
% 97.99/13.27 ((
% 97.99/13.27 (binintersectT_lem) =>
% 97.99/13.27 ((
% 97.99/13.27 (binunionT_lem) =>
% 97.99/13.27 ((
% 97.99/13.27 (powersetT_lem) =>
% 97.99/13.27 ((
% 97.99/13.27 (setminusT_lem) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementT_lem) =>
% 97.99/13.27 ((
% 97.99/13.27 (setextT) =>
% 97.99/13.27 ((
% 97.99/13.27 (subsetTI) =>
% 97.99/13.27 ((
% 97.99/13.27 (powersetTI1) =>
% 97.99/13.27 ((
% 97.99/13.27 (powersetTE1) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementTI1) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementTE1) =>
% 97.99/13.27 ((
% 97.99/13.27 (binintersectTELcontra) =>
% 97.99/13.27 ((
% 97.99/13.27 (binintersectTERcontra) =>
% 97.99/13.27 ((
% 97.99/13.27 (contrasubsetT) =>
% 97.99/13.27 ((
% 97.99/13.27 (contrasubsetT1) =>
% 97.99/13.27 ((
% 97.99/13.27 (contrasubsetT2) =>
% 97.99/13.27 ((
% 97.99/13.27 (contrasubsetT3) =>
% 97.99/13.27 ((
% 97.99/13.27 (doubleComplementI1) =>
% 97.99/13.27 ((
% 97.99/13.27 (doubleComplementE1) =>
% 97.99/13.27 ((
% 97.99/13.27 (doubleComplementSub1) =>
% 97.99/13.27 ((
% 97.99/13.27 (doubleComplementSub2) =>
% 97.99/13.27 ((
% 97.99/13.27 (doubleComplementEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementTnotintersectT) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementImpComplementIntersect) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementSubsetComplementIntersect) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementInPowersetComplementIntersect) =>
% 97.99/13.27 ((
% 97.99/13.27 (contraSubsetComplement) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementTcontraSubset) =>
% 97.99/13.27 ((
% 97.99/13.27 (binunionTILcontra) =>
% 97.99/13.27 ((
% 97.99/13.27 (binunionTIRcontra) =>
% 97.99/13.27 ((
% 97.99/13.27 (inIntersectImpInUnion) =>
% 97.99/13.27 ((
% 97.99/13.27 (inIntersectImpInUnion2) =>
% 97.99/13.27 ((
% 97.99/13.27 (inIntersectImpInIntersectUnions) =>
% 97.99/13.27 ((
% 97.99/13.27 (intersectInPowersetIntersectUnions) =>
% 97.99/13.27 ((
% 97.99/13.27 (inComplementUnionImpNotIn1) =>
% 97.99/13.27 ((
% 97.99/13.27 (inComplementUnionImpInComplement1) =>
% 97.99/13.27 ((
% 97.99/13.27 (binunionTE) =>
% 97.99/13.27 ((
% 97.99/13.27 (binunionTEcontra) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan2a1) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementUnionInPowersetComplement) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan2a2) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan1a) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan1b) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan1) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan2a) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan2b2) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan2b) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan2) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz13rule0) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz13rule1) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz13rule2) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz13rule3) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz13rule4) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz1_1) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz1_2) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz1_3) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz1_4) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz1_5) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1all2) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1SetBreln1) =>
% 97.99/13.27 ((
% 97.99/13.27 (choice2fnsingleton) =>
% 97.99/13.27 ((
% 97.99/13.27 (setOfPairsIsBReln1) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1all1) =>
% 97.99/13.27 ((
% 97.99/13.27 (subbreln1) =>
% 97.99/13.27 ((
% 97.99/13.27 (eqbreln1) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1invprop) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1invI) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1invE) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1compprop) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1compI) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1compE) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1compEex) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionprop) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionIL) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionIR) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionI) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionE) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionEcases) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionCommutes) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz2Ex) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz2W) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz2A) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz2B) =>
% 97.99/13.27 ((
% 97.99/13.27 (image1Ex) =>
% 97.99/13.27 ((
% 97.99/13.27 (image1Ex1) =>
% 97.99/13.27 ((
% 97.99/13.27 (image1Equiv) =>
% 97.99/13.27 ((
% 97.99/13.27 (image1E) =>
% 97.99/13.27 ((
% 97.99/13.27 (image1I) =>
% 97.99/13.27 ((
% 97.99/13.27 (injFuncInInjFuncSet) =>
% 97.99/13.27 ((
% 97.99/13.27 (injFuncSetFuncIn) =>
% 97.99/13.27 ((
% 97.99/13.27 (injFuncSetFuncInj) =>
% 97.99/13.27 ((
% 97.99/13.27 (surjFuncSetFuncIn) =>
% 97.99/13.27 ((
% 97.99/13.27 (surjFuncSetFuncSurj) =>
% 97.99/13.27 ((
% 97.99/13.27 (leftInvIsSurj) =>
% 97.99/13.27 ((
% 97.99/13.27 (surjCantorThm) =>
% 97.99/13.27 ((
% 97.99/13.27 (foundation2) =>
% 97.99/13.27 ((
% 97.99/13.27 (notinself) =>
% 97.99/13.27 ((
% 97.99/13.27 (notinself2) =>
% 97.99/13.27 ((
% 97.99/13.27 (omegaSp) =>
% 97.99/13.27 ((
% 97.99/13.27 (omegaSclos) =>
% 97.99/13.27 ((
% 97.99/13.27 (peano0notS) =>
% 97.99/13.27 ((
% 97.99/13.27 (!!) @ (
% 97.99/13.27 (('#S') @ (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 =>) @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#C') @ in @
% 97.99/13.27 omega)))) @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 !!) @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 (
% 97.99/13.27 ('#S') @ (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 =>) @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#C') @ in @
% 97.99/13.27 omega)))))) @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#S') @ (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 '#S') @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 =>))) @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#C') @ (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 '#B') @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 =) @
% 97.99/13.27 omegaS)))) @
% 97.99/13.27 omegaS)))))) @
% 97.99/13.27 (
% 97.99/13.27 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.99/13.27 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1386])).
% 97.99/13.27 thf(zip_derived_cl1407, plain,
% 97.99/13.27 (~ (((kpairp) =>
% 97.99/13.27 (((singletonsubset) =>
% 97.99/13.27 (((singletoninpowerset) =>
% 97.99/13.27 (((singletoninpowunion) =>
% 97.99/13.27 (((upairset2E) =>
% 97.99/13.27 (((upairsubunion) =>
% 97.99/13.27 (((upairinpowunion) =>
% 97.99/13.27 (((ubforcartprodlem1) =>
% 97.99/13.27 (((ubforcartprodlem2) =>
% 97.99/13.27 (((ubforcartprodlem3) =>
% 97.99/13.27 (((cartprodpairin) =>
% 97.99/13.27 (((cartprodmempair1) =>
% 97.99/13.27 (((cartprodmempair) =>
% 97.99/13.27 (((setunionE2) =>
% 97.99/13.27 (((setunionsingleton1) =>
% 97.99/13.27 (((setunionsingleton2) =>
% 97.99/13.27 (((setunionsingleton) =>
% 97.99/13.27 (((singletonprop) =>
% 97.99/13.27 (((ex1E1) =>
% 97.99/13.27 (((ex1I) =>
% 97.99/13.27 (((ex1I2) =>
% 97.99/13.27 (((singletonsuniq) =>
% 97.99/13.27 (((setukpairinjL1) =>
% 97.99/13.27 (((kfstsingleton) =>
% 97.99/13.27 (((theprop) =>
% 97.99/13.27 (((kfstpairEq) =>
% 97.99/13.27 (((cartprodfstin) =>
% 97.99/13.27 (((setukpairinjL2) =>
% 97.99/13.27 (((setukpairinjL) =>
% 97.99/13.27 (((setukpairinjR11) =>
% 97.99/13.27 ((
% 97.99/13.27 (setukpairinjR12) =>
% 97.99/13.27 ((
% 97.99/13.27 (setukpairinjR1) =>
% 97.99/13.27 ((
% 97.99/13.27 (upairequniteq) =>
% 97.99/13.27 ((
% 97.99/13.27 (setukpairinjR2) =>
% 97.99/13.27 ((
% 97.99/13.27 (setukpairinjR) =>
% 97.99/13.27 ((
% 97.99/13.27 (ksndsingleton) =>
% 97.99/13.27 ((
% 97.99/13.27 (ksndpairEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (kpairsurjEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodsndin) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodpairmemEL) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodpairmemER) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodmempaircEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodfstpairEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodsndpairEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodpairsurjEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (dpsetconstrI) =>
% 97.99/13.27 ((
% 97.99/13.27 (dpsetconstrSub) =>
% 97.99/13.27 ((
% 97.99/13.27 (setOfPairsIsBReln) =>
% 97.99/13.27 ((
% 97.99/13.27 (dpsetconstrERa) =>
% 97.99/13.27 ((
% 97.99/13.27 (dpsetconstrEL1) =>
% 97.99/13.27 ((
% 97.99/13.27 (dpsetconstrEL2) =>
% 97.99/13.27 ((
% 97.99/13.27 (dpsetconstrER) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcImageSingleton) =>
% 97.99/13.27 ((
% 97.99/13.27 (apProp) =>
% 97.99/13.27 ((
% 97.99/13.27 (app) =>
% 97.99/13.27 ((
% 97.99/13.27 (infuncsetfunc) =>
% 97.99/13.27 ((
% 97.99/13.27 (ap2p) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcinfuncset) =>
% 97.99/13.27 ((
% 97.99/13.27 (lamProp) =>
% 97.99/13.27 ((
% 97.99/13.27 (lamp) =>
% 97.99/13.27 ((
% 97.99/13.27 (lam2p) =>
% 97.99/13.27 ((
% 97.99/13.27 (brelnall1) =>
% 97.99/13.27 ((
% 97.99/13.27 (brelnall2) =>
% 97.99/13.27 ((
% 97.99/13.27 (ex1E2) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcGraphProp1) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcGraphProp3) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcGraphProp2) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcextLem) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcGraphProp4) =>
% 97.99/13.27 ((
% 97.99/13.27 (subbreln) =>
% 97.99/13.27 ((
% 97.99/13.27 (eqbreln) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcext) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcext2) =>
% 97.99/13.27 ((
% 97.99/13.27 (ap2apEq1) =>
% 97.99/13.27 ((
% 97.99/13.27 (ap2apEq2) =>
% 97.99/13.27 ((
% 97.99/13.27 (beta1) =>
% 97.99/13.27 ((
% 97.99/13.27 (eta1) =>
% 97.99/13.27 ((
% 97.99/13.27 (lam2lamEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (beta2) =>
% 97.99/13.27 ((
% 97.99/13.27 (eta2) =>
% 97.99/13.27 ((
% 97.99/13.27 (iffalseProp1) =>
% 97.99/13.27 ((
% 97.99/13.27 (iffalseProp2) =>
% 97.99/13.27 ((
% 97.99/13.27 (iftrueProp1) =>
% 97.99/13.27 ((
% 97.99/13.27 (iftrueProp2) =>
% 97.99/13.27 ((
% 97.99/13.27 (ifSingleton) =>
% 97.99/13.27 ((
% 97.99/13.27 (ifp) =>
% 97.99/13.27 ((
% 97.99/13.27 (theeq) =>
% 97.99/13.27 ((
% 97.99/13.27 (iftrue) =>
% 97.99/13.27 ((
% 97.99/13.27 (iffalse) =>
% 97.99/13.27 ((
% 97.99/13.27 (iftrueorfalse) =>
% 97.99/13.27 ((
% 97.99/13.27 (binintersectT_lem) =>
% 97.99/13.27 ((
% 97.99/13.27 (binunionT_lem) =>
% 97.99/13.27 ((
% 97.99/13.27 (powersetT_lem) =>
% 97.99/13.27 ((
% 97.99/13.27 (setminusT_lem) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementT_lem) =>
% 97.99/13.27 ((
% 97.99/13.27 (setextT) =>
% 97.99/13.27 ((
% 97.99/13.27 (subsetTI) =>
% 97.99/13.27 ((
% 97.99/13.27 (powersetTI1) =>
% 97.99/13.27 ((
% 97.99/13.27 (powersetTE1) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementTI1) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementTE1) =>
% 97.99/13.27 ((
% 97.99/13.27 (binintersectTELcontra) =>
% 97.99/13.27 ((
% 97.99/13.27 (binintersectTERcontra) =>
% 97.99/13.27 ((
% 97.99/13.27 (contrasubsetT) =>
% 97.99/13.27 ((
% 97.99/13.27 (contrasubsetT1) =>
% 97.99/13.27 ((
% 97.99/13.27 (contrasubsetT2) =>
% 97.99/13.27 ((
% 97.99/13.27 (contrasubsetT3) =>
% 97.99/13.27 ((
% 97.99/13.27 (doubleComplementI1) =>
% 97.99/13.27 ((
% 97.99/13.27 (doubleComplementE1) =>
% 97.99/13.27 ((
% 97.99/13.27 (doubleComplementSub1) =>
% 97.99/13.27 ((
% 97.99/13.27 (doubleComplementSub2) =>
% 97.99/13.27 ((
% 97.99/13.27 (doubleComplementEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementTnotintersectT) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementImpComplementIntersect) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementSubsetComplementIntersect) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementInPowersetComplementIntersect) =>
% 97.99/13.27 ((
% 97.99/13.27 (contraSubsetComplement) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementTcontraSubset) =>
% 97.99/13.27 ((
% 97.99/13.27 (binunionTILcontra) =>
% 97.99/13.27 ((
% 97.99/13.27 (binunionTIRcontra) =>
% 97.99/13.27 ((
% 97.99/13.27 (inIntersectImpInUnion) =>
% 97.99/13.27 ((
% 97.99/13.27 (inIntersectImpInUnion2) =>
% 97.99/13.27 ((
% 97.99/13.27 (inIntersectImpInIntersectUnions) =>
% 97.99/13.27 ((
% 97.99/13.27 (intersectInPowersetIntersectUnions) =>
% 97.99/13.27 ((
% 97.99/13.27 (inComplementUnionImpNotIn1) =>
% 97.99/13.27 ((
% 97.99/13.27 (inComplementUnionImpInComplement1) =>
% 97.99/13.27 ((
% 97.99/13.27 (binunionTE) =>
% 97.99/13.27 ((
% 97.99/13.27 (binunionTEcontra) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan2a1) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementUnionInPowersetComplement) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan2a2) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan1a) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan1b) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan1) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan2a) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan2b2) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan2b) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan2) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz13rule0) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz13rule1) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz13rule2) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz13rule3) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz13rule4) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz1_1) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz1_2) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz1_3) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz1_4) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz1_5) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1all2) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1SetBreln1) =>
% 97.99/13.27 ((
% 97.99/13.27 (choice2fnsingleton) =>
% 97.99/13.27 ((
% 97.99/13.27 (setOfPairsIsBReln1) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1all1) =>
% 97.99/13.27 ((
% 97.99/13.27 (subbreln1) =>
% 97.99/13.27 ((
% 97.99/13.27 (eqbreln1) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1invprop) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1invI) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1invE) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1compprop) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1compI) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1compE) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1compEex) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionprop) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionIL) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionIR) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionI) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionE) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionEcases) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionCommutes) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz2Ex) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz2W) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz2A) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz2B) =>
% 97.99/13.27 ((
% 97.99/13.27 (image1Ex) =>
% 97.99/13.27 ((
% 97.99/13.27 (image1Ex1) =>
% 97.99/13.27 ((
% 97.99/13.27 (image1Equiv) =>
% 97.99/13.27 ((
% 97.99/13.27 (image1E) =>
% 97.99/13.27 ((
% 97.99/13.27 (image1I) =>
% 97.99/13.27 ((
% 97.99/13.27 (injFuncInInjFuncSet) =>
% 97.99/13.27 ((
% 97.99/13.27 (injFuncSetFuncIn) =>
% 97.99/13.27 ((
% 97.99/13.27 (injFuncSetFuncInj) =>
% 97.99/13.27 ((
% 97.99/13.27 (surjFuncSetFuncIn) =>
% 97.99/13.27 ((
% 97.99/13.27 (surjFuncSetFuncSurj) =>
% 97.99/13.27 ((
% 97.99/13.27 (leftInvIsSurj) =>
% 97.99/13.27 ((
% 97.99/13.27 (surjCantorThm) =>
% 97.99/13.27 ((
% 97.99/13.27 (foundation2) =>
% 97.99/13.27 ((
% 97.99/13.27 (notinself) =>
% 97.99/13.27 ((
% 97.99/13.27 (notinself2) =>
% 97.99/13.27 ((
% 97.99/13.27 (omegaSp) =>
% 97.99/13.27 ((
% 97.99/13.27 (omegaSclos) =>
% 97.99/13.27 ((
% 97.99/13.27 (peano0notS) =>
% 97.99/13.27 ((
% 97.99/13.27 (!!) @ (
% 97.99/13.27 (('#S') @ (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 =>) @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#C') @ in @
% 97.99/13.27 omega)))) @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 !!) @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 (
% 97.99/13.27 ('#S') @ (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 =>) @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#C') @ in @
% 97.99/13.27 omega)))))) @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#S') @ (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 '#S') @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 =>))) @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#C') @ (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 '#B') @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 =) @
% 97.99/13.27 omegaS)))) @
% 97.99/13.27 omegaS)))))) @
% 97.99/13.27 (
% 97.99/13.27 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.99/13.27 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1396])).
% 97.99/13.27 thf(zip_derived_cl1420, plain,
% 97.99/13.27 (~ (((singletonsubset) =>
% 97.99/13.27 (((singletoninpowerset) =>
% 97.99/13.27 (((singletoninpowunion) =>
% 97.99/13.27 (((upairset2E) =>
% 97.99/13.27 (((upairsubunion) =>
% 97.99/13.27 (((upairinpowunion) =>
% 97.99/13.27 (((ubforcartprodlem1) =>
% 97.99/13.27 (((ubforcartprodlem2) =>
% 97.99/13.27 (((ubforcartprodlem3) =>
% 97.99/13.27 (((cartprodpairin) =>
% 97.99/13.27 (((cartprodmempair1) =>
% 97.99/13.27 (((cartprodmempair) =>
% 97.99/13.27 (((setunionE2) =>
% 97.99/13.27 (((setunionsingleton1) =>
% 97.99/13.27 (((setunionsingleton2) =>
% 97.99/13.27 (((setunionsingleton) =>
% 97.99/13.27 (((singletonprop) =>
% 97.99/13.27 (((ex1E1) =>
% 97.99/13.27 (((ex1I) =>
% 97.99/13.27 (((ex1I2) =>
% 97.99/13.27 (((singletonsuniq) =>
% 97.99/13.27 (((setukpairinjL1) =>
% 97.99/13.27 (((kfstsingleton) =>
% 97.99/13.27 (((theprop) =>
% 97.99/13.27 (((kfstpairEq) =>
% 97.99/13.27 (((cartprodfstin) =>
% 97.99/13.27 (((setukpairinjL2) =>
% 97.99/13.27 (((setukpairinjL) =>
% 97.99/13.27 (((setukpairinjR11) =>
% 97.99/13.27 (((setukpairinjR12) =>
% 97.99/13.27 ((
% 97.99/13.27 (setukpairinjR1) =>
% 97.99/13.27 ((
% 97.99/13.27 (upairequniteq) =>
% 97.99/13.27 ((
% 97.99/13.27 (setukpairinjR2) =>
% 97.99/13.27 ((
% 97.99/13.27 (setukpairinjR) =>
% 97.99/13.27 ((
% 97.99/13.27 (ksndsingleton) =>
% 97.99/13.27 ((
% 97.99/13.27 (ksndpairEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (kpairsurjEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodsndin) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodpairmemEL) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodpairmemER) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodmempaircEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodfstpairEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodsndpairEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodpairsurjEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (dpsetconstrI) =>
% 97.99/13.27 ((
% 97.99/13.27 (dpsetconstrSub) =>
% 97.99/13.27 ((
% 97.99/13.27 (setOfPairsIsBReln) =>
% 97.99/13.27 ((
% 97.99/13.27 (dpsetconstrERa) =>
% 97.99/13.27 ((
% 97.99/13.27 (dpsetconstrEL1) =>
% 97.99/13.27 ((
% 97.99/13.27 (dpsetconstrEL2) =>
% 97.99/13.27 ((
% 97.99/13.27 (dpsetconstrER) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcImageSingleton) =>
% 97.99/13.27 ((
% 97.99/13.27 (apProp) =>
% 97.99/13.27 ((
% 97.99/13.27 (app) =>
% 97.99/13.27 ((
% 97.99/13.27 (infuncsetfunc) =>
% 97.99/13.27 ((
% 97.99/13.27 (ap2p) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcinfuncset) =>
% 97.99/13.27 ((
% 97.99/13.27 (lamProp) =>
% 97.99/13.27 ((
% 97.99/13.27 (lamp) =>
% 97.99/13.27 ((
% 97.99/13.27 (lam2p) =>
% 97.99/13.27 ((
% 97.99/13.27 (brelnall1) =>
% 97.99/13.27 ((
% 97.99/13.27 (brelnall2) =>
% 97.99/13.27 ((
% 97.99/13.27 (ex1E2) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcGraphProp1) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcGraphProp3) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcGraphProp2) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcextLem) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcGraphProp4) =>
% 97.99/13.27 ((
% 97.99/13.27 (subbreln) =>
% 97.99/13.27 ((
% 97.99/13.27 (eqbreln) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcext) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcext2) =>
% 97.99/13.27 ((
% 97.99/13.27 (ap2apEq1) =>
% 97.99/13.27 ((
% 97.99/13.27 (ap2apEq2) =>
% 97.99/13.27 ((
% 97.99/13.27 (beta1) =>
% 97.99/13.27 ((
% 97.99/13.27 (eta1) =>
% 97.99/13.27 ((
% 97.99/13.27 (lam2lamEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (beta2) =>
% 97.99/13.27 ((
% 97.99/13.27 (eta2) =>
% 97.99/13.27 ((
% 97.99/13.27 (iffalseProp1) =>
% 97.99/13.27 ((
% 97.99/13.27 (iffalseProp2) =>
% 97.99/13.27 ((
% 97.99/13.27 (iftrueProp1) =>
% 97.99/13.27 ((
% 97.99/13.27 (iftrueProp2) =>
% 97.99/13.27 ((
% 97.99/13.27 (ifSingleton) =>
% 97.99/13.27 ((
% 97.99/13.27 (ifp) =>
% 97.99/13.27 ((
% 97.99/13.27 (theeq) =>
% 97.99/13.27 ((
% 97.99/13.27 (iftrue) =>
% 97.99/13.27 ((
% 97.99/13.27 (iffalse) =>
% 97.99/13.27 ((
% 97.99/13.27 (iftrueorfalse) =>
% 97.99/13.27 ((
% 97.99/13.27 (binintersectT_lem) =>
% 97.99/13.27 ((
% 97.99/13.27 (binunionT_lem) =>
% 97.99/13.27 ((
% 97.99/13.27 (powersetT_lem) =>
% 97.99/13.27 ((
% 97.99/13.27 (setminusT_lem) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementT_lem) =>
% 97.99/13.27 ((
% 97.99/13.27 (setextT) =>
% 97.99/13.27 ((
% 97.99/13.27 (subsetTI) =>
% 97.99/13.27 ((
% 97.99/13.27 (powersetTI1) =>
% 97.99/13.27 ((
% 97.99/13.27 (powersetTE1) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementTI1) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementTE1) =>
% 97.99/13.27 ((
% 97.99/13.27 (binintersectTELcontra) =>
% 97.99/13.27 ((
% 97.99/13.27 (binintersectTERcontra) =>
% 97.99/13.27 ((
% 97.99/13.27 (contrasubsetT) =>
% 97.99/13.27 ((
% 97.99/13.27 (contrasubsetT1) =>
% 97.99/13.27 ((
% 97.99/13.27 (contrasubsetT2) =>
% 97.99/13.27 ((
% 97.99/13.27 (contrasubsetT3) =>
% 97.99/13.27 ((
% 97.99/13.27 (doubleComplementI1) =>
% 97.99/13.27 ((
% 97.99/13.27 (doubleComplementE1) =>
% 97.99/13.27 ((
% 97.99/13.27 (doubleComplementSub1) =>
% 97.99/13.27 ((
% 97.99/13.27 (doubleComplementSub2) =>
% 97.99/13.27 ((
% 97.99/13.27 (doubleComplementEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementTnotintersectT) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementImpComplementIntersect) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementSubsetComplementIntersect) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementInPowersetComplementIntersect) =>
% 97.99/13.27 ((
% 97.99/13.27 (contraSubsetComplement) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementTcontraSubset) =>
% 97.99/13.27 ((
% 97.99/13.27 (binunionTILcontra) =>
% 97.99/13.27 ((
% 97.99/13.27 (binunionTIRcontra) =>
% 97.99/13.27 ((
% 97.99/13.27 (inIntersectImpInUnion) =>
% 97.99/13.27 ((
% 97.99/13.27 (inIntersectImpInUnion2) =>
% 97.99/13.27 ((
% 97.99/13.27 (inIntersectImpInIntersectUnions) =>
% 97.99/13.27 ((
% 97.99/13.27 (intersectInPowersetIntersectUnions) =>
% 97.99/13.27 ((
% 97.99/13.27 (inComplementUnionImpNotIn1) =>
% 97.99/13.27 ((
% 97.99/13.27 (inComplementUnionImpInComplement1) =>
% 97.99/13.27 ((
% 97.99/13.27 (binunionTE) =>
% 97.99/13.27 ((
% 97.99/13.27 (binunionTEcontra) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan2a1) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementUnionInPowersetComplement) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan2a2) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan1a) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan1b) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan1) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan2a) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan2b2) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan2b) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan2) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz13rule0) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz13rule1) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz13rule2) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz13rule3) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz13rule4) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz1_1) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz1_2) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz1_3) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz1_4) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz1_5) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1all2) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1SetBreln1) =>
% 97.99/13.27 ((
% 97.99/13.27 (choice2fnsingleton) =>
% 97.99/13.27 ((
% 97.99/13.27 (setOfPairsIsBReln1) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1all1) =>
% 97.99/13.27 ((
% 97.99/13.27 (subbreln1) =>
% 97.99/13.27 ((
% 97.99/13.27 (eqbreln1) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1invprop) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1invI) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1invE) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1compprop) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1compI) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1compE) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1compEex) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionprop) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionIL) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionIR) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionI) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionE) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionEcases) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionCommutes) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz2Ex) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz2W) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz2A) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz2B) =>
% 97.99/13.27 ((
% 97.99/13.27 (image1Ex) =>
% 97.99/13.27 ((
% 97.99/13.27 (image1Ex1) =>
% 97.99/13.27 ((
% 97.99/13.27 (image1Equiv) =>
% 97.99/13.27 ((
% 97.99/13.27 (image1E) =>
% 97.99/13.27 ((
% 97.99/13.27 (image1I) =>
% 97.99/13.27 ((
% 97.99/13.27 (injFuncInInjFuncSet) =>
% 97.99/13.27 ((
% 97.99/13.27 (injFuncSetFuncIn) =>
% 97.99/13.27 ((
% 97.99/13.27 (injFuncSetFuncInj) =>
% 97.99/13.27 ((
% 97.99/13.27 (surjFuncSetFuncIn) =>
% 97.99/13.27 ((
% 97.99/13.27 (surjFuncSetFuncSurj) =>
% 97.99/13.27 ((
% 97.99/13.27 (leftInvIsSurj) =>
% 97.99/13.27 ((
% 97.99/13.27 (surjCantorThm) =>
% 97.99/13.27 ((
% 97.99/13.27 (foundation2) =>
% 97.99/13.27 ((
% 97.99/13.27 (notinself) =>
% 97.99/13.27 ((
% 97.99/13.27 (notinself2) =>
% 97.99/13.27 ((
% 97.99/13.27 (omegaSp) =>
% 97.99/13.27 ((
% 97.99/13.27 (omegaSclos) =>
% 97.99/13.27 ((
% 97.99/13.27 (peano0notS) =>
% 97.99/13.27 ((
% 97.99/13.27 (!!) @ (
% 97.99/13.27 (('#S') @ (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 =>) @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#C') @ in @
% 97.99/13.27 omega)))) @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 !!) @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 (
% 97.99/13.27 ('#S') @ (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 =>) @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#C') @ in @
% 97.99/13.27 omega)))))) @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#S') @ (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 '#S') @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 =>))) @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#C') @ (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 '#B') @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 =) @
% 97.99/13.27 omegaS)))) @
% 97.99/13.27 omegaS)))))) @
% 97.99/13.27 (
% 97.99/13.27 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.99/13.27 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1407])).
% 97.99/13.27 thf(zip_derived_cl1433, plain,
% 97.99/13.27 (~ (((singletoninpowerset) =>
% 97.99/13.27 (((singletoninpowunion) =>
% 97.99/13.27 (((upairset2E) =>
% 97.99/13.27 (((upairsubunion) =>
% 97.99/13.27 (((upairinpowunion) =>
% 97.99/13.27 (((ubforcartprodlem1) =>
% 97.99/13.27 (((ubforcartprodlem2) =>
% 97.99/13.27 (((ubforcartprodlem3) =>
% 97.99/13.27 (((cartprodpairin) =>
% 97.99/13.27 (((cartprodmempair1) =>
% 97.99/13.27 (((cartprodmempair) =>
% 97.99/13.27 (((setunionE2) =>
% 97.99/13.27 (((setunionsingleton1) =>
% 97.99/13.27 (((setunionsingleton2) =>
% 97.99/13.27 (((setunionsingleton) =>
% 97.99/13.27 (((singletonprop) =>
% 97.99/13.27 (((ex1E1) =>
% 97.99/13.27 (((ex1I) =>
% 97.99/13.27 (((ex1I2) =>
% 97.99/13.27 (((singletonsuniq) =>
% 97.99/13.27 (((setukpairinjL1) =>
% 97.99/13.27 (((kfstsingleton) =>
% 97.99/13.27 (((theprop) =>
% 97.99/13.27 (((kfstpairEq) =>
% 97.99/13.27 (((cartprodfstin) =>
% 97.99/13.27 (((setukpairinjL2) =>
% 97.99/13.27 (((setukpairinjL) =>
% 97.99/13.27 (((setukpairinjR11) =>
% 97.99/13.27 (((setukpairinjR12) =>
% 97.99/13.27 (((setukpairinjR1) =>
% 97.99/13.27 ((
% 97.99/13.27 (upairequniteq) =>
% 97.99/13.27 ((
% 97.99/13.27 (setukpairinjR2) =>
% 97.99/13.27 ((
% 97.99/13.27 (setukpairinjR) =>
% 97.99/13.27 ((
% 97.99/13.27 (ksndsingleton) =>
% 97.99/13.27 ((
% 97.99/13.27 (ksndpairEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (kpairsurjEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodsndin) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodpairmemEL) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodpairmemER) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodmempaircEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodfstpairEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodsndpairEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodpairsurjEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (dpsetconstrI) =>
% 97.99/13.27 ((
% 97.99/13.27 (dpsetconstrSub) =>
% 97.99/13.27 ((
% 97.99/13.27 (setOfPairsIsBReln) =>
% 97.99/13.27 ((
% 97.99/13.27 (dpsetconstrERa) =>
% 97.99/13.27 ((
% 97.99/13.27 (dpsetconstrEL1) =>
% 97.99/13.27 ((
% 97.99/13.27 (dpsetconstrEL2) =>
% 97.99/13.27 ((
% 97.99/13.27 (dpsetconstrER) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcImageSingleton) =>
% 97.99/13.27 ((
% 97.99/13.27 (apProp) =>
% 97.99/13.27 ((
% 97.99/13.27 (app) =>
% 97.99/13.27 ((
% 97.99/13.27 (infuncsetfunc) =>
% 97.99/13.27 ((
% 97.99/13.27 (ap2p) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcinfuncset) =>
% 97.99/13.27 ((
% 97.99/13.27 (lamProp) =>
% 97.99/13.27 ((
% 97.99/13.27 (lamp) =>
% 97.99/13.27 ((
% 97.99/13.27 (lam2p) =>
% 97.99/13.27 ((
% 97.99/13.27 (brelnall1) =>
% 97.99/13.27 ((
% 97.99/13.27 (brelnall2) =>
% 97.99/13.27 ((
% 97.99/13.27 (ex1E2) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcGraphProp1) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcGraphProp3) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcGraphProp2) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcextLem) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcGraphProp4) =>
% 97.99/13.27 ((
% 97.99/13.27 (subbreln) =>
% 97.99/13.27 ((
% 97.99/13.27 (eqbreln) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcext) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcext2) =>
% 97.99/13.27 ((
% 97.99/13.27 (ap2apEq1) =>
% 97.99/13.27 ((
% 97.99/13.27 (ap2apEq2) =>
% 97.99/13.27 ((
% 97.99/13.27 (beta1) =>
% 97.99/13.27 ((
% 97.99/13.27 (eta1) =>
% 97.99/13.27 ((
% 97.99/13.27 (lam2lamEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (beta2) =>
% 97.99/13.27 ((
% 97.99/13.27 (eta2) =>
% 97.99/13.27 ((
% 97.99/13.27 (iffalseProp1) =>
% 97.99/13.27 ((
% 97.99/13.27 (iffalseProp2) =>
% 97.99/13.27 ((
% 97.99/13.27 (iftrueProp1) =>
% 97.99/13.27 ((
% 97.99/13.27 (iftrueProp2) =>
% 97.99/13.27 ((
% 97.99/13.27 (ifSingleton) =>
% 97.99/13.27 ((
% 97.99/13.27 (ifp) =>
% 97.99/13.27 ((
% 97.99/13.27 (theeq) =>
% 97.99/13.27 ((
% 97.99/13.27 (iftrue) =>
% 97.99/13.27 ((
% 97.99/13.27 (iffalse) =>
% 97.99/13.27 ((
% 97.99/13.27 (iftrueorfalse) =>
% 97.99/13.27 ((
% 97.99/13.27 (binintersectT_lem) =>
% 97.99/13.27 ((
% 97.99/13.27 (binunionT_lem) =>
% 97.99/13.27 ((
% 97.99/13.27 (powersetT_lem) =>
% 97.99/13.27 ((
% 97.99/13.27 (setminusT_lem) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementT_lem) =>
% 97.99/13.27 ((
% 97.99/13.27 (setextT) =>
% 97.99/13.27 ((
% 97.99/13.27 (subsetTI) =>
% 97.99/13.27 ((
% 97.99/13.27 (powersetTI1) =>
% 97.99/13.27 ((
% 97.99/13.27 (powersetTE1) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementTI1) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementTE1) =>
% 97.99/13.27 ((
% 97.99/13.27 (binintersectTELcontra) =>
% 97.99/13.27 ((
% 97.99/13.27 (binintersectTERcontra) =>
% 97.99/13.27 ((
% 97.99/13.27 (contrasubsetT) =>
% 97.99/13.27 ((
% 97.99/13.27 (contrasubsetT1) =>
% 97.99/13.27 ((
% 97.99/13.27 (contrasubsetT2) =>
% 97.99/13.27 ((
% 97.99/13.27 (contrasubsetT3) =>
% 97.99/13.27 ((
% 97.99/13.27 (doubleComplementI1) =>
% 97.99/13.27 ((
% 97.99/13.27 (doubleComplementE1) =>
% 97.99/13.27 ((
% 97.99/13.27 (doubleComplementSub1) =>
% 97.99/13.27 ((
% 97.99/13.27 (doubleComplementSub2) =>
% 97.99/13.27 ((
% 97.99/13.27 (doubleComplementEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementTnotintersectT) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementImpComplementIntersect) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementSubsetComplementIntersect) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementInPowersetComplementIntersect) =>
% 97.99/13.27 ((
% 97.99/13.27 (contraSubsetComplement) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementTcontraSubset) =>
% 97.99/13.27 ((
% 97.99/13.27 (binunionTILcontra) =>
% 97.99/13.27 ((
% 97.99/13.27 (binunionTIRcontra) =>
% 97.99/13.27 ((
% 97.99/13.27 (inIntersectImpInUnion) =>
% 97.99/13.27 ((
% 97.99/13.27 (inIntersectImpInUnion2) =>
% 97.99/13.27 ((
% 97.99/13.27 (inIntersectImpInIntersectUnions) =>
% 97.99/13.27 ((
% 97.99/13.27 (intersectInPowersetIntersectUnions) =>
% 97.99/13.27 ((
% 97.99/13.27 (inComplementUnionImpNotIn1) =>
% 97.99/13.27 ((
% 97.99/13.27 (inComplementUnionImpInComplement1) =>
% 97.99/13.27 ((
% 97.99/13.27 (binunionTE) =>
% 97.99/13.27 ((
% 97.99/13.27 (binunionTEcontra) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan2a1) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementUnionInPowersetComplement) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan2a2) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan1a) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan1b) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan1) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan2a) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan2b2) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan2b) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan2) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz13rule0) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz13rule1) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz13rule2) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz13rule3) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz13rule4) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz1_1) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz1_2) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz1_3) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz1_4) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz1_5) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1all2) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1SetBreln1) =>
% 97.99/13.27 ((
% 97.99/13.27 (choice2fnsingleton) =>
% 97.99/13.27 ((
% 97.99/13.27 (setOfPairsIsBReln1) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1all1) =>
% 97.99/13.27 ((
% 97.99/13.27 (subbreln1) =>
% 97.99/13.27 ((
% 97.99/13.27 (eqbreln1) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1invprop) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1invI) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1invE) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1compprop) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1compI) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1compE) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1compEex) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionprop) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionIL) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionIR) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionI) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionE) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionEcases) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionCommutes) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz2Ex) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz2W) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz2A) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz2B) =>
% 97.99/13.27 ((
% 97.99/13.27 (image1Ex) =>
% 97.99/13.27 ((
% 97.99/13.27 (image1Ex1) =>
% 97.99/13.27 ((
% 97.99/13.27 (image1Equiv) =>
% 97.99/13.27 ((
% 97.99/13.27 (image1E) =>
% 97.99/13.27 ((
% 97.99/13.27 (image1I) =>
% 97.99/13.27 ((
% 97.99/13.27 (injFuncInInjFuncSet) =>
% 97.99/13.27 ((
% 97.99/13.27 (injFuncSetFuncIn) =>
% 97.99/13.27 ((
% 97.99/13.27 (injFuncSetFuncInj) =>
% 97.99/13.27 ((
% 97.99/13.27 (surjFuncSetFuncIn) =>
% 97.99/13.27 ((
% 97.99/13.27 (surjFuncSetFuncSurj) =>
% 97.99/13.27 ((
% 97.99/13.27 (leftInvIsSurj) =>
% 97.99/13.27 ((
% 97.99/13.27 (surjCantorThm) =>
% 97.99/13.27 ((
% 97.99/13.27 (foundation2) =>
% 97.99/13.27 ((
% 97.99/13.27 (notinself) =>
% 97.99/13.27 ((
% 97.99/13.27 (notinself2) =>
% 97.99/13.27 ((
% 97.99/13.27 (omegaSp) =>
% 97.99/13.27 ((
% 97.99/13.27 (omegaSclos) =>
% 97.99/13.27 ((
% 97.99/13.27 (peano0notS) =>
% 97.99/13.27 ((
% 97.99/13.27 (!!) @ (
% 97.99/13.27 (('#S') @ (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 =>) @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#C') @ in @
% 97.99/13.27 omega)))) @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 !!) @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 (
% 97.99/13.27 ('#S') @ (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 =>) @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#C') @ in @
% 97.99/13.27 omega)))))) @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#S') @ (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 '#S') @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 =>))) @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#C') @ (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 '#B') @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 =) @
% 97.99/13.27 omegaS)))) @
% 97.99/13.27 omegaS)))))) @
% 97.99/13.27 (
% 97.99/13.27 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.99/13.27 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1420])).
% 97.99/13.27 thf(zip_derived_cl1444, plain,
% 97.99/13.27 (~ (((singletoninpowunion) =>
% 97.99/13.27 (((upairset2E) =>
% 97.99/13.27 (((upairsubunion) =>
% 97.99/13.27 (((upairinpowunion) =>
% 97.99/13.27 (((ubforcartprodlem1) =>
% 97.99/13.27 (((ubforcartprodlem2) =>
% 97.99/13.27 (((ubforcartprodlem3) =>
% 97.99/13.27 (((cartprodpairin) =>
% 97.99/13.27 (((cartprodmempair1) =>
% 97.99/13.27 (((cartprodmempair) =>
% 97.99/13.27 (((setunionE2) =>
% 97.99/13.27 (((setunionsingleton1) =>
% 97.99/13.27 (((setunionsingleton2) =>
% 97.99/13.27 (((setunionsingleton) =>
% 97.99/13.27 (((singletonprop) =>
% 97.99/13.27 (((ex1E1) =>
% 97.99/13.27 (((ex1I) =>
% 97.99/13.27 (((ex1I2) =>
% 97.99/13.27 (((singletonsuniq) =>
% 97.99/13.27 (((setukpairinjL1) =>
% 97.99/13.27 (((kfstsingleton) =>
% 97.99/13.27 (((theprop) =>
% 97.99/13.27 (((kfstpairEq) =>
% 97.99/13.27 (((cartprodfstin) =>
% 97.99/13.27 (((setukpairinjL2) =>
% 97.99/13.27 (((setukpairinjL) =>
% 97.99/13.27 (((setukpairinjR11) =>
% 97.99/13.27 (((setukpairinjR12) =>
% 97.99/13.27 (((setukpairinjR1) =>
% 97.99/13.27 (((upairequniteq) =>
% 97.99/13.27 ((
% 97.99/13.27 (setukpairinjR2) =>
% 97.99/13.27 ((
% 97.99/13.27 (setukpairinjR) =>
% 97.99/13.27 ((
% 97.99/13.27 (ksndsingleton) =>
% 97.99/13.27 ((
% 97.99/13.27 (ksndpairEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (kpairsurjEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodsndin) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodpairmemEL) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodpairmemER) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodmempaircEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodfstpairEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodsndpairEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodpairsurjEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (dpsetconstrI) =>
% 97.99/13.27 ((
% 97.99/13.27 (dpsetconstrSub) =>
% 97.99/13.27 ((
% 97.99/13.27 (setOfPairsIsBReln) =>
% 97.99/13.27 ((
% 97.99/13.27 (dpsetconstrERa) =>
% 97.99/13.27 ((
% 97.99/13.27 (dpsetconstrEL1) =>
% 97.99/13.27 ((
% 97.99/13.27 (dpsetconstrEL2) =>
% 97.99/13.27 ((
% 97.99/13.27 (dpsetconstrER) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcImageSingleton) =>
% 97.99/13.27 ((
% 97.99/13.27 (apProp) =>
% 97.99/13.27 ((
% 97.99/13.27 (app) =>
% 97.99/13.27 ((
% 97.99/13.27 (infuncsetfunc) =>
% 97.99/13.27 ((
% 97.99/13.27 (ap2p) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcinfuncset) =>
% 97.99/13.27 ((
% 97.99/13.27 (lamProp) =>
% 97.99/13.27 ((
% 97.99/13.27 (lamp) =>
% 97.99/13.27 ((
% 97.99/13.27 (lam2p) =>
% 97.99/13.27 ((
% 97.99/13.27 (brelnall1) =>
% 97.99/13.27 ((
% 97.99/13.27 (brelnall2) =>
% 97.99/13.27 ((
% 97.99/13.27 (ex1E2) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcGraphProp1) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcGraphProp3) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcGraphProp2) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcextLem) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcGraphProp4) =>
% 97.99/13.27 ((
% 97.99/13.27 (subbreln) =>
% 97.99/13.27 ((
% 97.99/13.27 (eqbreln) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcext) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcext2) =>
% 97.99/13.27 ((
% 97.99/13.27 (ap2apEq1) =>
% 97.99/13.27 ((
% 97.99/13.27 (ap2apEq2) =>
% 97.99/13.27 ((
% 97.99/13.27 (beta1) =>
% 97.99/13.27 ((
% 97.99/13.27 (eta1) =>
% 97.99/13.27 ((
% 97.99/13.27 (lam2lamEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (beta2) =>
% 97.99/13.27 ((
% 97.99/13.27 (eta2) =>
% 97.99/13.27 ((
% 97.99/13.27 (iffalseProp1) =>
% 97.99/13.27 ((
% 97.99/13.27 (iffalseProp2) =>
% 97.99/13.27 ((
% 97.99/13.27 (iftrueProp1) =>
% 97.99/13.27 ((
% 97.99/13.27 (iftrueProp2) =>
% 97.99/13.27 ((
% 97.99/13.27 (ifSingleton) =>
% 97.99/13.27 ((
% 97.99/13.27 (ifp) =>
% 97.99/13.27 ((
% 97.99/13.27 (theeq) =>
% 97.99/13.27 ((
% 97.99/13.27 (iftrue) =>
% 97.99/13.27 ((
% 97.99/13.27 (iffalse) =>
% 97.99/13.27 ((
% 97.99/13.27 (iftrueorfalse) =>
% 97.99/13.27 ((
% 97.99/13.27 (binintersectT_lem) =>
% 97.99/13.27 ((
% 97.99/13.27 (binunionT_lem) =>
% 97.99/13.27 ((
% 97.99/13.27 (powersetT_lem) =>
% 97.99/13.27 ((
% 97.99/13.27 (setminusT_lem) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementT_lem) =>
% 97.99/13.27 ((
% 97.99/13.27 (setextT) =>
% 97.99/13.27 ((
% 97.99/13.27 (subsetTI) =>
% 97.99/13.27 ((
% 97.99/13.27 (powersetTI1) =>
% 97.99/13.27 ((
% 97.99/13.27 (powersetTE1) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementTI1) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementTE1) =>
% 97.99/13.27 ((
% 97.99/13.27 (binintersectTELcontra) =>
% 97.99/13.27 ((
% 97.99/13.27 (binintersectTERcontra) =>
% 97.99/13.27 ((
% 97.99/13.27 (contrasubsetT) =>
% 97.99/13.27 ((
% 97.99/13.27 (contrasubsetT1) =>
% 97.99/13.27 ((
% 97.99/13.27 (contrasubsetT2) =>
% 97.99/13.27 ((
% 97.99/13.27 (contrasubsetT3) =>
% 97.99/13.27 ((
% 97.99/13.27 (doubleComplementI1) =>
% 97.99/13.27 ((
% 97.99/13.27 (doubleComplementE1) =>
% 97.99/13.27 ((
% 97.99/13.27 (doubleComplementSub1) =>
% 97.99/13.27 ((
% 97.99/13.27 (doubleComplementSub2) =>
% 97.99/13.27 ((
% 97.99/13.27 (doubleComplementEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementTnotintersectT) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementImpComplementIntersect) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementSubsetComplementIntersect) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementInPowersetComplementIntersect) =>
% 97.99/13.27 ((
% 97.99/13.27 (contraSubsetComplement) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementTcontraSubset) =>
% 97.99/13.27 ((
% 97.99/13.27 (binunionTILcontra) =>
% 97.99/13.27 ((
% 97.99/13.27 (binunionTIRcontra) =>
% 97.99/13.27 ((
% 97.99/13.27 (inIntersectImpInUnion) =>
% 97.99/13.27 ((
% 97.99/13.27 (inIntersectImpInUnion2) =>
% 97.99/13.27 ((
% 97.99/13.27 (inIntersectImpInIntersectUnions) =>
% 97.99/13.27 ((
% 97.99/13.27 (intersectInPowersetIntersectUnions) =>
% 97.99/13.27 ((
% 97.99/13.27 (inComplementUnionImpNotIn1) =>
% 97.99/13.27 ((
% 97.99/13.27 (inComplementUnionImpInComplement1) =>
% 97.99/13.27 ((
% 97.99/13.27 (binunionTE) =>
% 97.99/13.27 ((
% 97.99/13.27 (binunionTEcontra) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan2a1) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementUnionInPowersetComplement) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan2a2) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan1a) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan1b) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan1) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan2a) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan2b2) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan2b) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan2) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz13rule0) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz13rule1) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz13rule2) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz13rule3) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz13rule4) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz1_1) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz1_2) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz1_3) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz1_4) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz1_5) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1all2) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1SetBreln1) =>
% 97.99/13.27 ((
% 97.99/13.27 (choice2fnsingleton) =>
% 97.99/13.27 ((
% 97.99/13.27 (setOfPairsIsBReln1) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1all1) =>
% 97.99/13.27 ((
% 97.99/13.27 (subbreln1) =>
% 97.99/13.27 ((
% 97.99/13.27 (eqbreln1) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1invprop) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1invI) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1invE) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1compprop) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1compI) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1compE) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1compEex) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionprop) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionIL) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionIR) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionI) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionE) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionEcases) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionCommutes) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz2Ex) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz2W) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz2A) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz2B) =>
% 97.99/13.27 ((
% 97.99/13.27 (image1Ex) =>
% 97.99/13.27 ((
% 97.99/13.27 (image1Ex1) =>
% 97.99/13.27 ((
% 97.99/13.27 (image1Equiv) =>
% 97.99/13.27 ((
% 97.99/13.27 (image1E) =>
% 97.99/13.27 ((
% 97.99/13.27 (image1I) =>
% 97.99/13.27 ((
% 97.99/13.27 (injFuncInInjFuncSet) =>
% 97.99/13.27 ((
% 97.99/13.27 (injFuncSetFuncIn) =>
% 97.99/13.27 ((
% 97.99/13.27 (injFuncSetFuncInj) =>
% 97.99/13.27 ((
% 97.99/13.27 (surjFuncSetFuncIn) =>
% 97.99/13.27 ((
% 97.99/13.27 (surjFuncSetFuncSurj) =>
% 97.99/13.27 ((
% 97.99/13.27 (leftInvIsSurj) =>
% 97.99/13.27 ((
% 97.99/13.27 (surjCantorThm) =>
% 97.99/13.27 ((
% 97.99/13.27 (foundation2) =>
% 97.99/13.27 ((
% 97.99/13.27 (notinself) =>
% 97.99/13.27 ((
% 97.99/13.27 (notinself2) =>
% 97.99/13.27 ((
% 97.99/13.27 (omegaSp) =>
% 97.99/13.27 ((
% 97.99/13.27 (omegaSclos) =>
% 97.99/13.27 ((
% 97.99/13.27 (peano0notS) =>
% 97.99/13.27 ((
% 97.99/13.27 (!!) @ (
% 97.99/13.27 (('#S') @ (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 =>) @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#C') @ in @
% 97.99/13.27 omega)))) @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 !!) @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 (
% 97.99/13.27 ('#S') @ (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 =>) @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#C') @ in @
% 97.99/13.27 omega)))))) @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#S') @ (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 '#S') @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 =>))) @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#C') @ (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 '#B') @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 =) @
% 97.99/13.27 omegaS)))) @
% 97.99/13.27 omegaS)))))) @
% 97.99/13.27 (
% 97.99/13.27 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.99/13.27 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1433])).
% 97.99/13.27 thf(zip_derived_cl1452, plain,
% 97.99/13.27 (~ (((upairset2E) =>
% 97.99/13.27 (((upairsubunion) =>
% 97.99/13.27 (((upairinpowunion) =>
% 97.99/13.27 (((ubforcartprodlem1) =>
% 97.99/13.27 (((ubforcartprodlem2) =>
% 97.99/13.27 (((ubforcartprodlem3) =>
% 97.99/13.27 (((cartprodpairin) =>
% 97.99/13.27 (((cartprodmempair1) =>
% 97.99/13.27 (((cartprodmempair) =>
% 97.99/13.27 (((setunionE2) =>
% 97.99/13.27 (((setunionsingleton1) =>
% 97.99/13.27 (((setunionsingleton2) =>
% 97.99/13.27 (((setunionsingleton) =>
% 97.99/13.27 (((singletonprop) =>
% 97.99/13.27 (((ex1E1) =>
% 97.99/13.27 (((ex1I) =>
% 97.99/13.27 (((ex1I2) =>
% 97.99/13.27 (((singletonsuniq) =>
% 97.99/13.27 (((setukpairinjL1) =>
% 97.99/13.27 (((kfstsingleton) =>
% 97.99/13.27 (((theprop) =>
% 97.99/13.27 (((kfstpairEq) =>
% 97.99/13.27 (((cartprodfstin) =>
% 97.99/13.27 (((setukpairinjL2) =>
% 97.99/13.27 (((setukpairinjL) =>
% 97.99/13.27 (((setukpairinjR11) =>
% 97.99/13.27 (((setukpairinjR12) =>
% 97.99/13.27 (((setukpairinjR1) =>
% 97.99/13.27 (((upairequniteq) =>
% 97.99/13.27 (((setukpairinjR2) =>
% 97.99/13.27 ((
% 97.99/13.27 (setukpairinjR) =>
% 97.99/13.27 ((
% 97.99/13.27 (ksndsingleton) =>
% 97.99/13.27 ((
% 97.99/13.27 (ksndpairEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (kpairsurjEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodsndin) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodpairmemEL) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodpairmemER) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodmempaircEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodfstpairEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodsndpairEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodpairsurjEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (dpsetconstrI) =>
% 97.99/13.27 ((
% 97.99/13.27 (dpsetconstrSub) =>
% 97.99/13.27 ((
% 97.99/13.27 (setOfPairsIsBReln) =>
% 97.99/13.27 ((
% 97.99/13.27 (dpsetconstrERa) =>
% 97.99/13.27 ((
% 97.99/13.27 (dpsetconstrEL1) =>
% 97.99/13.27 ((
% 97.99/13.27 (dpsetconstrEL2) =>
% 97.99/13.27 ((
% 97.99/13.27 (dpsetconstrER) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcImageSingleton) =>
% 97.99/13.27 ((
% 97.99/13.27 (apProp) =>
% 97.99/13.27 ((
% 97.99/13.27 (app) =>
% 97.99/13.27 ((
% 97.99/13.27 (infuncsetfunc) =>
% 97.99/13.27 ((
% 97.99/13.27 (ap2p) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcinfuncset) =>
% 97.99/13.27 ((
% 97.99/13.27 (lamProp) =>
% 97.99/13.27 ((
% 97.99/13.27 (lamp) =>
% 97.99/13.27 ((
% 97.99/13.27 (lam2p) =>
% 97.99/13.27 ((
% 97.99/13.27 (brelnall1) =>
% 97.99/13.27 ((
% 97.99/13.27 (brelnall2) =>
% 97.99/13.27 ((
% 97.99/13.27 (ex1E2) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcGraphProp1) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcGraphProp3) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcGraphProp2) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcextLem) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcGraphProp4) =>
% 97.99/13.27 ((
% 97.99/13.27 (subbreln) =>
% 97.99/13.27 ((
% 97.99/13.27 (eqbreln) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcext) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcext2) =>
% 97.99/13.27 ((
% 97.99/13.27 (ap2apEq1) =>
% 97.99/13.27 ((
% 97.99/13.27 (ap2apEq2) =>
% 97.99/13.27 ((
% 97.99/13.27 (beta1) =>
% 97.99/13.27 ((
% 97.99/13.27 (eta1) =>
% 97.99/13.27 ((
% 97.99/13.27 (lam2lamEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (beta2) =>
% 97.99/13.27 ((
% 97.99/13.27 (eta2) =>
% 97.99/13.27 ((
% 97.99/13.27 (iffalseProp1) =>
% 97.99/13.27 ((
% 97.99/13.27 (iffalseProp2) =>
% 97.99/13.27 ((
% 97.99/13.27 (iftrueProp1) =>
% 97.99/13.27 ((
% 97.99/13.27 (iftrueProp2) =>
% 97.99/13.27 ((
% 97.99/13.27 (ifSingleton) =>
% 97.99/13.27 ((
% 97.99/13.27 (ifp) =>
% 97.99/13.27 ((
% 97.99/13.27 (theeq) =>
% 97.99/13.27 ((
% 97.99/13.27 (iftrue) =>
% 97.99/13.27 ((
% 97.99/13.27 (iffalse) =>
% 97.99/13.27 ((
% 97.99/13.27 (iftrueorfalse) =>
% 97.99/13.27 ((
% 97.99/13.27 (binintersectT_lem) =>
% 97.99/13.27 ((
% 97.99/13.27 (binunionT_lem) =>
% 97.99/13.27 ((
% 97.99/13.27 (powersetT_lem) =>
% 97.99/13.27 ((
% 97.99/13.27 (setminusT_lem) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementT_lem) =>
% 97.99/13.27 ((
% 97.99/13.27 (setextT) =>
% 97.99/13.27 ((
% 97.99/13.27 (subsetTI) =>
% 97.99/13.27 ((
% 97.99/13.27 (powersetTI1) =>
% 97.99/13.27 ((
% 97.99/13.27 (powersetTE1) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementTI1) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementTE1) =>
% 97.99/13.27 ((
% 97.99/13.27 (binintersectTELcontra) =>
% 97.99/13.27 ((
% 97.99/13.27 (binintersectTERcontra) =>
% 97.99/13.27 ((
% 97.99/13.27 (contrasubsetT) =>
% 97.99/13.27 ((
% 97.99/13.27 (contrasubsetT1) =>
% 97.99/13.27 ((
% 97.99/13.27 (contrasubsetT2) =>
% 97.99/13.27 ((
% 97.99/13.27 (contrasubsetT3) =>
% 97.99/13.27 ((
% 97.99/13.27 (doubleComplementI1) =>
% 97.99/13.27 ((
% 97.99/13.27 (doubleComplementE1) =>
% 97.99/13.27 ((
% 97.99/13.27 (doubleComplementSub1) =>
% 97.99/13.27 ((
% 97.99/13.27 (doubleComplementSub2) =>
% 97.99/13.27 ((
% 97.99/13.27 (doubleComplementEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementTnotintersectT) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementImpComplementIntersect) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementSubsetComplementIntersect) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementInPowersetComplementIntersect) =>
% 97.99/13.27 ((
% 97.99/13.27 (contraSubsetComplement) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementTcontraSubset) =>
% 97.99/13.27 ((
% 97.99/13.27 (binunionTILcontra) =>
% 97.99/13.27 ((
% 97.99/13.27 (binunionTIRcontra) =>
% 97.99/13.27 ((
% 97.99/13.27 (inIntersectImpInUnion) =>
% 97.99/13.27 ((
% 97.99/13.27 (inIntersectImpInUnion2) =>
% 97.99/13.27 ((
% 97.99/13.27 (inIntersectImpInIntersectUnions) =>
% 97.99/13.27 ((
% 97.99/13.27 (intersectInPowersetIntersectUnions) =>
% 97.99/13.27 ((
% 97.99/13.27 (inComplementUnionImpNotIn1) =>
% 97.99/13.27 ((
% 97.99/13.27 (inComplementUnionImpInComplement1) =>
% 97.99/13.27 ((
% 97.99/13.27 (binunionTE) =>
% 97.99/13.27 ((
% 97.99/13.27 (binunionTEcontra) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan2a1) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementUnionInPowersetComplement) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan2a2) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan1a) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan1b) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan1) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan2a) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan2b2) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan2b) =>
% 97.99/13.27 ((
% 97.99/13.27 (demorgan2) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz13rule0) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz13rule1) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz13rule2) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz13rule3) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz13rule4) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz1_1) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz1_2) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz1_3) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz1_4) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz1_5) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1all2) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1SetBreln1) =>
% 97.99/13.27 ((
% 97.99/13.27 (choice2fnsingleton) =>
% 97.99/13.27 ((
% 97.99/13.27 (setOfPairsIsBReln1) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1all1) =>
% 97.99/13.27 ((
% 97.99/13.27 (subbreln1) =>
% 97.99/13.27 ((
% 97.99/13.27 (eqbreln1) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1invprop) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1invI) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1invE) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1compprop) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1compI) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1compE) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1compEex) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionprop) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionIL) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionIR) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionI) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionE) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionEcases) =>
% 97.99/13.27 ((
% 97.99/13.27 (breln1unionCommutes) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz2Ex) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz2W) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz2A) =>
% 97.99/13.27 ((
% 97.99/13.27 (woz2B) =>
% 97.99/13.27 ((
% 97.99/13.27 (image1Ex) =>
% 97.99/13.27 ((
% 97.99/13.27 (image1Ex1) =>
% 97.99/13.27 ((
% 97.99/13.27 (image1Equiv) =>
% 97.99/13.27 ((
% 97.99/13.27 (image1E) =>
% 97.99/13.27 ((
% 97.99/13.27 (image1I) =>
% 97.99/13.27 ((
% 97.99/13.27 (injFuncInInjFuncSet) =>
% 97.99/13.27 ((
% 97.99/13.27 (injFuncSetFuncIn) =>
% 97.99/13.27 ((
% 97.99/13.27 (injFuncSetFuncInj) =>
% 97.99/13.27 ((
% 97.99/13.27 (surjFuncSetFuncIn) =>
% 97.99/13.27 ((
% 97.99/13.27 (surjFuncSetFuncSurj) =>
% 97.99/13.27 ((
% 97.99/13.27 (leftInvIsSurj) =>
% 97.99/13.27 ((
% 97.99/13.27 (surjCantorThm) =>
% 97.99/13.27 ((
% 97.99/13.27 (foundation2) =>
% 97.99/13.27 ((
% 97.99/13.27 (notinself) =>
% 97.99/13.27 ((
% 97.99/13.27 (notinself2) =>
% 97.99/13.27 ((
% 97.99/13.27 (omegaSp) =>
% 97.99/13.27 ((
% 97.99/13.27 (omegaSclos) =>
% 97.99/13.27 ((
% 97.99/13.27 (peano0notS) =>
% 97.99/13.27 ((
% 97.99/13.27 (!!) @ (
% 97.99/13.27 (('#S') @ (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 =>) @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#C') @ in @
% 97.99/13.27 omega)))) @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 !!) @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 (
% 97.99/13.27 ('#S') @ (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 =>) @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#C') @ in @
% 97.99/13.27 omega)))))) @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#S') @ (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 '#S') @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 =>))) @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#C') @ (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 '#B') @
% 97.99/13.27 (
% 97.99/13.27 (
% 97.99/13.27 ('#B') @ (
% 97.99/13.27 =) @
% 97.99/13.27 omegaS)))) @
% 97.99/13.27 omegaS)))))) @
% 97.99/13.27 (
% 97.99/13.27 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.99/13.27 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1444])).
% 97.99/13.27 thf(zip_derived_cl1459, plain,
% 97.99/13.27 (~ (((upairsubunion) =>
% 97.99/13.27 (((upairinpowunion) =>
% 97.99/13.27 (((ubforcartprodlem1) =>
% 97.99/13.27 (((ubforcartprodlem2) =>
% 97.99/13.27 (((ubforcartprodlem3) =>
% 97.99/13.27 (((cartprodpairin) =>
% 97.99/13.27 (((cartprodmempair1) =>
% 97.99/13.27 (((cartprodmempair) =>
% 97.99/13.27 (((setunionE2) =>
% 97.99/13.27 (((setunionsingleton1) =>
% 97.99/13.27 (((setunionsingleton2) =>
% 97.99/13.27 (((setunionsingleton) =>
% 97.99/13.27 (((singletonprop) =>
% 97.99/13.27 (((ex1E1) =>
% 97.99/13.27 (((ex1I) =>
% 97.99/13.27 (((ex1I2) =>
% 97.99/13.27 (((singletonsuniq) =>
% 97.99/13.27 (((setukpairinjL1) =>
% 97.99/13.27 (((kfstsingleton) =>
% 97.99/13.27 (((theprop) =>
% 97.99/13.27 (((kfstpairEq) =>
% 97.99/13.27 (((cartprodfstin) =>
% 97.99/13.27 (((setukpairinjL2) =>
% 97.99/13.27 (((setukpairinjL) =>
% 97.99/13.27 (((setukpairinjR11) =>
% 97.99/13.27 (((setukpairinjR12) =>
% 97.99/13.27 (((setukpairinjR1) =>
% 97.99/13.27 (((upairequniteq) =>
% 97.99/13.27 (((setukpairinjR2) =>
% 97.99/13.27 (((setukpairinjR) =>
% 97.99/13.27 ((
% 97.99/13.27 (ksndsingleton) =>
% 97.99/13.27 ((
% 97.99/13.27 (ksndpairEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (kpairsurjEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodsndin) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodpairmemEL) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodpairmemER) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodmempaircEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodfstpairEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodsndpairEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (cartprodpairsurjEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (dpsetconstrI) =>
% 97.99/13.27 ((
% 97.99/13.27 (dpsetconstrSub) =>
% 97.99/13.27 ((
% 97.99/13.27 (setOfPairsIsBReln) =>
% 97.99/13.27 ((
% 97.99/13.27 (dpsetconstrERa) =>
% 97.99/13.27 ((
% 97.99/13.27 (dpsetconstrEL1) =>
% 97.99/13.27 ((
% 97.99/13.27 (dpsetconstrEL2) =>
% 97.99/13.27 ((
% 97.99/13.27 (dpsetconstrER) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcImageSingleton) =>
% 97.99/13.27 ((
% 97.99/13.27 (apProp) =>
% 97.99/13.27 ((
% 97.99/13.27 (app) =>
% 97.99/13.27 ((
% 97.99/13.27 (infuncsetfunc) =>
% 97.99/13.27 ((
% 97.99/13.27 (ap2p) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcinfuncset) =>
% 97.99/13.27 ((
% 97.99/13.27 (lamProp) =>
% 97.99/13.27 ((
% 97.99/13.27 (lamp) =>
% 97.99/13.27 ((
% 97.99/13.27 (lam2p) =>
% 97.99/13.27 ((
% 97.99/13.27 (brelnall1) =>
% 97.99/13.27 ((
% 97.99/13.27 (brelnall2) =>
% 97.99/13.27 ((
% 97.99/13.27 (ex1E2) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcGraphProp1) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcGraphProp3) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcGraphProp2) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcextLem) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcGraphProp4) =>
% 97.99/13.27 ((
% 97.99/13.27 (subbreln) =>
% 97.99/13.27 ((
% 97.99/13.27 (eqbreln) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcext) =>
% 97.99/13.27 ((
% 97.99/13.27 (funcext2) =>
% 97.99/13.27 ((
% 97.99/13.27 (ap2apEq1) =>
% 97.99/13.27 ((
% 97.99/13.27 (ap2apEq2) =>
% 97.99/13.27 ((
% 97.99/13.27 (beta1) =>
% 97.99/13.27 ((
% 97.99/13.27 (eta1) =>
% 97.99/13.27 ((
% 97.99/13.27 (lam2lamEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (beta2) =>
% 97.99/13.27 ((
% 97.99/13.27 (eta2) =>
% 97.99/13.27 ((
% 97.99/13.27 (iffalseProp1) =>
% 97.99/13.27 ((
% 97.99/13.27 (iffalseProp2) =>
% 97.99/13.27 ((
% 97.99/13.27 (iftrueProp1) =>
% 97.99/13.27 ((
% 97.99/13.27 (iftrueProp2) =>
% 97.99/13.27 ((
% 97.99/13.27 (ifSingleton) =>
% 97.99/13.27 ((
% 97.99/13.27 (ifp) =>
% 97.99/13.27 ((
% 97.99/13.27 (theeq) =>
% 97.99/13.27 ((
% 97.99/13.27 (iftrue) =>
% 97.99/13.27 ((
% 97.99/13.27 (iffalse) =>
% 97.99/13.27 ((
% 97.99/13.27 (iftrueorfalse) =>
% 97.99/13.27 ((
% 97.99/13.27 (binintersectT_lem) =>
% 97.99/13.27 ((
% 97.99/13.27 (binunionT_lem) =>
% 97.99/13.27 ((
% 97.99/13.27 (powersetT_lem) =>
% 97.99/13.27 ((
% 97.99/13.27 (setminusT_lem) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementT_lem) =>
% 97.99/13.27 ((
% 97.99/13.27 (setextT) =>
% 97.99/13.27 ((
% 97.99/13.27 (subsetTI) =>
% 97.99/13.27 ((
% 97.99/13.27 (powersetTI1) =>
% 97.99/13.27 ((
% 97.99/13.27 (powersetTE1) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementTI1) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementTE1) =>
% 97.99/13.27 ((
% 97.99/13.27 (binintersectTELcontra) =>
% 97.99/13.27 ((
% 97.99/13.27 (binintersectTERcontra) =>
% 97.99/13.27 ((
% 97.99/13.27 (contrasubsetT) =>
% 97.99/13.27 ((
% 97.99/13.27 (contrasubsetT1) =>
% 97.99/13.27 ((
% 97.99/13.27 (contrasubsetT2) =>
% 97.99/13.27 ((
% 97.99/13.27 (contrasubsetT3) =>
% 97.99/13.27 ((
% 97.99/13.27 (doubleComplementI1) =>
% 97.99/13.27 ((
% 97.99/13.27 (doubleComplementE1) =>
% 97.99/13.27 ((
% 97.99/13.27 (doubleComplementSub1) =>
% 97.99/13.27 ((
% 97.99/13.27 (doubleComplementSub2) =>
% 97.99/13.27 ((
% 97.99/13.27 (doubleComplementEq) =>
% 97.99/13.27 ((
% 97.99/13.27 (complementTnotintersectT) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementImpComplementIntersect) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementSubsetComplementIntersect) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementInPowersetComplementIntersect) =>
% 97.99/13.28 ((
% 97.99/13.28 (contraSubsetComplement) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementTcontraSubset) =>
% 97.99/13.28 ((
% 97.99/13.28 (binunionTILcontra) =>
% 97.99/13.28 ((
% 97.99/13.28 (binunionTIRcontra) =>
% 97.99/13.28 ((
% 97.99/13.28 (inIntersectImpInUnion) =>
% 97.99/13.28 ((
% 97.99/13.28 (inIntersectImpInUnion2) =>
% 97.99/13.28 ((
% 97.99/13.28 (inIntersectImpInIntersectUnions) =>
% 97.99/13.28 ((
% 97.99/13.28 (intersectInPowersetIntersectUnions) =>
% 97.99/13.28 ((
% 97.99/13.28 (inComplementUnionImpNotIn1) =>
% 97.99/13.28 ((
% 97.99/13.28 (inComplementUnionImpInComplement1) =>
% 97.99/13.28 ((
% 97.99/13.28 (binunionTE) =>
% 97.99/13.28 ((
% 97.99/13.28 (binunionTEcontra) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2a1) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementUnionInPowersetComplement) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2a2) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan1a) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan1b) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan1) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2a) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2b2) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2b) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz13rule0) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz13rule1) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz13rule2) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz13rule3) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz13rule4) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz1_1) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz1_2) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz1_3) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz1_4) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz1_5) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1all2) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1SetBreln1) =>
% 97.99/13.28 ((
% 97.99/13.28 (choice2fnsingleton) =>
% 97.99/13.28 ((
% 97.99/13.28 (setOfPairsIsBReln1) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1all1) =>
% 97.99/13.28 ((
% 97.99/13.28 (subbreln1) =>
% 97.99/13.28 ((
% 97.99/13.28 (eqbreln1) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1invprop) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1invI) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1invE) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1compprop) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1compI) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1compE) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1compEex) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionprop) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionIL) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionIR) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionI) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionE) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionEcases) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionCommutes) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz2Ex) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz2W) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz2A) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz2B) =>
% 97.99/13.28 ((
% 97.99/13.28 (image1Ex) =>
% 97.99/13.28 ((
% 97.99/13.28 (image1Ex1) =>
% 97.99/13.28 ((
% 97.99/13.28 (image1Equiv) =>
% 97.99/13.28 ((
% 97.99/13.28 (image1E) =>
% 97.99/13.28 ((
% 97.99/13.28 (image1I) =>
% 97.99/13.28 ((
% 97.99/13.28 (injFuncInInjFuncSet) =>
% 97.99/13.28 ((
% 97.99/13.28 (injFuncSetFuncIn) =>
% 97.99/13.28 ((
% 97.99/13.28 (injFuncSetFuncInj) =>
% 97.99/13.28 ((
% 97.99/13.28 (surjFuncSetFuncIn) =>
% 97.99/13.28 ((
% 97.99/13.28 (surjFuncSetFuncSurj) =>
% 97.99/13.28 ((
% 97.99/13.28 (leftInvIsSurj) =>
% 97.99/13.28 ((
% 97.99/13.28 (surjCantorThm) =>
% 97.99/13.28 ((
% 97.99/13.28 (foundation2) =>
% 97.99/13.28 ((
% 97.99/13.28 (notinself) =>
% 97.99/13.28 ((
% 97.99/13.28 (notinself2) =>
% 97.99/13.28 ((
% 97.99/13.28 (omegaSp) =>
% 97.99/13.28 ((
% 97.99/13.28 (omegaSclos) =>
% 97.99/13.28 ((
% 97.99/13.28 (peano0notS) =>
% 97.99/13.28 ((
% 97.99/13.28 (!!) @ (
% 97.99/13.28 (('#S') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 =>) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#C') @ in @
% 97.99/13.28 omega)))) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 !!) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#S') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 =>) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#C') @ in @
% 97.99/13.28 omega)))))) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#S') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 '#S') @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 =>))) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#C') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 '#B') @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 =) @
% 97.99/13.28 omegaS)))) @
% 97.99/13.28 omegaS)))))) @
% 97.99/13.28 (
% 97.99/13.28 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.99/13.28 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1452])).
% 97.99/13.28 thf(zip_derived_cl1466, plain,
% 97.99/13.28 (~ (((upairinpowunion) =>
% 97.99/13.28 (((ubforcartprodlem1) =>
% 97.99/13.28 (((ubforcartprodlem2) =>
% 97.99/13.28 (((ubforcartprodlem3) =>
% 97.99/13.28 (((cartprodpairin) =>
% 97.99/13.28 (((cartprodmempair1) =>
% 97.99/13.28 (((cartprodmempair) =>
% 97.99/13.28 (((setunionE2) =>
% 97.99/13.28 (((setunionsingleton1) =>
% 97.99/13.28 (((setunionsingleton2) =>
% 97.99/13.28 (((setunionsingleton) =>
% 97.99/13.28 (((singletonprop) =>
% 97.99/13.28 (((ex1E1) =>
% 97.99/13.28 (((ex1I) =>
% 97.99/13.28 (((ex1I2) =>
% 97.99/13.28 (((singletonsuniq) =>
% 97.99/13.28 (((setukpairinjL1) =>
% 97.99/13.28 (((kfstsingleton) =>
% 97.99/13.28 (((theprop) =>
% 97.99/13.28 (((kfstpairEq) =>
% 97.99/13.28 (((cartprodfstin) =>
% 97.99/13.28 (((setukpairinjL2) =>
% 97.99/13.28 (((setukpairinjL) =>
% 97.99/13.28 (((setukpairinjR11) =>
% 97.99/13.28 (((setukpairinjR12) =>
% 97.99/13.28 (((setukpairinjR1) =>
% 97.99/13.28 (((upairequniteq) =>
% 97.99/13.28 (((setukpairinjR2) =>
% 97.99/13.28 (((setukpairinjR) =>
% 97.99/13.28 (((ksndsingleton) =>
% 97.99/13.28 ((
% 97.99/13.28 (ksndpairEq) =>
% 97.99/13.28 ((
% 97.99/13.28 (kpairsurjEq) =>
% 97.99/13.28 ((
% 97.99/13.28 (cartprodsndin) =>
% 97.99/13.28 ((
% 97.99/13.28 (cartprodpairmemEL) =>
% 97.99/13.28 ((
% 97.99/13.28 (cartprodpairmemER) =>
% 97.99/13.28 ((
% 97.99/13.28 (cartprodmempaircEq) =>
% 97.99/13.28 ((
% 97.99/13.28 (cartprodfstpairEq) =>
% 97.99/13.28 ((
% 97.99/13.28 (cartprodsndpairEq) =>
% 97.99/13.28 ((
% 97.99/13.28 (cartprodpairsurjEq) =>
% 97.99/13.28 ((
% 97.99/13.28 (dpsetconstrI) =>
% 97.99/13.28 ((
% 97.99/13.28 (dpsetconstrSub) =>
% 97.99/13.28 ((
% 97.99/13.28 (setOfPairsIsBReln) =>
% 97.99/13.28 ((
% 97.99/13.28 (dpsetconstrERa) =>
% 97.99/13.28 ((
% 97.99/13.28 (dpsetconstrEL1) =>
% 97.99/13.28 ((
% 97.99/13.28 (dpsetconstrEL2) =>
% 97.99/13.28 ((
% 97.99/13.28 (dpsetconstrER) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcImageSingleton) =>
% 97.99/13.28 ((
% 97.99/13.28 (apProp) =>
% 97.99/13.28 ((
% 97.99/13.28 (app) =>
% 97.99/13.28 ((
% 97.99/13.28 (infuncsetfunc) =>
% 97.99/13.28 ((
% 97.99/13.28 (ap2p) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcinfuncset) =>
% 97.99/13.28 ((
% 97.99/13.28 (lamProp) =>
% 97.99/13.28 ((
% 97.99/13.28 (lamp) =>
% 97.99/13.28 ((
% 97.99/13.28 (lam2p) =>
% 97.99/13.28 ((
% 97.99/13.28 (brelnall1) =>
% 97.99/13.28 ((
% 97.99/13.28 (brelnall2) =>
% 97.99/13.28 ((
% 97.99/13.28 (ex1E2) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcGraphProp1) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcGraphProp3) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcGraphProp2) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcextLem) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcGraphProp4) =>
% 97.99/13.28 ((
% 97.99/13.28 (subbreln) =>
% 97.99/13.28 ((
% 97.99/13.28 (eqbreln) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcext) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcext2) =>
% 97.99/13.28 ((
% 97.99/13.28 (ap2apEq1) =>
% 97.99/13.28 ((
% 97.99/13.28 (ap2apEq2) =>
% 97.99/13.28 ((
% 97.99/13.28 (beta1) =>
% 97.99/13.28 ((
% 97.99/13.28 (eta1) =>
% 97.99/13.28 ((
% 97.99/13.28 (lam2lamEq) =>
% 97.99/13.28 ((
% 97.99/13.28 (beta2) =>
% 97.99/13.28 ((
% 97.99/13.28 (eta2) =>
% 97.99/13.28 ((
% 97.99/13.28 (iffalseProp1) =>
% 97.99/13.28 ((
% 97.99/13.28 (iffalseProp2) =>
% 97.99/13.28 ((
% 97.99/13.28 (iftrueProp1) =>
% 97.99/13.28 ((
% 97.99/13.28 (iftrueProp2) =>
% 97.99/13.28 ((
% 97.99/13.28 (ifSingleton) =>
% 97.99/13.28 ((
% 97.99/13.28 (ifp) =>
% 97.99/13.28 ((
% 97.99/13.28 (theeq) =>
% 97.99/13.28 ((
% 97.99/13.28 (iftrue) =>
% 97.99/13.28 ((
% 97.99/13.28 (iffalse) =>
% 97.99/13.28 ((
% 97.99/13.28 (iftrueorfalse) =>
% 97.99/13.28 ((
% 97.99/13.28 (binintersectT_lem) =>
% 97.99/13.28 ((
% 97.99/13.28 (binunionT_lem) =>
% 97.99/13.28 ((
% 97.99/13.28 (powersetT_lem) =>
% 97.99/13.28 ((
% 97.99/13.28 (setminusT_lem) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementT_lem) =>
% 97.99/13.28 ((
% 97.99/13.28 (setextT) =>
% 97.99/13.28 ((
% 97.99/13.28 (subsetTI) =>
% 97.99/13.28 ((
% 97.99/13.28 (powersetTI1) =>
% 97.99/13.28 ((
% 97.99/13.28 (powersetTE1) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementTI1) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementTE1) =>
% 97.99/13.28 ((
% 97.99/13.28 (binintersectTELcontra) =>
% 97.99/13.28 ((
% 97.99/13.28 (binintersectTERcontra) =>
% 97.99/13.28 ((
% 97.99/13.28 (contrasubsetT) =>
% 97.99/13.28 ((
% 97.99/13.28 (contrasubsetT1) =>
% 97.99/13.28 ((
% 97.99/13.28 (contrasubsetT2) =>
% 97.99/13.28 ((
% 97.99/13.28 (contrasubsetT3) =>
% 97.99/13.28 ((
% 97.99/13.28 (doubleComplementI1) =>
% 97.99/13.28 ((
% 97.99/13.28 (doubleComplementE1) =>
% 97.99/13.28 ((
% 97.99/13.28 (doubleComplementSub1) =>
% 97.99/13.28 ((
% 97.99/13.28 (doubleComplementSub2) =>
% 97.99/13.28 ((
% 97.99/13.28 (doubleComplementEq) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementTnotintersectT) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementImpComplementIntersect) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementSubsetComplementIntersect) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementInPowersetComplementIntersect) =>
% 97.99/13.28 ((
% 97.99/13.28 (contraSubsetComplement) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementTcontraSubset) =>
% 97.99/13.28 ((
% 97.99/13.28 (binunionTILcontra) =>
% 97.99/13.28 ((
% 97.99/13.28 (binunionTIRcontra) =>
% 97.99/13.28 ((
% 97.99/13.28 (inIntersectImpInUnion) =>
% 97.99/13.28 ((
% 97.99/13.28 (inIntersectImpInUnion2) =>
% 97.99/13.28 ((
% 97.99/13.28 (inIntersectImpInIntersectUnions) =>
% 97.99/13.28 ((
% 97.99/13.28 (intersectInPowersetIntersectUnions) =>
% 97.99/13.28 ((
% 97.99/13.28 (inComplementUnionImpNotIn1) =>
% 97.99/13.28 ((
% 97.99/13.28 (inComplementUnionImpInComplement1) =>
% 97.99/13.28 ((
% 97.99/13.28 (binunionTE) =>
% 97.99/13.28 ((
% 97.99/13.28 (binunionTEcontra) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2a1) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementUnionInPowersetComplement) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2a2) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan1a) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan1b) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan1) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2a) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2b2) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2b) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz13rule0) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz13rule1) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz13rule2) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz13rule3) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz13rule4) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz1_1) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz1_2) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz1_3) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz1_4) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz1_5) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1all2) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1SetBreln1) =>
% 97.99/13.28 ((
% 97.99/13.28 (choice2fnsingleton) =>
% 97.99/13.28 ((
% 97.99/13.28 (setOfPairsIsBReln1) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1all1) =>
% 97.99/13.28 ((
% 97.99/13.28 (subbreln1) =>
% 97.99/13.28 ((
% 97.99/13.28 (eqbreln1) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1invprop) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1invI) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1invE) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1compprop) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1compI) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1compE) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1compEex) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionprop) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionIL) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionIR) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionI) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionE) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionEcases) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionCommutes) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz2Ex) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz2W) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz2A) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz2B) =>
% 97.99/13.28 ((
% 97.99/13.28 (image1Ex) =>
% 97.99/13.28 ((
% 97.99/13.28 (image1Ex1) =>
% 97.99/13.28 ((
% 97.99/13.28 (image1Equiv) =>
% 97.99/13.28 ((
% 97.99/13.28 (image1E) =>
% 97.99/13.28 ((
% 97.99/13.28 (image1I) =>
% 97.99/13.28 ((
% 97.99/13.28 (injFuncInInjFuncSet) =>
% 97.99/13.28 ((
% 97.99/13.28 (injFuncSetFuncIn) =>
% 97.99/13.28 ((
% 97.99/13.28 (injFuncSetFuncInj) =>
% 97.99/13.28 ((
% 97.99/13.28 (surjFuncSetFuncIn) =>
% 97.99/13.28 ((
% 97.99/13.28 (surjFuncSetFuncSurj) =>
% 97.99/13.28 ((
% 97.99/13.28 (leftInvIsSurj) =>
% 97.99/13.28 ((
% 97.99/13.28 (surjCantorThm) =>
% 97.99/13.28 ((
% 97.99/13.28 (foundation2) =>
% 97.99/13.28 ((
% 97.99/13.28 (notinself) =>
% 97.99/13.28 ((
% 97.99/13.28 (notinself2) =>
% 97.99/13.28 ((
% 97.99/13.28 (omegaSp) =>
% 97.99/13.28 ((
% 97.99/13.28 (omegaSclos) =>
% 97.99/13.28 ((
% 97.99/13.28 (peano0notS) =>
% 97.99/13.28 ((
% 97.99/13.28 (!!) @ (
% 97.99/13.28 (('#S') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 =>) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#C') @ in @
% 97.99/13.28 omega)))) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 !!) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#S') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 =>) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#C') @ in @
% 97.99/13.28 omega)))))) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#S') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 '#S') @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 =>))) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#C') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 '#B') @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 =) @
% 97.99/13.28 omegaS)))) @
% 97.99/13.28 omegaS)))))) @
% 97.99/13.28 (
% 97.99/13.28 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.99/13.28 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1459])).
% 97.99/13.28 thf(zip_derived_cl1473, plain,
% 97.99/13.28 (~ (((ubforcartprodlem1) =>
% 97.99/13.28 (((ubforcartprodlem2) =>
% 97.99/13.28 (((ubforcartprodlem3) =>
% 97.99/13.28 (((cartprodpairin) =>
% 97.99/13.28 (((cartprodmempair1) =>
% 97.99/13.28 (((cartprodmempair) =>
% 97.99/13.28 (((setunionE2) =>
% 97.99/13.28 (((setunionsingleton1) =>
% 97.99/13.28 (((setunionsingleton2) =>
% 97.99/13.28 (((setunionsingleton) =>
% 97.99/13.28 (((singletonprop) =>
% 97.99/13.28 (((ex1E1) =>
% 97.99/13.28 (((ex1I) =>
% 97.99/13.28 (((ex1I2) =>
% 97.99/13.28 (((singletonsuniq) =>
% 97.99/13.28 (((setukpairinjL1) =>
% 97.99/13.28 (((kfstsingleton) =>
% 97.99/13.28 (((theprop) =>
% 97.99/13.28 (((kfstpairEq) =>
% 97.99/13.28 (((cartprodfstin) =>
% 97.99/13.28 (((setukpairinjL2) =>
% 97.99/13.28 (((setukpairinjL) =>
% 97.99/13.28 (((setukpairinjR11) =>
% 97.99/13.28 (((setukpairinjR12) =>
% 97.99/13.28 (((setukpairinjR1) =>
% 97.99/13.28 (((upairequniteq) =>
% 97.99/13.28 (((setukpairinjR2) =>
% 97.99/13.28 (((setukpairinjR) =>
% 97.99/13.28 (((ksndsingleton) =>
% 97.99/13.28 (((ksndpairEq) =>
% 97.99/13.28 ((
% 97.99/13.28 (kpairsurjEq) =>
% 97.99/13.28 ((
% 97.99/13.28 (cartprodsndin) =>
% 97.99/13.28 ((
% 97.99/13.28 (cartprodpairmemEL) =>
% 97.99/13.28 ((
% 97.99/13.28 (cartprodpairmemER) =>
% 97.99/13.28 ((
% 97.99/13.28 (cartprodmempaircEq) =>
% 97.99/13.28 ((
% 97.99/13.28 (cartprodfstpairEq) =>
% 97.99/13.28 ((
% 97.99/13.28 (cartprodsndpairEq) =>
% 97.99/13.28 ((
% 97.99/13.28 (cartprodpairsurjEq) =>
% 97.99/13.28 ((
% 97.99/13.28 (dpsetconstrI) =>
% 97.99/13.28 ((
% 97.99/13.28 (dpsetconstrSub) =>
% 97.99/13.28 ((
% 97.99/13.28 (setOfPairsIsBReln) =>
% 97.99/13.28 ((
% 97.99/13.28 (dpsetconstrERa) =>
% 97.99/13.28 ((
% 97.99/13.28 (dpsetconstrEL1) =>
% 97.99/13.28 ((
% 97.99/13.28 (dpsetconstrEL2) =>
% 97.99/13.28 ((
% 97.99/13.28 (dpsetconstrER) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcImageSingleton) =>
% 97.99/13.28 ((
% 97.99/13.28 (apProp) =>
% 97.99/13.28 ((
% 97.99/13.28 (app) =>
% 97.99/13.28 ((
% 97.99/13.28 (infuncsetfunc) =>
% 97.99/13.28 ((
% 97.99/13.28 (ap2p) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcinfuncset) =>
% 97.99/13.28 ((
% 97.99/13.28 (lamProp) =>
% 97.99/13.28 ((
% 97.99/13.28 (lamp) =>
% 97.99/13.28 ((
% 97.99/13.28 (lam2p) =>
% 97.99/13.28 ((
% 97.99/13.28 (brelnall1) =>
% 97.99/13.28 ((
% 97.99/13.28 (brelnall2) =>
% 97.99/13.28 ((
% 97.99/13.28 (ex1E2) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcGraphProp1) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcGraphProp3) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcGraphProp2) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcextLem) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcGraphProp4) =>
% 97.99/13.28 ((
% 97.99/13.28 (subbreln) =>
% 97.99/13.28 ((
% 97.99/13.28 (eqbreln) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcext) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcext2) =>
% 97.99/13.28 ((
% 97.99/13.28 (ap2apEq1) =>
% 97.99/13.28 ((
% 97.99/13.28 (ap2apEq2) =>
% 97.99/13.28 ((
% 97.99/13.28 (beta1) =>
% 97.99/13.28 ((
% 97.99/13.28 (eta1) =>
% 97.99/13.28 ((
% 97.99/13.28 (lam2lamEq) =>
% 97.99/13.28 ((
% 97.99/13.28 (beta2) =>
% 97.99/13.28 ((
% 97.99/13.28 (eta2) =>
% 97.99/13.28 ((
% 97.99/13.28 (iffalseProp1) =>
% 97.99/13.28 ((
% 97.99/13.28 (iffalseProp2) =>
% 97.99/13.28 ((
% 97.99/13.28 (iftrueProp1) =>
% 97.99/13.28 ((
% 97.99/13.28 (iftrueProp2) =>
% 97.99/13.28 ((
% 97.99/13.28 (ifSingleton) =>
% 97.99/13.28 ((
% 97.99/13.28 (ifp) =>
% 97.99/13.28 ((
% 97.99/13.28 (theeq) =>
% 97.99/13.28 ((
% 97.99/13.28 (iftrue) =>
% 97.99/13.28 ((
% 97.99/13.28 (iffalse) =>
% 97.99/13.28 ((
% 97.99/13.28 (iftrueorfalse) =>
% 97.99/13.28 ((
% 97.99/13.28 (binintersectT_lem) =>
% 97.99/13.28 ((
% 97.99/13.28 (binunionT_lem) =>
% 97.99/13.28 ((
% 97.99/13.28 (powersetT_lem) =>
% 97.99/13.28 ((
% 97.99/13.28 (setminusT_lem) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementT_lem) =>
% 97.99/13.28 ((
% 97.99/13.28 (setextT) =>
% 97.99/13.28 ((
% 97.99/13.28 (subsetTI) =>
% 97.99/13.28 ((
% 97.99/13.28 (powersetTI1) =>
% 97.99/13.28 ((
% 97.99/13.28 (powersetTE1) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementTI1) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementTE1) =>
% 97.99/13.28 ((
% 97.99/13.28 (binintersectTELcontra) =>
% 97.99/13.28 ((
% 97.99/13.28 (binintersectTERcontra) =>
% 97.99/13.28 ((
% 97.99/13.28 (contrasubsetT) =>
% 97.99/13.28 ((
% 97.99/13.28 (contrasubsetT1) =>
% 97.99/13.28 ((
% 97.99/13.28 (contrasubsetT2) =>
% 97.99/13.28 ((
% 97.99/13.28 (contrasubsetT3) =>
% 97.99/13.28 ((
% 97.99/13.28 (doubleComplementI1) =>
% 97.99/13.28 ((
% 97.99/13.28 (doubleComplementE1) =>
% 97.99/13.28 ((
% 97.99/13.28 (doubleComplementSub1) =>
% 97.99/13.28 ((
% 97.99/13.28 (doubleComplementSub2) =>
% 97.99/13.28 ((
% 97.99/13.28 (doubleComplementEq) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementTnotintersectT) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementImpComplementIntersect) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementSubsetComplementIntersect) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementInPowersetComplementIntersect) =>
% 97.99/13.28 ((
% 97.99/13.28 (contraSubsetComplement) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementTcontraSubset) =>
% 97.99/13.28 ((
% 97.99/13.28 (binunionTILcontra) =>
% 97.99/13.28 ((
% 97.99/13.28 (binunionTIRcontra) =>
% 97.99/13.28 ((
% 97.99/13.28 (inIntersectImpInUnion) =>
% 97.99/13.28 ((
% 97.99/13.28 (inIntersectImpInUnion2) =>
% 97.99/13.28 ((
% 97.99/13.28 (inIntersectImpInIntersectUnions) =>
% 97.99/13.28 ((
% 97.99/13.28 (intersectInPowersetIntersectUnions) =>
% 97.99/13.28 ((
% 97.99/13.28 (inComplementUnionImpNotIn1) =>
% 97.99/13.28 ((
% 97.99/13.28 (inComplementUnionImpInComplement1) =>
% 97.99/13.28 ((
% 97.99/13.28 (binunionTE) =>
% 97.99/13.28 ((
% 97.99/13.28 (binunionTEcontra) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2a1) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementUnionInPowersetComplement) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2a2) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan1a) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan1b) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan1) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2a) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2b2) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2b) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz13rule0) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz13rule1) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz13rule2) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz13rule3) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz13rule4) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz1_1) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz1_2) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz1_3) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz1_4) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz1_5) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1all2) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1SetBreln1) =>
% 97.99/13.28 ((
% 97.99/13.28 (choice2fnsingleton) =>
% 97.99/13.28 ((
% 97.99/13.28 (setOfPairsIsBReln1) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1all1) =>
% 97.99/13.28 ((
% 97.99/13.28 (subbreln1) =>
% 97.99/13.28 ((
% 97.99/13.28 (eqbreln1) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1invprop) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1invI) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1invE) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1compprop) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1compI) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1compE) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1compEex) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionprop) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionIL) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionIR) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionI) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionE) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionEcases) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionCommutes) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz2Ex) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz2W) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz2A) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz2B) =>
% 97.99/13.28 ((
% 97.99/13.28 (image1Ex) =>
% 97.99/13.28 ((
% 97.99/13.28 (image1Ex1) =>
% 97.99/13.28 ((
% 97.99/13.28 (image1Equiv) =>
% 97.99/13.28 ((
% 97.99/13.28 (image1E) =>
% 97.99/13.28 ((
% 97.99/13.28 (image1I) =>
% 97.99/13.28 ((
% 97.99/13.28 (injFuncInInjFuncSet) =>
% 97.99/13.28 ((
% 97.99/13.28 (injFuncSetFuncIn) =>
% 97.99/13.28 ((
% 97.99/13.28 (injFuncSetFuncInj) =>
% 97.99/13.28 ((
% 97.99/13.28 (surjFuncSetFuncIn) =>
% 97.99/13.28 ((
% 97.99/13.28 (surjFuncSetFuncSurj) =>
% 97.99/13.28 ((
% 97.99/13.28 (leftInvIsSurj) =>
% 97.99/13.28 ((
% 97.99/13.28 (surjCantorThm) =>
% 97.99/13.28 ((
% 97.99/13.28 (foundation2) =>
% 97.99/13.28 ((
% 97.99/13.28 (notinself) =>
% 97.99/13.28 ((
% 97.99/13.28 (notinself2) =>
% 97.99/13.28 ((
% 97.99/13.28 (omegaSp) =>
% 97.99/13.28 ((
% 97.99/13.28 (omegaSclos) =>
% 97.99/13.28 ((
% 97.99/13.28 (peano0notS) =>
% 97.99/13.28 ((
% 97.99/13.28 (!!) @ (
% 97.99/13.28 (('#S') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 =>) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#C') @ in @
% 97.99/13.28 omega)))) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 !!) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#S') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 =>) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#C') @ in @
% 97.99/13.28 omega)))))) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#S') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 '#S') @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 =>))) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#C') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 '#B') @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 =) @
% 97.99/13.28 omegaS)))) @
% 97.99/13.28 omegaS)))))) @
% 97.99/13.28 (
% 97.99/13.28 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.99/13.28 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1466])).
% 97.99/13.28 thf(zip_derived_cl1480, plain,
% 97.99/13.28 (~ (((ubforcartprodlem2) =>
% 97.99/13.28 (((ubforcartprodlem3) =>
% 97.99/13.28 (((cartprodpairin) =>
% 97.99/13.28 (((cartprodmempair1) =>
% 97.99/13.28 (((cartprodmempair) =>
% 97.99/13.28 (((setunionE2) =>
% 97.99/13.28 (((setunionsingleton1) =>
% 97.99/13.28 (((setunionsingleton2) =>
% 97.99/13.28 (((setunionsingleton) =>
% 97.99/13.28 (((singletonprop) =>
% 97.99/13.28 (((ex1E1) =>
% 97.99/13.28 (((ex1I) =>
% 97.99/13.28 (((ex1I2) =>
% 97.99/13.28 (((singletonsuniq) =>
% 97.99/13.28 (((setukpairinjL1) =>
% 97.99/13.28 (((kfstsingleton) =>
% 97.99/13.28 (((theprop) =>
% 97.99/13.28 (((kfstpairEq) =>
% 97.99/13.28 (((cartprodfstin) =>
% 97.99/13.28 (((setukpairinjL2) =>
% 97.99/13.28 (((setukpairinjL) =>
% 97.99/13.28 (((setukpairinjR11) =>
% 97.99/13.28 (((setukpairinjR12) =>
% 97.99/13.28 (((setukpairinjR1) =>
% 97.99/13.28 (((upairequniteq) =>
% 97.99/13.28 (((setukpairinjR2) =>
% 97.99/13.28 (((setukpairinjR) =>
% 97.99/13.28 (((ksndsingleton) =>
% 97.99/13.28 (((ksndpairEq) =>
% 97.99/13.28 (((kpairsurjEq) =>
% 97.99/13.28 ((
% 97.99/13.28 (cartprodsndin) =>
% 97.99/13.28 ((
% 97.99/13.28 (cartprodpairmemEL) =>
% 97.99/13.28 ((
% 97.99/13.28 (cartprodpairmemER) =>
% 97.99/13.28 ((
% 97.99/13.28 (cartprodmempaircEq) =>
% 97.99/13.28 ((
% 97.99/13.28 (cartprodfstpairEq) =>
% 97.99/13.28 ((
% 97.99/13.28 (cartprodsndpairEq) =>
% 97.99/13.28 ((
% 97.99/13.28 (cartprodpairsurjEq) =>
% 97.99/13.28 ((
% 97.99/13.28 (dpsetconstrI) =>
% 97.99/13.28 ((
% 97.99/13.28 (dpsetconstrSub) =>
% 97.99/13.28 ((
% 97.99/13.28 (setOfPairsIsBReln) =>
% 97.99/13.28 ((
% 97.99/13.28 (dpsetconstrERa) =>
% 97.99/13.28 ((
% 97.99/13.28 (dpsetconstrEL1) =>
% 97.99/13.28 ((
% 97.99/13.28 (dpsetconstrEL2) =>
% 97.99/13.28 ((
% 97.99/13.28 (dpsetconstrER) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcImageSingleton) =>
% 97.99/13.28 ((
% 97.99/13.28 (apProp) =>
% 97.99/13.28 ((
% 97.99/13.28 (app) =>
% 97.99/13.28 ((
% 97.99/13.28 (infuncsetfunc) =>
% 97.99/13.28 ((
% 97.99/13.28 (ap2p) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcinfuncset) =>
% 97.99/13.28 ((
% 97.99/13.28 (lamProp) =>
% 97.99/13.28 ((
% 97.99/13.28 (lamp) =>
% 97.99/13.28 ((
% 97.99/13.28 (lam2p) =>
% 97.99/13.28 ((
% 97.99/13.28 (brelnall1) =>
% 97.99/13.28 ((
% 97.99/13.28 (brelnall2) =>
% 97.99/13.28 ((
% 97.99/13.28 (ex1E2) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcGraphProp1) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcGraphProp3) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcGraphProp2) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcextLem) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcGraphProp4) =>
% 97.99/13.28 ((
% 97.99/13.28 (subbreln) =>
% 97.99/13.28 ((
% 97.99/13.28 (eqbreln) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcext) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcext2) =>
% 97.99/13.28 ((
% 97.99/13.28 (ap2apEq1) =>
% 97.99/13.28 ((
% 97.99/13.28 (ap2apEq2) =>
% 97.99/13.28 ((
% 97.99/13.28 (beta1) =>
% 97.99/13.28 ((
% 97.99/13.28 (eta1) =>
% 97.99/13.28 ((
% 97.99/13.28 (lam2lamEq) =>
% 97.99/13.28 ((
% 97.99/13.28 (beta2) =>
% 97.99/13.28 ((
% 97.99/13.28 (eta2) =>
% 97.99/13.28 ((
% 97.99/13.28 (iffalseProp1) =>
% 97.99/13.28 ((
% 97.99/13.28 (iffalseProp2) =>
% 97.99/13.28 ((
% 97.99/13.28 (iftrueProp1) =>
% 97.99/13.28 ((
% 97.99/13.28 (iftrueProp2) =>
% 97.99/13.28 ((
% 97.99/13.28 (ifSingleton) =>
% 97.99/13.28 ((
% 97.99/13.28 (ifp) =>
% 97.99/13.28 ((
% 97.99/13.28 (theeq) =>
% 97.99/13.28 ((
% 97.99/13.28 (iftrue) =>
% 97.99/13.28 ((
% 97.99/13.28 (iffalse) =>
% 97.99/13.28 ((
% 97.99/13.28 (iftrueorfalse) =>
% 97.99/13.28 ((
% 97.99/13.28 (binintersectT_lem) =>
% 97.99/13.28 ((
% 97.99/13.28 (binunionT_lem) =>
% 97.99/13.28 ((
% 97.99/13.28 (powersetT_lem) =>
% 97.99/13.28 ((
% 97.99/13.28 (setminusT_lem) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementT_lem) =>
% 97.99/13.28 ((
% 97.99/13.28 (setextT) =>
% 97.99/13.28 ((
% 97.99/13.28 (subsetTI) =>
% 97.99/13.28 ((
% 97.99/13.28 (powersetTI1) =>
% 97.99/13.28 ((
% 97.99/13.28 (powersetTE1) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementTI1) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementTE1) =>
% 97.99/13.28 ((
% 97.99/13.28 (binintersectTELcontra) =>
% 97.99/13.28 ((
% 97.99/13.28 (binintersectTERcontra) =>
% 97.99/13.28 ((
% 97.99/13.28 (contrasubsetT) =>
% 97.99/13.28 ((
% 97.99/13.28 (contrasubsetT1) =>
% 97.99/13.28 ((
% 97.99/13.28 (contrasubsetT2) =>
% 97.99/13.28 ((
% 97.99/13.28 (contrasubsetT3) =>
% 97.99/13.28 ((
% 97.99/13.28 (doubleComplementI1) =>
% 97.99/13.28 ((
% 97.99/13.28 (doubleComplementE1) =>
% 97.99/13.28 ((
% 97.99/13.28 (doubleComplementSub1) =>
% 97.99/13.28 ((
% 97.99/13.28 (doubleComplementSub2) =>
% 97.99/13.28 ((
% 97.99/13.28 (doubleComplementEq) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementTnotintersectT) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementImpComplementIntersect) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementSubsetComplementIntersect) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementInPowersetComplementIntersect) =>
% 97.99/13.28 ((
% 97.99/13.28 (contraSubsetComplement) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementTcontraSubset) =>
% 97.99/13.28 ((
% 97.99/13.28 (binunionTILcontra) =>
% 97.99/13.28 ((
% 97.99/13.28 (binunionTIRcontra) =>
% 97.99/13.28 ((
% 97.99/13.28 (inIntersectImpInUnion) =>
% 97.99/13.28 ((
% 97.99/13.28 (inIntersectImpInUnion2) =>
% 97.99/13.28 ((
% 97.99/13.28 (inIntersectImpInIntersectUnions) =>
% 97.99/13.28 ((
% 97.99/13.28 (intersectInPowersetIntersectUnions) =>
% 97.99/13.28 ((
% 97.99/13.28 (inComplementUnionImpNotIn1) =>
% 97.99/13.28 ((
% 97.99/13.28 (inComplementUnionImpInComplement1) =>
% 97.99/13.28 ((
% 97.99/13.28 (binunionTE) =>
% 97.99/13.28 ((
% 97.99/13.28 (binunionTEcontra) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2a1) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementUnionInPowersetComplement) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2a2) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan1a) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan1b) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan1) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2a) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2b2) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2b) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz13rule0) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz13rule1) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz13rule2) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz13rule3) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz13rule4) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz1_1) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz1_2) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz1_3) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz1_4) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz1_5) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1all2) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1SetBreln1) =>
% 97.99/13.28 ((
% 97.99/13.28 (choice2fnsingleton) =>
% 97.99/13.28 ((
% 97.99/13.28 (setOfPairsIsBReln1) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1all1) =>
% 97.99/13.28 ((
% 97.99/13.28 (subbreln1) =>
% 97.99/13.28 ((
% 97.99/13.28 (eqbreln1) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1invprop) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1invI) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1invE) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1compprop) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1compI) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1compE) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1compEex) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionprop) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionIL) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionIR) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionI) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionE) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionEcases) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionCommutes) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz2Ex) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz2W) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz2A) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz2B) =>
% 97.99/13.28 ((
% 97.99/13.28 (image1Ex) =>
% 97.99/13.28 ((
% 97.99/13.28 (image1Ex1) =>
% 97.99/13.28 ((
% 97.99/13.28 (image1Equiv) =>
% 97.99/13.28 ((
% 97.99/13.28 (image1E) =>
% 97.99/13.28 ((
% 97.99/13.28 (image1I) =>
% 97.99/13.28 ((
% 97.99/13.28 (injFuncInInjFuncSet) =>
% 97.99/13.28 ((
% 97.99/13.28 (injFuncSetFuncIn) =>
% 97.99/13.28 ((
% 97.99/13.28 (injFuncSetFuncInj) =>
% 97.99/13.28 ((
% 97.99/13.28 (surjFuncSetFuncIn) =>
% 97.99/13.28 ((
% 97.99/13.28 (surjFuncSetFuncSurj) =>
% 97.99/13.28 ((
% 97.99/13.28 (leftInvIsSurj) =>
% 97.99/13.28 ((
% 97.99/13.28 (surjCantorThm) =>
% 97.99/13.28 ((
% 97.99/13.28 (foundation2) =>
% 97.99/13.28 ((
% 97.99/13.28 (notinself) =>
% 97.99/13.28 ((
% 97.99/13.28 (notinself2) =>
% 97.99/13.28 ((
% 97.99/13.28 (omegaSp) =>
% 97.99/13.28 ((
% 97.99/13.28 (omegaSclos) =>
% 97.99/13.28 ((
% 97.99/13.28 (peano0notS) =>
% 97.99/13.28 ((
% 97.99/13.28 (!!) @ (
% 97.99/13.28 (('#S') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 =>) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#C') @ in @
% 97.99/13.28 omega)))) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 !!) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#S') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 =>) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#C') @ in @
% 97.99/13.28 omega)))))) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#S') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 '#S') @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 =>))) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#C') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 '#B') @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 =) @
% 97.99/13.28 omegaS)))) @
% 97.99/13.28 omegaS)))))) @
% 97.99/13.28 (
% 97.99/13.28 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.99/13.28 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1473])).
% 97.99/13.28 thf(zip_derived_cl1488, plain,
% 97.99/13.28 (~ (((ubforcartprodlem3) =>
% 97.99/13.28 (((cartprodpairin) =>
% 97.99/13.28 (((cartprodmempair1) =>
% 97.99/13.28 (((cartprodmempair) =>
% 97.99/13.28 (((setunionE2) =>
% 97.99/13.28 (((setunionsingleton1) =>
% 97.99/13.28 (((setunionsingleton2) =>
% 97.99/13.28 (((setunionsingleton) =>
% 97.99/13.28 (((singletonprop) =>
% 97.99/13.28 (((ex1E1) =>
% 97.99/13.28 (((ex1I) =>
% 97.99/13.28 (((ex1I2) =>
% 97.99/13.28 (((singletonsuniq) =>
% 97.99/13.28 (((setukpairinjL1) =>
% 97.99/13.28 (((kfstsingleton) =>
% 97.99/13.28 (((theprop) =>
% 97.99/13.28 (((kfstpairEq) =>
% 97.99/13.28 (((cartprodfstin) =>
% 97.99/13.28 (((setukpairinjL2) =>
% 97.99/13.28 (((setukpairinjL) =>
% 97.99/13.28 (((setukpairinjR11) =>
% 97.99/13.28 (((setukpairinjR12) =>
% 97.99/13.28 (((setukpairinjR1) =>
% 97.99/13.28 (((upairequniteq) =>
% 97.99/13.28 (((setukpairinjR2) =>
% 97.99/13.28 (((setukpairinjR) =>
% 97.99/13.28 (((ksndsingleton) =>
% 97.99/13.28 (((ksndpairEq) =>
% 97.99/13.28 (((kpairsurjEq) =>
% 97.99/13.28 (((cartprodsndin) =>
% 97.99/13.28 ((
% 97.99/13.28 (cartprodpairmemEL) =>
% 97.99/13.28 ((
% 97.99/13.28 (cartprodpairmemER) =>
% 97.99/13.28 ((
% 97.99/13.28 (cartprodmempaircEq) =>
% 97.99/13.28 ((
% 97.99/13.28 (cartprodfstpairEq) =>
% 97.99/13.28 ((
% 97.99/13.28 (cartprodsndpairEq) =>
% 97.99/13.28 ((
% 97.99/13.28 (cartprodpairsurjEq) =>
% 97.99/13.28 ((
% 97.99/13.28 (dpsetconstrI) =>
% 97.99/13.28 ((
% 97.99/13.28 (dpsetconstrSub) =>
% 97.99/13.28 ((
% 97.99/13.28 (setOfPairsIsBReln) =>
% 97.99/13.28 ((
% 97.99/13.28 (dpsetconstrERa) =>
% 97.99/13.28 ((
% 97.99/13.28 (dpsetconstrEL1) =>
% 97.99/13.28 ((
% 97.99/13.28 (dpsetconstrEL2) =>
% 97.99/13.28 ((
% 97.99/13.28 (dpsetconstrER) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcImageSingleton) =>
% 97.99/13.28 ((
% 97.99/13.28 (apProp) =>
% 97.99/13.28 ((
% 97.99/13.28 (app) =>
% 97.99/13.28 ((
% 97.99/13.28 (infuncsetfunc) =>
% 97.99/13.28 ((
% 97.99/13.28 (ap2p) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcinfuncset) =>
% 97.99/13.28 ((
% 97.99/13.28 (lamProp) =>
% 97.99/13.28 ((
% 97.99/13.28 (lamp) =>
% 97.99/13.28 ((
% 97.99/13.28 (lam2p) =>
% 97.99/13.28 ((
% 97.99/13.28 (brelnall1) =>
% 97.99/13.28 ((
% 97.99/13.28 (brelnall2) =>
% 97.99/13.28 ((
% 97.99/13.28 (ex1E2) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcGraphProp1) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcGraphProp3) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcGraphProp2) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcextLem) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcGraphProp4) =>
% 97.99/13.28 ((
% 97.99/13.28 (subbreln) =>
% 97.99/13.28 ((
% 97.99/13.28 (eqbreln) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcext) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcext2) =>
% 97.99/13.28 ((
% 97.99/13.28 (ap2apEq1) =>
% 97.99/13.28 ((
% 97.99/13.28 (ap2apEq2) =>
% 97.99/13.28 ((
% 97.99/13.28 (beta1) =>
% 97.99/13.28 ((
% 97.99/13.28 (eta1) =>
% 97.99/13.28 ((
% 97.99/13.28 (lam2lamEq) =>
% 97.99/13.28 ((
% 97.99/13.28 (beta2) =>
% 97.99/13.28 ((
% 97.99/13.28 (eta2) =>
% 97.99/13.28 ((
% 97.99/13.28 (iffalseProp1) =>
% 97.99/13.28 ((
% 97.99/13.28 (iffalseProp2) =>
% 97.99/13.28 ((
% 97.99/13.28 (iftrueProp1) =>
% 97.99/13.28 ((
% 97.99/13.28 (iftrueProp2) =>
% 97.99/13.28 ((
% 97.99/13.28 (ifSingleton) =>
% 97.99/13.28 ((
% 97.99/13.28 (ifp) =>
% 97.99/13.28 ((
% 97.99/13.28 (theeq) =>
% 97.99/13.28 ((
% 97.99/13.28 (iftrue) =>
% 97.99/13.28 ((
% 97.99/13.28 (iffalse) =>
% 97.99/13.28 ((
% 97.99/13.28 (iftrueorfalse) =>
% 97.99/13.28 ((
% 97.99/13.28 (binintersectT_lem) =>
% 97.99/13.28 ((
% 97.99/13.28 (binunionT_lem) =>
% 97.99/13.28 ((
% 97.99/13.28 (powersetT_lem) =>
% 97.99/13.28 ((
% 97.99/13.28 (setminusT_lem) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementT_lem) =>
% 97.99/13.28 ((
% 97.99/13.28 (setextT) =>
% 97.99/13.28 ((
% 97.99/13.28 (subsetTI) =>
% 97.99/13.28 ((
% 97.99/13.28 (powersetTI1) =>
% 97.99/13.28 ((
% 97.99/13.28 (powersetTE1) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementTI1) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementTE1) =>
% 97.99/13.28 ((
% 97.99/13.28 (binintersectTELcontra) =>
% 97.99/13.28 ((
% 97.99/13.28 (binintersectTERcontra) =>
% 97.99/13.28 ((
% 97.99/13.28 (contrasubsetT) =>
% 97.99/13.28 ((
% 97.99/13.28 (contrasubsetT1) =>
% 97.99/13.28 ((
% 97.99/13.28 (contrasubsetT2) =>
% 97.99/13.28 ((
% 97.99/13.28 (contrasubsetT3) =>
% 97.99/13.28 ((
% 97.99/13.28 (doubleComplementI1) =>
% 97.99/13.28 ((
% 97.99/13.28 (doubleComplementE1) =>
% 97.99/13.28 ((
% 97.99/13.28 (doubleComplementSub1) =>
% 97.99/13.28 ((
% 97.99/13.28 (doubleComplementSub2) =>
% 97.99/13.28 ((
% 97.99/13.28 (doubleComplementEq) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementTnotintersectT) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementImpComplementIntersect) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementSubsetComplementIntersect) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementInPowersetComplementIntersect) =>
% 97.99/13.28 ((
% 97.99/13.28 (contraSubsetComplement) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementTcontraSubset) =>
% 97.99/13.28 ((
% 97.99/13.28 (binunionTILcontra) =>
% 97.99/13.28 ((
% 97.99/13.28 (binunionTIRcontra) =>
% 97.99/13.28 ((
% 97.99/13.28 (inIntersectImpInUnion) =>
% 97.99/13.28 ((
% 97.99/13.28 (inIntersectImpInUnion2) =>
% 97.99/13.28 ((
% 97.99/13.28 (inIntersectImpInIntersectUnions) =>
% 97.99/13.28 ((
% 97.99/13.28 (intersectInPowersetIntersectUnions) =>
% 97.99/13.28 ((
% 97.99/13.28 (inComplementUnionImpNotIn1) =>
% 97.99/13.28 ((
% 97.99/13.28 (inComplementUnionImpInComplement1) =>
% 97.99/13.28 ((
% 97.99/13.28 (binunionTE) =>
% 97.99/13.28 ((
% 97.99/13.28 (binunionTEcontra) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2a1) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementUnionInPowersetComplement) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2a2) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan1a) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan1b) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan1) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2a) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2b2) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2b) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz13rule0) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz13rule1) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz13rule2) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz13rule3) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz13rule4) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz1_1) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz1_2) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz1_3) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz1_4) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz1_5) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1all2) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1SetBreln1) =>
% 97.99/13.28 ((
% 97.99/13.28 (choice2fnsingleton) =>
% 97.99/13.28 ((
% 97.99/13.28 (setOfPairsIsBReln1) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1all1) =>
% 97.99/13.28 ((
% 97.99/13.28 (subbreln1) =>
% 97.99/13.28 ((
% 97.99/13.28 (eqbreln1) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1invprop) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1invI) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1invE) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1compprop) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1compI) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1compE) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1compEex) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionprop) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionIL) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionIR) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionI) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionE) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionEcases) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionCommutes) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz2Ex) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz2W) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz2A) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz2B) =>
% 97.99/13.28 ((
% 97.99/13.28 (image1Ex) =>
% 97.99/13.28 ((
% 97.99/13.28 (image1Ex1) =>
% 97.99/13.28 ((
% 97.99/13.28 (image1Equiv) =>
% 97.99/13.28 ((
% 97.99/13.28 (image1E) =>
% 97.99/13.28 ((
% 97.99/13.28 (image1I) =>
% 97.99/13.28 ((
% 97.99/13.28 (injFuncInInjFuncSet) =>
% 97.99/13.28 ((
% 97.99/13.28 (injFuncSetFuncIn) =>
% 97.99/13.28 ((
% 97.99/13.28 (injFuncSetFuncInj) =>
% 97.99/13.28 ((
% 97.99/13.28 (surjFuncSetFuncIn) =>
% 97.99/13.28 ((
% 97.99/13.28 (surjFuncSetFuncSurj) =>
% 97.99/13.28 ((
% 97.99/13.28 (leftInvIsSurj) =>
% 97.99/13.28 ((
% 97.99/13.28 (surjCantorThm) =>
% 97.99/13.28 ((
% 97.99/13.28 (foundation2) =>
% 97.99/13.28 ((
% 97.99/13.28 (notinself) =>
% 97.99/13.28 ((
% 97.99/13.28 (notinself2) =>
% 97.99/13.28 ((
% 97.99/13.28 (omegaSp) =>
% 97.99/13.28 ((
% 97.99/13.28 (omegaSclos) =>
% 97.99/13.28 ((
% 97.99/13.28 (peano0notS) =>
% 97.99/13.28 ((
% 97.99/13.28 (!!) @ (
% 97.99/13.28 (('#S') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 =>) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#C') @ in @
% 97.99/13.28 omega)))) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 !!) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#S') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 =>) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#C') @ in @
% 97.99/13.28 omega)))))) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#S') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 '#S') @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 =>))) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#C') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 '#B') @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 =) @
% 97.99/13.28 omegaS)))) @
% 97.99/13.28 omegaS)))))) @
% 97.99/13.28 (
% 97.99/13.28 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.99/13.28 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1480])).
% 97.99/13.28 thf(zip_derived_cl1496, plain,
% 97.99/13.28 (~ (((cartprodpairin) =>
% 97.99/13.28 (((cartprodmempair1) =>
% 97.99/13.28 (((cartprodmempair) =>
% 97.99/13.28 (((setunionE2) =>
% 97.99/13.28 (((setunionsingleton1) =>
% 97.99/13.28 (((setunionsingleton2) =>
% 97.99/13.28 (((setunionsingleton) =>
% 97.99/13.28 (((singletonprop) =>
% 97.99/13.28 (((ex1E1) =>
% 97.99/13.28 (((ex1I) =>
% 97.99/13.28 (((ex1I2) =>
% 97.99/13.28 (((singletonsuniq) =>
% 97.99/13.28 (((setukpairinjL1) =>
% 97.99/13.28 (((kfstsingleton) =>
% 97.99/13.28 (((theprop) =>
% 97.99/13.28 (((kfstpairEq) =>
% 97.99/13.28 (((cartprodfstin) =>
% 97.99/13.28 (((setukpairinjL2) =>
% 97.99/13.28 (((setukpairinjL) =>
% 97.99/13.28 (((setukpairinjR11) =>
% 97.99/13.28 (((setukpairinjR12) =>
% 97.99/13.28 (((setukpairinjR1) =>
% 97.99/13.28 (((upairequniteq) =>
% 97.99/13.28 (((setukpairinjR2) =>
% 97.99/13.28 (((setukpairinjR) =>
% 97.99/13.28 (((ksndsingleton) =>
% 97.99/13.28 (((ksndpairEq) =>
% 97.99/13.28 (((kpairsurjEq) =>
% 97.99/13.28 (((cartprodsndin) =>
% 97.99/13.28 (((cartprodpairmemEL) =>
% 97.99/13.28 ((
% 97.99/13.28 (cartprodpairmemER) =>
% 97.99/13.28 ((
% 97.99/13.28 (cartprodmempaircEq) =>
% 97.99/13.28 ((
% 97.99/13.28 (cartprodfstpairEq) =>
% 97.99/13.28 ((
% 97.99/13.28 (cartprodsndpairEq) =>
% 97.99/13.28 ((
% 97.99/13.28 (cartprodpairsurjEq) =>
% 97.99/13.28 ((
% 97.99/13.28 (dpsetconstrI) =>
% 97.99/13.28 ((
% 97.99/13.28 (dpsetconstrSub) =>
% 97.99/13.28 ((
% 97.99/13.28 (setOfPairsIsBReln) =>
% 97.99/13.28 ((
% 97.99/13.28 (dpsetconstrERa) =>
% 97.99/13.28 ((
% 97.99/13.28 (dpsetconstrEL1) =>
% 97.99/13.28 ((
% 97.99/13.28 (dpsetconstrEL2) =>
% 97.99/13.28 ((
% 97.99/13.28 (dpsetconstrER) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcImageSingleton) =>
% 97.99/13.28 ((
% 97.99/13.28 (apProp) =>
% 97.99/13.28 ((
% 97.99/13.28 (app) =>
% 97.99/13.28 ((
% 97.99/13.28 (infuncsetfunc) =>
% 97.99/13.28 ((
% 97.99/13.28 (ap2p) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcinfuncset) =>
% 97.99/13.28 ((
% 97.99/13.28 (lamProp) =>
% 97.99/13.28 ((
% 97.99/13.28 (lamp) =>
% 97.99/13.28 ((
% 97.99/13.28 (lam2p) =>
% 97.99/13.28 ((
% 97.99/13.28 (brelnall1) =>
% 97.99/13.28 ((
% 97.99/13.28 (brelnall2) =>
% 97.99/13.28 ((
% 97.99/13.28 (ex1E2) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcGraphProp1) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcGraphProp3) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcGraphProp2) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcextLem) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcGraphProp4) =>
% 97.99/13.28 ((
% 97.99/13.28 (subbreln) =>
% 97.99/13.28 ((
% 97.99/13.28 (eqbreln) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcext) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcext2) =>
% 97.99/13.28 ((
% 97.99/13.28 (ap2apEq1) =>
% 97.99/13.28 ((
% 97.99/13.28 (ap2apEq2) =>
% 97.99/13.28 ((
% 97.99/13.28 (beta1) =>
% 97.99/13.28 ((
% 97.99/13.28 (eta1) =>
% 97.99/13.28 ((
% 97.99/13.28 (lam2lamEq) =>
% 97.99/13.28 ((
% 97.99/13.28 (beta2) =>
% 97.99/13.28 ((
% 97.99/13.28 (eta2) =>
% 97.99/13.28 ((
% 97.99/13.28 (iffalseProp1) =>
% 97.99/13.28 ((
% 97.99/13.28 (iffalseProp2) =>
% 97.99/13.28 ((
% 97.99/13.28 (iftrueProp1) =>
% 97.99/13.28 ((
% 97.99/13.28 (iftrueProp2) =>
% 97.99/13.28 ((
% 97.99/13.28 (ifSingleton) =>
% 97.99/13.28 ((
% 97.99/13.28 (ifp) =>
% 97.99/13.28 ((
% 97.99/13.28 (theeq) =>
% 97.99/13.28 ((
% 97.99/13.28 (iftrue) =>
% 97.99/13.28 ((
% 97.99/13.28 (iffalse) =>
% 97.99/13.28 ((
% 97.99/13.28 (iftrueorfalse) =>
% 97.99/13.28 ((
% 97.99/13.28 (binintersectT_lem) =>
% 97.99/13.28 ((
% 97.99/13.28 (binunionT_lem) =>
% 97.99/13.28 ((
% 97.99/13.28 (powersetT_lem) =>
% 97.99/13.28 ((
% 97.99/13.28 (setminusT_lem) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementT_lem) =>
% 97.99/13.28 ((
% 97.99/13.28 (setextT) =>
% 97.99/13.28 ((
% 97.99/13.28 (subsetTI) =>
% 97.99/13.28 ((
% 97.99/13.28 (powersetTI1) =>
% 97.99/13.28 ((
% 97.99/13.28 (powersetTE1) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementTI1) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementTE1) =>
% 97.99/13.28 ((
% 97.99/13.28 (binintersectTELcontra) =>
% 97.99/13.28 ((
% 97.99/13.28 (binintersectTERcontra) =>
% 97.99/13.28 ((
% 97.99/13.28 (contrasubsetT) =>
% 97.99/13.28 ((
% 97.99/13.28 (contrasubsetT1) =>
% 97.99/13.28 ((
% 97.99/13.28 (contrasubsetT2) =>
% 97.99/13.28 ((
% 97.99/13.28 (contrasubsetT3) =>
% 97.99/13.28 ((
% 97.99/13.28 (doubleComplementI1) =>
% 97.99/13.28 ((
% 97.99/13.28 (doubleComplementE1) =>
% 97.99/13.28 ((
% 97.99/13.28 (doubleComplementSub1) =>
% 97.99/13.28 ((
% 97.99/13.28 (doubleComplementSub2) =>
% 97.99/13.28 ((
% 97.99/13.28 (doubleComplementEq) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementTnotintersectT) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementImpComplementIntersect) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementSubsetComplementIntersect) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementInPowersetComplementIntersect) =>
% 97.99/13.28 ((
% 97.99/13.28 (contraSubsetComplement) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementTcontraSubset) =>
% 97.99/13.28 ((
% 97.99/13.28 (binunionTILcontra) =>
% 97.99/13.28 ((
% 97.99/13.28 (binunionTIRcontra) =>
% 97.99/13.28 ((
% 97.99/13.28 (inIntersectImpInUnion) =>
% 97.99/13.28 ((
% 97.99/13.28 (inIntersectImpInUnion2) =>
% 97.99/13.28 ((
% 97.99/13.28 (inIntersectImpInIntersectUnions) =>
% 97.99/13.28 ((
% 97.99/13.28 (intersectInPowersetIntersectUnions) =>
% 97.99/13.28 ((
% 97.99/13.28 (inComplementUnionImpNotIn1) =>
% 97.99/13.28 ((
% 97.99/13.28 (inComplementUnionImpInComplement1) =>
% 97.99/13.28 ((
% 97.99/13.28 (binunionTE) =>
% 97.99/13.28 ((
% 97.99/13.28 (binunionTEcontra) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2a1) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementUnionInPowersetComplement) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2a2) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan1a) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan1b) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan1) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2a) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2b2) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2b) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz13rule0) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz13rule1) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz13rule2) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz13rule3) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz13rule4) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz1_1) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz1_2) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz1_3) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz1_4) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz1_5) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1all2) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1SetBreln1) =>
% 97.99/13.28 ((
% 97.99/13.28 (choice2fnsingleton) =>
% 97.99/13.28 ((
% 97.99/13.28 (setOfPairsIsBReln1) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1all1) =>
% 97.99/13.28 ((
% 97.99/13.28 (subbreln1) =>
% 97.99/13.28 ((
% 97.99/13.28 (eqbreln1) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1invprop) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1invI) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1invE) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1compprop) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1compI) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1compE) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1compEex) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionprop) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionIL) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionIR) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionI) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionE) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionEcases) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionCommutes) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz2Ex) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz2W) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz2A) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz2B) =>
% 97.99/13.28 ((
% 97.99/13.28 (image1Ex) =>
% 97.99/13.28 ((
% 97.99/13.28 (image1Ex1) =>
% 97.99/13.28 ((
% 97.99/13.28 (image1Equiv) =>
% 97.99/13.28 ((
% 97.99/13.28 (image1E) =>
% 97.99/13.28 ((
% 97.99/13.28 (image1I) =>
% 97.99/13.28 ((
% 97.99/13.28 (injFuncInInjFuncSet) =>
% 97.99/13.28 ((
% 97.99/13.28 (injFuncSetFuncIn) =>
% 97.99/13.28 ((
% 97.99/13.28 (injFuncSetFuncInj) =>
% 97.99/13.28 ((
% 97.99/13.28 (surjFuncSetFuncIn) =>
% 97.99/13.28 ((
% 97.99/13.28 (surjFuncSetFuncSurj) =>
% 97.99/13.28 ((
% 97.99/13.28 (leftInvIsSurj) =>
% 97.99/13.28 ((
% 97.99/13.28 (surjCantorThm) =>
% 97.99/13.28 ((
% 97.99/13.28 (foundation2) =>
% 97.99/13.28 ((
% 97.99/13.28 (notinself) =>
% 97.99/13.28 ((
% 97.99/13.28 (notinself2) =>
% 97.99/13.28 ((
% 97.99/13.28 (omegaSp) =>
% 97.99/13.28 ((
% 97.99/13.28 (omegaSclos) =>
% 97.99/13.28 ((
% 97.99/13.28 (peano0notS) =>
% 97.99/13.28 ((
% 97.99/13.28 (!!) @ (
% 97.99/13.28 (('#S') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 =>) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#C') @ in @
% 97.99/13.28 omega)))) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 !!) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#S') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 =>) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#C') @ in @
% 97.99/13.28 omega)))))) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#S') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 '#S') @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 =>))) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#C') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 '#B') @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 =) @
% 97.99/13.28 omegaS)))) @
% 97.99/13.28 omegaS)))))) @
% 97.99/13.28 (
% 97.99/13.28 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.99/13.28 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1488])).
% 97.99/13.28 thf(zip_derived_cl1505, plain,
% 97.99/13.28 (~ (((cartprodmempair1) =>
% 97.99/13.28 (((cartprodmempair) =>
% 97.99/13.28 (((setunionE2) =>
% 97.99/13.28 (((setunionsingleton1) =>
% 97.99/13.28 (((setunionsingleton2) =>
% 97.99/13.28 (((setunionsingleton) =>
% 97.99/13.28 (((singletonprop) =>
% 97.99/13.28 (((ex1E1) =>
% 97.99/13.28 (((ex1I) =>
% 97.99/13.28 (((ex1I2) =>
% 97.99/13.28 (((singletonsuniq) =>
% 97.99/13.28 (((setukpairinjL1) =>
% 97.99/13.28 (((kfstsingleton) =>
% 97.99/13.28 (((theprop) =>
% 97.99/13.28 (((kfstpairEq) =>
% 97.99/13.28 (((cartprodfstin) =>
% 97.99/13.28 (((setukpairinjL2) =>
% 97.99/13.28 (((setukpairinjL) =>
% 97.99/13.28 (((setukpairinjR11) =>
% 97.99/13.28 (((setukpairinjR12) =>
% 97.99/13.28 (((setukpairinjR1) =>
% 97.99/13.28 (((upairequniteq) =>
% 97.99/13.28 (((setukpairinjR2) =>
% 97.99/13.28 (((setukpairinjR) =>
% 97.99/13.28 (((ksndsingleton) =>
% 97.99/13.28 (((ksndpairEq) =>
% 97.99/13.28 (((kpairsurjEq) =>
% 97.99/13.28 (((cartprodsndin) =>
% 97.99/13.28 (((cartprodpairmemEL) =>
% 97.99/13.28 (((cartprodpairmemER) =>
% 97.99/13.28 ((
% 97.99/13.28 (cartprodmempaircEq) =>
% 97.99/13.28 ((
% 97.99/13.28 (cartprodfstpairEq) =>
% 97.99/13.28 ((
% 97.99/13.28 (cartprodsndpairEq) =>
% 97.99/13.28 ((
% 97.99/13.28 (cartprodpairsurjEq) =>
% 97.99/13.28 ((
% 97.99/13.28 (dpsetconstrI) =>
% 97.99/13.28 ((
% 97.99/13.28 (dpsetconstrSub) =>
% 97.99/13.28 ((
% 97.99/13.28 (setOfPairsIsBReln) =>
% 97.99/13.28 ((
% 97.99/13.28 (dpsetconstrERa) =>
% 97.99/13.28 ((
% 97.99/13.28 (dpsetconstrEL1) =>
% 97.99/13.28 ((
% 97.99/13.28 (dpsetconstrEL2) =>
% 97.99/13.28 ((
% 97.99/13.28 (dpsetconstrER) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcImageSingleton) =>
% 97.99/13.28 ((
% 97.99/13.28 (apProp) =>
% 97.99/13.28 ((
% 97.99/13.28 (app) =>
% 97.99/13.28 ((
% 97.99/13.28 (infuncsetfunc) =>
% 97.99/13.28 ((
% 97.99/13.28 (ap2p) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcinfuncset) =>
% 97.99/13.28 ((
% 97.99/13.28 (lamProp) =>
% 97.99/13.28 ((
% 97.99/13.28 (lamp) =>
% 97.99/13.28 ((
% 97.99/13.28 (lam2p) =>
% 97.99/13.28 ((
% 97.99/13.28 (brelnall1) =>
% 97.99/13.28 ((
% 97.99/13.28 (brelnall2) =>
% 97.99/13.28 ((
% 97.99/13.28 (ex1E2) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcGraphProp1) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcGraphProp3) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcGraphProp2) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcextLem) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcGraphProp4) =>
% 97.99/13.28 ((
% 97.99/13.28 (subbreln) =>
% 97.99/13.28 ((
% 97.99/13.28 (eqbreln) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcext) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcext2) =>
% 97.99/13.28 ((
% 97.99/13.28 (ap2apEq1) =>
% 97.99/13.28 ((
% 97.99/13.28 (ap2apEq2) =>
% 97.99/13.28 ((
% 97.99/13.28 (beta1) =>
% 97.99/13.28 ((
% 97.99/13.28 (eta1) =>
% 97.99/13.28 ((
% 97.99/13.28 (lam2lamEq) =>
% 97.99/13.28 ((
% 97.99/13.28 (beta2) =>
% 97.99/13.28 ((
% 97.99/13.28 (eta2) =>
% 97.99/13.28 ((
% 97.99/13.28 (iffalseProp1) =>
% 97.99/13.28 ((
% 97.99/13.28 (iffalseProp2) =>
% 97.99/13.28 ((
% 97.99/13.28 (iftrueProp1) =>
% 97.99/13.28 ((
% 97.99/13.28 (iftrueProp2) =>
% 97.99/13.28 ((
% 97.99/13.28 (ifSingleton) =>
% 97.99/13.28 ((
% 97.99/13.28 (ifp) =>
% 97.99/13.28 ((
% 97.99/13.28 (theeq) =>
% 97.99/13.28 ((
% 97.99/13.28 (iftrue) =>
% 97.99/13.28 ((
% 97.99/13.28 (iffalse) =>
% 97.99/13.28 ((
% 97.99/13.28 (iftrueorfalse) =>
% 97.99/13.28 ((
% 97.99/13.28 (binintersectT_lem) =>
% 97.99/13.28 ((
% 97.99/13.28 (binunionT_lem) =>
% 97.99/13.28 ((
% 97.99/13.28 (powersetT_lem) =>
% 97.99/13.28 ((
% 97.99/13.28 (setminusT_lem) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementT_lem) =>
% 97.99/13.28 ((
% 97.99/13.28 (setextT) =>
% 97.99/13.28 ((
% 97.99/13.28 (subsetTI) =>
% 97.99/13.28 ((
% 97.99/13.28 (powersetTI1) =>
% 97.99/13.28 ((
% 97.99/13.28 (powersetTE1) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementTI1) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementTE1) =>
% 97.99/13.28 ((
% 97.99/13.28 (binintersectTELcontra) =>
% 97.99/13.28 ((
% 97.99/13.28 (binintersectTERcontra) =>
% 97.99/13.28 ((
% 97.99/13.28 (contrasubsetT) =>
% 97.99/13.28 ((
% 97.99/13.28 (contrasubsetT1) =>
% 97.99/13.28 ((
% 97.99/13.28 (contrasubsetT2) =>
% 97.99/13.28 ((
% 97.99/13.28 (contrasubsetT3) =>
% 97.99/13.28 ((
% 97.99/13.28 (doubleComplementI1) =>
% 97.99/13.28 ((
% 97.99/13.28 (doubleComplementE1) =>
% 97.99/13.28 ((
% 97.99/13.28 (doubleComplementSub1) =>
% 97.99/13.28 ((
% 97.99/13.28 (doubleComplementSub2) =>
% 97.99/13.28 ((
% 97.99/13.28 (doubleComplementEq) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementTnotintersectT) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementImpComplementIntersect) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementSubsetComplementIntersect) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementInPowersetComplementIntersect) =>
% 97.99/13.28 ((
% 97.99/13.28 (contraSubsetComplement) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementTcontraSubset) =>
% 97.99/13.28 ((
% 97.99/13.28 (binunionTILcontra) =>
% 97.99/13.28 ((
% 97.99/13.28 (binunionTIRcontra) =>
% 97.99/13.28 ((
% 97.99/13.28 (inIntersectImpInUnion) =>
% 97.99/13.28 ((
% 97.99/13.28 (inIntersectImpInUnion2) =>
% 97.99/13.28 ((
% 97.99/13.28 (inIntersectImpInIntersectUnions) =>
% 97.99/13.28 ((
% 97.99/13.28 (intersectInPowersetIntersectUnions) =>
% 97.99/13.28 ((
% 97.99/13.28 (inComplementUnionImpNotIn1) =>
% 97.99/13.28 ((
% 97.99/13.28 (inComplementUnionImpInComplement1) =>
% 97.99/13.28 ((
% 97.99/13.28 (binunionTE) =>
% 97.99/13.28 ((
% 97.99/13.28 (binunionTEcontra) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2a1) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementUnionInPowersetComplement) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2a2) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan1a) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan1b) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan1) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2a) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2b2) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2b) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz13rule0) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz13rule1) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz13rule2) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz13rule3) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz13rule4) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz1_1) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz1_2) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz1_3) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz1_4) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz1_5) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1all2) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1SetBreln1) =>
% 97.99/13.28 ((
% 97.99/13.28 (choice2fnsingleton) =>
% 97.99/13.28 ((
% 97.99/13.28 (setOfPairsIsBReln1) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1all1) =>
% 97.99/13.28 ((
% 97.99/13.28 (subbreln1) =>
% 97.99/13.28 ((
% 97.99/13.28 (eqbreln1) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1invprop) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1invI) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1invE) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1compprop) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1compI) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1compE) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1compEex) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionprop) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionIL) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionIR) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionI) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionE) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionEcases) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionCommutes) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz2Ex) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz2W) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz2A) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz2B) =>
% 97.99/13.28 ((
% 97.99/13.28 (image1Ex) =>
% 97.99/13.28 ((
% 97.99/13.28 (image1Ex1) =>
% 97.99/13.28 ((
% 97.99/13.28 (image1Equiv) =>
% 97.99/13.28 ((
% 97.99/13.28 (image1E) =>
% 97.99/13.28 ((
% 97.99/13.28 (image1I) =>
% 97.99/13.28 ((
% 97.99/13.28 (injFuncInInjFuncSet) =>
% 97.99/13.28 ((
% 97.99/13.28 (injFuncSetFuncIn) =>
% 97.99/13.28 ((
% 97.99/13.28 (injFuncSetFuncInj) =>
% 97.99/13.28 ((
% 97.99/13.28 (surjFuncSetFuncIn) =>
% 97.99/13.28 ((
% 97.99/13.28 (surjFuncSetFuncSurj) =>
% 97.99/13.28 ((
% 97.99/13.28 (leftInvIsSurj) =>
% 97.99/13.28 ((
% 97.99/13.28 (surjCantorThm) =>
% 97.99/13.28 ((
% 97.99/13.28 (foundation2) =>
% 97.99/13.28 ((
% 97.99/13.28 (notinself) =>
% 97.99/13.28 ((
% 97.99/13.28 (notinself2) =>
% 97.99/13.28 ((
% 97.99/13.28 (omegaSp) =>
% 97.99/13.28 ((
% 97.99/13.28 (omegaSclos) =>
% 97.99/13.28 ((
% 97.99/13.28 (peano0notS) =>
% 97.99/13.28 ((
% 97.99/13.28 (!!) @ (
% 97.99/13.28 (('#S') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 =>) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#C') @ in @
% 97.99/13.28 omega)))) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 !!) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#S') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 =>) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#C') @ in @
% 97.99/13.28 omega)))))) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#S') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 '#S') @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 =>))) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#C') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 '#B') @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 =) @
% 97.99/13.28 omegaS)))) @
% 97.99/13.28 omegaS)))))) @
% 97.99/13.28 (
% 97.99/13.28 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.99/13.28 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1496])).
% 97.99/13.28 thf(zip_derived_cl1515, plain,
% 97.99/13.28 (~ (((cartprodmempair) =>
% 97.99/13.28 (((setunionE2) =>
% 97.99/13.28 (((setunionsingleton1) =>
% 97.99/13.28 (((setunionsingleton2) =>
% 97.99/13.28 (((setunionsingleton) =>
% 97.99/13.28 (((singletonprop) =>
% 97.99/13.28 (((ex1E1) =>
% 97.99/13.28 (((ex1I) =>
% 97.99/13.28 (((ex1I2) =>
% 97.99/13.28 (((singletonsuniq) =>
% 97.99/13.28 (((setukpairinjL1) =>
% 97.99/13.28 (((kfstsingleton) =>
% 97.99/13.28 (((theprop) =>
% 97.99/13.28 (((kfstpairEq) =>
% 97.99/13.28 (((cartprodfstin) =>
% 97.99/13.28 (((setukpairinjL2) =>
% 97.99/13.28 (((setukpairinjL) =>
% 97.99/13.28 (((setukpairinjR11) =>
% 97.99/13.28 (((setukpairinjR12) =>
% 97.99/13.28 (((setukpairinjR1) =>
% 97.99/13.28 (((upairequniteq) =>
% 97.99/13.28 (((setukpairinjR2) =>
% 97.99/13.28 (((setukpairinjR) =>
% 97.99/13.28 (((ksndsingleton) =>
% 97.99/13.28 (((ksndpairEq) =>
% 97.99/13.28 (((kpairsurjEq) =>
% 97.99/13.28 (((cartprodsndin) =>
% 97.99/13.28 (((cartprodpairmemEL) =>
% 97.99/13.28 (((cartprodpairmemER) =>
% 97.99/13.28 (((cartprodmempaircEq) =>
% 97.99/13.28 ((
% 97.99/13.28 (cartprodfstpairEq) =>
% 97.99/13.28 ((
% 97.99/13.28 (cartprodsndpairEq) =>
% 97.99/13.28 ((
% 97.99/13.28 (cartprodpairsurjEq) =>
% 97.99/13.28 ((
% 97.99/13.28 (dpsetconstrI) =>
% 97.99/13.28 ((
% 97.99/13.28 (dpsetconstrSub) =>
% 97.99/13.28 ((
% 97.99/13.28 (setOfPairsIsBReln) =>
% 97.99/13.28 ((
% 97.99/13.28 (dpsetconstrERa) =>
% 97.99/13.28 ((
% 97.99/13.28 (dpsetconstrEL1) =>
% 97.99/13.28 ((
% 97.99/13.28 (dpsetconstrEL2) =>
% 97.99/13.28 ((
% 97.99/13.28 (dpsetconstrER) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcImageSingleton) =>
% 97.99/13.28 ((
% 97.99/13.28 (apProp) =>
% 97.99/13.28 ((
% 97.99/13.28 (app) =>
% 97.99/13.28 ((
% 97.99/13.28 (infuncsetfunc) =>
% 97.99/13.28 ((
% 97.99/13.28 (ap2p) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcinfuncset) =>
% 97.99/13.28 ((
% 97.99/13.28 (lamProp) =>
% 97.99/13.28 ((
% 97.99/13.28 (lamp) =>
% 97.99/13.28 ((
% 97.99/13.28 (lam2p) =>
% 97.99/13.28 ((
% 97.99/13.28 (brelnall1) =>
% 97.99/13.28 ((
% 97.99/13.28 (brelnall2) =>
% 97.99/13.28 ((
% 97.99/13.28 (ex1E2) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcGraphProp1) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcGraphProp3) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcGraphProp2) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcextLem) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcGraphProp4) =>
% 97.99/13.28 ((
% 97.99/13.28 (subbreln) =>
% 97.99/13.28 ((
% 97.99/13.28 (eqbreln) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcext) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcext2) =>
% 97.99/13.28 ((
% 97.99/13.28 (ap2apEq1) =>
% 97.99/13.28 ((
% 97.99/13.28 (ap2apEq2) =>
% 97.99/13.28 ((
% 97.99/13.28 (beta1) =>
% 97.99/13.28 ((
% 97.99/13.28 (eta1) =>
% 97.99/13.28 ((
% 97.99/13.28 (lam2lamEq) =>
% 97.99/13.28 ((
% 97.99/13.28 (beta2) =>
% 97.99/13.28 ((
% 97.99/13.28 (eta2) =>
% 97.99/13.28 ((
% 97.99/13.28 (iffalseProp1) =>
% 97.99/13.28 ((
% 97.99/13.28 (iffalseProp2) =>
% 97.99/13.28 ((
% 97.99/13.28 (iftrueProp1) =>
% 97.99/13.28 ((
% 97.99/13.28 (iftrueProp2) =>
% 97.99/13.28 ((
% 97.99/13.28 (ifSingleton) =>
% 97.99/13.28 ((
% 97.99/13.28 (ifp) =>
% 97.99/13.28 ((
% 97.99/13.28 (theeq) =>
% 97.99/13.28 ((
% 97.99/13.28 (iftrue) =>
% 97.99/13.28 ((
% 97.99/13.28 (iffalse) =>
% 97.99/13.28 ((
% 97.99/13.28 (iftrueorfalse) =>
% 97.99/13.28 ((
% 97.99/13.28 (binintersectT_lem) =>
% 97.99/13.28 ((
% 97.99/13.28 (binunionT_lem) =>
% 97.99/13.28 ((
% 97.99/13.28 (powersetT_lem) =>
% 97.99/13.28 ((
% 97.99/13.28 (setminusT_lem) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementT_lem) =>
% 97.99/13.28 ((
% 97.99/13.28 (setextT) =>
% 97.99/13.28 ((
% 97.99/13.28 (subsetTI) =>
% 97.99/13.28 ((
% 97.99/13.28 (powersetTI1) =>
% 97.99/13.28 ((
% 97.99/13.28 (powersetTE1) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementTI1) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementTE1) =>
% 97.99/13.28 ((
% 97.99/13.28 (binintersectTELcontra) =>
% 97.99/13.28 ((
% 97.99/13.28 (binintersectTERcontra) =>
% 97.99/13.28 ((
% 97.99/13.28 (contrasubsetT) =>
% 97.99/13.28 ((
% 97.99/13.28 (contrasubsetT1) =>
% 97.99/13.28 ((
% 97.99/13.28 (contrasubsetT2) =>
% 97.99/13.28 ((
% 97.99/13.28 (contrasubsetT3) =>
% 97.99/13.28 ((
% 97.99/13.28 (doubleComplementI1) =>
% 97.99/13.28 ((
% 97.99/13.28 (doubleComplementE1) =>
% 97.99/13.28 ((
% 97.99/13.28 (doubleComplementSub1) =>
% 97.99/13.28 ((
% 97.99/13.28 (doubleComplementSub2) =>
% 97.99/13.28 ((
% 97.99/13.28 (doubleComplementEq) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementTnotintersectT) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementImpComplementIntersect) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementSubsetComplementIntersect) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementInPowersetComplementIntersect) =>
% 97.99/13.28 ((
% 97.99/13.28 (contraSubsetComplement) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementTcontraSubset) =>
% 97.99/13.28 ((
% 97.99/13.28 (binunionTILcontra) =>
% 97.99/13.28 ((
% 97.99/13.28 (binunionTIRcontra) =>
% 97.99/13.28 ((
% 97.99/13.28 (inIntersectImpInUnion) =>
% 97.99/13.28 ((
% 97.99/13.28 (inIntersectImpInUnion2) =>
% 97.99/13.28 ((
% 97.99/13.28 (inIntersectImpInIntersectUnions) =>
% 97.99/13.28 ((
% 97.99/13.28 (intersectInPowersetIntersectUnions) =>
% 97.99/13.28 ((
% 97.99/13.28 (inComplementUnionImpNotIn1) =>
% 97.99/13.28 ((
% 97.99/13.28 (inComplementUnionImpInComplement1) =>
% 97.99/13.28 ((
% 97.99/13.28 (binunionTE) =>
% 97.99/13.28 ((
% 97.99/13.28 (binunionTEcontra) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2a1) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementUnionInPowersetComplement) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2a2) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan1a) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan1b) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan1) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2a) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2b2) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2b) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz13rule0) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz13rule1) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz13rule2) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz13rule3) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz13rule4) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz1_1) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz1_2) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz1_3) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz1_4) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz1_5) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1all2) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1SetBreln1) =>
% 97.99/13.28 ((
% 97.99/13.28 (choice2fnsingleton) =>
% 97.99/13.28 ((
% 97.99/13.28 (setOfPairsIsBReln1) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1all1) =>
% 97.99/13.28 ((
% 97.99/13.28 (subbreln1) =>
% 97.99/13.28 ((
% 97.99/13.28 (eqbreln1) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1invprop) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1invI) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1invE) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1compprop) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1compI) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1compE) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1compEex) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionprop) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionIL) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionIR) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionI) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionE) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionEcases) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionCommutes) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz2Ex) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz2W) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz2A) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz2B) =>
% 97.99/13.28 ((
% 97.99/13.28 (image1Ex) =>
% 97.99/13.28 ((
% 97.99/13.28 (image1Ex1) =>
% 97.99/13.28 ((
% 97.99/13.28 (image1Equiv) =>
% 97.99/13.28 ((
% 97.99/13.28 (image1E) =>
% 97.99/13.28 ((
% 97.99/13.28 (image1I) =>
% 97.99/13.28 ((
% 97.99/13.28 (injFuncInInjFuncSet) =>
% 97.99/13.28 ((
% 97.99/13.28 (injFuncSetFuncIn) =>
% 97.99/13.28 ((
% 97.99/13.28 (injFuncSetFuncInj) =>
% 97.99/13.28 ((
% 97.99/13.28 (surjFuncSetFuncIn) =>
% 97.99/13.28 ((
% 97.99/13.28 (surjFuncSetFuncSurj) =>
% 97.99/13.28 ((
% 97.99/13.28 (leftInvIsSurj) =>
% 97.99/13.28 ((
% 97.99/13.28 (surjCantorThm) =>
% 97.99/13.28 ((
% 97.99/13.28 (foundation2) =>
% 97.99/13.28 ((
% 97.99/13.28 (notinself) =>
% 97.99/13.28 ((
% 97.99/13.28 (notinself2) =>
% 97.99/13.28 ((
% 97.99/13.28 (omegaSp) =>
% 97.99/13.28 ((
% 97.99/13.28 (omegaSclos) =>
% 97.99/13.28 ((
% 97.99/13.28 (peano0notS) =>
% 97.99/13.28 ((
% 97.99/13.28 (!!) @ (
% 97.99/13.28 (('#S') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 =>) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#C') @ in @
% 97.99/13.28 omega)))) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 !!) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#S') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 =>) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#C') @ in @
% 97.99/13.28 omega)))))) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#S') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 '#S') @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 =>))) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#C') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 '#B') @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 =) @
% 97.99/13.28 omegaS)))) @
% 97.99/13.28 omegaS)))))) @
% 97.99/13.28 (
% 97.99/13.28 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.99/13.28 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1505])).
% 97.99/13.28 thf(zip_derived_cl1525, plain,
% 97.99/13.28 (~ (((setunionE2) =>
% 97.99/13.28 (((setunionsingleton1) =>
% 97.99/13.28 (((setunionsingleton2) =>
% 97.99/13.28 (((setunionsingleton) =>
% 97.99/13.28 (((singletonprop) =>
% 97.99/13.28 (((ex1E1) =>
% 97.99/13.28 (((ex1I) =>
% 97.99/13.28 (((ex1I2) =>
% 97.99/13.28 (((singletonsuniq) =>
% 97.99/13.28 (((setukpairinjL1) =>
% 97.99/13.28 (((kfstsingleton) =>
% 97.99/13.28 (((theprop) =>
% 97.99/13.28 (((kfstpairEq) =>
% 97.99/13.28 (((cartprodfstin) =>
% 97.99/13.28 (((setukpairinjL2) =>
% 97.99/13.28 (((setukpairinjL) =>
% 97.99/13.28 (((setukpairinjR11) =>
% 97.99/13.28 (((setukpairinjR12) =>
% 97.99/13.28 (((setukpairinjR1) =>
% 97.99/13.28 (((upairequniteq) =>
% 97.99/13.28 (((setukpairinjR2) =>
% 97.99/13.28 (((setukpairinjR) =>
% 97.99/13.28 (((ksndsingleton) =>
% 97.99/13.28 (((ksndpairEq) =>
% 97.99/13.28 (((kpairsurjEq) =>
% 97.99/13.28 (((cartprodsndin) =>
% 97.99/13.28 (((cartprodpairmemEL) =>
% 97.99/13.28 (((cartprodpairmemER) =>
% 97.99/13.28 (((cartprodmempaircEq) =>
% 97.99/13.28 (((cartprodfstpairEq) =>
% 97.99/13.28 ((
% 97.99/13.28 (cartprodsndpairEq) =>
% 97.99/13.28 ((
% 97.99/13.28 (cartprodpairsurjEq) =>
% 97.99/13.28 ((
% 97.99/13.28 (dpsetconstrI) =>
% 97.99/13.28 ((
% 97.99/13.28 (dpsetconstrSub) =>
% 97.99/13.28 ((
% 97.99/13.28 (setOfPairsIsBReln) =>
% 97.99/13.28 ((
% 97.99/13.28 (dpsetconstrERa) =>
% 97.99/13.28 ((
% 97.99/13.28 (dpsetconstrEL1) =>
% 97.99/13.28 ((
% 97.99/13.28 (dpsetconstrEL2) =>
% 97.99/13.28 ((
% 97.99/13.28 (dpsetconstrER) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcImageSingleton) =>
% 97.99/13.28 ((
% 97.99/13.28 (apProp) =>
% 97.99/13.28 ((
% 97.99/13.28 (app) =>
% 97.99/13.28 ((
% 97.99/13.28 (infuncsetfunc) =>
% 97.99/13.28 ((
% 97.99/13.28 (ap2p) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcinfuncset) =>
% 97.99/13.28 ((
% 97.99/13.28 (lamProp) =>
% 97.99/13.28 ((
% 97.99/13.28 (lamp) =>
% 97.99/13.28 ((
% 97.99/13.28 (lam2p) =>
% 97.99/13.28 ((
% 97.99/13.28 (brelnall1) =>
% 97.99/13.28 ((
% 97.99/13.28 (brelnall2) =>
% 97.99/13.28 ((
% 97.99/13.28 (ex1E2) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcGraphProp1) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcGraphProp3) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcGraphProp2) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcextLem) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcGraphProp4) =>
% 97.99/13.28 ((
% 97.99/13.28 (subbreln) =>
% 97.99/13.28 ((
% 97.99/13.28 (eqbreln) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcext) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcext2) =>
% 97.99/13.28 ((
% 97.99/13.28 (ap2apEq1) =>
% 97.99/13.28 ((
% 97.99/13.28 (ap2apEq2) =>
% 97.99/13.28 ((
% 97.99/13.28 (beta1) =>
% 97.99/13.28 ((
% 97.99/13.28 (eta1) =>
% 97.99/13.28 ((
% 97.99/13.28 (lam2lamEq) =>
% 97.99/13.28 ((
% 97.99/13.28 (beta2) =>
% 97.99/13.28 ((
% 97.99/13.28 (eta2) =>
% 97.99/13.28 ((
% 97.99/13.28 (iffalseProp1) =>
% 97.99/13.28 ((
% 97.99/13.28 (iffalseProp2) =>
% 97.99/13.28 ((
% 97.99/13.28 (iftrueProp1) =>
% 97.99/13.28 ((
% 97.99/13.28 (iftrueProp2) =>
% 97.99/13.28 ((
% 97.99/13.28 (ifSingleton) =>
% 97.99/13.28 ((
% 97.99/13.28 (ifp) =>
% 97.99/13.28 ((
% 97.99/13.28 (theeq) =>
% 97.99/13.28 ((
% 97.99/13.28 (iftrue) =>
% 97.99/13.28 ((
% 97.99/13.28 (iffalse) =>
% 97.99/13.28 ((
% 97.99/13.28 (iftrueorfalse) =>
% 97.99/13.28 ((
% 97.99/13.28 (binintersectT_lem) =>
% 97.99/13.28 ((
% 97.99/13.28 (binunionT_lem) =>
% 97.99/13.28 ((
% 97.99/13.28 (powersetT_lem) =>
% 97.99/13.28 ((
% 97.99/13.28 (setminusT_lem) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementT_lem) =>
% 97.99/13.28 ((
% 97.99/13.28 (setextT) =>
% 97.99/13.28 ((
% 97.99/13.28 (subsetTI) =>
% 97.99/13.28 ((
% 97.99/13.28 (powersetTI1) =>
% 97.99/13.28 ((
% 97.99/13.28 (powersetTE1) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementTI1) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementTE1) =>
% 97.99/13.28 ((
% 97.99/13.28 (binintersectTELcontra) =>
% 97.99/13.28 ((
% 97.99/13.28 (binintersectTERcontra) =>
% 97.99/13.28 ((
% 97.99/13.28 (contrasubsetT) =>
% 97.99/13.28 ((
% 97.99/13.28 (contrasubsetT1) =>
% 97.99/13.28 ((
% 97.99/13.28 (contrasubsetT2) =>
% 97.99/13.28 ((
% 97.99/13.28 (contrasubsetT3) =>
% 97.99/13.28 ((
% 97.99/13.28 (doubleComplementI1) =>
% 97.99/13.28 ((
% 97.99/13.28 (doubleComplementE1) =>
% 97.99/13.28 ((
% 97.99/13.28 (doubleComplementSub1) =>
% 97.99/13.28 ((
% 97.99/13.28 (doubleComplementSub2) =>
% 97.99/13.28 ((
% 97.99/13.28 (doubleComplementEq) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementTnotintersectT) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementImpComplementIntersect) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementSubsetComplementIntersect) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementInPowersetComplementIntersect) =>
% 97.99/13.28 ((
% 97.99/13.28 (contraSubsetComplement) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementTcontraSubset) =>
% 97.99/13.28 ((
% 97.99/13.28 (binunionTILcontra) =>
% 97.99/13.28 ((
% 97.99/13.28 (binunionTIRcontra) =>
% 97.99/13.28 ((
% 97.99/13.28 (inIntersectImpInUnion) =>
% 97.99/13.28 ((
% 97.99/13.28 (inIntersectImpInUnion2) =>
% 97.99/13.28 ((
% 97.99/13.28 (inIntersectImpInIntersectUnions) =>
% 97.99/13.28 ((
% 97.99/13.28 (intersectInPowersetIntersectUnions) =>
% 97.99/13.28 ((
% 97.99/13.28 (inComplementUnionImpNotIn1) =>
% 97.99/13.28 ((
% 97.99/13.28 (inComplementUnionImpInComplement1) =>
% 97.99/13.28 ((
% 97.99/13.28 (binunionTE) =>
% 97.99/13.28 ((
% 97.99/13.28 (binunionTEcontra) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2a1) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementUnionInPowersetComplement) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2a2) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan1a) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan1b) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan1) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2a) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2b2) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2b) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz13rule0) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz13rule1) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz13rule2) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz13rule3) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz13rule4) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz1_1) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz1_2) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz1_3) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz1_4) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz1_5) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1all2) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1SetBreln1) =>
% 97.99/13.28 ((
% 97.99/13.28 (choice2fnsingleton) =>
% 97.99/13.28 ((
% 97.99/13.28 (setOfPairsIsBReln1) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1all1) =>
% 97.99/13.28 ((
% 97.99/13.28 (subbreln1) =>
% 97.99/13.28 ((
% 97.99/13.28 (eqbreln1) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1invprop) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1invI) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1invE) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1compprop) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1compI) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1compE) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1compEex) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionprop) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionIL) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionIR) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionI) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionE) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionEcases) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionCommutes) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz2Ex) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz2W) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz2A) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz2B) =>
% 97.99/13.28 ((
% 97.99/13.28 (image1Ex) =>
% 97.99/13.28 ((
% 97.99/13.28 (image1Ex1) =>
% 97.99/13.28 ((
% 97.99/13.28 (image1Equiv) =>
% 97.99/13.28 ((
% 97.99/13.28 (image1E) =>
% 97.99/13.28 ((
% 97.99/13.28 (image1I) =>
% 97.99/13.28 ((
% 97.99/13.28 (injFuncInInjFuncSet) =>
% 97.99/13.28 ((
% 97.99/13.28 (injFuncSetFuncIn) =>
% 97.99/13.28 ((
% 97.99/13.28 (injFuncSetFuncInj) =>
% 97.99/13.28 ((
% 97.99/13.28 (surjFuncSetFuncIn) =>
% 97.99/13.28 ((
% 97.99/13.28 (surjFuncSetFuncSurj) =>
% 97.99/13.28 ((
% 97.99/13.28 (leftInvIsSurj) =>
% 97.99/13.28 ((
% 97.99/13.28 (surjCantorThm) =>
% 97.99/13.28 ((
% 97.99/13.28 (foundation2) =>
% 97.99/13.28 ((
% 97.99/13.28 (notinself) =>
% 97.99/13.28 ((
% 97.99/13.28 (notinself2) =>
% 97.99/13.28 ((
% 97.99/13.28 (omegaSp) =>
% 97.99/13.28 ((
% 97.99/13.28 (omegaSclos) =>
% 97.99/13.28 ((
% 97.99/13.28 (peano0notS) =>
% 97.99/13.28 ((
% 97.99/13.28 (!!) @ (
% 97.99/13.28 (('#S') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 =>) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#C') @ in @
% 97.99/13.28 omega)))) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 !!) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#S') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 =>) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#C') @ in @
% 97.99/13.28 omega)))))) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#S') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 '#S') @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 =>))) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#C') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 '#B') @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 =) @
% 97.99/13.28 omegaS)))) @
% 97.99/13.28 omegaS)))))) @
% 97.99/13.28 (
% 97.99/13.28 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.99/13.28 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1515])).
% 97.99/13.28 thf(zip_derived_cl1535, plain,
% 97.99/13.28 (~ (((setunionsingleton1) =>
% 97.99/13.28 (((setunionsingleton2) =>
% 97.99/13.28 (((setunionsingleton) =>
% 97.99/13.28 (((singletonprop) =>
% 97.99/13.28 (((ex1E1) =>
% 97.99/13.28 (((ex1I) =>
% 97.99/13.28 (((ex1I2) =>
% 97.99/13.28 (((singletonsuniq) =>
% 97.99/13.28 (((setukpairinjL1) =>
% 97.99/13.28 (((kfstsingleton) =>
% 97.99/13.28 (((theprop) =>
% 97.99/13.28 (((kfstpairEq) =>
% 97.99/13.28 (((cartprodfstin) =>
% 97.99/13.28 (((setukpairinjL2) =>
% 97.99/13.28 (((setukpairinjL) =>
% 97.99/13.28 (((setukpairinjR11) =>
% 97.99/13.28 (((setukpairinjR12) =>
% 97.99/13.28 (((setukpairinjR1) =>
% 97.99/13.28 (((upairequniteq) =>
% 97.99/13.28 (((setukpairinjR2) =>
% 97.99/13.28 (((setukpairinjR) =>
% 97.99/13.28 (((ksndsingleton) =>
% 97.99/13.28 (((ksndpairEq) =>
% 97.99/13.28 (((kpairsurjEq) =>
% 97.99/13.28 (((cartprodsndin) =>
% 97.99/13.28 (((cartprodpairmemEL) =>
% 97.99/13.28 (((cartprodpairmemER) =>
% 97.99/13.28 (((cartprodmempaircEq) =>
% 97.99/13.28 (((cartprodfstpairEq) =>
% 97.99/13.28 (((cartprodsndpairEq) =>
% 97.99/13.28 ((
% 97.99/13.28 (cartprodpairsurjEq) =>
% 97.99/13.28 ((
% 97.99/13.28 (dpsetconstrI) =>
% 97.99/13.28 ((
% 97.99/13.28 (dpsetconstrSub) =>
% 97.99/13.28 ((
% 97.99/13.28 (setOfPairsIsBReln) =>
% 97.99/13.28 ((
% 97.99/13.28 (dpsetconstrERa) =>
% 97.99/13.28 ((
% 97.99/13.28 (dpsetconstrEL1) =>
% 97.99/13.28 ((
% 97.99/13.28 (dpsetconstrEL2) =>
% 97.99/13.28 ((
% 97.99/13.28 (dpsetconstrER) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcImageSingleton) =>
% 97.99/13.28 ((
% 97.99/13.28 (apProp) =>
% 97.99/13.28 ((
% 97.99/13.28 (app) =>
% 97.99/13.28 ((
% 97.99/13.28 (infuncsetfunc) =>
% 97.99/13.28 ((
% 97.99/13.28 (ap2p) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcinfuncset) =>
% 97.99/13.28 ((
% 97.99/13.28 (lamProp) =>
% 97.99/13.28 ((
% 97.99/13.28 (lamp) =>
% 97.99/13.28 ((
% 97.99/13.28 (lam2p) =>
% 97.99/13.28 ((
% 97.99/13.28 (brelnall1) =>
% 97.99/13.28 ((
% 97.99/13.28 (brelnall2) =>
% 97.99/13.28 ((
% 97.99/13.28 (ex1E2) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcGraphProp1) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcGraphProp3) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcGraphProp2) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcextLem) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcGraphProp4) =>
% 97.99/13.28 ((
% 97.99/13.28 (subbreln) =>
% 97.99/13.28 ((
% 97.99/13.28 (eqbreln) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcext) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcext2) =>
% 97.99/13.28 ((
% 97.99/13.28 (ap2apEq1) =>
% 97.99/13.28 ((
% 97.99/13.28 (ap2apEq2) =>
% 97.99/13.28 ((
% 97.99/13.28 (beta1) =>
% 97.99/13.28 ((
% 97.99/13.28 (eta1) =>
% 97.99/13.28 ((
% 97.99/13.28 (lam2lamEq) =>
% 97.99/13.28 ((
% 97.99/13.28 (beta2) =>
% 97.99/13.28 ((
% 97.99/13.28 (eta2) =>
% 97.99/13.28 ((
% 97.99/13.28 (iffalseProp1) =>
% 97.99/13.28 ((
% 97.99/13.28 (iffalseProp2) =>
% 97.99/13.28 ((
% 97.99/13.28 (iftrueProp1) =>
% 97.99/13.28 ((
% 97.99/13.28 (iftrueProp2) =>
% 97.99/13.28 ((
% 97.99/13.28 (ifSingleton) =>
% 97.99/13.28 ((
% 97.99/13.28 (ifp) =>
% 97.99/13.28 ((
% 97.99/13.28 (theeq) =>
% 97.99/13.28 ((
% 97.99/13.28 (iftrue) =>
% 97.99/13.28 ((
% 97.99/13.28 (iffalse) =>
% 97.99/13.28 ((
% 97.99/13.28 (iftrueorfalse) =>
% 97.99/13.28 ((
% 97.99/13.28 (binintersectT_lem) =>
% 97.99/13.28 ((
% 97.99/13.28 (binunionT_lem) =>
% 97.99/13.28 ((
% 97.99/13.28 (powersetT_lem) =>
% 97.99/13.28 ((
% 97.99/13.28 (setminusT_lem) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementT_lem) =>
% 97.99/13.28 ((
% 97.99/13.28 (setextT) =>
% 97.99/13.28 ((
% 97.99/13.28 (subsetTI) =>
% 97.99/13.28 ((
% 97.99/13.28 (powersetTI1) =>
% 97.99/13.28 ((
% 97.99/13.28 (powersetTE1) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementTI1) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementTE1) =>
% 97.99/13.28 ((
% 97.99/13.28 (binintersectTELcontra) =>
% 97.99/13.28 ((
% 97.99/13.28 (binintersectTERcontra) =>
% 97.99/13.28 ((
% 97.99/13.28 (contrasubsetT) =>
% 97.99/13.28 ((
% 97.99/13.28 (contrasubsetT1) =>
% 97.99/13.28 ((
% 97.99/13.28 (contrasubsetT2) =>
% 97.99/13.28 ((
% 97.99/13.28 (contrasubsetT3) =>
% 97.99/13.28 ((
% 97.99/13.28 (doubleComplementI1) =>
% 97.99/13.28 ((
% 97.99/13.28 (doubleComplementE1) =>
% 97.99/13.28 ((
% 97.99/13.28 (doubleComplementSub1) =>
% 97.99/13.28 ((
% 97.99/13.28 (doubleComplementSub2) =>
% 97.99/13.28 ((
% 97.99/13.28 (doubleComplementEq) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementTnotintersectT) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementImpComplementIntersect) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementSubsetComplementIntersect) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementInPowersetComplementIntersect) =>
% 97.99/13.28 ((
% 97.99/13.28 (contraSubsetComplement) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementTcontraSubset) =>
% 97.99/13.28 ((
% 97.99/13.28 (binunionTILcontra) =>
% 97.99/13.28 ((
% 97.99/13.28 (binunionTIRcontra) =>
% 97.99/13.28 ((
% 97.99/13.28 (inIntersectImpInUnion) =>
% 97.99/13.28 ((
% 97.99/13.28 (inIntersectImpInUnion2) =>
% 97.99/13.28 ((
% 97.99/13.28 (inIntersectImpInIntersectUnions) =>
% 97.99/13.28 ((
% 97.99/13.28 (intersectInPowersetIntersectUnions) =>
% 97.99/13.28 ((
% 97.99/13.28 (inComplementUnionImpNotIn1) =>
% 97.99/13.28 ((
% 97.99/13.28 (inComplementUnionImpInComplement1) =>
% 97.99/13.28 ((
% 97.99/13.28 (binunionTE) =>
% 97.99/13.28 ((
% 97.99/13.28 (binunionTEcontra) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2a1) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementUnionInPowersetComplement) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2a2) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan1a) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan1b) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan1) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2a) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2b2) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2b) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz13rule0) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz13rule1) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz13rule2) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz13rule3) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz13rule4) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz1_1) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz1_2) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz1_3) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz1_4) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz1_5) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1all2) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1SetBreln1) =>
% 97.99/13.28 ((
% 97.99/13.28 (choice2fnsingleton) =>
% 97.99/13.28 ((
% 97.99/13.28 (setOfPairsIsBReln1) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1all1) =>
% 97.99/13.28 ((
% 97.99/13.28 (subbreln1) =>
% 97.99/13.28 ((
% 97.99/13.28 (eqbreln1) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1invprop) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1invI) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1invE) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1compprop) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1compI) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1compE) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1compEex) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionprop) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionIL) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionIR) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionI) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionE) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionEcases) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionCommutes) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz2Ex) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz2W) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz2A) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz2B) =>
% 97.99/13.28 ((
% 97.99/13.28 (image1Ex) =>
% 97.99/13.28 ((
% 97.99/13.28 (image1Ex1) =>
% 97.99/13.28 ((
% 97.99/13.28 (image1Equiv) =>
% 97.99/13.28 ((
% 97.99/13.28 (image1E) =>
% 97.99/13.28 ((
% 97.99/13.28 (image1I) =>
% 97.99/13.28 ((
% 97.99/13.28 (injFuncInInjFuncSet) =>
% 97.99/13.28 ((
% 97.99/13.28 (injFuncSetFuncIn) =>
% 97.99/13.28 ((
% 97.99/13.28 (injFuncSetFuncInj) =>
% 97.99/13.28 ((
% 97.99/13.28 (surjFuncSetFuncIn) =>
% 97.99/13.28 ((
% 97.99/13.28 (surjFuncSetFuncSurj) =>
% 97.99/13.28 ((
% 97.99/13.28 (leftInvIsSurj) =>
% 97.99/13.28 ((
% 97.99/13.28 (surjCantorThm) =>
% 97.99/13.28 ((
% 97.99/13.28 (foundation2) =>
% 97.99/13.28 ((
% 97.99/13.28 (notinself) =>
% 97.99/13.28 ((
% 97.99/13.28 (notinself2) =>
% 97.99/13.28 ((
% 97.99/13.28 (omegaSp) =>
% 97.99/13.28 ((
% 97.99/13.28 (omegaSclos) =>
% 97.99/13.28 ((
% 97.99/13.28 (peano0notS) =>
% 97.99/13.28 ((
% 97.99/13.28 (!!) @ (
% 97.99/13.28 (('#S') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 =>) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#C') @ in @
% 97.99/13.28 omega)))) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 !!) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#S') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 =>) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#C') @ in @
% 97.99/13.28 omega)))))) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#S') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 '#S') @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 =>))) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#C') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 '#B') @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 =) @
% 97.99/13.28 omegaS)))) @
% 97.99/13.28 omegaS)))))) @
% 97.99/13.28 (
% 97.99/13.28 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.99/13.28 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1525])).
% 97.99/13.28 thf(zip_derived_cl1545, plain,
% 97.99/13.28 (~ (((setunionsingleton2) =>
% 97.99/13.28 (((setunionsingleton) =>
% 97.99/13.28 (((singletonprop) =>
% 97.99/13.28 (((ex1E1) =>
% 97.99/13.28 (((ex1I) =>
% 97.99/13.28 (((ex1I2) =>
% 97.99/13.28 (((singletonsuniq) =>
% 97.99/13.28 (((setukpairinjL1) =>
% 97.99/13.28 (((kfstsingleton) =>
% 97.99/13.28 (((theprop) =>
% 97.99/13.28 (((kfstpairEq) =>
% 97.99/13.28 (((cartprodfstin) =>
% 97.99/13.28 (((setukpairinjL2) =>
% 97.99/13.28 (((setukpairinjL) =>
% 97.99/13.28 (((setukpairinjR11) =>
% 97.99/13.28 (((setukpairinjR12) =>
% 97.99/13.28 (((setukpairinjR1) =>
% 97.99/13.28 (((upairequniteq) =>
% 97.99/13.28 (((setukpairinjR2) =>
% 97.99/13.28 (((setukpairinjR) =>
% 97.99/13.28 (((ksndsingleton) =>
% 97.99/13.28 (((ksndpairEq) =>
% 97.99/13.28 (((kpairsurjEq) =>
% 97.99/13.28 (((cartprodsndin) =>
% 97.99/13.28 (((cartprodpairmemEL) =>
% 97.99/13.28 (((cartprodpairmemER) =>
% 97.99/13.28 (((cartprodmempaircEq) =>
% 97.99/13.28 (((cartprodfstpairEq) =>
% 97.99/13.28 (((cartprodsndpairEq) =>
% 97.99/13.28 (((cartprodpairsurjEq) =>
% 97.99/13.28 ((
% 97.99/13.28 (dpsetconstrI) =>
% 97.99/13.28 ((
% 97.99/13.28 (dpsetconstrSub) =>
% 97.99/13.28 ((
% 97.99/13.28 (setOfPairsIsBReln) =>
% 97.99/13.28 ((
% 97.99/13.28 (dpsetconstrERa) =>
% 97.99/13.28 ((
% 97.99/13.28 (dpsetconstrEL1) =>
% 97.99/13.28 ((
% 97.99/13.28 (dpsetconstrEL2) =>
% 97.99/13.28 ((
% 97.99/13.28 (dpsetconstrER) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcImageSingleton) =>
% 97.99/13.28 ((
% 97.99/13.28 (apProp) =>
% 97.99/13.28 ((
% 97.99/13.28 (app) =>
% 97.99/13.28 ((
% 97.99/13.28 (infuncsetfunc) =>
% 97.99/13.28 ((
% 97.99/13.28 (ap2p) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcinfuncset) =>
% 97.99/13.28 ((
% 97.99/13.28 (lamProp) =>
% 97.99/13.28 ((
% 97.99/13.28 (lamp) =>
% 97.99/13.28 ((
% 97.99/13.28 (lam2p) =>
% 97.99/13.28 ((
% 97.99/13.28 (brelnall1) =>
% 97.99/13.28 ((
% 97.99/13.28 (brelnall2) =>
% 97.99/13.28 ((
% 97.99/13.28 (ex1E2) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcGraphProp1) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcGraphProp3) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcGraphProp2) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcextLem) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcGraphProp4) =>
% 97.99/13.28 ((
% 97.99/13.28 (subbreln) =>
% 97.99/13.28 ((
% 97.99/13.28 (eqbreln) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcext) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcext2) =>
% 97.99/13.28 ((
% 97.99/13.28 (ap2apEq1) =>
% 97.99/13.28 ((
% 97.99/13.28 (ap2apEq2) =>
% 97.99/13.28 ((
% 97.99/13.28 (beta1) =>
% 97.99/13.28 ((
% 97.99/13.28 (eta1) =>
% 97.99/13.28 ((
% 97.99/13.28 (lam2lamEq) =>
% 97.99/13.28 ((
% 97.99/13.28 (beta2) =>
% 97.99/13.28 ((
% 97.99/13.28 (eta2) =>
% 97.99/13.28 ((
% 97.99/13.28 (iffalseProp1) =>
% 97.99/13.28 ((
% 97.99/13.28 (iffalseProp2) =>
% 97.99/13.28 ((
% 97.99/13.28 (iftrueProp1) =>
% 97.99/13.28 ((
% 97.99/13.28 (iftrueProp2) =>
% 97.99/13.28 ((
% 97.99/13.28 (ifSingleton) =>
% 97.99/13.28 ((
% 97.99/13.28 (ifp) =>
% 97.99/13.28 ((
% 97.99/13.28 (theeq) =>
% 97.99/13.28 ((
% 97.99/13.28 (iftrue) =>
% 97.99/13.28 ((
% 97.99/13.28 (iffalse) =>
% 97.99/13.28 ((
% 97.99/13.28 (iftrueorfalse) =>
% 97.99/13.28 ((
% 97.99/13.28 (binintersectT_lem) =>
% 97.99/13.28 ((
% 97.99/13.28 (binunionT_lem) =>
% 97.99/13.28 ((
% 97.99/13.28 (powersetT_lem) =>
% 97.99/13.28 ((
% 97.99/13.28 (setminusT_lem) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementT_lem) =>
% 97.99/13.28 ((
% 97.99/13.28 (setextT) =>
% 97.99/13.28 ((
% 97.99/13.28 (subsetTI) =>
% 97.99/13.28 ((
% 97.99/13.28 (powersetTI1) =>
% 97.99/13.28 ((
% 97.99/13.28 (powersetTE1) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementTI1) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementTE1) =>
% 97.99/13.28 ((
% 97.99/13.28 (binintersectTELcontra) =>
% 97.99/13.28 ((
% 97.99/13.28 (binintersectTERcontra) =>
% 97.99/13.28 ((
% 97.99/13.28 (contrasubsetT) =>
% 97.99/13.28 ((
% 97.99/13.28 (contrasubsetT1) =>
% 97.99/13.28 ((
% 97.99/13.28 (contrasubsetT2) =>
% 97.99/13.28 ((
% 97.99/13.28 (contrasubsetT3) =>
% 97.99/13.28 ((
% 97.99/13.28 (doubleComplementI1) =>
% 97.99/13.28 ((
% 97.99/13.28 (doubleComplementE1) =>
% 97.99/13.28 ((
% 97.99/13.28 (doubleComplementSub1) =>
% 97.99/13.28 ((
% 97.99/13.28 (doubleComplementSub2) =>
% 97.99/13.28 ((
% 97.99/13.28 (doubleComplementEq) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementTnotintersectT) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementImpComplementIntersect) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementSubsetComplementIntersect) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementInPowersetComplementIntersect) =>
% 97.99/13.28 ((
% 97.99/13.28 (contraSubsetComplement) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementTcontraSubset) =>
% 97.99/13.28 ((
% 97.99/13.28 (binunionTILcontra) =>
% 97.99/13.28 ((
% 97.99/13.28 (binunionTIRcontra) =>
% 97.99/13.28 ((
% 97.99/13.28 (inIntersectImpInUnion) =>
% 97.99/13.28 ((
% 97.99/13.28 (inIntersectImpInUnion2) =>
% 97.99/13.28 ((
% 97.99/13.28 (inIntersectImpInIntersectUnions) =>
% 97.99/13.28 ((
% 97.99/13.28 (intersectInPowersetIntersectUnions) =>
% 97.99/13.28 ((
% 97.99/13.28 (inComplementUnionImpNotIn1) =>
% 97.99/13.28 ((
% 97.99/13.28 (inComplementUnionImpInComplement1) =>
% 97.99/13.28 ((
% 97.99/13.28 (binunionTE) =>
% 97.99/13.28 ((
% 97.99/13.28 (binunionTEcontra) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2a1) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementUnionInPowersetComplement) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2a2) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan1a) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan1b) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan1) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2a) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2b2) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2b) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz13rule0) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz13rule1) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz13rule2) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz13rule3) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz13rule4) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz1_1) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz1_2) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz1_3) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz1_4) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz1_5) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1all2) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1SetBreln1) =>
% 97.99/13.28 ((
% 97.99/13.28 (choice2fnsingleton) =>
% 97.99/13.28 ((
% 97.99/13.28 (setOfPairsIsBReln1) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1all1) =>
% 97.99/13.28 ((
% 97.99/13.28 (subbreln1) =>
% 97.99/13.28 ((
% 97.99/13.28 (eqbreln1) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1invprop) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1invI) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1invE) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1compprop) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1compI) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1compE) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1compEex) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionprop) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionIL) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionIR) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionI) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionE) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionEcases) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionCommutes) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz2Ex) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz2W) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz2A) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz2B) =>
% 97.99/13.28 ((
% 97.99/13.28 (image1Ex) =>
% 97.99/13.28 ((
% 97.99/13.28 (image1Ex1) =>
% 97.99/13.28 ((
% 97.99/13.28 (image1Equiv) =>
% 97.99/13.28 ((
% 97.99/13.28 (image1E) =>
% 97.99/13.28 ((
% 97.99/13.28 (image1I) =>
% 97.99/13.28 ((
% 97.99/13.28 (injFuncInInjFuncSet) =>
% 97.99/13.28 ((
% 97.99/13.28 (injFuncSetFuncIn) =>
% 97.99/13.28 ((
% 97.99/13.28 (injFuncSetFuncInj) =>
% 97.99/13.28 ((
% 97.99/13.28 (surjFuncSetFuncIn) =>
% 97.99/13.28 ((
% 97.99/13.28 (surjFuncSetFuncSurj) =>
% 97.99/13.28 ((
% 97.99/13.28 (leftInvIsSurj) =>
% 97.99/13.28 ((
% 97.99/13.28 (surjCantorThm) =>
% 97.99/13.28 ((
% 97.99/13.28 (foundation2) =>
% 97.99/13.28 ((
% 97.99/13.28 (notinself) =>
% 97.99/13.28 ((
% 97.99/13.28 (notinself2) =>
% 97.99/13.28 ((
% 97.99/13.28 (omegaSp) =>
% 97.99/13.28 ((
% 97.99/13.28 (omegaSclos) =>
% 97.99/13.28 ((
% 97.99/13.28 (peano0notS) =>
% 97.99/13.28 ((
% 97.99/13.28 (!!) @ (
% 97.99/13.28 (('#S') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 =>) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#C') @ in @
% 97.99/13.28 omega)))) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 !!) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#S') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 =>) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#C') @ in @
% 97.99/13.28 omega)))))) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#S') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 '#S') @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 =>))) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#C') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 '#B') @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 =) @
% 97.99/13.28 omegaS)))) @
% 97.99/13.28 omegaS)))))) @
% 97.99/13.28 (
% 97.99/13.28 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.99/13.28 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1535])).
% 97.99/13.28 thf(zip_derived_cl1555, plain,
% 97.99/13.28 (~ (((setunionsingleton) =>
% 97.99/13.28 (((singletonprop) =>
% 97.99/13.28 (((ex1E1) =>
% 97.99/13.28 (((ex1I) =>
% 97.99/13.28 (((ex1I2) =>
% 97.99/13.28 (((singletonsuniq) =>
% 97.99/13.28 (((setukpairinjL1) =>
% 97.99/13.28 (((kfstsingleton) =>
% 97.99/13.28 (((theprop) =>
% 97.99/13.28 (((kfstpairEq) =>
% 97.99/13.28 (((cartprodfstin) =>
% 97.99/13.28 (((setukpairinjL2) =>
% 97.99/13.28 (((setukpairinjL) =>
% 97.99/13.28 (((setukpairinjR11) =>
% 97.99/13.28 (((setukpairinjR12) =>
% 97.99/13.28 (((setukpairinjR1) =>
% 97.99/13.28 (((upairequniteq) =>
% 97.99/13.28 (((setukpairinjR2) =>
% 97.99/13.28 (((setukpairinjR) =>
% 97.99/13.28 (((ksndsingleton) =>
% 97.99/13.28 (((ksndpairEq) =>
% 97.99/13.28 (((kpairsurjEq) =>
% 97.99/13.28 (((cartprodsndin) =>
% 97.99/13.28 (((cartprodpairmemEL) =>
% 97.99/13.28 (((cartprodpairmemER) =>
% 97.99/13.28 (((cartprodmempaircEq) =>
% 97.99/13.28 (((cartprodfstpairEq) =>
% 97.99/13.28 (((cartprodsndpairEq) =>
% 97.99/13.28 (((cartprodpairsurjEq) =>
% 97.99/13.28 (((dpsetconstrI) =>
% 97.99/13.28 ((
% 97.99/13.28 (dpsetconstrSub) =>
% 97.99/13.28 ((
% 97.99/13.28 (setOfPairsIsBReln) =>
% 97.99/13.28 ((
% 97.99/13.28 (dpsetconstrERa) =>
% 97.99/13.28 ((
% 97.99/13.28 (dpsetconstrEL1) =>
% 97.99/13.28 ((
% 97.99/13.28 (dpsetconstrEL2) =>
% 97.99/13.28 ((
% 97.99/13.28 (dpsetconstrER) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcImageSingleton) =>
% 97.99/13.28 ((
% 97.99/13.28 (apProp) =>
% 97.99/13.28 ((
% 97.99/13.28 (app) =>
% 97.99/13.28 ((
% 97.99/13.28 (infuncsetfunc) =>
% 97.99/13.28 ((
% 97.99/13.28 (ap2p) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcinfuncset) =>
% 97.99/13.28 ((
% 97.99/13.28 (lamProp) =>
% 97.99/13.28 ((
% 97.99/13.28 (lamp) =>
% 97.99/13.28 ((
% 97.99/13.28 (lam2p) =>
% 97.99/13.28 ((
% 97.99/13.28 (brelnall1) =>
% 97.99/13.28 ((
% 97.99/13.28 (brelnall2) =>
% 97.99/13.28 ((
% 97.99/13.28 (ex1E2) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcGraphProp1) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcGraphProp3) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcGraphProp2) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcextLem) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcGraphProp4) =>
% 97.99/13.28 ((
% 97.99/13.28 (subbreln) =>
% 97.99/13.28 ((
% 97.99/13.28 (eqbreln) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcext) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcext2) =>
% 97.99/13.28 ((
% 97.99/13.28 (ap2apEq1) =>
% 97.99/13.28 ((
% 97.99/13.28 (ap2apEq2) =>
% 97.99/13.28 ((
% 97.99/13.28 (beta1) =>
% 97.99/13.28 ((
% 97.99/13.28 (eta1) =>
% 97.99/13.28 ((
% 97.99/13.28 (lam2lamEq) =>
% 97.99/13.28 ((
% 97.99/13.28 (beta2) =>
% 97.99/13.28 ((
% 97.99/13.28 (eta2) =>
% 97.99/13.28 ((
% 97.99/13.28 (iffalseProp1) =>
% 97.99/13.28 ((
% 97.99/13.28 (iffalseProp2) =>
% 97.99/13.28 ((
% 97.99/13.28 (iftrueProp1) =>
% 97.99/13.28 ((
% 97.99/13.28 (iftrueProp2) =>
% 97.99/13.28 ((
% 97.99/13.28 (ifSingleton) =>
% 97.99/13.28 ((
% 97.99/13.28 (ifp) =>
% 97.99/13.28 ((
% 97.99/13.28 (theeq) =>
% 97.99/13.28 ((
% 97.99/13.28 (iftrue) =>
% 97.99/13.28 ((
% 97.99/13.28 (iffalse) =>
% 97.99/13.28 ((
% 97.99/13.28 (iftrueorfalse) =>
% 97.99/13.28 ((
% 97.99/13.28 (binintersectT_lem) =>
% 97.99/13.28 ((
% 97.99/13.28 (binunionT_lem) =>
% 97.99/13.28 ((
% 97.99/13.28 (powersetT_lem) =>
% 97.99/13.28 ((
% 97.99/13.28 (setminusT_lem) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementT_lem) =>
% 97.99/13.28 ((
% 97.99/13.28 (setextT) =>
% 97.99/13.28 ((
% 97.99/13.28 (subsetTI) =>
% 97.99/13.28 ((
% 97.99/13.28 (powersetTI1) =>
% 97.99/13.28 ((
% 97.99/13.28 (powersetTE1) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementTI1) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementTE1) =>
% 97.99/13.28 ((
% 97.99/13.28 (binintersectTELcontra) =>
% 97.99/13.28 ((
% 97.99/13.28 (binintersectTERcontra) =>
% 97.99/13.28 ((
% 97.99/13.28 (contrasubsetT) =>
% 97.99/13.28 ((
% 97.99/13.28 (contrasubsetT1) =>
% 97.99/13.28 ((
% 97.99/13.28 (contrasubsetT2) =>
% 97.99/13.28 ((
% 97.99/13.28 (contrasubsetT3) =>
% 97.99/13.28 ((
% 97.99/13.28 (doubleComplementI1) =>
% 97.99/13.28 ((
% 97.99/13.28 (doubleComplementE1) =>
% 97.99/13.28 ((
% 97.99/13.28 (doubleComplementSub1) =>
% 97.99/13.28 ((
% 97.99/13.28 (doubleComplementSub2) =>
% 97.99/13.28 ((
% 97.99/13.28 (doubleComplementEq) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementTnotintersectT) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementImpComplementIntersect) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementSubsetComplementIntersect) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementInPowersetComplementIntersect) =>
% 97.99/13.28 ((
% 97.99/13.28 (contraSubsetComplement) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementTcontraSubset) =>
% 97.99/13.28 ((
% 97.99/13.28 (binunionTILcontra) =>
% 97.99/13.28 ((
% 97.99/13.28 (binunionTIRcontra) =>
% 97.99/13.28 ((
% 97.99/13.28 (inIntersectImpInUnion) =>
% 97.99/13.28 ((
% 97.99/13.28 (inIntersectImpInUnion2) =>
% 97.99/13.28 ((
% 97.99/13.28 (inIntersectImpInIntersectUnions) =>
% 97.99/13.28 ((
% 97.99/13.28 (intersectInPowersetIntersectUnions) =>
% 97.99/13.28 ((
% 97.99/13.28 (inComplementUnionImpNotIn1) =>
% 97.99/13.28 ((
% 97.99/13.28 (inComplementUnionImpInComplement1) =>
% 97.99/13.28 ((
% 97.99/13.28 (binunionTE) =>
% 97.99/13.28 ((
% 97.99/13.28 (binunionTEcontra) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2a1) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementUnionInPowersetComplement) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2a2) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan1a) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan1b) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan1) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2a) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2b2) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2b) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz13rule0) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz13rule1) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz13rule2) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz13rule3) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz13rule4) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz1_1) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz1_2) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz1_3) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz1_4) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz1_5) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1all2) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1SetBreln1) =>
% 97.99/13.28 ((
% 97.99/13.28 (choice2fnsingleton) =>
% 97.99/13.28 ((
% 97.99/13.28 (setOfPairsIsBReln1) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1all1) =>
% 97.99/13.28 ((
% 97.99/13.28 (subbreln1) =>
% 97.99/13.28 ((
% 97.99/13.28 (eqbreln1) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1invprop) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1invI) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1invE) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1compprop) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1compI) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1compE) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1compEex) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionprop) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionIL) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionIR) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionI) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionE) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionEcases) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionCommutes) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz2Ex) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz2W) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz2A) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz2B) =>
% 97.99/13.28 ((
% 97.99/13.28 (image1Ex) =>
% 97.99/13.28 ((
% 97.99/13.28 (image1Ex1) =>
% 97.99/13.28 ((
% 97.99/13.28 (image1Equiv) =>
% 97.99/13.28 ((
% 97.99/13.28 (image1E) =>
% 97.99/13.28 ((
% 97.99/13.28 (image1I) =>
% 97.99/13.28 ((
% 97.99/13.28 (injFuncInInjFuncSet) =>
% 97.99/13.28 ((
% 97.99/13.28 (injFuncSetFuncIn) =>
% 97.99/13.28 ((
% 97.99/13.28 (injFuncSetFuncInj) =>
% 97.99/13.28 ((
% 97.99/13.28 (surjFuncSetFuncIn) =>
% 97.99/13.28 ((
% 97.99/13.28 (surjFuncSetFuncSurj) =>
% 97.99/13.28 ((
% 97.99/13.28 (leftInvIsSurj) =>
% 97.99/13.28 ((
% 97.99/13.28 (surjCantorThm) =>
% 97.99/13.28 ((
% 97.99/13.28 (foundation2) =>
% 97.99/13.28 ((
% 97.99/13.28 (notinself) =>
% 97.99/13.28 ((
% 97.99/13.28 (notinself2) =>
% 97.99/13.28 ((
% 97.99/13.28 (omegaSp) =>
% 97.99/13.28 ((
% 97.99/13.28 (omegaSclos) =>
% 97.99/13.28 ((
% 97.99/13.28 (peano0notS) =>
% 97.99/13.28 ((
% 97.99/13.28 (!!) @ (
% 97.99/13.28 (('#S') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 =>) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#C') @ in @
% 97.99/13.28 omega)))) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 !!) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#S') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 =>) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#C') @ in @
% 97.99/13.28 omega)))))) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#S') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 '#S') @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 =>))) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#C') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 '#B') @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 =) @
% 97.99/13.28 omegaS)))) @
% 97.99/13.28 omegaS)))))) @
% 97.99/13.28 (
% 97.99/13.28 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.99/13.28 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1545])).
% 97.99/13.28 thf(zip_derived_cl1565, plain,
% 97.99/13.28 (~ (((singletonprop) =>
% 97.99/13.28 (((ex1E1) =>
% 97.99/13.28 (((ex1I) =>
% 97.99/13.28 (((ex1I2) =>
% 97.99/13.28 (((singletonsuniq) =>
% 97.99/13.28 (((setukpairinjL1) =>
% 97.99/13.28 (((kfstsingleton) =>
% 97.99/13.28 (((theprop) =>
% 97.99/13.28 (((kfstpairEq) =>
% 97.99/13.28 (((cartprodfstin) =>
% 97.99/13.28 (((setukpairinjL2) =>
% 97.99/13.28 (((setukpairinjL) =>
% 97.99/13.28 (((setukpairinjR11) =>
% 97.99/13.28 (((setukpairinjR12) =>
% 97.99/13.28 (((setukpairinjR1) =>
% 97.99/13.28 (((upairequniteq) =>
% 97.99/13.28 (((setukpairinjR2) =>
% 97.99/13.28 (((setukpairinjR) =>
% 97.99/13.28 (((ksndsingleton) =>
% 97.99/13.28 (((ksndpairEq) =>
% 97.99/13.28 (((kpairsurjEq) =>
% 97.99/13.28 (((cartprodsndin) =>
% 97.99/13.28 (((cartprodpairmemEL) =>
% 97.99/13.28 (((cartprodpairmemER) =>
% 97.99/13.28 (((cartprodmempaircEq) =>
% 97.99/13.28 (((cartprodfstpairEq) =>
% 97.99/13.28 (((cartprodsndpairEq) =>
% 97.99/13.28 (((cartprodpairsurjEq) =>
% 97.99/13.28 (((dpsetconstrI) =>
% 97.99/13.28 (((dpsetconstrSub) =>
% 97.99/13.28 ((
% 97.99/13.28 (setOfPairsIsBReln) =>
% 97.99/13.28 ((
% 97.99/13.28 (dpsetconstrERa) =>
% 97.99/13.28 ((
% 97.99/13.28 (dpsetconstrEL1) =>
% 97.99/13.28 ((
% 97.99/13.28 (dpsetconstrEL2) =>
% 97.99/13.28 ((
% 97.99/13.28 (dpsetconstrER) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcImageSingleton) =>
% 97.99/13.28 ((
% 97.99/13.28 (apProp) =>
% 97.99/13.28 ((
% 97.99/13.28 (app) =>
% 97.99/13.28 ((
% 97.99/13.28 (infuncsetfunc) =>
% 97.99/13.28 ((
% 97.99/13.28 (ap2p) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcinfuncset) =>
% 97.99/13.28 ((
% 97.99/13.28 (lamProp) =>
% 97.99/13.28 ((
% 97.99/13.28 (lamp) =>
% 97.99/13.28 ((
% 97.99/13.28 (lam2p) =>
% 97.99/13.28 ((
% 97.99/13.28 (brelnall1) =>
% 97.99/13.28 ((
% 97.99/13.28 (brelnall2) =>
% 97.99/13.28 ((
% 97.99/13.28 (ex1E2) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcGraphProp1) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcGraphProp3) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcGraphProp2) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcextLem) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcGraphProp4) =>
% 97.99/13.28 ((
% 97.99/13.28 (subbreln) =>
% 97.99/13.28 ((
% 97.99/13.28 (eqbreln) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcext) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcext2) =>
% 97.99/13.28 ((
% 97.99/13.28 (ap2apEq1) =>
% 97.99/13.28 ((
% 97.99/13.28 (ap2apEq2) =>
% 97.99/13.28 ((
% 97.99/13.28 (beta1) =>
% 97.99/13.28 ((
% 97.99/13.28 (eta1) =>
% 97.99/13.28 ((
% 97.99/13.28 (lam2lamEq) =>
% 97.99/13.28 ((
% 97.99/13.28 (beta2) =>
% 97.99/13.28 ((
% 97.99/13.28 (eta2) =>
% 97.99/13.28 ((
% 97.99/13.28 (iffalseProp1) =>
% 97.99/13.28 ((
% 97.99/13.28 (iffalseProp2) =>
% 97.99/13.28 ((
% 97.99/13.28 (iftrueProp1) =>
% 97.99/13.28 ((
% 97.99/13.28 (iftrueProp2) =>
% 97.99/13.28 ((
% 97.99/13.28 (ifSingleton) =>
% 97.99/13.28 ((
% 97.99/13.28 (ifp) =>
% 97.99/13.28 ((
% 97.99/13.28 (theeq) =>
% 97.99/13.28 ((
% 97.99/13.28 (iftrue) =>
% 97.99/13.28 ((
% 97.99/13.28 (iffalse) =>
% 97.99/13.28 ((
% 97.99/13.28 (iftrueorfalse) =>
% 97.99/13.28 ((
% 97.99/13.28 (binintersectT_lem) =>
% 97.99/13.28 ((
% 97.99/13.28 (binunionT_lem) =>
% 97.99/13.28 ((
% 97.99/13.28 (powersetT_lem) =>
% 97.99/13.28 ((
% 97.99/13.28 (setminusT_lem) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementT_lem) =>
% 97.99/13.28 ((
% 97.99/13.28 (setextT) =>
% 97.99/13.28 ((
% 97.99/13.28 (subsetTI) =>
% 97.99/13.28 ((
% 97.99/13.28 (powersetTI1) =>
% 97.99/13.28 ((
% 97.99/13.28 (powersetTE1) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementTI1) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementTE1) =>
% 97.99/13.28 ((
% 97.99/13.28 (binintersectTELcontra) =>
% 97.99/13.28 ((
% 97.99/13.28 (binintersectTERcontra) =>
% 97.99/13.28 ((
% 97.99/13.28 (contrasubsetT) =>
% 97.99/13.28 ((
% 97.99/13.28 (contrasubsetT1) =>
% 97.99/13.28 ((
% 97.99/13.28 (contrasubsetT2) =>
% 97.99/13.28 ((
% 97.99/13.28 (contrasubsetT3) =>
% 97.99/13.28 ((
% 97.99/13.28 (doubleComplementI1) =>
% 97.99/13.28 ((
% 97.99/13.28 (doubleComplementE1) =>
% 97.99/13.28 ((
% 97.99/13.28 (doubleComplementSub1) =>
% 97.99/13.28 ((
% 97.99/13.28 (doubleComplementSub2) =>
% 97.99/13.28 ((
% 97.99/13.28 (doubleComplementEq) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementTnotintersectT) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementImpComplementIntersect) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementSubsetComplementIntersect) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementInPowersetComplementIntersect) =>
% 97.99/13.28 ((
% 97.99/13.28 (contraSubsetComplement) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementTcontraSubset) =>
% 97.99/13.28 ((
% 97.99/13.28 (binunionTILcontra) =>
% 97.99/13.28 ((
% 97.99/13.28 (binunionTIRcontra) =>
% 97.99/13.28 ((
% 97.99/13.28 (inIntersectImpInUnion) =>
% 97.99/13.28 ((
% 97.99/13.28 (inIntersectImpInUnion2) =>
% 97.99/13.28 ((
% 97.99/13.28 (inIntersectImpInIntersectUnions) =>
% 97.99/13.28 ((
% 97.99/13.28 (intersectInPowersetIntersectUnions) =>
% 97.99/13.28 ((
% 97.99/13.28 (inComplementUnionImpNotIn1) =>
% 97.99/13.28 ((
% 97.99/13.28 (inComplementUnionImpInComplement1) =>
% 97.99/13.28 ((
% 97.99/13.28 (binunionTE) =>
% 97.99/13.28 ((
% 97.99/13.28 (binunionTEcontra) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2a1) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementUnionInPowersetComplement) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2a2) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan1a) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan1b) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan1) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2a) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2b2) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2b) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz13rule0) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz13rule1) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz13rule2) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz13rule3) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz13rule4) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz1_1) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz1_2) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz1_3) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz1_4) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz1_5) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1all2) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1SetBreln1) =>
% 97.99/13.28 ((
% 97.99/13.28 (choice2fnsingleton) =>
% 97.99/13.28 ((
% 97.99/13.28 (setOfPairsIsBReln1) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1all1) =>
% 97.99/13.28 ((
% 97.99/13.28 (subbreln1) =>
% 97.99/13.28 ((
% 97.99/13.28 (eqbreln1) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1invprop) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1invI) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1invE) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1compprop) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1compI) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1compE) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1compEex) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionprop) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionIL) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionIR) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionI) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionE) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionEcases) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionCommutes) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz2Ex) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz2W) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz2A) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz2B) =>
% 97.99/13.28 ((
% 97.99/13.28 (image1Ex) =>
% 97.99/13.28 ((
% 97.99/13.28 (image1Ex1) =>
% 97.99/13.28 ((
% 97.99/13.28 (image1Equiv) =>
% 97.99/13.28 ((
% 97.99/13.28 (image1E) =>
% 97.99/13.28 ((
% 97.99/13.28 (image1I) =>
% 97.99/13.28 ((
% 97.99/13.28 (injFuncInInjFuncSet) =>
% 97.99/13.28 ((
% 97.99/13.28 (injFuncSetFuncIn) =>
% 97.99/13.28 ((
% 97.99/13.28 (injFuncSetFuncInj) =>
% 97.99/13.28 ((
% 97.99/13.28 (surjFuncSetFuncIn) =>
% 97.99/13.28 ((
% 97.99/13.28 (surjFuncSetFuncSurj) =>
% 97.99/13.28 ((
% 97.99/13.28 (leftInvIsSurj) =>
% 97.99/13.28 ((
% 97.99/13.28 (surjCantorThm) =>
% 97.99/13.28 ((
% 97.99/13.28 (foundation2) =>
% 97.99/13.28 ((
% 97.99/13.28 (notinself) =>
% 97.99/13.28 ((
% 97.99/13.28 (notinself2) =>
% 97.99/13.28 ((
% 97.99/13.28 (omegaSp) =>
% 97.99/13.28 ((
% 97.99/13.28 (omegaSclos) =>
% 97.99/13.28 ((
% 97.99/13.28 (peano0notS) =>
% 97.99/13.28 ((
% 97.99/13.28 (!!) @ (
% 97.99/13.28 (('#S') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 =>) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#C') @ in @
% 97.99/13.28 omega)))) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 !!) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#S') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 =>) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#C') @ in @
% 97.99/13.28 omega)))))) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#S') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 '#S') @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 =>))) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#C') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 '#B') @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 =) @
% 97.99/13.28 omegaS)))) @
% 97.99/13.28 omegaS)))))) @
% 97.99/13.28 (
% 97.99/13.28 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.99/13.28 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1555])).
% 97.99/13.28 thf(zip_derived_cl1574, plain,
% 97.99/13.28 (~ (((ex1E1) =>
% 97.99/13.28 (((ex1I) =>
% 97.99/13.28 (((ex1I2) =>
% 97.99/13.28 (((singletonsuniq) =>
% 97.99/13.28 (((setukpairinjL1) =>
% 97.99/13.28 (((kfstsingleton) =>
% 97.99/13.28 (((theprop) =>
% 97.99/13.28 (((kfstpairEq) =>
% 97.99/13.28 (((cartprodfstin) =>
% 97.99/13.28 (((setukpairinjL2) =>
% 97.99/13.28 (((setukpairinjL) =>
% 97.99/13.28 (((setukpairinjR11) =>
% 97.99/13.28 (((setukpairinjR12) =>
% 97.99/13.28 (((setukpairinjR1) =>
% 97.99/13.28 (((upairequniteq) =>
% 97.99/13.28 (((setukpairinjR2) =>
% 97.99/13.28 (((setukpairinjR) =>
% 97.99/13.28 (((ksndsingleton) =>
% 97.99/13.28 (((ksndpairEq) =>
% 97.99/13.28 (((kpairsurjEq) =>
% 97.99/13.28 (((cartprodsndin) =>
% 97.99/13.28 (((cartprodpairmemEL) =>
% 97.99/13.28 (((cartprodpairmemER) =>
% 97.99/13.28 (((cartprodmempaircEq) =>
% 97.99/13.28 (((cartprodfstpairEq) =>
% 97.99/13.28 (((cartprodsndpairEq) =>
% 97.99/13.28 (((cartprodpairsurjEq) =>
% 97.99/13.28 (((dpsetconstrI) =>
% 97.99/13.28 (((dpsetconstrSub) =>
% 97.99/13.28 (((setOfPairsIsBReln) =>
% 97.99/13.28 ((
% 97.99/13.28 (dpsetconstrERa) =>
% 97.99/13.28 ((
% 97.99/13.28 (dpsetconstrEL1) =>
% 97.99/13.28 ((
% 97.99/13.28 (dpsetconstrEL2) =>
% 97.99/13.28 ((
% 97.99/13.28 (dpsetconstrER) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcImageSingleton) =>
% 97.99/13.28 ((
% 97.99/13.28 (apProp) =>
% 97.99/13.28 ((
% 97.99/13.28 (app) =>
% 97.99/13.28 ((
% 97.99/13.28 (infuncsetfunc) =>
% 97.99/13.28 ((
% 97.99/13.28 (ap2p) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcinfuncset) =>
% 97.99/13.28 ((
% 97.99/13.28 (lamProp) =>
% 97.99/13.28 ((
% 97.99/13.28 (lamp) =>
% 97.99/13.28 ((
% 97.99/13.28 (lam2p) =>
% 97.99/13.28 ((
% 97.99/13.28 (brelnall1) =>
% 97.99/13.28 ((
% 97.99/13.28 (brelnall2) =>
% 97.99/13.28 ((
% 97.99/13.28 (ex1E2) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcGraphProp1) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcGraphProp3) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcGraphProp2) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcextLem) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcGraphProp4) =>
% 97.99/13.28 ((
% 97.99/13.28 (subbreln) =>
% 97.99/13.28 ((
% 97.99/13.28 (eqbreln) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcext) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcext2) =>
% 97.99/13.28 ((
% 97.99/13.28 (ap2apEq1) =>
% 97.99/13.28 ((
% 97.99/13.28 (ap2apEq2) =>
% 97.99/13.28 ((
% 97.99/13.28 (beta1) =>
% 97.99/13.28 ((
% 97.99/13.28 (eta1) =>
% 97.99/13.28 ((
% 97.99/13.28 (lam2lamEq) =>
% 97.99/13.28 ((
% 97.99/13.28 (beta2) =>
% 97.99/13.28 ((
% 97.99/13.28 (eta2) =>
% 97.99/13.28 ((
% 97.99/13.28 (iffalseProp1) =>
% 97.99/13.28 ((
% 97.99/13.28 (iffalseProp2) =>
% 97.99/13.28 ((
% 97.99/13.28 (iftrueProp1) =>
% 97.99/13.28 ((
% 97.99/13.28 (iftrueProp2) =>
% 97.99/13.28 ((
% 97.99/13.28 (ifSingleton) =>
% 97.99/13.28 ((
% 97.99/13.28 (ifp) =>
% 97.99/13.28 ((
% 97.99/13.28 (theeq) =>
% 97.99/13.28 ((
% 97.99/13.28 (iftrue) =>
% 97.99/13.28 ((
% 97.99/13.28 (iffalse) =>
% 97.99/13.28 ((
% 97.99/13.28 (iftrueorfalse) =>
% 97.99/13.28 ((
% 97.99/13.28 (binintersectT_lem) =>
% 97.99/13.28 ((
% 97.99/13.28 (binunionT_lem) =>
% 97.99/13.28 ((
% 97.99/13.28 (powersetT_lem) =>
% 97.99/13.28 ((
% 97.99/13.28 (setminusT_lem) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementT_lem) =>
% 97.99/13.28 ((
% 97.99/13.28 (setextT) =>
% 97.99/13.28 ((
% 97.99/13.28 (subsetTI) =>
% 97.99/13.28 ((
% 97.99/13.28 (powersetTI1) =>
% 97.99/13.28 ((
% 97.99/13.28 (powersetTE1) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementTI1) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementTE1) =>
% 97.99/13.28 ((
% 97.99/13.28 (binintersectTELcontra) =>
% 97.99/13.28 ((
% 97.99/13.28 (binintersectTERcontra) =>
% 97.99/13.28 ((
% 97.99/13.28 (contrasubsetT) =>
% 97.99/13.28 ((
% 97.99/13.28 (contrasubsetT1) =>
% 97.99/13.28 ((
% 97.99/13.28 (contrasubsetT2) =>
% 97.99/13.28 ((
% 97.99/13.28 (contrasubsetT3) =>
% 97.99/13.28 ((
% 97.99/13.28 (doubleComplementI1) =>
% 97.99/13.28 ((
% 97.99/13.28 (doubleComplementE1) =>
% 97.99/13.28 ((
% 97.99/13.28 (doubleComplementSub1) =>
% 97.99/13.28 ((
% 97.99/13.28 (doubleComplementSub2) =>
% 97.99/13.28 ((
% 97.99/13.28 (doubleComplementEq) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementTnotintersectT) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementImpComplementIntersect) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementSubsetComplementIntersect) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementInPowersetComplementIntersect) =>
% 97.99/13.28 ((
% 97.99/13.28 (contraSubsetComplement) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementTcontraSubset) =>
% 97.99/13.28 ((
% 97.99/13.28 (binunionTILcontra) =>
% 97.99/13.28 ((
% 97.99/13.28 (binunionTIRcontra) =>
% 97.99/13.28 ((
% 97.99/13.28 (inIntersectImpInUnion) =>
% 97.99/13.28 ((
% 97.99/13.28 (inIntersectImpInUnion2) =>
% 97.99/13.28 ((
% 97.99/13.28 (inIntersectImpInIntersectUnions) =>
% 97.99/13.28 ((
% 97.99/13.28 (intersectInPowersetIntersectUnions) =>
% 97.99/13.28 ((
% 97.99/13.28 (inComplementUnionImpNotIn1) =>
% 97.99/13.28 ((
% 97.99/13.28 (inComplementUnionImpInComplement1) =>
% 97.99/13.28 ((
% 97.99/13.28 (binunionTE) =>
% 97.99/13.28 ((
% 97.99/13.28 (binunionTEcontra) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2a1) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementUnionInPowersetComplement) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2a2) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan1a) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan1b) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan1) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2a) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2b2) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2b) =>
% 97.99/13.28 ((
% 97.99/13.28 (demorgan2) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz13rule0) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz13rule1) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz13rule2) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz13rule3) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz13rule4) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz1_1) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz1_2) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz1_3) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz1_4) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz1_5) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1all2) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1SetBreln1) =>
% 97.99/13.28 ((
% 97.99/13.28 (choice2fnsingleton) =>
% 97.99/13.28 ((
% 97.99/13.28 (setOfPairsIsBReln1) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1all1) =>
% 97.99/13.28 ((
% 97.99/13.28 (subbreln1) =>
% 97.99/13.28 ((
% 97.99/13.28 (eqbreln1) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1invprop) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1invI) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1invE) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1compprop) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1compI) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1compE) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1compEex) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionprop) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionIL) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionIR) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionI) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionE) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionEcases) =>
% 97.99/13.28 ((
% 97.99/13.28 (breln1unionCommutes) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz2Ex) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz2W) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz2A) =>
% 97.99/13.28 ((
% 97.99/13.28 (woz2B) =>
% 97.99/13.28 ((
% 97.99/13.28 (image1Ex) =>
% 97.99/13.28 ((
% 97.99/13.28 (image1Ex1) =>
% 97.99/13.28 ((
% 97.99/13.28 (image1Equiv) =>
% 97.99/13.28 ((
% 97.99/13.28 (image1E) =>
% 97.99/13.28 ((
% 97.99/13.28 (image1I) =>
% 97.99/13.28 ((
% 97.99/13.28 (injFuncInInjFuncSet) =>
% 97.99/13.28 ((
% 97.99/13.28 (injFuncSetFuncIn) =>
% 97.99/13.28 ((
% 97.99/13.28 (injFuncSetFuncInj) =>
% 97.99/13.28 ((
% 97.99/13.28 (surjFuncSetFuncIn) =>
% 97.99/13.28 ((
% 97.99/13.28 (surjFuncSetFuncSurj) =>
% 97.99/13.28 ((
% 97.99/13.28 (leftInvIsSurj) =>
% 97.99/13.28 ((
% 97.99/13.28 (surjCantorThm) =>
% 97.99/13.28 ((
% 97.99/13.28 (foundation2) =>
% 97.99/13.28 ((
% 97.99/13.28 (notinself) =>
% 97.99/13.28 ((
% 97.99/13.28 (notinself2) =>
% 97.99/13.28 ((
% 97.99/13.28 (omegaSp) =>
% 97.99/13.28 ((
% 97.99/13.28 (omegaSclos) =>
% 97.99/13.28 ((
% 97.99/13.28 (peano0notS) =>
% 97.99/13.28 ((
% 97.99/13.28 (!!) @ (
% 97.99/13.28 (('#S') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 =>) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#C') @ in @
% 97.99/13.28 omega)))) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 !!) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#S') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 =>) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#C') @ in @
% 97.99/13.28 omega)))))) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#S') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 '#S') @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 =>))) @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#C') @ (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 '#B') @
% 97.99/13.28 (
% 97.99/13.28 (
% 97.99/13.28 ('#B') @ (
% 97.99/13.28 =) @
% 97.99/13.28 omegaS)))) @
% 97.99/13.28 omegaS)))))) @
% 97.99/13.28 (
% 97.99/13.28 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.99/13.28 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1565])).
% 97.99/13.28 thf(zip_derived_cl1582, plain,
% 97.99/13.28 (~ (((ex1I) =>
% 97.99/13.28 (((ex1I2) =>
% 97.99/13.28 (((singletonsuniq) =>
% 97.99/13.28 (((setukpairinjL1) =>
% 97.99/13.28 (((kfstsingleton) =>
% 97.99/13.28 (((theprop) =>
% 97.99/13.28 (((kfstpairEq) =>
% 97.99/13.28 (((cartprodfstin) =>
% 97.99/13.28 (((setukpairinjL2) =>
% 97.99/13.28 (((setukpairinjL) =>
% 97.99/13.28 (((setukpairinjR11) =>
% 97.99/13.28 (((setukpairinjR12) =>
% 97.99/13.28 (((setukpairinjR1) =>
% 97.99/13.28 (((upairequniteq) =>
% 97.99/13.28 (((setukpairinjR2) =>
% 97.99/13.28 (((setukpairinjR) =>
% 97.99/13.28 (((ksndsingleton) =>
% 97.99/13.28 (((ksndpairEq) =>
% 97.99/13.28 (((kpairsurjEq) =>
% 97.99/13.28 (((cartprodsndin) =>
% 97.99/13.28 (((cartprodpairmemEL) =>
% 97.99/13.28 (((cartprodpairmemER) =>
% 97.99/13.28 (((cartprodmempaircEq) =>
% 97.99/13.28 (((cartprodfstpairEq) =>
% 97.99/13.28 (((cartprodsndpairEq) =>
% 97.99/13.28 (((cartprodpairsurjEq) =>
% 97.99/13.28 (((dpsetconstrI) =>
% 97.99/13.28 (((dpsetconstrSub) =>
% 97.99/13.28 (((setOfPairsIsBReln) =>
% 97.99/13.28 (((dpsetconstrERa) =>
% 97.99/13.28 ((
% 97.99/13.28 (dpsetconstrEL1) =>
% 97.99/13.28 ((
% 97.99/13.28 (dpsetconstrEL2) =>
% 97.99/13.28 ((
% 97.99/13.28 (dpsetconstrER) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcImageSingleton) =>
% 97.99/13.28 ((
% 97.99/13.28 (apProp) =>
% 97.99/13.28 ((
% 97.99/13.28 (app) =>
% 97.99/13.28 ((
% 97.99/13.28 (infuncsetfunc) =>
% 97.99/13.28 ((
% 97.99/13.28 (ap2p) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcinfuncset) =>
% 97.99/13.28 ((
% 97.99/13.28 (lamProp) =>
% 97.99/13.28 ((
% 97.99/13.28 (lamp) =>
% 97.99/13.28 ((
% 97.99/13.28 (lam2p) =>
% 97.99/13.28 ((
% 97.99/13.28 (brelnall1) =>
% 97.99/13.28 ((
% 97.99/13.28 (brelnall2) =>
% 97.99/13.28 ((
% 97.99/13.28 (ex1E2) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcGraphProp1) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcGraphProp3) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcGraphProp2) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcextLem) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcGraphProp4) =>
% 97.99/13.28 ((
% 97.99/13.28 (subbreln) =>
% 97.99/13.28 ((
% 97.99/13.28 (eqbreln) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcext) =>
% 97.99/13.28 ((
% 97.99/13.28 (funcext2) =>
% 97.99/13.28 ((
% 97.99/13.28 (ap2apEq1) =>
% 97.99/13.28 ((
% 97.99/13.28 (ap2apEq2) =>
% 97.99/13.28 ((
% 97.99/13.28 (beta1) =>
% 97.99/13.28 ((
% 97.99/13.28 (eta1) =>
% 97.99/13.28 ((
% 97.99/13.28 (lam2lamEq) =>
% 97.99/13.28 ((
% 97.99/13.28 (beta2) =>
% 97.99/13.28 ((
% 97.99/13.28 (eta2) =>
% 97.99/13.28 ((
% 97.99/13.28 (iffalseProp1) =>
% 97.99/13.28 ((
% 97.99/13.28 (iffalseProp2) =>
% 97.99/13.28 ((
% 97.99/13.28 (iftrueProp1) =>
% 97.99/13.28 ((
% 97.99/13.28 (iftrueProp2) =>
% 97.99/13.28 ((
% 97.99/13.28 (ifSingleton) =>
% 97.99/13.28 ((
% 97.99/13.28 (ifp) =>
% 97.99/13.28 ((
% 97.99/13.28 (theeq) =>
% 97.99/13.28 ((
% 97.99/13.28 (iftrue) =>
% 97.99/13.28 ((
% 97.99/13.28 (iffalse) =>
% 97.99/13.28 ((
% 97.99/13.28 (iftrueorfalse) =>
% 97.99/13.28 ((
% 97.99/13.28 (binintersectT_lem) =>
% 97.99/13.28 ((
% 97.99/13.28 (binunionT_lem) =>
% 97.99/13.28 ((
% 97.99/13.28 (powersetT_lem) =>
% 97.99/13.28 ((
% 97.99/13.28 (setminusT_lem) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementT_lem) =>
% 97.99/13.28 ((
% 97.99/13.28 (setextT) =>
% 97.99/13.28 ((
% 97.99/13.28 (subsetTI) =>
% 97.99/13.28 ((
% 97.99/13.28 (powersetTI1) =>
% 97.99/13.28 ((
% 97.99/13.28 (powersetTE1) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementTI1) =>
% 97.99/13.28 ((
% 97.99/13.28 (complementTE1) =>
% 97.99/13.28 ((
% 97.99/13.28 (binintersectTELcontra) =>
% 97.99/13.28 ((
% 97.99/13.28 (binintersectTERcontra) =>
% 97.99/13.28 ((
% 97.99/13.28 (contrasubsetT) =>
% 97.99/13.28 ((
% 97.99/13.28 (contrasubsetT1) =>
% 97.99/13.28 ((
% 97.99/13.28 (contrasubsetT2) =>
% 97.99/13.28 ((
% 97.99/13.28 (contrasubsetT3) =>
% 97.99/13.28 ((
% 97.99/13.28 (doubleComplementI1) =>
% 97.99/13.28 ((
% 97.99/13.28 (doubleComplementE1) =>
% 97.99/13.28 ((
% 97.99/13.28 (doubleComplementSub1) =>
% 97.99/13.28 ((
% 97.99/13.28 (doubleComplementSub2) =>
% 97.99/13.29 ((
% 97.99/13.29 (doubleComplementEq) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementTnotintersectT) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementImpComplementIntersect) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementSubsetComplementIntersect) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementInPowersetComplementIntersect) =>
% 97.99/13.29 ((
% 97.99/13.29 (contraSubsetComplement) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementTcontraSubset) =>
% 97.99/13.29 ((
% 97.99/13.29 (binunionTILcontra) =>
% 97.99/13.29 ((
% 97.99/13.29 (binunionTIRcontra) =>
% 97.99/13.29 ((
% 97.99/13.29 (inIntersectImpInUnion) =>
% 97.99/13.29 ((
% 97.99/13.29 (inIntersectImpInUnion2) =>
% 97.99/13.29 ((
% 97.99/13.29 (inIntersectImpInIntersectUnions) =>
% 97.99/13.29 ((
% 97.99/13.29 (intersectInPowersetIntersectUnions) =>
% 97.99/13.29 ((
% 97.99/13.29 (inComplementUnionImpNotIn1) =>
% 97.99/13.29 ((
% 97.99/13.29 (inComplementUnionImpInComplement1) =>
% 97.99/13.29 ((
% 97.99/13.29 (binunionTE) =>
% 97.99/13.29 ((
% 97.99/13.29 (binunionTEcontra) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2a1) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementUnionInPowersetComplement) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2a2) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan1a) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan1b) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan1) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2a) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2b2) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2b) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz13rule0) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz13rule1) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz13rule2) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz13rule3) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz13rule4) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz1_1) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz1_2) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz1_3) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz1_4) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz1_5) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1all2) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1SetBreln1) =>
% 97.99/13.29 ((
% 97.99/13.29 (choice2fnsingleton) =>
% 97.99/13.29 ((
% 97.99/13.29 (setOfPairsIsBReln1) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1all1) =>
% 97.99/13.29 ((
% 97.99/13.29 (subbreln1) =>
% 97.99/13.29 ((
% 97.99/13.29 (eqbreln1) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1invprop) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1invI) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1invE) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1compprop) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1compI) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1compE) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1compEex) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionprop) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionIL) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionIR) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionI) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionE) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionEcases) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionCommutes) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz2Ex) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz2W) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz2A) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz2B) =>
% 97.99/13.29 ((
% 97.99/13.29 (image1Ex) =>
% 97.99/13.29 ((
% 97.99/13.29 (image1Ex1) =>
% 97.99/13.29 ((
% 97.99/13.29 (image1Equiv) =>
% 97.99/13.29 ((
% 97.99/13.29 (image1E) =>
% 97.99/13.29 ((
% 97.99/13.29 (image1I) =>
% 97.99/13.29 ((
% 97.99/13.29 (injFuncInInjFuncSet) =>
% 97.99/13.29 ((
% 97.99/13.29 (injFuncSetFuncIn) =>
% 97.99/13.29 ((
% 97.99/13.29 (injFuncSetFuncInj) =>
% 97.99/13.29 ((
% 97.99/13.29 (surjFuncSetFuncIn) =>
% 97.99/13.29 ((
% 97.99/13.29 (surjFuncSetFuncSurj) =>
% 97.99/13.29 ((
% 97.99/13.29 (leftInvIsSurj) =>
% 97.99/13.29 ((
% 97.99/13.29 (surjCantorThm) =>
% 97.99/13.29 ((
% 97.99/13.29 (foundation2) =>
% 97.99/13.29 ((
% 97.99/13.29 (notinself) =>
% 97.99/13.29 ((
% 97.99/13.29 (notinself2) =>
% 97.99/13.29 ((
% 97.99/13.29 (omegaSp) =>
% 97.99/13.29 ((
% 97.99/13.29 (omegaSclos) =>
% 97.99/13.29 ((
% 97.99/13.29 (peano0notS) =>
% 97.99/13.29 ((
% 97.99/13.29 (!!) @ (
% 97.99/13.29 (('#S') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 =>) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#C') @ in @
% 97.99/13.29 omega)))) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 !!) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#S') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 =>) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#C') @ in @
% 97.99/13.29 omega)))))) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#S') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 '#S') @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 =>))) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#C') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 '#B') @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 =) @
% 97.99/13.29 omegaS)))) @
% 97.99/13.29 omegaS)))))) @
% 97.99/13.29 (
% 97.99/13.29 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.99/13.29 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1574])).
% 97.99/13.29 thf(zip_derived_cl1591, plain,
% 97.99/13.29 (~ (((ex1I2) =>
% 97.99/13.29 (((singletonsuniq) =>
% 97.99/13.29 (((setukpairinjL1) =>
% 97.99/13.29 (((kfstsingleton) =>
% 97.99/13.29 (((theprop) =>
% 97.99/13.29 (((kfstpairEq) =>
% 97.99/13.29 (((cartprodfstin) =>
% 97.99/13.29 (((setukpairinjL2) =>
% 97.99/13.29 (((setukpairinjL) =>
% 97.99/13.29 (((setukpairinjR11) =>
% 97.99/13.29 (((setukpairinjR12) =>
% 97.99/13.29 (((setukpairinjR1) =>
% 97.99/13.29 (((upairequniteq) =>
% 97.99/13.29 (((setukpairinjR2) =>
% 97.99/13.29 (((setukpairinjR) =>
% 97.99/13.29 (((ksndsingleton) =>
% 97.99/13.29 (((ksndpairEq) =>
% 97.99/13.29 (((kpairsurjEq) =>
% 97.99/13.29 (((cartprodsndin) =>
% 97.99/13.29 (((cartprodpairmemEL) =>
% 97.99/13.29 (((cartprodpairmemER) =>
% 97.99/13.29 (((cartprodmempaircEq) =>
% 97.99/13.29 (((cartprodfstpairEq) =>
% 97.99/13.29 (((cartprodsndpairEq) =>
% 97.99/13.29 (((cartprodpairsurjEq) =>
% 97.99/13.29 (((dpsetconstrI) =>
% 97.99/13.29 (((dpsetconstrSub) =>
% 97.99/13.29 (((setOfPairsIsBReln) =>
% 97.99/13.29 (((dpsetconstrERa) =>
% 97.99/13.29 (((dpsetconstrEL1) =>
% 97.99/13.29 ((
% 97.99/13.29 (dpsetconstrEL2) =>
% 97.99/13.29 ((
% 97.99/13.29 (dpsetconstrER) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcImageSingleton) =>
% 97.99/13.29 ((
% 97.99/13.29 (apProp) =>
% 97.99/13.29 ((
% 97.99/13.29 (app) =>
% 97.99/13.29 ((
% 97.99/13.29 (infuncsetfunc) =>
% 97.99/13.29 ((
% 97.99/13.29 (ap2p) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcinfuncset) =>
% 97.99/13.29 ((
% 97.99/13.29 (lamProp) =>
% 97.99/13.29 ((
% 97.99/13.29 (lamp) =>
% 97.99/13.29 ((
% 97.99/13.29 (lam2p) =>
% 97.99/13.29 ((
% 97.99/13.29 (brelnall1) =>
% 97.99/13.29 ((
% 97.99/13.29 (brelnall2) =>
% 97.99/13.29 ((
% 97.99/13.29 (ex1E2) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcGraphProp1) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcGraphProp3) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcGraphProp2) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcextLem) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcGraphProp4) =>
% 97.99/13.29 ((
% 97.99/13.29 (subbreln) =>
% 97.99/13.29 ((
% 97.99/13.29 (eqbreln) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcext) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcext2) =>
% 97.99/13.29 ((
% 97.99/13.29 (ap2apEq1) =>
% 97.99/13.29 ((
% 97.99/13.29 (ap2apEq2) =>
% 97.99/13.29 ((
% 97.99/13.29 (beta1) =>
% 97.99/13.29 ((
% 97.99/13.29 (eta1) =>
% 97.99/13.29 ((
% 97.99/13.29 (lam2lamEq) =>
% 97.99/13.29 ((
% 97.99/13.29 (beta2) =>
% 97.99/13.29 ((
% 97.99/13.29 (eta2) =>
% 97.99/13.29 ((
% 97.99/13.29 (iffalseProp1) =>
% 97.99/13.29 ((
% 97.99/13.29 (iffalseProp2) =>
% 97.99/13.29 ((
% 97.99/13.29 (iftrueProp1) =>
% 97.99/13.29 ((
% 97.99/13.29 (iftrueProp2) =>
% 97.99/13.29 ((
% 97.99/13.29 (ifSingleton) =>
% 97.99/13.29 ((
% 97.99/13.29 (ifp) =>
% 97.99/13.29 ((
% 97.99/13.29 (theeq) =>
% 97.99/13.29 ((
% 97.99/13.29 (iftrue) =>
% 97.99/13.29 ((
% 97.99/13.29 (iffalse) =>
% 97.99/13.29 ((
% 97.99/13.29 (iftrueorfalse) =>
% 97.99/13.29 ((
% 97.99/13.29 (binintersectT_lem) =>
% 97.99/13.29 ((
% 97.99/13.29 (binunionT_lem) =>
% 97.99/13.29 ((
% 97.99/13.29 (powersetT_lem) =>
% 97.99/13.29 ((
% 97.99/13.29 (setminusT_lem) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementT_lem) =>
% 97.99/13.29 ((
% 97.99/13.29 (setextT) =>
% 97.99/13.29 ((
% 97.99/13.29 (subsetTI) =>
% 97.99/13.29 ((
% 97.99/13.29 (powersetTI1) =>
% 97.99/13.29 ((
% 97.99/13.29 (powersetTE1) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementTI1) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementTE1) =>
% 97.99/13.29 ((
% 97.99/13.29 (binintersectTELcontra) =>
% 97.99/13.29 ((
% 97.99/13.29 (binintersectTERcontra) =>
% 97.99/13.29 ((
% 97.99/13.29 (contrasubsetT) =>
% 97.99/13.29 ((
% 97.99/13.29 (contrasubsetT1) =>
% 97.99/13.29 ((
% 97.99/13.29 (contrasubsetT2) =>
% 97.99/13.29 ((
% 97.99/13.29 (contrasubsetT3) =>
% 97.99/13.29 ((
% 97.99/13.29 (doubleComplementI1) =>
% 97.99/13.29 ((
% 97.99/13.29 (doubleComplementE1) =>
% 97.99/13.29 ((
% 97.99/13.29 (doubleComplementSub1) =>
% 97.99/13.29 ((
% 97.99/13.29 (doubleComplementSub2) =>
% 97.99/13.29 ((
% 97.99/13.29 (doubleComplementEq) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementTnotintersectT) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementImpComplementIntersect) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementSubsetComplementIntersect) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementInPowersetComplementIntersect) =>
% 97.99/13.29 ((
% 97.99/13.29 (contraSubsetComplement) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementTcontraSubset) =>
% 97.99/13.29 ((
% 97.99/13.29 (binunionTILcontra) =>
% 97.99/13.29 ((
% 97.99/13.29 (binunionTIRcontra) =>
% 97.99/13.29 ((
% 97.99/13.29 (inIntersectImpInUnion) =>
% 97.99/13.29 ((
% 97.99/13.29 (inIntersectImpInUnion2) =>
% 97.99/13.29 ((
% 97.99/13.29 (inIntersectImpInIntersectUnions) =>
% 97.99/13.29 ((
% 97.99/13.29 (intersectInPowersetIntersectUnions) =>
% 97.99/13.29 ((
% 97.99/13.29 (inComplementUnionImpNotIn1) =>
% 97.99/13.29 ((
% 97.99/13.29 (inComplementUnionImpInComplement1) =>
% 97.99/13.29 ((
% 97.99/13.29 (binunionTE) =>
% 97.99/13.29 ((
% 97.99/13.29 (binunionTEcontra) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2a1) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementUnionInPowersetComplement) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2a2) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan1a) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan1b) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan1) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2a) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2b2) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2b) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz13rule0) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz13rule1) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz13rule2) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz13rule3) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz13rule4) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz1_1) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz1_2) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz1_3) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz1_4) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz1_5) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1all2) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1SetBreln1) =>
% 97.99/13.29 ((
% 97.99/13.29 (choice2fnsingleton) =>
% 97.99/13.29 ((
% 97.99/13.29 (setOfPairsIsBReln1) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1all1) =>
% 97.99/13.29 ((
% 97.99/13.29 (subbreln1) =>
% 97.99/13.29 ((
% 97.99/13.29 (eqbreln1) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1invprop) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1invI) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1invE) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1compprop) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1compI) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1compE) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1compEex) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionprop) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionIL) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionIR) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionI) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionE) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionEcases) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionCommutes) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz2Ex) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz2W) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz2A) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz2B) =>
% 97.99/13.29 ((
% 97.99/13.29 (image1Ex) =>
% 97.99/13.29 ((
% 97.99/13.29 (image1Ex1) =>
% 97.99/13.29 ((
% 97.99/13.29 (image1Equiv) =>
% 97.99/13.29 ((
% 97.99/13.29 (image1E) =>
% 97.99/13.29 ((
% 97.99/13.29 (image1I) =>
% 97.99/13.29 ((
% 97.99/13.29 (injFuncInInjFuncSet) =>
% 97.99/13.29 ((
% 97.99/13.29 (injFuncSetFuncIn) =>
% 97.99/13.29 ((
% 97.99/13.29 (injFuncSetFuncInj) =>
% 97.99/13.29 ((
% 97.99/13.29 (surjFuncSetFuncIn) =>
% 97.99/13.29 ((
% 97.99/13.29 (surjFuncSetFuncSurj) =>
% 97.99/13.29 ((
% 97.99/13.29 (leftInvIsSurj) =>
% 97.99/13.29 ((
% 97.99/13.29 (surjCantorThm) =>
% 97.99/13.29 ((
% 97.99/13.29 (foundation2) =>
% 97.99/13.29 ((
% 97.99/13.29 (notinself) =>
% 97.99/13.29 ((
% 97.99/13.29 (notinself2) =>
% 97.99/13.29 ((
% 97.99/13.29 (omegaSp) =>
% 97.99/13.29 ((
% 97.99/13.29 (omegaSclos) =>
% 97.99/13.29 ((
% 97.99/13.29 (peano0notS) =>
% 97.99/13.29 ((
% 97.99/13.29 (!!) @ (
% 97.99/13.29 (('#S') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 =>) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#C') @ in @
% 97.99/13.29 omega)))) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 !!) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#S') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 =>) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#C') @ in @
% 97.99/13.29 omega)))))) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#S') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 '#S') @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 =>))) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#C') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 '#B') @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 =) @
% 97.99/13.29 omegaS)))) @
% 97.99/13.29 omegaS)))))) @
% 97.99/13.29 (
% 97.99/13.29 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.99/13.29 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1582])).
% 97.99/13.29 thf(zip_derived_cl1599, plain,
% 97.99/13.29 (~ (((singletonsuniq) =>
% 97.99/13.29 (((setukpairinjL1) =>
% 97.99/13.29 (((kfstsingleton) =>
% 97.99/13.29 (((theprop) =>
% 97.99/13.29 (((kfstpairEq) =>
% 97.99/13.29 (((cartprodfstin) =>
% 97.99/13.29 (((setukpairinjL2) =>
% 97.99/13.29 (((setukpairinjL) =>
% 97.99/13.29 (((setukpairinjR11) =>
% 97.99/13.29 (((setukpairinjR12) =>
% 97.99/13.29 (((setukpairinjR1) =>
% 97.99/13.29 (((upairequniteq) =>
% 97.99/13.29 (((setukpairinjR2) =>
% 97.99/13.29 (((setukpairinjR) =>
% 97.99/13.29 (((ksndsingleton) =>
% 97.99/13.29 (((ksndpairEq) =>
% 97.99/13.29 (((kpairsurjEq) =>
% 97.99/13.29 (((cartprodsndin) =>
% 97.99/13.29 (((cartprodpairmemEL) =>
% 97.99/13.29 (((cartprodpairmemER) =>
% 97.99/13.29 (((cartprodmempaircEq) =>
% 97.99/13.29 (((cartprodfstpairEq) =>
% 97.99/13.29 (((cartprodsndpairEq) =>
% 97.99/13.29 (((cartprodpairsurjEq) =>
% 97.99/13.29 (((dpsetconstrI) =>
% 97.99/13.29 (((dpsetconstrSub) =>
% 97.99/13.29 (((setOfPairsIsBReln) =>
% 97.99/13.29 (((dpsetconstrERa) =>
% 97.99/13.29 (((dpsetconstrEL1) =>
% 97.99/13.29 (((dpsetconstrEL2) =>
% 97.99/13.29 ((
% 97.99/13.29 (dpsetconstrER) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcImageSingleton) =>
% 97.99/13.29 ((
% 97.99/13.29 (apProp) =>
% 97.99/13.29 ((
% 97.99/13.29 (app) =>
% 97.99/13.29 ((
% 97.99/13.29 (infuncsetfunc) =>
% 97.99/13.29 ((
% 97.99/13.29 (ap2p) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcinfuncset) =>
% 97.99/13.29 ((
% 97.99/13.29 (lamProp) =>
% 97.99/13.29 ((
% 97.99/13.29 (lamp) =>
% 97.99/13.29 ((
% 97.99/13.29 (lam2p) =>
% 97.99/13.29 ((
% 97.99/13.29 (brelnall1) =>
% 97.99/13.29 ((
% 97.99/13.29 (brelnall2) =>
% 97.99/13.29 ((
% 97.99/13.29 (ex1E2) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcGraphProp1) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcGraphProp3) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcGraphProp2) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcextLem) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcGraphProp4) =>
% 97.99/13.29 ((
% 97.99/13.29 (subbreln) =>
% 97.99/13.29 ((
% 97.99/13.29 (eqbreln) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcext) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcext2) =>
% 97.99/13.29 ((
% 97.99/13.29 (ap2apEq1) =>
% 97.99/13.29 ((
% 97.99/13.29 (ap2apEq2) =>
% 97.99/13.29 ((
% 97.99/13.29 (beta1) =>
% 97.99/13.29 ((
% 97.99/13.29 (eta1) =>
% 97.99/13.29 ((
% 97.99/13.29 (lam2lamEq) =>
% 97.99/13.29 ((
% 97.99/13.29 (beta2) =>
% 97.99/13.29 ((
% 97.99/13.29 (eta2) =>
% 97.99/13.29 ((
% 97.99/13.29 (iffalseProp1) =>
% 97.99/13.29 ((
% 97.99/13.29 (iffalseProp2) =>
% 97.99/13.29 ((
% 97.99/13.29 (iftrueProp1) =>
% 97.99/13.29 ((
% 97.99/13.29 (iftrueProp2) =>
% 97.99/13.29 ((
% 97.99/13.29 (ifSingleton) =>
% 97.99/13.29 ((
% 97.99/13.29 (ifp) =>
% 97.99/13.29 ((
% 97.99/13.29 (theeq) =>
% 97.99/13.29 ((
% 97.99/13.29 (iftrue) =>
% 97.99/13.29 ((
% 97.99/13.29 (iffalse) =>
% 97.99/13.29 ((
% 97.99/13.29 (iftrueorfalse) =>
% 97.99/13.29 ((
% 97.99/13.29 (binintersectT_lem) =>
% 97.99/13.29 ((
% 97.99/13.29 (binunionT_lem) =>
% 97.99/13.29 ((
% 97.99/13.29 (powersetT_lem) =>
% 97.99/13.29 ((
% 97.99/13.29 (setminusT_lem) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementT_lem) =>
% 97.99/13.29 ((
% 97.99/13.29 (setextT) =>
% 97.99/13.29 ((
% 97.99/13.29 (subsetTI) =>
% 97.99/13.29 ((
% 97.99/13.29 (powersetTI1) =>
% 97.99/13.29 ((
% 97.99/13.29 (powersetTE1) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementTI1) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementTE1) =>
% 97.99/13.29 ((
% 97.99/13.29 (binintersectTELcontra) =>
% 97.99/13.29 ((
% 97.99/13.29 (binintersectTERcontra) =>
% 97.99/13.29 ((
% 97.99/13.29 (contrasubsetT) =>
% 97.99/13.29 ((
% 97.99/13.29 (contrasubsetT1) =>
% 97.99/13.29 ((
% 97.99/13.29 (contrasubsetT2) =>
% 97.99/13.29 ((
% 97.99/13.29 (contrasubsetT3) =>
% 97.99/13.29 ((
% 97.99/13.29 (doubleComplementI1) =>
% 97.99/13.29 ((
% 97.99/13.29 (doubleComplementE1) =>
% 97.99/13.29 ((
% 97.99/13.29 (doubleComplementSub1) =>
% 97.99/13.29 ((
% 97.99/13.29 (doubleComplementSub2) =>
% 97.99/13.29 ((
% 97.99/13.29 (doubleComplementEq) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementTnotintersectT) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementImpComplementIntersect) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementSubsetComplementIntersect) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementInPowersetComplementIntersect) =>
% 97.99/13.29 ((
% 97.99/13.29 (contraSubsetComplement) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementTcontraSubset) =>
% 97.99/13.29 ((
% 97.99/13.29 (binunionTILcontra) =>
% 97.99/13.29 ((
% 97.99/13.29 (binunionTIRcontra) =>
% 97.99/13.29 ((
% 97.99/13.29 (inIntersectImpInUnion) =>
% 97.99/13.29 ((
% 97.99/13.29 (inIntersectImpInUnion2) =>
% 97.99/13.29 ((
% 97.99/13.29 (inIntersectImpInIntersectUnions) =>
% 97.99/13.29 ((
% 97.99/13.29 (intersectInPowersetIntersectUnions) =>
% 97.99/13.29 ((
% 97.99/13.29 (inComplementUnionImpNotIn1) =>
% 97.99/13.29 ((
% 97.99/13.29 (inComplementUnionImpInComplement1) =>
% 97.99/13.29 ((
% 97.99/13.29 (binunionTE) =>
% 97.99/13.29 ((
% 97.99/13.29 (binunionTEcontra) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2a1) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementUnionInPowersetComplement) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2a2) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan1a) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan1b) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan1) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2a) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2b2) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2b) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz13rule0) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz13rule1) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz13rule2) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz13rule3) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz13rule4) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz1_1) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz1_2) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz1_3) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz1_4) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz1_5) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1all2) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1SetBreln1) =>
% 97.99/13.29 ((
% 97.99/13.29 (choice2fnsingleton) =>
% 97.99/13.29 ((
% 97.99/13.29 (setOfPairsIsBReln1) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1all1) =>
% 97.99/13.29 ((
% 97.99/13.29 (subbreln1) =>
% 97.99/13.29 ((
% 97.99/13.29 (eqbreln1) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1invprop) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1invI) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1invE) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1compprop) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1compI) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1compE) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1compEex) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionprop) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionIL) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionIR) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionI) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionE) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionEcases) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionCommutes) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz2Ex) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz2W) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz2A) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz2B) =>
% 97.99/13.29 ((
% 97.99/13.29 (image1Ex) =>
% 97.99/13.29 ((
% 97.99/13.29 (image1Ex1) =>
% 97.99/13.29 ((
% 97.99/13.29 (image1Equiv) =>
% 97.99/13.29 ((
% 97.99/13.29 (image1E) =>
% 97.99/13.29 ((
% 97.99/13.29 (image1I) =>
% 97.99/13.29 ((
% 97.99/13.29 (injFuncInInjFuncSet) =>
% 97.99/13.29 ((
% 97.99/13.29 (injFuncSetFuncIn) =>
% 97.99/13.29 ((
% 97.99/13.29 (injFuncSetFuncInj) =>
% 97.99/13.29 ((
% 97.99/13.29 (surjFuncSetFuncIn) =>
% 97.99/13.29 ((
% 97.99/13.29 (surjFuncSetFuncSurj) =>
% 97.99/13.29 ((
% 97.99/13.29 (leftInvIsSurj) =>
% 97.99/13.29 ((
% 97.99/13.29 (surjCantorThm) =>
% 97.99/13.29 ((
% 97.99/13.29 (foundation2) =>
% 97.99/13.29 ((
% 97.99/13.29 (notinself) =>
% 97.99/13.29 ((
% 97.99/13.29 (notinself2) =>
% 97.99/13.29 ((
% 97.99/13.29 (omegaSp) =>
% 97.99/13.29 ((
% 97.99/13.29 (omegaSclos) =>
% 97.99/13.29 ((
% 97.99/13.29 (peano0notS) =>
% 97.99/13.29 ((
% 97.99/13.29 (!!) @ (
% 97.99/13.29 (('#S') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 =>) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#C') @ in @
% 97.99/13.29 omega)))) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 !!) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#S') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 =>) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#C') @ in @
% 97.99/13.29 omega)))))) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#S') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 '#S') @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 =>))) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#C') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 '#B') @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 =) @
% 97.99/13.29 omegaS)))) @
% 97.99/13.29 omegaS)))))) @
% 97.99/13.29 (
% 97.99/13.29 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.99/13.29 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1591])).
% 97.99/13.29 thf(zip_derived_cl1607, plain,
% 97.99/13.29 (~ (((setukpairinjL1) =>
% 97.99/13.29 (((kfstsingleton) =>
% 97.99/13.29 (((theprop) =>
% 97.99/13.29 (((kfstpairEq) =>
% 97.99/13.29 (((cartprodfstin) =>
% 97.99/13.29 (((setukpairinjL2) =>
% 97.99/13.29 (((setukpairinjL) =>
% 97.99/13.29 (((setukpairinjR11) =>
% 97.99/13.29 (((setukpairinjR12) =>
% 97.99/13.29 (((setukpairinjR1) =>
% 97.99/13.29 (((upairequniteq) =>
% 97.99/13.29 (((setukpairinjR2) =>
% 97.99/13.29 (((setukpairinjR) =>
% 97.99/13.29 (((ksndsingleton) =>
% 97.99/13.29 (((ksndpairEq) =>
% 97.99/13.29 (((kpairsurjEq) =>
% 97.99/13.29 (((cartprodsndin) =>
% 97.99/13.29 (((cartprodpairmemEL) =>
% 97.99/13.29 (((cartprodpairmemER) =>
% 97.99/13.29 (((cartprodmempaircEq) =>
% 97.99/13.29 (((cartprodfstpairEq) =>
% 97.99/13.29 (((cartprodsndpairEq) =>
% 97.99/13.29 (((cartprodpairsurjEq) =>
% 97.99/13.29 (((dpsetconstrI) =>
% 97.99/13.29 (((dpsetconstrSub) =>
% 97.99/13.29 (((setOfPairsIsBReln) =>
% 97.99/13.29 (((dpsetconstrERa) =>
% 97.99/13.29 (((dpsetconstrEL1) =>
% 97.99/13.29 (((dpsetconstrEL2) =>
% 97.99/13.29 (((dpsetconstrER) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcImageSingleton) =>
% 97.99/13.29 ((
% 97.99/13.29 (apProp) =>
% 97.99/13.29 ((
% 97.99/13.29 (app) =>
% 97.99/13.29 ((
% 97.99/13.29 (infuncsetfunc) =>
% 97.99/13.29 ((
% 97.99/13.29 (ap2p) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcinfuncset) =>
% 97.99/13.29 ((
% 97.99/13.29 (lamProp) =>
% 97.99/13.29 ((
% 97.99/13.29 (lamp) =>
% 97.99/13.29 ((
% 97.99/13.29 (lam2p) =>
% 97.99/13.29 ((
% 97.99/13.29 (brelnall1) =>
% 97.99/13.29 ((
% 97.99/13.29 (brelnall2) =>
% 97.99/13.29 ((
% 97.99/13.29 (ex1E2) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcGraphProp1) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcGraphProp3) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcGraphProp2) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcextLem) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcGraphProp4) =>
% 97.99/13.29 ((
% 97.99/13.29 (subbreln) =>
% 97.99/13.29 ((
% 97.99/13.29 (eqbreln) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcext) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcext2) =>
% 97.99/13.29 ((
% 97.99/13.29 (ap2apEq1) =>
% 97.99/13.29 ((
% 97.99/13.29 (ap2apEq2) =>
% 97.99/13.29 ((
% 97.99/13.29 (beta1) =>
% 97.99/13.29 ((
% 97.99/13.29 (eta1) =>
% 97.99/13.29 ((
% 97.99/13.29 (lam2lamEq) =>
% 97.99/13.29 ((
% 97.99/13.29 (beta2) =>
% 97.99/13.29 ((
% 97.99/13.29 (eta2) =>
% 97.99/13.29 ((
% 97.99/13.29 (iffalseProp1) =>
% 97.99/13.29 ((
% 97.99/13.29 (iffalseProp2) =>
% 97.99/13.29 ((
% 97.99/13.29 (iftrueProp1) =>
% 97.99/13.29 ((
% 97.99/13.29 (iftrueProp2) =>
% 97.99/13.29 ((
% 97.99/13.29 (ifSingleton) =>
% 97.99/13.29 ((
% 97.99/13.29 (ifp) =>
% 97.99/13.29 ((
% 97.99/13.29 (theeq) =>
% 97.99/13.29 ((
% 97.99/13.29 (iftrue) =>
% 97.99/13.29 ((
% 97.99/13.29 (iffalse) =>
% 97.99/13.29 ((
% 97.99/13.29 (iftrueorfalse) =>
% 97.99/13.29 ((
% 97.99/13.29 (binintersectT_lem) =>
% 97.99/13.29 ((
% 97.99/13.29 (binunionT_lem) =>
% 97.99/13.29 ((
% 97.99/13.29 (powersetT_lem) =>
% 97.99/13.29 ((
% 97.99/13.29 (setminusT_lem) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementT_lem) =>
% 97.99/13.29 ((
% 97.99/13.29 (setextT) =>
% 97.99/13.29 ((
% 97.99/13.29 (subsetTI) =>
% 97.99/13.29 ((
% 97.99/13.29 (powersetTI1) =>
% 97.99/13.29 ((
% 97.99/13.29 (powersetTE1) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementTI1) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementTE1) =>
% 97.99/13.29 ((
% 97.99/13.29 (binintersectTELcontra) =>
% 97.99/13.29 ((
% 97.99/13.29 (binintersectTERcontra) =>
% 97.99/13.29 ((
% 97.99/13.29 (contrasubsetT) =>
% 97.99/13.29 ((
% 97.99/13.29 (contrasubsetT1) =>
% 97.99/13.29 ((
% 97.99/13.29 (contrasubsetT2) =>
% 97.99/13.29 ((
% 97.99/13.29 (contrasubsetT3) =>
% 97.99/13.29 ((
% 97.99/13.29 (doubleComplementI1) =>
% 97.99/13.29 ((
% 97.99/13.29 (doubleComplementE1) =>
% 97.99/13.29 ((
% 97.99/13.29 (doubleComplementSub1) =>
% 97.99/13.29 ((
% 97.99/13.29 (doubleComplementSub2) =>
% 97.99/13.29 ((
% 97.99/13.29 (doubleComplementEq) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementTnotintersectT) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementImpComplementIntersect) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementSubsetComplementIntersect) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementInPowersetComplementIntersect) =>
% 97.99/13.29 ((
% 97.99/13.29 (contraSubsetComplement) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementTcontraSubset) =>
% 97.99/13.29 ((
% 97.99/13.29 (binunionTILcontra) =>
% 97.99/13.29 ((
% 97.99/13.29 (binunionTIRcontra) =>
% 97.99/13.29 ((
% 97.99/13.29 (inIntersectImpInUnion) =>
% 97.99/13.29 ((
% 97.99/13.29 (inIntersectImpInUnion2) =>
% 97.99/13.29 ((
% 97.99/13.29 (inIntersectImpInIntersectUnions) =>
% 97.99/13.29 ((
% 97.99/13.29 (intersectInPowersetIntersectUnions) =>
% 97.99/13.29 ((
% 97.99/13.29 (inComplementUnionImpNotIn1) =>
% 97.99/13.29 ((
% 97.99/13.29 (inComplementUnionImpInComplement1) =>
% 97.99/13.29 ((
% 97.99/13.29 (binunionTE) =>
% 97.99/13.29 ((
% 97.99/13.29 (binunionTEcontra) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2a1) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementUnionInPowersetComplement) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2a2) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan1a) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan1b) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan1) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2a) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2b2) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2b) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz13rule0) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz13rule1) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz13rule2) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz13rule3) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz13rule4) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz1_1) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz1_2) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz1_3) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz1_4) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz1_5) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1all2) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1SetBreln1) =>
% 97.99/13.29 ((
% 97.99/13.29 (choice2fnsingleton) =>
% 97.99/13.29 ((
% 97.99/13.29 (setOfPairsIsBReln1) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1all1) =>
% 97.99/13.29 ((
% 97.99/13.29 (subbreln1) =>
% 97.99/13.29 ((
% 97.99/13.29 (eqbreln1) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1invprop) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1invI) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1invE) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1compprop) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1compI) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1compE) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1compEex) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionprop) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionIL) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionIR) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionI) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionE) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionEcases) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionCommutes) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz2Ex) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz2W) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz2A) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz2B) =>
% 97.99/13.29 ((
% 97.99/13.29 (image1Ex) =>
% 97.99/13.29 ((
% 97.99/13.29 (image1Ex1) =>
% 97.99/13.29 ((
% 97.99/13.29 (image1Equiv) =>
% 97.99/13.29 ((
% 97.99/13.29 (image1E) =>
% 97.99/13.29 ((
% 97.99/13.29 (image1I) =>
% 97.99/13.29 ((
% 97.99/13.29 (injFuncInInjFuncSet) =>
% 97.99/13.29 ((
% 97.99/13.29 (injFuncSetFuncIn) =>
% 97.99/13.29 ((
% 97.99/13.29 (injFuncSetFuncInj) =>
% 97.99/13.29 ((
% 97.99/13.29 (surjFuncSetFuncIn) =>
% 97.99/13.29 ((
% 97.99/13.29 (surjFuncSetFuncSurj) =>
% 97.99/13.29 ((
% 97.99/13.29 (leftInvIsSurj) =>
% 97.99/13.29 ((
% 97.99/13.29 (surjCantorThm) =>
% 97.99/13.29 ((
% 97.99/13.29 (foundation2) =>
% 97.99/13.29 ((
% 97.99/13.29 (notinself) =>
% 97.99/13.29 ((
% 97.99/13.29 (notinself2) =>
% 97.99/13.29 ((
% 97.99/13.29 (omegaSp) =>
% 97.99/13.29 ((
% 97.99/13.29 (omegaSclos) =>
% 97.99/13.29 ((
% 97.99/13.29 (peano0notS) =>
% 97.99/13.29 ((
% 97.99/13.29 (!!) @ (
% 97.99/13.29 (('#S') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 =>) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#C') @ in @
% 97.99/13.29 omega)))) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 !!) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#S') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 =>) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#C') @ in @
% 97.99/13.29 omega)))))) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#S') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 '#S') @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 =>))) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#C') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 '#B') @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 =) @
% 97.99/13.29 omegaS)))) @
% 97.99/13.29 omegaS)))))) @
% 97.99/13.29 (
% 97.99/13.29 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.99/13.29 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1599])).
% 97.99/13.29 thf(zip_derived_cl1615, plain,
% 97.99/13.29 (~ (((kfstsingleton) =>
% 97.99/13.29 (((theprop) =>
% 97.99/13.29 (((kfstpairEq) =>
% 97.99/13.29 (((cartprodfstin) =>
% 97.99/13.29 (((setukpairinjL2) =>
% 97.99/13.29 (((setukpairinjL) =>
% 97.99/13.29 (((setukpairinjR11) =>
% 97.99/13.29 (((setukpairinjR12) =>
% 97.99/13.29 (((setukpairinjR1) =>
% 97.99/13.29 (((upairequniteq) =>
% 97.99/13.29 (((setukpairinjR2) =>
% 97.99/13.29 (((setukpairinjR) =>
% 97.99/13.29 (((ksndsingleton) =>
% 97.99/13.29 (((ksndpairEq) =>
% 97.99/13.29 (((kpairsurjEq) =>
% 97.99/13.29 (((cartprodsndin) =>
% 97.99/13.29 (((cartprodpairmemEL) =>
% 97.99/13.29 (((cartprodpairmemER) =>
% 97.99/13.29 (((cartprodmempaircEq) =>
% 97.99/13.29 (((cartprodfstpairEq) =>
% 97.99/13.29 (((cartprodsndpairEq) =>
% 97.99/13.29 (((cartprodpairsurjEq) =>
% 97.99/13.29 (((dpsetconstrI) =>
% 97.99/13.29 (((dpsetconstrSub) =>
% 97.99/13.29 (((setOfPairsIsBReln) =>
% 97.99/13.29 (((dpsetconstrERa) =>
% 97.99/13.29 (((dpsetconstrEL1) =>
% 97.99/13.29 (((dpsetconstrEL2) =>
% 97.99/13.29 (((dpsetconstrER) =>
% 97.99/13.29 (((funcImageSingleton) =>
% 97.99/13.29 ((
% 97.99/13.29 (apProp) =>
% 97.99/13.29 ((
% 97.99/13.29 (app) =>
% 97.99/13.29 ((
% 97.99/13.29 (infuncsetfunc) =>
% 97.99/13.29 ((
% 97.99/13.29 (ap2p) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcinfuncset) =>
% 97.99/13.29 ((
% 97.99/13.29 (lamProp) =>
% 97.99/13.29 ((
% 97.99/13.29 (lamp) =>
% 97.99/13.29 ((
% 97.99/13.29 (lam2p) =>
% 97.99/13.29 ((
% 97.99/13.29 (brelnall1) =>
% 97.99/13.29 ((
% 97.99/13.29 (brelnall2) =>
% 97.99/13.29 ((
% 97.99/13.29 (ex1E2) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcGraphProp1) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcGraphProp3) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcGraphProp2) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcextLem) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcGraphProp4) =>
% 97.99/13.29 ((
% 97.99/13.29 (subbreln) =>
% 97.99/13.29 ((
% 97.99/13.29 (eqbreln) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcext) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcext2) =>
% 97.99/13.29 ((
% 97.99/13.29 (ap2apEq1) =>
% 97.99/13.29 ((
% 97.99/13.29 (ap2apEq2) =>
% 97.99/13.29 ((
% 97.99/13.29 (beta1) =>
% 97.99/13.29 ((
% 97.99/13.29 (eta1) =>
% 97.99/13.29 ((
% 97.99/13.29 (lam2lamEq) =>
% 97.99/13.29 ((
% 97.99/13.29 (beta2) =>
% 97.99/13.29 ((
% 97.99/13.29 (eta2) =>
% 97.99/13.29 ((
% 97.99/13.29 (iffalseProp1) =>
% 97.99/13.29 ((
% 97.99/13.29 (iffalseProp2) =>
% 97.99/13.29 ((
% 97.99/13.29 (iftrueProp1) =>
% 97.99/13.29 ((
% 97.99/13.29 (iftrueProp2) =>
% 97.99/13.29 ((
% 97.99/13.29 (ifSingleton) =>
% 97.99/13.29 ((
% 97.99/13.29 (ifp) =>
% 97.99/13.29 ((
% 97.99/13.29 (theeq) =>
% 97.99/13.29 ((
% 97.99/13.29 (iftrue) =>
% 97.99/13.29 ((
% 97.99/13.29 (iffalse) =>
% 97.99/13.29 ((
% 97.99/13.29 (iftrueorfalse) =>
% 97.99/13.29 ((
% 97.99/13.29 (binintersectT_lem) =>
% 97.99/13.29 ((
% 97.99/13.29 (binunionT_lem) =>
% 97.99/13.29 ((
% 97.99/13.29 (powersetT_lem) =>
% 97.99/13.29 ((
% 97.99/13.29 (setminusT_lem) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementT_lem) =>
% 97.99/13.29 ((
% 97.99/13.29 (setextT) =>
% 97.99/13.29 ((
% 97.99/13.29 (subsetTI) =>
% 97.99/13.29 ((
% 97.99/13.29 (powersetTI1) =>
% 97.99/13.29 ((
% 97.99/13.29 (powersetTE1) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementTI1) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementTE1) =>
% 97.99/13.29 ((
% 97.99/13.29 (binintersectTELcontra) =>
% 97.99/13.29 ((
% 97.99/13.29 (binintersectTERcontra) =>
% 97.99/13.29 ((
% 97.99/13.29 (contrasubsetT) =>
% 97.99/13.29 ((
% 97.99/13.29 (contrasubsetT1) =>
% 97.99/13.29 ((
% 97.99/13.29 (contrasubsetT2) =>
% 97.99/13.29 ((
% 97.99/13.29 (contrasubsetT3) =>
% 97.99/13.29 ((
% 97.99/13.29 (doubleComplementI1) =>
% 97.99/13.29 ((
% 97.99/13.29 (doubleComplementE1) =>
% 97.99/13.29 ((
% 97.99/13.29 (doubleComplementSub1) =>
% 97.99/13.29 ((
% 97.99/13.29 (doubleComplementSub2) =>
% 97.99/13.29 ((
% 97.99/13.29 (doubleComplementEq) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementTnotintersectT) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementImpComplementIntersect) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementSubsetComplementIntersect) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementInPowersetComplementIntersect) =>
% 97.99/13.29 ((
% 97.99/13.29 (contraSubsetComplement) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementTcontraSubset) =>
% 97.99/13.29 ((
% 97.99/13.29 (binunionTILcontra) =>
% 97.99/13.29 ((
% 97.99/13.29 (binunionTIRcontra) =>
% 97.99/13.29 ((
% 97.99/13.29 (inIntersectImpInUnion) =>
% 97.99/13.29 ((
% 97.99/13.29 (inIntersectImpInUnion2) =>
% 97.99/13.29 ((
% 97.99/13.29 (inIntersectImpInIntersectUnions) =>
% 97.99/13.29 ((
% 97.99/13.29 (intersectInPowersetIntersectUnions) =>
% 97.99/13.29 ((
% 97.99/13.29 (inComplementUnionImpNotIn1) =>
% 97.99/13.29 ((
% 97.99/13.29 (inComplementUnionImpInComplement1) =>
% 97.99/13.29 ((
% 97.99/13.29 (binunionTE) =>
% 97.99/13.29 ((
% 97.99/13.29 (binunionTEcontra) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2a1) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementUnionInPowersetComplement) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2a2) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan1a) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan1b) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan1) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2a) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2b2) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2b) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz13rule0) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz13rule1) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz13rule2) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz13rule3) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz13rule4) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz1_1) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz1_2) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz1_3) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz1_4) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz1_5) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1all2) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1SetBreln1) =>
% 97.99/13.29 ((
% 97.99/13.29 (choice2fnsingleton) =>
% 97.99/13.29 ((
% 97.99/13.29 (setOfPairsIsBReln1) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1all1) =>
% 97.99/13.29 ((
% 97.99/13.29 (subbreln1) =>
% 97.99/13.29 ((
% 97.99/13.29 (eqbreln1) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1invprop) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1invI) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1invE) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1compprop) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1compI) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1compE) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1compEex) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionprop) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionIL) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionIR) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionI) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionE) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionEcases) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionCommutes) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz2Ex) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz2W) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz2A) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz2B) =>
% 97.99/13.29 ((
% 97.99/13.29 (image1Ex) =>
% 97.99/13.29 ((
% 97.99/13.29 (image1Ex1) =>
% 97.99/13.29 ((
% 97.99/13.29 (image1Equiv) =>
% 97.99/13.29 ((
% 97.99/13.29 (image1E) =>
% 97.99/13.29 ((
% 97.99/13.29 (image1I) =>
% 97.99/13.29 ((
% 97.99/13.29 (injFuncInInjFuncSet) =>
% 97.99/13.29 ((
% 97.99/13.29 (injFuncSetFuncIn) =>
% 97.99/13.29 ((
% 97.99/13.29 (injFuncSetFuncInj) =>
% 97.99/13.29 ((
% 97.99/13.29 (surjFuncSetFuncIn) =>
% 97.99/13.29 ((
% 97.99/13.29 (surjFuncSetFuncSurj) =>
% 97.99/13.29 ((
% 97.99/13.29 (leftInvIsSurj) =>
% 97.99/13.29 ((
% 97.99/13.29 (surjCantorThm) =>
% 97.99/13.29 ((
% 97.99/13.29 (foundation2) =>
% 97.99/13.29 ((
% 97.99/13.29 (notinself) =>
% 97.99/13.29 ((
% 97.99/13.29 (notinself2) =>
% 97.99/13.29 ((
% 97.99/13.29 (omegaSp) =>
% 97.99/13.29 ((
% 97.99/13.29 (omegaSclos) =>
% 97.99/13.29 ((
% 97.99/13.29 (peano0notS) =>
% 97.99/13.29 ((
% 97.99/13.29 (!!) @ (
% 97.99/13.29 (('#S') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 =>) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#C') @ in @
% 97.99/13.29 omega)))) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 !!) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#S') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 =>) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#C') @ in @
% 97.99/13.29 omega)))))) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#S') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 '#S') @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 =>))) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#C') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 '#B') @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 =) @
% 97.99/13.29 omegaS)))) @
% 97.99/13.29 omegaS)))))) @
% 97.99/13.29 (
% 97.99/13.29 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.99/13.29 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1607])).
% 97.99/13.29 thf(zip_derived_cl1625, plain,
% 97.99/13.29 (~ (((theprop) =>
% 97.99/13.29 (((kfstpairEq) =>
% 97.99/13.29 (((cartprodfstin) =>
% 97.99/13.29 (((setukpairinjL2) =>
% 97.99/13.29 (((setukpairinjL) =>
% 97.99/13.29 (((setukpairinjR11) =>
% 97.99/13.29 (((setukpairinjR12) =>
% 97.99/13.29 (((setukpairinjR1) =>
% 97.99/13.29 (((upairequniteq) =>
% 97.99/13.29 (((setukpairinjR2) =>
% 97.99/13.29 (((setukpairinjR) =>
% 97.99/13.29 (((ksndsingleton) =>
% 97.99/13.29 (((ksndpairEq) =>
% 97.99/13.29 (((kpairsurjEq) =>
% 97.99/13.29 (((cartprodsndin) =>
% 97.99/13.29 (((cartprodpairmemEL) =>
% 97.99/13.29 (((cartprodpairmemER) =>
% 97.99/13.29 (((cartprodmempaircEq) =>
% 97.99/13.29 (((cartprodfstpairEq) =>
% 97.99/13.29 (((cartprodsndpairEq) =>
% 97.99/13.29 (((cartprodpairsurjEq) =>
% 97.99/13.29 (((dpsetconstrI) =>
% 97.99/13.29 (((dpsetconstrSub) =>
% 97.99/13.29 (((setOfPairsIsBReln) =>
% 97.99/13.29 (((dpsetconstrERa) =>
% 97.99/13.29 (((dpsetconstrEL1) =>
% 97.99/13.29 (((dpsetconstrEL2) =>
% 97.99/13.29 (((dpsetconstrER) =>
% 97.99/13.29 (((funcImageSingleton) =>
% 97.99/13.29 (((apProp) =>
% 97.99/13.29 ((
% 97.99/13.29 (app) =>
% 97.99/13.29 ((
% 97.99/13.29 (infuncsetfunc) =>
% 97.99/13.29 ((
% 97.99/13.29 (ap2p) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcinfuncset) =>
% 97.99/13.29 ((
% 97.99/13.29 (lamProp) =>
% 97.99/13.29 ((
% 97.99/13.29 (lamp) =>
% 97.99/13.29 ((
% 97.99/13.29 (lam2p) =>
% 97.99/13.29 ((
% 97.99/13.29 (brelnall1) =>
% 97.99/13.29 ((
% 97.99/13.29 (brelnall2) =>
% 97.99/13.29 ((
% 97.99/13.29 (ex1E2) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcGraphProp1) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcGraphProp3) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcGraphProp2) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcextLem) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcGraphProp4) =>
% 97.99/13.29 ((
% 97.99/13.29 (subbreln) =>
% 97.99/13.29 ((
% 97.99/13.29 (eqbreln) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcext) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcext2) =>
% 97.99/13.29 ((
% 97.99/13.29 (ap2apEq1) =>
% 97.99/13.29 ((
% 97.99/13.29 (ap2apEq2) =>
% 97.99/13.29 ((
% 97.99/13.29 (beta1) =>
% 97.99/13.29 ((
% 97.99/13.29 (eta1) =>
% 97.99/13.29 ((
% 97.99/13.29 (lam2lamEq) =>
% 97.99/13.29 ((
% 97.99/13.29 (beta2) =>
% 97.99/13.29 ((
% 97.99/13.29 (eta2) =>
% 97.99/13.29 ((
% 97.99/13.29 (iffalseProp1) =>
% 97.99/13.29 ((
% 97.99/13.29 (iffalseProp2) =>
% 97.99/13.29 ((
% 97.99/13.29 (iftrueProp1) =>
% 97.99/13.29 ((
% 97.99/13.29 (iftrueProp2) =>
% 97.99/13.29 ((
% 97.99/13.29 (ifSingleton) =>
% 97.99/13.29 ((
% 97.99/13.29 (ifp) =>
% 97.99/13.29 ((
% 97.99/13.29 (theeq) =>
% 97.99/13.29 ((
% 97.99/13.29 (iftrue) =>
% 97.99/13.29 ((
% 97.99/13.29 (iffalse) =>
% 97.99/13.29 ((
% 97.99/13.29 (iftrueorfalse) =>
% 97.99/13.29 ((
% 97.99/13.29 (binintersectT_lem) =>
% 97.99/13.29 ((
% 97.99/13.29 (binunionT_lem) =>
% 97.99/13.29 ((
% 97.99/13.29 (powersetT_lem) =>
% 97.99/13.29 ((
% 97.99/13.29 (setminusT_lem) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementT_lem) =>
% 97.99/13.29 ((
% 97.99/13.29 (setextT) =>
% 97.99/13.29 ((
% 97.99/13.29 (subsetTI) =>
% 97.99/13.29 ((
% 97.99/13.29 (powersetTI1) =>
% 97.99/13.29 ((
% 97.99/13.29 (powersetTE1) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementTI1) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementTE1) =>
% 97.99/13.29 ((
% 97.99/13.29 (binintersectTELcontra) =>
% 97.99/13.29 ((
% 97.99/13.29 (binintersectTERcontra) =>
% 97.99/13.29 ((
% 97.99/13.29 (contrasubsetT) =>
% 97.99/13.29 ((
% 97.99/13.29 (contrasubsetT1) =>
% 97.99/13.29 ((
% 97.99/13.29 (contrasubsetT2) =>
% 97.99/13.29 ((
% 97.99/13.29 (contrasubsetT3) =>
% 97.99/13.29 ((
% 97.99/13.29 (doubleComplementI1) =>
% 97.99/13.29 ((
% 97.99/13.29 (doubleComplementE1) =>
% 97.99/13.29 ((
% 97.99/13.29 (doubleComplementSub1) =>
% 97.99/13.29 ((
% 97.99/13.29 (doubleComplementSub2) =>
% 97.99/13.29 ((
% 97.99/13.29 (doubleComplementEq) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementTnotintersectT) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementImpComplementIntersect) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementSubsetComplementIntersect) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementInPowersetComplementIntersect) =>
% 97.99/13.29 ((
% 97.99/13.29 (contraSubsetComplement) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementTcontraSubset) =>
% 97.99/13.29 ((
% 97.99/13.29 (binunionTILcontra) =>
% 97.99/13.29 ((
% 97.99/13.29 (binunionTIRcontra) =>
% 97.99/13.29 ((
% 97.99/13.29 (inIntersectImpInUnion) =>
% 97.99/13.29 ((
% 97.99/13.29 (inIntersectImpInUnion2) =>
% 97.99/13.29 ((
% 97.99/13.29 (inIntersectImpInIntersectUnions) =>
% 97.99/13.29 ((
% 97.99/13.29 (intersectInPowersetIntersectUnions) =>
% 97.99/13.29 ((
% 97.99/13.29 (inComplementUnionImpNotIn1) =>
% 97.99/13.29 ((
% 97.99/13.29 (inComplementUnionImpInComplement1) =>
% 97.99/13.29 ((
% 97.99/13.29 (binunionTE) =>
% 97.99/13.29 ((
% 97.99/13.29 (binunionTEcontra) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2a1) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementUnionInPowersetComplement) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2a2) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan1a) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan1b) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan1) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2a) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2b2) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2b) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz13rule0) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz13rule1) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz13rule2) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz13rule3) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz13rule4) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz1_1) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz1_2) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz1_3) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz1_4) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz1_5) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1all2) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1SetBreln1) =>
% 97.99/13.29 ((
% 97.99/13.29 (choice2fnsingleton) =>
% 97.99/13.29 ((
% 97.99/13.29 (setOfPairsIsBReln1) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1all1) =>
% 97.99/13.29 ((
% 97.99/13.29 (subbreln1) =>
% 97.99/13.29 ((
% 97.99/13.29 (eqbreln1) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1invprop) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1invI) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1invE) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1compprop) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1compI) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1compE) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1compEex) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionprop) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionIL) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionIR) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionI) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionE) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionEcases) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionCommutes) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz2Ex) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz2W) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz2A) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz2B) =>
% 97.99/13.29 ((
% 97.99/13.29 (image1Ex) =>
% 97.99/13.29 ((
% 97.99/13.29 (image1Ex1) =>
% 97.99/13.29 ((
% 97.99/13.29 (image1Equiv) =>
% 97.99/13.29 ((
% 97.99/13.29 (image1E) =>
% 97.99/13.29 ((
% 97.99/13.29 (image1I) =>
% 97.99/13.29 ((
% 97.99/13.29 (injFuncInInjFuncSet) =>
% 97.99/13.29 ((
% 97.99/13.29 (injFuncSetFuncIn) =>
% 97.99/13.29 ((
% 97.99/13.29 (injFuncSetFuncInj) =>
% 97.99/13.29 ((
% 97.99/13.29 (surjFuncSetFuncIn) =>
% 97.99/13.29 ((
% 97.99/13.29 (surjFuncSetFuncSurj) =>
% 97.99/13.29 ((
% 97.99/13.29 (leftInvIsSurj) =>
% 97.99/13.29 ((
% 97.99/13.29 (surjCantorThm) =>
% 97.99/13.29 ((
% 97.99/13.29 (foundation2) =>
% 97.99/13.29 ((
% 97.99/13.29 (notinself) =>
% 97.99/13.29 ((
% 97.99/13.29 (notinself2) =>
% 97.99/13.29 ((
% 97.99/13.29 (omegaSp) =>
% 97.99/13.29 ((
% 97.99/13.29 (omegaSclos) =>
% 97.99/13.29 ((
% 97.99/13.29 (peano0notS) =>
% 97.99/13.29 ((
% 97.99/13.29 (!!) @ (
% 97.99/13.29 (('#S') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 =>) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#C') @ in @
% 97.99/13.29 omega)))) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 !!) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#S') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 =>) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#C') @ in @
% 97.99/13.29 omega)))))) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#S') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 '#S') @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 =>))) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#C') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 '#B') @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 =) @
% 97.99/13.29 omegaS)))) @
% 97.99/13.29 omegaS)))))) @
% 97.99/13.29 (
% 97.99/13.29 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.99/13.29 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1615])).
% 97.99/13.29 thf(zip_derived_cl1637, plain,
% 97.99/13.29 (~ (((kfstpairEq) =>
% 97.99/13.29 (((cartprodfstin) =>
% 97.99/13.29 (((setukpairinjL2) =>
% 97.99/13.29 (((setukpairinjL) =>
% 97.99/13.29 (((setukpairinjR11) =>
% 97.99/13.29 (((setukpairinjR12) =>
% 97.99/13.29 (((setukpairinjR1) =>
% 97.99/13.29 (((upairequniteq) =>
% 97.99/13.29 (((setukpairinjR2) =>
% 97.99/13.29 (((setukpairinjR) =>
% 97.99/13.29 (((ksndsingleton) =>
% 97.99/13.29 (((ksndpairEq) =>
% 97.99/13.29 (((kpairsurjEq) =>
% 97.99/13.29 (((cartprodsndin) =>
% 97.99/13.29 (((cartprodpairmemEL) =>
% 97.99/13.29 (((cartprodpairmemER) =>
% 97.99/13.29 (((cartprodmempaircEq) =>
% 97.99/13.29 (((cartprodfstpairEq) =>
% 97.99/13.29 (((cartprodsndpairEq) =>
% 97.99/13.29 (((cartprodpairsurjEq) =>
% 97.99/13.29 (((dpsetconstrI) =>
% 97.99/13.29 (((dpsetconstrSub) =>
% 97.99/13.29 (((setOfPairsIsBReln) =>
% 97.99/13.29 (((dpsetconstrERa) =>
% 97.99/13.29 (((dpsetconstrEL1) =>
% 97.99/13.29 (((dpsetconstrEL2) =>
% 97.99/13.29 (((dpsetconstrER) =>
% 97.99/13.29 (((funcImageSingleton) =>
% 97.99/13.29 (((apProp) =>
% 97.99/13.29 (((app) =>
% 97.99/13.29 ((
% 97.99/13.29 (infuncsetfunc) =>
% 97.99/13.29 ((
% 97.99/13.29 (ap2p) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcinfuncset) =>
% 97.99/13.29 ((
% 97.99/13.29 (lamProp) =>
% 97.99/13.29 ((
% 97.99/13.29 (lamp) =>
% 97.99/13.29 ((
% 97.99/13.29 (lam2p) =>
% 97.99/13.29 ((
% 97.99/13.29 (brelnall1) =>
% 97.99/13.29 ((
% 97.99/13.29 (brelnall2) =>
% 97.99/13.29 ((
% 97.99/13.29 (ex1E2) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcGraphProp1) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcGraphProp3) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcGraphProp2) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcextLem) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcGraphProp4) =>
% 97.99/13.29 ((
% 97.99/13.29 (subbreln) =>
% 97.99/13.29 ((
% 97.99/13.29 (eqbreln) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcext) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcext2) =>
% 97.99/13.29 ((
% 97.99/13.29 (ap2apEq1) =>
% 97.99/13.29 ((
% 97.99/13.29 (ap2apEq2) =>
% 97.99/13.29 ((
% 97.99/13.29 (beta1) =>
% 97.99/13.29 ((
% 97.99/13.29 (eta1) =>
% 97.99/13.29 ((
% 97.99/13.29 (lam2lamEq) =>
% 97.99/13.29 ((
% 97.99/13.29 (beta2) =>
% 97.99/13.29 ((
% 97.99/13.29 (eta2) =>
% 97.99/13.29 ((
% 97.99/13.29 (iffalseProp1) =>
% 97.99/13.29 ((
% 97.99/13.29 (iffalseProp2) =>
% 97.99/13.29 ((
% 97.99/13.29 (iftrueProp1) =>
% 97.99/13.29 ((
% 97.99/13.29 (iftrueProp2) =>
% 97.99/13.29 ((
% 97.99/13.29 (ifSingleton) =>
% 97.99/13.29 ((
% 97.99/13.29 (ifp) =>
% 97.99/13.29 ((
% 97.99/13.29 (theeq) =>
% 97.99/13.29 ((
% 97.99/13.29 (iftrue) =>
% 97.99/13.29 ((
% 97.99/13.29 (iffalse) =>
% 97.99/13.29 ((
% 97.99/13.29 (iftrueorfalse) =>
% 97.99/13.29 ((
% 97.99/13.29 (binintersectT_lem) =>
% 97.99/13.29 ((
% 97.99/13.29 (binunionT_lem) =>
% 97.99/13.29 ((
% 97.99/13.29 (powersetT_lem) =>
% 97.99/13.29 ((
% 97.99/13.29 (setminusT_lem) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementT_lem) =>
% 97.99/13.29 ((
% 97.99/13.29 (setextT) =>
% 97.99/13.29 ((
% 97.99/13.29 (subsetTI) =>
% 97.99/13.29 ((
% 97.99/13.29 (powersetTI1) =>
% 97.99/13.29 ((
% 97.99/13.29 (powersetTE1) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementTI1) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementTE1) =>
% 97.99/13.29 ((
% 97.99/13.29 (binintersectTELcontra) =>
% 97.99/13.29 ((
% 97.99/13.29 (binintersectTERcontra) =>
% 97.99/13.29 ((
% 97.99/13.29 (contrasubsetT) =>
% 97.99/13.29 ((
% 97.99/13.29 (contrasubsetT1) =>
% 97.99/13.29 ((
% 97.99/13.29 (contrasubsetT2) =>
% 97.99/13.29 ((
% 97.99/13.29 (contrasubsetT3) =>
% 97.99/13.29 ((
% 97.99/13.29 (doubleComplementI1) =>
% 97.99/13.29 ((
% 97.99/13.29 (doubleComplementE1) =>
% 97.99/13.29 ((
% 97.99/13.29 (doubleComplementSub1) =>
% 97.99/13.29 ((
% 97.99/13.29 (doubleComplementSub2) =>
% 97.99/13.29 ((
% 97.99/13.29 (doubleComplementEq) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementTnotintersectT) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementImpComplementIntersect) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementSubsetComplementIntersect) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementInPowersetComplementIntersect) =>
% 97.99/13.29 ((
% 97.99/13.29 (contraSubsetComplement) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementTcontraSubset) =>
% 97.99/13.29 ((
% 97.99/13.29 (binunionTILcontra) =>
% 97.99/13.29 ((
% 97.99/13.29 (binunionTIRcontra) =>
% 97.99/13.29 ((
% 97.99/13.29 (inIntersectImpInUnion) =>
% 97.99/13.29 ((
% 97.99/13.29 (inIntersectImpInUnion2) =>
% 97.99/13.29 ((
% 97.99/13.29 (inIntersectImpInIntersectUnions) =>
% 97.99/13.29 ((
% 97.99/13.29 (intersectInPowersetIntersectUnions) =>
% 97.99/13.29 ((
% 97.99/13.29 (inComplementUnionImpNotIn1) =>
% 97.99/13.29 ((
% 97.99/13.29 (inComplementUnionImpInComplement1) =>
% 97.99/13.29 ((
% 97.99/13.29 (binunionTE) =>
% 97.99/13.29 ((
% 97.99/13.29 (binunionTEcontra) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2a1) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementUnionInPowersetComplement) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2a2) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan1a) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan1b) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan1) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2a) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2b2) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2b) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz13rule0) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz13rule1) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz13rule2) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz13rule3) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz13rule4) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz1_1) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz1_2) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz1_3) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz1_4) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz1_5) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1all2) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1SetBreln1) =>
% 97.99/13.29 ((
% 97.99/13.29 (choice2fnsingleton) =>
% 97.99/13.29 ((
% 97.99/13.29 (setOfPairsIsBReln1) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1all1) =>
% 97.99/13.29 ((
% 97.99/13.29 (subbreln1) =>
% 97.99/13.29 ((
% 97.99/13.29 (eqbreln1) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1invprop) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1invI) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1invE) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1compprop) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1compI) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1compE) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1compEex) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionprop) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionIL) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionIR) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionI) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionE) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionEcases) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionCommutes) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz2Ex) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz2W) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz2A) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz2B) =>
% 97.99/13.29 ((
% 97.99/13.29 (image1Ex) =>
% 97.99/13.29 ((
% 97.99/13.29 (image1Ex1) =>
% 97.99/13.29 ((
% 97.99/13.29 (image1Equiv) =>
% 97.99/13.29 ((
% 97.99/13.29 (image1E) =>
% 97.99/13.29 ((
% 97.99/13.29 (image1I) =>
% 97.99/13.29 ((
% 97.99/13.29 (injFuncInInjFuncSet) =>
% 97.99/13.29 ((
% 97.99/13.29 (injFuncSetFuncIn) =>
% 97.99/13.29 ((
% 97.99/13.29 (injFuncSetFuncInj) =>
% 97.99/13.29 ((
% 97.99/13.29 (surjFuncSetFuncIn) =>
% 97.99/13.29 ((
% 97.99/13.29 (surjFuncSetFuncSurj) =>
% 97.99/13.29 ((
% 97.99/13.29 (leftInvIsSurj) =>
% 97.99/13.29 ((
% 97.99/13.29 (surjCantorThm) =>
% 97.99/13.29 ((
% 97.99/13.29 (foundation2) =>
% 97.99/13.29 ((
% 97.99/13.29 (notinself) =>
% 97.99/13.29 ((
% 97.99/13.29 (notinself2) =>
% 97.99/13.29 ((
% 97.99/13.29 (omegaSp) =>
% 97.99/13.29 ((
% 97.99/13.29 (omegaSclos) =>
% 97.99/13.29 ((
% 97.99/13.29 (peano0notS) =>
% 97.99/13.29 ((
% 97.99/13.29 (!!) @ (
% 97.99/13.29 (('#S') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 =>) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#C') @ in @
% 97.99/13.29 omega)))) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 !!) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#S') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 =>) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#C') @ in @
% 97.99/13.29 omega)))))) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#S') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 '#S') @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 =>))) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#C') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 '#B') @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 =) @
% 97.99/13.29 omegaS)))) @
% 97.99/13.29 omegaS)))))) @
% 97.99/13.29 (
% 97.99/13.29 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.99/13.29 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1625])).
% 97.99/13.29 thf(zip_derived_cl1649, plain,
% 97.99/13.29 (~ (((cartprodfstin) =>
% 97.99/13.29 (((setukpairinjL2) =>
% 97.99/13.29 (((setukpairinjL) =>
% 97.99/13.29 (((setukpairinjR11) =>
% 97.99/13.29 (((setukpairinjR12) =>
% 97.99/13.29 (((setukpairinjR1) =>
% 97.99/13.29 (((upairequniteq) =>
% 97.99/13.29 (((setukpairinjR2) =>
% 97.99/13.29 (((setukpairinjR) =>
% 97.99/13.29 (((ksndsingleton) =>
% 97.99/13.29 (((ksndpairEq) =>
% 97.99/13.29 (((kpairsurjEq) =>
% 97.99/13.29 (((cartprodsndin) =>
% 97.99/13.29 (((cartprodpairmemEL) =>
% 97.99/13.29 (((cartprodpairmemER) =>
% 97.99/13.29 (((cartprodmempaircEq) =>
% 97.99/13.29 (((cartprodfstpairEq) =>
% 97.99/13.29 (((cartprodsndpairEq) =>
% 97.99/13.29 (((cartprodpairsurjEq) =>
% 97.99/13.29 (((dpsetconstrI) =>
% 97.99/13.29 (((dpsetconstrSub) =>
% 97.99/13.29 (((setOfPairsIsBReln) =>
% 97.99/13.29 (((dpsetconstrERa) =>
% 97.99/13.29 (((dpsetconstrEL1) =>
% 97.99/13.29 (((dpsetconstrEL2) =>
% 97.99/13.29 (((dpsetconstrER) =>
% 97.99/13.29 (((funcImageSingleton) =>
% 97.99/13.29 (((apProp) =>
% 97.99/13.29 (((app) =>
% 97.99/13.29 (((infuncsetfunc) =>
% 97.99/13.29 ((
% 97.99/13.29 (ap2p) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcinfuncset) =>
% 97.99/13.29 ((
% 97.99/13.29 (lamProp) =>
% 97.99/13.29 ((
% 97.99/13.29 (lamp) =>
% 97.99/13.29 ((
% 97.99/13.29 (lam2p) =>
% 97.99/13.29 ((
% 97.99/13.29 (brelnall1) =>
% 97.99/13.29 ((
% 97.99/13.29 (brelnall2) =>
% 97.99/13.29 ((
% 97.99/13.29 (ex1E2) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcGraphProp1) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcGraphProp3) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcGraphProp2) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcextLem) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcGraphProp4) =>
% 97.99/13.29 ((
% 97.99/13.29 (subbreln) =>
% 97.99/13.29 ((
% 97.99/13.29 (eqbreln) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcext) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcext2) =>
% 97.99/13.29 ((
% 97.99/13.29 (ap2apEq1) =>
% 97.99/13.29 ((
% 97.99/13.29 (ap2apEq2) =>
% 97.99/13.29 ((
% 97.99/13.29 (beta1) =>
% 97.99/13.29 ((
% 97.99/13.29 (eta1) =>
% 97.99/13.29 ((
% 97.99/13.29 (lam2lamEq) =>
% 97.99/13.29 ((
% 97.99/13.29 (beta2) =>
% 97.99/13.29 ((
% 97.99/13.29 (eta2) =>
% 97.99/13.29 ((
% 97.99/13.29 (iffalseProp1) =>
% 97.99/13.29 ((
% 97.99/13.29 (iffalseProp2) =>
% 97.99/13.29 ((
% 97.99/13.29 (iftrueProp1) =>
% 97.99/13.29 ((
% 97.99/13.29 (iftrueProp2) =>
% 97.99/13.29 ((
% 97.99/13.29 (ifSingleton) =>
% 97.99/13.29 ((
% 97.99/13.29 (ifp) =>
% 97.99/13.29 ((
% 97.99/13.29 (theeq) =>
% 97.99/13.29 ((
% 97.99/13.29 (iftrue) =>
% 97.99/13.29 ((
% 97.99/13.29 (iffalse) =>
% 97.99/13.29 ((
% 97.99/13.29 (iftrueorfalse) =>
% 97.99/13.29 ((
% 97.99/13.29 (binintersectT_lem) =>
% 97.99/13.29 ((
% 97.99/13.29 (binunionT_lem) =>
% 97.99/13.29 ((
% 97.99/13.29 (powersetT_lem) =>
% 97.99/13.29 ((
% 97.99/13.29 (setminusT_lem) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementT_lem) =>
% 97.99/13.29 ((
% 97.99/13.29 (setextT) =>
% 97.99/13.29 ((
% 97.99/13.29 (subsetTI) =>
% 97.99/13.29 ((
% 97.99/13.29 (powersetTI1) =>
% 97.99/13.29 ((
% 97.99/13.29 (powersetTE1) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementTI1) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementTE1) =>
% 97.99/13.29 ((
% 97.99/13.29 (binintersectTELcontra) =>
% 97.99/13.29 ((
% 97.99/13.29 (binintersectTERcontra) =>
% 97.99/13.29 ((
% 97.99/13.29 (contrasubsetT) =>
% 97.99/13.29 ((
% 97.99/13.29 (contrasubsetT1) =>
% 97.99/13.29 ((
% 97.99/13.29 (contrasubsetT2) =>
% 97.99/13.29 ((
% 97.99/13.29 (contrasubsetT3) =>
% 97.99/13.29 ((
% 97.99/13.29 (doubleComplementI1) =>
% 97.99/13.29 ((
% 97.99/13.29 (doubleComplementE1) =>
% 97.99/13.29 ((
% 97.99/13.29 (doubleComplementSub1) =>
% 97.99/13.29 ((
% 97.99/13.29 (doubleComplementSub2) =>
% 97.99/13.29 ((
% 97.99/13.29 (doubleComplementEq) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementTnotintersectT) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementImpComplementIntersect) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementSubsetComplementIntersect) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementInPowersetComplementIntersect) =>
% 97.99/13.29 ((
% 97.99/13.29 (contraSubsetComplement) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementTcontraSubset) =>
% 97.99/13.29 ((
% 97.99/13.29 (binunionTILcontra) =>
% 97.99/13.29 ((
% 97.99/13.29 (binunionTIRcontra) =>
% 97.99/13.29 ((
% 97.99/13.29 (inIntersectImpInUnion) =>
% 97.99/13.29 ((
% 97.99/13.29 (inIntersectImpInUnion2) =>
% 97.99/13.29 ((
% 97.99/13.29 (inIntersectImpInIntersectUnions) =>
% 97.99/13.29 ((
% 97.99/13.29 (intersectInPowersetIntersectUnions) =>
% 97.99/13.29 ((
% 97.99/13.29 (inComplementUnionImpNotIn1) =>
% 97.99/13.29 ((
% 97.99/13.29 (inComplementUnionImpInComplement1) =>
% 97.99/13.29 ((
% 97.99/13.29 (binunionTE) =>
% 97.99/13.29 ((
% 97.99/13.29 (binunionTEcontra) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2a1) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementUnionInPowersetComplement) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2a2) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan1a) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan1b) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan1) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2a) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2b2) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2b) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz13rule0) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz13rule1) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz13rule2) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz13rule3) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz13rule4) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz1_1) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz1_2) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz1_3) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz1_4) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz1_5) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1all2) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1SetBreln1) =>
% 97.99/13.29 ((
% 97.99/13.29 (choice2fnsingleton) =>
% 97.99/13.29 ((
% 97.99/13.29 (setOfPairsIsBReln1) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1all1) =>
% 97.99/13.29 ((
% 97.99/13.29 (subbreln1) =>
% 97.99/13.29 ((
% 97.99/13.29 (eqbreln1) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1invprop) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1invI) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1invE) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1compprop) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1compI) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1compE) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1compEex) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionprop) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionIL) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionIR) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionI) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionE) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionEcases) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionCommutes) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz2Ex) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz2W) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz2A) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz2B) =>
% 97.99/13.29 ((
% 97.99/13.29 (image1Ex) =>
% 97.99/13.29 ((
% 97.99/13.29 (image1Ex1) =>
% 97.99/13.29 ((
% 97.99/13.29 (image1Equiv) =>
% 97.99/13.29 ((
% 97.99/13.29 (image1E) =>
% 97.99/13.29 ((
% 97.99/13.29 (image1I) =>
% 97.99/13.29 ((
% 97.99/13.29 (injFuncInInjFuncSet) =>
% 97.99/13.29 ((
% 97.99/13.29 (injFuncSetFuncIn) =>
% 97.99/13.29 ((
% 97.99/13.29 (injFuncSetFuncInj) =>
% 97.99/13.29 ((
% 97.99/13.29 (surjFuncSetFuncIn) =>
% 97.99/13.29 ((
% 97.99/13.29 (surjFuncSetFuncSurj) =>
% 97.99/13.29 ((
% 97.99/13.29 (leftInvIsSurj) =>
% 97.99/13.29 ((
% 97.99/13.29 (surjCantorThm) =>
% 97.99/13.29 ((
% 97.99/13.29 (foundation2) =>
% 97.99/13.29 ((
% 97.99/13.29 (notinself) =>
% 97.99/13.29 ((
% 97.99/13.29 (notinself2) =>
% 97.99/13.29 ((
% 97.99/13.29 (omegaSp) =>
% 97.99/13.29 ((
% 97.99/13.29 (omegaSclos) =>
% 97.99/13.29 ((
% 97.99/13.29 (peano0notS) =>
% 97.99/13.29 ((
% 97.99/13.29 (!!) @ (
% 97.99/13.29 (('#S') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 =>) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#C') @ in @
% 97.99/13.29 omega)))) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 !!) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#S') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 =>) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#C') @ in @
% 97.99/13.29 omega)))))) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#S') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 '#S') @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 =>))) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#C') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 '#B') @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 =) @
% 97.99/13.29 omegaS)))) @
% 97.99/13.29 omegaS)))))) @
% 97.99/13.29 (
% 97.99/13.29 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.99/13.29 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1637])).
% 97.99/13.29 thf(zip_derived_cl1664, plain,
% 97.99/13.29 (~ (((setukpairinjL2) =>
% 97.99/13.29 (((setukpairinjL) =>
% 97.99/13.29 (((setukpairinjR11) =>
% 97.99/13.29 (((setukpairinjR12) =>
% 97.99/13.29 (((setukpairinjR1) =>
% 97.99/13.29 (((upairequniteq) =>
% 97.99/13.29 (((setukpairinjR2) =>
% 97.99/13.29 (((setukpairinjR) =>
% 97.99/13.29 (((ksndsingleton) =>
% 97.99/13.29 (((ksndpairEq) =>
% 97.99/13.29 (((kpairsurjEq) =>
% 97.99/13.29 (((cartprodsndin) =>
% 97.99/13.29 (((cartprodpairmemEL) =>
% 97.99/13.29 (((cartprodpairmemER) =>
% 97.99/13.29 (((cartprodmempaircEq) =>
% 97.99/13.29 (((cartprodfstpairEq) =>
% 97.99/13.29 (((cartprodsndpairEq) =>
% 97.99/13.29 (((cartprodpairsurjEq) =>
% 97.99/13.29 (((dpsetconstrI) =>
% 97.99/13.29 (((dpsetconstrSub) =>
% 97.99/13.29 (((setOfPairsIsBReln) =>
% 97.99/13.29 (((dpsetconstrERa) =>
% 97.99/13.29 (((dpsetconstrEL1) =>
% 97.99/13.29 (((dpsetconstrEL2) =>
% 97.99/13.29 (((dpsetconstrER) =>
% 97.99/13.29 (((funcImageSingleton) =>
% 97.99/13.29 (((apProp) =>
% 97.99/13.29 (((app) =>
% 97.99/13.29 (((infuncsetfunc) =>
% 97.99/13.29 (((ap2p) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcinfuncset) =>
% 97.99/13.29 ((
% 97.99/13.29 (lamProp) =>
% 97.99/13.29 ((
% 97.99/13.29 (lamp) =>
% 97.99/13.29 ((
% 97.99/13.29 (lam2p) =>
% 97.99/13.29 ((
% 97.99/13.29 (brelnall1) =>
% 97.99/13.29 ((
% 97.99/13.29 (brelnall2) =>
% 97.99/13.29 ((
% 97.99/13.29 (ex1E2) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcGraphProp1) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcGraphProp3) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcGraphProp2) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcextLem) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcGraphProp4) =>
% 97.99/13.29 ((
% 97.99/13.29 (subbreln) =>
% 97.99/13.29 ((
% 97.99/13.29 (eqbreln) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcext) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcext2) =>
% 97.99/13.29 ((
% 97.99/13.29 (ap2apEq1) =>
% 97.99/13.29 ((
% 97.99/13.29 (ap2apEq2) =>
% 97.99/13.29 ((
% 97.99/13.29 (beta1) =>
% 97.99/13.29 ((
% 97.99/13.29 (eta1) =>
% 97.99/13.29 ((
% 97.99/13.29 (lam2lamEq) =>
% 97.99/13.29 ((
% 97.99/13.29 (beta2) =>
% 97.99/13.29 ((
% 97.99/13.29 (eta2) =>
% 97.99/13.29 ((
% 97.99/13.29 (iffalseProp1) =>
% 97.99/13.29 ((
% 97.99/13.29 (iffalseProp2) =>
% 97.99/13.29 ((
% 97.99/13.29 (iftrueProp1) =>
% 97.99/13.29 ((
% 97.99/13.29 (iftrueProp2) =>
% 97.99/13.29 ((
% 97.99/13.29 (ifSingleton) =>
% 97.99/13.29 ((
% 97.99/13.29 (ifp) =>
% 97.99/13.29 ((
% 97.99/13.29 (theeq) =>
% 97.99/13.29 ((
% 97.99/13.29 (iftrue) =>
% 97.99/13.29 ((
% 97.99/13.29 (iffalse) =>
% 97.99/13.29 ((
% 97.99/13.29 (iftrueorfalse) =>
% 97.99/13.29 ((
% 97.99/13.29 (binintersectT_lem) =>
% 97.99/13.29 ((
% 97.99/13.29 (binunionT_lem) =>
% 97.99/13.29 ((
% 97.99/13.29 (powersetT_lem) =>
% 97.99/13.29 ((
% 97.99/13.29 (setminusT_lem) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementT_lem) =>
% 97.99/13.29 ((
% 97.99/13.29 (setextT) =>
% 97.99/13.29 ((
% 97.99/13.29 (subsetTI) =>
% 97.99/13.29 ((
% 97.99/13.29 (powersetTI1) =>
% 97.99/13.29 ((
% 97.99/13.29 (powersetTE1) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementTI1) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementTE1) =>
% 97.99/13.29 ((
% 97.99/13.29 (binintersectTELcontra) =>
% 97.99/13.29 ((
% 97.99/13.29 (binintersectTERcontra) =>
% 97.99/13.29 ((
% 97.99/13.29 (contrasubsetT) =>
% 97.99/13.29 ((
% 97.99/13.29 (contrasubsetT1) =>
% 97.99/13.29 ((
% 97.99/13.29 (contrasubsetT2) =>
% 97.99/13.29 ((
% 97.99/13.29 (contrasubsetT3) =>
% 97.99/13.29 ((
% 97.99/13.29 (doubleComplementI1) =>
% 97.99/13.29 ((
% 97.99/13.29 (doubleComplementE1) =>
% 97.99/13.29 ((
% 97.99/13.29 (doubleComplementSub1) =>
% 97.99/13.29 ((
% 97.99/13.29 (doubleComplementSub2) =>
% 97.99/13.29 ((
% 97.99/13.29 (doubleComplementEq) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementTnotintersectT) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementImpComplementIntersect) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementSubsetComplementIntersect) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementInPowersetComplementIntersect) =>
% 97.99/13.29 ((
% 97.99/13.29 (contraSubsetComplement) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementTcontraSubset) =>
% 97.99/13.29 ((
% 97.99/13.29 (binunionTILcontra) =>
% 97.99/13.29 ((
% 97.99/13.29 (binunionTIRcontra) =>
% 97.99/13.29 ((
% 97.99/13.29 (inIntersectImpInUnion) =>
% 97.99/13.29 ((
% 97.99/13.29 (inIntersectImpInUnion2) =>
% 97.99/13.29 ((
% 97.99/13.29 (inIntersectImpInIntersectUnions) =>
% 97.99/13.29 ((
% 97.99/13.29 (intersectInPowersetIntersectUnions) =>
% 97.99/13.29 ((
% 97.99/13.29 (inComplementUnionImpNotIn1) =>
% 97.99/13.29 ((
% 97.99/13.29 (inComplementUnionImpInComplement1) =>
% 97.99/13.29 ((
% 97.99/13.29 (binunionTE) =>
% 97.99/13.29 ((
% 97.99/13.29 (binunionTEcontra) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2a1) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementUnionInPowersetComplement) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2a2) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan1a) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan1b) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan1) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2a) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2b2) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2b) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz13rule0) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz13rule1) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz13rule2) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz13rule3) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz13rule4) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz1_1) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz1_2) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz1_3) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz1_4) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz1_5) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1all2) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1SetBreln1) =>
% 97.99/13.29 ((
% 97.99/13.29 (choice2fnsingleton) =>
% 97.99/13.29 ((
% 97.99/13.29 (setOfPairsIsBReln1) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1all1) =>
% 97.99/13.29 ((
% 97.99/13.29 (subbreln1) =>
% 97.99/13.29 ((
% 97.99/13.29 (eqbreln1) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1invprop) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1invI) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1invE) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1compprop) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1compI) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1compE) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1compEex) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionprop) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionIL) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionIR) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionI) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionE) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionEcases) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionCommutes) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz2Ex) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz2W) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz2A) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz2B) =>
% 97.99/13.29 ((
% 97.99/13.29 (image1Ex) =>
% 97.99/13.29 ((
% 97.99/13.29 (image1Ex1) =>
% 97.99/13.29 ((
% 97.99/13.29 (image1Equiv) =>
% 97.99/13.29 ((
% 97.99/13.29 (image1E) =>
% 97.99/13.29 ((
% 97.99/13.29 (image1I) =>
% 97.99/13.29 ((
% 97.99/13.29 (injFuncInInjFuncSet) =>
% 97.99/13.29 ((
% 97.99/13.29 (injFuncSetFuncIn) =>
% 97.99/13.29 ((
% 97.99/13.29 (injFuncSetFuncInj) =>
% 97.99/13.29 ((
% 97.99/13.29 (surjFuncSetFuncIn) =>
% 97.99/13.29 ((
% 97.99/13.29 (surjFuncSetFuncSurj) =>
% 97.99/13.29 ((
% 97.99/13.29 (leftInvIsSurj) =>
% 97.99/13.29 ((
% 97.99/13.29 (surjCantorThm) =>
% 97.99/13.29 ((
% 97.99/13.29 (foundation2) =>
% 97.99/13.29 ((
% 97.99/13.29 (notinself) =>
% 97.99/13.29 ((
% 97.99/13.29 (notinself2) =>
% 97.99/13.29 ((
% 97.99/13.29 (omegaSp) =>
% 97.99/13.29 ((
% 97.99/13.29 (omegaSclos) =>
% 97.99/13.29 ((
% 97.99/13.29 (peano0notS) =>
% 97.99/13.29 ((
% 97.99/13.29 (!!) @ (
% 97.99/13.29 (('#S') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 =>) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#C') @ in @
% 97.99/13.29 omega)))) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 !!) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#S') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 =>) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#C') @ in @
% 97.99/13.29 omega)))))) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#S') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 '#S') @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 =>))) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#C') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 '#B') @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 =) @
% 97.99/13.29 omegaS)))) @
% 97.99/13.29 omegaS)))))) @
% 97.99/13.29 (
% 97.99/13.29 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.99/13.29 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1649])).
% 97.99/13.29 thf(zip_derived_cl1678, plain,
% 97.99/13.29 (~ (((setukpairinjL) =>
% 97.99/13.29 (((setukpairinjR11) =>
% 97.99/13.29 (((setukpairinjR12) =>
% 97.99/13.29 (((setukpairinjR1) =>
% 97.99/13.29 (((upairequniteq) =>
% 97.99/13.29 (((setukpairinjR2) =>
% 97.99/13.29 (((setukpairinjR) =>
% 97.99/13.29 (((ksndsingleton) =>
% 97.99/13.29 (((ksndpairEq) =>
% 97.99/13.29 (((kpairsurjEq) =>
% 97.99/13.29 (((cartprodsndin) =>
% 97.99/13.29 (((cartprodpairmemEL) =>
% 97.99/13.29 (((cartprodpairmemER) =>
% 97.99/13.29 (((cartprodmempaircEq) =>
% 97.99/13.29 (((cartprodfstpairEq) =>
% 97.99/13.29 (((cartprodsndpairEq) =>
% 97.99/13.29 (((cartprodpairsurjEq) =>
% 97.99/13.29 (((dpsetconstrI) =>
% 97.99/13.29 (((dpsetconstrSub) =>
% 97.99/13.29 (((setOfPairsIsBReln) =>
% 97.99/13.29 (((dpsetconstrERa) =>
% 97.99/13.29 (((dpsetconstrEL1) =>
% 97.99/13.29 (((dpsetconstrEL2) =>
% 97.99/13.29 (((dpsetconstrER) =>
% 97.99/13.29 (((funcImageSingleton) =>
% 97.99/13.29 (((apProp) =>
% 97.99/13.29 (((app) =>
% 97.99/13.29 (((infuncsetfunc) =>
% 97.99/13.29 (((ap2p) =>
% 97.99/13.29 (((funcinfuncset) =>
% 97.99/13.29 ((
% 97.99/13.29 (lamProp) =>
% 97.99/13.29 ((
% 97.99/13.29 (lamp) =>
% 97.99/13.29 ((
% 97.99/13.29 (lam2p) =>
% 97.99/13.29 ((
% 97.99/13.29 (brelnall1) =>
% 97.99/13.29 ((
% 97.99/13.29 (brelnall2) =>
% 97.99/13.29 ((
% 97.99/13.29 (ex1E2) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcGraphProp1) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcGraphProp3) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcGraphProp2) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcextLem) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcGraphProp4) =>
% 97.99/13.29 ((
% 97.99/13.29 (subbreln) =>
% 97.99/13.29 ((
% 97.99/13.29 (eqbreln) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcext) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcext2) =>
% 97.99/13.29 ((
% 97.99/13.29 (ap2apEq1) =>
% 97.99/13.29 ((
% 97.99/13.29 (ap2apEq2) =>
% 97.99/13.29 ((
% 97.99/13.29 (beta1) =>
% 97.99/13.29 ((
% 97.99/13.29 (eta1) =>
% 97.99/13.29 ((
% 97.99/13.29 (lam2lamEq) =>
% 97.99/13.29 ((
% 97.99/13.29 (beta2) =>
% 97.99/13.29 ((
% 97.99/13.29 (eta2) =>
% 97.99/13.29 ((
% 97.99/13.29 (iffalseProp1) =>
% 97.99/13.29 ((
% 97.99/13.29 (iffalseProp2) =>
% 97.99/13.29 ((
% 97.99/13.29 (iftrueProp1) =>
% 97.99/13.29 ((
% 97.99/13.29 (iftrueProp2) =>
% 97.99/13.29 ((
% 97.99/13.29 (ifSingleton) =>
% 97.99/13.29 ((
% 97.99/13.29 (ifp) =>
% 97.99/13.29 ((
% 97.99/13.29 (theeq) =>
% 97.99/13.29 ((
% 97.99/13.29 (iftrue) =>
% 97.99/13.29 ((
% 97.99/13.29 (iffalse) =>
% 97.99/13.29 ((
% 97.99/13.29 (iftrueorfalse) =>
% 97.99/13.29 ((
% 97.99/13.29 (binintersectT_lem) =>
% 97.99/13.29 ((
% 97.99/13.29 (binunionT_lem) =>
% 97.99/13.29 ((
% 97.99/13.29 (powersetT_lem) =>
% 97.99/13.29 ((
% 97.99/13.29 (setminusT_lem) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementT_lem) =>
% 97.99/13.29 ((
% 97.99/13.29 (setextT) =>
% 97.99/13.29 ((
% 97.99/13.29 (subsetTI) =>
% 97.99/13.29 ((
% 97.99/13.29 (powersetTI1) =>
% 97.99/13.29 ((
% 97.99/13.29 (powersetTE1) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementTI1) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementTE1) =>
% 97.99/13.29 ((
% 97.99/13.29 (binintersectTELcontra) =>
% 97.99/13.29 ((
% 97.99/13.29 (binintersectTERcontra) =>
% 97.99/13.29 ((
% 97.99/13.29 (contrasubsetT) =>
% 97.99/13.29 ((
% 97.99/13.29 (contrasubsetT1) =>
% 97.99/13.29 ((
% 97.99/13.29 (contrasubsetT2) =>
% 97.99/13.29 ((
% 97.99/13.29 (contrasubsetT3) =>
% 97.99/13.29 ((
% 97.99/13.29 (doubleComplementI1) =>
% 97.99/13.29 ((
% 97.99/13.29 (doubleComplementE1) =>
% 97.99/13.29 ((
% 97.99/13.29 (doubleComplementSub1) =>
% 97.99/13.29 ((
% 97.99/13.29 (doubleComplementSub2) =>
% 97.99/13.29 ((
% 97.99/13.29 (doubleComplementEq) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementTnotintersectT) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementImpComplementIntersect) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementSubsetComplementIntersect) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementInPowersetComplementIntersect) =>
% 97.99/13.29 ((
% 97.99/13.29 (contraSubsetComplement) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementTcontraSubset) =>
% 97.99/13.29 ((
% 97.99/13.29 (binunionTILcontra) =>
% 97.99/13.29 ((
% 97.99/13.29 (binunionTIRcontra) =>
% 97.99/13.29 ((
% 97.99/13.29 (inIntersectImpInUnion) =>
% 97.99/13.29 ((
% 97.99/13.29 (inIntersectImpInUnion2) =>
% 97.99/13.29 ((
% 97.99/13.29 (inIntersectImpInIntersectUnions) =>
% 97.99/13.29 ((
% 97.99/13.29 (intersectInPowersetIntersectUnions) =>
% 97.99/13.29 ((
% 97.99/13.29 (inComplementUnionImpNotIn1) =>
% 97.99/13.29 ((
% 97.99/13.29 (inComplementUnionImpInComplement1) =>
% 97.99/13.29 ((
% 97.99/13.29 (binunionTE) =>
% 97.99/13.29 ((
% 97.99/13.29 (binunionTEcontra) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2a1) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementUnionInPowersetComplement) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2a2) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan1a) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan1b) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan1) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2a) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2b2) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2b) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz13rule0) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz13rule1) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz13rule2) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz13rule3) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz13rule4) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz1_1) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz1_2) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz1_3) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz1_4) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz1_5) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1all2) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1SetBreln1) =>
% 97.99/13.29 ((
% 97.99/13.29 (choice2fnsingleton) =>
% 97.99/13.29 ((
% 97.99/13.29 (setOfPairsIsBReln1) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1all1) =>
% 97.99/13.29 ((
% 97.99/13.29 (subbreln1) =>
% 97.99/13.29 ((
% 97.99/13.29 (eqbreln1) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1invprop) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1invI) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1invE) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1compprop) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1compI) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1compE) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1compEex) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionprop) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionIL) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionIR) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionI) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionE) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionEcases) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionCommutes) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz2Ex) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz2W) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz2A) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz2B) =>
% 97.99/13.29 ((
% 97.99/13.29 (image1Ex) =>
% 97.99/13.29 ((
% 97.99/13.29 (image1Ex1) =>
% 97.99/13.29 ((
% 97.99/13.29 (image1Equiv) =>
% 97.99/13.29 ((
% 97.99/13.29 (image1E) =>
% 97.99/13.29 ((
% 97.99/13.29 (image1I) =>
% 97.99/13.29 ((
% 97.99/13.29 (injFuncInInjFuncSet) =>
% 97.99/13.29 ((
% 97.99/13.29 (injFuncSetFuncIn) =>
% 97.99/13.29 ((
% 97.99/13.29 (injFuncSetFuncInj) =>
% 97.99/13.29 ((
% 97.99/13.29 (surjFuncSetFuncIn) =>
% 97.99/13.29 ((
% 97.99/13.29 (surjFuncSetFuncSurj) =>
% 97.99/13.29 ((
% 97.99/13.29 (leftInvIsSurj) =>
% 97.99/13.29 ((
% 97.99/13.29 (surjCantorThm) =>
% 97.99/13.29 ((
% 97.99/13.29 (foundation2) =>
% 97.99/13.29 ((
% 97.99/13.29 (notinself) =>
% 97.99/13.29 ((
% 97.99/13.29 (notinself2) =>
% 97.99/13.29 ((
% 97.99/13.29 (omegaSp) =>
% 97.99/13.29 ((
% 97.99/13.29 (omegaSclos) =>
% 97.99/13.29 ((
% 97.99/13.29 (peano0notS) =>
% 97.99/13.29 ((
% 97.99/13.29 (!!) @ (
% 97.99/13.29 (('#S') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 =>) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#C') @ in @
% 97.99/13.29 omega)))) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 !!) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#S') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 =>) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#C') @ in @
% 97.99/13.29 omega)))))) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#S') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 '#S') @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 =>))) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#C') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 '#B') @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 =) @
% 97.99/13.29 omegaS)))) @
% 97.99/13.29 omegaS)))))) @
% 97.99/13.29 (
% 97.99/13.29 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.99/13.29 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1664])).
% 97.99/13.29 thf(zip_derived_cl1695, plain,
% 97.99/13.29 (~ (((setukpairinjR11) =>
% 97.99/13.29 (((setukpairinjR12) =>
% 97.99/13.29 (((setukpairinjR1) =>
% 97.99/13.29 (((upairequniteq) =>
% 97.99/13.29 (((setukpairinjR2) =>
% 97.99/13.29 (((setukpairinjR) =>
% 97.99/13.29 (((ksndsingleton) =>
% 97.99/13.29 (((ksndpairEq) =>
% 97.99/13.29 (((kpairsurjEq) =>
% 97.99/13.29 (((cartprodsndin) =>
% 97.99/13.29 (((cartprodpairmemEL) =>
% 97.99/13.29 (((cartprodpairmemER) =>
% 97.99/13.29 (((cartprodmempaircEq) =>
% 97.99/13.29 (((cartprodfstpairEq) =>
% 97.99/13.29 (((cartprodsndpairEq) =>
% 97.99/13.29 (((cartprodpairsurjEq) =>
% 97.99/13.29 (((dpsetconstrI) =>
% 97.99/13.29 (((dpsetconstrSub) =>
% 97.99/13.29 (((setOfPairsIsBReln) =>
% 97.99/13.29 (((dpsetconstrERa) =>
% 97.99/13.29 (((dpsetconstrEL1) =>
% 97.99/13.29 (((dpsetconstrEL2) =>
% 97.99/13.29 (((dpsetconstrER) =>
% 97.99/13.29 (((funcImageSingleton) =>
% 97.99/13.29 (((apProp) =>
% 97.99/13.29 (((app) =>
% 97.99/13.29 (((infuncsetfunc) =>
% 97.99/13.29 (((ap2p) =>
% 97.99/13.29 (((funcinfuncset) =>
% 97.99/13.29 (((lamProp) =>
% 97.99/13.29 ((
% 97.99/13.29 (lamp) =>
% 97.99/13.29 ((
% 97.99/13.29 (lam2p) =>
% 97.99/13.29 ((
% 97.99/13.29 (brelnall1) =>
% 97.99/13.29 ((
% 97.99/13.29 (brelnall2) =>
% 97.99/13.29 ((
% 97.99/13.29 (ex1E2) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcGraphProp1) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcGraphProp3) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcGraphProp2) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcextLem) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcGraphProp4) =>
% 97.99/13.29 ((
% 97.99/13.29 (subbreln) =>
% 97.99/13.29 ((
% 97.99/13.29 (eqbreln) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcext) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcext2) =>
% 97.99/13.29 ((
% 97.99/13.29 (ap2apEq1) =>
% 97.99/13.29 ((
% 97.99/13.29 (ap2apEq2) =>
% 97.99/13.29 ((
% 97.99/13.29 (beta1) =>
% 97.99/13.29 ((
% 97.99/13.29 (eta1) =>
% 97.99/13.29 ((
% 97.99/13.29 (lam2lamEq) =>
% 97.99/13.29 ((
% 97.99/13.29 (beta2) =>
% 97.99/13.29 ((
% 97.99/13.29 (eta2) =>
% 97.99/13.29 ((
% 97.99/13.29 (iffalseProp1) =>
% 97.99/13.29 ((
% 97.99/13.29 (iffalseProp2) =>
% 97.99/13.29 ((
% 97.99/13.29 (iftrueProp1) =>
% 97.99/13.29 ((
% 97.99/13.29 (iftrueProp2) =>
% 97.99/13.29 ((
% 97.99/13.29 (ifSingleton) =>
% 97.99/13.29 ((
% 97.99/13.29 (ifp) =>
% 97.99/13.29 ((
% 97.99/13.29 (theeq) =>
% 97.99/13.29 ((
% 97.99/13.29 (iftrue) =>
% 97.99/13.29 ((
% 97.99/13.29 (iffalse) =>
% 97.99/13.29 ((
% 97.99/13.29 (iftrueorfalse) =>
% 97.99/13.29 ((
% 97.99/13.29 (binintersectT_lem) =>
% 97.99/13.29 ((
% 97.99/13.29 (binunionT_lem) =>
% 97.99/13.29 ((
% 97.99/13.29 (powersetT_lem) =>
% 97.99/13.29 ((
% 97.99/13.29 (setminusT_lem) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementT_lem) =>
% 97.99/13.29 ((
% 97.99/13.29 (setextT) =>
% 97.99/13.29 ((
% 97.99/13.29 (subsetTI) =>
% 97.99/13.29 ((
% 97.99/13.29 (powersetTI1) =>
% 97.99/13.29 ((
% 97.99/13.29 (powersetTE1) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementTI1) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementTE1) =>
% 97.99/13.29 ((
% 97.99/13.29 (binintersectTELcontra) =>
% 97.99/13.29 ((
% 97.99/13.29 (binintersectTERcontra) =>
% 97.99/13.29 ((
% 97.99/13.29 (contrasubsetT) =>
% 97.99/13.29 ((
% 97.99/13.29 (contrasubsetT1) =>
% 97.99/13.29 ((
% 97.99/13.29 (contrasubsetT2) =>
% 97.99/13.29 ((
% 97.99/13.29 (contrasubsetT3) =>
% 97.99/13.29 ((
% 97.99/13.29 (doubleComplementI1) =>
% 97.99/13.29 ((
% 97.99/13.29 (doubleComplementE1) =>
% 97.99/13.29 ((
% 97.99/13.29 (doubleComplementSub1) =>
% 97.99/13.29 ((
% 97.99/13.29 (doubleComplementSub2) =>
% 97.99/13.29 ((
% 97.99/13.29 (doubleComplementEq) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementTnotintersectT) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementImpComplementIntersect) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementSubsetComplementIntersect) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementInPowersetComplementIntersect) =>
% 97.99/13.29 ((
% 97.99/13.29 (contraSubsetComplement) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementTcontraSubset) =>
% 97.99/13.29 ((
% 97.99/13.29 (binunionTILcontra) =>
% 97.99/13.29 ((
% 97.99/13.29 (binunionTIRcontra) =>
% 97.99/13.29 ((
% 97.99/13.29 (inIntersectImpInUnion) =>
% 97.99/13.29 ((
% 97.99/13.29 (inIntersectImpInUnion2) =>
% 97.99/13.29 ((
% 97.99/13.29 (inIntersectImpInIntersectUnions) =>
% 97.99/13.29 ((
% 97.99/13.29 (intersectInPowersetIntersectUnions) =>
% 97.99/13.29 ((
% 97.99/13.29 (inComplementUnionImpNotIn1) =>
% 97.99/13.29 ((
% 97.99/13.29 (inComplementUnionImpInComplement1) =>
% 97.99/13.29 ((
% 97.99/13.29 (binunionTE) =>
% 97.99/13.29 ((
% 97.99/13.29 (binunionTEcontra) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2a1) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementUnionInPowersetComplement) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2a2) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan1a) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan1b) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan1) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2a) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2b2) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2b) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz13rule0) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz13rule1) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz13rule2) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz13rule3) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz13rule4) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz1_1) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz1_2) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz1_3) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz1_4) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz1_5) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1all2) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1SetBreln1) =>
% 97.99/13.29 ((
% 97.99/13.29 (choice2fnsingleton) =>
% 97.99/13.29 ((
% 97.99/13.29 (setOfPairsIsBReln1) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1all1) =>
% 97.99/13.29 ((
% 97.99/13.29 (subbreln1) =>
% 97.99/13.29 ((
% 97.99/13.29 (eqbreln1) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1invprop) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1invI) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1invE) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1compprop) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1compI) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1compE) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1compEex) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionprop) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionIL) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionIR) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionI) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionE) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionEcases) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionCommutes) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz2Ex) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz2W) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz2A) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz2B) =>
% 97.99/13.29 ((
% 97.99/13.29 (image1Ex) =>
% 97.99/13.29 ((
% 97.99/13.29 (image1Ex1) =>
% 97.99/13.29 ((
% 97.99/13.29 (image1Equiv) =>
% 97.99/13.29 ((
% 97.99/13.29 (image1E) =>
% 97.99/13.29 ((
% 97.99/13.29 (image1I) =>
% 97.99/13.29 ((
% 97.99/13.29 (injFuncInInjFuncSet) =>
% 97.99/13.29 ((
% 97.99/13.29 (injFuncSetFuncIn) =>
% 97.99/13.29 ((
% 97.99/13.29 (injFuncSetFuncInj) =>
% 97.99/13.29 ((
% 97.99/13.29 (surjFuncSetFuncIn) =>
% 97.99/13.29 ((
% 97.99/13.29 (surjFuncSetFuncSurj) =>
% 97.99/13.29 ((
% 97.99/13.29 (leftInvIsSurj) =>
% 97.99/13.29 ((
% 97.99/13.29 (surjCantorThm) =>
% 97.99/13.29 ((
% 97.99/13.29 (foundation2) =>
% 97.99/13.29 ((
% 97.99/13.29 (notinself) =>
% 97.99/13.29 ((
% 97.99/13.29 (notinself2) =>
% 97.99/13.29 ((
% 97.99/13.29 (omegaSp) =>
% 97.99/13.29 ((
% 97.99/13.29 (omegaSclos) =>
% 97.99/13.29 ((
% 97.99/13.29 (peano0notS) =>
% 97.99/13.29 ((
% 97.99/13.29 (!!) @ (
% 97.99/13.29 (('#S') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 =>) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#C') @ in @
% 97.99/13.29 omega)))) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 !!) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#S') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 =>) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#C') @ in @
% 97.99/13.29 omega)))))) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#S') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 '#S') @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 =>))) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#C') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 '#B') @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 =) @
% 97.99/13.29 omegaS)))) @
% 97.99/13.29 omegaS)))))) @
% 97.99/13.29 (
% 97.99/13.29 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.99/13.29 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1678])).
% 97.99/13.29 thf(zip_derived_cl1711, plain,
% 97.99/13.29 (~ (((setukpairinjR12) =>
% 97.99/13.29 (((setukpairinjR1) =>
% 97.99/13.29 (((upairequniteq) =>
% 97.99/13.29 (((setukpairinjR2) =>
% 97.99/13.29 (((setukpairinjR) =>
% 97.99/13.29 (((ksndsingleton) =>
% 97.99/13.29 (((ksndpairEq) =>
% 97.99/13.29 (((kpairsurjEq) =>
% 97.99/13.29 (((cartprodsndin) =>
% 97.99/13.29 (((cartprodpairmemEL) =>
% 97.99/13.29 (((cartprodpairmemER) =>
% 97.99/13.29 (((cartprodmempaircEq) =>
% 97.99/13.29 (((cartprodfstpairEq) =>
% 97.99/13.29 (((cartprodsndpairEq) =>
% 97.99/13.29 (((cartprodpairsurjEq) =>
% 97.99/13.29 (((dpsetconstrI) =>
% 97.99/13.29 (((dpsetconstrSub) =>
% 97.99/13.29 (((setOfPairsIsBReln) =>
% 97.99/13.29 (((dpsetconstrERa) =>
% 97.99/13.29 (((dpsetconstrEL1) =>
% 97.99/13.29 (((dpsetconstrEL2) =>
% 97.99/13.29 (((dpsetconstrER) =>
% 97.99/13.29 (((funcImageSingleton) =>
% 97.99/13.29 (((apProp) =>
% 97.99/13.29 (((app) =>
% 97.99/13.29 (((infuncsetfunc) =>
% 97.99/13.29 (((ap2p) =>
% 97.99/13.29 (((funcinfuncset) =>
% 97.99/13.29 (((lamProp) =>
% 97.99/13.29 (((lamp) =>
% 97.99/13.29 ((
% 97.99/13.29 (lam2p) =>
% 97.99/13.29 ((
% 97.99/13.29 (brelnall1) =>
% 97.99/13.29 ((
% 97.99/13.29 (brelnall2) =>
% 97.99/13.29 ((
% 97.99/13.29 (ex1E2) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcGraphProp1) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcGraphProp3) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcGraphProp2) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcextLem) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcGraphProp4) =>
% 97.99/13.29 ((
% 97.99/13.29 (subbreln) =>
% 97.99/13.29 ((
% 97.99/13.29 (eqbreln) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcext) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcext2) =>
% 97.99/13.29 ((
% 97.99/13.29 (ap2apEq1) =>
% 97.99/13.29 ((
% 97.99/13.29 (ap2apEq2) =>
% 97.99/13.29 ((
% 97.99/13.29 (beta1) =>
% 97.99/13.29 ((
% 97.99/13.29 (eta1) =>
% 97.99/13.29 ((
% 97.99/13.29 (lam2lamEq) =>
% 97.99/13.29 ((
% 97.99/13.29 (beta2) =>
% 97.99/13.29 ((
% 97.99/13.29 (eta2) =>
% 97.99/13.29 ((
% 97.99/13.29 (iffalseProp1) =>
% 97.99/13.29 ((
% 97.99/13.29 (iffalseProp2) =>
% 97.99/13.29 ((
% 97.99/13.29 (iftrueProp1) =>
% 97.99/13.29 ((
% 97.99/13.29 (iftrueProp2) =>
% 97.99/13.29 ((
% 97.99/13.29 (ifSingleton) =>
% 97.99/13.29 ((
% 97.99/13.29 (ifp) =>
% 97.99/13.29 ((
% 97.99/13.29 (theeq) =>
% 97.99/13.29 ((
% 97.99/13.29 (iftrue) =>
% 97.99/13.29 ((
% 97.99/13.29 (iffalse) =>
% 97.99/13.29 ((
% 97.99/13.29 (iftrueorfalse) =>
% 97.99/13.29 ((
% 97.99/13.29 (binintersectT_lem) =>
% 97.99/13.29 ((
% 97.99/13.29 (binunionT_lem) =>
% 97.99/13.29 ((
% 97.99/13.29 (powersetT_lem) =>
% 97.99/13.29 ((
% 97.99/13.29 (setminusT_lem) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementT_lem) =>
% 97.99/13.29 ((
% 97.99/13.29 (setextT) =>
% 97.99/13.29 ((
% 97.99/13.29 (subsetTI) =>
% 97.99/13.29 ((
% 97.99/13.29 (powersetTI1) =>
% 97.99/13.29 ((
% 97.99/13.29 (powersetTE1) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementTI1) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementTE1) =>
% 97.99/13.29 ((
% 97.99/13.29 (binintersectTELcontra) =>
% 97.99/13.29 ((
% 97.99/13.29 (binintersectTERcontra) =>
% 97.99/13.29 ((
% 97.99/13.29 (contrasubsetT) =>
% 97.99/13.29 ((
% 97.99/13.29 (contrasubsetT1) =>
% 97.99/13.29 ((
% 97.99/13.29 (contrasubsetT2) =>
% 97.99/13.29 ((
% 97.99/13.29 (contrasubsetT3) =>
% 97.99/13.29 ((
% 97.99/13.29 (doubleComplementI1) =>
% 97.99/13.29 ((
% 97.99/13.29 (doubleComplementE1) =>
% 97.99/13.29 ((
% 97.99/13.29 (doubleComplementSub1) =>
% 97.99/13.29 ((
% 97.99/13.29 (doubleComplementSub2) =>
% 97.99/13.29 ((
% 97.99/13.29 (doubleComplementEq) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementTnotintersectT) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementImpComplementIntersect) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementSubsetComplementIntersect) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementInPowersetComplementIntersect) =>
% 97.99/13.29 ((
% 97.99/13.29 (contraSubsetComplement) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementTcontraSubset) =>
% 97.99/13.29 ((
% 97.99/13.29 (binunionTILcontra) =>
% 97.99/13.29 ((
% 97.99/13.29 (binunionTIRcontra) =>
% 97.99/13.29 ((
% 97.99/13.29 (inIntersectImpInUnion) =>
% 97.99/13.29 ((
% 97.99/13.29 (inIntersectImpInUnion2) =>
% 97.99/13.29 ((
% 97.99/13.29 (inIntersectImpInIntersectUnions) =>
% 97.99/13.29 ((
% 97.99/13.29 (intersectInPowersetIntersectUnions) =>
% 97.99/13.29 ((
% 97.99/13.29 (inComplementUnionImpNotIn1) =>
% 97.99/13.29 ((
% 97.99/13.29 (inComplementUnionImpInComplement1) =>
% 97.99/13.29 ((
% 97.99/13.29 (binunionTE) =>
% 97.99/13.29 ((
% 97.99/13.29 (binunionTEcontra) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2a1) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementUnionInPowersetComplement) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2a2) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan1a) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan1b) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan1) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2a) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2b2) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2b) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz13rule0) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz13rule1) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz13rule2) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz13rule3) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz13rule4) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz1_1) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz1_2) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz1_3) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz1_4) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz1_5) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1all2) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1SetBreln1) =>
% 97.99/13.29 ((
% 97.99/13.29 (choice2fnsingleton) =>
% 97.99/13.29 ((
% 97.99/13.29 (setOfPairsIsBReln1) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1all1) =>
% 97.99/13.29 ((
% 97.99/13.29 (subbreln1) =>
% 97.99/13.29 ((
% 97.99/13.29 (eqbreln1) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1invprop) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1invI) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1invE) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1compprop) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1compI) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1compE) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1compEex) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionprop) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionIL) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionIR) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionI) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionE) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionEcases) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionCommutes) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz2Ex) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz2W) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz2A) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz2B) =>
% 97.99/13.29 ((
% 97.99/13.29 (image1Ex) =>
% 97.99/13.29 ((
% 97.99/13.29 (image1Ex1) =>
% 97.99/13.29 ((
% 97.99/13.29 (image1Equiv) =>
% 97.99/13.29 ((
% 97.99/13.29 (image1E) =>
% 97.99/13.29 ((
% 97.99/13.29 (image1I) =>
% 97.99/13.29 ((
% 97.99/13.29 (injFuncInInjFuncSet) =>
% 97.99/13.29 ((
% 97.99/13.29 (injFuncSetFuncIn) =>
% 97.99/13.29 ((
% 97.99/13.29 (injFuncSetFuncInj) =>
% 97.99/13.29 ((
% 97.99/13.29 (surjFuncSetFuncIn) =>
% 97.99/13.29 ((
% 97.99/13.29 (surjFuncSetFuncSurj) =>
% 97.99/13.29 ((
% 97.99/13.29 (leftInvIsSurj) =>
% 97.99/13.29 ((
% 97.99/13.29 (surjCantorThm) =>
% 97.99/13.29 ((
% 97.99/13.29 (foundation2) =>
% 97.99/13.29 ((
% 97.99/13.29 (notinself) =>
% 97.99/13.29 ((
% 97.99/13.29 (notinself2) =>
% 97.99/13.29 ((
% 97.99/13.29 (omegaSp) =>
% 97.99/13.29 ((
% 97.99/13.29 (omegaSclos) =>
% 97.99/13.29 ((
% 97.99/13.29 (peano0notS) =>
% 97.99/13.29 ((
% 97.99/13.29 (!!) @ (
% 97.99/13.29 (('#S') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 =>) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#C') @ in @
% 97.99/13.29 omega)))) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 !!) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#S') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 =>) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#C') @ in @
% 97.99/13.29 omega)))))) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#S') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 '#S') @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 =>))) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#C') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 '#B') @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 =) @
% 97.99/13.29 omegaS)))) @
% 97.99/13.29 omegaS)))))) @
% 97.99/13.29 (
% 97.99/13.29 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.99/13.29 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1695])).
% 97.99/13.29 thf(zip_derived_cl1725, plain,
% 97.99/13.29 (~ (((setukpairinjR1) =>
% 97.99/13.29 (((upairequniteq) =>
% 97.99/13.29 (((setukpairinjR2) =>
% 97.99/13.29 (((setukpairinjR) =>
% 97.99/13.29 (((ksndsingleton) =>
% 97.99/13.29 (((ksndpairEq) =>
% 97.99/13.29 (((kpairsurjEq) =>
% 97.99/13.29 (((cartprodsndin) =>
% 97.99/13.29 (((cartprodpairmemEL) =>
% 97.99/13.29 (((cartprodpairmemER) =>
% 97.99/13.29 (((cartprodmempaircEq) =>
% 97.99/13.29 (((cartprodfstpairEq) =>
% 97.99/13.29 (((cartprodsndpairEq) =>
% 97.99/13.29 (((cartprodpairsurjEq) =>
% 97.99/13.29 (((dpsetconstrI) =>
% 97.99/13.29 (((dpsetconstrSub) =>
% 97.99/13.29 (((setOfPairsIsBReln) =>
% 97.99/13.29 (((dpsetconstrERa) =>
% 97.99/13.29 (((dpsetconstrEL1) =>
% 97.99/13.29 (((dpsetconstrEL2) =>
% 97.99/13.29 (((dpsetconstrER) =>
% 97.99/13.29 (((funcImageSingleton) =>
% 97.99/13.29 (((apProp) =>
% 97.99/13.29 (((app) =>
% 97.99/13.29 (((infuncsetfunc) =>
% 97.99/13.29 (((ap2p) =>
% 97.99/13.29 (((funcinfuncset) =>
% 97.99/13.29 (((lamProp) =>
% 97.99/13.29 (((lamp) =>
% 97.99/13.29 (((lam2p) =>
% 97.99/13.29 ((
% 97.99/13.29 (brelnall1) =>
% 97.99/13.29 ((
% 97.99/13.29 (brelnall2) =>
% 97.99/13.29 ((
% 97.99/13.29 (ex1E2) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcGraphProp1) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcGraphProp3) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcGraphProp2) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcextLem) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcGraphProp4) =>
% 97.99/13.29 ((
% 97.99/13.29 (subbreln) =>
% 97.99/13.29 ((
% 97.99/13.29 (eqbreln) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcext) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcext2) =>
% 97.99/13.29 ((
% 97.99/13.29 (ap2apEq1) =>
% 97.99/13.29 ((
% 97.99/13.29 (ap2apEq2) =>
% 97.99/13.29 ((
% 97.99/13.29 (beta1) =>
% 97.99/13.29 ((
% 97.99/13.29 (eta1) =>
% 97.99/13.29 ((
% 97.99/13.29 (lam2lamEq) =>
% 97.99/13.29 ((
% 97.99/13.29 (beta2) =>
% 97.99/13.29 ((
% 97.99/13.29 (eta2) =>
% 97.99/13.29 ((
% 97.99/13.29 (iffalseProp1) =>
% 97.99/13.29 ((
% 97.99/13.29 (iffalseProp2) =>
% 97.99/13.29 ((
% 97.99/13.29 (iftrueProp1) =>
% 97.99/13.29 ((
% 97.99/13.29 (iftrueProp2) =>
% 97.99/13.29 ((
% 97.99/13.29 (ifSingleton) =>
% 97.99/13.29 ((
% 97.99/13.29 (ifp) =>
% 97.99/13.29 ((
% 97.99/13.29 (theeq) =>
% 97.99/13.29 ((
% 97.99/13.29 (iftrue) =>
% 97.99/13.29 ((
% 97.99/13.29 (iffalse) =>
% 97.99/13.29 ((
% 97.99/13.29 (iftrueorfalse) =>
% 97.99/13.29 ((
% 97.99/13.29 (binintersectT_lem) =>
% 97.99/13.29 ((
% 97.99/13.29 (binunionT_lem) =>
% 97.99/13.29 ((
% 97.99/13.29 (powersetT_lem) =>
% 97.99/13.29 ((
% 97.99/13.29 (setminusT_lem) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementT_lem) =>
% 97.99/13.29 ((
% 97.99/13.29 (setextT) =>
% 97.99/13.29 ((
% 97.99/13.29 (subsetTI) =>
% 97.99/13.29 ((
% 97.99/13.29 (powersetTI1) =>
% 97.99/13.29 ((
% 97.99/13.29 (powersetTE1) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementTI1) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementTE1) =>
% 97.99/13.29 ((
% 97.99/13.29 (binintersectTELcontra) =>
% 97.99/13.29 ((
% 97.99/13.29 (binintersectTERcontra) =>
% 97.99/13.29 ((
% 97.99/13.29 (contrasubsetT) =>
% 97.99/13.29 ((
% 97.99/13.29 (contrasubsetT1) =>
% 97.99/13.29 ((
% 97.99/13.29 (contrasubsetT2) =>
% 97.99/13.29 ((
% 97.99/13.29 (contrasubsetT3) =>
% 97.99/13.29 ((
% 97.99/13.29 (doubleComplementI1) =>
% 97.99/13.29 ((
% 97.99/13.29 (doubleComplementE1) =>
% 97.99/13.29 ((
% 97.99/13.29 (doubleComplementSub1) =>
% 97.99/13.29 ((
% 97.99/13.29 (doubleComplementSub2) =>
% 97.99/13.29 ((
% 97.99/13.29 (doubleComplementEq) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementTnotintersectT) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementImpComplementIntersect) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementSubsetComplementIntersect) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementInPowersetComplementIntersect) =>
% 97.99/13.29 ((
% 97.99/13.29 (contraSubsetComplement) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementTcontraSubset) =>
% 97.99/13.29 ((
% 97.99/13.29 (binunionTILcontra) =>
% 97.99/13.29 ((
% 97.99/13.29 (binunionTIRcontra) =>
% 97.99/13.29 ((
% 97.99/13.29 (inIntersectImpInUnion) =>
% 97.99/13.29 ((
% 97.99/13.29 (inIntersectImpInUnion2) =>
% 97.99/13.29 ((
% 97.99/13.29 (inIntersectImpInIntersectUnions) =>
% 97.99/13.29 ((
% 97.99/13.29 (intersectInPowersetIntersectUnions) =>
% 97.99/13.29 ((
% 97.99/13.29 (inComplementUnionImpNotIn1) =>
% 97.99/13.29 ((
% 97.99/13.29 (inComplementUnionImpInComplement1) =>
% 97.99/13.29 ((
% 97.99/13.29 (binunionTE) =>
% 97.99/13.29 ((
% 97.99/13.29 (binunionTEcontra) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2a1) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementUnionInPowersetComplement) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2a2) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan1a) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan1b) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan1) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2a) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2b2) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2b) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz13rule0) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz13rule1) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz13rule2) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz13rule3) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz13rule4) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz1_1) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz1_2) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz1_3) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz1_4) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz1_5) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1all2) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1SetBreln1) =>
% 97.99/13.29 ((
% 97.99/13.29 (choice2fnsingleton) =>
% 97.99/13.29 ((
% 97.99/13.29 (setOfPairsIsBReln1) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1all1) =>
% 97.99/13.29 ((
% 97.99/13.29 (subbreln1) =>
% 97.99/13.29 ((
% 97.99/13.29 (eqbreln1) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1invprop) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1invI) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1invE) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1compprop) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1compI) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1compE) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1compEex) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionprop) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionIL) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionIR) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionI) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionE) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionEcases) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionCommutes) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz2Ex) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz2W) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz2A) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz2B) =>
% 97.99/13.29 ((
% 97.99/13.29 (image1Ex) =>
% 97.99/13.29 ((
% 97.99/13.29 (image1Ex1) =>
% 97.99/13.29 ((
% 97.99/13.29 (image1Equiv) =>
% 97.99/13.29 ((
% 97.99/13.29 (image1E) =>
% 97.99/13.29 ((
% 97.99/13.29 (image1I) =>
% 97.99/13.29 ((
% 97.99/13.29 (injFuncInInjFuncSet) =>
% 97.99/13.29 ((
% 97.99/13.29 (injFuncSetFuncIn) =>
% 97.99/13.29 ((
% 97.99/13.29 (injFuncSetFuncInj) =>
% 97.99/13.29 ((
% 97.99/13.29 (surjFuncSetFuncIn) =>
% 97.99/13.29 ((
% 97.99/13.29 (surjFuncSetFuncSurj) =>
% 97.99/13.29 ((
% 97.99/13.29 (leftInvIsSurj) =>
% 97.99/13.29 ((
% 97.99/13.29 (surjCantorThm) =>
% 97.99/13.29 ((
% 97.99/13.29 (foundation2) =>
% 97.99/13.29 ((
% 97.99/13.29 (notinself) =>
% 97.99/13.29 ((
% 97.99/13.29 (notinself2) =>
% 97.99/13.29 ((
% 97.99/13.29 (omegaSp) =>
% 97.99/13.29 ((
% 97.99/13.29 (omegaSclos) =>
% 97.99/13.29 ((
% 97.99/13.29 (peano0notS) =>
% 97.99/13.29 ((
% 97.99/13.29 (!!) @ (
% 97.99/13.29 (('#S') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 =>) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#C') @ in @
% 97.99/13.29 omega)))) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 !!) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#S') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 =>) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#C') @ in @
% 97.99/13.29 omega)))))) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#S') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 '#S') @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 =>))) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#C') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 '#B') @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 =) @
% 97.99/13.29 omegaS)))) @
% 97.99/13.29 omegaS)))))) @
% 97.99/13.29 (
% 97.99/13.29 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.99/13.29 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1711])).
% 97.99/13.29 thf(zip_derived_cl1738, plain,
% 97.99/13.29 (~ (((upairequniteq) =>
% 97.99/13.29 (((setukpairinjR2) =>
% 97.99/13.29 (((setukpairinjR) =>
% 97.99/13.29 (((ksndsingleton) =>
% 97.99/13.29 (((ksndpairEq) =>
% 97.99/13.29 (((kpairsurjEq) =>
% 97.99/13.29 (((cartprodsndin) =>
% 97.99/13.29 (((cartprodpairmemEL) =>
% 97.99/13.29 (((cartprodpairmemER) =>
% 97.99/13.29 (((cartprodmempaircEq) =>
% 97.99/13.29 (((cartprodfstpairEq) =>
% 97.99/13.29 (((cartprodsndpairEq) =>
% 97.99/13.29 (((cartprodpairsurjEq) =>
% 97.99/13.29 (((dpsetconstrI) =>
% 97.99/13.29 (((dpsetconstrSub) =>
% 97.99/13.29 (((setOfPairsIsBReln) =>
% 97.99/13.29 (((dpsetconstrERa) =>
% 97.99/13.29 (((dpsetconstrEL1) =>
% 97.99/13.29 (((dpsetconstrEL2) =>
% 97.99/13.29 (((dpsetconstrER) =>
% 97.99/13.29 (((funcImageSingleton) =>
% 97.99/13.29 (((apProp) =>
% 97.99/13.29 (((app) =>
% 97.99/13.29 (((infuncsetfunc) =>
% 97.99/13.29 (((ap2p) =>
% 97.99/13.29 (((funcinfuncset) =>
% 97.99/13.29 (((lamProp) =>
% 97.99/13.29 (((lamp) =>
% 97.99/13.29 (((lam2p) =>
% 97.99/13.29 (((brelnall1) =>
% 97.99/13.29 ((
% 97.99/13.29 (brelnall2) =>
% 97.99/13.29 ((
% 97.99/13.29 (ex1E2) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcGraphProp1) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcGraphProp3) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcGraphProp2) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcextLem) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcGraphProp4) =>
% 97.99/13.29 ((
% 97.99/13.29 (subbreln) =>
% 97.99/13.29 ((
% 97.99/13.29 (eqbreln) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcext) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcext2) =>
% 97.99/13.29 ((
% 97.99/13.29 (ap2apEq1) =>
% 97.99/13.29 ((
% 97.99/13.29 (ap2apEq2) =>
% 97.99/13.29 ((
% 97.99/13.29 (beta1) =>
% 97.99/13.29 ((
% 97.99/13.29 (eta1) =>
% 97.99/13.29 ((
% 97.99/13.29 (lam2lamEq) =>
% 97.99/13.29 ((
% 97.99/13.29 (beta2) =>
% 97.99/13.29 ((
% 97.99/13.29 (eta2) =>
% 97.99/13.29 ((
% 97.99/13.29 (iffalseProp1) =>
% 97.99/13.29 ((
% 97.99/13.29 (iffalseProp2) =>
% 97.99/13.29 ((
% 97.99/13.29 (iftrueProp1) =>
% 97.99/13.29 ((
% 97.99/13.29 (iftrueProp2) =>
% 97.99/13.29 ((
% 97.99/13.29 (ifSingleton) =>
% 97.99/13.29 ((
% 97.99/13.29 (ifp) =>
% 97.99/13.29 ((
% 97.99/13.29 (theeq) =>
% 97.99/13.29 ((
% 97.99/13.29 (iftrue) =>
% 97.99/13.29 ((
% 97.99/13.29 (iffalse) =>
% 97.99/13.29 ((
% 97.99/13.29 (iftrueorfalse) =>
% 97.99/13.29 ((
% 97.99/13.29 (binintersectT_lem) =>
% 97.99/13.29 ((
% 97.99/13.29 (binunionT_lem) =>
% 97.99/13.29 ((
% 97.99/13.29 (powersetT_lem) =>
% 97.99/13.29 ((
% 97.99/13.29 (setminusT_lem) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementT_lem) =>
% 97.99/13.29 ((
% 97.99/13.29 (setextT) =>
% 97.99/13.29 ((
% 97.99/13.29 (subsetTI) =>
% 97.99/13.29 ((
% 97.99/13.29 (powersetTI1) =>
% 97.99/13.29 ((
% 97.99/13.29 (powersetTE1) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementTI1) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementTE1) =>
% 97.99/13.29 ((
% 97.99/13.29 (binintersectTELcontra) =>
% 97.99/13.29 ((
% 97.99/13.29 (binintersectTERcontra) =>
% 97.99/13.29 ((
% 97.99/13.29 (contrasubsetT) =>
% 97.99/13.29 ((
% 97.99/13.29 (contrasubsetT1) =>
% 97.99/13.29 ((
% 97.99/13.29 (contrasubsetT2) =>
% 97.99/13.29 ((
% 97.99/13.29 (contrasubsetT3) =>
% 97.99/13.29 ((
% 97.99/13.29 (doubleComplementI1) =>
% 97.99/13.29 ((
% 97.99/13.29 (doubleComplementE1) =>
% 97.99/13.29 ((
% 97.99/13.29 (doubleComplementSub1) =>
% 97.99/13.29 ((
% 97.99/13.29 (doubleComplementSub2) =>
% 97.99/13.29 ((
% 97.99/13.29 (doubleComplementEq) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementTnotintersectT) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementImpComplementIntersect) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementSubsetComplementIntersect) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementInPowersetComplementIntersect) =>
% 97.99/13.29 ((
% 97.99/13.29 (contraSubsetComplement) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementTcontraSubset) =>
% 97.99/13.29 ((
% 97.99/13.29 (binunionTILcontra) =>
% 97.99/13.29 ((
% 97.99/13.29 (binunionTIRcontra) =>
% 97.99/13.29 ((
% 97.99/13.29 (inIntersectImpInUnion) =>
% 97.99/13.29 ((
% 97.99/13.29 (inIntersectImpInUnion2) =>
% 97.99/13.29 ((
% 97.99/13.29 (inIntersectImpInIntersectUnions) =>
% 97.99/13.29 ((
% 97.99/13.29 (intersectInPowersetIntersectUnions) =>
% 97.99/13.29 ((
% 97.99/13.29 (inComplementUnionImpNotIn1) =>
% 97.99/13.29 ((
% 97.99/13.29 (inComplementUnionImpInComplement1) =>
% 97.99/13.29 ((
% 97.99/13.29 (binunionTE) =>
% 97.99/13.29 ((
% 97.99/13.29 (binunionTEcontra) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2a1) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementUnionInPowersetComplement) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2a2) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan1a) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan1b) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan1) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2a) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2b2) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2b) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz13rule0) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz13rule1) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz13rule2) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz13rule3) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz13rule4) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz1_1) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz1_2) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz1_3) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz1_4) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz1_5) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1all2) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1SetBreln1) =>
% 97.99/13.29 ((
% 97.99/13.29 (choice2fnsingleton) =>
% 97.99/13.29 ((
% 97.99/13.29 (setOfPairsIsBReln1) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1all1) =>
% 97.99/13.29 ((
% 97.99/13.29 (subbreln1) =>
% 97.99/13.29 ((
% 97.99/13.29 (eqbreln1) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1invprop) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1invI) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1invE) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1compprop) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1compI) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1compE) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1compEex) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionprop) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionIL) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionIR) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionI) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionE) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionEcases) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionCommutes) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz2Ex) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz2W) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz2A) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz2B) =>
% 97.99/13.29 ((
% 97.99/13.29 (image1Ex) =>
% 97.99/13.29 ((
% 97.99/13.29 (image1Ex1) =>
% 97.99/13.29 ((
% 97.99/13.29 (image1Equiv) =>
% 97.99/13.29 ((
% 97.99/13.29 (image1E) =>
% 97.99/13.29 ((
% 97.99/13.29 (image1I) =>
% 97.99/13.29 ((
% 97.99/13.29 (injFuncInInjFuncSet) =>
% 97.99/13.29 ((
% 97.99/13.29 (injFuncSetFuncIn) =>
% 97.99/13.29 ((
% 97.99/13.29 (injFuncSetFuncInj) =>
% 97.99/13.29 ((
% 97.99/13.29 (surjFuncSetFuncIn) =>
% 97.99/13.29 ((
% 97.99/13.29 (surjFuncSetFuncSurj) =>
% 97.99/13.29 ((
% 97.99/13.29 (leftInvIsSurj) =>
% 97.99/13.29 ((
% 97.99/13.29 (surjCantorThm) =>
% 97.99/13.29 ((
% 97.99/13.29 (foundation2) =>
% 97.99/13.29 ((
% 97.99/13.29 (notinself) =>
% 97.99/13.29 ((
% 97.99/13.29 (notinself2) =>
% 97.99/13.29 ((
% 97.99/13.29 (omegaSp) =>
% 97.99/13.29 ((
% 97.99/13.29 (omegaSclos) =>
% 97.99/13.29 ((
% 97.99/13.29 (peano0notS) =>
% 97.99/13.29 ((
% 97.99/13.29 (!!) @ (
% 97.99/13.29 (('#S') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 =>) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#C') @ in @
% 97.99/13.29 omega)))) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 !!) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#S') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 =>) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#C') @ in @
% 97.99/13.29 omega)))))) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#S') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 '#S') @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 =>))) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#C') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 '#B') @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 =) @
% 97.99/13.29 omegaS)))) @
% 97.99/13.29 omegaS)))))) @
% 97.99/13.29 (
% 97.99/13.29 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.99/13.29 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1725])).
% 97.99/13.29 thf(zip_derived_cl1749, plain,
% 97.99/13.29 (~ (((setukpairinjR2) =>
% 97.99/13.29 (((setukpairinjR) =>
% 97.99/13.29 (((ksndsingleton) =>
% 97.99/13.29 (((ksndpairEq) =>
% 97.99/13.29 (((kpairsurjEq) =>
% 97.99/13.29 (((cartprodsndin) =>
% 97.99/13.29 (((cartprodpairmemEL) =>
% 97.99/13.29 (((cartprodpairmemER) =>
% 97.99/13.29 (((cartprodmempaircEq) =>
% 97.99/13.29 (((cartprodfstpairEq) =>
% 97.99/13.29 (((cartprodsndpairEq) =>
% 97.99/13.29 (((cartprodpairsurjEq) =>
% 97.99/13.29 (((dpsetconstrI) =>
% 97.99/13.29 (((dpsetconstrSub) =>
% 97.99/13.29 (((setOfPairsIsBReln) =>
% 97.99/13.29 (((dpsetconstrERa) =>
% 97.99/13.29 (((dpsetconstrEL1) =>
% 97.99/13.29 (((dpsetconstrEL2) =>
% 97.99/13.29 (((dpsetconstrER) =>
% 97.99/13.29 (((funcImageSingleton) =>
% 97.99/13.29 (((apProp) =>
% 97.99/13.29 (((app) =>
% 97.99/13.29 (((infuncsetfunc) =>
% 97.99/13.29 (((ap2p) =>
% 97.99/13.29 (((funcinfuncset) =>
% 97.99/13.29 (((lamProp) =>
% 97.99/13.29 (((lamp) =>
% 97.99/13.29 (((lam2p) =>
% 97.99/13.29 (((brelnall1) =>
% 97.99/13.29 (((brelnall2) =>
% 97.99/13.29 ((
% 97.99/13.29 (ex1E2) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcGraphProp1) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcGraphProp3) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcGraphProp2) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcextLem) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcGraphProp4) =>
% 97.99/13.29 ((
% 97.99/13.29 (subbreln) =>
% 97.99/13.29 ((
% 97.99/13.29 (eqbreln) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcext) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcext2) =>
% 97.99/13.29 ((
% 97.99/13.29 (ap2apEq1) =>
% 97.99/13.29 ((
% 97.99/13.29 (ap2apEq2) =>
% 97.99/13.29 ((
% 97.99/13.29 (beta1) =>
% 97.99/13.29 ((
% 97.99/13.29 (eta1) =>
% 97.99/13.29 ((
% 97.99/13.29 (lam2lamEq) =>
% 97.99/13.29 ((
% 97.99/13.29 (beta2) =>
% 97.99/13.29 ((
% 97.99/13.29 (eta2) =>
% 97.99/13.29 ((
% 97.99/13.29 (iffalseProp1) =>
% 97.99/13.29 ((
% 97.99/13.29 (iffalseProp2) =>
% 97.99/13.29 ((
% 97.99/13.29 (iftrueProp1) =>
% 97.99/13.29 ((
% 97.99/13.29 (iftrueProp2) =>
% 97.99/13.29 ((
% 97.99/13.29 (ifSingleton) =>
% 97.99/13.29 ((
% 97.99/13.29 (ifp) =>
% 97.99/13.29 ((
% 97.99/13.29 (theeq) =>
% 97.99/13.29 ((
% 97.99/13.29 (iftrue) =>
% 97.99/13.29 ((
% 97.99/13.29 (iffalse) =>
% 97.99/13.29 ((
% 97.99/13.29 (iftrueorfalse) =>
% 97.99/13.29 ((
% 97.99/13.29 (binintersectT_lem) =>
% 97.99/13.29 ((
% 97.99/13.29 (binunionT_lem) =>
% 97.99/13.29 ((
% 97.99/13.29 (powersetT_lem) =>
% 97.99/13.29 ((
% 97.99/13.29 (setminusT_lem) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementT_lem) =>
% 97.99/13.29 ((
% 97.99/13.29 (setextT) =>
% 97.99/13.29 ((
% 97.99/13.29 (subsetTI) =>
% 97.99/13.29 ((
% 97.99/13.29 (powersetTI1) =>
% 97.99/13.29 ((
% 97.99/13.29 (powersetTE1) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementTI1) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementTE1) =>
% 97.99/13.29 ((
% 97.99/13.29 (binintersectTELcontra) =>
% 97.99/13.29 ((
% 97.99/13.29 (binintersectTERcontra) =>
% 97.99/13.29 ((
% 97.99/13.29 (contrasubsetT) =>
% 97.99/13.29 ((
% 97.99/13.29 (contrasubsetT1) =>
% 97.99/13.29 ((
% 97.99/13.29 (contrasubsetT2) =>
% 97.99/13.29 ((
% 97.99/13.29 (contrasubsetT3) =>
% 97.99/13.29 ((
% 97.99/13.29 (doubleComplementI1) =>
% 97.99/13.29 ((
% 97.99/13.29 (doubleComplementE1) =>
% 97.99/13.29 ((
% 97.99/13.29 (doubleComplementSub1) =>
% 97.99/13.29 ((
% 97.99/13.29 (doubleComplementSub2) =>
% 97.99/13.29 ((
% 97.99/13.29 (doubleComplementEq) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementTnotintersectT) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementImpComplementIntersect) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementSubsetComplementIntersect) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementInPowersetComplementIntersect) =>
% 97.99/13.29 ((
% 97.99/13.29 (contraSubsetComplement) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementTcontraSubset) =>
% 97.99/13.29 ((
% 97.99/13.29 (binunionTILcontra) =>
% 97.99/13.29 ((
% 97.99/13.29 (binunionTIRcontra) =>
% 97.99/13.29 ((
% 97.99/13.29 (inIntersectImpInUnion) =>
% 97.99/13.29 ((
% 97.99/13.29 (inIntersectImpInUnion2) =>
% 97.99/13.29 ((
% 97.99/13.29 (inIntersectImpInIntersectUnions) =>
% 97.99/13.29 ((
% 97.99/13.29 (intersectInPowersetIntersectUnions) =>
% 97.99/13.29 ((
% 97.99/13.29 (inComplementUnionImpNotIn1) =>
% 97.99/13.29 ((
% 97.99/13.29 (inComplementUnionImpInComplement1) =>
% 97.99/13.29 ((
% 97.99/13.29 (binunionTE) =>
% 97.99/13.29 ((
% 97.99/13.29 (binunionTEcontra) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2a1) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementUnionInPowersetComplement) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2a2) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan1a) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan1b) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan1) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2a) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2b2) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2b) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz13rule0) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz13rule1) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz13rule2) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz13rule3) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz13rule4) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz1_1) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz1_2) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz1_3) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz1_4) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz1_5) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1all2) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1SetBreln1) =>
% 97.99/13.29 ((
% 97.99/13.29 (choice2fnsingleton) =>
% 97.99/13.29 ((
% 97.99/13.29 (setOfPairsIsBReln1) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1all1) =>
% 97.99/13.29 ((
% 97.99/13.29 (subbreln1) =>
% 97.99/13.29 ((
% 97.99/13.29 (eqbreln1) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1invprop) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1invI) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1invE) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1compprop) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1compI) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1compE) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1compEex) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionprop) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionIL) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionIR) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionI) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionE) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionEcases) =>
% 97.99/13.29 ((
% 97.99/13.29 (breln1unionCommutes) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz2Ex) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz2W) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz2A) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz2B) =>
% 97.99/13.29 ((
% 97.99/13.29 (image1Ex) =>
% 97.99/13.29 ((
% 97.99/13.29 (image1Ex1) =>
% 97.99/13.29 ((
% 97.99/13.29 (image1Equiv) =>
% 97.99/13.29 ((
% 97.99/13.29 (image1E) =>
% 97.99/13.29 ((
% 97.99/13.29 (image1I) =>
% 97.99/13.29 ((
% 97.99/13.29 (injFuncInInjFuncSet) =>
% 97.99/13.29 ((
% 97.99/13.29 (injFuncSetFuncIn) =>
% 97.99/13.29 ((
% 97.99/13.29 (injFuncSetFuncInj) =>
% 97.99/13.29 ((
% 97.99/13.29 (surjFuncSetFuncIn) =>
% 97.99/13.29 ((
% 97.99/13.29 (surjFuncSetFuncSurj) =>
% 97.99/13.29 ((
% 97.99/13.29 (leftInvIsSurj) =>
% 97.99/13.29 ((
% 97.99/13.29 (surjCantorThm) =>
% 97.99/13.29 ((
% 97.99/13.29 (foundation2) =>
% 97.99/13.29 ((
% 97.99/13.29 (notinself) =>
% 97.99/13.29 ((
% 97.99/13.29 (notinself2) =>
% 97.99/13.29 ((
% 97.99/13.29 (omegaSp) =>
% 97.99/13.29 ((
% 97.99/13.29 (omegaSclos) =>
% 97.99/13.29 ((
% 97.99/13.29 (peano0notS) =>
% 97.99/13.29 ((
% 97.99/13.29 (!!) @ (
% 97.99/13.29 (('#S') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 =>) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#C') @ in @
% 97.99/13.29 omega)))) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 !!) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#S') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 =>) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#C') @ in @
% 97.99/13.29 omega)))))) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#S') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 '#S') @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 =>))) @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#C') @ (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 '#B') @
% 97.99/13.29 (
% 97.99/13.29 (
% 97.99/13.29 ('#B') @ (
% 97.99/13.29 =) @
% 97.99/13.29 omegaS)))) @
% 97.99/13.29 omegaS)))))) @
% 97.99/13.29 (
% 97.99/13.29 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.99/13.29 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1738])).
% 97.99/13.29 thf(zip_derived_cl1760, plain,
% 97.99/13.29 (~ (((setukpairinjR) =>
% 97.99/13.29 (((ksndsingleton) =>
% 97.99/13.29 (((ksndpairEq) =>
% 97.99/13.29 (((kpairsurjEq) =>
% 97.99/13.29 (((cartprodsndin) =>
% 97.99/13.29 (((cartprodpairmemEL) =>
% 97.99/13.29 (((cartprodpairmemER) =>
% 97.99/13.29 (((cartprodmempaircEq) =>
% 97.99/13.29 (((cartprodfstpairEq) =>
% 97.99/13.29 (((cartprodsndpairEq) =>
% 97.99/13.29 (((cartprodpairsurjEq) =>
% 97.99/13.29 (((dpsetconstrI) =>
% 97.99/13.29 (((dpsetconstrSub) =>
% 97.99/13.29 (((setOfPairsIsBReln) =>
% 97.99/13.29 (((dpsetconstrERa) =>
% 97.99/13.29 (((dpsetconstrEL1) =>
% 97.99/13.29 (((dpsetconstrEL2) =>
% 97.99/13.29 (((dpsetconstrER) =>
% 97.99/13.29 (((funcImageSingleton) =>
% 97.99/13.29 (((apProp) =>
% 97.99/13.29 (((app) =>
% 97.99/13.29 (((infuncsetfunc) =>
% 97.99/13.29 (((ap2p) =>
% 97.99/13.29 (((funcinfuncset) =>
% 97.99/13.29 (((lamProp) =>
% 97.99/13.29 (((lamp) =>
% 97.99/13.29 (((lam2p) =>
% 97.99/13.29 (((brelnall1) =>
% 97.99/13.29 (((brelnall2) =>
% 97.99/13.29 (((ex1E2) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcGraphProp1) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcGraphProp3) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcGraphProp2) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcextLem) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcGraphProp4) =>
% 97.99/13.29 ((
% 97.99/13.29 (subbreln) =>
% 97.99/13.29 ((
% 97.99/13.29 (eqbreln) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcext) =>
% 97.99/13.29 ((
% 97.99/13.29 (funcext2) =>
% 97.99/13.29 ((
% 97.99/13.29 (ap2apEq1) =>
% 97.99/13.29 ((
% 97.99/13.29 (ap2apEq2) =>
% 97.99/13.29 ((
% 97.99/13.29 (beta1) =>
% 97.99/13.29 ((
% 97.99/13.29 (eta1) =>
% 97.99/13.29 ((
% 97.99/13.29 (lam2lamEq) =>
% 97.99/13.29 ((
% 97.99/13.29 (beta2) =>
% 97.99/13.29 ((
% 97.99/13.29 (eta2) =>
% 97.99/13.29 ((
% 97.99/13.29 (iffalseProp1) =>
% 97.99/13.29 ((
% 97.99/13.29 (iffalseProp2) =>
% 97.99/13.29 ((
% 97.99/13.29 (iftrueProp1) =>
% 97.99/13.29 ((
% 97.99/13.29 (iftrueProp2) =>
% 97.99/13.29 ((
% 97.99/13.29 (ifSingleton) =>
% 97.99/13.29 ((
% 97.99/13.29 (ifp) =>
% 97.99/13.29 ((
% 97.99/13.29 (theeq) =>
% 97.99/13.29 ((
% 97.99/13.29 (iftrue) =>
% 97.99/13.29 ((
% 97.99/13.29 (iffalse) =>
% 97.99/13.29 ((
% 97.99/13.29 (iftrueorfalse) =>
% 97.99/13.29 ((
% 97.99/13.29 (binintersectT_lem) =>
% 97.99/13.29 ((
% 97.99/13.29 (binunionT_lem) =>
% 97.99/13.29 ((
% 97.99/13.29 (powersetT_lem) =>
% 97.99/13.29 ((
% 97.99/13.29 (setminusT_lem) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementT_lem) =>
% 97.99/13.29 ((
% 97.99/13.29 (setextT) =>
% 97.99/13.29 ((
% 97.99/13.29 (subsetTI) =>
% 97.99/13.29 ((
% 97.99/13.29 (powersetTI1) =>
% 97.99/13.29 ((
% 97.99/13.29 (powersetTE1) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementTI1) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementTE1) =>
% 97.99/13.29 ((
% 97.99/13.29 (binintersectTELcontra) =>
% 97.99/13.29 ((
% 97.99/13.29 (binintersectTERcontra) =>
% 97.99/13.29 ((
% 97.99/13.29 (contrasubsetT) =>
% 97.99/13.29 ((
% 97.99/13.29 (contrasubsetT1) =>
% 97.99/13.29 ((
% 97.99/13.29 (contrasubsetT2) =>
% 97.99/13.29 ((
% 97.99/13.29 (contrasubsetT3) =>
% 97.99/13.29 ((
% 97.99/13.29 (doubleComplementI1) =>
% 97.99/13.29 ((
% 97.99/13.29 (doubleComplementE1) =>
% 97.99/13.29 ((
% 97.99/13.29 (doubleComplementSub1) =>
% 97.99/13.29 ((
% 97.99/13.29 (doubleComplementSub2) =>
% 97.99/13.29 ((
% 97.99/13.29 (doubleComplementEq) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementTnotintersectT) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementImpComplementIntersect) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementSubsetComplementIntersect) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementInPowersetComplementIntersect) =>
% 97.99/13.29 ((
% 97.99/13.29 (contraSubsetComplement) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementTcontraSubset) =>
% 97.99/13.29 ((
% 97.99/13.29 (binunionTILcontra) =>
% 97.99/13.29 ((
% 97.99/13.29 (binunionTIRcontra) =>
% 97.99/13.29 ((
% 97.99/13.29 (inIntersectImpInUnion) =>
% 97.99/13.29 ((
% 97.99/13.29 (inIntersectImpInUnion2) =>
% 97.99/13.29 ((
% 97.99/13.29 (inIntersectImpInIntersectUnions) =>
% 97.99/13.29 ((
% 97.99/13.29 (intersectInPowersetIntersectUnions) =>
% 97.99/13.29 ((
% 97.99/13.29 (inComplementUnionImpNotIn1) =>
% 97.99/13.29 ((
% 97.99/13.29 (inComplementUnionImpInComplement1) =>
% 97.99/13.29 ((
% 97.99/13.29 (binunionTE) =>
% 97.99/13.29 ((
% 97.99/13.29 (binunionTEcontra) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2a1) =>
% 97.99/13.29 ((
% 97.99/13.29 (complementUnionInPowersetComplement) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2a2) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan1a) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan1b) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan1) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2a) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2b2) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2b) =>
% 97.99/13.29 ((
% 97.99/13.29 (demorgan2) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz13rule0) =>
% 97.99/13.29 ((
% 97.99/13.29 (woz13rule1) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz13rule2) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz13rule3) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz13rule4) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz1_1) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz1_2) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz1_3) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz1_4) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz1_5) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1all2) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1SetBreln1) =>
% 97.99/13.30 ((
% 97.99/13.30 (choice2fnsingleton) =>
% 97.99/13.30 ((
% 97.99/13.30 (setOfPairsIsBReln1) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1all1) =>
% 97.99/13.30 ((
% 97.99/13.30 (subbreln1) =>
% 97.99/13.30 ((
% 97.99/13.30 (eqbreln1) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1invprop) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1invI) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1invE) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1compprop) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1compI) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1compE) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1compEex) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionprop) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionIL) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionIR) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionI) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionE) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionEcases) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionCommutes) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz2Ex) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz2W) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz2A) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz2B) =>
% 97.99/13.30 ((
% 97.99/13.30 (image1Ex) =>
% 97.99/13.30 ((
% 97.99/13.30 (image1Ex1) =>
% 97.99/13.30 ((
% 97.99/13.30 (image1Equiv) =>
% 97.99/13.30 ((
% 97.99/13.30 (image1E) =>
% 97.99/13.30 ((
% 97.99/13.30 (image1I) =>
% 97.99/13.30 ((
% 97.99/13.30 (injFuncInInjFuncSet) =>
% 97.99/13.30 ((
% 97.99/13.30 (injFuncSetFuncIn) =>
% 97.99/13.30 ((
% 97.99/13.30 (injFuncSetFuncInj) =>
% 97.99/13.30 ((
% 97.99/13.30 (surjFuncSetFuncIn) =>
% 97.99/13.30 ((
% 97.99/13.30 (surjFuncSetFuncSurj) =>
% 97.99/13.30 ((
% 97.99/13.30 (leftInvIsSurj) =>
% 97.99/13.30 ((
% 97.99/13.30 (surjCantorThm) =>
% 97.99/13.30 ((
% 97.99/13.30 (foundation2) =>
% 97.99/13.30 ((
% 97.99/13.30 (notinself) =>
% 97.99/13.30 ((
% 97.99/13.30 (notinself2) =>
% 97.99/13.30 ((
% 97.99/13.30 (omegaSp) =>
% 97.99/13.30 ((
% 97.99/13.30 (omegaSclos) =>
% 97.99/13.30 ((
% 97.99/13.30 (peano0notS) =>
% 97.99/13.30 ((
% 97.99/13.30 (!!) @ (
% 97.99/13.30 (('#S') @ (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 =>) @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#C') @ in @
% 97.99/13.30 omega)))) @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 !!) @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 (
% 97.99/13.30 ('#S') @ (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 =>) @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#C') @ in @
% 97.99/13.30 omega)))))) @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#S') @ (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 '#S') @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 =>))) @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#C') @ (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 '#B') @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 =) @
% 97.99/13.30 omegaS)))) @
% 97.99/13.30 omegaS)))))) @
% 97.99/13.30 (
% 97.99/13.30 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.99/13.30 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1749])).
% 97.99/13.30 thf(zip_derived_cl1770, plain,
% 97.99/13.30 (~ (((ksndsingleton) =>
% 97.99/13.30 (((ksndpairEq) =>
% 97.99/13.30 (((kpairsurjEq) =>
% 97.99/13.30 (((cartprodsndin) =>
% 97.99/13.30 (((cartprodpairmemEL) =>
% 97.99/13.30 (((cartprodpairmemER) =>
% 97.99/13.30 (((cartprodmempaircEq) =>
% 97.99/13.30 (((cartprodfstpairEq) =>
% 97.99/13.30 (((cartprodsndpairEq) =>
% 97.99/13.30 (((cartprodpairsurjEq) =>
% 97.99/13.30 (((dpsetconstrI) =>
% 97.99/13.30 (((dpsetconstrSub) =>
% 97.99/13.30 (((setOfPairsIsBReln) =>
% 97.99/13.30 (((dpsetconstrERa) =>
% 97.99/13.30 (((dpsetconstrEL1) =>
% 97.99/13.30 (((dpsetconstrEL2) =>
% 97.99/13.30 (((dpsetconstrER) =>
% 97.99/13.30 (((funcImageSingleton) =>
% 97.99/13.30 (((apProp) =>
% 97.99/13.30 (((app) =>
% 97.99/13.30 (((infuncsetfunc) =>
% 97.99/13.30 (((ap2p) =>
% 97.99/13.30 (((funcinfuncset) =>
% 97.99/13.30 (((lamProp) =>
% 97.99/13.30 (((lamp) =>
% 97.99/13.30 (((lam2p) =>
% 97.99/13.30 (((brelnall1) =>
% 97.99/13.30 (((brelnall2) =>
% 97.99/13.30 (((ex1E2) =>
% 97.99/13.30 (((funcGraphProp1) =>
% 97.99/13.30 ((
% 97.99/13.30 (funcGraphProp3) =>
% 97.99/13.30 ((
% 97.99/13.30 (funcGraphProp2) =>
% 97.99/13.30 ((
% 97.99/13.30 (funcextLem) =>
% 97.99/13.30 ((
% 97.99/13.30 (funcGraphProp4) =>
% 97.99/13.30 ((
% 97.99/13.30 (subbreln) =>
% 97.99/13.30 ((
% 97.99/13.30 (eqbreln) =>
% 97.99/13.30 ((
% 97.99/13.30 (funcext) =>
% 97.99/13.30 ((
% 97.99/13.30 (funcext2) =>
% 97.99/13.30 ((
% 97.99/13.30 (ap2apEq1) =>
% 97.99/13.30 ((
% 97.99/13.30 (ap2apEq2) =>
% 97.99/13.30 ((
% 97.99/13.30 (beta1) =>
% 97.99/13.30 ((
% 97.99/13.30 (eta1) =>
% 97.99/13.30 ((
% 97.99/13.30 (lam2lamEq) =>
% 97.99/13.30 ((
% 97.99/13.30 (beta2) =>
% 97.99/13.30 ((
% 97.99/13.30 (eta2) =>
% 97.99/13.30 ((
% 97.99/13.30 (iffalseProp1) =>
% 97.99/13.30 ((
% 97.99/13.30 (iffalseProp2) =>
% 97.99/13.30 ((
% 97.99/13.30 (iftrueProp1) =>
% 97.99/13.30 ((
% 97.99/13.30 (iftrueProp2) =>
% 97.99/13.30 ((
% 97.99/13.30 (ifSingleton) =>
% 97.99/13.30 ((
% 97.99/13.30 (ifp) =>
% 97.99/13.30 ((
% 97.99/13.30 (theeq) =>
% 97.99/13.30 ((
% 97.99/13.30 (iftrue) =>
% 97.99/13.30 ((
% 97.99/13.30 (iffalse) =>
% 97.99/13.30 ((
% 97.99/13.30 (iftrueorfalse) =>
% 97.99/13.30 ((
% 97.99/13.30 (binintersectT_lem) =>
% 97.99/13.30 ((
% 97.99/13.30 (binunionT_lem) =>
% 97.99/13.30 ((
% 97.99/13.30 (powersetT_lem) =>
% 97.99/13.30 ((
% 97.99/13.30 (setminusT_lem) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementT_lem) =>
% 97.99/13.30 ((
% 97.99/13.30 (setextT) =>
% 97.99/13.30 ((
% 97.99/13.30 (subsetTI) =>
% 97.99/13.30 ((
% 97.99/13.30 (powersetTI1) =>
% 97.99/13.30 ((
% 97.99/13.30 (powersetTE1) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementTI1) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementTE1) =>
% 97.99/13.30 ((
% 97.99/13.30 (binintersectTELcontra) =>
% 97.99/13.30 ((
% 97.99/13.30 (binintersectTERcontra) =>
% 97.99/13.30 ((
% 97.99/13.30 (contrasubsetT) =>
% 97.99/13.30 ((
% 97.99/13.30 (contrasubsetT1) =>
% 97.99/13.30 ((
% 97.99/13.30 (contrasubsetT2) =>
% 97.99/13.30 ((
% 97.99/13.30 (contrasubsetT3) =>
% 97.99/13.30 ((
% 97.99/13.30 (doubleComplementI1) =>
% 97.99/13.30 ((
% 97.99/13.30 (doubleComplementE1) =>
% 97.99/13.30 ((
% 97.99/13.30 (doubleComplementSub1) =>
% 97.99/13.30 ((
% 97.99/13.30 (doubleComplementSub2) =>
% 97.99/13.30 ((
% 97.99/13.30 (doubleComplementEq) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementTnotintersectT) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementImpComplementIntersect) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementSubsetComplementIntersect) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementInPowersetComplementIntersect) =>
% 97.99/13.30 ((
% 97.99/13.30 (contraSubsetComplement) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementTcontraSubset) =>
% 97.99/13.30 ((
% 97.99/13.30 (binunionTILcontra) =>
% 97.99/13.30 ((
% 97.99/13.30 (binunionTIRcontra) =>
% 97.99/13.30 ((
% 97.99/13.30 (inIntersectImpInUnion) =>
% 97.99/13.30 ((
% 97.99/13.30 (inIntersectImpInUnion2) =>
% 97.99/13.30 ((
% 97.99/13.30 (inIntersectImpInIntersectUnions) =>
% 97.99/13.30 ((
% 97.99/13.30 (intersectInPowersetIntersectUnions) =>
% 97.99/13.30 ((
% 97.99/13.30 (inComplementUnionImpNotIn1) =>
% 97.99/13.30 ((
% 97.99/13.30 (inComplementUnionImpInComplement1) =>
% 97.99/13.30 ((
% 97.99/13.30 (binunionTE) =>
% 97.99/13.30 ((
% 97.99/13.30 (binunionTEcontra) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan2a1) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementUnionInPowersetComplement) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan2a2) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan1a) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan1b) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan1) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan2a) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan2b2) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan2b) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan2) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz13rule0) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz13rule1) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz13rule2) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz13rule3) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz13rule4) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz1_1) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz1_2) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz1_3) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz1_4) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz1_5) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1all2) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1SetBreln1) =>
% 97.99/13.30 ((
% 97.99/13.30 (choice2fnsingleton) =>
% 97.99/13.30 ((
% 97.99/13.30 (setOfPairsIsBReln1) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1all1) =>
% 97.99/13.30 ((
% 97.99/13.30 (subbreln1) =>
% 97.99/13.30 ((
% 97.99/13.30 (eqbreln1) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1invprop) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1invI) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1invE) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1compprop) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1compI) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1compE) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1compEex) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionprop) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionIL) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionIR) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionI) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionE) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionEcases) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionCommutes) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz2Ex) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz2W) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz2A) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz2B) =>
% 97.99/13.30 ((
% 97.99/13.30 (image1Ex) =>
% 97.99/13.30 ((
% 97.99/13.30 (image1Ex1) =>
% 97.99/13.30 ((
% 97.99/13.30 (image1Equiv) =>
% 97.99/13.30 ((
% 97.99/13.30 (image1E) =>
% 97.99/13.30 ((
% 97.99/13.30 (image1I) =>
% 97.99/13.30 ((
% 97.99/13.30 (injFuncInInjFuncSet) =>
% 97.99/13.30 ((
% 97.99/13.30 (injFuncSetFuncIn) =>
% 97.99/13.30 ((
% 97.99/13.30 (injFuncSetFuncInj) =>
% 97.99/13.30 ((
% 97.99/13.30 (surjFuncSetFuncIn) =>
% 97.99/13.30 ((
% 97.99/13.30 (surjFuncSetFuncSurj) =>
% 97.99/13.30 ((
% 97.99/13.30 (leftInvIsSurj) =>
% 97.99/13.30 ((
% 97.99/13.30 (surjCantorThm) =>
% 97.99/13.30 ((
% 97.99/13.30 (foundation2) =>
% 97.99/13.30 ((
% 97.99/13.30 (notinself) =>
% 97.99/13.30 ((
% 97.99/13.30 (notinself2) =>
% 97.99/13.30 ((
% 97.99/13.30 (omegaSp) =>
% 97.99/13.30 ((
% 97.99/13.30 (omegaSclos) =>
% 97.99/13.30 ((
% 97.99/13.30 (peano0notS) =>
% 97.99/13.30 ((
% 97.99/13.30 (!!) @ (
% 97.99/13.30 (('#S') @ (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 =>) @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#C') @ in @
% 97.99/13.30 omega)))) @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 !!) @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 (
% 97.99/13.30 ('#S') @ (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 =>) @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#C') @ in @
% 97.99/13.30 omega)))))) @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#S') @ (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 '#S') @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 =>))) @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#C') @ (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 '#B') @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 =) @
% 97.99/13.30 omegaS)))) @
% 97.99/13.30 omegaS)))))) @
% 97.99/13.30 (
% 97.99/13.30 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.99/13.30 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1760])).
% 97.99/13.30 thf(zip_derived_cl1779, plain,
% 97.99/13.30 (~ (((ksndpairEq) =>
% 97.99/13.30 (((kpairsurjEq) =>
% 97.99/13.30 (((cartprodsndin) =>
% 97.99/13.30 (((cartprodpairmemEL) =>
% 97.99/13.30 (((cartprodpairmemER) =>
% 97.99/13.30 (((cartprodmempaircEq) =>
% 97.99/13.30 (((cartprodfstpairEq) =>
% 97.99/13.30 (((cartprodsndpairEq) =>
% 97.99/13.30 (((cartprodpairsurjEq) =>
% 97.99/13.30 (((dpsetconstrI) =>
% 97.99/13.30 (((dpsetconstrSub) =>
% 97.99/13.30 (((setOfPairsIsBReln) =>
% 97.99/13.30 (((dpsetconstrERa) =>
% 97.99/13.30 (((dpsetconstrEL1) =>
% 97.99/13.30 (((dpsetconstrEL2) =>
% 97.99/13.30 (((dpsetconstrER) =>
% 97.99/13.30 (((funcImageSingleton) =>
% 97.99/13.30 (((apProp) =>
% 97.99/13.30 (((app) =>
% 97.99/13.30 (((infuncsetfunc) =>
% 97.99/13.30 (((ap2p) =>
% 97.99/13.30 (((funcinfuncset) =>
% 97.99/13.30 (((lamProp) =>
% 97.99/13.30 (((lamp) =>
% 97.99/13.30 (((lam2p) =>
% 97.99/13.30 (((brelnall1) =>
% 97.99/13.30 (((brelnall2) =>
% 97.99/13.30 (((ex1E2) =>
% 97.99/13.30 (((funcGraphProp1) =>
% 97.99/13.30 (((funcGraphProp3) =>
% 97.99/13.30 ((
% 97.99/13.30 (funcGraphProp2) =>
% 97.99/13.30 ((
% 97.99/13.30 (funcextLem) =>
% 97.99/13.30 ((
% 97.99/13.30 (funcGraphProp4) =>
% 97.99/13.30 ((
% 97.99/13.30 (subbreln) =>
% 97.99/13.30 ((
% 97.99/13.30 (eqbreln) =>
% 97.99/13.30 ((
% 97.99/13.30 (funcext) =>
% 97.99/13.30 ((
% 97.99/13.30 (funcext2) =>
% 97.99/13.30 ((
% 97.99/13.30 (ap2apEq1) =>
% 97.99/13.30 ((
% 97.99/13.30 (ap2apEq2) =>
% 97.99/13.30 ((
% 97.99/13.30 (beta1) =>
% 97.99/13.30 ((
% 97.99/13.30 (eta1) =>
% 97.99/13.30 ((
% 97.99/13.30 (lam2lamEq) =>
% 97.99/13.30 ((
% 97.99/13.30 (beta2) =>
% 97.99/13.30 ((
% 97.99/13.30 (eta2) =>
% 97.99/13.30 ((
% 97.99/13.30 (iffalseProp1) =>
% 97.99/13.30 ((
% 97.99/13.30 (iffalseProp2) =>
% 97.99/13.30 ((
% 97.99/13.30 (iftrueProp1) =>
% 97.99/13.30 ((
% 97.99/13.30 (iftrueProp2) =>
% 97.99/13.30 ((
% 97.99/13.30 (ifSingleton) =>
% 97.99/13.30 ((
% 97.99/13.30 (ifp) =>
% 97.99/13.30 ((
% 97.99/13.30 (theeq) =>
% 97.99/13.30 ((
% 97.99/13.30 (iftrue) =>
% 97.99/13.30 ((
% 97.99/13.30 (iffalse) =>
% 97.99/13.30 ((
% 97.99/13.30 (iftrueorfalse) =>
% 97.99/13.30 ((
% 97.99/13.30 (binintersectT_lem) =>
% 97.99/13.30 ((
% 97.99/13.30 (binunionT_lem) =>
% 97.99/13.30 ((
% 97.99/13.30 (powersetT_lem) =>
% 97.99/13.30 ((
% 97.99/13.30 (setminusT_lem) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementT_lem) =>
% 97.99/13.30 ((
% 97.99/13.30 (setextT) =>
% 97.99/13.30 ((
% 97.99/13.30 (subsetTI) =>
% 97.99/13.30 ((
% 97.99/13.30 (powersetTI1) =>
% 97.99/13.30 ((
% 97.99/13.30 (powersetTE1) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementTI1) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementTE1) =>
% 97.99/13.30 ((
% 97.99/13.30 (binintersectTELcontra) =>
% 97.99/13.30 ((
% 97.99/13.30 (binintersectTERcontra) =>
% 97.99/13.30 ((
% 97.99/13.30 (contrasubsetT) =>
% 97.99/13.30 ((
% 97.99/13.30 (contrasubsetT1) =>
% 97.99/13.30 ((
% 97.99/13.30 (contrasubsetT2) =>
% 97.99/13.30 ((
% 97.99/13.30 (contrasubsetT3) =>
% 97.99/13.30 ((
% 97.99/13.30 (doubleComplementI1) =>
% 97.99/13.30 ((
% 97.99/13.30 (doubleComplementE1) =>
% 97.99/13.30 ((
% 97.99/13.30 (doubleComplementSub1) =>
% 97.99/13.30 ((
% 97.99/13.30 (doubleComplementSub2) =>
% 97.99/13.30 ((
% 97.99/13.30 (doubleComplementEq) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementTnotintersectT) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementImpComplementIntersect) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementSubsetComplementIntersect) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementInPowersetComplementIntersect) =>
% 97.99/13.30 ((
% 97.99/13.30 (contraSubsetComplement) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementTcontraSubset) =>
% 97.99/13.30 ((
% 97.99/13.30 (binunionTILcontra) =>
% 97.99/13.30 ((
% 97.99/13.30 (binunionTIRcontra) =>
% 97.99/13.30 ((
% 97.99/13.30 (inIntersectImpInUnion) =>
% 97.99/13.30 ((
% 97.99/13.30 (inIntersectImpInUnion2) =>
% 97.99/13.30 ((
% 97.99/13.30 (inIntersectImpInIntersectUnions) =>
% 97.99/13.30 ((
% 97.99/13.30 (intersectInPowersetIntersectUnions) =>
% 97.99/13.30 ((
% 97.99/13.30 (inComplementUnionImpNotIn1) =>
% 97.99/13.30 ((
% 97.99/13.30 (inComplementUnionImpInComplement1) =>
% 97.99/13.30 ((
% 97.99/13.30 (binunionTE) =>
% 97.99/13.30 ((
% 97.99/13.30 (binunionTEcontra) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan2a1) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementUnionInPowersetComplement) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan2a2) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan1a) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan1b) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan1) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan2a) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan2b2) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan2b) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan2) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz13rule0) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz13rule1) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz13rule2) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz13rule3) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz13rule4) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz1_1) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz1_2) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz1_3) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz1_4) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz1_5) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1all2) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1SetBreln1) =>
% 97.99/13.30 ((
% 97.99/13.30 (choice2fnsingleton) =>
% 97.99/13.30 ((
% 97.99/13.30 (setOfPairsIsBReln1) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1all1) =>
% 97.99/13.30 ((
% 97.99/13.30 (subbreln1) =>
% 97.99/13.30 ((
% 97.99/13.30 (eqbreln1) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1invprop) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1invI) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1invE) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1compprop) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1compI) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1compE) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1compEex) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionprop) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionIL) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionIR) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionI) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionE) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionEcases) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionCommutes) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz2Ex) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz2W) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz2A) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz2B) =>
% 97.99/13.30 ((
% 97.99/13.30 (image1Ex) =>
% 97.99/13.30 ((
% 97.99/13.30 (image1Ex1) =>
% 97.99/13.30 ((
% 97.99/13.30 (image1Equiv) =>
% 97.99/13.30 ((
% 97.99/13.30 (image1E) =>
% 97.99/13.30 ((
% 97.99/13.30 (image1I) =>
% 97.99/13.30 ((
% 97.99/13.30 (injFuncInInjFuncSet) =>
% 97.99/13.30 ((
% 97.99/13.30 (injFuncSetFuncIn) =>
% 97.99/13.30 ((
% 97.99/13.30 (injFuncSetFuncInj) =>
% 97.99/13.30 ((
% 97.99/13.30 (surjFuncSetFuncIn) =>
% 97.99/13.30 ((
% 97.99/13.30 (surjFuncSetFuncSurj) =>
% 97.99/13.30 ((
% 97.99/13.30 (leftInvIsSurj) =>
% 97.99/13.30 ((
% 97.99/13.30 (surjCantorThm) =>
% 97.99/13.30 ((
% 97.99/13.30 (foundation2) =>
% 97.99/13.30 ((
% 97.99/13.30 (notinself) =>
% 97.99/13.30 ((
% 97.99/13.30 (notinself2) =>
% 97.99/13.30 ((
% 97.99/13.30 (omegaSp) =>
% 97.99/13.30 ((
% 97.99/13.30 (omegaSclos) =>
% 97.99/13.30 ((
% 97.99/13.30 (peano0notS) =>
% 97.99/13.30 ((
% 97.99/13.30 (!!) @ (
% 97.99/13.30 (('#S') @ (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 =>) @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#C') @ in @
% 97.99/13.30 omega)))) @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 !!) @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 (
% 97.99/13.30 ('#S') @ (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 =>) @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#C') @ in @
% 97.99/13.30 omega)))))) @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#S') @ (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 '#S') @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 =>))) @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#C') @ (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 '#B') @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 =) @
% 97.99/13.30 omegaS)))) @
% 97.99/13.30 omegaS)))))) @
% 97.99/13.30 (
% 97.99/13.30 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.99/13.30 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1770])).
% 97.99/13.30 thf(zip_derived_cl1787, plain,
% 97.99/13.30 (~ (((kpairsurjEq) =>
% 97.99/13.30 (((cartprodsndin) =>
% 97.99/13.30 (((cartprodpairmemEL) =>
% 97.99/13.30 (((cartprodpairmemER) =>
% 97.99/13.30 (((cartprodmempaircEq) =>
% 97.99/13.30 (((cartprodfstpairEq) =>
% 97.99/13.30 (((cartprodsndpairEq) =>
% 97.99/13.30 (((cartprodpairsurjEq) =>
% 97.99/13.30 (((dpsetconstrI) =>
% 97.99/13.30 (((dpsetconstrSub) =>
% 97.99/13.30 (((setOfPairsIsBReln) =>
% 97.99/13.30 (((dpsetconstrERa) =>
% 97.99/13.30 (((dpsetconstrEL1) =>
% 97.99/13.30 (((dpsetconstrEL2) =>
% 97.99/13.30 (((dpsetconstrER) =>
% 97.99/13.30 (((funcImageSingleton) =>
% 97.99/13.30 (((apProp) =>
% 97.99/13.30 (((app) =>
% 97.99/13.30 (((infuncsetfunc) =>
% 97.99/13.30 (((ap2p) =>
% 97.99/13.30 (((funcinfuncset) =>
% 97.99/13.30 (((lamProp) =>
% 97.99/13.30 (((lamp) =>
% 97.99/13.30 (((lam2p) =>
% 97.99/13.30 (((brelnall1) =>
% 97.99/13.30 (((brelnall2) =>
% 97.99/13.30 (((ex1E2) =>
% 97.99/13.30 (((funcGraphProp1) =>
% 97.99/13.30 (((funcGraphProp3) =>
% 97.99/13.30 (((funcGraphProp2) =>
% 97.99/13.30 ((
% 97.99/13.30 (funcextLem) =>
% 97.99/13.30 ((
% 97.99/13.30 (funcGraphProp4) =>
% 97.99/13.30 ((
% 97.99/13.30 (subbreln) =>
% 97.99/13.30 ((
% 97.99/13.30 (eqbreln) =>
% 97.99/13.30 ((
% 97.99/13.30 (funcext) =>
% 97.99/13.30 ((
% 97.99/13.30 (funcext2) =>
% 97.99/13.30 ((
% 97.99/13.30 (ap2apEq1) =>
% 97.99/13.30 ((
% 97.99/13.30 (ap2apEq2) =>
% 97.99/13.30 ((
% 97.99/13.30 (beta1) =>
% 97.99/13.30 ((
% 97.99/13.30 (eta1) =>
% 97.99/13.30 ((
% 97.99/13.30 (lam2lamEq) =>
% 97.99/13.30 ((
% 97.99/13.30 (beta2) =>
% 97.99/13.30 ((
% 97.99/13.30 (eta2) =>
% 97.99/13.30 ((
% 97.99/13.30 (iffalseProp1) =>
% 97.99/13.30 ((
% 97.99/13.30 (iffalseProp2) =>
% 97.99/13.30 ((
% 97.99/13.30 (iftrueProp1) =>
% 97.99/13.30 ((
% 97.99/13.30 (iftrueProp2) =>
% 97.99/13.30 ((
% 97.99/13.30 (ifSingleton) =>
% 97.99/13.30 ((
% 97.99/13.30 (ifp) =>
% 97.99/13.30 ((
% 97.99/13.30 (theeq) =>
% 97.99/13.30 ((
% 97.99/13.30 (iftrue) =>
% 97.99/13.30 ((
% 97.99/13.30 (iffalse) =>
% 97.99/13.30 ((
% 97.99/13.30 (iftrueorfalse) =>
% 97.99/13.30 ((
% 97.99/13.30 (binintersectT_lem) =>
% 97.99/13.30 ((
% 97.99/13.30 (binunionT_lem) =>
% 97.99/13.30 ((
% 97.99/13.30 (powersetT_lem) =>
% 97.99/13.30 ((
% 97.99/13.30 (setminusT_lem) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementT_lem) =>
% 97.99/13.30 ((
% 97.99/13.30 (setextT) =>
% 97.99/13.30 ((
% 97.99/13.30 (subsetTI) =>
% 97.99/13.30 ((
% 97.99/13.30 (powersetTI1) =>
% 97.99/13.30 ((
% 97.99/13.30 (powersetTE1) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementTI1) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementTE1) =>
% 97.99/13.30 ((
% 97.99/13.30 (binintersectTELcontra) =>
% 97.99/13.30 ((
% 97.99/13.30 (binintersectTERcontra) =>
% 97.99/13.30 ((
% 97.99/13.30 (contrasubsetT) =>
% 97.99/13.30 ((
% 97.99/13.30 (contrasubsetT1) =>
% 97.99/13.30 ((
% 97.99/13.30 (contrasubsetT2) =>
% 97.99/13.30 ((
% 97.99/13.30 (contrasubsetT3) =>
% 97.99/13.30 ((
% 97.99/13.30 (doubleComplementI1) =>
% 97.99/13.30 ((
% 97.99/13.30 (doubleComplementE1) =>
% 97.99/13.30 ((
% 97.99/13.30 (doubleComplementSub1) =>
% 97.99/13.30 ((
% 97.99/13.30 (doubleComplementSub2) =>
% 97.99/13.30 ((
% 97.99/13.30 (doubleComplementEq) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementTnotintersectT) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementImpComplementIntersect) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementSubsetComplementIntersect) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementInPowersetComplementIntersect) =>
% 97.99/13.30 ((
% 97.99/13.30 (contraSubsetComplement) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementTcontraSubset) =>
% 97.99/13.30 ((
% 97.99/13.30 (binunionTILcontra) =>
% 97.99/13.30 ((
% 97.99/13.30 (binunionTIRcontra) =>
% 97.99/13.30 ((
% 97.99/13.30 (inIntersectImpInUnion) =>
% 97.99/13.30 ((
% 97.99/13.30 (inIntersectImpInUnion2) =>
% 97.99/13.30 ((
% 97.99/13.30 (inIntersectImpInIntersectUnions) =>
% 97.99/13.30 ((
% 97.99/13.30 (intersectInPowersetIntersectUnions) =>
% 97.99/13.30 ((
% 97.99/13.30 (inComplementUnionImpNotIn1) =>
% 97.99/13.30 ((
% 97.99/13.30 (inComplementUnionImpInComplement1) =>
% 97.99/13.30 ((
% 97.99/13.30 (binunionTE) =>
% 97.99/13.30 ((
% 97.99/13.30 (binunionTEcontra) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan2a1) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementUnionInPowersetComplement) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan2a2) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan1a) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan1b) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan1) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan2a) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan2b2) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan2b) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan2) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz13rule0) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz13rule1) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz13rule2) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz13rule3) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz13rule4) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz1_1) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz1_2) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz1_3) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz1_4) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz1_5) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1all2) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1SetBreln1) =>
% 97.99/13.30 ((
% 97.99/13.30 (choice2fnsingleton) =>
% 97.99/13.30 ((
% 97.99/13.30 (setOfPairsIsBReln1) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1all1) =>
% 97.99/13.30 ((
% 97.99/13.30 (subbreln1) =>
% 97.99/13.30 ((
% 97.99/13.30 (eqbreln1) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1invprop) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1invI) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1invE) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1compprop) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1compI) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1compE) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1compEex) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionprop) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionIL) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionIR) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionI) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionE) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionEcases) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionCommutes) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz2Ex) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz2W) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz2A) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz2B) =>
% 97.99/13.30 ((
% 97.99/13.30 (image1Ex) =>
% 97.99/13.30 ((
% 97.99/13.30 (image1Ex1) =>
% 97.99/13.30 ((
% 97.99/13.30 (image1Equiv) =>
% 97.99/13.30 ((
% 97.99/13.30 (image1E) =>
% 97.99/13.30 ((
% 97.99/13.30 (image1I) =>
% 97.99/13.30 ((
% 97.99/13.30 (injFuncInInjFuncSet) =>
% 97.99/13.30 ((
% 97.99/13.30 (injFuncSetFuncIn) =>
% 97.99/13.30 ((
% 97.99/13.30 (injFuncSetFuncInj) =>
% 97.99/13.30 ((
% 97.99/13.30 (surjFuncSetFuncIn) =>
% 97.99/13.30 ((
% 97.99/13.30 (surjFuncSetFuncSurj) =>
% 97.99/13.30 ((
% 97.99/13.30 (leftInvIsSurj) =>
% 97.99/13.30 ((
% 97.99/13.30 (surjCantorThm) =>
% 97.99/13.30 ((
% 97.99/13.30 (foundation2) =>
% 97.99/13.30 ((
% 97.99/13.30 (notinself) =>
% 97.99/13.30 ((
% 97.99/13.30 (notinself2) =>
% 97.99/13.30 ((
% 97.99/13.30 (omegaSp) =>
% 97.99/13.30 ((
% 97.99/13.30 (omegaSclos) =>
% 97.99/13.30 ((
% 97.99/13.30 (peano0notS) =>
% 97.99/13.30 ((
% 97.99/13.30 (!!) @ (
% 97.99/13.30 (('#S') @ (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 =>) @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#C') @ in @
% 97.99/13.30 omega)))) @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 !!) @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 (
% 97.99/13.30 ('#S') @ (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 =>) @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#C') @ in @
% 97.99/13.30 omega)))))) @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#S') @ (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 '#S') @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 =>))) @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#C') @ (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 '#B') @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 =) @
% 97.99/13.30 omegaS)))) @
% 97.99/13.30 omegaS)))))) @
% 97.99/13.30 (
% 97.99/13.30 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.99/13.30 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1779])).
% 97.99/13.30 thf(zip_derived_cl1796, plain,
% 97.99/13.30 (~ (((cartprodsndin) =>
% 97.99/13.30 (((cartprodpairmemEL) =>
% 97.99/13.30 (((cartprodpairmemER) =>
% 97.99/13.30 (((cartprodmempaircEq) =>
% 97.99/13.30 (((cartprodfstpairEq) =>
% 97.99/13.30 (((cartprodsndpairEq) =>
% 97.99/13.30 (((cartprodpairsurjEq) =>
% 97.99/13.30 (((dpsetconstrI) =>
% 97.99/13.30 (((dpsetconstrSub) =>
% 97.99/13.30 (((setOfPairsIsBReln) =>
% 97.99/13.30 (((dpsetconstrERa) =>
% 97.99/13.30 (((dpsetconstrEL1) =>
% 97.99/13.30 (((dpsetconstrEL2) =>
% 97.99/13.30 (((dpsetconstrER) =>
% 97.99/13.30 (((funcImageSingleton) =>
% 97.99/13.30 (((apProp) =>
% 97.99/13.30 (((app) =>
% 97.99/13.30 (((infuncsetfunc) =>
% 97.99/13.30 (((ap2p) =>
% 97.99/13.30 (((funcinfuncset) =>
% 97.99/13.30 (((lamProp) =>
% 97.99/13.30 (((lamp) =>
% 97.99/13.30 (((lam2p) =>
% 97.99/13.30 (((brelnall1) =>
% 97.99/13.30 (((brelnall2) =>
% 97.99/13.30 (((ex1E2) =>
% 97.99/13.30 (((funcGraphProp1) =>
% 97.99/13.30 (((funcGraphProp3) =>
% 97.99/13.30 (((funcGraphProp2) =>
% 97.99/13.30 (((funcextLem) =>
% 97.99/13.30 ((
% 97.99/13.30 (funcGraphProp4) =>
% 97.99/13.30 ((
% 97.99/13.30 (subbreln) =>
% 97.99/13.30 ((
% 97.99/13.30 (eqbreln) =>
% 97.99/13.30 ((
% 97.99/13.30 (funcext) =>
% 97.99/13.30 ((
% 97.99/13.30 (funcext2) =>
% 97.99/13.30 ((
% 97.99/13.30 (ap2apEq1) =>
% 97.99/13.30 ((
% 97.99/13.30 (ap2apEq2) =>
% 97.99/13.30 ((
% 97.99/13.30 (beta1) =>
% 97.99/13.30 ((
% 97.99/13.30 (eta1) =>
% 97.99/13.30 ((
% 97.99/13.30 (lam2lamEq) =>
% 97.99/13.30 ((
% 97.99/13.30 (beta2) =>
% 97.99/13.30 ((
% 97.99/13.30 (eta2) =>
% 97.99/13.30 ((
% 97.99/13.30 (iffalseProp1) =>
% 97.99/13.30 ((
% 97.99/13.30 (iffalseProp2) =>
% 97.99/13.30 ((
% 97.99/13.30 (iftrueProp1) =>
% 97.99/13.30 ((
% 97.99/13.30 (iftrueProp2) =>
% 97.99/13.30 ((
% 97.99/13.30 (ifSingleton) =>
% 97.99/13.30 ((
% 97.99/13.30 (ifp) =>
% 97.99/13.30 ((
% 97.99/13.30 (theeq) =>
% 97.99/13.30 ((
% 97.99/13.30 (iftrue) =>
% 97.99/13.30 ((
% 97.99/13.30 (iffalse) =>
% 97.99/13.30 ((
% 97.99/13.30 (iftrueorfalse) =>
% 97.99/13.30 ((
% 97.99/13.30 (binintersectT_lem) =>
% 97.99/13.30 ((
% 97.99/13.30 (binunionT_lem) =>
% 97.99/13.30 ((
% 97.99/13.30 (powersetT_lem) =>
% 97.99/13.30 ((
% 97.99/13.30 (setminusT_lem) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementT_lem) =>
% 97.99/13.30 ((
% 97.99/13.30 (setextT) =>
% 97.99/13.30 ((
% 97.99/13.30 (subsetTI) =>
% 97.99/13.30 ((
% 97.99/13.30 (powersetTI1) =>
% 97.99/13.30 ((
% 97.99/13.30 (powersetTE1) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementTI1) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementTE1) =>
% 97.99/13.30 ((
% 97.99/13.30 (binintersectTELcontra) =>
% 97.99/13.30 ((
% 97.99/13.30 (binintersectTERcontra) =>
% 97.99/13.30 ((
% 97.99/13.30 (contrasubsetT) =>
% 97.99/13.30 ((
% 97.99/13.30 (contrasubsetT1) =>
% 97.99/13.30 ((
% 97.99/13.30 (contrasubsetT2) =>
% 97.99/13.30 ((
% 97.99/13.30 (contrasubsetT3) =>
% 97.99/13.30 ((
% 97.99/13.30 (doubleComplementI1) =>
% 97.99/13.30 ((
% 97.99/13.30 (doubleComplementE1) =>
% 97.99/13.30 ((
% 97.99/13.30 (doubleComplementSub1) =>
% 97.99/13.30 ((
% 97.99/13.30 (doubleComplementSub2) =>
% 97.99/13.30 ((
% 97.99/13.30 (doubleComplementEq) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementTnotintersectT) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementImpComplementIntersect) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementSubsetComplementIntersect) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementInPowersetComplementIntersect) =>
% 97.99/13.30 ((
% 97.99/13.30 (contraSubsetComplement) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementTcontraSubset) =>
% 97.99/13.30 ((
% 97.99/13.30 (binunionTILcontra) =>
% 97.99/13.30 ((
% 97.99/13.30 (binunionTIRcontra) =>
% 97.99/13.30 ((
% 97.99/13.30 (inIntersectImpInUnion) =>
% 97.99/13.30 ((
% 97.99/13.30 (inIntersectImpInUnion2) =>
% 97.99/13.30 ((
% 97.99/13.30 (inIntersectImpInIntersectUnions) =>
% 97.99/13.30 ((
% 97.99/13.30 (intersectInPowersetIntersectUnions) =>
% 97.99/13.30 ((
% 97.99/13.30 (inComplementUnionImpNotIn1) =>
% 97.99/13.30 ((
% 97.99/13.30 (inComplementUnionImpInComplement1) =>
% 97.99/13.30 ((
% 97.99/13.30 (binunionTE) =>
% 97.99/13.30 ((
% 97.99/13.30 (binunionTEcontra) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan2a1) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementUnionInPowersetComplement) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan2a2) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan1a) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan1b) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan1) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan2a) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan2b2) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan2b) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan2) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz13rule0) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz13rule1) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz13rule2) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz13rule3) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz13rule4) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz1_1) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz1_2) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz1_3) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz1_4) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz1_5) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1all2) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1SetBreln1) =>
% 97.99/13.30 ((
% 97.99/13.30 (choice2fnsingleton) =>
% 97.99/13.30 ((
% 97.99/13.30 (setOfPairsIsBReln1) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1all1) =>
% 97.99/13.30 ((
% 97.99/13.30 (subbreln1) =>
% 97.99/13.30 ((
% 97.99/13.30 (eqbreln1) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1invprop) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1invI) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1invE) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1compprop) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1compI) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1compE) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1compEex) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionprop) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionIL) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionIR) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionI) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionE) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionEcases) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionCommutes) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz2Ex) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz2W) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz2A) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz2B) =>
% 97.99/13.30 ((
% 97.99/13.30 (image1Ex) =>
% 97.99/13.30 ((
% 97.99/13.30 (image1Ex1) =>
% 97.99/13.30 ((
% 97.99/13.30 (image1Equiv) =>
% 97.99/13.30 ((
% 97.99/13.30 (image1E) =>
% 97.99/13.30 ((
% 97.99/13.30 (image1I) =>
% 97.99/13.30 ((
% 97.99/13.30 (injFuncInInjFuncSet) =>
% 97.99/13.30 ((
% 97.99/13.30 (injFuncSetFuncIn) =>
% 97.99/13.30 ((
% 97.99/13.30 (injFuncSetFuncInj) =>
% 97.99/13.30 ((
% 97.99/13.30 (surjFuncSetFuncIn) =>
% 97.99/13.30 ((
% 97.99/13.30 (surjFuncSetFuncSurj) =>
% 97.99/13.30 ((
% 97.99/13.30 (leftInvIsSurj) =>
% 97.99/13.30 ((
% 97.99/13.30 (surjCantorThm) =>
% 97.99/13.30 ((
% 97.99/13.30 (foundation2) =>
% 97.99/13.30 ((
% 97.99/13.30 (notinself) =>
% 97.99/13.30 ((
% 97.99/13.30 (notinself2) =>
% 97.99/13.30 ((
% 97.99/13.30 (omegaSp) =>
% 97.99/13.30 ((
% 97.99/13.30 (omegaSclos) =>
% 97.99/13.30 ((
% 97.99/13.30 (peano0notS) =>
% 97.99/13.30 ((
% 97.99/13.30 (!!) @ (
% 97.99/13.30 (('#S') @ (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 =>) @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#C') @ in @
% 97.99/13.30 omega)))) @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 !!) @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 (
% 97.99/13.30 ('#S') @ (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 =>) @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#C') @ in @
% 97.99/13.30 omega)))))) @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#S') @ (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 '#S') @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 =>))) @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#C') @ (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 '#B') @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 =) @
% 97.99/13.30 omegaS)))) @
% 97.99/13.30 omegaS)))))) @
% 97.99/13.30 (
% 97.99/13.30 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.99/13.30 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1787])).
% 97.99/13.30 thf(zip_derived_cl1807, plain,
% 97.99/13.30 (~ (((cartprodpairmemEL) =>
% 97.99/13.30 (((cartprodpairmemER) =>
% 97.99/13.30 (((cartprodmempaircEq) =>
% 97.99/13.30 (((cartprodfstpairEq) =>
% 97.99/13.30 (((cartprodsndpairEq) =>
% 97.99/13.30 (((cartprodpairsurjEq) =>
% 97.99/13.30 (((dpsetconstrI) =>
% 97.99/13.30 (((dpsetconstrSub) =>
% 97.99/13.30 (((setOfPairsIsBReln) =>
% 97.99/13.30 (((dpsetconstrERa) =>
% 97.99/13.30 (((dpsetconstrEL1) =>
% 97.99/13.30 (((dpsetconstrEL2) =>
% 97.99/13.30 (((dpsetconstrER) =>
% 97.99/13.30 (((funcImageSingleton) =>
% 97.99/13.30 (((apProp) =>
% 97.99/13.30 (((app) =>
% 97.99/13.30 (((infuncsetfunc) =>
% 97.99/13.30 (((ap2p) =>
% 97.99/13.30 (((funcinfuncset) =>
% 97.99/13.30 (((lamProp) =>
% 97.99/13.30 (((lamp) =>
% 97.99/13.30 (((lam2p) =>
% 97.99/13.30 (((brelnall1) =>
% 97.99/13.30 (((brelnall2) =>
% 97.99/13.30 (((ex1E2) =>
% 97.99/13.30 (((funcGraphProp1) =>
% 97.99/13.30 (((funcGraphProp3) =>
% 97.99/13.30 (((funcGraphProp2) =>
% 97.99/13.30 (((funcextLem) =>
% 97.99/13.30 (((funcGraphProp4) =>
% 97.99/13.30 ((
% 97.99/13.30 (subbreln) =>
% 97.99/13.30 ((
% 97.99/13.30 (eqbreln) =>
% 97.99/13.30 ((
% 97.99/13.30 (funcext) =>
% 97.99/13.30 ((
% 97.99/13.30 (funcext2) =>
% 97.99/13.30 ((
% 97.99/13.30 (ap2apEq1) =>
% 97.99/13.30 ((
% 97.99/13.30 (ap2apEq2) =>
% 97.99/13.30 ((
% 97.99/13.30 (beta1) =>
% 97.99/13.30 ((
% 97.99/13.30 (eta1) =>
% 97.99/13.30 ((
% 97.99/13.30 (lam2lamEq) =>
% 97.99/13.30 ((
% 97.99/13.30 (beta2) =>
% 97.99/13.30 ((
% 97.99/13.30 (eta2) =>
% 97.99/13.30 ((
% 97.99/13.30 (iffalseProp1) =>
% 97.99/13.30 ((
% 97.99/13.30 (iffalseProp2) =>
% 97.99/13.30 ((
% 97.99/13.30 (iftrueProp1) =>
% 97.99/13.30 ((
% 97.99/13.30 (iftrueProp2) =>
% 97.99/13.30 ((
% 97.99/13.30 (ifSingleton) =>
% 97.99/13.30 ((
% 97.99/13.30 (ifp) =>
% 97.99/13.30 ((
% 97.99/13.30 (theeq) =>
% 97.99/13.30 ((
% 97.99/13.30 (iftrue) =>
% 97.99/13.30 ((
% 97.99/13.30 (iffalse) =>
% 97.99/13.30 ((
% 97.99/13.30 (iftrueorfalse) =>
% 97.99/13.30 ((
% 97.99/13.30 (binintersectT_lem) =>
% 97.99/13.30 ((
% 97.99/13.30 (binunionT_lem) =>
% 97.99/13.30 ((
% 97.99/13.30 (powersetT_lem) =>
% 97.99/13.30 ((
% 97.99/13.30 (setminusT_lem) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementT_lem) =>
% 97.99/13.30 ((
% 97.99/13.30 (setextT) =>
% 97.99/13.30 ((
% 97.99/13.30 (subsetTI) =>
% 97.99/13.30 ((
% 97.99/13.30 (powersetTI1) =>
% 97.99/13.30 ((
% 97.99/13.30 (powersetTE1) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementTI1) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementTE1) =>
% 97.99/13.30 ((
% 97.99/13.30 (binintersectTELcontra) =>
% 97.99/13.30 ((
% 97.99/13.30 (binintersectTERcontra) =>
% 97.99/13.30 ((
% 97.99/13.30 (contrasubsetT) =>
% 97.99/13.30 ((
% 97.99/13.30 (contrasubsetT1) =>
% 97.99/13.30 ((
% 97.99/13.30 (contrasubsetT2) =>
% 97.99/13.30 ((
% 97.99/13.30 (contrasubsetT3) =>
% 97.99/13.30 ((
% 97.99/13.30 (doubleComplementI1) =>
% 97.99/13.30 ((
% 97.99/13.30 (doubleComplementE1) =>
% 97.99/13.30 ((
% 97.99/13.30 (doubleComplementSub1) =>
% 97.99/13.30 ((
% 97.99/13.30 (doubleComplementSub2) =>
% 97.99/13.30 ((
% 97.99/13.30 (doubleComplementEq) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementTnotintersectT) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementImpComplementIntersect) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementSubsetComplementIntersect) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementInPowersetComplementIntersect) =>
% 97.99/13.30 ((
% 97.99/13.30 (contraSubsetComplement) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementTcontraSubset) =>
% 97.99/13.30 ((
% 97.99/13.30 (binunionTILcontra) =>
% 97.99/13.30 ((
% 97.99/13.30 (binunionTIRcontra) =>
% 97.99/13.30 ((
% 97.99/13.30 (inIntersectImpInUnion) =>
% 97.99/13.30 ((
% 97.99/13.30 (inIntersectImpInUnion2) =>
% 97.99/13.30 ((
% 97.99/13.30 (inIntersectImpInIntersectUnions) =>
% 97.99/13.30 ((
% 97.99/13.30 (intersectInPowersetIntersectUnions) =>
% 97.99/13.30 ((
% 97.99/13.30 (inComplementUnionImpNotIn1) =>
% 97.99/13.30 ((
% 97.99/13.30 (inComplementUnionImpInComplement1) =>
% 97.99/13.30 ((
% 97.99/13.30 (binunionTE) =>
% 97.99/13.30 ((
% 97.99/13.30 (binunionTEcontra) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan2a1) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementUnionInPowersetComplement) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan2a2) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan1a) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan1b) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan1) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan2a) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan2b2) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan2b) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan2) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz13rule0) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz13rule1) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz13rule2) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz13rule3) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz13rule4) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz1_1) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz1_2) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz1_3) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz1_4) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz1_5) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1all2) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1SetBreln1) =>
% 97.99/13.30 ((
% 97.99/13.30 (choice2fnsingleton) =>
% 97.99/13.30 ((
% 97.99/13.30 (setOfPairsIsBReln1) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1all1) =>
% 97.99/13.30 ((
% 97.99/13.30 (subbreln1) =>
% 97.99/13.30 ((
% 97.99/13.30 (eqbreln1) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1invprop) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1invI) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1invE) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1compprop) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1compI) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1compE) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1compEex) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionprop) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionIL) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionIR) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionI) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionE) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionEcases) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionCommutes) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz2Ex) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz2W) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz2A) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz2B) =>
% 97.99/13.30 ((
% 97.99/13.30 (image1Ex) =>
% 97.99/13.30 ((
% 97.99/13.30 (image1Ex1) =>
% 97.99/13.30 ((
% 97.99/13.30 (image1Equiv) =>
% 97.99/13.30 ((
% 97.99/13.30 (image1E) =>
% 97.99/13.30 ((
% 97.99/13.30 (image1I) =>
% 97.99/13.30 ((
% 97.99/13.30 (injFuncInInjFuncSet) =>
% 97.99/13.30 ((
% 97.99/13.30 (injFuncSetFuncIn) =>
% 97.99/13.30 ((
% 97.99/13.30 (injFuncSetFuncInj) =>
% 97.99/13.30 ((
% 97.99/13.30 (surjFuncSetFuncIn) =>
% 97.99/13.30 ((
% 97.99/13.30 (surjFuncSetFuncSurj) =>
% 97.99/13.30 ((
% 97.99/13.30 (leftInvIsSurj) =>
% 97.99/13.30 ((
% 97.99/13.30 (surjCantorThm) =>
% 97.99/13.30 ((
% 97.99/13.30 (foundation2) =>
% 97.99/13.30 ((
% 97.99/13.30 (notinself) =>
% 97.99/13.30 ((
% 97.99/13.30 (notinself2) =>
% 97.99/13.30 ((
% 97.99/13.30 (omegaSp) =>
% 97.99/13.30 ((
% 97.99/13.30 (omegaSclos) =>
% 97.99/13.30 ((
% 97.99/13.30 (peano0notS) =>
% 97.99/13.30 ((
% 97.99/13.30 (!!) @ (
% 97.99/13.30 (('#S') @ (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 =>) @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#C') @ in @
% 97.99/13.30 omega)))) @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 !!) @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 (
% 97.99/13.30 ('#S') @ (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 =>) @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#C') @ in @
% 97.99/13.30 omega)))))) @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#S') @ (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 '#S') @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 =>))) @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#C') @ (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 '#B') @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 =) @
% 97.99/13.30 omegaS)))) @
% 97.99/13.30 omegaS)))))) @
% 97.99/13.30 (
% 97.99/13.30 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.99/13.30 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1796])).
% 97.99/13.30 thf(zip_derived_cl1816, plain,
% 97.99/13.30 (~ (((cartprodpairmemER) =>
% 97.99/13.30 (((cartprodmempaircEq) =>
% 97.99/13.30 (((cartprodfstpairEq) =>
% 97.99/13.30 (((cartprodsndpairEq) =>
% 97.99/13.30 (((cartprodpairsurjEq) =>
% 97.99/13.30 (((dpsetconstrI) =>
% 97.99/13.30 (((dpsetconstrSub) =>
% 97.99/13.30 (((setOfPairsIsBReln) =>
% 97.99/13.30 (((dpsetconstrERa) =>
% 97.99/13.30 (((dpsetconstrEL1) =>
% 97.99/13.30 (((dpsetconstrEL2) =>
% 97.99/13.30 (((dpsetconstrER) =>
% 97.99/13.30 (((funcImageSingleton) =>
% 97.99/13.30 (((apProp) =>
% 97.99/13.30 (((app) =>
% 97.99/13.30 (((infuncsetfunc) =>
% 97.99/13.30 (((ap2p) =>
% 97.99/13.30 (((funcinfuncset) =>
% 97.99/13.30 (((lamProp) =>
% 97.99/13.30 (((lamp) =>
% 97.99/13.30 (((lam2p) =>
% 97.99/13.30 (((brelnall1) =>
% 97.99/13.30 (((brelnall2) =>
% 97.99/13.30 (((ex1E2) =>
% 97.99/13.30 (((funcGraphProp1) =>
% 97.99/13.30 (((funcGraphProp3) =>
% 97.99/13.30 (((funcGraphProp2) =>
% 97.99/13.30 (((funcextLem) =>
% 97.99/13.30 (((funcGraphProp4) =>
% 97.99/13.30 (((subbreln) =>
% 97.99/13.30 ((
% 97.99/13.30 (eqbreln) =>
% 97.99/13.30 ((
% 97.99/13.30 (funcext) =>
% 97.99/13.30 ((
% 97.99/13.30 (funcext2) =>
% 97.99/13.30 ((
% 97.99/13.30 (ap2apEq1) =>
% 97.99/13.30 ((
% 97.99/13.30 (ap2apEq2) =>
% 97.99/13.30 ((
% 97.99/13.30 (beta1) =>
% 97.99/13.30 ((
% 97.99/13.30 (eta1) =>
% 97.99/13.30 ((
% 97.99/13.30 (lam2lamEq) =>
% 97.99/13.30 ((
% 97.99/13.30 (beta2) =>
% 97.99/13.30 ((
% 97.99/13.30 (eta2) =>
% 97.99/13.30 ((
% 97.99/13.30 (iffalseProp1) =>
% 97.99/13.30 ((
% 97.99/13.30 (iffalseProp2) =>
% 97.99/13.30 ((
% 97.99/13.30 (iftrueProp1) =>
% 97.99/13.30 ((
% 97.99/13.30 (iftrueProp2) =>
% 97.99/13.30 ((
% 97.99/13.30 (ifSingleton) =>
% 97.99/13.30 ((
% 97.99/13.30 (ifp) =>
% 97.99/13.30 ((
% 97.99/13.30 (theeq) =>
% 97.99/13.30 ((
% 97.99/13.30 (iftrue) =>
% 97.99/13.30 ((
% 97.99/13.30 (iffalse) =>
% 97.99/13.30 ((
% 97.99/13.30 (iftrueorfalse) =>
% 97.99/13.30 ((
% 97.99/13.30 (binintersectT_lem) =>
% 97.99/13.30 ((
% 97.99/13.30 (binunionT_lem) =>
% 97.99/13.30 ((
% 97.99/13.30 (powersetT_lem) =>
% 97.99/13.30 ((
% 97.99/13.30 (setminusT_lem) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementT_lem) =>
% 97.99/13.30 ((
% 97.99/13.30 (setextT) =>
% 97.99/13.30 ((
% 97.99/13.30 (subsetTI) =>
% 97.99/13.30 ((
% 97.99/13.30 (powersetTI1) =>
% 97.99/13.30 ((
% 97.99/13.30 (powersetTE1) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementTI1) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementTE1) =>
% 97.99/13.30 ((
% 97.99/13.30 (binintersectTELcontra) =>
% 97.99/13.30 ((
% 97.99/13.30 (binintersectTERcontra) =>
% 97.99/13.30 ((
% 97.99/13.30 (contrasubsetT) =>
% 97.99/13.30 ((
% 97.99/13.30 (contrasubsetT1) =>
% 97.99/13.30 ((
% 97.99/13.30 (contrasubsetT2) =>
% 97.99/13.30 ((
% 97.99/13.30 (contrasubsetT3) =>
% 97.99/13.30 ((
% 97.99/13.30 (doubleComplementI1) =>
% 97.99/13.30 ((
% 97.99/13.30 (doubleComplementE1) =>
% 97.99/13.30 ((
% 97.99/13.30 (doubleComplementSub1) =>
% 97.99/13.30 ((
% 97.99/13.30 (doubleComplementSub2) =>
% 97.99/13.30 ((
% 97.99/13.30 (doubleComplementEq) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementTnotintersectT) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementImpComplementIntersect) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementSubsetComplementIntersect) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementInPowersetComplementIntersect) =>
% 97.99/13.30 ((
% 97.99/13.30 (contraSubsetComplement) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementTcontraSubset) =>
% 97.99/13.30 ((
% 97.99/13.30 (binunionTILcontra) =>
% 97.99/13.30 ((
% 97.99/13.30 (binunionTIRcontra) =>
% 97.99/13.30 ((
% 97.99/13.30 (inIntersectImpInUnion) =>
% 97.99/13.30 ((
% 97.99/13.30 (inIntersectImpInUnion2) =>
% 97.99/13.30 ((
% 97.99/13.30 (inIntersectImpInIntersectUnions) =>
% 97.99/13.30 ((
% 97.99/13.30 (intersectInPowersetIntersectUnions) =>
% 97.99/13.30 ((
% 97.99/13.30 (inComplementUnionImpNotIn1) =>
% 97.99/13.30 ((
% 97.99/13.30 (inComplementUnionImpInComplement1) =>
% 97.99/13.30 ((
% 97.99/13.30 (binunionTE) =>
% 97.99/13.30 ((
% 97.99/13.30 (binunionTEcontra) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan2a1) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementUnionInPowersetComplement) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan2a2) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan1a) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan1b) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan1) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan2a) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan2b2) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan2b) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan2) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz13rule0) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz13rule1) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz13rule2) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz13rule3) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz13rule4) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz1_1) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz1_2) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz1_3) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz1_4) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz1_5) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1all2) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1SetBreln1) =>
% 97.99/13.30 ((
% 97.99/13.30 (choice2fnsingleton) =>
% 97.99/13.30 ((
% 97.99/13.30 (setOfPairsIsBReln1) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1all1) =>
% 97.99/13.30 ((
% 97.99/13.30 (subbreln1) =>
% 97.99/13.30 ((
% 97.99/13.30 (eqbreln1) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1invprop) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1invI) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1invE) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1compprop) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1compI) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1compE) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1compEex) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionprop) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionIL) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionIR) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionI) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionE) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionEcases) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionCommutes) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz2Ex) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz2W) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz2A) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz2B) =>
% 97.99/13.30 ((
% 97.99/13.30 (image1Ex) =>
% 97.99/13.30 ((
% 97.99/13.30 (image1Ex1) =>
% 97.99/13.30 ((
% 97.99/13.30 (image1Equiv) =>
% 97.99/13.30 ((
% 97.99/13.30 (image1E) =>
% 97.99/13.30 ((
% 97.99/13.30 (image1I) =>
% 97.99/13.30 ((
% 97.99/13.30 (injFuncInInjFuncSet) =>
% 97.99/13.30 ((
% 97.99/13.30 (injFuncSetFuncIn) =>
% 97.99/13.30 ((
% 97.99/13.30 (injFuncSetFuncInj) =>
% 97.99/13.30 ((
% 97.99/13.30 (surjFuncSetFuncIn) =>
% 97.99/13.30 ((
% 97.99/13.30 (surjFuncSetFuncSurj) =>
% 97.99/13.30 ((
% 97.99/13.30 (leftInvIsSurj) =>
% 97.99/13.30 ((
% 97.99/13.30 (surjCantorThm) =>
% 97.99/13.30 ((
% 97.99/13.30 (foundation2) =>
% 97.99/13.30 ((
% 97.99/13.30 (notinself) =>
% 97.99/13.30 ((
% 97.99/13.30 (notinself2) =>
% 97.99/13.30 ((
% 97.99/13.30 (omegaSp) =>
% 97.99/13.30 ((
% 97.99/13.30 (omegaSclos) =>
% 97.99/13.30 ((
% 97.99/13.30 (peano0notS) =>
% 97.99/13.30 ((
% 97.99/13.30 (!!) @ (
% 97.99/13.30 (('#S') @ (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 =>) @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#C') @ in @
% 97.99/13.30 omega)))) @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 !!) @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 (
% 97.99/13.30 ('#S') @ (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 =>) @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#C') @ in @
% 97.99/13.30 omega)))))) @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#S') @ (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 '#S') @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 =>))) @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#C') @ (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 '#B') @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 =) @
% 97.99/13.30 omegaS)))) @
% 97.99/13.30 omegaS)))))) @
% 97.99/13.30 (
% 97.99/13.30 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.99/13.30 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1807])).
% 97.99/13.30 thf(zip_derived_cl1825, plain,
% 97.99/13.30 (~ (((cartprodmempaircEq) =>
% 97.99/13.30 (((cartprodfstpairEq) =>
% 97.99/13.30 (((cartprodsndpairEq) =>
% 97.99/13.30 (((cartprodpairsurjEq) =>
% 97.99/13.30 (((dpsetconstrI) =>
% 97.99/13.30 (((dpsetconstrSub) =>
% 97.99/13.30 (((setOfPairsIsBReln) =>
% 97.99/13.30 (((dpsetconstrERa) =>
% 97.99/13.30 (((dpsetconstrEL1) =>
% 97.99/13.30 (((dpsetconstrEL2) =>
% 97.99/13.30 (((dpsetconstrER) =>
% 97.99/13.30 (((funcImageSingleton) =>
% 97.99/13.30 (((apProp) =>
% 97.99/13.30 (((app) =>
% 97.99/13.30 (((infuncsetfunc) =>
% 97.99/13.30 (((ap2p) =>
% 97.99/13.30 (((funcinfuncset) =>
% 97.99/13.30 (((lamProp) =>
% 97.99/13.30 (((lamp) =>
% 97.99/13.30 (((lam2p) =>
% 97.99/13.30 (((brelnall1) =>
% 97.99/13.30 (((brelnall2) =>
% 97.99/13.30 (((ex1E2) =>
% 97.99/13.30 (((funcGraphProp1) =>
% 97.99/13.30 (((funcGraphProp3) =>
% 97.99/13.30 (((funcGraphProp2) =>
% 97.99/13.30 (((funcextLem) =>
% 97.99/13.30 (((funcGraphProp4) =>
% 97.99/13.30 (((subbreln) =>
% 97.99/13.30 (((eqbreln) =>
% 97.99/13.30 ((
% 97.99/13.30 (funcext) =>
% 97.99/13.30 ((
% 97.99/13.30 (funcext2) =>
% 97.99/13.30 ((
% 97.99/13.30 (ap2apEq1) =>
% 97.99/13.30 ((
% 97.99/13.30 (ap2apEq2) =>
% 97.99/13.30 ((
% 97.99/13.30 (beta1) =>
% 97.99/13.30 ((
% 97.99/13.30 (eta1) =>
% 97.99/13.30 ((
% 97.99/13.30 (lam2lamEq) =>
% 97.99/13.30 ((
% 97.99/13.30 (beta2) =>
% 97.99/13.30 ((
% 97.99/13.30 (eta2) =>
% 97.99/13.30 ((
% 97.99/13.30 (iffalseProp1) =>
% 97.99/13.30 ((
% 97.99/13.30 (iffalseProp2) =>
% 97.99/13.30 ((
% 97.99/13.30 (iftrueProp1) =>
% 97.99/13.30 ((
% 97.99/13.30 (iftrueProp2) =>
% 97.99/13.30 ((
% 97.99/13.30 (ifSingleton) =>
% 97.99/13.30 ((
% 97.99/13.30 (ifp) =>
% 97.99/13.30 ((
% 97.99/13.30 (theeq) =>
% 97.99/13.30 ((
% 97.99/13.30 (iftrue) =>
% 97.99/13.30 ((
% 97.99/13.30 (iffalse) =>
% 97.99/13.30 ((
% 97.99/13.30 (iftrueorfalse) =>
% 97.99/13.30 ((
% 97.99/13.30 (binintersectT_lem) =>
% 97.99/13.30 ((
% 97.99/13.30 (binunionT_lem) =>
% 97.99/13.30 ((
% 97.99/13.30 (powersetT_lem) =>
% 97.99/13.30 ((
% 97.99/13.30 (setminusT_lem) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementT_lem) =>
% 97.99/13.30 ((
% 97.99/13.30 (setextT) =>
% 97.99/13.30 ((
% 97.99/13.30 (subsetTI) =>
% 97.99/13.30 ((
% 97.99/13.30 (powersetTI1) =>
% 97.99/13.30 ((
% 97.99/13.30 (powersetTE1) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementTI1) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementTE1) =>
% 97.99/13.30 ((
% 97.99/13.30 (binintersectTELcontra) =>
% 97.99/13.30 ((
% 97.99/13.30 (binintersectTERcontra) =>
% 97.99/13.30 ((
% 97.99/13.30 (contrasubsetT) =>
% 97.99/13.30 ((
% 97.99/13.30 (contrasubsetT1) =>
% 97.99/13.30 ((
% 97.99/13.30 (contrasubsetT2) =>
% 97.99/13.30 ((
% 97.99/13.30 (contrasubsetT3) =>
% 97.99/13.30 ((
% 97.99/13.30 (doubleComplementI1) =>
% 97.99/13.30 ((
% 97.99/13.30 (doubleComplementE1) =>
% 97.99/13.30 ((
% 97.99/13.30 (doubleComplementSub1) =>
% 97.99/13.30 ((
% 97.99/13.30 (doubleComplementSub2) =>
% 97.99/13.30 ((
% 97.99/13.30 (doubleComplementEq) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementTnotintersectT) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementImpComplementIntersect) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementSubsetComplementIntersect) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementInPowersetComplementIntersect) =>
% 97.99/13.30 ((
% 97.99/13.30 (contraSubsetComplement) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementTcontraSubset) =>
% 97.99/13.30 ((
% 97.99/13.30 (binunionTILcontra) =>
% 97.99/13.30 ((
% 97.99/13.30 (binunionTIRcontra) =>
% 97.99/13.30 ((
% 97.99/13.30 (inIntersectImpInUnion) =>
% 97.99/13.30 ((
% 97.99/13.30 (inIntersectImpInUnion2) =>
% 97.99/13.30 ((
% 97.99/13.30 (inIntersectImpInIntersectUnions) =>
% 97.99/13.30 ((
% 97.99/13.30 (intersectInPowersetIntersectUnions) =>
% 97.99/13.30 ((
% 97.99/13.30 (inComplementUnionImpNotIn1) =>
% 97.99/13.30 ((
% 97.99/13.30 (inComplementUnionImpInComplement1) =>
% 97.99/13.30 ((
% 97.99/13.30 (binunionTE) =>
% 97.99/13.30 ((
% 97.99/13.30 (binunionTEcontra) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan2a1) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementUnionInPowersetComplement) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan2a2) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan1a) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan1b) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan1) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan2a) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan2b2) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan2b) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan2) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz13rule0) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz13rule1) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz13rule2) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz13rule3) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz13rule4) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz1_1) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz1_2) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz1_3) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz1_4) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz1_5) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1all2) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1SetBreln1) =>
% 97.99/13.30 ((
% 97.99/13.30 (choice2fnsingleton) =>
% 97.99/13.30 ((
% 97.99/13.30 (setOfPairsIsBReln1) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1all1) =>
% 97.99/13.30 ((
% 97.99/13.30 (subbreln1) =>
% 97.99/13.30 ((
% 97.99/13.30 (eqbreln1) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1invprop) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1invI) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1invE) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1compprop) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1compI) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1compE) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1compEex) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionprop) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionIL) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionIR) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionI) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionE) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionEcases) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionCommutes) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz2Ex) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz2W) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz2A) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz2B) =>
% 97.99/13.30 ((
% 97.99/13.30 (image1Ex) =>
% 97.99/13.30 ((
% 97.99/13.30 (image1Ex1) =>
% 97.99/13.30 ((
% 97.99/13.30 (image1Equiv) =>
% 97.99/13.30 ((
% 97.99/13.30 (image1E) =>
% 97.99/13.30 ((
% 97.99/13.30 (image1I) =>
% 97.99/13.30 ((
% 97.99/13.30 (injFuncInInjFuncSet) =>
% 97.99/13.30 ((
% 97.99/13.30 (injFuncSetFuncIn) =>
% 97.99/13.30 ((
% 97.99/13.30 (injFuncSetFuncInj) =>
% 97.99/13.30 ((
% 97.99/13.30 (surjFuncSetFuncIn) =>
% 97.99/13.30 ((
% 97.99/13.30 (surjFuncSetFuncSurj) =>
% 97.99/13.30 ((
% 97.99/13.30 (leftInvIsSurj) =>
% 97.99/13.30 ((
% 97.99/13.30 (surjCantorThm) =>
% 97.99/13.30 ((
% 97.99/13.30 (foundation2) =>
% 97.99/13.30 ((
% 97.99/13.30 (notinself) =>
% 97.99/13.30 ((
% 97.99/13.30 (notinself2) =>
% 97.99/13.30 ((
% 97.99/13.30 (omegaSp) =>
% 97.99/13.30 ((
% 97.99/13.30 (omegaSclos) =>
% 97.99/13.30 ((
% 97.99/13.30 (peano0notS) =>
% 97.99/13.30 ((
% 97.99/13.30 (!!) @ (
% 97.99/13.30 (('#S') @ (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 =>) @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#C') @ in @
% 97.99/13.30 omega)))) @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 !!) @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 (
% 97.99/13.30 ('#S') @ (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 =>) @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#C') @ in @
% 97.99/13.30 omega)))))) @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#S') @ (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 '#S') @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 =>))) @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#C') @ (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 '#B') @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 =) @
% 97.99/13.30 omegaS)))) @
% 97.99/13.30 omegaS)))))) @
% 97.99/13.30 (
% 97.99/13.30 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.99/13.30 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1816])).
% 97.99/13.30 thf(zip_derived_cl1833, plain,
% 97.99/13.30 (~ (((cartprodfstpairEq) =>
% 97.99/13.30 (((cartprodsndpairEq) =>
% 97.99/13.30 (((cartprodpairsurjEq) =>
% 97.99/13.30 (((dpsetconstrI) =>
% 97.99/13.30 (((dpsetconstrSub) =>
% 97.99/13.30 (((setOfPairsIsBReln) =>
% 97.99/13.30 (((dpsetconstrERa) =>
% 97.99/13.30 (((dpsetconstrEL1) =>
% 97.99/13.30 (((dpsetconstrEL2) =>
% 97.99/13.30 (((dpsetconstrER) =>
% 97.99/13.30 (((funcImageSingleton) =>
% 97.99/13.30 (((apProp) =>
% 97.99/13.30 (((app) =>
% 97.99/13.30 (((infuncsetfunc) =>
% 97.99/13.30 (((ap2p) =>
% 97.99/13.30 (((funcinfuncset) =>
% 97.99/13.30 (((lamProp) =>
% 97.99/13.30 (((lamp) =>
% 97.99/13.30 (((lam2p) =>
% 97.99/13.30 (((brelnall1) =>
% 97.99/13.30 (((brelnall2) =>
% 97.99/13.30 (((ex1E2) =>
% 97.99/13.30 (((funcGraphProp1) =>
% 97.99/13.30 (((funcGraphProp3) =>
% 97.99/13.30 (((funcGraphProp2) =>
% 97.99/13.30 (((funcextLem) =>
% 97.99/13.30 (((funcGraphProp4) =>
% 97.99/13.30 (((subbreln) =>
% 97.99/13.30 (((eqbreln) =>
% 97.99/13.30 (((funcext) =>
% 97.99/13.30 ((
% 97.99/13.30 (funcext2) =>
% 97.99/13.30 ((
% 97.99/13.30 (ap2apEq1) =>
% 97.99/13.30 ((
% 97.99/13.30 (ap2apEq2) =>
% 97.99/13.30 ((
% 97.99/13.30 (beta1) =>
% 97.99/13.30 ((
% 97.99/13.30 (eta1) =>
% 97.99/13.30 ((
% 97.99/13.30 (lam2lamEq) =>
% 97.99/13.30 ((
% 97.99/13.30 (beta2) =>
% 97.99/13.30 ((
% 97.99/13.30 (eta2) =>
% 97.99/13.30 ((
% 97.99/13.30 (iffalseProp1) =>
% 97.99/13.30 ((
% 97.99/13.30 (iffalseProp2) =>
% 97.99/13.30 ((
% 97.99/13.30 (iftrueProp1) =>
% 97.99/13.30 ((
% 97.99/13.30 (iftrueProp2) =>
% 97.99/13.30 ((
% 97.99/13.30 (ifSingleton) =>
% 97.99/13.30 ((
% 97.99/13.30 (ifp) =>
% 97.99/13.30 ((
% 97.99/13.30 (theeq) =>
% 97.99/13.30 ((
% 97.99/13.30 (iftrue) =>
% 97.99/13.30 ((
% 97.99/13.30 (iffalse) =>
% 97.99/13.30 ((
% 97.99/13.30 (iftrueorfalse) =>
% 97.99/13.30 ((
% 97.99/13.30 (binintersectT_lem) =>
% 97.99/13.30 ((
% 97.99/13.30 (binunionT_lem) =>
% 97.99/13.30 ((
% 97.99/13.30 (powersetT_lem) =>
% 97.99/13.30 ((
% 97.99/13.30 (setminusT_lem) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementT_lem) =>
% 97.99/13.30 ((
% 97.99/13.30 (setextT) =>
% 97.99/13.30 ((
% 97.99/13.30 (subsetTI) =>
% 97.99/13.30 ((
% 97.99/13.30 (powersetTI1) =>
% 97.99/13.30 ((
% 97.99/13.30 (powersetTE1) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementTI1) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementTE1) =>
% 97.99/13.30 ((
% 97.99/13.30 (binintersectTELcontra) =>
% 97.99/13.30 ((
% 97.99/13.30 (binintersectTERcontra) =>
% 97.99/13.30 ((
% 97.99/13.30 (contrasubsetT) =>
% 97.99/13.30 ((
% 97.99/13.30 (contrasubsetT1) =>
% 97.99/13.30 ((
% 97.99/13.30 (contrasubsetT2) =>
% 97.99/13.30 ((
% 97.99/13.30 (contrasubsetT3) =>
% 97.99/13.30 ((
% 97.99/13.30 (doubleComplementI1) =>
% 97.99/13.30 ((
% 97.99/13.30 (doubleComplementE1) =>
% 97.99/13.30 ((
% 97.99/13.30 (doubleComplementSub1) =>
% 97.99/13.30 ((
% 97.99/13.30 (doubleComplementSub2) =>
% 97.99/13.30 ((
% 97.99/13.30 (doubleComplementEq) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementTnotintersectT) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementImpComplementIntersect) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementSubsetComplementIntersect) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementInPowersetComplementIntersect) =>
% 97.99/13.30 ((
% 97.99/13.30 (contraSubsetComplement) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementTcontraSubset) =>
% 97.99/13.30 ((
% 97.99/13.30 (binunionTILcontra) =>
% 97.99/13.30 ((
% 97.99/13.30 (binunionTIRcontra) =>
% 97.99/13.30 ((
% 97.99/13.30 (inIntersectImpInUnion) =>
% 97.99/13.30 ((
% 97.99/13.30 (inIntersectImpInUnion2) =>
% 97.99/13.30 ((
% 97.99/13.30 (inIntersectImpInIntersectUnions) =>
% 97.99/13.30 ((
% 97.99/13.30 (intersectInPowersetIntersectUnions) =>
% 97.99/13.30 ((
% 97.99/13.30 (inComplementUnionImpNotIn1) =>
% 97.99/13.30 ((
% 97.99/13.30 (inComplementUnionImpInComplement1) =>
% 97.99/13.30 ((
% 97.99/13.30 (binunionTE) =>
% 97.99/13.30 ((
% 97.99/13.30 (binunionTEcontra) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan2a1) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementUnionInPowersetComplement) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan2a2) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan1a) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan1b) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan1) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan2a) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan2b2) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan2b) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan2) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz13rule0) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz13rule1) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz13rule2) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz13rule3) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz13rule4) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz1_1) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz1_2) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz1_3) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz1_4) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz1_5) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1all2) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1SetBreln1) =>
% 97.99/13.30 ((
% 97.99/13.30 (choice2fnsingleton) =>
% 97.99/13.30 ((
% 97.99/13.30 (setOfPairsIsBReln1) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1all1) =>
% 97.99/13.30 ((
% 97.99/13.30 (subbreln1) =>
% 97.99/13.30 ((
% 97.99/13.30 (eqbreln1) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1invprop) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1invI) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1invE) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1compprop) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1compI) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1compE) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1compEex) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionprop) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionIL) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionIR) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionI) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionE) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionEcases) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionCommutes) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz2Ex) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz2W) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz2A) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz2B) =>
% 97.99/13.30 ((
% 97.99/13.30 (image1Ex) =>
% 97.99/13.30 ((
% 97.99/13.30 (image1Ex1) =>
% 97.99/13.30 ((
% 97.99/13.30 (image1Equiv) =>
% 97.99/13.30 ((
% 97.99/13.30 (image1E) =>
% 97.99/13.30 ((
% 97.99/13.30 (image1I) =>
% 97.99/13.30 ((
% 97.99/13.30 (injFuncInInjFuncSet) =>
% 97.99/13.30 ((
% 97.99/13.30 (injFuncSetFuncIn) =>
% 97.99/13.30 ((
% 97.99/13.30 (injFuncSetFuncInj) =>
% 97.99/13.30 ((
% 97.99/13.30 (surjFuncSetFuncIn) =>
% 97.99/13.30 ((
% 97.99/13.30 (surjFuncSetFuncSurj) =>
% 97.99/13.30 ((
% 97.99/13.30 (leftInvIsSurj) =>
% 97.99/13.30 ((
% 97.99/13.30 (surjCantorThm) =>
% 97.99/13.30 ((
% 97.99/13.30 (foundation2) =>
% 97.99/13.30 ((
% 97.99/13.30 (notinself) =>
% 97.99/13.30 ((
% 97.99/13.30 (notinself2) =>
% 97.99/13.30 ((
% 97.99/13.30 (omegaSp) =>
% 97.99/13.30 ((
% 97.99/13.30 (omegaSclos) =>
% 97.99/13.30 ((
% 97.99/13.30 (peano0notS) =>
% 97.99/13.30 ((
% 97.99/13.30 (!!) @ (
% 97.99/13.30 (('#S') @ (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 =>) @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#C') @ in @
% 97.99/13.30 omega)))) @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 !!) @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 (
% 97.99/13.30 ('#S') @ (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 =>) @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#C') @ in @
% 97.99/13.30 omega)))))) @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#S') @ (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 '#S') @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 =>))) @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#C') @ (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 '#B') @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 =) @
% 97.99/13.30 omegaS)))) @
% 97.99/13.30 omegaS)))))) @
% 97.99/13.30 (
% 97.99/13.30 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.99/13.30 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1825])).
% 97.99/13.30 thf(zip_derived_cl1840, plain,
% 97.99/13.30 (~ (((cartprodsndpairEq) =>
% 97.99/13.30 (((cartprodpairsurjEq) =>
% 97.99/13.30 (((dpsetconstrI) =>
% 97.99/13.30 (((dpsetconstrSub) =>
% 97.99/13.30 (((setOfPairsIsBReln) =>
% 97.99/13.30 (((dpsetconstrERa) =>
% 97.99/13.30 (((dpsetconstrEL1) =>
% 97.99/13.30 (((dpsetconstrEL2) =>
% 97.99/13.30 (((dpsetconstrER) =>
% 97.99/13.30 (((funcImageSingleton) =>
% 97.99/13.30 (((apProp) =>
% 97.99/13.30 (((app) =>
% 97.99/13.30 (((infuncsetfunc) =>
% 97.99/13.30 (((ap2p) =>
% 97.99/13.30 (((funcinfuncset) =>
% 97.99/13.30 (((lamProp) =>
% 97.99/13.30 (((lamp) =>
% 97.99/13.30 (((lam2p) =>
% 97.99/13.30 (((brelnall1) =>
% 97.99/13.30 (((brelnall2) =>
% 97.99/13.30 (((ex1E2) =>
% 97.99/13.30 (((funcGraphProp1) =>
% 97.99/13.30 (((funcGraphProp3) =>
% 97.99/13.30 (((funcGraphProp2) =>
% 97.99/13.30 (((funcextLem) =>
% 97.99/13.30 (((funcGraphProp4) =>
% 97.99/13.30 (((subbreln) =>
% 97.99/13.30 (((eqbreln) =>
% 97.99/13.30 (((funcext) =>
% 97.99/13.30 (((funcext2) =>
% 97.99/13.30 ((
% 97.99/13.30 (ap2apEq1) =>
% 97.99/13.30 ((
% 97.99/13.30 (ap2apEq2) =>
% 97.99/13.30 ((
% 97.99/13.30 (beta1) =>
% 97.99/13.30 ((
% 97.99/13.30 (eta1) =>
% 97.99/13.30 ((
% 97.99/13.30 (lam2lamEq) =>
% 97.99/13.30 ((
% 97.99/13.30 (beta2) =>
% 97.99/13.30 ((
% 97.99/13.30 (eta2) =>
% 97.99/13.30 ((
% 97.99/13.30 (iffalseProp1) =>
% 97.99/13.30 ((
% 97.99/13.30 (iffalseProp2) =>
% 97.99/13.30 ((
% 97.99/13.30 (iftrueProp1) =>
% 97.99/13.30 ((
% 97.99/13.30 (iftrueProp2) =>
% 97.99/13.30 ((
% 97.99/13.30 (ifSingleton) =>
% 97.99/13.30 ((
% 97.99/13.30 (ifp) =>
% 97.99/13.30 ((
% 97.99/13.30 (theeq) =>
% 97.99/13.30 ((
% 97.99/13.30 (iftrue) =>
% 97.99/13.30 ((
% 97.99/13.30 (iffalse) =>
% 97.99/13.30 ((
% 97.99/13.30 (iftrueorfalse) =>
% 97.99/13.30 ((
% 97.99/13.30 (binintersectT_lem) =>
% 97.99/13.30 ((
% 97.99/13.30 (binunionT_lem) =>
% 97.99/13.30 ((
% 97.99/13.30 (powersetT_lem) =>
% 97.99/13.30 ((
% 97.99/13.30 (setminusT_lem) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementT_lem) =>
% 97.99/13.30 ((
% 97.99/13.30 (setextT) =>
% 97.99/13.30 ((
% 97.99/13.30 (subsetTI) =>
% 97.99/13.30 ((
% 97.99/13.30 (powersetTI1) =>
% 97.99/13.30 ((
% 97.99/13.30 (powersetTE1) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementTI1) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementTE1) =>
% 97.99/13.30 ((
% 97.99/13.30 (binintersectTELcontra) =>
% 97.99/13.30 ((
% 97.99/13.30 (binintersectTERcontra) =>
% 97.99/13.30 ((
% 97.99/13.30 (contrasubsetT) =>
% 97.99/13.30 ((
% 97.99/13.30 (contrasubsetT1) =>
% 97.99/13.30 ((
% 97.99/13.30 (contrasubsetT2) =>
% 97.99/13.30 ((
% 97.99/13.30 (contrasubsetT3) =>
% 97.99/13.30 ((
% 97.99/13.30 (doubleComplementI1) =>
% 97.99/13.30 ((
% 97.99/13.30 (doubleComplementE1) =>
% 97.99/13.30 ((
% 97.99/13.30 (doubleComplementSub1) =>
% 97.99/13.30 ((
% 97.99/13.30 (doubleComplementSub2) =>
% 97.99/13.30 ((
% 97.99/13.30 (doubleComplementEq) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementTnotintersectT) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementImpComplementIntersect) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementSubsetComplementIntersect) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementInPowersetComplementIntersect) =>
% 97.99/13.30 ((
% 97.99/13.30 (contraSubsetComplement) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementTcontraSubset) =>
% 97.99/13.30 ((
% 97.99/13.30 (binunionTILcontra) =>
% 97.99/13.30 ((
% 97.99/13.30 (binunionTIRcontra) =>
% 97.99/13.30 ((
% 97.99/13.30 (inIntersectImpInUnion) =>
% 97.99/13.30 ((
% 97.99/13.30 (inIntersectImpInUnion2) =>
% 97.99/13.30 ((
% 97.99/13.30 (inIntersectImpInIntersectUnions) =>
% 97.99/13.30 ((
% 97.99/13.30 (intersectInPowersetIntersectUnions) =>
% 97.99/13.30 ((
% 97.99/13.30 (inComplementUnionImpNotIn1) =>
% 97.99/13.30 ((
% 97.99/13.30 (inComplementUnionImpInComplement1) =>
% 97.99/13.30 ((
% 97.99/13.30 (binunionTE) =>
% 97.99/13.30 ((
% 97.99/13.30 (binunionTEcontra) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan2a1) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementUnionInPowersetComplement) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan2a2) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan1a) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan1b) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan1) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan2a) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan2b2) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan2b) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan2) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz13rule0) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz13rule1) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz13rule2) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz13rule3) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz13rule4) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz1_1) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz1_2) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz1_3) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz1_4) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz1_5) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1all2) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1SetBreln1) =>
% 97.99/13.30 ((
% 97.99/13.30 (choice2fnsingleton) =>
% 97.99/13.30 ((
% 97.99/13.30 (setOfPairsIsBReln1) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1all1) =>
% 97.99/13.30 ((
% 97.99/13.30 (subbreln1) =>
% 97.99/13.30 ((
% 97.99/13.30 (eqbreln1) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1invprop) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1invI) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1invE) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1compprop) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1compI) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1compE) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1compEex) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionprop) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionIL) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionIR) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionI) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionE) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionEcases) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionCommutes) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz2Ex) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz2W) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz2A) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz2B) =>
% 97.99/13.30 ((
% 97.99/13.30 (image1Ex) =>
% 97.99/13.30 ((
% 97.99/13.30 (image1Ex1) =>
% 97.99/13.30 ((
% 97.99/13.30 (image1Equiv) =>
% 97.99/13.30 ((
% 97.99/13.30 (image1E) =>
% 97.99/13.30 ((
% 97.99/13.30 (image1I) =>
% 97.99/13.30 ((
% 97.99/13.30 (injFuncInInjFuncSet) =>
% 97.99/13.30 ((
% 97.99/13.30 (injFuncSetFuncIn) =>
% 97.99/13.30 ((
% 97.99/13.30 (injFuncSetFuncInj) =>
% 97.99/13.30 ((
% 97.99/13.30 (surjFuncSetFuncIn) =>
% 97.99/13.30 ((
% 97.99/13.30 (surjFuncSetFuncSurj) =>
% 97.99/13.30 ((
% 97.99/13.30 (leftInvIsSurj) =>
% 97.99/13.30 ((
% 97.99/13.30 (surjCantorThm) =>
% 97.99/13.30 ((
% 97.99/13.30 (foundation2) =>
% 97.99/13.30 ((
% 97.99/13.30 (notinself) =>
% 97.99/13.30 ((
% 97.99/13.30 (notinself2) =>
% 97.99/13.30 ((
% 97.99/13.30 (omegaSp) =>
% 97.99/13.30 ((
% 97.99/13.30 (omegaSclos) =>
% 97.99/13.30 ((
% 97.99/13.30 (peano0notS) =>
% 97.99/13.30 ((
% 97.99/13.30 (!!) @ (
% 97.99/13.30 (('#S') @ (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 =>) @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#C') @ in @
% 97.99/13.30 omega)))) @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 !!) @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 (
% 97.99/13.30 ('#S') @ (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 =>) @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#C') @ in @
% 97.99/13.30 omega)))))) @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#S') @ (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 '#S') @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 =>))) @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#C') @ (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 '#B') @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 =) @
% 97.99/13.30 omegaS)))) @
% 97.99/13.30 omegaS)))))) @
% 97.99/13.30 (
% 97.99/13.30 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.99/13.30 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1833])).
% 97.99/13.30 thf(zip_derived_cl1848, plain,
% 97.99/13.30 (~ (((cartprodpairsurjEq) =>
% 97.99/13.30 (((dpsetconstrI) =>
% 97.99/13.30 (((dpsetconstrSub) =>
% 97.99/13.30 (((setOfPairsIsBReln) =>
% 97.99/13.30 (((dpsetconstrERa) =>
% 97.99/13.30 (((dpsetconstrEL1) =>
% 97.99/13.30 (((dpsetconstrEL2) =>
% 97.99/13.30 (((dpsetconstrER) =>
% 97.99/13.30 (((funcImageSingleton) =>
% 97.99/13.30 (((apProp) =>
% 97.99/13.30 (((app) =>
% 97.99/13.30 (((infuncsetfunc) =>
% 97.99/13.30 (((ap2p) =>
% 97.99/13.30 (((funcinfuncset) =>
% 97.99/13.30 (((lamProp) =>
% 97.99/13.30 (((lamp) =>
% 97.99/13.30 (((lam2p) =>
% 97.99/13.30 (((brelnall1) =>
% 97.99/13.30 (((brelnall2) =>
% 97.99/13.30 (((ex1E2) =>
% 97.99/13.30 (((funcGraphProp1) =>
% 97.99/13.30 (((funcGraphProp3) =>
% 97.99/13.30 (((funcGraphProp2) =>
% 97.99/13.30 (((funcextLem) =>
% 97.99/13.30 (((funcGraphProp4) =>
% 97.99/13.30 (((subbreln) =>
% 97.99/13.30 (((eqbreln) =>
% 97.99/13.30 (((funcext) =>
% 97.99/13.30 (((funcext2) =>
% 97.99/13.30 (((ap2apEq1) =>
% 97.99/13.30 ((
% 97.99/13.30 (ap2apEq2) =>
% 97.99/13.30 ((
% 97.99/13.30 (beta1) =>
% 97.99/13.30 ((
% 97.99/13.30 (eta1) =>
% 97.99/13.30 ((
% 97.99/13.30 (lam2lamEq) =>
% 97.99/13.30 ((
% 97.99/13.30 (beta2) =>
% 97.99/13.30 ((
% 97.99/13.30 (eta2) =>
% 97.99/13.30 ((
% 97.99/13.30 (iffalseProp1) =>
% 97.99/13.30 ((
% 97.99/13.30 (iffalseProp2) =>
% 97.99/13.30 ((
% 97.99/13.30 (iftrueProp1) =>
% 97.99/13.30 ((
% 97.99/13.30 (iftrueProp2) =>
% 97.99/13.30 ((
% 97.99/13.30 (ifSingleton) =>
% 97.99/13.30 ((
% 97.99/13.30 (ifp) =>
% 97.99/13.30 ((
% 97.99/13.30 (theeq) =>
% 97.99/13.30 ((
% 97.99/13.30 (iftrue) =>
% 97.99/13.30 ((
% 97.99/13.30 (iffalse) =>
% 97.99/13.30 ((
% 97.99/13.30 (iftrueorfalse) =>
% 97.99/13.30 ((
% 97.99/13.30 (binintersectT_lem) =>
% 97.99/13.30 ((
% 97.99/13.30 (binunionT_lem) =>
% 97.99/13.30 ((
% 97.99/13.30 (powersetT_lem) =>
% 97.99/13.30 ((
% 97.99/13.30 (setminusT_lem) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementT_lem) =>
% 97.99/13.30 ((
% 97.99/13.30 (setextT) =>
% 97.99/13.30 ((
% 97.99/13.30 (subsetTI) =>
% 97.99/13.30 ((
% 97.99/13.30 (powersetTI1) =>
% 97.99/13.30 ((
% 97.99/13.30 (powersetTE1) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementTI1) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementTE1) =>
% 97.99/13.30 ((
% 97.99/13.30 (binintersectTELcontra) =>
% 97.99/13.30 ((
% 97.99/13.30 (binintersectTERcontra) =>
% 97.99/13.30 ((
% 97.99/13.30 (contrasubsetT) =>
% 97.99/13.30 ((
% 97.99/13.30 (contrasubsetT1) =>
% 97.99/13.30 ((
% 97.99/13.30 (contrasubsetT2) =>
% 97.99/13.30 ((
% 97.99/13.30 (contrasubsetT3) =>
% 97.99/13.30 ((
% 97.99/13.30 (doubleComplementI1) =>
% 97.99/13.30 ((
% 97.99/13.30 (doubleComplementE1) =>
% 97.99/13.30 ((
% 97.99/13.30 (doubleComplementSub1) =>
% 97.99/13.30 ((
% 97.99/13.30 (doubleComplementSub2) =>
% 97.99/13.30 ((
% 97.99/13.30 (doubleComplementEq) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementTnotintersectT) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementImpComplementIntersect) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementSubsetComplementIntersect) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementInPowersetComplementIntersect) =>
% 97.99/13.30 ((
% 97.99/13.30 (contraSubsetComplement) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementTcontraSubset) =>
% 97.99/13.30 ((
% 97.99/13.30 (binunionTILcontra) =>
% 97.99/13.30 ((
% 97.99/13.30 (binunionTIRcontra) =>
% 97.99/13.30 ((
% 97.99/13.30 (inIntersectImpInUnion) =>
% 97.99/13.30 ((
% 97.99/13.30 (inIntersectImpInUnion2) =>
% 97.99/13.30 ((
% 97.99/13.30 (inIntersectImpInIntersectUnions) =>
% 97.99/13.30 ((
% 97.99/13.30 (intersectInPowersetIntersectUnions) =>
% 97.99/13.30 ((
% 97.99/13.30 (inComplementUnionImpNotIn1) =>
% 97.99/13.30 ((
% 97.99/13.30 (inComplementUnionImpInComplement1) =>
% 97.99/13.30 ((
% 97.99/13.30 (binunionTE) =>
% 97.99/13.30 ((
% 97.99/13.30 (binunionTEcontra) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan2a1) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementUnionInPowersetComplement) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan2a2) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan1a) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan1b) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan1) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan2a) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan2b2) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan2b) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan2) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz13rule0) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz13rule1) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz13rule2) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz13rule3) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz13rule4) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz1_1) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz1_2) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz1_3) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz1_4) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz1_5) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1all2) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1SetBreln1) =>
% 97.99/13.30 ((
% 97.99/13.30 (choice2fnsingleton) =>
% 97.99/13.30 ((
% 97.99/13.30 (setOfPairsIsBReln1) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1all1) =>
% 97.99/13.30 ((
% 97.99/13.30 (subbreln1) =>
% 97.99/13.30 ((
% 97.99/13.30 (eqbreln1) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1invprop) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1invI) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1invE) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1compprop) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1compI) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1compE) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1compEex) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionprop) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionIL) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionIR) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionI) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionE) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionEcases) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionCommutes) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz2Ex) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz2W) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz2A) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz2B) =>
% 97.99/13.30 ((
% 97.99/13.30 (image1Ex) =>
% 97.99/13.30 ((
% 97.99/13.30 (image1Ex1) =>
% 97.99/13.30 ((
% 97.99/13.30 (image1Equiv) =>
% 97.99/13.30 ((
% 97.99/13.30 (image1E) =>
% 97.99/13.30 ((
% 97.99/13.30 (image1I) =>
% 97.99/13.30 ((
% 97.99/13.30 (injFuncInInjFuncSet) =>
% 97.99/13.30 ((
% 97.99/13.30 (injFuncSetFuncIn) =>
% 97.99/13.30 ((
% 97.99/13.30 (injFuncSetFuncInj) =>
% 97.99/13.30 ((
% 97.99/13.30 (surjFuncSetFuncIn) =>
% 97.99/13.30 ((
% 97.99/13.30 (surjFuncSetFuncSurj) =>
% 97.99/13.30 ((
% 97.99/13.30 (leftInvIsSurj) =>
% 97.99/13.30 ((
% 97.99/13.30 (surjCantorThm) =>
% 97.99/13.30 ((
% 97.99/13.30 (foundation2) =>
% 97.99/13.30 ((
% 97.99/13.30 (notinself) =>
% 97.99/13.30 ((
% 97.99/13.30 (notinself2) =>
% 97.99/13.30 ((
% 97.99/13.30 (omegaSp) =>
% 97.99/13.30 ((
% 97.99/13.30 (omegaSclos) =>
% 97.99/13.30 ((
% 97.99/13.30 (peano0notS) =>
% 97.99/13.30 ((
% 97.99/13.30 (!!) @ (
% 97.99/13.30 (('#S') @ (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 =>) @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#C') @ in @
% 97.99/13.30 omega)))) @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 !!) @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 (
% 97.99/13.30 ('#S') @ (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 =>) @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#C') @ in @
% 97.99/13.30 omega)))))) @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#S') @ (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 '#S') @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 =>))) @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#C') @ (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 '#B') @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 =) @
% 97.99/13.30 omegaS)))) @
% 97.99/13.30 omegaS)))))) @
% 97.99/13.30 (
% 97.99/13.30 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.99/13.30 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1840])).
% 97.99/13.30 thf(zip_derived_cl1856, plain,
% 97.99/13.30 (~ (((dpsetconstrI) =>
% 97.99/13.30 (((dpsetconstrSub) =>
% 97.99/13.30 (((setOfPairsIsBReln) =>
% 97.99/13.30 (((dpsetconstrERa) =>
% 97.99/13.30 (((dpsetconstrEL1) =>
% 97.99/13.30 (((dpsetconstrEL2) =>
% 97.99/13.30 (((dpsetconstrER) =>
% 97.99/13.30 (((funcImageSingleton) =>
% 97.99/13.30 (((apProp) =>
% 97.99/13.30 (((app) =>
% 97.99/13.30 (((infuncsetfunc) =>
% 97.99/13.30 (((ap2p) =>
% 97.99/13.30 (((funcinfuncset) =>
% 97.99/13.30 (((lamProp) =>
% 97.99/13.30 (((lamp) =>
% 97.99/13.30 (((lam2p) =>
% 97.99/13.30 (((brelnall1) =>
% 97.99/13.30 (((brelnall2) =>
% 97.99/13.30 (((ex1E2) =>
% 97.99/13.30 (((funcGraphProp1) =>
% 97.99/13.30 (((funcGraphProp3) =>
% 97.99/13.30 (((funcGraphProp2) =>
% 97.99/13.30 (((funcextLem) =>
% 97.99/13.30 (((funcGraphProp4) =>
% 97.99/13.30 (((subbreln) =>
% 97.99/13.30 (((eqbreln) =>
% 97.99/13.30 (((funcext) =>
% 97.99/13.30 (((funcext2) =>
% 97.99/13.30 (((ap2apEq1) =>
% 97.99/13.30 (((ap2apEq2) =>
% 97.99/13.30 ((
% 97.99/13.30 (beta1) =>
% 97.99/13.30 ((
% 97.99/13.30 (eta1) =>
% 97.99/13.30 ((
% 97.99/13.30 (lam2lamEq) =>
% 97.99/13.30 ((
% 97.99/13.30 (beta2) =>
% 97.99/13.30 ((
% 97.99/13.30 (eta2) =>
% 97.99/13.30 ((
% 97.99/13.30 (iffalseProp1) =>
% 97.99/13.30 ((
% 97.99/13.30 (iffalseProp2) =>
% 97.99/13.30 ((
% 97.99/13.30 (iftrueProp1) =>
% 97.99/13.30 ((
% 97.99/13.30 (iftrueProp2) =>
% 97.99/13.30 ((
% 97.99/13.30 (ifSingleton) =>
% 97.99/13.30 ((
% 97.99/13.30 (ifp) =>
% 97.99/13.30 ((
% 97.99/13.30 (theeq) =>
% 97.99/13.30 ((
% 97.99/13.30 (iftrue) =>
% 97.99/13.30 ((
% 97.99/13.30 (iffalse) =>
% 97.99/13.30 ((
% 97.99/13.30 (iftrueorfalse) =>
% 97.99/13.30 ((
% 97.99/13.30 (binintersectT_lem) =>
% 97.99/13.30 ((
% 97.99/13.30 (binunionT_lem) =>
% 97.99/13.30 ((
% 97.99/13.30 (powersetT_lem) =>
% 97.99/13.30 ((
% 97.99/13.30 (setminusT_lem) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementT_lem) =>
% 97.99/13.30 ((
% 97.99/13.30 (setextT) =>
% 97.99/13.30 ((
% 97.99/13.30 (subsetTI) =>
% 97.99/13.30 ((
% 97.99/13.30 (powersetTI1) =>
% 97.99/13.30 ((
% 97.99/13.30 (powersetTE1) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementTI1) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementTE1) =>
% 97.99/13.30 ((
% 97.99/13.30 (binintersectTELcontra) =>
% 97.99/13.30 ((
% 97.99/13.30 (binintersectTERcontra) =>
% 97.99/13.30 ((
% 97.99/13.30 (contrasubsetT) =>
% 97.99/13.30 ((
% 97.99/13.30 (contrasubsetT1) =>
% 97.99/13.30 ((
% 97.99/13.30 (contrasubsetT2) =>
% 97.99/13.30 ((
% 97.99/13.30 (contrasubsetT3) =>
% 97.99/13.30 ((
% 97.99/13.30 (doubleComplementI1) =>
% 97.99/13.30 ((
% 97.99/13.30 (doubleComplementE1) =>
% 97.99/13.30 ((
% 97.99/13.30 (doubleComplementSub1) =>
% 97.99/13.30 ((
% 97.99/13.30 (doubleComplementSub2) =>
% 97.99/13.30 ((
% 97.99/13.30 (doubleComplementEq) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementTnotintersectT) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementImpComplementIntersect) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementSubsetComplementIntersect) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementInPowersetComplementIntersect) =>
% 97.99/13.30 ((
% 97.99/13.30 (contraSubsetComplement) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementTcontraSubset) =>
% 97.99/13.30 ((
% 97.99/13.30 (binunionTILcontra) =>
% 97.99/13.30 ((
% 97.99/13.30 (binunionTIRcontra) =>
% 97.99/13.30 ((
% 97.99/13.30 (inIntersectImpInUnion) =>
% 97.99/13.30 ((
% 97.99/13.30 (inIntersectImpInUnion2) =>
% 97.99/13.30 ((
% 97.99/13.30 (inIntersectImpInIntersectUnions) =>
% 97.99/13.30 ((
% 97.99/13.30 (intersectInPowersetIntersectUnions) =>
% 97.99/13.30 ((
% 97.99/13.30 (inComplementUnionImpNotIn1) =>
% 97.99/13.30 ((
% 97.99/13.30 (inComplementUnionImpInComplement1) =>
% 97.99/13.30 ((
% 97.99/13.30 (binunionTE) =>
% 97.99/13.30 ((
% 97.99/13.30 (binunionTEcontra) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan2a1) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementUnionInPowersetComplement) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan2a2) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan1a) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan1b) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan1) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan2a) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan2b2) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan2b) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan2) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz13rule0) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz13rule1) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz13rule2) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz13rule3) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz13rule4) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz1_1) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz1_2) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz1_3) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz1_4) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz1_5) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1all2) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1SetBreln1) =>
% 97.99/13.30 ((
% 97.99/13.30 (choice2fnsingleton) =>
% 97.99/13.30 ((
% 97.99/13.30 (setOfPairsIsBReln1) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1all1) =>
% 97.99/13.30 ((
% 97.99/13.30 (subbreln1) =>
% 97.99/13.30 ((
% 97.99/13.30 (eqbreln1) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1invprop) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1invI) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1invE) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1compprop) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1compI) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1compE) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1compEex) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionprop) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionIL) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionIR) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionI) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionE) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionEcases) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionCommutes) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz2Ex) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz2W) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz2A) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz2B) =>
% 97.99/13.30 ((
% 97.99/13.30 (image1Ex) =>
% 97.99/13.30 ((
% 97.99/13.30 (image1Ex1) =>
% 97.99/13.30 ((
% 97.99/13.30 (image1Equiv) =>
% 97.99/13.30 ((
% 97.99/13.30 (image1E) =>
% 97.99/13.30 ((
% 97.99/13.30 (image1I) =>
% 97.99/13.30 ((
% 97.99/13.30 (injFuncInInjFuncSet) =>
% 97.99/13.30 ((
% 97.99/13.30 (injFuncSetFuncIn) =>
% 97.99/13.30 ((
% 97.99/13.30 (injFuncSetFuncInj) =>
% 97.99/13.30 ((
% 97.99/13.30 (surjFuncSetFuncIn) =>
% 97.99/13.30 ((
% 97.99/13.30 (surjFuncSetFuncSurj) =>
% 97.99/13.30 ((
% 97.99/13.30 (leftInvIsSurj) =>
% 97.99/13.30 ((
% 97.99/13.30 (surjCantorThm) =>
% 97.99/13.30 ((
% 97.99/13.30 (foundation2) =>
% 97.99/13.30 ((
% 97.99/13.30 (notinself) =>
% 97.99/13.30 ((
% 97.99/13.30 (notinself2) =>
% 97.99/13.30 ((
% 97.99/13.30 (omegaSp) =>
% 97.99/13.30 ((
% 97.99/13.30 (omegaSclos) =>
% 97.99/13.30 ((
% 97.99/13.30 (peano0notS) =>
% 97.99/13.30 ((
% 97.99/13.30 (!!) @ (
% 97.99/13.30 (('#S') @ (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 =>) @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#C') @ in @
% 97.99/13.30 omega)))) @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 !!) @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 (
% 97.99/13.30 ('#S') @ (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 =>) @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#C') @ in @
% 97.99/13.30 omega)))))) @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#S') @ (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 '#S') @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 =>))) @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#C') @ (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 '#B') @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 =) @
% 97.99/13.30 omegaS)))) @
% 97.99/13.30 omegaS)))))) @
% 97.99/13.30 (
% 97.99/13.30 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.99/13.30 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1848])).
% 97.99/13.30 thf(zip_derived_cl1865, plain,
% 97.99/13.30 (~ (((dpsetconstrSub) =>
% 97.99/13.30 (((setOfPairsIsBReln) =>
% 97.99/13.30 (((dpsetconstrERa) =>
% 97.99/13.30 (((dpsetconstrEL1) =>
% 97.99/13.30 (((dpsetconstrEL2) =>
% 97.99/13.30 (((dpsetconstrER) =>
% 97.99/13.30 (((funcImageSingleton) =>
% 97.99/13.30 (((apProp) =>
% 97.99/13.30 (((app) =>
% 97.99/13.30 (((infuncsetfunc) =>
% 97.99/13.30 (((ap2p) =>
% 97.99/13.30 (((funcinfuncset) =>
% 97.99/13.30 (((lamProp) =>
% 97.99/13.30 (((lamp) =>
% 97.99/13.30 (((lam2p) =>
% 97.99/13.30 (((brelnall1) =>
% 97.99/13.30 (((brelnall2) =>
% 97.99/13.30 (((ex1E2) =>
% 97.99/13.30 (((funcGraphProp1) =>
% 97.99/13.30 (((funcGraphProp3) =>
% 97.99/13.30 (((funcGraphProp2) =>
% 97.99/13.30 (((funcextLem) =>
% 97.99/13.30 (((funcGraphProp4) =>
% 97.99/13.30 (((subbreln) =>
% 97.99/13.30 (((eqbreln) =>
% 97.99/13.30 (((funcext) =>
% 97.99/13.30 (((funcext2) =>
% 97.99/13.30 (((ap2apEq1) =>
% 97.99/13.30 (((ap2apEq2) =>
% 97.99/13.30 (((beta1) =>
% 97.99/13.30 ((
% 97.99/13.30 (eta1) =>
% 97.99/13.30 ((
% 97.99/13.30 (lam2lamEq) =>
% 97.99/13.30 ((
% 97.99/13.30 (beta2) =>
% 97.99/13.30 ((
% 97.99/13.30 (eta2) =>
% 97.99/13.30 ((
% 97.99/13.30 (iffalseProp1) =>
% 97.99/13.30 ((
% 97.99/13.30 (iffalseProp2) =>
% 97.99/13.30 ((
% 97.99/13.30 (iftrueProp1) =>
% 97.99/13.30 ((
% 97.99/13.30 (iftrueProp2) =>
% 97.99/13.30 ((
% 97.99/13.30 (ifSingleton) =>
% 97.99/13.30 ((
% 97.99/13.30 (ifp) =>
% 97.99/13.30 ((
% 97.99/13.30 (theeq) =>
% 97.99/13.30 ((
% 97.99/13.30 (iftrue) =>
% 97.99/13.30 ((
% 97.99/13.30 (iffalse) =>
% 97.99/13.30 ((
% 97.99/13.30 (iftrueorfalse) =>
% 97.99/13.30 ((
% 97.99/13.30 (binintersectT_lem) =>
% 97.99/13.30 ((
% 97.99/13.30 (binunionT_lem) =>
% 97.99/13.30 ((
% 97.99/13.30 (powersetT_lem) =>
% 97.99/13.30 ((
% 97.99/13.30 (setminusT_lem) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementT_lem) =>
% 97.99/13.30 ((
% 97.99/13.30 (setextT) =>
% 97.99/13.30 ((
% 97.99/13.30 (subsetTI) =>
% 97.99/13.30 ((
% 97.99/13.30 (powersetTI1) =>
% 97.99/13.30 ((
% 97.99/13.30 (powersetTE1) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementTI1) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementTE1) =>
% 97.99/13.30 ((
% 97.99/13.30 (binintersectTELcontra) =>
% 97.99/13.30 ((
% 97.99/13.30 (binintersectTERcontra) =>
% 97.99/13.30 ((
% 97.99/13.30 (contrasubsetT) =>
% 97.99/13.30 ((
% 97.99/13.30 (contrasubsetT1) =>
% 97.99/13.30 ((
% 97.99/13.30 (contrasubsetT2) =>
% 97.99/13.30 ((
% 97.99/13.30 (contrasubsetT3) =>
% 97.99/13.30 ((
% 97.99/13.30 (doubleComplementI1) =>
% 97.99/13.30 ((
% 97.99/13.30 (doubleComplementE1) =>
% 97.99/13.30 ((
% 97.99/13.30 (doubleComplementSub1) =>
% 97.99/13.30 ((
% 97.99/13.30 (doubleComplementSub2) =>
% 97.99/13.30 ((
% 97.99/13.30 (doubleComplementEq) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementTnotintersectT) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementImpComplementIntersect) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementSubsetComplementIntersect) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementInPowersetComplementIntersect) =>
% 97.99/13.30 ((
% 97.99/13.30 (contraSubsetComplement) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementTcontraSubset) =>
% 97.99/13.30 ((
% 97.99/13.30 (binunionTILcontra) =>
% 97.99/13.30 ((
% 97.99/13.30 (binunionTIRcontra) =>
% 97.99/13.30 ((
% 97.99/13.30 (inIntersectImpInUnion) =>
% 97.99/13.30 ((
% 97.99/13.30 (inIntersectImpInUnion2) =>
% 97.99/13.30 ((
% 97.99/13.30 (inIntersectImpInIntersectUnions) =>
% 97.99/13.30 ((
% 97.99/13.30 (intersectInPowersetIntersectUnions) =>
% 97.99/13.30 ((
% 97.99/13.30 (inComplementUnionImpNotIn1) =>
% 97.99/13.30 ((
% 97.99/13.30 (inComplementUnionImpInComplement1) =>
% 97.99/13.30 ((
% 97.99/13.30 (binunionTE) =>
% 97.99/13.30 ((
% 97.99/13.30 (binunionTEcontra) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan2a1) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementUnionInPowersetComplement) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan2a2) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan1a) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan1b) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan1) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan2a) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan2b2) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan2b) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan2) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz13rule0) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz13rule1) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz13rule2) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz13rule3) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz13rule4) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz1_1) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz1_2) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz1_3) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz1_4) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz1_5) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1all2) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1SetBreln1) =>
% 97.99/13.30 ((
% 97.99/13.30 (choice2fnsingleton) =>
% 97.99/13.30 ((
% 97.99/13.30 (setOfPairsIsBReln1) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1all1) =>
% 97.99/13.30 ((
% 97.99/13.30 (subbreln1) =>
% 97.99/13.30 ((
% 97.99/13.30 (eqbreln1) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1invprop) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1invI) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1invE) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1compprop) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1compI) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1compE) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1compEex) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionprop) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionIL) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionIR) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionI) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionE) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionEcases) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionCommutes) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz2Ex) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz2W) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz2A) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz2B) =>
% 97.99/13.30 ((
% 97.99/13.30 (image1Ex) =>
% 97.99/13.30 ((
% 97.99/13.30 (image1Ex1) =>
% 97.99/13.30 ((
% 97.99/13.30 (image1Equiv) =>
% 97.99/13.30 ((
% 97.99/13.30 (image1E) =>
% 97.99/13.30 ((
% 97.99/13.30 (image1I) =>
% 97.99/13.30 ((
% 97.99/13.30 (injFuncInInjFuncSet) =>
% 97.99/13.30 ((
% 97.99/13.30 (injFuncSetFuncIn) =>
% 97.99/13.30 ((
% 97.99/13.30 (injFuncSetFuncInj) =>
% 97.99/13.30 ((
% 97.99/13.30 (surjFuncSetFuncIn) =>
% 97.99/13.30 ((
% 97.99/13.30 (surjFuncSetFuncSurj) =>
% 97.99/13.30 ((
% 97.99/13.30 (leftInvIsSurj) =>
% 97.99/13.30 ((
% 97.99/13.30 (surjCantorThm) =>
% 97.99/13.30 ((
% 97.99/13.30 (foundation2) =>
% 97.99/13.30 ((
% 97.99/13.30 (notinself) =>
% 97.99/13.30 ((
% 97.99/13.30 (notinself2) =>
% 97.99/13.30 ((
% 97.99/13.30 (omegaSp) =>
% 97.99/13.30 ((
% 97.99/13.30 (omegaSclos) =>
% 97.99/13.30 ((
% 97.99/13.30 (peano0notS) =>
% 97.99/13.30 ((
% 97.99/13.30 (!!) @ (
% 97.99/13.30 (('#S') @ (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 =>) @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#C') @ in @
% 97.99/13.30 omega)))) @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 !!) @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 (
% 97.99/13.30 ('#S') @ (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 =>) @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#C') @ in @
% 97.99/13.30 omega)))))) @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#S') @ (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 '#S') @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 =>))) @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#C') @ (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 '#B') @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 =) @
% 97.99/13.30 omegaS)))) @
% 97.99/13.30 omegaS)))))) @
% 97.99/13.30 (
% 97.99/13.30 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 97.99/13.30 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1856])).
% 97.99/13.30 thf(zip_derived_cl1874, plain,
% 97.99/13.30 (~ (((setOfPairsIsBReln) =>
% 97.99/13.30 (((dpsetconstrERa) =>
% 97.99/13.30 (((dpsetconstrEL1) =>
% 97.99/13.30 (((dpsetconstrEL2) =>
% 97.99/13.30 (((dpsetconstrER) =>
% 97.99/13.30 (((funcImageSingleton) =>
% 97.99/13.30 (((apProp) =>
% 97.99/13.30 (((app) =>
% 97.99/13.30 (((infuncsetfunc) =>
% 97.99/13.30 (((ap2p) =>
% 97.99/13.30 (((funcinfuncset) =>
% 97.99/13.30 (((lamProp) =>
% 97.99/13.30 (((lamp) =>
% 97.99/13.30 (((lam2p) =>
% 97.99/13.30 (((brelnall1) =>
% 97.99/13.30 (((brelnall2) =>
% 97.99/13.30 (((ex1E2) =>
% 97.99/13.30 (((funcGraphProp1) =>
% 97.99/13.30 (((funcGraphProp3) =>
% 97.99/13.30 (((funcGraphProp2) =>
% 97.99/13.30 (((funcextLem) =>
% 97.99/13.30 (((funcGraphProp4) =>
% 97.99/13.30 (((subbreln) =>
% 97.99/13.30 (((eqbreln) =>
% 97.99/13.30 (((funcext) =>
% 97.99/13.30 (((funcext2) =>
% 97.99/13.30 (((ap2apEq1) =>
% 97.99/13.30 (((ap2apEq2) =>
% 97.99/13.30 (((beta1) =>
% 97.99/13.30 (((eta1) =>
% 97.99/13.30 ((
% 97.99/13.30 (lam2lamEq) =>
% 97.99/13.30 ((
% 97.99/13.30 (beta2) =>
% 97.99/13.30 ((
% 97.99/13.30 (eta2) =>
% 97.99/13.30 ((
% 97.99/13.30 (iffalseProp1) =>
% 97.99/13.30 ((
% 97.99/13.30 (iffalseProp2) =>
% 97.99/13.30 ((
% 97.99/13.30 (iftrueProp1) =>
% 97.99/13.30 ((
% 97.99/13.30 (iftrueProp2) =>
% 97.99/13.30 ((
% 97.99/13.30 (ifSingleton) =>
% 97.99/13.30 ((
% 97.99/13.30 (ifp) =>
% 97.99/13.30 ((
% 97.99/13.30 (theeq) =>
% 97.99/13.30 ((
% 97.99/13.30 (iftrue) =>
% 97.99/13.30 ((
% 97.99/13.30 (iffalse) =>
% 97.99/13.30 ((
% 97.99/13.30 (iftrueorfalse) =>
% 97.99/13.30 ((
% 97.99/13.30 (binintersectT_lem) =>
% 97.99/13.30 ((
% 97.99/13.30 (binunionT_lem) =>
% 97.99/13.30 ((
% 97.99/13.30 (powersetT_lem) =>
% 97.99/13.30 ((
% 97.99/13.30 (setminusT_lem) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementT_lem) =>
% 97.99/13.30 ((
% 97.99/13.30 (setextT) =>
% 97.99/13.30 ((
% 97.99/13.30 (subsetTI) =>
% 97.99/13.30 ((
% 97.99/13.30 (powersetTI1) =>
% 97.99/13.30 ((
% 97.99/13.30 (powersetTE1) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementTI1) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementTE1) =>
% 97.99/13.30 ((
% 97.99/13.30 (binintersectTELcontra) =>
% 97.99/13.30 ((
% 97.99/13.30 (binintersectTERcontra) =>
% 97.99/13.30 ((
% 97.99/13.30 (contrasubsetT) =>
% 97.99/13.30 ((
% 97.99/13.30 (contrasubsetT1) =>
% 97.99/13.30 ((
% 97.99/13.30 (contrasubsetT2) =>
% 97.99/13.30 ((
% 97.99/13.30 (contrasubsetT3) =>
% 97.99/13.30 ((
% 97.99/13.30 (doubleComplementI1) =>
% 97.99/13.30 ((
% 97.99/13.30 (doubleComplementE1) =>
% 97.99/13.30 ((
% 97.99/13.30 (doubleComplementSub1) =>
% 97.99/13.30 ((
% 97.99/13.30 (doubleComplementSub2) =>
% 97.99/13.30 ((
% 97.99/13.30 (doubleComplementEq) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementTnotintersectT) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementImpComplementIntersect) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementSubsetComplementIntersect) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementInPowersetComplementIntersect) =>
% 97.99/13.30 ((
% 97.99/13.30 (contraSubsetComplement) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementTcontraSubset) =>
% 97.99/13.30 ((
% 97.99/13.30 (binunionTILcontra) =>
% 97.99/13.30 ((
% 97.99/13.30 (binunionTIRcontra) =>
% 97.99/13.30 ((
% 97.99/13.30 (inIntersectImpInUnion) =>
% 97.99/13.30 ((
% 97.99/13.30 (inIntersectImpInUnion2) =>
% 97.99/13.30 ((
% 97.99/13.30 (inIntersectImpInIntersectUnions) =>
% 97.99/13.30 ((
% 97.99/13.30 (intersectInPowersetIntersectUnions) =>
% 97.99/13.30 ((
% 97.99/13.30 (inComplementUnionImpNotIn1) =>
% 97.99/13.30 ((
% 97.99/13.30 (inComplementUnionImpInComplement1) =>
% 97.99/13.30 ((
% 97.99/13.30 (binunionTE) =>
% 97.99/13.30 ((
% 97.99/13.30 (binunionTEcontra) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan2a1) =>
% 97.99/13.30 ((
% 97.99/13.30 (complementUnionInPowersetComplement) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan2a2) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan1a) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan1b) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan1) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan2a) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan2b2) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan2b) =>
% 97.99/13.30 ((
% 97.99/13.30 (demorgan2) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz13rule0) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz13rule1) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz13rule2) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz13rule3) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz13rule4) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz1_1) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz1_2) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz1_3) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz1_4) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz1_5) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1all2) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1SetBreln1) =>
% 97.99/13.30 ((
% 97.99/13.30 (choice2fnsingleton) =>
% 97.99/13.30 ((
% 97.99/13.30 (setOfPairsIsBReln1) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1all1) =>
% 97.99/13.30 ((
% 97.99/13.30 (subbreln1) =>
% 97.99/13.30 ((
% 97.99/13.30 (eqbreln1) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1invprop) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1invI) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1invE) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1compprop) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1compI) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1compE) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1compEex) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionprop) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionIL) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionIR) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionI) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionE) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionEcases) =>
% 97.99/13.30 ((
% 97.99/13.30 (breln1unionCommutes) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz2Ex) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz2W) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz2A) =>
% 97.99/13.30 ((
% 97.99/13.30 (woz2B) =>
% 97.99/13.30 ((
% 97.99/13.30 (image1Ex) =>
% 97.99/13.30 ((
% 97.99/13.30 (image1Ex1) =>
% 97.99/13.30 ((
% 97.99/13.30 (image1Equiv) =>
% 97.99/13.30 ((
% 97.99/13.30 (image1E) =>
% 97.99/13.30 ((
% 97.99/13.30 (image1I) =>
% 97.99/13.30 ((
% 97.99/13.30 (injFuncInInjFuncSet) =>
% 97.99/13.30 ((
% 97.99/13.30 (injFuncSetFuncIn) =>
% 97.99/13.30 ((
% 97.99/13.30 (injFuncSetFuncInj) =>
% 97.99/13.30 ((
% 97.99/13.30 (surjFuncSetFuncIn) =>
% 97.99/13.30 ((
% 97.99/13.30 (surjFuncSetFuncSurj) =>
% 97.99/13.30 ((
% 97.99/13.30 (leftInvIsSurj) =>
% 97.99/13.30 ((
% 97.99/13.30 (surjCantorThm) =>
% 97.99/13.30 ((
% 97.99/13.30 (foundation2) =>
% 97.99/13.30 ((
% 97.99/13.30 (notinself) =>
% 97.99/13.30 ((
% 97.99/13.30 (notinself2) =>
% 97.99/13.30 ((
% 97.99/13.30 (omegaSp) =>
% 97.99/13.30 ((
% 97.99/13.30 (omegaSclos) =>
% 97.99/13.30 ((
% 97.99/13.30 (peano0notS) =>
% 97.99/13.30 ((
% 97.99/13.30 (!!) @ (
% 97.99/13.30 (('#S') @ (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 =>) @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#C') @ in @
% 97.99/13.30 omega)))) @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 !!) @
% 97.99/13.30 (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 (
% 97.99/13.30 ('#S') @ (
% 97.99/13.30 (
% 97.99/13.30 ('#B') @ (
% 97.99/13.30 =>) @
% 97.99/13.30 (
% 98.38/13.30 (
% 98.38/13.30 ('#C') @ in @
% 98.38/13.30 omega)))))) @
% 98.38/13.30 (
% 98.38/13.30 (
% 98.38/13.30 ('#S') @ (
% 98.38/13.30 (
% 98.38/13.30 ('#B') @ (
% 98.38/13.30 '#S') @
% 98.38/13.30 (
% 98.38/13.30 (
% 98.38/13.30 ('#B') @ (
% 98.38/13.30 (
% 98.38/13.30 ('#B') @ (
% 98.38/13.30 =>))) @
% 98.38/13.30 (
% 98.38/13.30 (
% 98.38/13.30 ('#C') @ (
% 98.38/13.30 (
% 98.38/13.30 ('#B') @ (
% 98.38/13.30 '#B') @
% 98.38/13.30 (
% 98.38/13.30 (
% 98.38/13.30 ('#B') @ (
% 98.38/13.30 =) @
% 98.38/13.30 omegaS)))) @
% 98.38/13.30 omegaS)))))) @
% 98.38/13.30 (
% 98.38/13.30 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.38/13.30 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1865])).
% 98.38/13.30 thf(zip_derived_cl1883, plain,
% 98.38/13.30 (~ (((dpsetconstrERa) =>
% 98.38/13.30 (((dpsetconstrEL1) =>
% 98.38/13.30 (((dpsetconstrEL2) =>
% 98.38/13.30 (((dpsetconstrER) =>
% 98.38/13.30 (((funcImageSingleton) =>
% 98.38/13.30 (((apProp) =>
% 98.38/13.30 (((app) =>
% 98.38/13.30 (((infuncsetfunc) =>
% 98.38/13.30 (((ap2p) =>
% 98.38/13.30 (((funcinfuncset) =>
% 98.38/13.30 (((lamProp) =>
% 98.38/13.30 (((lamp) =>
% 98.38/13.30 (((lam2p) =>
% 98.38/13.30 (((brelnall1) =>
% 98.38/13.30 (((brelnall2) =>
% 98.38/13.30 (((ex1E2) =>
% 98.38/13.30 (((funcGraphProp1) =>
% 98.38/13.30 (((funcGraphProp3) =>
% 98.38/13.30 (((funcGraphProp2) =>
% 98.38/13.30 (((funcextLem) =>
% 98.38/13.30 (((funcGraphProp4) =>
% 98.38/13.30 (((subbreln) =>
% 98.38/13.30 (((eqbreln) =>
% 98.38/13.30 (((funcext) =>
% 98.38/13.30 (((funcext2) =>
% 98.38/13.30 (((ap2apEq1) =>
% 98.38/13.30 (((ap2apEq2) =>
% 98.38/13.30 (((beta1) =>
% 98.38/13.30 (((eta1) =>
% 98.38/13.30 (((lam2lamEq) =>
% 98.38/13.30 ((
% 98.38/13.30 (beta2) =>
% 98.38/13.30 ((
% 98.38/13.30 (eta2) =>
% 98.38/13.30 ((
% 98.38/13.30 (iffalseProp1) =>
% 98.38/13.30 ((
% 98.38/13.30 (iffalseProp2) =>
% 98.38/13.30 ((
% 98.38/13.30 (iftrueProp1) =>
% 98.38/13.30 ((
% 98.38/13.30 (iftrueProp2) =>
% 98.38/13.30 ((
% 98.38/13.30 (ifSingleton) =>
% 98.38/13.30 ((
% 98.38/13.30 (ifp) =>
% 98.38/13.30 ((
% 98.38/13.30 (theeq) =>
% 98.38/13.30 ((
% 98.38/13.30 (iftrue) =>
% 98.38/13.30 ((
% 98.38/13.30 (iffalse) =>
% 98.38/13.30 ((
% 98.38/13.30 (iftrueorfalse) =>
% 98.38/13.30 ((
% 98.38/13.30 (binintersectT_lem) =>
% 98.38/13.30 ((
% 98.38/13.30 (binunionT_lem) =>
% 98.38/13.30 ((
% 98.38/13.30 (powersetT_lem) =>
% 98.38/13.30 ((
% 98.38/13.30 (setminusT_lem) =>
% 98.38/13.30 ((
% 98.38/13.30 (complementT_lem) =>
% 98.38/13.30 ((
% 98.38/13.30 (setextT) =>
% 98.38/13.30 ((
% 98.38/13.30 (subsetTI) =>
% 98.38/13.30 ((
% 98.38/13.30 (powersetTI1) =>
% 98.38/13.30 ((
% 98.38/13.30 (powersetTE1) =>
% 98.38/13.30 ((
% 98.38/13.30 (complementTI1) =>
% 98.38/13.30 ((
% 98.38/13.30 (complementTE1) =>
% 98.38/13.30 ((
% 98.38/13.30 (binintersectTELcontra) =>
% 98.38/13.30 ((
% 98.38/13.30 (binintersectTERcontra) =>
% 98.38/13.30 ((
% 98.38/13.30 (contrasubsetT) =>
% 98.38/13.30 ((
% 98.38/13.30 (contrasubsetT1) =>
% 98.38/13.30 ((
% 98.38/13.30 (contrasubsetT2) =>
% 98.38/13.30 ((
% 98.38/13.30 (contrasubsetT3) =>
% 98.38/13.30 ((
% 98.38/13.30 (doubleComplementI1) =>
% 98.38/13.30 ((
% 98.38/13.30 (doubleComplementE1) =>
% 98.38/13.30 ((
% 98.38/13.30 (doubleComplementSub1) =>
% 98.38/13.30 ((
% 98.38/13.30 (doubleComplementSub2) =>
% 98.38/13.30 ((
% 98.38/13.30 (doubleComplementEq) =>
% 98.38/13.30 ((
% 98.38/13.30 (complementTnotintersectT) =>
% 98.38/13.30 ((
% 98.38/13.30 (complementImpComplementIntersect) =>
% 98.38/13.30 ((
% 98.38/13.30 (complementSubsetComplementIntersect) =>
% 98.38/13.30 ((
% 98.38/13.30 (complementInPowersetComplementIntersect) =>
% 98.38/13.30 ((
% 98.38/13.30 (contraSubsetComplement) =>
% 98.38/13.30 ((
% 98.38/13.30 (complementTcontraSubset) =>
% 98.38/13.30 ((
% 98.38/13.30 (binunionTILcontra) =>
% 98.38/13.30 ((
% 98.38/13.30 (binunionTIRcontra) =>
% 98.38/13.30 ((
% 98.38/13.30 (inIntersectImpInUnion) =>
% 98.38/13.30 ((
% 98.38/13.30 (inIntersectImpInUnion2) =>
% 98.38/13.30 ((
% 98.38/13.30 (inIntersectImpInIntersectUnions) =>
% 98.38/13.30 ((
% 98.38/13.30 (intersectInPowersetIntersectUnions) =>
% 98.38/13.30 ((
% 98.38/13.30 (inComplementUnionImpNotIn1) =>
% 98.38/13.30 ((
% 98.38/13.30 (inComplementUnionImpInComplement1) =>
% 98.38/13.30 ((
% 98.38/13.30 (binunionTE) =>
% 98.38/13.30 ((
% 98.38/13.30 (binunionTEcontra) =>
% 98.38/13.30 ((
% 98.38/13.30 (demorgan2a1) =>
% 98.38/13.30 ((
% 98.38/13.30 (complementUnionInPowersetComplement) =>
% 98.38/13.30 ((
% 98.38/13.30 (demorgan2a2) =>
% 98.38/13.30 ((
% 98.38/13.30 (demorgan1a) =>
% 98.38/13.30 ((
% 98.38/13.30 (demorgan1b) =>
% 98.38/13.30 ((
% 98.38/13.30 (demorgan1) =>
% 98.38/13.30 ((
% 98.38/13.30 (demorgan2a) =>
% 98.38/13.30 ((
% 98.38/13.30 (demorgan2b2) =>
% 98.38/13.30 ((
% 98.38/13.30 (demorgan2b) =>
% 98.38/13.30 ((
% 98.38/13.30 (demorgan2) =>
% 98.38/13.30 ((
% 98.38/13.30 (woz13rule0) =>
% 98.38/13.30 ((
% 98.38/13.30 (woz13rule1) =>
% 98.38/13.30 ((
% 98.38/13.30 (woz13rule2) =>
% 98.38/13.30 ((
% 98.38/13.30 (woz13rule3) =>
% 98.38/13.30 ((
% 98.38/13.30 (woz13rule4) =>
% 98.38/13.30 ((
% 98.38/13.30 (woz1_1) =>
% 98.38/13.30 ((
% 98.38/13.30 (woz1_2) =>
% 98.38/13.30 ((
% 98.38/13.30 (woz1_3) =>
% 98.38/13.30 ((
% 98.38/13.30 (woz1_4) =>
% 98.38/13.30 ((
% 98.38/13.30 (woz1_5) =>
% 98.38/13.30 ((
% 98.38/13.30 (breln1all2) =>
% 98.38/13.30 ((
% 98.38/13.30 (breln1SetBreln1) =>
% 98.38/13.30 ((
% 98.38/13.30 (choice2fnsingleton) =>
% 98.38/13.30 ((
% 98.38/13.30 (setOfPairsIsBReln1) =>
% 98.38/13.30 ((
% 98.38/13.30 (breln1all1) =>
% 98.38/13.30 ((
% 98.38/13.30 (subbreln1) =>
% 98.38/13.30 ((
% 98.38/13.30 (eqbreln1) =>
% 98.38/13.30 ((
% 98.38/13.30 (breln1invprop) =>
% 98.38/13.30 ((
% 98.38/13.30 (breln1invI) =>
% 98.38/13.30 ((
% 98.38/13.30 (breln1invE) =>
% 98.38/13.30 ((
% 98.38/13.30 (breln1compprop) =>
% 98.38/13.30 ((
% 98.38/13.30 (breln1compI) =>
% 98.38/13.30 ((
% 98.38/13.30 (breln1compE) =>
% 98.38/13.30 ((
% 98.38/13.30 (breln1compEex) =>
% 98.38/13.30 ((
% 98.38/13.30 (breln1unionprop) =>
% 98.38/13.30 ((
% 98.38/13.30 (breln1unionIL) =>
% 98.38/13.30 ((
% 98.38/13.30 (breln1unionIR) =>
% 98.38/13.30 ((
% 98.38/13.30 (breln1unionI) =>
% 98.38/13.30 ((
% 98.38/13.30 (breln1unionE) =>
% 98.38/13.30 ((
% 98.38/13.30 (breln1unionEcases) =>
% 98.38/13.30 ((
% 98.38/13.30 (breln1unionCommutes) =>
% 98.38/13.30 ((
% 98.38/13.30 (woz2Ex) =>
% 98.38/13.30 ((
% 98.38/13.30 (woz2W) =>
% 98.38/13.30 ((
% 98.38/13.30 (woz2A) =>
% 98.38/13.30 ((
% 98.38/13.30 (woz2B) =>
% 98.38/13.30 ((
% 98.38/13.30 (image1Ex) =>
% 98.38/13.30 ((
% 98.38/13.30 (image1Ex1) =>
% 98.38/13.30 ((
% 98.38/13.30 (image1Equiv) =>
% 98.38/13.30 ((
% 98.38/13.30 (image1E) =>
% 98.38/13.30 ((
% 98.38/13.30 (image1I) =>
% 98.38/13.30 ((
% 98.38/13.30 (injFuncInInjFuncSet) =>
% 98.38/13.30 ((
% 98.38/13.30 (injFuncSetFuncIn) =>
% 98.38/13.30 ((
% 98.38/13.30 (injFuncSetFuncInj) =>
% 98.38/13.30 ((
% 98.38/13.30 (surjFuncSetFuncIn) =>
% 98.38/13.30 ((
% 98.38/13.30 (surjFuncSetFuncSurj) =>
% 98.38/13.30 ((
% 98.38/13.30 (leftInvIsSurj) =>
% 98.38/13.30 ((
% 98.38/13.30 (surjCantorThm) =>
% 98.38/13.30 ((
% 98.38/13.30 (foundation2) =>
% 98.38/13.30 ((
% 98.38/13.30 (notinself) =>
% 98.38/13.30 ((
% 98.38/13.30 (notinself2) =>
% 98.38/13.30 ((
% 98.38/13.30 (omegaSp) =>
% 98.38/13.30 ((
% 98.38/13.30 (omegaSclos) =>
% 98.38/13.30 ((
% 98.38/13.30 (peano0notS) =>
% 98.38/13.30 ((
% 98.38/13.30 (!!) @ (
% 98.38/13.30 (('#S') @ (
% 98.38/13.30 (
% 98.38/13.30 ('#B') @ (
% 98.38/13.30 =>) @
% 98.38/13.30 (
% 98.38/13.30 (
% 98.38/13.30 ('#C') @ in @
% 98.38/13.30 omega)))) @
% 98.38/13.30 (
% 98.38/13.30 (
% 98.38/13.30 ('#B') @ (
% 98.38/13.30 !!) @
% 98.38/13.30 (
% 98.38/13.30 (
% 98.38/13.30 ('#B') @ (
% 98.38/13.30 (
% 98.38/13.30 ('#S') @ (
% 98.38/13.30 (
% 98.38/13.30 ('#B') @ (
% 98.38/13.30 =>) @
% 98.38/13.30 (
% 98.38/13.30 (
% 98.38/13.30 ('#C') @ in @
% 98.38/13.30 omega)))))) @
% 98.38/13.30 (
% 98.38/13.30 (
% 98.38/13.30 ('#S') @ (
% 98.38/13.30 (
% 98.38/13.30 ('#B') @ (
% 98.38/13.30 '#S') @
% 98.38/13.30 (
% 98.38/13.30 (
% 98.38/13.30 ('#B') @ (
% 98.38/13.30 (
% 98.38/13.30 ('#B') @ (
% 98.38/13.30 =>))) @
% 98.38/13.30 (
% 98.38/13.30 (
% 98.38/13.30 ('#C') @ (
% 98.38/13.30 (
% 98.38/13.30 ('#B') @ (
% 98.38/13.30 '#B') @
% 98.38/13.30 (
% 98.38/13.30 (
% 98.38/13.30 ('#B') @ (
% 98.38/13.30 =) @
% 98.38/13.30 omegaS)))) @
% 98.38/13.30 omegaS)))))) @
% 98.38/13.30 (
% 98.38/13.30 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.38/13.30 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1874])).
% 98.38/13.30 thf(zip_derived_cl1893, plain,
% 98.38/13.30 (~ (((dpsetconstrEL1) =>
% 98.38/13.30 (((dpsetconstrEL2) =>
% 98.38/13.30 (((dpsetconstrER) =>
% 98.38/13.30 (((funcImageSingleton) =>
% 98.38/13.30 (((apProp) =>
% 98.38/13.30 (((app) =>
% 98.38/13.30 (((infuncsetfunc) =>
% 98.38/13.30 (((ap2p) =>
% 98.38/13.30 (((funcinfuncset) =>
% 98.38/13.30 (((lamProp) =>
% 98.38/13.30 (((lamp) =>
% 98.38/13.30 (((lam2p) =>
% 98.38/13.30 (((brelnall1) =>
% 98.38/13.30 (((brelnall2) =>
% 98.38/13.30 (((ex1E2) =>
% 98.38/13.30 (((funcGraphProp1) =>
% 98.38/13.30 (((funcGraphProp3) =>
% 98.38/13.30 (((funcGraphProp2) =>
% 98.38/13.30 (((funcextLem) =>
% 98.38/13.30 (((funcGraphProp4) =>
% 98.38/13.30 (((subbreln) =>
% 98.38/13.30 (((eqbreln) =>
% 98.38/13.30 (((funcext) =>
% 98.38/13.30 (((funcext2) =>
% 98.38/13.30 (((ap2apEq1) =>
% 98.38/13.30 (((ap2apEq2) =>
% 98.38/13.30 (((beta1) =>
% 98.38/13.30 (((eta1) =>
% 98.38/13.30 (((lam2lamEq) =>
% 98.38/13.30 (((beta2) =>
% 98.38/13.30 ((
% 98.38/13.30 (eta2) =>
% 98.38/13.30 ((
% 98.38/13.30 (iffalseProp1) =>
% 98.38/13.30 ((
% 98.38/13.30 (iffalseProp2) =>
% 98.38/13.30 ((
% 98.38/13.30 (iftrueProp1) =>
% 98.38/13.30 ((
% 98.38/13.30 (iftrueProp2) =>
% 98.38/13.30 ((
% 98.38/13.30 (ifSingleton) =>
% 98.38/13.30 ((
% 98.38/13.30 (ifp) =>
% 98.38/13.30 ((
% 98.38/13.30 (theeq) =>
% 98.38/13.30 ((
% 98.38/13.30 (iftrue) =>
% 98.38/13.30 ((
% 98.38/13.30 (iffalse) =>
% 98.38/13.30 ((
% 98.38/13.30 (iftrueorfalse) =>
% 98.38/13.30 ((
% 98.38/13.30 (binintersectT_lem) =>
% 98.38/13.30 ((
% 98.38/13.30 (binunionT_lem) =>
% 98.38/13.30 ((
% 98.38/13.30 (powersetT_lem) =>
% 98.38/13.30 ((
% 98.38/13.30 (setminusT_lem) =>
% 98.38/13.30 ((
% 98.38/13.30 (complementT_lem) =>
% 98.38/13.30 ((
% 98.38/13.30 (setextT) =>
% 98.38/13.30 ((
% 98.38/13.30 (subsetTI) =>
% 98.38/13.30 ((
% 98.38/13.30 (powersetTI1) =>
% 98.38/13.30 ((
% 98.38/13.30 (powersetTE1) =>
% 98.38/13.30 ((
% 98.38/13.30 (complementTI1) =>
% 98.38/13.30 ((
% 98.38/13.30 (complementTE1) =>
% 98.38/13.30 ((
% 98.38/13.30 (binintersectTELcontra) =>
% 98.38/13.30 ((
% 98.38/13.30 (binintersectTERcontra) =>
% 98.38/13.30 ((
% 98.38/13.30 (contrasubsetT) =>
% 98.38/13.30 ((
% 98.38/13.30 (contrasubsetT1) =>
% 98.38/13.30 ((
% 98.38/13.30 (contrasubsetT2) =>
% 98.38/13.30 ((
% 98.38/13.30 (contrasubsetT3) =>
% 98.38/13.30 ((
% 98.38/13.30 (doubleComplementI1) =>
% 98.38/13.30 ((
% 98.38/13.30 (doubleComplementE1) =>
% 98.38/13.30 ((
% 98.38/13.30 (doubleComplementSub1) =>
% 98.38/13.30 ((
% 98.38/13.30 (doubleComplementSub2) =>
% 98.38/13.30 ((
% 98.38/13.30 (doubleComplementEq) =>
% 98.38/13.30 ((
% 98.38/13.30 (complementTnotintersectT) =>
% 98.38/13.30 ((
% 98.38/13.30 (complementImpComplementIntersect) =>
% 98.38/13.30 ((
% 98.38/13.30 (complementSubsetComplementIntersect) =>
% 98.38/13.30 ((
% 98.38/13.30 (complementInPowersetComplementIntersect) =>
% 98.38/13.30 ((
% 98.38/13.30 (contraSubsetComplement) =>
% 98.38/13.30 ((
% 98.38/13.30 (complementTcontraSubset) =>
% 98.38/13.30 ((
% 98.38/13.30 (binunionTILcontra) =>
% 98.38/13.30 ((
% 98.38/13.30 (binunionTIRcontra) =>
% 98.38/13.30 ((
% 98.38/13.30 (inIntersectImpInUnion) =>
% 98.38/13.30 ((
% 98.38/13.30 (inIntersectImpInUnion2) =>
% 98.38/13.30 ((
% 98.38/13.30 (inIntersectImpInIntersectUnions) =>
% 98.38/13.30 ((
% 98.38/13.30 (intersectInPowersetIntersectUnions) =>
% 98.38/13.30 ((
% 98.38/13.30 (inComplementUnionImpNotIn1) =>
% 98.38/13.30 ((
% 98.38/13.30 (inComplementUnionImpInComplement1) =>
% 98.38/13.30 ((
% 98.38/13.30 (binunionTE) =>
% 98.38/13.30 ((
% 98.38/13.30 (binunionTEcontra) =>
% 98.38/13.30 ((
% 98.38/13.30 (demorgan2a1) =>
% 98.38/13.30 ((
% 98.38/13.30 (complementUnionInPowersetComplement) =>
% 98.38/13.30 ((
% 98.38/13.30 (demorgan2a2) =>
% 98.38/13.30 ((
% 98.38/13.30 (demorgan1a) =>
% 98.38/13.30 ((
% 98.38/13.30 (demorgan1b) =>
% 98.38/13.30 ((
% 98.38/13.30 (demorgan1) =>
% 98.38/13.30 ((
% 98.38/13.30 (demorgan2a) =>
% 98.38/13.30 ((
% 98.38/13.30 (demorgan2b2) =>
% 98.38/13.30 ((
% 98.38/13.30 (demorgan2b) =>
% 98.38/13.30 ((
% 98.38/13.30 (demorgan2) =>
% 98.38/13.30 ((
% 98.38/13.30 (woz13rule0) =>
% 98.38/13.30 ((
% 98.38/13.30 (woz13rule1) =>
% 98.38/13.30 ((
% 98.38/13.30 (woz13rule2) =>
% 98.38/13.30 ((
% 98.38/13.30 (woz13rule3) =>
% 98.38/13.30 ((
% 98.38/13.30 (woz13rule4) =>
% 98.38/13.30 ((
% 98.38/13.30 (woz1_1) =>
% 98.38/13.30 ((
% 98.38/13.30 (woz1_2) =>
% 98.38/13.30 ((
% 98.38/13.30 (woz1_3) =>
% 98.38/13.30 ((
% 98.38/13.30 (woz1_4) =>
% 98.38/13.30 ((
% 98.38/13.30 (woz1_5) =>
% 98.38/13.30 ((
% 98.38/13.30 (breln1all2) =>
% 98.38/13.30 ((
% 98.38/13.30 (breln1SetBreln1) =>
% 98.38/13.30 ((
% 98.38/13.30 (choice2fnsingleton) =>
% 98.38/13.30 ((
% 98.38/13.30 (setOfPairsIsBReln1) =>
% 98.38/13.30 ((
% 98.38/13.30 (breln1all1) =>
% 98.38/13.30 ((
% 98.38/13.30 (subbreln1) =>
% 98.38/13.30 ((
% 98.38/13.30 (eqbreln1) =>
% 98.38/13.30 ((
% 98.38/13.30 (breln1invprop) =>
% 98.38/13.30 ((
% 98.38/13.30 (breln1invI) =>
% 98.38/13.30 ((
% 98.38/13.30 (breln1invE) =>
% 98.38/13.30 ((
% 98.38/13.30 (breln1compprop) =>
% 98.38/13.30 ((
% 98.38/13.30 (breln1compI) =>
% 98.38/13.30 ((
% 98.38/13.30 (breln1compE) =>
% 98.38/13.30 ((
% 98.38/13.30 (breln1compEex) =>
% 98.38/13.30 ((
% 98.38/13.30 (breln1unionprop) =>
% 98.38/13.30 ((
% 98.38/13.30 (breln1unionIL) =>
% 98.38/13.30 ((
% 98.38/13.30 (breln1unionIR) =>
% 98.38/13.30 ((
% 98.38/13.30 (breln1unionI) =>
% 98.38/13.30 ((
% 98.38/13.30 (breln1unionE) =>
% 98.38/13.30 ((
% 98.38/13.30 (breln1unionEcases) =>
% 98.38/13.30 ((
% 98.38/13.30 (breln1unionCommutes) =>
% 98.38/13.30 ((
% 98.38/13.30 (woz2Ex) =>
% 98.38/13.30 ((
% 98.38/13.30 (woz2W) =>
% 98.38/13.30 ((
% 98.38/13.30 (woz2A) =>
% 98.38/13.30 ((
% 98.38/13.30 (woz2B) =>
% 98.38/13.30 ((
% 98.38/13.30 (image1Ex) =>
% 98.38/13.30 ((
% 98.38/13.30 (image1Ex1) =>
% 98.38/13.30 ((
% 98.38/13.30 (image1Equiv) =>
% 98.38/13.30 ((
% 98.38/13.30 (image1E) =>
% 98.38/13.30 ((
% 98.38/13.30 (image1I) =>
% 98.38/13.30 ((
% 98.38/13.30 (injFuncInInjFuncSet) =>
% 98.38/13.30 ((
% 98.38/13.30 (injFuncSetFuncIn) =>
% 98.38/13.30 ((
% 98.38/13.30 (injFuncSetFuncInj) =>
% 98.38/13.30 ((
% 98.38/13.30 (surjFuncSetFuncIn) =>
% 98.38/13.30 ((
% 98.38/13.30 (surjFuncSetFuncSurj) =>
% 98.38/13.30 ((
% 98.38/13.30 (leftInvIsSurj) =>
% 98.38/13.30 ((
% 98.38/13.30 (surjCantorThm) =>
% 98.38/13.30 ((
% 98.38/13.30 (foundation2) =>
% 98.38/13.30 ((
% 98.38/13.30 (notinself) =>
% 98.38/13.30 ((
% 98.38/13.30 (notinself2) =>
% 98.38/13.30 ((
% 98.38/13.30 (omegaSp) =>
% 98.38/13.30 ((
% 98.38/13.30 (omegaSclos) =>
% 98.38/13.30 ((
% 98.38/13.30 (peano0notS) =>
% 98.38/13.30 ((
% 98.38/13.30 (!!) @ (
% 98.38/13.30 (('#S') @ (
% 98.38/13.30 (
% 98.38/13.30 ('#B') @ (
% 98.38/13.30 =>) @
% 98.38/13.30 (
% 98.38/13.30 (
% 98.38/13.30 ('#C') @ in @
% 98.38/13.30 omega)))) @
% 98.38/13.30 (
% 98.38/13.30 (
% 98.38/13.30 ('#B') @ (
% 98.38/13.30 !!) @
% 98.38/13.30 (
% 98.38/13.30 (
% 98.38/13.30 ('#B') @ (
% 98.38/13.30 (
% 98.38/13.30 ('#S') @ (
% 98.38/13.30 (
% 98.38/13.30 ('#B') @ (
% 98.38/13.30 =>) @
% 98.38/13.30 (
% 98.38/13.30 (
% 98.38/13.30 ('#C') @ in @
% 98.38/13.30 omega)))))) @
% 98.38/13.30 (
% 98.38/13.30 (
% 98.38/13.30 ('#S') @ (
% 98.38/13.30 (
% 98.38/13.30 ('#B') @ (
% 98.38/13.30 '#S') @
% 98.38/13.30 (
% 98.38/13.30 (
% 98.38/13.30 ('#B') @ (
% 98.38/13.30 (
% 98.38/13.30 ('#B') @ (
% 98.38/13.30 =>))) @
% 98.38/13.30 (
% 98.38/13.30 (
% 98.38/13.30 ('#C') @ (
% 98.38/13.30 (
% 98.38/13.30 ('#B') @ (
% 98.38/13.30 '#B') @
% 98.38/13.30 (
% 98.38/13.30 (
% 98.38/13.30 ('#B') @ (
% 98.38/13.30 =) @
% 98.38/13.30 omegaS)))) @
% 98.38/13.30 omegaS)))))) @
% 98.38/13.30 (
% 98.38/13.30 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.38/13.30 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1883])).
% 98.38/13.30 thf(zip_derived_cl1903, plain,
% 98.38/13.30 (~ (((dpsetconstrEL2) =>
% 98.38/13.30 (((dpsetconstrER) =>
% 98.38/13.30 (((funcImageSingleton) =>
% 98.38/13.30 (((apProp) =>
% 98.38/13.30 (((app) =>
% 98.38/13.30 (((infuncsetfunc) =>
% 98.38/13.30 (((ap2p) =>
% 98.38/13.30 (((funcinfuncset) =>
% 98.38/13.30 (((lamProp) =>
% 98.38/13.30 (((lamp) =>
% 98.38/13.30 (((lam2p) =>
% 98.38/13.30 (((brelnall1) =>
% 98.38/13.30 (((brelnall2) =>
% 98.38/13.30 (((ex1E2) =>
% 98.38/13.30 (((funcGraphProp1) =>
% 98.38/13.30 (((funcGraphProp3) =>
% 98.38/13.30 (((funcGraphProp2) =>
% 98.38/13.30 (((funcextLem) =>
% 98.38/13.30 (((funcGraphProp4) =>
% 98.38/13.30 (((subbreln) =>
% 98.38/13.30 (((eqbreln) =>
% 98.38/13.30 (((funcext) =>
% 98.38/13.30 (((funcext2) =>
% 98.38/13.30 (((ap2apEq1) =>
% 98.38/13.30 (((ap2apEq2) =>
% 98.38/13.30 (((beta1) =>
% 98.38/13.30 (((eta1) =>
% 98.38/13.30 (((lam2lamEq) =>
% 98.38/13.30 (((beta2) =>
% 98.38/13.30 (((eta2) =>
% 98.38/13.30 ((
% 98.38/13.30 (iffalseProp1) =>
% 98.38/13.30 ((
% 98.38/13.30 (iffalseProp2) =>
% 98.38/13.30 ((
% 98.38/13.30 (iftrueProp1) =>
% 98.38/13.30 ((
% 98.38/13.30 (iftrueProp2) =>
% 98.38/13.30 ((
% 98.38/13.30 (ifSingleton) =>
% 98.38/13.30 ((
% 98.38/13.30 (ifp) =>
% 98.38/13.30 ((
% 98.38/13.30 (theeq) =>
% 98.38/13.30 ((
% 98.38/13.30 (iftrue) =>
% 98.38/13.30 ((
% 98.38/13.30 (iffalse) =>
% 98.38/13.30 ((
% 98.38/13.30 (iftrueorfalse) =>
% 98.38/13.30 ((
% 98.38/13.30 (binintersectT_lem) =>
% 98.38/13.30 ((
% 98.38/13.30 (binunionT_lem) =>
% 98.38/13.30 ((
% 98.38/13.30 (powersetT_lem) =>
% 98.38/13.30 ((
% 98.38/13.30 (setminusT_lem) =>
% 98.38/13.30 ((
% 98.38/13.30 (complementT_lem) =>
% 98.38/13.30 ((
% 98.38/13.30 (setextT) =>
% 98.38/13.30 ((
% 98.38/13.30 (subsetTI) =>
% 98.38/13.30 ((
% 98.38/13.30 (powersetTI1) =>
% 98.38/13.30 ((
% 98.38/13.30 (powersetTE1) =>
% 98.38/13.30 ((
% 98.38/13.30 (complementTI1) =>
% 98.38/13.30 ((
% 98.38/13.30 (complementTE1) =>
% 98.38/13.30 ((
% 98.38/13.30 (binintersectTELcontra) =>
% 98.38/13.30 ((
% 98.38/13.30 (binintersectTERcontra) =>
% 98.38/13.30 ((
% 98.38/13.30 (contrasubsetT) =>
% 98.38/13.30 ((
% 98.38/13.30 (contrasubsetT1) =>
% 98.38/13.30 ((
% 98.38/13.30 (contrasubsetT2) =>
% 98.38/13.30 ((
% 98.38/13.30 (contrasubsetT3) =>
% 98.38/13.30 ((
% 98.38/13.30 (doubleComplementI1) =>
% 98.38/13.30 ((
% 98.38/13.30 (doubleComplementE1) =>
% 98.38/13.30 ((
% 98.38/13.30 (doubleComplementSub1) =>
% 98.38/13.30 ((
% 98.38/13.30 (doubleComplementSub2) =>
% 98.38/13.30 ((
% 98.38/13.30 (doubleComplementEq) =>
% 98.38/13.30 ((
% 98.38/13.30 (complementTnotintersectT) =>
% 98.38/13.30 ((
% 98.38/13.30 (complementImpComplementIntersect) =>
% 98.38/13.30 ((
% 98.38/13.30 (complementSubsetComplementIntersect) =>
% 98.38/13.30 ((
% 98.38/13.30 (complementInPowersetComplementIntersect) =>
% 98.38/13.30 ((
% 98.38/13.30 (contraSubsetComplement) =>
% 98.38/13.30 ((
% 98.38/13.30 (complementTcontraSubset) =>
% 98.38/13.30 ((
% 98.38/13.30 (binunionTILcontra) =>
% 98.38/13.30 ((
% 98.38/13.30 (binunionTIRcontra) =>
% 98.38/13.30 ((
% 98.38/13.30 (inIntersectImpInUnion) =>
% 98.38/13.30 ((
% 98.38/13.30 (inIntersectImpInUnion2) =>
% 98.38/13.30 ((
% 98.38/13.30 (inIntersectImpInIntersectUnions) =>
% 98.38/13.30 ((
% 98.38/13.30 (intersectInPowersetIntersectUnions) =>
% 98.38/13.30 ((
% 98.38/13.30 (inComplementUnionImpNotIn1) =>
% 98.38/13.30 ((
% 98.38/13.30 (inComplementUnionImpInComplement1) =>
% 98.38/13.30 ((
% 98.38/13.30 (binunionTE) =>
% 98.38/13.30 ((
% 98.38/13.30 (binunionTEcontra) =>
% 98.38/13.30 ((
% 98.38/13.30 (demorgan2a1) =>
% 98.38/13.30 ((
% 98.38/13.30 (complementUnionInPowersetComplement) =>
% 98.38/13.30 ((
% 98.38/13.30 (demorgan2a2) =>
% 98.38/13.30 ((
% 98.38/13.30 (demorgan1a) =>
% 98.38/13.30 ((
% 98.38/13.30 (demorgan1b) =>
% 98.38/13.30 ((
% 98.38/13.30 (demorgan1) =>
% 98.38/13.30 ((
% 98.38/13.30 (demorgan2a) =>
% 98.38/13.30 ((
% 98.38/13.30 (demorgan2b2) =>
% 98.38/13.30 ((
% 98.38/13.30 (demorgan2b) =>
% 98.38/13.30 ((
% 98.38/13.30 (demorgan2) =>
% 98.38/13.30 ((
% 98.38/13.30 (woz13rule0) =>
% 98.38/13.30 ((
% 98.38/13.30 (woz13rule1) =>
% 98.38/13.30 ((
% 98.38/13.30 (woz13rule2) =>
% 98.38/13.30 ((
% 98.38/13.30 (woz13rule3) =>
% 98.38/13.30 ((
% 98.38/13.30 (woz13rule4) =>
% 98.38/13.30 ((
% 98.38/13.30 (woz1_1) =>
% 98.38/13.30 ((
% 98.38/13.30 (woz1_2) =>
% 98.38/13.30 ((
% 98.38/13.30 (woz1_3) =>
% 98.38/13.30 ((
% 98.38/13.30 (woz1_4) =>
% 98.38/13.30 ((
% 98.38/13.30 (woz1_5) =>
% 98.38/13.30 ((
% 98.38/13.30 (breln1all2) =>
% 98.38/13.30 ((
% 98.38/13.30 (breln1SetBreln1) =>
% 98.38/13.30 ((
% 98.38/13.30 (choice2fnsingleton) =>
% 98.38/13.30 ((
% 98.38/13.30 (setOfPairsIsBReln1) =>
% 98.38/13.30 ((
% 98.38/13.30 (breln1all1) =>
% 98.38/13.30 ((
% 98.38/13.30 (subbreln1) =>
% 98.38/13.30 ((
% 98.38/13.30 (eqbreln1) =>
% 98.38/13.30 ((
% 98.38/13.30 (breln1invprop) =>
% 98.38/13.30 ((
% 98.38/13.30 (breln1invI) =>
% 98.38/13.30 ((
% 98.38/13.30 (breln1invE) =>
% 98.38/13.30 ((
% 98.38/13.30 (breln1compprop) =>
% 98.38/13.30 ((
% 98.38/13.30 (breln1compI) =>
% 98.38/13.30 ((
% 98.38/13.30 (breln1compE) =>
% 98.38/13.30 ((
% 98.38/13.30 (breln1compEex) =>
% 98.38/13.30 ((
% 98.38/13.30 (breln1unionprop) =>
% 98.38/13.30 ((
% 98.38/13.30 (breln1unionIL) =>
% 98.38/13.30 ((
% 98.38/13.30 (breln1unionIR) =>
% 98.38/13.30 ((
% 98.38/13.30 (breln1unionI) =>
% 98.38/13.30 ((
% 98.38/13.30 (breln1unionE) =>
% 98.38/13.30 ((
% 98.38/13.30 (breln1unionEcases) =>
% 98.38/13.30 ((
% 98.38/13.30 (breln1unionCommutes) =>
% 98.38/13.30 ((
% 98.38/13.30 (woz2Ex) =>
% 98.38/13.30 ((
% 98.38/13.30 (woz2W) =>
% 98.38/13.30 ((
% 98.38/13.30 (woz2A) =>
% 98.38/13.30 ((
% 98.38/13.30 (woz2B) =>
% 98.38/13.30 ((
% 98.38/13.30 (image1Ex) =>
% 98.38/13.30 ((
% 98.38/13.30 (image1Ex1) =>
% 98.38/13.30 ((
% 98.38/13.30 (image1Equiv) =>
% 98.38/13.30 ((
% 98.38/13.30 (image1E) =>
% 98.38/13.30 ((
% 98.38/13.30 (image1I) =>
% 98.38/13.30 ((
% 98.38/13.30 (injFuncInInjFuncSet) =>
% 98.38/13.30 ((
% 98.38/13.30 (injFuncSetFuncIn) =>
% 98.38/13.30 ((
% 98.38/13.30 (injFuncSetFuncInj) =>
% 98.38/13.30 ((
% 98.38/13.30 (surjFuncSetFuncIn) =>
% 98.38/13.30 ((
% 98.38/13.30 (surjFuncSetFuncSurj) =>
% 98.38/13.30 ((
% 98.38/13.30 (leftInvIsSurj) =>
% 98.38/13.30 ((
% 98.38/13.30 (surjCantorThm) =>
% 98.38/13.30 ((
% 98.38/13.30 (foundation2) =>
% 98.38/13.30 ((
% 98.38/13.30 (notinself) =>
% 98.38/13.30 ((
% 98.38/13.30 (notinself2) =>
% 98.38/13.30 ((
% 98.38/13.30 (omegaSp) =>
% 98.38/13.30 ((
% 98.38/13.30 (omegaSclos) =>
% 98.38/13.30 ((
% 98.38/13.30 (peano0notS) =>
% 98.38/13.30 ((
% 98.38/13.30 (!!) @ (
% 98.38/13.30 (('#S') @ (
% 98.38/13.30 (
% 98.38/13.30 ('#B') @ (
% 98.38/13.30 =>) @
% 98.38/13.30 (
% 98.38/13.30 (
% 98.38/13.30 ('#C') @ in @
% 98.38/13.30 omega)))) @
% 98.38/13.30 (
% 98.38/13.30 (
% 98.38/13.30 ('#B') @ (
% 98.38/13.30 !!) @
% 98.38/13.30 (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#S') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 =>) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#C') @ in @
% 98.38/13.31 omega)))))) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#S') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 '#S') @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 =>))) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#C') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 '#B') @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 =) @
% 98.38/13.31 omegaS)))) @
% 98.38/13.31 omegaS)))))) @
% 98.38/13.31 (
% 98.38/13.31 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.38/13.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1893])).
% 98.38/13.31 thf(zip_derived_cl1914, plain,
% 98.38/13.31 (~ (((dpsetconstrER) =>
% 98.38/13.31 (((funcImageSingleton) =>
% 98.38/13.31 (((apProp) =>
% 98.38/13.31 (((app) =>
% 98.38/13.31 (((infuncsetfunc) =>
% 98.38/13.31 (((ap2p) =>
% 98.38/13.31 (((funcinfuncset) =>
% 98.38/13.31 (((lamProp) =>
% 98.38/13.31 (((lamp) =>
% 98.38/13.31 (((lam2p) =>
% 98.38/13.31 (((brelnall1) =>
% 98.38/13.31 (((brelnall2) =>
% 98.38/13.31 (((ex1E2) =>
% 98.38/13.31 (((funcGraphProp1) =>
% 98.38/13.31 (((funcGraphProp3) =>
% 98.38/13.31 (((funcGraphProp2) =>
% 98.38/13.31 (((funcextLem) =>
% 98.38/13.31 (((funcGraphProp4) =>
% 98.38/13.31 (((subbreln) =>
% 98.38/13.31 (((eqbreln) =>
% 98.38/13.31 (((funcext) =>
% 98.38/13.31 (((funcext2) =>
% 98.38/13.31 (((ap2apEq1) =>
% 98.38/13.31 (((ap2apEq2) =>
% 98.38/13.31 (((beta1) =>
% 98.38/13.31 (((eta1) =>
% 98.38/13.31 (((lam2lamEq) =>
% 98.38/13.31 (((beta2) =>
% 98.38/13.31 (((eta2) =>
% 98.38/13.31 (((iffalseProp1) =>
% 98.38/13.31 ((
% 98.38/13.31 (iffalseProp2) =>
% 98.38/13.31 ((
% 98.38/13.31 (iftrueProp1) =>
% 98.38/13.31 ((
% 98.38/13.31 (iftrueProp2) =>
% 98.38/13.31 ((
% 98.38/13.31 (ifSingleton) =>
% 98.38/13.31 ((
% 98.38/13.31 (ifp) =>
% 98.38/13.31 ((
% 98.38/13.31 (theeq) =>
% 98.38/13.31 ((
% 98.38/13.31 (iftrue) =>
% 98.38/13.31 ((
% 98.38/13.31 (iffalse) =>
% 98.38/13.31 ((
% 98.38/13.31 (iftrueorfalse) =>
% 98.38/13.31 ((
% 98.38/13.31 (binintersectT_lem) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionT_lem) =>
% 98.38/13.31 ((
% 98.38/13.31 (powersetT_lem) =>
% 98.38/13.31 ((
% 98.38/13.31 (setminusT_lem) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementT_lem) =>
% 98.38/13.31 ((
% 98.38/13.31 (setextT) =>
% 98.38/13.31 ((
% 98.38/13.31 (subsetTI) =>
% 98.38/13.31 ((
% 98.38/13.31 (powersetTI1) =>
% 98.38/13.31 ((
% 98.38/13.31 (powersetTE1) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementTI1) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementTE1) =>
% 98.38/13.31 ((
% 98.38/13.31 (binintersectTELcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (binintersectTERcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (contrasubsetT) =>
% 98.38/13.31 ((
% 98.38/13.31 (contrasubsetT1) =>
% 98.38/13.31 ((
% 98.38/13.31 (contrasubsetT2) =>
% 98.38/13.31 ((
% 98.38/13.31 (contrasubsetT3) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementI1) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementE1) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementSub1) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementSub2) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementEq) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementTnotintersectT) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementImpComplementIntersect) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementSubsetComplementIntersect) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementInPowersetComplementIntersect) =>
% 98.38/13.31 ((
% 98.38/13.31 (contraSubsetComplement) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementTcontraSubset) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionTILcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionTIRcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (inIntersectImpInUnion) =>
% 98.38/13.31 ((
% 98.38/13.31 (inIntersectImpInUnion2) =>
% 98.38/13.31 ((
% 98.38/13.31 (inIntersectImpInIntersectUnions) =>
% 98.38/13.31 ((
% 98.38/13.31 (intersectInPowersetIntersectUnions) =>
% 98.38/13.31 ((
% 98.38/13.31 (inComplementUnionImpNotIn1) =>
% 98.38/13.31 ((
% 98.38/13.31 (inComplementUnionImpInComplement1) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionTE) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionTEcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2a1) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementUnionInPowersetComplement) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2a2) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan1a) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan1b) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan1) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2a) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2b2) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2b) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule0) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule1) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule2) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule3) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule4) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_1) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_2) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_3) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_4) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_5) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1all2) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1SetBreln1) =>
% 98.38/13.31 ((
% 98.38/13.31 (choice2fnsingleton) =>
% 98.38/13.31 ((
% 98.38/13.31 (setOfPairsIsBReln1) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1all1) =>
% 98.38/13.31 ((
% 98.38/13.31 (subbreln1) =>
% 98.38/13.31 ((
% 98.38/13.31 (eqbreln1) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1invprop) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1invI) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1invE) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1compprop) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1compI) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1compE) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1compEex) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionprop) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionIL) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionIR) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionI) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionE) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionEcases) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionCommutes) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz2Ex) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz2W) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz2A) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz2B) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1Ex) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1Ex1) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1Equiv) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1E) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1I) =>
% 98.38/13.31 ((
% 98.38/13.31 (injFuncInInjFuncSet) =>
% 98.38/13.31 ((
% 98.38/13.31 (injFuncSetFuncIn) =>
% 98.38/13.31 ((
% 98.38/13.31 (injFuncSetFuncInj) =>
% 98.38/13.31 ((
% 98.38/13.31 (surjFuncSetFuncIn) =>
% 98.38/13.31 ((
% 98.38/13.31 (surjFuncSetFuncSurj) =>
% 98.38/13.31 ((
% 98.38/13.31 (leftInvIsSurj) =>
% 98.38/13.31 ((
% 98.38/13.31 (surjCantorThm) =>
% 98.38/13.31 ((
% 98.38/13.31 (foundation2) =>
% 98.38/13.31 ((
% 98.38/13.31 (notinself) =>
% 98.38/13.31 ((
% 98.38/13.31 (notinself2) =>
% 98.38/13.31 ((
% 98.38/13.31 (omegaSp) =>
% 98.38/13.31 ((
% 98.38/13.31 (omegaSclos) =>
% 98.38/13.31 ((
% 98.38/13.31 (peano0notS) =>
% 98.38/13.31 ((
% 98.38/13.31 (!!) @ (
% 98.38/13.31 (('#S') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 =>) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#C') @ in @
% 98.38/13.31 omega)))) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 !!) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#S') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 =>) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#C') @ in @
% 98.38/13.31 omega)))))) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#S') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 '#S') @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 =>))) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#C') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 '#B') @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 =) @
% 98.38/13.31 omegaS)))) @
% 98.38/13.31 omegaS)))))) @
% 98.38/13.31 (
% 98.38/13.31 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.38/13.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1903])).
% 98.38/13.31 thf(zip_derived_cl1923, plain,
% 98.38/13.31 (~ (((funcImageSingleton) =>
% 98.38/13.31 (((apProp) =>
% 98.38/13.31 (((app) =>
% 98.38/13.31 (((infuncsetfunc) =>
% 98.38/13.31 (((ap2p) =>
% 98.38/13.31 (((funcinfuncset) =>
% 98.38/13.31 (((lamProp) =>
% 98.38/13.31 (((lamp) =>
% 98.38/13.31 (((lam2p) =>
% 98.38/13.31 (((brelnall1) =>
% 98.38/13.31 (((brelnall2) =>
% 98.38/13.31 (((ex1E2) =>
% 98.38/13.31 (((funcGraphProp1) =>
% 98.38/13.31 (((funcGraphProp3) =>
% 98.38/13.31 (((funcGraphProp2) =>
% 98.38/13.31 (((funcextLem) =>
% 98.38/13.31 (((funcGraphProp4) =>
% 98.38/13.31 (((subbreln) =>
% 98.38/13.31 (((eqbreln) =>
% 98.38/13.31 (((funcext) =>
% 98.38/13.31 (((funcext2) =>
% 98.38/13.31 (((ap2apEq1) =>
% 98.38/13.31 (((ap2apEq2) =>
% 98.38/13.31 (((beta1) =>
% 98.38/13.31 (((eta1) =>
% 98.38/13.31 (((lam2lamEq) =>
% 98.38/13.31 (((beta2) =>
% 98.38/13.31 (((eta2) =>
% 98.38/13.31 (((iffalseProp1) =>
% 98.38/13.31 (((iffalseProp2) =>
% 98.38/13.31 ((
% 98.38/13.31 (iftrueProp1) =>
% 98.38/13.31 ((
% 98.38/13.31 (iftrueProp2) =>
% 98.38/13.31 ((
% 98.38/13.31 (ifSingleton) =>
% 98.38/13.31 ((
% 98.38/13.31 (ifp) =>
% 98.38/13.31 ((
% 98.38/13.31 (theeq) =>
% 98.38/13.31 ((
% 98.38/13.31 (iftrue) =>
% 98.38/13.31 ((
% 98.38/13.31 (iffalse) =>
% 98.38/13.31 ((
% 98.38/13.31 (iftrueorfalse) =>
% 98.38/13.31 ((
% 98.38/13.31 (binintersectT_lem) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionT_lem) =>
% 98.38/13.31 ((
% 98.38/13.31 (powersetT_lem) =>
% 98.38/13.31 ((
% 98.38/13.31 (setminusT_lem) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementT_lem) =>
% 98.38/13.31 ((
% 98.38/13.31 (setextT) =>
% 98.38/13.31 ((
% 98.38/13.31 (subsetTI) =>
% 98.38/13.31 ((
% 98.38/13.31 (powersetTI1) =>
% 98.38/13.31 ((
% 98.38/13.31 (powersetTE1) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementTI1) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementTE1) =>
% 98.38/13.31 ((
% 98.38/13.31 (binintersectTELcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (binintersectTERcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (contrasubsetT) =>
% 98.38/13.31 ((
% 98.38/13.31 (contrasubsetT1) =>
% 98.38/13.31 ((
% 98.38/13.31 (contrasubsetT2) =>
% 98.38/13.31 ((
% 98.38/13.31 (contrasubsetT3) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementI1) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementE1) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementSub1) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementSub2) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementEq) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementTnotintersectT) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementImpComplementIntersect) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementSubsetComplementIntersect) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementInPowersetComplementIntersect) =>
% 98.38/13.31 ((
% 98.38/13.31 (contraSubsetComplement) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementTcontraSubset) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionTILcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionTIRcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (inIntersectImpInUnion) =>
% 98.38/13.31 ((
% 98.38/13.31 (inIntersectImpInUnion2) =>
% 98.38/13.31 ((
% 98.38/13.31 (inIntersectImpInIntersectUnions) =>
% 98.38/13.31 ((
% 98.38/13.31 (intersectInPowersetIntersectUnions) =>
% 98.38/13.31 ((
% 98.38/13.31 (inComplementUnionImpNotIn1) =>
% 98.38/13.31 ((
% 98.38/13.31 (inComplementUnionImpInComplement1) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionTE) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionTEcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2a1) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementUnionInPowersetComplement) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2a2) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan1a) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan1b) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan1) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2a) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2b2) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2b) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule0) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule1) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule2) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule3) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule4) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_1) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_2) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_3) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_4) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_5) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1all2) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1SetBreln1) =>
% 98.38/13.31 ((
% 98.38/13.31 (choice2fnsingleton) =>
% 98.38/13.31 ((
% 98.38/13.31 (setOfPairsIsBReln1) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1all1) =>
% 98.38/13.31 ((
% 98.38/13.31 (subbreln1) =>
% 98.38/13.31 ((
% 98.38/13.31 (eqbreln1) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1invprop) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1invI) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1invE) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1compprop) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1compI) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1compE) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1compEex) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionprop) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionIL) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionIR) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionI) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionE) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionEcases) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionCommutes) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz2Ex) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz2W) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz2A) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz2B) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1Ex) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1Ex1) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1Equiv) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1E) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1I) =>
% 98.38/13.31 ((
% 98.38/13.31 (injFuncInInjFuncSet) =>
% 98.38/13.31 ((
% 98.38/13.31 (injFuncSetFuncIn) =>
% 98.38/13.31 ((
% 98.38/13.31 (injFuncSetFuncInj) =>
% 98.38/13.31 ((
% 98.38/13.31 (surjFuncSetFuncIn) =>
% 98.38/13.31 ((
% 98.38/13.31 (surjFuncSetFuncSurj) =>
% 98.38/13.31 ((
% 98.38/13.31 (leftInvIsSurj) =>
% 98.38/13.31 ((
% 98.38/13.31 (surjCantorThm) =>
% 98.38/13.31 ((
% 98.38/13.31 (foundation2) =>
% 98.38/13.31 ((
% 98.38/13.31 (notinself) =>
% 98.38/13.31 ((
% 98.38/13.31 (notinself2) =>
% 98.38/13.31 ((
% 98.38/13.31 (omegaSp) =>
% 98.38/13.31 ((
% 98.38/13.31 (omegaSclos) =>
% 98.38/13.31 ((
% 98.38/13.31 (peano0notS) =>
% 98.38/13.31 ((
% 98.38/13.31 (!!) @ (
% 98.38/13.31 (('#S') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 =>) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#C') @ in @
% 98.38/13.31 omega)))) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 !!) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#S') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 =>) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#C') @ in @
% 98.38/13.31 omega)))))) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#S') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 '#S') @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 =>))) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#C') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 '#B') @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 =) @
% 98.38/13.31 omegaS)))) @
% 98.38/13.31 omegaS)))))) @
% 98.38/13.31 (
% 98.38/13.31 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.38/13.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1914])).
% 98.38/13.31 thf(zip_derived_cl1931, plain,
% 98.38/13.31 (~ (((apProp) =>
% 98.38/13.31 (((app) =>
% 98.38/13.31 (((infuncsetfunc) =>
% 98.38/13.31 (((ap2p) =>
% 98.38/13.31 (((funcinfuncset) =>
% 98.38/13.31 (((lamProp) =>
% 98.38/13.31 (((lamp) =>
% 98.38/13.31 (((lam2p) =>
% 98.38/13.31 (((brelnall1) =>
% 98.38/13.31 (((brelnall2) =>
% 98.38/13.31 (((ex1E2) =>
% 98.38/13.31 (((funcGraphProp1) =>
% 98.38/13.31 (((funcGraphProp3) =>
% 98.38/13.31 (((funcGraphProp2) =>
% 98.38/13.31 (((funcextLem) =>
% 98.38/13.31 (((funcGraphProp4) =>
% 98.38/13.31 (((subbreln) =>
% 98.38/13.31 (((eqbreln) =>
% 98.38/13.31 (((funcext) =>
% 98.38/13.31 (((funcext2) =>
% 98.38/13.31 (((ap2apEq1) =>
% 98.38/13.31 (((ap2apEq2) =>
% 98.38/13.31 (((beta1) =>
% 98.38/13.31 (((eta1) =>
% 98.38/13.31 (((lam2lamEq) =>
% 98.38/13.31 (((beta2) =>
% 98.38/13.31 (((eta2) =>
% 98.38/13.31 (((iffalseProp1) =>
% 98.38/13.31 (((iffalseProp2) =>
% 98.38/13.31 (((iftrueProp1) =>
% 98.38/13.31 ((
% 98.38/13.31 (iftrueProp2) =>
% 98.38/13.31 ((
% 98.38/13.31 (ifSingleton) =>
% 98.38/13.31 ((
% 98.38/13.31 (ifp) =>
% 98.38/13.31 ((
% 98.38/13.31 (theeq) =>
% 98.38/13.31 ((
% 98.38/13.31 (iftrue) =>
% 98.38/13.31 ((
% 98.38/13.31 (iffalse) =>
% 98.38/13.31 ((
% 98.38/13.31 (iftrueorfalse) =>
% 98.38/13.31 ((
% 98.38/13.31 (binintersectT_lem) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionT_lem) =>
% 98.38/13.31 ((
% 98.38/13.31 (powersetT_lem) =>
% 98.38/13.31 ((
% 98.38/13.31 (setminusT_lem) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementT_lem) =>
% 98.38/13.31 ((
% 98.38/13.31 (setextT) =>
% 98.38/13.31 ((
% 98.38/13.31 (subsetTI) =>
% 98.38/13.31 ((
% 98.38/13.31 (powersetTI1) =>
% 98.38/13.31 ((
% 98.38/13.31 (powersetTE1) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementTI1) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementTE1) =>
% 98.38/13.31 ((
% 98.38/13.31 (binintersectTELcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (binintersectTERcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (contrasubsetT) =>
% 98.38/13.31 ((
% 98.38/13.31 (contrasubsetT1) =>
% 98.38/13.31 ((
% 98.38/13.31 (contrasubsetT2) =>
% 98.38/13.31 ((
% 98.38/13.31 (contrasubsetT3) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementI1) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementE1) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementSub1) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementSub2) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementEq) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementTnotintersectT) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementImpComplementIntersect) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementSubsetComplementIntersect) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementInPowersetComplementIntersect) =>
% 98.38/13.31 ((
% 98.38/13.31 (contraSubsetComplement) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementTcontraSubset) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionTILcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionTIRcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (inIntersectImpInUnion) =>
% 98.38/13.31 ((
% 98.38/13.31 (inIntersectImpInUnion2) =>
% 98.38/13.31 ((
% 98.38/13.31 (inIntersectImpInIntersectUnions) =>
% 98.38/13.31 ((
% 98.38/13.31 (intersectInPowersetIntersectUnions) =>
% 98.38/13.31 ((
% 98.38/13.31 (inComplementUnionImpNotIn1) =>
% 98.38/13.31 ((
% 98.38/13.31 (inComplementUnionImpInComplement1) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionTE) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionTEcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2a1) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementUnionInPowersetComplement) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2a2) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan1a) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan1b) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan1) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2a) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2b2) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2b) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule0) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule1) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule2) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule3) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule4) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_1) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_2) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_3) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_4) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_5) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1all2) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1SetBreln1) =>
% 98.38/13.31 ((
% 98.38/13.31 (choice2fnsingleton) =>
% 98.38/13.31 ((
% 98.38/13.31 (setOfPairsIsBReln1) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1all1) =>
% 98.38/13.31 ((
% 98.38/13.31 (subbreln1) =>
% 98.38/13.31 ((
% 98.38/13.31 (eqbreln1) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1invprop) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1invI) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1invE) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1compprop) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1compI) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1compE) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1compEex) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionprop) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionIL) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionIR) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionI) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionE) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionEcases) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionCommutes) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz2Ex) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz2W) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz2A) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz2B) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1Ex) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1Ex1) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1Equiv) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1E) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1I) =>
% 98.38/13.31 ((
% 98.38/13.31 (injFuncInInjFuncSet) =>
% 98.38/13.31 ((
% 98.38/13.31 (injFuncSetFuncIn) =>
% 98.38/13.31 ((
% 98.38/13.31 (injFuncSetFuncInj) =>
% 98.38/13.31 ((
% 98.38/13.31 (surjFuncSetFuncIn) =>
% 98.38/13.31 ((
% 98.38/13.31 (surjFuncSetFuncSurj) =>
% 98.38/13.31 ((
% 98.38/13.31 (leftInvIsSurj) =>
% 98.38/13.31 ((
% 98.38/13.31 (surjCantorThm) =>
% 98.38/13.31 ((
% 98.38/13.31 (foundation2) =>
% 98.38/13.31 ((
% 98.38/13.31 (notinself) =>
% 98.38/13.31 ((
% 98.38/13.31 (notinself2) =>
% 98.38/13.31 ((
% 98.38/13.31 (omegaSp) =>
% 98.38/13.31 ((
% 98.38/13.31 (omegaSclos) =>
% 98.38/13.31 ((
% 98.38/13.31 (peano0notS) =>
% 98.38/13.31 ((
% 98.38/13.31 (!!) @ (
% 98.38/13.31 (('#S') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 =>) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#C') @ in @
% 98.38/13.31 omega)))) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 !!) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#S') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 =>) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#C') @ in @
% 98.38/13.31 omega)))))) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#S') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 '#S') @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 =>))) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#C') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 '#B') @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 =) @
% 98.38/13.31 omegaS)))) @
% 98.38/13.31 omegaS)))))) @
% 98.38/13.31 (
% 98.38/13.31 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.38/13.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1923])).
% 98.38/13.31 thf(zip_derived_cl1940, plain,
% 98.38/13.31 (~ (((app) =>
% 98.38/13.31 (((infuncsetfunc) =>
% 98.38/13.31 (((ap2p) =>
% 98.38/13.31 (((funcinfuncset) =>
% 98.38/13.31 (((lamProp) =>
% 98.38/13.31 (((lamp) =>
% 98.38/13.31 (((lam2p) =>
% 98.38/13.31 (((brelnall1) =>
% 98.38/13.31 (((brelnall2) =>
% 98.38/13.31 (((ex1E2) =>
% 98.38/13.31 (((funcGraphProp1) =>
% 98.38/13.31 (((funcGraphProp3) =>
% 98.38/13.31 (((funcGraphProp2) =>
% 98.38/13.31 (((funcextLem) =>
% 98.38/13.31 (((funcGraphProp4) =>
% 98.38/13.31 (((subbreln) =>
% 98.38/13.31 (((eqbreln) =>
% 98.38/13.31 (((funcext) =>
% 98.38/13.31 (((funcext2) =>
% 98.38/13.31 (((ap2apEq1) =>
% 98.38/13.31 (((ap2apEq2) =>
% 98.38/13.31 (((beta1) =>
% 98.38/13.31 (((eta1) =>
% 98.38/13.31 (((lam2lamEq) =>
% 98.38/13.31 (((beta2) =>
% 98.38/13.31 (((eta2) =>
% 98.38/13.31 (((iffalseProp1) =>
% 98.38/13.31 (((iffalseProp2) =>
% 98.38/13.31 (((iftrueProp1) =>
% 98.38/13.31 (((iftrueProp2) =>
% 98.38/13.31 ((
% 98.38/13.31 (ifSingleton) =>
% 98.38/13.31 ((
% 98.38/13.31 (ifp) =>
% 98.38/13.31 ((
% 98.38/13.31 (theeq) =>
% 98.38/13.31 ((
% 98.38/13.31 (iftrue) =>
% 98.38/13.31 ((
% 98.38/13.31 (iffalse) =>
% 98.38/13.31 ((
% 98.38/13.31 (iftrueorfalse) =>
% 98.38/13.31 ((
% 98.38/13.31 (binintersectT_lem) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionT_lem) =>
% 98.38/13.31 ((
% 98.38/13.31 (powersetT_lem) =>
% 98.38/13.31 ((
% 98.38/13.31 (setminusT_lem) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementT_lem) =>
% 98.38/13.31 ((
% 98.38/13.31 (setextT) =>
% 98.38/13.31 ((
% 98.38/13.31 (subsetTI) =>
% 98.38/13.31 ((
% 98.38/13.31 (powersetTI1) =>
% 98.38/13.31 ((
% 98.38/13.31 (powersetTE1) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementTI1) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementTE1) =>
% 98.38/13.31 ((
% 98.38/13.31 (binintersectTELcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (binintersectTERcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (contrasubsetT) =>
% 98.38/13.31 ((
% 98.38/13.31 (contrasubsetT1) =>
% 98.38/13.31 ((
% 98.38/13.31 (contrasubsetT2) =>
% 98.38/13.31 ((
% 98.38/13.31 (contrasubsetT3) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementI1) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementE1) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementSub1) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementSub2) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementEq) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementTnotintersectT) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementImpComplementIntersect) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementSubsetComplementIntersect) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementInPowersetComplementIntersect) =>
% 98.38/13.31 ((
% 98.38/13.31 (contraSubsetComplement) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementTcontraSubset) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionTILcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionTIRcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (inIntersectImpInUnion) =>
% 98.38/13.31 ((
% 98.38/13.31 (inIntersectImpInUnion2) =>
% 98.38/13.31 ((
% 98.38/13.31 (inIntersectImpInIntersectUnions) =>
% 98.38/13.31 ((
% 98.38/13.31 (intersectInPowersetIntersectUnions) =>
% 98.38/13.31 ((
% 98.38/13.31 (inComplementUnionImpNotIn1) =>
% 98.38/13.31 ((
% 98.38/13.31 (inComplementUnionImpInComplement1) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionTE) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionTEcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2a1) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementUnionInPowersetComplement) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2a2) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan1a) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan1b) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan1) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2a) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2b2) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2b) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule0) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule1) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule2) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule3) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule4) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_1) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_2) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_3) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_4) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_5) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1all2) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1SetBreln1) =>
% 98.38/13.31 ((
% 98.38/13.31 (choice2fnsingleton) =>
% 98.38/13.31 ((
% 98.38/13.31 (setOfPairsIsBReln1) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1all1) =>
% 98.38/13.31 ((
% 98.38/13.31 (subbreln1) =>
% 98.38/13.31 ((
% 98.38/13.31 (eqbreln1) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1invprop) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1invI) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1invE) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1compprop) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1compI) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1compE) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1compEex) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionprop) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionIL) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionIR) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionI) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionE) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionEcases) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionCommutes) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz2Ex) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz2W) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz2A) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz2B) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1Ex) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1Ex1) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1Equiv) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1E) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1I) =>
% 98.38/13.31 ((
% 98.38/13.31 (injFuncInInjFuncSet) =>
% 98.38/13.31 ((
% 98.38/13.31 (injFuncSetFuncIn) =>
% 98.38/13.31 ((
% 98.38/13.31 (injFuncSetFuncInj) =>
% 98.38/13.31 ((
% 98.38/13.31 (surjFuncSetFuncIn) =>
% 98.38/13.31 ((
% 98.38/13.31 (surjFuncSetFuncSurj) =>
% 98.38/13.31 ((
% 98.38/13.31 (leftInvIsSurj) =>
% 98.38/13.31 ((
% 98.38/13.31 (surjCantorThm) =>
% 98.38/13.31 ((
% 98.38/13.31 (foundation2) =>
% 98.38/13.31 ((
% 98.38/13.31 (notinself) =>
% 98.38/13.31 ((
% 98.38/13.31 (notinself2) =>
% 98.38/13.31 ((
% 98.38/13.31 (omegaSp) =>
% 98.38/13.31 ((
% 98.38/13.31 (omegaSclos) =>
% 98.38/13.31 ((
% 98.38/13.31 (peano0notS) =>
% 98.38/13.31 ((
% 98.38/13.31 (!!) @ (
% 98.38/13.31 (('#S') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 =>) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#C') @ in @
% 98.38/13.31 omega)))) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 !!) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#S') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 =>) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#C') @ in @
% 98.38/13.31 omega)))))) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#S') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 '#S') @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 =>))) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#C') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 '#B') @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 =) @
% 98.38/13.31 omegaS)))) @
% 98.38/13.31 omegaS)))))) @
% 98.38/13.31 (
% 98.38/13.31 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.38/13.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1931])).
% 98.38/13.31 thf(zip_derived_cl1950, plain,
% 98.38/13.31 (~ (((infuncsetfunc) =>
% 98.38/13.31 (((ap2p) =>
% 98.38/13.31 (((funcinfuncset) =>
% 98.38/13.31 (((lamProp) =>
% 98.38/13.31 (((lamp) =>
% 98.38/13.31 (((lam2p) =>
% 98.38/13.31 (((brelnall1) =>
% 98.38/13.31 (((brelnall2) =>
% 98.38/13.31 (((ex1E2) =>
% 98.38/13.31 (((funcGraphProp1) =>
% 98.38/13.31 (((funcGraphProp3) =>
% 98.38/13.31 (((funcGraphProp2) =>
% 98.38/13.31 (((funcextLem) =>
% 98.38/13.31 (((funcGraphProp4) =>
% 98.38/13.31 (((subbreln) =>
% 98.38/13.31 (((eqbreln) =>
% 98.38/13.31 (((funcext) =>
% 98.38/13.31 (((funcext2) =>
% 98.38/13.31 (((ap2apEq1) =>
% 98.38/13.31 (((ap2apEq2) =>
% 98.38/13.31 (((beta1) =>
% 98.38/13.31 (((eta1) =>
% 98.38/13.31 (((lam2lamEq) =>
% 98.38/13.31 (((beta2) =>
% 98.38/13.31 (((eta2) =>
% 98.38/13.31 (((iffalseProp1) =>
% 98.38/13.31 (((iffalseProp2) =>
% 98.38/13.31 (((iftrueProp1) =>
% 98.38/13.31 (((iftrueProp2) =>
% 98.38/13.31 (((ifSingleton) =>
% 98.38/13.31 ((
% 98.38/13.31 (ifp) =>
% 98.38/13.31 ((
% 98.38/13.31 (theeq) =>
% 98.38/13.31 ((
% 98.38/13.31 (iftrue) =>
% 98.38/13.31 ((
% 98.38/13.31 (iffalse) =>
% 98.38/13.31 ((
% 98.38/13.31 (iftrueorfalse) =>
% 98.38/13.31 ((
% 98.38/13.31 (binintersectT_lem) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionT_lem) =>
% 98.38/13.31 ((
% 98.38/13.31 (powersetT_lem) =>
% 98.38/13.31 ((
% 98.38/13.31 (setminusT_lem) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementT_lem) =>
% 98.38/13.31 ((
% 98.38/13.31 (setextT) =>
% 98.38/13.31 ((
% 98.38/13.31 (subsetTI) =>
% 98.38/13.31 ((
% 98.38/13.31 (powersetTI1) =>
% 98.38/13.31 ((
% 98.38/13.31 (powersetTE1) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementTI1) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementTE1) =>
% 98.38/13.31 ((
% 98.38/13.31 (binintersectTELcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (binintersectTERcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (contrasubsetT) =>
% 98.38/13.31 ((
% 98.38/13.31 (contrasubsetT1) =>
% 98.38/13.31 ((
% 98.38/13.31 (contrasubsetT2) =>
% 98.38/13.31 ((
% 98.38/13.31 (contrasubsetT3) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementI1) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementE1) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementSub1) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementSub2) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementEq) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementTnotintersectT) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementImpComplementIntersect) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementSubsetComplementIntersect) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementInPowersetComplementIntersect) =>
% 98.38/13.31 ((
% 98.38/13.31 (contraSubsetComplement) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementTcontraSubset) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionTILcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionTIRcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (inIntersectImpInUnion) =>
% 98.38/13.31 ((
% 98.38/13.31 (inIntersectImpInUnion2) =>
% 98.38/13.31 ((
% 98.38/13.31 (inIntersectImpInIntersectUnions) =>
% 98.38/13.31 ((
% 98.38/13.31 (intersectInPowersetIntersectUnions) =>
% 98.38/13.31 ((
% 98.38/13.31 (inComplementUnionImpNotIn1) =>
% 98.38/13.31 ((
% 98.38/13.31 (inComplementUnionImpInComplement1) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionTE) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionTEcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2a1) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementUnionInPowersetComplement) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2a2) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan1a) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan1b) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan1) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2a) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2b2) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2b) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule0) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule1) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule2) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule3) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule4) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_1) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_2) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_3) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_4) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_5) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1all2) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1SetBreln1) =>
% 98.38/13.31 ((
% 98.38/13.31 (choice2fnsingleton) =>
% 98.38/13.31 ((
% 98.38/13.31 (setOfPairsIsBReln1) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1all1) =>
% 98.38/13.31 ((
% 98.38/13.31 (subbreln1) =>
% 98.38/13.31 ((
% 98.38/13.31 (eqbreln1) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1invprop) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1invI) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1invE) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1compprop) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1compI) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1compE) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1compEex) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionprop) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionIL) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionIR) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionI) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionE) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionEcases) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionCommutes) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz2Ex) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz2W) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz2A) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz2B) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1Ex) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1Ex1) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1Equiv) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1E) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1I) =>
% 98.38/13.31 ((
% 98.38/13.31 (injFuncInInjFuncSet) =>
% 98.38/13.31 ((
% 98.38/13.31 (injFuncSetFuncIn) =>
% 98.38/13.31 ((
% 98.38/13.31 (injFuncSetFuncInj) =>
% 98.38/13.31 ((
% 98.38/13.31 (surjFuncSetFuncIn) =>
% 98.38/13.31 ((
% 98.38/13.31 (surjFuncSetFuncSurj) =>
% 98.38/13.31 ((
% 98.38/13.31 (leftInvIsSurj) =>
% 98.38/13.31 ((
% 98.38/13.31 (surjCantorThm) =>
% 98.38/13.31 ((
% 98.38/13.31 (foundation2) =>
% 98.38/13.31 ((
% 98.38/13.31 (notinself) =>
% 98.38/13.31 ((
% 98.38/13.31 (notinself2) =>
% 98.38/13.31 ((
% 98.38/13.31 (omegaSp) =>
% 98.38/13.31 ((
% 98.38/13.31 (omegaSclos) =>
% 98.38/13.31 ((
% 98.38/13.31 (peano0notS) =>
% 98.38/13.31 ((
% 98.38/13.31 (!!) @ (
% 98.38/13.31 (('#S') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 =>) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#C') @ in @
% 98.38/13.31 omega)))) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 !!) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#S') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 =>) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#C') @ in @
% 98.38/13.31 omega)))))) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#S') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 '#S') @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 =>))) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#C') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 '#B') @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 =) @
% 98.38/13.31 omegaS)))) @
% 98.38/13.31 omegaS)))))) @
% 98.38/13.31 (
% 98.38/13.31 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.38/13.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1940])).
% 98.38/13.31 thf(zip_derived_cl1960, plain,
% 98.38/13.31 (~ (((ap2p) =>
% 98.38/13.31 (((funcinfuncset) =>
% 98.38/13.31 (((lamProp) =>
% 98.38/13.31 (((lamp) =>
% 98.38/13.31 (((lam2p) =>
% 98.38/13.31 (((brelnall1) =>
% 98.38/13.31 (((brelnall2) =>
% 98.38/13.31 (((ex1E2) =>
% 98.38/13.31 (((funcGraphProp1) =>
% 98.38/13.31 (((funcGraphProp3) =>
% 98.38/13.31 (((funcGraphProp2) =>
% 98.38/13.31 (((funcextLem) =>
% 98.38/13.31 (((funcGraphProp4) =>
% 98.38/13.31 (((subbreln) =>
% 98.38/13.31 (((eqbreln) =>
% 98.38/13.31 (((funcext) =>
% 98.38/13.31 (((funcext2) =>
% 98.38/13.31 (((ap2apEq1) =>
% 98.38/13.31 (((ap2apEq2) =>
% 98.38/13.31 (((beta1) =>
% 98.38/13.31 (((eta1) =>
% 98.38/13.31 (((lam2lamEq) =>
% 98.38/13.31 (((beta2) =>
% 98.38/13.31 (((eta2) =>
% 98.38/13.31 (((iffalseProp1) =>
% 98.38/13.31 (((iffalseProp2) =>
% 98.38/13.31 (((iftrueProp1) =>
% 98.38/13.31 (((iftrueProp2) =>
% 98.38/13.31 (((ifSingleton) =>
% 98.38/13.31 (((ifp) =>
% 98.38/13.31 ((
% 98.38/13.31 (theeq) =>
% 98.38/13.31 ((
% 98.38/13.31 (iftrue) =>
% 98.38/13.31 ((
% 98.38/13.31 (iffalse) =>
% 98.38/13.31 ((
% 98.38/13.31 (iftrueorfalse) =>
% 98.38/13.31 ((
% 98.38/13.31 (binintersectT_lem) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionT_lem) =>
% 98.38/13.31 ((
% 98.38/13.31 (powersetT_lem) =>
% 98.38/13.31 ((
% 98.38/13.31 (setminusT_lem) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementT_lem) =>
% 98.38/13.31 ((
% 98.38/13.31 (setextT) =>
% 98.38/13.31 ((
% 98.38/13.31 (subsetTI) =>
% 98.38/13.31 ((
% 98.38/13.31 (powersetTI1) =>
% 98.38/13.31 ((
% 98.38/13.31 (powersetTE1) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementTI1) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementTE1) =>
% 98.38/13.31 ((
% 98.38/13.31 (binintersectTELcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (binintersectTERcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (contrasubsetT) =>
% 98.38/13.31 ((
% 98.38/13.31 (contrasubsetT1) =>
% 98.38/13.31 ((
% 98.38/13.31 (contrasubsetT2) =>
% 98.38/13.31 ((
% 98.38/13.31 (contrasubsetT3) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementI1) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementE1) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementSub1) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementSub2) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementEq) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementTnotintersectT) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementImpComplementIntersect) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementSubsetComplementIntersect) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementInPowersetComplementIntersect) =>
% 98.38/13.31 ((
% 98.38/13.31 (contraSubsetComplement) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementTcontraSubset) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionTILcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionTIRcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (inIntersectImpInUnion) =>
% 98.38/13.31 ((
% 98.38/13.31 (inIntersectImpInUnion2) =>
% 98.38/13.31 ((
% 98.38/13.31 (inIntersectImpInIntersectUnions) =>
% 98.38/13.31 ((
% 98.38/13.31 (intersectInPowersetIntersectUnions) =>
% 98.38/13.31 ((
% 98.38/13.31 (inComplementUnionImpNotIn1) =>
% 98.38/13.31 ((
% 98.38/13.31 (inComplementUnionImpInComplement1) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionTE) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionTEcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2a1) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementUnionInPowersetComplement) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2a2) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan1a) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan1b) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan1) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2a) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2b2) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2b) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule0) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule1) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule2) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule3) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule4) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_1) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_2) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_3) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_4) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_5) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1all2) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1SetBreln1) =>
% 98.38/13.31 ((
% 98.38/13.31 (choice2fnsingleton) =>
% 98.38/13.31 ((
% 98.38/13.31 (setOfPairsIsBReln1) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1all1) =>
% 98.38/13.31 ((
% 98.38/13.31 (subbreln1) =>
% 98.38/13.31 ((
% 98.38/13.31 (eqbreln1) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1invprop) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1invI) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1invE) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1compprop) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1compI) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1compE) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1compEex) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionprop) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionIL) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionIR) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionI) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionE) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionEcases) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionCommutes) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz2Ex) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz2W) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz2A) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz2B) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1Ex) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1Ex1) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1Equiv) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1E) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1I) =>
% 98.38/13.31 ((
% 98.38/13.31 (injFuncInInjFuncSet) =>
% 98.38/13.31 ((
% 98.38/13.31 (injFuncSetFuncIn) =>
% 98.38/13.31 ((
% 98.38/13.31 (injFuncSetFuncInj) =>
% 98.38/13.31 ((
% 98.38/13.31 (surjFuncSetFuncIn) =>
% 98.38/13.31 ((
% 98.38/13.31 (surjFuncSetFuncSurj) =>
% 98.38/13.31 ((
% 98.38/13.31 (leftInvIsSurj) =>
% 98.38/13.31 ((
% 98.38/13.31 (surjCantorThm) =>
% 98.38/13.31 ((
% 98.38/13.31 (foundation2) =>
% 98.38/13.31 ((
% 98.38/13.31 (notinself) =>
% 98.38/13.31 ((
% 98.38/13.31 (notinself2) =>
% 98.38/13.31 ((
% 98.38/13.31 (omegaSp) =>
% 98.38/13.31 ((
% 98.38/13.31 (omegaSclos) =>
% 98.38/13.31 ((
% 98.38/13.31 (peano0notS) =>
% 98.38/13.31 ((
% 98.38/13.31 (!!) @ (
% 98.38/13.31 (('#S') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 =>) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#C') @ in @
% 98.38/13.31 omega)))) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 !!) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#S') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 =>) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#C') @ in @
% 98.38/13.31 omega)))))) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#S') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 '#S') @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 =>))) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#C') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 '#B') @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 =) @
% 98.38/13.31 omegaS)))) @
% 98.38/13.31 omegaS)))))) @
% 98.38/13.31 (
% 98.38/13.31 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.38/13.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1950])).
% 98.38/13.31 thf(zip_derived_cl1971, plain,
% 98.38/13.31 (~ (((funcinfuncset) =>
% 98.38/13.31 (((lamProp) =>
% 98.38/13.31 (((lamp) =>
% 98.38/13.31 (((lam2p) =>
% 98.38/13.31 (((brelnall1) =>
% 98.38/13.31 (((brelnall2) =>
% 98.38/13.31 (((ex1E2) =>
% 98.38/13.31 (((funcGraphProp1) =>
% 98.38/13.31 (((funcGraphProp3) =>
% 98.38/13.31 (((funcGraphProp2) =>
% 98.38/13.31 (((funcextLem) =>
% 98.38/13.31 (((funcGraphProp4) =>
% 98.38/13.31 (((subbreln) =>
% 98.38/13.31 (((eqbreln) =>
% 98.38/13.31 (((funcext) =>
% 98.38/13.31 (((funcext2) =>
% 98.38/13.31 (((ap2apEq1) =>
% 98.38/13.31 (((ap2apEq2) =>
% 98.38/13.31 (((beta1) =>
% 98.38/13.31 (((eta1) =>
% 98.38/13.31 (((lam2lamEq) =>
% 98.38/13.31 (((beta2) =>
% 98.38/13.31 (((eta2) =>
% 98.38/13.31 (((iffalseProp1) =>
% 98.38/13.31 (((iffalseProp2) =>
% 98.38/13.31 (((iftrueProp1) =>
% 98.38/13.31 (((iftrueProp2) =>
% 98.38/13.31 (((ifSingleton) =>
% 98.38/13.31 (((ifp) =>
% 98.38/13.31 (((theeq) =>
% 98.38/13.31 ((
% 98.38/13.31 (iftrue) =>
% 98.38/13.31 ((
% 98.38/13.31 (iffalse) =>
% 98.38/13.31 ((
% 98.38/13.31 (iftrueorfalse) =>
% 98.38/13.31 ((
% 98.38/13.31 (binintersectT_lem) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionT_lem) =>
% 98.38/13.31 ((
% 98.38/13.31 (powersetT_lem) =>
% 98.38/13.31 ((
% 98.38/13.31 (setminusT_lem) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementT_lem) =>
% 98.38/13.31 ((
% 98.38/13.31 (setextT) =>
% 98.38/13.31 ((
% 98.38/13.31 (subsetTI) =>
% 98.38/13.31 ((
% 98.38/13.31 (powersetTI1) =>
% 98.38/13.31 ((
% 98.38/13.31 (powersetTE1) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementTI1) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementTE1) =>
% 98.38/13.31 ((
% 98.38/13.31 (binintersectTELcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (binintersectTERcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (contrasubsetT) =>
% 98.38/13.31 ((
% 98.38/13.31 (contrasubsetT1) =>
% 98.38/13.31 ((
% 98.38/13.31 (contrasubsetT2) =>
% 98.38/13.31 ((
% 98.38/13.31 (contrasubsetT3) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementI1) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementE1) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementSub1) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementSub2) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementEq) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementTnotintersectT) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementImpComplementIntersect) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementSubsetComplementIntersect) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementInPowersetComplementIntersect) =>
% 98.38/13.31 ((
% 98.38/13.31 (contraSubsetComplement) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementTcontraSubset) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionTILcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionTIRcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (inIntersectImpInUnion) =>
% 98.38/13.31 ((
% 98.38/13.31 (inIntersectImpInUnion2) =>
% 98.38/13.31 ((
% 98.38/13.31 (inIntersectImpInIntersectUnions) =>
% 98.38/13.31 ((
% 98.38/13.31 (intersectInPowersetIntersectUnions) =>
% 98.38/13.31 ((
% 98.38/13.31 (inComplementUnionImpNotIn1) =>
% 98.38/13.31 ((
% 98.38/13.31 (inComplementUnionImpInComplement1) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionTE) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionTEcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2a1) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementUnionInPowersetComplement) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2a2) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan1a) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan1b) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan1) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2a) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2b2) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2b) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule0) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule1) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule2) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule3) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule4) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_1) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_2) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_3) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_4) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_5) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1all2) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1SetBreln1) =>
% 98.38/13.31 ((
% 98.38/13.31 (choice2fnsingleton) =>
% 98.38/13.31 ((
% 98.38/13.31 (setOfPairsIsBReln1) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1all1) =>
% 98.38/13.31 ((
% 98.38/13.31 (subbreln1) =>
% 98.38/13.31 ((
% 98.38/13.31 (eqbreln1) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1invprop) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1invI) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1invE) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1compprop) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1compI) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1compE) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1compEex) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionprop) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionIL) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionIR) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionI) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionE) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionEcases) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionCommutes) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz2Ex) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz2W) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz2A) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz2B) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1Ex) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1Ex1) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1Equiv) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1E) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1I) =>
% 98.38/13.31 ((
% 98.38/13.31 (injFuncInInjFuncSet) =>
% 98.38/13.31 ((
% 98.38/13.31 (injFuncSetFuncIn) =>
% 98.38/13.31 ((
% 98.38/13.31 (injFuncSetFuncInj) =>
% 98.38/13.31 ((
% 98.38/13.31 (surjFuncSetFuncIn) =>
% 98.38/13.31 ((
% 98.38/13.31 (surjFuncSetFuncSurj) =>
% 98.38/13.31 ((
% 98.38/13.31 (leftInvIsSurj) =>
% 98.38/13.31 ((
% 98.38/13.31 (surjCantorThm) =>
% 98.38/13.31 ((
% 98.38/13.31 (foundation2) =>
% 98.38/13.31 ((
% 98.38/13.31 (notinself) =>
% 98.38/13.31 ((
% 98.38/13.31 (notinself2) =>
% 98.38/13.31 ((
% 98.38/13.31 (omegaSp) =>
% 98.38/13.31 ((
% 98.38/13.31 (omegaSclos) =>
% 98.38/13.31 ((
% 98.38/13.31 (peano0notS) =>
% 98.38/13.31 ((
% 98.38/13.31 (!!) @ (
% 98.38/13.31 (('#S') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 =>) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#C') @ in @
% 98.38/13.31 omega)))) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 !!) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#S') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 =>) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#C') @ in @
% 98.38/13.31 omega)))))) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#S') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 '#S') @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 =>))) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#C') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 '#B') @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 =) @
% 98.38/13.31 omegaS)))) @
% 98.38/13.31 omegaS)))))) @
% 98.38/13.31 (
% 98.38/13.31 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.38/13.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1960])).
% 98.38/13.31 thf(zip_derived_cl1982, plain,
% 98.38/13.31 (~ (((lamProp) =>
% 98.38/13.31 (((lamp) =>
% 98.38/13.31 (((lam2p) =>
% 98.38/13.31 (((brelnall1) =>
% 98.38/13.31 (((brelnall2) =>
% 98.38/13.31 (((ex1E2) =>
% 98.38/13.31 (((funcGraphProp1) =>
% 98.38/13.31 (((funcGraphProp3) =>
% 98.38/13.31 (((funcGraphProp2) =>
% 98.38/13.31 (((funcextLem) =>
% 98.38/13.31 (((funcGraphProp4) =>
% 98.38/13.31 (((subbreln) =>
% 98.38/13.31 (((eqbreln) =>
% 98.38/13.31 (((funcext) =>
% 98.38/13.31 (((funcext2) =>
% 98.38/13.31 (((ap2apEq1) =>
% 98.38/13.31 (((ap2apEq2) =>
% 98.38/13.31 (((beta1) =>
% 98.38/13.31 (((eta1) =>
% 98.38/13.31 (((lam2lamEq) =>
% 98.38/13.31 (((beta2) =>
% 98.38/13.31 (((eta2) =>
% 98.38/13.31 (((iffalseProp1) =>
% 98.38/13.31 (((iffalseProp2) =>
% 98.38/13.31 (((iftrueProp1) =>
% 98.38/13.31 (((iftrueProp2) =>
% 98.38/13.31 (((ifSingleton) =>
% 98.38/13.31 (((ifp) =>
% 98.38/13.31 (((theeq) =>
% 98.38/13.31 (((iftrue) =>
% 98.38/13.31 ((
% 98.38/13.31 (iffalse) =>
% 98.38/13.31 ((
% 98.38/13.31 (iftrueorfalse) =>
% 98.38/13.31 ((
% 98.38/13.31 (binintersectT_lem) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionT_lem) =>
% 98.38/13.31 ((
% 98.38/13.31 (powersetT_lem) =>
% 98.38/13.31 ((
% 98.38/13.31 (setminusT_lem) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementT_lem) =>
% 98.38/13.31 ((
% 98.38/13.31 (setextT) =>
% 98.38/13.31 ((
% 98.38/13.31 (subsetTI) =>
% 98.38/13.31 ((
% 98.38/13.31 (powersetTI1) =>
% 98.38/13.31 ((
% 98.38/13.31 (powersetTE1) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementTI1) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementTE1) =>
% 98.38/13.31 ((
% 98.38/13.31 (binintersectTELcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (binintersectTERcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (contrasubsetT) =>
% 98.38/13.31 ((
% 98.38/13.31 (contrasubsetT1) =>
% 98.38/13.31 ((
% 98.38/13.31 (contrasubsetT2) =>
% 98.38/13.31 ((
% 98.38/13.31 (contrasubsetT3) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementI1) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementE1) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementSub1) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementSub2) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementEq) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementTnotintersectT) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementImpComplementIntersect) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementSubsetComplementIntersect) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementInPowersetComplementIntersect) =>
% 98.38/13.31 ((
% 98.38/13.31 (contraSubsetComplement) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementTcontraSubset) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionTILcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionTIRcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (inIntersectImpInUnion) =>
% 98.38/13.31 ((
% 98.38/13.31 (inIntersectImpInUnion2) =>
% 98.38/13.31 ((
% 98.38/13.31 (inIntersectImpInIntersectUnions) =>
% 98.38/13.31 ((
% 98.38/13.31 (intersectInPowersetIntersectUnions) =>
% 98.38/13.31 ((
% 98.38/13.31 (inComplementUnionImpNotIn1) =>
% 98.38/13.31 ((
% 98.38/13.31 (inComplementUnionImpInComplement1) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionTE) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionTEcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2a1) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementUnionInPowersetComplement) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2a2) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan1a) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan1b) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan1) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2a) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2b2) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2b) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule0) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule1) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule2) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule3) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule4) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_1) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_2) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_3) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_4) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_5) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1all2) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1SetBreln1) =>
% 98.38/13.31 ((
% 98.38/13.31 (choice2fnsingleton) =>
% 98.38/13.31 ((
% 98.38/13.31 (setOfPairsIsBReln1) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1all1) =>
% 98.38/13.31 ((
% 98.38/13.31 (subbreln1) =>
% 98.38/13.31 ((
% 98.38/13.31 (eqbreln1) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1invprop) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1invI) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1invE) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1compprop) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1compI) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1compE) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1compEex) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionprop) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionIL) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionIR) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionI) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionE) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionEcases) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionCommutes) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz2Ex) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz2W) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz2A) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz2B) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1Ex) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1Ex1) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1Equiv) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1E) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1I) =>
% 98.38/13.31 ((
% 98.38/13.31 (injFuncInInjFuncSet) =>
% 98.38/13.31 ((
% 98.38/13.31 (injFuncSetFuncIn) =>
% 98.38/13.31 ((
% 98.38/13.31 (injFuncSetFuncInj) =>
% 98.38/13.31 ((
% 98.38/13.31 (surjFuncSetFuncIn) =>
% 98.38/13.31 ((
% 98.38/13.31 (surjFuncSetFuncSurj) =>
% 98.38/13.31 ((
% 98.38/13.31 (leftInvIsSurj) =>
% 98.38/13.31 ((
% 98.38/13.31 (surjCantorThm) =>
% 98.38/13.31 ((
% 98.38/13.31 (foundation2) =>
% 98.38/13.31 ((
% 98.38/13.31 (notinself) =>
% 98.38/13.31 ((
% 98.38/13.31 (notinself2) =>
% 98.38/13.31 ((
% 98.38/13.31 (omegaSp) =>
% 98.38/13.31 ((
% 98.38/13.31 (omegaSclos) =>
% 98.38/13.31 ((
% 98.38/13.31 (peano0notS) =>
% 98.38/13.31 ((
% 98.38/13.31 (!!) @ (
% 98.38/13.31 (('#S') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 =>) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#C') @ in @
% 98.38/13.31 omega)))) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 !!) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#S') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 =>) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#C') @ in @
% 98.38/13.31 omega)))))) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#S') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 '#S') @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 =>))) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#C') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 '#B') @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 =) @
% 98.38/13.31 omegaS)))) @
% 98.38/13.31 omegaS)))))) @
% 98.38/13.31 (
% 98.38/13.31 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.38/13.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1971])).
% 98.38/13.31 thf(zip_derived_cl1992, plain,
% 98.38/13.31 (~ (((lamp) =>
% 98.38/13.31 (((lam2p) =>
% 98.38/13.31 (((brelnall1) =>
% 98.38/13.31 (((brelnall2) =>
% 98.38/13.31 (((ex1E2) =>
% 98.38/13.31 (((funcGraphProp1) =>
% 98.38/13.31 (((funcGraphProp3) =>
% 98.38/13.31 (((funcGraphProp2) =>
% 98.38/13.31 (((funcextLem) =>
% 98.38/13.31 (((funcGraphProp4) =>
% 98.38/13.31 (((subbreln) =>
% 98.38/13.31 (((eqbreln) =>
% 98.38/13.31 (((funcext) =>
% 98.38/13.31 (((funcext2) =>
% 98.38/13.31 (((ap2apEq1) =>
% 98.38/13.31 (((ap2apEq2) =>
% 98.38/13.31 (((beta1) =>
% 98.38/13.31 (((eta1) =>
% 98.38/13.31 (((lam2lamEq) =>
% 98.38/13.31 (((beta2) =>
% 98.38/13.31 (((eta2) =>
% 98.38/13.31 (((iffalseProp1) =>
% 98.38/13.31 (((iffalseProp2) =>
% 98.38/13.31 (((iftrueProp1) =>
% 98.38/13.31 (((iftrueProp2) =>
% 98.38/13.31 (((ifSingleton) =>
% 98.38/13.31 (((ifp) =>
% 98.38/13.31 (((theeq) =>
% 98.38/13.31 (((iftrue) =>
% 98.38/13.31 (((iffalse) =>
% 98.38/13.31 ((
% 98.38/13.31 (iftrueorfalse) =>
% 98.38/13.31 ((
% 98.38/13.31 (binintersectT_lem) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionT_lem) =>
% 98.38/13.31 ((
% 98.38/13.31 (powersetT_lem) =>
% 98.38/13.31 ((
% 98.38/13.31 (setminusT_lem) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementT_lem) =>
% 98.38/13.31 ((
% 98.38/13.31 (setextT) =>
% 98.38/13.31 ((
% 98.38/13.31 (subsetTI) =>
% 98.38/13.31 ((
% 98.38/13.31 (powersetTI1) =>
% 98.38/13.31 ((
% 98.38/13.31 (powersetTE1) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementTI1) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementTE1) =>
% 98.38/13.31 ((
% 98.38/13.31 (binintersectTELcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (binintersectTERcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (contrasubsetT) =>
% 98.38/13.31 ((
% 98.38/13.31 (contrasubsetT1) =>
% 98.38/13.31 ((
% 98.38/13.31 (contrasubsetT2) =>
% 98.38/13.31 ((
% 98.38/13.31 (contrasubsetT3) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementI1) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementE1) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementSub1) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementSub2) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementEq) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementTnotintersectT) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementImpComplementIntersect) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementSubsetComplementIntersect) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementInPowersetComplementIntersect) =>
% 98.38/13.31 ((
% 98.38/13.31 (contraSubsetComplement) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementTcontraSubset) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionTILcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionTIRcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (inIntersectImpInUnion) =>
% 98.38/13.31 ((
% 98.38/13.31 (inIntersectImpInUnion2) =>
% 98.38/13.31 ((
% 98.38/13.31 (inIntersectImpInIntersectUnions) =>
% 98.38/13.31 ((
% 98.38/13.31 (intersectInPowersetIntersectUnions) =>
% 98.38/13.31 ((
% 98.38/13.31 (inComplementUnionImpNotIn1) =>
% 98.38/13.31 ((
% 98.38/13.31 (inComplementUnionImpInComplement1) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionTE) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionTEcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2a1) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementUnionInPowersetComplement) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2a2) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan1a) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan1b) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan1) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2a) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2b2) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2b) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule0) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule1) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule2) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule3) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule4) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_1) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_2) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_3) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_4) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_5) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1all2) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1SetBreln1) =>
% 98.38/13.31 ((
% 98.38/13.31 (choice2fnsingleton) =>
% 98.38/13.31 ((
% 98.38/13.31 (setOfPairsIsBReln1) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1all1) =>
% 98.38/13.31 ((
% 98.38/13.31 (subbreln1) =>
% 98.38/13.31 ((
% 98.38/13.31 (eqbreln1) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1invprop) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1invI) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1invE) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1compprop) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1compI) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1compE) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1compEex) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionprop) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionIL) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionIR) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionI) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionE) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionEcases) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionCommutes) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz2Ex) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz2W) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz2A) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz2B) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1Ex) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1Ex1) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1Equiv) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1E) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1I) =>
% 98.38/13.31 ((
% 98.38/13.31 (injFuncInInjFuncSet) =>
% 98.38/13.31 ((
% 98.38/13.31 (injFuncSetFuncIn) =>
% 98.38/13.31 ((
% 98.38/13.31 (injFuncSetFuncInj) =>
% 98.38/13.31 ((
% 98.38/13.31 (surjFuncSetFuncIn) =>
% 98.38/13.31 ((
% 98.38/13.31 (surjFuncSetFuncSurj) =>
% 98.38/13.31 ((
% 98.38/13.31 (leftInvIsSurj) =>
% 98.38/13.31 ((
% 98.38/13.31 (surjCantorThm) =>
% 98.38/13.31 ((
% 98.38/13.31 (foundation2) =>
% 98.38/13.31 ((
% 98.38/13.31 (notinself) =>
% 98.38/13.31 ((
% 98.38/13.31 (notinself2) =>
% 98.38/13.31 ((
% 98.38/13.31 (omegaSp) =>
% 98.38/13.31 ((
% 98.38/13.31 (omegaSclos) =>
% 98.38/13.31 ((
% 98.38/13.31 (peano0notS) =>
% 98.38/13.31 ((
% 98.38/13.31 (!!) @ (
% 98.38/13.31 (('#S') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 =>) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#C') @ in @
% 98.38/13.31 omega)))) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 !!) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#S') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 =>) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#C') @ in @
% 98.38/13.31 omega)))))) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#S') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 '#S') @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 =>))) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#C') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 '#B') @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 =) @
% 98.38/13.31 omegaS)))) @
% 98.38/13.31 omegaS)))))) @
% 98.38/13.31 (
% 98.38/13.31 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.38/13.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1982])).
% 98.38/13.31 thf(zip_derived_cl2002, plain,
% 98.38/13.31 (~ (((lam2p) =>
% 98.38/13.31 (((brelnall1) =>
% 98.38/13.31 (((brelnall2) =>
% 98.38/13.31 (((ex1E2) =>
% 98.38/13.31 (((funcGraphProp1) =>
% 98.38/13.31 (((funcGraphProp3) =>
% 98.38/13.31 (((funcGraphProp2) =>
% 98.38/13.31 (((funcextLem) =>
% 98.38/13.31 (((funcGraphProp4) =>
% 98.38/13.31 (((subbreln) =>
% 98.38/13.31 (((eqbreln) =>
% 98.38/13.31 (((funcext) =>
% 98.38/13.31 (((funcext2) =>
% 98.38/13.31 (((ap2apEq1) =>
% 98.38/13.31 (((ap2apEq2) =>
% 98.38/13.31 (((beta1) =>
% 98.38/13.31 (((eta1) =>
% 98.38/13.31 (((lam2lamEq) =>
% 98.38/13.31 (((beta2) =>
% 98.38/13.31 (((eta2) =>
% 98.38/13.31 (((iffalseProp1) =>
% 98.38/13.31 (((iffalseProp2) =>
% 98.38/13.31 (((iftrueProp1) =>
% 98.38/13.31 (((iftrueProp2) =>
% 98.38/13.31 (((ifSingleton) =>
% 98.38/13.31 (((ifp) =>
% 98.38/13.31 (((theeq) =>
% 98.38/13.31 (((iftrue) =>
% 98.38/13.31 (((iffalse) =>
% 98.38/13.31 (((iftrueorfalse) =>
% 98.38/13.31 ((
% 98.38/13.31 (binintersectT_lem) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionT_lem) =>
% 98.38/13.31 ((
% 98.38/13.31 (powersetT_lem) =>
% 98.38/13.31 ((
% 98.38/13.31 (setminusT_lem) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementT_lem) =>
% 98.38/13.31 ((
% 98.38/13.31 (setextT) =>
% 98.38/13.31 ((
% 98.38/13.31 (subsetTI) =>
% 98.38/13.31 ((
% 98.38/13.31 (powersetTI1) =>
% 98.38/13.31 ((
% 98.38/13.31 (powersetTE1) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementTI1) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementTE1) =>
% 98.38/13.31 ((
% 98.38/13.31 (binintersectTELcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (binintersectTERcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (contrasubsetT) =>
% 98.38/13.31 ((
% 98.38/13.31 (contrasubsetT1) =>
% 98.38/13.31 ((
% 98.38/13.31 (contrasubsetT2) =>
% 98.38/13.31 ((
% 98.38/13.31 (contrasubsetT3) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementI1) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementE1) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementSub1) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementSub2) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementEq) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementTnotintersectT) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementImpComplementIntersect) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementSubsetComplementIntersect) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementInPowersetComplementIntersect) =>
% 98.38/13.31 ((
% 98.38/13.31 (contraSubsetComplement) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementTcontraSubset) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionTILcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionTIRcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (inIntersectImpInUnion) =>
% 98.38/13.31 ((
% 98.38/13.31 (inIntersectImpInUnion2) =>
% 98.38/13.31 ((
% 98.38/13.31 (inIntersectImpInIntersectUnions) =>
% 98.38/13.31 ((
% 98.38/13.31 (intersectInPowersetIntersectUnions) =>
% 98.38/13.31 ((
% 98.38/13.31 (inComplementUnionImpNotIn1) =>
% 98.38/13.31 ((
% 98.38/13.31 (inComplementUnionImpInComplement1) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionTE) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionTEcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2a1) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementUnionInPowersetComplement) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2a2) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan1a) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan1b) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan1) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2a) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2b2) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2b) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule0) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule1) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule2) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule3) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule4) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_1) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_2) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_3) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_4) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_5) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1all2) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1SetBreln1) =>
% 98.38/13.31 ((
% 98.38/13.31 (choice2fnsingleton) =>
% 98.38/13.31 ((
% 98.38/13.31 (setOfPairsIsBReln1) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1all1) =>
% 98.38/13.31 ((
% 98.38/13.31 (subbreln1) =>
% 98.38/13.31 ((
% 98.38/13.31 (eqbreln1) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1invprop) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1invI) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1invE) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1compprop) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1compI) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1compE) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1compEex) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionprop) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionIL) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionIR) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionI) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionE) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionEcases) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionCommutes) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz2Ex) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz2W) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz2A) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz2B) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1Ex) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1Ex1) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1Equiv) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1E) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1I) =>
% 98.38/13.31 ((
% 98.38/13.31 (injFuncInInjFuncSet) =>
% 98.38/13.31 ((
% 98.38/13.31 (injFuncSetFuncIn) =>
% 98.38/13.31 ((
% 98.38/13.31 (injFuncSetFuncInj) =>
% 98.38/13.31 ((
% 98.38/13.31 (surjFuncSetFuncIn) =>
% 98.38/13.31 ((
% 98.38/13.31 (surjFuncSetFuncSurj) =>
% 98.38/13.31 ((
% 98.38/13.31 (leftInvIsSurj) =>
% 98.38/13.31 ((
% 98.38/13.31 (surjCantorThm) =>
% 98.38/13.31 ((
% 98.38/13.31 (foundation2) =>
% 98.38/13.31 ((
% 98.38/13.31 (notinself) =>
% 98.38/13.31 ((
% 98.38/13.31 (notinself2) =>
% 98.38/13.31 ((
% 98.38/13.31 (omegaSp) =>
% 98.38/13.31 ((
% 98.38/13.31 (omegaSclos) =>
% 98.38/13.31 ((
% 98.38/13.31 (peano0notS) =>
% 98.38/13.31 ((
% 98.38/13.31 (!!) @ (
% 98.38/13.31 (('#S') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 =>) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#C') @ in @
% 98.38/13.31 omega)))) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 !!) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#S') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 =>) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#C') @ in @
% 98.38/13.31 omega)))))) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#S') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 '#S') @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 =>))) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#C') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 '#B') @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 =) @
% 98.38/13.31 omegaS)))) @
% 98.38/13.31 omegaS)))))) @
% 98.38/13.31 (
% 98.38/13.31 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.38/13.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1992])).
% 98.38/13.31 thf(zip_derived_cl2012, plain,
% 98.38/13.31 (~ (((brelnall1) =>
% 98.38/13.31 (((brelnall2) =>
% 98.38/13.31 (((ex1E2) =>
% 98.38/13.31 (((funcGraphProp1) =>
% 98.38/13.31 (((funcGraphProp3) =>
% 98.38/13.31 (((funcGraphProp2) =>
% 98.38/13.31 (((funcextLem) =>
% 98.38/13.31 (((funcGraphProp4) =>
% 98.38/13.31 (((subbreln) =>
% 98.38/13.31 (((eqbreln) =>
% 98.38/13.31 (((funcext) =>
% 98.38/13.31 (((funcext2) =>
% 98.38/13.31 (((ap2apEq1) =>
% 98.38/13.31 (((ap2apEq2) =>
% 98.38/13.31 (((beta1) =>
% 98.38/13.31 (((eta1) =>
% 98.38/13.31 (((lam2lamEq) =>
% 98.38/13.31 (((beta2) =>
% 98.38/13.31 (((eta2) =>
% 98.38/13.31 (((iffalseProp1) =>
% 98.38/13.31 (((iffalseProp2) =>
% 98.38/13.31 (((iftrueProp1) =>
% 98.38/13.31 (((iftrueProp2) =>
% 98.38/13.31 (((ifSingleton) =>
% 98.38/13.31 (((ifp) =>
% 98.38/13.31 (((theeq) =>
% 98.38/13.31 (((iftrue) =>
% 98.38/13.31 (((iffalse) =>
% 98.38/13.31 (((iftrueorfalse) =>
% 98.38/13.31 (((binintersectT_lem) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionT_lem) =>
% 98.38/13.31 ((
% 98.38/13.31 (powersetT_lem) =>
% 98.38/13.31 ((
% 98.38/13.31 (setminusT_lem) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementT_lem) =>
% 98.38/13.31 ((
% 98.38/13.31 (setextT) =>
% 98.38/13.31 ((
% 98.38/13.31 (subsetTI) =>
% 98.38/13.31 ((
% 98.38/13.31 (powersetTI1) =>
% 98.38/13.31 ((
% 98.38/13.31 (powersetTE1) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementTI1) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementTE1) =>
% 98.38/13.31 ((
% 98.38/13.31 (binintersectTELcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (binintersectTERcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (contrasubsetT) =>
% 98.38/13.31 ((
% 98.38/13.31 (contrasubsetT1) =>
% 98.38/13.31 ((
% 98.38/13.31 (contrasubsetT2) =>
% 98.38/13.31 ((
% 98.38/13.31 (contrasubsetT3) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementI1) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementE1) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementSub1) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementSub2) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementEq) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementTnotintersectT) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementImpComplementIntersect) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementSubsetComplementIntersect) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementInPowersetComplementIntersect) =>
% 98.38/13.31 ((
% 98.38/13.31 (contraSubsetComplement) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementTcontraSubset) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionTILcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionTIRcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (inIntersectImpInUnion) =>
% 98.38/13.31 ((
% 98.38/13.31 (inIntersectImpInUnion2) =>
% 98.38/13.31 ((
% 98.38/13.31 (inIntersectImpInIntersectUnions) =>
% 98.38/13.31 ((
% 98.38/13.31 (intersectInPowersetIntersectUnions) =>
% 98.38/13.31 ((
% 98.38/13.31 (inComplementUnionImpNotIn1) =>
% 98.38/13.31 ((
% 98.38/13.31 (inComplementUnionImpInComplement1) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionTE) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionTEcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2a1) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementUnionInPowersetComplement) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2a2) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan1a) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan1b) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan1) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2a) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2b2) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2b) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule0) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule1) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule2) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule3) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule4) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_1) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_2) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_3) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_4) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_5) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1all2) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1SetBreln1) =>
% 98.38/13.31 ((
% 98.38/13.31 (choice2fnsingleton) =>
% 98.38/13.31 ((
% 98.38/13.31 (setOfPairsIsBReln1) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1all1) =>
% 98.38/13.31 ((
% 98.38/13.31 (subbreln1) =>
% 98.38/13.31 ((
% 98.38/13.31 (eqbreln1) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1invprop) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1invI) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1invE) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1compprop) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1compI) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1compE) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1compEex) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionprop) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionIL) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionIR) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionI) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionE) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionEcases) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionCommutes) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz2Ex) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz2W) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz2A) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz2B) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1Ex) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1Ex1) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1Equiv) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1E) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1I) =>
% 98.38/13.31 ((
% 98.38/13.31 (injFuncInInjFuncSet) =>
% 98.38/13.31 ((
% 98.38/13.31 (injFuncSetFuncIn) =>
% 98.38/13.31 ((
% 98.38/13.31 (injFuncSetFuncInj) =>
% 98.38/13.31 ((
% 98.38/13.31 (surjFuncSetFuncIn) =>
% 98.38/13.31 ((
% 98.38/13.31 (surjFuncSetFuncSurj) =>
% 98.38/13.31 ((
% 98.38/13.31 (leftInvIsSurj) =>
% 98.38/13.31 ((
% 98.38/13.31 (surjCantorThm) =>
% 98.38/13.31 ((
% 98.38/13.31 (foundation2) =>
% 98.38/13.31 ((
% 98.38/13.31 (notinself) =>
% 98.38/13.31 ((
% 98.38/13.31 (notinself2) =>
% 98.38/13.31 ((
% 98.38/13.31 (omegaSp) =>
% 98.38/13.31 ((
% 98.38/13.31 (omegaSclos) =>
% 98.38/13.31 ((
% 98.38/13.31 (peano0notS) =>
% 98.38/13.31 ((
% 98.38/13.31 (!!) @ (
% 98.38/13.31 (('#S') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 =>) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#C') @ in @
% 98.38/13.31 omega)))) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 !!) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#S') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 =>) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#C') @ in @
% 98.38/13.31 omega)))))) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#S') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 '#S') @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 =>))) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#C') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 '#B') @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 =) @
% 98.38/13.31 omegaS)))) @
% 98.38/13.31 omegaS)))))) @
% 98.38/13.31 (
% 98.38/13.31 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.38/13.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2002])).
% 98.38/13.31 thf(zip_derived_cl2021, plain,
% 98.38/13.31 (~ (((brelnall2) =>
% 98.38/13.31 (((ex1E2) =>
% 98.38/13.31 (((funcGraphProp1) =>
% 98.38/13.31 (((funcGraphProp3) =>
% 98.38/13.31 (((funcGraphProp2) =>
% 98.38/13.31 (((funcextLem) =>
% 98.38/13.31 (((funcGraphProp4) =>
% 98.38/13.31 (((subbreln) =>
% 98.38/13.31 (((eqbreln) =>
% 98.38/13.31 (((funcext) =>
% 98.38/13.31 (((funcext2) =>
% 98.38/13.31 (((ap2apEq1) =>
% 98.38/13.31 (((ap2apEq2) =>
% 98.38/13.31 (((beta1) =>
% 98.38/13.31 (((eta1) =>
% 98.38/13.31 (((lam2lamEq) =>
% 98.38/13.31 (((beta2) =>
% 98.38/13.31 (((eta2) =>
% 98.38/13.31 (((iffalseProp1) =>
% 98.38/13.31 (((iffalseProp2) =>
% 98.38/13.31 (((iftrueProp1) =>
% 98.38/13.31 (((iftrueProp2) =>
% 98.38/13.31 (((ifSingleton) =>
% 98.38/13.31 (((ifp) =>
% 98.38/13.31 (((theeq) =>
% 98.38/13.31 (((iftrue) =>
% 98.38/13.31 (((iffalse) =>
% 98.38/13.31 (((iftrueorfalse) =>
% 98.38/13.31 (((binintersectT_lem) =>
% 98.38/13.31 (((binunionT_lem) =>
% 98.38/13.31 ((
% 98.38/13.31 (powersetT_lem) =>
% 98.38/13.31 ((
% 98.38/13.31 (setminusT_lem) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementT_lem) =>
% 98.38/13.31 ((
% 98.38/13.31 (setextT) =>
% 98.38/13.31 ((
% 98.38/13.31 (subsetTI) =>
% 98.38/13.31 ((
% 98.38/13.31 (powersetTI1) =>
% 98.38/13.31 ((
% 98.38/13.31 (powersetTE1) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementTI1) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementTE1) =>
% 98.38/13.31 ((
% 98.38/13.31 (binintersectTELcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (binintersectTERcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (contrasubsetT) =>
% 98.38/13.31 ((
% 98.38/13.31 (contrasubsetT1) =>
% 98.38/13.31 ((
% 98.38/13.31 (contrasubsetT2) =>
% 98.38/13.31 ((
% 98.38/13.31 (contrasubsetT3) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementI1) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementE1) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementSub1) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementSub2) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementEq) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementTnotintersectT) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementImpComplementIntersect) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementSubsetComplementIntersect) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementInPowersetComplementIntersect) =>
% 98.38/13.31 ((
% 98.38/13.31 (contraSubsetComplement) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementTcontraSubset) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionTILcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionTIRcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (inIntersectImpInUnion) =>
% 98.38/13.31 ((
% 98.38/13.31 (inIntersectImpInUnion2) =>
% 98.38/13.31 ((
% 98.38/13.31 (inIntersectImpInIntersectUnions) =>
% 98.38/13.31 ((
% 98.38/13.31 (intersectInPowersetIntersectUnions) =>
% 98.38/13.31 ((
% 98.38/13.31 (inComplementUnionImpNotIn1) =>
% 98.38/13.31 ((
% 98.38/13.31 (inComplementUnionImpInComplement1) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionTE) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionTEcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2a1) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementUnionInPowersetComplement) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2a2) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan1a) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan1b) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan1) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2a) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2b2) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2b) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule0) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule1) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule2) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule3) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule4) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_1) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_2) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_3) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_4) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_5) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1all2) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1SetBreln1) =>
% 98.38/13.31 ((
% 98.38/13.31 (choice2fnsingleton) =>
% 98.38/13.31 ((
% 98.38/13.31 (setOfPairsIsBReln1) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1all1) =>
% 98.38/13.31 ((
% 98.38/13.31 (subbreln1) =>
% 98.38/13.31 ((
% 98.38/13.31 (eqbreln1) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1invprop) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1invI) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1invE) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1compprop) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1compI) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1compE) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1compEex) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionprop) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionIL) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionIR) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionI) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionE) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionEcases) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionCommutes) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz2Ex) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz2W) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz2A) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz2B) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1Ex) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1Ex1) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1Equiv) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1E) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1I) =>
% 98.38/13.31 ((
% 98.38/13.31 (injFuncInInjFuncSet) =>
% 98.38/13.31 ((
% 98.38/13.31 (injFuncSetFuncIn) =>
% 98.38/13.31 ((
% 98.38/13.31 (injFuncSetFuncInj) =>
% 98.38/13.31 ((
% 98.38/13.31 (surjFuncSetFuncIn) =>
% 98.38/13.31 ((
% 98.38/13.31 (surjFuncSetFuncSurj) =>
% 98.38/13.31 ((
% 98.38/13.31 (leftInvIsSurj) =>
% 98.38/13.31 ((
% 98.38/13.31 (surjCantorThm) =>
% 98.38/13.31 ((
% 98.38/13.31 (foundation2) =>
% 98.38/13.31 ((
% 98.38/13.31 (notinself) =>
% 98.38/13.31 ((
% 98.38/13.31 (notinself2) =>
% 98.38/13.31 ((
% 98.38/13.31 (omegaSp) =>
% 98.38/13.31 ((
% 98.38/13.31 (omegaSclos) =>
% 98.38/13.31 ((
% 98.38/13.31 (peano0notS) =>
% 98.38/13.31 ((
% 98.38/13.31 (!!) @ (
% 98.38/13.31 (('#S') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 =>) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#C') @ in @
% 98.38/13.31 omega)))) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 !!) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#S') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 =>) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#C') @ in @
% 98.38/13.31 omega)))))) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#S') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 '#S') @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 =>))) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#C') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 '#B') @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 =) @
% 98.38/13.31 omegaS)))) @
% 98.38/13.31 omegaS)))))) @
% 98.38/13.31 (
% 98.38/13.31 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.38/13.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2012])).
% 98.38/13.31 thf(zip_derived_cl2030, plain,
% 98.38/13.31 (~ (((ex1E2) =>
% 98.38/13.31 (((funcGraphProp1) =>
% 98.38/13.31 (((funcGraphProp3) =>
% 98.38/13.31 (((funcGraphProp2) =>
% 98.38/13.31 (((funcextLem) =>
% 98.38/13.31 (((funcGraphProp4) =>
% 98.38/13.31 (((subbreln) =>
% 98.38/13.31 (((eqbreln) =>
% 98.38/13.31 (((funcext) =>
% 98.38/13.31 (((funcext2) =>
% 98.38/13.31 (((ap2apEq1) =>
% 98.38/13.31 (((ap2apEq2) =>
% 98.38/13.31 (((beta1) =>
% 98.38/13.31 (((eta1) =>
% 98.38/13.31 (((lam2lamEq) =>
% 98.38/13.31 (((beta2) =>
% 98.38/13.31 (((eta2) =>
% 98.38/13.31 (((iffalseProp1) =>
% 98.38/13.31 (((iffalseProp2) =>
% 98.38/13.31 (((iftrueProp1) =>
% 98.38/13.31 (((iftrueProp2) =>
% 98.38/13.31 (((ifSingleton) =>
% 98.38/13.31 (((ifp) =>
% 98.38/13.31 (((theeq) =>
% 98.38/13.31 (((iftrue) =>
% 98.38/13.31 (((iffalse) =>
% 98.38/13.31 (((iftrueorfalse) =>
% 98.38/13.31 (((binintersectT_lem) =>
% 98.38/13.31 (((binunionT_lem) =>
% 98.38/13.31 (((powersetT_lem) =>
% 98.38/13.31 ((
% 98.38/13.31 (setminusT_lem) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementT_lem) =>
% 98.38/13.31 ((
% 98.38/13.31 (setextT) =>
% 98.38/13.31 ((
% 98.38/13.31 (subsetTI) =>
% 98.38/13.31 ((
% 98.38/13.31 (powersetTI1) =>
% 98.38/13.31 ((
% 98.38/13.31 (powersetTE1) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementTI1) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementTE1) =>
% 98.38/13.31 ((
% 98.38/13.31 (binintersectTELcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (binintersectTERcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (contrasubsetT) =>
% 98.38/13.31 ((
% 98.38/13.31 (contrasubsetT1) =>
% 98.38/13.31 ((
% 98.38/13.31 (contrasubsetT2) =>
% 98.38/13.31 ((
% 98.38/13.31 (contrasubsetT3) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementI1) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementE1) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementSub1) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementSub2) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementEq) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementTnotintersectT) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementImpComplementIntersect) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementSubsetComplementIntersect) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementInPowersetComplementIntersect) =>
% 98.38/13.31 ((
% 98.38/13.31 (contraSubsetComplement) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementTcontraSubset) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionTILcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionTIRcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (inIntersectImpInUnion) =>
% 98.38/13.31 ((
% 98.38/13.31 (inIntersectImpInUnion2) =>
% 98.38/13.31 ((
% 98.38/13.31 (inIntersectImpInIntersectUnions) =>
% 98.38/13.31 ((
% 98.38/13.31 (intersectInPowersetIntersectUnions) =>
% 98.38/13.31 ((
% 98.38/13.31 (inComplementUnionImpNotIn1) =>
% 98.38/13.31 ((
% 98.38/13.31 (inComplementUnionImpInComplement1) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionTE) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionTEcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2a1) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementUnionInPowersetComplement) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2a2) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan1a) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan1b) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan1) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2a) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2b2) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2b) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule0) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule1) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule2) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule3) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule4) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_1) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_2) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_3) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_4) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_5) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1all2) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1SetBreln1) =>
% 98.38/13.31 ((
% 98.38/13.31 (choice2fnsingleton) =>
% 98.38/13.31 ((
% 98.38/13.31 (setOfPairsIsBReln1) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1all1) =>
% 98.38/13.31 ((
% 98.38/13.31 (subbreln1) =>
% 98.38/13.31 ((
% 98.38/13.31 (eqbreln1) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1invprop) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1invI) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1invE) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1compprop) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1compI) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1compE) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1compEex) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionprop) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionIL) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionIR) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionI) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionE) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionEcases) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionCommutes) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz2Ex) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz2W) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz2A) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz2B) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1Ex) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1Ex1) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1Equiv) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1E) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1I) =>
% 98.38/13.31 ((
% 98.38/13.31 (injFuncInInjFuncSet) =>
% 98.38/13.31 ((
% 98.38/13.31 (injFuncSetFuncIn) =>
% 98.38/13.31 ((
% 98.38/13.31 (injFuncSetFuncInj) =>
% 98.38/13.31 ((
% 98.38/13.31 (surjFuncSetFuncIn) =>
% 98.38/13.31 ((
% 98.38/13.31 (surjFuncSetFuncSurj) =>
% 98.38/13.31 ((
% 98.38/13.31 (leftInvIsSurj) =>
% 98.38/13.31 ((
% 98.38/13.31 (surjCantorThm) =>
% 98.38/13.31 ((
% 98.38/13.31 (foundation2) =>
% 98.38/13.31 ((
% 98.38/13.31 (notinself) =>
% 98.38/13.31 ((
% 98.38/13.31 (notinself2) =>
% 98.38/13.31 ((
% 98.38/13.31 (omegaSp) =>
% 98.38/13.31 ((
% 98.38/13.31 (omegaSclos) =>
% 98.38/13.31 ((
% 98.38/13.31 (peano0notS) =>
% 98.38/13.31 ((
% 98.38/13.31 (!!) @ (
% 98.38/13.31 (('#S') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 =>) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#C') @ in @
% 98.38/13.31 omega)))) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 !!) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#S') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 =>) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#C') @ in @
% 98.38/13.31 omega)))))) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#S') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 '#S') @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 =>))) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#C') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 '#B') @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 =) @
% 98.38/13.31 omegaS)))) @
% 98.38/13.31 omegaS)))))) @
% 98.38/13.31 (
% 98.38/13.31 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.38/13.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2021])).
% 98.38/13.31 thf(zip_derived_cl2039, plain,
% 98.38/13.31 (~ (((funcGraphProp1) =>
% 98.38/13.31 (((funcGraphProp3) =>
% 98.38/13.31 (((funcGraphProp2) =>
% 98.38/13.31 (((funcextLem) =>
% 98.38/13.31 (((funcGraphProp4) =>
% 98.38/13.31 (((subbreln) =>
% 98.38/13.31 (((eqbreln) =>
% 98.38/13.31 (((funcext) =>
% 98.38/13.31 (((funcext2) =>
% 98.38/13.31 (((ap2apEq1) =>
% 98.38/13.31 (((ap2apEq2) =>
% 98.38/13.31 (((beta1) =>
% 98.38/13.31 (((eta1) =>
% 98.38/13.31 (((lam2lamEq) =>
% 98.38/13.31 (((beta2) =>
% 98.38/13.31 (((eta2) =>
% 98.38/13.31 (((iffalseProp1) =>
% 98.38/13.31 (((iffalseProp2) =>
% 98.38/13.31 (((iftrueProp1) =>
% 98.38/13.31 (((iftrueProp2) =>
% 98.38/13.31 (((ifSingleton) =>
% 98.38/13.31 (((ifp) =>
% 98.38/13.31 (((theeq) =>
% 98.38/13.31 (((iftrue) =>
% 98.38/13.31 (((iffalse) =>
% 98.38/13.31 (((iftrueorfalse) =>
% 98.38/13.31 (((binintersectT_lem) =>
% 98.38/13.31 (((binunionT_lem) =>
% 98.38/13.31 (((powersetT_lem) =>
% 98.38/13.31 (((setminusT_lem) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementT_lem) =>
% 98.38/13.31 ((
% 98.38/13.31 (setextT) =>
% 98.38/13.31 ((
% 98.38/13.31 (subsetTI) =>
% 98.38/13.31 ((
% 98.38/13.31 (powersetTI1) =>
% 98.38/13.31 ((
% 98.38/13.31 (powersetTE1) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementTI1) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementTE1) =>
% 98.38/13.31 ((
% 98.38/13.31 (binintersectTELcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (binintersectTERcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (contrasubsetT) =>
% 98.38/13.31 ((
% 98.38/13.31 (contrasubsetT1) =>
% 98.38/13.31 ((
% 98.38/13.31 (contrasubsetT2) =>
% 98.38/13.31 ((
% 98.38/13.31 (contrasubsetT3) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementI1) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementE1) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementSub1) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementSub2) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementEq) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementTnotintersectT) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementImpComplementIntersect) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementSubsetComplementIntersect) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementInPowersetComplementIntersect) =>
% 98.38/13.31 ((
% 98.38/13.31 (contraSubsetComplement) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementTcontraSubset) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionTILcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionTIRcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (inIntersectImpInUnion) =>
% 98.38/13.31 ((
% 98.38/13.31 (inIntersectImpInUnion2) =>
% 98.38/13.31 ((
% 98.38/13.31 (inIntersectImpInIntersectUnions) =>
% 98.38/13.31 ((
% 98.38/13.31 (intersectInPowersetIntersectUnions) =>
% 98.38/13.31 ((
% 98.38/13.31 (inComplementUnionImpNotIn1) =>
% 98.38/13.31 ((
% 98.38/13.31 (inComplementUnionImpInComplement1) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionTE) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionTEcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2a1) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementUnionInPowersetComplement) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2a2) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan1a) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan1b) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan1) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2a) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2b2) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2b) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule0) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule1) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule2) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule3) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule4) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_1) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_2) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_3) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_4) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_5) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1all2) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1SetBreln1) =>
% 98.38/13.31 ((
% 98.38/13.31 (choice2fnsingleton) =>
% 98.38/13.31 ((
% 98.38/13.31 (setOfPairsIsBReln1) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1all1) =>
% 98.38/13.31 ((
% 98.38/13.31 (subbreln1) =>
% 98.38/13.31 ((
% 98.38/13.31 (eqbreln1) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1invprop) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1invI) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1invE) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1compprop) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1compI) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1compE) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1compEex) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionprop) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionIL) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionIR) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionI) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionE) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionEcases) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionCommutes) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz2Ex) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz2W) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz2A) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz2B) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1Ex) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1Ex1) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1Equiv) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1E) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1I) =>
% 98.38/13.31 ((
% 98.38/13.31 (injFuncInInjFuncSet) =>
% 98.38/13.31 ((
% 98.38/13.31 (injFuncSetFuncIn) =>
% 98.38/13.31 ((
% 98.38/13.31 (injFuncSetFuncInj) =>
% 98.38/13.31 ((
% 98.38/13.31 (surjFuncSetFuncIn) =>
% 98.38/13.31 ((
% 98.38/13.31 (surjFuncSetFuncSurj) =>
% 98.38/13.31 ((
% 98.38/13.31 (leftInvIsSurj) =>
% 98.38/13.31 ((
% 98.38/13.31 (surjCantorThm) =>
% 98.38/13.31 ((
% 98.38/13.31 (foundation2) =>
% 98.38/13.31 ((
% 98.38/13.31 (notinself) =>
% 98.38/13.31 ((
% 98.38/13.31 (notinself2) =>
% 98.38/13.31 ((
% 98.38/13.31 (omegaSp) =>
% 98.38/13.31 ((
% 98.38/13.31 (omegaSclos) =>
% 98.38/13.31 ((
% 98.38/13.31 (peano0notS) =>
% 98.38/13.31 ((
% 98.38/13.31 (!!) @ (
% 98.38/13.31 (('#S') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 =>) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#C') @ in @
% 98.38/13.31 omega)))) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 !!) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#S') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 =>) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#C') @ in @
% 98.38/13.31 omega)))))) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#S') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 '#S') @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 =>))) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#C') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 '#B') @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 =) @
% 98.38/13.31 omegaS)))) @
% 98.38/13.31 omegaS)))))) @
% 98.38/13.31 (
% 98.38/13.31 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.38/13.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2030])).
% 98.38/13.31 thf(zip_derived_cl2048, plain,
% 98.38/13.31 (~ (((funcGraphProp3) =>
% 98.38/13.31 (((funcGraphProp2) =>
% 98.38/13.31 (((funcextLem) =>
% 98.38/13.31 (((funcGraphProp4) =>
% 98.38/13.31 (((subbreln) =>
% 98.38/13.31 (((eqbreln) =>
% 98.38/13.31 (((funcext) =>
% 98.38/13.31 (((funcext2) =>
% 98.38/13.31 (((ap2apEq1) =>
% 98.38/13.31 (((ap2apEq2) =>
% 98.38/13.31 (((beta1) =>
% 98.38/13.31 (((eta1) =>
% 98.38/13.31 (((lam2lamEq) =>
% 98.38/13.31 (((beta2) =>
% 98.38/13.31 (((eta2) =>
% 98.38/13.31 (((iffalseProp1) =>
% 98.38/13.31 (((iffalseProp2) =>
% 98.38/13.31 (((iftrueProp1) =>
% 98.38/13.31 (((iftrueProp2) =>
% 98.38/13.31 (((ifSingleton) =>
% 98.38/13.31 (((ifp) =>
% 98.38/13.31 (((theeq) =>
% 98.38/13.31 (((iftrue) =>
% 98.38/13.31 (((iffalse) =>
% 98.38/13.31 (((iftrueorfalse) =>
% 98.38/13.31 (((binintersectT_lem) =>
% 98.38/13.31 (((binunionT_lem) =>
% 98.38/13.31 (((powersetT_lem) =>
% 98.38/13.31 (((setminusT_lem) =>
% 98.38/13.31 (((complementT_lem) =>
% 98.38/13.31 ((
% 98.38/13.31 (setextT) =>
% 98.38/13.31 ((
% 98.38/13.31 (subsetTI) =>
% 98.38/13.31 ((
% 98.38/13.31 (powersetTI1) =>
% 98.38/13.31 ((
% 98.38/13.31 (powersetTE1) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementTI1) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementTE1) =>
% 98.38/13.31 ((
% 98.38/13.31 (binintersectTELcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (binintersectTERcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (contrasubsetT) =>
% 98.38/13.31 ((
% 98.38/13.31 (contrasubsetT1) =>
% 98.38/13.31 ((
% 98.38/13.31 (contrasubsetT2) =>
% 98.38/13.31 ((
% 98.38/13.31 (contrasubsetT3) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementI1) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementE1) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementSub1) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementSub2) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementEq) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementTnotintersectT) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementImpComplementIntersect) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementSubsetComplementIntersect) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementInPowersetComplementIntersect) =>
% 98.38/13.31 ((
% 98.38/13.31 (contraSubsetComplement) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementTcontraSubset) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionTILcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionTIRcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (inIntersectImpInUnion) =>
% 98.38/13.31 ((
% 98.38/13.31 (inIntersectImpInUnion2) =>
% 98.38/13.31 ((
% 98.38/13.31 (inIntersectImpInIntersectUnions) =>
% 98.38/13.31 ((
% 98.38/13.31 (intersectInPowersetIntersectUnions) =>
% 98.38/13.31 ((
% 98.38/13.31 (inComplementUnionImpNotIn1) =>
% 98.38/13.31 ((
% 98.38/13.31 (inComplementUnionImpInComplement1) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionTE) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionTEcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2a1) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementUnionInPowersetComplement) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2a2) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan1a) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan1b) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan1) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2a) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2b2) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2b) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule0) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule1) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule2) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule3) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule4) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_1) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_2) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_3) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_4) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_5) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1all2) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1SetBreln1) =>
% 98.38/13.31 ((
% 98.38/13.31 (choice2fnsingleton) =>
% 98.38/13.31 ((
% 98.38/13.31 (setOfPairsIsBReln1) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1all1) =>
% 98.38/13.31 ((
% 98.38/13.31 (subbreln1) =>
% 98.38/13.31 ((
% 98.38/13.31 (eqbreln1) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1invprop) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1invI) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1invE) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1compprop) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1compI) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1compE) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1compEex) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionprop) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionIL) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionIR) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionI) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionE) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionEcases) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionCommutes) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz2Ex) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz2W) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz2A) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz2B) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1Ex) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1Ex1) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1Equiv) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1E) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1I) =>
% 98.38/13.31 ((
% 98.38/13.31 (injFuncInInjFuncSet) =>
% 98.38/13.31 ((
% 98.38/13.31 (injFuncSetFuncIn) =>
% 98.38/13.31 ((
% 98.38/13.31 (injFuncSetFuncInj) =>
% 98.38/13.31 ((
% 98.38/13.31 (surjFuncSetFuncIn) =>
% 98.38/13.31 ((
% 98.38/13.31 (surjFuncSetFuncSurj) =>
% 98.38/13.31 ((
% 98.38/13.31 (leftInvIsSurj) =>
% 98.38/13.31 ((
% 98.38/13.31 (surjCantorThm) =>
% 98.38/13.31 ((
% 98.38/13.31 (foundation2) =>
% 98.38/13.31 ((
% 98.38/13.31 (notinself) =>
% 98.38/13.31 ((
% 98.38/13.31 (notinself2) =>
% 98.38/13.31 ((
% 98.38/13.31 (omegaSp) =>
% 98.38/13.31 ((
% 98.38/13.31 (omegaSclos) =>
% 98.38/13.31 ((
% 98.38/13.31 (peano0notS) =>
% 98.38/13.31 ((
% 98.38/13.31 (!!) @ (
% 98.38/13.31 (('#S') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 =>) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#C') @ in @
% 98.38/13.31 omega)))) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 !!) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#S') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 =>) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#C') @ in @
% 98.38/13.31 omega)))))) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#S') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 '#S') @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 =>))) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#C') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 '#B') @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 =) @
% 98.38/13.31 omegaS)))) @
% 98.38/13.31 omegaS)))))) @
% 98.38/13.31 (
% 98.38/13.31 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.38/13.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2039])).
% 98.38/13.31 thf(zip_derived_cl2059, plain,
% 98.38/13.31 (~ (((funcGraphProp2) =>
% 98.38/13.31 (((funcextLem) =>
% 98.38/13.31 (((funcGraphProp4) =>
% 98.38/13.31 (((subbreln) =>
% 98.38/13.31 (((eqbreln) =>
% 98.38/13.31 (((funcext) =>
% 98.38/13.31 (((funcext2) =>
% 98.38/13.31 (((ap2apEq1) =>
% 98.38/13.31 (((ap2apEq2) =>
% 98.38/13.31 (((beta1) =>
% 98.38/13.31 (((eta1) =>
% 98.38/13.31 (((lam2lamEq) =>
% 98.38/13.31 (((beta2) =>
% 98.38/13.31 (((eta2) =>
% 98.38/13.31 (((iffalseProp1) =>
% 98.38/13.31 (((iffalseProp2) =>
% 98.38/13.31 (((iftrueProp1) =>
% 98.38/13.31 (((iftrueProp2) =>
% 98.38/13.31 (((ifSingleton) =>
% 98.38/13.31 (((ifp) =>
% 98.38/13.31 (((theeq) =>
% 98.38/13.31 (((iftrue) =>
% 98.38/13.31 (((iffalse) =>
% 98.38/13.31 (((iftrueorfalse) =>
% 98.38/13.31 (((binintersectT_lem) =>
% 98.38/13.31 (((binunionT_lem) =>
% 98.38/13.31 (((powersetT_lem) =>
% 98.38/13.31 (((setminusT_lem) =>
% 98.38/13.31 (((complementT_lem) =>
% 98.38/13.31 (((setextT) =>
% 98.38/13.31 ((
% 98.38/13.31 (subsetTI) =>
% 98.38/13.31 ((
% 98.38/13.31 (powersetTI1) =>
% 98.38/13.31 ((
% 98.38/13.31 (powersetTE1) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementTI1) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementTE1) =>
% 98.38/13.31 ((
% 98.38/13.31 (binintersectTELcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (binintersectTERcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (contrasubsetT) =>
% 98.38/13.31 ((
% 98.38/13.31 (contrasubsetT1) =>
% 98.38/13.31 ((
% 98.38/13.31 (contrasubsetT2) =>
% 98.38/13.31 ((
% 98.38/13.31 (contrasubsetT3) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementI1) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementE1) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementSub1) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementSub2) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementEq) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementTnotintersectT) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementImpComplementIntersect) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementSubsetComplementIntersect) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementInPowersetComplementIntersect) =>
% 98.38/13.31 ((
% 98.38/13.31 (contraSubsetComplement) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementTcontraSubset) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionTILcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionTIRcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (inIntersectImpInUnion) =>
% 98.38/13.31 ((
% 98.38/13.31 (inIntersectImpInUnion2) =>
% 98.38/13.31 ((
% 98.38/13.31 (inIntersectImpInIntersectUnions) =>
% 98.38/13.31 ((
% 98.38/13.31 (intersectInPowersetIntersectUnions) =>
% 98.38/13.31 ((
% 98.38/13.31 (inComplementUnionImpNotIn1) =>
% 98.38/13.31 ((
% 98.38/13.31 (inComplementUnionImpInComplement1) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionTE) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionTEcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2a1) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementUnionInPowersetComplement) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2a2) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan1a) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan1b) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan1) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2a) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2b2) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2b) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule0) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule1) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule2) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule3) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule4) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_1) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_2) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_3) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_4) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_5) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1all2) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1SetBreln1) =>
% 98.38/13.31 ((
% 98.38/13.31 (choice2fnsingleton) =>
% 98.38/13.31 ((
% 98.38/13.31 (setOfPairsIsBReln1) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1all1) =>
% 98.38/13.31 ((
% 98.38/13.31 (subbreln1) =>
% 98.38/13.31 ((
% 98.38/13.31 (eqbreln1) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1invprop) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1invI) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1invE) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1compprop) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1compI) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1compE) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1compEex) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionprop) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionIL) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionIR) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionI) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionE) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionEcases) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionCommutes) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz2Ex) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz2W) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz2A) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz2B) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1Ex) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1Ex1) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1Equiv) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1E) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1I) =>
% 98.38/13.31 ((
% 98.38/13.31 (injFuncInInjFuncSet) =>
% 98.38/13.31 ((
% 98.38/13.31 (injFuncSetFuncIn) =>
% 98.38/13.31 ((
% 98.38/13.31 (injFuncSetFuncInj) =>
% 98.38/13.31 ((
% 98.38/13.31 (surjFuncSetFuncIn) =>
% 98.38/13.31 ((
% 98.38/13.31 (surjFuncSetFuncSurj) =>
% 98.38/13.31 ((
% 98.38/13.31 (leftInvIsSurj) =>
% 98.38/13.31 ((
% 98.38/13.31 (surjCantorThm) =>
% 98.38/13.31 ((
% 98.38/13.31 (foundation2) =>
% 98.38/13.31 ((
% 98.38/13.31 (notinself) =>
% 98.38/13.31 ((
% 98.38/13.31 (notinself2) =>
% 98.38/13.31 ((
% 98.38/13.31 (omegaSp) =>
% 98.38/13.31 ((
% 98.38/13.31 (omegaSclos) =>
% 98.38/13.31 ((
% 98.38/13.31 (peano0notS) =>
% 98.38/13.31 ((
% 98.38/13.31 (!!) @ (
% 98.38/13.31 (('#S') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 =>) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#C') @ in @
% 98.38/13.31 omega)))) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 !!) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#S') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 =>) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#C') @ in @
% 98.38/13.31 omega)))))) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#S') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 '#S') @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 =>))) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#C') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 '#B') @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 =) @
% 98.38/13.31 omegaS)))) @
% 98.38/13.31 omegaS)))))) @
% 98.38/13.31 (
% 98.38/13.31 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.38/13.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2048])).
% 98.38/13.31 thf(zip_derived_cl2070, plain,
% 98.38/13.31 (~ (((funcextLem) =>
% 98.38/13.31 (((funcGraphProp4) =>
% 98.38/13.31 (((subbreln) =>
% 98.38/13.31 (((eqbreln) =>
% 98.38/13.31 (((funcext) =>
% 98.38/13.31 (((funcext2) =>
% 98.38/13.31 (((ap2apEq1) =>
% 98.38/13.31 (((ap2apEq2) =>
% 98.38/13.31 (((beta1) =>
% 98.38/13.31 (((eta1) =>
% 98.38/13.31 (((lam2lamEq) =>
% 98.38/13.31 (((beta2) =>
% 98.38/13.31 (((eta2) =>
% 98.38/13.31 (((iffalseProp1) =>
% 98.38/13.31 (((iffalseProp2) =>
% 98.38/13.31 (((iftrueProp1) =>
% 98.38/13.31 (((iftrueProp2) =>
% 98.38/13.31 (((ifSingleton) =>
% 98.38/13.31 (((ifp) =>
% 98.38/13.31 (((theeq) =>
% 98.38/13.31 (((iftrue) =>
% 98.38/13.31 (((iffalse) =>
% 98.38/13.31 (((iftrueorfalse) =>
% 98.38/13.31 (((binintersectT_lem) =>
% 98.38/13.31 (((binunionT_lem) =>
% 98.38/13.31 (((powersetT_lem) =>
% 98.38/13.31 (((setminusT_lem) =>
% 98.38/13.31 (((complementT_lem) =>
% 98.38/13.31 (((setextT) =>
% 98.38/13.31 (((subsetTI) =>
% 98.38/13.31 ((
% 98.38/13.31 (powersetTI1) =>
% 98.38/13.31 ((
% 98.38/13.31 (powersetTE1) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementTI1) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementTE1) =>
% 98.38/13.31 ((
% 98.38/13.31 (binintersectTELcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (binintersectTERcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (contrasubsetT) =>
% 98.38/13.31 ((
% 98.38/13.31 (contrasubsetT1) =>
% 98.38/13.31 ((
% 98.38/13.31 (contrasubsetT2) =>
% 98.38/13.31 ((
% 98.38/13.31 (contrasubsetT3) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementI1) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementE1) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementSub1) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementSub2) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementEq) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementTnotintersectT) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementImpComplementIntersect) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementSubsetComplementIntersect) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementInPowersetComplementIntersect) =>
% 98.38/13.31 ((
% 98.38/13.31 (contraSubsetComplement) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementTcontraSubset) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionTILcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionTIRcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (inIntersectImpInUnion) =>
% 98.38/13.31 ((
% 98.38/13.31 (inIntersectImpInUnion2) =>
% 98.38/13.31 ((
% 98.38/13.31 (inIntersectImpInIntersectUnions) =>
% 98.38/13.31 ((
% 98.38/13.31 (intersectInPowersetIntersectUnions) =>
% 98.38/13.31 ((
% 98.38/13.31 (inComplementUnionImpNotIn1) =>
% 98.38/13.31 ((
% 98.38/13.31 (inComplementUnionImpInComplement1) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionTE) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionTEcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2a1) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementUnionInPowersetComplement) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2a2) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan1a) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan1b) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan1) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2a) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2b2) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2b) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule0) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule1) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule2) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule3) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule4) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_1) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_2) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_3) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_4) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_5) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1all2) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1SetBreln1) =>
% 98.38/13.31 ((
% 98.38/13.31 (choice2fnsingleton) =>
% 98.38/13.31 ((
% 98.38/13.31 (setOfPairsIsBReln1) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1all1) =>
% 98.38/13.31 ((
% 98.38/13.31 (subbreln1) =>
% 98.38/13.31 ((
% 98.38/13.31 (eqbreln1) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1invprop) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1invI) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1invE) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1compprop) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1compI) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1compE) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1compEex) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionprop) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionIL) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionIR) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionI) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionE) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionEcases) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionCommutes) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz2Ex) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz2W) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz2A) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz2B) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1Ex) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1Ex1) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1Equiv) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1E) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1I) =>
% 98.38/13.31 ((
% 98.38/13.31 (injFuncInInjFuncSet) =>
% 98.38/13.31 ((
% 98.38/13.31 (injFuncSetFuncIn) =>
% 98.38/13.31 ((
% 98.38/13.31 (injFuncSetFuncInj) =>
% 98.38/13.31 ((
% 98.38/13.31 (surjFuncSetFuncIn) =>
% 98.38/13.31 ((
% 98.38/13.31 (surjFuncSetFuncSurj) =>
% 98.38/13.31 ((
% 98.38/13.31 (leftInvIsSurj) =>
% 98.38/13.31 ((
% 98.38/13.31 (surjCantorThm) =>
% 98.38/13.31 ((
% 98.38/13.31 (foundation2) =>
% 98.38/13.31 ((
% 98.38/13.31 (notinself) =>
% 98.38/13.31 ((
% 98.38/13.31 (notinself2) =>
% 98.38/13.31 ((
% 98.38/13.31 (omegaSp) =>
% 98.38/13.31 ((
% 98.38/13.31 (omegaSclos) =>
% 98.38/13.31 ((
% 98.38/13.31 (peano0notS) =>
% 98.38/13.31 ((
% 98.38/13.31 (!!) @ (
% 98.38/13.31 (('#S') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 =>) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#C') @ in @
% 98.38/13.31 omega)))) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 !!) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#S') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 =>) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#C') @ in @
% 98.38/13.31 omega)))))) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#S') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 '#S') @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 =>))) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#C') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 '#B') @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 =) @
% 98.38/13.31 omegaS)))) @
% 98.38/13.31 omegaS)))))) @
% 98.38/13.31 (
% 98.38/13.31 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.38/13.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2059])).
% 98.38/13.31 thf(zip_derived_cl2081, plain,
% 98.38/13.31 (~ (((funcGraphProp4) =>
% 98.38/13.31 (((subbreln) =>
% 98.38/13.31 (((eqbreln) =>
% 98.38/13.31 (((funcext) =>
% 98.38/13.31 (((funcext2) =>
% 98.38/13.31 (((ap2apEq1) =>
% 98.38/13.31 (((ap2apEq2) =>
% 98.38/13.31 (((beta1) =>
% 98.38/13.31 (((eta1) =>
% 98.38/13.31 (((lam2lamEq) =>
% 98.38/13.31 (((beta2) =>
% 98.38/13.31 (((eta2) =>
% 98.38/13.31 (((iffalseProp1) =>
% 98.38/13.31 (((iffalseProp2) =>
% 98.38/13.31 (((iftrueProp1) =>
% 98.38/13.31 (((iftrueProp2) =>
% 98.38/13.31 (((ifSingleton) =>
% 98.38/13.31 (((ifp) =>
% 98.38/13.31 (((theeq) =>
% 98.38/13.31 (((iftrue) =>
% 98.38/13.31 (((iffalse) =>
% 98.38/13.31 (((iftrueorfalse) =>
% 98.38/13.31 (((binintersectT_lem) =>
% 98.38/13.31 (((binunionT_lem) =>
% 98.38/13.31 (((powersetT_lem) =>
% 98.38/13.31 (((setminusT_lem) =>
% 98.38/13.31 (((complementT_lem) =>
% 98.38/13.31 (((setextT) =>
% 98.38/13.31 (((subsetTI) =>
% 98.38/13.31 (((powersetTI1) =>
% 98.38/13.31 ((
% 98.38/13.31 (powersetTE1) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementTI1) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementTE1) =>
% 98.38/13.31 ((
% 98.38/13.31 (binintersectTELcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (binintersectTERcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (contrasubsetT) =>
% 98.38/13.31 ((
% 98.38/13.31 (contrasubsetT1) =>
% 98.38/13.31 ((
% 98.38/13.31 (contrasubsetT2) =>
% 98.38/13.31 ((
% 98.38/13.31 (contrasubsetT3) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementI1) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementE1) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementSub1) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementSub2) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementEq) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementTnotintersectT) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementImpComplementIntersect) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementSubsetComplementIntersect) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementInPowersetComplementIntersect) =>
% 98.38/13.31 ((
% 98.38/13.31 (contraSubsetComplement) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementTcontraSubset) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionTILcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionTIRcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (inIntersectImpInUnion) =>
% 98.38/13.31 ((
% 98.38/13.31 (inIntersectImpInUnion2) =>
% 98.38/13.31 ((
% 98.38/13.31 (inIntersectImpInIntersectUnions) =>
% 98.38/13.31 ((
% 98.38/13.31 (intersectInPowersetIntersectUnions) =>
% 98.38/13.31 ((
% 98.38/13.31 (inComplementUnionImpNotIn1) =>
% 98.38/13.31 ((
% 98.38/13.31 (inComplementUnionImpInComplement1) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionTE) =>
% 98.38/13.31 ((
% 98.38/13.31 (binunionTEcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2a1) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementUnionInPowersetComplement) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2a2) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan1a) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan1b) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan1) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2a) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2b2) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2b) =>
% 98.38/13.31 ((
% 98.38/13.31 (demorgan2) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule0) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule1) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule2) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule3) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz13rule4) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_1) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_2) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_3) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_4) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz1_5) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1all2) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1SetBreln1) =>
% 98.38/13.31 ((
% 98.38/13.31 (choice2fnsingleton) =>
% 98.38/13.31 ((
% 98.38/13.31 (setOfPairsIsBReln1) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1all1) =>
% 98.38/13.31 ((
% 98.38/13.31 (subbreln1) =>
% 98.38/13.31 ((
% 98.38/13.31 (eqbreln1) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1invprop) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1invI) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1invE) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1compprop) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1compI) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1compE) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1compEex) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionprop) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionIL) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionIR) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionI) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionE) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionEcases) =>
% 98.38/13.31 ((
% 98.38/13.31 (breln1unionCommutes) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz2Ex) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz2W) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz2A) =>
% 98.38/13.31 ((
% 98.38/13.31 (woz2B) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1Ex) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1Ex1) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1Equiv) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1E) =>
% 98.38/13.31 ((
% 98.38/13.31 (image1I) =>
% 98.38/13.31 ((
% 98.38/13.31 (injFuncInInjFuncSet) =>
% 98.38/13.31 ((
% 98.38/13.31 (injFuncSetFuncIn) =>
% 98.38/13.31 ((
% 98.38/13.31 (injFuncSetFuncInj) =>
% 98.38/13.31 ((
% 98.38/13.31 (surjFuncSetFuncIn) =>
% 98.38/13.31 ((
% 98.38/13.31 (surjFuncSetFuncSurj) =>
% 98.38/13.31 ((
% 98.38/13.31 (leftInvIsSurj) =>
% 98.38/13.31 ((
% 98.38/13.31 (surjCantorThm) =>
% 98.38/13.31 ((
% 98.38/13.31 (foundation2) =>
% 98.38/13.31 ((
% 98.38/13.31 (notinself) =>
% 98.38/13.31 ((
% 98.38/13.31 (notinself2) =>
% 98.38/13.31 ((
% 98.38/13.31 (omegaSp) =>
% 98.38/13.31 ((
% 98.38/13.31 (omegaSclos) =>
% 98.38/13.31 ((
% 98.38/13.31 (peano0notS) =>
% 98.38/13.31 ((
% 98.38/13.31 (!!) @ (
% 98.38/13.31 (('#S') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 =>) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#C') @ in @
% 98.38/13.31 omega)))) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 !!) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#S') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 =>) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#C') @ in @
% 98.38/13.31 omega)))))) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#S') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 '#S') @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 =>))) @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#C') @ (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 '#B') @
% 98.38/13.31 (
% 98.38/13.31 (
% 98.38/13.31 ('#B') @ (
% 98.38/13.31 =) @
% 98.38/13.31 omegaS)))) @
% 98.38/13.31 omegaS)))))) @
% 98.38/13.31 (
% 98.38/13.31 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.38/13.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2070])).
% 98.38/13.31 thf(zip_derived_cl2091, plain,
% 98.38/13.31 (~ (((subbreln) =>
% 98.38/13.31 (((eqbreln) =>
% 98.38/13.31 (((funcext) =>
% 98.38/13.31 (((funcext2) =>
% 98.38/13.31 (((ap2apEq1) =>
% 98.38/13.31 (((ap2apEq2) =>
% 98.38/13.31 (((beta1) =>
% 98.38/13.31 (((eta1) =>
% 98.38/13.31 (((lam2lamEq) =>
% 98.38/13.31 (((beta2) =>
% 98.38/13.31 (((eta2) =>
% 98.38/13.31 (((iffalseProp1) =>
% 98.38/13.31 (((iffalseProp2) =>
% 98.38/13.31 (((iftrueProp1) =>
% 98.38/13.31 (((iftrueProp2) =>
% 98.38/13.31 (((ifSingleton) =>
% 98.38/13.31 (((ifp) =>
% 98.38/13.31 (((theeq) =>
% 98.38/13.31 (((iftrue) =>
% 98.38/13.31 (((iffalse) =>
% 98.38/13.31 (((iftrueorfalse) =>
% 98.38/13.31 (((binintersectT_lem) =>
% 98.38/13.31 (((binunionT_lem) =>
% 98.38/13.31 (((powersetT_lem) =>
% 98.38/13.31 (((setminusT_lem) =>
% 98.38/13.31 (((complementT_lem) =>
% 98.38/13.31 (((setextT) =>
% 98.38/13.31 (((subsetTI) =>
% 98.38/13.31 (((powersetTI1) =>
% 98.38/13.31 (((powersetTE1) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementTI1) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementTE1) =>
% 98.38/13.31 ((
% 98.38/13.31 (binintersectTELcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (binintersectTERcontra) =>
% 98.38/13.31 ((
% 98.38/13.31 (contrasubsetT) =>
% 98.38/13.31 ((
% 98.38/13.31 (contrasubsetT1) =>
% 98.38/13.31 ((
% 98.38/13.31 (contrasubsetT2) =>
% 98.38/13.31 ((
% 98.38/13.31 (contrasubsetT3) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementI1) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementE1) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementSub1) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementSub2) =>
% 98.38/13.31 ((
% 98.38/13.31 (doubleComplementEq) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementTnotintersectT) =>
% 98.38/13.31 ((
% 98.38/13.31 (complementImpComplementIntersect) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementSubsetComplementIntersect) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementInPowersetComplementIntersect) =>
% 98.38/13.32 ((
% 98.38/13.32 (contraSubsetComplement) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementTcontraSubset) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTILcontra) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTIRcontra) =>
% 98.38/13.32 ((
% 98.38/13.32 (inIntersectImpInUnion) =>
% 98.38/13.32 ((
% 98.38/13.32 (inIntersectImpInUnion2) =>
% 98.38/13.32 ((
% 98.38/13.32 (inIntersectImpInIntersectUnions) =>
% 98.38/13.32 ((
% 98.38/13.32 (intersectInPowersetIntersectUnions) =>
% 98.38/13.32 ((
% 98.38/13.32 (inComplementUnionImpNotIn1) =>
% 98.38/13.32 ((
% 98.38/13.32 (inComplementUnionImpInComplement1) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTE) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTEcontra) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2a1) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementUnionInPowersetComplement) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2a2) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan1a) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan1b) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan1) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2a) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2b2) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2b) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule0) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule1) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule2) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule3) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule4) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_1) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_2) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_3) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_4) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_5) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1all2) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1SetBreln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (choice2fnsingleton) =>
% 98.38/13.32 ((
% 98.38/13.32 (setOfPairsIsBReln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1all1) =>
% 98.38/13.32 ((
% 98.38/13.32 (subbreln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (eqbreln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1invprop) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1invI) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1invE) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compprop) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compI) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compE) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compEex) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionprop) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionIL) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionIR) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionI) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionE) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionEcases) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionCommutes) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2Ex) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2W) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2A) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2B) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1Ex) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1Ex1) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1Equiv) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1E) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1I) =>
% 98.38/13.32 ((
% 98.38/13.32 (injFuncInInjFuncSet) =>
% 98.38/13.32 ((
% 98.38/13.32 (injFuncSetFuncIn) =>
% 98.38/13.32 ((
% 98.38/13.32 (injFuncSetFuncInj) =>
% 98.38/13.32 ((
% 98.38/13.32 (surjFuncSetFuncIn) =>
% 98.38/13.32 ((
% 98.38/13.32 (surjFuncSetFuncSurj) =>
% 98.38/13.32 ((
% 98.38/13.32 (leftInvIsSurj) =>
% 98.38/13.32 ((
% 98.38/13.32 (surjCantorThm) =>
% 98.38/13.32 ((
% 98.38/13.32 (foundation2) =>
% 98.38/13.32 ((
% 98.38/13.32 (notinself) =>
% 98.38/13.32 ((
% 98.38/13.32 (notinself2) =>
% 98.38/13.32 ((
% 98.38/13.32 (omegaSp) =>
% 98.38/13.32 ((
% 98.38/13.32 (omegaSclos) =>
% 98.38/13.32 ((
% 98.38/13.32 (peano0notS) =>
% 98.38/13.32 ((
% 98.38/13.32 (!!) @ (
% 98.38/13.32 (('#S') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =>) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#C') @ in @
% 98.38/13.32 omega)))) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 !!) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#S') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =>) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#C') @ in @
% 98.38/13.32 omega)))))) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#S') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 '#S') @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =>))) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#C') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 '#B') @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =) @
% 98.38/13.32 omegaS)))) @
% 98.38/13.32 omegaS)))))) @
% 98.38/13.32 (
% 98.38/13.32 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.38/13.32 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2081])).
% 98.38/13.32 thf(zip_derived_cl2102, plain,
% 98.38/13.32 (~ (((eqbreln) =>
% 98.38/13.32 (((funcext) =>
% 98.38/13.32 (((funcext2) =>
% 98.38/13.32 (((ap2apEq1) =>
% 98.38/13.32 (((ap2apEq2) =>
% 98.38/13.32 (((beta1) =>
% 98.38/13.32 (((eta1) =>
% 98.38/13.32 (((lam2lamEq) =>
% 98.38/13.32 (((beta2) =>
% 98.38/13.32 (((eta2) =>
% 98.38/13.32 (((iffalseProp1) =>
% 98.38/13.32 (((iffalseProp2) =>
% 98.38/13.32 (((iftrueProp1) =>
% 98.38/13.32 (((iftrueProp2) =>
% 98.38/13.32 (((ifSingleton) =>
% 98.38/13.32 (((ifp) =>
% 98.38/13.32 (((theeq) =>
% 98.38/13.32 (((iftrue) =>
% 98.38/13.32 (((iffalse) =>
% 98.38/13.32 (((iftrueorfalse) =>
% 98.38/13.32 (((binintersectT_lem) =>
% 98.38/13.32 (((binunionT_lem) =>
% 98.38/13.32 (((powersetT_lem) =>
% 98.38/13.32 (((setminusT_lem) =>
% 98.38/13.32 (((complementT_lem) =>
% 98.38/13.32 (((setextT) =>
% 98.38/13.32 (((subsetTI) =>
% 98.38/13.32 (((powersetTI1) =>
% 98.38/13.32 (((powersetTE1) =>
% 98.38/13.32 (((complementTI1) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementTE1) =>
% 98.38/13.32 ((
% 98.38/13.32 (binintersectTELcontra) =>
% 98.38/13.32 ((
% 98.38/13.32 (binintersectTERcontra) =>
% 98.38/13.32 ((
% 98.38/13.32 (contrasubsetT) =>
% 98.38/13.32 ((
% 98.38/13.32 (contrasubsetT1) =>
% 98.38/13.32 ((
% 98.38/13.32 (contrasubsetT2) =>
% 98.38/13.32 ((
% 98.38/13.32 (contrasubsetT3) =>
% 98.38/13.32 ((
% 98.38/13.32 (doubleComplementI1) =>
% 98.38/13.32 ((
% 98.38/13.32 (doubleComplementE1) =>
% 98.38/13.32 ((
% 98.38/13.32 (doubleComplementSub1) =>
% 98.38/13.32 ((
% 98.38/13.32 (doubleComplementSub2) =>
% 98.38/13.32 ((
% 98.38/13.32 (doubleComplementEq) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementTnotintersectT) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementImpComplementIntersect) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementSubsetComplementIntersect) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementInPowersetComplementIntersect) =>
% 98.38/13.32 ((
% 98.38/13.32 (contraSubsetComplement) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementTcontraSubset) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTILcontra) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTIRcontra) =>
% 98.38/13.32 ((
% 98.38/13.32 (inIntersectImpInUnion) =>
% 98.38/13.32 ((
% 98.38/13.32 (inIntersectImpInUnion2) =>
% 98.38/13.32 ((
% 98.38/13.32 (inIntersectImpInIntersectUnions) =>
% 98.38/13.32 ((
% 98.38/13.32 (intersectInPowersetIntersectUnions) =>
% 98.38/13.32 ((
% 98.38/13.32 (inComplementUnionImpNotIn1) =>
% 98.38/13.32 ((
% 98.38/13.32 (inComplementUnionImpInComplement1) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTE) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTEcontra) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2a1) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementUnionInPowersetComplement) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2a2) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan1a) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan1b) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan1) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2a) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2b2) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2b) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule0) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule1) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule2) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule3) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule4) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_1) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_2) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_3) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_4) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_5) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1all2) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1SetBreln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (choice2fnsingleton) =>
% 98.38/13.32 ((
% 98.38/13.32 (setOfPairsIsBReln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1all1) =>
% 98.38/13.32 ((
% 98.38/13.32 (subbreln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (eqbreln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1invprop) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1invI) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1invE) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compprop) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compI) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compE) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compEex) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionprop) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionIL) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionIR) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionI) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionE) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionEcases) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionCommutes) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2Ex) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2W) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2A) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2B) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1Ex) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1Ex1) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1Equiv) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1E) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1I) =>
% 98.38/13.32 ((
% 98.38/13.32 (injFuncInInjFuncSet) =>
% 98.38/13.32 ((
% 98.38/13.32 (injFuncSetFuncIn) =>
% 98.38/13.32 ((
% 98.38/13.32 (injFuncSetFuncInj) =>
% 98.38/13.32 ((
% 98.38/13.32 (surjFuncSetFuncIn) =>
% 98.38/13.32 ((
% 98.38/13.32 (surjFuncSetFuncSurj) =>
% 98.38/13.32 ((
% 98.38/13.32 (leftInvIsSurj) =>
% 98.38/13.32 ((
% 98.38/13.32 (surjCantorThm) =>
% 98.38/13.32 ((
% 98.38/13.32 (foundation2) =>
% 98.38/13.32 ((
% 98.38/13.32 (notinself) =>
% 98.38/13.32 ((
% 98.38/13.32 (notinself2) =>
% 98.38/13.32 ((
% 98.38/13.32 (omegaSp) =>
% 98.38/13.32 ((
% 98.38/13.32 (omegaSclos) =>
% 98.38/13.32 ((
% 98.38/13.32 (peano0notS) =>
% 98.38/13.32 ((
% 98.38/13.32 (!!) @ (
% 98.38/13.32 (('#S') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =>) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#C') @ in @
% 98.38/13.32 omega)))) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 !!) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#S') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =>) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#C') @ in @
% 98.38/13.32 omega)))))) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#S') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 '#S') @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =>))) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#C') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 '#B') @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =) @
% 98.38/13.32 omegaS)))) @
% 98.38/13.32 omegaS)))))) @
% 98.38/13.32 (
% 98.38/13.32 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.38/13.32 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2091])).
% 98.38/13.32 thf(zip_derived_cl2115, plain,
% 98.38/13.32 (~ (((funcext) =>
% 98.38/13.32 (((funcext2) =>
% 98.38/13.32 (((ap2apEq1) =>
% 98.38/13.32 (((ap2apEq2) =>
% 98.38/13.32 (((beta1) =>
% 98.38/13.32 (((eta1) =>
% 98.38/13.32 (((lam2lamEq) =>
% 98.38/13.32 (((beta2) =>
% 98.38/13.32 (((eta2) =>
% 98.38/13.32 (((iffalseProp1) =>
% 98.38/13.32 (((iffalseProp2) =>
% 98.38/13.32 (((iftrueProp1) =>
% 98.38/13.32 (((iftrueProp2) =>
% 98.38/13.32 (((ifSingleton) =>
% 98.38/13.32 (((ifp) =>
% 98.38/13.32 (((theeq) =>
% 98.38/13.32 (((iftrue) =>
% 98.38/13.32 (((iffalse) =>
% 98.38/13.32 (((iftrueorfalse) =>
% 98.38/13.32 (((binintersectT_lem) =>
% 98.38/13.32 (((binunionT_lem) =>
% 98.38/13.32 (((powersetT_lem) =>
% 98.38/13.32 (((setminusT_lem) =>
% 98.38/13.32 (((complementT_lem) =>
% 98.38/13.32 (((setextT) =>
% 98.38/13.32 (((subsetTI) =>
% 98.38/13.32 (((powersetTI1) =>
% 98.38/13.32 (((powersetTE1) =>
% 98.38/13.32 (((complementTI1) =>
% 98.38/13.32 (((complementTE1) =>
% 98.38/13.32 ((
% 98.38/13.32 (binintersectTELcontra) =>
% 98.38/13.32 ((
% 98.38/13.32 (binintersectTERcontra) =>
% 98.38/13.32 ((
% 98.38/13.32 (contrasubsetT) =>
% 98.38/13.32 ((
% 98.38/13.32 (contrasubsetT1) =>
% 98.38/13.32 ((
% 98.38/13.32 (contrasubsetT2) =>
% 98.38/13.32 ((
% 98.38/13.32 (contrasubsetT3) =>
% 98.38/13.32 ((
% 98.38/13.32 (doubleComplementI1) =>
% 98.38/13.32 ((
% 98.38/13.32 (doubleComplementE1) =>
% 98.38/13.32 ((
% 98.38/13.32 (doubleComplementSub1) =>
% 98.38/13.32 ((
% 98.38/13.32 (doubleComplementSub2) =>
% 98.38/13.32 ((
% 98.38/13.32 (doubleComplementEq) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementTnotintersectT) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementImpComplementIntersect) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementSubsetComplementIntersect) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementInPowersetComplementIntersect) =>
% 98.38/13.32 ((
% 98.38/13.32 (contraSubsetComplement) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementTcontraSubset) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTILcontra) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTIRcontra) =>
% 98.38/13.32 ((
% 98.38/13.32 (inIntersectImpInUnion) =>
% 98.38/13.32 ((
% 98.38/13.32 (inIntersectImpInUnion2) =>
% 98.38/13.32 ((
% 98.38/13.32 (inIntersectImpInIntersectUnions) =>
% 98.38/13.32 ((
% 98.38/13.32 (intersectInPowersetIntersectUnions) =>
% 98.38/13.32 ((
% 98.38/13.32 (inComplementUnionImpNotIn1) =>
% 98.38/13.32 ((
% 98.38/13.32 (inComplementUnionImpInComplement1) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTE) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTEcontra) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2a1) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementUnionInPowersetComplement) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2a2) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan1a) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan1b) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan1) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2a) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2b2) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2b) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule0) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule1) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule2) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule3) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule4) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_1) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_2) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_3) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_4) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_5) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1all2) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1SetBreln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (choice2fnsingleton) =>
% 98.38/13.32 ((
% 98.38/13.32 (setOfPairsIsBReln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1all1) =>
% 98.38/13.32 ((
% 98.38/13.32 (subbreln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (eqbreln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1invprop) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1invI) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1invE) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compprop) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compI) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compE) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compEex) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionprop) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionIL) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionIR) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionI) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionE) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionEcases) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionCommutes) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2Ex) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2W) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2A) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2B) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1Ex) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1Ex1) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1Equiv) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1E) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1I) =>
% 98.38/13.32 ((
% 98.38/13.32 (injFuncInInjFuncSet) =>
% 98.38/13.32 ((
% 98.38/13.32 (injFuncSetFuncIn) =>
% 98.38/13.32 ((
% 98.38/13.32 (injFuncSetFuncInj) =>
% 98.38/13.32 ((
% 98.38/13.32 (surjFuncSetFuncIn) =>
% 98.38/13.32 ((
% 98.38/13.32 (surjFuncSetFuncSurj) =>
% 98.38/13.32 ((
% 98.38/13.32 (leftInvIsSurj) =>
% 98.38/13.32 ((
% 98.38/13.32 (surjCantorThm) =>
% 98.38/13.32 ((
% 98.38/13.32 (foundation2) =>
% 98.38/13.32 ((
% 98.38/13.32 (notinself) =>
% 98.38/13.32 ((
% 98.38/13.32 (notinself2) =>
% 98.38/13.32 ((
% 98.38/13.32 (omegaSp) =>
% 98.38/13.32 ((
% 98.38/13.32 (omegaSclos) =>
% 98.38/13.32 ((
% 98.38/13.32 (peano0notS) =>
% 98.38/13.32 ((
% 98.38/13.32 (!!) @ (
% 98.38/13.32 (('#S') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =>) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#C') @ in @
% 98.38/13.32 omega)))) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 !!) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#S') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =>) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#C') @ in @
% 98.38/13.32 omega)))))) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#S') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 '#S') @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =>))) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#C') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 '#B') @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =) @
% 98.38/13.32 omegaS)))) @
% 98.38/13.32 omegaS)))))) @
% 98.38/13.32 (
% 98.38/13.32 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.38/13.32 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2102])).
% 98.38/13.32 thf(zip_derived_cl2130, plain,
% 98.38/13.32 (~ (((funcext2) =>
% 98.38/13.32 (((ap2apEq1) =>
% 98.38/13.32 (((ap2apEq2) =>
% 98.38/13.32 (((beta1) =>
% 98.38/13.32 (((eta1) =>
% 98.38/13.32 (((lam2lamEq) =>
% 98.38/13.32 (((beta2) =>
% 98.38/13.32 (((eta2) =>
% 98.38/13.32 (((iffalseProp1) =>
% 98.38/13.32 (((iffalseProp2) =>
% 98.38/13.32 (((iftrueProp1) =>
% 98.38/13.32 (((iftrueProp2) =>
% 98.38/13.32 (((ifSingleton) =>
% 98.38/13.32 (((ifp) =>
% 98.38/13.32 (((theeq) =>
% 98.38/13.32 (((iftrue) =>
% 98.38/13.32 (((iffalse) =>
% 98.38/13.32 (((iftrueorfalse) =>
% 98.38/13.32 (((binintersectT_lem) =>
% 98.38/13.32 (((binunionT_lem) =>
% 98.38/13.32 (((powersetT_lem) =>
% 98.38/13.32 (((setminusT_lem) =>
% 98.38/13.32 (((complementT_lem) =>
% 98.38/13.32 (((setextT) =>
% 98.38/13.32 (((subsetTI) =>
% 98.38/13.32 (((powersetTI1) =>
% 98.38/13.32 (((powersetTE1) =>
% 98.38/13.32 (((complementTI1) =>
% 98.38/13.32 (((complementTE1) =>
% 98.38/13.32 (((binintersectTELcontra) =>
% 98.38/13.32 ((
% 98.38/13.32 (binintersectTERcontra) =>
% 98.38/13.32 ((
% 98.38/13.32 (contrasubsetT) =>
% 98.38/13.32 ((
% 98.38/13.32 (contrasubsetT1) =>
% 98.38/13.32 ((
% 98.38/13.32 (contrasubsetT2) =>
% 98.38/13.32 ((
% 98.38/13.32 (contrasubsetT3) =>
% 98.38/13.32 ((
% 98.38/13.32 (doubleComplementI1) =>
% 98.38/13.32 ((
% 98.38/13.32 (doubleComplementE1) =>
% 98.38/13.32 ((
% 98.38/13.32 (doubleComplementSub1) =>
% 98.38/13.32 ((
% 98.38/13.32 (doubleComplementSub2) =>
% 98.38/13.32 ((
% 98.38/13.32 (doubleComplementEq) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementTnotintersectT) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementImpComplementIntersect) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementSubsetComplementIntersect) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementInPowersetComplementIntersect) =>
% 98.38/13.32 ((
% 98.38/13.32 (contraSubsetComplement) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementTcontraSubset) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTILcontra) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTIRcontra) =>
% 98.38/13.32 ((
% 98.38/13.32 (inIntersectImpInUnion) =>
% 98.38/13.32 ((
% 98.38/13.32 (inIntersectImpInUnion2) =>
% 98.38/13.32 ((
% 98.38/13.32 (inIntersectImpInIntersectUnions) =>
% 98.38/13.32 ((
% 98.38/13.32 (intersectInPowersetIntersectUnions) =>
% 98.38/13.32 ((
% 98.38/13.32 (inComplementUnionImpNotIn1) =>
% 98.38/13.32 ((
% 98.38/13.32 (inComplementUnionImpInComplement1) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTE) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTEcontra) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2a1) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementUnionInPowersetComplement) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2a2) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan1a) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan1b) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan1) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2a) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2b2) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2b) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule0) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule1) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule2) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule3) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule4) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_1) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_2) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_3) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_4) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_5) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1all2) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1SetBreln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (choice2fnsingleton) =>
% 98.38/13.32 ((
% 98.38/13.32 (setOfPairsIsBReln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1all1) =>
% 98.38/13.32 ((
% 98.38/13.32 (subbreln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (eqbreln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1invprop) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1invI) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1invE) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compprop) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compI) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compE) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compEex) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionprop) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionIL) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionIR) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionI) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionE) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionEcases) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionCommutes) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2Ex) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2W) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2A) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2B) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1Ex) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1Ex1) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1Equiv) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1E) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1I) =>
% 98.38/13.32 ((
% 98.38/13.32 (injFuncInInjFuncSet) =>
% 98.38/13.32 ((
% 98.38/13.32 (injFuncSetFuncIn) =>
% 98.38/13.32 ((
% 98.38/13.32 (injFuncSetFuncInj) =>
% 98.38/13.32 ((
% 98.38/13.32 (surjFuncSetFuncIn) =>
% 98.38/13.32 ((
% 98.38/13.32 (surjFuncSetFuncSurj) =>
% 98.38/13.32 ((
% 98.38/13.32 (leftInvIsSurj) =>
% 98.38/13.32 ((
% 98.38/13.32 (surjCantorThm) =>
% 98.38/13.32 ((
% 98.38/13.32 (foundation2) =>
% 98.38/13.32 ((
% 98.38/13.32 (notinself) =>
% 98.38/13.32 ((
% 98.38/13.32 (notinself2) =>
% 98.38/13.32 ((
% 98.38/13.32 (omegaSp) =>
% 98.38/13.32 ((
% 98.38/13.32 (omegaSclos) =>
% 98.38/13.32 ((
% 98.38/13.32 (peano0notS) =>
% 98.38/13.32 ((
% 98.38/13.32 (!!) @ (
% 98.38/13.32 (('#S') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =>) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#C') @ in @
% 98.38/13.32 omega)))) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 !!) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#S') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =>) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#C') @ in @
% 98.38/13.32 omega)))))) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#S') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 '#S') @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =>))) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#C') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 '#B') @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =) @
% 98.38/13.32 omegaS)))) @
% 98.38/13.32 omegaS)))))) @
% 98.38/13.32 (
% 98.38/13.32 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.38/13.32 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2115])).
% 98.38/13.32 thf(zip_derived_cl2146, plain,
% 98.38/13.32 (~ (((ap2apEq1) =>
% 98.38/13.32 (((ap2apEq2) =>
% 98.38/13.32 (((beta1) =>
% 98.38/13.32 (((eta1) =>
% 98.38/13.32 (((lam2lamEq) =>
% 98.38/13.32 (((beta2) =>
% 98.38/13.32 (((eta2) =>
% 98.38/13.32 (((iffalseProp1) =>
% 98.38/13.32 (((iffalseProp2) =>
% 98.38/13.32 (((iftrueProp1) =>
% 98.38/13.32 (((iftrueProp2) =>
% 98.38/13.32 (((ifSingleton) =>
% 98.38/13.32 (((ifp) =>
% 98.38/13.32 (((theeq) =>
% 98.38/13.32 (((iftrue) =>
% 98.38/13.32 (((iffalse) =>
% 98.38/13.32 (((iftrueorfalse) =>
% 98.38/13.32 (((binintersectT_lem) =>
% 98.38/13.32 (((binunionT_lem) =>
% 98.38/13.32 (((powersetT_lem) =>
% 98.38/13.32 (((setminusT_lem) =>
% 98.38/13.32 (((complementT_lem) =>
% 98.38/13.32 (((setextT) =>
% 98.38/13.32 (((subsetTI) =>
% 98.38/13.32 (((powersetTI1) =>
% 98.38/13.32 (((powersetTE1) =>
% 98.38/13.32 (((complementTI1) =>
% 98.38/13.32 (((complementTE1) =>
% 98.38/13.32 (((binintersectTELcontra) =>
% 98.38/13.32 (((binintersectTERcontra) =>
% 98.38/13.32 ((
% 98.38/13.32 (contrasubsetT) =>
% 98.38/13.32 ((
% 98.38/13.32 (contrasubsetT1) =>
% 98.38/13.32 ((
% 98.38/13.32 (contrasubsetT2) =>
% 98.38/13.32 ((
% 98.38/13.32 (contrasubsetT3) =>
% 98.38/13.32 ((
% 98.38/13.32 (doubleComplementI1) =>
% 98.38/13.32 ((
% 98.38/13.32 (doubleComplementE1) =>
% 98.38/13.32 ((
% 98.38/13.32 (doubleComplementSub1) =>
% 98.38/13.32 ((
% 98.38/13.32 (doubleComplementSub2) =>
% 98.38/13.32 ((
% 98.38/13.32 (doubleComplementEq) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementTnotintersectT) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementImpComplementIntersect) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementSubsetComplementIntersect) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementInPowersetComplementIntersect) =>
% 98.38/13.32 ((
% 98.38/13.32 (contraSubsetComplement) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementTcontraSubset) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTILcontra) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTIRcontra) =>
% 98.38/13.32 ((
% 98.38/13.32 (inIntersectImpInUnion) =>
% 98.38/13.32 ((
% 98.38/13.32 (inIntersectImpInUnion2) =>
% 98.38/13.32 ((
% 98.38/13.32 (inIntersectImpInIntersectUnions) =>
% 98.38/13.32 ((
% 98.38/13.32 (intersectInPowersetIntersectUnions) =>
% 98.38/13.32 ((
% 98.38/13.32 (inComplementUnionImpNotIn1) =>
% 98.38/13.32 ((
% 98.38/13.32 (inComplementUnionImpInComplement1) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTE) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTEcontra) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2a1) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementUnionInPowersetComplement) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2a2) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan1a) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan1b) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan1) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2a) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2b2) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2b) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule0) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule1) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule2) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule3) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule4) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_1) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_2) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_3) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_4) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_5) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1all2) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1SetBreln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (choice2fnsingleton) =>
% 98.38/13.32 ((
% 98.38/13.32 (setOfPairsIsBReln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1all1) =>
% 98.38/13.32 ((
% 98.38/13.32 (subbreln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (eqbreln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1invprop) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1invI) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1invE) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compprop) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compI) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compE) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compEex) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionprop) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionIL) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionIR) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionI) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionE) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionEcases) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionCommutes) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2Ex) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2W) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2A) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2B) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1Ex) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1Ex1) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1Equiv) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1E) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1I) =>
% 98.38/13.32 ((
% 98.38/13.32 (injFuncInInjFuncSet) =>
% 98.38/13.32 ((
% 98.38/13.32 (injFuncSetFuncIn) =>
% 98.38/13.32 ((
% 98.38/13.32 (injFuncSetFuncInj) =>
% 98.38/13.32 ((
% 98.38/13.32 (surjFuncSetFuncIn) =>
% 98.38/13.32 ((
% 98.38/13.32 (surjFuncSetFuncSurj) =>
% 98.38/13.32 ((
% 98.38/13.32 (leftInvIsSurj) =>
% 98.38/13.32 ((
% 98.38/13.32 (surjCantorThm) =>
% 98.38/13.32 ((
% 98.38/13.32 (foundation2) =>
% 98.38/13.32 ((
% 98.38/13.32 (notinself) =>
% 98.38/13.32 ((
% 98.38/13.32 (notinself2) =>
% 98.38/13.32 ((
% 98.38/13.32 (omegaSp) =>
% 98.38/13.32 ((
% 98.38/13.32 (omegaSclos) =>
% 98.38/13.32 ((
% 98.38/13.32 (peano0notS) =>
% 98.38/13.32 ((
% 98.38/13.32 (!!) @ (
% 98.38/13.32 (('#S') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =>) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#C') @ in @
% 98.38/13.32 omega)))) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 !!) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#S') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =>) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#C') @ in @
% 98.38/13.32 omega)))))) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#S') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 '#S') @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =>))) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#C') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 '#B') @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =) @
% 98.38/13.32 omegaS)))) @
% 98.38/13.32 omegaS)))))) @
% 98.38/13.32 (
% 98.38/13.32 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.38/13.32 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2130])).
% 98.38/13.32 thf(zip_derived_cl2163, plain,
% 98.38/13.32 (~ (((ap2apEq2) =>
% 98.38/13.32 (((beta1) =>
% 98.38/13.32 (((eta1) =>
% 98.38/13.32 (((lam2lamEq) =>
% 98.38/13.32 (((beta2) =>
% 98.38/13.32 (((eta2) =>
% 98.38/13.32 (((iffalseProp1) =>
% 98.38/13.32 (((iffalseProp2) =>
% 98.38/13.32 (((iftrueProp1) =>
% 98.38/13.32 (((iftrueProp2) =>
% 98.38/13.32 (((ifSingleton) =>
% 98.38/13.32 (((ifp) =>
% 98.38/13.32 (((theeq) =>
% 98.38/13.32 (((iftrue) =>
% 98.38/13.32 (((iffalse) =>
% 98.38/13.32 (((iftrueorfalse) =>
% 98.38/13.32 (((binintersectT_lem) =>
% 98.38/13.32 (((binunionT_lem) =>
% 98.38/13.32 (((powersetT_lem) =>
% 98.38/13.32 (((setminusT_lem) =>
% 98.38/13.32 (((complementT_lem) =>
% 98.38/13.32 (((setextT) =>
% 98.38/13.32 (((subsetTI) =>
% 98.38/13.32 (((powersetTI1) =>
% 98.38/13.32 (((powersetTE1) =>
% 98.38/13.32 (((complementTI1) =>
% 98.38/13.32 (((complementTE1) =>
% 98.38/13.32 (((binintersectTELcontra) =>
% 98.38/13.32 (((binintersectTERcontra) =>
% 98.38/13.32 (((contrasubsetT) =>
% 98.38/13.32 ((
% 98.38/13.32 (contrasubsetT1) =>
% 98.38/13.32 ((
% 98.38/13.32 (contrasubsetT2) =>
% 98.38/13.32 ((
% 98.38/13.32 (contrasubsetT3) =>
% 98.38/13.32 ((
% 98.38/13.32 (doubleComplementI1) =>
% 98.38/13.32 ((
% 98.38/13.32 (doubleComplementE1) =>
% 98.38/13.32 ((
% 98.38/13.32 (doubleComplementSub1) =>
% 98.38/13.32 ((
% 98.38/13.32 (doubleComplementSub2) =>
% 98.38/13.32 ((
% 98.38/13.32 (doubleComplementEq) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementTnotintersectT) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementImpComplementIntersect) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementSubsetComplementIntersect) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementInPowersetComplementIntersect) =>
% 98.38/13.32 ((
% 98.38/13.32 (contraSubsetComplement) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementTcontraSubset) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTILcontra) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTIRcontra) =>
% 98.38/13.32 ((
% 98.38/13.32 (inIntersectImpInUnion) =>
% 98.38/13.32 ((
% 98.38/13.32 (inIntersectImpInUnion2) =>
% 98.38/13.32 ((
% 98.38/13.32 (inIntersectImpInIntersectUnions) =>
% 98.38/13.32 ((
% 98.38/13.32 (intersectInPowersetIntersectUnions) =>
% 98.38/13.32 ((
% 98.38/13.32 (inComplementUnionImpNotIn1) =>
% 98.38/13.32 ((
% 98.38/13.32 (inComplementUnionImpInComplement1) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTE) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTEcontra) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2a1) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementUnionInPowersetComplement) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2a2) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan1a) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan1b) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan1) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2a) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2b2) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2b) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule0) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule1) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule2) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule3) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule4) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_1) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_2) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_3) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_4) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_5) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1all2) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1SetBreln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (choice2fnsingleton) =>
% 98.38/13.32 ((
% 98.38/13.32 (setOfPairsIsBReln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1all1) =>
% 98.38/13.32 ((
% 98.38/13.32 (subbreln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (eqbreln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1invprop) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1invI) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1invE) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compprop) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compI) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compE) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compEex) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionprop) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionIL) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionIR) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionI) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionE) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionEcases) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionCommutes) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2Ex) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2W) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2A) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2B) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1Ex) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1Ex1) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1Equiv) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1E) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1I) =>
% 98.38/13.32 ((
% 98.38/13.32 (injFuncInInjFuncSet) =>
% 98.38/13.32 ((
% 98.38/13.32 (injFuncSetFuncIn) =>
% 98.38/13.32 ((
% 98.38/13.32 (injFuncSetFuncInj) =>
% 98.38/13.32 ((
% 98.38/13.32 (surjFuncSetFuncIn) =>
% 98.38/13.32 ((
% 98.38/13.32 (surjFuncSetFuncSurj) =>
% 98.38/13.32 ((
% 98.38/13.32 (leftInvIsSurj) =>
% 98.38/13.32 ((
% 98.38/13.32 (surjCantorThm) =>
% 98.38/13.32 ((
% 98.38/13.32 (foundation2) =>
% 98.38/13.32 ((
% 98.38/13.32 (notinself) =>
% 98.38/13.32 ((
% 98.38/13.32 (notinself2) =>
% 98.38/13.32 ((
% 98.38/13.32 (omegaSp) =>
% 98.38/13.32 ((
% 98.38/13.32 (omegaSclos) =>
% 98.38/13.32 ((
% 98.38/13.32 (peano0notS) =>
% 98.38/13.32 ((
% 98.38/13.32 (!!) @ (
% 98.38/13.32 (('#S') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =>) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#C') @ in @
% 98.38/13.32 omega)))) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 !!) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#S') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =>) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#C') @ in @
% 98.38/13.32 omega)))))) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#S') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 '#S') @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =>))) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#C') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 '#B') @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =) @
% 98.38/13.32 omegaS)))) @
% 98.38/13.32 omegaS)))))) @
% 98.38/13.32 (
% 98.38/13.32 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.38/13.32 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2146])).
% 98.38/13.32 thf(zip_derived_cl2181, plain,
% 98.38/13.32 (~ (((beta1) =>
% 98.38/13.32 (((eta1) =>
% 98.38/13.32 (((lam2lamEq) =>
% 98.38/13.32 (((beta2) =>
% 98.38/13.32 (((eta2) =>
% 98.38/13.32 (((iffalseProp1) =>
% 98.38/13.32 (((iffalseProp2) =>
% 98.38/13.32 (((iftrueProp1) =>
% 98.38/13.32 (((iftrueProp2) =>
% 98.38/13.32 (((ifSingleton) =>
% 98.38/13.32 (((ifp) =>
% 98.38/13.32 (((theeq) =>
% 98.38/13.32 (((iftrue) =>
% 98.38/13.32 (((iffalse) =>
% 98.38/13.32 (((iftrueorfalse) =>
% 98.38/13.32 (((binintersectT_lem) =>
% 98.38/13.32 (((binunionT_lem) =>
% 98.38/13.32 (((powersetT_lem) =>
% 98.38/13.32 (((setminusT_lem) =>
% 98.38/13.32 (((complementT_lem) =>
% 98.38/13.32 (((setextT) =>
% 98.38/13.32 (((subsetTI) =>
% 98.38/13.32 (((powersetTI1) =>
% 98.38/13.32 (((powersetTE1) =>
% 98.38/13.32 (((complementTI1) =>
% 98.38/13.32 (((complementTE1) =>
% 98.38/13.32 (((binintersectTELcontra) =>
% 98.38/13.32 (((binintersectTERcontra) =>
% 98.38/13.32 (((contrasubsetT) =>
% 98.38/13.32 (((contrasubsetT1) =>
% 98.38/13.32 ((
% 98.38/13.32 (contrasubsetT2) =>
% 98.38/13.32 ((
% 98.38/13.32 (contrasubsetT3) =>
% 98.38/13.32 ((
% 98.38/13.32 (doubleComplementI1) =>
% 98.38/13.32 ((
% 98.38/13.32 (doubleComplementE1) =>
% 98.38/13.32 ((
% 98.38/13.32 (doubleComplementSub1) =>
% 98.38/13.32 ((
% 98.38/13.32 (doubleComplementSub2) =>
% 98.38/13.32 ((
% 98.38/13.32 (doubleComplementEq) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementTnotintersectT) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementImpComplementIntersect) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementSubsetComplementIntersect) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementInPowersetComplementIntersect) =>
% 98.38/13.32 ((
% 98.38/13.32 (contraSubsetComplement) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementTcontraSubset) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTILcontra) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTIRcontra) =>
% 98.38/13.32 ((
% 98.38/13.32 (inIntersectImpInUnion) =>
% 98.38/13.32 ((
% 98.38/13.32 (inIntersectImpInUnion2) =>
% 98.38/13.32 ((
% 98.38/13.32 (inIntersectImpInIntersectUnions) =>
% 98.38/13.32 ((
% 98.38/13.32 (intersectInPowersetIntersectUnions) =>
% 98.38/13.32 ((
% 98.38/13.32 (inComplementUnionImpNotIn1) =>
% 98.38/13.32 ((
% 98.38/13.32 (inComplementUnionImpInComplement1) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTE) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTEcontra) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2a1) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementUnionInPowersetComplement) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2a2) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan1a) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan1b) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan1) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2a) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2b2) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2b) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule0) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule1) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule2) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule3) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule4) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_1) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_2) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_3) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_4) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_5) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1all2) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1SetBreln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (choice2fnsingleton) =>
% 98.38/13.32 ((
% 98.38/13.32 (setOfPairsIsBReln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1all1) =>
% 98.38/13.32 ((
% 98.38/13.32 (subbreln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (eqbreln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1invprop) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1invI) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1invE) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compprop) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compI) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compE) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compEex) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionprop) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionIL) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionIR) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionI) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionE) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionEcases) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionCommutes) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2Ex) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2W) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2A) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2B) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1Ex) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1Ex1) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1Equiv) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1E) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1I) =>
% 98.38/13.32 ((
% 98.38/13.32 (injFuncInInjFuncSet) =>
% 98.38/13.32 ((
% 98.38/13.32 (injFuncSetFuncIn) =>
% 98.38/13.32 ((
% 98.38/13.32 (injFuncSetFuncInj) =>
% 98.38/13.32 ((
% 98.38/13.32 (surjFuncSetFuncIn) =>
% 98.38/13.32 ((
% 98.38/13.32 (surjFuncSetFuncSurj) =>
% 98.38/13.32 ((
% 98.38/13.32 (leftInvIsSurj) =>
% 98.38/13.32 ((
% 98.38/13.32 (surjCantorThm) =>
% 98.38/13.32 ((
% 98.38/13.32 (foundation2) =>
% 98.38/13.32 ((
% 98.38/13.32 (notinself) =>
% 98.38/13.32 ((
% 98.38/13.32 (notinself2) =>
% 98.38/13.32 ((
% 98.38/13.32 (omegaSp) =>
% 98.38/13.32 ((
% 98.38/13.32 (omegaSclos) =>
% 98.38/13.32 ((
% 98.38/13.32 (peano0notS) =>
% 98.38/13.32 ((
% 98.38/13.32 (!!) @ (
% 98.38/13.32 (('#S') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =>) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#C') @ in @
% 98.38/13.32 omega)))) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 !!) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#S') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =>) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#C') @ in @
% 98.38/13.32 omega)))))) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#S') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 '#S') @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =>))) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#C') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 '#B') @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =) @
% 98.38/13.32 omegaS)))) @
% 98.38/13.32 omegaS)))))) @
% 98.38/13.32 (
% 98.38/13.32 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.38/13.32 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2163])).
% 98.38/13.32 thf(zip_derived_cl2198, plain,
% 98.38/13.32 (~ (((eta1) =>
% 98.38/13.32 (((lam2lamEq) =>
% 98.38/13.32 (((beta2) =>
% 98.38/13.32 (((eta2) =>
% 98.38/13.32 (((iffalseProp1) =>
% 98.38/13.32 (((iffalseProp2) =>
% 98.38/13.32 (((iftrueProp1) =>
% 98.38/13.32 (((iftrueProp2) =>
% 98.38/13.32 (((ifSingleton) =>
% 98.38/13.32 (((ifp) =>
% 98.38/13.32 (((theeq) =>
% 98.38/13.32 (((iftrue) =>
% 98.38/13.32 (((iffalse) =>
% 98.38/13.32 (((iftrueorfalse) =>
% 98.38/13.32 (((binintersectT_lem) =>
% 98.38/13.32 (((binunionT_lem) =>
% 98.38/13.32 (((powersetT_lem) =>
% 98.38/13.32 (((setminusT_lem) =>
% 98.38/13.32 (((complementT_lem) =>
% 98.38/13.32 (((setextT) =>
% 98.38/13.32 (((subsetTI) =>
% 98.38/13.32 (((powersetTI1) =>
% 98.38/13.32 (((powersetTE1) =>
% 98.38/13.32 (((complementTI1) =>
% 98.38/13.32 (((complementTE1) =>
% 98.38/13.32 (((binintersectTELcontra) =>
% 98.38/13.32 (((binintersectTERcontra) =>
% 98.38/13.32 (((contrasubsetT) =>
% 98.38/13.32 (((contrasubsetT1) =>
% 98.38/13.32 (((contrasubsetT2) =>
% 98.38/13.32 ((
% 98.38/13.32 (contrasubsetT3) =>
% 98.38/13.32 ((
% 98.38/13.32 (doubleComplementI1) =>
% 98.38/13.32 ((
% 98.38/13.32 (doubleComplementE1) =>
% 98.38/13.32 ((
% 98.38/13.32 (doubleComplementSub1) =>
% 98.38/13.32 ((
% 98.38/13.32 (doubleComplementSub2) =>
% 98.38/13.32 ((
% 98.38/13.32 (doubleComplementEq) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementTnotintersectT) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementImpComplementIntersect) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementSubsetComplementIntersect) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementInPowersetComplementIntersect) =>
% 98.38/13.32 ((
% 98.38/13.32 (contraSubsetComplement) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementTcontraSubset) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTILcontra) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTIRcontra) =>
% 98.38/13.32 ((
% 98.38/13.32 (inIntersectImpInUnion) =>
% 98.38/13.32 ((
% 98.38/13.32 (inIntersectImpInUnion2) =>
% 98.38/13.32 ((
% 98.38/13.32 (inIntersectImpInIntersectUnions) =>
% 98.38/13.32 ((
% 98.38/13.32 (intersectInPowersetIntersectUnions) =>
% 98.38/13.32 ((
% 98.38/13.32 (inComplementUnionImpNotIn1) =>
% 98.38/13.32 ((
% 98.38/13.32 (inComplementUnionImpInComplement1) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTE) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTEcontra) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2a1) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementUnionInPowersetComplement) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2a2) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan1a) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan1b) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan1) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2a) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2b2) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2b) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule0) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule1) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule2) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule3) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule4) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_1) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_2) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_3) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_4) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_5) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1all2) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1SetBreln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (choice2fnsingleton) =>
% 98.38/13.32 ((
% 98.38/13.32 (setOfPairsIsBReln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1all1) =>
% 98.38/13.32 ((
% 98.38/13.32 (subbreln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (eqbreln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1invprop) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1invI) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1invE) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compprop) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compI) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compE) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compEex) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionprop) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionIL) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionIR) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionI) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionE) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionEcases) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionCommutes) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2Ex) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2W) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2A) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2B) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1Ex) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1Ex1) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1Equiv) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1E) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1I) =>
% 98.38/13.32 ((
% 98.38/13.32 (injFuncInInjFuncSet) =>
% 98.38/13.32 ((
% 98.38/13.32 (injFuncSetFuncIn) =>
% 98.38/13.32 ((
% 98.38/13.32 (injFuncSetFuncInj) =>
% 98.38/13.32 ((
% 98.38/13.32 (surjFuncSetFuncIn) =>
% 98.38/13.32 ((
% 98.38/13.32 (surjFuncSetFuncSurj) =>
% 98.38/13.32 ((
% 98.38/13.32 (leftInvIsSurj) =>
% 98.38/13.32 ((
% 98.38/13.32 (surjCantorThm) =>
% 98.38/13.32 ((
% 98.38/13.32 (foundation2) =>
% 98.38/13.32 ((
% 98.38/13.32 (notinself) =>
% 98.38/13.32 ((
% 98.38/13.32 (notinself2) =>
% 98.38/13.32 ((
% 98.38/13.32 (omegaSp) =>
% 98.38/13.32 ((
% 98.38/13.32 (omegaSclos) =>
% 98.38/13.32 ((
% 98.38/13.32 (peano0notS) =>
% 98.38/13.32 ((
% 98.38/13.32 (!!) @ (
% 98.38/13.32 (('#S') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =>) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#C') @ in @
% 98.38/13.32 omega)))) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 !!) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#S') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =>) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#C') @ in @
% 98.38/13.32 omega)))))) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#S') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 '#S') @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =>))) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#C') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 '#B') @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =) @
% 98.38/13.32 omegaS)))) @
% 98.38/13.32 omegaS)))))) @
% 98.38/13.32 (
% 98.38/13.32 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.38/13.32 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2181])).
% 98.38/13.32 thf(zip_derived_cl2213, plain,
% 98.38/13.32 (~ (((lam2lamEq) =>
% 98.38/13.32 (((beta2) =>
% 98.38/13.32 (((eta2) =>
% 98.38/13.32 (((iffalseProp1) =>
% 98.38/13.32 (((iffalseProp2) =>
% 98.38/13.32 (((iftrueProp1) =>
% 98.38/13.32 (((iftrueProp2) =>
% 98.38/13.32 (((ifSingleton) =>
% 98.38/13.32 (((ifp) =>
% 98.38/13.32 (((theeq) =>
% 98.38/13.32 (((iftrue) =>
% 98.38/13.32 (((iffalse) =>
% 98.38/13.32 (((iftrueorfalse) =>
% 98.38/13.32 (((binintersectT_lem) =>
% 98.38/13.32 (((binunionT_lem) =>
% 98.38/13.32 (((powersetT_lem) =>
% 98.38/13.32 (((setminusT_lem) =>
% 98.38/13.32 (((complementT_lem) =>
% 98.38/13.32 (((setextT) =>
% 98.38/13.32 (((subsetTI) =>
% 98.38/13.32 (((powersetTI1) =>
% 98.38/13.32 (((powersetTE1) =>
% 98.38/13.32 (((complementTI1) =>
% 98.38/13.32 (((complementTE1) =>
% 98.38/13.32 (((binintersectTELcontra) =>
% 98.38/13.32 (((binintersectTERcontra) =>
% 98.38/13.32 (((contrasubsetT) =>
% 98.38/13.32 (((contrasubsetT1) =>
% 98.38/13.32 (((contrasubsetT2) =>
% 98.38/13.32 (((contrasubsetT3) =>
% 98.38/13.32 ((
% 98.38/13.32 (doubleComplementI1) =>
% 98.38/13.32 ((
% 98.38/13.32 (doubleComplementE1) =>
% 98.38/13.32 ((
% 98.38/13.32 (doubleComplementSub1) =>
% 98.38/13.32 ((
% 98.38/13.32 (doubleComplementSub2) =>
% 98.38/13.32 ((
% 98.38/13.32 (doubleComplementEq) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementTnotintersectT) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementImpComplementIntersect) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementSubsetComplementIntersect) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementInPowersetComplementIntersect) =>
% 98.38/13.32 ((
% 98.38/13.32 (contraSubsetComplement) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementTcontraSubset) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTILcontra) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTIRcontra) =>
% 98.38/13.32 ((
% 98.38/13.32 (inIntersectImpInUnion) =>
% 98.38/13.32 ((
% 98.38/13.32 (inIntersectImpInUnion2) =>
% 98.38/13.32 ((
% 98.38/13.32 (inIntersectImpInIntersectUnions) =>
% 98.38/13.32 ((
% 98.38/13.32 (intersectInPowersetIntersectUnions) =>
% 98.38/13.32 ((
% 98.38/13.32 (inComplementUnionImpNotIn1) =>
% 98.38/13.32 ((
% 98.38/13.32 (inComplementUnionImpInComplement1) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTE) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTEcontra) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2a1) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementUnionInPowersetComplement) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2a2) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan1a) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan1b) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan1) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2a) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2b2) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2b) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule0) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule1) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule2) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule3) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule4) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_1) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_2) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_3) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_4) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_5) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1all2) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1SetBreln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (choice2fnsingleton) =>
% 98.38/13.32 ((
% 98.38/13.32 (setOfPairsIsBReln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1all1) =>
% 98.38/13.32 ((
% 98.38/13.32 (subbreln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (eqbreln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1invprop) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1invI) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1invE) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compprop) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compI) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compE) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compEex) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionprop) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionIL) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionIR) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionI) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionE) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionEcases) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionCommutes) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2Ex) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2W) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2A) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2B) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1Ex) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1Ex1) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1Equiv) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1E) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1I) =>
% 98.38/13.32 ((
% 98.38/13.32 (injFuncInInjFuncSet) =>
% 98.38/13.32 ((
% 98.38/13.32 (injFuncSetFuncIn) =>
% 98.38/13.32 ((
% 98.38/13.32 (injFuncSetFuncInj) =>
% 98.38/13.32 ((
% 98.38/13.32 (surjFuncSetFuncIn) =>
% 98.38/13.32 ((
% 98.38/13.32 (surjFuncSetFuncSurj) =>
% 98.38/13.32 ((
% 98.38/13.32 (leftInvIsSurj) =>
% 98.38/13.32 ((
% 98.38/13.32 (surjCantorThm) =>
% 98.38/13.32 ((
% 98.38/13.32 (foundation2) =>
% 98.38/13.32 ((
% 98.38/13.32 (notinself) =>
% 98.38/13.32 ((
% 98.38/13.32 (notinself2) =>
% 98.38/13.32 ((
% 98.38/13.32 (omegaSp) =>
% 98.38/13.32 ((
% 98.38/13.32 (omegaSclos) =>
% 98.38/13.32 ((
% 98.38/13.32 (peano0notS) =>
% 98.38/13.32 ((
% 98.38/13.32 (!!) @ (
% 98.38/13.32 (('#S') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =>) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#C') @ in @
% 98.38/13.32 omega)))) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 !!) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#S') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =>) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#C') @ in @
% 98.38/13.32 omega)))))) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#S') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 '#S') @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =>))) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#C') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 '#B') @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =) @
% 98.38/13.32 omegaS)))) @
% 98.38/13.32 omegaS)))))) @
% 98.38/13.32 (
% 98.38/13.32 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.38/13.32 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2198])).
% 98.38/13.32 thf(zip_derived_cl2228, plain,
% 98.38/13.32 (~ (((beta2) =>
% 98.38/13.32 (((eta2) =>
% 98.38/13.32 (((iffalseProp1) =>
% 98.38/13.32 (((iffalseProp2) =>
% 98.38/13.32 (((iftrueProp1) =>
% 98.38/13.32 (((iftrueProp2) =>
% 98.38/13.32 (((ifSingleton) =>
% 98.38/13.32 (((ifp) =>
% 98.38/13.32 (((theeq) =>
% 98.38/13.32 (((iftrue) =>
% 98.38/13.32 (((iffalse) =>
% 98.38/13.32 (((iftrueorfalse) =>
% 98.38/13.32 (((binintersectT_lem) =>
% 98.38/13.32 (((binunionT_lem) =>
% 98.38/13.32 (((powersetT_lem) =>
% 98.38/13.32 (((setminusT_lem) =>
% 98.38/13.32 (((complementT_lem) =>
% 98.38/13.32 (((setextT) =>
% 98.38/13.32 (((subsetTI) =>
% 98.38/13.32 (((powersetTI1) =>
% 98.38/13.32 (((powersetTE1) =>
% 98.38/13.32 (((complementTI1) =>
% 98.38/13.32 (((complementTE1) =>
% 98.38/13.32 (((binintersectTELcontra) =>
% 98.38/13.32 (((binintersectTERcontra) =>
% 98.38/13.32 (((contrasubsetT) =>
% 98.38/13.32 (((contrasubsetT1) =>
% 98.38/13.32 (((contrasubsetT2) =>
% 98.38/13.32 (((contrasubsetT3) =>
% 98.38/13.32 (((doubleComplementI1) =>
% 98.38/13.32 ((
% 98.38/13.32 (doubleComplementE1) =>
% 98.38/13.32 ((
% 98.38/13.32 (doubleComplementSub1) =>
% 98.38/13.32 ((
% 98.38/13.32 (doubleComplementSub2) =>
% 98.38/13.32 ((
% 98.38/13.32 (doubleComplementEq) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementTnotintersectT) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementImpComplementIntersect) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementSubsetComplementIntersect) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementInPowersetComplementIntersect) =>
% 98.38/13.32 ((
% 98.38/13.32 (contraSubsetComplement) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementTcontraSubset) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTILcontra) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTIRcontra) =>
% 98.38/13.32 ((
% 98.38/13.32 (inIntersectImpInUnion) =>
% 98.38/13.32 ((
% 98.38/13.32 (inIntersectImpInUnion2) =>
% 98.38/13.32 ((
% 98.38/13.32 (inIntersectImpInIntersectUnions) =>
% 98.38/13.32 ((
% 98.38/13.32 (intersectInPowersetIntersectUnions) =>
% 98.38/13.32 ((
% 98.38/13.32 (inComplementUnionImpNotIn1) =>
% 98.38/13.32 ((
% 98.38/13.32 (inComplementUnionImpInComplement1) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTE) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTEcontra) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2a1) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementUnionInPowersetComplement) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2a2) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan1a) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan1b) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan1) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2a) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2b2) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2b) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule0) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule1) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule2) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule3) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule4) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_1) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_2) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_3) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_4) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_5) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1all2) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1SetBreln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (choice2fnsingleton) =>
% 98.38/13.32 ((
% 98.38/13.32 (setOfPairsIsBReln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1all1) =>
% 98.38/13.32 ((
% 98.38/13.32 (subbreln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (eqbreln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1invprop) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1invI) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1invE) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compprop) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compI) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compE) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compEex) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionprop) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionIL) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionIR) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionI) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionE) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionEcases) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionCommutes) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2Ex) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2W) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2A) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2B) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1Ex) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1Ex1) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1Equiv) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1E) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1I) =>
% 98.38/13.32 ((
% 98.38/13.32 (injFuncInInjFuncSet) =>
% 98.38/13.32 ((
% 98.38/13.32 (injFuncSetFuncIn) =>
% 98.38/13.32 ((
% 98.38/13.32 (injFuncSetFuncInj) =>
% 98.38/13.32 ((
% 98.38/13.32 (surjFuncSetFuncIn) =>
% 98.38/13.32 ((
% 98.38/13.32 (surjFuncSetFuncSurj) =>
% 98.38/13.32 ((
% 98.38/13.32 (leftInvIsSurj) =>
% 98.38/13.32 ((
% 98.38/13.32 (surjCantorThm) =>
% 98.38/13.32 ((
% 98.38/13.32 (foundation2) =>
% 98.38/13.32 ((
% 98.38/13.32 (notinself) =>
% 98.38/13.32 ((
% 98.38/13.32 (notinself2) =>
% 98.38/13.32 ((
% 98.38/13.32 (omegaSp) =>
% 98.38/13.32 ((
% 98.38/13.32 (omegaSclos) =>
% 98.38/13.32 ((
% 98.38/13.32 (peano0notS) =>
% 98.38/13.32 ((
% 98.38/13.32 (!!) @ (
% 98.38/13.32 (('#S') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =>) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#C') @ in @
% 98.38/13.32 omega)))) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 !!) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#S') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =>) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#C') @ in @
% 98.38/13.32 omega)))))) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#S') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 '#S') @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =>))) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#C') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 '#B') @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =) @
% 98.38/13.32 omegaS)))) @
% 98.38/13.32 omegaS)))))) @
% 98.38/13.32 (
% 98.38/13.32 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.38/13.32 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2213])).
% 98.38/13.32 thf(zip_derived_cl2244, plain,
% 98.38/13.32 (~ (((eta2) =>
% 98.38/13.32 (((iffalseProp1) =>
% 98.38/13.32 (((iffalseProp2) =>
% 98.38/13.32 (((iftrueProp1) =>
% 98.38/13.32 (((iftrueProp2) =>
% 98.38/13.32 (((ifSingleton) =>
% 98.38/13.32 (((ifp) =>
% 98.38/13.32 (((theeq) =>
% 98.38/13.32 (((iftrue) =>
% 98.38/13.32 (((iffalse) =>
% 98.38/13.32 (((iftrueorfalse) =>
% 98.38/13.32 (((binintersectT_lem) =>
% 98.38/13.32 (((binunionT_lem) =>
% 98.38/13.32 (((powersetT_lem) =>
% 98.38/13.32 (((setminusT_lem) =>
% 98.38/13.32 (((complementT_lem) =>
% 98.38/13.32 (((setextT) =>
% 98.38/13.32 (((subsetTI) =>
% 98.38/13.32 (((powersetTI1) =>
% 98.38/13.32 (((powersetTE1) =>
% 98.38/13.32 (((complementTI1) =>
% 98.38/13.32 (((complementTE1) =>
% 98.38/13.32 (((binintersectTELcontra) =>
% 98.38/13.32 (((binintersectTERcontra) =>
% 98.38/13.32 (((contrasubsetT) =>
% 98.38/13.32 (((contrasubsetT1) =>
% 98.38/13.32 (((contrasubsetT2) =>
% 98.38/13.32 (((contrasubsetT3) =>
% 98.38/13.32 (((doubleComplementI1) =>
% 98.38/13.32 (((doubleComplementE1) =>
% 98.38/13.32 ((
% 98.38/13.32 (doubleComplementSub1) =>
% 98.38/13.32 ((
% 98.38/13.32 (doubleComplementSub2) =>
% 98.38/13.32 ((
% 98.38/13.32 (doubleComplementEq) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementTnotintersectT) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementImpComplementIntersect) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementSubsetComplementIntersect) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementInPowersetComplementIntersect) =>
% 98.38/13.32 ((
% 98.38/13.32 (contraSubsetComplement) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementTcontraSubset) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTILcontra) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTIRcontra) =>
% 98.38/13.32 ((
% 98.38/13.32 (inIntersectImpInUnion) =>
% 98.38/13.32 ((
% 98.38/13.32 (inIntersectImpInUnion2) =>
% 98.38/13.32 ((
% 98.38/13.32 (inIntersectImpInIntersectUnions) =>
% 98.38/13.32 ((
% 98.38/13.32 (intersectInPowersetIntersectUnions) =>
% 98.38/13.32 ((
% 98.38/13.32 (inComplementUnionImpNotIn1) =>
% 98.38/13.32 ((
% 98.38/13.32 (inComplementUnionImpInComplement1) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTE) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTEcontra) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2a1) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementUnionInPowersetComplement) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2a2) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan1a) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan1b) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan1) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2a) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2b2) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2b) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule0) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule1) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule2) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule3) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule4) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_1) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_2) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_3) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_4) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_5) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1all2) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1SetBreln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (choice2fnsingleton) =>
% 98.38/13.32 ((
% 98.38/13.32 (setOfPairsIsBReln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1all1) =>
% 98.38/13.32 ((
% 98.38/13.32 (subbreln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (eqbreln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1invprop) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1invI) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1invE) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compprop) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compI) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compE) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compEex) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionprop) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionIL) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionIR) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionI) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionE) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionEcases) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionCommutes) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2Ex) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2W) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2A) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2B) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1Ex) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1Ex1) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1Equiv) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1E) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1I) =>
% 98.38/13.32 ((
% 98.38/13.32 (injFuncInInjFuncSet) =>
% 98.38/13.32 ((
% 98.38/13.32 (injFuncSetFuncIn) =>
% 98.38/13.32 ((
% 98.38/13.32 (injFuncSetFuncInj) =>
% 98.38/13.32 ((
% 98.38/13.32 (surjFuncSetFuncIn) =>
% 98.38/13.32 ((
% 98.38/13.32 (surjFuncSetFuncSurj) =>
% 98.38/13.32 ((
% 98.38/13.32 (leftInvIsSurj) =>
% 98.38/13.32 ((
% 98.38/13.32 (surjCantorThm) =>
% 98.38/13.32 ((
% 98.38/13.32 (foundation2) =>
% 98.38/13.32 ((
% 98.38/13.32 (notinself) =>
% 98.38/13.32 ((
% 98.38/13.32 (notinself2) =>
% 98.38/13.32 ((
% 98.38/13.32 (omegaSp) =>
% 98.38/13.32 ((
% 98.38/13.32 (omegaSclos) =>
% 98.38/13.32 ((
% 98.38/13.32 (peano0notS) =>
% 98.38/13.32 ((
% 98.38/13.32 (!!) @ (
% 98.38/13.32 (('#S') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =>) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#C') @ in @
% 98.38/13.32 omega)))) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 !!) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#S') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =>) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#C') @ in @
% 98.38/13.32 omega)))))) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#S') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 '#S') @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =>))) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#C') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 '#B') @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =) @
% 98.38/13.32 omegaS)))) @
% 98.38/13.32 omegaS)))))) @
% 98.38/13.32 (
% 98.38/13.32 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.38/13.32 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2228])).
% 98.38/13.32 thf(zip_derived_cl2261, plain,
% 98.38/13.32 (~ (((iffalseProp1) =>
% 98.38/13.32 (((iffalseProp2) =>
% 98.38/13.32 (((iftrueProp1) =>
% 98.38/13.32 (((iftrueProp2) =>
% 98.38/13.32 (((ifSingleton) =>
% 98.38/13.32 (((ifp) =>
% 98.38/13.32 (((theeq) =>
% 98.38/13.32 (((iftrue) =>
% 98.38/13.32 (((iffalse) =>
% 98.38/13.32 (((iftrueorfalse) =>
% 98.38/13.32 (((binintersectT_lem) =>
% 98.38/13.32 (((binunionT_lem) =>
% 98.38/13.32 (((powersetT_lem) =>
% 98.38/13.32 (((setminusT_lem) =>
% 98.38/13.32 (((complementT_lem) =>
% 98.38/13.32 (((setextT) =>
% 98.38/13.32 (((subsetTI) =>
% 98.38/13.32 (((powersetTI1) =>
% 98.38/13.32 (((powersetTE1) =>
% 98.38/13.32 (((complementTI1) =>
% 98.38/13.32 (((complementTE1) =>
% 98.38/13.32 (((binintersectTELcontra) =>
% 98.38/13.32 (((binintersectTERcontra) =>
% 98.38/13.32 (((contrasubsetT) =>
% 98.38/13.32 (((contrasubsetT1) =>
% 98.38/13.32 (((contrasubsetT2) =>
% 98.38/13.32 (((contrasubsetT3) =>
% 98.38/13.32 (((doubleComplementI1) =>
% 98.38/13.32 (((doubleComplementE1) =>
% 98.38/13.32 (((doubleComplementSub1) =>
% 98.38/13.32 ((
% 98.38/13.32 (doubleComplementSub2) =>
% 98.38/13.32 ((
% 98.38/13.32 (doubleComplementEq) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementTnotintersectT) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementImpComplementIntersect) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementSubsetComplementIntersect) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementInPowersetComplementIntersect) =>
% 98.38/13.32 ((
% 98.38/13.32 (contraSubsetComplement) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementTcontraSubset) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTILcontra) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTIRcontra) =>
% 98.38/13.32 ((
% 98.38/13.32 (inIntersectImpInUnion) =>
% 98.38/13.32 ((
% 98.38/13.32 (inIntersectImpInUnion2) =>
% 98.38/13.32 ((
% 98.38/13.32 (inIntersectImpInIntersectUnions) =>
% 98.38/13.32 ((
% 98.38/13.32 (intersectInPowersetIntersectUnions) =>
% 98.38/13.32 ((
% 98.38/13.32 (inComplementUnionImpNotIn1) =>
% 98.38/13.32 ((
% 98.38/13.32 (inComplementUnionImpInComplement1) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTE) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTEcontra) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2a1) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementUnionInPowersetComplement) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2a2) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan1a) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan1b) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan1) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2a) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2b2) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2b) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule0) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule1) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule2) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule3) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule4) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_1) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_2) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_3) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_4) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_5) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1all2) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1SetBreln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (choice2fnsingleton) =>
% 98.38/13.32 ((
% 98.38/13.32 (setOfPairsIsBReln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1all1) =>
% 98.38/13.32 ((
% 98.38/13.32 (subbreln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (eqbreln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1invprop) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1invI) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1invE) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compprop) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compI) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compE) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compEex) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionprop) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionIL) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionIR) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionI) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionE) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionEcases) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionCommutes) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2Ex) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2W) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2A) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2B) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1Ex) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1Ex1) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1Equiv) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1E) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1I) =>
% 98.38/13.32 ((
% 98.38/13.32 (injFuncInInjFuncSet) =>
% 98.38/13.32 ((
% 98.38/13.32 (injFuncSetFuncIn) =>
% 98.38/13.32 ((
% 98.38/13.32 (injFuncSetFuncInj) =>
% 98.38/13.32 ((
% 98.38/13.32 (surjFuncSetFuncIn) =>
% 98.38/13.32 ((
% 98.38/13.32 (surjFuncSetFuncSurj) =>
% 98.38/13.32 ((
% 98.38/13.32 (leftInvIsSurj) =>
% 98.38/13.32 ((
% 98.38/13.32 (surjCantorThm) =>
% 98.38/13.32 ((
% 98.38/13.32 (foundation2) =>
% 98.38/13.32 ((
% 98.38/13.32 (notinself) =>
% 98.38/13.32 ((
% 98.38/13.32 (notinself2) =>
% 98.38/13.32 ((
% 98.38/13.32 (omegaSp) =>
% 98.38/13.32 ((
% 98.38/13.32 (omegaSclos) =>
% 98.38/13.32 ((
% 98.38/13.32 (peano0notS) =>
% 98.38/13.32 ((
% 98.38/13.32 (!!) @ (
% 98.38/13.32 (('#S') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =>) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#C') @ in @
% 98.38/13.32 omega)))) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 !!) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#S') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =>) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#C') @ in @
% 98.38/13.32 omega)))))) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#S') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 '#S') @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =>))) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#C') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 '#B') @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =) @
% 98.38/13.32 omegaS)))) @
% 98.38/13.32 omegaS)))))) @
% 98.38/13.32 (
% 98.38/13.32 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.38/13.32 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2244])).
% 98.38/13.32 thf(zip_derived_cl2279, plain,
% 98.38/13.32 (~ (((iffalseProp2) =>
% 98.38/13.32 (((iftrueProp1) =>
% 98.38/13.32 (((iftrueProp2) =>
% 98.38/13.32 (((ifSingleton) =>
% 98.38/13.32 (((ifp) =>
% 98.38/13.32 (((theeq) =>
% 98.38/13.32 (((iftrue) =>
% 98.38/13.32 (((iffalse) =>
% 98.38/13.32 (((iftrueorfalse) =>
% 98.38/13.32 (((binintersectT_lem) =>
% 98.38/13.32 (((binunionT_lem) =>
% 98.38/13.32 (((powersetT_lem) =>
% 98.38/13.32 (((setminusT_lem) =>
% 98.38/13.32 (((complementT_lem) =>
% 98.38/13.32 (((setextT) =>
% 98.38/13.32 (((subsetTI) =>
% 98.38/13.32 (((powersetTI1) =>
% 98.38/13.32 (((powersetTE1) =>
% 98.38/13.32 (((complementTI1) =>
% 98.38/13.32 (((complementTE1) =>
% 98.38/13.32 (((binintersectTELcontra) =>
% 98.38/13.32 (((binintersectTERcontra) =>
% 98.38/13.32 (((contrasubsetT) =>
% 98.38/13.32 (((contrasubsetT1) =>
% 98.38/13.32 (((contrasubsetT2) =>
% 98.38/13.32 (((contrasubsetT3) =>
% 98.38/13.32 (((doubleComplementI1) =>
% 98.38/13.32 (((doubleComplementE1) =>
% 98.38/13.32 (((doubleComplementSub1) =>
% 98.38/13.32 (((doubleComplementSub2) =>
% 98.38/13.32 ((
% 98.38/13.32 (doubleComplementEq) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementTnotintersectT) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementImpComplementIntersect) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementSubsetComplementIntersect) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementInPowersetComplementIntersect) =>
% 98.38/13.32 ((
% 98.38/13.32 (contraSubsetComplement) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementTcontraSubset) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTILcontra) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTIRcontra) =>
% 98.38/13.32 ((
% 98.38/13.32 (inIntersectImpInUnion) =>
% 98.38/13.32 ((
% 98.38/13.32 (inIntersectImpInUnion2) =>
% 98.38/13.32 ((
% 98.38/13.32 (inIntersectImpInIntersectUnions) =>
% 98.38/13.32 ((
% 98.38/13.32 (intersectInPowersetIntersectUnions) =>
% 98.38/13.32 ((
% 98.38/13.32 (inComplementUnionImpNotIn1) =>
% 98.38/13.32 ((
% 98.38/13.32 (inComplementUnionImpInComplement1) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTE) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTEcontra) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2a1) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementUnionInPowersetComplement) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2a2) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan1a) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan1b) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan1) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2a) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2b2) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2b) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule0) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule1) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule2) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule3) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule4) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_1) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_2) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_3) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_4) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_5) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1all2) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1SetBreln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (choice2fnsingleton) =>
% 98.38/13.32 ((
% 98.38/13.32 (setOfPairsIsBReln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1all1) =>
% 98.38/13.32 ((
% 98.38/13.32 (subbreln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (eqbreln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1invprop) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1invI) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1invE) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compprop) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compI) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compE) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compEex) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionprop) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionIL) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionIR) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionI) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionE) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionEcases) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionCommutes) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2Ex) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2W) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2A) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2B) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1Ex) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1Ex1) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1Equiv) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1E) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1I) =>
% 98.38/13.32 ((
% 98.38/13.32 (injFuncInInjFuncSet) =>
% 98.38/13.32 ((
% 98.38/13.32 (injFuncSetFuncIn) =>
% 98.38/13.32 ((
% 98.38/13.32 (injFuncSetFuncInj) =>
% 98.38/13.32 ((
% 98.38/13.32 (surjFuncSetFuncIn) =>
% 98.38/13.32 ((
% 98.38/13.32 (surjFuncSetFuncSurj) =>
% 98.38/13.32 ((
% 98.38/13.32 (leftInvIsSurj) =>
% 98.38/13.32 ((
% 98.38/13.32 (surjCantorThm) =>
% 98.38/13.32 ((
% 98.38/13.32 (foundation2) =>
% 98.38/13.32 ((
% 98.38/13.32 (notinself) =>
% 98.38/13.32 ((
% 98.38/13.32 (notinself2) =>
% 98.38/13.32 ((
% 98.38/13.32 (omegaSp) =>
% 98.38/13.32 ((
% 98.38/13.32 (omegaSclos) =>
% 98.38/13.32 ((
% 98.38/13.32 (peano0notS) =>
% 98.38/13.32 ((
% 98.38/13.32 (!!) @ (
% 98.38/13.32 (('#S') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =>) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#C') @ in @
% 98.38/13.32 omega)))) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 !!) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#S') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =>) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#C') @ in @
% 98.38/13.32 omega)))))) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#S') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 '#S') @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =>))) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#C') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 '#B') @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =) @
% 98.38/13.32 omegaS)))) @
% 98.38/13.32 omegaS)))))) @
% 98.38/13.32 (
% 98.38/13.32 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.38/13.32 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2261])).
% 98.38/13.32 thf(zip_derived_cl2299, plain,
% 98.38/13.32 (~ (((iftrueProp1) =>
% 98.38/13.32 (((iftrueProp2) =>
% 98.38/13.32 (((ifSingleton) =>
% 98.38/13.32 (((ifp) =>
% 98.38/13.32 (((theeq) =>
% 98.38/13.32 (((iftrue) =>
% 98.38/13.32 (((iffalse) =>
% 98.38/13.32 (((iftrueorfalse) =>
% 98.38/13.32 (((binintersectT_lem) =>
% 98.38/13.32 (((binunionT_lem) =>
% 98.38/13.32 (((powersetT_lem) =>
% 98.38/13.32 (((setminusT_lem) =>
% 98.38/13.32 (((complementT_lem) =>
% 98.38/13.32 (((setextT) =>
% 98.38/13.32 (((subsetTI) =>
% 98.38/13.32 (((powersetTI1) =>
% 98.38/13.32 (((powersetTE1) =>
% 98.38/13.32 (((complementTI1) =>
% 98.38/13.32 (((complementTE1) =>
% 98.38/13.32 (((binintersectTELcontra) =>
% 98.38/13.32 (((binintersectTERcontra) =>
% 98.38/13.32 (((contrasubsetT) =>
% 98.38/13.32 (((contrasubsetT1) =>
% 98.38/13.32 (((contrasubsetT2) =>
% 98.38/13.32 (((contrasubsetT3) =>
% 98.38/13.32 (((doubleComplementI1) =>
% 98.38/13.32 (((doubleComplementE1) =>
% 98.38/13.32 (((doubleComplementSub1) =>
% 98.38/13.32 (((doubleComplementSub2) =>
% 98.38/13.32 (((doubleComplementEq) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementTnotintersectT) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementImpComplementIntersect) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementSubsetComplementIntersect) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementInPowersetComplementIntersect) =>
% 98.38/13.32 ((
% 98.38/13.32 (contraSubsetComplement) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementTcontraSubset) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTILcontra) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTIRcontra) =>
% 98.38/13.32 ((
% 98.38/13.32 (inIntersectImpInUnion) =>
% 98.38/13.32 ((
% 98.38/13.32 (inIntersectImpInUnion2) =>
% 98.38/13.32 ((
% 98.38/13.32 (inIntersectImpInIntersectUnions) =>
% 98.38/13.32 ((
% 98.38/13.32 (intersectInPowersetIntersectUnions) =>
% 98.38/13.32 ((
% 98.38/13.32 (inComplementUnionImpNotIn1) =>
% 98.38/13.32 ((
% 98.38/13.32 (inComplementUnionImpInComplement1) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTE) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTEcontra) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2a1) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementUnionInPowersetComplement) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2a2) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan1a) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan1b) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan1) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2a) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2b2) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2b) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule0) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule1) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule2) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule3) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule4) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_1) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_2) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_3) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_4) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_5) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1all2) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1SetBreln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (choice2fnsingleton) =>
% 98.38/13.32 ((
% 98.38/13.32 (setOfPairsIsBReln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1all1) =>
% 98.38/13.32 ((
% 98.38/13.32 (subbreln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (eqbreln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1invprop) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1invI) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1invE) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compprop) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compI) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compE) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compEex) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionprop) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionIL) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionIR) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionI) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionE) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionEcases) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionCommutes) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2Ex) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2W) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2A) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2B) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1Ex) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1Ex1) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1Equiv) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1E) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1I) =>
% 98.38/13.32 ((
% 98.38/13.32 (injFuncInInjFuncSet) =>
% 98.38/13.32 ((
% 98.38/13.32 (injFuncSetFuncIn) =>
% 98.38/13.32 ((
% 98.38/13.32 (injFuncSetFuncInj) =>
% 98.38/13.32 ((
% 98.38/13.32 (surjFuncSetFuncIn) =>
% 98.38/13.32 ((
% 98.38/13.32 (surjFuncSetFuncSurj) =>
% 98.38/13.32 ((
% 98.38/13.32 (leftInvIsSurj) =>
% 98.38/13.32 ((
% 98.38/13.32 (surjCantorThm) =>
% 98.38/13.32 ((
% 98.38/13.32 (foundation2) =>
% 98.38/13.32 ((
% 98.38/13.32 (notinself) =>
% 98.38/13.32 ((
% 98.38/13.32 (notinself2) =>
% 98.38/13.32 ((
% 98.38/13.32 (omegaSp) =>
% 98.38/13.32 ((
% 98.38/13.32 (omegaSclos) =>
% 98.38/13.32 ((
% 98.38/13.32 (peano0notS) =>
% 98.38/13.32 ((
% 98.38/13.32 (!!) @ (
% 98.38/13.32 (('#S') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =>) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#C') @ in @
% 98.38/13.32 omega)))) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 !!) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#S') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =>) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#C') @ in @
% 98.38/13.32 omega)))))) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#S') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 '#S') @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =>))) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#C') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 '#B') @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =) @
% 98.38/13.32 omegaS)))) @
% 98.38/13.32 omegaS)))))) @
% 98.38/13.32 (
% 98.38/13.32 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.38/13.32 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2279])).
% 98.38/13.32 thf(zip_derived_cl2321, plain,
% 98.38/13.32 (~ (((iftrueProp2) =>
% 98.38/13.32 (((ifSingleton) =>
% 98.38/13.32 (((ifp) =>
% 98.38/13.32 (((theeq) =>
% 98.38/13.32 (((iftrue) =>
% 98.38/13.32 (((iffalse) =>
% 98.38/13.32 (((iftrueorfalse) =>
% 98.38/13.32 (((binintersectT_lem) =>
% 98.38/13.32 (((binunionT_lem) =>
% 98.38/13.32 (((powersetT_lem) =>
% 98.38/13.32 (((setminusT_lem) =>
% 98.38/13.32 (((complementT_lem) =>
% 98.38/13.32 (((setextT) =>
% 98.38/13.32 (((subsetTI) =>
% 98.38/13.32 (((powersetTI1) =>
% 98.38/13.32 (((powersetTE1) =>
% 98.38/13.32 (((complementTI1) =>
% 98.38/13.32 (((complementTE1) =>
% 98.38/13.32 (((binintersectTELcontra) =>
% 98.38/13.32 (((binintersectTERcontra) =>
% 98.38/13.32 (((contrasubsetT) =>
% 98.38/13.32 (((contrasubsetT1) =>
% 98.38/13.32 (((contrasubsetT2) =>
% 98.38/13.32 (((contrasubsetT3) =>
% 98.38/13.32 (((doubleComplementI1) =>
% 98.38/13.32 (((doubleComplementE1) =>
% 98.38/13.32 (((doubleComplementSub1) =>
% 98.38/13.32 (((doubleComplementSub2) =>
% 98.38/13.32 (((doubleComplementEq) =>
% 98.38/13.32 (((complementTnotintersectT) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementImpComplementIntersect) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementSubsetComplementIntersect) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementInPowersetComplementIntersect) =>
% 98.38/13.32 ((
% 98.38/13.32 (contraSubsetComplement) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementTcontraSubset) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTILcontra) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTIRcontra) =>
% 98.38/13.32 ((
% 98.38/13.32 (inIntersectImpInUnion) =>
% 98.38/13.32 ((
% 98.38/13.32 (inIntersectImpInUnion2) =>
% 98.38/13.32 ((
% 98.38/13.32 (inIntersectImpInIntersectUnions) =>
% 98.38/13.32 ((
% 98.38/13.32 (intersectInPowersetIntersectUnions) =>
% 98.38/13.32 ((
% 98.38/13.32 (inComplementUnionImpNotIn1) =>
% 98.38/13.32 ((
% 98.38/13.32 (inComplementUnionImpInComplement1) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTE) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTEcontra) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2a1) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementUnionInPowersetComplement) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2a2) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan1a) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan1b) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan1) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2a) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2b2) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2b) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule0) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule1) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule2) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule3) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule4) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_1) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_2) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_3) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_4) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_5) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1all2) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1SetBreln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (choice2fnsingleton) =>
% 98.38/13.32 ((
% 98.38/13.32 (setOfPairsIsBReln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1all1) =>
% 98.38/13.32 ((
% 98.38/13.32 (subbreln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (eqbreln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1invprop) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1invI) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1invE) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compprop) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compI) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compE) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compEex) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionprop) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionIL) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionIR) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionI) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionE) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionEcases) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionCommutes) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2Ex) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2W) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2A) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2B) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1Ex) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1Ex1) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1Equiv) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1E) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1I) =>
% 98.38/13.32 ((
% 98.38/13.32 (injFuncInInjFuncSet) =>
% 98.38/13.32 ((
% 98.38/13.32 (injFuncSetFuncIn) =>
% 98.38/13.32 ((
% 98.38/13.32 (injFuncSetFuncInj) =>
% 98.38/13.32 ((
% 98.38/13.32 (surjFuncSetFuncIn) =>
% 98.38/13.32 ((
% 98.38/13.32 (surjFuncSetFuncSurj) =>
% 98.38/13.32 ((
% 98.38/13.32 (leftInvIsSurj) =>
% 98.38/13.32 ((
% 98.38/13.32 (surjCantorThm) =>
% 98.38/13.32 ((
% 98.38/13.32 (foundation2) =>
% 98.38/13.32 ((
% 98.38/13.32 (notinself) =>
% 98.38/13.32 ((
% 98.38/13.32 (notinself2) =>
% 98.38/13.32 ((
% 98.38/13.32 (omegaSp) =>
% 98.38/13.32 ((
% 98.38/13.32 (omegaSclos) =>
% 98.38/13.32 ((
% 98.38/13.32 (peano0notS) =>
% 98.38/13.32 ((
% 98.38/13.32 (!!) @ (
% 98.38/13.32 (('#S') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =>) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#C') @ in @
% 98.38/13.32 omega)))) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 !!) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#S') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =>) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#C') @ in @
% 98.38/13.32 omega)))))) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#S') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 '#S') @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =>))) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#C') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 '#B') @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =) @
% 98.38/13.32 omegaS)))) @
% 98.38/13.32 omegaS)))))) @
% 98.38/13.32 (
% 98.38/13.32 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.38/13.32 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2299])).
% 98.38/13.32 thf(zip_derived_cl2337, plain,
% 98.38/13.32 (~ (((ifSingleton) =>
% 98.38/13.32 (((ifp) =>
% 98.38/13.32 (((theeq) =>
% 98.38/13.32 (((iftrue) =>
% 98.38/13.32 (((iffalse) =>
% 98.38/13.32 (((iftrueorfalse) =>
% 98.38/13.32 (((binintersectT_lem) =>
% 98.38/13.32 (((binunionT_lem) =>
% 98.38/13.32 (((powersetT_lem) =>
% 98.38/13.32 (((setminusT_lem) =>
% 98.38/13.32 (((complementT_lem) =>
% 98.38/13.32 (((setextT) =>
% 98.38/13.32 (((subsetTI) =>
% 98.38/13.32 (((powersetTI1) =>
% 98.38/13.32 (((powersetTE1) =>
% 98.38/13.32 (((complementTI1) =>
% 98.38/13.32 (((complementTE1) =>
% 98.38/13.32 (((binintersectTELcontra) =>
% 98.38/13.32 (((binintersectTERcontra) =>
% 98.38/13.32 (((contrasubsetT) =>
% 98.38/13.32 (((contrasubsetT1) =>
% 98.38/13.32 (((contrasubsetT2) =>
% 98.38/13.32 (((contrasubsetT3) =>
% 98.38/13.32 (((doubleComplementI1) =>
% 98.38/13.32 (((doubleComplementE1) =>
% 98.38/13.32 (((doubleComplementSub1) =>
% 98.38/13.32 (((doubleComplementSub2) =>
% 98.38/13.32 (((doubleComplementEq) =>
% 98.38/13.32 (((complementTnotintersectT) =>
% 98.38/13.32 (((complementImpComplementIntersect) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementSubsetComplementIntersect) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementInPowersetComplementIntersect) =>
% 98.38/13.32 ((
% 98.38/13.32 (contraSubsetComplement) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementTcontraSubset) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTILcontra) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTIRcontra) =>
% 98.38/13.32 ((
% 98.38/13.32 (inIntersectImpInUnion) =>
% 98.38/13.32 ((
% 98.38/13.32 (inIntersectImpInUnion2) =>
% 98.38/13.32 ((
% 98.38/13.32 (inIntersectImpInIntersectUnions) =>
% 98.38/13.32 ((
% 98.38/13.32 (intersectInPowersetIntersectUnions) =>
% 98.38/13.32 ((
% 98.38/13.32 (inComplementUnionImpNotIn1) =>
% 98.38/13.32 ((
% 98.38/13.32 (inComplementUnionImpInComplement1) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTE) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTEcontra) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2a1) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementUnionInPowersetComplement) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2a2) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan1a) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan1b) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan1) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2a) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2b2) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2b) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule0) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule1) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule2) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule3) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule4) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_1) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_2) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_3) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_4) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_5) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1all2) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1SetBreln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (choice2fnsingleton) =>
% 98.38/13.32 ((
% 98.38/13.32 (setOfPairsIsBReln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1all1) =>
% 98.38/13.32 ((
% 98.38/13.32 (subbreln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (eqbreln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1invprop) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1invI) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1invE) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compprop) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compI) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compE) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compEex) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionprop) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionIL) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionIR) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionI) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionE) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionEcases) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionCommutes) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2Ex) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2W) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2A) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2B) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1Ex) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1Ex1) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1Equiv) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1E) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1I) =>
% 98.38/13.32 ((
% 98.38/13.32 (injFuncInInjFuncSet) =>
% 98.38/13.32 ((
% 98.38/13.32 (injFuncSetFuncIn) =>
% 98.38/13.32 ((
% 98.38/13.32 (injFuncSetFuncInj) =>
% 98.38/13.32 ((
% 98.38/13.32 (surjFuncSetFuncIn) =>
% 98.38/13.32 ((
% 98.38/13.32 (surjFuncSetFuncSurj) =>
% 98.38/13.32 ((
% 98.38/13.32 (leftInvIsSurj) =>
% 98.38/13.32 ((
% 98.38/13.32 (surjCantorThm) =>
% 98.38/13.32 ((
% 98.38/13.32 (foundation2) =>
% 98.38/13.32 ((
% 98.38/13.32 (notinself) =>
% 98.38/13.32 ((
% 98.38/13.32 (notinself2) =>
% 98.38/13.32 ((
% 98.38/13.32 (omegaSp) =>
% 98.38/13.32 ((
% 98.38/13.32 (omegaSclos) =>
% 98.38/13.32 ((
% 98.38/13.32 (peano0notS) =>
% 98.38/13.32 ((
% 98.38/13.32 (!!) @ (
% 98.38/13.32 (('#S') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =>) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#C') @ in @
% 98.38/13.32 omega)))) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 !!) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#S') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =>) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#C') @ in @
% 98.38/13.32 omega)))))) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#S') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 '#S') @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =>))) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#C') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 '#B') @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =) @
% 98.38/13.32 omegaS)))) @
% 98.38/13.32 omegaS)))))) @
% 98.38/13.32 (
% 98.38/13.32 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.38/13.32 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2321])).
% 98.38/13.32 thf(zip_derived_cl2353, plain,
% 98.38/13.32 (~ (((ifp) =>
% 98.38/13.32 (((theeq) =>
% 98.38/13.32 (((iftrue) =>
% 98.38/13.32 (((iffalse) =>
% 98.38/13.32 (((iftrueorfalse) =>
% 98.38/13.32 (((binintersectT_lem) =>
% 98.38/13.32 (((binunionT_lem) =>
% 98.38/13.32 (((powersetT_lem) =>
% 98.38/13.32 (((setminusT_lem) =>
% 98.38/13.32 (((complementT_lem) =>
% 98.38/13.32 (((setextT) =>
% 98.38/13.32 (((subsetTI) =>
% 98.38/13.32 (((powersetTI1) =>
% 98.38/13.32 (((powersetTE1) =>
% 98.38/13.32 (((complementTI1) =>
% 98.38/13.32 (((complementTE1) =>
% 98.38/13.32 (((binintersectTELcontra) =>
% 98.38/13.32 (((binintersectTERcontra) =>
% 98.38/13.32 (((contrasubsetT) =>
% 98.38/13.32 (((contrasubsetT1) =>
% 98.38/13.32 (((contrasubsetT2) =>
% 98.38/13.32 (((contrasubsetT3) =>
% 98.38/13.32 (((doubleComplementI1) =>
% 98.38/13.32 (((doubleComplementE1) =>
% 98.38/13.32 (((doubleComplementSub1) =>
% 98.38/13.32 (((doubleComplementSub2) =>
% 98.38/13.32 (((doubleComplementEq) =>
% 98.38/13.32 (((complementTnotintersectT) =>
% 98.38/13.32 (((complementImpComplementIntersect) =>
% 98.38/13.32 (((complementSubsetComplementIntersect) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementInPowersetComplementIntersect) =>
% 98.38/13.32 ((
% 98.38/13.32 (contraSubsetComplement) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementTcontraSubset) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTILcontra) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTIRcontra) =>
% 98.38/13.32 ((
% 98.38/13.32 (inIntersectImpInUnion) =>
% 98.38/13.32 ((
% 98.38/13.32 (inIntersectImpInUnion2) =>
% 98.38/13.32 ((
% 98.38/13.32 (inIntersectImpInIntersectUnions) =>
% 98.38/13.32 ((
% 98.38/13.32 (intersectInPowersetIntersectUnions) =>
% 98.38/13.32 ((
% 98.38/13.32 (inComplementUnionImpNotIn1) =>
% 98.38/13.32 ((
% 98.38/13.32 (inComplementUnionImpInComplement1) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTE) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTEcontra) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2a1) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementUnionInPowersetComplement) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2a2) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan1a) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan1b) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan1) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2a) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2b2) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2b) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule0) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule1) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule2) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule3) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule4) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_1) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_2) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_3) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_4) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_5) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1all2) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1SetBreln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (choice2fnsingleton) =>
% 98.38/13.32 ((
% 98.38/13.32 (setOfPairsIsBReln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1all1) =>
% 98.38/13.32 ((
% 98.38/13.32 (subbreln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (eqbreln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1invprop) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1invI) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1invE) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compprop) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compI) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compE) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compEex) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionprop) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionIL) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionIR) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionI) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionE) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionEcases) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionCommutes) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2Ex) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2W) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2A) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2B) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1Ex) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1Ex1) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1Equiv) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1E) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1I) =>
% 98.38/13.32 ((
% 98.38/13.32 (injFuncInInjFuncSet) =>
% 98.38/13.32 ((
% 98.38/13.32 (injFuncSetFuncIn) =>
% 98.38/13.32 ((
% 98.38/13.32 (injFuncSetFuncInj) =>
% 98.38/13.32 ((
% 98.38/13.32 (surjFuncSetFuncIn) =>
% 98.38/13.32 ((
% 98.38/13.32 (surjFuncSetFuncSurj) =>
% 98.38/13.32 ((
% 98.38/13.32 (leftInvIsSurj) =>
% 98.38/13.32 ((
% 98.38/13.32 (surjCantorThm) =>
% 98.38/13.32 ((
% 98.38/13.32 (foundation2) =>
% 98.38/13.32 ((
% 98.38/13.32 (notinself) =>
% 98.38/13.32 ((
% 98.38/13.32 (notinself2) =>
% 98.38/13.32 ((
% 98.38/13.32 (omegaSp) =>
% 98.38/13.32 ((
% 98.38/13.32 (omegaSclos) =>
% 98.38/13.32 ((
% 98.38/13.32 (peano0notS) =>
% 98.38/13.32 ((
% 98.38/13.32 (!!) @ (
% 98.38/13.32 (('#S') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =>) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#C') @ in @
% 98.38/13.32 omega)))) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 !!) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#S') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =>) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#C') @ in @
% 98.38/13.32 omega)))))) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#S') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 '#S') @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =>))) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#C') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 '#B') @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =) @
% 98.38/13.32 omegaS)))) @
% 98.38/13.32 omegaS)))))) @
% 98.38/13.32 (
% 98.38/13.32 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.38/13.32 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2337])).
% 98.38/13.32 thf(zip_derived_cl2374, plain,
% 98.38/13.32 (~ (((theeq) =>
% 98.38/13.32 (((iftrue) =>
% 98.38/13.32 (((iffalse) =>
% 98.38/13.32 (((iftrueorfalse) =>
% 98.38/13.32 (((binintersectT_lem) =>
% 98.38/13.32 (((binunionT_lem) =>
% 98.38/13.32 (((powersetT_lem) =>
% 98.38/13.32 (((setminusT_lem) =>
% 98.38/13.32 (((complementT_lem) =>
% 98.38/13.32 (((setextT) =>
% 98.38/13.32 (((subsetTI) =>
% 98.38/13.32 (((powersetTI1) =>
% 98.38/13.32 (((powersetTE1) =>
% 98.38/13.32 (((complementTI1) =>
% 98.38/13.32 (((complementTE1) =>
% 98.38/13.32 (((binintersectTELcontra) =>
% 98.38/13.32 (((binintersectTERcontra) =>
% 98.38/13.32 (((contrasubsetT) =>
% 98.38/13.32 (((contrasubsetT1) =>
% 98.38/13.32 (((contrasubsetT2) =>
% 98.38/13.32 (((contrasubsetT3) =>
% 98.38/13.32 (((doubleComplementI1) =>
% 98.38/13.32 (((doubleComplementE1) =>
% 98.38/13.32 (((doubleComplementSub1) =>
% 98.38/13.32 (((doubleComplementSub2) =>
% 98.38/13.32 (((doubleComplementEq) =>
% 98.38/13.32 (((complementTnotintersectT) =>
% 98.38/13.32 (((complementImpComplementIntersect) =>
% 98.38/13.32 (((complementSubsetComplementIntersect) =>
% 98.38/13.32 (((complementInPowersetComplementIntersect) =>
% 98.38/13.32 ((
% 98.38/13.32 (contraSubsetComplement) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementTcontraSubset) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTILcontra) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTIRcontra) =>
% 98.38/13.32 ((
% 98.38/13.32 (inIntersectImpInUnion) =>
% 98.38/13.32 ((
% 98.38/13.32 (inIntersectImpInUnion2) =>
% 98.38/13.32 ((
% 98.38/13.32 (inIntersectImpInIntersectUnions) =>
% 98.38/13.32 ((
% 98.38/13.32 (intersectInPowersetIntersectUnions) =>
% 98.38/13.32 ((
% 98.38/13.32 (inComplementUnionImpNotIn1) =>
% 98.38/13.32 ((
% 98.38/13.32 (inComplementUnionImpInComplement1) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTE) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTEcontra) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2a1) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementUnionInPowersetComplement) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2a2) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan1a) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan1b) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan1) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2a) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2b2) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2b) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule0) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule1) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule2) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule3) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule4) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_1) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_2) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_3) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_4) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_5) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1all2) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1SetBreln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (choice2fnsingleton) =>
% 98.38/13.32 ((
% 98.38/13.32 (setOfPairsIsBReln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1all1) =>
% 98.38/13.32 ((
% 98.38/13.32 (subbreln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (eqbreln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1invprop) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1invI) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1invE) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compprop) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compI) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compE) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compEex) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionprop) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionIL) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionIR) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionI) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionE) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionEcases) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionCommutes) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2Ex) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2W) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2A) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2B) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1Ex) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1Ex1) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1Equiv) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1E) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1I) =>
% 98.38/13.32 ((
% 98.38/13.32 (injFuncInInjFuncSet) =>
% 98.38/13.32 ((
% 98.38/13.32 (injFuncSetFuncIn) =>
% 98.38/13.32 ((
% 98.38/13.32 (injFuncSetFuncInj) =>
% 98.38/13.32 ((
% 98.38/13.32 (surjFuncSetFuncIn) =>
% 98.38/13.32 ((
% 98.38/13.32 (surjFuncSetFuncSurj) =>
% 98.38/13.32 ((
% 98.38/13.32 (leftInvIsSurj) =>
% 98.38/13.32 ((
% 98.38/13.32 (surjCantorThm) =>
% 98.38/13.32 ((
% 98.38/13.32 (foundation2) =>
% 98.38/13.32 ((
% 98.38/13.32 (notinself) =>
% 98.38/13.32 ((
% 98.38/13.32 (notinself2) =>
% 98.38/13.32 ((
% 98.38/13.32 (omegaSp) =>
% 98.38/13.32 ((
% 98.38/13.32 (omegaSclos) =>
% 98.38/13.32 ((
% 98.38/13.32 (peano0notS) =>
% 98.38/13.32 ((
% 98.38/13.32 (!!) @ (
% 98.38/13.32 (('#S') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =>) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#C') @ in @
% 98.38/13.32 omega)))) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 !!) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#S') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =>) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#C') @ in @
% 98.38/13.32 omega)))))) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#S') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 '#S') @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =>))) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#C') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 '#B') @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =) @
% 98.38/13.32 omegaS)))) @
% 98.38/13.32 omegaS)))))) @
% 98.38/13.32 (
% 98.38/13.32 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.38/13.32 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2353])).
% 98.38/13.32 thf(zip_derived_cl2392, plain,
% 98.38/13.32 (~ (((iftrue) =>
% 98.38/13.32 (((iffalse) =>
% 98.38/13.32 (((iftrueorfalse) =>
% 98.38/13.32 (((binintersectT_lem) =>
% 98.38/13.32 (((binunionT_lem) =>
% 98.38/13.32 (((powersetT_lem) =>
% 98.38/13.32 (((setminusT_lem) =>
% 98.38/13.32 (((complementT_lem) =>
% 98.38/13.32 (((setextT) =>
% 98.38/13.32 (((subsetTI) =>
% 98.38/13.32 (((powersetTI1) =>
% 98.38/13.32 (((powersetTE1) =>
% 98.38/13.32 (((complementTI1) =>
% 98.38/13.32 (((complementTE1) =>
% 98.38/13.32 (((binintersectTELcontra) =>
% 98.38/13.32 (((binintersectTERcontra) =>
% 98.38/13.32 (((contrasubsetT) =>
% 98.38/13.32 (((contrasubsetT1) =>
% 98.38/13.32 (((contrasubsetT2) =>
% 98.38/13.32 (((contrasubsetT3) =>
% 98.38/13.32 (((doubleComplementI1) =>
% 98.38/13.32 (((doubleComplementE1) =>
% 98.38/13.32 (((doubleComplementSub1) =>
% 98.38/13.32 (((doubleComplementSub2) =>
% 98.38/13.32 (((doubleComplementEq) =>
% 98.38/13.32 (((complementTnotintersectT) =>
% 98.38/13.32 (((complementImpComplementIntersect) =>
% 98.38/13.32 (((complementSubsetComplementIntersect) =>
% 98.38/13.32 (((complementInPowersetComplementIntersect) =>
% 98.38/13.32 (((contraSubsetComplement) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementTcontraSubset) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTILcontra) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTIRcontra) =>
% 98.38/13.32 ((
% 98.38/13.32 (inIntersectImpInUnion) =>
% 98.38/13.32 ((
% 98.38/13.32 (inIntersectImpInUnion2) =>
% 98.38/13.32 ((
% 98.38/13.32 (inIntersectImpInIntersectUnions) =>
% 98.38/13.32 ((
% 98.38/13.32 (intersectInPowersetIntersectUnions) =>
% 98.38/13.32 ((
% 98.38/13.32 (inComplementUnionImpNotIn1) =>
% 98.38/13.32 ((
% 98.38/13.32 (inComplementUnionImpInComplement1) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTE) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTEcontra) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2a1) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementUnionInPowersetComplement) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2a2) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan1a) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan1b) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan1) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2a) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2b2) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2b) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule0) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule1) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule2) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule3) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule4) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_1) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_2) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_3) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_4) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_5) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1all2) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1SetBreln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (choice2fnsingleton) =>
% 98.38/13.32 ((
% 98.38/13.32 (setOfPairsIsBReln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1all1) =>
% 98.38/13.32 ((
% 98.38/13.32 (subbreln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (eqbreln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1invprop) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1invI) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1invE) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compprop) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compI) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compE) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compEex) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionprop) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionIL) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionIR) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionI) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionE) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionEcases) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionCommutes) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2Ex) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2W) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2A) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2B) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1Ex) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1Ex1) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1Equiv) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1E) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1I) =>
% 98.38/13.32 ((
% 98.38/13.32 (injFuncInInjFuncSet) =>
% 98.38/13.32 ((
% 98.38/13.32 (injFuncSetFuncIn) =>
% 98.38/13.32 ((
% 98.38/13.32 (injFuncSetFuncInj) =>
% 98.38/13.32 ((
% 98.38/13.32 (surjFuncSetFuncIn) =>
% 98.38/13.32 ((
% 98.38/13.32 (surjFuncSetFuncSurj) =>
% 98.38/13.32 ((
% 98.38/13.32 (leftInvIsSurj) =>
% 98.38/13.32 ((
% 98.38/13.32 (surjCantorThm) =>
% 98.38/13.32 ((
% 98.38/13.32 (foundation2) =>
% 98.38/13.32 ((
% 98.38/13.32 (notinself) =>
% 98.38/13.32 ((
% 98.38/13.32 (notinself2) =>
% 98.38/13.32 ((
% 98.38/13.32 (omegaSp) =>
% 98.38/13.32 ((
% 98.38/13.32 (omegaSclos) =>
% 98.38/13.32 ((
% 98.38/13.32 (peano0notS) =>
% 98.38/13.32 ((
% 98.38/13.32 (!!) @ (
% 98.38/13.32 (('#S') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =>) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#C') @ in @
% 98.38/13.32 omega)))) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 !!) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#S') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =>) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#C') @ in @
% 98.38/13.32 omega)))))) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#S') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 '#S') @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =>))) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#C') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 '#B') @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =) @
% 98.38/13.32 omegaS)))) @
% 98.38/13.32 omegaS)))))) @
% 98.38/13.32 (
% 98.38/13.32 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.38/13.32 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2374])).
% 98.38/13.32 thf(zip_derived_cl2408, plain,
% 98.38/13.32 (~ (((iffalse) =>
% 98.38/13.32 (((iftrueorfalse) =>
% 98.38/13.32 (((binintersectT_lem) =>
% 98.38/13.32 (((binunionT_lem) =>
% 98.38/13.32 (((powersetT_lem) =>
% 98.38/13.32 (((setminusT_lem) =>
% 98.38/13.32 (((complementT_lem) =>
% 98.38/13.32 (((setextT) =>
% 98.38/13.32 (((subsetTI) =>
% 98.38/13.32 (((powersetTI1) =>
% 98.38/13.32 (((powersetTE1) =>
% 98.38/13.32 (((complementTI1) =>
% 98.38/13.32 (((complementTE1) =>
% 98.38/13.32 (((binintersectTELcontra) =>
% 98.38/13.32 (((binintersectTERcontra) =>
% 98.38/13.32 (((contrasubsetT) =>
% 98.38/13.32 (((contrasubsetT1) =>
% 98.38/13.32 (((contrasubsetT2) =>
% 98.38/13.32 (((contrasubsetT3) =>
% 98.38/13.32 (((doubleComplementI1) =>
% 98.38/13.32 (((doubleComplementE1) =>
% 98.38/13.32 (((doubleComplementSub1) =>
% 98.38/13.32 (((doubleComplementSub2) =>
% 98.38/13.32 (((doubleComplementEq) =>
% 98.38/13.32 (((complementTnotintersectT) =>
% 98.38/13.32 (((complementImpComplementIntersect) =>
% 98.38/13.32 (((complementSubsetComplementIntersect) =>
% 98.38/13.32 (((complementInPowersetComplementIntersect) =>
% 98.38/13.32 (((contraSubsetComplement) =>
% 98.38/13.32 (((complementTcontraSubset) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTILcontra) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTIRcontra) =>
% 98.38/13.32 ((
% 98.38/13.32 (inIntersectImpInUnion) =>
% 98.38/13.32 ((
% 98.38/13.32 (inIntersectImpInUnion2) =>
% 98.38/13.32 ((
% 98.38/13.32 (inIntersectImpInIntersectUnions) =>
% 98.38/13.32 ((
% 98.38/13.32 (intersectInPowersetIntersectUnions) =>
% 98.38/13.32 ((
% 98.38/13.32 (inComplementUnionImpNotIn1) =>
% 98.38/13.32 ((
% 98.38/13.32 (inComplementUnionImpInComplement1) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTE) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTEcontra) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2a1) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementUnionInPowersetComplement) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2a2) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan1a) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan1b) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan1) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2a) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2b2) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2b) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule0) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule1) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule2) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule3) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule4) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_1) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_2) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_3) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_4) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_5) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1all2) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1SetBreln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (choice2fnsingleton) =>
% 98.38/13.32 ((
% 98.38/13.32 (setOfPairsIsBReln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1all1) =>
% 98.38/13.32 ((
% 98.38/13.32 (subbreln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (eqbreln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1invprop) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1invI) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1invE) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compprop) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compI) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compE) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compEex) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionprop) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionIL) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionIR) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionI) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionE) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionEcases) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionCommutes) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2Ex) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2W) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2A) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2B) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1Ex) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1Ex1) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1Equiv) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1E) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1I) =>
% 98.38/13.32 ((
% 98.38/13.32 (injFuncInInjFuncSet) =>
% 98.38/13.32 ((
% 98.38/13.32 (injFuncSetFuncIn) =>
% 98.38/13.32 ((
% 98.38/13.32 (injFuncSetFuncInj) =>
% 98.38/13.32 ((
% 98.38/13.32 (surjFuncSetFuncIn) =>
% 98.38/13.32 ((
% 98.38/13.32 (surjFuncSetFuncSurj) =>
% 98.38/13.32 ((
% 98.38/13.32 (leftInvIsSurj) =>
% 98.38/13.32 ((
% 98.38/13.32 (surjCantorThm) =>
% 98.38/13.32 ((
% 98.38/13.32 (foundation2) =>
% 98.38/13.32 ((
% 98.38/13.32 (notinself) =>
% 98.38/13.32 ((
% 98.38/13.32 (notinself2) =>
% 98.38/13.32 ((
% 98.38/13.32 (omegaSp) =>
% 98.38/13.32 ((
% 98.38/13.32 (omegaSclos) =>
% 98.38/13.32 ((
% 98.38/13.32 (peano0notS) =>
% 98.38/13.32 ((
% 98.38/13.32 (!!) @ (
% 98.38/13.32 (('#S') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =>) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#C') @ in @
% 98.38/13.32 omega)))) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 !!) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#S') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =>) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#C') @ in @
% 98.38/13.32 omega)))))) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#S') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 '#S') @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =>))) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#C') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 '#B') @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =) @
% 98.38/13.32 omegaS)))) @
% 98.38/13.32 omegaS)))))) @
% 98.38/13.32 (
% 98.38/13.32 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.38/13.32 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2392])).
% 98.38/13.32 thf(zip_derived_cl2427, plain,
% 98.38/13.32 (~ (((iftrueorfalse) =>
% 98.38/13.32 (((binintersectT_lem) =>
% 98.38/13.32 (((binunionT_lem) =>
% 98.38/13.32 (((powersetT_lem) =>
% 98.38/13.32 (((setminusT_lem) =>
% 98.38/13.32 (((complementT_lem) =>
% 98.38/13.32 (((setextT) =>
% 98.38/13.32 (((subsetTI) =>
% 98.38/13.32 (((powersetTI1) =>
% 98.38/13.32 (((powersetTE1) =>
% 98.38/13.32 (((complementTI1) =>
% 98.38/13.32 (((complementTE1) =>
% 98.38/13.32 (((binintersectTELcontra) =>
% 98.38/13.32 (((binintersectTERcontra) =>
% 98.38/13.32 (((contrasubsetT) =>
% 98.38/13.32 (((contrasubsetT1) =>
% 98.38/13.32 (((contrasubsetT2) =>
% 98.38/13.32 (((contrasubsetT3) =>
% 98.38/13.32 (((doubleComplementI1) =>
% 98.38/13.32 (((doubleComplementE1) =>
% 98.38/13.32 (((doubleComplementSub1) =>
% 98.38/13.32 (((doubleComplementSub2) =>
% 98.38/13.32 (((doubleComplementEq) =>
% 98.38/13.32 (((complementTnotintersectT) =>
% 98.38/13.32 (((complementImpComplementIntersect) =>
% 98.38/13.32 (((complementSubsetComplementIntersect) =>
% 98.38/13.32 (((complementInPowersetComplementIntersect) =>
% 98.38/13.32 (((contraSubsetComplement) =>
% 98.38/13.32 (((complementTcontraSubset) =>
% 98.38/13.32 (((binunionTILcontra) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTIRcontra) =>
% 98.38/13.32 ((
% 98.38/13.32 (inIntersectImpInUnion) =>
% 98.38/13.32 ((
% 98.38/13.32 (inIntersectImpInUnion2) =>
% 98.38/13.32 ((
% 98.38/13.32 (inIntersectImpInIntersectUnions) =>
% 98.38/13.32 ((
% 98.38/13.32 (intersectInPowersetIntersectUnions) =>
% 98.38/13.32 ((
% 98.38/13.32 (inComplementUnionImpNotIn1) =>
% 98.38/13.32 ((
% 98.38/13.32 (inComplementUnionImpInComplement1) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTE) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTEcontra) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2a1) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementUnionInPowersetComplement) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2a2) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan1a) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan1b) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan1) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2a) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2b2) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2b) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule0) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule1) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule2) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule3) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule4) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_1) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_2) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_3) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_4) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_5) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1all2) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1SetBreln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (choice2fnsingleton) =>
% 98.38/13.32 ((
% 98.38/13.32 (setOfPairsIsBReln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1all1) =>
% 98.38/13.32 ((
% 98.38/13.32 (subbreln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (eqbreln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1invprop) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1invI) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1invE) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compprop) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compI) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compE) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compEex) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionprop) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionIL) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionIR) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionI) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionE) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionEcases) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionCommutes) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2Ex) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2W) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2A) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz2B) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1Ex) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1Ex1) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1Equiv) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1E) =>
% 98.38/13.32 ((
% 98.38/13.32 (image1I) =>
% 98.38/13.32 ((
% 98.38/13.32 (injFuncInInjFuncSet) =>
% 98.38/13.32 ((
% 98.38/13.32 (injFuncSetFuncIn) =>
% 98.38/13.32 ((
% 98.38/13.32 (injFuncSetFuncInj) =>
% 98.38/13.32 ((
% 98.38/13.32 (surjFuncSetFuncIn) =>
% 98.38/13.32 ((
% 98.38/13.32 (surjFuncSetFuncSurj) =>
% 98.38/13.32 ((
% 98.38/13.32 (leftInvIsSurj) =>
% 98.38/13.32 ((
% 98.38/13.32 (surjCantorThm) =>
% 98.38/13.32 ((
% 98.38/13.32 (foundation2) =>
% 98.38/13.32 ((
% 98.38/13.32 (notinself) =>
% 98.38/13.32 ((
% 98.38/13.32 (notinself2) =>
% 98.38/13.32 ((
% 98.38/13.32 (omegaSp) =>
% 98.38/13.32 ((
% 98.38/13.32 (omegaSclos) =>
% 98.38/13.32 ((
% 98.38/13.32 (peano0notS) =>
% 98.38/13.32 ((
% 98.38/13.32 (!!) @ (
% 98.38/13.32 (('#S') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =>) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#C') @ in @
% 98.38/13.32 omega)))) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 !!) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#S') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =>) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#C') @ in @
% 98.38/13.32 omega)))))) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#S') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 '#S') @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =>))) @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#C') @ (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 '#B') @
% 98.38/13.32 (
% 98.38/13.32 (
% 98.38/13.32 ('#B') @ (
% 98.38/13.32 =) @
% 98.38/13.32 omegaS)))) @
% 98.38/13.32 omegaS)))))) @
% 98.38/13.32 (
% 98.38/13.32 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.38/13.32 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2408])).
% 98.38/13.32 thf(zip_derived_cl2442, plain,
% 98.38/13.32 (~ (((binintersectT_lem) =>
% 98.38/13.32 (((binunionT_lem) =>
% 98.38/13.32 (((powersetT_lem) =>
% 98.38/13.32 (((setminusT_lem) =>
% 98.38/13.32 (((complementT_lem) =>
% 98.38/13.32 (((setextT) =>
% 98.38/13.32 (((subsetTI) =>
% 98.38/13.32 (((powersetTI1) =>
% 98.38/13.32 (((powersetTE1) =>
% 98.38/13.32 (((complementTI1) =>
% 98.38/13.32 (((complementTE1) =>
% 98.38/13.32 (((binintersectTELcontra) =>
% 98.38/13.32 (((binintersectTERcontra) =>
% 98.38/13.32 (((contrasubsetT) =>
% 98.38/13.32 (((contrasubsetT1) =>
% 98.38/13.32 (((contrasubsetT2) =>
% 98.38/13.32 (((contrasubsetT3) =>
% 98.38/13.32 (((doubleComplementI1) =>
% 98.38/13.32 (((doubleComplementE1) =>
% 98.38/13.32 (((doubleComplementSub1) =>
% 98.38/13.32 (((doubleComplementSub2) =>
% 98.38/13.32 (((doubleComplementEq) =>
% 98.38/13.32 (((complementTnotintersectT) =>
% 98.38/13.32 (((complementImpComplementIntersect) =>
% 98.38/13.32 (((complementSubsetComplementIntersect) =>
% 98.38/13.32 (((complementInPowersetComplementIntersect) =>
% 98.38/13.32 (((contraSubsetComplement) =>
% 98.38/13.32 (((complementTcontraSubset) =>
% 98.38/13.32 (((binunionTILcontra) =>
% 98.38/13.32 (((binunionTIRcontra) =>
% 98.38/13.32 ((
% 98.38/13.32 (inIntersectImpInUnion) =>
% 98.38/13.32 ((
% 98.38/13.32 (inIntersectImpInUnion2) =>
% 98.38/13.32 ((
% 98.38/13.32 (inIntersectImpInIntersectUnions) =>
% 98.38/13.32 ((
% 98.38/13.32 (intersectInPowersetIntersectUnions) =>
% 98.38/13.32 ((
% 98.38/13.32 (inComplementUnionImpNotIn1) =>
% 98.38/13.32 ((
% 98.38/13.32 (inComplementUnionImpInComplement1) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTE) =>
% 98.38/13.32 ((
% 98.38/13.32 (binunionTEcontra) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2a1) =>
% 98.38/13.32 ((
% 98.38/13.32 (complementUnionInPowersetComplement) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2a2) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan1a) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan1b) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan1) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2a) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2b2) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2b) =>
% 98.38/13.32 ((
% 98.38/13.32 (demorgan2) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule0) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule1) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule2) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule3) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz13rule4) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_1) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_2) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_3) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_4) =>
% 98.38/13.32 ((
% 98.38/13.32 (woz1_5) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1all2) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1SetBreln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (choice2fnsingleton) =>
% 98.38/13.32 ((
% 98.38/13.32 (setOfPairsIsBReln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1all1) =>
% 98.38/13.32 ((
% 98.38/13.32 (subbreln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (eqbreln1) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1invprop) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1invI) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1invE) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compprop) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compI) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compE) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1compEex) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionprop) =>
% 98.38/13.32 ((
% 98.38/13.32 (breln1unionIL) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionIR) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionI) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionE) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionEcases) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionCommutes) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz2Ex) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz2W) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz2A) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz2B) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1Ex) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1Ex1) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1Equiv) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1E) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1I) =>
% 98.38/13.33 ((
% 98.38/13.33 (injFuncInInjFuncSet) =>
% 98.38/13.33 ((
% 98.38/13.33 (injFuncSetFuncIn) =>
% 98.38/13.33 ((
% 98.38/13.33 (injFuncSetFuncInj) =>
% 98.38/13.33 ((
% 98.38/13.33 (surjFuncSetFuncIn) =>
% 98.38/13.33 ((
% 98.38/13.33 (surjFuncSetFuncSurj) =>
% 98.38/13.33 ((
% 98.38/13.33 (leftInvIsSurj) =>
% 98.38/13.33 ((
% 98.38/13.33 (surjCantorThm) =>
% 98.38/13.33 ((
% 98.38/13.33 (foundation2) =>
% 98.38/13.33 ((
% 98.38/13.33 (notinself) =>
% 98.38/13.33 ((
% 98.38/13.33 (notinself2) =>
% 98.38/13.33 ((
% 98.38/13.33 (omegaSp) =>
% 98.38/13.33 ((
% 98.38/13.33 (omegaSclos) =>
% 98.38/13.33 ((
% 98.38/13.33 (peano0notS) =>
% 98.38/13.33 ((
% 98.38/13.33 (!!) @ (
% 98.38/13.33 (('#S') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 =>) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#C') @ in @
% 98.38/13.33 omega)))) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 !!) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#S') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 =>) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#C') @ in @
% 98.38/13.33 omega)))))) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#S') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 '#S') @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 =>))) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#C') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 '#B') @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 =) @
% 98.38/13.33 omegaS)))) @
% 98.38/13.33 omegaS)))))) @
% 98.38/13.33 (
% 98.38/13.33 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.38/13.33 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2427])).
% 98.38/13.33 thf(zip_derived_cl2454, plain,
% 98.38/13.33 (~ (((binunionT_lem) =>
% 98.38/13.33 (((powersetT_lem) =>
% 98.38/13.33 (((setminusT_lem) =>
% 98.38/13.33 (((complementT_lem) =>
% 98.38/13.33 (((setextT) =>
% 98.38/13.33 (((subsetTI) =>
% 98.38/13.33 (((powersetTI1) =>
% 98.38/13.33 (((powersetTE1) =>
% 98.38/13.33 (((complementTI1) =>
% 98.38/13.33 (((complementTE1) =>
% 98.38/13.33 (((binintersectTELcontra) =>
% 98.38/13.33 (((binintersectTERcontra) =>
% 98.38/13.33 (((contrasubsetT) =>
% 98.38/13.33 (((contrasubsetT1) =>
% 98.38/13.33 (((contrasubsetT2) =>
% 98.38/13.33 (((contrasubsetT3) =>
% 98.38/13.33 (((doubleComplementI1) =>
% 98.38/13.33 (((doubleComplementE1) =>
% 98.38/13.33 (((doubleComplementSub1) =>
% 98.38/13.33 (((doubleComplementSub2) =>
% 98.38/13.33 (((doubleComplementEq) =>
% 98.38/13.33 (((complementTnotintersectT) =>
% 98.38/13.33 (((complementImpComplementIntersect) =>
% 98.38/13.33 (((complementSubsetComplementIntersect) =>
% 98.38/13.33 (((complementInPowersetComplementIntersect) =>
% 98.38/13.33 (((contraSubsetComplement) =>
% 98.38/13.33 (((complementTcontraSubset) =>
% 98.38/13.33 (((binunionTILcontra) =>
% 98.38/13.33 (((binunionTIRcontra) =>
% 98.38/13.33 (((inIntersectImpInUnion) =>
% 98.38/13.33 ((
% 98.38/13.33 (inIntersectImpInUnion2) =>
% 98.38/13.33 ((
% 98.38/13.33 (inIntersectImpInIntersectUnions) =>
% 98.38/13.33 ((
% 98.38/13.33 (intersectInPowersetIntersectUnions) =>
% 98.38/13.33 ((
% 98.38/13.33 (inComplementUnionImpNotIn1) =>
% 98.38/13.33 ((
% 98.38/13.33 (inComplementUnionImpInComplement1) =>
% 98.38/13.33 ((
% 98.38/13.33 (binunionTE) =>
% 98.38/13.33 ((
% 98.38/13.33 (binunionTEcontra) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan2a1) =>
% 98.38/13.33 ((
% 98.38/13.33 (complementUnionInPowersetComplement) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan2a2) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan1a) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan1b) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan1) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan2a) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan2b2) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan2b) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan2) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz13rule0) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz13rule1) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz13rule2) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz13rule3) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz13rule4) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz1_1) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz1_2) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz1_3) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz1_4) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz1_5) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1all2) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1SetBreln1) =>
% 98.38/13.33 ((
% 98.38/13.33 (choice2fnsingleton) =>
% 98.38/13.33 ((
% 98.38/13.33 (setOfPairsIsBReln1) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1all1) =>
% 98.38/13.33 ((
% 98.38/13.33 (subbreln1) =>
% 98.38/13.33 ((
% 98.38/13.33 (eqbreln1) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1invprop) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1invI) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1invE) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1compprop) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1compI) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1compE) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1compEex) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionprop) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionIL) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionIR) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionI) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionE) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionEcases) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionCommutes) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz2Ex) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz2W) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz2A) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz2B) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1Ex) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1Ex1) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1Equiv) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1E) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1I) =>
% 98.38/13.33 ((
% 98.38/13.33 (injFuncInInjFuncSet) =>
% 98.38/13.33 ((
% 98.38/13.33 (injFuncSetFuncIn) =>
% 98.38/13.33 ((
% 98.38/13.33 (injFuncSetFuncInj) =>
% 98.38/13.33 ((
% 98.38/13.33 (surjFuncSetFuncIn) =>
% 98.38/13.33 ((
% 98.38/13.33 (surjFuncSetFuncSurj) =>
% 98.38/13.33 ((
% 98.38/13.33 (leftInvIsSurj) =>
% 98.38/13.33 ((
% 98.38/13.33 (surjCantorThm) =>
% 98.38/13.33 ((
% 98.38/13.33 (foundation2) =>
% 98.38/13.33 ((
% 98.38/13.33 (notinself) =>
% 98.38/13.33 ((
% 98.38/13.33 (notinself2) =>
% 98.38/13.33 ((
% 98.38/13.33 (omegaSp) =>
% 98.38/13.33 ((
% 98.38/13.33 (omegaSclos) =>
% 98.38/13.33 ((
% 98.38/13.33 (peano0notS) =>
% 98.38/13.33 ((
% 98.38/13.33 (!!) @ (
% 98.38/13.33 (('#S') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 =>) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#C') @ in @
% 98.38/13.33 omega)))) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 !!) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#S') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 =>) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#C') @ in @
% 98.38/13.33 omega)))))) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#S') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 '#S') @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 =>))) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#C') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 '#B') @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 =) @
% 98.38/13.33 omegaS)))) @
% 98.38/13.33 omegaS)))))) @
% 98.38/13.33 (
% 98.38/13.33 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.38/13.33 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2442])).
% 98.38/13.33 thf(zip_derived_cl2465, plain,
% 98.38/13.33 (~ (((powersetT_lem) =>
% 98.38/13.33 (((setminusT_lem) =>
% 98.38/13.33 (((complementT_lem) =>
% 98.38/13.33 (((setextT) =>
% 98.38/13.33 (((subsetTI) =>
% 98.38/13.33 (((powersetTI1) =>
% 98.38/13.33 (((powersetTE1) =>
% 98.38/13.33 (((complementTI1) =>
% 98.38/13.33 (((complementTE1) =>
% 98.38/13.33 (((binintersectTELcontra) =>
% 98.38/13.33 (((binintersectTERcontra) =>
% 98.38/13.33 (((contrasubsetT) =>
% 98.38/13.33 (((contrasubsetT1) =>
% 98.38/13.33 (((contrasubsetT2) =>
% 98.38/13.33 (((contrasubsetT3) =>
% 98.38/13.33 (((doubleComplementI1) =>
% 98.38/13.33 (((doubleComplementE1) =>
% 98.38/13.33 (((doubleComplementSub1) =>
% 98.38/13.33 (((doubleComplementSub2) =>
% 98.38/13.33 (((doubleComplementEq) =>
% 98.38/13.33 (((complementTnotintersectT) =>
% 98.38/13.33 (((complementImpComplementIntersect) =>
% 98.38/13.33 (((complementSubsetComplementIntersect) =>
% 98.38/13.33 (((complementInPowersetComplementIntersect) =>
% 98.38/13.33 (((contraSubsetComplement) =>
% 98.38/13.33 (((complementTcontraSubset) =>
% 98.38/13.33 (((binunionTILcontra) =>
% 98.38/13.33 (((binunionTIRcontra) =>
% 98.38/13.33 (((inIntersectImpInUnion) =>
% 98.38/13.33 (((inIntersectImpInUnion2) =>
% 98.38/13.33 ((
% 98.38/13.33 (inIntersectImpInIntersectUnions) =>
% 98.38/13.33 ((
% 98.38/13.33 (intersectInPowersetIntersectUnions) =>
% 98.38/13.33 ((
% 98.38/13.33 (inComplementUnionImpNotIn1) =>
% 98.38/13.33 ((
% 98.38/13.33 (inComplementUnionImpInComplement1) =>
% 98.38/13.33 ((
% 98.38/13.33 (binunionTE) =>
% 98.38/13.33 ((
% 98.38/13.33 (binunionTEcontra) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan2a1) =>
% 98.38/13.33 ((
% 98.38/13.33 (complementUnionInPowersetComplement) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan2a2) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan1a) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan1b) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan1) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan2a) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan2b2) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan2b) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan2) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz13rule0) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz13rule1) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz13rule2) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz13rule3) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz13rule4) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz1_1) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz1_2) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz1_3) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz1_4) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz1_5) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1all2) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1SetBreln1) =>
% 98.38/13.33 ((
% 98.38/13.33 (choice2fnsingleton) =>
% 98.38/13.33 ((
% 98.38/13.33 (setOfPairsIsBReln1) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1all1) =>
% 98.38/13.33 ((
% 98.38/13.33 (subbreln1) =>
% 98.38/13.33 ((
% 98.38/13.33 (eqbreln1) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1invprop) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1invI) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1invE) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1compprop) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1compI) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1compE) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1compEex) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionprop) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionIL) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionIR) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionI) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionE) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionEcases) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionCommutes) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz2Ex) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz2W) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz2A) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz2B) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1Ex) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1Ex1) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1Equiv) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1E) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1I) =>
% 98.38/13.33 ((
% 98.38/13.33 (injFuncInInjFuncSet) =>
% 98.38/13.33 ((
% 98.38/13.33 (injFuncSetFuncIn) =>
% 98.38/13.33 ((
% 98.38/13.33 (injFuncSetFuncInj) =>
% 98.38/13.33 ((
% 98.38/13.33 (surjFuncSetFuncIn) =>
% 98.38/13.33 ((
% 98.38/13.33 (surjFuncSetFuncSurj) =>
% 98.38/13.33 ((
% 98.38/13.33 (leftInvIsSurj) =>
% 98.38/13.33 ((
% 98.38/13.33 (surjCantorThm) =>
% 98.38/13.33 ((
% 98.38/13.33 (foundation2) =>
% 98.38/13.33 ((
% 98.38/13.33 (notinself) =>
% 98.38/13.33 ((
% 98.38/13.33 (notinself2) =>
% 98.38/13.33 ((
% 98.38/13.33 (omegaSp) =>
% 98.38/13.33 ((
% 98.38/13.33 (omegaSclos) =>
% 98.38/13.33 ((
% 98.38/13.33 (peano0notS) =>
% 98.38/13.33 ((
% 98.38/13.33 (!!) @ (
% 98.38/13.33 (('#S') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 =>) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#C') @ in @
% 98.38/13.33 omega)))) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 !!) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#S') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 =>) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#C') @ in @
% 98.38/13.33 omega)))))) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#S') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 '#S') @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 =>))) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#C') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 '#B') @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 =) @
% 98.38/13.33 omegaS)))) @
% 98.38/13.33 omegaS)))))) @
% 98.38/13.33 (
% 98.38/13.33 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.38/13.33 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2454])).
% 98.38/13.33 thf(zip_derived_cl2476, plain,
% 98.38/13.33 (~ (((setminusT_lem) =>
% 98.38/13.33 (((complementT_lem) =>
% 98.38/13.33 (((setextT) =>
% 98.38/13.33 (((subsetTI) =>
% 98.38/13.33 (((powersetTI1) =>
% 98.38/13.33 (((powersetTE1) =>
% 98.38/13.33 (((complementTI1) =>
% 98.38/13.33 (((complementTE1) =>
% 98.38/13.33 (((binintersectTELcontra) =>
% 98.38/13.33 (((binintersectTERcontra) =>
% 98.38/13.33 (((contrasubsetT) =>
% 98.38/13.33 (((contrasubsetT1) =>
% 98.38/13.33 (((contrasubsetT2) =>
% 98.38/13.33 (((contrasubsetT3) =>
% 98.38/13.33 (((doubleComplementI1) =>
% 98.38/13.33 (((doubleComplementE1) =>
% 98.38/13.33 (((doubleComplementSub1) =>
% 98.38/13.33 (((doubleComplementSub2) =>
% 98.38/13.33 (((doubleComplementEq) =>
% 98.38/13.33 (((complementTnotintersectT) =>
% 98.38/13.33 (((complementImpComplementIntersect) =>
% 98.38/13.33 (((complementSubsetComplementIntersect) =>
% 98.38/13.33 (((complementInPowersetComplementIntersect) =>
% 98.38/13.33 (((contraSubsetComplement) =>
% 98.38/13.33 (((complementTcontraSubset) =>
% 98.38/13.33 (((binunionTILcontra) =>
% 98.38/13.33 (((binunionTIRcontra) =>
% 98.38/13.33 (((inIntersectImpInUnion) =>
% 98.38/13.33 (((inIntersectImpInUnion2) =>
% 98.38/13.33 (((inIntersectImpInIntersectUnions) =>
% 98.38/13.33 ((
% 98.38/13.33 (intersectInPowersetIntersectUnions) =>
% 98.38/13.33 ((
% 98.38/13.33 (inComplementUnionImpNotIn1) =>
% 98.38/13.33 ((
% 98.38/13.33 (inComplementUnionImpInComplement1) =>
% 98.38/13.33 ((
% 98.38/13.33 (binunionTE) =>
% 98.38/13.33 ((
% 98.38/13.33 (binunionTEcontra) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan2a1) =>
% 98.38/13.33 ((
% 98.38/13.33 (complementUnionInPowersetComplement) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan2a2) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan1a) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan1b) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan1) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan2a) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan2b2) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan2b) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan2) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz13rule0) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz13rule1) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz13rule2) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz13rule3) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz13rule4) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz1_1) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz1_2) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz1_3) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz1_4) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz1_5) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1all2) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1SetBreln1) =>
% 98.38/13.33 ((
% 98.38/13.33 (choice2fnsingleton) =>
% 98.38/13.33 ((
% 98.38/13.33 (setOfPairsIsBReln1) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1all1) =>
% 98.38/13.33 ((
% 98.38/13.33 (subbreln1) =>
% 98.38/13.33 ((
% 98.38/13.33 (eqbreln1) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1invprop) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1invI) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1invE) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1compprop) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1compI) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1compE) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1compEex) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionprop) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionIL) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionIR) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionI) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionE) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionEcases) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionCommutes) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz2Ex) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz2W) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz2A) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz2B) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1Ex) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1Ex1) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1Equiv) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1E) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1I) =>
% 98.38/13.33 ((
% 98.38/13.33 (injFuncInInjFuncSet) =>
% 98.38/13.33 ((
% 98.38/13.33 (injFuncSetFuncIn) =>
% 98.38/13.33 ((
% 98.38/13.33 (injFuncSetFuncInj) =>
% 98.38/13.33 ((
% 98.38/13.33 (surjFuncSetFuncIn) =>
% 98.38/13.33 ((
% 98.38/13.33 (surjFuncSetFuncSurj) =>
% 98.38/13.33 ((
% 98.38/13.33 (leftInvIsSurj) =>
% 98.38/13.33 ((
% 98.38/13.33 (surjCantorThm) =>
% 98.38/13.33 ((
% 98.38/13.33 (foundation2) =>
% 98.38/13.33 ((
% 98.38/13.33 (notinself) =>
% 98.38/13.33 ((
% 98.38/13.33 (notinself2) =>
% 98.38/13.33 ((
% 98.38/13.33 (omegaSp) =>
% 98.38/13.33 ((
% 98.38/13.33 (omegaSclos) =>
% 98.38/13.33 ((
% 98.38/13.33 (peano0notS) =>
% 98.38/13.33 ((
% 98.38/13.33 (!!) @ (
% 98.38/13.33 (('#S') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 =>) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#C') @ in @
% 98.38/13.33 omega)))) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 !!) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#S') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 =>) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#C') @ in @
% 98.38/13.33 omega)))))) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#S') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 '#S') @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 =>))) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#C') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 '#B') @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 =) @
% 98.38/13.33 omegaS)))) @
% 98.38/13.33 omegaS)))))) @
% 98.38/13.33 (
% 98.38/13.33 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.38/13.33 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2465])).
% 98.38/13.33 thf(zip_derived_cl2485, plain,
% 98.38/13.33 (~ (((complementT_lem) =>
% 98.38/13.33 (((setextT) =>
% 98.38/13.33 (((subsetTI) =>
% 98.38/13.33 (((powersetTI1) =>
% 98.38/13.33 (((powersetTE1) =>
% 98.38/13.33 (((complementTI1) =>
% 98.38/13.33 (((complementTE1) =>
% 98.38/13.33 (((binintersectTELcontra) =>
% 98.38/13.33 (((binintersectTERcontra) =>
% 98.38/13.33 (((contrasubsetT) =>
% 98.38/13.33 (((contrasubsetT1) =>
% 98.38/13.33 (((contrasubsetT2) =>
% 98.38/13.33 (((contrasubsetT3) =>
% 98.38/13.33 (((doubleComplementI1) =>
% 98.38/13.33 (((doubleComplementE1) =>
% 98.38/13.33 (((doubleComplementSub1) =>
% 98.38/13.33 (((doubleComplementSub2) =>
% 98.38/13.33 (((doubleComplementEq) =>
% 98.38/13.33 (((complementTnotintersectT) =>
% 98.38/13.33 (((complementImpComplementIntersect) =>
% 98.38/13.33 (((complementSubsetComplementIntersect) =>
% 98.38/13.33 (((complementInPowersetComplementIntersect) =>
% 98.38/13.33 (((contraSubsetComplement) =>
% 98.38/13.33 (((complementTcontraSubset) =>
% 98.38/13.33 (((binunionTILcontra) =>
% 98.38/13.33 (((binunionTIRcontra) =>
% 98.38/13.33 (((inIntersectImpInUnion) =>
% 98.38/13.33 (((inIntersectImpInUnion2) =>
% 98.38/13.33 (((inIntersectImpInIntersectUnions) =>
% 98.38/13.33 (((intersectInPowersetIntersectUnions) =>
% 98.38/13.33 ((
% 98.38/13.33 (inComplementUnionImpNotIn1) =>
% 98.38/13.33 ((
% 98.38/13.33 (inComplementUnionImpInComplement1) =>
% 98.38/13.33 ((
% 98.38/13.33 (binunionTE) =>
% 98.38/13.33 ((
% 98.38/13.33 (binunionTEcontra) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan2a1) =>
% 98.38/13.33 ((
% 98.38/13.33 (complementUnionInPowersetComplement) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan2a2) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan1a) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan1b) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan1) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan2a) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan2b2) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan2b) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan2) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz13rule0) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz13rule1) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz13rule2) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz13rule3) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz13rule4) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz1_1) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz1_2) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz1_3) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz1_4) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz1_5) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1all2) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1SetBreln1) =>
% 98.38/13.33 ((
% 98.38/13.33 (choice2fnsingleton) =>
% 98.38/13.33 ((
% 98.38/13.33 (setOfPairsIsBReln1) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1all1) =>
% 98.38/13.33 ((
% 98.38/13.33 (subbreln1) =>
% 98.38/13.33 ((
% 98.38/13.33 (eqbreln1) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1invprop) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1invI) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1invE) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1compprop) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1compI) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1compE) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1compEex) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionprop) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionIL) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionIR) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionI) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionE) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionEcases) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionCommutes) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz2Ex) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz2W) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz2A) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz2B) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1Ex) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1Ex1) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1Equiv) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1E) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1I) =>
% 98.38/13.33 ((
% 98.38/13.33 (injFuncInInjFuncSet) =>
% 98.38/13.33 ((
% 98.38/13.33 (injFuncSetFuncIn) =>
% 98.38/13.33 ((
% 98.38/13.33 (injFuncSetFuncInj) =>
% 98.38/13.33 ((
% 98.38/13.33 (surjFuncSetFuncIn) =>
% 98.38/13.33 ((
% 98.38/13.33 (surjFuncSetFuncSurj) =>
% 98.38/13.33 ((
% 98.38/13.33 (leftInvIsSurj) =>
% 98.38/13.33 ((
% 98.38/13.33 (surjCantorThm) =>
% 98.38/13.33 ((
% 98.38/13.33 (foundation2) =>
% 98.38/13.33 ((
% 98.38/13.33 (notinself) =>
% 98.38/13.33 ((
% 98.38/13.33 (notinself2) =>
% 98.38/13.33 ((
% 98.38/13.33 (omegaSp) =>
% 98.38/13.33 ((
% 98.38/13.33 (omegaSclos) =>
% 98.38/13.33 ((
% 98.38/13.33 (peano0notS) =>
% 98.38/13.33 ((
% 98.38/13.33 (!!) @ (
% 98.38/13.33 (('#S') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 =>) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#C') @ in @
% 98.38/13.33 omega)))) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 !!) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#S') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 =>) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#C') @ in @
% 98.38/13.33 omega)))))) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#S') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 '#S') @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 =>))) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#C') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 '#B') @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 =) @
% 98.38/13.33 omegaS)))) @
% 98.38/13.33 omegaS)))))) @
% 98.38/13.33 (
% 98.38/13.33 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.38/13.33 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2476])).
% 98.38/13.33 thf(zip_derived_cl2495, plain,
% 98.38/13.33 (~ (((setextT) =>
% 98.38/13.33 (((subsetTI) =>
% 98.38/13.33 (((powersetTI1) =>
% 98.38/13.33 (((powersetTE1) =>
% 98.38/13.33 (((complementTI1) =>
% 98.38/13.33 (((complementTE1) =>
% 98.38/13.33 (((binintersectTELcontra) =>
% 98.38/13.33 (((binintersectTERcontra) =>
% 98.38/13.33 (((contrasubsetT) =>
% 98.38/13.33 (((contrasubsetT1) =>
% 98.38/13.33 (((contrasubsetT2) =>
% 98.38/13.33 (((contrasubsetT3) =>
% 98.38/13.33 (((doubleComplementI1) =>
% 98.38/13.33 (((doubleComplementE1) =>
% 98.38/13.33 (((doubleComplementSub1) =>
% 98.38/13.33 (((doubleComplementSub2) =>
% 98.38/13.33 (((doubleComplementEq) =>
% 98.38/13.33 (((complementTnotintersectT) =>
% 98.38/13.33 (((complementImpComplementIntersect) =>
% 98.38/13.33 (((complementSubsetComplementIntersect) =>
% 98.38/13.33 (((complementInPowersetComplementIntersect) =>
% 98.38/13.33 (((contraSubsetComplement) =>
% 98.38/13.33 (((complementTcontraSubset) =>
% 98.38/13.33 (((binunionTILcontra) =>
% 98.38/13.33 (((binunionTIRcontra) =>
% 98.38/13.33 (((inIntersectImpInUnion) =>
% 98.38/13.33 (((inIntersectImpInUnion2) =>
% 98.38/13.33 (((inIntersectImpInIntersectUnions) =>
% 98.38/13.33 (((intersectInPowersetIntersectUnions) =>
% 98.38/13.33 (((inComplementUnionImpNotIn1) =>
% 98.38/13.33 ((
% 98.38/13.33 (inComplementUnionImpInComplement1) =>
% 98.38/13.33 ((
% 98.38/13.33 (binunionTE) =>
% 98.38/13.33 ((
% 98.38/13.33 (binunionTEcontra) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan2a1) =>
% 98.38/13.33 ((
% 98.38/13.33 (complementUnionInPowersetComplement) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan2a2) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan1a) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan1b) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan1) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan2a) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan2b2) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan2b) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan2) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz13rule0) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz13rule1) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz13rule2) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz13rule3) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz13rule4) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz1_1) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz1_2) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz1_3) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz1_4) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz1_5) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1all2) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1SetBreln1) =>
% 98.38/13.33 ((
% 98.38/13.33 (choice2fnsingleton) =>
% 98.38/13.33 ((
% 98.38/13.33 (setOfPairsIsBReln1) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1all1) =>
% 98.38/13.33 ((
% 98.38/13.33 (subbreln1) =>
% 98.38/13.33 ((
% 98.38/13.33 (eqbreln1) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1invprop) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1invI) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1invE) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1compprop) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1compI) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1compE) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1compEex) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionprop) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionIL) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionIR) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionI) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionE) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionEcases) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionCommutes) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz2Ex) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz2W) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz2A) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz2B) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1Ex) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1Ex1) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1Equiv) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1E) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1I) =>
% 98.38/13.33 ((
% 98.38/13.33 (injFuncInInjFuncSet) =>
% 98.38/13.33 ((
% 98.38/13.33 (injFuncSetFuncIn) =>
% 98.38/13.33 ((
% 98.38/13.33 (injFuncSetFuncInj) =>
% 98.38/13.33 ((
% 98.38/13.33 (surjFuncSetFuncIn) =>
% 98.38/13.33 ((
% 98.38/13.33 (surjFuncSetFuncSurj) =>
% 98.38/13.33 ((
% 98.38/13.33 (leftInvIsSurj) =>
% 98.38/13.33 ((
% 98.38/13.33 (surjCantorThm) =>
% 98.38/13.33 ((
% 98.38/13.33 (foundation2) =>
% 98.38/13.33 ((
% 98.38/13.33 (notinself) =>
% 98.38/13.33 ((
% 98.38/13.33 (notinself2) =>
% 98.38/13.33 ((
% 98.38/13.33 (omegaSp) =>
% 98.38/13.33 ((
% 98.38/13.33 (omegaSclos) =>
% 98.38/13.33 ((
% 98.38/13.33 (peano0notS) =>
% 98.38/13.33 ((
% 98.38/13.33 (!!) @ (
% 98.38/13.33 (('#S') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 =>) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#C') @ in @
% 98.38/13.33 omega)))) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 !!) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#S') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 =>) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#C') @ in @
% 98.38/13.33 omega)))))) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#S') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 '#S') @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 =>))) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#C') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 '#B') @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 =) @
% 98.38/13.33 omegaS)))) @
% 98.38/13.33 omegaS)))))) @
% 98.38/13.33 (
% 98.38/13.33 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.38/13.33 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2485])).
% 98.38/13.33 thf(zip_derived_cl2506, plain,
% 98.38/13.33 (~ (((subsetTI) =>
% 98.38/13.33 (((powersetTI1) =>
% 98.38/13.33 (((powersetTE1) =>
% 98.38/13.33 (((complementTI1) =>
% 98.38/13.33 (((complementTE1) =>
% 98.38/13.33 (((binintersectTELcontra) =>
% 98.38/13.33 (((binintersectTERcontra) =>
% 98.38/13.33 (((contrasubsetT) =>
% 98.38/13.33 (((contrasubsetT1) =>
% 98.38/13.33 (((contrasubsetT2) =>
% 98.38/13.33 (((contrasubsetT3) =>
% 98.38/13.33 (((doubleComplementI1) =>
% 98.38/13.33 (((doubleComplementE1) =>
% 98.38/13.33 (((doubleComplementSub1) =>
% 98.38/13.33 (((doubleComplementSub2) =>
% 98.38/13.33 (((doubleComplementEq) =>
% 98.38/13.33 (((complementTnotintersectT) =>
% 98.38/13.33 (((complementImpComplementIntersect) =>
% 98.38/13.33 (((complementSubsetComplementIntersect) =>
% 98.38/13.33 (((complementInPowersetComplementIntersect) =>
% 98.38/13.33 (((contraSubsetComplement) =>
% 98.38/13.33 (((complementTcontraSubset) =>
% 98.38/13.33 (((binunionTILcontra) =>
% 98.38/13.33 (((binunionTIRcontra) =>
% 98.38/13.33 (((inIntersectImpInUnion) =>
% 98.38/13.33 (((inIntersectImpInUnion2) =>
% 98.38/13.33 (((inIntersectImpInIntersectUnions) =>
% 98.38/13.33 (((intersectInPowersetIntersectUnions) =>
% 98.38/13.33 (((inComplementUnionImpNotIn1) =>
% 98.38/13.33 (((inComplementUnionImpInComplement1) =>
% 98.38/13.33 ((
% 98.38/13.33 (binunionTE) =>
% 98.38/13.33 ((
% 98.38/13.33 (binunionTEcontra) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan2a1) =>
% 98.38/13.33 ((
% 98.38/13.33 (complementUnionInPowersetComplement) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan2a2) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan1a) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan1b) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan1) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan2a) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan2b2) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan2b) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan2) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz13rule0) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz13rule1) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz13rule2) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz13rule3) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz13rule4) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz1_1) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz1_2) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz1_3) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz1_4) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz1_5) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1all2) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1SetBreln1) =>
% 98.38/13.33 ((
% 98.38/13.33 (choice2fnsingleton) =>
% 98.38/13.33 ((
% 98.38/13.33 (setOfPairsIsBReln1) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1all1) =>
% 98.38/13.33 ((
% 98.38/13.33 (subbreln1) =>
% 98.38/13.33 ((
% 98.38/13.33 (eqbreln1) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1invprop) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1invI) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1invE) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1compprop) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1compI) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1compE) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1compEex) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionprop) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionIL) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionIR) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionI) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionE) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionEcases) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionCommutes) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz2Ex) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz2W) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz2A) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz2B) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1Ex) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1Ex1) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1Equiv) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1E) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1I) =>
% 98.38/13.33 ((
% 98.38/13.33 (injFuncInInjFuncSet) =>
% 98.38/13.33 ((
% 98.38/13.33 (injFuncSetFuncIn) =>
% 98.38/13.33 ((
% 98.38/13.33 (injFuncSetFuncInj) =>
% 98.38/13.33 ((
% 98.38/13.33 (surjFuncSetFuncIn) =>
% 98.38/13.33 ((
% 98.38/13.33 (surjFuncSetFuncSurj) =>
% 98.38/13.33 ((
% 98.38/13.33 (leftInvIsSurj) =>
% 98.38/13.33 ((
% 98.38/13.33 (surjCantorThm) =>
% 98.38/13.33 ((
% 98.38/13.33 (foundation2) =>
% 98.38/13.33 ((
% 98.38/13.33 (notinself) =>
% 98.38/13.33 ((
% 98.38/13.33 (notinself2) =>
% 98.38/13.33 ((
% 98.38/13.33 (omegaSp) =>
% 98.38/13.33 ((
% 98.38/13.33 (omegaSclos) =>
% 98.38/13.33 ((
% 98.38/13.33 (peano0notS) =>
% 98.38/13.33 ((
% 98.38/13.33 (!!) @ (
% 98.38/13.33 (('#S') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 =>) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#C') @ in @
% 98.38/13.33 omega)))) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 !!) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#S') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 =>) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#C') @ in @
% 98.38/13.33 omega)))))) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#S') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 '#S') @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 =>))) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#C') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 '#B') @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 =) @
% 98.38/13.33 omegaS)))) @
% 98.38/13.33 omegaS)))))) @
% 98.38/13.33 (
% 98.38/13.33 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.38/13.33 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2495])).
% 98.38/13.33 thf(zip_derived_cl2518, plain,
% 98.38/13.33 (~ (((powersetTI1) =>
% 98.38/13.33 (((powersetTE1) =>
% 98.38/13.33 (((complementTI1) =>
% 98.38/13.33 (((complementTE1) =>
% 98.38/13.33 (((binintersectTELcontra) =>
% 98.38/13.33 (((binintersectTERcontra) =>
% 98.38/13.33 (((contrasubsetT) =>
% 98.38/13.33 (((contrasubsetT1) =>
% 98.38/13.33 (((contrasubsetT2) =>
% 98.38/13.33 (((contrasubsetT3) =>
% 98.38/13.33 (((doubleComplementI1) =>
% 98.38/13.33 (((doubleComplementE1) =>
% 98.38/13.33 (((doubleComplementSub1) =>
% 98.38/13.33 (((doubleComplementSub2) =>
% 98.38/13.33 (((doubleComplementEq) =>
% 98.38/13.33 (((complementTnotintersectT) =>
% 98.38/13.33 (((complementImpComplementIntersect) =>
% 98.38/13.33 (((complementSubsetComplementIntersect) =>
% 98.38/13.33 (((complementInPowersetComplementIntersect) =>
% 98.38/13.33 (((contraSubsetComplement) =>
% 98.38/13.33 (((complementTcontraSubset) =>
% 98.38/13.33 (((binunionTILcontra) =>
% 98.38/13.33 (((binunionTIRcontra) =>
% 98.38/13.33 (((inIntersectImpInUnion) =>
% 98.38/13.33 (((inIntersectImpInUnion2) =>
% 98.38/13.33 (((inIntersectImpInIntersectUnions) =>
% 98.38/13.33 (((intersectInPowersetIntersectUnions) =>
% 98.38/13.33 (((inComplementUnionImpNotIn1) =>
% 98.38/13.33 (((inComplementUnionImpInComplement1) =>
% 98.38/13.33 (((binunionTE) =>
% 98.38/13.33 ((
% 98.38/13.33 (binunionTEcontra) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan2a1) =>
% 98.38/13.33 ((
% 98.38/13.33 (complementUnionInPowersetComplement) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan2a2) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan1a) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan1b) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan1) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan2a) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan2b2) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan2b) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan2) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz13rule0) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz13rule1) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz13rule2) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz13rule3) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz13rule4) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz1_1) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz1_2) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz1_3) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz1_4) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz1_5) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1all2) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1SetBreln1) =>
% 98.38/13.33 ((
% 98.38/13.33 (choice2fnsingleton) =>
% 98.38/13.33 ((
% 98.38/13.33 (setOfPairsIsBReln1) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1all1) =>
% 98.38/13.33 ((
% 98.38/13.33 (subbreln1) =>
% 98.38/13.33 ((
% 98.38/13.33 (eqbreln1) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1invprop) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1invI) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1invE) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1compprop) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1compI) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1compE) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1compEex) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionprop) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionIL) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionIR) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionI) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionE) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionEcases) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionCommutes) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz2Ex) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz2W) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz2A) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz2B) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1Ex) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1Ex1) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1Equiv) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1E) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1I) =>
% 98.38/13.33 ((
% 98.38/13.33 (injFuncInInjFuncSet) =>
% 98.38/13.33 ((
% 98.38/13.33 (injFuncSetFuncIn) =>
% 98.38/13.33 ((
% 98.38/13.33 (injFuncSetFuncInj) =>
% 98.38/13.33 ((
% 98.38/13.33 (surjFuncSetFuncIn) =>
% 98.38/13.33 ((
% 98.38/13.33 (surjFuncSetFuncSurj) =>
% 98.38/13.33 ((
% 98.38/13.33 (leftInvIsSurj) =>
% 98.38/13.33 ((
% 98.38/13.33 (surjCantorThm) =>
% 98.38/13.33 ((
% 98.38/13.33 (foundation2) =>
% 98.38/13.33 ((
% 98.38/13.33 (notinself) =>
% 98.38/13.33 ((
% 98.38/13.33 (notinself2) =>
% 98.38/13.33 ((
% 98.38/13.33 (omegaSp) =>
% 98.38/13.33 ((
% 98.38/13.33 (omegaSclos) =>
% 98.38/13.33 ((
% 98.38/13.33 (peano0notS) =>
% 98.38/13.33 ((
% 98.38/13.33 (!!) @ (
% 98.38/13.33 (('#S') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 =>) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#C') @ in @
% 98.38/13.33 omega)))) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 !!) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#S') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 =>) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#C') @ in @
% 98.38/13.33 omega)))))) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#S') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 '#S') @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 =>))) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#C') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 '#B') @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 =) @
% 98.38/13.33 omegaS)))) @
% 98.38/13.33 omegaS)))))) @
% 98.38/13.33 (
% 98.38/13.33 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.38/13.33 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2506])).
% 98.38/13.33 thf(zip_derived_cl2527, plain,
% 98.38/13.33 (~ (((powersetTE1) =>
% 98.38/13.33 (((complementTI1) =>
% 98.38/13.33 (((complementTE1) =>
% 98.38/13.33 (((binintersectTELcontra) =>
% 98.38/13.33 (((binintersectTERcontra) =>
% 98.38/13.33 (((contrasubsetT) =>
% 98.38/13.33 (((contrasubsetT1) =>
% 98.38/13.33 (((contrasubsetT2) =>
% 98.38/13.33 (((contrasubsetT3) =>
% 98.38/13.33 (((doubleComplementI1) =>
% 98.38/13.33 (((doubleComplementE1) =>
% 98.38/13.33 (((doubleComplementSub1) =>
% 98.38/13.33 (((doubleComplementSub2) =>
% 98.38/13.33 (((doubleComplementEq) =>
% 98.38/13.33 (((complementTnotintersectT) =>
% 98.38/13.33 (((complementImpComplementIntersect) =>
% 98.38/13.33 (((complementSubsetComplementIntersect) =>
% 98.38/13.33 (((complementInPowersetComplementIntersect) =>
% 98.38/13.33 (((contraSubsetComplement) =>
% 98.38/13.33 (((complementTcontraSubset) =>
% 98.38/13.33 (((binunionTILcontra) =>
% 98.38/13.33 (((binunionTIRcontra) =>
% 98.38/13.33 (((inIntersectImpInUnion) =>
% 98.38/13.33 (((inIntersectImpInUnion2) =>
% 98.38/13.33 (((inIntersectImpInIntersectUnions) =>
% 98.38/13.33 (((intersectInPowersetIntersectUnions) =>
% 98.38/13.33 (((inComplementUnionImpNotIn1) =>
% 98.38/13.33 (((inComplementUnionImpInComplement1) =>
% 98.38/13.33 (((binunionTE) =>
% 98.38/13.33 (((binunionTEcontra) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan2a1) =>
% 98.38/13.33 ((
% 98.38/13.33 (complementUnionInPowersetComplement) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan2a2) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan1a) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan1b) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan1) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan2a) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan2b2) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan2b) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan2) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz13rule0) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz13rule1) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz13rule2) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz13rule3) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz13rule4) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz1_1) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz1_2) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz1_3) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz1_4) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz1_5) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1all2) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1SetBreln1) =>
% 98.38/13.33 ((
% 98.38/13.33 (choice2fnsingleton) =>
% 98.38/13.33 ((
% 98.38/13.33 (setOfPairsIsBReln1) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1all1) =>
% 98.38/13.33 ((
% 98.38/13.33 (subbreln1) =>
% 98.38/13.33 ((
% 98.38/13.33 (eqbreln1) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1invprop) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1invI) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1invE) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1compprop) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1compI) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1compE) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1compEex) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionprop) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionIL) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionIR) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionI) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionE) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionEcases) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionCommutes) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz2Ex) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz2W) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz2A) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz2B) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1Ex) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1Ex1) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1Equiv) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1E) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1I) =>
% 98.38/13.33 ((
% 98.38/13.33 (injFuncInInjFuncSet) =>
% 98.38/13.33 ((
% 98.38/13.33 (injFuncSetFuncIn) =>
% 98.38/13.33 ((
% 98.38/13.33 (injFuncSetFuncInj) =>
% 98.38/13.33 ((
% 98.38/13.33 (surjFuncSetFuncIn) =>
% 98.38/13.33 ((
% 98.38/13.33 (surjFuncSetFuncSurj) =>
% 98.38/13.33 ((
% 98.38/13.33 (leftInvIsSurj) =>
% 98.38/13.33 ((
% 98.38/13.33 (surjCantorThm) =>
% 98.38/13.33 ((
% 98.38/13.33 (foundation2) =>
% 98.38/13.33 ((
% 98.38/13.33 (notinself) =>
% 98.38/13.33 ((
% 98.38/13.33 (notinself2) =>
% 98.38/13.33 ((
% 98.38/13.33 (omegaSp) =>
% 98.38/13.33 ((
% 98.38/13.33 (omegaSclos) =>
% 98.38/13.33 ((
% 98.38/13.33 (peano0notS) =>
% 98.38/13.33 ((
% 98.38/13.33 (!!) @ (
% 98.38/13.33 (('#S') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 =>) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#C') @ in @
% 98.38/13.33 omega)))) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 !!) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#S') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 =>) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#C') @ in @
% 98.38/13.33 omega)))))) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#S') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 '#S') @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 =>))) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#C') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 '#B') @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 =) @
% 98.38/13.33 omegaS)))) @
% 98.38/13.33 omegaS)))))) @
% 98.38/13.33 (
% 98.38/13.33 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.38/13.33 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2518])).
% 98.38/13.33 thf(zip_derived_cl2535, plain,
% 98.38/13.33 (~ (((complementTI1) =>
% 98.38/13.33 (((complementTE1) =>
% 98.38/13.33 (((binintersectTELcontra) =>
% 98.38/13.33 (((binintersectTERcontra) =>
% 98.38/13.33 (((contrasubsetT) =>
% 98.38/13.33 (((contrasubsetT1) =>
% 98.38/13.33 (((contrasubsetT2) =>
% 98.38/13.33 (((contrasubsetT3) =>
% 98.38/13.33 (((doubleComplementI1) =>
% 98.38/13.33 (((doubleComplementE1) =>
% 98.38/13.33 (((doubleComplementSub1) =>
% 98.38/13.33 (((doubleComplementSub2) =>
% 98.38/13.33 (((doubleComplementEq) =>
% 98.38/13.33 (((complementTnotintersectT) =>
% 98.38/13.33 (((complementImpComplementIntersect) =>
% 98.38/13.33 (((complementSubsetComplementIntersect) =>
% 98.38/13.33 (((complementInPowersetComplementIntersect) =>
% 98.38/13.33 (((contraSubsetComplement) =>
% 98.38/13.33 (((complementTcontraSubset) =>
% 98.38/13.33 (((binunionTILcontra) =>
% 98.38/13.33 (((binunionTIRcontra) =>
% 98.38/13.33 (((inIntersectImpInUnion) =>
% 98.38/13.33 (((inIntersectImpInUnion2) =>
% 98.38/13.33 (((inIntersectImpInIntersectUnions) =>
% 98.38/13.33 (((intersectInPowersetIntersectUnions) =>
% 98.38/13.33 (((inComplementUnionImpNotIn1) =>
% 98.38/13.33 (((inComplementUnionImpInComplement1) =>
% 98.38/13.33 (((binunionTE) =>
% 98.38/13.33 (((binunionTEcontra) =>
% 98.38/13.33 (((demorgan2a1) =>
% 98.38/13.33 ((
% 98.38/13.33 (complementUnionInPowersetComplement) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan2a2) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan1a) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan1b) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan1) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan2a) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan2b2) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan2b) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan2) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz13rule0) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz13rule1) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz13rule2) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz13rule3) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz13rule4) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz1_1) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz1_2) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz1_3) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz1_4) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz1_5) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1all2) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1SetBreln1) =>
% 98.38/13.33 ((
% 98.38/13.33 (choice2fnsingleton) =>
% 98.38/13.33 ((
% 98.38/13.33 (setOfPairsIsBReln1) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1all1) =>
% 98.38/13.33 ((
% 98.38/13.33 (subbreln1) =>
% 98.38/13.33 ((
% 98.38/13.33 (eqbreln1) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1invprop) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1invI) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1invE) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1compprop) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1compI) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1compE) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1compEex) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionprop) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionIL) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionIR) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionI) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionE) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionEcases) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionCommutes) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz2Ex) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz2W) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz2A) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz2B) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1Ex) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1Ex1) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1Equiv) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1E) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1I) =>
% 98.38/13.33 ((
% 98.38/13.33 (injFuncInInjFuncSet) =>
% 98.38/13.33 ((
% 98.38/13.33 (injFuncSetFuncIn) =>
% 98.38/13.33 ((
% 98.38/13.33 (injFuncSetFuncInj) =>
% 98.38/13.33 ((
% 98.38/13.33 (surjFuncSetFuncIn) =>
% 98.38/13.33 ((
% 98.38/13.33 (surjFuncSetFuncSurj) =>
% 98.38/13.33 ((
% 98.38/13.33 (leftInvIsSurj) =>
% 98.38/13.33 ((
% 98.38/13.33 (surjCantorThm) =>
% 98.38/13.33 ((
% 98.38/13.33 (foundation2) =>
% 98.38/13.33 ((
% 98.38/13.33 (notinself) =>
% 98.38/13.33 ((
% 98.38/13.33 (notinself2) =>
% 98.38/13.33 ((
% 98.38/13.33 (omegaSp) =>
% 98.38/13.33 ((
% 98.38/13.33 (omegaSclos) =>
% 98.38/13.33 ((
% 98.38/13.33 (peano0notS) =>
% 98.38/13.33 ((
% 98.38/13.33 (!!) @ (
% 98.38/13.33 (('#S') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 =>) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#C') @ in @
% 98.38/13.33 omega)))) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 !!) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#S') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 =>) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#C') @ in @
% 98.38/13.33 omega)))))) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#S') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 '#S') @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 =>))) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#C') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 '#B') @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 =) @
% 98.38/13.33 omegaS)))) @
% 98.38/13.33 omegaS)))))) @
% 98.38/13.33 (
% 98.38/13.33 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.38/13.33 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2527])).
% 98.38/13.33 thf(zip_derived_cl2543, plain,
% 98.38/13.33 (~ (((complementTE1) =>
% 98.38/13.33 (((binintersectTELcontra) =>
% 98.38/13.33 (((binintersectTERcontra) =>
% 98.38/13.33 (((contrasubsetT) =>
% 98.38/13.33 (((contrasubsetT1) =>
% 98.38/13.33 (((contrasubsetT2) =>
% 98.38/13.33 (((contrasubsetT3) =>
% 98.38/13.33 (((doubleComplementI1) =>
% 98.38/13.33 (((doubleComplementE1) =>
% 98.38/13.33 (((doubleComplementSub1) =>
% 98.38/13.33 (((doubleComplementSub2) =>
% 98.38/13.33 (((doubleComplementEq) =>
% 98.38/13.33 (((complementTnotintersectT) =>
% 98.38/13.33 (((complementImpComplementIntersect) =>
% 98.38/13.33 (((complementSubsetComplementIntersect) =>
% 98.38/13.33 (((complementInPowersetComplementIntersect) =>
% 98.38/13.33 (((contraSubsetComplement) =>
% 98.38/13.33 (((complementTcontraSubset) =>
% 98.38/13.33 (((binunionTILcontra) =>
% 98.38/13.33 (((binunionTIRcontra) =>
% 98.38/13.33 (((inIntersectImpInUnion) =>
% 98.38/13.33 (((inIntersectImpInUnion2) =>
% 98.38/13.33 (((inIntersectImpInIntersectUnions) =>
% 98.38/13.33 (((intersectInPowersetIntersectUnions) =>
% 98.38/13.33 (((inComplementUnionImpNotIn1) =>
% 98.38/13.33 (((inComplementUnionImpInComplement1) =>
% 98.38/13.33 (((binunionTE) =>
% 98.38/13.33 (((binunionTEcontra) =>
% 98.38/13.33 (((demorgan2a1) =>
% 98.38/13.33 (((complementUnionInPowersetComplement) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan2a2) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan1a) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan1b) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan1) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan2a) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan2b2) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan2b) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan2) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz13rule0) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz13rule1) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz13rule2) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz13rule3) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz13rule4) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz1_1) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz1_2) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz1_3) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz1_4) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz1_5) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1all2) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1SetBreln1) =>
% 98.38/13.33 ((
% 98.38/13.33 (choice2fnsingleton) =>
% 98.38/13.33 ((
% 98.38/13.33 (setOfPairsIsBReln1) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1all1) =>
% 98.38/13.33 ((
% 98.38/13.33 (subbreln1) =>
% 98.38/13.33 ((
% 98.38/13.33 (eqbreln1) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1invprop) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1invI) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1invE) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1compprop) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1compI) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1compE) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1compEex) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionprop) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionIL) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionIR) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionI) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionE) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionEcases) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionCommutes) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz2Ex) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz2W) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz2A) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz2B) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1Ex) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1Ex1) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1Equiv) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1E) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1I) =>
% 98.38/13.33 ((
% 98.38/13.33 (injFuncInInjFuncSet) =>
% 98.38/13.33 ((
% 98.38/13.33 (injFuncSetFuncIn) =>
% 98.38/13.33 ((
% 98.38/13.33 (injFuncSetFuncInj) =>
% 98.38/13.33 ((
% 98.38/13.33 (surjFuncSetFuncIn) =>
% 98.38/13.33 ((
% 98.38/13.33 (surjFuncSetFuncSurj) =>
% 98.38/13.33 ((
% 98.38/13.33 (leftInvIsSurj) =>
% 98.38/13.33 ((
% 98.38/13.33 (surjCantorThm) =>
% 98.38/13.33 ((
% 98.38/13.33 (foundation2) =>
% 98.38/13.33 ((
% 98.38/13.33 (notinself) =>
% 98.38/13.33 ((
% 98.38/13.33 (notinself2) =>
% 98.38/13.33 ((
% 98.38/13.33 (omegaSp) =>
% 98.38/13.33 ((
% 98.38/13.33 (omegaSclos) =>
% 98.38/13.33 ((
% 98.38/13.33 (peano0notS) =>
% 98.38/13.33 ((
% 98.38/13.33 (!!) @ (
% 98.38/13.33 (('#S') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 =>) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#C') @ in @
% 98.38/13.33 omega)))) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 !!) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#S') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 =>) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#C') @ in @
% 98.38/13.33 omega)))))) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#S') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 '#S') @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 =>))) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#C') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 '#B') @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 =) @
% 98.38/13.33 omegaS)))) @
% 98.38/13.33 omegaS)))))) @
% 98.38/13.33 (
% 98.38/13.33 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.38/13.33 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2535])).
% 98.38/13.33 thf(zip_derived_cl2551, plain,
% 98.38/13.33 (~ (((binintersectTELcontra) =>
% 98.38/13.33 (((binintersectTERcontra) =>
% 98.38/13.33 (((contrasubsetT) =>
% 98.38/13.33 (((contrasubsetT1) =>
% 98.38/13.33 (((contrasubsetT2) =>
% 98.38/13.33 (((contrasubsetT3) =>
% 98.38/13.33 (((doubleComplementI1) =>
% 98.38/13.33 (((doubleComplementE1) =>
% 98.38/13.33 (((doubleComplementSub1) =>
% 98.38/13.33 (((doubleComplementSub2) =>
% 98.38/13.33 (((doubleComplementEq) =>
% 98.38/13.33 (((complementTnotintersectT) =>
% 98.38/13.33 (((complementImpComplementIntersect) =>
% 98.38/13.33 (((complementSubsetComplementIntersect) =>
% 98.38/13.33 (((complementInPowersetComplementIntersect) =>
% 98.38/13.33 (((contraSubsetComplement) =>
% 98.38/13.33 (((complementTcontraSubset) =>
% 98.38/13.33 (((binunionTILcontra) =>
% 98.38/13.33 (((binunionTIRcontra) =>
% 98.38/13.33 (((inIntersectImpInUnion) =>
% 98.38/13.33 (((inIntersectImpInUnion2) =>
% 98.38/13.33 (((inIntersectImpInIntersectUnions) =>
% 98.38/13.33 (((intersectInPowersetIntersectUnions) =>
% 98.38/13.33 (((inComplementUnionImpNotIn1) =>
% 98.38/13.33 (((inComplementUnionImpInComplement1) =>
% 98.38/13.33 (((binunionTE) =>
% 98.38/13.33 (((binunionTEcontra) =>
% 98.38/13.33 (((demorgan2a1) =>
% 98.38/13.33 (((complementUnionInPowersetComplement) =>
% 98.38/13.33 (((demorgan2a2) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan1a) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan1b) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan1) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan2a) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan2b2) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan2b) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan2) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz13rule0) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz13rule1) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz13rule2) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz13rule3) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz13rule4) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz1_1) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz1_2) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz1_3) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz1_4) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz1_5) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1all2) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1SetBreln1) =>
% 98.38/13.33 ((
% 98.38/13.33 (choice2fnsingleton) =>
% 98.38/13.33 ((
% 98.38/13.33 (setOfPairsIsBReln1) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1all1) =>
% 98.38/13.33 ((
% 98.38/13.33 (subbreln1) =>
% 98.38/13.33 ((
% 98.38/13.33 (eqbreln1) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1invprop) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1invI) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1invE) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1compprop) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1compI) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1compE) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1compEex) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionprop) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionIL) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionIR) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionI) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionE) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionEcases) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionCommutes) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz2Ex) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz2W) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz2A) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz2B) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1Ex) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1Ex1) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1Equiv) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1E) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1I) =>
% 98.38/13.33 ((
% 98.38/13.33 (injFuncInInjFuncSet) =>
% 98.38/13.33 ((
% 98.38/13.33 (injFuncSetFuncIn) =>
% 98.38/13.33 ((
% 98.38/13.33 (injFuncSetFuncInj) =>
% 98.38/13.33 ((
% 98.38/13.33 (surjFuncSetFuncIn) =>
% 98.38/13.33 ((
% 98.38/13.33 (surjFuncSetFuncSurj) =>
% 98.38/13.33 ((
% 98.38/13.33 (leftInvIsSurj) =>
% 98.38/13.33 ((
% 98.38/13.33 (surjCantorThm) =>
% 98.38/13.33 ((
% 98.38/13.33 (foundation2) =>
% 98.38/13.33 ((
% 98.38/13.33 (notinself) =>
% 98.38/13.33 ((
% 98.38/13.33 (notinself2) =>
% 98.38/13.33 ((
% 98.38/13.33 (omegaSp) =>
% 98.38/13.33 ((
% 98.38/13.33 (omegaSclos) =>
% 98.38/13.33 ((
% 98.38/13.33 (peano0notS) =>
% 98.38/13.33 ((
% 98.38/13.33 (!!) @ (
% 98.38/13.33 (('#S') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 =>) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#C') @ in @
% 98.38/13.33 omega)))) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 !!) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#S') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 =>) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#C') @ in @
% 98.38/13.33 omega)))))) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#S') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 '#S') @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 =>))) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#C') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 '#B') @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 =) @
% 98.38/13.33 omegaS)))) @
% 98.38/13.33 omegaS)))))) @
% 98.38/13.33 (
% 98.38/13.33 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.38/13.33 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2543])).
% 98.38/13.33 thf(zip_derived_cl2560, plain,
% 98.38/13.33 (~ (((binintersectTERcontra) =>
% 98.38/13.33 (((contrasubsetT) =>
% 98.38/13.33 (((contrasubsetT1) =>
% 98.38/13.33 (((contrasubsetT2) =>
% 98.38/13.33 (((contrasubsetT3) =>
% 98.38/13.33 (((doubleComplementI1) =>
% 98.38/13.33 (((doubleComplementE1) =>
% 98.38/13.33 (((doubleComplementSub1) =>
% 98.38/13.33 (((doubleComplementSub2) =>
% 98.38/13.33 (((doubleComplementEq) =>
% 98.38/13.33 (((complementTnotintersectT) =>
% 98.38/13.33 (((complementImpComplementIntersect) =>
% 98.38/13.33 (((complementSubsetComplementIntersect) =>
% 98.38/13.33 (((complementInPowersetComplementIntersect) =>
% 98.38/13.33 (((contraSubsetComplement) =>
% 98.38/13.33 (((complementTcontraSubset) =>
% 98.38/13.33 (((binunionTILcontra) =>
% 98.38/13.33 (((binunionTIRcontra) =>
% 98.38/13.33 (((inIntersectImpInUnion) =>
% 98.38/13.33 (((inIntersectImpInUnion2) =>
% 98.38/13.33 (((inIntersectImpInIntersectUnions) =>
% 98.38/13.33 (((intersectInPowersetIntersectUnions) =>
% 98.38/13.33 (((inComplementUnionImpNotIn1) =>
% 98.38/13.33 (((inComplementUnionImpInComplement1) =>
% 98.38/13.33 (((binunionTE) =>
% 98.38/13.33 (((binunionTEcontra) =>
% 98.38/13.33 (((demorgan2a1) =>
% 98.38/13.33 (((complementUnionInPowersetComplement) =>
% 98.38/13.33 (((demorgan2a2) =>
% 98.38/13.33 (((demorgan1a) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan1b) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan1) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan2a) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan2b2) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan2b) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan2) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz13rule0) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz13rule1) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz13rule2) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz13rule3) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz13rule4) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz1_1) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz1_2) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz1_3) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz1_4) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz1_5) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1all2) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1SetBreln1) =>
% 98.38/13.33 ((
% 98.38/13.33 (choice2fnsingleton) =>
% 98.38/13.33 ((
% 98.38/13.33 (setOfPairsIsBReln1) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1all1) =>
% 98.38/13.33 ((
% 98.38/13.33 (subbreln1) =>
% 98.38/13.33 ((
% 98.38/13.33 (eqbreln1) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1invprop) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1invI) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1invE) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1compprop) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1compI) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1compE) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1compEex) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionprop) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionIL) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionIR) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionI) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionE) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionEcases) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionCommutes) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz2Ex) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz2W) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz2A) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz2B) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1Ex) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1Ex1) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1Equiv) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1E) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1I) =>
% 98.38/13.33 ((
% 98.38/13.33 (injFuncInInjFuncSet) =>
% 98.38/13.33 ((
% 98.38/13.33 (injFuncSetFuncIn) =>
% 98.38/13.33 ((
% 98.38/13.33 (injFuncSetFuncInj) =>
% 98.38/13.33 ((
% 98.38/13.33 (surjFuncSetFuncIn) =>
% 98.38/13.33 ((
% 98.38/13.33 (surjFuncSetFuncSurj) =>
% 98.38/13.33 ((
% 98.38/13.33 (leftInvIsSurj) =>
% 98.38/13.33 ((
% 98.38/13.33 (surjCantorThm) =>
% 98.38/13.33 ((
% 98.38/13.33 (foundation2) =>
% 98.38/13.33 ((
% 98.38/13.33 (notinself) =>
% 98.38/13.33 ((
% 98.38/13.33 (notinself2) =>
% 98.38/13.33 ((
% 98.38/13.33 (omegaSp) =>
% 98.38/13.33 ((
% 98.38/13.33 (omegaSclos) =>
% 98.38/13.33 ((
% 98.38/13.33 (peano0notS) =>
% 98.38/13.33 ((
% 98.38/13.33 (!!) @ (
% 98.38/13.33 (('#S') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 =>) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#C') @ in @
% 98.38/13.33 omega)))) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 !!) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#S') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 =>) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#C') @ in @
% 98.38/13.33 omega)))))) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#S') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 '#S') @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 =>))) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#C') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 '#B') @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 =) @
% 98.38/13.33 omegaS)))) @
% 98.38/13.33 omegaS)))))) @
% 98.38/13.33 (
% 98.38/13.33 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.38/13.33 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2551])).
% 98.38/13.33 thf(zip_derived_cl2570, plain,
% 98.38/13.33 (~ (((contrasubsetT) =>
% 98.38/13.33 (((contrasubsetT1) =>
% 98.38/13.33 (((contrasubsetT2) =>
% 98.38/13.33 (((contrasubsetT3) =>
% 98.38/13.33 (((doubleComplementI1) =>
% 98.38/13.33 (((doubleComplementE1) =>
% 98.38/13.33 (((doubleComplementSub1) =>
% 98.38/13.33 (((doubleComplementSub2) =>
% 98.38/13.33 (((doubleComplementEq) =>
% 98.38/13.33 (((complementTnotintersectT) =>
% 98.38/13.33 (((complementImpComplementIntersect) =>
% 98.38/13.33 (((complementSubsetComplementIntersect) =>
% 98.38/13.33 (((complementInPowersetComplementIntersect) =>
% 98.38/13.33 (((contraSubsetComplement) =>
% 98.38/13.33 (((complementTcontraSubset) =>
% 98.38/13.33 (((binunionTILcontra) =>
% 98.38/13.33 (((binunionTIRcontra) =>
% 98.38/13.33 (((inIntersectImpInUnion) =>
% 98.38/13.33 (((inIntersectImpInUnion2) =>
% 98.38/13.33 (((inIntersectImpInIntersectUnions) =>
% 98.38/13.33 (((intersectInPowersetIntersectUnions) =>
% 98.38/13.33 (((inComplementUnionImpNotIn1) =>
% 98.38/13.33 (((inComplementUnionImpInComplement1) =>
% 98.38/13.33 (((binunionTE) =>
% 98.38/13.33 (((binunionTEcontra) =>
% 98.38/13.33 (((demorgan2a1) =>
% 98.38/13.33 (((complementUnionInPowersetComplement) =>
% 98.38/13.33 (((demorgan2a2) =>
% 98.38/13.33 (((demorgan1a) =>
% 98.38/13.33 (((demorgan1b) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan1) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan2a) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan2b2) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan2b) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan2) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz13rule0) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz13rule1) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz13rule2) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz13rule3) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz13rule4) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz1_1) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz1_2) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz1_3) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz1_4) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz1_5) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1all2) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1SetBreln1) =>
% 98.38/13.33 ((
% 98.38/13.33 (choice2fnsingleton) =>
% 98.38/13.33 ((
% 98.38/13.33 (setOfPairsIsBReln1) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1all1) =>
% 98.38/13.33 ((
% 98.38/13.33 (subbreln1) =>
% 98.38/13.33 ((
% 98.38/13.33 (eqbreln1) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1invprop) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1invI) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1invE) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1compprop) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1compI) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1compE) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1compEex) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionprop) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionIL) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionIR) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionI) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionE) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionEcases) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionCommutes) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz2Ex) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz2W) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz2A) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz2B) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1Ex) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1Ex1) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1Equiv) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1E) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1I) =>
% 98.38/13.33 ((
% 98.38/13.33 (injFuncInInjFuncSet) =>
% 98.38/13.33 ((
% 98.38/13.33 (injFuncSetFuncIn) =>
% 98.38/13.33 ((
% 98.38/13.33 (injFuncSetFuncInj) =>
% 98.38/13.33 ((
% 98.38/13.33 (surjFuncSetFuncIn) =>
% 98.38/13.33 ((
% 98.38/13.33 (surjFuncSetFuncSurj) =>
% 98.38/13.33 ((
% 98.38/13.33 (leftInvIsSurj) =>
% 98.38/13.33 ((
% 98.38/13.33 (surjCantorThm) =>
% 98.38/13.33 ((
% 98.38/13.33 (foundation2) =>
% 98.38/13.33 ((
% 98.38/13.33 (notinself) =>
% 98.38/13.33 ((
% 98.38/13.33 (notinself2) =>
% 98.38/13.33 ((
% 98.38/13.33 (omegaSp) =>
% 98.38/13.33 ((
% 98.38/13.33 (omegaSclos) =>
% 98.38/13.33 ((
% 98.38/13.33 (peano0notS) =>
% 98.38/13.33 ((
% 98.38/13.33 (!!) @ (
% 98.38/13.33 (('#S') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 =>) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#C') @ in @
% 98.38/13.33 omega)))) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 !!) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#S') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 =>) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#C') @ in @
% 98.38/13.33 omega)))))) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#S') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 '#S') @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 =>))) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#C') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 '#B') @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 =) @
% 98.38/13.33 omegaS)))) @
% 98.38/13.33 omegaS)))))) @
% 98.38/13.33 (
% 98.38/13.33 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.38/13.33 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2560])).
% 98.38/13.33 thf(zip_derived_cl2581, plain,
% 98.38/13.33 (~ (((contrasubsetT1) =>
% 98.38/13.33 (((contrasubsetT2) =>
% 98.38/13.33 (((contrasubsetT3) =>
% 98.38/13.33 (((doubleComplementI1) =>
% 98.38/13.33 (((doubleComplementE1) =>
% 98.38/13.33 (((doubleComplementSub1) =>
% 98.38/13.33 (((doubleComplementSub2) =>
% 98.38/13.33 (((doubleComplementEq) =>
% 98.38/13.33 (((complementTnotintersectT) =>
% 98.38/13.33 (((complementImpComplementIntersect) =>
% 98.38/13.33 (((complementSubsetComplementIntersect) =>
% 98.38/13.33 (((complementInPowersetComplementIntersect) =>
% 98.38/13.33 (((contraSubsetComplement) =>
% 98.38/13.33 (((complementTcontraSubset) =>
% 98.38/13.33 (((binunionTILcontra) =>
% 98.38/13.33 (((binunionTIRcontra) =>
% 98.38/13.33 (((inIntersectImpInUnion) =>
% 98.38/13.33 (((inIntersectImpInUnion2) =>
% 98.38/13.33 (((inIntersectImpInIntersectUnions) =>
% 98.38/13.33 (((intersectInPowersetIntersectUnions) =>
% 98.38/13.33 (((inComplementUnionImpNotIn1) =>
% 98.38/13.33 (((inComplementUnionImpInComplement1) =>
% 98.38/13.33 (((binunionTE) =>
% 98.38/13.33 (((binunionTEcontra) =>
% 98.38/13.33 (((demorgan2a1) =>
% 98.38/13.33 (((complementUnionInPowersetComplement) =>
% 98.38/13.33 (((demorgan2a2) =>
% 98.38/13.33 (((demorgan1a) =>
% 98.38/13.33 (((demorgan1b) =>
% 98.38/13.33 (((demorgan1) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan2a) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan2b2) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan2b) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan2) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz13rule0) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz13rule1) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz13rule2) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz13rule3) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz13rule4) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz1_1) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz1_2) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz1_3) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz1_4) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz1_5) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1all2) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1SetBreln1) =>
% 98.38/13.33 ((
% 98.38/13.33 (choice2fnsingleton) =>
% 98.38/13.33 ((
% 98.38/13.33 (setOfPairsIsBReln1) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1all1) =>
% 98.38/13.33 ((
% 98.38/13.33 (subbreln1) =>
% 98.38/13.33 ((
% 98.38/13.33 (eqbreln1) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1invprop) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1invI) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1invE) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1compprop) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1compI) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1compE) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1compEex) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionprop) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionIL) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionIR) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionI) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionE) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionEcases) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionCommutes) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz2Ex) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz2W) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz2A) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz2B) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1Ex) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1Ex1) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1Equiv) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1E) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1I) =>
% 98.38/13.33 ((
% 98.38/13.33 (injFuncInInjFuncSet) =>
% 98.38/13.33 ((
% 98.38/13.33 (injFuncSetFuncIn) =>
% 98.38/13.33 ((
% 98.38/13.33 (injFuncSetFuncInj) =>
% 98.38/13.33 ((
% 98.38/13.33 (surjFuncSetFuncIn) =>
% 98.38/13.33 ((
% 98.38/13.33 (surjFuncSetFuncSurj) =>
% 98.38/13.33 ((
% 98.38/13.33 (leftInvIsSurj) =>
% 98.38/13.33 ((
% 98.38/13.33 (surjCantorThm) =>
% 98.38/13.33 ((
% 98.38/13.33 (foundation2) =>
% 98.38/13.33 ((
% 98.38/13.33 (notinself) =>
% 98.38/13.33 ((
% 98.38/13.33 (notinself2) =>
% 98.38/13.33 ((
% 98.38/13.33 (omegaSp) =>
% 98.38/13.33 ((
% 98.38/13.33 (omegaSclos) =>
% 98.38/13.33 ((
% 98.38/13.33 (peano0notS) =>
% 98.38/13.33 ((
% 98.38/13.33 (!!) @ (
% 98.38/13.33 (('#S') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 =>) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#C') @ in @
% 98.38/13.33 omega)))) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 !!) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#S') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 =>) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#C') @ in @
% 98.38/13.33 omega)))))) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#S') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 '#S') @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 =>))) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#C') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 '#B') @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 =) @
% 98.38/13.33 omegaS)))) @
% 98.38/13.33 omegaS)))))) @
% 98.38/13.33 (
% 98.38/13.33 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.38/13.33 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2570])).
% 98.38/13.33 thf(zip_derived_cl2594, plain,
% 98.38/13.33 (~ (((contrasubsetT2) =>
% 98.38/13.33 (((contrasubsetT3) =>
% 98.38/13.33 (((doubleComplementI1) =>
% 98.38/13.33 (((doubleComplementE1) =>
% 98.38/13.33 (((doubleComplementSub1) =>
% 98.38/13.33 (((doubleComplementSub2) =>
% 98.38/13.33 (((doubleComplementEq) =>
% 98.38/13.33 (((complementTnotintersectT) =>
% 98.38/13.33 (((complementImpComplementIntersect) =>
% 98.38/13.33 (((complementSubsetComplementIntersect) =>
% 98.38/13.33 (((complementInPowersetComplementIntersect) =>
% 98.38/13.33 (((contraSubsetComplement) =>
% 98.38/13.33 (((complementTcontraSubset) =>
% 98.38/13.33 (((binunionTILcontra) =>
% 98.38/13.33 (((binunionTIRcontra) =>
% 98.38/13.33 (((inIntersectImpInUnion) =>
% 98.38/13.33 (((inIntersectImpInUnion2) =>
% 98.38/13.33 (((inIntersectImpInIntersectUnions) =>
% 98.38/13.33 (((intersectInPowersetIntersectUnions) =>
% 98.38/13.33 (((inComplementUnionImpNotIn1) =>
% 98.38/13.33 (((inComplementUnionImpInComplement1) =>
% 98.38/13.33 (((binunionTE) =>
% 98.38/13.33 (((binunionTEcontra) =>
% 98.38/13.33 (((demorgan2a1) =>
% 98.38/13.33 (((complementUnionInPowersetComplement) =>
% 98.38/13.33 (((demorgan2a2) =>
% 98.38/13.33 (((demorgan1a) =>
% 98.38/13.33 (((demorgan1b) =>
% 98.38/13.33 (((demorgan1) =>
% 98.38/13.33 (((demorgan2a) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan2b2) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan2b) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan2) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz13rule0) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz13rule1) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz13rule2) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz13rule3) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz13rule4) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz1_1) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz1_2) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz1_3) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz1_4) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz1_5) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1all2) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1SetBreln1) =>
% 98.38/13.33 ((
% 98.38/13.33 (choice2fnsingleton) =>
% 98.38/13.33 ((
% 98.38/13.33 (setOfPairsIsBReln1) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1all1) =>
% 98.38/13.33 ((
% 98.38/13.33 (subbreln1) =>
% 98.38/13.33 ((
% 98.38/13.33 (eqbreln1) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1invprop) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1invI) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1invE) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1compprop) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1compI) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1compE) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1compEex) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionprop) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionIL) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionIR) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionI) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionE) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionEcases) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionCommutes) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz2Ex) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz2W) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz2A) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz2B) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1Ex) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1Ex1) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1Equiv) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1E) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1I) =>
% 98.38/13.33 ((
% 98.38/13.33 (injFuncInInjFuncSet) =>
% 98.38/13.33 ((
% 98.38/13.33 (injFuncSetFuncIn) =>
% 98.38/13.33 ((
% 98.38/13.33 (injFuncSetFuncInj) =>
% 98.38/13.33 ((
% 98.38/13.33 (surjFuncSetFuncIn) =>
% 98.38/13.33 ((
% 98.38/13.33 (surjFuncSetFuncSurj) =>
% 98.38/13.33 ((
% 98.38/13.33 (leftInvIsSurj) =>
% 98.38/13.33 ((
% 98.38/13.33 (surjCantorThm) =>
% 98.38/13.33 ((
% 98.38/13.33 (foundation2) =>
% 98.38/13.33 ((
% 98.38/13.33 (notinself) =>
% 98.38/13.33 ((
% 98.38/13.33 (notinself2) =>
% 98.38/13.33 ((
% 98.38/13.33 (omegaSp) =>
% 98.38/13.33 ((
% 98.38/13.33 (omegaSclos) =>
% 98.38/13.33 ((
% 98.38/13.33 (peano0notS) =>
% 98.38/13.33 ((
% 98.38/13.33 (!!) @ (
% 98.38/13.33 (('#S') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 =>) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#C') @ in @
% 98.38/13.33 omega)))) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 !!) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#S') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 =>) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#C') @ in @
% 98.38/13.33 omega)))))) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#S') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 '#S') @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 =>))) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#C') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 '#B') @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 =) @
% 98.38/13.33 omegaS)))) @
% 98.38/13.33 omegaS)))))) @
% 98.38/13.33 (
% 98.38/13.33 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.38/13.33 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2581])).
% 98.38/13.33 thf(zip_derived_cl2610, plain,
% 98.38/13.33 (~ (((contrasubsetT3) =>
% 98.38/13.33 (((doubleComplementI1) =>
% 98.38/13.33 (((doubleComplementE1) =>
% 98.38/13.33 (((doubleComplementSub1) =>
% 98.38/13.33 (((doubleComplementSub2) =>
% 98.38/13.33 (((doubleComplementEq) =>
% 98.38/13.33 (((complementTnotintersectT) =>
% 98.38/13.33 (((complementImpComplementIntersect) =>
% 98.38/13.33 (((complementSubsetComplementIntersect) =>
% 98.38/13.33 (((complementInPowersetComplementIntersect) =>
% 98.38/13.33 (((contraSubsetComplement) =>
% 98.38/13.33 (((complementTcontraSubset) =>
% 98.38/13.33 (((binunionTILcontra) =>
% 98.38/13.33 (((binunionTIRcontra) =>
% 98.38/13.33 (((inIntersectImpInUnion) =>
% 98.38/13.33 (((inIntersectImpInUnion2) =>
% 98.38/13.33 (((inIntersectImpInIntersectUnions) =>
% 98.38/13.33 (((intersectInPowersetIntersectUnions) =>
% 98.38/13.33 (((inComplementUnionImpNotIn1) =>
% 98.38/13.33 (((inComplementUnionImpInComplement1) =>
% 98.38/13.33 (((binunionTE) =>
% 98.38/13.33 (((binunionTEcontra) =>
% 98.38/13.33 (((demorgan2a1) =>
% 98.38/13.33 (((complementUnionInPowersetComplement) =>
% 98.38/13.33 (((demorgan2a2) =>
% 98.38/13.33 (((demorgan1a) =>
% 98.38/13.33 (((demorgan1b) =>
% 98.38/13.33 (((demorgan1) =>
% 98.38/13.33 (((demorgan2a) =>
% 98.38/13.33 (((demorgan2b2) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan2b) =>
% 98.38/13.33 ((
% 98.38/13.33 (demorgan2) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz13rule0) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz13rule1) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz13rule2) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz13rule3) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz13rule4) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz1_1) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz1_2) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz1_3) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz1_4) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz1_5) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1all2) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1SetBreln1) =>
% 98.38/13.33 ((
% 98.38/13.33 (choice2fnsingleton) =>
% 98.38/13.33 ((
% 98.38/13.33 (setOfPairsIsBReln1) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1all1) =>
% 98.38/13.33 ((
% 98.38/13.33 (subbreln1) =>
% 98.38/13.33 ((
% 98.38/13.33 (eqbreln1) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1invprop) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1invI) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1invE) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1compprop) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1compI) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1compE) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1compEex) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionprop) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionIL) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionIR) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionI) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionE) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionEcases) =>
% 98.38/13.33 ((
% 98.38/13.33 (breln1unionCommutes) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz2Ex) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz2W) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz2A) =>
% 98.38/13.33 ((
% 98.38/13.33 (woz2B) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1Ex) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1Ex1) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1Equiv) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1E) =>
% 98.38/13.33 ((
% 98.38/13.33 (image1I) =>
% 98.38/13.33 ((
% 98.38/13.33 (injFuncInInjFuncSet) =>
% 98.38/13.33 ((
% 98.38/13.33 (injFuncSetFuncIn) =>
% 98.38/13.33 ((
% 98.38/13.33 (injFuncSetFuncInj) =>
% 98.38/13.33 ((
% 98.38/13.33 (surjFuncSetFuncIn) =>
% 98.38/13.33 ((
% 98.38/13.33 (surjFuncSetFuncSurj) =>
% 98.38/13.33 ((
% 98.38/13.33 (leftInvIsSurj) =>
% 98.38/13.33 ((
% 98.38/13.33 (surjCantorThm) =>
% 98.38/13.33 ((
% 98.38/13.33 (foundation2) =>
% 98.38/13.33 ((
% 98.38/13.33 (notinself) =>
% 98.38/13.33 ((
% 98.38/13.33 (notinself2) =>
% 98.38/13.33 ((
% 98.38/13.33 (omegaSp) =>
% 98.38/13.33 ((
% 98.38/13.33 (omegaSclos) =>
% 98.38/13.33 ((
% 98.38/13.33 (peano0notS) =>
% 98.38/13.33 ((
% 98.38/13.33 (!!) @ (
% 98.38/13.33 (('#S') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 =>) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#C') @ in @
% 98.38/13.33 omega)))) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 !!) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#S') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 =>) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#C') @ in @
% 98.38/13.33 omega)))))) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#S') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 '#S') @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 =>))) @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#C') @ (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 '#B') @
% 98.38/13.33 (
% 98.38/13.33 (
% 98.38/13.33 ('#B') @ (
% 98.38/13.33 =) @
% 98.38/13.33 omegaS)))) @
% 98.38/13.33 omegaS)))))) @
% 98.38/13.33 (
% 98.38/13.33 =)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 98.38/13.33 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2594])).
% 98.38/13.33 thf(zip_derived_cl2629, plain,
% 98.38/13.33 (~ (((doubleComplementI1) =>
% 98.38/13.33 (((doubleComplementE1) =>
% 98.38/13.33 (((doubleComplementSub1) =>
% 98.38/13.33 (((doubleComplementSub2) =>
% 98.38/13.33 (((doubleComplementEq) =>
% 98.38/13.33 (((complementTnotintersectT) =>
% 98.38/13.33 (((complementImpComplementIntersect) =>
% 98.38/13.33 (((complementSubsetComplementIntersect) =>
% 98.38/13.33 (((complementInPowersetComplementIntersect) =>
% 98.38/13.33 (((contraSubsetComplement) =>
% 98.38/13.33 (((complementTcontraSubset) =>
% 98.38/13.33 (((binunionTILcontra) =>
% 98.38/13.33 (((binunionTIRcontra) =>
% 98.38/13.33 (((inIntersectImpInUnion) =>
% 98.38/13.33 (((inIntersectImpInUnion2) =>
% 98.38/13.33 (((inIntersectImpInIntersectUnions) =>
% 98.38/13.33 (((intersectInPowersetIntersectUnions) =>
% 98.38/13.33 (((inComplementUnionImpNotIn1) =>
% 98.38/13.33 (((inComplementUnionImpInComplement1) =>
% 98.38/13.33 (((binunionTE) =>
% 98.38/13.33 (((binunionTEcontra) =>
% 98.38/13.33 (((demorgan2a1) =>
% 98.38/13.33 (((complementUnionInPowersetComplement) =>
% 98.38/13.33 (((demorgan2a2) =>
% 98.38/13.33 (((demorgan1a) =>
% 98.38/13.33 (((demorgan1b) =>
% 98.38/13.33 (((demorgan1) =>
% 98.38/13.33 (((demorgan2a) =>
% 98.38/13.33