TSTP Solution File: SEU805^1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU805^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.gLUo6gQ9N5 true
% Computer : n005.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 19:17:59 EDT 2023
% Result : Theorem 106.14s 14.36s
% Output : Refutation 108.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU805^1 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.gLUo6gQ9N5 true
% 0.14/0.35 % Computer : n005.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Aug 23 22:03:54 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % Running portfolio for 300 s
% 0.14/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.36 % Number of cores: 8
% 0.14/0.36 % Python version: Python 3.6.8
% 0.14/0.36 % Running in HO mode
% 0.22/0.66 % Total configuration time : 828
% 0.22/0.66 % Estimated wc time : 1656
% 0.22/0.66 % Estimated cpu time (8 cpus) : 207.0
% 0.22/0.74 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.22/0.75 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.22/0.76 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.22/0.76 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.22/0.76 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.22/0.77 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.22/0.78 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.22/0.80 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 106.14/14.36 % Solved by lams/40_b.comb.sh.
% 106.14/14.36 % done 216 iterations in 13.222s
% 106.14/14.36 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 106.14/14.36 % SZS output start Refutation
% 106.14/14.36 thf(setadjoinAx_type, type, setadjoinAx: $o).
% 106.14/14.36 thf(cartprodfstpairEq_type, type, cartprodfstpairEq: $o).
% 106.14/14.36 thf(notdexE_type, type, notdexE: $o).
% 106.14/14.36 thf('#sk14_type', type, '#sk14': $i > $i).
% 106.14/14.36 thf(setunionAx_type, type, setunionAx: $o).
% 106.14/14.36 thf(setminusELneg_type, type, setminusELneg: $o).
% 106.14/14.36 thf(breln1unionEcases_type, type, breln1unionEcases: $o).
% 106.14/14.36 thf(powersetE_type, type, powersetE: $o).
% 106.14/14.36 thf(woz1_1_type, type, woz1_1: $o).
% 106.14/14.36 thf(omegaSAx_type, type, omegaSAx: $o).
% 106.14/14.36 thf(breln1unionI_type, type, breln1unionI: $o).
% 106.14/14.36 thf(complementSubsetComplementIntersect_type, type, complementSubsetComplementIntersect:
% 106.14/14.36 $o).
% 106.14/14.36 thf(surjCantorThm_type, type, surjCantorThm: $o).
% 106.14/14.36 thf(exuI1_type, type, exuI1: $o).
% 106.14/14.36 thf(exuI2_type, type, exuI2: $o).
% 106.14/14.36 thf(notequalI2_type, type, notequalI2: $o).
% 106.14/14.36 thf(kfstsingleton_type, type, kfstsingleton: $o).
% 106.14/14.36 thf(kpairiskpair_type, type, kpairiskpair: $o).
% 106.14/14.36 thf(upairsubunion_type, type, upairsubunion: $o).
% 106.14/14.36 thf(binunionTE_type, type, binunionTE: $o).
% 106.14/14.36 thf(binunionTEcontra_type, type, binunionTEcontra: $o).
% 106.14/14.36 thf(powerset__Cong_type, type, powerset__Cong: $o).
% 106.14/14.36 thf(setukpairinjR2_type, type, setukpairinjR2: $o).
% 106.14/14.36 thf(singletonsuniq_type, type, singletonsuniq: $o).
% 106.14/14.36 thf(setminusILneg_type, type, setminusILneg: $o).
% 106.14/14.36 thf(wellorderingAx_type, type, wellorderingAx: $o).
% 106.14/14.36 thf(kpairsurjEq_type, type, kpairsurjEq: $o).
% 106.14/14.36 thf(funcextLem_type, type, funcextLem: $o).
% 106.14/14.36 thf(setadjoinSub2_type, type, setadjoinSub2: $o).
% 106.14/14.36 thf(binintersectSubset5_type, type, binintersectSubset5: $o).
% 106.14/14.36 thf(upairinpowunion_type, type, upairinpowunion: $o).
% 106.14/14.36 thf(eta1_type, type, eta1: $o).
% 106.14/14.36 thf(complementTnotintersectT_type, type, complementTnotintersectT: $o).
% 106.14/14.36 thf(setoftrueEq_type, type, setoftrueEq: $o).
% 106.14/14.36 thf(apProp_type, type, apProp: $o).
% 106.14/14.36 thf(setextT_type, type, setextT: $o).
% 106.14/14.36 thf(inIntersectImpInIntersectUnions_type, type, inIntersectImpInIntersectUnions:
% 106.14/14.36 $o).
% 106.14/14.36 thf(emptyset__Cong_type, type, emptyset__Cong: $o).
% 106.14/14.36 thf(cartprodmempaircEq_type, type, cartprodmempaircEq: $o).
% 106.14/14.36 thf(breln1invprop_type, type, breln1invprop: $o).
% 106.14/14.36 thf(lamProp_type, type, lamProp: $o).
% 106.14/14.36 thf(dpsetconstrSub_type, type, dpsetconstrSub: $o).
% 106.14/14.36 thf('#sk29_type', type, '#sk29': $i > $i > $i).
% 106.14/14.36 thf(ex1E1_type, type, ex1E1: $o).
% 106.14/14.36 thf(sepInPowerset_type, type, sepInPowerset: $o).
% 106.14/14.36 thf(setukpairIR_type, type, setukpairIR: $o).
% 106.14/14.36 thf(brelnall1_type, type, brelnall1: $o).
% 106.14/14.36 thf(binunionE_type, type, binunionE: $o).
% 106.14/14.36 thf(setext_type, type, setext: $o).
% 106.14/14.36 thf(complementTcontraSubset_type, type, complementTcontraSubset: $o).
% 106.14/14.36 thf(emptyinPowerset_type, type, emptyinPowerset: $o).
% 106.14/14.36 thf(binintersectTELcontra_type, type, binintersectTELcontra: $o).
% 106.14/14.36 thf(ubforcartprodlem1_type, type, ubforcartprodlem1: $o).
% 106.14/14.36 thf(iftrue_type, type, iftrue: $o).
% 106.14/14.36 thf(woz13rule4_type, type, woz13rule4: $o).
% 106.14/14.36 thf(descr__Cong_type, type, descr__Cong: $o).
% 106.14/14.36 thf(funcGraphProp2_type, type, funcGraphProp2: $o).
% 106.14/14.36 thf(theprop_type, type, theprop: $o).
% 106.14/14.36 thf(image1I_type, type, image1I: $o).
% 106.14/14.36 thf(binintersectSubset1_type, type, binintersectSubset1: $o).
% 106.14/14.36 thf(in_type, type, in: $i > $i > $o).
% 106.14/14.36 thf(cartprodsndpairEq_type, type, cartprodsndpairEq: $o).
% 106.14/14.36 thf(quantDeMorgan1_type, type, quantDeMorgan1: $o).
% 106.14/14.36 thf(setukpairinjL2_type, type, setukpairinjL2: $o).
% 106.14/14.36 thf(demorgan1_type, type, demorgan1: $o).
% 106.14/14.36 thf(setadjoinIR_type, type, setadjoinIR: $o).
% 106.14/14.36 thf(complementInPowersetComplementIntersect_type, type, complementInPowersetComplementIntersect:
% 106.14/14.36 $o).
% 106.14/14.36 thf(inIntersectImpInUnion_type, type, inIntersectImpInUnion: $o).
% 106.14/14.36 thf(breln1SetBreln1_type, type, breln1SetBreln1: $o).
% 106.14/14.36 thf(setadjoin__Cong_type, type, setadjoin__Cong: $o).
% 106.14/14.36 thf(ksndpairEq_type, type, ksndpairEq: $o).
% 106.14/14.36 thf(ex1I2_type, type, ex1I2: $o).
% 106.14/14.36 thf(symdiffI2_type, type, symdiffI2: $o).
% 106.14/14.36 thf(ap2apEq2_type, type, ap2apEq2: $o).
% 106.14/14.36 thf(ifSingleton_type, type, ifSingleton: $o).
% 106.14/14.36 thf(upairset2IR_type, type, upairset2IR: $o).
% 106.14/14.36 thf(iftrueProp1_type, type, iftrueProp1: $o).
% 106.14/14.36 thf(complementTI1_type, type, complementTI1: $o).
% 106.14/14.36 thf(subsetE_type, type, subsetE: $o).
% 106.14/14.36 thf(prop2set2propI_type, type, prop2set2propI: $o).
% 106.14/14.36 thf(doubleComplementSub2_type, type, doubleComplementSub2: $o).
% 106.14/14.36 thf(complementUnionInPowersetComplement_type, type, complementUnionInPowersetComplement:
% 106.14/14.36 $o).
% 106.14/14.36 thf(iffalse_type, type, iffalse: $o).
% 106.14/14.36 thf(dsetconstrEL_type, type, dsetconstrEL: $o).
% 106.14/14.36 thf(setbeta_type, type, setbeta: $o).
% 106.14/14.36 thf(eqinunit_type, type, eqinunit: $o).
% 106.14/14.36 thf(upairsetIL_type, type, upairsetIL: $o).
% 106.14/14.36 thf(powersetI1_type, type, powersetI1: $o).
% 106.14/14.36 thf(cartprodfstin_type, type, cartprodfstin: $o).
% 106.14/14.36 thf(lamp_type, type, lamp: $o).
% 106.14/14.36 thf(iffalseProp1_type, type, iffalseProp1: $o).
% 106.14/14.36 thf(breln1invI_type, type, breln1invI: $o).
% 106.14/14.36 thf(binintersectSubset3_type, type, binintersectSubset3: $o).
% 106.14/14.36 thf(breln1unionE_type, type, breln1unionE: $o).
% 106.14/14.36 thf(ksndsingleton_type, type, ksndsingleton: $o).
% 106.14/14.36 thf(setminusIRneg_type, type, setminusIRneg: $o).
% 106.14/14.36 thf(lam2lamEq_type, type, lam2lamEq: $o).
% 106.14/14.36 thf(powersetAx_type, type, powersetAx: $o).
% 106.14/14.36 thf(woz2Ex_type, type, woz2Ex: $o).
% 106.14/14.36 thf(eta2_type, type, eta2: $o).
% 106.14/14.36 thf(binintersectSubset4_type, type, binintersectSubset4: $o).
% 106.14/14.36 thf(singletoninpowunion_type, type, singletoninpowunion: $o).
% 106.14/14.36 thf(image1Ex_type, type, image1Ex: $o).
% 106.14/14.36 thf(powersetI_type, type, powersetI: $o).
% 106.14/14.36 thf(cartprodmempair_type, type, cartprodmempair: $o).
% 106.14/14.36 thf(powersetTE1_type, type, powersetTE1: $o).
% 106.14/14.36 thf(upairsetIR_type, type, upairsetIR: $o).
% 106.14/14.36 thf(cartprodpairsurjEq_type, type, cartprodpairsurjEq: $o).
% 106.14/14.36 thf(lam2p_type, type, lam2p: $o).
% 106.14/14.36 thf(contraSubsetComplement_type, type, contraSubsetComplement: $o).
% 106.14/14.36 thf(doubleComplementSub1_type, type, doubleComplementSub1: $o).
% 106.14/14.36 thf(cartprodpairmemEL_type, type, cartprodpairmemEL: $o).
% 106.14/14.36 thf(setOfPairsIsBReln1_type, type, setOfPairsIsBReln1: $o).
% 106.14/14.36 thf(inCongP_type, type, inCongP: $o).
% 106.14/14.36 thf(setukpairinjR11_type, type, setukpairinjR11: $o).
% 106.14/14.36 thf(setadjoinSub_type, type, setadjoinSub: $o).
% 106.14/14.36 thf(exuE3e_type, type, exuE3e: $o).
% 106.14/14.36 thf(emptysetE_type, type, emptysetE: $o).
% 106.14/14.36 thf(woz13rule2_type, type, woz13rule2: $o).
% 106.14/14.36 thf(binintersectSubset2_type, type, binintersectSubset2: $o).
% 106.14/14.36 thf(image1E_type, type, image1E: $o).
% 106.14/14.36 thf(setunionI_type, type, setunionI: $o).
% 106.14/14.36 thf(breln1unionIR_type, type, breln1unionIR: $o).
% 106.14/14.36 thf(binintersectTERcontra_type, type, binintersectTERcontra: $o).
% 106.14/14.36 thf(setunion__Cong_type, type, setunion__Cong: $o).
% 106.14/14.36 thf(injFuncSetFuncInj_type, type, injFuncSetFuncInj: $o).
% 106.14/14.36 thf(prop2setI_type, type, prop2setI: $o).
% 106.14/14.36 thf(nonemptyImpWitness_type, type, nonemptyImpWitness: $o).
% 106.14/14.36 thf(setminusER_type, type, setminusER: $o).
% 106.14/14.36 thf(exuE2_type, type, exuE2: $o).
% 106.14/14.36 thf(woz1_2_type, type, woz1_2: $o).
% 106.14/14.36 thf(emptyset_type, type, emptyset: $i).
% 106.14/14.36 thf(setukpairinjR12_type, type, setukpairinjR12: $o).
% 106.14/14.36 thf(funcGraphProp1_type, type, funcGraphProp1: $o).
% 106.14/14.36 thf(powersetsubset_type, type, powersetsubset: $o).
% 106.14/14.36 thf(upairequniteq_type, type, upairequniteq: $o).
% 106.14/14.36 thf(dpsetconstrEL1_type, type, dpsetconstrEL1: $o).
% 106.14/14.36 thf(injFuncInInjFuncSet_type, type, injFuncInInjFuncSet: $o).
% 106.14/14.36 thf(subPowSU_type, type, subPowSU: $o).
% 106.14/14.36 thf(breln1compprop_type, type, breln1compprop: $o).
% 106.14/14.36 thf(woz2B_type, type, woz2B: $o).
% 106.14/14.36 thf(notequalI1_type, type, notequalI1: $o).
% 106.14/14.36 thf(demorgan2b_type, type, demorgan2b: $o).
% 106.14/14.36 thf(notinemptyset_type, type, notinemptyset: $o).
% 106.14/14.36 thf(nonemptyI1_type, type, nonemptyI1: $o).
% 106.14/14.36 thf(breln1unionIL_type, type, breln1unionIL: $o).
% 106.14/14.36 thf(subsetTrans_type, type, subsetTrans: $o).
% 106.14/14.36 thf(setukpairinjR_type, type, setukpairinjR: $o).
% 106.14/14.36 thf(infuncsetfunc_type, type, infuncsetfunc: $o).
% 106.14/14.36 thf(kpairp_type, type, kpairp: $o).
% 106.14/14.36 thf(setukpairinjR1_type, type, setukpairinjR1: $o).
% 106.14/14.36 thf(setminusI_type, type, setminusI: $o).
% 106.14/14.36 thf(binunionIL_type, type, binunionIL: $o).
% 106.14/14.36 thf(setOfPairsIsBReln_type, type, setOfPairsIsBReln: $o).
% 106.14/14.36 thf(setukpairinjL1_type, type, setukpairinjL1: $o).
% 106.14/14.36 thf(setunionsingleton_type, type, setunionsingleton: $o).
% 106.14/14.36 thf(powersetTI1_type, type, powersetTI1: $o).
% 106.14/14.36 thf(subsetE2_type, type, subsetE2: $o).
% 106.14/14.36 thf(image1Ex1_type, type, image1Ex1: $o).
% 106.14/14.36 thf(singletonsswitch_type, type, singletonsswitch: $o).
% 106.14/14.36 thf(ubforcartprodlem3_type, type, ubforcartprodlem3: $o).
% 106.14/14.36 thf(setextsub_type, type, setextsub: $o).
% 106.14/14.36 thf(binunionLsub_type, type, binunionLsub: $o).
% 106.14/14.36 thf(contrasubsetT1_type, type, contrasubsetT1: $o).
% 106.14/14.36 thf(setunionsingleton1_type, type, setunionsingleton1: $o).
% 106.14/14.36 thf(breln1compE_type, type, breln1compE: $o).
% 106.14/14.36 thf(binintersect_type, type, binintersect: $i > $i > $i).
% 106.14/14.36 thf(emptysetsubset_type, type, emptysetsubset: $o).
% 106.14/14.36 thf(quantDeMorgan3_type, type, quantDeMorgan3: $o).
% 106.14/14.36 thf(dpsetconstrERa_type, type, dpsetconstrERa: $o).
% 106.14/14.36 thf(setunionE_type, type, setunionE: $o).
% 106.14/14.36 thf(setminusSubset1_type, type, setminusSubset1: $o).
% 106.14/14.36 thf(complementT_lem_type, type, complementT_lem: $o).
% 106.14/14.36 thf(binintersectT_lem_type, type, binintersectT_lem: $o).
% 106.14/14.36 thf(emptyinunitempty_type, type, emptyinunitempty: $o).
% 106.14/14.36 thf(binunionIR_type, type, binunionIR: $o).
% 106.14/14.36 thf(injFuncSetFuncIn_type, type, injFuncSetFuncIn: $o).
% 106.14/14.36 thf(setadjoinE_type, type, setadjoinE: $o).
% 106.14/14.36 thf(doubleComplementEq_type, type, doubleComplementEq: $o).
% 106.14/14.36 thf(eqbreln1_type, type, eqbreln1: $o).
% 106.14/14.36 thf(cartprodpairmemER_type, type, cartprodpairmemER: $o).
% 106.14/14.36 thf(dpsetconstrER_type, type, dpsetconstrER: $o).
% 106.14/14.36 thf(leftInvIsSurj_type, type, leftInvIsSurj: $o).
% 106.14/14.36 thf(doubleComplementE1_type, type, doubleComplementE1: $o).
% 106.14/14.36 thf(setadjoinIL_type, type, setadjoinIL: $o).
% 106.14/14.36 thf(exuE1_type, type, exuE1: $o).
% 106.14/14.36 thf(ubforcartprodlem2_type, type, ubforcartprodlem2: $o).
% 106.14/14.36 thf(binintersectRsub_type, type, binintersectRsub: $o).
% 106.14/14.36 thf(setminusLsub_type, type, setminusLsub: $o).
% 106.14/14.36 thf(notinsingleton_type, type, notinsingleton: $o).
% 106.14/14.36 thf(intersectInPowersetIntersectUnions_type, type, intersectInPowersetIntersectUnions:
% 106.14/14.36 $o).
% 106.14/14.36 thf(dpsetconstrEL2_type, type, dpsetconstrEL2: $o).
% 106.14/14.36 thf(eqimpsubset2_type, type, eqimpsubset2: $o).
% 106.14/14.36 thf(exuEu_type, type, exuEu: $o).
% 106.14/14.36 thf(emptysetimpfalse_type, type, emptysetimpfalse: $o).
% 106.14/14.36 thf(upairsetE_type, type, upairsetE: $o).
% 106.14/14.36 thf(omega0Ax_type, type, omega0Ax: $o).
% 106.14/14.36 thf(breln1invE_type, type, breln1invE: $o).
% 106.14/14.36 thf(breln1unionCommutes_type, type, breln1unionCommutes: $o).
% 106.14/14.36 thf(funcGraphProp3_type, type, funcGraphProp3: $o).
% 106.14/14.36 thf(app_type, type, app: $o).
% 106.14/14.36 thf(funcImageSingleton_type, type, funcImageSingleton: $o).
% 106.14/14.36 thf(dpsetconstrI_type, type, dpsetconstrI: $o).
% 106.14/14.36 thf(notsubsetI_type, type, notsubsetI: $o).
% 106.14/14.36 thf(powersetT_lem_type, type, powersetT_lem: $o).
% 106.14/14.36 thf(woz2W_type, type, woz2W: $o).
% 106.14/14.36 thf(iffalseProp2_type, type, iffalseProp2: $o).
% 106.14/14.36 thf(quantDeMorgan4_type, type, quantDeMorgan4: $o).
% 106.14/14.36 thf(setextAx_type, type, setextAx: $o).
% 106.14/14.36 thf(breln1all1_type, type, breln1all1: $o).
% 106.14/14.36 thf('#sk49_type', type, '#sk49': $i).
% 106.14/14.36 thf(choice2fnsingleton_type, type, choice2fnsingleton: $o).
% 106.14/14.36 thf(breln1compI_type, type, breln1compI: $o).
% 106.14/14.36 thf(demorgan2a1_type, type, demorgan2a1: $o).
% 106.14/14.36 thf(powersetE1_type, type, powersetE1: $o).
% 106.14/14.36 thf(bs114d_type, type, bs114d: $o).
% 106.14/14.36 thf(complementTE1_type, type, complementTE1: $o).
% 106.14/14.36 thf(noeltsimpempty_type, type, noeltsimpempty: $o).
% 106.14/14.36 thf(breln1all2_type, type, breln1all2: $o).
% 106.14/14.36 thf(contrasubsetT2_type, type, contrasubsetT2: $o).
% 106.14/14.36 thf(inIntersectImpInUnion2_type, type, inIntersectImpInUnion2: $o).
% 106.14/14.36 thf(demorgan2b2_type, type, demorgan2b2: $o).
% 106.14/14.36 thf(binintersectLsub_type, type, binintersectLsub: $o).
% 106.14/14.36 thf(subsetI1_type, type, subsetI1: $o).
% 106.14/14.36 thf(symdiffE_type, type, symdiffE: $o).
% 106.14/14.36 thf(woz13rule1_type, type, woz13rule1: $o).
% 106.14/14.36 thf(breln1unionprop_type, type, breln1unionprop: $o).
% 106.14/14.36 thf(descrp_type, type, descrp: $o).
% 106.14/14.36 thf(dsetconstr__Cong_type, type, dsetconstr__Cong: $o).
% 106.14/14.36 thf(foundationAx_type, type, foundationAx: $o).
% 106.14/14.36 thf(brelnall2_type, type, brelnall2: $o).
% 106.14/14.36 thf(emptysetAx_type, type, emptysetAx: $o).
% 106.14/14.36 thf(emptyI_type, type, emptyI: $o).
% 106.14/14.36 thf(setadjoinOr_type, type, setadjoinOr: $o).
% 106.14/14.36 thf(binintersectEL_type, type, binintersectEL: $o).
% 106.14/14.36 thf(emptyE1_type, type, emptyE1: $o).
% 106.14/14.36 thf(demorgan2a_type, type, demorgan2a: $o).
% 106.14/14.36 thf(woz1_3_type, type, woz1_3: $o).
% 106.14/14.36 thf(emptyInPowerset_type, type, emptyInPowerset: $o).
% 106.14/14.36 thf(vacuousDall_type, type, vacuousDall: $o).
% 106.14/14.36 thf(dsetconstrER_type, type, dsetconstrER: $o).
% 106.14/14.36 thf(demorgan1a_type, type, demorgan1a: $o).
% 106.14/14.36 thf(ifp_type, type, ifp: $o).
% 106.14/14.36 thf(binintersectI_type, type, binintersectI: $o).
% 106.14/14.36 thf(beta1_type, type, beta1: $o).
% 106.14/14.36 thf(funcext2_type, type, funcext2: $o).
% 106.14/14.36 thf(subbreln_type, type, subbreln: $o).
% 106.14/14.36 thf(cartprodpairin_type, type, cartprodpairin: $o).
% 106.14/14.36 thf(cartprodmempair1_type, type, cartprodmempair1: $o).
% 106.14/14.36 thf(subbreln1_type, type, subbreln1: $o).
% 106.14/14.36 thf(demorgan2a2_type, type, demorgan2a2: $o).
% 106.14/14.36 thf(image1Equiv_type, type, image1Equiv: $o).
% 106.14/14.36 thf(subsetTI_type, type, subsetTI: $o).
% 106.14/14.36 thf(setminusT_lem_type, type, setminusT_lem: $o).
% 106.14/14.36 thf(ap2p_type, type, ap2p: $o).
% 106.14/14.36 thf(doubleComplementI1_type, type, doubleComplementI1: $o).
% 106.14/14.36 thf(binunionT_lem_type, type, binunionT_lem: $o).
% 106.14/14.36 thf(symdiffI1_type, type, symdiffI1: $o).
% 106.14/14.36 thf(woz1_4_type, type, woz1_4: $o).
% 106.14/14.36 thf(kfstpairEq_type, type, kfstpairEq: $o).
% 106.14/14.36 thf(subsetI2_type, type, subsetI2: $o).
% 106.14/14.36 thf(symdiffIneg1_type, type, symdiffIneg1: $o).
% 106.14/14.36 thf(theeq_type, type, theeq: $o).
% 106.14/14.36 thf(setminusERneg_type, type, setminusERneg: $o).
% 106.14/14.36 thf(symdiffIneg2_type, type, symdiffIneg2: $o).
% 106.14/14.36 thf(binunionTIRcontra_type, type, binunionTIRcontra: $o).
% 106.14/14.36 thf(omega__Cong_type, type, omega__Cong: $o).
% 106.14/14.36 thf(demorgan1b_type, type, demorgan1b: $o).
% 106.14/14.36 thf(subsetRefl_type, type, subsetRefl: $o).
% 106.14/14.36 thf(uniqinunit_type, type, uniqinunit: $o).
% 106.14/14.36 thf(eqbreln_type, type, eqbreln: $o).
% 106.14/14.36 thf(inComplementUnionImpNotIn1_type, type, inComplementUnionImpNotIn1: $o).
% 106.14/14.36 thf(funcinfuncset_type, type, funcinfuncset: $o).
% 106.14/14.36 thf(breln1compEex_type, type, breln1compEex: $o).
% 106.14/14.36 thf(contrasubsetT_type, type, contrasubsetT: $o).
% 106.14/14.36 thf(setminusSubset2_type, type, setminusSubset2: $o).
% 106.14/14.36 thf(prop2setE_type, type, prop2setE: $o).
% 106.14/14.36 thf('#sk5_type', type, '#sk5': $i > $i).
% 106.14/14.36 thf(binunionEcases_type, type, binunionEcases: $o).
% 106.14/14.36 thf(omega_type, type, omega: $i).
% 106.14/14.36 thf(nonemptyI_type, type, nonemptyI: $o).
% 106.14/14.36 thf(disjointsetsI1_type, type, disjointsetsI1: $o).
% 106.14/14.36 thf(woz2A_type, type, woz2A: $o).
% 106.14/14.36 thf(exuE3u_type, type, exuE3u: $o).
% 106.14/14.36 thf(setminusEL_type, type, setminusEL: $o).
% 106.14/14.36 thf(funcGraphProp4_type, type, funcGraphProp4: $o).
% 106.14/14.36 thf(woz1_5_type, type, woz1_5: $o).
% 106.14/14.36 thf(demorgan2_type, type, demorgan2: $o).
% 106.14/14.36 thf(setunionsingleton2_type, type, setunionsingleton2: $o).
% 106.14/14.36 thf(sepSubset_type, type, sepSubset: $o).
% 106.14/14.36 thf(inComplementUnionImpInComplement1_type, type, inComplementUnionImpInComplement1:
% 106.14/14.36 $o).
% 106.14/14.36 thf(funcext_type, type, funcext: $o).
% 106.14/14.36 thf(surjFuncSetFuncSurj_type, type, surjFuncSetFuncSurj: $o).
% 106.14/14.36 thf(upairset2E_type, type, upairset2E: $o).
% 106.14/14.36 thf(eqimpsubset1_type, type, eqimpsubset1: $o).
% 106.14/14.36 thf(exuI3_type, type, exuI3: $o).
% 106.14/14.36 thf(notdallE_type, type, notdallE: $o).
% 106.14/14.36 thf(iftrueProp2_type, type, iftrueProp2: $o).
% 106.14/14.36 thf(binintersectER_type, type, binintersectER: $o).
% 106.14/14.36 thf(woz13rule0_type, type, woz13rule0: $o).
% 106.14/14.36 thf(dsetconstrI_type, type, dsetconstrI: $o).
% 106.14/14.36 thf(nonempty_type, type, nonempty: $i > $o).
% 106.14/14.36 thf(beta2_type, type, beta2: $o).
% 106.14/14.36 thf(setadjoin_type, type, setadjoin: $i > $i > $i).
% 106.14/14.36 thf(exu__Cong_type, type, exu__Cong: $o).
% 106.14/14.36 thf(cartprodsndin_type, type, cartprodsndin: $o).
% 106.14/14.36 thf(iftrueorfalse_type, type, iftrueorfalse: $o).
% 106.14/14.36 thf(surjFuncSetFuncIn_type, type, surjFuncSetFuncIn: $o).
% 106.14/14.36 thf(quantDeMorgan2_type, type, quantDeMorgan2: $o).
% 106.14/14.36 thf(ex1I_type, type, ex1I: $o).
% 106.14/14.36 thf(secondinupair_type, type, secondinupair: $o).
% 106.14/14.36 thf(singletonprop_type, type, singletonprop: $o).
% 106.14/14.36 thf(singletonsubset_type, type, singletonsubset: $o).
% 106.14/14.36 thf(singletoninpowerset_type, type, singletoninpowerset: $o).
% 106.14/14.36 thf(subsetemptysetimpeq_type, type, subsetemptysetimpeq: $o).
% 106.14/14.36 thf(ex1E2_type, type, ex1E2: $o).
% 106.14/14.36 thf(replAx_type, type, replAx: $o).
% 106.14/14.36 thf(nonemptyE1_type, type, nonemptyE1: $o).
% 106.14/14.36 thf(omegaIndAx_type, type, omegaIndAx: $o).
% 106.14/14.36 thf(setukpairIL_type, type, setukpairIL: $o).
% 106.14/14.36 thf(setunionE2_type, type, setunionE2: $o).
% 106.14/14.36 thf(inPowerset_type, type, inPowerset: $o).
% 106.14/14.36 thf(binunionTILcontra_type, type, binunionTILcontra: $o).
% 106.14/14.36 thf(ap2apEq1_type, type, ap2apEq1: $o).
% 106.14/14.36 thf(contrasubsetT3_type, type, contrasubsetT3: $o).
% 106.14/14.36 thf(woz13rule3_type, type, woz13rule3: $o).
% 106.14/14.36 thf(complementImpComplementIntersect_type, type, complementImpComplementIntersect:
% 106.14/14.36 $o).
% 106.14/14.36 thf(in__Cong_type, type, in__Cong: $o).
% 106.14/14.36 thf(setukpairinjL_type, type, setukpairinjL: $o).
% 106.14/14.36 thf(binunionRsub_type, type, binunionRsub: $o).
% 106.14/14.36 thf(subset2powerset_type, type, subset2powerset: $o).
% 106.14/14.36 thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)).
% 106.14/14.36 thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)).
% 106.14/14.36 thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)).
% 106.14/14.36 thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)).
% 106.14/14.36 thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)).
% 106.14/14.36 thf(foundation2, conjecture,
% 106.14/14.36 (( setextAx ) =>
% 106.14/14.36 ( ( emptysetAx ) =>
% 106.14/14.36 ( ( setadjoinAx ) =>
% 106.14/14.36 ( ( powersetAx ) =>
% 106.14/14.36 ( ( setunionAx ) =>
% 106.14/14.36 ( ( omega0Ax ) =>
% 106.14/14.36 ( ( omegaSAx ) =>
% 106.14/14.36 ( ( omegaIndAx ) =>
% 106.14/14.36 ( ( replAx ) =>
% 106.14/14.36 ( ( foundationAx ) =>
% 106.14/14.36 ( ( wellorderingAx ) =>
% 106.14/14.36 ( ( descrp ) =>
% 106.14/14.36 ( ( dsetconstrI ) =>
% 106.14/14.36 ( ( dsetconstrEL ) =>
% 106.14/14.36 ( ( dsetconstrER ) =>
% 106.14/14.36 ( ( exuE1 ) =>
% 106.14/14.36 ( ( prop2setE ) =>
% 106.14/14.36 ( ( emptysetE ) =>
% 106.14/14.36 ( ( emptysetimpfalse ) =>
% 106.14/14.36 ( ( notinemptyset ) =>
% 106.14/14.36 ( ( exuE3e ) =>
% 106.14/14.36 ( ( setext ) =>
% 106.14/14.36 ( ( emptyI ) =>
% 106.14/14.36 ( ( noeltsimpempty ) =>
% 106.14/14.36 ( ( setbeta ) =>
% 106.14/14.36 ( ( nonemptyE1 ) =>
% 106.14/14.36 ( ( nonemptyI ) =>
% 106.14/14.36 ( ( nonemptyI1 ) =>
% 106.14/14.36 ( ( setadjoinIL ) =>
% 106.14/14.36 ( ( emptyinunitempty ) =>
% 106.14/14.36 ( ( setadjoinIR ) =>
% 106.14/14.36 ( ( setadjoinE ) =>
% 106.14/14.36 ( (
% 106.14/14.36 setadjoinOr ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 setoftrueEq ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 powersetI ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 emptyinPowerset ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 emptyInPowerset ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 powersetE ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 setunionI ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 setunionE ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 subPowSU ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 exuE2 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 nonemptyImpWitness ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 uniqinunit ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 notinsingleton ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 eqinunit ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 singletonsswitch ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 upairsetE ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 upairsetIL ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 upairsetIR ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 emptyE1 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 vacuousDall ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 quantDeMorgan1 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 quantDeMorgan2 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 quantDeMorgan3 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 quantDeMorgan4 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 prop2setI ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 prop2set2propI ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 notdexE ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 notdallE ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 exuI1 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 exuI3 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 exuI2 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 inCongP ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 in__Cong ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 exuE3u ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 exu__Cong ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 emptyset__Cong ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 setadjoin__Cong ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 powerset__Cong ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 setunion__Cong ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 omega__Cong ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 exuEu ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 descr__Cong ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 dsetconstr__Cong ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 subsetI1 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 eqimpsubset2 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 eqimpsubset1 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 subsetI2 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 emptysetsubset ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 subsetE ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 subsetE2 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 notsubsetI ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 notequalI1 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 notequalI2 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 subsetRefl ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 subsetTrans ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 setadjoinSub ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 setadjoinSub2 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 subset2powerset ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 setextsub ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 subsetemptysetimpeq ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 powersetI1 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 powersetE1 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 inPowerset ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 powersetsubset ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 sepInPowerset ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 sepSubset ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 binunionIL ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 upairset2IR ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 binunionIR ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 binunionEcases ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 binunionE ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 binunionLsub ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 binunionRsub ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 binintersectI ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 binintersectSubset5 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 binintersectEL ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 binintersectLsub ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 binintersectSubset2 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 binintersectSubset3 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 binintersectER ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 disjointsetsI1 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 binintersectRsub ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 binintersectSubset4 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 binintersectSubset1 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 bs114d ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 setminusI ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 setminusEL ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 setminusER ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 setminusSubset2 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 setminusERneg ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 setminusELneg ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 setminusILneg ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 setminusIRneg ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 setminusLsub ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 setminusSubset1 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 symdiffE ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 symdiffI1 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 symdiffI2 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 symdiffIneg1 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 symdiffIneg2 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 secondinupair ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 setukpairIL ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 setukpairIR ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 kpairiskpair ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 kpairp ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 singletonsubset ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 singletoninpowerset ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 singletoninpowunion ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 upairset2E ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 upairsubunion ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 upairinpowunion ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 ubforcartprodlem1 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 ubforcartprodlem2 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 ubforcartprodlem3 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 cartprodpairin ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 cartprodmempair1 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 cartprodmempair ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 setunionE2 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 setunionsingleton1 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 setunionsingleton2 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 setunionsingleton ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 singletonprop ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 ex1E1 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 ex1I ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 ex1I2 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 singletonsuniq ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 setukpairinjL1 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 kfstsingleton ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 theprop ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 kfstpairEq ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 cartprodfstin ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 setukpairinjL2 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 setukpairinjL ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 setukpairinjR11 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 setukpairinjR12 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 setukpairinjR1 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 upairequniteq ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 setukpairinjR2 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 setukpairinjR ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 ksndsingleton ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 ksndpairEq ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 kpairsurjEq ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 cartprodsndin ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 cartprodpairmemEL ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 cartprodpairmemER ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 cartprodmempaircEq ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 cartprodfstpairEq ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 cartprodsndpairEq ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 cartprodpairsurjEq ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 dpsetconstrI ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 dpsetconstrSub ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 setOfPairsIsBReln ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 dpsetconstrERa ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 dpsetconstrEL1 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 dpsetconstrEL2 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 dpsetconstrER ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 funcImageSingleton ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 apProp ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 app ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 infuncsetfunc ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 ap2p ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 funcinfuncset ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 lamProp ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 lamp ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 lam2p ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 brelnall1 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 brelnall2 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 ex1E2 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 funcGraphProp1 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 funcGraphProp3 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 funcGraphProp2 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 funcextLem ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 funcGraphProp4 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 subbreln ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 eqbreln ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 funcext ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 funcext2 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 ap2apEq1 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 ap2apEq2 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 beta1 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 eta1 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 lam2lamEq ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 beta2 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 eta2 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 iffalseProp1 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 iffalseProp2 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 iftrueProp1 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 iftrueProp2 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 ifSingleton ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 ifp ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 theeq ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 iftrue ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 iffalse ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 iftrueorfalse ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 binintersectT_lem ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 binunionT_lem ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 powersetT_lem ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 setminusT_lem ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 complementT_lem ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 setextT ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 subsetTI ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 powersetTI1 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 powersetTE1 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 complementTI1 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 complementTE1 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 binintersectTELcontra ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 binintersectTERcontra ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 contrasubsetT ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 contrasubsetT1 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 contrasubsetT2 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 contrasubsetT3 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 doubleComplementI1 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 doubleComplementE1 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 doubleComplementSub1 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 doubleComplementSub2 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 doubleComplementEq ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 complementTnotintersectT ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 complementImpComplementIntersect ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 complementSubsetComplementIntersect ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 complementInPowersetComplementIntersect ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 contraSubsetComplement ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 complementTcontraSubset ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 binunionTILcontra ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 binunionTIRcontra ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 inIntersectImpInUnion ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 inIntersectImpInUnion2 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 inIntersectImpInIntersectUnions ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 intersectInPowersetIntersectUnions ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 inComplementUnionImpNotIn1 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 inComplementUnionImpInComplement1 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 binunionTE ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 binunionTEcontra ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 demorgan2a1 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 complementUnionInPowersetComplement ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 demorgan2a2 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 demorgan1a ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 demorgan1b ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 demorgan1 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 demorgan2a ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 demorgan2b2 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 demorgan2b ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 demorgan2 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 woz13rule0 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 woz13rule1 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 woz13rule2 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 woz13rule3 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 woz13rule4 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 woz1_1 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 woz1_2 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 woz1_3 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 woz1_4 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 woz1_5 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 breln1all2 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 breln1SetBreln1 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 choice2fnsingleton ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 setOfPairsIsBReln1 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 breln1all1 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 subbreln1 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 eqbreln1 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 breln1invprop ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 breln1invI ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 breln1invE ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 breln1compprop ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 breln1compI ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 breln1compE ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 breln1compEex ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 breln1unionprop ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 breln1unionIL ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 breln1unionIR ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 breln1unionI ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 breln1unionE ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 breln1unionEcases ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 breln1unionCommutes ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 woz2Ex ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 woz2W ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 woz2A ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 woz2B ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 image1Ex ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 image1Ex1 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 image1Equiv ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 image1E ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 image1I ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 injFuncInInjFuncSet ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 injFuncSetFuncIn ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 injFuncSetFuncInj ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 surjFuncSetFuncIn ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 surjFuncSetFuncSurj ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 leftInvIsSurj ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 surjCantorThm ) =>
% 106.14/14.36 (
% 106.14/14.36 ![
% 106.14/14.36 A:$i]:
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 nonempty @
% 106.14/14.36 A ) =>
% 106.14/14.36 (
% 106.14/14.36 ?[
% 106.14/14.36 X:$i]:
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 in @ X @ A ) &
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 binintersect
% 106.14/14.36 @
% 106.14/14.36 X @ A ) =
% 106.14/14.36 (
% 106.14/14.36 emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 106.14/14.36 thf(zf_stmt_0, negated_conjecture,
% 106.14/14.36 (~( ( setextAx ) =>
% 106.14/14.36 ( ( emptysetAx ) =>
% 106.14/14.36 ( ( setadjoinAx ) =>
% 106.14/14.36 ( ( powersetAx ) =>
% 106.14/14.36 ( ( setunionAx ) =>
% 106.14/14.36 ( ( omega0Ax ) =>
% 106.14/14.36 ( ( omegaSAx ) =>
% 106.14/14.36 ( ( omegaIndAx ) =>
% 106.14/14.36 ( ( replAx ) =>
% 106.14/14.36 ( ( foundationAx ) =>
% 106.14/14.36 ( ( wellorderingAx ) =>
% 106.14/14.36 ( ( descrp ) =>
% 106.14/14.36 ( ( dsetconstrI ) =>
% 106.14/14.36 ( ( dsetconstrEL ) =>
% 106.14/14.36 ( ( dsetconstrER ) =>
% 106.14/14.36 ( ( exuE1 ) =>
% 106.14/14.36 ( ( prop2setE ) =>
% 106.14/14.36 ( ( emptysetE ) =>
% 106.14/14.36 ( ( emptysetimpfalse ) =>
% 106.14/14.36 ( ( notinemptyset ) =>
% 106.14/14.36 ( ( exuE3e ) =>
% 106.14/14.36 ( ( setext ) =>
% 106.14/14.36 ( ( emptyI ) =>
% 106.14/14.36 ( ( noeltsimpempty ) =>
% 106.14/14.36 ( ( setbeta ) =>
% 106.14/14.36 ( ( nonemptyE1 ) =>
% 106.14/14.36 ( ( nonemptyI ) =>
% 106.14/14.36 ( ( nonemptyI1 ) =>
% 106.14/14.36 ( ( setadjoinIL ) =>
% 106.14/14.36 ( ( emptyinunitempty ) =>
% 106.14/14.36 ( ( setadjoinIR ) =>
% 106.14/14.36 ( (
% 106.14/14.36 setadjoinE ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 setadjoinOr ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 setoftrueEq ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 powersetI ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 emptyinPowerset ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 emptyInPowerset ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 powersetE ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 setunionI ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 setunionE ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 subPowSU ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 exuE2 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 nonemptyImpWitness ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 uniqinunit ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 notinsingleton ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 eqinunit ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 singletonsswitch ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 upairsetE ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 upairsetIL ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 upairsetIR ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 emptyE1 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 vacuousDall ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 quantDeMorgan1 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 quantDeMorgan2 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 quantDeMorgan3 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 quantDeMorgan4 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 prop2setI ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 prop2set2propI ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 notdexE ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 notdallE ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 exuI1 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 exuI3 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 exuI2 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 inCongP ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 in__Cong ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 exuE3u ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 exu__Cong ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 emptyset__Cong ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 setadjoin__Cong ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 powerset__Cong ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 setunion__Cong ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 omega__Cong ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 exuEu ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 descr__Cong ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 dsetconstr__Cong ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 subsetI1 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 eqimpsubset2 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 eqimpsubset1 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 subsetI2 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 emptysetsubset ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 subsetE ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 subsetE2 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 notsubsetI ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 notequalI1 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 notequalI2 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 subsetRefl ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 subsetTrans ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 setadjoinSub ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 setadjoinSub2 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 subset2powerset ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 setextsub ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 subsetemptysetimpeq ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 powersetI1 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 powersetE1 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 inPowerset ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 powersetsubset ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 sepInPowerset ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 sepSubset ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 binunionIL ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 upairset2IR ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 binunionIR ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 binunionEcases ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 binunionE ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 binunionLsub ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 binunionRsub ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 binintersectI ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 binintersectSubset5 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 binintersectEL ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 binintersectLsub ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 binintersectSubset2 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 binintersectSubset3 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 binintersectER ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 disjointsetsI1 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 binintersectRsub ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 binintersectSubset4 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 binintersectSubset1 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 bs114d ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 setminusI ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 setminusEL ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 setminusER ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 setminusSubset2 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 setminusERneg ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 setminusELneg ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 setminusILneg ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 setminusIRneg ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 setminusLsub ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 setminusSubset1 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 symdiffE ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 symdiffI1 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 symdiffI2 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 symdiffIneg1 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 symdiffIneg2 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 secondinupair ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 setukpairIL ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 setukpairIR ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 kpairiskpair ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 kpairp ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 singletonsubset ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 singletoninpowerset ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 singletoninpowunion ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 upairset2E ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 upairsubunion ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 upairinpowunion ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 ubforcartprodlem1 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 ubforcartprodlem2 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 ubforcartprodlem3 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 cartprodpairin ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 cartprodmempair1 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 cartprodmempair ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 setunionE2 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 setunionsingleton1 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 setunionsingleton2 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 setunionsingleton ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 singletonprop ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 ex1E1 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 ex1I ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 ex1I2 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 singletonsuniq ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 setukpairinjL1 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 kfstsingleton ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 theprop ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 kfstpairEq ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 cartprodfstin ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 setukpairinjL2 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 setukpairinjL ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 setukpairinjR11 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 setukpairinjR12 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 setukpairinjR1 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 upairequniteq ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 setukpairinjR2 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 setukpairinjR ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 ksndsingleton ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 ksndpairEq ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 kpairsurjEq ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 cartprodsndin ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 cartprodpairmemEL ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 cartprodpairmemER ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 cartprodmempaircEq ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 cartprodfstpairEq ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 cartprodsndpairEq ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 cartprodpairsurjEq ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 dpsetconstrI ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 dpsetconstrSub ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 setOfPairsIsBReln ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 dpsetconstrERa ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 dpsetconstrEL1 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 dpsetconstrEL2 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 dpsetconstrER ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 funcImageSingleton ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 apProp ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 app ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 infuncsetfunc ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 ap2p ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 funcinfuncset ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 lamProp ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 lamp ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 lam2p ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 brelnall1 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 brelnall2 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 ex1E2 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 funcGraphProp1 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 funcGraphProp3 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 funcGraphProp2 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 funcextLem ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 funcGraphProp4 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 subbreln ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 eqbreln ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 funcext ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 funcext2 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 ap2apEq1 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 ap2apEq2 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 beta1 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 eta1 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 lam2lamEq ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 beta2 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 eta2 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 iffalseProp1 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 iffalseProp2 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 iftrueProp1 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 iftrueProp2 ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 ifSingleton ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 ifp ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 theeq ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 iftrue ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 iffalse ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 iftrueorfalse ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 binintersectT_lem ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 binunionT_lem ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 powersetT_lem ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 setminusT_lem ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 complementT_lem ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 setextT ) =>
% 106.14/14.36 (
% 106.14/14.36 (
% 106.14/14.36 subsetTI ) =>
% 106.14/14.36 (
% 106.14/14.37 (
% 106.14/14.37 powersetTI1 ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 powersetTE1 ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 complementTI1 ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 complementTE1 ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 binintersectTELcontra ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 binintersectTERcontra ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 contrasubsetT ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 contrasubsetT1 ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 contrasubsetT2 ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 contrasubsetT3 ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 doubleComplementI1 ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 doubleComplementE1 ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 doubleComplementSub1 ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 doubleComplementSub2 ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 doubleComplementEq ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 complementTnotintersectT ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 complementImpComplementIntersect ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 complementSubsetComplementIntersect ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 complementInPowersetComplementIntersect ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 contraSubsetComplement ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 complementTcontraSubset ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 binunionTILcontra ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 binunionTIRcontra ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 inIntersectImpInUnion ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 inIntersectImpInUnion2 ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 inIntersectImpInIntersectUnions ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 intersectInPowersetIntersectUnions ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 inComplementUnionImpNotIn1 ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 inComplementUnionImpInComplement1 ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 binunionTE ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 binunionTEcontra ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 demorgan2a1 ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 complementUnionInPowersetComplement ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 demorgan2a2 ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 demorgan1a ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 demorgan1b ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 demorgan1 ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 demorgan2a ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 demorgan2b2 ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 demorgan2b ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 demorgan2 ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 woz13rule0 ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 woz13rule1 ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 woz13rule2 ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 woz13rule3 ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 woz13rule4 ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 woz1_1 ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 woz1_2 ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 woz1_3 ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 woz1_4 ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 woz1_5 ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 breln1all2 ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 breln1SetBreln1 ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 choice2fnsingleton ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 setOfPairsIsBReln1 ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 breln1all1 ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 subbreln1 ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 eqbreln1 ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 breln1invprop ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 breln1invI ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 breln1invE ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 breln1compprop ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 breln1compI ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 breln1compE ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 breln1compEex ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 breln1unionprop ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 breln1unionIL ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 breln1unionIR ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 breln1unionI ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 breln1unionE ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 breln1unionEcases ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 breln1unionCommutes ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 woz2Ex ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 woz2W ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 woz2A ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 woz2B ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 image1Ex ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 image1Ex1 ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 image1Equiv ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 image1E ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 image1I ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 injFuncInInjFuncSet ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 injFuncSetFuncIn ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 injFuncSetFuncInj ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 surjFuncSetFuncIn ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 surjFuncSetFuncSurj ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 leftInvIsSurj ) =>
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 surjCantorThm ) =>
% 106.14/14.37 (
% 106.14/14.37 ![
% 106.14/14.37 A:$i]:
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 nonempty
% 106.14/14.37 @
% 106.14/14.37 A ) =>
% 106.14/14.37 (
% 106.14/14.37 ?[
% 106.14/14.37 X:$i]:
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 in @
% 106.14/14.37 X @ A ) &
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 binintersect
% 106.14/14.37 @
% 106.14/14.37 X @ A ) =
% 106.14/14.37 (
% 106.14/14.37 emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )),
% 106.14/14.37 inference('cnf.neg', [status(esa)], [foundation2])).
% 106.14/14.37 thf(zip_derived_cl0, plain,
% 106.14/14.37 (~ (((setextAx) =>
% 106.14/14.37 (((emptysetAx) =>
% 106.14/14.37 (((setadjoinAx) =>
% 106.14/14.37 (((powersetAx) =>
% 106.14/14.37 (((setunionAx) =>
% 106.14/14.37 (((omega0Ax) =>
% 106.14/14.37 (((omegaSAx) =>
% 106.14/14.37 (((omegaIndAx) =>
% 106.14/14.37 (((replAx) =>
% 106.14/14.37 (((foundationAx) =>
% 106.14/14.37 (((wellorderingAx) =>
% 106.14/14.37 (((descrp) =>
% 106.14/14.37 (((dsetconstrI) =>
% 106.14/14.37 (((dsetconstrEL) =>
% 106.14/14.37 (((dsetconstrER) =>
% 106.14/14.37 (((exuE1) =>
% 106.14/14.37 (((prop2setE) =>
% 106.14/14.37 (((emptysetE) =>
% 106.14/14.37 (((emptysetimpfalse) =>
% 106.14/14.37 (((notinemptyset) =>
% 106.14/14.37 (((exuE3e) =>
% 106.14/14.37 (((setext) =>
% 106.14/14.37 (((emptyI) =>
% 106.14/14.37 (((noeltsimpempty) =>
% 106.14/14.37 (((setbeta) =>
% 106.14/14.37 (((nonemptyE1) =>
% 106.14/14.37 (((nonemptyI) =>
% 106.14/14.37 (((nonemptyI1) =>
% 106.14/14.37 (((setadjoinIL) =>
% 106.14/14.37 (((emptyinunitempty) =>
% 106.14/14.37 ((
% 106.14/14.37 (setadjoinIR) =>
% 106.14/14.37 ((
% 106.14/14.37 (setadjoinE) =>
% 106.14/14.37 ((
% 106.14/14.37 (setadjoinOr) =>
% 106.14/14.37 ((
% 106.14/14.37 (setoftrueEq) =>
% 106.14/14.37 ((
% 106.14/14.37 (powersetI) =>
% 106.14/14.37 ((
% 106.14/14.37 (emptyinPowerset) =>
% 106.14/14.37 ((
% 106.14/14.37 (emptyInPowerset) =>
% 106.14/14.37 ((
% 106.14/14.37 (powersetE) =>
% 106.14/14.37 ((
% 106.14/14.37 (setunionI) =>
% 106.14/14.37 ((
% 106.14/14.37 (setunionE) =>
% 106.14/14.37 ((
% 106.14/14.37 (subPowSU) =>
% 106.14/14.37 ((
% 106.14/14.37 (exuE2) =>
% 106.14/14.37 ((
% 106.14/14.37 (nonemptyImpWitness) =>
% 106.14/14.37 ((
% 106.14/14.37 (uniqinunit) =>
% 106.14/14.37 ((
% 106.14/14.37 (notinsingleton) =>
% 106.14/14.37 ((
% 106.14/14.37 (eqinunit) =>
% 106.14/14.37 ((
% 106.14/14.37 (singletonsswitch) =>
% 106.14/14.37 ((
% 106.14/14.37 (upairsetE) =>
% 106.14/14.37 ((
% 106.14/14.37 (upairsetIL) =>
% 106.14/14.37 ((
% 106.14/14.37 (upairsetIR) =>
% 106.14/14.37 ((
% 106.14/14.37 (emptyE1) =>
% 106.14/14.37 ((
% 106.14/14.37 (vacuousDall) =>
% 106.14/14.37 ((
% 106.14/14.37 (quantDeMorgan1) =>
% 106.14/14.37 ((
% 106.14/14.37 (quantDeMorgan2) =>
% 106.14/14.37 ((
% 106.14/14.37 (quantDeMorgan3) =>
% 106.14/14.37 ((
% 106.14/14.37 (quantDeMorgan4) =>
% 106.14/14.37 ((
% 106.14/14.37 (prop2setI) =>
% 106.14/14.37 ((
% 106.14/14.37 (prop2set2propI) =>
% 106.14/14.37 ((
% 106.14/14.37 (notdexE) =>
% 106.14/14.37 ((
% 106.14/14.37 (notdallE) =>
% 106.14/14.37 ((
% 106.14/14.37 (exuI1) =>
% 106.14/14.37 ((
% 106.14/14.37 (exuI3) =>
% 106.14/14.37 ((
% 106.14/14.37 (exuI2) =>
% 106.14/14.37 ((
% 106.14/14.37 (inCongP) =>
% 106.14/14.37 ((
% 106.14/14.37 (in__Cong) =>
% 106.14/14.37 ((
% 106.14/14.37 (exuE3u) =>
% 106.14/14.37 ((
% 106.14/14.37 (exu__Cong) =>
% 106.14/14.37 ((
% 106.14/14.37 (emptyset__Cong) =>
% 106.14/14.37 ((
% 106.14/14.37 (setadjoin__Cong) =>
% 106.14/14.37 ((
% 106.14/14.37 (powerset__Cong) =>
% 106.14/14.37 ((
% 106.14/14.37 (setunion__Cong) =>
% 106.14/14.37 ((
% 106.14/14.37 (omega__Cong) =>
% 106.14/14.37 ((
% 106.14/14.37 (exuEu) =>
% 106.14/14.37 ((
% 106.14/14.37 (descr__Cong) =>
% 106.14/14.37 ((
% 106.14/14.37 (dsetconstr__Cong) =>
% 106.14/14.37 ((
% 106.14/14.37 (subsetI1) =>
% 106.14/14.37 ((
% 106.14/14.37 (eqimpsubset2) =>
% 106.14/14.37 ((
% 106.14/14.37 (eqimpsubset1) =>
% 106.14/14.37 ((
% 106.14/14.37 (subsetI2) =>
% 106.14/14.37 ((
% 106.14/14.37 (emptysetsubset) =>
% 106.14/14.37 ((
% 106.14/14.37 (subsetE) =>
% 106.14/14.37 ((
% 106.14/14.37 (subsetE2) =>
% 106.14/14.37 ((
% 106.14/14.37 (notsubsetI) =>
% 106.14/14.37 ((
% 106.14/14.37 (notequalI1) =>
% 106.14/14.37 ((
% 106.14/14.37 (notequalI2) =>
% 106.14/14.37 ((
% 106.14/14.37 (subsetRefl) =>
% 106.14/14.37 ((
% 106.14/14.37 (subsetTrans) =>
% 106.14/14.37 ((
% 106.14/14.37 (setadjoinSub) =>
% 106.14/14.37 ((
% 106.14/14.37 (setadjoinSub2) =>
% 106.14/14.37 ((
% 106.14/14.37 (subset2powerset) =>
% 106.14/14.37 ((
% 106.14/14.37 (setextsub) =>
% 106.14/14.37 ((
% 106.14/14.37 (subsetemptysetimpeq) =>
% 106.14/14.37 ((
% 106.14/14.37 (powersetI1) =>
% 106.14/14.37 ((
% 106.14/14.37 (powersetE1) =>
% 106.14/14.37 ((
% 106.14/14.37 (inPowerset) =>
% 106.14/14.37 ((
% 106.14/14.37 (powersetsubset) =>
% 106.14/14.37 ((
% 106.14/14.37 (sepInPowerset) =>
% 106.14/14.37 ((
% 106.14/14.37 (sepSubset) =>
% 106.14/14.37 ((
% 106.14/14.37 (binunionIL) =>
% 106.14/14.37 ((
% 106.14/14.37 (upairset2IR) =>
% 106.14/14.37 ((
% 106.14/14.37 (binunionIR) =>
% 106.14/14.37 ((
% 106.14/14.37 (binunionEcases) =>
% 106.14/14.37 ((
% 106.14/14.37 (binunionE) =>
% 106.14/14.37 ((
% 106.14/14.37 (binunionLsub) =>
% 106.14/14.37 ((
% 106.14/14.37 (binunionRsub) =>
% 106.14/14.37 ((
% 106.14/14.37 (binintersectI) =>
% 106.14/14.37 ((
% 106.14/14.37 (binintersectSubset5) =>
% 106.14/14.37 ((
% 106.14/14.37 (binintersectEL) =>
% 106.14/14.37 ((
% 106.14/14.37 (binintersectLsub) =>
% 106.14/14.37 ((
% 106.14/14.37 (binintersectSubset2) =>
% 106.14/14.37 ((
% 106.14/14.37 (binintersectSubset3) =>
% 106.14/14.37 ((
% 106.14/14.37 (binintersectER) =>
% 106.14/14.37 ((
% 106.14/14.37 (disjointsetsI1) =>
% 106.14/14.37 ((
% 106.14/14.37 (binintersectRsub) =>
% 106.14/14.37 ((
% 106.14/14.37 (binintersectSubset4) =>
% 106.14/14.37 ((
% 106.14/14.37 (binintersectSubset1) =>
% 106.14/14.37 ((
% 106.14/14.37 (bs114d) =>
% 106.14/14.37 ((
% 106.14/14.37 (setminusI) =>
% 106.14/14.37 ((
% 106.14/14.37 (setminusEL) =>
% 106.14/14.37 ((
% 106.14/14.37 (setminusER) =>
% 106.14/14.37 ((
% 106.14/14.37 (setminusSubset2) =>
% 106.14/14.37 ((
% 106.14/14.37 (setminusERneg) =>
% 106.14/14.37 ((
% 106.14/14.37 (setminusELneg) =>
% 106.14/14.37 ((
% 106.14/14.37 (setminusILneg) =>
% 106.14/14.37 ((
% 106.14/14.37 (setminusIRneg) =>
% 106.14/14.37 ((
% 106.14/14.37 (setminusLsub) =>
% 106.14/14.37 ((
% 106.14/14.37 (setminusSubset1) =>
% 106.14/14.37 ((
% 106.14/14.37 (symdiffE) =>
% 106.14/14.37 ((
% 106.14/14.37 (symdiffI1) =>
% 106.14/14.37 ((
% 106.14/14.37 (symdiffI2) =>
% 106.14/14.37 ((
% 106.14/14.37 (symdiffIneg1) =>
% 106.14/14.37 ((
% 106.14/14.37 (symdiffIneg2) =>
% 106.14/14.37 ((
% 106.14/14.37 (secondinupair) =>
% 106.14/14.37 ((
% 106.14/14.37 (setukpairIL) =>
% 106.14/14.37 ((
% 106.14/14.37 (setukpairIR) =>
% 106.14/14.37 ((
% 106.14/14.37 (kpairiskpair) =>
% 106.14/14.37 ((
% 106.14/14.37 (kpairp) =>
% 106.14/14.37 ((
% 106.14/14.37 (singletonsubset) =>
% 106.14/14.37 ((
% 106.14/14.37 (singletoninpowerset) =>
% 106.14/14.37 ((
% 106.14/14.37 (singletoninpowunion) =>
% 106.14/14.37 ((
% 106.14/14.37 (upairset2E) =>
% 106.14/14.37 ((
% 106.14/14.37 (upairsubunion) =>
% 106.14/14.37 ((
% 106.14/14.37 (upairinpowunion) =>
% 106.14/14.37 ((
% 106.14/14.37 (ubforcartprodlem1) =>
% 106.14/14.37 ((
% 106.14/14.37 (ubforcartprodlem2) =>
% 106.14/14.37 ((
% 106.14/14.37 (ubforcartprodlem3) =>
% 106.14/14.37 ((
% 106.14/14.37 (cartprodpairin) =>
% 106.14/14.37 ((
% 106.14/14.37 (cartprodmempair1) =>
% 106.14/14.37 ((
% 106.14/14.37 (cartprodmempair) =>
% 106.14/14.37 ((
% 106.14/14.37 (setunionE2) =>
% 106.14/14.37 ((
% 106.14/14.37 (setunionsingleton1) =>
% 106.14/14.37 ((
% 106.14/14.37 (setunionsingleton2) =>
% 106.14/14.37 ((
% 106.14/14.37 (setunionsingleton) =>
% 106.14/14.37 ((
% 106.14/14.37 (singletonprop) =>
% 106.14/14.37 ((
% 106.14/14.37 (ex1E1) =>
% 106.14/14.37 ((
% 106.14/14.37 (ex1I) =>
% 106.14/14.37 ((
% 106.14/14.37 (ex1I2) =>
% 106.14/14.37 ((
% 106.14/14.37 (singletonsuniq) =>
% 106.14/14.37 ((
% 106.14/14.37 (setukpairinjL1) =>
% 106.14/14.37 ((
% 106.14/14.37 (kfstsingleton) =>
% 106.14/14.37 ((
% 106.14/14.37 (theprop) =>
% 106.14/14.37 ((
% 106.14/14.37 (kfstpairEq) =>
% 106.14/14.37 ((
% 106.14/14.37 (cartprodfstin) =>
% 106.14/14.37 ((
% 106.14/14.37 (setukpairinjL2) =>
% 106.14/14.37 ((
% 106.14/14.37 (setukpairinjL) =>
% 106.14/14.37 ((
% 106.14/14.37 (setukpairinjR11) =>
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% 106.14/14.37 (setminusLsub) =>
% 106.14/14.37 ((
% 106.14/14.37 (setminusSubset1) =>
% 106.14/14.37 ((
% 106.14/14.37 (symdiffE) =>
% 106.14/14.37 ((
% 106.14/14.37 (symdiffI1) =>
% 106.14/14.37 ((
% 106.14/14.37 (symdiffI2) =>
% 106.14/14.37 ((
% 106.14/14.37 (symdiffIneg1) =>
% 106.14/14.37 ((
% 106.14/14.37 (symdiffIneg2) =>
% 106.14/14.37 ((
% 106.14/14.37 (secondinupair) =>
% 106.14/14.37 ((
% 106.14/14.37 (setukpairIL) =>
% 106.14/14.37 ((
% 106.14/14.37 (setukpairIR) =>
% 106.14/14.37 ((
% 106.14/14.37 (kpairiskpair) =>
% 106.14/14.37 ((
% 106.14/14.37 (kpairp) =>
% 106.14/14.37 ((
% 106.14/14.37 (singletonsubset) =>
% 106.14/14.37 ((
% 106.14/14.37 (singletoninpowerset) =>
% 106.14/14.37 ((
% 106.14/14.37 (singletoninpowunion) =>
% 106.14/14.37 ((
% 106.14/14.37 (upairset2E) =>
% 106.14/14.37 ((
% 106.14/14.37 (upairsubunion) =>
% 106.14/14.37 ((
% 106.14/14.37 (upairinpowunion) =>
% 106.14/14.37 ((
% 106.14/14.37 (ubforcartprodlem1) =>
% 106.14/14.37 ((
% 106.14/14.37 (ubforcartprodlem2) =>
% 106.14/14.37 ((
% 106.14/14.37 (ubforcartprodlem3) =>
% 106.14/14.37 ((
% 106.14/14.37 (cartprodpairin) =>
% 106.14/14.37 ((
% 106.14/14.37 (cartprodmempair1) =>
% 106.14/14.37 ((
% 106.14/14.37 (cartprodmempair) =>
% 106.14/14.37 ((
% 106.14/14.37 (setunionE2) =>
% 106.14/14.37 ((
% 106.14/14.37 (setunionsingleton1) =>
% 106.14/14.37 ((
% 106.14/14.37 (setunionsingleton2) =>
% 106.14/14.37 ((
% 106.14/14.37 (setunionsingleton) =>
% 106.14/14.37 ((
% 106.14/14.37 (singletonprop) =>
% 106.14/14.37 ((
% 106.14/14.37 (ex1E1) =>
% 106.14/14.37 ((
% 106.14/14.37 (ex1I) =>
% 106.14/14.37 ((
% 106.14/14.37 (ex1I2) =>
% 106.14/14.37 ((
% 106.14/14.37 (singletonsuniq) =>
% 106.14/14.37 ((
% 106.14/14.37 (setukpairinjL1) =>
% 106.14/14.37 ((
% 106.14/14.37 (kfstsingleton) =>
% 106.14/14.37 ((
% 106.14/14.37 (theprop) =>
% 106.14/14.37 ((
% 106.14/14.37 (kfstpairEq) =>
% 106.14/14.37 ((
% 106.14/14.37 (cartprodfstin) =>
% 106.14/14.37 ((
% 106.14/14.37 (setukpairinjL2) =>
% 106.14/14.37 ((
% 106.14/14.37 (setukpairinjL) =>
% 106.14/14.37 ((
% 106.14/14.37 (setukpairinjR11) =>
% 106.14/14.37 ((
% 106.14/14.37 (setukpairinjR12) =>
% 106.14/14.37 ((
% 106.14/14.37 (setukpairinjR1) =>
% 106.14/14.37 ((
% 106.14/14.37 (upairequniteq) =>
% 106.14/14.37 ((
% 106.14/14.37 (setukpairinjR2) =>
% 106.14/14.37 ((
% 106.14/14.37 (setukpairinjR) =>
% 106.14/14.37 ((
% 106.14/14.37 (ksndsingleton) =>
% 106.14/14.37 ((
% 106.14/14.37 (ksndpairEq) =>
% 106.14/14.37 ((
% 106.14/14.37 (kpairsurjEq) =>
% 106.14/14.37 ((
% 106.14/14.37 (cartprodsndin) =>
% 106.14/14.37 ((
% 106.14/14.37 (cartprodpairmemEL) =>
% 106.14/14.37 ((
% 106.14/14.37 (cartprodpairmemER) =>
% 106.14/14.37 ((
% 106.14/14.37 (cartprodmempaircEq) =>
% 106.14/14.37 ((
% 106.14/14.37 (cartprodfstpairEq) =>
% 106.14/14.37 ((
% 106.14/14.37 (cartprodsndpairEq) =>
% 106.14/14.37 ((
% 106.14/14.37 (cartprodpairsurjEq) =>
% 106.14/14.37 ((
% 106.14/14.37 (dpsetconstrI) =>
% 106.14/14.37 ((
% 106.14/14.37 (dpsetconstrSub) =>
% 106.14/14.37 ((
% 106.14/14.37 (setOfPairsIsBReln) =>
% 106.14/14.37 ((
% 106.14/14.37 (dpsetconstrERa) =>
% 106.14/14.37 ((
% 106.14/14.37 (dpsetconstrEL1) =>
% 106.14/14.37 ((
% 106.14/14.37 (dpsetconstrEL2) =>
% 106.14/14.37 ((
% 106.14/14.37 (dpsetconstrER) =>
% 106.14/14.37 ((
% 106.14/14.37 (funcImageSingleton) =>
% 106.14/14.37 ((
% 106.14/14.37 (apProp) =>
% 106.14/14.37 ((
% 106.14/14.37 (app) =>
% 106.14/14.37 ((
% 106.14/14.37 (infuncsetfunc) =>
% 106.14/14.37 ((
% 106.14/14.37 (ap2p) =>
% 106.14/14.37 ((
% 106.14/14.37 (funcinfuncset) =>
% 106.14/14.37 ((
% 106.14/14.37 (lamProp) =>
% 106.14/14.37 ((
% 106.14/14.37 (lamp) =>
% 106.14/14.37 ((
% 106.14/14.37 (lam2p) =>
% 106.14/14.37 ((
% 106.14/14.37 (brelnall1) =>
% 106.14/14.37 ((
% 106.14/14.37 (brelnall2) =>
% 106.14/14.37 ((
% 106.14/14.37 (ex1E2) =>
% 106.14/14.37 ((
% 106.14/14.37 (funcGraphProp1) =>
% 106.14/14.37 ((
% 106.14/14.37 (funcGraphProp3) =>
% 106.14/14.37 ((
% 106.14/14.37 (funcGraphProp2) =>
% 106.14/14.37 ((
% 106.14/14.37 (funcextLem) =>
% 106.14/14.37 ((
% 106.14/14.37 (funcGraphProp4) =>
% 106.14/14.37 ((
% 106.14/14.37 (subbreln) =>
% 106.14/14.37 ((
% 106.14/14.37 (eqbreln) =>
% 106.14/14.37 ((
% 106.14/14.37 (funcext) =>
% 106.14/14.37 ((
% 106.14/14.37 (funcext2) =>
% 106.14/14.37 ((
% 106.14/14.37 (ap2apEq1) =>
% 106.14/14.37 ((
% 106.14/14.37 (ap2apEq2) =>
% 106.14/14.37 ((
% 106.14/14.37 (beta1) =>
% 106.14/14.37 ((
% 106.14/14.37 (eta1) =>
% 106.14/14.37 ((
% 106.14/14.37 (lam2lamEq) =>
% 106.14/14.37 ((
% 106.14/14.37 (beta2) =>
% 106.14/14.37 ((
% 106.14/14.37 (eta2) =>
% 106.14/14.37 ((
% 106.14/14.37 (iffalseProp1) =>
% 106.14/14.37 ((
% 106.14/14.37 (iffalseProp2) =>
% 106.14/14.37 ((
% 106.14/14.37 (iftrueProp1) =>
% 106.14/14.37 ((
% 106.14/14.37 (iftrueProp2) =>
% 106.14/14.37 ((
% 106.14/14.37 (ifSingleton) =>
% 106.14/14.37 ((
% 106.14/14.37 (ifp) =>
% 106.14/14.37 ((
% 106.14/14.37 (theeq) =>
% 106.14/14.37 ((
% 106.14/14.37 (iftrue) =>
% 106.14/14.37 ((
% 106.14/14.37 (iffalse) =>
% 106.14/14.37 ((
% 106.14/14.37 (iftrueorfalse) =>
% 106.14/14.37 ((
% 106.14/14.37 (binintersectT_lem) =>
% 106.14/14.37 ((
% 106.14/14.37 (binunionT_lem) =>
% 106.14/14.37 ((
% 106.14/14.37 (powersetT_lem) =>
% 106.14/14.37 ((
% 106.14/14.37 (setminusT_lem) =>
% 106.14/14.37 ((
% 106.14/14.37 (complementT_lem) =>
% 106.14/14.37 ((
% 106.14/14.37 (setextT) =>
% 106.14/14.37 ((
% 106.14/14.37 (subsetTI) =>
% 106.14/14.37 ((
% 106.14/14.37 (powersetTI1) =>
% 106.14/14.37 ((
% 106.14/14.37 (powersetTE1) =>
% 106.14/14.37 ((
% 106.14/14.37 (complementTI1) =>
% 106.14/14.37 ((
% 106.14/14.37 (complementTE1) =>
% 106.14/14.37 ((
% 106.14/14.37 (binintersectTELcontra) =>
% 106.14/14.37 ((
% 106.14/14.37 (binintersectTERcontra) =>
% 106.14/14.37 ((
% 106.14/14.37 (contrasubsetT) =>
% 106.14/14.37 ((
% 106.14/14.37 (contrasubsetT1) =>
% 106.14/14.37 ((
% 106.14/14.37 (contrasubsetT2) =>
% 106.14/14.37 ((
% 106.14/14.37 (contrasubsetT3) =>
% 106.14/14.37 ((
% 106.14/14.37 (doubleComplementI1) =>
% 106.14/14.37 ((
% 106.14/14.37 (doubleComplementE1) =>
% 106.14/14.37 ((
% 106.14/14.37 (doubleComplementSub1) =>
% 106.14/14.37 ((
% 106.14/14.37 (doubleComplementSub2) =>
% 106.14/14.37 ((
% 106.14/14.37 (doubleComplementEq) =>
% 106.14/14.37 ((
% 106.14/14.37 (complementTnotintersectT) =>
% 106.14/14.37 ((
% 106.14/14.37 (complementImpComplementIntersect) =>
% 106.14/14.37 ((
% 106.14/14.37 (complementSubsetComplementIntersect) =>
% 106.14/14.37 ((
% 106.14/14.37 (complementInPowersetComplementIntersect) =>
% 106.14/14.37 ((
% 106.14/14.37 (contraSubsetComplement) =>
% 106.14/14.37 ((
% 106.14/14.37 (complementTcontraSubset) =>
% 106.14/14.37 ((
% 106.14/14.37 (binunionTILcontra) =>
% 106.14/14.37 ((
% 106.14/14.37 (binunionTIRcontra) =>
% 106.14/14.37 ((
% 106.14/14.37 (inIntersectImpInUnion) =>
% 106.14/14.37 ((
% 106.14/14.37 (inIntersectImpInUnion2) =>
% 106.14/14.37 ((
% 106.14/14.37 (inIntersectImpInIntersectUnions) =>
% 106.14/14.37 ((
% 106.14/14.37 (intersectInPowersetIntersectUnions) =>
% 106.14/14.37 ((
% 106.14/14.37 (inComplementUnionImpNotIn1) =>
% 106.14/14.37 ((
% 106.14/14.37 (inComplementUnionImpInComplement1) =>
% 106.14/14.37 ((
% 106.14/14.37 (binunionTE) =>
% 106.14/14.37 ((
% 106.14/14.37 (binunionTEcontra) =>
% 106.14/14.37 ((
% 106.14/14.37 (demorgan2a1) =>
% 106.14/14.37 ((
% 106.14/14.37 (complementUnionInPowersetComplement) =>
% 106.14/14.37 ((
% 106.14/14.37 (demorgan2a2) =>
% 106.14/14.37 ((
% 106.14/14.37 (demorgan1a) =>
% 106.14/14.37 ((
% 106.14/14.37 (demorgan1b) =>
% 106.14/14.37 ((
% 106.14/14.37 (demorgan1) =>
% 106.14/14.37 ((
% 106.14/14.37 (demorgan2a) =>
% 106.14/14.37 ((
% 106.14/14.37 (demorgan2b2) =>
% 106.14/14.37 ((
% 106.14/14.37 (demorgan2b) =>
% 106.14/14.37 ((
% 106.14/14.37 (demorgan2) =>
% 106.14/14.37 ((
% 106.14/14.37 (woz13rule0) =>
% 106.14/14.37 ((
% 106.14/14.37 (woz13rule1) =>
% 106.14/14.37 ((
% 106.14/14.37 (woz13rule2) =>
% 106.14/14.37 ((
% 106.14/14.37 (woz13rule3) =>
% 106.14/14.37 ((
% 106.14/14.37 (woz13rule4) =>
% 106.14/14.37 ((
% 106.14/14.37 (woz1_1) =>
% 106.14/14.37 ((
% 106.14/14.37 (woz1_2) =>
% 106.14/14.37 ((
% 106.14/14.37 (woz1_3) =>
% 106.14/14.37 ((
% 106.14/14.37 (woz1_4) =>
% 106.14/14.37 ((
% 106.14/14.37 (woz1_5) =>
% 106.14/14.37 ((
% 106.14/14.37 (breln1all2) =>
% 106.14/14.37 ((
% 106.14/14.37 (breln1SetBreln1) =>
% 106.14/14.37 ((
% 106.14/14.37 (choice2fnsingleton) =>
% 106.14/14.37 ((
% 106.14/14.37 (setOfPairsIsBReln1) =>
% 106.14/14.37 ((
% 106.14/14.37 (breln1all1) =>
% 106.14/14.37 ((
% 106.14/14.37 (subbreln1) =>
% 106.14/14.37 ((
% 106.14/14.37 (eqbreln1) =>
% 106.14/14.37 ((
% 106.14/14.37 (breln1invprop) =>
% 106.14/14.37 ((
% 106.14/14.37 (breln1invI) =>
% 106.14/14.37 ((
% 106.14/14.37 (breln1invE) =>
% 106.14/14.37 ((
% 106.14/14.37 (breln1compprop) =>
% 106.14/14.37 ((
% 106.14/14.37 (breln1compI) =>
% 106.14/14.37 ((
% 106.14/14.37 (breln1compE) =>
% 106.14/14.37 ((
% 106.14/14.37 (breln1compEex) =>
% 106.14/14.37 ((
% 106.14/14.37 (breln1unionprop) =>
% 106.14/14.37 ((
% 106.14/14.37 (breln1unionIL) =>
% 106.14/14.37 ((
% 106.14/14.37 (breln1unionIR) =>
% 106.14/14.37 ((
% 106.14/14.37 (breln1unionI) =>
% 106.14/14.37 ((
% 106.14/14.37 (breln1unionE) =>
% 106.14/14.37 ((
% 106.14/14.37 (breln1unionEcases) =>
% 106.14/14.37 ((
% 106.14/14.37 (breln1unionCommutes) =>
% 106.14/14.37 ((
% 106.14/14.37 (woz2Ex) =>
% 106.14/14.37 ((
% 106.14/14.37 (woz2W) =>
% 106.14/14.37 ((
% 106.14/14.37 (woz2A) =>
% 106.14/14.37 ((
% 106.14/14.37 (woz2B) =>
% 106.14/14.37 ((
% 106.14/14.37 (image1Ex) =>
% 106.14/14.37 ((
% 106.14/14.37 (image1Ex1) =>
% 106.14/14.37 ((
% 106.14/14.37 (image1Equiv) =>
% 106.14/14.37 ((
% 106.14/14.37 (image1E) =>
% 106.14/14.37 ((
% 106.14/14.37 (image1I) =>
% 106.14/14.37 ((
% 106.14/14.37 (injFuncInInjFuncSet) =>
% 106.14/14.37 ((
% 106.14/14.37 (injFuncSetFuncIn) =>
% 106.14/14.37 ((
% 106.14/14.37 (injFuncSetFuncInj) =>
% 106.14/14.37 ((
% 106.14/14.37 (surjFuncSetFuncIn) =>
% 106.14/14.37 ((
% 106.14/14.37 (surjFuncSetFuncSurj) =>
% 106.14/14.37 ((
% 106.14/14.37 (leftInvIsSurj) =>
% 106.14/14.37 ((
% 106.14/14.37 (surjCantorThm) =>
% 106.14/14.37 ((
% 106.14/14.37 (!!) @ (
% 106.14/14.37 (('#S') @ (
% 106.14/14.37 (
% 106.14/14.37 ('#B') @ (
% 106.14/14.37 =>) @
% 106.14/14.37 nonempty)) @
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 ('#B') @ (
% 106.14/14.37 ??) @
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 ('#S') @ (
% 106.14/14.37 (
% 106.14/14.37 ('#B') @ (
% 106.14/14.37 '#S') @
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 ('#B') @ (
% 106.14/14.37 (
% 106.14/14.37 ('#B') @ (
% 106.14/14.37 &))) @
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 ('#C') @ in)))))) @
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 ('#C') @ (
% 106.14/14.37 (
% 106.14/14.37 ('#B') @ (
% 106.14/14.37 '#C') @
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 ('#B') @ (
% 106.14/14.37 (
% 106.14/14.37 ('#B') @ (
% 106.14/14.37 =))) @
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 ('#C') @ binintersect)))))) @
% 106.14/14.37 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.14/14.37 inference('lams2combs', [status(thm)], [zip_derived_cl0])).
% 106.14/14.37 thf(omega0Ax, axiom,(( omega0Ax ) = ((in @ emptyset @ omega)))).
% 106.14/14.37 thf('0', plain, (( omega0Ax ) = ( in @ emptyset @ omega )),
% 106.14/14.37 define([status(thm)])).
% 106.14/14.37 thf(emptyinunitempty, axiom,(( emptyinunitempty ) =
% 106.14/14.37 ((in @ emptyset @ (setadjoin @ emptyset @ emptyset))))).
% 106.14/14.37 thf('1', plain,
% 106.14/14.37 (( emptyinunitempty ) =
% 106.14/14.37 ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )),
% 106.14/14.37 define([status(thm)])).
% 106.14/14.37 thf(emptyset__Cong, axiom,(( emptyset__Cong ) =
% 106.14/14.37 ((((emptyset) = (emptyset)))))).
% 106.14/14.37 thf('2', plain, (( emptyset__Cong ) = ( ( emptyset ) = ( emptyset ) )),
% 106.14/14.37 define([status(thm)])).
% 106.14/14.37 thf(omega__Cong, axiom,(( omega__Cong ) = ((((omega) = (omega)))))).
% 106.14/14.37 thf('3', plain, (( omega__Cong ) = ( ( omega ) = ( omega ) )),
% 106.14/14.37 define([status(thm)])).
% 106.14/14.37 thf(zip_derived_cl2, plain,
% 106.14/14.37 (~ (((setextAx) =>
% 106.14/14.37 (((emptysetAx) =>
% 106.14/14.37 (((setadjoinAx) =>
% 106.14/14.37 (((powersetAx) =>
% 106.14/14.37 (((setunionAx) =>
% 106.14/14.37 (((in @ emptyset @ omega) =>
% 106.14/14.37 (((omegaSAx) =>
% 106.14/14.37 (((omegaIndAx) =>
% 106.14/14.37 (((replAx) =>
% 106.14/14.37 (((foundationAx) =>
% 106.14/14.37 (((wellorderingAx) =>
% 106.14/14.37 (((descrp) =>
% 106.14/14.37 (((dsetconstrI) =>
% 106.14/14.37 (((dsetconstrEL) =>
% 106.14/14.37 (((dsetconstrER) =>
% 106.14/14.37 (((exuE1) =>
% 106.14/14.37 (((prop2setE) =>
% 106.14/14.37 (((emptysetE) =>
% 106.14/14.37 (((emptysetimpfalse) =>
% 106.14/14.37 (((notinemptyset) =>
% 106.14/14.37 (((exuE3e) =>
% 106.14/14.37 (((setext) =>
% 106.14/14.37 (((emptyI) =>
% 106.14/14.37 (((noeltsimpempty) =>
% 106.14/14.37 (((setbeta) =>
% 106.14/14.37 (((nonemptyE1) =>
% 106.14/14.37 (((nonemptyI) =>
% 106.14/14.37 (((nonemptyI1) =>
% 106.14/14.37 (((setadjoinIL) =>
% 106.14/14.37 (((in @
% 106.14/14.37 emptyset @
% 106.14/14.37 (setadjoin @
% 106.14/14.37 emptyset @
% 106.14/14.37 emptyset)) =>
% 106.14/14.37 ((
% 106.14/14.37 (setadjoinIR) =>
% 106.14/14.37 ((
% 106.14/14.37 (setadjoinE) =>
% 106.14/14.37 ((
% 106.14/14.37 (setadjoinOr) =>
% 106.14/14.37 ((
% 106.14/14.37 (setoftrueEq) =>
% 106.14/14.37 ((
% 106.14/14.37 (powersetI) =>
% 106.14/14.37 ((
% 106.14/14.37 (emptyinPowerset) =>
% 106.14/14.37 ((
% 106.14/14.37 (emptyInPowerset) =>
% 106.14/14.37 ((
% 106.14/14.37 (powersetE) =>
% 106.14/14.37 ((
% 106.14/14.37 (setunionI) =>
% 106.14/14.37 ((
% 106.14/14.37 (setunionE) =>
% 106.14/14.37 ((
% 106.14/14.37 (subPowSU) =>
% 106.14/14.37 ((
% 106.14/14.37 (exuE2) =>
% 106.14/14.37 ((
% 106.14/14.37 (nonemptyImpWitness) =>
% 106.14/14.37 ((
% 106.14/14.37 (uniqinunit) =>
% 106.14/14.37 ((
% 106.14/14.37 (notinsingleton) =>
% 106.14/14.37 ((
% 106.14/14.37 (eqinunit) =>
% 106.14/14.37 ((
% 106.14/14.37 (singletonsswitch) =>
% 106.14/14.37 ((
% 106.14/14.37 (upairsetE) =>
% 106.14/14.37 ((
% 106.14/14.37 (upairsetIL) =>
% 106.14/14.37 ((
% 106.14/14.37 (upairsetIR) =>
% 106.14/14.37 ((
% 106.14/14.37 (emptyE1) =>
% 106.14/14.37 ((
% 106.14/14.37 (vacuousDall) =>
% 106.14/14.37 ((
% 106.14/14.37 (quantDeMorgan1) =>
% 106.14/14.37 ((
% 106.14/14.37 (quantDeMorgan2) =>
% 106.14/14.37 ((
% 106.14/14.37 (quantDeMorgan3) =>
% 106.14/14.37 ((
% 106.14/14.37 (quantDeMorgan4) =>
% 106.14/14.37 ((
% 106.14/14.37 (prop2setI) =>
% 106.14/14.37 ((
% 106.14/14.37 (prop2set2propI) =>
% 106.14/14.37 ((
% 106.14/14.37 (notdexE) =>
% 106.14/14.37 ((
% 106.14/14.37 (notdallE) =>
% 106.14/14.37 ((
% 106.14/14.37 (exuI1) =>
% 106.14/14.37 ((
% 106.14/14.37 (exuI3) =>
% 106.14/14.37 ((
% 106.14/14.37 (exuI2) =>
% 106.14/14.37 ((
% 106.14/14.37 (inCongP) =>
% 106.14/14.37 ((
% 106.14/14.37 (in__Cong) =>
% 106.14/14.37 ((
% 106.14/14.37 (exuE3u) =>
% 106.14/14.37 ((
% 106.14/14.37 (exu__Cong) =>
% 106.14/14.37 ((
% 106.14/14.37 ((
% 106.14/14.37 (emptyset) =
% 106.14/14.37 (emptyset))) =>
% 106.14/14.37 ((
% 106.14/14.37 (setadjoin__Cong) =>
% 106.14/14.37 ((
% 106.14/14.37 (powerset__Cong) =>
% 106.14/14.37 ((
% 106.14/14.37 (setunion__Cong) =>
% 106.14/14.37 ((
% 106.14/14.37 ((
% 106.14/14.37 (omega) =
% 106.14/14.37 (omega))) =>
% 106.14/14.37 ((
% 106.14/14.37 (exuEu) =>
% 106.14/14.37 ((
% 106.14/14.37 (descr__Cong) =>
% 106.14/14.37 ((
% 106.14/14.37 (dsetconstr__Cong) =>
% 106.14/14.37 ((
% 106.14/14.37 (subsetI1) =>
% 106.14/14.37 ((
% 106.14/14.37 (eqimpsubset2) =>
% 106.14/14.37 ((
% 106.14/14.37 (eqimpsubset1) =>
% 106.14/14.37 ((
% 106.14/14.37 (subsetI2) =>
% 106.14/14.37 ((
% 106.14/14.37 (emptysetsubset) =>
% 106.14/14.37 ((
% 106.14/14.37 (subsetE) =>
% 106.14/14.37 ((
% 106.14/14.37 (subsetE2) =>
% 106.14/14.37 ((
% 106.14/14.37 (notsubsetI) =>
% 106.14/14.37 ((
% 106.14/14.37 (notequalI1) =>
% 106.14/14.37 ((
% 106.14/14.37 (notequalI2) =>
% 106.14/14.37 ((
% 106.14/14.37 (subsetRefl) =>
% 106.14/14.37 ((
% 106.14/14.37 (subsetTrans) =>
% 106.14/14.37 ((
% 106.14/14.37 (setadjoinSub) =>
% 106.14/14.37 ((
% 106.14/14.37 (setadjoinSub2) =>
% 106.14/14.37 ((
% 106.14/14.37 (subset2powerset) =>
% 106.14/14.37 ((
% 106.14/14.37 (setextsub) =>
% 106.14/14.37 ((
% 106.14/14.37 (subsetemptysetimpeq) =>
% 106.14/14.37 ((
% 106.14/14.37 (powersetI1) =>
% 106.14/14.37 ((
% 106.14/14.37 (powersetE1) =>
% 106.14/14.37 ((
% 106.14/14.37 (inPowerset) =>
% 106.14/14.37 ((
% 106.14/14.37 (powersetsubset) =>
% 106.14/14.37 ((
% 106.14/14.37 (sepInPowerset) =>
% 106.14/14.37 ((
% 106.14/14.37 (sepSubset) =>
% 106.14/14.37 ((
% 106.14/14.37 (binunionIL) =>
% 106.14/14.37 ((
% 106.14/14.37 (upairset2IR) =>
% 106.14/14.37 ((
% 106.14/14.37 (binunionIR) =>
% 106.14/14.37 ((
% 106.14/14.37 (binunionEcases) =>
% 106.14/14.37 ((
% 106.14/14.37 (binunionE) =>
% 106.14/14.37 ((
% 106.14/14.37 (binunionLsub) =>
% 106.14/14.37 ((
% 106.14/14.37 (binunionRsub) =>
% 106.14/14.37 ((
% 106.14/14.37 (binintersectI) =>
% 106.14/14.37 ((
% 106.14/14.37 (binintersectSubset5) =>
% 106.14/14.37 ((
% 106.14/14.37 (binintersectEL) =>
% 106.14/14.37 ((
% 106.14/14.37 (binintersectLsub) =>
% 106.14/14.37 ((
% 106.14/14.37 (binintersectSubset2) =>
% 106.14/14.37 ((
% 106.14/14.37 (binintersectSubset3) =>
% 106.14/14.37 ((
% 106.14/14.37 (binintersectER) =>
% 106.14/14.37 ((
% 106.14/14.37 (disjointsetsI1) =>
% 106.14/14.37 ((
% 106.14/14.37 (binintersectRsub) =>
% 106.14/14.37 ((
% 106.14/14.37 (binintersectSubset4) =>
% 106.14/14.37 ((
% 106.14/14.37 (binintersectSubset1) =>
% 106.14/14.37 ((
% 106.14/14.37 (bs114d) =>
% 106.14/14.37 ((
% 106.14/14.37 (setminusI) =>
% 106.14/14.37 ((
% 106.14/14.37 (setminusEL) =>
% 106.14/14.37 ((
% 106.14/14.37 (setminusER) =>
% 106.14/14.37 ((
% 106.14/14.37 (setminusSubset2) =>
% 106.14/14.37 ((
% 106.14/14.37 (setminusERneg) =>
% 106.14/14.37 ((
% 106.14/14.37 (setminusELneg) =>
% 106.14/14.37 ((
% 106.14/14.37 (setminusILneg) =>
% 106.14/14.37 ((
% 106.14/14.37 (setminusIRneg) =>
% 106.14/14.37 ((
% 106.14/14.37 (setminusLsub) =>
% 106.14/14.37 ((
% 106.14/14.37 (setminusSubset1) =>
% 106.14/14.37 ((
% 106.14/14.37 (symdiffE) =>
% 106.14/14.37 ((
% 106.14/14.37 (symdiffI1) =>
% 106.14/14.37 ((
% 106.14/14.37 (symdiffI2) =>
% 106.14/14.37 ((
% 106.14/14.37 (symdiffIneg1) =>
% 106.14/14.37 ((
% 106.14/14.37 (symdiffIneg2) =>
% 106.14/14.37 ((
% 106.14/14.37 (secondinupair) =>
% 106.14/14.37 ((
% 106.14/14.37 (setukpairIL) =>
% 106.14/14.37 ((
% 106.14/14.37 (setukpairIR) =>
% 106.14/14.37 ((
% 106.14/14.37 (kpairiskpair) =>
% 106.14/14.37 ((
% 106.14/14.37 (kpairp) =>
% 106.14/14.37 ((
% 106.14/14.37 (singletonsubset) =>
% 106.14/14.37 ((
% 106.14/14.37 (singletoninpowerset) =>
% 106.14/14.37 ((
% 106.14/14.37 (singletoninpowunion) =>
% 106.14/14.37 ((
% 106.14/14.37 (upairset2E) =>
% 106.14/14.37 ((
% 106.14/14.37 (upairsubunion) =>
% 106.14/14.37 ((
% 106.14/14.37 (upairinpowunion) =>
% 106.14/14.37 ((
% 106.14/14.37 (ubforcartprodlem1) =>
% 106.14/14.37 ((
% 106.14/14.37 (ubforcartprodlem2) =>
% 106.14/14.37 ((
% 106.14/14.37 (ubforcartprodlem3) =>
% 106.14/14.37 ((
% 106.14/14.37 (cartprodpairin) =>
% 106.14/14.37 ((
% 106.14/14.37 (cartprodmempair1) =>
% 106.14/14.37 ((
% 106.14/14.37 (cartprodmempair) =>
% 106.14/14.37 ((
% 106.14/14.37 (setunionE2) =>
% 106.14/14.37 ((
% 106.14/14.37 (setunionsingleton1) =>
% 106.14/14.37 ((
% 106.14/14.37 (setunionsingleton2) =>
% 106.14/14.37 ((
% 106.14/14.37 (setunionsingleton) =>
% 106.14/14.37 ((
% 106.14/14.37 (singletonprop) =>
% 106.14/14.37 ((
% 106.14/14.37 (ex1E1) =>
% 106.14/14.37 ((
% 106.14/14.37 (ex1I) =>
% 106.14/14.37 ((
% 106.14/14.37 (ex1I2) =>
% 106.14/14.37 ((
% 106.14/14.37 (singletonsuniq) =>
% 106.14/14.37 ((
% 106.14/14.37 (setukpairinjL1) =>
% 106.14/14.37 ((
% 106.14/14.37 (kfstsingleton) =>
% 106.14/14.37 ((
% 106.14/14.37 (theprop) =>
% 106.14/14.37 ((
% 106.14/14.37 (kfstpairEq) =>
% 106.14/14.37 ((
% 106.14/14.37 (cartprodfstin) =>
% 106.14/14.37 ((
% 106.14/14.37 (setukpairinjL2) =>
% 106.14/14.37 ((
% 106.14/14.37 (setukpairinjL) =>
% 106.14/14.37 ((
% 106.14/14.37 (setukpairinjR11) =>
% 106.14/14.37 ((
% 106.14/14.37 (setukpairinjR12) =>
% 106.14/14.37 ((
% 106.14/14.37 (setukpairinjR1) =>
% 106.14/14.37 ((
% 106.14/14.37 (upairequniteq) =>
% 106.14/14.37 ((
% 106.14/14.37 (setukpairinjR2) =>
% 106.14/14.37 ((
% 106.14/14.37 (setukpairinjR) =>
% 106.14/14.37 ((
% 106.14/14.37 (ksndsingleton) =>
% 106.14/14.37 ((
% 106.14/14.37 (ksndpairEq) =>
% 106.14/14.37 ((
% 106.14/14.37 (kpairsurjEq) =>
% 106.14/14.37 ((
% 106.14/14.37 (cartprodsndin) =>
% 106.14/14.37 ((
% 106.14/14.37 (cartprodpairmemEL) =>
% 106.14/14.37 ((
% 106.14/14.37 (cartprodpairmemER) =>
% 106.14/14.37 ((
% 106.14/14.37 (cartprodmempaircEq) =>
% 106.14/14.37 ((
% 106.14/14.37 (cartprodfstpairEq) =>
% 106.14/14.37 ((
% 106.14/14.37 (cartprodsndpairEq) =>
% 106.14/14.37 ((
% 106.14/14.37 (cartprodpairsurjEq) =>
% 106.14/14.37 ((
% 106.14/14.37 (dpsetconstrI) =>
% 106.14/14.37 ((
% 106.14/14.37 (dpsetconstrSub) =>
% 106.14/14.37 ((
% 106.14/14.37 (setOfPairsIsBReln) =>
% 106.14/14.37 ((
% 106.14/14.37 (dpsetconstrERa) =>
% 106.14/14.37 ((
% 106.14/14.37 (dpsetconstrEL1) =>
% 106.14/14.37 ((
% 106.14/14.37 (dpsetconstrEL2) =>
% 106.14/14.37 ((
% 106.14/14.37 (dpsetconstrER) =>
% 106.14/14.37 ((
% 106.14/14.37 (funcImageSingleton) =>
% 106.14/14.37 ((
% 106.14/14.37 (apProp) =>
% 106.14/14.37 ((
% 106.14/14.37 (app) =>
% 106.14/14.37 ((
% 106.14/14.37 (infuncsetfunc) =>
% 106.14/14.37 ((
% 106.14/14.37 (ap2p) =>
% 106.14/14.37 ((
% 106.14/14.37 (funcinfuncset) =>
% 106.14/14.37 ((
% 106.14/14.37 (lamProp) =>
% 106.14/14.37 ((
% 106.14/14.37 (lamp) =>
% 106.14/14.37 ((
% 106.14/14.37 (lam2p) =>
% 106.14/14.37 ((
% 106.14/14.37 (brelnall1) =>
% 106.14/14.37 ((
% 106.14/14.37 (brelnall2) =>
% 106.14/14.37 ((
% 106.14/14.37 (ex1E2) =>
% 106.14/14.37 ((
% 106.14/14.37 (funcGraphProp1) =>
% 106.14/14.37 ((
% 106.14/14.37 (funcGraphProp3) =>
% 106.14/14.37 ((
% 106.14/14.37 (funcGraphProp2) =>
% 106.14/14.37 ((
% 106.14/14.37 (funcextLem) =>
% 106.14/14.37 ((
% 106.14/14.37 (funcGraphProp4) =>
% 106.14/14.37 ((
% 106.14/14.37 (subbreln) =>
% 106.14/14.37 ((
% 106.14/14.37 (eqbreln) =>
% 106.14/14.37 ((
% 106.14/14.37 (funcext) =>
% 106.14/14.37 ((
% 106.14/14.37 (funcext2) =>
% 106.14/14.37 ((
% 106.14/14.37 (ap2apEq1) =>
% 106.14/14.37 ((
% 106.14/14.37 (ap2apEq2) =>
% 106.14/14.37 ((
% 106.14/14.37 (beta1) =>
% 106.14/14.37 ((
% 106.14/14.37 (eta1) =>
% 106.14/14.37 ((
% 106.14/14.37 (lam2lamEq) =>
% 106.14/14.37 ((
% 106.14/14.37 (beta2) =>
% 106.14/14.37 ((
% 106.14/14.37 (eta2) =>
% 106.14/14.37 ((
% 106.14/14.37 (iffalseProp1) =>
% 106.14/14.37 ((
% 106.14/14.37 (iffalseProp2) =>
% 106.14/14.37 ((
% 106.14/14.37 (iftrueProp1) =>
% 106.14/14.37 ((
% 106.14/14.37 (iftrueProp2) =>
% 106.14/14.37 ((
% 106.14/14.37 (ifSingleton) =>
% 106.14/14.37 ((
% 106.14/14.37 (ifp) =>
% 106.14/14.37 ((
% 106.14/14.37 (theeq) =>
% 106.14/14.37 ((
% 106.14/14.37 (iftrue) =>
% 106.14/14.37 ((
% 106.14/14.37 (iffalse) =>
% 106.14/14.37 ((
% 106.14/14.37 (iftrueorfalse) =>
% 106.14/14.37 ((
% 106.14/14.37 (binintersectT_lem) =>
% 106.14/14.37 ((
% 106.14/14.37 (binunionT_lem) =>
% 106.14/14.37 ((
% 106.14/14.37 (powersetT_lem) =>
% 106.14/14.37 ((
% 106.14/14.37 (setminusT_lem) =>
% 106.14/14.37 ((
% 106.14/14.37 (complementT_lem) =>
% 106.14/14.37 ((
% 106.14/14.37 (setextT) =>
% 106.14/14.37 ((
% 106.14/14.37 (subsetTI) =>
% 106.14/14.37 ((
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% 106.14/14.37 ((
% 106.14/14.37 (powersetTE1) =>
% 106.14/14.37 ((
% 106.14/14.37 (complementTI1) =>
% 106.14/14.37 ((
% 106.14/14.37 (complementTE1) =>
% 106.14/14.37 ((
% 106.14/14.37 (binintersectTELcontra) =>
% 106.14/14.37 ((
% 106.14/14.37 (binintersectTERcontra) =>
% 106.14/14.37 ((
% 106.14/14.37 (contrasubsetT) =>
% 106.14/14.37 ((
% 106.14/14.37 (contrasubsetT1) =>
% 106.14/14.37 ((
% 106.14/14.37 (contrasubsetT2) =>
% 106.14/14.37 ((
% 106.14/14.37 (contrasubsetT3) =>
% 106.14/14.37 ((
% 106.14/14.37 (doubleComplementI1) =>
% 106.14/14.37 ((
% 106.14/14.37 (doubleComplementE1) =>
% 106.14/14.37 ((
% 106.14/14.37 (doubleComplementSub1) =>
% 106.14/14.37 ((
% 106.14/14.37 (doubleComplementSub2) =>
% 106.14/14.37 ((
% 106.14/14.37 (doubleComplementEq) =>
% 106.14/14.37 ((
% 106.14/14.37 (complementTnotintersectT) =>
% 106.14/14.37 ((
% 106.14/14.37 (complementImpComplementIntersect) =>
% 106.14/14.37 ((
% 106.14/14.37 (complementSubsetComplementIntersect) =>
% 106.14/14.37 ((
% 106.14/14.37 (complementInPowersetComplementIntersect) =>
% 106.14/14.37 ((
% 106.14/14.37 (contraSubsetComplement) =>
% 106.14/14.37 ((
% 106.14/14.37 (complementTcontraSubset) =>
% 106.14/14.37 ((
% 106.14/14.37 (binunionTILcontra) =>
% 106.14/14.37 ((
% 106.14/14.37 (binunionTIRcontra) =>
% 106.14/14.37 ((
% 106.14/14.37 (inIntersectImpInUnion) =>
% 106.14/14.37 ((
% 106.14/14.37 (inIntersectImpInUnion2) =>
% 106.14/14.37 ((
% 106.14/14.37 (inIntersectImpInIntersectUnions) =>
% 106.14/14.37 ((
% 106.14/14.37 (intersectInPowersetIntersectUnions) =>
% 106.14/14.37 ((
% 106.14/14.37 (inComplementUnionImpNotIn1) =>
% 106.14/14.37 ((
% 106.14/14.37 (inComplementUnionImpInComplement1) =>
% 106.14/14.37 ((
% 106.14/14.37 (binunionTE) =>
% 106.14/14.37 ((
% 106.14/14.37 (binunionTEcontra) =>
% 106.14/14.37 ((
% 106.14/14.37 (demorgan2a1) =>
% 106.14/14.37 ((
% 106.14/14.37 (complementUnionInPowersetComplement) =>
% 106.14/14.37 ((
% 106.14/14.37 (demorgan2a2) =>
% 106.14/14.37 ((
% 106.14/14.37 (demorgan1a) =>
% 106.14/14.37 ((
% 106.14/14.37 (demorgan1b) =>
% 106.14/14.37 ((
% 106.14/14.37 (demorgan1) =>
% 106.14/14.37 ((
% 106.14/14.37 (demorgan2a) =>
% 106.14/14.37 ((
% 106.14/14.37 (demorgan2b2) =>
% 106.14/14.37 ((
% 106.14/14.37 (demorgan2b) =>
% 106.14/14.37 ((
% 106.14/14.37 (demorgan2) =>
% 106.14/14.37 ((
% 106.14/14.37 (woz13rule0) =>
% 106.14/14.37 ((
% 106.14/14.37 (woz13rule1) =>
% 106.14/14.37 ((
% 106.14/14.37 (woz13rule2) =>
% 106.14/14.37 ((
% 106.14/14.37 (woz13rule3) =>
% 106.14/14.37 ((
% 106.14/14.37 (woz13rule4) =>
% 106.14/14.37 ((
% 106.14/14.37 (woz1_1) =>
% 106.14/14.37 ((
% 106.14/14.37 (woz1_2) =>
% 106.14/14.37 ((
% 106.14/14.37 (woz1_3) =>
% 106.14/14.37 ((
% 106.14/14.37 (woz1_4) =>
% 106.14/14.37 ((
% 106.14/14.37 (woz1_5) =>
% 106.14/14.37 ((
% 106.14/14.37 (breln1all2) =>
% 106.14/14.37 ((
% 106.14/14.37 (breln1SetBreln1) =>
% 106.14/14.37 ((
% 106.14/14.37 (choice2fnsingleton) =>
% 106.14/14.37 ((
% 106.14/14.37 (setOfPairsIsBReln1) =>
% 106.14/14.37 ((
% 106.14/14.37 (breln1all1) =>
% 106.14/14.37 ((
% 106.14/14.37 (subbreln1) =>
% 106.14/14.37 ((
% 106.14/14.37 (eqbreln1) =>
% 106.14/14.37 ((
% 106.14/14.37 (breln1invprop) =>
% 106.14/14.37 ((
% 106.14/14.37 (breln1invI) =>
% 106.14/14.37 ((
% 106.14/14.37 (breln1invE) =>
% 106.14/14.37 ((
% 106.14/14.37 (breln1compprop) =>
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% 106.14/14.37 ((
% 106.14/14.37 (breln1compE) =>
% 106.14/14.37 ((
% 106.14/14.37 (breln1compEex) =>
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% 106.14/14.37 (breln1unionprop) =>
% 106.14/14.37 ((
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% 106.14/14.37 ((
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% 106.14/14.37 ((
% 106.14/14.37 (breln1unionI) =>
% 106.14/14.37 ((
% 106.14/14.37 (breln1unionE) =>
% 106.14/14.37 ((
% 106.14/14.37 (breln1unionEcases) =>
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% 106.14/14.37 (breln1unionCommutes) =>
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% 106.14/14.37 ((
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% 106.14/14.37 ((
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% 106.14/14.37 ((
% 106.14/14.37 (image1Equiv) =>
% 106.14/14.37 ((
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% 106.14/14.37 (image1I) =>
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% 106.14/14.37 ((
% 106.14/14.37 (injFuncSetFuncIn) =>
% 106.14/14.37 ((
% 106.14/14.37 (injFuncSetFuncInj) =>
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% 106.14/14.37 ((
% 106.14/14.37 (surjFuncSetFuncSurj) =>
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% 106.14/14.37 (leftInvIsSurj) =>
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% 106.14/14.37 ('#B') @ (
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% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 ('#C') @ binintersect)))))) @
% 106.14/14.37 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.14/14.37 inference('rw', [status(thm)], [zip_derived_cl1, '0', '1', '2', '3'])).
% 106.14/14.37 thf(zip_derived_cl3, plain,
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% 106.14/14.37 (((setbeta) =>
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% 106.14/14.37 ((
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% 106.14/14.37 ((
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% 106.14/14.37 ((
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% 106.14/14.37 ((
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% 106.14/14.37 ((
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% 106.14/14.37 ((
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% 106.14/14.37 ((
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% 106.14/14.37 ((
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% 106.14/14.37 ((
% 106.14/14.37 (exuEu) =>
% 106.14/14.37 ((
% 106.14/14.37 (descr__Cong) =>
% 106.14/14.37 ((
% 106.14/14.37 (dsetconstr__Cong) =>
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% 106.14/14.37 ((
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% 106.14/14.37 ((
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% 106.14/14.37 ((
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% 106.14/14.37 ((
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% 106.14/14.37 ((
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% 106.14/14.37 ((
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% 106.14/14.37 ((
% 106.14/14.37 (binunionEcases) =>
% 106.14/14.37 ((
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% 106.14/14.37 ((
% 106.14/14.37 (binunionLsub) =>
% 106.14/14.37 ((
% 106.14/14.37 (binunionRsub) =>
% 106.14/14.37 ((
% 106.14/14.37 (binintersectI) =>
% 106.14/14.37 ((
% 106.14/14.37 (binintersectSubset5) =>
% 106.14/14.37 ((
% 106.14/14.37 (binintersectEL) =>
% 106.14/14.37 ((
% 106.14/14.37 (binintersectLsub) =>
% 106.14/14.37 ((
% 106.14/14.37 (binintersectSubset2) =>
% 106.14/14.37 ((
% 106.14/14.37 (binintersectSubset3) =>
% 106.14/14.37 ((
% 106.14/14.37 (binintersectER) =>
% 106.14/14.37 ((
% 106.14/14.37 (disjointsetsI1) =>
% 106.14/14.37 ((
% 106.14/14.37 (binintersectRsub) =>
% 106.14/14.37 ((
% 106.14/14.37 (binintersectSubset4) =>
% 106.14/14.37 ((
% 106.14/14.37 (binintersectSubset1) =>
% 106.14/14.37 ((
% 106.14/14.37 (bs114d) =>
% 106.14/14.37 ((
% 106.14/14.37 (setminusI) =>
% 106.14/14.37 ((
% 106.14/14.37 (setminusEL) =>
% 106.14/14.37 ((
% 106.14/14.37 (setminusER) =>
% 106.14/14.37 ((
% 106.14/14.37 (setminusSubset2) =>
% 106.14/14.37 ((
% 106.14/14.37 (setminusERneg) =>
% 106.14/14.37 ((
% 106.14/14.37 (setminusELneg) =>
% 106.14/14.37 ((
% 106.14/14.37 (setminusILneg) =>
% 106.14/14.37 ((
% 106.14/14.37 (setminusIRneg) =>
% 106.14/14.37 ((
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% 106.14/14.37 ((
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% 106.14/14.37 ((
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% 106.14/14.37 ((
% 106.14/14.37 (symdiffIneg2) =>
% 106.14/14.37 ((
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% 106.14/14.37 ((
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% 106.14/14.37 ((
% 106.14/14.37 (singletoninpowerset) =>
% 106.14/14.37 ((
% 106.14/14.37 (singletoninpowunion) =>
% 106.14/14.37 ((
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% 106.14/14.37 ((
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% 106.14/14.37 ((
% 106.14/14.37 (upairinpowunion) =>
% 106.14/14.37 ((
% 106.14/14.37 (ubforcartprodlem1) =>
% 106.14/14.37 ((
% 106.14/14.37 (ubforcartprodlem2) =>
% 106.14/14.37 ((
% 106.14/14.37 (ubforcartprodlem3) =>
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% 106.14/14.37 (cartprodpairin) =>
% 106.14/14.37 ((
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% 106.14/14.37 ((
% 106.14/14.37 (cartprodmempair) =>
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% 106.14/14.37 (setunionE2) =>
% 106.14/14.37 ((
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% 106.14/14.37 ((
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% 106.14/14.37 (eqbreln1) =>
% 106.14/14.37 ((
% 106.14/14.37 (breln1invprop) =>
% 106.14/14.37 ((
% 106.14/14.37 (breln1invI) =>
% 106.14/14.37 ((
% 106.14/14.37 (breln1invE) =>
% 106.14/14.37 ((
% 106.14/14.37 (breln1compprop) =>
% 106.14/14.37 ((
% 106.14/14.37 (breln1compI) =>
% 106.14/14.37 ((
% 106.14/14.37 (breln1compE) =>
% 106.14/14.37 ((
% 106.14/14.37 (breln1compEex) =>
% 106.14/14.37 ((
% 106.14/14.37 (breln1unionprop) =>
% 106.14/14.37 ((
% 106.14/14.37 (breln1unionIL) =>
% 106.14/14.37 ((
% 106.14/14.37 (breln1unionIR) =>
% 106.14/14.37 ((
% 106.14/14.37 (breln1unionI) =>
% 106.14/14.37 ((
% 106.14/14.37 (breln1unionE) =>
% 106.14/14.37 ((
% 106.14/14.37 (breln1unionEcases) =>
% 106.14/14.37 ((
% 106.14/14.37 (breln1unionCommutes) =>
% 106.14/14.37 ((
% 106.14/14.37 (woz2Ex) =>
% 106.14/14.37 ((
% 106.14/14.37 (woz2W) =>
% 106.14/14.37 ((
% 106.14/14.37 (woz2A) =>
% 106.14/14.37 ((
% 106.14/14.37 (woz2B) =>
% 106.14/14.37 ((
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% 106.14/14.37 ((
% 106.14/14.37 (image1Ex1) =>
% 106.14/14.37 ((
% 106.14/14.37 (image1Equiv) =>
% 106.14/14.37 ((
% 106.14/14.37 (image1E) =>
% 106.14/14.37 ((
% 106.14/14.37 (image1I) =>
% 106.14/14.37 ((
% 106.14/14.37 (injFuncInInjFuncSet) =>
% 106.14/14.37 ((
% 106.14/14.37 (injFuncSetFuncIn) =>
% 106.14/14.37 ((
% 106.14/14.37 (injFuncSetFuncInj) =>
% 106.14/14.37 ((
% 106.14/14.37 (surjFuncSetFuncIn) =>
% 106.14/14.37 ((
% 106.14/14.37 (surjFuncSetFuncSurj) =>
% 106.14/14.37 ((
% 106.14/14.37 (leftInvIsSurj) =>
% 106.14/14.37 ((
% 106.14/14.37 (surjCantorThm) =>
% 106.14/14.37 ((
% 106.14/14.37 (!!) @ (
% 106.14/14.37 (('#S') @ (
% 106.14/14.37 (
% 106.14/14.37 ('#B') @ (
% 106.14/14.37 =>) @
% 106.14/14.37 nonempty)) @
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 ('#B') @ (
% 106.14/14.37 ??) @
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 ('#S') @ (
% 106.14/14.37 (
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% 106.14/14.37 '#S') @
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 ('#B') @ (
% 106.14/14.37 (
% 106.14/14.37 ('#B') @ (
% 106.14/14.37 &))) @
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 ('#C') @ in)))))) @
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 ('#C') @ (
% 106.14/14.37 (
% 106.14/14.37 ('#B') @ (
% 106.14/14.37 '#C') @
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 ('#B') @ (
% 106.14/14.37 (
% 106.14/14.37 ('#B') @ (
% 106.14/14.37 =))) @
% 106.14/14.37 (
% 106.14/14.37 (
% 106.14/14.37 ('#C') @ binintersect)))))) @
% 106.14/14.37 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.14/14.37 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl2])).
% 106.14/14.37 thf(zip_derived_cl5, plain,
% 106.14/14.37 (~ (((emptysetAx) =>
% 106.14/14.37 (((setadjoinAx) =>
% 106.14/14.37 (((powersetAx) =>
% 106.14/14.37 (((setunionAx) =>
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% 106.14/14.37 (((omegaIndAx) =>
% 106.14/14.37 (((replAx) =>
% 106.14/14.37 (((foundationAx) =>
% 106.14/14.37 (((wellorderingAx) =>
% 106.14/14.37 (((descrp) =>
% 106.14/14.37 (((dsetconstrI) =>
% 106.14/14.37 (((dsetconstrEL) =>
% 106.14/14.37 (((dsetconstrER) =>
% 106.14/14.37 (((exuE1) =>
% 106.14/14.37 (((prop2setE) =>
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% 106.14/14.37 (((emptyI) =>
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% 106.14/14.37 (((setbeta) =>
% 106.14/14.37 (((nonemptyE1) =>
% 106.14/14.37 (((nonemptyI) =>
% 106.14/14.37 (((nonemptyI1) =>
% 106.14/14.37 (((setadjoinIL) =>
% 106.14/14.37 (((in @
% 106.14/14.37 emptyset @
% 106.14/14.37 (setadjoin @
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% 106.14/14.37 ((
% 106.14/14.37 (setadjoinOr) =>
% 106.14/14.37 ((
% 106.14/14.37 (setoftrueEq) =>
% 106.14/14.37 ((
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% 106.14/14.37 ((
% 106.14/14.37 (emptyinPowerset) =>
% 106.14/14.37 ((
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% 106.14/14.37 ((
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% 106.14/14.37 ((
% 106.14/14.37 (exuE2) =>
% 106.14/14.37 ((
% 106.14/14.37 (nonemptyImpWitness) =>
% 106.14/14.37 ((
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% 106.14/14.37 ((
% 106.14/14.37 (notinsingleton) =>
% 106.14/14.37 ((
% 106.14/14.37 (eqinunit) =>
% 106.14/14.37 ((
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% 106.14/14.37 ((
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% 106.14/14.37 ((
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% 106.14/14.37 ((
% 106.14/14.37 (quantDeMorgan2) =>
% 106.14/14.37 ((
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% 106.14/14.37 ((
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% 106.14/14.37 ((
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% 106.14/14.37 ((
% 106.14/14.37 (prop2set2propI) =>
% 106.14/14.37 ((
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% 106.14/14.37 ((
% 106.14/14.37 (notdallE) =>
% 106.14/14.37 ((
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% 106.14/14.37 ((
% 106.14/14.37 (exuI3) =>
% 106.14/14.37 ((
% 106.14/14.37 (exuI2) =>
% 106.14/14.37 ((
% 106.14/14.37 (inCongP) =>
% 106.14/14.37 ((
% 106.14/14.37 (in__Cong) =>
% 106.14/14.37 ((
% 106.14/14.37 (exuE3u) =>
% 106.14/14.37 ((
% 106.14/14.37 (exu__Cong) =>
% 106.14/14.37 ((
% 106.14/14.37 (setadjoin__Cong) =>
% 106.14/14.37 ((
% 106.14/14.37 (powerset__Cong) =>
% 106.14/14.37 ((
% 106.14/14.37 (setunion__Cong) =>
% 106.14/14.37 ((
% 106.14/14.37 (exuEu) =>
% 106.14/14.37 ((
% 106.14/14.37 (descr__Cong) =>
% 106.14/14.37 ((
% 106.14/14.37 (dsetconstr__Cong) =>
% 106.14/14.37 ((
% 106.14/14.37 (subsetI1) =>
% 106.14/14.37 ((
% 106.14/14.37 (eqimpsubset2) =>
% 106.14/14.37 ((
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% 106.14/14.37 ((
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% 106.14/14.37 ((
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% 106.14/14.37 ((
% 106.14/14.37 (subsetE) =>
% 106.14/14.37 ((
% 106.14/14.37 (subsetE2) =>
% 106.14/14.37 ((
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% 106.14/14.37 ((
% 106.14/14.37 (notequalI1) =>
% 106.14/14.37 ((
% 106.14/14.37 (notequalI2) =>
% 106.14/14.37 ((
% 106.14/14.37 (subsetRefl) =>
% 106.14/14.37 ((
% 106.14/14.37 (subsetTrans) =>
% 106.14/14.37 ((
% 106.14/14.37 (setadjoinSub) =>
% 106.14/14.37 ((
% 106.14/14.37 (setadjoinSub2) =>
% 106.14/14.37 ((
% 106.14/14.37 (subset2powerset) =>
% 106.14/14.37 ((
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% 106.14/14.37 ((
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% 106.14/14.37 ((
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% 106.14/14.37 ((
% 106.14/14.37 (powersetE1) =>
% 106.14/14.37 ((
% 106.14/14.37 (inPowerset) =>
% 106.14/14.37 ((
% 106.14/14.37 (powersetsubset) =>
% 106.14/14.37 ((
% 106.14/14.37 (sepInPowerset) =>
% 106.14/14.37 ((
% 106.14/14.37 (sepSubset) =>
% 106.14/14.37 ((
% 106.14/14.37 (binunionIL) =>
% 106.14/14.37 ((
% 106.14/14.37 (upairset2IR) =>
% 106.14/14.37 ((
% 106.14/14.37 (binunionIR) =>
% 106.14/14.37 ((
% 106.14/14.37 (binunionEcases) =>
% 106.14/14.37 ((
% 106.14/14.37 (binunionE) =>
% 106.14/14.37 ((
% 106.14/14.37 (binunionLsub) =>
% 106.14/14.37 ((
% 106.14/14.37 (binunionRsub) =>
% 106.14/14.37 ((
% 106.14/14.37 (binintersectI) =>
% 106.14/14.37 ((
% 106.14/14.37 (binintersectSubset5) =>
% 106.14/14.37 ((
% 106.14/14.37 (binintersectEL) =>
% 106.14/14.37 ((
% 106.14/14.37 (binintersectLsub) =>
% 106.14/14.37 ((
% 106.14/14.37 (binintersectSubset2) =>
% 106.14/14.37 ((
% 106.14/14.37 (binintersectSubset3) =>
% 106.14/14.37 ((
% 106.14/14.37 (binintersectER) =>
% 106.14/14.37 ((
% 106.14/14.37 (disjointsetsI1) =>
% 106.14/14.37 ((
% 106.14/14.37 (binintersectRsub) =>
% 106.14/14.37 ((
% 106.14/14.37 (binintersectSubset4) =>
% 106.14/14.37 ((
% 106.14/14.37 (binintersectSubset1) =>
% 106.14/14.37 ((
% 106.14/14.37 (bs114d) =>
% 106.14/14.37 ((
% 106.14/14.37 (setminusI) =>
% 106.14/14.37 ((
% 106.14/14.37 (setminusEL) =>
% 106.14/14.37 ((
% 106.14/14.37 (setminusER) =>
% 106.14/14.37 ((
% 106.14/14.37 (setminusSubset2) =>
% 106.14/14.37 ((
% 106.14/14.37 (setminusERneg) =>
% 106.14/14.37 ((
% 106.14/14.37 (setminusELneg) =>
% 106.14/14.37 ((
% 106.14/14.37 (setminusILneg) =>
% 106.14/14.37 ((
% 106.14/14.37 (setminusIRneg) =>
% 106.14/14.37 ((
% 106.14/14.37 (setminusLsub) =>
% 106.14/14.37 ((
% 106.14/14.37 (setminusSubset1) =>
% 106.14/14.37 ((
% 106.14/14.37 (symdiffE) =>
% 106.14/14.37 ((
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% 106.14/14.37 ((
% 106.14/14.37 (symdiffI2) =>
% 106.14/14.37 ((
% 106.14/14.37 (symdiffIneg1) =>
% 106.14/14.37 ((
% 106.14/14.37 (symdiffIneg2) =>
% 106.14/14.37 ((
% 106.14/14.37 (secondinupair) =>
% 106.14/14.37 ((
% 106.14/14.37 (setukpairIL) =>
% 106.14/14.37 ((
% 106.14/14.37 (setukpairIR) =>
% 106.14/14.37 ((
% 106.14/14.37 (kpairiskpair) =>
% 106.14/14.37 ((
% 106.14/14.37 (kpairp) =>
% 106.14/14.37 ((
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% 106.14/14.37 ((
% 106.14/14.37 (singletoninpowerset) =>
% 106.14/14.37 ((
% 106.14/14.37 (singletoninpowunion) =>
% 106.14/14.37 ((
% 106.14/14.37 (upairset2E) =>
% 106.14/14.37 ((
% 106.14/14.37 (upairsubunion) =>
% 106.14/14.37 ((
% 106.14/14.37 (upairinpowunion) =>
% 106.14/14.37 ((
% 106.14/14.37 (ubforcartprodlem1) =>
% 106.14/14.37 ((
% 106.14/14.37 (ubforcartprodlem2) =>
% 106.14/14.37 ((
% 106.14/14.37 (ubforcartprodlem3) =>
% 106.14/14.37 ((
% 106.14/14.37 (cartprodpairin) =>
% 106.14/14.37 ((
% 106.14/14.37 (cartprodmempair1) =>
% 106.14/14.37 ((
% 106.14/14.37 (cartprodmempair) =>
% 106.14/14.37 ((
% 106.14/14.37 (setunionE2) =>
% 106.14/14.37 ((
% 106.14/14.37 (setunionsingleton1) =>
% 106.14/14.37 ((
% 106.14/14.37 (setunionsingleton2) =>
% 106.14/14.37 ((
% 106.14/14.37 (setunionsingleton) =>
% 106.14/14.37 ((
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% 106.14/14.37 ((
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% 106.14/14.37 ((
% 106.14/14.37 (ex1I2) =>
% 106.14/14.37 ((
% 106.14/14.37 (singletonsuniq) =>
% 106.14/14.37 ((
% 106.14/14.37 (setukpairinjL1) =>
% 106.14/14.37 ((
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% 106.14/14.37 ((
% 106.14/14.37 (theprop) =>
% 106.14/14.37 ((
% 106.14/14.37 (kfstpairEq) =>
% 106.14/14.37 ((
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% 106.14/14.37 (setukpairinjR) =>
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% 106.14/14.37 ((
% 106.14/14.37 (cartprodmempaircEq) =>
% 106.14/14.37 ((
% 106.14/14.37 (cartprodfstpairEq) =>
% 106.14/14.37 ((
% 106.14/14.37 (cartprodsndpairEq) =>
% 106.14/14.37 ((
% 106.14/14.37 (cartprodpairsurjEq) =>
% 106.14/14.37 ((
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% 106.14/14.37 ((
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% 106.14/14.37 ((
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% 106.14/14.37 ((
% 106.14/14.37 (lamp) =>
% 106.14/14.37 ((
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% 106.14/14.37 ((
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% 106.14/14.37 ((
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% 106.14/14.37 ((
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% 106.14/14.37 ((
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% 106.14/14.37 ((
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% 106.14/14.37 ((
% 106.14/14.37 (doubleComplementE1) =>
% 106.14/14.37 ((
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% 106.14/14.37 (inComplementUnionImpInComplement1) =>
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% 106.14/14.37 (setOfPairsIsBReln1) =>
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% 106.14/14.37 (breln1all1) =>
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% 106.14/14.37 (breln1compEex) =>
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% 106.14/14.37 (breln1unionIR) =>
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% 106.14/14.37 (breln1unionI) =>
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% 106.14/14.37 ((
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% 106.14/14.37 ((
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% 106.14/14.37 (injFuncSetFuncInj) =>
% 106.14/14.37 ((
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% 106.14/14.37 ((
% 106.14/14.37 (surjFuncSetFuncSurj) =>
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% 106.14/14.37 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3])).
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% 106.14/14.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl5])).
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% 106.14/14.38 (cartprodsndpairEq) =>
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% 106.14/14.38 ((
% 106.14/14.38 (brelnall2) =>
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% 106.14/14.38 (contrasubsetT3) =>
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% 106.14/14.38 ((
% 106.14/14.38 (doubleComplementE1) =>
% 106.14/14.38 ((
% 106.14/14.38 (doubleComplementSub1) =>
% 106.14/14.38 ((
% 106.14/14.38 (doubleComplementSub2) =>
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% 106.14/14.38 (complementSubsetComplementIntersect) =>
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% 106.14/14.38 (complementInPowersetComplementIntersect) =>
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% 106.14/14.38 (inIntersectImpInIntersectUnions) =>
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% 106.14/14.38 (intersectInPowersetIntersectUnions) =>
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% 106.14/14.38 (inComplementUnionImpNotIn1) =>
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% 106.14/14.38 (inComplementUnionImpInComplement1) =>
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% 106.14/14.38 (binunionTE) =>
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% 106.14/14.38 (demorgan2a1) =>
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% 106.14/14.38 ((
% 106.14/14.38 (demorgan2a) =>
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% 106.14/14.38 (demorgan2b2) =>
% 106.14/14.38 ((
% 106.14/14.38 (demorgan2b) =>
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% 106.14/14.38 (demorgan2) =>
% 106.14/14.38 ((
% 106.14/14.38 (woz13rule0) =>
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% 106.14/14.38 (woz13rule3) =>
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% 106.14/14.38 (woz13rule4) =>
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% 106.14/14.38 ((
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% 106.14/14.38 (woz1_5) =>
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% 106.14/14.38 (breln1SetBreln1) =>
% 106.14/14.38 ((
% 106.14/14.38 (choice2fnsingleton) =>
% 106.14/14.38 ((
% 106.14/14.38 (setOfPairsIsBReln1) =>
% 106.14/14.38 ((
% 106.14/14.38 (breln1all1) =>
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% 106.14/14.38 (breln1compprop) =>
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% 106.14/14.38 ((
% 106.14/14.38 (breln1compE) =>
% 106.14/14.38 ((
% 106.14/14.38 (breln1compEex) =>
% 106.14/14.38 ((
% 106.14/14.38 (breln1unionprop) =>
% 106.14/14.38 ((
% 106.14/14.38 (breln1unionIL) =>
% 106.14/14.38 ((
% 106.14/14.38 (breln1unionIR) =>
% 106.14/14.38 ((
% 106.14/14.38 (breln1unionI) =>
% 106.14/14.38 ((
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% 106.14/14.38 (breln1unionEcases) =>
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% 106.14/14.38 (breln1unionCommutes) =>
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% 106.14/14.38 ((
% 106.14/14.38 (image1I) =>
% 106.14/14.38 ((
% 106.14/14.38 (injFuncInInjFuncSet) =>
% 106.14/14.38 ((
% 106.14/14.38 (injFuncSetFuncIn) =>
% 106.14/14.38 ((
% 106.14/14.38 (injFuncSetFuncInj) =>
% 106.14/14.38 ((
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% 106.14/14.38 (surjFuncSetFuncSurj) =>
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% 106.14/14.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl8])).
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% 106.14/14.38 (upairset2IR) =>
% 106.14/14.38 ((
% 106.14/14.38 (binunionIR) =>
% 106.14/14.38 ((
% 106.14/14.38 (binunionEcases) =>
% 106.14/14.38 ((
% 106.14/14.38 (binunionE) =>
% 106.14/14.38 ((
% 106.14/14.38 (binunionLsub) =>
% 106.14/14.38 ((
% 106.14/14.38 (binunionRsub) =>
% 106.14/14.38 ((
% 106.14/14.38 (binintersectI) =>
% 106.14/14.38 ((
% 106.14/14.38 (binintersectSubset5) =>
% 106.14/14.38 ((
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% 106.14/14.38 ((
% 106.14/14.38 (binintersectLsub) =>
% 106.14/14.38 ((
% 106.14/14.38 (binintersectSubset2) =>
% 106.14/14.38 ((
% 106.14/14.38 (binintersectSubset3) =>
% 106.14/14.38 ((
% 106.14/14.38 (binintersectER) =>
% 106.14/14.38 ((
% 106.14/14.38 (disjointsetsI1) =>
% 106.14/14.38 ((
% 106.14/14.38 (binintersectRsub) =>
% 106.14/14.38 ((
% 106.14/14.38 (binintersectSubset4) =>
% 106.14/14.38 ((
% 106.14/14.38 (binintersectSubset1) =>
% 106.14/14.38 ((
% 106.14/14.38 (bs114d) =>
% 106.14/14.38 ((
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% 106.14/14.38 ((
% 106.14/14.38 (setminusEL) =>
% 106.14/14.38 ((
% 106.14/14.38 (setminusER) =>
% 106.14/14.38 ((
% 106.14/14.38 (setminusSubset2) =>
% 106.14/14.38 ((
% 106.14/14.38 (setminusERneg) =>
% 106.14/14.38 ((
% 106.14/14.38 (setminusELneg) =>
% 106.14/14.38 ((
% 106.14/14.38 (setminusILneg) =>
% 106.14/14.38 ((
% 106.14/14.38 (setminusIRneg) =>
% 106.14/14.38 ((
% 106.14/14.38 (setminusLsub) =>
% 106.14/14.38 ((
% 106.14/14.38 (setminusSubset1) =>
% 106.14/14.38 ((
% 106.14/14.38 (symdiffE) =>
% 106.14/14.38 ((
% 106.14/14.38 (symdiffI1) =>
% 106.14/14.38 ((
% 106.14/14.38 (symdiffI2) =>
% 106.14/14.38 ((
% 106.14/14.38 (symdiffIneg1) =>
% 106.14/14.38 ((
% 106.14/14.38 (symdiffIneg2) =>
% 106.14/14.38 ((
% 106.14/14.38 (secondinupair) =>
% 106.14/14.38 ((
% 106.14/14.38 (setukpairIL) =>
% 106.14/14.38 ((
% 106.14/14.38 (setukpairIR) =>
% 106.14/14.38 ((
% 106.14/14.38 (kpairiskpair) =>
% 106.14/14.38 ((
% 106.14/14.38 (kpairp) =>
% 106.14/14.38 ((
% 106.14/14.38 (singletonsubset) =>
% 106.14/14.38 ((
% 106.14/14.38 (singletoninpowerset) =>
% 106.14/14.38 ((
% 106.14/14.38 (singletoninpowunion) =>
% 106.14/14.38 ((
% 106.14/14.38 (upairset2E) =>
% 106.14/14.38 ((
% 106.14/14.38 (upairsubunion) =>
% 106.14/14.38 ((
% 106.14/14.38 (upairinpowunion) =>
% 106.14/14.38 ((
% 106.14/14.38 (ubforcartprodlem1) =>
% 106.14/14.38 ((
% 106.14/14.38 (ubforcartprodlem2) =>
% 106.14/14.38 ((
% 106.14/14.38 (ubforcartprodlem3) =>
% 106.14/14.38 ((
% 106.14/14.38 (cartprodpairin) =>
% 106.14/14.38 ((
% 106.14/14.38 (cartprodmempair1) =>
% 106.14/14.38 ((
% 106.14/14.38 (cartprodmempair) =>
% 106.14/14.38 ((
% 106.14/14.38 (setunionE2) =>
% 106.14/14.38 ((
% 106.14/14.38 (setunionsingleton1) =>
% 106.14/14.38 ((
% 106.14/14.38 (setunionsingleton2) =>
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% 106.14/14.38 (setunionsingleton) =>
% 106.14/14.38 ((
% 106.14/14.38 (singletonprop) =>
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% 106.14/14.38 (ex1I2) =>
% 106.14/14.38 ((
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% 106.14/14.38 ((
% 106.14/14.38 (setukpairinjL1) =>
% 106.14/14.38 ((
% 106.14/14.38 (kfstsingleton) =>
% 106.14/14.38 ((
% 106.14/14.38 (theprop) =>
% 106.14/14.38 ((
% 106.14/14.38 (kfstpairEq) =>
% 106.14/14.38 ((
% 106.14/14.38 (cartprodfstin) =>
% 106.14/14.38 ((
% 106.14/14.38 (setukpairinjL2) =>
% 106.14/14.38 ((
% 106.14/14.38 (setukpairinjL) =>
% 106.14/14.38 ((
% 106.14/14.38 (setukpairinjR11) =>
% 106.14/14.38 ((
% 106.14/14.38 (setukpairinjR12) =>
% 106.14/14.38 ((
% 106.14/14.38 (setukpairinjR1) =>
% 106.14/14.38 ((
% 106.14/14.38 (upairequniteq) =>
% 106.14/14.38 ((
% 106.14/14.38 (setukpairinjR2) =>
% 106.14/14.38 ((
% 106.14/14.38 (setukpairinjR) =>
% 106.14/14.38 ((
% 106.14/14.38 (ksndsingleton) =>
% 106.14/14.38 ((
% 106.14/14.38 (ksndpairEq) =>
% 106.14/14.38 ((
% 106.14/14.38 (kpairsurjEq) =>
% 106.14/14.38 ((
% 106.14/14.38 (cartprodsndin) =>
% 106.14/14.38 ((
% 106.14/14.38 (cartprodpairmemEL) =>
% 106.14/14.38 ((
% 106.14/14.38 (cartprodpairmemER) =>
% 106.14/14.38 ((
% 106.14/14.38 (cartprodmempaircEq) =>
% 106.14/14.38 ((
% 106.14/14.38 (cartprodfstpairEq) =>
% 106.14/14.38 ((
% 106.14/14.38 (cartprodsndpairEq) =>
% 106.14/14.38 ((
% 106.14/14.38 (cartprodpairsurjEq) =>
% 106.14/14.38 ((
% 106.14/14.38 (dpsetconstrI) =>
% 106.14/14.38 ((
% 106.14/14.38 (dpsetconstrSub) =>
% 106.14/14.38 ((
% 106.14/14.38 (setOfPairsIsBReln) =>
% 106.14/14.38 ((
% 106.14/14.38 (dpsetconstrERa) =>
% 106.14/14.38 ((
% 106.14/14.38 (dpsetconstrEL1) =>
% 106.14/14.38 ((
% 106.14/14.38 (dpsetconstrEL2) =>
% 106.14/14.38 ((
% 106.14/14.38 (dpsetconstrER) =>
% 106.14/14.38 ((
% 106.14/14.38 (funcImageSingleton) =>
% 106.14/14.38 ((
% 106.14/14.38 (apProp) =>
% 106.14/14.38 ((
% 106.14/14.38 (app) =>
% 106.14/14.38 ((
% 106.14/14.38 (infuncsetfunc) =>
% 106.14/14.38 ((
% 106.14/14.38 (ap2p) =>
% 106.14/14.38 ((
% 106.14/14.38 (funcinfuncset) =>
% 106.14/14.38 ((
% 106.14/14.38 (lamProp) =>
% 106.14/14.38 ((
% 106.14/14.38 (lamp) =>
% 106.14/14.38 ((
% 106.14/14.38 (lam2p) =>
% 106.14/14.38 ((
% 106.14/14.38 (brelnall1) =>
% 106.14/14.38 ((
% 106.14/14.38 (brelnall2) =>
% 106.14/14.38 ((
% 106.14/14.38 (ex1E2) =>
% 106.14/14.38 ((
% 106.14/14.38 (funcGraphProp1) =>
% 106.14/14.38 ((
% 106.14/14.38 (funcGraphProp3) =>
% 106.14/14.38 ((
% 106.14/14.38 (funcGraphProp2) =>
% 106.14/14.38 ((
% 106.14/14.38 (funcextLem) =>
% 106.14/14.38 ((
% 106.14/14.38 (funcGraphProp4) =>
% 106.14/14.38 ((
% 106.14/14.38 (subbreln) =>
% 106.14/14.38 ((
% 106.14/14.38 (eqbreln) =>
% 106.14/14.38 ((
% 106.14/14.38 (funcext) =>
% 106.14/14.38 ((
% 106.14/14.38 (funcext2) =>
% 106.14/14.38 ((
% 106.14/14.38 (ap2apEq1) =>
% 106.14/14.38 ((
% 106.14/14.38 (ap2apEq2) =>
% 106.14/14.38 ((
% 106.14/14.38 (beta1) =>
% 106.14/14.38 ((
% 106.14/14.38 (eta1) =>
% 106.14/14.38 ((
% 106.14/14.38 (lam2lamEq) =>
% 106.14/14.38 ((
% 106.14/14.38 (beta2) =>
% 106.14/14.38 ((
% 106.14/14.38 (eta2) =>
% 106.14/14.38 ((
% 106.14/14.38 (iffalseProp1) =>
% 106.14/14.38 ((
% 106.14/14.38 (iffalseProp2) =>
% 106.14/14.38 ((
% 106.14/14.38 (iftrueProp1) =>
% 106.14/14.38 ((
% 106.14/14.38 (iftrueProp2) =>
% 106.14/14.38 ((
% 106.14/14.38 (ifSingleton) =>
% 106.14/14.38 ((
% 106.14/14.38 (ifp) =>
% 106.14/14.38 ((
% 106.14/14.38 (theeq) =>
% 106.14/14.38 ((
% 106.14/14.38 (iftrue) =>
% 106.14/14.38 ((
% 106.14/14.38 (iffalse) =>
% 106.14/14.38 ((
% 106.14/14.38 (iftrueorfalse) =>
% 106.14/14.38 ((
% 106.14/14.38 (binintersectT_lem) =>
% 106.14/14.38 ((
% 106.14/14.38 (binunionT_lem) =>
% 106.14/14.38 ((
% 106.14/14.38 (powersetT_lem) =>
% 106.14/14.38 ((
% 106.14/14.38 (setminusT_lem) =>
% 106.14/14.38 ((
% 106.14/14.38 (complementT_lem) =>
% 106.14/14.38 ((
% 106.14/14.38 (setextT) =>
% 106.14/14.38 ((
% 106.14/14.38 (subsetTI) =>
% 106.14/14.38 ((
% 106.14/14.38 (powersetTI1) =>
% 106.14/14.38 ((
% 106.14/14.38 (powersetTE1) =>
% 106.14/14.38 ((
% 106.14/14.38 (complementTI1) =>
% 106.14/14.38 ((
% 106.14/14.38 (complementTE1) =>
% 106.14/14.38 ((
% 106.14/14.38 (binintersectTELcontra) =>
% 106.14/14.38 ((
% 106.14/14.38 (binintersectTERcontra) =>
% 106.14/14.38 ((
% 106.14/14.38 (contrasubsetT) =>
% 106.14/14.38 ((
% 106.14/14.38 (contrasubsetT1) =>
% 106.14/14.38 ((
% 106.14/14.38 (contrasubsetT2) =>
% 106.14/14.38 ((
% 106.14/14.38 (contrasubsetT3) =>
% 106.14/14.38 ((
% 106.14/14.38 (doubleComplementI1) =>
% 106.14/14.38 ((
% 106.14/14.38 (doubleComplementE1) =>
% 106.14/14.38 ((
% 106.14/14.38 (doubleComplementSub1) =>
% 106.14/14.38 ((
% 106.14/14.38 (doubleComplementSub2) =>
% 106.14/14.38 ((
% 106.14/14.38 (doubleComplementEq) =>
% 106.14/14.38 ((
% 106.14/14.38 (complementTnotintersectT) =>
% 106.14/14.38 ((
% 106.14/14.38 (complementImpComplementIntersect) =>
% 106.14/14.38 ((
% 106.14/14.38 (complementSubsetComplementIntersect) =>
% 106.14/14.38 ((
% 106.14/14.38 (complementInPowersetComplementIntersect) =>
% 106.14/14.38 ((
% 106.14/14.38 (contraSubsetComplement) =>
% 106.14/14.38 ((
% 106.14/14.38 (complementTcontraSubset) =>
% 106.14/14.38 ((
% 106.14/14.38 (binunionTILcontra) =>
% 106.14/14.38 ((
% 106.14/14.38 (binunionTIRcontra) =>
% 106.14/14.38 ((
% 106.14/14.38 (inIntersectImpInUnion) =>
% 106.14/14.38 ((
% 106.14/14.38 (inIntersectImpInUnion2) =>
% 106.14/14.38 ((
% 106.14/14.38 (inIntersectImpInIntersectUnions) =>
% 106.14/14.38 ((
% 106.14/14.38 (intersectInPowersetIntersectUnions) =>
% 106.14/14.38 ((
% 106.14/14.38 (inComplementUnionImpNotIn1) =>
% 106.14/14.38 ((
% 106.14/14.38 (inComplementUnionImpInComplement1) =>
% 106.14/14.38 ((
% 106.14/14.38 (binunionTE) =>
% 106.14/14.38 ((
% 106.14/14.38 (binunionTEcontra) =>
% 106.14/14.38 ((
% 106.14/14.38 (demorgan2a1) =>
% 106.14/14.38 ((
% 106.14/14.38 (complementUnionInPowersetComplement) =>
% 106.14/14.38 ((
% 106.14/14.38 (demorgan2a2) =>
% 106.14/14.38 ((
% 106.14/14.38 (demorgan1a) =>
% 106.14/14.38 ((
% 106.14/14.38 (demorgan1b) =>
% 106.14/14.38 ((
% 106.14/14.38 (demorgan1) =>
% 106.14/14.38 ((
% 106.14/14.38 (demorgan2a) =>
% 106.14/14.38 ((
% 106.14/14.38 (demorgan2b2) =>
% 106.14/14.38 ((
% 106.14/14.38 (demorgan2b) =>
% 106.14/14.38 ((
% 106.14/14.38 (demorgan2) =>
% 106.14/14.38 ((
% 106.14/14.38 (woz13rule0) =>
% 106.14/14.38 ((
% 106.14/14.38 (woz13rule1) =>
% 106.14/14.38 ((
% 106.14/14.38 (woz13rule2) =>
% 106.14/14.38 ((
% 106.14/14.38 (woz13rule3) =>
% 106.14/14.38 ((
% 106.14/14.38 (woz13rule4) =>
% 106.14/14.38 ((
% 106.14/14.38 (woz1_1) =>
% 106.14/14.38 ((
% 106.14/14.38 (woz1_2) =>
% 106.14/14.38 ((
% 106.14/14.38 (woz1_3) =>
% 106.14/14.38 ((
% 106.14/14.38 (woz1_4) =>
% 106.14/14.38 ((
% 106.14/14.38 (woz1_5) =>
% 106.14/14.38 ((
% 106.14/14.38 (breln1all2) =>
% 106.14/14.38 ((
% 106.14/14.38 (breln1SetBreln1) =>
% 106.14/14.38 ((
% 106.14/14.38 (choice2fnsingleton) =>
% 106.14/14.38 ((
% 106.14/14.38 (setOfPairsIsBReln1) =>
% 106.14/14.38 ((
% 106.14/14.38 (breln1all1) =>
% 106.14/14.38 ((
% 106.14/14.38 (subbreln1) =>
% 106.14/14.38 ((
% 106.14/14.38 (eqbreln1) =>
% 106.14/14.38 ((
% 106.14/14.38 (breln1invprop) =>
% 106.14/14.38 ((
% 106.14/14.38 (breln1invI) =>
% 106.14/14.38 ((
% 106.14/14.38 (breln1invE) =>
% 106.14/14.38 ((
% 106.14/14.38 (breln1compprop) =>
% 106.14/14.38 ((
% 106.14/14.38 (breln1compI) =>
% 106.14/14.38 ((
% 106.14/14.38 (breln1compE) =>
% 106.14/14.38 ((
% 106.14/14.38 (breln1compEex) =>
% 106.14/14.38 ((
% 106.14/14.38 (breln1unionprop) =>
% 106.14/14.38 ((
% 106.14/14.38 (breln1unionIL) =>
% 106.14/14.38 ((
% 106.14/14.38 (breln1unionIR) =>
% 106.14/14.38 ((
% 106.14/14.38 (breln1unionI) =>
% 106.14/14.38 ((
% 106.14/14.38 (breln1unionE) =>
% 106.14/14.38 ((
% 106.14/14.38 (breln1unionEcases) =>
% 106.14/14.38 ((
% 106.14/14.38 (breln1unionCommutes) =>
% 106.14/14.38 ((
% 106.14/14.38 (woz2Ex) =>
% 106.14/14.38 ((
% 106.14/14.38 (woz2W) =>
% 106.14/14.38 ((
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% 106.14/14.38 ((
% 106.14/14.38 (woz2B) =>
% 106.14/14.38 ((
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% 106.14/14.38 ((
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% 106.14/14.38 ((
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% 106.14/14.38 ((
% 106.14/14.38 (image1E) =>
% 106.14/14.38 ((
% 106.14/14.38 (image1I) =>
% 106.14/14.38 ((
% 106.14/14.38 (injFuncInInjFuncSet) =>
% 106.14/14.38 ((
% 106.14/14.38 (injFuncSetFuncIn) =>
% 106.14/14.38 ((
% 106.14/14.38 (injFuncSetFuncInj) =>
% 106.14/14.38 ((
% 106.14/14.38 (surjFuncSetFuncIn) =>
% 106.14/14.38 ((
% 106.14/14.38 (surjFuncSetFuncSurj) =>
% 106.14/14.38 ((
% 106.14/14.38 (leftInvIsSurj) =>
% 106.14/14.38 ((
% 106.14/14.38 (surjCantorThm) =>
% 106.14/14.38 ((
% 106.14/14.38 (!!) @ (
% 106.14/14.38 (('#S') @ (
% 106.14/14.38 (
% 106.14/14.38 ('#B') @ (
% 106.14/14.38 =>) @
% 106.14/14.38 nonempty)) @
% 106.14/14.38 (
% 106.14/14.38 (
% 106.14/14.38 ('#B') @ (
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% 106.14/14.38 (
% 106.14/14.38 (
% 106.14/14.38 ('#S') @ (
% 106.14/14.38 (
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% 106.14/14.38 (
% 106.14/14.38 (
% 106.14/14.38 ('#B') @ (
% 106.14/14.38 (
% 106.14/14.38 ('#B') @ (
% 106.14/14.38 &))) @
% 106.14/14.38 (
% 106.14/14.38 (
% 106.14/14.38 ('#C') @ in)))))) @
% 106.14/14.38 (
% 106.14/14.38 (
% 106.14/14.38 ('#C') @ (
% 106.14/14.38 (
% 106.14/14.38 ('#B') @ (
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% 106.14/14.38 (
% 106.14/14.38 (
% 106.14/14.38 ('#B') @ (
% 106.14/14.38 (
% 106.14/14.38 ('#B') @ (
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% 106.14/14.38 (
% 106.14/14.38 (
% 106.14/14.38 ('#C') @ binintersect)))))) @
% 106.14/14.38 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.14/14.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl13])).
% 106.14/14.38 thf(zip_derived_cl25, plain,
% 106.14/14.38 (~ (((in @ emptyset @ omega) =>
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% 106.14/14.38 (((replAx) =>
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% 106.14/14.38 (((dsetconstrER) =>
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% 106.14/14.38 (((in @ emptyset @
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% 106.14/14.38 ((
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% 106.14/14.38 ((
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% 106.14/14.38 ((
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% 106.14/14.38 ((
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% 106.14/14.38 ((
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% 106.14/14.38 ((
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% 106.14/14.38 ((
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% 106.14/14.38 ((
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% 106.14/14.38 ((
% 106.14/14.38 (upairsetIR) =>
% 106.14/14.38 ((
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% 106.14/14.38 ('#B') @ (
% 106.14/14.38 =))) @
% 106.14/14.38 (
% 106.14/14.38 (
% 106.14/14.38 ('#C') @ binintersect)))))) @
% 106.14/14.38 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.14/14.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl19])).
% 106.14/14.38 thf(zip_derived_cl33, plain,
% 106.14/14.38 (~ (((omegaSAx) =>
% 106.14/14.38 (((omegaIndAx) =>
% 106.14/14.38 (((replAx) =>
% 106.14/14.38 (((foundationAx) =>
% 106.14/14.38 (((wellorderingAx) =>
% 106.14/14.38 (((descrp) =>
% 106.14/14.38 (((dsetconstrI) =>
% 106.14/14.38 (((dsetconstrEL) =>
% 106.14/14.38 (((dsetconstrER) =>
% 106.14/14.38 (((exuE1) =>
% 106.14/14.38 (((prop2setE) =>
% 106.14/14.38 (((emptysetE) =>
% 106.14/14.38 (((emptysetimpfalse) =>
% 106.14/14.38 (((notinemptyset) =>
% 106.14/14.38 (((exuE3e) =>
% 106.14/14.38 (((setext) =>
% 106.14/14.38 (((emptyI) =>
% 106.14/14.38 (((noeltsimpempty) =>
% 106.14/14.38 (((setbeta) =>
% 106.14/14.38 (((nonemptyE1) =>
% 106.14/14.38 (((nonemptyI) =>
% 106.14/14.38 (((nonemptyI1) =>
% 106.14/14.38 (((setadjoinIL) =>
% 106.14/14.38 (((in @ emptyset @
% 106.14/14.38 (setadjoin @
% 106.14/14.38 emptyset @ emptyset)) =>
% 106.14/14.38 (((setadjoinIR) =>
% 106.14/14.38 (((setadjoinE) =>
% 106.14/14.38 (((setadjoinOr) =>
% 106.14/14.38 (((setoftrueEq) =>
% 106.14/14.38 (((powersetI) =>
% 106.14/14.38 (((emptyinPowerset) =>
% 106.14/14.38 ((
% 106.14/14.38 (emptyInPowerset) =>
% 106.14/14.38 ((
% 106.14/14.38 (powersetE) =>
% 106.14/14.38 ((
% 106.14/14.38 (setunionI) =>
% 106.14/14.38 ((
% 106.14/14.38 (setunionE) =>
% 106.14/14.38 ((
% 106.14/14.38 (subPowSU) =>
% 106.14/14.38 ((
% 106.14/14.38 (exuE2) =>
% 106.14/14.38 ((
% 106.14/14.38 (nonemptyImpWitness) =>
% 106.14/14.38 ((
% 106.14/14.38 (uniqinunit) =>
% 106.14/14.38 ((
% 106.14/14.38 (notinsingleton) =>
% 106.14/14.38 ((
% 106.14/14.38 (eqinunit) =>
% 106.14/14.38 ((
% 106.14/14.38 (singletonsswitch) =>
% 106.14/14.38 ((
% 106.14/14.38 (upairsetE) =>
% 106.14/14.38 ((
% 106.14/14.38 (upairsetIL) =>
% 106.14/14.38 ((
% 106.14/14.38 (upairsetIR) =>
% 106.14/14.38 ((
% 106.14/14.38 (emptyE1) =>
% 106.14/14.38 ((
% 106.14/14.38 (vacuousDall) =>
% 106.14/14.38 ((
% 106.14/14.38 (quantDeMorgan1) =>
% 106.14/14.38 ((
% 106.14/14.38 (quantDeMorgan2) =>
% 106.14/14.38 ((
% 106.14/14.38 (quantDeMorgan3) =>
% 106.14/14.38 ((
% 106.14/14.38 (quantDeMorgan4) =>
% 106.14/14.38 ((
% 106.14/14.38 (prop2setI) =>
% 106.14/14.38 ((
% 106.14/14.38 (prop2set2propI) =>
% 106.14/14.38 ((
% 106.14/14.38 (notdexE) =>
% 106.14/14.38 ((
% 106.14/14.38 (notdallE) =>
% 106.14/14.38 ((
% 106.14/14.38 (exuI1) =>
% 106.14/14.38 ((
% 106.14/14.38 (exuI3) =>
% 106.14/14.38 ((
% 106.14/14.38 (exuI2) =>
% 106.14/14.38 ((
% 106.14/14.38 (inCongP) =>
% 106.14/14.38 ((
% 106.14/14.38 (in__Cong) =>
% 106.14/14.38 ((
% 106.14/14.38 (exuE3u) =>
% 106.14/14.38 ((
% 106.14/14.38 (exu__Cong) =>
% 106.14/14.38 ((
% 106.14/14.38 (setadjoin__Cong) =>
% 106.14/14.38 ((
% 106.14/14.38 (powerset__Cong) =>
% 106.14/14.38 ((
% 106.14/14.38 (setunion__Cong) =>
% 106.14/14.38 ((
% 106.14/14.38 (exuEu) =>
% 106.14/14.38 ((
% 106.14/14.38 (descr__Cong) =>
% 106.14/14.38 ((
% 106.14/14.38 (dsetconstr__Cong) =>
% 106.14/14.38 ((
% 106.14/14.38 (subsetI1) =>
% 106.14/14.38 ((
% 106.14/14.38 (eqimpsubset2) =>
% 106.14/14.38 ((
% 106.14/14.38 (eqimpsubset1) =>
% 106.14/14.38 ((
% 106.14/14.38 (subsetI2) =>
% 106.14/14.38 ((
% 106.14/14.38 (emptysetsubset) =>
% 106.14/14.38 ((
% 106.14/14.38 (subsetE) =>
% 106.14/14.38 ((
% 106.14/14.38 (subsetE2) =>
% 106.14/14.38 ((
% 106.14/14.38 (notsubsetI) =>
% 106.14/14.38 ((
% 106.14/14.38 (notequalI1) =>
% 106.14/14.38 ((
% 106.14/14.38 (notequalI2) =>
% 106.14/14.38 ((
% 106.14/14.38 (subsetRefl) =>
% 106.14/14.38 ((
% 106.14/14.38 (subsetTrans) =>
% 106.14/14.38 ((
% 106.14/14.38 (setadjoinSub) =>
% 106.14/14.38 ((
% 106.14/14.38 (setadjoinSub2) =>
% 106.14/14.38 ((
% 106.14/14.38 (subset2powerset) =>
% 106.14/14.38 ((
% 106.14/14.38 (setextsub) =>
% 106.14/14.38 ((
% 106.14/14.38 (subsetemptysetimpeq) =>
% 106.14/14.38 ((
% 106.14/14.38 (powersetI1) =>
% 106.14/14.38 ((
% 106.14/14.38 (powersetE1) =>
% 106.14/14.38 ((
% 106.14/14.38 (inPowerset) =>
% 106.14/14.38 ((
% 106.14/14.38 (powersetsubset) =>
% 106.14/14.38 ((
% 106.14/14.38 (sepInPowerset) =>
% 106.14/14.38 ((
% 106.14/14.38 (sepSubset) =>
% 106.14/14.38 ((
% 106.14/14.38 (binunionIL) =>
% 106.14/14.38 ((
% 106.14/14.38 (upairset2IR) =>
% 106.14/14.38 ((
% 106.14/14.38 (binunionIR) =>
% 106.14/14.38 ((
% 106.14/14.38 (binunionEcases) =>
% 106.14/14.38 ((
% 106.14/14.38 (binunionE) =>
% 106.14/14.38 ((
% 106.14/14.38 (binunionLsub) =>
% 106.14/14.38 ((
% 106.14/14.38 (binunionRsub) =>
% 106.14/14.38 ((
% 106.14/14.38 (binintersectI) =>
% 106.14/14.38 ((
% 106.14/14.38 (binintersectSubset5) =>
% 106.14/14.38 ((
% 106.14/14.38 (binintersectEL) =>
% 106.14/14.38 ((
% 106.14/14.38 (binintersectLsub) =>
% 106.14/14.38 ((
% 106.14/14.38 (binintersectSubset2) =>
% 106.14/14.38 ((
% 106.14/14.38 (binintersectSubset3) =>
% 106.14/14.38 ((
% 106.14/14.38 (binintersectER) =>
% 106.14/14.38 ((
% 106.14/14.38 (disjointsetsI1) =>
% 106.14/14.38 ((
% 106.14/14.38 (binintersectRsub) =>
% 106.14/14.38 ((
% 106.14/14.38 (binintersectSubset4) =>
% 106.14/14.38 ((
% 106.14/14.38 (binintersectSubset1) =>
% 106.14/14.38 ((
% 106.14/14.38 (bs114d) =>
% 106.14/14.38 ((
% 106.14/14.38 (setminusI) =>
% 106.14/14.38 ((
% 106.14/14.38 (setminusEL) =>
% 106.14/14.38 ((
% 106.14/14.38 (setminusER) =>
% 106.14/14.38 ((
% 106.14/14.38 (setminusSubset2) =>
% 106.14/14.38 ((
% 106.14/14.38 (setminusERneg) =>
% 106.14/14.38 ((
% 106.14/14.38 (setminusELneg) =>
% 106.14/14.38 ((
% 106.14/14.38 (setminusILneg) =>
% 106.14/14.38 ((
% 106.14/14.38 (setminusIRneg) =>
% 106.14/14.38 ((
% 106.14/14.38 (setminusLsub) =>
% 106.14/14.38 ((
% 106.14/14.38 (setminusSubset1) =>
% 106.14/14.38 ((
% 106.14/14.38 (symdiffE) =>
% 106.14/14.38 ((
% 106.14/14.38 (symdiffI1) =>
% 106.14/14.38 ((
% 106.14/14.38 (symdiffI2) =>
% 106.14/14.38 ((
% 106.14/14.38 (symdiffIneg1) =>
% 106.14/14.38 ((
% 106.14/14.38 (symdiffIneg2) =>
% 106.14/14.38 ((
% 106.14/14.38 (secondinupair) =>
% 106.14/14.38 ((
% 106.14/14.38 (setukpairIL) =>
% 106.14/14.38 ((
% 106.14/14.38 (setukpairIR) =>
% 106.14/14.38 ((
% 106.14/14.38 (kpairiskpair) =>
% 106.14/14.38 ((
% 106.14/14.38 (kpairp) =>
% 106.14/14.38 ((
% 106.14/14.38 (singletonsubset) =>
% 106.14/14.38 ((
% 106.14/14.38 (singletoninpowerset) =>
% 106.14/14.38 ((
% 106.14/14.38 (singletoninpowunion) =>
% 106.14/14.38 ((
% 106.14/14.38 (upairset2E) =>
% 106.14/14.38 ((
% 106.14/14.38 (upairsubunion) =>
% 106.14/14.38 ((
% 106.14/14.38 (upairinpowunion) =>
% 106.14/14.38 ((
% 106.14/14.38 (ubforcartprodlem1) =>
% 106.14/14.38 ((
% 106.14/14.38 (ubforcartprodlem2) =>
% 106.14/14.38 ((
% 106.14/14.38 (ubforcartprodlem3) =>
% 106.14/14.38 ((
% 106.14/14.38 (cartprodpairin) =>
% 106.14/14.38 ((
% 106.14/14.38 (cartprodmempair1) =>
% 106.14/14.38 ((
% 106.14/14.38 (cartprodmempair) =>
% 106.14/14.38 ((
% 106.14/14.38 (setunionE2) =>
% 106.14/14.38 ((
% 106.14/14.38 (setunionsingleton1) =>
% 106.14/14.38 ((
% 106.14/14.38 (setunionsingleton2) =>
% 106.14/14.38 ((
% 106.14/14.38 (setunionsingleton) =>
% 106.14/14.38 ((
% 106.14/14.38 (singletonprop) =>
% 106.14/14.38 ((
% 106.14/14.38 (ex1E1) =>
% 106.14/14.38 ((
% 106.14/14.38 (ex1I) =>
% 106.14/14.38 ((
% 106.14/14.38 (ex1I2) =>
% 106.14/14.38 ((
% 106.14/14.38 (singletonsuniq) =>
% 106.14/14.38 ((
% 106.14/14.38 (setukpairinjL1) =>
% 106.14/14.38 ((
% 106.14/14.38 (kfstsingleton) =>
% 106.14/14.38 ((
% 106.14/14.38 (theprop) =>
% 106.14/14.38 ((
% 106.14/14.38 (kfstpairEq) =>
% 106.14/14.38 ((
% 106.14/14.38 (cartprodfstin) =>
% 106.14/14.38 ((
% 106.14/14.38 (setukpairinjL2) =>
% 106.14/14.38 ((
% 106.14/14.38 (setukpairinjL) =>
% 106.14/14.38 ((
% 106.14/14.38 (setukpairinjR11) =>
% 106.14/14.38 ((
% 106.14/14.38 (setukpairinjR12) =>
% 106.14/14.38 ((
% 106.14/14.38 (setukpairinjR1) =>
% 106.14/14.38 ((
% 106.14/14.38 (upairequniteq) =>
% 106.14/14.38 ((
% 106.14/14.38 (setukpairinjR2) =>
% 106.14/14.38 ((
% 106.14/14.38 (setukpairinjR) =>
% 106.14/14.38 ((
% 106.14/14.38 (ksndsingleton) =>
% 106.14/14.38 ((
% 106.14/14.38 (ksndpairEq) =>
% 106.14/14.38 ((
% 106.14/14.38 (kpairsurjEq) =>
% 106.14/14.38 ((
% 106.14/14.38 (cartprodsndin) =>
% 106.14/14.38 ((
% 106.14/14.38 (cartprodpairmemEL) =>
% 106.14/14.38 ((
% 106.14/14.38 (cartprodpairmemER) =>
% 106.14/14.38 ((
% 106.14/14.38 (cartprodmempaircEq) =>
% 106.14/14.38 ((
% 106.14/14.38 (cartprodfstpairEq) =>
% 106.14/14.38 ((
% 106.14/14.38 (cartprodsndpairEq) =>
% 106.14/14.38 ((
% 106.14/14.38 (cartprodpairsurjEq) =>
% 106.14/14.38 ((
% 106.14/14.38 (dpsetconstrI) =>
% 106.14/14.38 ((
% 106.14/14.38 (dpsetconstrSub) =>
% 106.14/14.38 ((
% 106.14/14.38 (setOfPairsIsBReln) =>
% 106.14/14.38 ((
% 106.14/14.38 (dpsetconstrERa) =>
% 106.14/14.38 ((
% 106.14/14.38 (dpsetconstrEL1) =>
% 106.14/14.38 ((
% 106.14/14.38 (dpsetconstrEL2) =>
% 106.14/14.38 ((
% 106.14/14.38 (dpsetconstrER) =>
% 106.14/14.38 ((
% 106.14/14.38 (funcImageSingleton) =>
% 106.14/14.38 ((
% 106.14/14.38 (apProp) =>
% 106.14/14.38 ((
% 106.14/14.38 (app) =>
% 106.14/14.38 ((
% 106.14/14.38 (infuncsetfunc) =>
% 106.14/14.38 ((
% 106.14/14.38 (ap2p) =>
% 106.14/14.38 ((
% 106.14/14.38 (funcinfuncset) =>
% 106.14/14.38 ((
% 106.14/14.38 (lamProp) =>
% 106.14/14.38 ((
% 106.14/14.38 (lamp) =>
% 106.14/14.38 ((
% 106.14/14.38 (lam2p) =>
% 106.14/14.38 ((
% 106.14/14.38 (brelnall1) =>
% 106.14/14.38 ((
% 106.14/14.38 (brelnall2) =>
% 106.14/14.38 ((
% 106.14/14.38 (ex1E2) =>
% 106.14/14.38 ((
% 106.14/14.38 (funcGraphProp1) =>
% 106.14/14.38 ((
% 106.14/14.38 (funcGraphProp3) =>
% 106.14/14.38 ((
% 106.14/14.38 (funcGraphProp2) =>
% 106.14/14.38 ((
% 106.14/14.38 (funcextLem) =>
% 106.14/14.38 ((
% 106.14/14.38 (funcGraphProp4) =>
% 106.14/14.38 ((
% 106.14/14.38 (subbreln) =>
% 106.14/14.38 ((
% 106.14/14.38 (eqbreln) =>
% 106.14/14.38 ((
% 106.14/14.38 (funcext) =>
% 106.14/14.38 ((
% 106.14/14.38 (funcext2) =>
% 106.14/14.38 ((
% 106.14/14.38 (ap2apEq1) =>
% 106.14/14.38 ((
% 106.14/14.38 (ap2apEq2) =>
% 106.14/14.38 ((
% 106.14/14.38 (beta1) =>
% 106.14/14.38 ((
% 106.14/14.38 (eta1) =>
% 106.14/14.38 ((
% 106.14/14.38 (lam2lamEq) =>
% 106.14/14.38 ((
% 106.14/14.38 (beta2) =>
% 106.14/14.38 ((
% 106.14/14.38 (eta2) =>
% 106.14/14.38 ((
% 106.14/14.38 (iffalseProp1) =>
% 106.14/14.38 ((
% 106.14/14.38 (iffalseProp2) =>
% 106.14/14.38 ((
% 106.14/14.38 (iftrueProp1) =>
% 106.14/14.38 ((
% 106.14/14.38 (iftrueProp2) =>
% 106.14/14.38 ((
% 106.14/14.38 (ifSingleton) =>
% 106.14/14.38 ((
% 106.14/14.38 (ifp) =>
% 106.14/14.38 ((
% 106.14/14.38 (theeq) =>
% 106.14/14.38 ((
% 106.14/14.38 (iftrue) =>
% 106.14/14.38 ((
% 106.14/14.38 (iffalse) =>
% 106.14/14.38 ((
% 106.14/14.38 (iftrueorfalse) =>
% 106.14/14.38 ((
% 106.14/14.38 (binintersectT_lem) =>
% 106.14/14.38 ((
% 106.14/14.38 (binunionT_lem) =>
% 106.14/14.38 ((
% 106.14/14.38 (powersetT_lem) =>
% 106.14/14.38 ((
% 106.14/14.38 (setminusT_lem) =>
% 106.14/14.38 ((
% 106.14/14.38 (complementT_lem) =>
% 106.14/14.38 ((
% 106.14/14.38 (setextT) =>
% 106.14/14.38 ((
% 106.14/14.38 (subsetTI) =>
% 106.14/14.38 ((
% 106.14/14.38 (powersetTI1) =>
% 106.14/14.38 ((
% 106.14/14.38 (powersetTE1) =>
% 106.14/14.38 ((
% 106.14/14.38 (complementTI1) =>
% 106.14/14.38 ((
% 106.14/14.38 (complementTE1) =>
% 106.14/14.38 ((
% 106.14/14.38 (binintersectTELcontra) =>
% 106.14/14.38 ((
% 106.14/14.38 (binintersectTERcontra) =>
% 106.14/14.38 ((
% 106.14/14.38 (contrasubsetT) =>
% 106.14/14.38 ((
% 106.14/14.38 (contrasubsetT1) =>
% 106.14/14.38 ((
% 106.14/14.38 (contrasubsetT2) =>
% 106.14/14.38 ((
% 106.14/14.38 (contrasubsetT3) =>
% 106.14/14.38 ((
% 106.14/14.38 (doubleComplementI1) =>
% 106.14/14.38 ((
% 106.14/14.38 (doubleComplementE1) =>
% 106.14/14.38 ((
% 106.14/14.38 (doubleComplementSub1) =>
% 106.14/14.38 ((
% 106.14/14.38 (doubleComplementSub2) =>
% 106.14/14.38 ((
% 106.14/14.38 (doubleComplementEq) =>
% 106.14/14.38 ((
% 106.14/14.38 (complementTnotintersectT) =>
% 106.14/14.38 ((
% 106.14/14.38 (complementImpComplementIntersect) =>
% 106.14/14.38 ((
% 106.14/14.38 (complementSubsetComplementIntersect) =>
% 106.14/14.38 ((
% 106.14/14.38 (complementInPowersetComplementIntersect) =>
% 106.14/14.38 ((
% 106.14/14.38 (contraSubsetComplement) =>
% 106.14/14.38 ((
% 106.14/14.38 (complementTcontraSubset) =>
% 106.14/14.38 ((
% 106.14/14.38 (binunionTILcontra) =>
% 106.14/14.38 ((
% 106.14/14.38 (binunionTIRcontra) =>
% 106.14/14.38 ((
% 106.14/14.38 (inIntersectImpInUnion) =>
% 106.14/14.38 ((
% 106.14/14.38 (inIntersectImpInUnion2) =>
% 106.14/14.38 ((
% 106.14/14.38 (inIntersectImpInIntersectUnions) =>
% 106.14/14.38 ((
% 106.14/14.38 (intersectInPowersetIntersectUnions) =>
% 106.14/14.38 ((
% 106.14/14.38 (inComplementUnionImpNotIn1) =>
% 106.14/14.38 ((
% 106.14/14.38 (inComplementUnionImpInComplement1) =>
% 106.14/14.38 ((
% 106.14/14.38 (binunionTE) =>
% 106.14/14.38 ((
% 106.14/14.38 (binunionTEcontra) =>
% 106.14/14.38 ((
% 106.14/14.38 (demorgan2a1) =>
% 106.14/14.38 ((
% 106.14/14.38 (complementUnionInPowersetComplement) =>
% 106.14/14.38 ((
% 106.14/14.38 (demorgan2a2) =>
% 106.14/14.38 ((
% 106.14/14.38 (demorgan1a) =>
% 106.14/14.38 ((
% 106.14/14.38 (demorgan1b) =>
% 106.14/14.38 ((
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% 106.14/14.38 ((
% 106.14/14.38 (demorgan2a) =>
% 106.14/14.38 ((
% 106.14/14.38 (demorgan2b2) =>
% 106.14/14.38 ((
% 106.14/14.38 (demorgan2b) =>
% 106.14/14.38 ((
% 106.14/14.38 (demorgan2) =>
% 106.14/14.38 ((
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% 106.14/14.38 ((
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% 106.14/14.38 ((
% 106.14/14.38 (woz13rule2) =>
% 106.14/14.38 ((
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% 106.14/14.38 ((
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% 106.14/14.38 ((
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% 106.14/14.38 ((
% 106.14/14.38 (woz1_2) =>
% 106.14/14.38 ((
% 106.14/14.38 (woz1_3) =>
% 106.14/14.38 ((
% 106.14/14.38 (woz1_4) =>
% 106.14/14.38 ((
% 106.14/14.38 (woz1_5) =>
% 106.14/14.38 ((
% 106.14/14.38 (breln1all2) =>
% 106.14/14.38 ((
% 106.14/14.38 (breln1SetBreln1) =>
% 106.14/14.38 ((
% 106.14/14.38 (choice2fnsingleton) =>
% 106.14/14.38 ((
% 106.14/14.38 (setOfPairsIsBReln1) =>
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% 106.14/14.38 (breln1all1) =>
% 106.14/14.38 ((
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% 106.14/14.38 ((
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% 106.14/14.38 ((
% 106.14/14.38 (breln1invprop) =>
% 106.14/14.38 ((
% 106.14/14.38 (breln1invI) =>
% 106.14/14.38 ((
% 106.14/14.38 (breln1invE) =>
% 106.14/14.38 ((
% 106.14/14.38 (breln1compprop) =>
% 106.14/14.38 ((
% 106.14/14.38 (breln1compI) =>
% 106.14/14.38 ((
% 106.14/14.38 (breln1compE) =>
% 106.14/14.38 ((
% 106.14/14.38 (breln1compEex) =>
% 106.14/14.38 ((
% 106.14/14.38 (breln1unionprop) =>
% 106.14/14.38 ((
% 106.14/14.38 (breln1unionIL) =>
% 106.14/14.38 ((
% 106.14/14.38 (breln1unionIR) =>
% 106.14/14.38 ((
% 106.14/14.38 (breln1unionI) =>
% 106.14/14.38 ((
% 106.14/14.38 (breln1unionE) =>
% 106.14/14.38 ((
% 106.14/14.38 (breln1unionEcases) =>
% 106.14/14.38 ((
% 106.14/14.38 (breln1unionCommutes) =>
% 106.14/14.38 ((
% 106.14/14.38 (woz2Ex) =>
% 106.14/14.38 ((
% 106.14/14.38 (woz2W) =>
% 106.14/14.38 ((
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% 106.14/14.38 ((
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% 106.14/14.38 ((
% 106.14/14.38 (image1E) =>
% 106.14/14.38 ((
% 106.14/14.38 (image1I) =>
% 106.14/14.38 ((
% 106.14/14.38 (injFuncInInjFuncSet) =>
% 106.14/14.38 ((
% 106.14/14.38 (injFuncSetFuncIn) =>
% 106.14/14.38 ((
% 106.14/14.38 (injFuncSetFuncInj) =>
% 106.14/14.38 ((
% 106.14/14.38 (surjFuncSetFuncIn) =>
% 106.14/14.38 ((
% 106.14/14.38 (surjFuncSetFuncSurj) =>
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% 106.14/14.38 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl25])).
% 106.14/14.38 thf(zip_derived_cl40, plain,
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% 106.14/14.38 ((
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% 106.14/14.38 ((
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% 106.14/14.38 (exuE3u) =>
% 106.14/14.38 ((
% 106.14/14.38 (exu__Cong) =>
% 106.14/14.38 ((
% 106.14/14.38 (setadjoin__Cong) =>
% 106.14/14.38 ((
% 106.14/14.38 (powerset__Cong) =>
% 106.14/14.38 ((
% 106.14/14.38 (setunion__Cong) =>
% 106.14/14.38 ((
% 106.14/14.38 (exuEu) =>
% 106.14/14.38 ((
% 106.14/14.38 (descr__Cong) =>
% 106.14/14.38 ((
% 106.14/14.38 (dsetconstr__Cong) =>
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% 106.14/14.38 ((
% 106.14/14.38 (upairset2IR) =>
% 106.14/14.38 ((
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% 106.14/14.38 ((
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% 106.14/14.38 ((
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% 106.14/14.38 ((
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% 106.14/14.38 ((
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% 106.14/14.38 ((
% 106.14/14.38 (binintersectI) =>
% 106.14/14.38 ((
% 106.14/14.38 (binintersectSubset5) =>
% 106.14/14.38 ((
% 106.14/14.38 (binintersectEL) =>
% 106.14/14.38 ((
% 106.14/14.38 (binintersectLsub) =>
% 106.14/14.38 ((
% 106.14/14.38 (binintersectSubset2) =>
% 106.14/14.38 ((
% 106.14/14.38 (binintersectSubset3) =>
% 106.14/14.38 ((
% 106.14/14.38 (binintersectER) =>
% 106.14/14.38 ((
% 106.14/14.38 (disjointsetsI1) =>
% 106.14/14.38 ((
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% 106.14/14.38 ((
% 106.14/14.38 (binintersectSubset4) =>
% 106.14/14.38 ((
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% 106.14/14.38 ((
% 106.14/14.38 (bs114d) =>
% 106.14/14.38 ((
% 106.14/14.38 (setminusI) =>
% 106.14/14.38 ((
% 106.14/14.38 (setminusEL) =>
% 106.14/14.38 ((
% 106.14/14.38 (setminusER) =>
% 106.14/14.38 ((
% 106.14/14.38 (setminusSubset2) =>
% 106.14/14.38 ((
% 106.14/14.38 (setminusERneg) =>
% 106.14/14.38 ((
% 106.14/14.38 (setminusELneg) =>
% 106.14/14.38 ((
% 106.14/14.38 (setminusILneg) =>
% 106.14/14.38 ((
% 106.14/14.38 (setminusIRneg) =>
% 106.14/14.38 ((
% 106.14/14.38 (setminusLsub) =>
% 106.14/14.38 ((
% 106.14/14.38 (setminusSubset1) =>
% 106.14/14.38 ((
% 106.14/14.38 (symdiffE) =>
% 106.14/14.38 ((
% 106.14/14.38 (symdiffI1) =>
% 106.14/14.38 ((
% 106.14/14.38 (symdiffI2) =>
% 106.14/14.38 ((
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% 106.14/14.38 ((
% 106.14/14.38 (symdiffIneg2) =>
% 106.14/14.38 ((
% 106.14/14.38 (secondinupair) =>
% 106.14/14.38 ((
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% 106.14/14.38 ((
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% 106.14/14.38 ((
% 106.14/14.38 (kpairp) =>
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% 106.14/14.38 (singletonsubset) =>
% 106.14/14.38 ((
% 106.14/14.38 (singletoninpowerset) =>
% 106.14/14.38 ((
% 106.14/14.38 (singletoninpowunion) =>
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% 106.14/14.38 ((
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% 106.14/14.38 ((
% 106.14/14.38 (ubforcartprodlem2) =>
% 106.14/14.38 ((
% 106.14/14.38 (ubforcartprodlem3) =>
% 106.14/14.38 ((
% 106.14/14.38 (cartprodpairin) =>
% 106.14/14.38 ((
% 106.14/14.38 (cartprodmempair1) =>
% 106.14/14.38 ((
% 106.14/14.38 (cartprodmempair) =>
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% 106.14/14.38 ((
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% 106.14/14.38 (complementTcontraSubset) =>
% 106.14/14.38 ((
% 106.14/14.38 (binunionTILcontra) =>
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% 106.14/14.38 (binunionTIRcontra) =>
% 106.14/14.38 ((
% 106.14/14.38 (inIntersectImpInUnion) =>
% 106.14/14.38 ((
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% 106.14/14.38 ((
% 106.14/14.38 (inIntersectImpInIntersectUnions) =>
% 106.14/14.38 ((
% 106.14/14.38 (intersectInPowersetIntersectUnions) =>
% 106.14/14.38 ((
% 106.14/14.38 (inComplementUnionImpNotIn1) =>
% 106.14/14.38 ((
% 106.14/14.38 (inComplementUnionImpInComplement1) =>
% 106.14/14.38 ((
% 106.14/14.38 (binunionTE) =>
% 106.14/14.38 ((
% 106.14/14.38 (binunionTEcontra) =>
% 106.14/14.38 ((
% 106.14/14.38 (demorgan2a1) =>
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% 106.14/14.38 (complementUnionInPowersetComplement) =>
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% 106.14/14.38 ((
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% 106.14/14.38 (demorgan1b) =>
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% 106.14/14.38 ((
% 106.14/14.38 (demorgan2a) =>
% 106.14/14.38 ((
% 106.14/14.38 (demorgan2b2) =>
% 106.14/14.38 ((
% 106.14/14.38 (demorgan2b) =>
% 106.14/14.38 ((
% 106.14/14.38 (demorgan2) =>
% 106.14/14.38 ((
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% 106.14/14.38 ((
% 106.14/14.38 (woz13rule2) =>
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% 106.14/14.38 (woz13rule3) =>
% 106.14/14.38 ((
% 106.14/14.38 (woz13rule4) =>
% 106.14/14.38 ((
% 106.14/14.38 (woz1_1) =>
% 106.14/14.38 ((
% 106.14/14.38 (woz1_2) =>
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% 106.14/14.38 (woz1_3) =>
% 106.14/14.38 ((
% 106.14/14.38 (woz1_4) =>
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% 106.14/14.38 (woz1_5) =>
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% 106.14/14.38 (breln1all2) =>
% 106.14/14.38 ((
% 106.14/14.38 (breln1SetBreln1) =>
% 106.14/14.38 ((
% 106.14/14.38 (choice2fnsingleton) =>
% 106.14/14.38 ((
% 106.14/14.38 (setOfPairsIsBReln1) =>
% 106.14/14.38 ((
% 106.14/14.38 (breln1all1) =>
% 106.14/14.38 ((
% 106.14/14.38 (subbreln1) =>
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% 106.14/14.38 (eqbreln1) =>
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% 106.14/14.38 ((
% 106.14/14.38 (breln1invI) =>
% 106.14/14.38 ((
% 106.14/14.38 (breln1invE) =>
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% 106.14/14.38 (breln1compprop) =>
% 106.14/14.38 ((
% 106.14/14.38 (breln1compI) =>
% 106.14/14.38 ((
% 106.14/14.38 (breln1compE) =>
% 106.14/14.38 ((
% 106.14/14.38 (breln1compEex) =>
% 106.14/14.38 ((
% 106.14/14.38 (breln1unionprop) =>
% 106.14/14.38 ((
% 106.14/14.38 (breln1unionIL) =>
% 106.14/14.38 ((
% 106.14/14.38 (breln1unionIR) =>
% 106.14/14.38 ((
% 106.14/14.38 (breln1unionI) =>
% 106.14/14.38 ((
% 106.14/14.38 (breln1unionE) =>
% 106.14/14.38 ((
% 106.14/14.38 (breln1unionEcases) =>
% 106.14/14.38 ((
% 106.14/14.38 (breln1unionCommutes) =>
% 106.14/14.38 ((
% 106.14/14.38 (woz2Ex) =>
% 106.14/14.38 ((
% 106.14/14.38 (woz2W) =>
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% 106.14/14.38 ((
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% 106.14/14.38 ((
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% 106.14/14.38 ((
% 106.14/14.38 (image1E) =>
% 106.14/14.38 ((
% 106.14/14.38 (image1I) =>
% 106.14/14.38 ((
% 106.14/14.38 (injFuncInInjFuncSet) =>
% 106.14/14.38 ((
% 106.14/14.38 (injFuncSetFuncIn) =>
% 106.14/14.38 ((
% 106.14/14.38 (injFuncSetFuncInj) =>
% 106.14/14.38 ((
% 106.14/14.38 (surjFuncSetFuncIn) =>
% 106.14/14.38 ((
% 106.14/14.38 (surjFuncSetFuncSurj) =>
% 106.14/14.38 ((
% 106.14/14.38 (leftInvIsSurj) =>
% 106.14/14.38 ((
% 106.14/14.38 (surjCantorThm) =>
% 106.14/14.38 ((
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% 106.14/14.38 nonempty)) @
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% 106.14/14.39 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl33])).
% 106.14/14.39 thf(zip_derived_cl46, plain,
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% 106.14/14.39 ((
% 106.14/14.39 (quantDeMorgan1) =>
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% 106.14/14.39 ((
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% 106.14/14.39 (exu__Cong) =>
% 106.14/14.39 ((
% 106.14/14.39 (setadjoin__Cong) =>
% 106.14/14.39 ((
% 106.14/14.39 (powerset__Cong) =>
% 106.14/14.39 ((
% 106.14/14.39 (setunion__Cong) =>
% 106.14/14.39 ((
% 106.14/14.39 (exuEu) =>
% 106.14/14.39 ((
% 106.14/14.39 (descr__Cong) =>
% 106.14/14.39 ((
% 106.14/14.39 (dsetconstr__Cong) =>
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% 106.14/14.39 ((
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% 106.14/14.39 ((
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% 106.14/14.39 ((
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% 106.14/14.39 ((
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% 106.14/14.39 ((
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% 106.14/14.39 ((
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% 106.14/14.39 ((
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% 106.14/14.39 ((
% 106.14/14.39 (setminusSubset2) =>
% 106.14/14.39 ((
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% 106.14/14.39 ((
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% 106.14/14.39 ((
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% 106.14/14.39 ((
% 106.14/14.39 (setminusIRneg) =>
% 106.14/14.39 ((
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% 106.14/14.39 ((
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% 106.14/14.39 ((
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% 106.14/14.39 ((
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% 106.14/14.39 ((
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% 106.14/14.39 ((
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% 106.14/14.39 ((
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% 106.14/14.39 ((
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% 106.14/14.39 ((
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% 106.14/14.39 ((
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% 106.14/14.39 (beta1) =>
% 106.14/14.39 ((
% 106.14/14.39 (eta1) =>
% 106.14/14.39 ((
% 106.14/14.39 (lam2lamEq) =>
% 106.14/14.39 ((
% 106.14/14.39 (beta2) =>
% 106.14/14.39 ((
% 106.14/14.39 (eta2) =>
% 106.14/14.39 ((
% 106.14/14.39 (iffalseProp1) =>
% 106.14/14.39 ((
% 106.14/14.39 (iffalseProp2) =>
% 106.14/14.39 ((
% 106.14/14.39 (iftrueProp1) =>
% 106.14/14.39 ((
% 106.14/14.39 (iftrueProp2) =>
% 106.14/14.39 ((
% 106.14/14.39 (ifSingleton) =>
% 106.14/14.39 ((
% 106.14/14.39 (ifp) =>
% 106.14/14.39 ((
% 106.14/14.39 (theeq) =>
% 106.14/14.39 ((
% 106.14/14.39 (iftrue) =>
% 106.14/14.39 ((
% 106.14/14.39 (iffalse) =>
% 106.14/14.39 ((
% 106.14/14.39 (iftrueorfalse) =>
% 106.14/14.39 ((
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% 106.14/14.39 ((
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% 106.14/14.39 ((
% 106.14/14.39 (complementT_lem) =>
% 106.14/14.39 ((
% 106.14/14.39 (setextT) =>
% 106.14/14.39 ((
% 106.14/14.39 (subsetTI) =>
% 106.14/14.39 ((
% 106.14/14.39 (powersetTI1) =>
% 106.14/14.39 ((
% 106.14/14.39 (powersetTE1) =>
% 106.14/14.39 ((
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% 106.14/14.39 ((
% 106.14/14.39 (complementTE1) =>
% 106.14/14.39 ((
% 106.14/14.39 (binintersectTELcontra) =>
% 106.14/14.39 ((
% 106.14/14.39 (binintersectTERcontra) =>
% 106.14/14.39 ((
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% 106.14/14.39 (contrasubsetT1) =>
% 106.14/14.39 ((
% 106.14/14.39 (contrasubsetT2) =>
% 106.14/14.39 ((
% 106.14/14.39 (contrasubsetT3) =>
% 106.14/14.39 ((
% 106.14/14.39 (doubleComplementI1) =>
% 106.14/14.39 ((
% 106.14/14.39 (doubleComplementE1) =>
% 106.14/14.39 ((
% 106.14/14.39 (doubleComplementSub1) =>
% 106.14/14.39 ((
% 106.14/14.39 (doubleComplementSub2) =>
% 106.14/14.39 ((
% 106.14/14.39 (doubleComplementEq) =>
% 106.14/14.39 ((
% 106.14/14.39 (complementTnotintersectT) =>
% 106.14/14.39 ((
% 106.14/14.39 (complementImpComplementIntersect) =>
% 106.14/14.39 ((
% 106.14/14.39 (complementSubsetComplementIntersect) =>
% 106.14/14.39 ((
% 106.14/14.39 (complementInPowersetComplementIntersect) =>
% 106.14/14.39 ((
% 106.14/14.39 (contraSubsetComplement) =>
% 106.14/14.39 ((
% 106.14/14.39 (complementTcontraSubset) =>
% 106.14/14.39 ((
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% 106.14/14.39 (binunionTIRcontra) =>
% 106.14/14.39 ((
% 106.14/14.39 (inIntersectImpInUnion) =>
% 106.14/14.39 ((
% 106.14/14.39 (inIntersectImpInUnion2) =>
% 106.14/14.39 ((
% 106.14/14.39 (inIntersectImpInIntersectUnions) =>
% 106.14/14.39 ((
% 106.14/14.39 (intersectInPowersetIntersectUnions) =>
% 106.14/14.39 ((
% 106.14/14.39 (inComplementUnionImpNotIn1) =>
% 106.14/14.39 ((
% 106.14/14.39 (inComplementUnionImpInComplement1) =>
% 106.14/14.39 ((
% 106.14/14.39 (binunionTE) =>
% 106.14/14.39 ((
% 106.14/14.39 (binunionTEcontra) =>
% 106.14/14.39 ((
% 106.14/14.39 (demorgan2a1) =>
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% 106.14/14.39 ((
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% 106.14/14.39 ((
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% 106.14/14.39 ((
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% 106.14/14.39 ((
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% 106.14/14.39 ((
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% 106.14/14.39 ((
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% 106.14/14.39 ((
% 106.14/14.39 (woz13rule2) =>
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% 106.14/14.39 (woz13rule3) =>
% 106.14/14.39 ((
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% 106.14/14.39 ((
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% 106.14/14.39 ((
% 106.14/14.39 (woz1_2) =>
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% 106.14/14.39 (woz1_3) =>
% 106.14/14.39 ((
% 106.14/14.39 (woz1_4) =>
% 106.14/14.39 ((
% 106.14/14.39 (woz1_5) =>
% 106.14/14.39 ((
% 106.14/14.39 (breln1all2) =>
% 106.14/14.39 ((
% 106.14/14.39 (breln1SetBreln1) =>
% 106.14/14.39 ((
% 106.14/14.39 (choice2fnsingleton) =>
% 106.14/14.39 ((
% 106.14/14.39 (setOfPairsIsBReln1) =>
% 106.14/14.39 ((
% 106.14/14.39 (breln1all1) =>
% 106.14/14.39 ((
% 106.14/14.39 (subbreln1) =>
% 106.14/14.39 ((
% 106.14/14.39 (eqbreln1) =>
% 106.14/14.39 ((
% 106.14/14.39 (breln1invprop) =>
% 106.14/14.39 ((
% 106.14/14.39 (breln1invI) =>
% 106.14/14.39 ((
% 106.14/14.39 (breln1invE) =>
% 106.14/14.39 ((
% 106.14/14.39 (breln1compprop) =>
% 106.14/14.39 ((
% 106.14/14.39 (breln1compI) =>
% 106.14/14.39 ((
% 106.14/14.39 (breln1compE) =>
% 106.14/14.39 ((
% 106.14/14.39 (breln1compEex) =>
% 106.14/14.39 ((
% 106.14/14.39 (breln1unionprop) =>
% 106.14/14.39 ((
% 106.14/14.39 (breln1unionIL) =>
% 106.14/14.39 ((
% 106.14/14.39 (breln1unionIR) =>
% 106.14/14.39 ((
% 106.14/14.39 (breln1unionI) =>
% 106.14/14.39 ((
% 106.14/14.39 (breln1unionE) =>
% 106.14/14.39 ((
% 106.14/14.39 (breln1unionEcases) =>
% 106.14/14.39 ((
% 106.14/14.39 (breln1unionCommutes) =>
% 106.14/14.39 ((
% 106.14/14.39 (woz2Ex) =>
% 106.14/14.39 ((
% 106.14/14.39 (woz2W) =>
% 106.14/14.39 ((
% 106.14/14.39 (woz2A) =>
% 106.14/14.39 ((
% 106.14/14.39 (woz2B) =>
% 106.14/14.39 ((
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% 106.14/14.39 ((
% 106.14/14.39 (image1Ex1) =>
% 106.14/14.39 ((
% 106.14/14.39 (image1Equiv) =>
% 106.14/14.39 ((
% 106.14/14.39 (image1E) =>
% 106.14/14.39 ((
% 106.14/14.39 (image1I) =>
% 106.14/14.39 ((
% 106.14/14.39 (injFuncInInjFuncSet) =>
% 106.14/14.39 ((
% 106.14/14.39 (injFuncSetFuncIn) =>
% 106.14/14.39 ((
% 106.14/14.39 (injFuncSetFuncInj) =>
% 106.14/14.39 ((
% 106.14/14.39 (surjFuncSetFuncIn) =>
% 106.14/14.39 ((
% 106.14/14.39 (surjFuncSetFuncSurj) =>
% 106.14/14.39 ((
% 106.14/14.39 (leftInvIsSurj) =>
% 106.14/14.39 ((
% 106.14/14.39 (surjCantorThm) =>
% 106.14/14.39 ((
% 106.14/14.39 (!!) @ (
% 106.14/14.39 (('#S') @ (
% 106.14/14.39 (
% 106.14/14.39 ('#B') @ (
% 106.14/14.39 =>) @
% 106.14/14.39 nonempty)) @
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% 106.14/14.39 (
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% 106.14/14.39 (
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% 106.14/14.39 (
% 106.14/14.39 ('#B') @ (
% 106.14/14.39 &))) @
% 106.14/14.39 (
% 106.14/14.39 (
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% 106.14/14.39 (
% 106.14/14.39 (
% 106.14/14.39 ('#C') @ (
% 106.14/14.39 (
% 106.14/14.39 ('#B') @ (
% 106.14/14.39 '#C') @
% 106.14/14.39 (
% 106.14/14.39 (
% 106.14/14.39 ('#B') @ (
% 106.14/14.39 (
% 106.14/14.39 ('#B') @ (
% 106.14/14.39 =))) @
% 106.14/14.39 (
% 106.14/14.39 (
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% 106.14/14.39 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl40])).
% 106.14/14.39 thf(zip_derived_cl52, plain,
% 106.14/14.39 (~ (((foundationAx) =>
% 106.14/14.39 (((wellorderingAx) =>
% 106.14/14.39 (((descrp) =>
% 106.14/14.39 (((dsetconstrI) =>
% 106.14/14.39 (((dsetconstrEL) =>
% 106.14/14.39 (((dsetconstrER) =>
% 106.14/14.39 (((exuE1) =>
% 106.14/14.39 (((prop2setE) =>
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% 106.14/14.39 (((emptyI) =>
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% 106.14/14.39 (((setbeta) =>
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% 106.14/14.39 (((in @ emptyset @
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% 106.14/14.39 (((setadjoinIR) =>
% 106.14/14.39 (((setadjoinE) =>
% 106.14/14.39 (((setadjoinOr) =>
% 106.14/14.39 (((setoftrueEq) =>
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% 106.14/14.39 (((powersetE) =>
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% 106.14/14.39 ((
% 106.14/14.39 (exuE2) =>
% 106.14/14.39 ((
% 106.14/14.39 (nonemptyImpWitness) =>
% 106.14/14.39 ((
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% 106.14/14.39 ((
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% 106.14/14.39 ((
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% 106.14/14.39 ((
% 106.14/14.39 (emptyE1) =>
% 106.14/14.39 ((
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% 106.14/14.39 ((
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% 106.14/14.39 ((
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% 106.14/14.39 ((
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% 106.14/14.39 ((
% 106.14/14.39 (inCongP) =>
% 106.14/14.39 ((
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% 106.14/14.39 ((
% 106.14/14.39 (exuE3u) =>
% 106.14/14.39 ((
% 106.14/14.39 (exu__Cong) =>
% 106.14/14.39 ((
% 106.14/14.39 (setadjoin__Cong) =>
% 106.14/14.39 ((
% 106.14/14.39 (powerset__Cong) =>
% 106.14/14.39 ((
% 106.14/14.39 (setunion__Cong) =>
% 106.14/14.39 ((
% 106.14/14.39 (exuEu) =>
% 106.14/14.39 ((
% 106.14/14.39 (descr__Cong) =>
% 106.14/14.39 ((
% 106.14/14.39 (dsetconstr__Cong) =>
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% 106.14/14.39 ((
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% 106.14/14.39 ((
% 106.14/14.39 (upairset2IR) =>
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% 106.14/14.39 ((
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% 106.14/14.39 ((
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% 106.14/14.39 ((
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% 106.14/14.39 ((
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% 106.14/14.39 ((
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% 106.14/14.39 ((
% 106.14/14.39 (binintersectSubset3) =>
% 106.14/14.39 ((
% 106.14/14.39 (binintersectER) =>
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% 106.14/14.39 ((
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% 106.14/14.39 ((
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% 106.14/14.39 ((
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% 106.14/14.39 ((
% 106.14/14.39 (setminusSubset2) =>
% 106.14/14.39 ((
% 106.14/14.39 (setminusERneg) =>
% 106.14/14.39 ((
% 106.14/14.39 (setminusELneg) =>
% 106.14/14.39 ((
% 106.14/14.39 (setminusILneg) =>
% 106.14/14.39 ((
% 106.14/14.39 (setminusIRneg) =>
% 106.14/14.39 ((
% 106.14/14.39 (setminusLsub) =>
% 106.14/14.39 ((
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% 106.14/14.39 ((
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% 106.14/14.39 ((
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% 106.14/14.39 ((
% 106.14/14.39 (symdiffI2) =>
% 106.14/14.39 ((
% 106.14/14.39 (symdiffIneg1) =>
% 106.14/14.39 ((
% 106.14/14.39 (symdiffIneg2) =>
% 106.14/14.39 ((
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% 106.14/14.39 ((
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% 106.14/14.39 ((
% 106.14/14.39 (setukpairIR) =>
% 106.14/14.39 ((
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% 106.14/14.39 ((
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% 106.14/14.39 ((
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% 106.14/14.39 ((
% 106.14/14.39 (singletoninpowunion) =>
% 106.14/14.39 ((
% 106.14/14.39 (upairset2E) =>
% 106.14/14.39 ((
% 106.14/14.39 (upairsubunion) =>
% 106.14/14.39 ((
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% 106.14/14.39 ((
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% 106.14/14.39 ((
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% 106.14/14.39 ((
% 106.14/14.39 (cartprodmempair1) =>
% 106.14/14.39 ((
% 106.14/14.39 (cartprodmempair) =>
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% 106.14/14.39 ((
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% 106.14/14.39 ((
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% 106.14/14.39 ((
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% 106.14/14.39 ((
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% 106.14/14.39 ((
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% 106.14/14.39 (setukpairinjR12) =>
% 106.14/14.39 ((
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% 106.14/14.39 ((
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% 106.14/14.39 ((
% 106.14/14.39 (setukpairinjR2) =>
% 106.14/14.39 ((
% 106.14/14.39 (setukpairinjR) =>
% 106.14/14.39 ((
% 106.14/14.39 (ksndsingleton) =>
% 106.14/14.39 ((
% 106.14/14.39 (ksndpairEq) =>
% 106.14/14.39 ((
% 106.14/14.39 (kpairsurjEq) =>
% 106.14/14.39 ((
% 106.14/14.39 (cartprodsndin) =>
% 106.14/14.39 ((
% 106.14/14.39 (cartprodpairmemEL) =>
% 106.14/14.39 ((
% 106.14/14.39 (cartprodpairmemER) =>
% 106.14/14.39 ((
% 106.14/14.39 (cartprodmempaircEq) =>
% 106.14/14.39 ((
% 106.14/14.39 (cartprodfstpairEq) =>
% 106.14/14.39 ((
% 106.14/14.39 (cartprodsndpairEq) =>
% 106.14/14.39 ((
% 106.14/14.39 (cartprodpairsurjEq) =>
% 106.14/14.39 ((
% 106.14/14.39 (dpsetconstrI) =>
% 106.14/14.39 ((
% 106.14/14.39 (dpsetconstrSub) =>
% 106.14/14.39 ((
% 106.14/14.39 (setOfPairsIsBReln) =>
% 106.14/14.39 ((
% 106.14/14.39 (dpsetconstrERa) =>
% 106.14/14.39 ((
% 106.14/14.39 (dpsetconstrEL1) =>
% 106.14/14.39 ((
% 106.14/14.39 (dpsetconstrEL2) =>
% 106.14/14.39 ((
% 106.14/14.39 (dpsetconstrER) =>
% 106.14/14.39 ((
% 106.14/14.39 (funcImageSingleton) =>
% 106.14/14.39 ((
% 106.14/14.39 (apProp) =>
% 106.14/14.39 ((
% 106.14/14.39 (app) =>
% 106.14/14.39 ((
% 106.14/14.39 (infuncsetfunc) =>
% 106.14/14.39 ((
% 106.14/14.39 (ap2p) =>
% 106.14/14.39 ((
% 106.14/14.39 (funcinfuncset) =>
% 106.14/14.39 ((
% 106.14/14.39 (lamProp) =>
% 106.14/14.39 ((
% 106.14/14.39 (lamp) =>
% 106.14/14.39 ((
% 106.14/14.39 (lam2p) =>
% 106.14/14.39 ((
% 106.14/14.39 (brelnall1) =>
% 106.14/14.39 ((
% 106.14/14.39 (brelnall2) =>
% 106.14/14.39 ((
% 106.14/14.39 (ex1E2) =>
% 106.14/14.39 ((
% 106.14/14.39 (funcGraphProp1) =>
% 106.14/14.39 ((
% 106.14/14.39 (funcGraphProp3) =>
% 106.14/14.39 ((
% 106.14/14.39 (funcGraphProp2) =>
% 106.14/14.39 ((
% 106.14/14.39 (funcextLem) =>
% 106.14/14.39 ((
% 106.14/14.39 (funcGraphProp4) =>
% 106.14/14.39 ((
% 106.14/14.39 (subbreln) =>
% 106.14/14.39 ((
% 106.14/14.39 (eqbreln) =>
% 106.14/14.39 ((
% 106.14/14.39 (funcext) =>
% 106.14/14.39 ((
% 106.14/14.39 (funcext2) =>
% 106.14/14.39 ((
% 106.14/14.39 (ap2apEq1) =>
% 106.14/14.39 ((
% 106.14/14.39 (ap2apEq2) =>
% 106.14/14.39 ((
% 106.14/14.39 (beta1) =>
% 106.14/14.39 ((
% 106.14/14.39 (eta1) =>
% 106.14/14.39 ((
% 106.14/14.39 (lam2lamEq) =>
% 106.14/14.39 ((
% 106.14/14.39 (beta2) =>
% 106.14/14.39 ((
% 106.14/14.39 (eta2) =>
% 106.14/14.39 ((
% 106.14/14.39 (iffalseProp1) =>
% 106.14/14.39 ((
% 106.14/14.39 (iffalseProp2) =>
% 106.14/14.39 ((
% 106.14/14.39 (iftrueProp1) =>
% 106.14/14.39 ((
% 106.14/14.39 (iftrueProp2) =>
% 106.14/14.39 ((
% 106.14/14.39 (ifSingleton) =>
% 106.14/14.39 ((
% 106.14/14.39 (ifp) =>
% 106.14/14.39 ((
% 106.14/14.39 (theeq) =>
% 106.14/14.39 ((
% 106.14/14.39 (iftrue) =>
% 106.14/14.39 ((
% 106.14/14.39 (iffalse) =>
% 106.14/14.39 ((
% 106.14/14.39 (iftrueorfalse) =>
% 106.14/14.39 ((
% 106.14/14.39 (binintersectT_lem) =>
% 106.14/14.39 ((
% 106.14/14.39 (binunionT_lem) =>
% 106.14/14.39 ((
% 106.14/14.39 (powersetT_lem) =>
% 106.14/14.39 ((
% 106.14/14.39 (setminusT_lem) =>
% 106.14/14.39 ((
% 106.14/14.39 (complementT_lem) =>
% 106.14/14.39 ((
% 106.14/14.39 (setextT) =>
% 106.14/14.39 ((
% 106.14/14.39 (subsetTI) =>
% 106.14/14.39 ((
% 106.14/14.39 (powersetTI1) =>
% 106.14/14.39 ((
% 106.14/14.39 (powersetTE1) =>
% 106.14/14.39 ((
% 106.14/14.39 (complementTI1) =>
% 106.14/14.39 ((
% 106.14/14.39 (complementTE1) =>
% 106.14/14.39 ((
% 106.14/14.39 (binintersectTELcontra) =>
% 106.14/14.39 ((
% 106.14/14.39 (binintersectTERcontra) =>
% 106.14/14.39 ((
% 106.14/14.39 (contrasubsetT) =>
% 106.14/14.39 ((
% 106.14/14.39 (contrasubsetT1) =>
% 106.14/14.39 ((
% 106.14/14.39 (contrasubsetT2) =>
% 106.14/14.39 ((
% 106.14/14.39 (contrasubsetT3) =>
% 106.14/14.39 ((
% 106.14/14.39 (doubleComplementI1) =>
% 106.14/14.39 ((
% 106.14/14.39 (doubleComplementE1) =>
% 106.14/14.39 ((
% 106.14/14.39 (doubleComplementSub1) =>
% 106.14/14.39 ((
% 106.14/14.39 (doubleComplementSub2) =>
% 106.14/14.39 ((
% 106.14/14.39 (doubleComplementEq) =>
% 106.14/14.39 ((
% 106.14/14.39 (complementTnotintersectT) =>
% 106.14/14.39 ((
% 106.14/14.39 (complementImpComplementIntersect) =>
% 106.14/14.39 ((
% 106.14/14.39 (complementSubsetComplementIntersect) =>
% 106.14/14.39 ((
% 106.14/14.39 (complementInPowersetComplementIntersect) =>
% 106.14/14.39 ((
% 106.14/14.39 (contraSubsetComplement) =>
% 106.14/14.39 ((
% 106.14/14.39 (complementTcontraSubset) =>
% 106.14/14.39 ((
% 106.14/14.39 (binunionTILcontra) =>
% 106.14/14.39 ((
% 106.14/14.39 (binunionTIRcontra) =>
% 106.14/14.39 ((
% 106.14/14.39 (inIntersectImpInUnion) =>
% 106.14/14.39 ((
% 106.14/14.39 (inIntersectImpInUnion2) =>
% 106.14/14.39 ((
% 106.14/14.39 (inIntersectImpInIntersectUnions) =>
% 106.14/14.39 ((
% 106.14/14.39 (intersectInPowersetIntersectUnions) =>
% 106.14/14.39 ((
% 106.14/14.39 (inComplementUnionImpNotIn1) =>
% 106.14/14.39 ((
% 106.14/14.39 (inComplementUnionImpInComplement1) =>
% 106.14/14.39 ((
% 106.14/14.39 (binunionTE) =>
% 106.14/14.39 ((
% 106.14/14.39 (binunionTEcontra) =>
% 106.14/14.39 ((
% 106.14/14.39 (demorgan2a1) =>
% 106.14/14.39 ((
% 106.14/14.39 (complementUnionInPowersetComplement) =>
% 106.14/14.39 ((
% 106.14/14.39 (demorgan2a2) =>
% 106.14/14.39 ((
% 106.14/14.39 (demorgan1a) =>
% 106.14/14.39 ((
% 106.14/14.39 (demorgan1b) =>
% 106.14/14.39 ((
% 106.14/14.39 (demorgan1) =>
% 106.14/14.39 ((
% 106.14/14.39 (demorgan2a) =>
% 106.14/14.39 ((
% 106.14/14.39 (demorgan2b2) =>
% 106.14/14.39 ((
% 106.14/14.39 (demorgan2b) =>
% 106.14/14.39 ((
% 106.14/14.39 (demorgan2) =>
% 106.14/14.39 ((
% 106.14/14.39 (woz13rule0) =>
% 106.14/14.39 ((
% 106.14/14.39 (woz13rule1) =>
% 106.14/14.39 ((
% 106.14/14.39 (woz13rule2) =>
% 106.14/14.39 ((
% 106.14/14.39 (woz13rule3) =>
% 106.14/14.39 ((
% 106.14/14.39 (woz13rule4) =>
% 106.14/14.39 ((
% 106.14/14.39 (woz1_1) =>
% 106.14/14.39 ((
% 106.14/14.39 (woz1_2) =>
% 106.14/14.39 ((
% 106.14/14.39 (woz1_3) =>
% 106.14/14.39 ((
% 106.14/14.39 (woz1_4) =>
% 106.14/14.39 ((
% 106.14/14.39 (woz1_5) =>
% 106.14/14.39 ((
% 106.14/14.39 (breln1all2) =>
% 106.14/14.39 ((
% 106.14/14.39 (breln1SetBreln1) =>
% 106.14/14.39 ((
% 106.14/14.39 (choice2fnsingleton) =>
% 106.14/14.39 ((
% 106.14/14.39 (setOfPairsIsBReln1) =>
% 106.14/14.39 ((
% 106.14/14.39 (breln1all1) =>
% 106.14/14.39 ((
% 106.14/14.39 (subbreln1) =>
% 106.14/14.39 ((
% 106.14/14.39 (eqbreln1) =>
% 106.14/14.39 ((
% 106.14/14.39 (breln1invprop) =>
% 106.14/14.39 ((
% 106.14/14.39 (breln1invI) =>
% 106.14/14.39 ((
% 106.14/14.39 (breln1invE) =>
% 106.14/14.39 ((
% 106.14/14.39 (breln1compprop) =>
% 106.14/14.39 ((
% 106.14/14.39 (breln1compI) =>
% 106.14/14.39 ((
% 106.14/14.39 (breln1compE) =>
% 106.14/14.39 ((
% 106.14/14.39 (breln1compEex) =>
% 106.14/14.39 ((
% 106.14/14.39 (breln1unionprop) =>
% 106.14/14.39 ((
% 106.14/14.39 (breln1unionIL) =>
% 106.14/14.39 ((
% 106.14/14.39 (breln1unionIR) =>
% 106.14/14.39 ((
% 106.14/14.39 (breln1unionI) =>
% 106.14/14.39 ((
% 106.14/14.39 (breln1unionE) =>
% 106.14/14.39 ((
% 106.14/14.39 (breln1unionEcases) =>
% 106.14/14.39 ((
% 106.14/14.39 (breln1unionCommutes) =>
% 106.14/14.39 ((
% 106.14/14.39 (woz2Ex) =>
% 106.14/14.39 ((
% 106.14/14.39 (woz2W) =>
% 106.14/14.39 ((
% 106.14/14.39 (woz2A) =>
% 106.14/14.39 ((
% 106.14/14.39 (woz2B) =>
% 106.14/14.39 ((
% 106.14/14.39 (image1Ex) =>
% 106.14/14.39 ((
% 106.14/14.39 (image1Ex1) =>
% 106.14/14.39 ((
% 106.14/14.39 (image1Equiv) =>
% 106.14/14.39 ((
% 106.14/14.39 (image1E) =>
% 106.14/14.39 ((
% 106.14/14.39 (image1I) =>
% 106.14/14.39 ((
% 106.14/14.39 (injFuncInInjFuncSet) =>
% 106.14/14.39 ((
% 106.14/14.39 (injFuncSetFuncIn) =>
% 106.14/14.39 ((
% 106.14/14.39 (injFuncSetFuncInj) =>
% 106.14/14.39 ((
% 106.14/14.39 (surjFuncSetFuncIn) =>
% 106.14/14.39 ((
% 106.14/14.39 (surjFuncSetFuncSurj) =>
% 106.14/14.39 ((
% 106.14/14.39 (leftInvIsSurj) =>
% 106.14/14.39 ((
% 106.14/14.39 (surjCantorThm) =>
% 106.14/14.39 ((
% 106.14/14.39 (!!) @ (
% 106.14/14.39 (('#S') @ (
% 106.14/14.39 (
% 106.14/14.39 ('#B') @ (
% 106.14/14.39 =>) @
% 106.14/14.39 nonempty)) @
% 106.14/14.39 (
% 106.14/14.39 (
% 106.14/14.39 ('#B') @ (
% 106.14/14.39 ??) @
% 106.14/14.39 (
% 106.14/14.39 (
% 106.14/14.39 ('#S') @ (
% 106.14/14.39 (
% 106.14/14.39 ('#B') @ (
% 106.14/14.39 '#S') @
% 106.14/14.39 (
% 106.14/14.39 (
% 106.14/14.39 ('#B') @ (
% 106.14/14.39 (
% 106.14/14.39 ('#B') @ (
% 106.14/14.39 &))) @
% 106.14/14.39 (
% 106.14/14.39 (
% 106.14/14.39 ('#C') @ in)))))) @
% 106.14/14.39 (
% 106.14/14.39 (
% 106.14/14.39 ('#C') @ (
% 106.14/14.39 (
% 106.14/14.39 ('#B') @ (
% 106.14/14.39 '#C') @
% 106.14/14.39 (
% 106.14/14.39 (
% 106.14/14.39 ('#B') @ (
% 106.14/14.39 (
% 106.14/14.39 ('#B') @ (
% 106.14/14.39 =))) @
% 106.14/14.39 (
% 106.14/14.39 (
% 106.14/14.39 ('#C') @ binintersect)))))) @
% 106.14/14.39 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.14/14.39 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl46])).
% 106.14/14.39 thf(zip_derived_cl58, plain,
% 106.14/14.39 (~ (((wellorderingAx) =>
% 106.14/14.39 (((descrp) =>
% 106.14/14.39 (((dsetconstrI) =>
% 106.14/14.39 (((dsetconstrEL) =>
% 106.14/14.39 (((dsetconstrER) =>
% 106.14/14.39 (((exuE1) =>
% 106.14/14.39 (((prop2setE) =>
% 106.14/14.39 (((emptysetE) =>
% 106.14/14.39 (((emptysetimpfalse) =>
% 106.14/14.39 (((notinemptyset) =>
% 106.14/14.39 (((exuE3e) =>
% 106.14/14.39 (((setext) =>
% 106.14/14.39 (((emptyI) =>
% 106.14/14.39 (((noeltsimpempty) =>
% 106.14/14.39 (((setbeta) =>
% 106.14/14.39 (((nonemptyE1) =>
% 106.14/14.39 (((nonemptyI) =>
% 106.14/14.39 (((nonemptyI1) =>
% 106.14/14.39 (((setadjoinIL) =>
% 106.14/14.39 (((in @ emptyset @
% 106.14/14.39 (setadjoin @ emptyset @
% 106.14/14.39 emptyset)) =>
% 106.14/14.39 (((setadjoinIR) =>
% 106.14/14.39 (((setadjoinE) =>
% 106.14/14.39 (((setadjoinOr) =>
% 106.14/14.39 (((setoftrueEq) =>
% 106.14/14.39 (((powersetI) =>
% 106.14/14.39 (((emptyinPowerset) =>
% 106.14/14.39 (((emptyInPowerset) =>
% 106.14/14.39 (((powersetE) =>
% 106.14/14.39 (((setunionI) =>
% 106.14/14.39 (((setunionE) =>
% 106.14/14.39 ((
% 106.14/14.39 (subPowSU) =>
% 106.14/14.39 ((
% 106.14/14.39 (exuE2) =>
% 106.14/14.39 ((
% 106.14/14.39 (nonemptyImpWitness) =>
% 106.14/14.39 ((
% 106.14/14.39 (uniqinunit) =>
% 106.14/14.39 ((
% 106.14/14.39 (notinsingleton) =>
% 106.14/14.39 ((
% 106.14/14.39 (eqinunit) =>
% 106.14/14.39 ((
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% 106.14/14.39 ((
% 106.14/14.39 (upairsetE) =>
% 106.14/14.39 ((
% 106.14/14.39 (upairsetIL) =>
% 106.14/14.39 ((
% 106.14/14.39 (upairsetIR) =>
% 106.14/14.39 ((
% 106.14/14.39 (emptyE1) =>
% 106.14/14.39 ((
% 106.14/14.39 (vacuousDall) =>
% 106.14/14.39 ((
% 106.14/14.39 (quantDeMorgan1) =>
% 106.14/14.39 ((
% 106.14/14.39 (quantDeMorgan2) =>
% 106.14/14.39 ((
% 106.14/14.39 (quantDeMorgan3) =>
% 106.14/14.39 ((
% 106.14/14.39 (quantDeMorgan4) =>
% 106.14/14.39 ((
% 106.14/14.39 (prop2setI) =>
% 106.14/14.39 ((
% 106.14/14.39 (prop2set2propI) =>
% 106.14/14.39 ((
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% 106.14/14.39 ((
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% 106.14/14.39 ((
% 106.14/14.39 (exuI3) =>
% 106.14/14.39 ((
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% 106.14/14.39 ((
% 106.14/14.39 (inCongP) =>
% 106.14/14.39 ((
% 106.14/14.39 (in__Cong) =>
% 106.14/14.39 ((
% 106.14/14.39 (exuE3u) =>
% 106.14/14.39 ((
% 106.14/14.39 (exu__Cong) =>
% 106.14/14.39 ((
% 106.14/14.39 (setadjoin__Cong) =>
% 106.14/14.39 ((
% 106.14/14.39 (powerset__Cong) =>
% 106.14/14.39 ((
% 106.14/14.39 (setunion__Cong) =>
% 106.14/14.39 ((
% 106.14/14.39 (exuEu) =>
% 106.14/14.39 ((
% 106.14/14.39 (descr__Cong) =>
% 106.14/14.39 ((
% 106.14/14.39 (dsetconstr__Cong) =>
% 106.14/14.39 ((
% 106.14/14.39 (subsetI1) =>
% 106.14/14.39 ((
% 106.14/14.39 (eqimpsubset2) =>
% 106.14/14.39 ((
% 106.14/14.39 (eqimpsubset1) =>
% 106.14/14.39 ((
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% 106.14/14.39 (subsetE2) =>
% 106.14/14.39 ((
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% 106.14/14.39 ((
% 106.14/14.39 (notequalI1) =>
% 106.14/14.39 ((
% 106.14/14.39 (notequalI2) =>
% 106.14/14.39 ((
% 106.14/14.39 (subsetRefl) =>
% 106.14/14.39 ((
% 106.14/14.39 (subsetTrans) =>
% 106.14/14.39 ((
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% 106.14/14.39 ((
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% 106.14/14.39 ((
% 106.14/14.39 (setextsub) =>
% 106.14/14.39 ((
% 106.14/14.39 (subsetemptysetimpeq) =>
% 106.14/14.39 ((
% 106.14/14.39 (powersetI1) =>
% 106.14/14.39 ((
% 106.14/14.39 (powersetE1) =>
% 106.14/14.39 ((
% 106.14/14.39 (inPowerset) =>
% 106.14/14.39 ((
% 106.14/14.39 (powersetsubset) =>
% 106.14/14.39 ((
% 106.14/14.39 (sepInPowerset) =>
% 106.14/14.39 ((
% 106.14/14.39 (sepSubset) =>
% 106.14/14.39 ((
% 106.14/14.39 (binunionIL) =>
% 106.14/14.39 ((
% 106.14/14.39 (upairset2IR) =>
% 106.14/14.39 ((
% 106.14/14.39 (binunionIR) =>
% 106.14/14.39 ((
% 106.14/14.39 (binunionEcases) =>
% 106.14/14.39 ((
% 106.14/14.39 (binunionE) =>
% 106.14/14.39 ((
% 106.14/14.39 (binunionLsub) =>
% 106.14/14.39 ((
% 106.14/14.39 (binunionRsub) =>
% 106.14/14.39 ((
% 106.14/14.39 (binintersectI) =>
% 106.14/14.39 ((
% 106.14/14.39 (binintersectSubset5) =>
% 106.14/14.39 ((
% 106.14/14.39 (binintersectEL) =>
% 106.14/14.39 ((
% 106.14/14.39 (binintersectLsub) =>
% 106.14/14.39 ((
% 106.14/14.39 (binintersectSubset2) =>
% 106.14/14.39 ((
% 106.14/14.39 (binintersectSubset3) =>
% 106.14/14.39 ((
% 106.14/14.39 (binintersectER) =>
% 106.14/14.39 ((
% 106.14/14.39 (disjointsetsI1) =>
% 106.14/14.39 ((
% 106.14/14.39 (binintersectRsub) =>
% 106.14/14.39 ((
% 106.14/14.39 (binintersectSubset4) =>
% 106.14/14.39 ((
% 106.14/14.39 (binintersectSubset1) =>
% 106.14/14.39 ((
% 106.14/14.39 (bs114d) =>
% 106.14/14.39 ((
% 106.14/14.39 (setminusI) =>
% 106.14/14.39 ((
% 106.14/14.39 (setminusEL) =>
% 106.14/14.39 ((
% 106.14/14.39 (setminusER) =>
% 106.14/14.39 ((
% 106.14/14.39 (setminusSubset2) =>
% 106.14/14.39 ((
% 106.14/14.39 (setminusERneg) =>
% 106.14/14.39 ((
% 106.14/14.39 (setminusELneg) =>
% 106.14/14.39 ((
% 106.14/14.39 (setminusILneg) =>
% 106.14/14.39 ((
% 106.14/14.39 (setminusIRneg) =>
% 106.14/14.39 ((
% 106.14/14.39 (setminusLsub) =>
% 106.14/14.39 ((
% 106.14/14.39 (setminusSubset1) =>
% 106.14/14.39 ((
% 106.14/14.39 (symdiffE) =>
% 106.14/14.39 ((
% 106.14/14.39 (symdiffI1) =>
% 106.14/14.39 ((
% 106.14/14.39 (symdiffI2) =>
% 106.14/14.39 ((
% 106.14/14.39 (symdiffIneg1) =>
% 106.14/14.39 ((
% 106.14/14.39 (symdiffIneg2) =>
% 106.14/14.39 ((
% 106.14/14.39 (secondinupair) =>
% 106.14/14.39 ((
% 106.14/14.39 (setukpairIL) =>
% 106.14/14.39 ((
% 106.14/14.39 (setukpairIR) =>
% 106.14/14.39 ((
% 106.14/14.39 (kpairiskpair) =>
% 106.14/14.39 ((
% 106.14/14.39 (kpairp) =>
% 106.14/14.39 ((
% 106.14/14.39 (singletonsubset) =>
% 106.14/14.39 ((
% 106.14/14.39 (singletoninpowerset) =>
% 106.14/14.39 ((
% 106.14/14.39 (singletoninpowunion) =>
% 106.14/14.39 ((
% 106.14/14.39 (upairset2E) =>
% 106.14/14.39 ((
% 106.14/14.39 (upairsubunion) =>
% 106.14/14.39 ((
% 106.14/14.39 (upairinpowunion) =>
% 106.14/14.39 ((
% 106.14/14.39 (ubforcartprodlem1) =>
% 106.14/14.39 ((
% 106.14/14.39 (ubforcartprodlem2) =>
% 106.14/14.39 ((
% 106.14/14.39 (ubforcartprodlem3) =>
% 106.14/14.39 ((
% 106.14/14.39 (cartprodpairin) =>
% 106.14/14.39 ((
% 106.14/14.39 (cartprodmempair1) =>
% 106.14/14.39 ((
% 106.14/14.39 (cartprodmempair) =>
% 106.14/14.39 ((
% 106.14/14.39 (setunionE2) =>
% 106.14/14.39 ((
% 106.14/14.39 (setunionsingleton1) =>
% 106.14/14.39 ((
% 106.14/14.39 (setunionsingleton2) =>
% 106.14/14.39 ((
% 106.14/14.39 (setunionsingleton) =>
% 106.14/14.39 ((
% 106.14/14.39 (singletonprop) =>
% 106.14/14.39 ((
% 106.14/14.39 (ex1E1) =>
% 106.14/14.39 ((
% 106.14/14.39 (ex1I) =>
% 106.14/14.39 ((
% 106.14/14.39 (ex1I2) =>
% 106.14/14.39 ((
% 106.14/14.39 (singletonsuniq) =>
% 106.14/14.39 ((
% 106.14/14.39 (setukpairinjL1) =>
% 106.14/14.39 ((
% 106.14/14.39 (kfstsingleton) =>
% 106.14/14.39 ((
% 106.14/14.39 (theprop) =>
% 106.14/14.39 ((
% 106.14/14.39 (kfstpairEq) =>
% 106.14/14.39 ((
% 106.14/14.39 (cartprodfstin) =>
% 106.14/14.39 ((
% 106.14/14.39 (setukpairinjL2) =>
% 106.14/14.39 ((
% 106.14/14.39 (setukpairinjL) =>
% 106.14/14.39 ((
% 106.14/14.39 (setukpairinjR11) =>
% 106.14/14.39 ((
% 106.14/14.39 (setukpairinjR12) =>
% 106.14/14.39 ((
% 106.14/14.39 (setukpairinjR1) =>
% 106.14/14.39 ((
% 106.14/14.39 (upairequniteq) =>
% 106.14/14.39 ((
% 106.14/14.39 (setukpairinjR2) =>
% 106.14/14.39 ((
% 106.14/14.39 (setukpairinjR) =>
% 106.14/14.39 ((
% 106.14/14.39 (ksndsingleton) =>
% 106.14/14.39 ((
% 106.14/14.39 (ksndpairEq) =>
% 106.14/14.39 ((
% 106.14/14.39 (kpairsurjEq) =>
% 106.14/14.39 ((
% 106.14/14.39 (cartprodsndin) =>
% 106.14/14.39 ((
% 106.14/14.39 (cartprodpairmemEL) =>
% 106.14/14.39 ((
% 106.14/14.39 (cartprodpairmemER) =>
% 106.14/14.39 ((
% 106.14/14.39 (cartprodmempaircEq) =>
% 106.14/14.39 ((
% 106.14/14.39 (cartprodfstpairEq) =>
% 106.14/14.39 ((
% 106.14/14.39 (cartprodsndpairEq) =>
% 106.14/14.39 ((
% 106.14/14.39 (cartprodpairsurjEq) =>
% 106.14/14.39 ((
% 106.14/14.39 (dpsetconstrI) =>
% 106.14/14.39 ((
% 106.14/14.39 (dpsetconstrSub) =>
% 106.14/14.39 ((
% 106.14/14.39 (setOfPairsIsBReln) =>
% 106.14/14.39 ((
% 106.14/14.39 (dpsetconstrERa) =>
% 106.14/14.39 ((
% 106.14/14.39 (dpsetconstrEL1) =>
% 106.14/14.39 ((
% 106.14/14.39 (dpsetconstrEL2) =>
% 106.14/14.39 ((
% 106.14/14.39 (dpsetconstrER) =>
% 106.14/14.39 ((
% 106.14/14.39 (funcImageSingleton) =>
% 106.14/14.39 ((
% 106.14/14.39 (apProp) =>
% 106.14/14.39 ((
% 106.14/14.39 (app) =>
% 106.14/14.39 ((
% 106.14/14.39 (infuncsetfunc) =>
% 106.14/14.39 ((
% 106.14/14.39 (ap2p) =>
% 106.14/14.39 ((
% 106.14/14.39 (funcinfuncset) =>
% 106.14/14.39 ((
% 106.14/14.39 (lamProp) =>
% 106.14/14.39 ((
% 106.14/14.39 (lamp) =>
% 106.14/14.39 ((
% 106.14/14.39 (lam2p) =>
% 106.14/14.39 ((
% 106.14/14.39 (brelnall1) =>
% 106.14/14.39 ((
% 106.14/14.39 (brelnall2) =>
% 106.14/14.39 ((
% 106.14/14.39 (ex1E2) =>
% 106.14/14.39 ((
% 106.14/14.39 (funcGraphProp1) =>
% 106.14/14.39 ((
% 106.14/14.39 (funcGraphProp3) =>
% 106.14/14.39 ((
% 106.14/14.39 (funcGraphProp2) =>
% 106.14/14.39 ((
% 106.14/14.39 (funcextLem) =>
% 106.14/14.39 ((
% 106.14/14.39 (funcGraphProp4) =>
% 106.14/14.39 ((
% 106.14/14.39 (subbreln) =>
% 106.14/14.39 ((
% 106.14/14.39 (eqbreln) =>
% 106.14/14.39 ((
% 106.14/14.39 (funcext) =>
% 106.14/14.39 ((
% 106.14/14.39 (funcext2) =>
% 106.14/14.39 ((
% 106.14/14.39 (ap2apEq1) =>
% 106.14/14.39 ((
% 106.14/14.39 (ap2apEq2) =>
% 106.14/14.39 ((
% 106.14/14.39 (beta1) =>
% 106.14/14.39 ((
% 106.14/14.39 (eta1) =>
% 106.14/14.39 ((
% 106.14/14.39 (lam2lamEq) =>
% 106.14/14.39 ((
% 106.14/14.39 (beta2) =>
% 106.14/14.39 ((
% 106.14/14.39 (eta2) =>
% 106.14/14.39 ((
% 106.14/14.39 (iffalseProp1) =>
% 106.14/14.39 ((
% 106.14/14.39 (iffalseProp2) =>
% 106.14/14.39 ((
% 106.14/14.39 (iftrueProp1) =>
% 106.14/14.39 ((
% 106.14/14.39 (iftrueProp2) =>
% 106.14/14.39 ((
% 106.14/14.39 (ifSingleton) =>
% 106.14/14.39 ((
% 106.14/14.39 (ifp) =>
% 106.14/14.39 ((
% 106.14/14.39 (theeq) =>
% 106.14/14.39 ((
% 106.14/14.39 (iftrue) =>
% 106.14/14.39 ((
% 106.14/14.39 (iffalse) =>
% 106.14/14.39 ((
% 106.14/14.39 (iftrueorfalse) =>
% 106.14/14.39 ((
% 106.14/14.39 (binintersectT_lem) =>
% 106.14/14.39 ((
% 106.14/14.39 (binunionT_lem) =>
% 106.14/14.39 ((
% 106.14/14.39 (powersetT_lem) =>
% 106.14/14.39 ((
% 106.14/14.39 (setminusT_lem) =>
% 106.14/14.39 ((
% 106.14/14.39 (complementT_lem) =>
% 106.14/14.39 ((
% 106.14/14.39 (setextT) =>
% 106.14/14.39 ((
% 106.14/14.39 (subsetTI) =>
% 106.14/14.39 ((
% 106.14/14.39 (powersetTI1) =>
% 106.14/14.39 ((
% 106.14/14.39 (powersetTE1) =>
% 106.14/14.39 ((
% 106.14/14.39 (complementTI1) =>
% 106.14/14.39 ((
% 106.14/14.39 (complementTE1) =>
% 106.14/14.39 ((
% 106.14/14.39 (binintersectTELcontra) =>
% 106.14/14.39 ((
% 106.14/14.39 (binintersectTERcontra) =>
% 106.14/14.39 ((
% 106.14/14.39 (contrasubsetT) =>
% 106.14/14.39 ((
% 106.14/14.39 (contrasubsetT1) =>
% 106.14/14.39 ((
% 106.14/14.39 (contrasubsetT2) =>
% 106.14/14.39 ((
% 106.14/14.39 (contrasubsetT3) =>
% 106.14/14.39 ((
% 106.14/14.39 (doubleComplementI1) =>
% 106.14/14.39 ((
% 106.14/14.39 (doubleComplementE1) =>
% 106.14/14.39 ((
% 106.14/14.39 (doubleComplementSub1) =>
% 106.14/14.39 ((
% 106.14/14.39 (doubleComplementSub2) =>
% 106.14/14.39 ((
% 106.14/14.39 (doubleComplementEq) =>
% 106.14/14.39 ((
% 106.14/14.39 (complementTnotintersectT) =>
% 106.14/14.39 ((
% 106.14/14.39 (complementImpComplementIntersect) =>
% 106.14/14.39 ((
% 106.14/14.39 (complementSubsetComplementIntersect) =>
% 106.14/14.39 ((
% 106.14/14.39 (complementInPowersetComplementIntersect) =>
% 106.14/14.39 ((
% 106.14/14.39 (contraSubsetComplement) =>
% 106.14/14.39 ((
% 106.14/14.39 (complementTcontraSubset) =>
% 106.14/14.39 ((
% 106.14/14.39 (binunionTILcontra) =>
% 106.14/14.39 ((
% 106.14/14.39 (binunionTIRcontra) =>
% 106.14/14.39 ((
% 106.14/14.39 (inIntersectImpInUnion) =>
% 106.14/14.39 ((
% 106.14/14.39 (inIntersectImpInUnion2) =>
% 106.14/14.39 ((
% 106.14/14.39 (inIntersectImpInIntersectUnions) =>
% 106.14/14.39 ((
% 106.14/14.39 (intersectInPowersetIntersectUnions) =>
% 106.14/14.39 ((
% 106.14/14.39 (inComplementUnionImpNotIn1) =>
% 106.14/14.39 ((
% 106.14/14.39 (inComplementUnionImpInComplement1) =>
% 106.14/14.39 ((
% 106.14/14.39 (binunionTE) =>
% 106.14/14.39 ((
% 106.14/14.39 (binunionTEcontra) =>
% 106.14/14.39 ((
% 106.14/14.39 (demorgan2a1) =>
% 106.14/14.39 ((
% 106.14/14.39 (complementUnionInPowersetComplement) =>
% 106.14/14.39 ((
% 106.14/14.39 (demorgan2a2) =>
% 106.14/14.39 ((
% 106.14/14.39 (demorgan1a) =>
% 106.14/14.39 ((
% 106.14/14.39 (demorgan1b) =>
% 106.14/14.39 ((
% 106.14/14.39 (demorgan1) =>
% 106.14/14.39 ((
% 106.14/14.39 (demorgan2a) =>
% 106.14/14.39 ((
% 106.14/14.39 (demorgan2b2) =>
% 106.14/14.39 ((
% 106.14/14.39 (demorgan2b) =>
% 106.14/14.39 ((
% 106.14/14.39 (demorgan2) =>
% 106.14/14.39 ((
% 106.14/14.39 (woz13rule0) =>
% 106.14/14.39 ((
% 106.14/14.39 (woz13rule1) =>
% 106.14/14.39 ((
% 106.14/14.39 (woz13rule2) =>
% 106.14/14.39 ((
% 106.14/14.39 (woz13rule3) =>
% 106.14/14.39 ((
% 106.14/14.39 (woz13rule4) =>
% 106.14/14.39 ((
% 106.14/14.39 (woz1_1) =>
% 106.14/14.39 ((
% 106.14/14.39 (woz1_2) =>
% 106.14/14.39 ((
% 106.14/14.39 (woz1_3) =>
% 106.14/14.39 ((
% 106.14/14.39 (woz1_4) =>
% 106.14/14.39 ((
% 106.14/14.39 (woz1_5) =>
% 106.14/14.39 ((
% 106.14/14.39 (breln1all2) =>
% 106.14/14.39 ((
% 106.14/14.39 (breln1SetBreln1) =>
% 106.14/14.39 ((
% 106.14/14.39 (choice2fnsingleton) =>
% 106.14/14.39 ((
% 106.14/14.39 (setOfPairsIsBReln1) =>
% 106.14/14.39 ((
% 106.14/14.39 (breln1all1) =>
% 106.14/14.39 ((
% 106.14/14.39 (subbreln1) =>
% 106.14/14.39 ((
% 106.14/14.39 (eqbreln1) =>
% 106.14/14.39 ((
% 106.14/14.39 (breln1invprop) =>
% 106.14/14.39 ((
% 106.14/14.39 (breln1invI) =>
% 106.14/14.39 ((
% 106.14/14.39 (breln1invE) =>
% 106.14/14.39 ((
% 106.14/14.39 (breln1compprop) =>
% 106.14/14.39 ((
% 106.14/14.39 (breln1compI) =>
% 106.14/14.39 ((
% 106.14/14.39 (breln1compE) =>
% 106.14/14.39 ((
% 106.14/14.39 (breln1compEex) =>
% 106.14/14.39 ((
% 106.14/14.39 (breln1unionprop) =>
% 106.14/14.39 ((
% 106.14/14.39 (breln1unionIL) =>
% 106.14/14.39 ((
% 106.14/14.39 (breln1unionIR) =>
% 106.14/14.39 ((
% 106.14/14.39 (breln1unionI) =>
% 106.14/14.39 ((
% 106.14/14.39 (breln1unionE) =>
% 106.14/14.39 ((
% 106.14/14.39 (breln1unionEcases) =>
% 106.14/14.39 ((
% 106.14/14.39 (breln1unionCommutes) =>
% 106.14/14.39 ((
% 106.14/14.39 (woz2Ex) =>
% 106.14/14.39 ((
% 106.14/14.39 (woz2W) =>
% 106.14/14.39 ((
% 106.14/14.39 (woz2A) =>
% 106.14/14.39 ((
% 106.14/14.39 (woz2B) =>
% 106.14/14.39 ((
% 106.14/14.39 (image1Ex) =>
% 106.14/14.39 ((
% 106.14/14.39 (image1Ex1) =>
% 106.14/14.39 ((
% 106.14/14.39 (image1Equiv) =>
% 106.14/14.39 ((
% 106.14/14.39 (image1E) =>
% 106.14/14.39 ((
% 106.14/14.39 (image1I) =>
% 106.14/14.39 ((
% 106.14/14.39 (injFuncInInjFuncSet) =>
% 106.14/14.39 ((
% 106.14/14.39 (injFuncSetFuncIn) =>
% 106.14/14.39 ((
% 106.14/14.39 (injFuncSetFuncInj) =>
% 106.14/14.39 ((
% 106.14/14.39 (surjFuncSetFuncIn) =>
% 106.14/14.39 ((
% 106.14/14.39 (surjFuncSetFuncSurj) =>
% 106.14/14.39 ((
% 106.14/14.39 (leftInvIsSurj) =>
% 106.14/14.39 ((
% 106.14/14.39 (surjCantorThm) =>
% 106.14/14.39 ((
% 106.14/14.39 (!!) @ (
% 106.14/14.39 (('#S') @ (
% 106.14/14.39 (
% 106.14/14.39 ('#B') @ (
% 106.14/14.39 =>) @
% 106.14/14.39 nonempty)) @
% 106.14/14.39 (
% 106.14/14.39 (
% 106.14/14.39 ('#B') @ (
% 106.14/14.39 ??) @
% 106.14/14.39 (
% 106.14/14.39 (
% 106.14/14.39 ('#S') @ (
% 106.14/14.39 (
% 106.14/14.39 ('#B') @ (
% 106.14/14.39 '#S') @
% 106.14/14.39 (
% 106.14/14.39 (
% 106.14/14.39 ('#B') @ (
% 106.14/14.39 (
% 106.14/14.39 ('#B') @ (
% 106.14/14.39 &))) @
% 106.14/14.39 (
% 106.14/14.39 (
% 106.14/14.39 ('#C') @ in)))))) @
% 106.14/14.39 (
% 106.14/14.39 (
% 106.14/14.39 ('#C') @ (
% 106.14/14.39 (
% 106.14/14.39 ('#B') @ (
% 106.14/14.39 '#C') @
% 106.14/14.39 (
% 106.14/14.39 (
% 106.14/14.39 ('#B') @ (
% 106.14/14.39 (
% 106.14/14.39 ('#B') @ (
% 106.14/14.39 =))) @
% 106.14/14.39 (
% 106.14/14.39 (
% 106.14/14.39 ('#C') @ binintersect)))))) @
% 106.14/14.39 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.14/14.39 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl52])).
% 106.14/14.39 thf(zip_derived_cl64, plain,
% 106.14/14.39 (~ (((descrp) =>
% 106.14/14.39 (((dsetconstrI) =>
% 106.14/14.39 (((dsetconstrEL) =>
% 106.14/14.39 (((dsetconstrER) =>
% 106.14/14.39 (((exuE1) =>
% 106.14/14.39 (((prop2setE) =>
% 106.14/14.39 (((emptysetE) =>
% 106.14/14.39 (((emptysetimpfalse) =>
% 106.14/14.39 (((notinemptyset) =>
% 106.14/14.39 (((exuE3e) =>
% 106.14/14.39 (((setext) =>
% 106.14/14.39 (((emptyI) =>
% 106.14/14.39 (((noeltsimpempty) =>
% 106.14/14.39 (((setbeta) =>
% 106.14/14.39 (((nonemptyE1) =>
% 106.14/14.39 (((nonemptyI) =>
% 106.14/14.39 (((nonemptyI1) =>
% 106.14/14.39 (((setadjoinIL) =>
% 106.14/14.39 (((in @ emptyset @
% 106.14/14.39 (setadjoin @ emptyset @ emptyset)) =>
% 106.14/14.39 (((setadjoinIR) =>
% 106.14/14.39 (((setadjoinE) =>
% 106.14/14.39 (((setadjoinOr) =>
% 106.14/14.39 (((setoftrueEq) =>
% 106.14/14.39 (((powersetI) =>
% 106.14/14.39 (((emptyinPowerset) =>
% 106.14/14.39 (((emptyInPowerset) =>
% 106.14/14.39 (((powersetE) =>
% 106.14/14.39 (((setunionI) =>
% 106.14/14.39 (((setunionE) =>
% 106.14/14.39 (((subPowSU) =>
% 106.14/14.39 ((
% 106.14/14.39 (exuE2) =>
% 106.14/14.39 ((
% 106.14/14.39 (nonemptyImpWitness) =>
% 106.14/14.39 ((
% 106.14/14.39 (uniqinunit) =>
% 106.14/14.39 ((
% 106.14/14.39 (notinsingleton) =>
% 106.14/14.39 ((
% 106.14/14.39 (eqinunit) =>
% 106.14/14.39 ((
% 106.14/14.39 (singletonsswitch) =>
% 106.14/14.39 ((
% 106.14/14.39 (upairsetE) =>
% 106.14/14.39 ((
% 106.14/14.39 (upairsetIL) =>
% 106.14/14.39 ((
% 106.14/14.39 (upairsetIR) =>
% 106.14/14.39 ((
% 106.14/14.39 (emptyE1) =>
% 106.14/14.39 ((
% 106.14/14.39 (vacuousDall) =>
% 106.14/14.39 ((
% 106.14/14.39 (quantDeMorgan1) =>
% 106.14/14.39 ((
% 106.14/14.39 (quantDeMorgan2) =>
% 106.14/14.39 ((
% 106.14/14.39 (quantDeMorgan3) =>
% 106.14/14.39 ((
% 106.14/14.39 (quantDeMorgan4) =>
% 106.14/14.39 ((
% 106.14/14.39 (prop2setI) =>
% 106.14/14.39 ((
% 106.14/14.39 (prop2set2propI) =>
% 106.14/14.39 ((
% 106.14/14.39 (notdexE) =>
% 106.14/14.39 ((
% 106.14/14.39 (notdallE) =>
% 106.14/14.39 ((
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% 106.14/14.39 ((
% 106.14/14.39 (exuI3) =>
% 106.14/14.39 ((
% 106.14/14.39 (exuI2) =>
% 106.14/14.39 ((
% 106.14/14.39 (inCongP) =>
% 106.14/14.39 ((
% 106.14/14.39 (in__Cong) =>
% 106.14/14.39 ((
% 106.14/14.39 (exuE3u) =>
% 106.14/14.39 ((
% 106.14/14.39 (exu__Cong) =>
% 106.14/14.39 ((
% 106.14/14.39 (setadjoin__Cong) =>
% 106.14/14.39 ((
% 106.14/14.39 (powerset__Cong) =>
% 106.14/14.39 ((
% 106.14/14.39 (setunion__Cong) =>
% 106.14/14.39 ((
% 106.14/14.39 (exuEu) =>
% 106.14/14.39 ((
% 106.14/14.39 (descr__Cong) =>
% 106.14/14.39 ((
% 106.14/14.39 (dsetconstr__Cong) =>
% 106.14/14.39 ((
% 106.14/14.39 (subsetI1) =>
% 106.14/14.39 ((
% 106.14/14.39 (eqimpsubset2) =>
% 106.14/14.39 ((
% 106.14/14.39 (eqimpsubset1) =>
% 106.14/14.39 ((
% 106.14/14.39 (subsetI2) =>
% 106.14/14.39 ((
% 106.14/14.39 (emptysetsubset) =>
% 106.14/14.39 ((
% 106.14/14.39 (subsetE) =>
% 106.14/14.39 ((
% 106.14/14.39 (subsetE2) =>
% 106.14/14.39 ((
% 106.14/14.39 (notsubsetI) =>
% 106.14/14.39 ((
% 106.14/14.39 (notequalI1) =>
% 106.14/14.39 ((
% 106.14/14.39 (notequalI2) =>
% 106.14/14.39 ((
% 106.14/14.39 (subsetRefl) =>
% 106.14/14.39 ((
% 106.14/14.39 (subsetTrans) =>
% 106.14/14.39 ((
% 106.14/14.39 (setadjoinSub) =>
% 106.14/14.39 ((
% 106.14/14.39 (setadjoinSub2) =>
% 106.14/14.39 ((
% 106.14/14.39 (subset2powerset) =>
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% 106.14/14.39 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl58])).
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% 106.14/14.39 ('#B') @ (
% 106.14/14.39 (
% 106.14/14.39 ('#B') @ (
% 106.14/14.39 =))) @
% 106.14/14.39 (
% 106.14/14.39 (
% 106.14/14.39 ('#C') @ binintersect)))))) @
% 106.14/14.39 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.14/14.39 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl64])).
% 106.14/14.39 thf(zip_derived_cl79, plain,
% 106.14/14.39 (~ (((dsetconstrEL) =>
% 106.14/14.39 (((dsetconstrER) =>
% 106.14/14.39 (((exuE1) =>
% 106.14/14.39 (((prop2setE) =>
% 106.14/14.39 (((emptysetE) =>
% 106.14/14.39 (((emptysetimpfalse) =>
% 106.14/14.39 (((notinemptyset) =>
% 106.14/14.39 (((exuE3e) =>
% 106.14/14.39 (((setext) =>
% 106.14/14.39 (((emptyI) =>
% 106.14/14.39 (((noeltsimpempty) =>
% 106.14/14.39 (((setbeta) =>
% 106.14/14.39 (((nonemptyE1) =>
% 106.14/14.39 (((nonemptyI) =>
% 106.14/14.39 (((nonemptyI1) =>
% 106.14/14.39 (((setadjoinIL) =>
% 106.14/14.39 (((in @ emptyset @
% 106.14/14.39 (setadjoin @ emptyset @ emptyset)) =>
% 106.14/14.39 (((setadjoinIR) =>
% 106.14/14.39 (((setadjoinE) =>
% 106.14/14.39 (((setadjoinOr) =>
% 106.14/14.39 (((setoftrueEq) =>
% 106.14/14.39 (((powersetI) =>
% 106.14/14.39 (((emptyinPowerset) =>
% 106.14/14.39 (((emptyInPowerset) =>
% 106.14/14.39 (((powersetE) =>
% 106.14/14.39 (((setunionI) =>
% 106.14/14.39 (((setunionE) =>
% 106.14/14.39 (((subPowSU) =>
% 106.14/14.39 (((exuE2) =>
% 106.14/14.39 (((nonemptyImpWitness) =>
% 106.14/14.39 ((
% 106.14/14.39 (uniqinunit) =>
% 106.14/14.39 ((
% 106.14/14.39 (notinsingleton) =>
% 106.14/14.39 ((
% 106.14/14.39 (eqinunit) =>
% 106.14/14.39 ((
% 106.14/14.39 (singletonsswitch) =>
% 106.14/14.39 ((
% 106.14/14.39 (upairsetE) =>
% 106.14/14.39 ((
% 106.14/14.39 (upairsetIL) =>
% 106.14/14.39 ((
% 106.14/14.39 (upairsetIR) =>
% 106.14/14.39 ((
% 106.14/14.39 (emptyE1) =>
% 106.14/14.39 ((
% 106.14/14.39 (vacuousDall) =>
% 106.14/14.39 ((
% 106.14/14.39 (quantDeMorgan1) =>
% 106.14/14.39 ((
% 106.14/14.39 (quantDeMorgan2) =>
% 106.14/14.39 ((
% 106.14/14.39 (quantDeMorgan3) =>
% 106.14/14.39 ((
% 106.14/14.39 (quantDeMorgan4) =>
% 106.14/14.39 ((
% 106.14/14.39 (prop2setI) =>
% 106.14/14.39 ((
% 106.14/14.39 (prop2set2propI) =>
% 106.14/14.39 ((
% 106.14/14.39 (notdexE) =>
% 106.14/14.39 ((
% 106.14/14.39 (notdallE) =>
% 106.14/14.39 ((
% 106.14/14.39 (exuI1) =>
% 106.14/14.39 ((
% 106.14/14.39 (exuI3) =>
% 106.14/14.39 ((
% 106.14/14.39 (exuI2) =>
% 106.14/14.39 ((
% 106.14/14.39 (inCongP) =>
% 106.14/14.39 ((
% 106.14/14.39 (in__Cong) =>
% 106.14/14.39 ((
% 106.14/14.39 (exuE3u) =>
% 106.14/14.39 ((
% 106.14/14.39 (exu__Cong) =>
% 106.14/14.39 ((
% 106.14/14.39 (setadjoin__Cong) =>
% 106.14/14.39 ((
% 106.14/14.39 (powerset__Cong) =>
% 106.14/14.39 ((
% 106.14/14.39 (setunion__Cong) =>
% 106.14/14.39 ((
% 106.14/14.39 (exuEu) =>
% 106.14/14.39 ((
% 106.14/14.39 (descr__Cong) =>
% 106.14/14.39 ((
% 106.14/14.39 (dsetconstr__Cong) =>
% 106.14/14.39 ((
% 106.14/14.39 (subsetI1) =>
% 106.14/14.39 ((
% 106.14/14.39 (eqimpsubset2) =>
% 106.14/14.39 ((
% 106.14/14.39 (eqimpsubset1) =>
% 106.14/14.39 ((
% 106.14/14.39 (subsetI2) =>
% 106.14/14.39 ((
% 106.14/14.39 (emptysetsubset) =>
% 106.14/14.39 ((
% 106.14/14.39 (subsetE) =>
% 106.14/14.39 ((
% 106.14/14.39 (subsetE2) =>
% 106.14/14.39 ((
% 106.14/14.39 (notsubsetI) =>
% 106.14/14.39 ((
% 106.14/14.39 (notequalI1) =>
% 106.14/14.39 ((
% 106.14/14.39 (notequalI2) =>
% 106.14/14.39 ((
% 106.14/14.39 (subsetRefl) =>
% 106.14/14.39 ((
% 106.14/14.39 (subsetTrans) =>
% 106.14/14.39 ((
% 106.14/14.39 (setadjoinSub) =>
% 106.14/14.39 ((
% 106.14/14.39 (setadjoinSub2) =>
% 106.14/14.39 ((
% 106.14/14.39 (subset2powerset) =>
% 106.14/14.39 ((
% 106.14/14.39 (setextsub) =>
% 106.14/14.39 ((
% 106.14/14.39 (subsetemptysetimpeq) =>
% 106.14/14.39 ((
% 106.14/14.39 (powersetI1) =>
% 106.14/14.39 ((
% 106.14/14.39 (powersetE1) =>
% 106.14/14.39 ((
% 106.14/14.39 (inPowerset) =>
% 106.14/14.39 ((
% 106.14/14.39 (powersetsubset) =>
% 106.14/14.39 ((
% 106.14/14.39 (sepInPowerset) =>
% 106.14/14.39 ((
% 106.14/14.39 (sepSubset) =>
% 106.14/14.39 ((
% 106.14/14.39 (binunionIL) =>
% 106.14/14.39 ((
% 106.14/14.39 (upairset2IR) =>
% 106.14/14.39 ((
% 106.14/14.39 (binunionIR) =>
% 106.14/14.39 ((
% 106.14/14.39 (binunionEcases) =>
% 106.14/14.39 ((
% 106.14/14.39 (binunionE) =>
% 106.14/14.39 ((
% 106.14/14.39 (binunionLsub) =>
% 106.14/14.39 ((
% 106.14/14.39 (binunionRsub) =>
% 106.14/14.39 ((
% 106.14/14.39 (binintersectI) =>
% 106.14/14.39 ((
% 106.14/14.39 (binintersectSubset5) =>
% 106.14/14.39 ((
% 106.14/14.39 (binintersectEL) =>
% 106.14/14.39 ((
% 106.14/14.39 (binintersectLsub) =>
% 106.14/14.39 ((
% 106.14/14.39 (binintersectSubset2) =>
% 106.14/14.39 ((
% 106.14/14.39 (binintersectSubset3) =>
% 106.14/14.39 ((
% 106.14/14.39 (binintersectER) =>
% 106.14/14.39 ((
% 106.14/14.39 (disjointsetsI1) =>
% 106.14/14.39 ((
% 106.14/14.39 (binintersectRsub) =>
% 106.14/14.39 ((
% 106.14/14.39 (binintersectSubset4) =>
% 106.14/14.39 ((
% 106.14/14.39 (binintersectSubset1) =>
% 106.14/14.39 ((
% 106.14/14.39 (bs114d) =>
% 106.14/14.39 ((
% 106.14/14.39 (setminusI) =>
% 106.14/14.39 ((
% 106.14/14.39 (setminusEL) =>
% 106.14/14.39 ((
% 106.14/14.39 (setminusER) =>
% 106.14/14.39 ((
% 106.14/14.39 (setminusSubset2) =>
% 106.14/14.39 ((
% 106.14/14.39 (setminusERneg) =>
% 106.14/14.39 ((
% 106.14/14.39 (setminusELneg) =>
% 106.14/14.39 ((
% 106.14/14.39 (setminusILneg) =>
% 106.14/14.39 ((
% 106.14/14.39 (setminusIRneg) =>
% 106.14/14.39 ((
% 106.14/14.39 (setminusLsub) =>
% 106.14/14.39 ((
% 106.14/14.39 (setminusSubset1) =>
% 106.14/14.39 ((
% 106.14/14.39 (symdiffE) =>
% 106.14/14.39 ((
% 106.14/14.39 (symdiffI1) =>
% 106.14/14.39 ((
% 106.14/14.39 (symdiffI2) =>
% 106.14/14.39 ((
% 106.14/14.39 (symdiffIneg1) =>
% 106.14/14.39 ((
% 106.14/14.39 (symdiffIneg2) =>
% 106.14/14.39 ((
% 106.14/14.39 (secondinupair) =>
% 106.14/14.39 ((
% 106.14/14.39 (setukpairIL) =>
% 106.14/14.39 ((
% 106.14/14.39 (setukpairIR) =>
% 106.14/14.39 ((
% 106.14/14.39 (kpairiskpair) =>
% 106.14/14.39 ((
% 106.14/14.39 (kpairp) =>
% 106.14/14.39 ((
% 106.14/14.39 (singletonsubset) =>
% 106.14/14.39 ((
% 106.14/14.39 (singletoninpowerset) =>
% 106.14/14.39 ((
% 106.14/14.39 (singletoninpowunion) =>
% 106.14/14.39 ((
% 106.14/14.39 (upairset2E) =>
% 106.14/14.39 ((
% 106.14/14.39 (upairsubunion) =>
% 106.14/14.39 ((
% 106.14/14.39 (upairinpowunion) =>
% 106.14/14.39 ((
% 106.14/14.39 (ubforcartprodlem1) =>
% 106.14/14.39 ((
% 106.14/14.39 (ubforcartprodlem2) =>
% 106.14/14.39 ((
% 106.14/14.39 (ubforcartprodlem3) =>
% 106.14/14.39 ((
% 106.14/14.39 (cartprodpairin) =>
% 106.14/14.39 ((
% 106.14/14.39 (cartprodmempair1) =>
% 106.14/14.39 ((
% 106.14/14.39 (cartprodmempair) =>
% 106.14/14.39 ((
% 106.14/14.39 (setunionE2) =>
% 106.14/14.39 ((
% 106.14/14.39 (setunionsingleton1) =>
% 106.14/14.39 ((
% 106.14/14.39 (setunionsingleton2) =>
% 106.14/14.39 ((
% 106.14/14.39 (setunionsingleton) =>
% 106.14/14.39 ((
% 106.14/14.39 (singletonprop) =>
% 106.14/14.39 ((
% 106.14/14.39 (ex1E1) =>
% 106.14/14.39 ((
% 106.14/14.39 (ex1I) =>
% 106.14/14.39 ((
% 106.14/14.39 (ex1I2) =>
% 106.14/14.39 ((
% 106.14/14.39 (singletonsuniq) =>
% 106.14/14.39 ((
% 106.14/14.39 (setukpairinjL1) =>
% 106.14/14.39 ((
% 106.14/14.39 (kfstsingleton) =>
% 106.14/14.39 ((
% 106.14/14.39 (theprop) =>
% 106.14/14.39 ((
% 106.14/14.39 (kfstpairEq) =>
% 106.14/14.39 ((
% 106.14/14.39 (cartprodfstin) =>
% 106.14/14.39 ((
% 106.14/14.39 (setukpairinjL2) =>
% 106.14/14.39 ((
% 106.14/14.39 (setukpairinjL) =>
% 106.14/14.39 ((
% 106.14/14.39 (setukpairinjR11) =>
% 106.14/14.39 ((
% 106.14/14.39 (setukpairinjR12) =>
% 106.14/14.39 ((
% 106.14/14.39 (setukpairinjR1) =>
% 106.14/14.39 ((
% 106.14/14.39 (upairequniteq) =>
% 106.14/14.39 ((
% 106.14/14.39 (setukpairinjR2) =>
% 106.14/14.39 ((
% 106.14/14.39 (setukpairinjR) =>
% 106.14/14.39 ((
% 106.14/14.39 (ksndsingleton) =>
% 106.14/14.39 ((
% 106.14/14.39 (ksndpairEq) =>
% 106.14/14.39 ((
% 106.14/14.39 (kpairsurjEq) =>
% 106.14/14.39 ((
% 106.14/14.39 (cartprodsndin) =>
% 106.14/14.39 ((
% 106.14/14.39 (cartprodpairmemEL) =>
% 106.14/14.39 ((
% 106.14/14.39 (cartprodpairmemER) =>
% 106.14/14.39 ((
% 106.14/14.39 (cartprodmempaircEq) =>
% 106.14/14.39 ((
% 106.14/14.39 (cartprodfstpairEq) =>
% 106.14/14.39 ((
% 106.14/14.39 (cartprodsndpairEq) =>
% 106.14/14.39 ((
% 106.14/14.39 (cartprodpairsurjEq) =>
% 106.14/14.39 ((
% 106.14/14.39 (dpsetconstrI) =>
% 106.14/14.39 ((
% 106.14/14.39 (dpsetconstrSub) =>
% 106.14/14.39 ((
% 106.14/14.39 (setOfPairsIsBReln) =>
% 106.14/14.39 ((
% 106.14/14.39 (dpsetconstrERa) =>
% 106.14/14.39 ((
% 106.14/14.39 (dpsetconstrEL1) =>
% 106.14/14.39 ((
% 106.14/14.39 (dpsetconstrEL2) =>
% 106.14/14.39 ((
% 106.14/14.39 (dpsetconstrER) =>
% 106.14/14.39 ((
% 106.14/14.39 (funcImageSingleton) =>
% 106.14/14.39 ((
% 106.14/14.39 (apProp) =>
% 106.14/14.39 ((
% 106.14/14.39 (app) =>
% 106.14/14.39 ((
% 106.14/14.39 (infuncsetfunc) =>
% 106.14/14.39 ((
% 106.14/14.39 (ap2p) =>
% 106.14/14.39 ((
% 106.14/14.39 (funcinfuncset) =>
% 106.14/14.39 ((
% 106.14/14.39 (lamProp) =>
% 106.14/14.39 ((
% 106.14/14.39 (lamp) =>
% 106.14/14.39 ((
% 106.14/14.39 (lam2p) =>
% 106.14/14.39 ((
% 106.14/14.39 (brelnall1) =>
% 106.14/14.39 ((
% 106.14/14.39 (brelnall2) =>
% 106.14/14.39 ((
% 106.14/14.39 (ex1E2) =>
% 106.14/14.39 ((
% 106.14/14.39 (funcGraphProp1) =>
% 106.14/14.39 ((
% 106.14/14.39 (funcGraphProp3) =>
% 106.14/14.39 ((
% 106.14/14.39 (funcGraphProp2) =>
% 106.14/14.39 ((
% 106.14/14.39 (funcextLem) =>
% 106.14/14.39 ((
% 106.14/14.39 (funcGraphProp4) =>
% 106.14/14.39 ((
% 106.14/14.39 (subbreln) =>
% 106.14/14.39 ((
% 106.14/14.39 (eqbreln) =>
% 106.14/14.39 ((
% 106.14/14.39 (funcext) =>
% 106.14/14.39 ((
% 106.14/14.39 (funcext2) =>
% 106.14/14.39 ((
% 106.14/14.39 (ap2apEq1) =>
% 106.14/14.39 ((
% 106.14/14.39 (ap2apEq2) =>
% 106.14/14.39 ((
% 106.14/14.39 (beta1) =>
% 106.14/14.39 ((
% 106.14/14.39 (eta1) =>
% 106.14/14.39 ((
% 106.14/14.39 (lam2lamEq) =>
% 106.14/14.39 ((
% 106.14/14.39 (beta2) =>
% 106.14/14.39 ((
% 106.14/14.39 (eta2) =>
% 106.14/14.39 ((
% 106.14/14.39 (iffalseProp1) =>
% 106.14/14.39 ((
% 106.14/14.39 (iffalseProp2) =>
% 106.14/14.39 ((
% 106.14/14.39 (iftrueProp1) =>
% 106.14/14.39 ((
% 106.14/14.39 (iftrueProp2) =>
% 106.14/14.39 ((
% 106.14/14.39 (ifSingleton) =>
% 106.14/14.39 ((
% 106.14/14.39 (ifp) =>
% 106.14/14.39 ((
% 106.14/14.39 (theeq) =>
% 106.14/14.39 ((
% 106.14/14.39 (iftrue) =>
% 106.14/14.39 ((
% 106.14/14.39 (iffalse) =>
% 106.14/14.39 ((
% 106.14/14.39 (iftrueorfalse) =>
% 106.14/14.39 ((
% 106.14/14.39 (binintersectT_lem) =>
% 106.14/14.39 ((
% 106.14/14.39 (binunionT_lem) =>
% 106.14/14.39 ((
% 106.14/14.39 (powersetT_lem) =>
% 106.14/14.39 ((
% 106.14/14.39 (setminusT_lem) =>
% 106.14/14.39 ((
% 106.14/14.39 (complementT_lem) =>
% 106.14/14.39 ((
% 106.14/14.39 (setextT) =>
% 106.14/14.39 ((
% 106.14/14.39 (subsetTI) =>
% 106.14/14.39 ((
% 106.14/14.39 (powersetTI1) =>
% 106.14/14.39 ((
% 106.14/14.39 (powersetTE1) =>
% 106.14/14.39 ((
% 106.14/14.39 (complementTI1) =>
% 106.14/14.39 ((
% 106.14/14.39 (complementTE1) =>
% 106.14/14.39 ((
% 106.14/14.39 (binintersectTELcontra) =>
% 106.14/14.39 ((
% 106.14/14.39 (binintersectTERcontra) =>
% 106.14/14.39 ((
% 106.14/14.39 (contrasubsetT) =>
% 106.14/14.39 ((
% 106.14/14.39 (contrasubsetT1) =>
% 106.14/14.39 ((
% 106.14/14.39 (contrasubsetT2) =>
% 106.14/14.39 ((
% 106.14/14.39 (contrasubsetT3) =>
% 106.14/14.39 ((
% 106.14/14.39 (doubleComplementI1) =>
% 106.14/14.39 ((
% 106.14/14.39 (doubleComplementE1) =>
% 106.14/14.39 ((
% 106.14/14.39 (doubleComplementSub1) =>
% 106.14/14.39 ((
% 106.14/14.39 (doubleComplementSub2) =>
% 106.14/14.39 ((
% 106.14/14.39 (doubleComplementEq) =>
% 106.14/14.39 ((
% 106.14/14.39 (complementTnotintersectT) =>
% 106.14/14.40 ((
% 106.14/14.40 (complementImpComplementIntersect) =>
% 106.14/14.40 ((
% 106.14/14.40 (complementSubsetComplementIntersect) =>
% 106.14/14.40 ((
% 106.14/14.40 (complementInPowersetComplementIntersect) =>
% 106.14/14.40 ((
% 106.14/14.40 (contraSubsetComplement) =>
% 106.14/14.40 ((
% 106.14/14.40 (complementTcontraSubset) =>
% 106.14/14.40 ((
% 106.14/14.40 (binunionTILcontra) =>
% 106.14/14.40 ((
% 106.14/14.40 (binunionTIRcontra) =>
% 106.14/14.40 ((
% 106.14/14.40 (inIntersectImpInUnion) =>
% 106.14/14.40 ((
% 106.14/14.40 (inIntersectImpInUnion2) =>
% 106.14/14.40 ((
% 106.14/14.40 (inIntersectImpInIntersectUnions) =>
% 106.14/14.40 ((
% 106.14/14.40 (intersectInPowersetIntersectUnions) =>
% 106.14/14.40 ((
% 106.14/14.40 (inComplementUnionImpNotIn1) =>
% 106.14/14.40 ((
% 106.14/14.40 (inComplementUnionImpInComplement1) =>
% 106.14/14.40 ((
% 106.14/14.40 (binunionTE) =>
% 106.14/14.40 ((
% 106.14/14.40 (binunionTEcontra) =>
% 106.14/14.40 ((
% 106.14/14.40 (demorgan2a1) =>
% 106.14/14.40 ((
% 106.14/14.40 (complementUnionInPowersetComplement) =>
% 106.14/14.40 ((
% 106.14/14.40 (demorgan2a2) =>
% 106.14/14.40 ((
% 106.14/14.40 (demorgan1a) =>
% 106.14/14.40 ((
% 106.14/14.40 (demorgan1b) =>
% 106.14/14.40 ((
% 106.14/14.40 (demorgan1) =>
% 106.14/14.40 ((
% 106.14/14.40 (demorgan2a) =>
% 106.14/14.40 ((
% 106.14/14.40 (demorgan2b2) =>
% 106.14/14.40 ((
% 106.14/14.40 (demorgan2b) =>
% 106.14/14.40 ((
% 106.14/14.40 (demorgan2) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz13rule0) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz13rule1) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz13rule2) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz13rule3) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz13rule4) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz1_1) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz1_2) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz1_3) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz1_4) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz1_5) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1all2) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1SetBreln1) =>
% 106.14/14.40 ((
% 106.14/14.40 (choice2fnsingleton) =>
% 106.14/14.40 ((
% 106.14/14.40 (setOfPairsIsBReln1) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1all1) =>
% 106.14/14.40 ((
% 106.14/14.40 (subbreln1) =>
% 106.14/14.40 ((
% 106.14/14.40 (eqbreln1) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1invprop) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1invI) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1invE) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1compprop) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1compI) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1compE) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1compEex) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1unionprop) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1unionIL) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1unionIR) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1unionI) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1unionE) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1unionEcases) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1unionCommutes) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz2Ex) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz2W) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz2A) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz2B) =>
% 106.14/14.40 ((
% 106.14/14.40 (image1Ex) =>
% 106.14/14.40 ((
% 106.14/14.40 (image1Ex1) =>
% 106.14/14.40 ((
% 106.14/14.40 (image1Equiv) =>
% 106.14/14.40 ((
% 106.14/14.40 (image1E) =>
% 106.14/14.40 ((
% 106.14/14.40 (image1I) =>
% 106.14/14.40 ((
% 106.14/14.40 (injFuncInInjFuncSet) =>
% 106.14/14.40 ((
% 106.14/14.40 (injFuncSetFuncIn) =>
% 106.14/14.40 ((
% 106.14/14.40 (injFuncSetFuncInj) =>
% 106.14/14.40 ((
% 106.14/14.40 (surjFuncSetFuncIn) =>
% 106.14/14.40 ((
% 106.14/14.40 (surjFuncSetFuncSurj) =>
% 106.14/14.40 ((
% 106.14/14.40 (leftInvIsSurj) =>
% 106.14/14.40 ((
% 106.14/14.40 (surjCantorThm) =>
% 106.14/14.40 ((
% 106.14/14.40 (!!) @ (
% 106.14/14.40 (('#S') @ (
% 106.14/14.40 (
% 106.14/14.40 ('#B') @ (
% 106.14/14.40 =>) @
% 106.14/14.40 nonempty)) @
% 106.14/14.40 (
% 106.14/14.40 (
% 106.14/14.40 ('#B') @ (
% 106.14/14.40 ??) @
% 106.14/14.40 (
% 106.14/14.40 (
% 106.14/14.40 ('#S') @ (
% 106.14/14.40 (
% 106.14/14.40 ('#B') @ (
% 106.14/14.40 '#S') @
% 106.14/14.40 (
% 106.14/14.40 (
% 106.14/14.40 ('#B') @ (
% 106.14/14.40 (
% 106.14/14.40 ('#B') @ (
% 106.14/14.40 &))) @
% 106.14/14.40 (
% 106.14/14.40 (
% 106.14/14.40 ('#C') @ in)))))) @
% 106.14/14.40 (
% 106.14/14.40 (
% 106.14/14.40 ('#C') @ (
% 106.14/14.40 (
% 106.14/14.40 ('#B') @ (
% 106.14/14.40 '#C') @
% 106.14/14.40 (
% 106.14/14.40 (
% 106.14/14.40 ('#B') @ (
% 106.14/14.40 (
% 106.14/14.40 ('#B') @ (
% 106.14/14.40 =))) @
% 106.14/14.40 (
% 106.14/14.40 (
% 106.14/14.40 ('#C') @ binintersect)))))) @
% 106.14/14.40 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.14/14.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl71])).
% 106.14/14.40 thf(zip_derived_cl89, plain,
% 106.14/14.40 (~ (((dsetconstrER) =>
% 106.14/14.40 (((exuE1) =>
% 106.14/14.40 (((prop2setE) =>
% 106.14/14.40 (((emptysetE) =>
% 106.14/14.40 (((emptysetimpfalse) =>
% 106.14/14.40 (((notinemptyset) =>
% 106.14/14.40 (((exuE3e) =>
% 106.14/14.40 (((setext) =>
% 106.14/14.40 (((emptyI) =>
% 106.14/14.40 (((noeltsimpempty) =>
% 106.14/14.40 (((setbeta) =>
% 106.14/14.40 (((nonemptyE1) =>
% 106.14/14.40 (((nonemptyI) =>
% 106.14/14.40 (((nonemptyI1) =>
% 106.14/14.40 (((setadjoinIL) =>
% 106.14/14.40 (((in @ emptyset @
% 106.14/14.40 (setadjoin @ emptyset @ emptyset)) =>
% 106.14/14.40 (((setadjoinIR) =>
% 106.14/14.40 (((setadjoinE) =>
% 106.14/14.40 (((setadjoinOr) =>
% 106.14/14.40 (((setoftrueEq) =>
% 106.14/14.40 (((powersetI) =>
% 106.14/14.40 (((emptyinPowerset) =>
% 106.14/14.40 (((emptyInPowerset) =>
% 106.14/14.40 (((powersetE) =>
% 106.14/14.40 (((setunionI) =>
% 106.14/14.40 (((setunionE) =>
% 106.14/14.40 (((subPowSU) =>
% 106.14/14.40 (((exuE2) =>
% 106.14/14.40 (((nonemptyImpWitness) =>
% 106.14/14.40 (((uniqinunit) =>
% 106.14/14.40 ((
% 106.14/14.40 (notinsingleton) =>
% 106.14/14.40 ((
% 106.14/14.40 (eqinunit) =>
% 106.14/14.40 ((
% 106.14/14.40 (singletonsswitch) =>
% 106.14/14.40 ((
% 106.14/14.40 (upairsetE) =>
% 106.14/14.40 ((
% 106.14/14.40 (upairsetIL) =>
% 106.14/14.40 ((
% 106.14/14.40 (upairsetIR) =>
% 106.14/14.40 ((
% 106.14/14.40 (emptyE1) =>
% 106.14/14.40 ((
% 106.14/14.40 (vacuousDall) =>
% 106.14/14.40 ((
% 106.14/14.40 (quantDeMorgan1) =>
% 106.14/14.40 ((
% 106.14/14.40 (quantDeMorgan2) =>
% 106.14/14.40 ((
% 106.14/14.40 (quantDeMorgan3) =>
% 106.14/14.40 ((
% 106.14/14.40 (quantDeMorgan4) =>
% 106.14/14.40 ((
% 106.14/14.40 (prop2setI) =>
% 106.14/14.40 ((
% 106.14/14.40 (prop2set2propI) =>
% 106.14/14.40 ((
% 106.14/14.40 (notdexE) =>
% 106.14/14.40 ((
% 106.14/14.40 (notdallE) =>
% 106.14/14.40 ((
% 106.14/14.40 (exuI1) =>
% 106.14/14.40 ((
% 106.14/14.40 (exuI3) =>
% 106.14/14.40 ((
% 106.14/14.40 (exuI2) =>
% 106.14/14.40 ((
% 106.14/14.40 (inCongP) =>
% 106.14/14.40 ((
% 106.14/14.40 (in__Cong) =>
% 106.14/14.40 ((
% 106.14/14.40 (exuE3u) =>
% 106.14/14.40 ((
% 106.14/14.40 (exu__Cong) =>
% 106.14/14.40 ((
% 106.14/14.40 (setadjoin__Cong) =>
% 106.14/14.40 ((
% 106.14/14.40 (powerset__Cong) =>
% 106.14/14.40 ((
% 106.14/14.40 (setunion__Cong) =>
% 106.14/14.40 ((
% 106.14/14.40 (exuEu) =>
% 106.14/14.40 ((
% 106.14/14.40 (descr__Cong) =>
% 106.14/14.40 ((
% 106.14/14.40 (dsetconstr__Cong) =>
% 106.14/14.40 ((
% 106.14/14.40 (subsetI1) =>
% 106.14/14.40 ((
% 106.14/14.40 (eqimpsubset2) =>
% 106.14/14.40 ((
% 106.14/14.40 (eqimpsubset1) =>
% 106.14/14.40 ((
% 106.14/14.40 (subsetI2) =>
% 106.14/14.40 ((
% 106.14/14.40 (emptysetsubset) =>
% 106.14/14.40 ((
% 106.14/14.40 (subsetE) =>
% 106.14/14.40 ((
% 106.14/14.40 (subsetE2) =>
% 106.14/14.40 ((
% 106.14/14.40 (notsubsetI) =>
% 106.14/14.40 ((
% 106.14/14.40 (notequalI1) =>
% 106.14/14.40 ((
% 106.14/14.40 (notequalI2) =>
% 106.14/14.40 ((
% 106.14/14.40 (subsetRefl) =>
% 106.14/14.40 ((
% 106.14/14.40 (subsetTrans) =>
% 106.14/14.40 ((
% 106.14/14.40 (setadjoinSub) =>
% 106.14/14.40 ((
% 106.14/14.40 (setadjoinSub2) =>
% 106.14/14.40 ((
% 106.14/14.40 (subset2powerset) =>
% 106.14/14.40 ((
% 106.14/14.40 (setextsub) =>
% 106.14/14.40 ((
% 106.14/14.40 (subsetemptysetimpeq) =>
% 106.14/14.40 ((
% 106.14/14.40 (powersetI1) =>
% 106.14/14.40 ((
% 106.14/14.40 (powersetE1) =>
% 106.14/14.40 ((
% 106.14/14.40 (inPowerset) =>
% 106.14/14.40 ((
% 106.14/14.40 (powersetsubset) =>
% 106.14/14.40 ((
% 106.14/14.40 (sepInPowerset) =>
% 106.14/14.40 ((
% 106.14/14.40 (sepSubset) =>
% 106.14/14.40 ((
% 106.14/14.40 (binunionIL) =>
% 106.14/14.40 ((
% 106.14/14.40 (upairset2IR) =>
% 106.14/14.40 ((
% 106.14/14.40 (binunionIR) =>
% 106.14/14.40 ((
% 106.14/14.40 (binunionEcases) =>
% 106.14/14.40 ((
% 106.14/14.40 (binunionE) =>
% 106.14/14.40 ((
% 106.14/14.40 (binunionLsub) =>
% 106.14/14.40 ((
% 106.14/14.40 (binunionRsub) =>
% 106.14/14.40 ((
% 106.14/14.40 (binintersectI) =>
% 106.14/14.40 ((
% 106.14/14.40 (binintersectSubset5) =>
% 106.14/14.40 ((
% 106.14/14.40 (binintersectEL) =>
% 106.14/14.40 ((
% 106.14/14.40 (binintersectLsub) =>
% 106.14/14.40 ((
% 106.14/14.40 (binintersectSubset2) =>
% 106.14/14.40 ((
% 106.14/14.40 (binintersectSubset3) =>
% 106.14/14.40 ((
% 106.14/14.40 (binintersectER) =>
% 106.14/14.40 ((
% 106.14/14.40 (disjointsetsI1) =>
% 106.14/14.40 ((
% 106.14/14.40 (binintersectRsub) =>
% 106.14/14.40 ((
% 106.14/14.40 (binintersectSubset4) =>
% 106.14/14.40 ((
% 106.14/14.40 (binintersectSubset1) =>
% 106.14/14.40 ((
% 106.14/14.40 (bs114d) =>
% 106.14/14.40 ((
% 106.14/14.40 (setminusI) =>
% 106.14/14.40 ((
% 106.14/14.40 (setminusEL) =>
% 106.14/14.40 ((
% 106.14/14.40 (setminusER) =>
% 106.14/14.40 ((
% 106.14/14.40 (setminusSubset2) =>
% 106.14/14.40 ((
% 106.14/14.40 (setminusERneg) =>
% 106.14/14.40 ((
% 106.14/14.40 (setminusELneg) =>
% 106.14/14.40 ((
% 106.14/14.40 (setminusILneg) =>
% 106.14/14.40 ((
% 106.14/14.40 (setminusIRneg) =>
% 106.14/14.40 ((
% 106.14/14.40 (setminusLsub) =>
% 106.14/14.40 ((
% 106.14/14.40 (setminusSubset1) =>
% 106.14/14.40 ((
% 106.14/14.40 (symdiffE) =>
% 106.14/14.40 ((
% 106.14/14.40 (symdiffI1) =>
% 106.14/14.40 ((
% 106.14/14.40 (symdiffI2) =>
% 106.14/14.40 ((
% 106.14/14.40 (symdiffIneg1) =>
% 106.14/14.40 ((
% 106.14/14.40 (symdiffIneg2) =>
% 106.14/14.40 ((
% 106.14/14.40 (secondinupair) =>
% 106.14/14.40 ((
% 106.14/14.40 (setukpairIL) =>
% 106.14/14.40 ((
% 106.14/14.40 (setukpairIR) =>
% 106.14/14.40 ((
% 106.14/14.40 (kpairiskpair) =>
% 106.14/14.40 ((
% 106.14/14.40 (kpairp) =>
% 106.14/14.40 ((
% 106.14/14.40 (singletonsubset) =>
% 106.14/14.40 ((
% 106.14/14.40 (singletoninpowerset) =>
% 106.14/14.40 ((
% 106.14/14.40 (singletoninpowunion) =>
% 106.14/14.40 ((
% 106.14/14.40 (upairset2E) =>
% 106.14/14.40 ((
% 106.14/14.40 (upairsubunion) =>
% 106.14/14.40 ((
% 106.14/14.40 (upairinpowunion) =>
% 106.14/14.40 ((
% 106.14/14.40 (ubforcartprodlem1) =>
% 106.14/14.40 ((
% 106.14/14.40 (ubforcartprodlem2) =>
% 106.14/14.40 ((
% 106.14/14.40 (ubforcartprodlem3) =>
% 106.14/14.40 ((
% 106.14/14.40 (cartprodpairin) =>
% 106.14/14.40 ((
% 106.14/14.40 (cartprodmempair1) =>
% 106.14/14.40 ((
% 106.14/14.40 (cartprodmempair) =>
% 106.14/14.40 ((
% 106.14/14.40 (setunionE2) =>
% 106.14/14.40 ((
% 106.14/14.40 (setunionsingleton1) =>
% 106.14/14.40 ((
% 106.14/14.40 (setunionsingleton2) =>
% 106.14/14.40 ((
% 106.14/14.40 (setunionsingleton) =>
% 106.14/14.40 ((
% 106.14/14.40 (singletonprop) =>
% 106.14/14.40 ((
% 106.14/14.40 (ex1E1) =>
% 106.14/14.40 ((
% 106.14/14.40 (ex1I) =>
% 106.14/14.40 ((
% 106.14/14.40 (ex1I2) =>
% 106.14/14.40 ((
% 106.14/14.40 (singletonsuniq) =>
% 106.14/14.40 ((
% 106.14/14.40 (setukpairinjL1) =>
% 106.14/14.40 ((
% 106.14/14.40 (kfstsingleton) =>
% 106.14/14.40 ((
% 106.14/14.40 (theprop) =>
% 106.14/14.40 ((
% 106.14/14.40 (kfstpairEq) =>
% 106.14/14.40 ((
% 106.14/14.40 (cartprodfstin) =>
% 106.14/14.40 ((
% 106.14/14.40 (setukpairinjL2) =>
% 106.14/14.40 ((
% 106.14/14.40 (setukpairinjL) =>
% 106.14/14.40 ((
% 106.14/14.40 (setukpairinjR11) =>
% 106.14/14.40 ((
% 106.14/14.40 (setukpairinjR12) =>
% 106.14/14.40 ((
% 106.14/14.40 (setukpairinjR1) =>
% 106.14/14.40 ((
% 106.14/14.40 (upairequniteq) =>
% 106.14/14.40 ((
% 106.14/14.40 (setukpairinjR2) =>
% 106.14/14.40 ((
% 106.14/14.40 (setukpairinjR) =>
% 106.14/14.40 ((
% 106.14/14.40 (ksndsingleton) =>
% 106.14/14.40 ((
% 106.14/14.40 (ksndpairEq) =>
% 106.14/14.40 ((
% 106.14/14.40 (kpairsurjEq) =>
% 106.14/14.40 ((
% 106.14/14.40 (cartprodsndin) =>
% 106.14/14.40 ((
% 106.14/14.40 (cartprodpairmemEL) =>
% 106.14/14.40 ((
% 106.14/14.40 (cartprodpairmemER) =>
% 106.14/14.40 ((
% 106.14/14.40 (cartprodmempaircEq) =>
% 106.14/14.40 ((
% 106.14/14.40 (cartprodfstpairEq) =>
% 106.14/14.40 ((
% 106.14/14.40 (cartprodsndpairEq) =>
% 106.14/14.40 ((
% 106.14/14.40 (cartprodpairsurjEq) =>
% 106.14/14.40 ((
% 106.14/14.40 (dpsetconstrI) =>
% 106.14/14.40 ((
% 106.14/14.40 (dpsetconstrSub) =>
% 106.14/14.40 ((
% 106.14/14.40 (setOfPairsIsBReln) =>
% 106.14/14.40 ((
% 106.14/14.40 (dpsetconstrERa) =>
% 106.14/14.40 ((
% 106.14/14.40 (dpsetconstrEL1) =>
% 106.14/14.40 ((
% 106.14/14.40 (dpsetconstrEL2) =>
% 106.14/14.40 ((
% 106.14/14.40 (dpsetconstrER) =>
% 106.14/14.40 ((
% 106.14/14.40 (funcImageSingleton) =>
% 106.14/14.40 ((
% 106.14/14.40 (apProp) =>
% 106.14/14.40 ((
% 106.14/14.40 (app) =>
% 106.14/14.40 ((
% 106.14/14.40 (infuncsetfunc) =>
% 106.14/14.40 ((
% 106.14/14.40 (ap2p) =>
% 106.14/14.40 ((
% 106.14/14.40 (funcinfuncset) =>
% 106.14/14.40 ((
% 106.14/14.40 (lamProp) =>
% 106.14/14.40 ((
% 106.14/14.40 (lamp) =>
% 106.14/14.40 ((
% 106.14/14.40 (lam2p) =>
% 106.14/14.40 ((
% 106.14/14.40 (brelnall1) =>
% 106.14/14.40 ((
% 106.14/14.40 (brelnall2) =>
% 106.14/14.40 ((
% 106.14/14.40 (ex1E2) =>
% 106.14/14.40 ((
% 106.14/14.40 (funcGraphProp1) =>
% 106.14/14.40 ((
% 106.14/14.40 (funcGraphProp3) =>
% 106.14/14.40 ((
% 106.14/14.40 (funcGraphProp2) =>
% 106.14/14.40 ((
% 106.14/14.40 (funcextLem) =>
% 106.14/14.40 ((
% 106.14/14.40 (funcGraphProp4) =>
% 106.14/14.40 ((
% 106.14/14.40 (subbreln) =>
% 106.14/14.40 ((
% 106.14/14.40 (eqbreln) =>
% 106.14/14.40 ((
% 106.14/14.40 (funcext) =>
% 106.14/14.40 ((
% 106.14/14.40 (funcext2) =>
% 106.14/14.40 ((
% 106.14/14.40 (ap2apEq1) =>
% 106.14/14.40 ((
% 106.14/14.40 (ap2apEq2) =>
% 106.14/14.40 ((
% 106.14/14.40 (beta1) =>
% 106.14/14.40 ((
% 106.14/14.40 (eta1) =>
% 106.14/14.40 ((
% 106.14/14.40 (lam2lamEq) =>
% 106.14/14.40 ((
% 106.14/14.40 (beta2) =>
% 106.14/14.40 ((
% 106.14/14.40 (eta2) =>
% 106.14/14.40 ((
% 106.14/14.40 (iffalseProp1) =>
% 106.14/14.40 ((
% 106.14/14.40 (iffalseProp2) =>
% 106.14/14.40 ((
% 106.14/14.40 (iftrueProp1) =>
% 106.14/14.40 ((
% 106.14/14.40 (iftrueProp2) =>
% 106.14/14.40 ((
% 106.14/14.40 (ifSingleton) =>
% 106.14/14.40 ((
% 106.14/14.40 (ifp) =>
% 106.14/14.40 ((
% 106.14/14.40 (theeq) =>
% 106.14/14.40 ((
% 106.14/14.40 (iftrue) =>
% 106.14/14.40 ((
% 106.14/14.40 (iffalse) =>
% 106.14/14.40 ((
% 106.14/14.40 (iftrueorfalse) =>
% 106.14/14.40 ((
% 106.14/14.40 (binintersectT_lem) =>
% 106.14/14.40 ((
% 106.14/14.40 (binunionT_lem) =>
% 106.14/14.40 ((
% 106.14/14.40 (powersetT_lem) =>
% 106.14/14.40 ((
% 106.14/14.40 (setminusT_lem) =>
% 106.14/14.40 ((
% 106.14/14.40 (complementT_lem) =>
% 106.14/14.40 ((
% 106.14/14.40 (setextT) =>
% 106.14/14.40 ((
% 106.14/14.40 (subsetTI) =>
% 106.14/14.40 ((
% 106.14/14.40 (powersetTI1) =>
% 106.14/14.40 ((
% 106.14/14.40 (powersetTE1) =>
% 106.14/14.40 ((
% 106.14/14.40 (complementTI1) =>
% 106.14/14.40 ((
% 106.14/14.40 (complementTE1) =>
% 106.14/14.40 ((
% 106.14/14.40 (binintersectTELcontra) =>
% 106.14/14.40 ((
% 106.14/14.40 (binintersectTERcontra) =>
% 106.14/14.40 ((
% 106.14/14.40 (contrasubsetT) =>
% 106.14/14.40 ((
% 106.14/14.40 (contrasubsetT1) =>
% 106.14/14.40 ((
% 106.14/14.40 (contrasubsetT2) =>
% 106.14/14.40 ((
% 106.14/14.40 (contrasubsetT3) =>
% 106.14/14.40 ((
% 106.14/14.40 (doubleComplementI1) =>
% 106.14/14.40 ((
% 106.14/14.40 (doubleComplementE1) =>
% 106.14/14.40 ((
% 106.14/14.40 (doubleComplementSub1) =>
% 106.14/14.40 ((
% 106.14/14.40 (doubleComplementSub2) =>
% 106.14/14.40 ((
% 106.14/14.40 (doubleComplementEq) =>
% 106.14/14.40 ((
% 106.14/14.40 (complementTnotintersectT) =>
% 106.14/14.40 ((
% 106.14/14.40 (complementImpComplementIntersect) =>
% 106.14/14.40 ((
% 106.14/14.40 (complementSubsetComplementIntersect) =>
% 106.14/14.40 ((
% 106.14/14.40 (complementInPowersetComplementIntersect) =>
% 106.14/14.40 ((
% 106.14/14.40 (contraSubsetComplement) =>
% 106.14/14.40 ((
% 106.14/14.40 (complementTcontraSubset) =>
% 106.14/14.40 ((
% 106.14/14.40 (binunionTILcontra) =>
% 106.14/14.40 ((
% 106.14/14.40 (binunionTIRcontra) =>
% 106.14/14.40 ((
% 106.14/14.40 (inIntersectImpInUnion) =>
% 106.14/14.40 ((
% 106.14/14.40 (inIntersectImpInUnion2) =>
% 106.14/14.40 ((
% 106.14/14.40 (inIntersectImpInIntersectUnions) =>
% 106.14/14.40 ((
% 106.14/14.40 (intersectInPowersetIntersectUnions) =>
% 106.14/14.40 ((
% 106.14/14.40 (inComplementUnionImpNotIn1) =>
% 106.14/14.40 ((
% 106.14/14.40 (inComplementUnionImpInComplement1) =>
% 106.14/14.40 ((
% 106.14/14.40 (binunionTE) =>
% 106.14/14.40 ((
% 106.14/14.40 (binunionTEcontra) =>
% 106.14/14.40 ((
% 106.14/14.40 (demorgan2a1) =>
% 106.14/14.40 ((
% 106.14/14.40 (complementUnionInPowersetComplement) =>
% 106.14/14.40 ((
% 106.14/14.40 (demorgan2a2) =>
% 106.14/14.40 ((
% 106.14/14.40 (demorgan1a) =>
% 106.14/14.40 ((
% 106.14/14.40 (demorgan1b) =>
% 106.14/14.40 ((
% 106.14/14.40 (demorgan1) =>
% 106.14/14.40 ((
% 106.14/14.40 (demorgan2a) =>
% 106.14/14.40 ((
% 106.14/14.40 (demorgan2b2) =>
% 106.14/14.40 ((
% 106.14/14.40 (demorgan2b) =>
% 106.14/14.40 ((
% 106.14/14.40 (demorgan2) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz13rule0) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz13rule1) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz13rule2) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz13rule3) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz13rule4) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz1_1) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz1_2) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz1_3) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz1_4) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz1_5) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1all2) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1SetBreln1) =>
% 106.14/14.40 ((
% 106.14/14.40 (choice2fnsingleton) =>
% 106.14/14.40 ((
% 106.14/14.40 (setOfPairsIsBReln1) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1all1) =>
% 106.14/14.40 ((
% 106.14/14.40 (subbreln1) =>
% 106.14/14.40 ((
% 106.14/14.40 (eqbreln1) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1invprop) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1invI) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1invE) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1compprop) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1compI) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1compE) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1compEex) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1unionprop) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1unionIL) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1unionIR) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1unionI) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1unionE) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1unionEcases) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1unionCommutes) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz2Ex) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz2W) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz2A) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz2B) =>
% 106.14/14.40 ((
% 106.14/14.40 (image1Ex) =>
% 106.14/14.40 ((
% 106.14/14.40 (image1Ex1) =>
% 106.14/14.40 ((
% 106.14/14.40 (image1Equiv) =>
% 106.14/14.40 ((
% 106.14/14.40 (image1E) =>
% 106.14/14.40 ((
% 106.14/14.40 (image1I) =>
% 106.14/14.40 ((
% 106.14/14.40 (injFuncInInjFuncSet) =>
% 106.14/14.40 ((
% 106.14/14.40 (injFuncSetFuncIn) =>
% 106.14/14.40 ((
% 106.14/14.40 (injFuncSetFuncInj) =>
% 106.14/14.40 ((
% 106.14/14.40 (surjFuncSetFuncIn) =>
% 106.14/14.40 ((
% 106.14/14.40 (surjFuncSetFuncSurj) =>
% 106.14/14.40 ((
% 106.14/14.40 (leftInvIsSurj) =>
% 106.14/14.40 ((
% 106.14/14.40 (surjCantorThm) =>
% 106.14/14.40 ((
% 106.14/14.40 (!!) @ (
% 106.14/14.40 (('#S') @ (
% 106.14/14.40 (
% 106.14/14.40 ('#B') @ (
% 106.14/14.40 =>) @
% 106.14/14.40 nonempty)) @
% 106.14/14.40 (
% 106.14/14.40 (
% 106.14/14.40 ('#B') @ (
% 106.14/14.40 ??) @
% 106.14/14.40 (
% 106.14/14.40 (
% 106.14/14.40 ('#S') @ (
% 106.14/14.40 (
% 106.14/14.40 ('#B') @ (
% 106.14/14.40 '#S') @
% 106.14/14.40 (
% 106.14/14.40 (
% 106.14/14.40 ('#B') @ (
% 106.14/14.40 (
% 106.14/14.40 ('#B') @ (
% 106.14/14.40 &))) @
% 106.14/14.40 (
% 106.14/14.40 (
% 106.14/14.40 ('#C') @ in)))))) @
% 106.14/14.40 (
% 106.14/14.40 (
% 106.14/14.40 ('#C') @ (
% 106.14/14.40 (
% 106.14/14.40 ('#B') @ (
% 106.14/14.40 '#C') @
% 106.14/14.40 (
% 106.14/14.40 (
% 106.14/14.40 ('#B') @ (
% 106.14/14.40 (
% 106.14/14.40 ('#B') @ (
% 106.14/14.40 =))) @
% 106.14/14.40 (
% 106.14/14.40 (
% 106.14/14.40 ('#C') @ binintersect)))))) @
% 106.14/14.40 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.14/14.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl79])).
% 106.14/14.40 thf(zip_derived_cl105, plain,
% 106.14/14.40 (~ (((exuE1) =>
% 106.14/14.40 (((prop2setE) =>
% 106.14/14.40 (((emptysetE) =>
% 106.14/14.40 (((emptysetimpfalse) =>
% 106.14/14.40 (((notinemptyset) =>
% 106.14/14.40 (((exuE3e) =>
% 106.14/14.40 (((setext) =>
% 106.14/14.40 (((emptyI) =>
% 106.14/14.40 (((noeltsimpempty) =>
% 106.14/14.40 (((setbeta) =>
% 106.14/14.40 (((nonemptyE1) =>
% 106.14/14.40 (((nonemptyI) =>
% 106.14/14.40 (((nonemptyI1) =>
% 106.14/14.40 (((setadjoinIL) =>
% 106.14/14.40 (((in @ emptyset @
% 106.14/14.40 (setadjoin @ emptyset @ emptyset)) =>
% 106.14/14.40 (((setadjoinIR) =>
% 106.14/14.40 (((setadjoinE) =>
% 106.14/14.40 (((setadjoinOr) =>
% 106.14/14.40 (((setoftrueEq) =>
% 106.14/14.40 (((powersetI) =>
% 106.14/14.40 (((emptyinPowerset) =>
% 106.14/14.40 (((emptyInPowerset) =>
% 106.14/14.40 (((powersetE) =>
% 106.14/14.40 (((setunionI) =>
% 106.14/14.40 (((setunionE) =>
% 106.14/14.40 (((subPowSU) =>
% 106.14/14.40 (((exuE2) =>
% 106.14/14.40 (((nonemptyImpWitness) =>
% 106.14/14.40 (((uniqinunit) =>
% 106.14/14.40 (((notinsingleton) =>
% 106.14/14.40 ((
% 106.14/14.40 (eqinunit) =>
% 106.14/14.40 ((
% 106.14/14.40 (singletonsswitch) =>
% 106.14/14.40 ((
% 106.14/14.40 (upairsetE) =>
% 106.14/14.40 ((
% 106.14/14.40 (upairsetIL) =>
% 106.14/14.40 ((
% 106.14/14.40 (upairsetIR) =>
% 106.14/14.40 ((
% 106.14/14.40 (emptyE1) =>
% 106.14/14.40 ((
% 106.14/14.40 (vacuousDall) =>
% 106.14/14.40 ((
% 106.14/14.40 (quantDeMorgan1) =>
% 106.14/14.40 ((
% 106.14/14.40 (quantDeMorgan2) =>
% 106.14/14.40 ((
% 106.14/14.40 (quantDeMorgan3) =>
% 106.14/14.40 ((
% 106.14/14.40 (quantDeMorgan4) =>
% 106.14/14.40 ((
% 106.14/14.40 (prop2setI) =>
% 106.14/14.40 ((
% 106.14/14.40 (prop2set2propI) =>
% 106.14/14.40 ((
% 106.14/14.40 (notdexE) =>
% 106.14/14.40 ((
% 106.14/14.40 (notdallE) =>
% 106.14/14.40 ((
% 106.14/14.40 (exuI1) =>
% 106.14/14.40 ((
% 106.14/14.40 (exuI3) =>
% 106.14/14.40 ((
% 106.14/14.40 (exuI2) =>
% 106.14/14.40 ((
% 106.14/14.40 (inCongP) =>
% 106.14/14.40 ((
% 106.14/14.40 (in__Cong) =>
% 106.14/14.40 ((
% 106.14/14.40 (exuE3u) =>
% 106.14/14.40 ((
% 106.14/14.40 (exu__Cong) =>
% 106.14/14.40 ((
% 106.14/14.40 (setadjoin__Cong) =>
% 106.14/14.40 ((
% 106.14/14.40 (powerset__Cong) =>
% 106.14/14.40 ((
% 106.14/14.40 (setunion__Cong) =>
% 106.14/14.40 ((
% 106.14/14.40 (exuEu) =>
% 106.14/14.40 ((
% 106.14/14.40 (descr__Cong) =>
% 106.14/14.40 ((
% 106.14/14.40 (dsetconstr__Cong) =>
% 106.14/14.40 ((
% 106.14/14.40 (subsetI1) =>
% 106.14/14.40 ((
% 106.14/14.40 (eqimpsubset2) =>
% 106.14/14.40 ((
% 106.14/14.40 (eqimpsubset1) =>
% 106.14/14.40 ((
% 106.14/14.40 (subsetI2) =>
% 106.14/14.40 ((
% 106.14/14.40 (emptysetsubset) =>
% 106.14/14.40 ((
% 106.14/14.40 (subsetE) =>
% 106.14/14.40 ((
% 106.14/14.40 (subsetE2) =>
% 106.14/14.40 ((
% 106.14/14.40 (notsubsetI) =>
% 106.14/14.40 ((
% 106.14/14.40 (notequalI1) =>
% 106.14/14.40 ((
% 106.14/14.40 (notequalI2) =>
% 106.14/14.40 ((
% 106.14/14.40 (subsetRefl) =>
% 106.14/14.40 ((
% 106.14/14.40 (subsetTrans) =>
% 106.14/14.40 ((
% 106.14/14.40 (setadjoinSub) =>
% 106.14/14.40 ((
% 106.14/14.40 (setadjoinSub2) =>
% 106.14/14.40 ((
% 106.14/14.40 (subset2powerset) =>
% 106.14/14.40 ((
% 106.14/14.40 (setextsub) =>
% 106.14/14.40 ((
% 106.14/14.40 (subsetemptysetimpeq) =>
% 106.14/14.40 ((
% 106.14/14.40 (powersetI1) =>
% 106.14/14.40 ((
% 106.14/14.40 (powersetE1) =>
% 106.14/14.40 ((
% 106.14/14.40 (inPowerset) =>
% 106.14/14.40 ((
% 106.14/14.40 (powersetsubset) =>
% 106.14/14.40 ((
% 106.14/14.40 (sepInPowerset) =>
% 106.14/14.40 ((
% 106.14/14.40 (sepSubset) =>
% 106.14/14.40 ((
% 106.14/14.40 (binunionIL) =>
% 106.14/14.40 ((
% 106.14/14.40 (upairset2IR) =>
% 106.14/14.40 ((
% 106.14/14.40 (binunionIR) =>
% 106.14/14.40 ((
% 106.14/14.40 (binunionEcases) =>
% 106.14/14.40 ((
% 106.14/14.40 (binunionE) =>
% 106.14/14.40 ((
% 106.14/14.40 (binunionLsub) =>
% 106.14/14.40 ((
% 106.14/14.40 (binunionRsub) =>
% 106.14/14.40 ((
% 106.14/14.40 (binintersectI) =>
% 106.14/14.40 ((
% 106.14/14.40 (binintersectSubset5) =>
% 106.14/14.40 ((
% 106.14/14.40 (binintersectEL) =>
% 106.14/14.40 ((
% 106.14/14.40 (binintersectLsub) =>
% 106.14/14.40 ((
% 106.14/14.40 (binintersectSubset2) =>
% 106.14/14.40 ((
% 106.14/14.40 (binintersectSubset3) =>
% 106.14/14.40 ((
% 106.14/14.40 (binintersectER) =>
% 106.14/14.40 ((
% 106.14/14.40 (disjointsetsI1) =>
% 106.14/14.40 ((
% 106.14/14.40 (binintersectRsub) =>
% 106.14/14.40 ((
% 106.14/14.40 (binintersectSubset4) =>
% 106.14/14.40 ((
% 106.14/14.40 (binintersectSubset1) =>
% 106.14/14.40 ((
% 106.14/14.40 (bs114d) =>
% 106.14/14.40 ((
% 106.14/14.40 (setminusI) =>
% 106.14/14.40 ((
% 106.14/14.40 (setminusEL) =>
% 106.14/14.40 ((
% 106.14/14.40 (setminusER) =>
% 106.14/14.40 ((
% 106.14/14.40 (setminusSubset2) =>
% 106.14/14.40 ((
% 106.14/14.40 (setminusERneg) =>
% 106.14/14.40 ((
% 106.14/14.40 (setminusELneg) =>
% 106.14/14.40 ((
% 106.14/14.40 (setminusILneg) =>
% 106.14/14.40 ((
% 106.14/14.40 (setminusIRneg) =>
% 106.14/14.40 ((
% 106.14/14.40 (setminusLsub) =>
% 106.14/14.40 ((
% 106.14/14.40 (setminusSubset1) =>
% 106.14/14.40 ((
% 106.14/14.40 (symdiffE) =>
% 106.14/14.40 ((
% 106.14/14.40 (symdiffI1) =>
% 106.14/14.40 ((
% 106.14/14.40 (symdiffI2) =>
% 106.14/14.40 ((
% 106.14/14.40 (symdiffIneg1) =>
% 106.14/14.40 ((
% 106.14/14.40 (symdiffIneg2) =>
% 106.14/14.40 ((
% 106.14/14.40 (secondinupair) =>
% 106.14/14.40 ((
% 106.14/14.40 (setukpairIL) =>
% 106.14/14.40 ((
% 106.14/14.40 (setukpairIR) =>
% 106.14/14.40 ((
% 106.14/14.40 (kpairiskpair) =>
% 106.14/14.40 ((
% 106.14/14.40 (kpairp) =>
% 106.14/14.40 ((
% 106.14/14.40 (singletonsubset) =>
% 106.14/14.40 ((
% 106.14/14.40 (singletoninpowerset) =>
% 106.14/14.40 ((
% 106.14/14.40 (singletoninpowunion) =>
% 106.14/14.40 ((
% 106.14/14.40 (upairset2E) =>
% 106.14/14.40 ((
% 106.14/14.40 (upairsubunion) =>
% 106.14/14.40 ((
% 106.14/14.40 (upairinpowunion) =>
% 106.14/14.40 ((
% 106.14/14.40 (ubforcartprodlem1) =>
% 106.14/14.40 ((
% 106.14/14.40 (ubforcartprodlem2) =>
% 106.14/14.40 ((
% 106.14/14.40 (ubforcartprodlem3) =>
% 106.14/14.40 ((
% 106.14/14.40 (cartprodpairin) =>
% 106.14/14.40 ((
% 106.14/14.40 (cartprodmempair1) =>
% 106.14/14.40 ((
% 106.14/14.40 (cartprodmempair) =>
% 106.14/14.40 ((
% 106.14/14.40 (setunionE2) =>
% 106.14/14.40 ((
% 106.14/14.40 (setunionsingleton1) =>
% 106.14/14.40 ((
% 106.14/14.40 (setunionsingleton2) =>
% 106.14/14.40 ((
% 106.14/14.40 (setunionsingleton) =>
% 106.14/14.40 ((
% 106.14/14.40 (singletonprop) =>
% 106.14/14.40 ((
% 106.14/14.40 (ex1E1) =>
% 106.14/14.40 ((
% 106.14/14.40 (ex1I) =>
% 106.14/14.40 ((
% 106.14/14.40 (ex1I2) =>
% 106.14/14.40 ((
% 106.14/14.40 (singletonsuniq) =>
% 106.14/14.40 ((
% 106.14/14.40 (setukpairinjL1) =>
% 106.14/14.40 ((
% 106.14/14.40 (kfstsingleton) =>
% 106.14/14.40 ((
% 106.14/14.40 (theprop) =>
% 106.14/14.40 ((
% 106.14/14.40 (kfstpairEq) =>
% 106.14/14.40 ((
% 106.14/14.40 (cartprodfstin) =>
% 106.14/14.40 ((
% 106.14/14.40 (setukpairinjL2) =>
% 106.14/14.40 ((
% 106.14/14.40 (setukpairinjL) =>
% 106.14/14.40 ((
% 106.14/14.40 (setukpairinjR11) =>
% 106.14/14.40 ((
% 106.14/14.40 (setukpairinjR12) =>
% 106.14/14.40 ((
% 106.14/14.40 (setukpairinjR1) =>
% 106.14/14.40 ((
% 106.14/14.40 (upairequniteq) =>
% 106.14/14.40 ((
% 106.14/14.40 (setukpairinjR2) =>
% 106.14/14.40 ((
% 106.14/14.40 (setukpairinjR) =>
% 106.14/14.40 ((
% 106.14/14.40 (ksndsingleton) =>
% 106.14/14.40 ((
% 106.14/14.40 (ksndpairEq) =>
% 106.14/14.40 ((
% 106.14/14.40 (kpairsurjEq) =>
% 106.14/14.40 ((
% 106.14/14.40 (cartprodsndin) =>
% 106.14/14.40 ((
% 106.14/14.40 (cartprodpairmemEL) =>
% 106.14/14.40 ((
% 106.14/14.40 (cartprodpairmemER) =>
% 106.14/14.40 ((
% 106.14/14.40 (cartprodmempaircEq) =>
% 106.14/14.40 ((
% 106.14/14.40 (cartprodfstpairEq) =>
% 106.14/14.40 ((
% 106.14/14.40 (cartprodsndpairEq) =>
% 106.14/14.40 ((
% 106.14/14.40 (cartprodpairsurjEq) =>
% 106.14/14.40 ((
% 106.14/14.40 (dpsetconstrI) =>
% 106.14/14.40 ((
% 106.14/14.40 (dpsetconstrSub) =>
% 106.14/14.40 ((
% 106.14/14.40 (setOfPairsIsBReln) =>
% 106.14/14.40 ((
% 106.14/14.40 (dpsetconstrERa) =>
% 106.14/14.40 ((
% 106.14/14.40 (dpsetconstrEL1) =>
% 106.14/14.40 ((
% 106.14/14.40 (dpsetconstrEL2) =>
% 106.14/14.40 ((
% 106.14/14.40 (dpsetconstrER) =>
% 106.14/14.40 ((
% 106.14/14.40 (funcImageSingleton) =>
% 106.14/14.40 ((
% 106.14/14.40 (apProp) =>
% 106.14/14.40 ((
% 106.14/14.40 (app) =>
% 106.14/14.40 ((
% 106.14/14.40 (infuncsetfunc) =>
% 106.14/14.40 ((
% 106.14/14.40 (ap2p) =>
% 106.14/14.40 ((
% 106.14/14.40 (funcinfuncset) =>
% 106.14/14.40 ((
% 106.14/14.40 (lamProp) =>
% 106.14/14.40 ((
% 106.14/14.40 (lamp) =>
% 106.14/14.40 ((
% 106.14/14.40 (lam2p) =>
% 106.14/14.40 ((
% 106.14/14.40 (brelnall1) =>
% 106.14/14.40 ((
% 106.14/14.40 (brelnall2) =>
% 106.14/14.40 ((
% 106.14/14.40 (ex1E2) =>
% 106.14/14.40 ((
% 106.14/14.40 (funcGraphProp1) =>
% 106.14/14.40 ((
% 106.14/14.40 (funcGraphProp3) =>
% 106.14/14.40 ((
% 106.14/14.40 (funcGraphProp2) =>
% 106.14/14.40 ((
% 106.14/14.40 (funcextLem) =>
% 106.14/14.40 ((
% 106.14/14.40 (funcGraphProp4) =>
% 106.14/14.40 ((
% 106.14/14.40 (subbreln) =>
% 106.14/14.40 ((
% 106.14/14.40 (eqbreln) =>
% 106.14/14.40 ((
% 106.14/14.40 (funcext) =>
% 106.14/14.40 ((
% 106.14/14.40 (funcext2) =>
% 106.14/14.40 ((
% 106.14/14.40 (ap2apEq1) =>
% 106.14/14.40 ((
% 106.14/14.40 (ap2apEq2) =>
% 106.14/14.40 ((
% 106.14/14.40 (beta1) =>
% 106.14/14.40 ((
% 106.14/14.40 (eta1) =>
% 106.14/14.40 ((
% 106.14/14.40 (lam2lamEq) =>
% 106.14/14.40 ((
% 106.14/14.40 (beta2) =>
% 106.14/14.40 ((
% 106.14/14.40 (eta2) =>
% 106.14/14.40 ((
% 106.14/14.40 (iffalseProp1) =>
% 106.14/14.40 ((
% 106.14/14.40 (iffalseProp2) =>
% 106.14/14.40 ((
% 106.14/14.40 (iftrueProp1) =>
% 106.14/14.40 ((
% 106.14/14.40 (iftrueProp2) =>
% 106.14/14.40 ((
% 106.14/14.40 (ifSingleton) =>
% 106.14/14.40 ((
% 106.14/14.40 (ifp) =>
% 106.14/14.40 ((
% 106.14/14.40 (theeq) =>
% 106.14/14.40 ((
% 106.14/14.40 (iftrue) =>
% 106.14/14.40 ((
% 106.14/14.40 (iffalse) =>
% 106.14/14.40 ((
% 106.14/14.40 (iftrueorfalse) =>
% 106.14/14.40 ((
% 106.14/14.40 (binintersectT_lem) =>
% 106.14/14.40 ((
% 106.14/14.40 (binunionT_lem) =>
% 106.14/14.40 ((
% 106.14/14.40 (powersetT_lem) =>
% 106.14/14.40 ((
% 106.14/14.40 (setminusT_lem) =>
% 106.14/14.40 ((
% 106.14/14.40 (complementT_lem) =>
% 106.14/14.40 ((
% 106.14/14.40 (setextT) =>
% 106.14/14.40 ((
% 106.14/14.40 (subsetTI) =>
% 106.14/14.40 ((
% 106.14/14.40 (powersetTI1) =>
% 106.14/14.40 ((
% 106.14/14.40 (powersetTE1) =>
% 106.14/14.40 ((
% 106.14/14.40 (complementTI1) =>
% 106.14/14.40 ((
% 106.14/14.40 (complementTE1) =>
% 106.14/14.40 ((
% 106.14/14.40 (binintersectTELcontra) =>
% 106.14/14.40 ((
% 106.14/14.40 (binintersectTERcontra) =>
% 106.14/14.40 ((
% 106.14/14.40 (contrasubsetT) =>
% 106.14/14.40 ((
% 106.14/14.40 (contrasubsetT1) =>
% 106.14/14.40 ((
% 106.14/14.40 (contrasubsetT2) =>
% 106.14/14.40 ((
% 106.14/14.40 (contrasubsetT3) =>
% 106.14/14.40 ((
% 106.14/14.40 (doubleComplementI1) =>
% 106.14/14.40 ((
% 106.14/14.40 (doubleComplementE1) =>
% 106.14/14.40 ((
% 106.14/14.40 (doubleComplementSub1) =>
% 106.14/14.40 ((
% 106.14/14.40 (doubleComplementSub2) =>
% 106.14/14.40 ((
% 106.14/14.40 (doubleComplementEq) =>
% 106.14/14.40 ((
% 106.14/14.40 (complementTnotintersectT) =>
% 106.14/14.40 ((
% 106.14/14.40 (complementImpComplementIntersect) =>
% 106.14/14.40 ((
% 106.14/14.40 (complementSubsetComplementIntersect) =>
% 106.14/14.40 ((
% 106.14/14.40 (complementInPowersetComplementIntersect) =>
% 106.14/14.40 ((
% 106.14/14.40 (contraSubsetComplement) =>
% 106.14/14.40 ((
% 106.14/14.40 (complementTcontraSubset) =>
% 106.14/14.40 ((
% 106.14/14.40 (binunionTILcontra) =>
% 106.14/14.40 ((
% 106.14/14.40 (binunionTIRcontra) =>
% 106.14/14.40 ((
% 106.14/14.40 (inIntersectImpInUnion) =>
% 106.14/14.40 ((
% 106.14/14.40 (inIntersectImpInUnion2) =>
% 106.14/14.40 ((
% 106.14/14.40 (inIntersectImpInIntersectUnions) =>
% 106.14/14.40 ((
% 106.14/14.40 (intersectInPowersetIntersectUnions) =>
% 106.14/14.40 ((
% 106.14/14.40 (inComplementUnionImpNotIn1) =>
% 106.14/14.40 ((
% 106.14/14.40 (inComplementUnionImpInComplement1) =>
% 106.14/14.40 ((
% 106.14/14.40 (binunionTE) =>
% 106.14/14.40 ((
% 106.14/14.40 (binunionTEcontra) =>
% 106.14/14.40 ((
% 106.14/14.40 (demorgan2a1) =>
% 106.14/14.40 ((
% 106.14/14.40 (complementUnionInPowersetComplement) =>
% 106.14/14.40 ((
% 106.14/14.40 (demorgan2a2) =>
% 106.14/14.40 ((
% 106.14/14.40 (demorgan1a) =>
% 106.14/14.40 ((
% 106.14/14.40 (demorgan1b) =>
% 106.14/14.40 ((
% 106.14/14.40 (demorgan1) =>
% 106.14/14.40 ((
% 106.14/14.40 (demorgan2a) =>
% 106.14/14.40 ((
% 106.14/14.40 (demorgan2b2) =>
% 106.14/14.40 ((
% 106.14/14.40 (demorgan2b) =>
% 106.14/14.40 ((
% 106.14/14.40 (demorgan2) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz13rule0) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz13rule1) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz13rule2) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz13rule3) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz13rule4) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz1_1) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz1_2) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz1_3) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz1_4) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz1_5) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1all2) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1SetBreln1) =>
% 106.14/14.40 ((
% 106.14/14.40 (choice2fnsingleton) =>
% 106.14/14.40 ((
% 106.14/14.40 (setOfPairsIsBReln1) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1all1) =>
% 106.14/14.40 ((
% 106.14/14.40 (subbreln1) =>
% 106.14/14.40 ((
% 106.14/14.40 (eqbreln1) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1invprop) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1invI) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1invE) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1compprop) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1compI) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1compE) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1compEex) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1unionprop) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1unionIL) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1unionIR) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1unionI) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1unionE) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1unionEcases) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1unionCommutes) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz2Ex) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz2W) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz2A) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz2B) =>
% 106.14/14.40 ((
% 106.14/14.40 (image1Ex) =>
% 106.14/14.40 ((
% 106.14/14.40 (image1Ex1) =>
% 106.14/14.40 ((
% 106.14/14.40 (image1Equiv) =>
% 106.14/14.40 ((
% 106.14/14.40 (image1E) =>
% 106.14/14.40 ((
% 106.14/14.40 (image1I) =>
% 106.14/14.40 ((
% 106.14/14.40 (injFuncInInjFuncSet) =>
% 106.14/14.40 ((
% 106.14/14.40 (injFuncSetFuncIn) =>
% 106.14/14.40 ((
% 106.14/14.40 (injFuncSetFuncInj) =>
% 106.14/14.40 ((
% 106.14/14.40 (surjFuncSetFuncIn) =>
% 106.14/14.40 ((
% 106.14/14.40 (surjFuncSetFuncSurj) =>
% 106.14/14.40 ((
% 106.14/14.40 (leftInvIsSurj) =>
% 106.14/14.40 ((
% 106.14/14.40 (surjCantorThm) =>
% 106.14/14.40 ((
% 106.14/14.40 (!!) @ (
% 106.14/14.40 (('#S') @ (
% 106.14/14.40 (
% 106.14/14.40 ('#B') @ (
% 106.14/14.40 =>) @
% 106.14/14.40 nonempty)) @
% 106.14/14.40 (
% 106.14/14.40 (
% 106.14/14.40 ('#B') @ (
% 106.14/14.40 ??) @
% 106.14/14.40 (
% 106.14/14.40 (
% 106.14/14.40 ('#S') @ (
% 106.14/14.40 (
% 106.14/14.40 ('#B') @ (
% 106.14/14.40 '#S') @
% 106.14/14.40 (
% 106.14/14.40 (
% 106.14/14.40 ('#B') @ (
% 106.14/14.40 (
% 106.14/14.40 ('#B') @ (
% 106.14/14.40 &))) @
% 106.14/14.40 (
% 106.14/14.40 (
% 106.14/14.40 ('#C') @ in)))))) @
% 106.14/14.40 (
% 106.14/14.40 (
% 106.14/14.40 ('#C') @ (
% 106.14/14.40 (
% 106.14/14.40 ('#B') @ (
% 106.14/14.40 '#C') @
% 106.14/14.40 (
% 106.14/14.40 (
% 106.14/14.40 ('#B') @ (
% 106.14/14.40 (
% 106.14/14.40 ('#B') @ (
% 106.14/14.40 =))) @
% 106.14/14.40 (
% 106.14/14.40 (
% 106.14/14.40 ('#C') @ binintersect)))))) @
% 106.14/14.40 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.14/14.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl89])).
% 106.14/14.40 thf(zip_derived_cl123, plain,
% 106.14/14.40 (~ (((prop2setE) =>
% 106.14/14.40 (((emptysetE) =>
% 106.14/14.40 (((emptysetimpfalse) =>
% 106.14/14.40 (((notinemptyset) =>
% 106.14/14.40 (((exuE3e) =>
% 106.14/14.40 (((setext) =>
% 106.14/14.40 (((emptyI) =>
% 106.14/14.40 (((noeltsimpempty) =>
% 106.14/14.40 (((setbeta) =>
% 106.14/14.40 (((nonemptyE1) =>
% 106.14/14.40 (((nonemptyI) =>
% 106.14/14.40 (((nonemptyI1) =>
% 106.14/14.40 (((setadjoinIL) =>
% 106.14/14.40 (((in @ emptyset @
% 106.14/14.40 (setadjoin @ emptyset @ emptyset)) =>
% 106.14/14.40 (((setadjoinIR) =>
% 106.14/14.40 (((setadjoinE) =>
% 106.14/14.40 (((setadjoinOr) =>
% 106.14/14.40 (((setoftrueEq) =>
% 106.14/14.40 (((powersetI) =>
% 106.14/14.40 (((emptyinPowerset) =>
% 106.14/14.40 (((emptyInPowerset) =>
% 106.14/14.40 (((powersetE) =>
% 106.14/14.40 (((setunionI) =>
% 106.14/14.40 (((setunionE) =>
% 106.14/14.40 (((subPowSU) =>
% 106.14/14.40 (((exuE2) =>
% 106.14/14.40 (((nonemptyImpWitness) =>
% 106.14/14.40 (((uniqinunit) =>
% 106.14/14.40 (((notinsingleton) =>
% 106.14/14.40 (((eqinunit) =>
% 106.14/14.40 ((
% 106.14/14.40 (singletonsswitch) =>
% 106.14/14.40 ((
% 106.14/14.40 (upairsetE) =>
% 106.14/14.40 ((
% 106.14/14.40 (upairsetIL) =>
% 106.14/14.40 ((
% 106.14/14.40 (upairsetIR) =>
% 106.14/14.40 ((
% 106.14/14.40 (emptyE1) =>
% 106.14/14.40 ((
% 106.14/14.40 (vacuousDall) =>
% 106.14/14.40 ((
% 106.14/14.40 (quantDeMorgan1) =>
% 106.14/14.40 ((
% 106.14/14.40 (quantDeMorgan2) =>
% 106.14/14.40 ((
% 106.14/14.40 (quantDeMorgan3) =>
% 106.14/14.40 ((
% 106.14/14.40 (quantDeMorgan4) =>
% 106.14/14.40 ((
% 106.14/14.40 (prop2setI) =>
% 106.14/14.40 ((
% 106.14/14.40 (prop2set2propI) =>
% 106.14/14.40 ((
% 106.14/14.40 (notdexE) =>
% 106.14/14.40 ((
% 106.14/14.40 (notdallE) =>
% 106.14/14.40 ((
% 106.14/14.40 (exuI1) =>
% 106.14/14.40 ((
% 106.14/14.40 (exuI3) =>
% 106.14/14.40 ((
% 106.14/14.40 (exuI2) =>
% 106.14/14.40 ((
% 106.14/14.40 (inCongP) =>
% 106.14/14.40 ((
% 106.14/14.40 (in__Cong) =>
% 106.14/14.40 ((
% 106.14/14.40 (exuE3u) =>
% 106.14/14.40 ((
% 106.14/14.40 (exu__Cong) =>
% 106.14/14.40 ((
% 106.14/14.40 (setadjoin__Cong) =>
% 106.14/14.40 ((
% 106.14/14.40 (powerset__Cong) =>
% 106.14/14.40 ((
% 106.14/14.40 (setunion__Cong) =>
% 106.14/14.40 ((
% 106.14/14.40 (exuEu) =>
% 106.14/14.40 ((
% 106.14/14.40 (descr__Cong) =>
% 106.14/14.40 ((
% 106.14/14.40 (dsetconstr__Cong) =>
% 106.14/14.40 ((
% 106.14/14.40 (subsetI1) =>
% 106.14/14.40 ((
% 106.14/14.40 (eqimpsubset2) =>
% 106.14/14.40 ((
% 106.14/14.40 (eqimpsubset1) =>
% 106.14/14.40 ((
% 106.14/14.40 (subsetI2) =>
% 106.14/14.40 ((
% 106.14/14.40 (emptysetsubset) =>
% 106.14/14.40 ((
% 106.14/14.40 (subsetE) =>
% 106.14/14.40 ((
% 106.14/14.40 (subsetE2) =>
% 106.14/14.40 ((
% 106.14/14.40 (notsubsetI) =>
% 106.14/14.40 ((
% 106.14/14.40 (notequalI1) =>
% 106.14/14.40 ((
% 106.14/14.40 (notequalI2) =>
% 106.14/14.40 ((
% 106.14/14.40 (subsetRefl) =>
% 106.14/14.40 ((
% 106.14/14.40 (subsetTrans) =>
% 106.14/14.40 ((
% 106.14/14.40 (setadjoinSub) =>
% 106.14/14.40 ((
% 106.14/14.40 (setadjoinSub2) =>
% 106.14/14.40 ((
% 106.14/14.40 (subset2powerset) =>
% 106.14/14.40 ((
% 106.14/14.40 (setextsub) =>
% 106.14/14.40 ((
% 106.14/14.40 (subsetemptysetimpeq) =>
% 106.14/14.40 ((
% 106.14/14.40 (powersetI1) =>
% 106.14/14.40 ((
% 106.14/14.40 (powersetE1) =>
% 106.14/14.40 ((
% 106.14/14.40 (inPowerset) =>
% 106.14/14.40 ((
% 106.14/14.40 (powersetsubset) =>
% 106.14/14.40 ((
% 106.14/14.40 (sepInPowerset) =>
% 106.14/14.40 ((
% 106.14/14.40 (sepSubset) =>
% 106.14/14.40 ((
% 106.14/14.40 (binunionIL) =>
% 106.14/14.40 ((
% 106.14/14.40 (upairset2IR) =>
% 106.14/14.40 ((
% 106.14/14.40 (binunionIR) =>
% 106.14/14.40 ((
% 106.14/14.40 (binunionEcases) =>
% 106.14/14.40 ((
% 106.14/14.40 (binunionE) =>
% 106.14/14.40 ((
% 106.14/14.40 (binunionLsub) =>
% 106.14/14.40 ((
% 106.14/14.40 (binunionRsub) =>
% 106.14/14.40 ((
% 106.14/14.40 (binintersectI) =>
% 106.14/14.40 ((
% 106.14/14.40 (binintersectSubset5) =>
% 106.14/14.40 ((
% 106.14/14.40 (binintersectEL) =>
% 106.14/14.40 ((
% 106.14/14.40 (binintersectLsub) =>
% 106.14/14.40 ((
% 106.14/14.40 (binintersectSubset2) =>
% 106.14/14.40 ((
% 106.14/14.40 (binintersectSubset3) =>
% 106.14/14.40 ((
% 106.14/14.40 (binintersectER) =>
% 106.14/14.40 ((
% 106.14/14.40 (disjointsetsI1) =>
% 106.14/14.40 ((
% 106.14/14.40 (binintersectRsub) =>
% 106.14/14.40 ((
% 106.14/14.40 (binintersectSubset4) =>
% 106.14/14.40 ((
% 106.14/14.40 (binintersectSubset1) =>
% 106.14/14.40 ((
% 106.14/14.40 (bs114d) =>
% 106.14/14.40 ((
% 106.14/14.40 (setminusI) =>
% 106.14/14.40 ((
% 106.14/14.40 (setminusEL) =>
% 106.14/14.40 ((
% 106.14/14.40 (setminusER) =>
% 106.14/14.40 ((
% 106.14/14.40 (setminusSubset2) =>
% 106.14/14.40 ((
% 106.14/14.40 (setminusERneg) =>
% 106.14/14.40 ((
% 106.14/14.40 (setminusELneg) =>
% 106.14/14.40 ((
% 106.14/14.40 (setminusILneg) =>
% 106.14/14.40 ((
% 106.14/14.40 (setminusIRneg) =>
% 106.14/14.40 ((
% 106.14/14.40 (setminusLsub) =>
% 106.14/14.40 ((
% 106.14/14.40 (setminusSubset1) =>
% 106.14/14.40 ((
% 106.14/14.40 (symdiffE) =>
% 106.14/14.40 ((
% 106.14/14.40 (symdiffI1) =>
% 106.14/14.40 ((
% 106.14/14.40 (symdiffI2) =>
% 106.14/14.40 ((
% 106.14/14.40 (symdiffIneg1) =>
% 106.14/14.40 ((
% 106.14/14.40 (symdiffIneg2) =>
% 106.14/14.40 ((
% 106.14/14.40 (secondinupair) =>
% 106.14/14.40 ((
% 106.14/14.40 (setukpairIL) =>
% 106.14/14.40 ((
% 106.14/14.40 (setukpairIR) =>
% 106.14/14.40 ((
% 106.14/14.40 (kpairiskpair) =>
% 106.14/14.40 ((
% 106.14/14.40 (kpairp) =>
% 106.14/14.40 ((
% 106.14/14.40 (singletonsubset) =>
% 106.14/14.40 ((
% 106.14/14.40 (singletoninpowerset) =>
% 106.14/14.40 ((
% 106.14/14.40 (singletoninpowunion) =>
% 106.14/14.40 ((
% 106.14/14.40 (upairset2E) =>
% 106.14/14.40 ((
% 106.14/14.40 (upairsubunion) =>
% 106.14/14.40 ((
% 106.14/14.40 (upairinpowunion) =>
% 106.14/14.40 ((
% 106.14/14.40 (ubforcartprodlem1) =>
% 106.14/14.40 ((
% 106.14/14.40 (ubforcartprodlem2) =>
% 106.14/14.40 ((
% 106.14/14.40 (ubforcartprodlem3) =>
% 106.14/14.40 ((
% 106.14/14.40 (cartprodpairin) =>
% 106.14/14.40 ((
% 106.14/14.40 (cartprodmempair1) =>
% 106.14/14.40 ((
% 106.14/14.40 (cartprodmempair) =>
% 106.14/14.40 ((
% 106.14/14.40 (setunionE2) =>
% 106.14/14.40 ((
% 106.14/14.40 (setunionsingleton1) =>
% 106.14/14.40 ((
% 106.14/14.40 (setunionsingleton2) =>
% 106.14/14.40 ((
% 106.14/14.40 (setunionsingleton) =>
% 106.14/14.40 ((
% 106.14/14.40 (singletonprop) =>
% 106.14/14.40 ((
% 106.14/14.40 (ex1E1) =>
% 106.14/14.40 ((
% 106.14/14.40 (ex1I) =>
% 106.14/14.40 ((
% 106.14/14.40 (ex1I2) =>
% 106.14/14.40 ((
% 106.14/14.40 (singletonsuniq) =>
% 106.14/14.40 ((
% 106.14/14.40 (setukpairinjL1) =>
% 106.14/14.40 ((
% 106.14/14.40 (kfstsingleton) =>
% 106.14/14.40 ((
% 106.14/14.40 (theprop) =>
% 106.14/14.40 ((
% 106.14/14.40 (kfstpairEq) =>
% 106.14/14.40 ((
% 106.14/14.40 (cartprodfstin) =>
% 106.14/14.40 ((
% 106.14/14.40 (setukpairinjL2) =>
% 106.14/14.40 ((
% 106.14/14.40 (setukpairinjL) =>
% 106.14/14.40 ((
% 106.14/14.40 (setukpairinjR11) =>
% 106.14/14.40 ((
% 106.14/14.40 (setukpairinjR12) =>
% 106.14/14.40 ((
% 106.14/14.40 (setukpairinjR1) =>
% 106.14/14.40 ((
% 106.14/14.40 (upairequniteq) =>
% 106.14/14.40 ((
% 106.14/14.40 (setukpairinjR2) =>
% 106.14/14.40 ((
% 106.14/14.40 (setukpairinjR) =>
% 106.14/14.40 ((
% 106.14/14.40 (ksndsingleton) =>
% 106.14/14.40 ((
% 106.14/14.40 (ksndpairEq) =>
% 106.14/14.40 ((
% 106.14/14.40 (kpairsurjEq) =>
% 106.14/14.40 ((
% 106.14/14.40 (cartprodsndin) =>
% 106.14/14.40 ((
% 106.14/14.40 (cartprodpairmemEL) =>
% 106.14/14.40 ((
% 106.14/14.40 (cartprodpairmemER) =>
% 106.14/14.40 ((
% 106.14/14.40 (cartprodmempaircEq) =>
% 106.14/14.40 ((
% 106.14/14.40 (cartprodfstpairEq) =>
% 106.14/14.40 ((
% 106.14/14.40 (cartprodsndpairEq) =>
% 106.14/14.40 ((
% 106.14/14.40 (cartprodpairsurjEq) =>
% 106.14/14.40 ((
% 106.14/14.40 (dpsetconstrI) =>
% 106.14/14.40 ((
% 106.14/14.40 (dpsetconstrSub) =>
% 106.14/14.40 ((
% 106.14/14.40 (setOfPairsIsBReln) =>
% 106.14/14.40 ((
% 106.14/14.40 (dpsetconstrERa) =>
% 106.14/14.40 ((
% 106.14/14.40 (dpsetconstrEL1) =>
% 106.14/14.40 ((
% 106.14/14.40 (dpsetconstrEL2) =>
% 106.14/14.40 ((
% 106.14/14.40 (dpsetconstrER) =>
% 106.14/14.40 ((
% 106.14/14.40 (funcImageSingleton) =>
% 106.14/14.40 ((
% 106.14/14.40 (apProp) =>
% 106.14/14.40 ((
% 106.14/14.40 (app) =>
% 106.14/14.40 ((
% 106.14/14.40 (infuncsetfunc) =>
% 106.14/14.40 ((
% 106.14/14.40 (ap2p) =>
% 106.14/14.40 ((
% 106.14/14.40 (funcinfuncset) =>
% 106.14/14.40 ((
% 106.14/14.40 (lamProp) =>
% 106.14/14.40 ((
% 106.14/14.40 (lamp) =>
% 106.14/14.40 ((
% 106.14/14.40 (lam2p) =>
% 106.14/14.40 ((
% 106.14/14.40 (brelnall1) =>
% 106.14/14.40 ((
% 106.14/14.40 (brelnall2) =>
% 106.14/14.40 ((
% 106.14/14.40 (ex1E2) =>
% 106.14/14.40 ((
% 106.14/14.40 (funcGraphProp1) =>
% 106.14/14.40 ((
% 106.14/14.40 (funcGraphProp3) =>
% 106.14/14.40 ((
% 106.14/14.40 (funcGraphProp2) =>
% 106.14/14.40 ((
% 106.14/14.40 (funcextLem) =>
% 106.14/14.40 ((
% 106.14/14.40 (funcGraphProp4) =>
% 106.14/14.40 ((
% 106.14/14.40 (subbreln) =>
% 106.14/14.40 ((
% 106.14/14.40 (eqbreln) =>
% 106.14/14.40 ((
% 106.14/14.40 (funcext) =>
% 106.14/14.40 ((
% 106.14/14.40 (funcext2) =>
% 106.14/14.40 ((
% 106.14/14.40 (ap2apEq1) =>
% 106.14/14.40 ((
% 106.14/14.40 (ap2apEq2) =>
% 106.14/14.40 ((
% 106.14/14.40 (beta1) =>
% 106.14/14.40 ((
% 106.14/14.40 (eta1) =>
% 106.14/14.40 ((
% 106.14/14.40 (lam2lamEq) =>
% 106.14/14.40 ((
% 106.14/14.40 (beta2) =>
% 106.14/14.40 ((
% 106.14/14.40 (eta2) =>
% 106.14/14.40 ((
% 106.14/14.40 (iffalseProp1) =>
% 106.14/14.40 ((
% 106.14/14.40 (iffalseProp2) =>
% 106.14/14.40 ((
% 106.14/14.40 (iftrueProp1) =>
% 106.14/14.40 ((
% 106.14/14.40 (iftrueProp2) =>
% 106.14/14.40 ((
% 106.14/14.40 (ifSingleton) =>
% 106.14/14.40 ((
% 106.14/14.40 (ifp) =>
% 106.14/14.40 ((
% 106.14/14.40 (theeq) =>
% 106.14/14.40 ((
% 106.14/14.40 (iftrue) =>
% 106.14/14.40 ((
% 106.14/14.40 (iffalse) =>
% 106.14/14.40 ((
% 106.14/14.40 (iftrueorfalse) =>
% 106.14/14.40 ((
% 106.14/14.40 (binintersectT_lem) =>
% 106.14/14.40 ((
% 106.14/14.40 (binunionT_lem) =>
% 106.14/14.40 ((
% 106.14/14.40 (powersetT_lem) =>
% 106.14/14.40 ((
% 106.14/14.40 (setminusT_lem) =>
% 106.14/14.40 ((
% 106.14/14.40 (complementT_lem) =>
% 106.14/14.40 ((
% 106.14/14.40 (setextT) =>
% 106.14/14.40 ((
% 106.14/14.40 (subsetTI) =>
% 106.14/14.40 ((
% 106.14/14.40 (powersetTI1) =>
% 106.14/14.40 ((
% 106.14/14.40 (powersetTE1) =>
% 106.14/14.40 ((
% 106.14/14.40 (complementTI1) =>
% 106.14/14.40 ((
% 106.14/14.40 (complementTE1) =>
% 106.14/14.40 ((
% 106.14/14.40 (binintersectTELcontra) =>
% 106.14/14.40 ((
% 106.14/14.40 (binintersectTERcontra) =>
% 106.14/14.40 ((
% 106.14/14.40 (contrasubsetT) =>
% 106.14/14.40 ((
% 106.14/14.40 (contrasubsetT1) =>
% 106.14/14.40 ((
% 106.14/14.40 (contrasubsetT2) =>
% 106.14/14.40 ((
% 106.14/14.40 (contrasubsetT3) =>
% 106.14/14.40 ((
% 106.14/14.40 (doubleComplementI1) =>
% 106.14/14.40 ((
% 106.14/14.40 (doubleComplementE1) =>
% 106.14/14.40 ((
% 106.14/14.40 (doubleComplementSub1) =>
% 106.14/14.40 ((
% 106.14/14.40 (doubleComplementSub2) =>
% 106.14/14.40 ((
% 106.14/14.40 (doubleComplementEq) =>
% 106.14/14.40 ((
% 106.14/14.40 (complementTnotintersectT) =>
% 106.14/14.40 ((
% 106.14/14.40 (complementImpComplementIntersect) =>
% 106.14/14.40 ((
% 106.14/14.40 (complementSubsetComplementIntersect) =>
% 106.14/14.40 ((
% 106.14/14.40 (complementInPowersetComplementIntersect) =>
% 106.14/14.40 ((
% 106.14/14.40 (contraSubsetComplement) =>
% 106.14/14.40 ((
% 106.14/14.40 (complementTcontraSubset) =>
% 106.14/14.40 ((
% 106.14/14.40 (binunionTILcontra) =>
% 106.14/14.40 ((
% 106.14/14.40 (binunionTIRcontra) =>
% 106.14/14.40 ((
% 106.14/14.40 (inIntersectImpInUnion) =>
% 106.14/14.40 ((
% 106.14/14.40 (inIntersectImpInUnion2) =>
% 106.14/14.40 ((
% 106.14/14.40 (inIntersectImpInIntersectUnions) =>
% 106.14/14.40 ((
% 106.14/14.40 (intersectInPowersetIntersectUnions) =>
% 106.14/14.40 ((
% 106.14/14.40 (inComplementUnionImpNotIn1) =>
% 106.14/14.40 ((
% 106.14/14.40 (inComplementUnionImpInComplement1) =>
% 106.14/14.40 ((
% 106.14/14.40 (binunionTE) =>
% 106.14/14.40 ((
% 106.14/14.40 (binunionTEcontra) =>
% 106.14/14.40 ((
% 106.14/14.40 (demorgan2a1) =>
% 106.14/14.40 ((
% 106.14/14.40 (complementUnionInPowersetComplement) =>
% 106.14/14.40 ((
% 106.14/14.40 (demorgan2a2) =>
% 106.14/14.40 ((
% 106.14/14.40 (demorgan1a) =>
% 106.14/14.40 ((
% 106.14/14.40 (demorgan1b) =>
% 106.14/14.40 ((
% 106.14/14.40 (demorgan1) =>
% 106.14/14.40 ((
% 106.14/14.40 (demorgan2a) =>
% 106.14/14.40 ((
% 106.14/14.40 (demorgan2b2) =>
% 106.14/14.40 ((
% 106.14/14.40 (demorgan2b) =>
% 106.14/14.40 ((
% 106.14/14.40 (demorgan2) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz13rule0) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz13rule1) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz13rule2) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz13rule3) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz13rule4) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz1_1) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz1_2) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz1_3) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz1_4) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz1_5) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1all2) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1SetBreln1) =>
% 106.14/14.40 ((
% 106.14/14.40 (choice2fnsingleton) =>
% 106.14/14.40 ((
% 106.14/14.40 (setOfPairsIsBReln1) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1all1) =>
% 106.14/14.40 ((
% 106.14/14.40 (subbreln1) =>
% 106.14/14.40 ((
% 106.14/14.40 (eqbreln1) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1invprop) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1invI) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1invE) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1compprop) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1compI) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1compE) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1compEex) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1unionprop) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1unionIL) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1unionIR) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1unionI) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1unionE) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1unionEcases) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1unionCommutes) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz2Ex) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz2W) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz2A) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz2B) =>
% 106.14/14.40 ((
% 106.14/14.40 (image1Ex) =>
% 106.14/14.40 ((
% 106.14/14.40 (image1Ex1) =>
% 106.14/14.40 ((
% 106.14/14.40 (image1Equiv) =>
% 106.14/14.40 ((
% 106.14/14.40 (image1E) =>
% 106.14/14.40 ((
% 106.14/14.40 (image1I) =>
% 106.14/14.40 ((
% 106.14/14.40 (injFuncInInjFuncSet) =>
% 106.14/14.40 ((
% 106.14/14.40 (injFuncSetFuncIn) =>
% 106.14/14.40 ((
% 106.14/14.40 (injFuncSetFuncInj) =>
% 106.14/14.40 ((
% 106.14/14.40 (surjFuncSetFuncIn) =>
% 106.14/14.40 ((
% 106.14/14.40 (surjFuncSetFuncSurj) =>
% 106.14/14.40 ((
% 106.14/14.40 (leftInvIsSurj) =>
% 106.14/14.40 ((
% 106.14/14.40 (surjCantorThm) =>
% 106.14/14.40 ((
% 106.14/14.40 (!!) @ (
% 106.14/14.40 (('#S') @ (
% 106.14/14.40 (
% 106.14/14.40 ('#B') @ (
% 106.14/14.40 =>) @
% 106.14/14.40 nonempty)) @
% 106.14/14.40 (
% 106.14/14.40 (
% 106.14/14.40 ('#B') @ (
% 106.14/14.40 ??) @
% 106.14/14.40 (
% 106.14/14.40 (
% 106.14/14.40 ('#S') @ (
% 106.14/14.40 (
% 106.14/14.40 ('#B') @ (
% 106.14/14.40 '#S') @
% 106.14/14.40 (
% 106.14/14.40 (
% 106.14/14.40 ('#B') @ (
% 106.14/14.40 (
% 106.14/14.40 ('#B') @ (
% 106.14/14.40 &))) @
% 106.14/14.40 (
% 106.14/14.40 (
% 106.14/14.40 ('#C') @ in)))))) @
% 106.14/14.40 (
% 106.14/14.40 (
% 106.14/14.40 ('#C') @ (
% 106.14/14.40 (
% 106.14/14.40 ('#B') @ (
% 106.14/14.40 '#C') @
% 106.14/14.40 (
% 106.14/14.40 (
% 106.14/14.40 ('#B') @ (
% 106.14/14.40 (
% 106.14/14.40 ('#B') @ (
% 106.14/14.40 =))) @
% 106.14/14.40 (
% 106.14/14.40 (
% 106.14/14.40 ('#C') @ binintersect)))))) @
% 106.14/14.40 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.14/14.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl105])).
% 106.14/14.40 thf(zip_derived_cl142, plain,
% 106.14/14.40 (~ (((emptysetE) =>
% 106.14/14.40 (((emptysetimpfalse) =>
% 106.14/14.40 (((notinemptyset) =>
% 106.14/14.40 (((exuE3e) =>
% 106.14/14.40 (((setext) =>
% 106.14/14.40 (((emptyI) =>
% 106.14/14.40 (((noeltsimpempty) =>
% 106.14/14.40 (((setbeta) =>
% 106.14/14.40 (((nonemptyE1) =>
% 106.14/14.40 (((nonemptyI) =>
% 106.14/14.40 (((nonemptyI1) =>
% 106.14/14.40 (((setadjoinIL) =>
% 106.14/14.40 (((in @ emptyset @
% 106.14/14.40 (setadjoin @ emptyset @ emptyset)) =>
% 106.14/14.40 (((setadjoinIR) =>
% 106.14/14.40 (((setadjoinE) =>
% 106.14/14.40 (((setadjoinOr) =>
% 106.14/14.40 (((setoftrueEq) =>
% 106.14/14.40 (((powersetI) =>
% 106.14/14.40 (((emptyinPowerset) =>
% 106.14/14.40 (((emptyInPowerset) =>
% 106.14/14.40 (((powersetE) =>
% 106.14/14.40 (((setunionI) =>
% 106.14/14.40 (((setunionE) =>
% 106.14/14.40 (((subPowSU) =>
% 106.14/14.40 (((exuE2) =>
% 106.14/14.40 (((nonemptyImpWitness) =>
% 106.14/14.40 (((uniqinunit) =>
% 106.14/14.40 (((notinsingleton) =>
% 106.14/14.40 (((eqinunit) =>
% 106.14/14.40 (((singletonsswitch) =>
% 106.14/14.40 ((
% 106.14/14.40 (upairsetE) =>
% 106.14/14.40 ((
% 106.14/14.40 (upairsetIL) =>
% 106.14/14.40 ((
% 106.14/14.40 (upairsetIR) =>
% 106.14/14.40 ((
% 106.14/14.40 (emptyE1) =>
% 106.14/14.40 ((
% 106.14/14.40 (vacuousDall) =>
% 106.14/14.40 ((
% 106.14/14.40 (quantDeMorgan1) =>
% 106.14/14.40 ((
% 106.14/14.40 (quantDeMorgan2) =>
% 106.14/14.40 ((
% 106.14/14.40 (quantDeMorgan3) =>
% 106.14/14.40 ((
% 106.14/14.40 (quantDeMorgan4) =>
% 106.14/14.40 ((
% 106.14/14.40 (prop2setI) =>
% 106.14/14.40 ((
% 106.14/14.40 (prop2set2propI) =>
% 106.14/14.40 ((
% 106.14/14.40 (notdexE) =>
% 106.14/14.40 ((
% 106.14/14.40 (notdallE) =>
% 106.14/14.40 ((
% 106.14/14.40 (exuI1) =>
% 106.14/14.40 ((
% 106.14/14.40 (exuI3) =>
% 106.14/14.40 ((
% 106.14/14.40 (exuI2) =>
% 106.14/14.40 ((
% 106.14/14.40 (inCongP) =>
% 106.14/14.40 ((
% 106.14/14.40 (in__Cong) =>
% 106.14/14.40 ((
% 106.14/14.40 (exuE3u) =>
% 106.14/14.40 ((
% 106.14/14.40 (exu__Cong) =>
% 106.14/14.40 ((
% 106.14/14.40 (setadjoin__Cong) =>
% 106.14/14.40 ((
% 106.14/14.40 (powerset__Cong) =>
% 106.14/14.40 ((
% 106.14/14.40 (setunion__Cong) =>
% 106.14/14.40 ((
% 106.14/14.40 (exuEu) =>
% 106.14/14.40 ((
% 106.14/14.40 (descr__Cong) =>
% 106.14/14.40 ((
% 106.14/14.40 (dsetconstr__Cong) =>
% 106.14/14.40 ((
% 106.14/14.40 (subsetI1) =>
% 106.14/14.40 ((
% 106.14/14.40 (eqimpsubset2) =>
% 106.14/14.40 ((
% 106.14/14.40 (eqimpsubset1) =>
% 106.14/14.40 ((
% 106.14/14.40 (subsetI2) =>
% 106.14/14.40 ((
% 106.14/14.40 (emptysetsubset) =>
% 106.14/14.40 ((
% 106.14/14.40 (subsetE) =>
% 106.14/14.40 ((
% 106.14/14.40 (subsetE2) =>
% 106.14/14.40 ((
% 106.14/14.40 (notsubsetI) =>
% 106.14/14.40 ((
% 106.14/14.40 (notequalI1) =>
% 106.14/14.40 ((
% 106.14/14.40 (notequalI2) =>
% 106.14/14.40 ((
% 106.14/14.40 (subsetRefl) =>
% 106.14/14.40 ((
% 106.14/14.40 (subsetTrans) =>
% 106.14/14.40 ((
% 106.14/14.40 (setadjoinSub) =>
% 106.14/14.40 ((
% 106.14/14.40 (setadjoinSub2) =>
% 106.14/14.40 ((
% 106.14/14.40 (subset2powerset) =>
% 106.14/14.40 ((
% 106.14/14.40 (setextsub) =>
% 106.14/14.40 ((
% 106.14/14.40 (subsetemptysetimpeq) =>
% 106.14/14.40 ((
% 106.14/14.40 (powersetI1) =>
% 106.14/14.40 ((
% 106.14/14.40 (powersetE1) =>
% 106.14/14.40 ((
% 106.14/14.40 (inPowerset) =>
% 106.14/14.40 ((
% 106.14/14.40 (powersetsubset) =>
% 106.14/14.40 ((
% 106.14/14.40 (sepInPowerset) =>
% 106.14/14.40 ((
% 106.14/14.40 (sepSubset) =>
% 106.14/14.40 ((
% 106.14/14.40 (binunionIL) =>
% 106.14/14.40 ((
% 106.14/14.40 (upairset2IR) =>
% 106.14/14.40 ((
% 106.14/14.40 (binunionIR) =>
% 106.14/14.40 ((
% 106.14/14.40 (binunionEcases) =>
% 106.14/14.40 ((
% 106.14/14.40 (binunionE) =>
% 106.14/14.40 ((
% 106.14/14.40 (binunionLsub) =>
% 106.14/14.40 ((
% 106.14/14.40 (binunionRsub) =>
% 106.14/14.40 ((
% 106.14/14.40 (binintersectI) =>
% 106.14/14.40 ((
% 106.14/14.40 (binintersectSubset5) =>
% 106.14/14.40 ((
% 106.14/14.40 (binintersectEL) =>
% 106.14/14.40 ((
% 106.14/14.40 (binintersectLsub) =>
% 106.14/14.40 ((
% 106.14/14.40 (binintersectSubset2) =>
% 106.14/14.40 ((
% 106.14/14.40 (binintersectSubset3) =>
% 106.14/14.40 ((
% 106.14/14.40 (binintersectER) =>
% 106.14/14.40 ((
% 106.14/14.40 (disjointsetsI1) =>
% 106.14/14.40 ((
% 106.14/14.40 (binintersectRsub) =>
% 106.14/14.40 ((
% 106.14/14.40 (binintersectSubset4) =>
% 106.14/14.40 ((
% 106.14/14.40 (binintersectSubset1) =>
% 106.14/14.40 ((
% 106.14/14.40 (bs114d) =>
% 106.14/14.40 ((
% 106.14/14.40 (setminusI) =>
% 106.14/14.40 ((
% 106.14/14.40 (setminusEL) =>
% 106.14/14.40 ((
% 106.14/14.40 (setminusER) =>
% 106.14/14.40 ((
% 106.14/14.40 (setminusSubset2) =>
% 106.14/14.40 ((
% 106.14/14.40 (setminusERneg) =>
% 106.14/14.40 ((
% 106.14/14.40 (setminusELneg) =>
% 106.14/14.40 ((
% 106.14/14.40 (setminusILneg) =>
% 106.14/14.40 ((
% 106.14/14.40 (setminusIRneg) =>
% 106.14/14.40 ((
% 106.14/14.40 (setminusLsub) =>
% 106.14/14.40 ((
% 106.14/14.40 (setminusSubset1) =>
% 106.14/14.40 ((
% 106.14/14.40 (symdiffE) =>
% 106.14/14.40 ((
% 106.14/14.40 (symdiffI1) =>
% 106.14/14.40 ((
% 106.14/14.40 (symdiffI2) =>
% 106.14/14.40 ((
% 106.14/14.40 (symdiffIneg1) =>
% 106.14/14.40 ((
% 106.14/14.40 (symdiffIneg2) =>
% 106.14/14.40 ((
% 106.14/14.40 (secondinupair) =>
% 106.14/14.40 ((
% 106.14/14.40 (setukpairIL) =>
% 106.14/14.40 ((
% 106.14/14.40 (setukpairIR) =>
% 106.14/14.40 ((
% 106.14/14.40 (kpairiskpair) =>
% 106.14/14.40 ((
% 106.14/14.40 (kpairp) =>
% 106.14/14.40 ((
% 106.14/14.40 (singletonsubset) =>
% 106.14/14.40 ((
% 106.14/14.40 (singletoninpowerset) =>
% 106.14/14.40 ((
% 106.14/14.40 (singletoninpowunion) =>
% 106.14/14.40 ((
% 106.14/14.40 (upairset2E) =>
% 106.14/14.40 ((
% 106.14/14.40 (upairsubunion) =>
% 106.14/14.40 ((
% 106.14/14.40 (upairinpowunion) =>
% 106.14/14.40 ((
% 106.14/14.40 (ubforcartprodlem1) =>
% 106.14/14.40 ((
% 106.14/14.40 (ubforcartprodlem2) =>
% 106.14/14.40 ((
% 106.14/14.40 (ubforcartprodlem3) =>
% 106.14/14.40 ((
% 106.14/14.40 (cartprodpairin) =>
% 106.14/14.40 ((
% 106.14/14.40 (cartprodmempair1) =>
% 106.14/14.40 ((
% 106.14/14.40 (cartprodmempair) =>
% 106.14/14.40 ((
% 106.14/14.40 (setunionE2) =>
% 106.14/14.40 ((
% 106.14/14.40 (setunionsingleton1) =>
% 106.14/14.40 ((
% 106.14/14.40 (setunionsingleton2) =>
% 106.14/14.40 ((
% 106.14/14.40 (setunionsingleton) =>
% 106.14/14.40 ((
% 106.14/14.40 (singletonprop) =>
% 106.14/14.40 ((
% 106.14/14.40 (ex1E1) =>
% 106.14/14.40 ((
% 106.14/14.40 (ex1I) =>
% 106.14/14.40 ((
% 106.14/14.40 (ex1I2) =>
% 106.14/14.40 ((
% 106.14/14.40 (singletonsuniq) =>
% 106.14/14.40 ((
% 106.14/14.40 (setukpairinjL1) =>
% 106.14/14.40 ((
% 106.14/14.40 (kfstsingleton) =>
% 106.14/14.40 ((
% 106.14/14.40 (theprop) =>
% 106.14/14.40 ((
% 106.14/14.40 (kfstpairEq) =>
% 106.14/14.40 ((
% 106.14/14.40 (cartprodfstin) =>
% 106.14/14.40 ((
% 106.14/14.40 (setukpairinjL2) =>
% 106.14/14.40 ((
% 106.14/14.40 (setukpairinjL) =>
% 106.14/14.40 ((
% 106.14/14.40 (setukpairinjR11) =>
% 106.14/14.40 ((
% 106.14/14.40 (setukpairinjR12) =>
% 106.14/14.40 ((
% 106.14/14.40 (setukpairinjR1) =>
% 106.14/14.40 ((
% 106.14/14.40 (upairequniteq) =>
% 106.14/14.40 ((
% 106.14/14.40 (setukpairinjR2) =>
% 106.14/14.40 ((
% 106.14/14.40 (setukpairinjR) =>
% 106.14/14.40 ((
% 106.14/14.40 (ksndsingleton) =>
% 106.14/14.40 ((
% 106.14/14.40 (ksndpairEq) =>
% 106.14/14.40 ((
% 106.14/14.40 (kpairsurjEq) =>
% 106.14/14.40 ((
% 106.14/14.40 (cartprodsndin) =>
% 106.14/14.40 ((
% 106.14/14.40 (cartprodpairmemEL) =>
% 106.14/14.40 ((
% 106.14/14.40 (cartprodpairmemER) =>
% 106.14/14.40 ((
% 106.14/14.40 (cartprodmempaircEq) =>
% 106.14/14.40 ((
% 106.14/14.40 (cartprodfstpairEq) =>
% 106.14/14.40 ((
% 106.14/14.40 (cartprodsndpairEq) =>
% 106.14/14.40 ((
% 106.14/14.40 (cartprodpairsurjEq) =>
% 106.14/14.40 ((
% 106.14/14.40 (dpsetconstrI) =>
% 106.14/14.40 ((
% 106.14/14.40 (dpsetconstrSub) =>
% 106.14/14.40 ((
% 106.14/14.40 (setOfPairsIsBReln) =>
% 106.14/14.40 ((
% 106.14/14.40 (dpsetconstrERa) =>
% 106.14/14.40 ((
% 106.14/14.40 (dpsetconstrEL1) =>
% 106.14/14.40 ((
% 106.14/14.40 (dpsetconstrEL2) =>
% 106.14/14.40 ((
% 106.14/14.40 (dpsetconstrER) =>
% 106.14/14.40 ((
% 106.14/14.40 (funcImageSingleton) =>
% 106.14/14.40 ((
% 106.14/14.40 (apProp) =>
% 106.14/14.40 ((
% 106.14/14.40 (app) =>
% 106.14/14.40 ((
% 106.14/14.40 (infuncsetfunc) =>
% 106.14/14.40 ((
% 106.14/14.40 (ap2p) =>
% 106.14/14.40 ((
% 106.14/14.40 (funcinfuncset) =>
% 106.14/14.40 ((
% 106.14/14.40 (lamProp) =>
% 106.14/14.40 ((
% 106.14/14.40 (lamp) =>
% 106.14/14.40 ((
% 106.14/14.40 (lam2p) =>
% 106.14/14.40 ((
% 106.14/14.40 (brelnall1) =>
% 106.14/14.40 ((
% 106.14/14.40 (brelnall2) =>
% 106.14/14.40 ((
% 106.14/14.40 (ex1E2) =>
% 106.14/14.40 ((
% 106.14/14.40 (funcGraphProp1) =>
% 106.14/14.40 ((
% 106.14/14.40 (funcGraphProp3) =>
% 106.14/14.40 ((
% 106.14/14.40 (funcGraphProp2) =>
% 106.14/14.40 ((
% 106.14/14.40 (funcextLem) =>
% 106.14/14.40 ((
% 106.14/14.40 (funcGraphProp4) =>
% 106.14/14.40 ((
% 106.14/14.40 (subbreln) =>
% 106.14/14.40 ((
% 106.14/14.40 (eqbreln) =>
% 106.14/14.40 ((
% 106.14/14.40 (funcext) =>
% 106.14/14.40 ((
% 106.14/14.40 (funcext2) =>
% 106.14/14.40 ((
% 106.14/14.40 (ap2apEq1) =>
% 106.14/14.40 ((
% 106.14/14.40 (ap2apEq2) =>
% 106.14/14.40 ((
% 106.14/14.40 (beta1) =>
% 106.14/14.40 ((
% 106.14/14.40 (eta1) =>
% 106.14/14.40 ((
% 106.14/14.40 (lam2lamEq) =>
% 106.14/14.40 ((
% 106.14/14.40 (beta2) =>
% 106.14/14.40 ((
% 106.14/14.40 (eta2) =>
% 106.14/14.40 ((
% 106.14/14.40 (iffalseProp1) =>
% 106.14/14.40 ((
% 106.14/14.40 (iffalseProp2) =>
% 106.14/14.40 ((
% 106.14/14.40 (iftrueProp1) =>
% 106.14/14.40 ((
% 106.14/14.40 (iftrueProp2) =>
% 106.14/14.40 ((
% 106.14/14.40 (ifSingleton) =>
% 106.14/14.40 ((
% 106.14/14.40 (ifp) =>
% 106.14/14.40 ((
% 106.14/14.40 (theeq) =>
% 106.14/14.40 ((
% 106.14/14.40 (iftrue) =>
% 106.14/14.40 ((
% 106.14/14.40 (iffalse) =>
% 106.14/14.40 ((
% 106.14/14.40 (iftrueorfalse) =>
% 106.14/14.40 ((
% 106.14/14.40 (binintersectT_lem) =>
% 106.14/14.40 ((
% 106.14/14.40 (binunionT_lem) =>
% 106.14/14.40 ((
% 106.14/14.40 (powersetT_lem) =>
% 106.14/14.40 ((
% 106.14/14.40 (setminusT_lem) =>
% 106.14/14.40 ((
% 106.14/14.40 (complementT_lem) =>
% 106.14/14.40 ((
% 106.14/14.40 (setextT) =>
% 106.14/14.40 ((
% 106.14/14.40 (subsetTI) =>
% 106.14/14.40 ((
% 106.14/14.40 (powersetTI1) =>
% 106.14/14.40 ((
% 106.14/14.40 (powersetTE1) =>
% 106.14/14.40 ((
% 106.14/14.40 (complementTI1) =>
% 106.14/14.40 ((
% 106.14/14.40 (complementTE1) =>
% 106.14/14.40 ((
% 106.14/14.40 (binintersectTELcontra) =>
% 106.14/14.40 ((
% 106.14/14.40 (binintersectTERcontra) =>
% 106.14/14.40 ((
% 106.14/14.40 (contrasubsetT) =>
% 106.14/14.40 ((
% 106.14/14.40 (contrasubsetT1) =>
% 106.14/14.40 ((
% 106.14/14.40 (contrasubsetT2) =>
% 106.14/14.40 ((
% 106.14/14.40 (contrasubsetT3) =>
% 106.14/14.40 ((
% 106.14/14.40 (doubleComplementI1) =>
% 106.14/14.40 ((
% 106.14/14.40 (doubleComplementE1) =>
% 106.14/14.40 ((
% 106.14/14.40 (doubleComplementSub1) =>
% 106.14/14.40 ((
% 106.14/14.40 (doubleComplementSub2) =>
% 106.14/14.40 ((
% 106.14/14.40 (doubleComplementEq) =>
% 106.14/14.40 ((
% 106.14/14.40 (complementTnotintersectT) =>
% 106.14/14.40 ((
% 106.14/14.40 (complementImpComplementIntersect) =>
% 106.14/14.40 ((
% 106.14/14.40 (complementSubsetComplementIntersect) =>
% 106.14/14.40 ((
% 106.14/14.40 (complementInPowersetComplementIntersect) =>
% 106.14/14.40 ((
% 106.14/14.40 (contraSubsetComplement) =>
% 106.14/14.40 ((
% 106.14/14.40 (complementTcontraSubset) =>
% 106.14/14.40 ((
% 106.14/14.40 (binunionTILcontra) =>
% 106.14/14.40 ((
% 106.14/14.40 (binunionTIRcontra) =>
% 106.14/14.40 ((
% 106.14/14.40 (inIntersectImpInUnion) =>
% 106.14/14.40 ((
% 106.14/14.40 (inIntersectImpInUnion2) =>
% 106.14/14.40 ((
% 106.14/14.40 (inIntersectImpInIntersectUnions) =>
% 106.14/14.40 ((
% 106.14/14.40 (intersectInPowersetIntersectUnions) =>
% 106.14/14.40 ((
% 106.14/14.40 (inComplementUnionImpNotIn1) =>
% 106.14/14.40 ((
% 106.14/14.40 (inComplementUnionImpInComplement1) =>
% 106.14/14.40 ((
% 106.14/14.40 (binunionTE) =>
% 106.14/14.40 ((
% 106.14/14.40 (binunionTEcontra) =>
% 106.14/14.40 ((
% 106.14/14.40 (demorgan2a1) =>
% 106.14/14.40 ((
% 106.14/14.40 (complementUnionInPowersetComplement) =>
% 106.14/14.40 ((
% 106.14/14.40 (demorgan2a2) =>
% 106.14/14.40 ((
% 106.14/14.40 (demorgan1a) =>
% 106.14/14.40 ((
% 106.14/14.40 (demorgan1b) =>
% 106.14/14.40 ((
% 106.14/14.40 (demorgan1) =>
% 106.14/14.40 ((
% 106.14/14.40 (demorgan2a) =>
% 106.14/14.40 ((
% 106.14/14.40 (demorgan2b2) =>
% 106.14/14.40 ((
% 106.14/14.40 (demorgan2b) =>
% 106.14/14.40 ((
% 106.14/14.40 (demorgan2) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz13rule0) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz13rule1) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz13rule2) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz13rule3) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz13rule4) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz1_1) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz1_2) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz1_3) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz1_4) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz1_5) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1all2) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1SetBreln1) =>
% 106.14/14.40 ((
% 106.14/14.40 (choice2fnsingleton) =>
% 106.14/14.40 ((
% 106.14/14.40 (setOfPairsIsBReln1) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1all1) =>
% 106.14/14.40 ((
% 106.14/14.40 (subbreln1) =>
% 106.14/14.40 ((
% 106.14/14.40 (eqbreln1) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1invprop) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1invI) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1invE) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1compprop) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1compI) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1compE) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1compEex) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1unionprop) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1unionIL) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1unionIR) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1unionI) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1unionE) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1unionEcases) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1unionCommutes) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz2Ex) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz2W) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz2A) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz2B) =>
% 106.14/14.40 ((
% 106.14/14.40 (image1Ex) =>
% 106.14/14.40 ((
% 106.14/14.40 (image1Ex1) =>
% 106.14/14.40 ((
% 106.14/14.40 (image1Equiv) =>
% 106.14/14.40 ((
% 106.14/14.40 (image1E) =>
% 106.14/14.40 ((
% 106.14/14.40 (image1I) =>
% 106.14/14.40 ((
% 106.14/14.40 (injFuncInInjFuncSet) =>
% 106.14/14.40 ((
% 106.14/14.40 (injFuncSetFuncIn) =>
% 106.14/14.40 ((
% 106.14/14.40 (injFuncSetFuncInj) =>
% 106.14/14.40 ((
% 106.14/14.40 (surjFuncSetFuncIn) =>
% 106.14/14.40 ((
% 106.14/14.40 (surjFuncSetFuncSurj) =>
% 106.14/14.40 ((
% 106.14/14.40 (leftInvIsSurj) =>
% 106.14/14.40 ((
% 106.14/14.40 (surjCantorThm) =>
% 106.14/14.40 ((
% 106.14/14.40 (!!) @ (
% 106.14/14.40 (('#S') @ (
% 106.14/14.40 (
% 106.14/14.40 ('#B') @ (
% 106.14/14.40 =>) @
% 106.14/14.40 nonempty)) @
% 106.14/14.40 (
% 106.14/14.40 (
% 106.14/14.40 ('#B') @ (
% 106.14/14.40 ??) @
% 106.14/14.40 (
% 106.14/14.40 (
% 106.14/14.40 ('#S') @ (
% 106.14/14.40 (
% 106.14/14.40 ('#B') @ (
% 106.14/14.40 '#S') @
% 106.14/14.40 (
% 106.14/14.40 (
% 106.14/14.40 ('#B') @ (
% 106.14/14.40 (
% 106.14/14.40 ('#B') @ (
% 106.14/14.40 &))) @
% 106.14/14.40 (
% 106.14/14.40 (
% 106.14/14.40 ('#C') @ in)))))) @
% 106.14/14.40 (
% 106.14/14.40 (
% 106.14/14.40 ('#C') @ (
% 106.14/14.40 (
% 106.14/14.40 ('#B') @ (
% 106.14/14.40 '#C') @
% 106.14/14.40 (
% 106.14/14.40 (
% 106.14/14.40 ('#B') @ (
% 106.14/14.40 (
% 106.14/14.40 ('#B') @ (
% 106.14/14.40 =))) @
% 106.14/14.40 (
% 106.14/14.40 (
% 106.14/14.40 ('#C') @ binintersect)))))) @
% 106.14/14.40 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.14/14.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl123])).
% 106.14/14.40 thf(zip_derived_cl158, plain,
% 106.14/14.40 (~ (((emptysetimpfalse) =>
% 106.14/14.40 (((notinemptyset) =>
% 106.14/14.40 (((exuE3e) =>
% 106.14/14.40 (((setext) =>
% 106.14/14.40 (((emptyI) =>
% 106.14/14.40 (((noeltsimpempty) =>
% 106.14/14.40 (((setbeta) =>
% 106.14/14.40 (((nonemptyE1) =>
% 106.14/14.40 (((nonemptyI) =>
% 106.14/14.40 (((nonemptyI1) =>
% 106.14/14.40 (((setadjoinIL) =>
% 106.14/14.40 (((in @ emptyset @
% 106.14/14.40 (setadjoin @ emptyset @ emptyset)) =>
% 106.14/14.40 (((setadjoinIR) =>
% 106.14/14.40 (((setadjoinE) =>
% 106.14/14.40 (((setadjoinOr) =>
% 106.14/14.40 (((setoftrueEq) =>
% 106.14/14.40 (((powersetI) =>
% 106.14/14.40 (((emptyinPowerset) =>
% 106.14/14.40 (((emptyInPowerset) =>
% 106.14/14.40 (((powersetE) =>
% 106.14/14.40 (((setunionI) =>
% 106.14/14.40 (((setunionE) =>
% 106.14/14.40 (((subPowSU) =>
% 106.14/14.40 (((exuE2) =>
% 106.14/14.40 (((nonemptyImpWitness) =>
% 106.14/14.40 (((uniqinunit) =>
% 106.14/14.40 (((notinsingleton) =>
% 106.14/14.40 (((eqinunit) =>
% 106.14/14.40 (((singletonsswitch) =>
% 106.14/14.40 (((upairsetE) =>
% 106.14/14.40 ((
% 106.14/14.40 (upairsetIL) =>
% 106.14/14.40 ((
% 106.14/14.40 (upairsetIR) =>
% 106.14/14.40 ((
% 106.14/14.40 (emptyE1) =>
% 106.14/14.40 ((
% 106.14/14.40 (vacuousDall) =>
% 106.14/14.40 ((
% 106.14/14.40 (quantDeMorgan1) =>
% 106.14/14.40 ((
% 106.14/14.40 (quantDeMorgan2) =>
% 106.14/14.40 ((
% 106.14/14.40 (quantDeMorgan3) =>
% 106.14/14.40 ((
% 106.14/14.40 (quantDeMorgan4) =>
% 106.14/14.40 ((
% 106.14/14.40 (prop2setI) =>
% 106.14/14.40 ((
% 106.14/14.40 (prop2set2propI) =>
% 106.14/14.40 ((
% 106.14/14.40 (notdexE) =>
% 106.14/14.40 ((
% 106.14/14.40 (notdallE) =>
% 106.14/14.40 ((
% 106.14/14.40 (exuI1) =>
% 106.14/14.40 ((
% 106.14/14.40 (exuI3) =>
% 106.14/14.40 ((
% 106.14/14.40 (exuI2) =>
% 106.14/14.40 ((
% 106.14/14.40 (inCongP) =>
% 106.14/14.40 ((
% 106.14/14.40 (in__Cong) =>
% 106.14/14.40 ((
% 106.14/14.40 (exuE3u) =>
% 106.14/14.40 ((
% 106.14/14.40 (exu__Cong) =>
% 106.14/14.40 ((
% 106.14/14.40 (setadjoin__Cong) =>
% 106.14/14.40 ((
% 106.14/14.40 (powerset__Cong) =>
% 106.14/14.40 ((
% 106.14/14.40 (setunion__Cong) =>
% 106.14/14.40 ((
% 106.14/14.40 (exuEu) =>
% 106.14/14.40 ((
% 106.14/14.40 (descr__Cong) =>
% 106.14/14.40 ((
% 106.14/14.40 (dsetconstr__Cong) =>
% 106.14/14.40 ((
% 106.14/14.40 (subsetI1) =>
% 106.14/14.40 ((
% 106.14/14.40 (eqimpsubset2) =>
% 106.14/14.40 ((
% 106.14/14.40 (eqimpsubset1) =>
% 106.14/14.40 ((
% 106.14/14.40 (subsetI2) =>
% 106.14/14.40 ((
% 106.14/14.40 (emptysetsubset) =>
% 106.14/14.40 ((
% 106.14/14.40 (subsetE) =>
% 106.14/14.40 ((
% 106.14/14.40 (subsetE2) =>
% 106.14/14.40 ((
% 106.14/14.40 (notsubsetI) =>
% 106.14/14.40 ((
% 106.14/14.40 (notequalI1) =>
% 106.14/14.40 ((
% 106.14/14.40 (notequalI2) =>
% 106.14/14.40 ((
% 106.14/14.40 (subsetRefl) =>
% 106.14/14.40 ((
% 106.14/14.40 (subsetTrans) =>
% 106.14/14.40 ((
% 106.14/14.40 (setadjoinSub) =>
% 106.14/14.40 ((
% 106.14/14.40 (setadjoinSub2) =>
% 106.14/14.40 ((
% 106.14/14.40 (subset2powerset) =>
% 106.14/14.40 ((
% 106.14/14.40 (setextsub) =>
% 106.14/14.40 ((
% 106.14/14.40 (subsetemptysetimpeq) =>
% 106.14/14.40 ((
% 106.14/14.40 (powersetI1) =>
% 106.14/14.40 ((
% 106.14/14.40 (powersetE1) =>
% 106.14/14.40 ((
% 106.14/14.40 (inPowerset) =>
% 106.14/14.40 ((
% 106.14/14.40 (powersetsubset) =>
% 106.14/14.40 ((
% 106.14/14.40 (sepInPowerset) =>
% 106.14/14.40 ((
% 106.14/14.40 (sepSubset) =>
% 106.14/14.40 ((
% 106.14/14.40 (binunionIL) =>
% 106.14/14.40 ((
% 106.14/14.40 (upairset2IR) =>
% 106.14/14.40 ((
% 106.14/14.40 (binunionIR) =>
% 106.14/14.40 ((
% 106.14/14.40 (binunionEcases) =>
% 106.14/14.40 ((
% 106.14/14.40 (binunionE) =>
% 106.14/14.40 ((
% 106.14/14.40 (binunionLsub) =>
% 106.14/14.40 ((
% 106.14/14.40 (binunionRsub) =>
% 106.14/14.40 ((
% 106.14/14.40 (binintersectI) =>
% 106.14/14.40 ((
% 106.14/14.40 (binintersectSubset5) =>
% 106.14/14.40 ((
% 106.14/14.40 (binintersectEL) =>
% 106.14/14.40 ((
% 106.14/14.40 (binintersectLsub) =>
% 106.14/14.40 ((
% 106.14/14.40 (binintersectSubset2) =>
% 106.14/14.40 ((
% 106.14/14.40 (binintersectSubset3) =>
% 106.14/14.40 ((
% 106.14/14.40 (binintersectER) =>
% 106.14/14.40 ((
% 106.14/14.40 (disjointsetsI1) =>
% 106.14/14.40 ((
% 106.14/14.40 (binintersectRsub) =>
% 106.14/14.40 ((
% 106.14/14.40 (binintersectSubset4) =>
% 106.14/14.40 ((
% 106.14/14.40 (binintersectSubset1) =>
% 106.14/14.40 ((
% 106.14/14.40 (bs114d) =>
% 106.14/14.40 ((
% 106.14/14.40 (setminusI) =>
% 106.14/14.40 ((
% 106.14/14.40 (setminusEL) =>
% 106.14/14.40 ((
% 106.14/14.40 (setminusER) =>
% 106.14/14.40 ((
% 106.14/14.40 (setminusSubset2) =>
% 106.14/14.40 ((
% 106.14/14.40 (setminusERneg) =>
% 106.14/14.40 ((
% 106.14/14.40 (setminusELneg) =>
% 106.14/14.40 ((
% 106.14/14.40 (setminusILneg) =>
% 106.14/14.40 ((
% 106.14/14.40 (setminusIRneg) =>
% 106.14/14.40 ((
% 106.14/14.40 (setminusLsub) =>
% 106.14/14.40 ((
% 106.14/14.40 (setminusSubset1) =>
% 106.14/14.40 ((
% 106.14/14.40 (symdiffE) =>
% 106.14/14.40 ((
% 106.14/14.40 (symdiffI1) =>
% 106.14/14.40 ((
% 106.14/14.40 (symdiffI2) =>
% 106.14/14.40 ((
% 106.14/14.40 (symdiffIneg1) =>
% 106.14/14.40 ((
% 106.14/14.40 (symdiffIneg2) =>
% 106.14/14.40 ((
% 106.14/14.40 (secondinupair) =>
% 106.14/14.40 ((
% 106.14/14.40 (setukpairIL) =>
% 106.14/14.40 ((
% 106.14/14.40 (setukpairIR) =>
% 106.14/14.40 ((
% 106.14/14.40 (kpairiskpair) =>
% 106.14/14.40 ((
% 106.14/14.40 (kpairp) =>
% 106.14/14.40 ((
% 106.14/14.40 (singletonsubset) =>
% 106.14/14.40 ((
% 106.14/14.40 (singletoninpowerset) =>
% 106.14/14.40 ((
% 106.14/14.40 (singletoninpowunion) =>
% 106.14/14.40 ((
% 106.14/14.40 (upairset2E) =>
% 106.14/14.40 ((
% 106.14/14.40 (upairsubunion) =>
% 106.14/14.40 ((
% 106.14/14.40 (upairinpowunion) =>
% 106.14/14.40 ((
% 106.14/14.40 (ubforcartprodlem1) =>
% 106.14/14.40 ((
% 106.14/14.40 (ubforcartprodlem2) =>
% 106.14/14.40 ((
% 106.14/14.40 (ubforcartprodlem3) =>
% 106.14/14.40 ((
% 106.14/14.40 (cartprodpairin) =>
% 106.14/14.40 ((
% 106.14/14.40 (cartprodmempair1) =>
% 106.14/14.40 ((
% 106.14/14.40 (cartprodmempair) =>
% 106.14/14.40 ((
% 106.14/14.40 (setunionE2) =>
% 106.14/14.40 ((
% 106.14/14.40 (setunionsingleton1) =>
% 106.14/14.40 ((
% 106.14/14.40 (setunionsingleton2) =>
% 106.14/14.40 ((
% 106.14/14.40 (setunionsingleton) =>
% 106.14/14.40 ((
% 106.14/14.40 (singletonprop) =>
% 106.14/14.40 ((
% 106.14/14.40 (ex1E1) =>
% 106.14/14.40 ((
% 106.14/14.40 (ex1I) =>
% 106.14/14.40 ((
% 106.14/14.40 (ex1I2) =>
% 106.14/14.40 ((
% 106.14/14.40 (singletonsuniq) =>
% 106.14/14.40 ((
% 106.14/14.40 (setukpairinjL1) =>
% 106.14/14.40 ((
% 106.14/14.40 (kfstsingleton) =>
% 106.14/14.40 ((
% 106.14/14.40 (theprop) =>
% 106.14/14.40 ((
% 106.14/14.40 (kfstpairEq) =>
% 106.14/14.40 ((
% 106.14/14.40 (cartprodfstin) =>
% 106.14/14.40 ((
% 106.14/14.40 (setukpairinjL2) =>
% 106.14/14.40 ((
% 106.14/14.40 (setukpairinjL) =>
% 106.14/14.40 ((
% 106.14/14.40 (setukpairinjR11) =>
% 106.14/14.40 ((
% 106.14/14.40 (setukpairinjR12) =>
% 106.14/14.40 ((
% 106.14/14.40 (setukpairinjR1) =>
% 106.14/14.40 ((
% 106.14/14.40 (upairequniteq) =>
% 106.14/14.40 ((
% 106.14/14.40 (setukpairinjR2) =>
% 106.14/14.40 ((
% 106.14/14.40 (setukpairinjR) =>
% 106.14/14.40 ((
% 106.14/14.40 (ksndsingleton) =>
% 106.14/14.40 ((
% 106.14/14.40 (ksndpairEq) =>
% 106.14/14.40 ((
% 106.14/14.40 (kpairsurjEq) =>
% 106.14/14.40 ((
% 106.14/14.40 (cartprodsndin) =>
% 106.14/14.40 ((
% 106.14/14.40 (cartprodpairmemEL) =>
% 106.14/14.40 ((
% 106.14/14.40 (cartprodpairmemER) =>
% 106.14/14.40 ((
% 106.14/14.40 (cartprodmempaircEq) =>
% 106.14/14.40 ((
% 106.14/14.40 (cartprodfstpairEq) =>
% 106.14/14.40 ((
% 106.14/14.40 (cartprodsndpairEq) =>
% 106.14/14.40 ((
% 106.14/14.40 (cartprodpairsurjEq) =>
% 106.14/14.40 ((
% 106.14/14.40 (dpsetconstrI) =>
% 106.14/14.40 ((
% 106.14/14.40 (dpsetconstrSub) =>
% 106.14/14.40 ((
% 106.14/14.40 (setOfPairsIsBReln) =>
% 106.14/14.40 ((
% 106.14/14.40 (dpsetconstrERa) =>
% 106.14/14.40 ((
% 106.14/14.40 (dpsetconstrEL1) =>
% 106.14/14.40 ((
% 106.14/14.40 (dpsetconstrEL2) =>
% 106.14/14.40 ((
% 106.14/14.40 (dpsetconstrER) =>
% 106.14/14.40 ((
% 106.14/14.40 (funcImageSingleton) =>
% 106.14/14.40 ((
% 106.14/14.40 (apProp) =>
% 106.14/14.40 ((
% 106.14/14.40 (app) =>
% 106.14/14.40 ((
% 106.14/14.40 (infuncsetfunc) =>
% 106.14/14.40 ((
% 106.14/14.40 (ap2p) =>
% 106.14/14.40 ((
% 106.14/14.40 (funcinfuncset) =>
% 106.14/14.40 ((
% 106.14/14.40 (lamProp) =>
% 106.14/14.40 ((
% 106.14/14.40 (lamp) =>
% 106.14/14.40 ((
% 106.14/14.40 (lam2p) =>
% 106.14/14.40 ((
% 106.14/14.40 (brelnall1) =>
% 106.14/14.40 ((
% 106.14/14.40 (brelnall2) =>
% 106.14/14.40 ((
% 106.14/14.40 (ex1E2) =>
% 106.14/14.40 ((
% 106.14/14.40 (funcGraphProp1) =>
% 106.14/14.40 ((
% 106.14/14.40 (funcGraphProp3) =>
% 106.14/14.40 ((
% 106.14/14.40 (funcGraphProp2) =>
% 106.14/14.40 ((
% 106.14/14.40 (funcextLem) =>
% 106.14/14.40 ((
% 106.14/14.40 (funcGraphProp4) =>
% 106.14/14.40 ((
% 106.14/14.40 (subbreln) =>
% 106.14/14.40 ((
% 106.14/14.40 (eqbreln) =>
% 106.14/14.40 ((
% 106.14/14.40 (funcext) =>
% 106.14/14.40 ((
% 106.14/14.40 (funcext2) =>
% 106.14/14.40 ((
% 106.14/14.40 (ap2apEq1) =>
% 106.14/14.40 ((
% 106.14/14.40 (ap2apEq2) =>
% 106.14/14.40 ((
% 106.14/14.40 (beta1) =>
% 106.14/14.40 ((
% 106.14/14.40 (eta1) =>
% 106.14/14.40 ((
% 106.14/14.40 (lam2lamEq) =>
% 106.14/14.40 ((
% 106.14/14.40 (beta2) =>
% 106.14/14.40 ((
% 106.14/14.40 (eta2) =>
% 106.14/14.40 ((
% 106.14/14.40 (iffalseProp1) =>
% 106.14/14.40 ((
% 106.14/14.40 (iffalseProp2) =>
% 106.14/14.40 ((
% 106.14/14.40 (iftrueProp1) =>
% 106.14/14.40 ((
% 106.14/14.40 (iftrueProp2) =>
% 106.14/14.40 ((
% 106.14/14.40 (ifSingleton) =>
% 106.14/14.40 ((
% 106.14/14.40 (ifp) =>
% 106.14/14.40 ((
% 106.14/14.40 (theeq) =>
% 106.14/14.40 ((
% 106.14/14.40 (iftrue) =>
% 106.14/14.40 ((
% 106.14/14.40 (iffalse) =>
% 106.14/14.40 ((
% 106.14/14.40 (iftrueorfalse) =>
% 106.14/14.40 ((
% 106.14/14.40 (binintersectT_lem) =>
% 106.14/14.40 ((
% 106.14/14.40 (binunionT_lem) =>
% 106.14/14.40 ((
% 106.14/14.40 (powersetT_lem) =>
% 106.14/14.40 ((
% 106.14/14.40 (setminusT_lem) =>
% 106.14/14.40 ((
% 106.14/14.40 (complementT_lem) =>
% 106.14/14.40 ((
% 106.14/14.40 (setextT) =>
% 106.14/14.40 ((
% 106.14/14.40 (subsetTI) =>
% 106.14/14.40 ((
% 106.14/14.40 (powersetTI1) =>
% 106.14/14.40 ((
% 106.14/14.40 (powersetTE1) =>
% 106.14/14.40 ((
% 106.14/14.40 (complementTI1) =>
% 106.14/14.40 ((
% 106.14/14.40 (complementTE1) =>
% 106.14/14.40 ((
% 106.14/14.40 (binintersectTELcontra) =>
% 106.14/14.40 ((
% 106.14/14.40 (binintersectTERcontra) =>
% 106.14/14.40 ((
% 106.14/14.40 (contrasubsetT) =>
% 106.14/14.40 ((
% 106.14/14.40 (contrasubsetT1) =>
% 106.14/14.40 ((
% 106.14/14.40 (contrasubsetT2) =>
% 106.14/14.40 ((
% 106.14/14.40 (contrasubsetT3) =>
% 106.14/14.40 ((
% 106.14/14.40 (doubleComplementI1) =>
% 106.14/14.40 ((
% 106.14/14.40 (doubleComplementE1) =>
% 106.14/14.40 ((
% 106.14/14.40 (doubleComplementSub1) =>
% 106.14/14.40 ((
% 106.14/14.40 (doubleComplementSub2) =>
% 106.14/14.40 ((
% 106.14/14.40 (doubleComplementEq) =>
% 106.14/14.40 ((
% 106.14/14.40 (complementTnotintersectT) =>
% 106.14/14.40 ((
% 106.14/14.40 (complementImpComplementIntersect) =>
% 106.14/14.40 ((
% 106.14/14.40 (complementSubsetComplementIntersect) =>
% 106.14/14.40 ((
% 106.14/14.40 (complementInPowersetComplementIntersect) =>
% 106.14/14.40 ((
% 106.14/14.40 (contraSubsetComplement) =>
% 106.14/14.40 ((
% 106.14/14.40 (complementTcontraSubset) =>
% 106.14/14.40 ((
% 106.14/14.40 (binunionTILcontra) =>
% 106.14/14.40 ((
% 106.14/14.40 (binunionTIRcontra) =>
% 106.14/14.40 ((
% 106.14/14.40 (inIntersectImpInUnion) =>
% 106.14/14.40 ((
% 106.14/14.40 (inIntersectImpInUnion2) =>
% 106.14/14.40 ((
% 106.14/14.40 (inIntersectImpInIntersectUnions) =>
% 106.14/14.40 ((
% 106.14/14.40 (intersectInPowersetIntersectUnions) =>
% 106.14/14.40 ((
% 106.14/14.40 (inComplementUnionImpNotIn1) =>
% 106.14/14.40 ((
% 106.14/14.40 (inComplementUnionImpInComplement1) =>
% 106.14/14.40 ((
% 106.14/14.40 (binunionTE) =>
% 106.14/14.40 ((
% 106.14/14.40 (binunionTEcontra) =>
% 106.14/14.40 ((
% 106.14/14.40 (demorgan2a1) =>
% 106.14/14.40 ((
% 106.14/14.40 (complementUnionInPowersetComplement) =>
% 106.14/14.40 ((
% 106.14/14.40 (demorgan2a2) =>
% 106.14/14.40 ((
% 106.14/14.40 (demorgan1a) =>
% 106.14/14.40 ((
% 106.14/14.40 (demorgan1b) =>
% 106.14/14.40 ((
% 106.14/14.40 (demorgan1) =>
% 106.14/14.40 ((
% 106.14/14.40 (demorgan2a) =>
% 106.14/14.40 ((
% 106.14/14.40 (demorgan2b2) =>
% 106.14/14.40 ((
% 106.14/14.40 (demorgan2b) =>
% 106.14/14.40 ((
% 106.14/14.40 (demorgan2) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz13rule0) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz13rule1) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz13rule2) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz13rule3) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz13rule4) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz1_1) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz1_2) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz1_3) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz1_4) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz1_5) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1all2) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1SetBreln1) =>
% 106.14/14.40 ((
% 106.14/14.40 (choice2fnsingleton) =>
% 106.14/14.40 ((
% 106.14/14.40 (setOfPairsIsBReln1) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1all1) =>
% 106.14/14.40 ((
% 106.14/14.40 (subbreln1) =>
% 106.14/14.40 ((
% 106.14/14.40 (eqbreln1) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1invprop) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1invI) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1invE) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1compprop) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1compI) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1compE) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1compEex) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1unionprop) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1unionIL) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1unionIR) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1unionI) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1unionE) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1unionEcases) =>
% 106.14/14.40 ((
% 106.14/14.40 (breln1unionCommutes) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz2Ex) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz2W) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz2A) =>
% 106.14/14.40 ((
% 106.14/14.40 (woz2B) =>
% 106.14/14.40 ((
% 106.14/14.40 (image1Ex) =>
% 106.14/14.40 ((
% 106.14/14.40 (image1Ex1) =>
% 106.14/14.40 ((
% 106.14/14.40 (image1Equiv) =>
% 106.14/14.40 ((
% 106.14/14.40 (image1E) =>
% 106.14/14.40 ((
% 106.14/14.40 (image1I) =>
% 106.14/14.40 ((
% 106.14/14.40 (injFuncInInjFuncSet) =>
% 106.14/14.40 ((
% 106.14/14.40 (injFuncSetFuncIn) =>
% 106.14/14.40 ((
% 106.14/14.40 (injFuncSetFuncInj) =>
% 106.14/14.40 ((
% 106.14/14.40 (surjFuncSetFuncIn) =>
% 106.14/14.40 ((
% 106.14/14.40 (surjFuncSetFuncSurj) =>
% 106.14/14.40 ((
% 106.14/14.40 (leftInvIsSurj) =>
% 106.14/14.40 ((
% 106.14/14.40 (surjCantorThm) =>
% 106.14/14.40 ((
% 106.14/14.40 (!!) @ (
% 106.14/14.40 (('#S') @ (
% 106.14/14.40 (
% 106.14/14.40 ('#B') @ (
% 106.14/14.40 =>) @
% 106.14/14.40 nonempty)) @
% 106.14/14.40 (
% 106.14/14.40 (
% 106.14/14.40 ('#B') @ (
% 106.14/14.40 ??) @
% 106.14/14.40 (
% 106.14/14.40 (
% 106.14/14.40 ('#S') @ (
% 106.14/14.40 (
% 106.14/14.40 ('#B') @ (
% 106.14/14.40 '#S') @
% 106.14/14.40 (
% 106.14/14.40 (
% 106.14/14.40 ('#B') @ (
% 106.14/14.40 (
% 106.14/14.40 ('#B') @ (
% 106.14/14.40 &))) @
% 106.14/14.40 (
% 106.14/14.40 (
% 106.14/14.40 ('#C') @ in)))))) @
% 106.14/14.40 (
% 106.14/14.40 (
% 106.14/14.40 ('#C') @ (
% 106.14/14.40 (
% 106.14/14.40 ('#B') @ (
% 106.14/14.40 '#C') @
% 106.14/14.40 (
% 106.14/14.40 (
% 106.14/14.40 ('#B') @ (
% 106.14/14.40 (
% 106.14/14.40 ('#B') @ (
% 106.14/14.40 =))) @
% 106.14/14.40 (
% 106.14/14.40 (
% 106.14/14.40 ('#C') @ binintersect)))))) @
% 106.14/14.40 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.14/14.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl142])).
% 106.14/14.40 thf(zip_derived_cl174, plain,
% 106.14/14.40 (~ (((notinemptyset) =>
% 106.14/14.40 (((exuE3e) =>
% 106.14/14.40 (((setext) =>
% 106.14/14.40 (((emptyI) =>
% 106.14/14.40 (((noeltsimpempty) =>
% 106.14/14.40 (((setbeta) =>
% 106.14/14.40 (((nonemptyE1) =>
% 106.14/14.40 (((nonemptyI) =>
% 106.14/14.40 (((nonemptyI1) =>
% 106.14/14.40 (((setadjoinIL) =>
% 106.14/14.40 (((in @ emptyset @
% 106.14/14.40 (setadjoin @ emptyset @ emptyset)) =>
% 106.14/14.40 (((setadjoinIR) =>
% 106.14/14.40 (((setadjoinE) =>
% 106.14/14.40 (((setadjoinOr) =>
% 106.14/14.40 (((setoftrueEq) =>
% 106.14/14.40 (((powersetI) =>
% 106.14/14.40 (((emptyinPowerset) =>
% 106.14/14.40 (((emptyInPowerset) =>
% 106.14/14.40 (((powersetE) =>
% 106.14/14.40 (((setunionI) =>
% 106.14/14.40 (((setunionE) =>
% 106.14/14.40 (((subPowSU) =>
% 106.14/14.40 (((exuE2) =>
% 106.14/14.40 (((nonemptyImpWitness) =>
% 106.14/14.40 (((uniqinunit) =>
% 106.14/14.40 (((notinsingleton) =>
% 106.14/14.40 (((eqinunit) =>
% 106.14/14.40 (((singletonsswitch) =>
% 106.14/14.40 (((upairsetE) =>
% 106.14/14.40 (((upairsetIL) =>
% 106.14/14.40 ((
% 106.14/14.40 (upairsetIR) =>
% 106.14/14.40 ((
% 106.14/14.40 (emptyE1) =>
% 106.14/14.40 ((
% 106.14/14.40 (vacuousDall) =>
% 106.14/14.40 ((
% 106.14/14.40 (quantDeMorgan1) =>
% 106.14/14.40 ((
% 106.14/14.40 (quantDeMorgan2) =>
% 106.14/14.40 ((
% 106.14/14.40 (quantDeMorgan3) =>
% 106.14/14.40 ((
% 106.14/14.40 (quantDeMorgan4) =>
% 106.14/14.40 ((
% 106.14/14.40 (prop2setI) =>
% 106.14/14.40 ((
% 106.14/14.40 (prop2set2propI) =>
% 106.14/14.40 ((
% 106.14/14.40 (notdexE) =>
% 106.14/14.40 ((
% 106.14/14.40 (notdallE) =>
% 106.14/14.40 ((
% 106.14/14.40 (exuI1) =>
% 106.14/14.40 ((
% 106.14/14.40 (exuI3) =>
% 106.14/14.40 ((
% 106.14/14.40 (exuI2) =>
% 106.14/14.40 ((
% 106.14/14.40 (inCongP) =>
% 106.14/14.40 ((
% 106.14/14.40 (in__Cong) =>
% 106.14/14.40 ((
% 106.14/14.40 (exuE3u) =>
% 106.14/14.40 ((
% 106.14/14.40 (exu__Cong) =>
% 106.14/14.40 ((
% 106.14/14.40 (setadjoin__Cong) =>
% 106.14/14.40 ((
% 106.14/14.40 (powerset__Cong) =>
% 106.14/14.40 ((
% 106.14/14.40 (setunion__Cong) =>
% 106.14/14.40 ((
% 106.14/14.40 (exuEu) =>
% 106.14/14.40 ((
% 106.14/14.40 (descr__Cong) =>
% 106.14/14.40 ((
% 106.14/14.40 (dsetconstr__Cong) =>
% 106.14/14.40 ((
% 106.14/14.40 (subsetI1) =>
% 106.14/14.40 ((
% 106.14/14.40 (eqimpsubset2) =>
% 106.14/14.40 ((
% 106.14/14.40 (eqimpsubset1) =>
% 106.14/14.40 ((
% 106.14/14.40 (subsetI2) =>
% 106.14/14.40 ((
% 106.14/14.40 (emptysetsubset) =>
% 106.14/14.40 ((
% 106.14/14.40 (subsetE) =>
% 106.14/14.40 ((
% 106.14/14.40 (subsetE2) =>
% 106.14/14.40 ((
% 106.14/14.40 (notsubsetI) =>
% 106.14/14.40 ((
% 106.14/14.40 (notequalI1) =>
% 106.14/14.40 ((
% 106.14/14.40 (notequalI2) =>
% 106.14/14.40 ((
% 106.14/14.40 (subsetRefl) =>
% 106.14/14.40 ((
% 106.14/14.40 (subsetTrans) =>
% 106.14/14.40 ((
% 106.14/14.40 (setadjoinSub) =>
% 106.14/14.40 ((
% 106.14/14.40 (setadjoinSub2) =>
% 106.14/14.40 ((
% 106.14/14.40 (subset2powerset) =>
% 106.14/14.40 ((
% 106.14/14.40 (setextsub) =>
% 106.14/14.40 ((
% 106.14/14.40 (subsetemptysetimpeq) =>
% 106.14/14.40 ((
% 106.14/14.40 (powersetI1) =>
% 106.14/14.40 ((
% 106.14/14.40 (powersetE1) =>
% 106.14/14.40 ((
% 106.14/14.40 (inPowerset) =>
% 106.14/14.40 ((
% 106.14/14.40 (powersetsubset) =>
% 106.14/14.40 ((
% 106.14/14.40 (sepInPowerset) =>
% 106.14/14.40 ((
% 106.14/14.40 (sepSubset) =>
% 106.14/14.40 ((
% 106.14/14.40 (binunionIL) =>
% 106.14/14.40 ((
% 106.14/14.40 (upairset2IR) =>
% 106.14/14.40 ((
% 106.14/14.40 (binunionIR) =>
% 106.14/14.40 ((
% 106.14/14.40 (binunionEcases) =>
% 106.14/14.40 ((
% 106.14/14.40 (binunionE) =>
% 106.14/14.40 ((
% 106.14/14.40 (binunionLsub) =>
% 106.14/14.40 ((
% 106.14/14.40 (binunionRsub) =>
% 106.14/14.40 ((
% 106.14/14.40 (binintersectI) =>
% 106.14/14.40 ((
% 106.14/14.40 (binintersectSubset5) =>
% 106.14/14.40 ((
% 106.14/14.40 (binintersectEL) =>
% 106.14/14.40 ((
% 106.14/14.40 (binintersectLsub) =>
% 106.14/14.40 ((
% 106.14/14.40 (binintersectSubset2) =>
% 106.14/14.40 ((
% 106.14/14.40 (binintersectSubset3) =>
% 106.14/14.40 ((
% 106.14/14.40 (binintersectER) =>
% 106.14/14.40 ((
% 106.14/14.40 (disjointsetsI1) =>
% 106.14/14.40 ((
% 106.14/14.40 (binintersectRsub) =>
% 106.14/14.40 ((
% 106.14/14.40 (binintersectSubset4) =>
% 106.14/14.40 ((
% 106.14/14.40 (binintersectSubset1) =>
% 106.14/14.40 ((
% 106.14/14.40 (bs114d) =>
% 106.14/14.40 ((
% 106.14/14.40 (setminusI) =>
% 106.14/14.40 ((
% 106.14/14.40 (setminusEL) =>
% 106.14/14.40 ((
% 106.14/14.40 (setminusER) =>
% 106.14/14.40 ((
% 106.14/14.40 (setminusSubset2) =>
% 106.14/14.40 ((
% 106.14/14.40 (setminusERneg) =>
% 106.14/14.40 ((
% 106.14/14.40 (setminusELneg) =>
% 106.14/14.40 ((
% 106.14/14.40 (setminusILneg) =>
% 106.14/14.40 ((
% 106.14/14.40 (setminusIRneg) =>
% 106.14/14.40 ((
% 106.14/14.40 (setminusLsub) =>
% 106.14/14.40 ((
% 106.14/14.40 (setminusSubset1) =>
% 106.14/14.40 ((
% 106.14/14.40 (symdiffE) =>
% 106.14/14.40 ((
% 106.14/14.40 (symdiffI1) =>
% 106.14/14.40 ((
% 106.14/14.40 (symdiffI2) =>
% 106.14/14.40 ((
% 106.14/14.40 (symdiffIneg1) =>
% 106.14/14.40 ((
% 106.14/14.40 (symdiffIneg2) =>
% 106.14/14.40 ((
% 106.14/14.40 (secondinupair) =>
% 106.14/14.40 ((
% 106.14/14.40 (setukpairIL) =>
% 106.14/14.40 ((
% 106.14/14.40 (setukpairIR) =>
% 106.14/14.40 ((
% 106.14/14.40 (kpairiskpair) =>
% 106.14/14.40 ((
% 106.14/14.40 (kpairp) =>
% 106.14/14.40 ((
% 106.14/14.40 (singletonsubset) =>
% 106.14/14.40 ((
% 106.14/14.40 (singletoninpowerset) =>
% 106.14/14.40 ((
% 106.14/14.40 (singletoninpowunion) =>
% 106.14/14.40 ((
% 106.14/14.40 (upairset2E) =>
% 106.14/14.40 ((
% 106.14/14.40 (upairsubunion) =>
% 106.14/14.40 ((
% 106.14/14.40 (upairinpowunion) =>
% 106.14/14.40 ((
% 106.14/14.40 (ubforcartprodlem1) =>
% 106.14/14.40 ((
% 106.14/14.40 (ubforcartprodlem2) =>
% 106.14/14.40 ((
% 106.14/14.40 (ubforcartprodlem3) =>
% 106.14/14.40 ((
% 106.14/14.40 (cartprodpairin) =>
% 106.14/14.40 ((
% 106.14/14.40 (cartprodmempair1) =>
% 106.14/14.40 ((
% 106.14/14.40 (cartprodmempair) =>
% 106.14/14.40 ((
% 106.14/14.40 (setunionE2) =>
% 106.14/14.40 ((
% 106.14/14.40 (setunionsingleton1) =>
% 106.14/14.40 ((
% 106.14/14.40 (setunionsingleton2) =>
% 106.14/14.40 ((
% 106.14/14.40 (setunionsingleton) =>
% 106.14/14.40 ((
% 106.14/14.40 (singletonprop) =>
% 106.14/14.40 ((
% 106.14/14.40 (ex1E1) =>
% 106.14/14.40 ((
% 106.14/14.40 (ex1I) =>
% 106.14/14.40 ((
% 106.14/14.40 (ex1I2) =>
% 106.14/14.40 ((
% 106.14/14.40 (singletonsuniq) =>
% 106.14/14.40 ((
% 106.14/14.40 (setukpairinjL1) =>
% 106.14/14.40 ((
% 106.14/14.40 (kfstsingleton) =>
% 106.14/14.40 ((
% 106.14/14.40 (theprop) =>
% 106.14/14.40 ((
% 106.14/14.40 (kfstpairEq) =>
% 106.14/14.40 ((
% 106.14/14.40 (cartprodfstin) =>
% 106.14/14.40 ((
% 106.14/14.40 (setukpairinjL2) =>
% 106.14/14.40 ((
% 106.14/14.40 (setukpairinjL) =>
% 106.14/14.40 ((
% 106.14/14.40 (setukpairinjR11) =>
% 106.14/14.40 ((
% 106.14/14.40 (setukpairinjR12) =>
% 106.14/14.40 ((
% 106.14/14.40 (setukpairinjR1) =>
% 106.14/14.40 ((
% 106.14/14.40 (upairequniteq) =>
% 106.14/14.40 ((
% 106.14/14.40 (setukpairinjR2) =>
% 106.14/14.40 ((
% 106.14/14.40 (setukpairinjR) =>
% 106.14/14.40 ((
% 106.14/14.40 (ksndsingleton) =>
% 106.14/14.40 ((
% 106.14/14.40 (ksndpairEq) =>
% 106.14/14.40 ((
% 106.14/14.40 (kpairsurjEq) =>
% 106.14/14.40 ((
% 106.14/14.40 (cartprodsndin) =>
% 106.14/14.40 ((
% 106.14/14.40 (cartprodpairmemEL) =>
% 106.14/14.40 ((
% 106.14/14.40 (cartprodpairmemER) =>
% 106.14/14.40 ((
% 106.14/14.40 (cartprodmempaircEq) =>
% 106.14/14.40 ((
% 106.14/14.40 (cartprodfstpairEq) =>
% 106.14/14.40 ((
% 106.14/14.40 (cartprodsndpairEq) =>
% 106.14/14.40 ((
% 106.14/14.40 (cartprodpairsurjEq) =>
% 106.14/14.40 ((
% 106.14/14.40 (dpsetconstrI) =>
% 106.14/14.40 ((
% 106.14/14.40 (dpsetconstrSub) =>
% 106.14/14.40 ((
% 106.14/14.40 (setOfPairsIsBReln) =>
% 106.14/14.40 ((
% 106.14/14.40 (dpsetconstrERa) =>
% 106.14/14.40 ((
% 106.14/14.40 (dpsetconstrEL1) =>
% 106.14/14.40 ((
% 106.14/14.40 (dpsetconstrEL2) =>
% 106.14/14.40 ((
% 106.14/14.40 (dpsetconstrER) =>
% 106.14/14.40 ((
% 106.14/14.40 (funcImageSingleton) =>
% 106.14/14.40 ((
% 106.14/14.40 (apProp) =>
% 106.14/14.40 ((
% 106.14/14.40 (app) =>
% 106.14/14.40 ((
% 106.14/14.40 (infuncsetfunc) =>
% 106.14/14.40 ((
% 106.14/14.40 (ap2p) =>
% 106.14/14.40 ((
% 106.14/14.40 (funcinfuncset) =>
% 106.14/14.40 ((
% 106.14/14.40 (lamProp) =>
% 106.14/14.40 ((
% 106.14/14.40 (lamp) =>
% 106.14/14.40 ((
% 106.14/14.40 (lam2p) =>
% 106.14/14.40 ((
% 106.14/14.40 (brelnall1) =>
% 106.14/14.40 ((
% 106.14/14.40 (brelnall2) =>
% 106.14/14.40 ((
% 106.14/14.40 (ex1E2) =>
% 106.14/14.40 ((
% 106.14/14.40 (funcGraphProp1) =>
% 106.14/14.40 ((
% 106.14/14.40 (funcGraphProp3) =>
% 106.14/14.40 ((
% 106.14/14.40 (funcGraphProp2) =>
% 106.14/14.40 ((
% 106.14/14.40 (funcextLem) =>
% 106.14/14.40 ((
% 106.14/14.40 (funcGraphProp4) =>
% 106.14/14.40 ((
% 106.14/14.40 (subbreln) =>
% 106.14/14.40 ((
% 106.14/14.40 (eqbreln) =>
% 106.14/14.40 ((
% 106.14/14.40 (funcext) =>
% 106.14/14.40 ((
% 106.14/14.40 (funcext2) =>
% 106.14/14.40 ((
% 106.14/14.40 (ap2apEq1) =>
% 106.14/14.40 ((
% 106.14/14.40 (ap2apEq2) =>
% 106.14/14.40 ((
% 106.14/14.40 (beta1) =>
% 106.14/14.40 ((
% 106.14/14.40 (eta1) =>
% 106.14/14.40 ((
% 106.14/14.40 (lam2lamEq) =>
% 106.14/14.40 ((
% 106.14/14.40 (beta2) =>
% 106.14/14.40 ((
% 106.14/14.40 (eta2) =>
% 106.14/14.40 ((
% 106.14/14.40 (iffalseProp1) =>
% 106.14/14.40 ((
% 106.14/14.40 (iffalseProp2) =>
% 106.14/14.40 ((
% 106.14/14.40 (iftrueProp1) =>
% 106.14/14.40 ((
% 106.14/14.40 (iftrueProp2) =>
% 106.14/14.40 ((
% 106.14/14.40 (ifSingleton) =>
% 106.14/14.40 ((
% 106.14/14.40 (ifp) =>
% 106.14/14.40 ((
% 106.14/14.40 (theeq) =>
% 106.14/14.40 ((
% 106.14/14.40 (iftrue) =>
% 106.14/14.40 ((
% 106.14/14.40 (iffalse) =>
% 106.14/14.40 ((
% 106.14/14.40 (iftrueorfalse) =>
% 106.14/14.40 ((
% 106.14/14.40 (binintersectT_lem) =>
% 106.14/14.40 ((
% 106.14/14.40 (binunionT_lem) =>
% 106.14/14.40 ((
% 106.14/14.40 (powersetT_lem) =>
% 106.14/14.40 ((
% 106.14/14.41 (setminusT_lem) =>
% 106.14/14.41 ((
% 106.14/14.41 (complementT_lem) =>
% 106.14/14.41 ((
% 106.14/14.41 (setextT) =>
% 106.14/14.41 ((
% 106.14/14.41 (subsetTI) =>
% 106.14/14.41 ((
% 106.14/14.41 (powersetTI1) =>
% 106.14/14.41 ((
% 106.14/14.41 (powersetTE1) =>
% 106.14/14.41 ((
% 106.14/14.41 (complementTI1) =>
% 106.14/14.41 ((
% 106.14/14.41 (complementTE1) =>
% 106.14/14.41 ((
% 106.14/14.41 (binintersectTELcontra) =>
% 106.14/14.41 ((
% 106.14/14.41 (binintersectTERcontra) =>
% 106.14/14.41 ((
% 106.14/14.41 (contrasubsetT) =>
% 106.14/14.41 ((
% 106.14/14.41 (contrasubsetT1) =>
% 106.14/14.41 ((
% 106.14/14.41 (contrasubsetT2) =>
% 106.14/14.41 ((
% 106.14/14.41 (contrasubsetT3) =>
% 106.14/14.41 ((
% 106.14/14.41 (doubleComplementI1) =>
% 106.14/14.41 ((
% 106.14/14.41 (doubleComplementE1) =>
% 106.14/14.41 ((
% 106.14/14.41 (doubleComplementSub1) =>
% 106.14/14.41 ((
% 106.14/14.41 (doubleComplementSub2) =>
% 106.14/14.41 ((
% 106.14/14.41 (doubleComplementEq) =>
% 106.14/14.41 ((
% 106.14/14.41 (complementTnotintersectT) =>
% 106.14/14.41 ((
% 106.14/14.41 (complementImpComplementIntersect) =>
% 106.14/14.41 ((
% 106.14/14.41 (complementSubsetComplementIntersect) =>
% 106.14/14.41 ((
% 106.14/14.41 (complementInPowersetComplementIntersect) =>
% 106.14/14.41 ((
% 106.14/14.41 (contraSubsetComplement) =>
% 106.14/14.41 ((
% 106.14/14.41 (complementTcontraSubset) =>
% 106.14/14.41 ((
% 106.14/14.41 (binunionTILcontra) =>
% 106.14/14.41 ((
% 106.14/14.41 (binunionTIRcontra) =>
% 106.14/14.41 ((
% 106.14/14.41 (inIntersectImpInUnion) =>
% 106.14/14.41 ((
% 106.14/14.41 (inIntersectImpInUnion2) =>
% 106.14/14.41 ((
% 106.14/14.41 (inIntersectImpInIntersectUnions) =>
% 106.14/14.41 ((
% 106.14/14.41 (intersectInPowersetIntersectUnions) =>
% 106.14/14.41 ((
% 106.14/14.41 (inComplementUnionImpNotIn1) =>
% 106.14/14.41 ((
% 106.14/14.41 (inComplementUnionImpInComplement1) =>
% 106.14/14.41 ((
% 106.14/14.41 (binunionTE) =>
% 106.14/14.41 ((
% 106.14/14.41 (binunionTEcontra) =>
% 106.14/14.41 ((
% 106.14/14.41 (demorgan2a1) =>
% 106.14/14.41 ((
% 106.14/14.41 (complementUnionInPowersetComplement) =>
% 106.14/14.41 ((
% 106.14/14.41 (demorgan2a2) =>
% 106.14/14.41 ((
% 106.14/14.41 (demorgan1a) =>
% 106.14/14.41 ((
% 106.14/14.41 (demorgan1b) =>
% 106.14/14.41 ((
% 106.14/14.41 (demorgan1) =>
% 106.14/14.41 ((
% 106.14/14.41 (demorgan2a) =>
% 106.14/14.41 ((
% 106.14/14.41 (demorgan2b2) =>
% 106.14/14.41 ((
% 106.14/14.41 (demorgan2b) =>
% 106.14/14.41 ((
% 106.14/14.41 (demorgan2) =>
% 106.14/14.41 ((
% 106.14/14.41 (woz13rule0) =>
% 106.14/14.41 ((
% 106.14/14.41 (woz13rule1) =>
% 106.14/14.41 ((
% 106.14/14.41 (woz13rule2) =>
% 106.14/14.41 ((
% 106.14/14.41 (woz13rule3) =>
% 106.14/14.41 ((
% 106.14/14.41 (woz13rule4) =>
% 106.14/14.41 ((
% 106.14/14.41 (woz1_1) =>
% 106.14/14.41 ((
% 106.14/14.41 (woz1_2) =>
% 106.14/14.41 ((
% 106.14/14.41 (woz1_3) =>
% 106.14/14.41 ((
% 106.14/14.41 (woz1_4) =>
% 106.14/14.41 ((
% 106.14/14.41 (woz1_5) =>
% 106.14/14.41 ((
% 106.14/14.41 (breln1all2) =>
% 106.14/14.41 ((
% 106.14/14.41 (breln1SetBreln1) =>
% 106.14/14.41 ((
% 106.14/14.41 (choice2fnsingleton) =>
% 106.14/14.41 ((
% 106.14/14.41 (setOfPairsIsBReln1) =>
% 106.14/14.41 ((
% 106.14/14.41 (breln1all1) =>
% 106.14/14.41 ((
% 106.14/14.41 (subbreln1) =>
% 106.14/14.41 ((
% 106.14/14.41 (eqbreln1) =>
% 106.14/14.41 ((
% 106.14/14.41 (breln1invprop) =>
% 106.14/14.41 ((
% 106.14/14.41 (breln1invI) =>
% 106.14/14.41 ((
% 106.14/14.41 (breln1invE) =>
% 106.14/14.41 ((
% 106.14/14.41 (breln1compprop) =>
% 106.14/14.41 ((
% 106.14/14.41 (breln1compI) =>
% 106.14/14.41 ((
% 106.14/14.41 (breln1compE) =>
% 106.14/14.41 ((
% 106.14/14.41 (breln1compEex) =>
% 106.14/14.41 ((
% 106.14/14.41 (breln1unionprop) =>
% 106.14/14.41 ((
% 106.14/14.41 (breln1unionIL) =>
% 106.14/14.41 ((
% 106.14/14.41 (breln1unionIR) =>
% 106.14/14.41 ((
% 106.14/14.41 (breln1unionI) =>
% 106.14/14.41 ((
% 106.14/14.41 (breln1unionE) =>
% 106.14/14.41 ((
% 106.14/14.41 (breln1unionEcases) =>
% 106.14/14.41 ((
% 106.14/14.41 (breln1unionCommutes) =>
% 106.14/14.41 ((
% 106.14/14.41 (woz2Ex) =>
% 106.14/14.41 ((
% 106.14/14.41 (woz2W) =>
% 106.14/14.41 ((
% 106.14/14.41 (woz2A) =>
% 106.14/14.41 ((
% 106.14/14.41 (woz2B) =>
% 106.14/14.41 ((
% 106.14/14.41 (image1Ex) =>
% 106.14/14.41 ((
% 106.14/14.41 (image1Ex1) =>
% 106.14/14.41 ((
% 106.14/14.41 (image1Equiv) =>
% 106.14/14.41 ((
% 106.14/14.41 (image1E) =>
% 106.14/14.41 ((
% 106.14/14.41 (image1I) =>
% 106.14/14.41 ((
% 106.14/14.41 (injFuncInInjFuncSet) =>
% 106.14/14.41 ((
% 106.14/14.41 (injFuncSetFuncIn) =>
% 106.14/14.41 ((
% 106.14/14.41 (injFuncSetFuncInj) =>
% 106.14/14.41 ((
% 106.14/14.41 (surjFuncSetFuncIn) =>
% 106.14/14.41 ((
% 106.14/14.41 (surjFuncSetFuncSurj) =>
% 106.14/14.41 ((
% 106.14/14.41 (leftInvIsSurj) =>
% 106.14/14.41 ((
% 106.14/14.41 (surjCantorThm) =>
% 106.14/14.41 ((
% 106.14/14.41 (!!) @ (
% 106.14/14.41 (('#S') @ (
% 106.14/14.41 (
% 106.14/14.41 ('#B') @ (
% 106.14/14.41 =>) @
% 106.14/14.41 nonempty)) @
% 106.14/14.41 (
% 106.14/14.41 (
% 106.14/14.41 ('#B') @ (
% 106.14/14.41 ??) @
% 106.14/14.41 (
% 106.14/14.41 (
% 106.14/14.41 ('#S') @ (
% 106.14/14.41 (
% 106.14/14.41 ('#B') @ (
% 106.14/14.41 '#S') @
% 106.14/14.41 (
% 106.14/14.41 (
% 106.14/14.41 ('#B') @ (
% 106.14/14.41 (
% 106.14/14.41 ('#B') @ (
% 106.14/14.41 &))) @
% 106.14/14.41 (
% 106.14/14.41 (
% 106.14/14.41 ('#C') @ in)))))) @
% 106.14/14.41 (
% 106.14/14.41 (
% 106.14/14.41 ('#C') @ (
% 106.14/14.41 (
% 106.14/14.41 ('#B') @ (
% 106.14/14.41 '#C') @
% 106.14/14.41 (
% 106.14/14.41 (
% 106.14/14.41 ('#B') @ (
% 106.14/14.41 (
% 106.14/14.41 ('#B') @ (
% 106.14/14.41 =))) @
% 106.14/14.41 (
% 106.14/14.41 (
% 106.14/14.41 ('#C') @ binintersect)))))) @
% 106.14/14.41 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.14/14.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl158])).
% 106.14/14.41 thf(zip_derived_cl189, plain,
% 106.14/14.41 (~ (((exuE3e) =>
% 106.14/14.41 (((setext) =>
% 106.14/14.41 (((emptyI) =>
% 106.14/14.41 (((noeltsimpempty) =>
% 106.14/14.41 (((setbeta) =>
% 106.14/14.41 (((nonemptyE1) =>
% 106.14/14.41 (((nonemptyI) =>
% 106.14/14.41 (((nonemptyI1) =>
% 106.14/14.41 (((setadjoinIL) =>
% 106.14/14.41 (((in @ emptyset @
% 106.14/14.41 (setadjoin @ emptyset @ emptyset)) =>
% 106.14/14.41 (((setadjoinIR) =>
% 106.14/14.41 (((setadjoinE) =>
% 106.14/14.41 (((setadjoinOr) =>
% 106.14/14.41 (((setoftrueEq) =>
% 106.14/14.41 (((powersetI) =>
% 106.14/14.41 (((emptyinPowerset) =>
% 106.14/14.41 (((emptyInPowerset) =>
% 106.14/14.41 (((powersetE) =>
% 106.14/14.41 (((setunionI) =>
% 106.14/14.41 (((setunionE) =>
% 106.14/14.41 (((subPowSU) =>
% 106.14/14.41 (((exuE2) =>
% 106.14/14.41 (((nonemptyImpWitness) =>
% 106.14/14.41 (((uniqinunit) =>
% 106.14/14.41 (((notinsingleton) =>
% 106.14/14.41 (((eqinunit) =>
% 106.14/14.41 (((singletonsswitch) =>
% 106.14/14.41 (((upairsetE) =>
% 106.14/14.41 (((upairsetIL) =>
% 106.14/14.41 (((upairsetIR) =>
% 106.14/14.41 ((
% 106.14/14.41 (emptyE1) =>
% 106.14/14.41 ((
% 106.14/14.41 (vacuousDall) =>
% 106.14/14.41 ((
% 106.14/14.41 (quantDeMorgan1) =>
% 106.14/14.41 ((
% 106.14/14.41 (quantDeMorgan2) =>
% 106.14/14.41 ((
% 106.14/14.41 (quantDeMorgan3) =>
% 106.14/14.41 ((
% 106.14/14.41 (quantDeMorgan4) =>
% 106.14/14.41 ((
% 106.14/14.41 (prop2setI) =>
% 106.14/14.41 ((
% 106.14/14.41 (prop2set2propI) =>
% 106.14/14.41 ((
% 106.14/14.41 (notdexE) =>
% 106.14/14.41 ((
% 106.14/14.41 (notdallE) =>
% 106.14/14.41 ((
% 106.14/14.41 (exuI1) =>
% 106.14/14.41 ((
% 106.14/14.41 (exuI3) =>
% 106.14/14.41 ((
% 106.14/14.41 (exuI2) =>
% 106.14/14.41 ((
% 106.14/14.41 (inCongP) =>
% 106.14/14.41 ((
% 106.14/14.41 (in__Cong) =>
% 106.14/14.41 ((
% 106.14/14.41 (exuE3u) =>
% 106.14/14.41 ((
% 106.14/14.41 (exu__Cong) =>
% 106.14/14.41 ((
% 106.14/14.41 (setadjoin__Cong) =>
% 106.14/14.41 ((
% 106.14/14.41 (powerset__Cong) =>
% 106.14/14.41 ((
% 106.14/14.41 (setunion__Cong) =>
% 106.14/14.41 ((
% 106.14/14.41 (exuEu) =>
% 106.14/14.41 ((
% 106.14/14.41 (descr__Cong) =>
% 106.14/14.41 ((
% 106.14/14.41 (dsetconstr__Cong) =>
% 106.14/14.41 ((
% 106.14/14.41 (subsetI1) =>
% 106.14/14.41 ((
% 106.14/14.41 (eqimpsubset2) =>
% 106.14/14.41 ((
% 106.14/14.41 (eqimpsubset1) =>
% 106.14/14.41 ((
% 106.14/14.41 (subsetI2) =>
% 106.14/14.41 ((
% 106.14/14.41 (emptysetsubset) =>
% 106.14/14.41 ((
% 106.14/14.41 (subsetE) =>
% 106.14/14.41 ((
% 106.14/14.41 (subsetE2) =>
% 106.14/14.41 ((
% 106.14/14.41 (notsubsetI) =>
% 106.14/14.41 ((
% 106.14/14.41 (notequalI1) =>
% 106.14/14.41 ((
% 106.14/14.41 (notequalI2) =>
% 106.14/14.41 ((
% 106.14/14.41 (subsetRefl) =>
% 106.14/14.41 ((
% 106.14/14.41 (subsetTrans) =>
% 106.14/14.41 ((
% 106.14/14.41 (setadjoinSub) =>
% 106.14/14.41 ((
% 106.14/14.41 (setadjoinSub2) =>
% 106.14/14.41 ((
% 106.14/14.41 (subset2powerset) =>
% 106.14/14.41 ((
% 106.14/14.41 (setextsub) =>
% 106.14/14.41 ((
% 106.14/14.41 (subsetemptysetimpeq) =>
% 106.14/14.41 ((
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% 106.14/14.41 ((
% 106.14/14.41 (powersetE1) =>
% 106.14/14.41 ((
% 106.14/14.41 (inPowerset) =>
% 106.14/14.41 ((
% 106.14/14.41 (powersetsubset) =>
% 106.14/14.41 ((
% 106.14/14.41 (sepInPowerset) =>
% 106.14/14.41 ((
% 106.14/14.41 (sepSubset) =>
% 106.14/14.41 ((
% 106.14/14.41 (binunionIL) =>
% 106.14/14.41 ((
% 106.14/14.41 (upairset2IR) =>
% 106.14/14.41 ((
% 106.14/14.41 (binunionIR) =>
% 106.14/14.41 ((
% 106.14/14.41 (binunionEcases) =>
% 106.14/14.41 ((
% 106.14/14.41 (binunionE) =>
% 106.14/14.41 ((
% 106.14/14.41 (binunionLsub) =>
% 106.14/14.41 ((
% 106.14/14.41 (binunionRsub) =>
% 106.14/14.41 ((
% 106.14/14.41 (binintersectI) =>
% 106.14/14.41 ((
% 106.14/14.41 (binintersectSubset5) =>
% 106.14/14.41 ((
% 106.14/14.41 (binintersectEL) =>
% 106.14/14.41 ((
% 106.14/14.41 (binintersectLsub) =>
% 106.14/14.41 ((
% 106.14/14.41 (binintersectSubset2) =>
% 106.14/14.41 ((
% 106.14/14.41 (binintersectSubset3) =>
% 106.14/14.41 ((
% 106.14/14.41 (binintersectER) =>
% 106.14/14.41 ((
% 106.14/14.41 (disjointsetsI1) =>
% 106.14/14.41 ((
% 106.14/14.41 (binintersectRsub) =>
% 106.14/14.41 ((
% 106.14/14.41 (binintersectSubset4) =>
% 106.14/14.41 ((
% 106.14/14.41 (binintersectSubset1) =>
% 106.14/14.41 ((
% 106.14/14.41 (bs114d) =>
% 106.14/14.41 ((
% 106.14/14.41 (setminusI) =>
% 106.14/14.41 ((
% 106.14/14.41 (setminusEL) =>
% 106.14/14.41 ((
% 106.14/14.41 (setminusER) =>
% 106.14/14.41 ((
% 106.14/14.41 (setminusSubset2) =>
% 106.14/14.41 ((
% 106.14/14.41 (setminusERneg) =>
% 106.14/14.41 ((
% 106.14/14.41 (setminusELneg) =>
% 106.14/14.41 ((
% 106.14/14.41 (setminusILneg) =>
% 106.14/14.41 ((
% 106.14/14.41 (setminusIRneg) =>
% 106.14/14.41 ((
% 106.14/14.41 (setminusLsub) =>
% 106.14/14.41 ((
% 106.14/14.41 (setminusSubset1) =>
% 106.14/14.41 ((
% 106.14/14.41 (symdiffE) =>
% 106.14/14.41 ((
% 106.14/14.41 (symdiffI1) =>
% 106.14/14.41 ((
% 106.14/14.41 (symdiffI2) =>
% 106.14/14.41 ((
% 106.14/14.41 (symdiffIneg1) =>
% 106.14/14.41 ((
% 106.14/14.41 (symdiffIneg2) =>
% 106.14/14.41 ((
% 106.14/14.41 (secondinupair) =>
% 106.14/14.41 ((
% 106.14/14.41 (setukpairIL) =>
% 106.14/14.41 ((
% 106.14/14.41 (setukpairIR) =>
% 106.14/14.41 ((
% 106.14/14.41 (kpairiskpair) =>
% 106.14/14.41 ((
% 106.14/14.41 (kpairp) =>
% 106.14/14.41 ((
% 106.14/14.41 (singletonsubset) =>
% 106.14/14.41 ((
% 106.14/14.41 (singletoninpowerset) =>
% 106.14/14.41 ((
% 106.14/14.41 (singletoninpowunion) =>
% 106.14/14.41 ((
% 106.14/14.41 (upairset2E) =>
% 106.14/14.41 ((
% 106.14/14.41 (upairsubunion) =>
% 106.14/14.41 ((
% 106.14/14.41 (upairinpowunion) =>
% 106.14/14.41 ((
% 106.14/14.41 (ubforcartprodlem1) =>
% 106.14/14.41 ((
% 106.14/14.41 (ubforcartprodlem2) =>
% 106.14/14.41 ((
% 106.14/14.41 (ubforcartprodlem3) =>
% 106.14/14.41 ((
% 106.14/14.41 (cartprodpairin) =>
% 106.14/14.41 ((
% 106.14/14.41 (cartprodmempair1) =>
% 106.14/14.41 ((
% 106.14/14.41 (cartprodmempair) =>
% 106.14/14.41 ((
% 106.14/14.41 (setunionE2) =>
% 106.14/14.41 ((
% 106.14/14.41 (setunionsingleton1) =>
% 106.14/14.41 ((
% 106.14/14.41 (setunionsingleton2) =>
% 106.14/14.41 ((
% 106.14/14.41 (setunionsingleton) =>
% 106.14/14.41 ((
% 106.14/14.41 (singletonprop) =>
% 106.14/14.41 ((
% 106.14/14.41 (ex1E1) =>
% 106.14/14.41 ((
% 106.14/14.41 (ex1I) =>
% 106.14/14.41 ((
% 106.14/14.41 (ex1I2) =>
% 106.14/14.41 ((
% 106.14/14.41 (singletonsuniq) =>
% 106.14/14.41 ((
% 106.14/14.41 (setukpairinjL1) =>
% 106.14/14.41 ((
% 106.14/14.41 (kfstsingleton) =>
% 106.14/14.41 ((
% 106.14/14.41 (theprop) =>
% 106.14/14.41 ((
% 106.14/14.41 (kfstpairEq) =>
% 106.14/14.41 ((
% 106.14/14.41 (cartprodfstin) =>
% 106.14/14.41 ((
% 106.14/14.41 (setukpairinjL2) =>
% 106.14/14.41 ((
% 106.14/14.41 (setukpairinjL) =>
% 106.14/14.41 ((
% 106.14/14.41 (setukpairinjR11) =>
% 106.14/14.41 ((
% 106.14/14.41 (setukpairinjR12) =>
% 106.14/14.41 ((
% 106.14/14.41 (setukpairinjR1) =>
% 106.14/14.41 ((
% 106.14/14.41 (upairequniteq) =>
% 106.14/14.41 ((
% 106.14/14.41 (setukpairinjR2) =>
% 106.14/14.41 ((
% 106.14/14.41 (setukpairinjR) =>
% 106.14/14.41 ((
% 106.14/14.41 (ksndsingleton) =>
% 106.14/14.41 ((
% 106.14/14.41 (ksndpairEq) =>
% 106.14/14.41 ((
% 106.14/14.41 (kpairsurjEq) =>
% 106.14/14.41 ((
% 106.14/14.41 (cartprodsndin) =>
% 106.14/14.41 ((
% 106.14/14.41 (cartprodpairmemEL) =>
% 106.14/14.41 ((
% 106.14/14.41 (cartprodpairmemER) =>
% 106.14/14.41 ((
% 106.14/14.41 (cartprodmempaircEq) =>
% 106.14/14.41 ((
% 106.14/14.41 (cartprodfstpairEq) =>
% 106.14/14.41 ((
% 106.14/14.41 (cartprodsndpairEq) =>
% 106.14/14.41 ((
% 106.14/14.41 (cartprodpairsurjEq) =>
% 106.14/14.41 ((
% 106.14/14.41 (dpsetconstrI) =>
% 106.14/14.41 ((
% 106.14/14.41 (dpsetconstrSub) =>
% 106.14/14.41 ((
% 106.14/14.41 (setOfPairsIsBReln) =>
% 106.14/14.41 ((
% 106.14/14.41 (dpsetconstrERa) =>
% 106.14/14.41 ((
% 106.14/14.41 (dpsetconstrEL1) =>
% 106.14/14.41 ((
% 106.14/14.41 (dpsetconstrEL2) =>
% 106.14/14.41 ((
% 106.14/14.41 (dpsetconstrER) =>
% 106.14/14.41 ((
% 106.14/14.41 (funcImageSingleton) =>
% 106.14/14.41 ((
% 106.14/14.41 (apProp) =>
% 106.14/14.41 ((
% 106.14/14.41 (app) =>
% 106.14/14.41 ((
% 106.14/14.41 (infuncsetfunc) =>
% 106.14/14.41 ((
% 106.14/14.41 (ap2p) =>
% 106.14/14.41 ((
% 106.14/14.41 (funcinfuncset) =>
% 106.14/14.41 ((
% 106.14/14.41 (lamProp) =>
% 106.14/14.41 ((
% 106.14/14.41 (lamp) =>
% 106.14/14.41 ((
% 106.14/14.41 (lam2p) =>
% 106.14/14.41 ((
% 106.14/14.41 (brelnall1) =>
% 106.14/14.41 ((
% 106.14/14.41 (brelnall2) =>
% 106.14/14.41 ((
% 106.14/14.41 (ex1E2) =>
% 106.14/14.41 ((
% 106.14/14.41 (funcGraphProp1) =>
% 106.14/14.41 ((
% 106.14/14.41 (funcGraphProp3) =>
% 106.14/14.41 ((
% 106.14/14.41 (funcGraphProp2) =>
% 106.14/14.41 ((
% 106.14/14.41 (funcextLem) =>
% 106.14/14.41 ((
% 106.14/14.41 (funcGraphProp4) =>
% 106.14/14.41 ((
% 106.14/14.41 (subbreln) =>
% 106.14/14.41 ((
% 106.14/14.41 (eqbreln) =>
% 106.14/14.41 ((
% 106.14/14.41 (funcext) =>
% 106.14/14.41 ((
% 106.14/14.41 (funcext2) =>
% 106.14/14.41 ((
% 106.14/14.41 (ap2apEq1) =>
% 106.14/14.41 ((
% 106.14/14.41 (ap2apEq2) =>
% 106.14/14.41 ((
% 106.14/14.41 (beta1) =>
% 106.14/14.41 ((
% 106.14/14.41 (eta1) =>
% 106.14/14.41 ((
% 106.14/14.41 (lam2lamEq) =>
% 106.14/14.41 ((
% 106.14/14.41 (beta2) =>
% 106.14/14.41 ((
% 106.14/14.41 (eta2) =>
% 106.14/14.41 ((
% 106.14/14.41 (iffalseProp1) =>
% 106.14/14.41 ((
% 106.14/14.41 (iffalseProp2) =>
% 106.14/14.41 ((
% 106.14/14.41 (iftrueProp1) =>
% 106.14/14.41 ((
% 106.14/14.41 (iftrueProp2) =>
% 106.14/14.41 ((
% 106.14/14.41 (ifSingleton) =>
% 106.14/14.41 ((
% 106.14/14.41 (ifp) =>
% 106.14/14.41 ((
% 106.14/14.41 (theeq) =>
% 106.14/14.41 ((
% 106.14/14.41 (iftrue) =>
% 106.14/14.41 ((
% 106.14/14.41 (iffalse) =>
% 106.14/14.41 ((
% 106.14/14.41 (iftrueorfalse) =>
% 106.14/14.41 ((
% 106.14/14.41 (binintersectT_lem) =>
% 106.14/14.41 ((
% 106.14/14.41 (binunionT_lem) =>
% 106.14/14.41 ((
% 106.14/14.41 (powersetT_lem) =>
% 106.14/14.41 ((
% 106.14/14.41 (setminusT_lem) =>
% 106.14/14.41 ((
% 106.14/14.41 (complementT_lem) =>
% 106.14/14.41 ((
% 106.14/14.41 (setextT) =>
% 106.14/14.41 ((
% 106.14/14.41 (subsetTI) =>
% 106.14/14.41 ((
% 106.14/14.41 (powersetTI1) =>
% 106.14/14.41 ((
% 106.14/14.41 (powersetTE1) =>
% 106.14/14.41 ((
% 106.14/14.41 (complementTI1) =>
% 106.14/14.41 ((
% 106.14/14.41 (complementTE1) =>
% 106.14/14.41 ((
% 106.14/14.41 (binintersectTELcontra) =>
% 106.14/14.41 ((
% 106.14/14.41 (binintersectTERcontra) =>
% 106.14/14.41 ((
% 106.14/14.41 (contrasubsetT) =>
% 106.14/14.41 ((
% 106.14/14.41 (contrasubsetT1) =>
% 106.14/14.41 ((
% 106.14/14.41 (contrasubsetT2) =>
% 106.14/14.41 ((
% 106.14/14.41 (contrasubsetT3) =>
% 106.14/14.41 ((
% 106.14/14.41 (doubleComplementI1) =>
% 106.14/14.41 ((
% 106.14/14.41 (doubleComplementE1) =>
% 106.14/14.41 ((
% 106.14/14.41 (doubleComplementSub1) =>
% 106.14/14.41 ((
% 106.14/14.41 (doubleComplementSub2) =>
% 106.14/14.41 ((
% 106.14/14.41 (doubleComplementEq) =>
% 106.14/14.41 ((
% 106.14/14.41 (complementTnotintersectT) =>
% 106.14/14.41 ((
% 106.14/14.41 (complementImpComplementIntersect) =>
% 106.14/14.41 ((
% 106.14/14.41 (complementSubsetComplementIntersect) =>
% 106.14/14.41 ((
% 106.14/14.41 (complementInPowersetComplementIntersect) =>
% 106.14/14.41 ((
% 106.14/14.41 (contraSubsetComplement) =>
% 106.14/14.41 ((
% 106.14/14.41 (complementTcontraSubset) =>
% 106.14/14.41 ((
% 106.14/14.41 (binunionTILcontra) =>
% 106.14/14.41 ((
% 106.14/14.41 (binunionTIRcontra) =>
% 106.14/14.41 ((
% 106.14/14.41 (inIntersectImpInUnion) =>
% 106.14/14.41 ((
% 106.14/14.41 (inIntersectImpInUnion2) =>
% 106.14/14.41 ((
% 106.14/14.41 (inIntersectImpInIntersectUnions) =>
% 106.14/14.41 ((
% 106.14/14.41 (intersectInPowersetIntersectUnions) =>
% 106.14/14.41 ((
% 106.14/14.41 (inComplementUnionImpNotIn1) =>
% 106.14/14.41 ((
% 106.14/14.41 (inComplementUnionImpInComplement1) =>
% 106.14/14.41 ((
% 106.14/14.41 (binunionTE) =>
% 106.14/14.41 ((
% 106.14/14.41 (binunionTEcontra) =>
% 106.14/14.41 ((
% 106.14/14.41 (demorgan2a1) =>
% 106.14/14.41 ((
% 106.14/14.41 (complementUnionInPowersetComplement) =>
% 106.14/14.41 ((
% 106.14/14.41 (demorgan2a2) =>
% 106.14/14.41 ((
% 106.14/14.41 (demorgan1a) =>
% 106.14/14.41 ((
% 106.14/14.41 (demorgan1b) =>
% 106.14/14.41 ((
% 106.14/14.41 (demorgan1) =>
% 106.14/14.41 ((
% 106.14/14.41 (demorgan2a) =>
% 106.14/14.41 ((
% 106.14/14.41 (demorgan2b2) =>
% 106.14/14.41 ((
% 106.14/14.41 (demorgan2b) =>
% 106.14/14.41 ((
% 106.14/14.41 (demorgan2) =>
% 106.14/14.41 ((
% 106.14/14.41 (woz13rule0) =>
% 106.14/14.41 ((
% 106.14/14.41 (woz13rule1) =>
% 106.14/14.41 ((
% 106.14/14.41 (woz13rule2) =>
% 106.14/14.41 ((
% 106.14/14.41 (woz13rule3) =>
% 106.14/14.41 ((
% 106.14/14.41 (woz13rule4) =>
% 106.14/14.41 ((
% 106.14/14.41 (woz1_1) =>
% 106.14/14.41 ((
% 106.14/14.41 (woz1_2) =>
% 106.14/14.41 ((
% 106.14/14.41 (woz1_3) =>
% 106.14/14.41 ((
% 106.14/14.41 (woz1_4) =>
% 106.14/14.41 ((
% 106.14/14.41 (woz1_5) =>
% 106.14/14.41 ((
% 106.14/14.41 (breln1all2) =>
% 106.14/14.41 ((
% 106.14/14.41 (breln1SetBreln1) =>
% 106.14/14.41 ((
% 106.14/14.41 (choice2fnsingleton) =>
% 106.14/14.41 ((
% 106.14/14.41 (setOfPairsIsBReln1) =>
% 106.14/14.41 ((
% 106.14/14.41 (breln1all1) =>
% 106.14/14.41 ((
% 106.14/14.41 (subbreln1) =>
% 106.14/14.41 ((
% 106.14/14.41 (eqbreln1) =>
% 106.14/14.41 ((
% 106.14/14.41 (breln1invprop) =>
% 106.14/14.41 ((
% 106.14/14.41 (breln1invI) =>
% 106.14/14.41 ((
% 106.14/14.41 (breln1invE) =>
% 106.14/14.41 ((
% 106.14/14.41 (breln1compprop) =>
% 106.14/14.41 ((
% 106.14/14.41 (breln1compI) =>
% 106.14/14.41 ((
% 106.14/14.41 (breln1compE) =>
% 106.14/14.41 ((
% 106.14/14.41 (breln1compEex) =>
% 106.14/14.41 ((
% 106.14/14.41 (breln1unionprop) =>
% 106.14/14.41 ((
% 106.14/14.41 (breln1unionIL) =>
% 106.14/14.41 ((
% 106.14/14.41 (breln1unionIR) =>
% 106.14/14.41 ((
% 106.14/14.41 (breln1unionI) =>
% 106.14/14.41 ((
% 106.14/14.41 (breln1unionE) =>
% 106.14/14.41 ((
% 106.14/14.41 (breln1unionEcases) =>
% 106.14/14.41 ((
% 106.14/14.41 (breln1unionCommutes) =>
% 106.14/14.41 ((
% 106.14/14.41 (woz2Ex) =>
% 106.14/14.41 ((
% 106.14/14.41 (woz2W) =>
% 106.14/14.41 ((
% 106.14/14.41 (woz2A) =>
% 106.14/14.41 ((
% 106.14/14.41 (woz2B) =>
% 106.14/14.41 ((
% 106.14/14.41 (image1Ex) =>
% 106.14/14.41 ((
% 106.14/14.41 (image1Ex1) =>
% 106.14/14.41 ((
% 106.14/14.41 (image1Equiv) =>
% 106.14/14.41 ((
% 106.14/14.41 (image1E) =>
% 106.14/14.41 ((
% 106.14/14.41 (image1I) =>
% 106.14/14.41 ((
% 106.14/14.41 (injFuncInInjFuncSet) =>
% 106.14/14.41 ((
% 106.14/14.41 (injFuncSetFuncIn) =>
% 106.14/14.41 ((
% 106.14/14.41 (injFuncSetFuncInj) =>
% 106.14/14.41 ((
% 106.14/14.41 (surjFuncSetFuncIn) =>
% 106.14/14.41 ((
% 106.14/14.41 (surjFuncSetFuncSurj) =>
% 106.14/14.41 ((
% 106.14/14.41 (leftInvIsSurj) =>
% 106.14/14.41 ((
% 106.14/14.41 (surjCantorThm) =>
% 106.14/14.41 ((
% 106.14/14.41 (!!) @ (
% 106.14/14.41 (('#S') @ (
% 106.14/14.41 (
% 106.14/14.41 ('#B') @ (
% 106.14/14.41 =>) @
% 106.14/14.41 nonempty)) @
% 106.14/14.41 (
% 106.14/14.41 (
% 106.14/14.41 ('#B') @ (
% 106.14/14.41 ??) @
% 106.14/14.41 (
% 106.14/14.41 (
% 106.14/14.41 ('#S') @ (
% 106.14/14.41 (
% 106.14/14.41 ('#B') @ (
% 106.14/14.41 '#S') @
% 106.14/14.41 (
% 106.14/14.41 (
% 106.14/14.41 ('#B') @ (
% 106.14/14.41 (
% 106.14/14.41 ('#B') @ (
% 106.14/14.41 &))) @
% 106.14/14.41 (
% 106.14/14.41 (
% 106.14/14.41 ('#C') @ in)))))) @
% 106.14/14.41 (
% 106.14/14.41 (
% 106.14/14.41 ('#C') @ (
% 106.14/14.41 (
% 106.14/14.41 ('#B') @ (
% 106.14/14.41 '#C') @
% 106.14/14.41 (
% 106.14/14.41 (
% 106.14/14.41 ('#B') @ (
% 106.14/14.41 (
% 106.14/14.41 ('#B') @ (
% 106.14/14.41 =))) @
% 106.14/14.41 (
% 106.14/14.41 (
% 106.14/14.41 ('#C') @ binintersect)))))) @
% 106.14/14.41 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.14/14.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl174])).
% 106.14/14.41 thf(zip_derived_cl206, plain,
% 106.14/14.41 (~ (((setext) =>
% 106.14/14.41 (((emptyI) =>
% 106.14/14.41 (((noeltsimpempty) =>
% 106.14/14.41 (((setbeta) =>
% 106.14/14.41 (((nonemptyE1) =>
% 106.14/14.41 (((nonemptyI) =>
% 106.14/14.41 (((nonemptyI1) =>
% 106.14/14.41 (((setadjoinIL) =>
% 106.14/14.41 (((in @ emptyset @
% 106.14/14.41 (setadjoin @ emptyset @ emptyset)) =>
% 106.14/14.41 (((setadjoinIR) =>
% 106.14/14.41 (((setadjoinE) =>
% 106.14/14.41 (((setadjoinOr) =>
% 106.14/14.41 (((setoftrueEq) =>
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% 106.65/14.41 '#S') @
% 106.65/14.41 (
% 106.65/14.41 (
% 106.65/14.41 ('#B') @ (
% 106.65/14.41 (
% 106.65/14.41 ('#B') @ (
% 106.65/14.41 &))) @
% 106.65/14.41 (
% 106.65/14.41 (
% 106.65/14.41 ('#C') @ in)))))) @
% 106.65/14.41 (
% 106.65/14.41 (
% 106.65/14.41 ('#C') @ (
% 106.65/14.41 (
% 106.65/14.41 ('#B') @ (
% 106.65/14.41 '#C') @
% 106.65/14.41 (
% 106.65/14.41 (
% 106.65/14.41 ('#B') @ (
% 106.65/14.41 (
% 106.65/14.41 ('#B') @ (
% 106.65/14.41 =))) @
% 106.65/14.41 (
% 106.65/14.41 (
% 106.65/14.41 ('#C') @ binintersect)))))) @
% 106.65/14.41 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.65/14.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl189])).
% 106.65/14.41 thf(zip_derived_cl222, plain,
% 106.65/14.41 (~ (((emptyI) =>
% 106.65/14.41 (((noeltsimpempty) =>
% 106.65/14.41 (((setbeta) =>
% 106.65/14.41 (((nonemptyE1) =>
% 106.65/14.41 (((nonemptyI) =>
% 106.65/14.41 (((nonemptyI1) =>
% 106.65/14.41 (((setadjoinIL) =>
% 106.65/14.41 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 106.65/14.41 (((setadjoinIR) =>
% 106.65/14.41 (((setadjoinE) =>
% 106.65/14.41 (((setadjoinOr) =>
% 106.65/14.41 (((setoftrueEq) =>
% 106.65/14.41 (((powersetI) =>
% 106.65/14.41 (((emptyinPowerset) =>
% 106.65/14.41 (((emptyInPowerset) =>
% 106.65/14.41 (((powersetE) =>
% 106.65/14.41 (((setunionI) =>
% 106.65/14.41 (((setunionE) =>
% 106.65/14.41 (((subPowSU) =>
% 106.65/14.41 (((exuE2) =>
% 106.65/14.41 (((nonemptyImpWitness) =>
% 106.65/14.41 (((uniqinunit) =>
% 106.65/14.41 (((notinsingleton) =>
% 106.65/14.41 (((eqinunit) =>
% 106.65/14.41 (((singletonsswitch) =>
% 106.65/14.41 (((upairsetE) =>
% 106.65/14.41 (((upairsetIL) =>
% 106.65/14.41 (((upairsetIR) =>
% 106.65/14.41 (((emptyE1) =>
% 106.65/14.41 (((vacuousDall) =>
% 106.65/14.41 ((
% 106.65/14.41 (quantDeMorgan1) =>
% 106.65/14.41 ((
% 106.65/14.41 (quantDeMorgan2) =>
% 106.65/14.41 ((
% 106.65/14.41 (quantDeMorgan3) =>
% 106.65/14.41 ((
% 106.65/14.41 (quantDeMorgan4) =>
% 106.65/14.41 ((
% 106.65/14.41 (prop2setI) =>
% 106.65/14.41 ((
% 106.65/14.41 (prop2set2propI) =>
% 106.65/14.41 ((
% 106.65/14.41 (notdexE) =>
% 106.65/14.41 ((
% 106.65/14.41 (notdallE) =>
% 106.65/14.41 ((
% 106.65/14.41 (exuI1) =>
% 106.65/14.41 ((
% 106.65/14.41 (exuI3) =>
% 106.65/14.41 ((
% 106.65/14.41 (exuI2) =>
% 106.65/14.41 ((
% 106.65/14.41 (inCongP) =>
% 106.65/14.41 ((
% 106.65/14.41 (in__Cong) =>
% 106.65/14.41 ((
% 106.65/14.41 (exuE3u) =>
% 106.65/14.41 ((
% 106.65/14.41 (exu__Cong) =>
% 106.65/14.41 ((
% 106.65/14.41 (setadjoin__Cong) =>
% 106.65/14.41 ((
% 106.65/14.41 (powerset__Cong) =>
% 106.65/14.41 ((
% 106.65/14.41 (setunion__Cong) =>
% 106.65/14.41 ((
% 106.65/14.41 (exuEu) =>
% 106.65/14.41 ((
% 106.65/14.41 (descr__Cong) =>
% 106.65/14.41 ((
% 106.65/14.41 (dsetconstr__Cong) =>
% 106.65/14.41 ((
% 106.65/14.41 (subsetI1) =>
% 106.65/14.41 ((
% 106.65/14.41 (eqimpsubset2) =>
% 106.65/14.41 ((
% 106.65/14.41 (eqimpsubset1) =>
% 106.65/14.41 ((
% 106.65/14.41 (subsetI2) =>
% 106.65/14.41 ((
% 106.65/14.41 (emptysetsubset) =>
% 106.65/14.41 ((
% 106.65/14.41 (subsetE) =>
% 106.65/14.41 ((
% 106.65/14.41 (subsetE2) =>
% 106.65/14.41 ((
% 106.65/14.41 (notsubsetI) =>
% 106.65/14.41 ((
% 106.65/14.41 (notequalI1) =>
% 106.65/14.41 ((
% 106.65/14.41 (notequalI2) =>
% 106.65/14.41 ((
% 106.65/14.41 (subsetRefl) =>
% 106.65/14.41 ((
% 106.65/14.41 (subsetTrans) =>
% 106.65/14.41 ((
% 106.65/14.41 (setadjoinSub) =>
% 106.65/14.41 ((
% 106.65/14.41 (setadjoinSub2) =>
% 106.65/14.41 ((
% 106.65/14.41 (subset2powerset) =>
% 106.65/14.41 ((
% 106.65/14.41 (setextsub) =>
% 106.65/14.41 ((
% 106.65/14.41 (subsetemptysetimpeq) =>
% 106.65/14.41 ((
% 106.65/14.41 (powersetI1) =>
% 106.65/14.41 ((
% 106.65/14.41 (powersetE1) =>
% 106.65/14.41 ((
% 106.65/14.41 (inPowerset) =>
% 106.65/14.41 ((
% 106.65/14.41 (powersetsubset) =>
% 106.65/14.41 ((
% 106.65/14.41 (sepInPowerset) =>
% 106.65/14.41 ((
% 106.65/14.41 (sepSubset) =>
% 106.65/14.41 ((
% 106.65/14.41 (binunionIL) =>
% 106.65/14.41 ((
% 106.65/14.41 (upairset2IR) =>
% 106.65/14.41 ((
% 106.65/14.41 (binunionIR) =>
% 106.65/14.41 ((
% 106.65/14.41 (binunionEcases) =>
% 106.65/14.41 ((
% 106.65/14.41 (binunionE) =>
% 106.65/14.41 ((
% 106.65/14.41 (binunionLsub) =>
% 106.65/14.41 ((
% 106.65/14.41 (binunionRsub) =>
% 106.65/14.41 ((
% 106.65/14.41 (binintersectI) =>
% 106.65/14.41 ((
% 106.65/14.41 (binintersectSubset5) =>
% 106.65/14.41 ((
% 106.65/14.41 (binintersectEL) =>
% 106.65/14.41 ((
% 106.65/14.41 (binintersectLsub) =>
% 106.65/14.41 ((
% 106.65/14.41 (binintersectSubset2) =>
% 106.65/14.41 ((
% 106.65/14.41 (binintersectSubset3) =>
% 106.65/14.41 ((
% 106.65/14.41 (binintersectER) =>
% 106.65/14.41 ((
% 106.65/14.41 (disjointsetsI1) =>
% 106.65/14.41 ((
% 106.65/14.41 (binintersectRsub) =>
% 106.65/14.41 ((
% 106.65/14.41 (binintersectSubset4) =>
% 106.65/14.41 ((
% 106.65/14.41 (binintersectSubset1) =>
% 106.65/14.41 ((
% 106.65/14.41 (bs114d) =>
% 106.65/14.41 ((
% 106.65/14.41 (setminusI) =>
% 106.65/14.41 ((
% 106.65/14.41 (setminusEL) =>
% 106.65/14.41 ((
% 106.65/14.41 (setminusER) =>
% 106.65/14.41 ((
% 106.65/14.41 (setminusSubset2) =>
% 106.65/14.41 ((
% 106.65/14.41 (setminusERneg) =>
% 106.65/14.41 ((
% 106.65/14.41 (setminusELneg) =>
% 106.65/14.41 ((
% 106.65/14.41 (setminusILneg) =>
% 106.65/14.41 ((
% 106.65/14.41 (setminusIRneg) =>
% 106.65/14.41 ((
% 106.65/14.41 (setminusLsub) =>
% 106.65/14.41 ((
% 106.65/14.41 (setminusSubset1) =>
% 106.65/14.41 ((
% 106.65/14.41 (symdiffE) =>
% 106.65/14.41 ((
% 106.65/14.41 (symdiffI1) =>
% 106.65/14.41 ((
% 106.65/14.41 (symdiffI2) =>
% 106.65/14.41 ((
% 106.65/14.41 (symdiffIneg1) =>
% 106.65/14.41 ((
% 106.65/14.41 (symdiffIneg2) =>
% 106.65/14.41 ((
% 106.65/14.41 (secondinupair) =>
% 106.65/14.41 ((
% 106.65/14.41 (setukpairIL) =>
% 106.65/14.41 ((
% 106.65/14.41 (setukpairIR) =>
% 106.65/14.41 ((
% 106.65/14.41 (kpairiskpair) =>
% 106.65/14.41 ((
% 106.65/14.41 (kpairp) =>
% 106.65/14.41 ((
% 106.65/14.41 (singletonsubset) =>
% 106.65/14.41 ((
% 106.65/14.41 (singletoninpowerset) =>
% 106.65/14.41 ((
% 106.65/14.41 (singletoninpowunion) =>
% 106.65/14.41 ((
% 106.65/14.41 (upairset2E) =>
% 106.65/14.41 ((
% 106.65/14.41 (upairsubunion) =>
% 106.65/14.41 ((
% 106.65/14.41 (upairinpowunion) =>
% 106.65/14.41 ((
% 106.65/14.41 (ubforcartprodlem1) =>
% 106.65/14.41 ((
% 106.65/14.41 (ubforcartprodlem2) =>
% 106.65/14.41 ((
% 106.65/14.41 (ubforcartprodlem3) =>
% 106.65/14.41 ((
% 106.65/14.41 (cartprodpairin) =>
% 106.65/14.41 ((
% 106.65/14.41 (cartprodmempair1) =>
% 106.65/14.41 ((
% 106.65/14.41 (cartprodmempair) =>
% 106.65/14.41 ((
% 106.65/14.41 (setunionE2) =>
% 106.65/14.41 ((
% 106.65/14.41 (setunionsingleton1) =>
% 106.65/14.41 ((
% 106.65/14.41 (setunionsingleton2) =>
% 106.65/14.41 ((
% 106.65/14.41 (setunionsingleton) =>
% 106.65/14.41 ((
% 106.65/14.41 (singletonprop) =>
% 106.65/14.41 ((
% 106.65/14.41 (ex1E1) =>
% 106.65/14.41 ((
% 106.65/14.41 (ex1I) =>
% 106.65/14.41 ((
% 106.65/14.41 (ex1I2) =>
% 106.65/14.41 ((
% 106.65/14.41 (singletonsuniq) =>
% 106.65/14.41 ((
% 106.65/14.41 (setukpairinjL1) =>
% 106.65/14.41 ((
% 106.65/14.41 (kfstsingleton) =>
% 106.65/14.41 ((
% 106.65/14.41 (theprop) =>
% 106.65/14.41 ((
% 106.65/14.41 (kfstpairEq) =>
% 106.65/14.41 ((
% 106.65/14.41 (cartprodfstin) =>
% 106.65/14.41 ((
% 106.65/14.41 (setukpairinjL2) =>
% 106.65/14.41 ((
% 106.65/14.41 (setukpairinjL) =>
% 106.65/14.41 ((
% 106.65/14.41 (setukpairinjR11) =>
% 106.65/14.41 ((
% 106.65/14.41 (setukpairinjR12) =>
% 106.65/14.41 ((
% 106.65/14.41 (setukpairinjR1) =>
% 106.65/14.41 ((
% 106.65/14.41 (upairequniteq) =>
% 106.65/14.41 ((
% 106.65/14.41 (setukpairinjR2) =>
% 106.65/14.41 ((
% 106.65/14.41 (setukpairinjR) =>
% 106.65/14.41 ((
% 106.65/14.41 (ksndsingleton) =>
% 106.65/14.41 ((
% 106.65/14.41 (ksndpairEq) =>
% 106.65/14.41 ((
% 106.65/14.41 (kpairsurjEq) =>
% 106.65/14.41 ((
% 106.65/14.41 (cartprodsndin) =>
% 106.65/14.41 ((
% 106.65/14.41 (cartprodpairmemEL) =>
% 106.65/14.41 ((
% 106.65/14.41 (cartprodpairmemER) =>
% 106.65/14.41 ((
% 106.65/14.41 (cartprodmempaircEq) =>
% 106.65/14.41 ((
% 106.65/14.41 (cartprodfstpairEq) =>
% 106.65/14.41 ((
% 106.65/14.41 (cartprodsndpairEq) =>
% 106.65/14.41 ((
% 106.65/14.41 (cartprodpairsurjEq) =>
% 106.65/14.41 ((
% 106.65/14.41 (dpsetconstrI) =>
% 106.65/14.41 ((
% 106.65/14.41 (dpsetconstrSub) =>
% 106.65/14.41 ((
% 106.65/14.41 (setOfPairsIsBReln) =>
% 106.65/14.41 ((
% 106.65/14.41 (dpsetconstrERa) =>
% 106.65/14.41 ((
% 106.65/14.41 (dpsetconstrEL1) =>
% 106.65/14.41 ((
% 106.65/14.41 (dpsetconstrEL2) =>
% 106.65/14.41 ((
% 106.65/14.41 (dpsetconstrER) =>
% 106.65/14.41 ((
% 106.65/14.41 (funcImageSingleton) =>
% 106.65/14.41 ((
% 106.65/14.41 (apProp) =>
% 106.65/14.41 ((
% 106.65/14.41 (app) =>
% 106.65/14.41 ((
% 106.65/14.41 (infuncsetfunc) =>
% 106.65/14.41 ((
% 106.65/14.41 (ap2p) =>
% 106.65/14.41 ((
% 106.65/14.41 (funcinfuncset) =>
% 106.65/14.41 ((
% 106.65/14.41 (lamProp) =>
% 106.65/14.41 ((
% 106.65/14.41 (lamp) =>
% 106.65/14.41 ((
% 106.65/14.41 (lam2p) =>
% 106.65/14.41 ((
% 106.65/14.41 (brelnall1) =>
% 106.65/14.41 ((
% 106.65/14.41 (brelnall2) =>
% 106.65/14.41 ((
% 106.65/14.41 (ex1E2) =>
% 106.65/14.41 ((
% 106.65/14.41 (funcGraphProp1) =>
% 106.65/14.41 ((
% 106.65/14.41 (funcGraphProp3) =>
% 106.65/14.41 ((
% 106.65/14.41 (funcGraphProp2) =>
% 106.65/14.41 ((
% 106.65/14.41 (funcextLem) =>
% 106.65/14.41 ((
% 106.65/14.41 (funcGraphProp4) =>
% 106.65/14.41 ((
% 106.65/14.41 (subbreln) =>
% 106.65/14.41 ((
% 106.65/14.41 (eqbreln) =>
% 106.65/14.41 ((
% 106.65/14.41 (funcext) =>
% 106.65/14.41 ((
% 106.65/14.41 (funcext2) =>
% 106.65/14.41 ((
% 106.65/14.41 (ap2apEq1) =>
% 106.65/14.41 ((
% 106.65/14.41 (ap2apEq2) =>
% 106.65/14.41 ((
% 106.65/14.41 (beta1) =>
% 106.65/14.41 ((
% 106.65/14.41 (eta1) =>
% 106.65/14.41 ((
% 106.65/14.41 (lam2lamEq) =>
% 106.65/14.41 ((
% 106.65/14.41 (beta2) =>
% 106.65/14.41 ((
% 106.65/14.41 (eta2) =>
% 106.65/14.41 ((
% 106.65/14.41 (iffalseProp1) =>
% 106.65/14.41 ((
% 106.65/14.41 (iffalseProp2) =>
% 106.65/14.41 ((
% 106.65/14.41 (iftrueProp1) =>
% 106.65/14.41 ((
% 106.65/14.41 (iftrueProp2) =>
% 106.65/14.41 ((
% 106.65/14.41 (ifSingleton) =>
% 106.65/14.41 ((
% 106.65/14.41 (ifp) =>
% 106.65/14.41 ((
% 106.65/14.41 (theeq) =>
% 106.65/14.41 ((
% 106.65/14.41 (iftrue) =>
% 106.65/14.41 ((
% 106.65/14.41 (iffalse) =>
% 106.65/14.41 ((
% 106.65/14.41 (iftrueorfalse) =>
% 106.65/14.41 ((
% 106.65/14.41 (binintersectT_lem) =>
% 106.65/14.41 ((
% 106.65/14.41 (binunionT_lem) =>
% 106.65/14.41 ((
% 106.65/14.41 (powersetT_lem) =>
% 106.65/14.41 ((
% 106.65/14.41 (setminusT_lem) =>
% 106.65/14.41 ((
% 106.65/14.41 (complementT_lem) =>
% 106.65/14.41 ((
% 106.65/14.41 (setextT) =>
% 106.65/14.41 ((
% 106.65/14.41 (subsetTI) =>
% 106.65/14.41 ((
% 106.65/14.41 (powersetTI1) =>
% 106.65/14.41 ((
% 106.65/14.41 (powersetTE1) =>
% 106.65/14.41 ((
% 106.65/14.41 (complementTI1) =>
% 106.65/14.41 ((
% 106.65/14.41 (complementTE1) =>
% 106.65/14.41 ((
% 106.65/14.41 (binintersectTELcontra) =>
% 106.65/14.41 ((
% 106.65/14.41 (binintersectTERcontra) =>
% 106.65/14.41 ((
% 106.65/14.41 (contrasubsetT) =>
% 106.65/14.41 ((
% 106.65/14.41 (contrasubsetT1) =>
% 106.65/14.41 ((
% 106.65/14.41 (contrasubsetT2) =>
% 106.65/14.41 ((
% 106.65/14.41 (contrasubsetT3) =>
% 106.65/14.41 ((
% 106.65/14.41 (doubleComplementI1) =>
% 106.65/14.41 ((
% 106.65/14.41 (doubleComplementE1) =>
% 106.65/14.41 ((
% 106.65/14.41 (doubleComplementSub1) =>
% 106.65/14.41 ((
% 106.65/14.41 (doubleComplementSub2) =>
% 106.65/14.41 ((
% 106.65/14.41 (doubleComplementEq) =>
% 106.65/14.41 ((
% 106.65/14.41 (complementTnotintersectT) =>
% 106.65/14.41 ((
% 106.65/14.41 (complementImpComplementIntersect) =>
% 106.65/14.41 ((
% 106.65/14.41 (complementSubsetComplementIntersect) =>
% 106.65/14.41 ((
% 106.65/14.41 (complementInPowersetComplementIntersect) =>
% 106.65/14.41 ((
% 106.65/14.41 (contraSubsetComplement) =>
% 106.65/14.41 ((
% 106.65/14.41 (complementTcontraSubset) =>
% 106.65/14.41 ((
% 106.65/14.41 (binunionTILcontra) =>
% 106.65/14.41 ((
% 106.65/14.41 (binunionTIRcontra) =>
% 106.65/14.41 ((
% 106.65/14.41 (inIntersectImpInUnion) =>
% 106.65/14.41 ((
% 106.65/14.41 (inIntersectImpInUnion2) =>
% 106.65/14.41 ((
% 106.65/14.41 (inIntersectImpInIntersectUnions) =>
% 106.65/14.41 ((
% 106.65/14.41 (intersectInPowersetIntersectUnions) =>
% 106.65/14.41 ((
% 106.65/14.41 (inComplementUnionImpNotIn1) =>
% 106.65/14.41 ((
% 106.65/14.41 (inComplementUnionImpInComplement1) =>
% 106.65/14.41 ((
% 106.65/14.41 (binunionTE) =>
% 106.65/14.41 ((
% 106.65/14.41 (binunionTEcontra) =>
% 106.65/14.41 ((
% 106.65/14.41 (demorgan2a1) =>
% 106.65/14.41 ((
% 106.65/14.41 (complementUnionInPowersetComplement) =>
% 106.65/14.41 ((
% 106.65/14.41 (demorgan2a2) =>
% 106.65/14.41 ((
% 106.65/14.41 (demorgan1a) =>
% 106.65/14.41 ((
% 106.65/14.41 (demorgan1b) =>
% 106.65/14.41 ((
% 106.65/14.41 (demorgan1) =>
% 106.65/14.41 ((
% 106.65/14.41 (demorgan2a) =>
% 106.65/14.41 ((
% 106.65/14.41 (demorgan2b2) =>
% 106.65/14.41 ((
% 106.65/14.41 (demorgan2b) =>
% 106.65/14.41 ((
% 106.65/14.41 (demorgan2) =>
% 106.65/14.41 ((
% 106.65/14.41 (woz13rule0) =>
% 106.65/14.41 ((
% 106.65/14.41 (woz13rule1) =>
% 106.65/14.41 ((
% 106.65/14.41 (woz13rule2) =>
% 106.65/14.41 ((
% 106.65/14.41 (woz13rule3) =>
% 106.65/14.41 ((
% 106.65/14.41 (woz13rule4) =>
% 106.65/14.41 ((
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% 106.65/14.41 ((
% 106.65/14.41 (woz1_2) =>
% 106.65/14.41 ((
% 106.65/14.41 (woz1_3) =>
% 106.65/14.41 ((
% 106.65/14.41 (woz1_4) =>
% 106.65/14.41 ((
% 106.65/14.41 (woz1_5) =>
% 106.65/14.41 ((
% 106.65/14.41 (breln1all2) =>
% 106.65/14.41 ((
% 106.65/14.41 (breln1SetBreln1) =>
% 106.65/14.41 ((
% 106.65/14.41 (choice2fnsingleton) =>
% 106.65/14.41 ((
% 106.65/14.41 (setOfPairsIsBReln1) =>
% 106.65/14.41 ((
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% 106.65/14.41 ((
% 106.65/14.41 (subbreln1) =>
% 106.65/14.41 ((
% 106.65/14.41 (eqbreln1) =>
% 106.65/14.41 ((
% 106.65/14.41 (breln1invprop) =>
% 106.65/14.41 ((
% 106.65/14.41 (breln1invI) =>
% 106.65/14.41 ((
% 106.65/14.41 (breln1invE) =>
% 106.65/14.41 ((
% 106.65/14.41 (breln1compprop) =>
% 106.65/14.41 ((
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% 106.65/14.41 ((
% 106.65/14.41 (breln1compE) =>
% 106.65/14.41 ((
% 106.65/14.41 (breln1compEex) =>
% 106.65/14.41 ((
% 106.65/14.41 (breln1unionprop) =>
% 106.65/14.41 ((
% 106.65/14.41 (breln1unionIL) =>
% 106.65/14.41 ((
% 106.65/14.41 (breln1unionIR) =>
% 106.65/14.41 ((
% 106.65/14.41 (breln1unionI) =>
% 106.65/14.41 ((
% 106.65/14.41 (breln1unionE) =>
% 106.65/14.41 ((
% 106.65/14.41 (breln1unionEcases) =>
% 106.65/14.41 ((
% 106.65/14.41 (breln1unionCommutes) =>
% 106.65/14.41 ((
% 106.65/14.41 (woz2Ex) =>
% 106.65/14.41 ((
% 106.65/14.41 (woz2W) =>
% 106.65/14.41 ((
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% 106.65/14.41 ((
% 106.65/14.41 (woz2B) =>
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% 106.65/14.41 ((
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% 106.65/14.41 ((
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% 106.65/14.41 ((
% 106.65/14.41 (image1E) =>
% 106.65/14.41 ((
% 106.65/14.41 (image1I) =>
% 106.65/14.41 ((
% 106.65/14.41 (injFuncInInjFuncSet) =>
% 106.65/14.41 ((
% 106.65/14.41 (injFuncSetFuncIn) =>
% 106.65/14.41 ((
% 106.65/14.41 (injFuncSetFuncInj) =>
% 106.65/14.41 ((
% 106.65/14.41 (surjFuncSetFuncIn) =>
% 106.65/14.41 ((
% 106.65/14.41 (surjFuncSetFuncSurj) =>
% 106.65/14.41 ((
% 106.65/14.41 (leftInvIsSurj) =>
% 106.65/14.41 ((
% 106.65/14.41 (surjCantorThm) =>
% 106.65/14.41 ((
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% 106.65/14.41 (('#S') @ (
% 106.65/14.41 (
% 106.65/14.41 ('#B') @ (
% 106.65/14.41 =>) @
% 106.65/14.41 nonempty)) @
% 106.65/14.41 (
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% 106.65/14.41 ('#B') @ (
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% 106.65/14.41 (
% 106.65/14.41 (
% 106.65/14.41 ('#C') @ (
% 106.65/14.41 (
% 106.65/14.41 ('#B') @ (
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% 106.65/14.41 (
% 106.65/14.41 ('#B') @ (
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% 106.65/14.41 =))) @
% 106.65/14.41 (
% 106.65/14.41 (
% 106.65/14.41 ('#C') @ binintersect)))))) @
% 106.65/14.41 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.65/14.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl206])).
% 106.65/14.41 thf(zip_derived_cl236, plain,
% 106.65/14.41 (~ (((noeltsimpempty) =>
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% 106.65/14.41 (quantDeMorgan2) =>
% 106.65/14.41 ((
% 106.65/14.41 (quantDeMorgan3) =>
% 106.65/14.41 ((
% 106.65/14.41 (quantDeMorgan4) =>
% 106.65/14.41 ((
% 106.65/14.41 (prop2setI) =>
% 106.65/14.41 ((
% 106.65/14.41 (prop2set2propI) =>
% 106.65/14.41 ((
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% 106.65/14.41 ((
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% 106.65/14.41 ((
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% 106.65/14.41 ((
% 106.65/14.41 (exuI3) =>
% 106.65/14.41 ((
% 106.65/14.41 (exuI2) =>
% 106.65/14.41 ((
% 106.65/14.41 (inCongP) =>
% 106.65/14.41 ((
% 106.65/14.41 (in__Cong) =>
% 106.65/14.41 ((
% 106.65/14.41 (exuE3u) =>
% 106.65/14.41 ((
% 106.65/14.41 (exu__Cong) =>
% 106.65/14.41 ((
% 106.65/14.41 (setadjoin__Cong) =>
% 106.65/14.41 ((
% 106.65/14.41 (powerset__Cong) =>
% 106.65/14.41 ((
% 106.65/14.41 (setunion__Cong) =>
% 106.65/14.41 ((
% 106.65/14.41 (exuEu) =>
% 106.65/14.41 ((
% 106.65/14.41 (descr__Cong) =>
% 106.65/14.41 ((
% 106.65/14.41 (dsetconstr__Cong) =>
% 106.65/14.41 ((
% 106.65/14.41 (subsetI1) =>
% 106.65/14.41 ((
% 106.65/14.41 (eqimpsubset2) =>
% 106.65/14.41 ((
% 106.65/14.41 (eqimpsubset1) =>
% 106.65/14.41 ((
% 106.65/14.41 (subsetI2) =>
% 106.65/14.41 ((
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% 106.65/14.41 ((
% 106.65/14.41 (subsetE) =>
% 106.65/14.41 ((
% 106.65/14.41 (subsetE2) =>
% 106.65/14.41 ((
% 106.65/14.41 (notsubsetI) =>
% 106.65/14.41 ((
% 106.65/14.41 (notequalI1) =>
% 106.65/14.41 ((
% 106.65/14.41 (notequalI2) =>
% 106.65/14.41 ((
% 106.65/14.41 (subsetRefl) =>
% 106.65/14.41 ((
% 106.65/14.41 (subsetTrans) =>
% 106.65/14.41 ((
% 106.65/14.41 (setadjoinSub) =>
% 106.65/14.41 ((
% 106.65/14.41 (setadjoinSub2) =>
% 106.65/14.41 ((
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% 106.65/14.41 ((
% 106.65/14.41 (setextsub) =>
% 106.65/14.41 ((
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% 106.65/14.41 ((
% 106.65/14.41 (powersetE1) =>
% 106.65/14.41 ((
% 106.65/14.41 (inPowerset) =>
% 106.65/14.41 ((
% 106.65/14.41 (powersetsubset) =>
% 106.65/14.41 ((
% 106.65/14.41 (sepInPowerset) =>
% 106.65/14.41 ((
% 106.65/14.41 (sepSubset) =>
% 106.65/14.41 ((
% 106.65/14.41 (binunionIL) =>
% 106.65/14.41 ((
% 106.65/14.41 (upairset2IR) =>
% 106.65/14.41 ((
% 106.65/14.41 (binunionIR) =>
% 106.65/14.41 ((
% 106.65/14.41 (binunionEcases) =>
% 106.65/14.41 ((
% 106.65/14.41 (binunionE) =>
% 106.65/14.41 ((
% 106.65/14.41 (binunionLsub) =>
% 106.65/14.41 ((
% 106.65/14.41 (binunionRsub) =>
% 106.65/14.41 ((
% 106.65/14.41 (binintersectI) =>
% 106.65/14.41 ((
% 106.65/14.41 (binintersectSubset5) =>
% 106.65/14.41 ((
% 106.65/14.41 (binintersectEL) =>
% 106.65/14.41 ((
% 106.65/14.41 (binintersectLsub) =>
% 106.65/14.41 ((
% 106.65/14.41 (binintersectSubset2) =>
% 106.65/14.41 ((
% 106.65/14.41 (binintersectSubset3) =>
% 106.65/14.41 ((
% 106.65/14.41 (binintersectER) =>
% 106.65/14.41 ((
% 106.65/14.41 (disjointsetsI1) =>
% 106.65/14.41 ((
% 106.65/14.41 (binintersectRsub) =>
% 106.65/14.41 ((
% 106.65/14.41 (binintersectSubset4) =>
% 106.65/14.41 ((
% 106.65/14.41 (binintersectSubset1) =>
% 106.65/14.41 ((
% 106.65/14.41 (bs114d) =>
% 106.65/14.41 ((
% 106.65/14.41 (setminusI) =>
% 106.65/14.41 ((
% 106.65/14.41 (setminusEL) =>
% 106.65/14.41 ((
% 106.65/14.41 (setminusER) =>
% 106.65/14.41 ((
% 106.65/14.41 (setminusSubset2) =>
% 106.65/14.41 ((
% 106.65/14.41 (setminusERneg) =>
% 106.65/14.41 ((
% 106.65/14.41 (setminusELneg) =>
% 106.65/14.41 ((
% 106.65/14.41 (setminusILneg) =>
% 106.65/14.41 ((
% 106.65/14.41 (setminusIRneg) =>
% 106.65/14.41 ((
% 106.65/14.41 (setminusLsub) =>
% 106.65/14.41 ((
% 106.65/14.41 (setminusSubset1) =>
% 106.65/14.41 ((
% 106.65/14.41 (symdiffE) =>
% 106.65/14.41 ((
% 106.65/14.41 (symdiffI1) =>
% 106.65/14.41 ((
% 106.65/14.41 (symdiffI2) =>
% 106.65/14.41 ((
% 106.65/14.41 (symdiffIneg1) =>
% 106.65/14.41 ((
% 106.65/14.41 (symdiffIneg2) =>
% 106.65/14.41 ((
% 106.65/14.41 (secondinupair) =>
% 106.65/14.41 ((
% 106.65/14.41 (setukpairIL) =>
% 106.65/14.41 ((
% 106.65/14.41 (setukpairIR) =>
% 106.65/14.41 ((
% 106.65/14.41 (kpairiskpair) =>
% 106.65/14.41 ((
% 106.65/14.41 (kpairp) =>
% 106.65/14.41 ((
% 106.65/14.41 (singletonsubset) =>
% 106.65/14.41 ((
% 106.65/14.41 (singletoninpowerset) =>
% 106.65/14.41 ((
% 106.65/14.41 (singletoninpowunion) =>
% 106.65/14.41 ((
% 106.65/14.41 (upairset2E) =>
% 106.65/14.41 ((
% 106.65/14.41 (upairsubunion) =>
% 106.65/14.41 ((
% 106.65/14.41 (upairinpowunion) =>
% 106.65/14.41 ((
% 106.65/14.41 (ubforcartprodlem1) =>
% 106.65/14.41 ((
% 106.65/14.41 (ubforcartprodlem2) =>
% 106.65/14.41 ((
% 106.65/14.41 (ubforcartprodlem3) =>
% 106.65/14.41 ((
% 106.65/14.41 (cartprodpairin) =>
% 106.65/14.41 ((
% 106.65/14.41 (cartprodmempair1) =>
% 106.65/14.41 ((
% 106.65/14.41 (cartprodmempair) =>
% 106.65/14.41 ((
% 106.65/14.41 (setunionE2) =>
% 106.65/14.41 ((
% 106.65/14.41 (setunionsingleton1) =>
% 106.65/14.41 ((
% 106.65/14.41 (setunionsingleton2) =>
% 106.65/14.41 ((
% 106.65/14.41 (setunionsingleton) =>
% 106.65/14.41 ((
% 106.65/14.41 (singletonprop) =>
% 106.65/14.41 ((
% 106.65/14.41 (ex1E1) =>
% 106.65/14.41 ((
% 106.65/14.41 (ex1I) =>
% 106.65/14.41 ((
% 106.65/14.41 (ex1I2) =>
% 106.65/14.41 ((
% 106.65/14.41 (singletonsuniq) =>
% 106.65/14.41 ((
% 106.65/14.41 (setukpairinjL1) =>
% 106.65/14.41 ((
% 106.65/14.41 (kfstsingleton) =>
% 106.65/14.41 ((
% 106.65/14.41 (theprop) =>
% 106.65/14.41 ((
% 106.65/14.41 (kfstpairEq) =>
% 106.65/14.41 ((
% 106.65/14.41 (cartprodfstin) =>
% 106.65/14.41 ((
% 106.65/14.41 (setukpairinjL2) =>
% 106.65/14.41 ((
% 106.65/14.41 (setukpairinjL) =>
% 106.65/14.41 ((
% 106.65/14.41 (setukpairinjR11) =>
% 106.65/14.41 ((
% 106.65/14.41 (setukpairinjR12) =>
% 106.65/14.41 ((
% 106.65/14.41 (setukpairinjR1) =>
% 106.65/14.41 ((
% 106.65/14.41 (upairequniteq) =>
% 106.65/14.41 ((
% 106.65/14.41 (setukpairinjR2) =>
% 106.65/14.41 ((
% 106.65/14.41 (setukpairinjR) =>
% 106.65/14.41 ((
% 106.65/14.41 (ksndsingleton) =>
% 106.65/14.41 ((
% 106.65/14.41 (ksndpairEq) =>
% 106.65/14.41 ((
% 106.65/14.41 (kpairsurjEq) =>
% 106.65/14.41 ((
% 106.65/14.41 (cartprodsndin) =>
% 106.65/14.41 ((
% 106.65/14.41 (cartprodpairmemEL) =>
% 106.65/14.41 ((
% 106.65/14.41 (cartprodpairmemER) =>
% 106.65/14.41 ((
% 106.65/14.41 (cartprodmempaircEq) =>
% 106.65/14.41 ((
% 106.65/14.41 (cartprodfstpairEq) =>
% 106.65/14.41 ((
% 106.65/14.41 (cartprodsndpairEq) =>
% 106.65/14.41 ((
% 106.65/14.41 (cartprodpairsurjEq) =>
% 106.65/14.41 ((
% 106.65/14.41 (dpsetconstrI) =>
% 106.65/14.41 ((
% 106.65/14.41 (dpsetconstrSub) =>
% 106.65/14.41 ((
% 106.65/14.41 (setOfPairsIsBReln) =>
% 106.65/14.41 ((
% 106.65/14.41 (dpsetconstrERa) =>
% 106.65/14.41 ((
% 106.65/14.41 (dpsetconstrEL1) =>
% 106.65/14.41 ((
% 106.65/14.41 (dpsetconstrEL2) =>
% 106.65/14.41 ((
% 106.65/14.41 (dpsetconstrER) =>
% 106.65/14.41 ((
% 106.65/14.41 (funcImageSingleton) =>
% 106.65/14.41 ((
% 106.65/14.41 (apProp) =>
% 106.65/14.41 ((
% 106.65/14.41 (app) =>
% 106.65/14.41 ((
% 106.65/14.41 (infuncsetfunc) =>
% 106.65/14.41 ((
% 106.65/14.41 (ap2p) =>
% 106.65/14.41 ((
% 106.65/14.41 (funcinfuncset) =>
% 106.65/14.41 ((
% 106.65/14.41 (lamProp) =>
% 106.65/14.41 ((
% 106.65/14.41 (lamp) =>
% 106.65/14.41 ((
% 106.65/14.41 (lam2p) =>
% 106.65/14.41 ((
% 106.65/14.41 (brelnall1) =>
% 106.65/14.41 ((
% 106.65/14.41 (brelnall2) =>
% 106.65/14.41 ((
% 106.65/14.41 (ex1E2) =>
% 106.65/14.41 ((
% 106.65/14.41 (funcGraphProp1) =>
% 106.65/14.41 ((
% 106.65/14.41 (funcGraphProp3) =>
% 106.65/14.41 ((
% 106.65/14.41 (funcGraphProp2) =>
% 106.65/14.41 ((
% 106.65/14.41 (funcextLem) =>
% 106.65/14.41 ((
% 106.65/14.41 (funcGraphProp4) =>
% 106.65/14.41 ((
% 106.65/14.41 (subbreln) =>
% 106.65/14.41 ((
% 106.65/14.41 (eqbreln) =>
% 106.65/14.41 ((
% 106.65/14.41 (funcext) =>
% 106.65/14.41 ((
% 106.65/14.41 (funcext2) =>
% 106.65/14.41 ((
% 106.65/14.41 (ap2apEq1) =>
% 106.65/14.41 ((
% 106.65/14.41 (ap2apEq2) =>
% 106.65/14.41 ((
% 106.65/14.41 (beta1) =>
% 106.65/14.41 ((
% 106.65/14.41 (eta1) =>
% 106.65/14.41 ((
% 106.65/14.41 (lam2lamEq) =>
% 106.65/14.41 ((
% 106.65/14.41 (beta2) =>
% 106.65/14.41 ((
% 106.65/14.41 (eta2) =>
% 106.65/14.41 ((
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% 106.65/14.41 ((
% 106.65/14.41 (iffalseProp2) =>
% 106.65/14.41 ((
% 106.65/14.41 (iftrueProp1) =>
% 106.65/14.41 ((
% 106.65/14.41 (iftrueProp2) =>
% 106.65/14.41 ((
% 106.65/14.41 (ifSingleton) =>
% 106.65/14.41 ((
% 106.65/14.41 (ifp) =>
% 106.65/14.41 ((
% 106.65/14.41 (theeq) =>
% 106.65/14.41 ((
% 106.65/14.41 (iftrue) =>
% 106.65/14.41 ((
% 106.65/14.41 (iffalse) =>
% 106.65/14.41 ((
% 106.65/14.41 (iftrueorfalse) =>
% 106.65/14.41 ((
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% 106.65/14.41 ((
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% 106.65/14.41 ((
% 106.65/14.41 (powersetT_lem) =>
% 106.65/14.41 ((
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% 106.65/14.41 ((
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% 106.65/14.41 ((
% 106.65/14.41 (setextT) =>
% 106.65/14.41 ((
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% 106.65/14.41 ((
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% 106.65/14.41 ((
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% 106.65/14.41 ((
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% 106.65/14.41 ((
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% 106.65/14.41 ((
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% 106.65/14.41 ((
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% 106.65/14.41 ((
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% 106.65/14.41 (contrasubsetT3) =>
% 106.65/14.41 ((
% 106.65/14.41 (doubleComplementI1) =>
% 106.65/14.41 ((
% 106.65/14.41 (doubleComplementE1) =>
% 106.65/14.41 ((
% 106.65/14.41 (doubleComplementSub1) =>
% 106.65/14.41 ((
% 106.65/14.41 (doubleComplementSub2) =>
% 106.65/14.41 ((
% 106.65/14.41 (doubleComplementEq) =>
% 106.65/14.41 ((
% 106.65/14.41 (complementTnotintersectT) =>
% 106.65/14.41 ((
% 106.65/14.41 (complementImpComplementIntersect) =>
% 106.65/14.41 ((
% 106.65/14.41 (complementSubsetComplementIntersect) =>
% 106.65/14.41 ((
% 106.65/14.41 (complementInPowersetComplementIntersect) =>
% 106.65/14.41 ((
% 106.65/14.41 (contraSubsetComplement) =>
% 106.65/14.41 ((
% 106.65/14.41 (complementTcontraSubset) =>
% 106.65/14.41 ((
% 106.65/14.41 (binunionTILcontra) =>
% 106.65/14.41 ((
% 106.65/14.41 (binunionTIRcontra) =>
% 106.65/14.41 ((
% 106.65/14.41 (inIntersectImpInUnion) =>
% 106.65/14.41 ((
% 106.65/14.41 (inIntersectImpInUnion2) =>
% 106.65/14.41 ((
% 106.65/14.41 (inIntersectImpInIntersectUnions) =>
% 106.65/14.41 ((
% 106.65/14.41 (intersectInPowersetIntersectUnions) =>
% 106.65/14.41 ((
% 106.65/14.41 (inComplementUnionImpNotIn1) =>
% 106.65/14.41 ((
% 106.65/14.41 (inComplementUnionImpInComplement1) =>
% 106.65/14.41 ((
% 106.65/14.41 (binunionTE) =>
% 106.65/14.41 ((
% 106.65/14.41 (binunionTEcontra) =>
% 106.65/14.41 ((
% 106.65/14.41 (demorgan2a1) =>
% 106.65/14.41 ((
% 106.65/14.41 (complementUnionInPowersetComplement) =>
% 106.65/14.41 ((
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% 106.65/14.41 ((
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% 106.65/14.41 ((
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% 106.65/14.41 ((
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% 106.65/14.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl222])).
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% 106.65/14.41 (exu__Cong) =>
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% 106.65/14.41 (powerset__Cong) =>
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% 106.65/14.41 (exuEu) =>
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% 106.65/14.41 ((
% 106.65/14.41 (ubforcartprodlem2) =>
% 106.65/14.41 ((
% 106.65/14.41 (ubforcartprodlem3) =>
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% 106.65/14.41 (complementInPowersetComplementIntersect) =>
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% 106.65/14.41 (inComplementUnionImpNotIn1) =>
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% 106.65/14.41 (inComplementUnionImpInComplement1) =>
% 106.65/14.41 ((
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% 106.65/14.41 ((
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% 106.65/14.41 ((
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% 106.65/14.41 (demorgan1) =>
% 106.65/14.41 ((
% 106.65/14.41 (demorgan2a) =>
% 106.65/14.41 ((
% 106.65/14.41 (demorgan2b2) =>
% 106.65/14.41 ((
% 106.65/14.41 (demorgan2b) =>
% 106.65/14.41 ((
% 106.65/14.41 (demorgan2) =>
% 106.65/14.41 ((
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% 106.65/14.41 ((
% 106.65/14.41 (woz13rule1) =>
% 106.65/14.41 ((
% 106.65/14.41 (woz13rule2) =>
% 106.65/14.41 ((
% 106.65/14.41 (woz13rule3) =>
% 106.65/14.41 ((
% 106.65/14.41 (woz13rule4) =>
% 106.65/14.41 ((
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% 106.65/14.41 ((
% 106.65/14.41 (woz1_2) =>
% 106.65/14.41 ((
% 106.65/14.41 (woz1_3) =>
% 106.65/14.41 ((
% 106.65/14.41 (woz1_4) =>
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% 106.65/14.41 (woz1_5) =>
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% 106.65/14.41 (breln1SetBreln1) =>
% 106.65/14.41 ((
% 106.65/14.41 (choice2fnsingleton) =>
% 106.65/14.41 ((
% 106.65/14.41 (setOfPairsIsBReln1) =>
% 106.65/14.41 ((
% 106.65/14.41 (breln1all1) =>
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% 106.65/14.41 ((
% 106.65/14.41 (breln1invI) =>
% 106.65/14.41 ((
% 106.65/14.41 (breln1invE) =>
% 106.65/14.41 ((
% 106.65/14.41 (breln1compprop) =>
% 106.65/14.41 ((
% 106.65/14.41 (breln1compI) =>
% 106.65/14.41 ((
% 106.65/14.41 (breln1compE) =>
% 106.65/14.41 ((
% 106.65/14.41 (breln1compEex) =>
% 106.65/14.41 ((
% 106.65/14.41 (breln1unionprop) =>
% 106.65/14.41 ((
% 106.65/14.41 (breln1unionIL) =>
% 106.65/14.41 ((
% 106.65/14.41 (breln1unionIR) =>
% 106.65/14.41 ((
% 106.65/14.41 (breln1unionI) =>
% 106.65/14.41 ((
% 106.65/14.41 (breln1unionE) =>
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% 106.65/14.41 (breln1unionEcases) =>
% 106.65/14.41 ((
% 106.65/14.41 (breln1unionCommutes) =>
% 106.65/14.41 ((
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% 106.65/14.41 ((
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% 106.65/14.41 ((
% 106.65/14.41 (image1E) =>
% 106.65/14.41 ((
% 106.65/14.41 (image1I) =>
% 106.65/14.41 ((
% 106.65/14.41 (injFuncInInjFuncSet) =>
% 106.65/14.41 ((
% 106.65/14.41 (injFuncSetFuncIn) =>
% 106.65/14.41 ((
% 106.65/14.41 (injFuncSetFuncInj) =>
% 106.65/14.41 ((
% 106.65/14.41 (surjFuncSetFuncIn) =>
% 106.65/14.41 ((
% 106.65/14.41 (surjFuncSetFuncSurj) =>
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% 106.65/14.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl236])).
% 106.65/14.41 thf(zip_derived_cl264, plain,
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% 106.65/14.41 ((
% 106.65/14.41 (prop2set2propI) =>
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% 106.65/14.41 ((
% 106.65/14.41 (notdallE) =>
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% 106.65/14.41 ((
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% 106.65/14.41 ((
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% 106.65/14.41 ((
% 106.65/14.41 (in__Cong) =>
% 106.65/14.41 ((
% 106.65/14.41 (exuE3u) =>
% 106.65/14.41 ((
% 106.65/14.41 (exu__Cong) =>
% 106.65/14.41 ((
% 106.65/14.41 (setadjoin__Cong) =>
% 106.65/14.41 ((
% 106.65/14.41 (powerset__Cong) =>
% 106.65/14.41 ((
% 106.65/14.41 (setunion__Cong) =>
% 106.65/14.41 ((
% 106.65/14.41 (exuEu) =>
% 106.65/14.41 ((
% 106.65/14.41 (descr__Cong) =>
% 106.65/14.41 ((
% 106.65/14.41 (dsetconstr__Cong) =>
% 106.65/14.41 ((
% 106.65/14.41 (subsetI1) =>
% 106.65/14.41 ((
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% 106.65/14.41 (subsetE2) =>
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% 106.65/14.41 ((
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% 106.65/14.41 ((
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% 106.65/14.41 ((
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% 106.65/14.41 ((
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% 106.65/14.41 ((
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% 106.65/14.41 ((
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% 106.65/14.41 (binintersectI) =>
% 106.65/14.41 ((
% 106.65/14.41 (binintersectSubset5) =>
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% 106.65/14.41 ((
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% 106.65/14.41 (binintersectSubset2) =>
% 106.65/14.41 ((
% 106.65/14.41 (binintersectSubset3) =>
% 106.65/14.41 ((
% 106.65/14.41 (binintersectER) =>
% 106.65/14.41 ((
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% 106.65/14.41 ((
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% 106.65/14.41 ((
% 106.65/14.41 (setminusER) =>
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% 106.65/14.41 (setminusSubset2) =>
% 106.65/14.41 ((
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% 106.65/14.41 ((
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% 106.65/14.41 ((
% 106.65/14.41 (setminusILneg) =>
% 106.65/14.41 ((
% 106.65/14.41 (setminusIRneg) =>
% 106.65/14.41 ((
% 106.65/14.41 (setminusLsub) =>
% 106.65/14.41 ((
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% 106.65/14.41 ((
% 106.65/14.41 (symdiffE) =>
% 106.65/14.41 ((
% 106.65/14.41 (symdiffI1) =>
% 106.65/14.41 ((
% 106.65/14.41 (symdiffI2) =>
% 106.65/14.41 ((
% 106.65/14.41 (symdiffIneg1) =>
% 106.65/14.41 ((
% 106.65/14.41 (symdiffIneg2) =>
% 106.65/14.41 ((
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% 106.65/14.41 ((
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% 106.65/14.41 ((
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% 106.65/14.41 (kpairp) =>
% 106.65/14.41 ((
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% 106.65/14.41 ((
% 106.65/14.41 (singletoninpowerset) =>
% 106.65/14.41 ((
% 106.65/14.41 (singletoninpowunion) =>
% 106.65/14.41 ((
% 106.65/14.41 (upairset2E) =>
% 106.65/14.41 ((
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% 106.65/14.41 ((
% 106.65/14.41 (upairinpowunion) =>
% 106.65/14.41 ((
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% 106.65/14.41 ((
% 106.65/14.41 (ubforcartprodlem2) =>
% 106.65/14.41 ((
% 106.65/14.41 (ubforcartprodlem3) =>
% 106.65/14.41 ((
% 106.65/14.41 (cartprodpairin) =>
% 106.65/14.41 ((
% 106.65/14.41 (cartprodmempair1) =>
% 106.65/14.41 ((
% 106.65/14.41 (cartprodmempair) =>
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% 106.65/14.41 ((
% 106.65/14.41 (setukpairinjL2) =>
% 106.65/14.41 ((
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% 106.65/14.41 ((
% 106.65/14.41 (setukpairinjR11) =>
% 106.65/14.41 ((
% 106.65/14.41 (setukpairinjR12) =>
% 106.65/14.41 ((
% 106.65/14.41 (setukpairinjR1) =>
% 106.65/14.41 ((
% 106.65/14.41 (upairequniteq) =>
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% 106.65/14.41 ((
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% 106.65/14.41 ((
% 106.65/14.41 (kpairsurjEq) =>
% 106.65/14.41 ((
% 106.65/14.41 (cartprodsndin) =>
% 106.65/14.41 ((
% 106.65/14.41 (cartprodpairmemEL) =>
% 106.65/14.41 ((
% 106.65/14.41 (cartprodpairmemER) =>
% 106.65/14.41 ((
% 106.65/14.41 (cartprodmempaircEq) =>
% 106.65/14.41 ((
% 106.65/14.41 (cartprodfstpairEq) =>
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% 106.65/14.41 (cartprodsndpairEq) =>
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% 106.65/14.41 (cartprodpairsurjEq) =>
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% 106.65/14.41 ((
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% 106.65/14.42 ((
% 106.65/14.42 (doubleComplementE1) =>
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% 106.65/14.42 (inComplementUnionImpInComplement1) =>
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% 106.65/14.42 ((
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% 106.65/14.42 (woz13rule4) =>
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% 106.65/14.42 (woz1_4) =>
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% 106.65/14.42 (breln1SetBreln1) =>
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% 106.65/14.42 (choice2fnsingleton) =>
% 106.65/14.42 ((
% 106.65/14.42 (setOfPairsIsBReln1) =>
% 106.65/14.42 ((
% 106.65/14.42 (breln1all1) =>
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% 106.65/14.42 (subbreln1) =>
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% 106.65/14.42 ((
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% 106.65/14.42 (breln1invE) =>
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% 106.65/14.42 ((
% 106.65/14.42 (breln1compE) =>
% 106.65/14.42 ((
% 106.65/14.42 (breln1compEex) =>
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% 106.65/14.42 (breln1unionprop) =>
% 106.65/14.42 ((
% 106.65/14.42 (breln1unionIL) =>
% 106.65/14.42 ((
% 106.65/14.42 (breln1unionIR) =>
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% 106.65/14.42 (breln1unionI) =>
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% 106.65/14.42 (breln1unionE) =>
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% 106.65/14.42 (breln1unionCommutes) =>
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% 106.65/14.42 ((
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% 106.65/14.42 (image1I) =>
% 106.65/14.42 ((
% 106.65/14.42 (injFuncInInjFuncSet) =>
% 106.65/14.42 ((
% 106.65/14.42 (injFuncSetFuncIn) =>
% 106.65/14.42 ((
% 106.65/14.42 (injFuncSetFuncInj) =>
% 106.65/14.42 ((
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% 106.65/14.42 ((
% 106.65/14.42 (surjFuncSetFuncSurj) =>
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% 106.65/14.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl251])).
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% 106.65/14.42 (prop2set2propI) =>
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% 106.65/14.42 ((
% 106.65/14.42 (exuE3u) =>
% 106.65/14.42 ((
% 106.65/14.42 (exu__Cong) =>
% 106.65/14.42 ((
% 106.65/14.42 (setadjoin__Cong) =>
% 106.65/14.42 ((
% 106.65/14.42 (powerset__Cong) =>
% 106.65/14.42 ((
% 106.65/14.42 (setunion__Cong) =>
% 106.65/14.42 ((
% 106.65/14.42 (exuEu) =>
% 106.65/14.42 ((
% 106.65/14.42 (descr__Cong) =>
% 106.65/14.42 ((
% 106.65/14.42 (dsetconstr__Cong) =>
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% 106.65/14.42 ((
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% 106.65/14.42 ((
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% 106.65/14.42 ((
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% 106.65/14.42 ((
% 106.65/14.42 (singletoninpowunion) =>
% 106.65/14.42 ((
% 106.65/14.42 (upairset2E) =>
% 106.65/14.42 ((
% 106.65/14.42 (upairsubunion) =>
% 106.65/14.42 ((
% 106.65/14.42 (upairinpowunion) =>
% 106.65/14.42 ((
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% 106.65/14.42 ((
% 106.65/14.42 (ubforcartprodlem2) =>
% 106.65/14.42 ((
% 106.65/14.42 (ubforcartprodlem3) =>
% 106.65/14.42 ((
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% 106.65/14.42 ((
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% 106.65/14.42 ((
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% 106.65/14.42 ((
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% 106.65/14.42 (cartprodpairmemER) =>
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% 106.65/14.42 (cartprodmempaircEq) =>
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% 106.65/14.42 (cartprodfstpairEq) =>
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% 106.65/14.42 (funcGraphProp2) =>
% 106.65/14.42 ((
% 106.65/14.42 (funcextLem) =>
% 106.65/14.42 ((
% 106.65/14.42 (funcGraphProp4) =>
% 106.65/14.42 ((
% 106.65/14.42 (subbreln) =>
% 106.65/14.42 ((
% 106.65/14.42 (eqbreln) =>
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% 106.65/14.42 (ap2apEq2) =>
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% 106.65/14.42 (lam2lamEq) =>
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% 106.65/14.42 (beta2) =>
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% 106.65/14.42 (contrasubsetT2) =>
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% 106.65/14.42 (contrasubsetT3) =>
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% 106.65/14.42 ((
% 106.65/14.42 (doubleComplementE1) =>
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% 106.65/14.42 (inComplementUnionImpNotIn1) =>
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% 106.65/14.42 (inComplementUnionImpInComplement1) =>
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% 106.65/14.42 ((
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% 106.65/14.42 (demorgan2) =>
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% 106.65/14.42 ((
% 106.65/14.42 (woz13rule1) =>
% 106.65/14.42 ((
% 106.65/14.42 (woz13rule2) =>
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% 106.65/14.42 (woz13rule3) =>
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% 106.65/14.42 (woz13rule4) =>
% 106.65/14.42 ((
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% 106.65/14.42 ((
% 106.65/14.42 (woz1_2) =>
% 106.65/14.42 ((
% 106.65/14.42 (woz1_3) =>
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% 106.65/14.42 (woz1_4) =>
% 106.65/14.42 ((
% 106.65/14.42 (woz1_5) =>
% 106.65/14.42 ((
% 106.65/14.42 (breln1all2) =>
% 106.65/14.42 ((
% 106.65/14.42 (breln1SetBreln1) =>
% 106.65/14.42 ((
% 106.65/14.42 (choice2fnsingleton) =>
% 106.65/14.42 ((
% 106.65/14.42 (setOfPairsIsBReln1) =>
% 106.65/14.42 ((
% 106.65/14.42 (breln1all1) =>
% 106.65/14.42 ((
% 106.65/14.42 (subbreln1) =>
% 106.65/14.42 ((
% 106.65/14.42 (eqbreln1) =>
% 106.65/14.42 ((
% 106.65/14.42 (breln1invprop) =>
% 106.65/14.42 ((
% 106.65/14.42 (breln1invI) =>
% 106.65/14.42 ((
% 106.65/14.42 (breln1invE) =>
% 106.65/14.42 ((
% 106.65/14.42 (breln1compprop) =>
% 106.65/14.42 ((
% 106.65/14.42 (breln1compI) =>
% 106.65/14.42 ((
% 106.65/14.42 (breln1compE) =>
% 106.65/14.42 ((
% 106.65/14.42 (breln1compEex) =>
% 106.65/14.42 ((
% 106.65/14.42 (breln1unionprop) =>
% 106.65/14.42 ((
% 106.65/14.42 (breln1unionIL) =>
% 106.65/14.42 ((
% 106.65/14.42 (breln1unionIR) =>
% 106.65/14.42 ((
% 106.65/14.42 (breln1unionI) =>
% 106.65/14.42 ((
% 106.65/14.42 (breln1unionE) =>
% 106.65/14.42 ((
% 106.65/14.42 (breln1unionEcases) =>
% 106.65/14.42 ((
% 106.65/14.42 (breln1unionCommutes) =>
% 106.65/14.42 ((
% 106.65/14.42 (woz2Ex) =>
% 106.65/14.42 ((
% 106.65/14.42 (woz2W) =>
% 106.65/14.42 ((
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% 106.65/14.42 ((
% 106.65/14.42 (woz2B) =>
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% 106.65/14.42 ((
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% 106.65/14.42 ((
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% 106.65/14.42 ((
% 106.65/14.42 (image1E) =>
% 106.65/14.42 ((
% 106.65/14.42 (image1I) =>
% 106.65/14.42 ((
% 106.65/14.42 (injFuncInInjFuncSet) =>
% 106.65/14.42 ((
% 106.65/14.42 (injFuncSetFuncIn) =>
% 106.65/14.42 ((
% 106.65/14.42 (injFuncSetFuncInj) =>
% 106.65/14.42 ((
% 106.65/14.42 (surjFuncSetFuncIn) =>
% 106.65/14.42 ((
% 106.65/14.42 (surjFuncSetFuncSurj) =>
% 106.65/14.42 ((
% 106.65/14.42 (leftInvIsSurj) =>
% 106.65/14.42 ((
% 106.65/14.42 (surjCantorThm) =>
% 106.65/14.42 ((
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% 106.65/14.42 (('#S') @ (
% 106.65/14.42 (
% 106.65/14.42 ('#B') @ (
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% 106.65/14.42 nonempty)) @
% 106.65/14.42 (
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% 106.65/14.42 (
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% 106.65/14.42 ('#B') @ (
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% 106.65/14.42 (
% 106.65/14.42 (
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% 106.65/14.42 (
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% 106.65/14.42 ('#B') @ (
% 106.65/14.42 (
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% 106.65/14.42 =))) @
% 106.65/14.42 (
% 106.65/14.42 (
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% 106.65/14.42 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.65/14.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl264])).
% 106.65/14.42 thf(zip_derived_cl293, plain,
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% 106.65/14.42 ((
% 106.65/14.42 (notdallE) =>
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% 106.65/14.42 ((
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% 106.65/14.42 ((
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% 106.65/14.42 ((
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% 106.65/14.42 ((
% 106.65/14.42 (exuE3u) =>
% 106.65/14.42 ((
% 106.65/14.42 (exu__Cong) =>
% 106.65/14.42 ((
% 106.65/14.42 (setadjoin__Cong) =>
% 106.65/14.42 ((
% 106.65/14.42 (powerset__Cong) =>
% 106.65/14.42 ((
% 106.65/14.42 (setunion__Cong) =>
% 106.65/14.42 ((
% 106.65/14.42 (exuEu) =>
% 106.65/14.42 ((
% 106.65/14.42 (descr__Cong) =>
% 106.65/14.42 ((
% 106.65/14.42 (dsetconstr__Cong) =>
% 106.65/14.42 ((
% 106.65/14.42 (subsetI1) =>
% 106.65/14.42 ((
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% 106.65/14.42 ((
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% 106.65/14.42 ((
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% 106.65/14.42 ((
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% 106.65/14.42 ((
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% 106.65/14.42 ((
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% 106.65/14.42 ((
% 106.65/14.42 (symdiffI2) =>
% 106.65/14.42 ((
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% 106.65/14.42 ((
% 106.65/14.42 (symdiffIneg2) =>
% 106.65/14.42 ((
% 106.65/14.42 (secondinupair) =>
% 106.65/14.42 ((
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% 106.65/14.42 ((
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% 106.65/14.42 ((
% 106.65/14.42 (singletoninpowerset) =>
% 106.65/14.42 ((
% 106.65/14.42 (singletoninpowunion) =>
% 106.65/14.42 ((
% 106.65/14.42 (upairset2E) =>
% 106.65/14.42 ((
% 106.65/14.42 (upairsubunion) =>
% 106.65/14.42 ((
% 106.65/14.42 (upairinpowunion) =>
% 106.65/14.42 ((
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% 106.65/14.42 ((
% 106.65/14.42 (ubforcartprodlem2) =>
% 106.65/14.42 ((
% 106.65/14.42 (ubforcartprodlem3) =>
% 106.65/14.42 ((
% 106.65/14.42 (cartprodpairin) =>
% 106.65/14.42 ((
% 106.65/14.42 (cartprodmempair1) =>
% 106.65/14.42 ((
% 106.65/14.42 (cartprodmempair) =>
% 106.65/14.42 ((
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% 106.65/14.42 ((
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% 106.65/14.42 ((
% 106.65/14.42 (setunionsingleton2) =>
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% 106.65/14.42 (setunionsingleton) =>
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% 106.65/14.42 ((
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% 106.65/14.42 ((
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% 106.65/14.42 ((
% 106.65/14.42 (kfstsingleton) =>
% 106.65/14.42 ((
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% 106.65/14.42 (kfstpairEq) =>
% 106.65/14.42 ((
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% 106.65/14.42 ((
% 106.65/14.42 (setukpairinjL) =>
% 106.65/14.42 ((
% 106.65/14.42 (setukpairinjR11) =>
% 106.65/14.42 ((
% 106.65/14.42 (setukpairinjR12) =>
% 106.65/14.42 ((
% 106.65/14.42 (setukpairinjR1) =>
% 106.65/14.42 ((
% 106.65/14.42 (upairequniteq) =>
% 106.65/14.42 ((
% 106.65/14.42 (setukpairinjR2) =>
% 106.65/14.42 ((
% 106.65/14.42 (setukpairinjR) =>
% 106.65/14.42 ((
% 106.65/14.42 (ksndsingleton) =>
% 106.65/14.42 ((
% 106.65/14.42 (ksndpairEq) =>
% 106.65/14.42 ((
% 106.65/14.42 (kpairsurjEq) =>
% 106.65/14.42 ((
% 106.65/14.42 (cartprodsndin) =>
% 106.65/14.42 ((
% 106.65/14.42 (cartprodpairmemEL) =>
% 106.65/14.42 ((
% 106.65/14.42 (cartprodpairmemER) =>
% 106.65/14.42 ((
% 106.65/14.42 (cartprodmempaircEq) =>
% 106.65/14.42 ((
% 106.65/14.42 (cartprodfstpairEq) =>
% 106.65/14.42 ((
% 106.65/14.42 (cartprodsndpairEq) =>
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% 106.65/14.42 (woz1_4) =>
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% 106.65/14.42 (breln1invE) =>
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% 106.65/14.42 ((
% 106.65/14.42 (breln1compE) =>
% 106.65/14.42 ((
% 106.65/14.42 (breln1compEex) =>
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% 106.65/14.42 (breln1unionprop) =>
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% 106.65/14.42 ((
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% 106.65/14.42 (breln1unionCommutes) =>
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% 106.65/14.42 (image1I) =>
% 106.65/14.42 ((
% 106.65/14.42 (injFuncInInjFuncSet) =>
% 106.65/14.42 ((
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% 106.65/14.42 (injFuncSetFuncInj) =>
% 106.65/14.42 ((
% 106.65/14.42 (surjFuncSetFuncIn) =>
% 106.65/14.42 ((
% 106.65/14.42 (surjFuncSetFuncSurj) =>
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% 106.65/14.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl280])).
% 106.65/14.42 thf(zip_derived_cl307, plain,
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% 106.65/14.42 ((
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% 106.65/14.42 ((
% 106.65/14.42 (upairsubunion) =>
% 106.65/14.42 ((
% 106.65/14.42 (upairinpowunion) =>
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% 106.65/14.42 ((
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% 106.65/14.42 (ubforcartprodlem3) =>
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% 106.65/14.42 ((
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% 106.65/14.42 (funcGraphProp4) =>
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% 106.65/14.42 ((
% 106.65/14.42 (doubleComplementE1) =>
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% 106.65/14.42 (inComplementUnionImpInComplement1) =>
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% 106.65/14.42 (woz13rule4) =>
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% 106.65/14.42 (woz1_4) =>
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% 106.65/14.42 (woz1_5) =>
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% 106.65/14.42 (breln1SetBreln1) =>
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% 106.65/14.42 (choice2fnsingleton) =>
% 106.65/14.42 ((
% 106.65/14.42 (setOfPairsIsBReln1) =>
% 106.65/14.42 ((
% 106.65/14.42 (breln1all1) =>
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% 106.65/14.42 ((
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% 106.65/14.42 (breln1invE) =>
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% 106.65/14.42 (breln1compI) =>
% 106.65/14.42 ((
% 106.65/14.42 (breln1compE) =>
% 106.65/14.42 ((
% 106.65/14.42 (breln1compEex) =>
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% 106.65/14.42 (breln1unionprop) =>
% 106.65/14.42 ((
% 106.65/14.42 (breln1unionIL) =>
% 106.65/14.42 ((
% 106.65/14.42 (breln1unionIR) =>
% 106.65/14.42 ((
% 106.65/14.42 (breln1unionI) =>
% 106.65/14.42 ((
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% 106.65/14.42 (breln1unionCommutes) =>
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% 106.65/14.42 (image1E) =>
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% 106.65/14.42 (image1I) =>
% 106.65/14.42 ((
% 106.65/14.42 (injFuncInInjFuncSet) =>
% 106.65/14.42 ((
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% 106.65/14.42 (injFuncSetFuncInj) =>
% 106.65/14.42 ((
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% 106.65/14.42 ((
% 106.65/14.42 (surjFuncSetFuncSurj) =>
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% 106.65/14.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl293])).
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% 106.65/14.42 (descr__Cong) =>
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% 106.65/14.42 ((
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% 106.65/14.42 ((
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% 106.65/14.42 ((
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% 106.65/14.42 ((
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% 106.65/14.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl307])).
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% 106.65/14.42 (setminusERneg) =>
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% 106.65/14.42 (setminusELneg) =>
% 106.65/14.42 ((
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% 106.65/14.42 (setminusIRneg) =>
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% 106.65/14.42 (setminusLsub) =>
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% 106.65/14.42 (symdiffE) =>
% 106.65/14.42 ((
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% 106.65/14.42 (symdiffI2) =>
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% 106.65/14.42 (symdiffIneg2) =>
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% 106.65/14.42 (setukpairIR) =>
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% 106.65/14.42 (kpairp) =>
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% 106.65/14.42 (singletoninpowerset) =>
% 106.65/14.42 ((
% 106.65/14.42 (singletoninpowunion) =>
% 106.65/14.42 ((
% 106.65/14.42 (upairset2E) =>
% 106.65/14.42 ((
% 106.65/14.42 (upairsubunion) =>
% 106.65/14.42 ((
% 106.65/14.42 (upairinpowunion) =>
% 106.65/14.42 ((
% 106.65/14.42 (ubforcartprodlem1) =>
% 106.65/14.42 ((
% 106.65/14.42 (ubforcartprodlem2) =>
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% 106.65/14.42 (ubforcartprodlem3) =>
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% 106.65/14.42 (cartprodpairin) =>
% 106.65/14.42 ((
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% 106.65/14.42 ((
% 106.65/14.42 (cartprodmempair) =>
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% 106.65/14.42 ((
% 106.65/14.42 (setunionsingleton1) =>
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% 106.65/14.42 (setunionsingleton2) =>
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% 106.65/14.42 (theprop) =>
% 106.65/14.42 ((
% 106.65/14.42 (kfstpairEq) =>
% 106.65/14.42 ((
% 106.65/14.42 (cartprodfstin) =>
% 106.65/14.42 ((
% 106.65/14.42 (setukpairinjL2) =>
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% 106.65/14.42 (setukpairinjL) =>
% 106.65/14.42 ((
% 106.65/14.42 (setukpairinjR11) =>
% 106.65/14.42 ((
% 106.65/14.42 (setukpairinjR12) =>
% 106.65/14.42 ((
% 106.65/14.42 (setukpairinjR1) =>
% 106.65/14.42 ((
% 106.65/14.42 (upairequniteq) =>
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% 106.65/14.42 (setukpairinjR2) =>
% 106.65/14.42 ((
% 106.65/14.42 (setukpairinjR) =>
% 106.65/14.42 ((
% 106.65/14.42 (ksndsingleton) =>
% 106.65/14.42 ((
% 106.65/14.42 (ksndpairEq) =>
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% 106.65/14.42 (kpairsurjEq) =>
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% 106.65/14.42 (cartprodsndin) =>
% 106.65/14.42 ((
% 106.65/14.42 (cartprodpairmemEL) =>
% 106.65/14.42 ((
% 106.65/14.42 (cartprodpairmemER) =>
% 106.65/14.42 ((
% 106.65/14.42 (cartprodmempaircEq) =>
% 106.65/14.42 ((
% 106.65/14.42 (cartprodfstpairEq) =>
% 106.65/14.42 ((
% 106.65/14.42 (cartprodsndpairEq) =>
% 106.65/14.42 ((
% 106.65/14.42 (cartprodpairsurjEq) =>
% 106.65/14.42 ((
% 106.65/14.42 (dpsetconstrI) =>
% 106.65/14.42 ((
% 106.65/14.42 (dpsetconstrSub) =>
% 106.65/14.42 ((
% 106.65/14.42 (setOfPairsIsBReln) =>
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% 106.65/14.42 (dpsetconstrERa) =>
% 106.65/14.42 ((
% 106.65/14.42 (dpsetconstrEL1) =>
% 106.65/14.42 ((
% 106.65/14.42 (dpsetconstrEL2) =>
% 106.65/14.42 ((
% 106.65/14.42 (dpsetconstrER) =>
% 106.65/14.42 ((
% 106.65/14.42 (funcImageSingleton) =>
% 106.65/14.42 ((
% 106.65/14.42 (apProp) =>
% 106.65/14.42 ((
% 106.65/14.42 (app) =>
% 106.65/14.42 ((
% 106.65/14.42 (infuncsetfunc) =>
% 106.65/14.42 ((
% 106.65/14.42 (ap2p) =>
% 106.65/14.42 ((
% 106.65/14.42 (funcinfuncset) =>
% 106.65/14.42 ((
% 106.65/14.42 (lamProp) =>
% 106.65/14.42 ((
% 106.65/14.42 (lamp) =>
% 106.65/14.42 ((
% 106.65/14.42 (lam2p) =>
% 106.65/14.42 ((
% 106.65/14.42 (brelnall1) =>
% 106.65/14.42 ((
% 106.65/14.42 (brelnall2) =>
% 106.65/14.42 ((
% 106.65/14.42 (ex1E2) =>
% 106.65/14.42 ((
% 106.65/14.42 (funcGraphProp1) =>
% 106.65/14.42 ((
% 106.65/14.42 (funcGraphProp3) =>
% 106.65/14.42 ((
% 106.65/14.42 (funcGraphProp2) =>
% 106.65/14.42 ((
% 106.65/14.42 (funcextLem) =>
% 106.65/14.42 ((
% 106.65/14.42 (funcGraphProp4) =>
% 106.65/14.42 ((
% 106.65/14.42 (subbreln) =>
% 106.65/14.42 ((
% 106.65/14.42 (eqbreln) =>
% 106.65/14.42 ((
% 106.65/14.42 (funcext) =>
% 106.65/14.42 ((
% 106.65/14.42 (funcext2) =>
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% 106.65/14.42 (ap2apEq1) =>
% 106.65/14.42 ((
% 106.65/14.42 (ap2apEq2) =>
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% 106.65/14.42 (beta1) =>
% 106.65/14.42 ((
% 106.65/14.42 (eta1) =>
% 106.65/14.42 ((
% 106.65/14.42 (lam2lamEq) =>
% 106.65/14.42 ((
% 106.65/14.42 (beta2) =>
% 106.65/14.42 ((
% 106.65/14.42 (eta2) =>
% 106.65/14.42 ((
% 106.65/14.42 (iffalseProp1) =>
% 106.65/14.42 ((
% 106.65/14.42 (iffalseProp2) =>
% 106.65/14.42 ((
% 106.65/14.42 (iftrueProp1) =>
% 106.65/14.42 ((
% 106.65/14.42 (iftrueProp2) =>
% 106.65/14.42 ((
% 106.65/14.42 (ifSingleton) =>
% 106.65/14.42 ((
% 106.65/14.42 (ifp) =>
% 106.65/14.42 ((
% 106.65/14.42 (theeq) =>
% 106.65/14.42 ((
% 106.65/14.42 (iftrue) =>
% 106.65/14.42 ((
% 106.65/14.42 (iffalse) =>
% 106.65/14.42 ((
% 106.65/14.42 (iftrueorfalse) =>
% 106.65/14.42 ((
% 106.65/14.42 (binintersectT_lem) =>
% 106.65/14.42 ((
% 106.65/14.42 (binunionT_lem) =>
% 106.65/14.42 ((
% 106.65/14.42 (powersetT_lem) =>
% 106.65/14.42 ((
% 106.65/14.42 (setminusT_lem) =>
% 106.65/14.42 ((
% 106.65/14.42 (complementT_lem) =>
% 106.65/14.42 ((
% 106.65/14.42 (setextT) =>
% 106.65/14.42 ((
% 106.65/14.42 (subsetTI) =>
% 106.65/14.42 ((
% 106.65/14.42 (powersetTI1) =>
% 106.65/14.42 ((
% 106.65/14.42 (powersetTE1) =>
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% 106.65/14.42 (complementTI1) =>
% 106.65/14.42 ((
% 106.65/14.42 (complementTE1) =>
% 106.65/14.42 ((
% 106.65/14.42 (binintersectTELcontra) =>
% 106.65/14.42 ((
% 106.65/14.42 (binintersectTERcontra) =>
% 106.65/14.42 ((
% 106.65/14.42 (contrasubsetT) =>
% 106.65/14.42 ((
% 106.65/14.42 (contrasubsetT1) =>
% 106.65/14.42 ((
% 106.65/14.42 (contrasubsetT2) =>
% 106.65/14.42 ((
% 106.65/14.42 (contrasubsetT3) =>
% 106.65/14.42 ((
% 106.65/14.42 (doubleComplementI1) =>
% 106.65/14.42 ((
% 106.65/14.42 (doubleComplementE1) =>
% 106.65/14.42 ((
% 106.65/14.42 (doubleComplementSub1) =>
% 106.65/14.42 ((
% 106.65/14.42 (doubleComplementSub2) =>
% 106.65/14.42 ((
% 106.65/14.42 (doubleComplementEq) =>
% 106.65/14.42 ((
% 106.65/14.42 (complementTnotintersectT) =>
% 106.65/14.42 ((
% 106.65/14.42 (complementImpComplementIntersect) =>
% 106.65/14.42 ((
% 106.65/14.42 (complementSubsetComplementIntersect) =>
% 106.65/14.42 ((
% 106.65/14.42 (complementInPowersetComplementIntersect) =>
% 106.65/14.42 ((
% 106.65/14.42 (contraSubsetComplement) =>
% 106.65/14.42 ((
% 106.65/14.42 (complementTcontraSubset) =>
% 106.65/14.42 ((
% 106.65/14.42 (binunionTILcontra) =>
% 106.65/14.42 ((
% 106.65/14.42 (binunionTIRcontra) =>
% 106.65/14.42 ((
% 106.65/14.42 (inIntersectImpInUnion) =>
% 106.65/14.42 ((
% 106.65/14.42 (inIntersectImpInUnion2) =>
% 106.65/14.42 ((
% 106.65/14.42 (inIntersectImpInIntersectUnions) =>
% 106.65/14.42 ((
% 106.65/14.42 (intersectInPowersetIntersectUnions) =>
% 106.65/14.42 ((
% 106.65/14.42 (inComplementUnionImpNotIn1) =>
% 106.65/14.42 ((
% 106.65/14.42 (inComplementUnionImpInComplement1) =>
% 106.65/14.42 ((
% 106.65/14.42 (binunionTE) =>
% 106.65/14.42 ((
% 106.65/14.42 (binunionTEcontra) =>
% 106.65/14.42 ((
% 106.65/14.42 (demorgan2a1) =>
% 106.65/14.42 ((
% 106.65/14.42 (complementUnionInPowersetComplement) =>
% 106.65/14.42 ((
% 106.65/14.42 (demorgan2a2) =>
% 106.65/14.42 ((
% 106.65/14.42 (demorgan1a) =>
% 106.65/14.42 ((
% 106.65/14.42 (demorgan1b) =>
% 106.65/14.42 ((
% 106.65/14.42 (demorgan1) =>
% 106.65/14.42 ((
% 106.65/14.42 (demorgan2a) =>
% 106.65/14.42 ((
% 106.65/14.42 (demorgan2b2) =>
% 106.65/14.42 ((
% 106.65/14.42 (demorgan2b) =>
% 106.65/14.42 ((
% 106.65/14.42 (demorgan2) =>
% 106.65/14.42 ((
% 106.65/14.42 (woz13rule0) =>
% 106.65/14.42 ((
% 106.65/14.42 (woz13rule1) =>
% 106.65/14.42 ((
% 106.65/14.42 (woz13rule2) =>
% 106.65/14.42 ((
% 106.65/14.42 (woz13rule3) =>
% 106.65/14.42 ((
% 106.65/14.42 (woz13rule4) =>
% 106.65/14.42 ((
% 106.65/14.42 (woz1_1) =>
% 106.65/14.42 ((
% 106.65/14.42 (woz1_2) =>
% 106.65/14.42 ((
% 106.65/14.42 (woz1_3) =>
% 106.65/14.42 ((
% 106.65/14.42 (woz1_4) =>
% 106.65/14.42 ((
% 106.65/14.42 (woz1_5) =>
% 106.65/14.42 ((
% 106.65/14.42 (breln1all2) =>
% 106.65/14.42 ((
% 106.65/14.42 (breln1SetBreln1) =>
% 106.65/14.42 ((
% 106.65/14.42 (choice2fnsingleton) =>
% 106.65/14.42 ((
% 106.65/14.42 (setOfPairsIsBReln1) =>
% 106.65/14.42 ((
% 106.65/14.42 (breln1all1) =>
% 106.65/14.42 ((
% 106.65/14.42 (subbreln1) =>
% 106.65/14.42 ((
% 106.65/14.42 (eqbreln1) =>
% 106.65/14.42 ((
% 106.65/14.42 (breln1invprop) =>
% 106.65/14.42 ((
% 106.65/14.42 (breln1invI) =>
% 106.65/14.42 ((
% 106.65/14.42 (breln1invE) =>
% 106.65/14.42 ((
% 106.65/14.42 (breln1compprop) =>
% 106.65/14.42 ((
% 106.65/14.42 (breln1compI) =>
% 106.65/14.42 ((
% 106.65/14.42 (breln1compE) =>
% 106.65/14.42 ((
% 106.65/14.42 (breln1compEex) =>
% 106.65/14.42 ((
% 106.65/14.42 (breln1unionprop) =>
% 106.65/14.42 ((
% 106.65/14.42 (breln1unionIL) =>
% 106.65/14.42 ((
% 106.65/14.42 (breln1unionIR) =>
% 106.65/14.42 ((
% 106.65/14.42 (breln1unionI) =>
% 106.65/14.42 ((
% 106.65/14.42 (breln1unionE) =>
% 106.65/14.42 ((
% 106.65/14.42 (breln1unionEcases) =>
% 106.65/14.42 ((
% 106.65/14.42 (breln1unionCommutes) =>
% 106.65/14.42 ((
% 106.65/14.42 (woz2Ex) =>
% 106.65/14.42 ((
% 106.65/14.42 (woz2W) =>
% 106.65/14.42 ((
% 106.65/14.42 (woz2A) =>
% 106.65/14.42 ((
% 106.65/14.42 (woz2B) =>
% 106.65/14.42 ((
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% 106.65/14.42 ((
% 106.65/14.42 (image1Ex1) =>
% 106.65/14.42 ((
% 106.65/14.42 (image1Equiv) =>
% 106.65/14.42 ((
% 106.65/14.42 (image1E) =>
% 106.65/14.42 ((
% 106.65/14.42 (image1I) =>
% 106.65/14.42 ((
% 106.65/14.42 (injFuncInInjFuncSet) =>
% 106.65/14.42 ((
% 106.65/14.42 (injFuncSetFuncIn) =>
% 106.65/14.42 ((
% 106.65/14.42 (injFuncSetFuncInj) =>
% 106.65/14.42 ((
% 106.65/14.42 (surjFuncSetFuncIn) =>
% 106.65/14.42 ((
% 106.65/14.42 (surjFuncSetFuncSurj) =>
% 106.65/14.42 ((
% 106.65/14.42 (leftInvIsSurj) =>
% 106.65/14.42 ((
% 106.65/14.42 (surjCantorThm) =>
% 106.65/14.42 ((
% 106.65/14.42 (!!) @ (
% 106.65/14.42 (('#S') @ (
% 106.65/14.42 (
% 106.65/14.42 ('#B') @ (
% 106.65/14.42 =>) @
% 106.65/14.42 nonempty)) @
% 106.65/14.42 (
% 106.65/14.42 (
% 106.65/14.42 ('#B') @ (
% 106.65/14.42 ??) @
% 106.65/14.42 (
% 106.65/14.42 (
% 106.65/14.42 ('#S') @ (
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% 106.65/14.42 '#S') @
% 106.65/14.42 (
% 106.65/14.42 (
% 106.65/14.42 ('#B') @ (
% 106.65/14.42 (
% 106.65/14.42 ('#B') @ (
% 106.65/14.42 &))) @
% 106.65/14.42 (
% 106.65/14.42 (
% 106.65/14.42 ('#C') @ in)))))) @
% 106.65/14.42 (
% 106.65/14.42 (
% 106.65/14.42 ('#C') @ (
% 106.65/14.42 (
% 106.65/14.42 ('#B') @ (
% 106.65/14.42 '#C') @
% 106.65/14.42 (
% 106.65/14.42 (
% 106.65/14.42 ('#B') @ (
% 106.65/14.42 (
% 106.65/14.42 ('#B') @ (
% 106.65/14.42 =))) @
% 106.65/14.42 (
% 106.65/14.42 (
% 106.65/14.42 ('#C') @ binintersect)))))) @
% 106.65/14.42 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.65/14.42 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl322])).
% 106.65/14.42 thf(zip_derived_cl349, plain,
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% 106.65/14.42 (((emptyInPowerset) =>
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% 106.65/14.42 (((setunionE) =>
% 106.65/14.42 (((subPowSU) =>
% 106.65/14.42 (((exuE2) =>
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% 106.65/14.42 (((quantDeMorgan3) =>
% 106.65/14.42 (((quantDeMorgan4) =>
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% 106.65/14.42 ((
% 106.65/14.42 (inCongP) =>
% 106.65/14.42 ((
% 106.65/14.42 (in__Cong) =>
% 106.65/14.42 ((
% 106.65/14.42 (exuE3u) =>
% 106.65/14.42 ((
% 106.65/14.42 (exu__Cong) =>
% 106.65/14.42 ((
% 106.65/14.42 (setadjoin__Cong) =>
% 106.65/14.42 ((
% 106.65/14.42 (powerset__Cong) =>
% 106.65/14.42 ((
% 106.65/14.42 (setunion__Cong) =>
% 106.65/14.42 ((
% 106.65/14.42 (exuEu) =>
% 106.65/14.42 ((
% 106.65/14.42 (descr__Cong) =>
% 106.65/14.42 ((
% 106.65/14.42 (dsetconstr__Cong) =>
% 106.65/14.42 ((
% 106.65/14.42 (subsetI1) =>
% 106.65/14.42 ((
% 106.65/14.42 (eqimpsubset2) =>
% 106.65/14.42 ((
% 106.65/14.42 (eqimpsubset1) =>
% 106.65/14.42 ((
% 106.65/14.42 (subsetI2) =>
% 106.65/14.42 ((
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% 106.65/14.42 (subsetE) =>
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% 106.65/14.42 ((
% 106.65/14.42 (subsetTrans) =>
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% 106.65/14.42 ((
% 106.65/14.42 (setadjoinSub2) =>
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% 106.65/14.42 ((
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% 106.65/14.42 ((
% 106.65/14.42 (subsetemptysetimpeq) =>
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% 106.65/14.42 ((
% 106.65/14.42 (powersetE1) =>
% 106.65/14.42 ((
% 106.65/14.42 (inPowerset) =>
% 106.65/14.42 ((
% 106.65/14.42 (powersetsubset) =>
% 106.65/14.42 ((
% 106.65/14.42 (sepInPowerset) =>
% 106.65/14.42 ((
% 106.65/14.42 (sepSubset) =>
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% 106.65/14.42 ((
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% 106.65/14.42 (setminusELneg) =>
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% 106.65/14.42 (setukpairinjR1) =>
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% 106.65/14.42 (cartprodpairmemER) =>
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% 106.65/14.42 (cartprodmempaircEq) =>
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% 106.65/14.42 (cartprodfstpairEq) =>
% 106.65/14.42 ((
% 106.65/14.42 (cartprodsndpairEq) =>
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% 106.65/14.42 (cartprodpairsurjEq) =>
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% 106.65/14.42 (dpsetconstrEL2) =>
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% 106.65/14.42 (dpsetconstrER) =>
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% 106.65/14.42 (lamProp) =>
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% 106.65/14.42 (lamp) =>
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% 106.65/14.42 (lam2p) =>
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% 106.65/14.42 (brelnall1) =>
% 106.65/14.42 ((
% 106.65/14.42 (brelnall2) =>
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% 106.65/14.42 (funcGraphProp3) =>
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% 106.65/14.42 (funcGraphProp2) =>
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% 106.65/14.42 ((
% 106.65/14.42 (funcGraphProp4) =>
% 106.65/14.42 ((
% 106.65/14.42 (subbreln) =>
% 106.65/14.42 ((
% 106.65/14.42 (eqbreln) =>
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% 106.65/14.42 (lam2lamEq) =>
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% 106.65/14.42 (beta2) =>
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% 106.65/14.42 (iftrue) =>
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% 106.65/14.42 (subsetTI) =>
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% 106.65/14.42 ((
% 106.65/14.42 (binintersectTERcontra) =>
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% 106.65/14.42 ((
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% 106.65/14.42 ((
% 106.65/14.42 (contrasubsetT2) =>
% 106.65/14.42 ((
% 106.65/14.42 (contrasubsetT3) =>
% 106.65/14.42 ((
% 106.65/14.42 (doubleComplementI1) =>
% 106.65/14.42 ((
% 106.65/14.42 (doubleComplementE1) =>
% 106.65/14.42 ((
% 106.65/14.42 (doubleComplementSub1) =>
% 106.65/14.42 ((
% 106.65/14.42 (doubleComplementSub2) =>
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% 106.65/14.42 (doubleComplementEq) =>
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% 106.65/14.42 (complementTnotintersectT) =>
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% 106.65/14.42 (complementImpComplementIntersect) =>
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% 106.65/14.42 (complementSubsetComplementIntersect) =>
% 106.65/14.42 ((
% 106.65/14.42 (complementInPowersetComplementIntersect) =>
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% 106.65/14.42 (contraSubsetComplement) =>
% 106.65/14.42 ((
% 106.65/14.42 (complementTcontraSubset) =>
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% 106.65/14.42 (binunionTIRcontra) =>
% 106.65/14.42 ((
% 106.65/14.42 (inIntersectImpInUnion) =>
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% 106.65/14.42 (inIntersectImpInUnion2) =>
% 106.65/14.42 ((
% 106.65/14.42 (inIntersectImpInIntersectUnions) =>
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% 106.65/14.42 (intersectInPowersetIntersectUnions) =>
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% 106.65/14.42 (inComplementUnionImpNotIn1) =>
% 106.65/14.42 ((
% 106.65/14.42 (inComplementUnionImpInComplement1) =>
% 106.65/14.42 ((
% 106.65/14.42 (binunionTE) =>
% 106.65/14.42 ((
% 106.65/14.42 (binunionTEcontra) =>
% 106.65/14.42 ((
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% 106.65/14.42 ((
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% 106.65/14.42 ((
% 106.65/14.42 (demorgan1) =>
% 106.65/14.42 ((
% 106.65/14.42 (demorgan2a) =>
% 106.65/14.42 ((
% 106.65/14.42 (demorgan2b2) =>
% 106.65/14.42 ((
% 106.65/14.42 (demorgan2b) =>
% 106.65/14.42 ((
% 106.65/14.42 (demorgan2) =>
% 106.65/14.42 ((
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% 106.65/14.42 ((
% 106.65/14.42 (woz13rule1) =>
% 106.65/14.42 ((
% 106.65/14.42 (woz13rule2) =>
% 106.65/14.42 ((
% 106.65/14.42 (woz13rule3) =>
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% 106.65/14.43 (woz13rule4) =>
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% 106.65/14.43 ((
% 106.65/14.43 (woz1_2) =>
% 106.65/14.43 ((
% 106.65/14.43 (woz1_3) =>
% 106.65/14.43 ((
% 106.65/14.43 (woz1_4) =>
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% 106.65/14.43 (woz1_5) =>
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% 106.65/14.43 (breln1all2) =>
% 106.65/14.43 ((
% 106.65/14.43 (breln1SetBreln1) =>
% 106.65/14.43 ((
% 106.65/14.43 (choice2fnsingleton) =>
% 106.65/14.43 ((
% 106.65/14.43 (setOfPairsIsBReln1) =>
% 106.65/14.43 ((
% 106.65/14.43 (breln1all1) =>
% 106.65/14.43 ((
% 106.65/14.43 (subbreln1) =>
% 106.65/14.43 ((
% 106.65/14.43 (eqbreln1) =>
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% 106.65/14.43 ((
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% 106.65/14.43 ((
% 106.65/14.43 (breln1invE) =>
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% 106.65/14.43 (breln1compprop) =>
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% 106.65/14.43 (breln1compI) =>
% 106.65/14.43 ((
% 106.65/14.43 (breln1compE) =>
% 106.65/14.43 ((
% 106.65/14.43 (breln1compEex) =>
% 106.65/14.43 ((
% 106.65/14.43 (breln1unionprop) =>
% 106.65/14.43 ((
% 106.65/14.43 (breln1unionIL) =>
% 106.65/14.43 ((
% 106.65/14.43 (breln1unionIR) =>
% 106.65/14.43 ((
% 106.65/14.43 (breln1unionI) =>
% 106.65/14.43 ((
% 106.65/14.43 (breln1unionE) =>
% 106.65/14.43 ((
% 106.65/14.43 (breln1unionEcases) =>
% 106.65/14.43 ((
% 106.65/14.43 (breln1unionCommutes) =>
% 106.65/14.43 ((
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% 106.65/14.43 ((
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% 106.65/14.43 ((
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% 106.65/14.43 ((
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% 106.65/14.43 ((
% 106.65/14.43 (image1E) =>
% 106.65/14.43 ((
% 106.65/14.43 (image1I) =>
% 106.65/14.43 ((
% 106.65/14.43 (injFuncInInjFuncSet) =>
% 106.65/14.43 ((
% 106.65/14.43 (injFuncSetFuncIn) =>
% 106.65/14.43 ((
% 106.65/14.43 (injFuncSetFuncInj) =>
% 106.65/14.43 ((
% 106.65/14.43 (surjFuncSetFuncIn) =>
% 106.65/14.43 ((
% 106.65/14.43 (surjFuncSetFuncSurj) =>
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% 106.65/14.43 (leftInvIsSurj) =>
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% 106.65/14.43 ((
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% 106.65/14.43 ('#B') @ (
% 106.65/14.43 =>) @
% 106.65/14.43 nonempty)) @
% 106.65/14.43 (
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% 106.65/14.43 (
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% 106.65/14.43 (
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% 106.65/14.43 (
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% 106.65/14.43 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl337])).
% 106.65/14.43 thf(zip_derived_cl355, plain,
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% 106.65/14.43 ((
% 106.65/14.43 (exuE3u) =>
% 106.65/14.43 ((
% 106.65/14.43 (exu__Cong) =>
% 106.65/14.43 ((
% 106.65/14.43 (setadjoin__Cong) =>
% 106.65/14.43 ((
% 106.65/14.43 (powerset__Cong) =>
% 106.65/14.43 ((
% 106.65/14.43 (setunion__Cong) =>
% 106.65/14.43 ((
% 106.65/14.43 (exuEu) =>
% 106.65/14.43 ((
% 106.65/14.43 (descr__Cong) =>
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% 106.65/14.43 (cartprodmempaircEq) =>
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% 106.65/14.43 (cartprodfstpairEq) =>
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% 106.65/14.43 (cartprodsndpairEq) =>
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% 106.65/14.43 (brelnall1) =>
% 106.65/14.43 ((
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% 106.65/14.43 (funcGraphProp3) =>
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% 106.65/14.43 ((
% 106.65/14.43 (funcGraphProp4) =>
% 106.65/14.43 ((
% 106.65/14.43 (subbreln) =>
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% 106.65/14.43 (contrasubsetT3) =>
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% 106.65/14.43 (doubleComplementI1) =>
% 106.65/14.43 ((
% 106.65/14.43 (doubleComplementE1) =>
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% 106.65/14.43 (complementSubsetComplementIntersect) =>
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% 106.65/14.43 (contraSubsetComplement) =>
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% 106.65/14.43 (inIntersectImpInIntersectUnions) =>
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% 106.65/14.43 (inComplementUnionImpNotIn1) =>
% 106.65/14.43 ((
% 106.65/14.43 (inComplementUnionImpInComplement1) =>
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% 106.65/14.43 ((
% 106.65/14.43 (breln1compE) =>
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% 106.65/14.43 (breln1compEex) =>
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% 106.65/14.43 (breln1unionprop) =>
% 106.65/14.43 ((
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% 106.65/14.43 ((
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% 106.65/14.43 ((
% 106.65/14.43 (breln1unionI) =>
% 106.65/14.43 ((
% 106.65/14.43 (breln1unionE) =>
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% 106.65/14.43 (breln1unionCommutes) =>
% 106.65/14.43 ((
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% 106.65/14.43 ((
% 106.65/14.43 (image1E) =>
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% 106.65/14.43 (image1I) =>
% 106.65/14.43 ((
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% 106.65/14.43 ((
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% 106.65/14.43 ((
% 106.65/14.43 (injFuncSetFuncInj) =>
% 106.65/14.43 ((
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% 106.65/14.43 ((
% 106.65/14.43 (surjFuncSetFuncSurj) =>
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% 106.65/14.43 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl355])).
% 106.65/14.43 thf(zip_derived_cl369, plain,
% 106.65/14.43 (~ (((powersetI) =>
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% 106.65/14.43 (
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% 106.65/14.43 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.65/14.43 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl362])).
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% 106.65/14.43 ((
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% 106.65/14.43 ((
% 106.65/14.43 (kpairp) =>
% 106.65/14.43 ((
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% 106.65/14.43 ((
% 106.65/14.43 (singletoninpowerset) =>
% 106.65/14.43 ((
% 106.65/14.43 (singletoninpowunion) =>
% 106.65/14.43 ((
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% 106.65/14.43 ((
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% 106.65/14.43 ((
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% 106.65/14.43 ((
% 106.65/14.43 (ubforcartprodlem1) =>
% 106.65/14.43 ((
% 106.65/14.43 (ubforcartprodlem2) =>
% 106.65/14.43 ((
% 106.65/14.43 (ubforcartprodlem3) =>
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% 106.65/14.43 (cartprodpairin) =>
% 106.65/14.43 ((
% 106.65/14.43 (cartprodmempair1) =>
% 106.65/14.43 ((
% 106.65/14.43 (cartprodmempair) =>
% 106.65/14.43 ((
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% 106.65/14.43 ((
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% 106.65/14.43 ((
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% 106.65/14.43 (setunionsingleton) =>
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% 106.65/14.43 ((
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% 106.65/14.43 ((
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% 106.65/14.43 ((
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% 106.65/14.43 ((
% 106.65/14.43 (kfstpairEq) =>
% 106.65/14.43 ((
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% 106.65/14.43 ((
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% 106.65/14.43 ((
% 106.65/14.43 (kpairsurjEq) =>
% 106.65/14.43 ((
% 106.65/14.43 (cartprodsndin) =>
% 106.65/14.43 ((
% 106.65/14.43 (cartprodpairmemEL) =>
% 106.65/14.43 ((
% 106.65/14.43 (cartprodpairmemER) =>
% 106.65/14.43 ((
% 106.65/14.43 (cartprodmempaircEq) =>
% 106.65/14.43 ((
% 106.65/14.43 (cartprodfstpairEq) =>
% 106.65/14.43 ((
% 106.65/14.43 (cartprodsndpairEq) =>
% 106.65/14.43 ((
% 106.65/14.43 (cartprodpairsurjEq) =>
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% 106.65/14.43 (surjCantorThm) =>
% 106.65/14.43 ((
% 106.65/14.43 (!!) @ (
% 106.65/14.43 (('#S') @ (
% 106.65/14.43 (
% 106.65/14.43 ('#B') @ (
% 106.65/14.43 =>) @
% 106.65/14.43 nonempty)) @
% 106.65/14.43 (
% 106.65/14.43 (
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% 106.65/14.43 (
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% 106.65/14.43 (
% 106.65/14.43 ('#B') @ (
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% 106.65/14.43 (
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% 106.65/14.43 (
% 106.65/14.43 (
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% 106.65/14.43 (
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% 106.65/14.43 (
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% 106.65/14.43 (
% 106.65/14.43 (
% 106.65/14.43 ('#C') @ binintersect)))))) @
% 106.65/14.43 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.65/14.43 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl369])).
% 106.65/14.43 thf(zip_derived_cl384, plain,
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% 106.65/14.43 ((
% 106.65/14.43 (exu__Cong) =>
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% 106.65/14.43 (setadjoin__Cong) =>
% 106.65/14.43 ((
% 106.65/14.43 (powerset__Cong) =>
% 106.65/14.43 ((
% 106.65/14.43 (setunion__Cong) =>
% 106.65/14.43 ((
% 106.65/14.43 (exuEu) =>
% 106.65/14.43 ((
% 106.65/14.43 (descr__Cong) =>
% 106.65/14.43 ((
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% 106.65/14.43 ((
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% 106.65/14.43 ((
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% 106.65/14.43 ((
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% 106.65/14.43 ((
% 106.65/14.43 (upairset2IR) =>
% 106.65/14.43 ((
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% 106.65/14.43 ((
% 106.65/14.43 (binunionEcases) =>
% 106.65/14.43 ((
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% 106.65/14.43 ((
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% 106.65/14.43 ((
% 106.65/14.43 (binunionRsub) =>
% 106.65/14.43 ((
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% 106.65/14.43 ((
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% 106.65/14.43 ((
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% 106.65/14.43 ((
% 106.65/14.43 (binintersectLsub) =>
% 106.65/14.43 ((
% 106.65/14.43 (binintersectSubset2) =>
% 106.65/14.43 ((
% 106.65/14.43 (binintersectSubset3) =>
% 106.65/14.43 ((
% 106.65/14.43 (binintersectER) =>
% 106.65/14.43 ((
% 106.65/14.43 (disjointsetsI1) =>
% 106.65/14.43 ((
% 106.65/14.43 (binintersectRsub) =>
% 106.65/14.43 ((
% 106.65/14.43 (binintersectSubset4) =>
% 106.65/14.43 ((
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% 106.65/14.43 (bs114d) =>
% 106.65/14.43 ((
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% 106.65/14.43 ((
% 106.65/14.43 (setminusEL) =>
% 106.65/14.43 ((
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% 106.65/14.43 ((
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% 106.65/14.43 ((
% 106.65/14.43 (setminusERneg) =>
% 106.65/14.43 ((
% 106.65/14.43 (setminusELneg) =>
% 106.65/14.43 ((
% 106.65/14.43 (setminusILneg) =>
% 106.65/14.43 ((
% 106.65/14.43 (setminusIRneg) =>
% 106.65/14.43 ((
% 106.65/14.43 (setminusLsub) =>
% 106.65/14.43 ((
% 106.65/14.43 (setminusSubset1) =>
% 106.65/14.43 ((
% 106.65/14.43 (symdiffE) =>
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% 106.65/14.43 (symdiffI1) =>
% 106.65/14.43 ((
% 106.65/14.43 (symdiffI2) =>
% 106.65/14.43 ((
% 106.65/14.43 (symdiffIneg1) =>
% 106.65/14.43 ((
% 106.65/14.43 (symdiffIneg2) =>
% 106.65/14.43 ((
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% 106.65/14.43 ((
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% 106.65/14.43 ((
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% 106.65/14.43 ((
% 106.65/14.43 (kpairiskpair) =>
% 106.65/14.43 ((
% 106.65/14.43 (kpairp) =>
% 106.65/14.43 ((
% 106.65/14.43 (singletonsubset) =>
% 106.65/14.43 ((
% 106.65/14.43 (singletoninpowerset) =>
% 106.65/14.43 ((
% 106.65/14.43 (singletoninpowunion) =>
% 106.65/14.43 ((
% 106.65/14.43 (upairset2E) =>
% 106.65/14.43 ((
% 106.65/14.43 (upairsubunion) =>
% 106.65/14.43 ((
% 106.65/14.43 (upairinpowunion) =>
% 106.65/14.43 ((
% 106.65/14.43 (ubforcartprodlem1) =>
% 106.65/14.43 ((
% 106.65/14.43 (ubforcartprodlem2) =>
% 106.65/14.43 ((
% 106.65/14.43 (ubforcartprodlem3) =>
% 106.65/14.43 ((
% 106.65/14.43 (cartprodpairin) =>
% 106.65/14.43 ((
% 106.65/14.43 (cartprodmempair1) =>
% 106.65/14.43 ((
% 106.65/14.43 (cartprodmempair) =>
% 106.65/14.43 ((
% 106.65/14.43 (setunionE2) =>
% 106.65/14.43 ((
% 106.65/14.43 (setunionsingleton1) =>
% 106.65/14.43 ((
% 106.65/14.43 (setunionsingleton2) =>
% 106.65/14.43 ((
% 106.65/14.43 (setunionsingleton) =>
% 106.65/14.43 ((
% 106.65/14.43 (singletonprop) =>
% 106.65/14.43 ((
% 106.65/14.43 (ex1E1) =>
% 106.65/14.43 ((
% 106.65/14.43 (ex1I) =>
% 106.65/14.43 ((
% 106.65/14.43 (ex1I2) =>
% 106.65/14.43 ((
% 106.65/14.43 (singletonsuniq) =>
% 106.65/14.43 ((
% 106.65/14.43 (setukpairinjL1) =>
% 106.65/14.43 ((
% 106.65/14.43 (kfstsingleton) =>
% 106.65/14.43 ((
% 106.65/14.43 (theprop) =>
% 106.65/14.43 ((
% 106.65/14.43 (kfstpairEq) =>
% 106.65/14.43 ((
% 106.65/14.43 (cartprodfstin) =>
% 106.65/14.43 ((
% 106.65/14.43 (setukpairinjL2) =>
% 106.65/14.43 ((
% 106.65/14.43 (setukpairinjL) =>
% 106.65/14.43 ((
% 106.65/14.43 (setukpairinjR11) =>
% 106.65/14.43 ((
% 106.65/14.43 (setukpairinjR12) =>
% 106.65/14.43 ((
% 106.65/14.43 (setukpairinjR1) =>
% 106.65/14.43 ((
% 106.65/14.43 (upairequniteq) =>
% 106.65/14.43 ((
% 106.65/14.43 (setukpairinjR2) =>
% 106.65/14.43 ((
% 106.65/14.43 (setukpairinjR) =>
% 106.65/14.43 ((
% 106.65/14.43 (ksndsingleton) =>
% 106.65/14.43 ((
% 106.65/14.43 (ksndpairEq) =>
% 106.65/14.43 ((
% 106.65/14.43 (kpairsurjEq) =>
% 106.65/14.43 ((
% 106.65/14.43 (cartprodsndin) =>
% 106.65/14.43 ((
% 106.65/14.43 (cartprodpairmemEL) =>
% 106.65/14.43 ((
% 106.65/14.43 (cartprodpairmemER) =>
% 106.65/14.43 ((
% 106.65/14.43 (cartprodmempaircEq) =>
% 106.65/14.43 ((
% 106.65/14.43 (cartprodfstpairEq) =>
% 106.65/14.43 ((
% 106.65/14.43 (cartprodsndpairEq) =>
% 106.65/14.43 ((
% 106.65/14.43 (cartprodpairsurjEq) =>
% 106.65/14.43 ((
% 106.65/14.43 (dpsetconstrI) =>
% 106.65/14.43 ((
% 106.65/14.43 (dpsetconstrSub) =>
% 106.65/14.43 ((
% 106.65/14.43 (setOfPairsIsBReln) =>
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% 106.65/14.43 (dpsetconstrERa) =>
% 106.65/14.43 ((
% 106.65/14.43 (dpsetconstrEL1) =>
% 106.65/14.43 ((
% 106.65/14.43 (dpsetconstrEL2) =>
% 106.65/14.43 ((
% 106.65/14.43 (dpsetconstrER) =>
% 106.65/14.43 ((
% 106.65/14.43 (funcImageSingleton) =>
% 106.65/14.43 ((
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% 106.65/14.43 ((
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% 106.65/14.43 ((
% 106.65/14.43 (infuncsetfunc) =>
% 106.65/14.43 ((
% 106.65/14.43 (ap2p) =>
% 106.65/14.43 ((
% 106.65/14.43 (funcinfuncset) =>
% 106.65/14.43 ((
% 106.65/14.43 (lamProp) =>
% 106.65/14.43 ((
% 106.65/14.43 (lamp) =>
% 106.65/14.43 ((
% 106.65/14.43 (lam2p) =>
% 106.65/14.43 ((
% 106.65/14.43 (brelnall1) =>
% 106.65/14.43 ((
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% 106.65/14.43 (funcGraphProp3) =>
% 106.65/14.43 ((
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% 106.65/14.43 ((
% 106.65/14.43 (funcGraphProp4) =>
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% 106.65/14.43 (subbreln) =>
% 106.65/14.43 ((
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% 106.65/14.43 ((
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% 106.65/14.43 ((
% 106.65/14.43 (eta1) =>
% 106.65/14.43 ((
% 106.65/14.43 (lam2lamEq) =>
% 106.65/14.43 ((
% 106.65/14.43 (beta2) =>
% 106.65/14.43 ((
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% 106.65/14.43 (iftrueProp1) =>
% 106.65/14.43 ((
% 106.65/14.43 (iftrueProp2) =>
% 106.65/14.43 ((
% 106.65/14.43 (ifSingleton) =>
% 106.65/14.43 ((
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% 106.65/14.43 ((
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% 106.65/14.43 ((
% 106.65/14.43 (subsetTI) =>
% 106.65/14.43 ((
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% 106.65/14.43 ((
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% 106.65/14.43 ((
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% 106.65/14.43 ((
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% 106.65/14.43 ((
% 106.65/14.43 (complementSubsetComplementIntersect) =>
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% 106.65/14.43 ((
% 106.65/14.43 (inIntersectImpInUnion2) =>
% 106.65/14.43 ((
% 106.65/14.43 (inIntersectImpInIntersectUnions) =>
% 106.65/14.43 ((
% 106.65/14.43 (intersectInPowersetIntersectUnions) =>
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% 106.65/14.43 ((
% 106.65/14.43 (inComplementUnionImpInComplement1) =>
% 106.65/14.43 ((
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% 106.65/14.43 ((
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% 106.65/14.43 ((
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% 106.65/14.43 ((
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% 106.65/14.43 ((
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% 106.65/14.43 ((
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% 106.65/14.44 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl400])).
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% 106.65/14.44 ((
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% 106.65/14.44 ((
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% 106.65/14.44 ((
% 106.65/14.44 (demorgan2a2) =>
% 106.65/14.44 ((
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% 106.65/14.44 ((
% 106.65/14.44 (demorgan1b) =>
% 106.65/14.44 ((
% 106.65/14.44 (demorgan1) =>
% 106.65/14.44 ((
% 106.65/14.44 (demorgan2a) =>
% 106.65/14.44 ((
% 106.65/14.44 (demorgan2b2) =>
% 106.65/14.44 ((
% 106.65/14.44 (demorgan2b) =>
% 106.65/14.44 ((
% 106.65/14.44 (demorgan2) =>
% 106.65/14.44 ((
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% 106.65/14.44 ((
% 106.65/14.44 (woz13rule1) =>
% 106.65/14.44 ((
% 106.65/14.44 (woz13rule2) =>
% 106.65/14.44 ((
% 106.65/14.44 (woz13rule3) =>
% 106.65/14.44 ((
% 106.65/14.44 (woz13rule4) =>
% 106.65/14.44 ((
% 106.65/14.44 (woz1_1) =>
% 106.65/14.44 ((
% 106.65/14.44 (woz1_2) =>
% 106.65/14.44 ((
% 106.65/14.44 (woz1_3) =>
% 106.65/14.44 ((
% 106.65/14.44 (woz1_4) =>
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% 106.65/14.44 (woz1_5) =>
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% 106.65/14.44 ((
% 106.65/14.44 (breln1SetBreln1) =>
% 106.65/14.44 ((
% 106.65/14.44 (choice2fnsingleton) =>
% 106.65/14.44 ((
% 106.65/14.44 (setOfPairsIsBReln1) =>
% 106.65/14.44 ((
% 106.65/14.44 (breln1all1) =>
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% 106.65/14.44 (breln1invE) =>
% 106.65/14.44 ((
% 106.65/14.44 (breln1compprop) =>
% 106.65/14.44 ((
% 106.65/14.44 (breln1compI) =>
% 106.65/14.44 ((
% 106.65/14.44 (breln1compE) =>
% 106.65/14.44 ((
% 106.65/14.44 (breln1compEex) =>
% 106.65/14.44 ((
% 106.65/14.44 (breln1unionprop) =>
% 106.65/14.44 ((
% 106.65/14.44 (breln1unionIL) =>
% 106.65/14.44 ((
% 106.65/14.44 (breln1unionIR) =>
% 106.65/14.44 ((
% 106.65/14.44 (breln1unionI) =>
% 106.65/14.44 ((
% 106.65/14.44 (breln1unionE) =>
% 106.65/14.44 ((
% 106.65/14.44 (breln1unionEcases) =>
% 106.65/14.44 ((
% 106.65/14.44 (breln1unionCommutes) =>
% 106.65/14.44 ((
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% 106.65/14.44 ((
% 106.65/14.44 (image1E) =>
% 106.65/14.44 ((
% 106.65/14.44 (image1I) =>
% 106.65/14.44 ((
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% 106.65/14.44 ((
% 106.65/14.44 (injFuncSetFuncIn) =>
% 106.65/14.44 ((
% 106.65/14.44 (injFuncSetFuncInj) =>
% 106.65/14.44 ((
% 106.65/14.44 (surjFuncSetFuncIn) =>
% 106.65/14.44 ((
% 106.65/14.44 (surjFuncSetFuncSurj) =>
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% 106.65/14.44 (leftInvIsSurj) =>
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% 106.65/14.44 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.65/14.44 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl408])).
% 106.65/14.44 thf(zip_derived_cl428, plain,
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% 106.65/14.44 (((exuE3u) =>
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% 106.65/14.44 (((powerset__Cong) =>
% 106.65/14.44 (((setunion__Cong) =>
% 106.65/14.44 (((exuEu) =>
% 106.65/14.44 ((
% 106.65/14.44 (descr__Cong) =>
% 106.65/14.44 ((
% 106.65/14.44 (dsetconstr__Cong) =>
% 106.65/14.44 ((
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% 106.65/14.44 ((
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% 106.65/14.44 ((
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% 106.65/14.44 ((
% 106.65/14.44 (subsetTrans) =>
% 106.65/14.44 ((
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% 106.65/14.44 ((
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% 106.65/14.44 ((
% 106.65/14.44 (sepInPowerset) =>
% 106.65/14.44 ((
% 106.65/14.44 (sepSubset) =>
% 106.65/14.44 ((
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% 106.65/14.44 ((
% 106.65/14.44 (upairset2IR) =>
% 106.65/14.44 ((
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% 106.65/14.44 ((
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% 106.65/14.44 ((
% 106.65/14.44 (binunionE) =>
% 106.65/14.44 ((
% 106.65/14.44 (binunionLsub) =>
% 106.65/14.44 ((
% 106.65/14.44 (binunionRsub) =>
% 106.65/14.44 ((
% 106.65/14.44 (binintersectI) =>
% 106.65/14.44 ((
% 106.65/14.44 (binintersectSubset5) =>
% 106.65/14.44 ((
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% 106.65/14.44 ((
% 106.65/14.44 (binintersectLsub) =>
% 106.65/14.44 ((
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% 106.65/14.44 ((
% 106.65/14.44 (binintersectSubset3) =>
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% 106.65/14.44 ((
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% 106.65/14.44 ((
% 106.65/14.44 (binintersectSubset4) =>
% 106.65/14.44 ((
% 106.65/14.44 (binintersectSubset1) =>
% 106.65/14.44 ((
% 106.65/14.44 (bs114d) =>
% 106.65/14.44 ((
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% 106.65/14.44 ((
% 106.65/14.44 (setminusEL) =>
% 106.65/14.44 ((
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% 106.65/14.44 ((
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% 106.65/14.44 ((
% 106.65/14.44 (setminusILneg) =>
% 106.65/14.44 ((
% 106.65/14.44 (setminusIRneg) =>
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% 106.65/14.44 ((
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% 106.65/14.44 (symdiffE) =>
% 106.65/14.44 ((
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% 106.65/14.44 ((
% 106.65/14.44 (symdiffI2) =>
% 106.65/14.44 ((
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% 106.65/14.44 ((
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% 106.65/14.44 ((
% 106.65/14.44 (setukpairIR) =>
% 106.65/14.44 ((
% 106.65/14.44 (kpairiskpair) =>
% 106.65/14.44 ((
% 106.65/14.44 (kpairp) =>
% 106.65/14.44 ((
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% 106.65/14.44 ((
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% 106.65/14.44 ((
% 106.65/14.44 (singletoninpowunion) =>
% 106.65/14.44 ((
% 106.65/14.44 (upairset2E) =>
% 106.65/14.44 ((
% 106.65/14.44 (upairsubunion) =>
% 106.65/14.44 ((
% 106.65/14.44 (upairinpowunion) =>
% 106.65/14.44 ((
% 106.65/14.44 (ubforcartprodlem1) =>
% 106.65/14.44 ((
% 106.65/14.44 (ubforcartprodlem2) =>
% 106.65/14.44 ((
% 106.65/14.44 (ubforcartprodlem3) =>
% 106.65/14.44 ((
% 106.65/14.44 (cartprodpairin) =>
% 106.65/14.44 ((
% 106.65/14.44 (cartprodmempair1) =>
% 106.65/14.44 ((
% 106.65/14.44 (cartprodmempair) =>
% 106.65/14.44 ((
% 106.65/14.44 (setunionE2) =>
% 106.65/14.44 ((
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% 106.65/14.44 ((
% 106.65/14.44 (setunionsingleton2) =>
% 106.65/14.44 ((
% 106.65/14.44 (setunionsingleton) =>
% 106.65/14.44 ((
% 106.65/14.44 (singletonprop) =>
% 106.65/14.44 ((
% 106.65/14.44 (ex1E1) =>
% 106.65/14.44 ((
% 106.65/14.44 (ex1I) =>
% 106.65/14.44 ((
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% 106.65/14.44 ((
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% 106.65/14.44 ((
% 106.65/14.44 (setukpairinjL1) =>
% 106.65/14.44 ((
% 106.65/14.44 (kfstsingleton) =>
% 106.65/14.44 ((
% 106.65/14.44 (theprop) =>
% 106.65/14.44 ((
% 106.65/14.44 (kfstpairEq) =>
% 106.65/14.44 ((
% 106.65/14.44 (cartprodfstin) =>
% 106.65/14.44 ((
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% 106.65/14.44 ((
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% 106.65/14.44 ((
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% 106.65/14.44 ((
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% 106.65/14.44 (setukpairinjR) =>
% 106.65/14.44 ((
% 106.65/14.44 (ksndsingleton) =>
% 106.65/14.44 ((
% 106.65/14.44 (ksndpairEq) =>
% 106.65/14.44 ((
% 106.65/14.44 (kpairsurjEq) =>
% 106.65/14.44 ((
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% 106.65/14.44 ((
% 106.65/14.44 (cartprodpairmemEL) =>
% 106.65/14.44 ((
% 106.65/14.44 (cartprodpairmemER) =>
% 106.65/14.44 ((
% 106.65/14.44 (cartprodmempaircEq) =>
% 106.65/14.44 ((
% 106.65/14.44 (cartprodfstpairEq) =>
% 106.65/14.44 ((
% 106.65/14.44 (cartprodsndpairEq) =>
% 106.65/14.44 ((
% 106.65/14.44 (cartprodpairsurjEq) =>
% 106.65/14.44 ((
% 106.65/14.44 (dpsetconstrI) =>
% 106.65/14.44 ((
% 106.65/14.44 (dpsetconstrSub) =>
% 106.65/14.44 ((
% 106.65/14.44 (setOfPairsIsBReln) =>
% 106.65/14.44 ((
% 106.65/14.44 (dpsetconstrERa) =>
% 106.65/14.44 ((
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% 106.65/14.44 ((
% 106.65/14.44 (dpsetconstrEL2) =>
% 106.65/14.44 ((
% 106.65/14.44 (dpsetconstrER) =>
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% 106.65/14.44 ((
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% 106.65/14.44 ((
% 106.65/14.44 (lam2p) =>
% 106.65/14.44 ((
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% 106.65/14.44 ((
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% 106.65/14.44 (inIntersectImpInUnion2) =>
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% 106.65/14.44 (inComplementUnionImpNotIn1) =>
% 106.65/14.44 ((
% 106.65/14.44 (inComplementUnionImpInComplement1) =>
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% 106.65/14.44 (demorgan1) =>
% 106.65/14.44 ((
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% 106.65/14.44 (demorgan2b2) =>
% 106.65/14.44 ((
% 106.65/14.44 (demorgan2b) =>
% 106.65/14.44 ((
% 106.65/14.44 (demorgan2) =>
% 106.65/14.44 ((
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% 106.65/14.44 ((
% 106.65/14.44 (woz13rule1) =>
% 106.65/14.44 ((
% 106.65/14.44 (woz13rule2) =>
% 106.65/14.44 ((
% 106.65/14.44 (woz13rule3) =>
% 106.65/14.44 ((
% 106.65/14.44 (woz13rule4) =>
% 106.65/14.44 ((
% 106.65/14.44 (woz1_1) =>
% 106.65/14.44 ((
% 106.65/14.44 (woz1_2) =>
% 106.65/14.44 ((
% 106.65/14.44 (woz1_3) =>
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% 106.65/14.44 (woz1_5) =>
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% 106.65/14.44 ((
% 106.65/14.44 (breln1SetBreln1) =>
% 106.65/14.44 ((
% 106.65/14.44 (choice2fnsingleton) =>
% 106.65/14.44 ((
% 106.65/14.44 (setOfPairsIsBReln1) =>
% 106.65/14.44 ((
% 106.65/14.44 (breln1all1) =>
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% 106.65/14.44 (breln1invE) =>
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% 106.65/14.44 (breln1compprop) =>
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% 106.65/14.44 (breln1compI) =>
% 106.65/14.44 ((
% 106.65/14.44 (breln1compE) =>
% 106.65/14.44 ((
% 106.65/14.44 (breln1compEex) =>
% 106.65/14.44 ((
% 106.65/14.44 (breln1unionprop) =>
% 106.65/14.44 ((
% 106.65/14.44 (breln1unionIL) =>
% 106.65/14.44 ((
% 106.65/14.44 (breln1unionIR) =>
% 106.65/14.44 ((
% 106.65/14.44 (breln1unionI) =>
% 106.65/14.44 ((
% 106.65/14.44 (breln1unionE) =>
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% 106.65/14.44 (breln1unionEcases) =>
% 106.65/14.44 ((
% 106.65/14.44 (breln1unionCommutes) =>
% 106.65/14.44 ((
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% 106.65/14.44 (image1I) =>
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% 106.65/14.44 ((
% 106.65/14.44 (injFuncSetFuncIn) =>
% 106.65/14.44 ((
% 106.65/14.44 (injFuncSetFuncInj) =>
% 106.65/14.44 ((
% 106.65/14.44 (surjFuncSetFuncIn) =>
% 106.65/14.44 ((
% 106.65/14.44 (surjFuncSetFuncSurj) =>
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% 106.65/14.44 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl417])).
% 106.65/14.44 thf(zip_derived_cl439, plain,
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% 106.65/14.44 (((descr__Cong) =>
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% 106.65/14.44 (dsetconstr__Cong) =>
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% 106.65/14.44 ((
% 106.65/14.44 (subsetTrans) =>
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% 106.65/14.44 ((
% 106.65/14.44 (setadjoinSub2) =>
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% 106.65/14.44 ((
% 106.65/14.44 (setextsub) =>
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% 106.65/14.44 ((
% 106.65/14.44 (sepSubset) =>
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% 106.65/14.44 ((
% 106.65/14.44 (upairset2IR) =>
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% 106.65/14.44 ((
% 106.65/14.44 (binunionEcases) =>
% 106.65/14.44 ((
% 106.65/14.44 (binunionE) =>
% 106.65/14.44 ((
% 106.65/14.44 (binunionLsub) =>
% 106.65/14.44 ((
% 106.65/14.44 (binunionRsub) =>
% 106.65/14.44 ((
% 106.65/14.44 (binintersectI) =>
% 106.65/14.44 ((
% 106.65/14.44 (binintersectSubset5) =>
% 106.65/14.44 ((
% 106.65/14.44 (binintersectEL) =>
% 106.65/14.44 ((
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% 106.65/14.44 ((
% 106.65/14.44 (binintersectSubset2) =>
% 106.65/14.44 ((
% 106.65/14.44 (binintersectSubset3) =>
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% 106.65/14.44 ((
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% 106.65/14.44 ((
% 106.65/14.44 (binintersectSubset1) =>
% 106.65/14.44 ((
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% 106.65/14.44 ((
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% 106.65/14.44 ((
% 106.65/14.44 (setminusEL) =>
% 106.65/14.44 ((
% 106.65/14.44 (setminusER) =>
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% 106.65/14.44 (setminusSubset2) =>
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% 106.65/14.44 (setminusELneg) =>
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% 106.65/14.44 (setminusIRneg) =>
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% 106.65/14.44 (setminusLsub) =>
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% 106.65/14.44 (symdiffI1) =>
% 106.65/14.44 ((
% 106.65/14.44 (symdiffI2) =>
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% 106.65/14.44 (kpairiskpair) =>
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% 106.65/14.44 (kpairp) =>
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% 106.65/14.44 ((
% 106.65/14.44 (upairsubunion) =>
% 106.65/14.44 ((
% 106.65/14.44 (upairinpowunion) =>
% 106.65/14.44 ((
% 106.65/14.44 (ubforcartprodlem1) =>
% 106.65/14.44 ((
% 106.65/14.44 (ubforcartprodlem2) =>
% 106.65/14.44 ((
% 106.65/14.44 (ubforcartprodlem3) =>
% 106.65/14.44 ((
% 106.65/14.44 (cartprodpairin) =>
% 106.65/14.44 ((
% 106.65/14.44 (cartprodmempair1) =>
% 106.65/14.44 ((
% 106.65/14.44 (cartprodmempair) =>
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% 106.65/14.44 (setunionE2) =>
% 106.65/14.44 ((
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% 106.65/14.44 ((
% 106.65/14.44 (setunionsingleton2) =>
% 106.65/14.44 ((
% 106.65/14.44 (setunionsingleton) =>
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% 106.65/14.44 ((
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% 106.65/14.44 ((
% 106.65/14.44 (ex1I) =>
% 106.65/14.44 ((
% 106.65/14.44 (ex1I2) =>
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% 106.65/14.44 ((
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% 106.65/14.44 ((
% 106.65/14.44 (theprop) =>
% 106.65/14.44 ((
% 106.65/14.44 (kfstpairEq) =>
% 106.65/14.44 ((
% 106.65/14.44 (cartprodfstin) =>
% 106.65/14.44 ((
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% 106.65/14.44 ((
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% 106.65/14.44 ((
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% 106.65/14.44 ((
% 106.65/14.44 (kpairsurjEq) =>
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% 106.65/14.44 (cartprodpairmemER) =>
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% 106.65/14.44 (cartprodmempaircEq) =>
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% 106.65/14.44 (cartprodfstpairEq) =>
% 106.65/14.44 ((
% 106.65/14.44 (cartprodsndpairEq) =>
% 106.65/14.44 ((
% 106.65/14.44 (cartprodpairsurjEq) =>
% 106.65/14.44 ((
% 106.65/14.44 (dpsetconstrI) =>
% 106.65/14.44 ((
% 106.65/14.44 (dpsetconstrSub) =>
% 106.65/14.44 ((
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% 106.65/14.44 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl428])).
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% 106.65/14.44 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl439])).
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% 106.65/14.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl467])).
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% 106.65/14.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl485])).
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% 106.65/14.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl507])).
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% 106.65/14.46 (breln1compEex) =>
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% 106.65/14.46 (breln1unionI) =>
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% 106.65/14.46 (breln1unionCommutes) =>
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% 106.65/14.46 (injFuncSetFuncInj) =>
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% 106.65/14.46 (surjFuncSetFuncSurj) =>
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% 106.65/14.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl537])).
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% 106.65/14.46 (((exuE3u) =>
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% 106.65/14.46 (((powerset__Cong) =>
% 106.65/14.46 (((setunion__Cong) =>
% 106.65/14.46 (((exuEu) =>
% 106.65/14.46 (((descr__Cong) =>
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% 106.65/14.46 ((
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% 106.65/14.46 (kpairsurjEq) =>
% 106.65/14.46 ((
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% 106.65/14.46 ((
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% 106.65/14.46 ((
% 106.65/14.46 (cartprodpairmemER) =>
% 106.65/14.46 ((
% 106.65/14.46 (cartprodmempaircEq) =>
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% 106.65/14.46 (cartprodfstpairEq) =>
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% 106.65/14.46 (cartprodsndpairEq) =>
% 106.65/14.46 ((
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% 106.65/14.46 (inComplementUnionImpInComplement1) =>
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% 106.65/14.46 ((
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% 106.65/14.46 (demorgan2a) =>
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% 106.65/14.46 (demorgan2b2) =>
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% 106.65/14.46 (demorgan2b) =>
% 106.65/14.46 ((
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% 106.65/14.46 ((
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% 106.65/14.46 ((
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% 106.65/14.46 (breln1compI) =>
% 106.65/14.46 ((
% 106.65/14.46 (breln1compE) =>
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% 106.65/14.46 (breln1compEex) =>
% 106.65/14.46 ((
% 106.65/14.46 (breln1unionprop) =>
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% 106.65/14.46 (breln1unionI) =>
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% 106.65/14.46 (breln1unionCommutes) =>
% 106.65/14.46 ((
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% 106.65/14.46 (image1I) =>
% 106.65/14.46 ((
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% 106.65/14.46 ((
% 106.65/14.46 (injFuncSetFuncIn) =>
% 106.65/14.46 ((
% 106.65/14.46 (injFuncSetFuncInj) =>
% 106.65/14.46 ((
% 106.65/14.46 (surjFuncSetFuncIn) =>
% 106.65/14.46 ((
% 106.65/14.46 (surjFuncSetFuncSurj) =>
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% 106.65/14.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl546])).
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% 106.65/14.46 (((exuI2) =>
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% 106.65/14.46 (((in__Cong) =>
% 106.65/14.46 (((exuE3u) =>
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% 106.65/14.46 (((setadjoin__Cong) =>
% 106.65/14.46 (((powerset__Cong) =>
% 106.65/14.46 (((setunion__Cong) =>
% 106.65/14.46 (((exuEu) =>
% 106.65/14.46 (((descr__Cong) =>
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% 106.65/14.46 ((
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% 106.65/14.46 (binunionRsub) =>
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% 106.65/14.46 (binintersectSubset3) =>
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% 106.65/14.46 ((
% 106.65/14.46 (binintersectRsub) =>
% 106.65/14.46 ((
% 106.65/14.46 (binintersectSubset4) =>
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% 106.65/14.46 ((
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% 106.65/14.46 (symdiffI2) =>
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% 106.65/14.46 (upairinpowunion) =>
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% 106.65/14.46 (ubforcartprodlem2) =>
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% 106.65/14.46 ((
% 106.65/14.46 (setukpairinjR1) =>
% 106.65/14.46 ((
% 106.65/14.46 (upairequniteq) =>
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% 106.65/14.46 (kpairsurjEq) =>
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% 106.65/14.46 (cartprodsndin) =>
% 106.65/14.46 ((
% 106.65/14.46 (cartprodpairmemEL) =>
% 106.65/14.46 ((
% 106.65/14.46 (cartprodpairmemER) =>
% 106.65/14.46 ((
% 106.65/14.46 (cartprodmempaircEq) =>
% 106.65/14.46 ((
% 106.65/14.46 (cartprodfstpairEq) =>
% 106.65/14.46 ((
% 106.65/14.46 (cartprodsndpairEq) =>
% 106.65/14.46 ((
% 106.65/14.46 (cartprodpairsurjEq) =>
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% 106.65/14.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl553])).
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% 106.65/14.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl561])).
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% 106.65/14.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl570])).
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% 106.65/14.47 (demorgan2a2) =>
% 106.65/14.47 ((
% 106.65/14.47 (demorgan1a) =>
% 106.65/14.47 ((
% 106.65/14.47 (demorgan1b) =>
% 106.65/14.47 ((
% 106.65/14.47 (demorgan1) =>
% 106.65/14.47 ((
% 106.65/14.47 (demorgan2a) =>
% 106.65/14.47 ((
% 106.65/14.47 (demorgan2b2) =>
% 106.65/14.47 ((
% 106.65/14.47 (demorgan2b) =>
% 106.65/14.47 ((
% 106.65/14.47 (demorgan2) =>
% 106.65/14.47 ((
% 106.65/14.47 (woz13rule0) =>
% 106.65/14.47 ((
% 106.65/14.47 (woz13rule1) =>
% 106.65/14.47 ((
% 106.65/14.47 (woz13rule2) =>
% 106.65/14.47 ((
% 106.65/14.47 (woz13rule3) =>
% 106.65/14.47 ((
% 106.65/14.47 (woz13rule4) =>
% 106.65/14.47 ((
% 106.65/14.47 (woz1_1) =>
% 106.65/14.47 ((
% 106.65/14.47 (woz1_2) =>
% 106.65/14.47 ((
% 106.65/14.47 (woz1_3) =>
% 106.65/14.47 ((
% 106.65/14.47 (woz1_4) =>
% 106.65/14.47 ((
% 106.65/14.47 (woz1_5) =>
% 106.65/14.47 ((
% 106.65/14.47 (breln1all2) =>
% 106.65/14.47 ((
% 106.65/14.47 (breln1SetBreln1) =>
% 106.65/14.47 ((
% 106.65/14.47 (choice2fnsingleton) =>
% 106.65/14.47 ((
% 106.65/14.47 (setOfPairsIsBReln1) =>
% 106.65/14.47 ((
% 106.65/14.47 (breln1all1) =>
% 106.65/14.47 ((
% 106.65/14.47 (subbreln1) =>
% 106.65/14.47 ((
% 106.65/14.47 (eqbreln1) =>
% 106.65/14.47 ((
% 106.65/14.47 (breln1invprop) =>
% 106.65/14.47 ((
% 106.65/14.47 (breln1invI) =>
% 106.65/14.47 ((
% 106.65/14.47 (breln1invE) =>
% 106.65/14.47 ((
% 106.65/14.47 (breln1compprop) =>
% 106.65/14.47 ((
% 106.65/14.47 (breln1compI) =>
% 106.65/14.47 ((
% 106.65/14.47 (breln1compE) =>
% 106.65/14.47 ((
% 106.65/14.47 (breln1compEex) =>
% 106.65/14.47 ((
% 106.65/14.47 (breln1unionprop) =>
% 106.65/14.47 ((
% 106.65/14.47 (breln1unionIL) =>
% 106.65/14.47 ((
% 106.65/14.47 (breln1unionIR) =>
% 106.65/14.47 ((
% 106.65/14.47 (breln1unionI) =>
% 106.65/14.47 ((
% 106.65/14.47 (breln1unionE) =>
% 106.65/14.47 ((
% 106.65/14.47 (breln1unionEcases) =>
% 106.65/14.47 ((
% 106.65/14.47 (breln1unionCommutes) =>
% 106.65/14.47 ((
% 106.65/14.47 (woz2Ex) =>
% 106.65/14.47 ((
% 106.65/14.47 (woz2W) =>
% 106.65/14.47 ((
% 106.65/14.47 (woz2A) =>
% 106.65/14.47 ((
% 106.65/14.47 (woz2B) =>
% 106.65/14.47 ((
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% 106.65/14.47 ((
% 106.65/14.47 (image1Ex1) =>
% 106.65/14.47 ((
% 106.65/14.47 (image1Equiv) =>
% 106.65/14.47 ((
% 106.65/14.47 (image1E) =>
% 106.65/14.47 ((
% 106.65/14.47 (image1I) =>
% 106.65/14.47 ((
% 106.65/14.47 (injFuncInInjFuncSet) =>
% 106.65/14.47 ((
% 106.65/14.47 (injFuncSetFuncIn) =>
% 106.65/14.47 ((
% 106.65/14.47 (injFuncSetFuncInj) =>
% 106.65/14.47 ((
% 106.65/14.47 (surjFuncSetFuncIn) =>
% 106.65/14.47 ((
% 106.65/14.47 (surjFuncSetFuncSurj) =>
% 106.65/14.47 ((
% 106.65/14.47 (leftInvIsSurj) =>
% 106.65/14.47 ((
% 106.65/14.47 (surjCantorThm) =>
% 106.65/14.47 ((
% 106.65/14.47 (!!) @ (
% 106.65/14.47 (('#S') @ (
% 106.65/14.47 (
% 106.65/14.47 ('#B') @ (
% 106.65/14.47 =>) @
% 106.65/14.47 nonempty)) @
% 106.65/14.47 (
% 106.65/14.47 (
% 106.65/14.47 ('#B') @ (
% 106.65/14.47 ??) @
% 106.65/14.47 (
% 106.65/14.47 (
% 106.65/14.47 ('#S') @ (
% 106.65/14.47 (
% 106.65/14.47 ('#B') @ (
% 106.65/14.47 '#S') @
% 106.65/14.47 (
% 106.65/14.47 (
% 106.65/14.47 ('#B') @ (
% 106.65/14.47 (
% 106.65/14.47 ('#B') @ (
% 106.65/14.47 &))) @
% 106.65/14.47 (
% 106.65/14.47 (
% 106.65/14.47 ('#C') @ in)))))) @
% 106.65/14.47 (
% 106.65/14.47 (
% 106.65/14.47 ('#C') @ (
% 106.65/14.47 (
% 106.65/14.47 ('#B') @ (
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% 106.65/14.47 (
% 106.65/14.47 (
% 106.65/14.47 ('#B') @ (
% 106.65/14.47 (
% 106.65/14.47 ('#B') @ (
% 106.65/14.47 =))) @
% 106.65/14.47 (
% 106.65/14.47 (
% 106.65/14.47 ('#C') @ binintersect)))))) @
% 106.65/14.47 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.65/14.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl578])).
% 106.65/14.47 thf(zip_derived_cl595, plain,
% 106.65/14.47 (~ (((notdallE) =>
% 106.65/14.47 (((exuI1) =>
% 106.65/14.47 (((exuI3) =>
% 106.65/14.47 (((exuI2) =>
% 106.65/14.47 (((inCongP) =>
% 106.65/14.47 (((in__Cong) =>
% 106.65/14.47 (((exuE3u) =>
% 106.65/14.47 (((exu__Cong) =>
% 106.65/14.47 (((setadjoin__Cong) =>
% 106.65/14.47 (((powerset__Cong) =>
% 106.65/14.47 (((setunion__Cong) =>
% 106.65/14.47 (((exuEu) =>
% 106.65/14.47 (((descr__Cong) =>
% 106.65/14.47 (((dsetconstr__Cong) =>
% 106.65/14.47 (((subsetI1) =>
% 106.65/14.47 (((eqimpsubset2) =>
% 106.65/14.47 (((eqimpsubset1) =>
% 106.65/14.47 (((subsetI2) =>
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% 106.65/14.47 (((subsetE) =>
% 106.65/14.47 (((subsetE2) =>
% 106.65/14.47 (((notsubsetI) =>
% 106.65/14.47 (((notequalI1) =>
% 106.65/14.47 (((notequalI2) =>
% 106.65/14.47 (((subsetRefl) =>
% 106.65/14.47 (((subsetTrans) =>
% 106.65/14.47 (((setadjoinSub) =>
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% 106.65/14.47 (((setextsub) =>
% 106.65/14.47 ((
% 106.65/14.47 (subsetemptysetimpeq) =>
% 106.65/14.47 ((
% 106.65/14.47 (powersetI1) =>
% 106.65/14.47 ((
% 106.65/14.47 (powersetE1) =>
% 106.65/14.47 ((
% 106.65/14.47 (inPowerset) =>
% 106.65/14.47 ((
% 106.65/14.47 (powersetsubset) =>
% 106.65/14.47 ((
% 106.65/14.47 (sepInPowerset) =>
% 106.65/14.47 ((
% 106.65/14.47 (sepSubset) =>
% 106.65/14.47 ((
% 106.65/14.47 (binunionIL) =>
% 106.65/14.47 ((
% 106.65/14.47 (upairset2IR) =>
% 106.65/14.47 ((
% 106.65/14.47 (binunionIR) =>
% 106.65/14.47 ((
% 106.65/14.47 (binunionEcases) =>
% 106.65/14.47 ((
% 106.65/14.47 (binunionE) =>
% 106.65/14.47 ((
% 106.65/14.47 (binunionLsub) =>
% 106.65/14.47 ((
% 106.65/14.47 (binunionRsub) =>
% 106.65/14.47 ((
% 106.65/14.47 (binintersectI) =>
% 106.65/14.47 ((
% 106.65/14.47 (binintersectSubset5) =>
% 106.65/14.47 ((
% 106.65/14.47 (binintersectEL) =>
% 106.65/14.47 ((
% 106.65/14.47 (binintersectLsub) =>
% 106.65/14.47 ((
% 106.65/14.47 (binintersectSubset2) =>
% 106.65/14.47 ((
% 106.65/14.47 (binintersectSubset3) =>
% 106.65/14.47 ((
% 106.65/14.47 (binintersectER) =>
% 106.65/14.47 ((
% 106.65/14.47 (disjointsetsI1) =>
% 106.65/14.47 ((
% 106.65/14.47 (binintersectRsub) =>
% 106.65/14.47 ((
% 106.65/14.47 (binintersectSubset4) =>
% 106.65/14.47 ((
% 106.65/14.47 (binintersectSubset1) =>
% 106.65/14.47 ((
% 106.65/14.47 (bs114d) =>
% 106.65/14.47 ((
% 106.65/14.47 (setminusI) =>
% 106.65/14.47 ((
% 106.65/14.47 (setminusEL) =>
% 106.65/14.47 ((
% 106.65/14.47 (setminusER) =>
% 106.65/14.47 ((
% 106.65/14.47 (setminusSubset2) =>
% 106.65/14.47 ((
% 106.65/14.47 (setminusERneg) =>
% 106.65/14.47 ((
% 106.65/14.47 (setminusELneg) =>
% 106.65/14.47 ((
% 106.65/14.47 (setminusILneg) =>
% 106.65/14.47 ((
% 106.65/14.47 (setminusIRneg) =>
% 106.65/14.47 ((
% 106.65/14.47 (setminusLsub) =>
% 106.65/14.47 ((
% 106.65/14.47 (setminusSubset1) =>
% 106.65/14.47 ((
% 106.65/14.47 (symdiffE) =>
% 106.65/14.47 ((
% 106.65/14.47 (symdiffI1) =>
% 106.65/14.47 ((
% 106.65/14.47 (symdiffI2) =>
% 106.65/14.47 ((
% 106.65/14.47 (symdiffIneg1) =>
% 106.65/14.47 ((
% 106.65/14.47 (symdiffIneg2) =>
% 106.65/14.47 ((
% 106.65/14.47 (secondinupair) =>
% 106.65/14.47 ((
% 106.65/14.47 (setukpairIL) =>
% 106.65/14.47 ((
% 106.65/14.47 (setukpairIR) =>
% 106.65/14.47 ((
% 106.65/14.47 (kpairiskpair) =>
% 106.65/14.47 ((
% 106.65/14.47 (kpairp) =>
% 106.65/14.47 ((
% 106.65/14.47 (singletonsubset) =>
% 106.65/14.47 ((
% 106.65/14.47 (singletoninpowerset) =>
% 106.65/14.47 ((
% 106.65/14.47 (singletoninpowunion) =>
% 106.65/14.47 ((
% 106.65/14.47 (upairset2E) =>
% 106.65/14.47 ((
% 106.65/14.47 (upairsubunion) =>
% 106.65/14.47 ((
% 106.65/14.47 (upairinpowunion) =>
% 106.65/14.47 ((
% 106.65/14.47 (ubforcartprodlem1) =>
% 106.65/14.47 ((
% 106.65/14.47 (ubforcartprodlem2) =>
% 106.65/14.47 ((
% 106.65/14.47 (ubforcartprodlem3) =>
% 106.65/14.47 ((
% 106.65/14.47 (cartprodpairin) =>
% 106.65/14.47 ((
% 106.65/14.47 (cartprodmempair1) =>
% 106.65/14.47 ((
% 106.65/14.47 (cartprodmempair) =>
% 106.65/14.47 ((
% 106.65/14.47 (setunionE2) =>
% 106.65/14.47 ((
% 106.65/14.47 (setunionsingleton1) =>
% 106.65/14.47 ((
% 106.65/14.47 (setunionsingleton2) =>
% 106.65/14.47 ((
% 106.65/14.47 (setunionsingleton) =>
% 106.65/14.47 ((
% 106.65/14.47 (singletonprop) =>
% 106.65/14.47 ((
% 106.65/14.47 (ex1E1) =>
% 106.65/14.47 ((
% 106.65/14.47 (ex1I) =>
% 106.65/14.47 ((
% 106.65/14.47 (ex1I2) =>
% 106.65/14.47 ((
% 106.65/14.47 (singletonsuniq) =>
% 106.65/14.47 ((
% 106.65/14.47 (setukpairinjL1) =>
% 106.65/14.47 ((
% 106.65/14.47 (kfstsingleton) =>
% 106.65/14.47 ((
% 106.65/14.47 (theprop) =>
% 106.65/14.47 ((
% 106.65/14.47 (kfstpairEq) =>
% 106.65/14.47 ((
% 106.65/14.47 (cartprodfstin) =>
% 106.65/14.47 ((
% 106.65/14.47 (setukpairinjL2) =>
% 106.65/14.47 ((
% 106.65/14.47 (setukpairinjL) =>
% 106.65/14.47 ((
% 106.65/14.47 (setukpairinjR11) =>
% 106.65/14.47 ((
% 106.65/14.47 (setukpairinjR12) =>
% 106.65/14.47 ((
% 106.65/14.47 (setukpairinjR1) =>
% 106.65/14.47 ((
% 106.65/14.47 (upairequniteq) =>
% 106.65/14.47 ((
% 106.65/14.47 (setukpairinjR2) =>
% 106.65/14.47 ((
% 106.65/14.47 (setukpairinjR) =>
% 106.65/14.47 ((
% 106.65/14.47 (ksndsingleton) =>
% 106.65/14.47 ((
% 106.65/14.47 (ksndpairEq) =>
% 106.65/14.47 ((
% 106.65/14.47 (kpairsurjEq) =>
% 106.65/14.47 ((
% 106.65/14.47 (cartprodsndin) =>
% 106.65/14.47 ((
% 106.65/14.47 (cartprodpairmemEL) =>
% 106.65/14.47 ((
% 106.65/14.47 (cartprodpairmemER) =>
% 106.65/14.47 ((
% 106.65/14.47 (cartprodmempaircEq) =>
% 106.65/14.47 ((
% 106.65/14.47 (cartprodfstpairEq) =>
% 106.65/14.47 ((
% 106.65/14.47 (cartprodsndpairEq) =>
% 106.65/14.47 ((
% 106.65/14.47 (cartprodpairsurjEq) =>
% 106.65/14.47 ((
% 106.65/14.47 (dpsetconstrI) =>
% 106.65/14.47 ((
% 106.65/14.47 (dpsetconstrSub) =>
% 106.65/14.47 ((
% 106.65/14.47 (setOfPairsIsBReln) =>
% 106.65/14.47 ((
% 106.65/14.47 (dpsetconstrERa) =>
% 106.65/14.47 ((
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% 106.65/14.47 ((
% 106.65/14.47 (dpsetconstrEL2) =>
% 106.65/14.47 ((
% 106.65/14.47 (dpsetconstrER) =>
% 106.65/14.47 ((
% 106.65/14.47 (funcImageSingleton) =>
% 106.65/14.47 ((
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% 106.65/14.47 ((
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% 106.65/14.47 ((
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% 106.65/14.47 (ap2p) =>
% 106.65/14.47 ((
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% 106.65/14.47 ((
% 106.65/14.47 (lamp) =>
% 106.65/14.47 ((
% 106.65/14.47 (lam2p) =>
% 106.65/14.47 ((
% 106.65/14.47 (brelnall1) =>
% 106.65/14.47 ((
% 106.65/14.47 (brelnall2) =>
% 106.65/14.47 ((
% 106.65/14.47 (ex1E2) =>
% 106.65/14.47 ((
% 106.65/14.47 (funcGraphProp1) =>
% 106.65/14.47 ((
% 106.65/14.47 (funcGraphProp3) =>
% 106.65/14.47 ((
% 106.65/14.47 (funcGraphProp2) =>
% 106.65/14.47 ((
% 106.65/14.47 (funcextLem) =>
% 106.65/14.47 ((
% 106.65/14.47 (funcGraphProp4) =>
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% 106.65/14.47 ((
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% 106.65/14.47 ((
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% 106.65/14.47 ((
% 106.65/14.47 (funcext2) =>
% 106.65/14.47 ((
% 106.65/14.47 (ap2apEq1) =>
% 106.65/14.47 ((
% 106.65/14.47 (ap2apEq2) =>
% 106.65/14.47 ((
% 106.65/14.47 (beta1) =>
% 106.65/14.47 ((
% 106.65/14.47 (eta1) =>
% 106.65/14.47 ((
% 106.65/14.47 (lam2lamEq) =>
% 106.65/14.47 ((
% 106.65/14.47 (beta2) =>
% 106.65/14.47 ((
% 106.65/14.47 (eta2) =>
% 106.65/14.47 ((
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% 106.65/14.47 ((
% 106.65/14.47 (iffalseProp2) =>
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% 106.65/14.47 (iftrueProp1) =>
% 106.65/14.47 ((
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% 106.65/14.47 ((
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% 106.65/14.47 ((
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% 106.65/14.47 ((
% 106.65/14.47 (setminusT_lem) =>
% 106.65/14.47 ((
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% 106.65/14.47 ((
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% 106.65/14.47 ((
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% 106.65/14.47 ((
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% 106.65/14.47 ((
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% 106.65/14.47 ((
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% 106.65/14.47 ((
% 106.65/14.47 (contrasubsetT3) =>
% 106.65/14.47 ((
% 106.65/14.47 (doubleComplementI1) =>
% 106.65/14.47 ((
% 106.65/14.47 (doubleComplementE1) =>
% 106.65/14.47 ((
% 106.65/14.47 (doubleComplementSub1) =>
% 106.65/14.47 ((
% 106.65/14.47 (doubleComplementSub2) =>
% 106.65/14.47 ((
% 106.65/14.47 (doubleComplementEq) =>
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% 106.65/14.47 (complementInPowersetComplementIntersect) =>
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% 106.65/14.47 ((
% 106.65/14.47 (complementTcontraSubset) =>
% 106.65/14.47 ((
% 106.65/14.47 (binunionTILcontra) =>
% 106.65/14.47 ((
% 106.65/14.47 (binunionTIRcontra) =>
% 106.65/14.47 ((
% 106.65/14.47 (inIntersectImpInUnion) =>
% 106.65/14.47 ((
% 106.65/14.47 (inIntersectImpInUnion2) =>
% 106.65/14.47 ((
% 106.65/14.47 (inIntersectImpInIntersectUnions) =>
% 106.65/14.47 ((
% 106.65/14.47 (intersectInPowersetIntersectUnions) =>
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% 106.65/14.47 (inComplementUnionImpNotIn1) =>
% 106.65/14.47 ((
% 106.65/14.47 (inComplementUnionImpInComplement1) =>
% 106.65/14.47 ((
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% 106.65/14.47 ((
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% 106.65/14.47 ((
% 106.65/14.47 (complementUnionInPowersetComplement) =>
% 106.65/14.47 ((
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% 106.65/14.47 ((
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% 106.65/14.47 (breln1compEex) =>
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% 106.65/14.47 (breln1unionCommutes) =>
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% 106.65/14.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl595])).
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% 106.65/14.47 ((
% 106.65/14.47 (kpairsurjEq) =>
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% 106.65/14.47 (cartprodsndin) =>
% 106.65/14.47 ((
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% 106.65/14.47 (cartprodpairmemER) =>
% 106.65/14.47 ((
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% 106.65/14.47 (cartprodpairsurjEq) =>
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% 106.65/14.47 (breln1compEex) =>
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% 106.65/14.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl606])).
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% 106.65/14.47 (kpairsurjEq) =>
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% 106.65/14.47 ((
% 106.65/14.47 (cartprodpairmemEL) =>
% 106.65/14.47 ((
% 106.65/14.47 (cartprodpairmemER) =>
% 106.65/14.47 ((
% 106.65/14.47 (cartprodmempaircEq) =>
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% 106.65/14.47 (cartprodsndpairEq) =>
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% 106.65/14.47 ('#B') @ (
% 106.65/14.47 =>) @
% 106.65/14.47 nonempty)) @
% 106.65/14.47 (
% 106.65/14.47 (
% 106.65/14.47 ('#B') @ (
% 106.65/14.47 ??) @
% 106.65/14.47 (
% 106.65/14.47 (
% 106.65/14.47 ('#S') @ (
% 106.65/14.47 (
% 106.65/14.47 ('#B') @ (
% 106.65/14.47 '#S') @
% 106.65/14.47 (
% 106.65/14.47 (
% 106.65/14.47 ('#B') @ (
% 106.65/14.47 (
% 106.65/14.47 ('#B') @ (
% 106.65/14.47 &))) @
% 106.65/14.47 (
% 106.65/14.47 (
% 106.65/14.47 ('#C') @ in)))))) @
% 106.65/14.47 (
% 106.65/14.47 (
% 106.65/14.47 ('#C') @ (
% 106.65/14.47 (
% 106.65/14.47 ('#B') @ (
% 106.65/14.47 '#C') @
% 106.65/14.47 (
% 106.65/14.47 (
% 106.65/14.47 ('#B') @ (
% 106.65/14.47 (
% 106.65/14.47 ('#B') @ (
% 106.65/14.47 =))) @
% 106.65/14.47 (
% 106.65/14.47 (
% 106.65/14.47 ('#C') @ binintersect)))))) @
% 106.65/14.47 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 106.65/14.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl630])).
% 106.65/14.47 thf(zip_derived_cl650, plain,
% 106.65/14.47 (~ (((in__Cong) =>
% 106.65/14.47 (((exuE3u) =>
% 106.65/14.47 (((exu__Cong) =>
% 106.65/14.47 (((setadjoin__Cong) =>
% 106.65/14.47 (((powerset__Cong) =>
% 106.65/14.47 (((setunion__Cong) =>
% 106.65/14.47 (((exuEu) =>
% 106.65/14.47 (((descr__Cong) =>
% 106.65/14.47 (((dsetconstr__Cong) =>
% 106.65/14.47 (((subsetI1) =>
% 106.65/14.47 (((eqimpsubset2) =>
% 106.65/14.47 (((eqimpsubset1) =>
% 106.65/14.47 (((subsetI2) =>
% 106.65/14.47 (((emptysetsubset) =>
% 106.65/14.47 (((subsetE) =>
% 106.65/14.47 (((subsetE2) =>
% 106.65/14.47 (((notsubsetI) =>
% 106.65/14.47 (((notequalI1) =>
% 106.65/14.47 (((notequalI2) =>
% 106.65/14.47 (((subsetRefl) =>
% 106.65/14.47 (((subsetTrans) =>
% 106.65/14.47 (((setadjoinSub) =>
% 106.65/14.47 (((setadjoinSub2) =>
% 106.65/14.47 (((subset2powerset) =>
% 106.65/14.47 (((setextsub) =>
% 106.65/14.47 (((subsetemptysetimpeq) =>
% 106.65/14.47 (((powersetI1) =>
% 106.65/14.47 (((powersetE1) =>
% 106.65/14.47 (((inPowerset) =>
% 106.65/14.47 (((powersetsubset) =>
% 106.65/14.47 ((
% 106.65/14.47 (sepInPowerset) =>
% 106.65/14.47 ((
% 106.65/14.47 (sepSubset) =>
% 106.65/14.47 ((
% 106.65/14.47 (binunionIL) =>
% 106.65/14.47 ((
% 106.65/14.47 (upairset2IR) =>
% 106.65/14.47 ((
% 106.65/14.47 (binunionIR) =>
% 106.65/14.47 ((
% 106.65/14.47 (binunionEcases) =>
% 106.65/14.47 ((
% 106.65/14.47 (binunionE) =>
% 106.65/14.47 ((
% 106.65/14.47 (binunionLsub) =>
% 106.65/14.47 ((
% 106.65/14.47 (binunionRsub) =>
% 106.65/14.47 ((
% 106.65/14.47 (binintersectI) =>
% 106.65/14.47 ((
% 106.65/14.47 (binintersectSubset5) =>
% 106.65/14.47 ((
% 106.65/14.47 (binintersectEL) =>
% 106.65/14.47 ((
% 106.65/14.47 (binintersectLsub) =>
% 106.65/14.47 ((
% 106.65/14.47 (binintersectSubset2) =>
% 106.65/14.47 ((
% 106.65/14.47 (binintersectSubset3) =>
% 106.65/14.47 ((
% 106.65/14.47 (binintersectER) =>
% 106.65/14.47 ((
% 106.65/14.47 (disjointsetsI1) =>
% 106.65/14.47 ((
% 106.65/14.47 (binintersectRsub) =>
% 106.65/14.47 ((
% 106.65/14.47 (binintersectSubset4) =>
% 106.65/14.47 ((
% 106.65/14.47 (binintersectSubset1) =>
% 106.65/14.47 ((
% 106.65/14.47 (bs114d) =>
% 106.65/14.47 ((
% 106.65/14.47 (setminusI) =>
% 106.65/14.47 ((
% 106.65/14.47 (setminusEL) =>
% 106.65/14.47 ((
% 106.65/14.47 (setminusER) =>
% 106.65/14.47 ((
% 106.65/14.47 (setminusSubset2) =>
% 106.65/14.47 ((
% 106.65/14.47 (setminusERneg) =>
% 106.65/14.47 ((
% 106.65/14.47 (setminusELneg) =>
% 106.65/14.47 ((
% 106.65/14.47 (setminusILneg) =>
% 106.65/14.47 ((
% 106.65/14.47 (setminusIRneg) =>
% 106.65/14.47 ((
% 106.65/14.47 (setminusLsub) =>
% 106.65/14.47 ((
% 106.65/14.47 (setminusSubset1) =>
% 106.65/14.47 ((
% 106.65/14.47 (symdiffE) =>
% 106.65/14.47 ((
% 106.65/14.47 (symdiffI1) =>
% 106.65/14.47 ((
% 106.65/14.47 (symdiffI2) =>
% 106.65/14.47 ((
% 106.65/14.47 (symdiffIneg1) =>
% 106.65/14.47 ((
% 106.65/14.47 (symdiffIneg2) =>
% 106.65/14.47 ((
% 106.65/14.47 (secondinupair) =>
% 106.65/14.47 ((
% 106.65/14.47 (setukpairIL) =>
% 106.65/14.47 ((
% 106.65/14.47 (setukpairIR) =>
% 106.65/14.47 ((
% 106.65/14.47 (kpairiskpair) =>
% 106.65/14.47 ((
% 106.65/14.47 (kpairp) =>
% 106.65/14.47 ((
% 106.65/14.47 (singletonsubset) =>
% 106.65/14.47 ((
% 106.65/14.47 (singletoninpowerset) =>
% 106.65/14.47 ((
% 106.65/14.47 (singletoninpowunion) =>
% 106.65/14.47 ((
% 106.65/14.47 (upairset2E) =>
% 106.65/14.47 ((
% 106.65/14.47 (upairsubunion) =>
% 106.65/14.47 ((
% 106.65/14.47 (upairinpowunion) =>
% 106.65/14.47 ((
% 106.65/14.47 (ubforcartprodlem1) =>
% 106.65/14.47 ((
% 106.65/14.47 (ubforcartprodlem2) =>
% 106.65/14.47 ((
% 106.65/14.47 (ubforcartprodlem3) =>
% 106.65/14.47 ((
% 106.65/14.47 (cartprodpairin) =>
% 106.65/14.47 ((
% 106.65/14.47 (cartprodmempair1) =>
% 106.65/14.47 ((
% 106.65/14.47 (cartprodmempair) =>
% 106.65/14.47 ((
% 106.65/14.47 (setunionE2) =>
% 106.65/14.47 ((
% 106.65/14.47 (setunionsingleton1) =>
% 106.65/14.47 ((
% 106.65/14.47 (setunionsingleton2) =>
% 106.65/14.47 ((
% 106.65/14.47 (setunionsingleton) =>
% 106.65/14.47 ((
% 106.65/14.47 (singletonprop) =>
% 106.65/14.47 ((
% 106.65/14.47 (ex1E1) =>
% 106.65/14.47 ((
% 106.65/14.47 (ex1I) =>
% 106.65/14.47 ((
% 106.65/14.47 (ex1I2) =>
% 106.65/14.47 ((
% 106.65/14.47 (singletonsuniq) =>
% 106.65/14.47 ((
% 106.65/14.47 (setukpairinjL1) =>
% 106.65/14.47 ((
% 106.65/14.47 (kfstsingleton) =>
% 106.65/14.47 ((
% 106.65/14.47 (theprop) =>
% 106.65/14.47 ((
% 106.65/14.47 (kfstpairEq) =>
% 106.65/14.47 ((
% 106.65/14.47 (cartprodfstin) =>
% 106.65/14.47 ((
% 106.65/14.47 (setukpairinjL2) =>
% 106.65/14.47 ((
% 106.65/14.47 (setukpairinjL) =>
% 106.65/14.47 ((
% 106.65/14.47 (setukpairinjR11) =>
% 106.65/14.47 ((
% 106.65/14.47 (setukpairinjR12) =>
% 106.65/14.47 ((
% 106.65/14.47 (setukpairinjR1) =>
% 106.65/14.47 ((
% 106.65/14.47 (upairequniteq) =>
% 106.65/14.47 ((
% 106.65/14.47 (setukpairinjR2) =>
% 106.65/14.47 ((
% 106.65/14.47 (setukpairinjR) =>
% 106.65/14.47 ((
% 106.65/14.47 (ksndsingleton) =>
% 106.65/14.47 ((
% 106.65/14.47 (ksndpairEq) =>
% 106.65/14.47 ((
% 106.65/14.47 (kpairsurjEq) =>
% 106.65/14.47 ((
% 106.65/14.47 (cartprodsndin) =>
% 106.65/14.47 ((
% 106.65/14.47 (cartprodpairmemEL) =>
% 106.65/14.47 ((
% 106.65/14.47 (cartprodpairmemER) =>
% 106.65/14.47 ((
% 106.65/14.47 (cartprodmempaircEq) =>
% 106.65/14.47 ((
% 106.65/14.47 (cartprodfstpairEq) =>
% 106.65/14.47 ((
% 106.65/14.47 (cartprodsndpairEq) =>
% 106.65/14.47 ((
% 106.65/14.47 (cartprodpairsurjEq) =>
% 106.65/14.47 ((
% 106.65/14.47 (dpsetconstrI) =>
% 106.65/14.47 ((
% 106.65/14.47 (dpsetconstrSub) =>
% 106.65/14.47 ((
% 106.65/14.47 (setOfPairsIsBReln) =>
% 106.65/14.47 ((
% 106.65/14.47 (dpsetconstrERa) =>
% 106.65/14.47 ((
% 106.65/14.47 (dpsetconstrEL1) =>
% 106.65/14.47 ((
% 106.65/14.47 (dpsetconstrEL2) =>
% 106.65/14.47 ((
% 106.65/14.47 (dpsetconstrER) =>
% 106.65/14.47 ((
% 106.65/14.47 (funcImageSingleton) =>
% 106.65/14.47 ((
% 106.65/14.47 (apProp) =>
% 106.65/14.47 ((
% 106.65/14.47 (app) =>
% 106.65/14.47 ((
% 106.65/14.47 (infuncsetfunc) =>
% 106.65/14.47 ((
% 106.65/14.47 (ap2p) =>
% 106.65/14.47 ((
% 106.65/14.47 (funcinfuncset) =>
% 106.65/14.47 ((
% 106.65/14.47 (lamProp) =>
% 106.65/14.47 ((
% 106.65/14.47 (lamp) =>
% 106.65/14.47 ((
% 106.65/14.47 (lam2p) =>
% 106.65/14.47 ((
% 106.65/14.47 (brelnall1) =>
% 106.65/14.47 ((
% 106.65/14.47 (brelnall2) =>
% 106.65/14.47 ((
% 106.65/14.47 (ex1E2) =>
% 106.65/14.47 ((
% 106.65/14.47 (funcGraphProp1) =>
% 106.65/14.48 ((
% 106.65/14.48 (funcGraphProp3) =>
% 106.65/14.48 ((
% 106.65/14.48 (funcGraphProp2) =>
% 106.65/14.48 ((
% 106.65/14.48 (funcextLem) =>
% 106.65/14.48 ((
% 106.65/14.48 (funcGraphProp4) =>
% 106.65/14.48 ((
% 106.65/14.48 (subbreln) =>
% 106.65/14.48 ((
% 106.65/14.48 (eqbreln) =>
% 106.65/14.48 ((
% 106.65/14.48 (funcext) =>
% 106.65/14.48 ((
% 106.65/14.48 (funcext2) =>
% 106.65/14.48 ((
% 106.65/14.48 (ap2apEq1) =>
% 106.65/14.48 ((
% 106.65/14.48 (ap2apEq2) =>
% 106.65/14.48 ((
% 106.65/14.48 (beta1) =>
% 106.65/14.48 ((
% 106.65/14.48 (eta1) =>
% 106.65/14.48 ((
% 106.65/14.48 (lam2lamEq) =>
% 106.65/14.48 ((
% 106.65/14.48 (beta2) =>
% 106.65/14.48 ((
% 106.65/14.48 (eta2) =>
% 106.65/14.48 ((
% 106.65/14.48 (iffalseProp1) =>
% 106.65/14.48 ((
% 106.65/14.48 (iffalseProp2) =>
% 106.65/14.48 ((
% 106.65/14.48 (iftrueProp1) =>
% 106.65/14.48 ((
% 106.65/14.48 (iftrueProp2) =>
% 106.65/14.48 ((
% 106.65/14.48 (ifSingleton) =>
% 106.65/14.48 ((
% 106.65/14.48 (ifp) =>
% 106.65/14.48 ((
% 106.65/14.48 (theeq) =>
% 106.65/14.48 ((
% 106.65/14.48 (iftrue) =>
% 106.65/14.48 ((
% 106.65/14.48 (iffalse) =>
% 106.65/14.48 ((
% 106.65/14.48 (iftrueorfalse) =>
% 106.65/14.48 ((
% 106.65/14.48 (binintersectT_lem) =>
% 106.65/14.48 ((
% 106.65/14.48 (binunionT_lem) =>
% 106.65/14.48 ((
% 106.65/14.48 (powersetT_lem) =>
% 106.65/14.48 ((
% 106.65/14.48 (setminusT_lem) =>
% 106.65/14.48 ((
% 106.65/14.48 (complementT_lem) =>
% 106.65/14.48 ((
% 106.65/14.48 (setextT) =>
% 106.65/14.48 ((
% 106.65/14.48 (subsetTI) =>
% 106.65/14.48 ((
% 106.65/14.48 (powersetTI1) =>
% 106.65/14.48 ((
% 106.65/14.48 (powersetTE1) =>
% 106.65/14.48 ((
% 106.65/14.48 (complementTI1) =>
% 106.65/14.48 ((
% 106.65/14.48 (complementTE1) =>
% 106.65/14.48 ((
% 106.65/14.48 (binintersectTELcontra) =>
% 106.65/14.48 ((
% 106.65/14.48 (binintersectTERcontra) =>
% 106.65/14.48 ((
% 106.65/14.48 (contrasubsetT) =>
% 106.65/14.48 ((
% 106.65/14.48 (contrasubsetT1) =>
% 107.13/14.48 ((
% 107.13/14.48 (contrasubsetT2) =>
% 107.13/14.48 ((
% 107.13/14.48 (contrasubsetT3) =>
% 107.13/14.48 ((
% 107.13/14.48 (doubleComplementI1) =>
% 107.13/14.48 ((
% 107.13/14.48 (doubleComplementE1) =>
% 107.13/14.48 ((
% 107.13/14.48 (doubleComplementSub1) =>
% 107.13/14.48 ((
% 107.13/14.48 (doubleComplementSub2) =>
% 107.13/14.48 ((
% 107.13/14.48 (doubleComplementEq) =>
% 107.13/14.48 ((
% 107.13/14.48 (complementTnotintersectT) =>
% 107.13/14.48 ((
% 107.13/14.48 (complementImpComplementIntersect) =>
% 107.13/14.48 ((
% 107.13/14.48 (complementSubsetComplementIntersect) =>
% 107.13/14.48 ((
% 107.13/14.48 (complementInPowersetComplementIntersect) =>
% 107.13/14.48 ((
% 107.13/14.48 (contraSubsetComplement) =>
% 107.13/14.48 ((
% 107.13/14.48 (complementTcontraSubset) =>
% 107.13/14.48 ((
% 107.13/14.48 (binunionTILcontra) =>
% 107.13/14.48 ((
% 107.13/14.48 (binunionTIRcontra) =>
% 107.13/14.48 ((
% 107.13/14.48 (inIntersectImpInUnion) =>
% 107.13/14.48 ((
% 107.13/14.48 (inIntersectImpInUnion2) =>
% 107.13/14.48 ((
% 107.13/14.48 (inIntersectImpInIntersectUnions) =>
% 107.13/14.48 ((
% 107.13/14.48 (intersectInPowersetIntersectUnions) =>
% 107.13/14.48 ((
% 107.13/14.48 (inComplementUnionImpNotIn1) =>
% 107.13/14.48 ((
% 107.13/14.48 (inComplementUnionImpInComplement1) =>
% 107.13/14.48 ((
% 107.13/14.48 (binunionTE) =>
% 107.13/14.48 ((
% 107.13/14.48 (binunionTEcontra) =>
% 107.13/14.48 ((
% 107.13/14.48 (demorgan2a1) =>
% 107.13/14.48 ((
% 107.13/14.48 (complementUnionInPowersetComplement) =>
% 107.13/14.48 ((
% 107.13/14.48 (demorgan2a2) =>
% 107.13/14.48 ((
% 107.13/14.48 (demorgan1a) =>
% 107.13/14.48 ((
% 107.13/14.48 (demorgan1b) =>
% 107.13/14.48 ((
% 107.13/14.48 (demorgan1) =>
% 107.13/14.48 ((
% 107.13/14.48 (demorgan2a) =>
% 107.13/14.48 ((
% 107.13/14.48 (demorgan2b2) =>
% 107.13/14.48 ((
% 107.13/14.48 (demorgan2b) =>
% 107.13/14.48 ((
% 107.13/14.48 (demorgan2) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz13rule0) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz13rule1) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz13rule2) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz13rule3) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz13rule4) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz1_1) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz1_2) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz1_3) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz1_4) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz1_5) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1all2) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1SetBreln1) =>
% 107.13/14.48 ((
% 107.13/14.48 (choice2fnsingleton) =>
% 107.13/14.48 ((
% 107.13/14.48 (setOfPairsIsBReln1) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1all1) =>
% 107.13/14.48 ((
% 107.13/14.48 (subbreln1) =>
% 107.13/14.48 ((
% 107.13/14.48 (eqbreln1) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1invprop) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1invI) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1invE) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1compprop) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1compI) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1compE) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1compEex) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1unionprop) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1unionIL) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1unionIR) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1unionI) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1unionE) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1unionEcases) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1unionCommutes) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz2Ex) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz2W) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz2A) =>
% 107.13/14.48 ((
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% 107.13/14.48 ((
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% 107.13/14.48 ((
% 107.13/14.48 (image1Ex1) =>
% 107.13/14.48 ((
% 107.13/14.48 (image1Equiv) =>
% 107.13/14.48 ((
% 107.13/14.48 (image1E) =>
% 107.13/14.48 ((
% 107.13/14.48 (image1I) =>
% 107.13/14.48 ((
% 107.13/14.48 (injFuncInInjFuncSet) =>
% 107.13/14.48 ((
% 107.13/14.48 (injFuncSetFuncIn) =>
% 107.13/14.48 ((
% 107.13/14.48 (injFuncSetFuncInj) =>
% 107.13/14.48 ((
% 107.13/14.48 (surjFuncSetFuncIn) =>
% 107.13/14.48 ((
% 107.13/14.48 (surjFuncSetFuncSurj) =>
% 107.13/14.48 ((
% 107.13/14.48 (leftInvIsSurj) =>
% 107.13/14.48 ((
% 107.13/14.48 (surjCantorThm) =>
% 107.13/14.48 ((
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% 107.13/14.48 ('#B') @ (
% 107.13/14.48 =>) @
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% 107.13/14.48 ('#S') @ (
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% 107.13/14.48 (
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% 107.13/14.48 (
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% 107.13/14.48 ('#B') @ (
% 107.13/14.48 (
% 107.13/14.48 ('#B') @ (
% 107.13/14.48 =))) @
% 107.13/14.48 (
% 107.13/14.48 (
% 107.13/14.48 ('#C') @ binintersect)))))) @
% 107.13/14.48 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 107.13/14.48 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl640])).
% 107.13/14.48 thf(zip_derived_cl660, plain,
% 107.13/14.48 (~ (((exuE3u) =>
% 107.13/14.48 (((exu__Cong) =>
% 107.13/14.48 (((setadjoin__Cong) =>
% 107.13/14.48 (((powerset__Cong) =>
% 107.13/14.48 (((setunion__Cong) =>
% 107.13/14.48 (((exuEu) =>
% 107.13/14.48 (((descr__Cong) =>
% 107.13/14.48 (((dsetconstr__Cong) =>
% 107.13/14.48 (((subsetI1) =>
% 107.13/14.48 (((eqimpsubset2) =>
% 107.13/14.48 (((eqimpsubset1) =>
% 107.13/14.48 (((subsetI2) =>
% 107.13/14.48 (((emptysetsubset) =>
% 107.13/14.48 (((subsetE) =>
% 107.13/14.48 (((subsetE2) =>
% 107.13/14.48 (((notsubsetI) =>
% 107.13/14.48 (((notequalI1) =>
% 107.13/14.48 (((notequalI2) =>
% 107.13/14.48 (((subsetRefl) =>
% 107.13/14.48 (((subsetTrans) =>
% 107.13/14.48 (((setadjoinSub) =>
% 107.13/14.48 (((setadjoinSub2) =>
% 107.13/14.48 (((subset2powerset) =>
% 107.13/14.48 (((setextsub) =>
% 107.13/14.48 (((subsetemptysetimpeq) =>
% 107.13/14.48 (((powersetI1) =>
% 107.13/14.48 (((powersetE1) =>
% 107.13/14.48 (((inPowerset) =>
% 107.13/14.48 (((powersetsubset) =>
% 107.13/14.48 (((sepInPowerset) =>
% 107.13/14.48 ((
% 107.13/14.48 (sepSubset) =>
% 107.13/14.48 ((
% 107.13/14.48 (binunionIL) =>
% 107.13/14.48 ((
% 107.13/14.48 (upairset2IR) =>
% 107.13/14.48 ((
% 107.13/14.48 (binunionIR) =>
% 107.13/14.48 ((
% 107.13/14.48 (binunionEcases) =>
% 107.13/14.48 ((
% 107.13/14.48 (binunionE) =>
% 107.13/14.48 ((
% 107.13/14.48 (binunionLsub) =>
% 107.13/14.48 ((
% 107.13/14.48 (binunionRsub) =>
% 107.13/14.48 ((
% 107.13/14.48 (binintersectI) =>
% 107.13/14.48 ((
% 107.13/14.48 (binintersectSubset5) =>
% 107.13/14.48 ((
% 107.13/14.48 (binintersectEL) =>
% 107.13/14.48 ((
% 107.13/14.48 (binintersectLsub) =>
% 107.13/14.48 ((
% 107.13/14.48 (binintersectSubset2) =>
% 107.13/14.48 ((
% 107.13/14.48 (binintersectSubset3) =>
% 107.13/14.48 ((
% 107.13/14.48 (binintersectER) =>
% 107.13/14.48 ((
% 107.13/14.48 (disjointsetsI1) =>
% 107.13/14.48 ((
% 107.13/14.48 (binintersectRsub) =>
% 107.13/14.48 ((
% 107.13/14.48 (binintersectSubset4) =>
% 107.13/14.48 ((
% 107.13/14.48 (binintersectSubset1) =>
% 107.13/14.48 ((
% 107.13/14.48 (bs114d) =>
% 107.13/14.48 ((
% 107.13/14.48 (setminusI) =>
% 107.13/14.48 ((
% 107.13/14.48 (setminusEL) =>
% 107.13/14.48 ((
% 107.13/14.48 (setminusER) =>
% 107.13/14.48 ((
% 107.13/14.48 (setminusSubset2) =>
% 107.13/14.48 ((
% 107.13/14.48 (setminusERneg) =>
% 107.13/14.48 ((
% 107.13/14.48 (setminusELneg) =>
% 107.13/14.48 ((
% 107.13/14.48 (setminusILneg) =>
% 107.13/14.48 ((
% 107.13/14.48 (setminusIRneg) =>
% 107.13/14.48 ((
% 107.13/14.48 (setminusLsub) =>
% 107.13/14.48 ((
% 107.13/14.48 (setminusSubset1) =>
% 107.13/14.48 ((
% 107.13/14.48 (symdiffE) =>
% 107.13/14.48 ((
% 107.13/14.48 (symdiffI1) =>
% 107.13/14.48 ((
% 107.13/14.48 (symdiffI2) =>
% 107.13/14.48 ((
% 107.13/14.48 (symdiffIneg1) =>
% 107.13/14.48 ((
% 107.13/14.48 (symdiffIneg2) =>
% 107.13/14.48 ((
% 107.13/14.48 (secondinupair) =>
% 107.13/14.48 ((
% 107.13/14.48 (setukpairIL) =>
% 107.13/14.48 ((
% 107.13/14.48 (setukpairIR) =>
% 107.13/14.48 ((
% 107.13/14.48 (kpairiskpair) =>
% 107.13/14.48 ((
% 107.13/14.48 (kpairp) =>
% 107.13/14.48 ((
% 107.13/14.48 (singletonsubset) =>
% 107.13/14.48 ((
% 107.13/14.48 (singletoninpowerset) =>
% 107.13/14.48 ((
% 107.13/14.48 (singletoninpowunion) =>
% 107.13/14.48 ((
% 107.13/14.48 (upairset2E) =>
% 107.13/14.48 ((
% 107.13/14.48 (upairsubunion) =>
% 107.13/14.48 ((
% 107.13/14.48 (upairinpowunion) =>
% 107.13/14.48 ((
% 107.13/14.48 (ubforcartprodlem1) =>
% 107.13/14.48 ((
% 107.13/14.48 (ubforcartprodlem2) =>
% 107.13/14.48 ((
% 107.13/14.48 (ubforcartprodlem3) =>
% 107.13/14.48 ((
% 107.13/14.48 (cartprodpairin) =>
% 107.13/14.48 ((
% 107.13/14.48 (cartprodmempair1) =>
% 107.13/14.48 ((
% 107.13/14.48 (cartprodmempair) =>
% 107.13/14.48 ((
% 107.13/14.48 (setunionE2) =>
% 107.13/14.48 ((
% 107.13/14.48 (setunionsingleton1) =>
% 107.13/14.48 ((
% 107.13/14.48 (setunionsingleton2) =>
% 107.13/14.48 ((
% 107.13/14.48 (setunionsingleton) =>
% 107.13/14.48 ((
% 107.13/14.48 (singletonprop) =>
% 107.13/14.48 ((
% 107.13/14.48 (ex1E1) =>
% 107.13/14.48 ((
% 107.13/14.48 (ex1I) =>
% 107.13/14.48 ((
% 107.13/14.48 (ex1I2) =>
% 107.13/14.48 ((
% 107.13/14.48 (singletonsuniq) =>
% 107.13/14.48 ((
% 107.13/14.48 (setukpairinjL1) =>
% 107.13/14.48 ((
% 107.13/14.48 (kfstsingleton) =>
% 107.13/14.48 ((
% 107.13/14.48 (theprop) =>
% 107.13/14.48 ((
% 107.13/14.48 (kfstpairEq) =>
% 107.13/14.48 ((
% 107.13/14.48 (cartprodfstin) =>
% 107.13/14.48 ((
% 107.13/14.48 (setukpairinjL2) =>
% 107.13/14.48 ((
% 107.13/14.48 (setukpairinjL) =>
% 107.13/14.48 ((
% 107.13/14.48 (setukpairinjR11) =>
% 107.13/14.48 ((
% 107.13/14.48 (setukpairinjR12) =>
% 107.13/14.48 ((
% 107.13/14.48 (setukpairinjR1) =>
% 107.13/14.48 ((
% 107.13/14.48 (upairequniteq) =>
% 107.13/14.48 ((
% 107.13/14.48 (setukpairinjR2) =>
% 107.13/14.48 ((
% 107.13/14.48 (setukpairinjR) =>
% 107.13/14.48 ((
% 107.13/14.48 (ksndsingleton) =>
% 107.13/14.48 ((
% 107.13/14.48 (ksndpairEq) =>
% 107.13/14.48 ((
% 107.13/14.48 (kpairsurjEq) =>
% 107.13/14.48 ((
% 107.13/14.48 (cartprodsndin) =>
% 107.13/14.48 ((
% 107.13/14.48 (cartprodpairmemEL) =>
% 107.13/14.48 ((
% 107.13/14.48 (cartprodpairmemER) =>
% 107.13/14.48 ((
% 107.13/14.48 (cartprodmempaircEq) =>
% 107.13/14.48 ((
% 107.13/14.48 (cartprodfstpairEq) =>
% 107.13/14.48 ((
% 107.13/14.48 (cartprodsndpairEq) =>
% 107.13/14.48 ((
% 107.13/14.48 (cartprodpairsurjEq) =>
% 107.13/14.48 ((
% 107.13/14.48 (dpsetconstrI) =>
% 107.13/14.48 ((
% 107.13/14.48 (dpsetconstrSub) =>
% 107.13/14.48 ((
% 107.13/14.48 (setOfPairsIsBReln) =>
% 107.13/14.48 ((
% 107.13/14.48 (dpsetconstrERa) =>
% 107.13/14.48 ((
% 107.13/14.48 (dpsetconstrEL1) =>
% 107.13/14.48 ((
% 107.13/14.48 (dpsetconstrEL2) =>
% 107.13/14.48 ((
% 107.13/14.48 (dpsetconstrER) =>
% 107.13/14.48 ((
% 107.13/14.48 (funcImageSingleton) =>
% 107.13/14.48 ((
% 107.13/14.48 (apProp) =>
% 107.13/14.48 ((
% 107.13/14.48 (app) =>
% 107.13/14.48 ((
% 107.13/14.48 (infuncsetfunc) =>
% 107.13/14.48 ((
% 107.13/14.48 (ap2p) =>
% 107.13/14.48 ((
% 107.13/14.48 (funcinfuncset) =>
% 107.13/14.48 ((
% 107.13/14.48 (lamProp) =>
% 107.13/14.48 ((
% 107.13/14.48 (lamp) =>
% 107.13/14.48 ((
% 107.13/14.48 (lam2p) =>
% 107.13/14.48 ((
% 107.13/14.48 (brelnall1) =>
% 107.13/14.48 ((
% 107.13/14.48 (brelnall2) =>
% 107.13/14.48 ((
% 107.13/14.48 (ex1E2) =>
% 107.13/14.48 ((
% 107.13/14.48 (funcGraphProp1) =>
% 107.13/14.48 ((
% 107.13/14.48 (funcGraphProp3) =>
% 107.13/14.48 ((
% 107.13/14.48 (funcGraphProp2) =>
% 107.13/14.48 ((
% 107.13/14.48 (funcextLem) =>
% 107.13/14.48 ((
% 107.13/14.48 (funcGraphProp4) =>
% 107.13/14.48 ((
% 107.13/14.48 (subbreln) =>
% 107.13/14.48 ((
% 107.13/14.48 (eqbreln) =>
% 107.13/14.48 ((
% 107.13/14.48 (funcext) =>
% 107.13/14.48 ((
% 107.13/14.48 (funcext2) =>
% 107.13/14.48 ((
% 107.13/14.48 (ap2apEq1) =>
% 107.13/14.48 ((
% 107.13/14.48 (ap2apEq2) =>
% 107.13/14.48 ((
% 107.13/14.48 (beta1) =>
% 107.13/14.48 ((
% 107.13/14.48 (eta1) =>
% 107.13/14.48 ((
% 107.13/14.48 (lam2lamEq) =>
% 107.13/14.48 ((
% 107.13/14.48 (beta2) =>
% 107.13/14.48 ((
% 107.13/14.48 (eta2) =>
% 107.13/14.48 ((
% 107.13/14.48 (iffalseProp1) =>
% 107.13/14.48 ((
% 107.13/14.48 (iffalseProp2) =>
% 107.13/14.48 ((
% 107.13/14.48 (iftrueProp1) =>
% 107.13/14.48 ((
% 107.13/14.48 (iftrueProp2) =>
% 107.13/14.48 ((
% 107.13/14.48 (ifSingleton) =>
% 107.13/14.48 ((
% 107.13/14.48 (ifp) =>
% 107.13/14.48 ((
% 107.13/14.48 (theeq) =>
% 107.13/14.48 ((
% 107.13/14.48 (iftrue) =>
% 107.13/14.48 ((
% 107.13/14.48 (iffalse) =>
% 107.13/14.48 ((
% 107.13/14.48 (iftrueorfalse) =>
% 107.13/14.48 ((
% 107.13/14.48 (binintersectT_lem) =>
% 107.13/14.48 ((
% 107.13/14.48 (binunionT_lem) =>
% 107.13/14.48 ((
% 107.13/14.48 (powersetT_lem) =>
% 107.13/14.48 ((
% 107.13/14.48 (setminusT_lem) =>
% 107.13/14.48 ((
% 107.13/14.48 (complementT_lem) =>
% 107.13/14.48 ((
% 107.13/14.48 (setextT) =>
% 107.13/14.48 ((
% 107.13/14.48 (subsetTI) =>
% 107.13/14.48 ((
% 107.13/14.48 (powersetTI1) =>
% 107.13/14.48 ((
% 107.13/14.48 (powersetTE1) =>
% 107.13/14.48 ((
% 107.13/14.48 (complementTI1) =>
% 107.13/14.48 ((
% 107.13/14.48 (complementTE1) =>
% 107.13/14.48 ((
% 107.13/14.48 (binintersectTELcontra) =>
% 107.13/14.48 ((
% 107.13/14.48 (binintersectTERcontra) =>
% 107.13/14.48 ((
% 107.13/14.48 (contrasubsetT) =>
% 107.13/14.48 ((
% 107.13/14.48 (contrasubsetT1) =>
% 107.13/14.48 ((
% 107.13/14.48 (contrasubsetT2) =>
% 107.13/14.48 ((
% 107.13/14.48 (contrasubsetT3) =>
% 107.13/14.48 ((
% 107.13/14.48 (doubleComplementI1) =>
% 107.13/14.48 ((
% 107.13/14.48 (doubleComplementE1) =>
% 107.13/14.48 ((
% 107.13/14.48 (doubleComplementSub1) =>
% 107.13/14.48 ((
% 107.13/14.48 (doubleComplementSub2) =>
% 107.13/14.48 ((
% 107.13/14.48 (doubleComplementEq) =>
% 107.13/14.48 ((
% 107.13/14.48 (complementTnotintersectT) =>
% 107.13/14.48 ((
% 107.13/14.48 (complementImpComplementIntersect) =>
% 107.13/14.48 ((
% 107.13/14.48 (complementSubsetComplementIntersect) =>
% 107.13/14.48 ((
% 107.13/14.48 (complementInPowersetComplementIntersect) =>
% 107.13/14.48 ((
% 107.13/14.48 (contraSubsetComplement) =>
% 107.13/14.48 ((
% 107.13/14.48 (complementTcontraSubset) =>
% 107.13/14.48 ((
% 107.13/14.48 (binunionTILcontra) =>
% 107.13/14.48 ((
% 107.13/14.48 (binunionTIRcontra) =>
% 107.13/14.48 ((
% 107.13/14.48 (inIntersectImpInUnion) =>
% 107.13/14.48 ((
% 107.13/14.48 (inIntersectImpInUnion2) =>
% 107.13/14.48 ((
% 107.13/14.48 (inIntersectImpInIntersectUnions) =>
% 107.13/14.48 ((
% 107.13/14.48 (intersectInPowersetIntersectUnions) =>
% 107.13/14.48 ((
% 107.13/14.48 (inComplementUnionImpNotIn1) =>
% 107.13/14.48 ((
% 107.13/14.48 (inComplementUnionImpInComplement1) =>
% 107.13/14.48 ((
% 107.13/14.48 (binunionTE) =>
% 107.13/14.48 ((
% 107.13/14.48 (binunionTEcontra) =>
% 107.13/14.48 ((
% 107.13/14.48 (demorgan2a1) =>
% 107.13/14.48 ((
% 107.13/14.48 (complementUnionInPowersetComplement) =>
% 107.13/14.48 ((
% 107.13/14.48 (demorgan2a2) =>
% 107.13/14.48 ((
% 107.13/14.48 (demorgan1a) =>
% 107.13/14.48 ((
% 107.13/14.48 (demorgan1b) =>
% 107.13/14.48 ((
% 107.13/14.48 (demorgan1) =>
% 107.13/14.48 ((
% 107.13/14.48 (demorgan2a) =>
% 107.13/14.48 ((
% 107.13/14.48 (demorgan2b2) =>
% 107.13/14.48 ((
% 107.13/14.48 (demorgan2b) =>
% 107.13/14.48 ((
% 107.13/14.48 (demorgan2) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz13rule0) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz13rule1) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz13rule2) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz13rule3) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz13rule4) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz1_1) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz1_2) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz1_3) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz1_4) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz1_5) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1all2) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1SetBreln1) =>
% 107.13/14.48 ((
% 107.13/14.48 (choice2fnsingleton) =>
% 107.13/14.48 ((
% 107.13/14.48 (setOfPairsIsBReln1) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1all1) =>
% 107.13/14.48 ((
% 107.13/14.48 (subbreln1) =>
% 107.13/14.48 ((
% 107.13/14.48 (eqbreln1) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1invprop) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1invI) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1invE) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1compprop) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1compI) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1compE) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1compEex) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1unionprop) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1unionIL) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1unionIR) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1unionI) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1unionE) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1unionEcases) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1unionCommutes) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz2Ex) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz2W) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz2A) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz2B) =>
% 107.13/14.48 ((
% 107.13/14.48 (image1Ex) =>
% 107.13/14.48 ((
% 107.13/14.48 (image1Ex1) =>
% 107.13/14.48 ((
% 107.13/14.48 (image1Equiv) =>
% 107.13/14.48 ((
% 107.13/14.48 (image1E) =>
% 107.13/14.48 ((
% 107.13/14.48 (image1I) =>
% 107.13/14.48 ((
% 107.13/14.48 (injFuncInInjFuncSet) =>
% 107.13/14.48 ((
% 107.13/14.48 (injFuncSetFuncIn) =>
% 107.13/14.48 ((
% 107.13/14.48 (injFuncSetFuncInj) =>
% 107.13/14.48 ((
% 107.13/14.48 (surjFuncSetFuncIn) =>
% 107.13/14.48 ((
% 107.13/14.48 (surjFuncSetFuncSurj) =>
% 107.13/14.48 ((
% 107.13/14.48 (leftInvIsSurj) =>
% 107.13/14.48 ((
% 107.13/14.48 (surjCantorThm) =>
% 107.13/14.48 ((
% 107.13/14.48 (!!) @ (
% 107.13/14.48 (('#S') @ (
% 107.13/14.48 (
% 107.13/14.48 ('#B') @ (
% 107.13/14.48 =>) @
% 107.13/14.48 nonempty)) @
% 107.13/14.48 (
% 107.13/14.48 (
% 107.13/14.48 ('#B') @ (
% 107.13/14.48 ??) @
% 107.13/14.48 (
% 107.13/14.48 (
% 107.13/14.48 ('#S') @ (
% 107.13/14.48 (
% 107.13/14.48 ('#B') @ (
% 107.13/14.48 '#S') @
% 107.13/14.48 (
% 107.13/14.48 (
% 107.13/14.48 ('#B') @ (
% 107.13/14.48 (
% 107.13/14.48 ('#B') @ (
% 107.13/14.48 &))) @
% 107.13/14.48 (
% 107.13/14.48 (
% 107.13/14.48 ('#C') @ in)))))) @
% 107.13/14.48 (
% 107.13/14.48 (
% 107.13/14.48 ('#C') @ (
% 107.13/14.48 (
% 107.13/14.48 ('#B') @ (
% 107.13/14.48 '#C') @
% 107.13/14.48 (
% 107.13/14.48 (
% 107.13/14.48 ('#B') @ (
% 107.13/14.48 (
% 107.13/14.48 ('#B') @ (
% 107.13/14.48 =))) @
% 107.13/14.48 (
% 107.13/14.48 (
% 107.13/14.48 ('#C') @ binintersect)))))) @
% 107.13/14.48 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 107.13/14.48 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl650])).
% 107.13/14.48 thf(zip_derived_cl672, plain,
% 107.13/14.48 (~ (((exu__Cong) =>
% 107.13/14.48 (((setadjoin__Cong) =>
% 107.13/14.48 (((powerset__Cong) =>
% 107.13/14.48 (((setunion__Cong) =>
% 107.13/14.48 (((exuEu) =>
% 107.13/14.48 (((descr__Cong) =>
% 107.13/14.48 (((dsetconstr__Cong) =>
% 107.13/14.48 (((subsetI1) =>
% 107.13/14.48 (((eqimpsubset2) =>
% 107.13/14.48 (((eqimpsubset1) =>
% 107.13/14.48 (((subsetI2) =>
% 107.13/14.48 (((emptysetsubset) =>
% 107.13/14.48 (((subsetE) =>
% 107.13/14.48 (((subsetE2) =>
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% 107.13/14.48 (((notequalI1) =>
% 107.13/14.48 (((notequalI2) =>
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% 107.13/14.48 (((subsetTrans) =>
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% 107.13/14.48 (((setextsub) =>
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% 107.13/14.48 (((powersetE1) =>
% 107.13/14.48 (((inPowerset) =>
% 107.13/14.48 (((powersetsubset) =>
% 107.13/14.48 (((sepInPowerset) =>
% 107.13/14.48 (((sepSubset) =>
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% 107.13/14.48 ((
% 107.13/14.48 (upairset2IR) =>
% 107.13/14.48 ((
% 107.13/14.48 (binunionIR) =>
% 107.13/14.48 ((
% 107.13/14.48 (binunionEcases) =>
% 107.13/14.48 ((
% 107.13/14.48 (binunionE) =>
% 107.13/14.48 ((
% 107.13/14.48 (binunionLsub) =>
% 107.13/14.48 ((
% 107.13/14.48 (binunionRsub) =>
% 107.13/14.48 ((
% 107.13/14.48 (binintersectI) =>
% 107.13/14.48 ((
% 107.13/14.48 (binintersectSubset5) =>
% 107.13/14.48 ((
% 107.13/14.48 (binintersectEL) =>
% 107.13/14.48 ((
% 107.13/14.48 (binintersectLsub) =>
% 107.13/14.48 ((
% 107.13/14.48 (binintersectSubset2) =>
% 107.13/14.48 ((
% 107.13/14.48 (binintersectSubset3) =>
% 107.13/14.48 ((
% 107.13/14.48 (binintersectER) =>
% 107.13/14.48 ((
% 107.13/14.48 (disjointsetsI1) =>
% 107.13/14.48 ((
% 107.13/14.48 (binintersectRsub) =>
% 107.13/14.48 ((
% 107.13/14.48 (binintersectSubset4) =>
% 107.13/14.48 ((
% 107.13/14.48 (binintersectSubset1) =>
% 107.13/14.48 ((
% 107.13/14.48 (bs114d) =>
% 107.13/14.48 ((
% 107.13/14.48 (setminusI) =>
% 107.13/14.48 ((
% 107.13/14.48 (setminusEL) =>
% 107.13/14.48 ((
% 107.13/14.48 (setminusER) =>
% 107.13/14.48 ((
% 107.13/14.48 (setminusSubset2) =>
% 107.13/14.48 ((
% 107.13/14.48 (setminusERneg) =>
% 107.13/14.48 ((
% 107.13/14.48 (setminusELneg) =>
% 107.13/14.48 ((
% 107.13/14.48 (setminusILneg) =>
% 107.13/14.48 ((
% 107.13/14.48 (setminusIRneg) =>
% 107.13/14.48 ((
% 107.13/14.48 (setminusLsub) =>
% 107.13/14.48 ((
% 107.13/14.48 (setminusSubset1) =>
% 107.13/14.48 ((
% 107.13/14.48 (symdiffE) =>
% 107.13/14.48 ((
% 107.13/14.48 (symdiffI1) =>
% 107.13/14.48 ((
% 107.13/14.48 (symdiffI2) =>
% 107.13/14.48 ((
% 107.13/14.48 (symdiffIneg1) =>
% 107.13/14.48 ((
% 107.13/14.48 (symdiffIneg2) =>
% 107.13/14.48 ((
% 107.13/14.48 (secondinupair) =>
% 107.13/14.48 ((
% 107.13/14.48 (setukpairIL) =>
% 107.13/14.48 ((
% 107.13/14.48 (setukpairIR) =>
% 107.13/14.48 ((
% 107.13/14.48 (kpairiskpair) =>
% 107.13/14.48 ((
% 107.13/14.48 (kpairp) =>
% 107.13/14.48 ((
% 107.13/14.48 (singletonsubset) =>
% 107.13/14.48 ((
% 107.13/14.48 (singletoninpowerset) =>
% 107.13/14.48 ((
% 107.13/14.48 (singletoninpowunion) =>
% 107.13/14.48 ((
% 107.13/14.48 (upairset2E) =>
% 107.13/14.48 ((
% 107.13/14.48 (upairsubunion) =>
% 107.13/14.48 ((
% 107.13/14.48 (upairinpowunion) =>
% 107.13/14.48 ((
% 107.13/14.48 (ubforcartprodlem1) =>
% 107.13/14.48 ((
% 107.13/14.48 (ubforcartprodlem2) =>
% 107.13/14.48 ((
% 107.13/14.48 (ubforcartprodlem3) =>
% 107.13/14.48 ((
% 107.13/14.48 (cartprodpairin) =>
% 107.13/14.48 ((
% 107.13/14.48 (cartprodmempair1) =>
% 107.13/14.48 ((
% 107.13/14.48 (cartprodmempair) =>
% 107.13/14.48 ((
% 107.13/14.48 (setunionE2) =>
% 107.13/14.48 ((
% 107.13/14.48 (setunionsingleton1) =>
% 107.13/14.48 ((
% 107.13/14.48 (setunionsingleton2) =>
% 107.13/14.48 ((
% 107.13/14.48 (setunionsingleton) =>
% 107.13/14.48 ((
% 107.13/14.48 (singletonprop) =>
% 107.13/14.48 ((
% 107.13/14.48 (ex1E1) =>
% 107.13/14.48 ((
% 107.13/14.48 (ex1I) =>
% 107.13/14.48 ((
% 107.13/14.48 (ex1I2) =>
% 107.13/14.48 ((
% 107.13/14.48 (singletonsuniq) =>
% 107.13/14.48 ((
% 107.13/14.48 (setukpairinjL1) =>
% 107.13/14.48 ((
% 107.13/14.48 (kfstsingleton) =>
% 107.13/14.48 ((
% 107.13/14.48 (theprop) =>
% 107.13/14.48 ((
% 107.13/14.48 (kfstpairEq) =>
% 107.13/14.48 ((
% 107.13/14.48 (cartprodfstin) =>
% 107.13/14.48 ((
% 107.13/14.48 (setukpairinjL2) =>
% 107.13/14.48 ((
% 107.13/14.48 (setukpairinjL) =>
% 107.13/14.48 ((
% 107.13/14.48 (setukpairinjR11) =>
% 107.13/14.48 ((
% 107.13/14.48 (setukpairinjR12) =>
% 107.13/14.48 ((
% 107.13/14.48 (setukpairinjR1) =>
% 107.13/14.48 ((
% 107.13/14.48 (upairequniteq) =>
% 107.13/14.48 ((
% 107.13/14.48 (setukpairinjR2) =>
% 107.13/14.48 ((
% 107.13/14.48 (setukpairinjR) =>
% 107.13/14.48 ((
% 107.13/14.48 (ksndsingleton) =>
% 107.13/14.48 ((
% 107.13/14.48 (ksndpairEq) =>
% 107.13/14.48 ((
% 107.13/14.48 (kpairsurjEq) =>
% 107.13/14.48 ((
% 107.13/14.48 (cartprodsndin) =>
% 107.13/14.48 ((
% 107.13/14.48 (cartprodpairmemEL) =>
% 107.13/14.48 ((
% 107.13/14.48 (cartprodpairmemER) =>
% 107.13/14.48 ((
% 107.13/14.48 (cartprodmempaircEq) =>
% 107.13/14.48 ((
% 107.13/14.48 (cartprodfstpairEq) =>
% 107.13/14.48 ((
% 107.13/14.48 (cartprodsndpairEq) =>
% 107.13/14.48 ((
% 107.13/14.48 (cartprodpairsurjEq) =>
% 107.13/14.48 ((
% 107.13/14.48 (dpsetconstrI) =>
% 107.13/14.48 ((
% 107.13/14.48 (dpsetconstrSub) =>
% 107.13/14.48 ((
% 107.13/14.48 (setOfPairsIsBReln) =>
% 107.13/14.48 ((
% 107.13/14.48 (dpsetconstrERa) =>
% 107.13/14.48 ((
% 107.13/14.48 (dpsetconstrEL1) =>
% 107.13/14.48 ((
% 107.13/14.48 (dpsetconstrEL2) =>
% 107.13/14.48 ((
% 107.13/14.48 (dpsetconstrER) =>
% 107.13/14.48 ((
% 107.13/14.48 (funcImageSingleton) =>
% 107.13/14.48 ((
% 107.13/14.48 (apProp) =>
% 107.13/14.48 ((
% 107.13/14.48 (app) =>
% 107.13/14.48 ((
% 107.13/14.48 (infuncsetfunc) =>
% 107.13/14.48 ((
% 107.13/14.48 (ap2p) =>
% 107.13/14.48 ((
% 107.13/14.48 (funcinfuncset) =>
% 107.13/14.48 ((
% 107.13/14.48 (lamProp) =>
% 107.13/14.48 ((
% 107.13/14.48 (lamp) =>
% 107.13/14.48 ((
% 107.13/14.48 (lam2p) =>
% 107.13/14.48 ((
% 107.13/14.48 (brelnall1) =>
% 107.13/14.48 ((
% 107.13/14.48 (brelnall2) =>
% 107.13/14.48 ((
% 107.13/14.48 (ex1E2) =>
% 107.13/14.48 ((
% 107.13/14.48 (funcGraphProp1) =>
% 107.13/14.48 ((
% 107.13/14.48 (funcGraphProp3) =>
% 107.13/14.48 ((
% 107.13/14.48 (funcGraphProp2) =>
% 107.13/14.48 ((
% 107.13/14.48 (funcextLem) =>
% 107.13/14.48 ((
% 107.13/14.48 (funcGraphProp4) =>
% 107.13/14.48 ((
% 107.13/14.48 (subbreln) =>
% 107.13/14.48 ((
% 107.13/14.48 (eqbreln) =>
% 107.13/14.48 ((
% 107.13/14.48 (funcext) =>
% 107.13/14.48 ((
% 107.13/14.48 (funcext2) =>
% 107.13/14.48 ((
% 107.13/14.48 (ap2apEq1) =>
% 107.13/14.48 ((
% 107.13/14.48 (ap2apEq2) =>
% 107.13/14.48 ((
% 107.13/14.48 (beta1) =>
% 107.13/14.48 ((
% 107.13/14.48 (eta1) =>
% 107.13/14.48 ((
% 107.13/14.48 (lam2lamEq) =>
% 107.13/14.48 ((
% 107.13/14.48 (beta2) =>
% 107.13/14.48 ((
% 107.13/14.48 (eta2) =>
% 107.13/14.48 ((
% 107.13/14.48 (iffalseProp1) =>
% 107.13/14.48 ((
% 107.13/14.48 (iffalseProp2) =>
% 107.13/14.48 ((
% 107.13/14.48 (iftrueProp1) =>
% 107.13/14.48 ((
% 107.13/14.48 (iftrueProp2) =>
% 107.13/14.48 ((
% 107.13/14.48 (ifSingleton) =>
% 107.13/14.48 ((
% 107.13/14.48 (ifp) =>
% 107.13/14.48 ((
% 107.13/14.48 (theeq) =>
% 107.13/14.48 ((
% 107.13/14.48 (iftrue) =>
% 107.13/14.48 ((
% 107.13/14.48 (iffalse) =>
% 107.13/14.48 ((
% 107.13/14.48 (iftrueorfalse) =>
% 107.13/14.48 ((
% 107.13/14.48 (binintersectT_lem) =>
% 107.13/14.48 ((
% 107.13/14.48 (binunionT_lem) =>
% 107.13/14.48 ((
% 107.13/14.48 (powersetT_lem) =>
% 107.13/14.48 ((
% 107.13/14.48 (setminusT_lem) =>
% 107.13/14.48 ((
% 107.13/14.48 (complementT_lem) =>
% 107.13/14.48 ((
% 107.13/14.48 (setextT) =>
% 107.13/14.48 ((
% 107.13/14.48 (subsetTI) =>
% 107.13/14.48 ((
% 107.13/14.48 (powersetTI1) =>
% 107.13/14.48 ((
% 107.13/14.48 (powersetTE1) =>
% 107.13/14.48 ((
% 107.13/14.48 (complementTI1) =>
% 107.13/14.48 ((
% 107.13/14.48 (complementTE1) =>
% 107.13/14.48 ((
% 107.13/14.48 (binintersectTELcontra) =>
% 107.13/14.48 ((
% 107.13/14.48 (binintersectTERcontra) =>
% 107.13/14.48 ((
% 107.13/14.48 (contrasubsetT) =>
% 107.13/14.48 ((
% 107.13/14.48 (contrasubsetT1) =>
% 107.13/14.48 ((
% 107.13/14.48 (contrasubsetT2) =>
% 107.13/14.48 ((
% 107.13/14.48 (contrasubsetT3) =>
% 107.13/14.48 ((
% 107.13/14.48 (doubleComplementI1) =>
% 107.13/14.48 ((
% 107.13/14.48 (doubleComplementE1) =>
% 107.13/14.48 ((
% 107.13/14.48 (doubleComplementSub1) =>
% 107.13/14.48 ((
% 107.13/14.48 (doubleComplementSub2) =>
% 107.13/14.48 ((
% 107.13/14.48 (doubleComplementEq) =>
% 107.13/14.48 ((
% 107.13/14.48 (complementTnotintersectT) =>
% 107.13/14.48 ((
% 107.13/14.48 (complementImpComplementIntersect) =>
% 107.13/14.48 ((
% 107.13/14.48 (complementSubsetComplementIntersect) =>
% 107.13/14.48 ((
% 107.13/14.48 (complementInPowersetComplementIntersect) =>
% 107.13/14.48 ((
% 107.13/14.48 (contraSubsetComplement) =>
% 107.13/14.48 ((
% 107.13/14.48 (complementTcontraSubset) =>
% 107.13/14.48 ((
% 107.13/14.48 (binunionTILcontra) =>
% 107.13/14.48 ((
% 107.13/14.48 (binunionTIRcontra) =>
% 107.13/14.48 ((
% 107.13/14.48 (inIntersectImpInUnion) =>
% 107.13/14.48 ((
% 107.13/14.48 (inIntersectImpInUnion2) =>
% 107.13/14.48 ((
% 107.13/14.48 (inIntersectImpInIntersectUnions) =>
% 107.13/14.48 ((
% 107.13/14.48 (intersectInPowersetIntersectUnions) =>
% 107.13/14.48 ((
% 107.13/14.48 (inComplementUnionImpNotIn1) =>
% 107.13/14.48 ((
% 107.13/14.48 (inComplementUnionImpInComplement1) =>
% 107.13/14.48 ((
% 107.13/14.48 (binunionTE) =>
% 107.13/14.48 ((
% 107.13/14.48 (binunionTEcontra) =>
% 107.13/14.48 ((
% 107.13/14.48 (demorgan2a1) =>
% 107.13/14.48 ((
% 107.13/14.48 (complementUnionInPowersetComplement) =>
% 107.13/14.48 ((
% 107.13/14.48 (demorgan2a2) =>
% 107.13/14.48 ((
% 107.13/14.48 (demorgan1a) =>
% 107.13/14.48 ((
% 107.13/14.48 (demorgan1b) =>
% 107.13/14.48 ((
% 107.13/14.48 (demorgan1) =>
% 107.13/14.48 ((
% 107.13/14.48 (demorgan2a) =>
% 107.13/14.48 ((
% 107.13/14.48 (demorgan2b2) =>
% 107.13/14.48 ((
% 107.13/14.48 (demorgan2b) =>
% 107.13/14.48 ((
% 107.13/14.48 (demorgan2) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz13rule0) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz13rule1) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz13rule2) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz13rule3) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz13rule4) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz1_1) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz1_2) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz1_3) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz1_4) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz1_5) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1all2) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1SetBreln1) =>
% 107.13/14.48 ((
% 107.13/14.48 (choice2fnsingleton) =>
% 107.13/14.48 ((
% 107.13/14.48 (setOfPairsIsBReln1) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1all1) =>
% 107.13/14.48 ((
% 107.13/14.48 (subbreln1) =>
% 107.13/14.48 ((
% 107.13/14.48 (eqbreln1) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1invprop) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1invI) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1invE) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1compprop) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1compI) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1compE) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1compEex) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1unionprop) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1unionIL) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1unionIR) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1unionI) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1unionE) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1unionEcases) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1unionCommutes) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz2Ex) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz2W) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz2A) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz2B) =>
% 107.13/14.48 ((
% 107.13/14.48 (image1Ex) =>
% 107.13/14.48 ((
% 107.13/14.48 (image1Ex1) =>
% 107.13/14.48 ((
% 107.13/14.48 (image1Equiv) =>
% 107.13/14.48 ((
% 107.13/14.48 (image1E) =>
% 107.13/14.48 ((
% 107.13/14.48 (image1I) =>
% 107.13/14.48 ((
% 107.13/14.48 (injFuncInInjFuncSet) =>
% 107.13/14.48 ((
% 107.13/14.48 (injFuncSetFuncIn) =>
% 107.13/14.48 ((
% 107.13/14.48 (injFuncSetFuncInj) =>
% 107.13/14.48 ((
% 107.13/14.48 (surjFuncSetFuncIn) =>
% 107.13/14.48 ((
% 107.13/14.48 (surjFuncSetFuncSurj) =>
% 107.13/14.48 ((
% 107.13/14.48 (leftInvIsSurj) =>
% 107.13/14.48 ((
% 107.13/14.48 (surjCantorThm) =>
% 107.13/14.48 ((
% 107.13/14.48 (!!) @ (
% 107.13/14.48 (('#S') @ (
% 107.13/14.48 (
% 107.13/14.48 ('#B') @ (
% 107.13/14.48 =>) @
% 107.13/14.48 nonempty)) @
% 107.13/14.48 (
% 107.13/14.48 (
% 107.13/14.48 ('#B') @ (
% 107.13/14.48 ??) @
% 107.13/14.48 (
% 107.13/14.48 (
% 107.13/14.48 ('#S') @ (
% 107.13/14.48 (
% 107.13/14.48 ('#B') @ (
% 107.13/14.48 '#S') @
% 107.13/14.48 (
% 107.13/14.48 (
% 107.13/14.48 ('#B') @ (
% 107.13/14.48 (
% 107.13/14.48 ('#B') @ (
% 107.13/14.48 &))) @
% 107.13/14.48 (
% 107.13/14.48 (
% 107.13/14.48 ('#C') @ in)))))) @
% 107.13/14.48 (
% 107.13/14.48 (
% 107.13/14.48 ('#C') @ (
% 107.13/14.48 (
% 107.13/14.48 ('#B') @ (
% 107.13/14.48 '#C') @
% 107.13/14.48 (
% 107.13/14.48 (
% 107.13/14.48 ('#B') @ (
% 107.13/14.48 (
% 107.13/14.48 ('#B') @ (
% 107.13/14.48 =))) @
% 107.13/14.48 (
% 107.13/14.48 (
% 107.13/14.48 ('#C') @ binintersect)))))) @
% 107.13/14.48 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 107.13/14.48 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl660])).
% 107.13/14.48 thf(zip_derived_cl685, plain,
% 107.13/14.48 (~ (((setadjoin__Cong) =>
% 107.13/14.48 (((powerset__Cong) =>
% 107.13/14.48 (((setunion__Cong) =>
% 107.13/14.48 (((exuEu) =>
% 107.13/14.48 (((descr__Cong) =>
% 107.13/14.48 (((dsetconstr__Cong) =>
% 107.13/14.48 (((subsetI1) =>
% 107.13/14.48 (((eqimpsubset2) =>
% 107.13/14.48 (((eqimpsubset1) =>
% 107.13/14.48 (((subsetI2) =>
% 107.13/14.48 (((emptysetsubset) =>
% 107.13/14.48 (((subsetE) =>
% 107.13/14.48 (((subsetE2) =>
% 107.13/14.48 (((notsubsetI) =>
% 107.13/14.48 (((notequalI1) =>
% 107.13/14.48 (((notequalI2) =>
% 107.13/14.48 (((subsetRefl) =>
% 107.13/14.48 (((subsetTrans) =>
% 107.13/14.48 (((setadjoinSub) =>
% 107.13/14.48 (((setadjoinSub2) =>
% 107.13/14.48 (((subset2powerset) =>
% 107.13/14.48 (((setextsub) =>
% 107.13/14.48 (((subsetemptysetimpeq) =>
% 107.13/14.48 (((powersetI1) =>
% 107.13/14.48 (((powersetE1) =>
% 107.13/14.48 (((inPowerset) =>
% 107.13/14.48 (((powersetsubset) =>
% 107.13/14.48 (((sepInPowerset) =>
% 107.13/14.48 (((sepSubset) =>
% 107.13/14.48 (((binunionIL) =>
% 107.13/14.48 ((
% 107.13/14.48 (upairset2IR) =>
% 107.13/14.48 ((
% 107.13/14.48 (binunionIR) =>
% 107.13/14.48 ((
% 107.13/14.48 (binunionEcases) =>
% 107.13/14.48 ((
% 107.13/14.48 (binunionE) =>
% 107.13/14.48 ((
% 107.13/14.48 (binunionLsub) =>
% 107.13/14.48 ((
% 107.13/14.48 (binunionRsub) =>
% 107.13/14.48 ((
% 107.13/14.48 (binintersectI) =>
% 107.13/14.48 ((
% 107.13/14.48 (binintersectSubset5) =>
% 107.13/14.48 ((
% 107.13/14.48 (binintersectEL) =>
% 107.13/14.48 ((
% 107.13/14.48 (binintersectLsub) =>
% 107.13/14.48 ((
% 107.13/14.48 (binintersectSubset2) =>
% 107.13/14.48 ((
% 107.13/14.48 (binintersectSubset3) =>
% 107.13/14.48 ((
% 107.13/14.48 (binintersectER) =>
% 107.13/14.48 ((
% 107.13/14.48 (disjointsetsI1) =>
% 107.13/14.48 ((
% 107.13/14.48 (binintersectRsub) =>
% 107.13/14.48 ((
% 107.13/14.48 (binintersectSubset4) =>
% 107.13/14.48 ((
% 107.13/14.48 (binintersectSubset1) =>
% 107.13/14.48 ((
% 107.13/14.48 (bs114d) =>
% 107.13/14.48 ((
% 107.13/14.48 (setminusI) =>
% 107.13/14.48 ((
% 107.13/14.48 (setminusEL) =>
% 107.13/14.48 ((
% 107.13/14.48 (setminusER) =>
% 107.13/14.48 ((
% 107.13/14.48 (setminusSubset2) =>
% 107.13/14.48 ((
% 107.13/14.48 (setminusERneg) =>
% 107.13/14.48 ((
% 107.13/14.48 (setminusELneg) =>
% 107.13/14.48 ((
% 107.13/14.48 (setminusILneg) =>
% 107.13/14.48 ((
% 107.13/14.48 (setminusIRneg) =>
% 107.13/14.48 ((
% 107.13/14.48 (setminusLsub) =>
% 107.13/14.48 ((
% 107.13/14.48 (setminusSubset1) =>
% 107.13/14.48 ((
% 107.13/14.48 (symdiffE) =>
% 107.13/14.48 ((
% 107.13/14.48 (symdiffI1) =>
% 107.13/14.48 ((
% 107.13/14.48 (symdiffI2) =>
% 107.13/14.48 ((
% 107.13/14.48 (symdiffIneg1) =>
% 107.13/14.48 ((
% 107.13/14.48 (symdiffIneg2) =>
% 107.13/14.48 ((
% 107.13/14.48 (secondinupair) =>
% 107.13/14.48 ((
% 107.13/14.48 (setukpairIL) =>
% 107.13/14.48 ((
% 107.13/14.48 (setukpairIR) =>
% 107.13/14.48 ((
% 107.13/14.48 (kpairiskpair) =>
% 107.13/14.48 ((
% 107.13/14.48 (kpairp) =>
% 107.13/14.48 ((
% 107.13/14.48 (singletonsubset) =>
% 107.13/14.48 ((
% 107.13/14.48 (singletoninpowerset) =>
% 107.13/14.48 ((
% 107.13/14.48 (singletoninpowunion) =>
% 107.13/14.48 ((
% 107.13/14.48 (upairset2E) =>
% 107.13/14.48 ((
% 107.13/14.48 (upairsubunion) =>
% 107.13/14.48 ((
% 107.13/14.48 (upairinpowunion) =>
% 107.13/14.48 ((
% 107.13/14.48 (ubforcartprodlem1) =>
% 107.13/14.48 ((
% 107.13/14.48 (ubforcartprodlem2) =>
% 107.13/14.48 ((
% 107.13/14.48 (ubforcartprodlem3) =>
% 107.13/14.48 ((
% 107.13/14.48 (cartprodpairin) =>
% 107.13/14.48 ((
% 107.13/14.48 (cartprodmempair1) =>
% 107.13/14.48 ((
% 107.13/14.48 (cartprodmempair) =>
% 107.13/14.48 ((
% 107.13/14.48 (setunionE2) =>
% 107.13/14.48 ((
% 107.13/14.48 (setunionsingleton1) =>
% 107.13/14.48 ((
% 107.13/14.48 (setunionsingleton2) =>
% 107.13/14.48 ((
% 107.13/14.48 (setunionsingleton) =>
% 107.13/14.48 ((
% 107.13/14.48 (singletonprop) =>
% 107.13/14.48 ((
% 107.13/14.48 (ex1E1) =>
% 107.13/14.48 ((
% 107.13/14.48 (ex1I) =>
% 107.13/14.48 ((
% 107.13/14.48 (ex1I2) =>
% 107.13/14.48 ((
% 107.13/14.48 (singletonsuniq) =>
% 107.13/14.48 ((
% 107.13/14.48 (setukpairinjL1) =>
% 107.13/14.48 ((
% 107.13/14.48 (kfstsingleton) =>
% 107.13/14.48 ((
% 107.13/14.48 (theprop) =>
% 107.13/14.48 ((
% 107.13/14.48 (kfstpairEq) =>
% 107.13/14.48 ((
% 107.13/14.48 (cartprodfstin) =>
% 107.13/14.48 ((
% 107.13/14.48 (setukpairinjL2) =>
% 107.13/14.48 ((
% 107.13/14.48 (setukpairinjL) =>
% 107.13/14.48 ((
% 107.13/14.48 (setukpairinjR11) =>
% 107.13/14.48 ((
% 107.13/14.48 (setukpairinjR12) =>
% 107.13/14.48 ((
% 107.13/14.48 (setukpairinjR1) =>
% 107.13/14.48 ((
% 107.13/14.48 (upairequniteq) =>
% 107.13/14.48 ((
% 107.13/14.48 (setukpairinjR2) =>
% 107.13/14.48 ((
% 107.13/14.48 (setukpairinjR) =>
% 107.13/14.48 ((
% 107.13/14.48 (ksndsingleton) =>
% 107.13/14.48 ((
% 107.13/14.48 (ksndpairEq) =>
% 107.13/14.48 ((
% 107.13/14.48 (kpairsurjEq) =>
% 107.13/14.48 ((
% 107.13/14.48 (cartprodsndin) =>
% 107.13/14.48 ((
% 107.13/14.48 (cartprodpairmemEL) =>
% 107.13/14.48 ((
% 107.13/14.48 (cartprodpairmemER) =>
% 107.13/14.48 ((
% 107.13/14.48 (cartprodmempaircEq) =>
% 107.13/14.48 ((
% 107.13/14.48 (cartprodfstpairEq) =>
% 107.13/14.48 ((
% 107.13/14.48 (cartprodsndpairEq) =>
% 107.13/14.48 ((
% 107.13/14.48 (cartprodpairsurjEq) =>
% 107.13/14.48 ((
% 107.13/14.48 (dpsetconstrI) =>
% 107.13/14.48 ((
% 107.13/14.48 (dpsetconstrSub) =>
% 107.13/14.48 ((
% 107.13/14.48 (setOfPairsIsBReln) =>
% 107.13/14.48 ((
% 107.13/14.48 (dpsetconstrERa) =>
% 107.13/14.48 ((
% 107.13/14.48 (dpsetconstrEL1) =>
% 107.13/14.48 ((
% 107.13/14.48 (dpsetconstrEL2) =>
% 107.13/14.48 ((
% 107.13/14.48 (dpsetconstrER) =>
% 107.13/14.48 ((
% 107.13/14.48 (funcImageSingleton) =>
% 107.13/14.48 ((
% 107.13/14.48 (apProp) =>
% 107.13/14.48 ((
% 107.13/14.48 (app) =>
% 107.13/14.48 ((
% 107.13/14.48 (infuncsetfunc) =>
% 107.13/14.48 ((
% 107.13/14.48 (ap2p) =>
% 107.13/14.48 ((
% 107.13/14.48 (funcinfuncset) =>
% 107.13/14.48 ((
% 107.13/14.48 (lamProp) =>
% 107.13/14.48 ((
% 107.13/14.48 (lamp) =>
% 107.13/14.48 ((
% 107.13/14.48 (lam2p) =>
% 107.13/14.48 ((
% 107.13/14.48 (brelnall1) =>
% 107.13/14.48 ((
% 107.13/14.48 (brelnall2) =>
% 107.13/14.48 ((
% 107.13/14.48 (ex1E2) =>
% 107.13/14.48 ((
% 107.13/14.48 (funcGraphProp1) =>
% 107.13/14.48 ((
% 107.13/14.48 (funcGraphProp3) =>
% 107.13/14.48 ((
% 107.13/14.48 (funcGraphProp2) =>
% 107.13/14.48 ((
% 107.13/14.48 (funcextLem) =>
% 107.13/14.48 ((
% 107.13/14.48 (funcGraphProp4) =>
% 107.13/14.48 ((
% 107.13/14.48 (subbreln) =>
% 107.13/14.48 ((
% 107.13/14.48 (eqbreln) =>
% 107.13/14.48 ((
% 107.13/14.48 (funcext) =>
% 107.13/14.48 ((
% 107.13/14.48 (funcext2) =>
% 107.13/14.48 ((
% 107.13/14.48 (ap2apEq1) =>
% 107.13/14.48 ((
% 107.13/14.48 (ap2apEq2) =>
% 107.13/14.48 ((
% 107.13/14.48 (beta1) =>
% 107.13/14.48 ((
% 107.13/14.48 (eta1) =>
% 107.13/14.48 ((
% 107.13/14.48 (lam2lamEq) =>
% 107.13/14.48 ((
% 107.13/14.48 (beta2) =>
% 107.13/14.48 ((
% 107.13/14.48 (eta2) =>
% 107.13/14.48 ((
% 107.13/14.48 (iffalseProp1) =>
% 107.13/14.48 ((
% 107.13/14.48 (iffalseProp2) =>
% 107.13/14.48 ((
% 107.13/14.48 (iftrueProp1) =>
% 107.13/14.48 ((
% 107.13/14.48 (iftrueProp2) =>
% 107.13/14.48 ((
% 107.13/14.48 (ifSingleton) =>
% 107.13/14.48 ((
% 107.13/14.48 (ifp) =>
% 107.13/14.48 ((
% 107.13/14.48 (theeq) =>
% 107.13/14.48 ((
% 107.13/14.48 (iftrue) =>
% 107.13/14.48 ((
% 107.13/14.48 (iffalse) =>
% 107.13/14.48 ((
% 107.13/14.48 (iftrueorfalse) =>
% 107.13/14.48 ((
% 107.13/14.48 (binintersectT_lem) =>
% 107.13/14.48 ((
% 107.13/14.48 (binunionT_lem) =>
% 107.13/14.48 ((
% 107.13/14.48 (powersetT_lem) =>
% 107.13/14.48 ((
% 107.13/14.48 (setminusT_lem) =>
% 107.13/14.48 ((
% 107.13/14.48 (complementT_lem) =>
% 107.13/14.48 ((
% 107.13/14.48 (setextT) =>
% 107.13/14.48 ((
% 107.13/14.48 (subsetTI) =>
% 107.13/14.48 ((
% 107.13/14.48 (powersetTI1) =>
% 107.13/14.48 ((
% 107.13/14.48 (powersetTE1) =>
% 107.13/14.48 ((
% 107.13/14.48 (complementTI1) =>
% 107.13/14.48 ((
% 107.13/14.48 (complementTE1) =>
% 107.13/14.48 ((
% 107.13/14.48 (binintersectTELcontra) =>
% 107.13/14.48 ((
% 107.13/14.48 (binintersectTERcontra) =>
% 107.13/14.48 ((
% 107.13/14.48 (contrasubsetT) =>
% 107.13/14.48 ((
% 107.13/14.48 (contrasubsetT1) =>
% 107.13/14.48 ((
% 107.13/14.48 (contrasubsetT2) =>
% 107.13/14.48 ((
% 107.13/14.48 (contrasubsetT3) =>
% 107.13/14.48 ((
% 107.13/14.48 (doubleComplementI1) =>
% 107.13/14.48 ((
% 107.13/14.48 (doubleComplementE1) =>
% 107.13/14.48 ((
% 107.13/14.48 (doubleComplementSub1) =>
% 107.13/14.48 ((
% 107.13/14.48 (doubleComplementSub2) =>
% 107.13/14.48 ((
% 107.13/14.48 (doubleComplementEq) =>
% 107.13/14.48 ((
% 107.13/14.48 (complementTnotintersectT) =>
% 107.13/14.48 ((
% 107.13/14.48 (complementImpComplementIntersect) =>
% 107.13/14.48 ((
% 107.13/14.48 (complementSubsetComplementIntersect) =>
% 107.13/14.48 ((
% 107.13/14.48 (complementInPowersetComplementIntersect) =>
% 107.13/14.48 ((
% 107.13/14.48 (contraSubsetComplement) =>
% 107.13/14.48 ((
% 107.13/14.48 (complementTcontraSubset) =>
% 107.13/14.48 ((
% 107.13/14.48 (binunionTILcontra) =>
% 107.13/14.48 ((
% 107.13/14.48 (binunionTIRcontra) =>
% 107.13/14.48 ((
% 107.13/14.48 (inIntersectImpInUnion) =>
% 107.13/14.48 ((
% 107.13/14.48 (inIntersectImpInUnion2) =>
% 107.13/14.48 ((
% 107.13/14.48 (inIntersectImpInIntersectUnions) =>
% 107.13/14.48 ((
% 107.13/14.48 (intersectInPowersetIntersectUnions) =>
% 107.13/14.48 ((
% 107.13/14.48 (inComplementUnionImpNotIn1) =>
% 107.13/14.48 ((
% 107.13/14.48 (inComplementUnionImpInComplement1) =>
% 107.13/14.48 ((
% 107.13/14.48 (binunionTE) =>
% 107.13/14.48 ((
% 107.13/14.48 (binunionTEcontra) =>
% 107.13/14.48 ((
% 107.13/14.48 (demorgan2a1) =>
% 107.13/14.48 ((
% 107.13/14.48 (complementUnionInPowersetComplement) =>
% 107.13/14.48 ((
% 107.13/14.48 (demorgan2a2) =>
% 107.13/14.48 ((
% 107.13/14.48 (demorgan1a) =>
% 107.13/14.48 ((
% 107.13/14.48 (demorgan1b) =>
% 107.13/14.48 ((
% 107.13/14.48 (demorgan1) =>
% 107.13/14.48 ((
% 107.13/14.48 (demorgan2a) =>
% 107.13/14.48 ((
% 107.13/14.48 (demorgan2b2) =>
% 107.13/14.48 ((
% 107.13/14.48 (demorgan2b) =>
% 107.13/14.48 ((
% 107.13/14.48 (demorgan2) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz13rule0) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz13rule1) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz13rule2) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz13rule3) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz13rule4) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz1_1) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz1_2) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz1_3) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz1_4) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz1_5) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1all2) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1SetBreln1) =>
% 107.13/14.48 ((
% 107.13/14.48 (choice2fnsingleton) =>
% 107.13/14.48 ((
% 107.13/14.48 (setOfPairsIsBReln1) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1all1) =>
% 107.13/14.48 ((
% 107.13/14.48 (subbreln1) =>
% 107.13/14.48 ((
% 107.13/14.48 (eqbreln1) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1invprop) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1invI) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1invE) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1compprop) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1compI) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1compE) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1compEex) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1unionprop) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1unionIL) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1unionIR) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1unionI) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1unionE) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1unionEcases) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1unionCommutes) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz2Ex) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz2W) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz2A) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz2B) =>
% 107.13/14.48 ((
% 107.13/14.48 (image1Ex) =>
% 107.13/14.48 ((
% 107.13/14.48 (image1Ex1) =>
% 107.13/14.48 ((
% 107.13/14.48 (image1Equiv) =>
% 107.13/14.48 ((
% 107.13/14.48 (image1E) =>
% 107.13/14.48 ((
% 107.13/14.48 (image1I) =>
% 107.13/14.48 ((
% 107.13/14.48 (injFuncInInjFuncSet) =>
% 107.13/14.48 ((
% 107.13/14.48 (injFuncSetFuncIn) =>
% 107.13/14.48 ((
% 107.13/14.48 (injFuncSetFuncInj) =>
% 107.13/14.48 ((
% 107.13/14.48 (surjFuncSetFuncIn) =>
% 107.13/14.48 ((
% 107.13/14.48 (surjFuncSetFuncSurj) =>
% 107.13/14.48 ((
% 107.13/14.48 (leftInvIsSurj) =>
% 107.13/14.48 ((
% 107.13/14.48 (surjCantorThm) =>
% 107.13/14.48 ((
% 107.13/14.48 (!!) @ (
% 107.13/14.48 (('#S') @ (
% 107.13/14.48 (
% 107.13/14.48 ('#B') @ (
% 107.13/14.48 =>) @
% 107.13/14.48 nonempty)) @
% 107.13/14.48 (
% 107.13/14.48 (
% 107.13/14.48 ('#B') @ (
% 107.13/14.48 ??) @
% 107.13/14.48 (
% 107.13/14.48 (
% 107.13/14.48 ('#S') @ (
% 107.13/14.48 (
% 107.13/14.48 ('#B') @ (
% 107.13/14.48 '#S') @
% 107.13/14.48 (
% 107.13/14.48 (
% 107.13/14.48 ('#B') @ (
% 107.13/14.48 (
% 107.13/14.48 ('#B') @ (
% 107.13/14.48 &))) @
% 107.13/14.48 (
% 107.13/14.48 (
% 107.13/14.48 ('#C') @ in)))))) @
% 107.13/14.48 (
% 107.13/14.48 (
% 107.13/14.48 ('#C') @ (
% 107.13/14.48 (
% 107.13/14.48 ('#B') @ (
% 107.13/14.48 '#C') @
% 107.13/14.48 (
% 107.13/14.48 (
% 107.13/14.48 ('#B') @ (
% 107.13/14.48 (
% 107.13/14.48 ('#B') @ (
% 107.13/14.48 =))) @
% 107.13/14.48 (
% 107.13/14.48 (
% 107.13/14.48 ('#C') @ binintersect)))))) @
% 107.13/14.48 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 107.13/14.48 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl672])).
% 107.13/14.48 thf(zip_derived_cl699, plain,
% 107.13/14.48 (~ (((powerset__Cong) =>
% 107.13/14.48 (((setunion__Cong) =>
% 107.13/14.48 (((exuEu) =>
% 107.13/14.48 (((descr__Cong) =>
% 107.13/14.48 (((dsetconstr__Cong) =>
% 107.13/14.48 (((subsetI1) =>
% 107.13/14.48 (((eqimpsubset2) =>
% 107.13/14.48 (((eqimpsubset1) =>
% 107.13/14.48 (((subsetI2) =>
% 107.13/14.48 (((emptysetsubset) =>
% 107.13/14.48 (((subsetE) =>
% 107.13/14.48 (((subsetE2) =>
% 107.13/14.48 (((notsubsetI) =>
% 107.13/14.48 (((notequalI1) =>
% 107.13/14.48 (((notequalI2) =>
% 107.13/14.48 (((subsetRefl) =>
% 107.13/14.48 (((subsetTrans) =>
% 107.13/14.48 (((setadjoinSub) =>
% 107.13/14.48 (((setadjoinSub2) =>
% 107.13/14.48 (((subset2powerset) =>
% 107.13/14.48 (((setextsub) =>
% 107.13/14.48 (((subsetemptysetimpeq) =>
% 107.13/14.48 (((powersetI1) =>
% 107.13/14.48 (((powersetE1) =>
% 107.13/14.48 (((inPowerset) =>
% 107.13/14.48 (((powersetsubset) =>
% 107.13/14.48 (((sepInPowerset) =>
% 107.13/14.48 (((sepSubset) =>
% 107.13/14.48 (((binunionIL) =>
% 107.13/14.48 (((upairset2IR) =>
% 107.13/14.48 ((
% 107.13/14.48 (binunionIR) =>
% 107.13/14.48 ((
% 107.13/14.48 (binunionEcases) =>
% 107.13/14.48 ((
% 107.13/14.48 (binunionE) =>
% 107.13/14.48 ((
% 107.13/14.48 (binunionLsub) =>
% 107.13/14.48 ((
% 107.13/14.48 (binunionRsub) =>
% 107.13/14.48 ((
% 107.13/14.48 (binintersectI) =>
% 107.13/14.48 ((
% 107.13/14.48 (binintersectSubset5) =>
% 107.13/14.48 ((
% 107.13/14.48 (binintersectEL) =>
% 107.13/14.48 ((
% 107.13/14.48 (binintersectLsub) =>
% 107.13/14.48 ((
% 107.13/14.48 (binintersectSubset2) =>
% 107.13/14.48 ((
% 107.13/14.48 (binintersectSubset3) =>
% 107.13/14.48 ((
% 107.13/14.48 (binintersectER) =>
% 107.13/14.48 ((
% 107.13/14.48 (disjointsetsI1) =>
% 107.13/14.48 ((
% 107.13/14.48 (binintersectRsub) =>
% 107.13/14.48 ((
% 107.13/14.48 (binintersectSubset4) =>
% 107.13/14.48 ((
% 107.13/14.48 (binintersectSubset1) =>
% 107.13/14.48 ((
% 107.13/14.48 (bs114d) =>
% 107.13/14.48 ((
% 107.13/14.48 (setminusI) =>
% 107.13/14.48 ((
% 107.13/14.48 (setminusEL) =>
% 107.13/14.48 ((
% 107.13/14.48 (setminusER) =>
% 107.13/14.48 ((
% 107.13/14.48 (setminusSubset2) =>
% 107.13/14.48 ((
% 107.13/14.48 (setminusERneg) =>
% 107.13/14.48 ((
% 107.13/14.48 (setminusELneg) =>
% 107.13/14.48 ((
% 107.13/14.48 (setminusILneg) =>
% 107.13/14.48 ((
% 107.13/14.48 (setminusIRneg) =>
% 107.13/14.48 ((
% 107.13/14.48 (setminusLsub) =>
% 107.13/14.48 ((
% 107.13/14.48 (setminusSubset1) =>
% 107.13/14.48 ((
% 107.13/14.48 (symdiffE) =>
% 107.13/14.48 ((
% 107.13/14.48 (symdiffI1) =>
% 107.13/14.48 ((
% 107.13/14.48 (symdiffI2) =>
% 107.13/14.48 ((
% 107.13/14.48 (symdiffIneg1) =>
% 107.13/14.48 ((
% 107.13/14.48 (symdiffIneg2) =>
% 107.13/14.48 ((
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% 107.13/14.48 ((
% 107.13/14.48 (setukpairIR) =>
% 107.13/14.48 ((
% 107.13/14.48 (kpairiskpair) =>
% 107.13/14.48 ((
% 107.13/14.48 (kpairp) =>
% 107.13/14.48 ((
% 107.13/14.48 (singletonsubset) =>
% 107.13/14.48 ((
% 107.13/14.48 (singletoninpowerset) =>
% 107.13/14.48 ((
% 107.13/14.48 (singletoninpowunion) =>
% 107.13/14.48 ((
% 107.13/14.48 (upairset2E) =>
% 107.13/14.48 ((
% 107.13/14.48 (upairsubunion) =>
% 107.13/14.48 ((
% 107.13/14.48 (upairinpowunion) =>
% 107.13/14.48 ((
% 107.13/14.48 (ubforcartprodlem1) =>
% 107.13/14.48 ((
% 107.13/14.48 (ubforcartprodlem2) =>
% 107.13/14.48 ((
% 107.13/14.48 (ubforcartprodlem3) =>
% 107.13/14.48 ((
% 107.13/14.48 (cartprodpairin) =>
% 107.13/14.48 ((
% 107.13/14.48 (cartprodmempair1) =>
% 107.13/14.48 ((
% 107.13/14.48 (cartprodmempair) =>
% 107.13/14.48 ((
% 107.13/14.48 (setunionE2) =>
% 107.13/14.48 ((
% 107.13/14.48 (setunionsingleton1) =>
% 107.13/14.48 ((
% 107.13/14.48 (setunionsingleton2) =>
% 107.13/14.48 ((
% 107.13/14.48 (setunionsingleton) =>
% 107.13/14.48 ((
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% 107.13/14.48 ((
% 107.13/14.48 (ex1I) =>
% 107.13/14.48 ((
% 107.13/14.48 (ex1I2) =>
% 107.13/14.48 ((
% 107.13/14.48 (singletonsuniq) =>
% 107.13/14.48 ((
% 107.13/14.48 (setukpairinjL1) =>
% 107.13/14.48 ((
% 107.13/14.48 (kfstsingleton) =>
% 107.13/14.48 ((
% 107.13/14.48 (theprop) =>
% 107.13/14.48 ((
% 107.13/14.48 (kfstpairEq) =>
% 107.13/14.48 ((
% 107.13/14.48 (cartprodfstin) =>
% 107.13/14.48 ((
% 107.13/14.48 (setukpairinjL2) =>
% 107.13/14.48 ((
% 107.13/14.48 (setukpairinjL) =>
% 107.13/14.48 ((
% 107.13/14.48 (setukpairinjR11) =>
% 107.13/14.48 ((
% 107.13/14.48 (setukpairinjR12) =>
% 107.13/14.48 ((
% 107.13/14.48 (setukpairinjR1) =>
% 107.13/14.48 ((
% 107.13/14.48 (upairequniteq) =>
% 107.13/14.48 ((
% 107.13/14.48 (setukpairinjR2) =>
% 107.13/14.48 ((
% 107.13/14.48 (setukpairinjR) =>
% 107.13/14.48 ((
% 107.13/14.48 (ksndsingleton) =>
% 107.13/14.48 ((
% 107.13/14.48 (ksndpairEq) =>
% 107.13/14.48 ((
% 107.13/14.48 (kpairsurjEq) =>
% 107.13/14.48 ((
% 107.13/14.48 (cartprodsndin) =>
% 107.13/14.48 ((
% 107.13/14.48 (cartprodpairmemEL) =>
% 107.13/14.48 ((
% 107.13/14.48 (cartprodpairmemER) =>
% 107.13/14.48 ((
% 107.13/14.48 (cartprodmempaircEq) =>
% 107.13/14.48 ((
% 107.13/14.48 (cartprodfstpairEq) =>
% 107.13/14.48 ((
% 107.13/14.48 (cartprodsndpairEq) =>
% 107.13/14.48 ((
% 107.13/14.48 (cartprodpairsurjEq) =>
% 107.13/14.48 ((
% 107.13/14.48 (dpsetconstrI) =>
% 107.13/14.48 ((
% 107.13/14.48 (dpsetconstrSub) =>
% 107.13/14.48 ((
% 107.13/14.48 (setOfPairsIsBReln) =>
% 107.13/14.48 ((
% 107.13/14.48 (dpsetconstrERa) =>
% 107.13/14.48 ((
% 107.13/14.48 (dpsetconstrEL1) =>
% 107.13/14.48 ((
% 107.13/14.48 (dpsetconstrEL2) =>
% 107.13/14.48 ((
% 107.13/14.48 (dpsetconstrER) =>
% 107.13/14.48 ((
% 107.13/14.48 (funcImageSingleton) =>
% 107.13/14.48 ((
% 107.13/14.48 (apProp) =>
% 107.13/14.48 ((
% 107.13/14.48 (app) =>
% 107.13/14.48 ((
% 107.13/14.48 (infuncsetfunc) =>
% 107.13/14.48 ((
% 107.13/14.48 (ap2p) =>
% 107.13/14.48 ((
% 107.13/14.48 (funcinfuncset) =>
% 107.13/14.48 ((
% 107.13/14.48 (lamProp) =>
% 107.13/14.48 ((
% 107.13/14.48 (lamp) =>
% 107.13/14.48 ((
% 107.13/14.48 (lam2p) =>
% 107.13/14.48 ((
% 107.13/14.48 (brelnall1) =>
% 107.13/14.48 ((
% 107.13/14.48 (brelnall2) =>
% 107.13/14.48 ((
% 107.13/14.48 (ex1E2) =>
% 107.13/14.48 ((
% 107.13/14.48 (funcGraphProp1) =>
% 107.13/14.48 ((
% 107.13/14.48 (funcGraphProp3) =>
% 107.13/14.48 ((
% 107.13/14.48 (funcGraphProp2) =>
% 107.13/14.48 ((
% 107.13/14.48 (funcextLem) =>
% 107.13/14.48 ((
% 107.13/14.48 (funcGraphProp4) =>
% 107.13/14.48 ((
% 107.13/14.48 (subbreln) =>
% 107.13/14.48 ((
% 107.13/14.48 (eqbreln) =>
% 107.13/14.48 ((
% 107.13/14.48 (funcext) =>
% 107.13/14.48 ((
% 107.13/14.48 (funcext2) =>
% 107.13/14.48 ((
% 107.13/14.48 (ap2apEq1) =>
% 107.13/14.48 ((
% 107.13/14.48 (ap2apEq2) =>
% 107.13/14.48 ((
% 107.13/14.48 (beta1) =>
% 107.13/14.48 ((
% 107.13/14.48 (eta1) =>
% 107.13/14.48 ((
% 107.13/14.48 (lam2lamEq) =>
% 107.13/14.48 ((
% 107.13/14.48 (beta2) =>
% 107.13/14.48 ((
% 107.13/14.48 (eta2) =>
% 107.13/14.48 ((
% 107.13/14.48 (iffalseProp1) =>
% 107.13/14.48 ((
% 107.13/14.48 (iffalseProp2) =>
% 107.13/14.48 ((
% 107.13/14.48 (iftrueProp1) =>
% 107.13/14.48 ((
% 107.13/14.48 (iftrueProp2) =>
% 107.13/14.48 ((
% 107.13/14.48 (ifSingleton) =>
% 107.13/14.48 ((
% 107.13/14.48 (ifp) =>
% 107.13/14.48 ((
% 107.13/14.48 (theeq) =>
% 107.13/14.48 ((
% 107.13/14.48 (iftrue) =>
% 107.13/14.48 ((
% 107.13/14.48 (iffalse) =>
% 107.13/14.48 ((
% 107.13/14.48 (iftrueorfalse) =>
% 107.13/14.48 ((
% 107.13/14.48 (binintersectT_lem) =>
% 107.13/14.48 ((
% 107.13/14.48 (binunionT_lem) =>
% 107.13/14.48 ((
% 107.13/14.48 (powersetT_lem) =>
% 107.13/14.48 ((
% 107.13/14.48 (setminusT_lem) =>
% 107.13/14.48 ((
% 107.13/14.48 (complementT_lem) =>
% 107.13/14.48 ((
% 107.13/14.48 (setextT) =>
% 107.13/14.48 ((
% 107.13/14.48 (subsetTI) =>
% 107.13/14.48 ((
% 107.13/14.48 (powersetTI1) =>
% 107.13/14.48 ((
% 107.13/14.48 (powersetTE1) =>
% 107.13/14.48 ((
% 107.13/14.48 (complementTI1) =>
% 107.13/14.48 ((
% 107.13/14.48 (complementTE1) =>
% 107.13/14.48 ((
% 107.13/14.48 (binintersectTELcontra) =>
% 107.13/14.48 ((
% 107.13/14.48 (binintersectTERcontra) =>
% 107.13/14.48 ((
% 107.13/14.48 (contrasubsetT) =>
% 107.13/14.48 ((
% 107.13/14.48 (contrasubsetT1) =>
% 107.13/14.48 ((
% 107.13/14.48 (contrasubsetT2) =>
% 107.13/14.48 ((
% 107.13/14.48 (contrasubsetT3) =>
% 107.13/14.48 ((
% 107.13/14.48 (doubleComplementI1) =>
% 107.13/14.48 ((
% 107.13/14.48 (doubleComplementE1) =>
% 107.13/14.48 ((
% 107.13/14.48 (doubleComplementSub1) =>
% 107.13/14.48 ((
% 107.13/14.48 (doubleComplementSub2) =>
% 107.13/14.48 ((
% 107.13/14.48 (doubleComplementEq) =>
% 107.13/14.48 ((
% 107.13/14.48 (complementTnotintersectT) =>
% 107.13/14.48 ((
% 107.13/14.48 (complementImpComplementIntersect) =>
% 107.13/14.48 ((
% 107.13/14.48 (complementSubsetComplementIntersect) =>
% 107.13/14.48 ((
% 107.13/14.48 (complementInPowersetComplementIntersect) =>
% 107.13/14.48 ((
% 107.13/14.48 (contraSubsetComplement) =>
% 107.13/14.48 ((
% 107.13/14.48 (complementTcontraSubset) =>
% 107.13/14.48 ((
% 107.13/14.48 (binunionTILcontra) =>
% 107.13/14.48 ((
% 107.13/14.48 (binunionTIRcontra) =>
% 107.13/14.48 ((
% 107.13/14.48 (inIntersectImpInUnion) =>
% 107.13/14.48 ((
% 107.13/14.48 (inIntersectImpInUnion2) =>
% 107.13/14.48 ((
% 107.13/14.48 (inIntersectImpInIntersectUnions) =>
% 107.13/14.48 ((
% 107.13/14.48 (intersectInPowersetIntersectUnions) =>
% 107.13/14.48 ((
% 107.13/14.48 (inComplementUnionImpNotIn1) =>
% 107.13/14.48 ((
% 107.13/14.48 (inComplementUnionImpInComplement1) =>
% 107.13/14.48 ((
% 107.13/14.48 (binunionTE) =>
% 107.13/14.48 ((
% 107.13/14.48 (binunionTEcontra) =>
% 107.13/14.48 ((
% 107.13/14.48 (demorgan2a1) =>
% 107.13/14.48 ((
% 107.13/14.48 (complementUnionInPowersetComplement) =>
% 107.13/14.48 ((
% 107.13/14.48 (demorgan2a2) =>
% 107.13/14.48 ((
% 107.13/14.48 (demorgan1a) =>
% 107.13/14.48 ((
% 107.13/14.48 (demorgan1b) =>
% 107.13/14.48 ((
% 107.13/14.48 (demorgan1) =>
% 107.13/14.48 ((
% 107.13/14.48 (demorgan2a) =>
% 107.13/14.48 ((
% 107.13/14.48 (demorgan2b2) =>
% 107.13/14.48 ((
% 107.13/14.48 (demorgan2b) =>
% 107.13/14.48 ((
% 107.13/14.48 (demorgan2) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz13rule0) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz13rule1) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz13rule2) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz13rule3) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz13rule4) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz1_1) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz1_2) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz1_3) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz1_4) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz1_5) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1all2) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1SetBreln1) =>
% 107.13/14.48 ((
% 107.13/14.48 (choice2fnsingleton) =>
% 107.13/14.48 ((
% 107.13/14.48 (setOfPairsIsBReln1) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1all1) =>
% 107.13/14.48 ((
% 107.13/14.48 (subbreln1) =>
% 107.13/14.48 ((
% 107.13/14.48 (eqbreln1) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1invprop) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1invI) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1invE) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1compprop) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1compI) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1compE) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1compEex) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1unionprop) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1unionIL) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1unionIR) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1unionI) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1unionE) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1unionEcases) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1unionCommutes) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz2Ex) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz2W) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz2A) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz2B) =>
% 107.13/14.48 ((
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% 107.13/14.48 ((
% 107.13/14.48 (image1Ex1) =>
% 107.13/14.48 ((
% 107.13/14.48 (image1Equiv) =>
% 107.13/14.48 ((
% 107.13/14.48 (image1E) =>
% 107.13/14.48 ((
% 107.13/14.48 (image1I) =>
% 107.13/14.48 ((
% 107.13/14.48 (injFuncInInjFuncSet) =>
% 107.13/14.48 ((
% 107.13/14.48 (injFuncSetFuncIn) =>
% 107.13/14.48 ((
% 107.13/14.48 (injFuncSetFuncInj) =>
% 107.13/14.48 ((
% 107.13/14.48 (surjFuncSetFuncIn) =>
% 107.13/14.48 ((
% 107.13/14.48 (surjFuncSetFuncSurj) =>
% 107.13/14.48 ((
% 107.13/14.48 (leftInvIsSurj) =>
% 107.13/14.48 ((
% 107.13/14.48 (surjCantorThm) =>
% 107.13/14.48 ((
% 107.13/14.48 (!!) @ (
% 107.13/14.48 (('#S') @ (
% 107.13/14.48 (
% 107.13/14.48 ('#B') @ (
% 107.13/14.48 =>) @
% 107.13/14.48 nonempty)) @
% 107.13/14.48 (
% 107.13/14.48 (
% 107.13/14.48 ('#B') @ (
% 107.13/14.48 ??) @
% 107.13/14.48 (
% 107.13/14.48 (
% 107.13/14.48 ('#S') @ (
% 107.13/14.48 (
% 107.13/14.48 ('#B') @ (
% 107.13/14.48 '#S') @
% 107.13/14.48 (
% 107.13/14.48 (
% 107.13/14.48 ('#B') @ (
% 107.13/14.48 (
% 107.13/14.48 ('#B') @ (
% 107.13/14.48 &))) @
% 107.13/14.48 (
% 107.13/14.48 (
% 107.13/14.48 ('#C') @ in)))))) @
% 107.13/14.48 (
% 107.13/14.48 (
% 107.13/14.48 ('#C') @ (
% 107.13/14.48 (
% 107.13/14.48 ('#B') @ (
% 107.13/14.48 '#C') @
% 107.13/14.48 (
% 107.13/14.48 (
% 107.13/14.48 ('#B') @ (
% 107.13/14.48 (
% 107.13/14.48 ('#B') @ (
% 107.13/14.48 =))) @
% 107.13/14.48 (
% 107.13/14.48 (
% 107.13/14.48 ('#C') @ binintersect)))))) @
% 107.13/14.48 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 107.13/14.48 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl685])).
% 107.13/14.48 thf(zip_derived_cl714, plain,
% 107.13/14.48 (~ (((setunion__Cong) =>
% 107.13/14.48 (((exuEu) =>
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% 107.13/14.48 (((eqimpsubset2) =>
% 107.13/14.48 (((eqimpsubset1) =>
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% 107.13/14.48 (((notequalI1) =>
% 107.13/14.48 (((notequalI2) =>
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% 107.13/14.48 (((subsetTrans) =>
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% 107.13/14.48 (((binunionIR) =>
% 107.13/14.48 ((
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% 107.13/14.48 ((
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% 107.13/14.48 ((
% 107.13/14.48 (binunionRsub) =>
% 107.13/14.48 ((
% 107.13/14.48 (binintersectI) =>
% 107.13/14.48 ((
% 107.13/14.48 (binintersectSubset5) =>
% 107.13/14.48 ((
% 107.13/14.48 (binintersectEL) =>
% 107.13/14.48 ((
% 107.13/14.48 (binintersectLsub) =>
% 107.13/14.48 ((
% 107.13/14.48 (binintersectSubset2) =>
% 107.13/14.48 ((
% 107.13/14.48 (binintersectSubset3) =>
% 107.13/14.48 ((
% 107.13/14.48 (binintersectER) =>
% 107.13/14.48 ((
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% 107.13/14.48 ((
% 107.13/14.48 (binintersectRsub) =>
% 107.13/14.48 ((
% 107.13/14.48 (binintersectSubset4) =>
% 107.13/14.48 ((
% 107.13/14.48 (binintersectSubset1) =>
% 107.13/14.48 ((
% 107.13/14.48 (bs114d) =>
% 107.13/14.48 ((
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% 107.13/14.48 ((
% 107.13/14.48 (setminusEL) =>
% 107.13/14.48 ((
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% 107.13/14.48 ((
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% 107.13/14.48 ((
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% 107.13/14.48 ((
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% 107.13/14.48 ((
% 107.13/14.48 (setminusIRneg) =>
% 107.13/14.48 ((
% 107.13/14.48 (setminusLsub) =>
% 107.13/14.48 ((
% 107.13/14.48 (setminusSubset1) =>
% 107.13/14.48 ((
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% 107.13/14.48 ((
% 107.13/14.48 (symdiffI1) =>
% 107.13/14.48 ((
% 107.13/14.48 (symdiffI2) =>
% 107.13/14.48 ((
% 107.13/14.48 (symdiffIneg1) =>
% 107.13/14.48 ((
% 107.13/14.48 (symdiffIneg2) =>
% 107.13/14.48 ((
% 107.13/14.48 (secondinupair) =>
% 107.13/14.48 ((
% 107.13/14.48 (setukpairIL) =>
% 107.13/14.48 ((
% 107.13/14.48 (setukpairIR) =>
% 107.13/14.48 ((
% 107.13/14.48 (kpairiskpair) =>
% 107.13/14.48 ((
% 107.13/14.48 (kpairp) =>
% 107.13/14.48 ((
% 107.13/14.48 (singletonsubset) =>
% 107.13/14.48 ((
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% 107.13/14.48 ((
% 107.13/14.48 (singletoninpowunion) =>
% 107.13/14.48 ((
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% 107.13/14.48 ((
% 107.13/14.48 (upairsubunion) =>
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% 107.13/14.48 (setukpairinjL) =>
% 107.13/14.48 ((
% 107.13/14.48 (setukpairinjR11) =>
% 107.13/14.48 ((
% 107.13/14.48 (setukpairinjR12) =>
% 107.13/14.48 ((
% 107.13/14.48 (setukpairinjR1) =>
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% 107.13/14.48 (cartprodpairmemER) =>
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% 107.13/14.48 (cartprodmempaircEq) =>
% 107.13/14.48 ((
% 107.13/14.48 (cartprodfstpairEq) =>
% 107.13/14.48 ((
% 107.13/14.48 (cartprodsndpairEq) =>
% 107.13/14.48 ((
% 107.13/14.48 (cartprodpairsurjEq) =>
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% 107.13/14.48 (dpsetconstrSub) =>
% 107.13/14.48 ((
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% 107.13/14.48 (dpsetconstrEL2) =>
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% 107.13/14.48 (dpsetconstrER) =>
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% 107.13/14.48 ((
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% 107.13/14.48 (lamp) =>
% 107.13/14.48 ((
% 107.13/14.48 (lam2p) =>
% 107.13/14.48 ((
% 107.13/14.48 (brelnall1) =>
% 107.13/14.48 ((
% 107.13/14.48 (brelnall2) =>
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% 107.13/14.48 (ex1E2) =>
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% 107.13/14.48 ((
% 107.13/14.48 (funcGraphProp3) =>
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% 107.13/14.48 (funcGraphProp2) =>
% 107.13/14.48 ((
% 107.13/14.48 (funcextLem) =>
% 107.13/14.48 ((
% 107.13/14.48 (funcGraphProp4) =>
% 107.13/14.48 ((
% 107.13/14.48 (subbreln) =>
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% 107.13/14.48 (ap2apEq2) =>
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% 107.13/14.48 (eta1) =>
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% 107.13/14.48 (lam2lamEq) =>
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% 107.13/14.48 (beta2) =>
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% 107.13/14.48 (eta2) =>
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% 107.13/14.48 (iffalseProp1) =>
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% 107.13/14.48 (iffalseProp2) =>
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% 107.13/14.48 (iftrueProp1) =>
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% 107.13/14.48 ((
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% 107.13/14.48 ((
% 107.13/14.48 (contrasubsetT2) =>
% 107.13/14.48 ((
% 107.13/14.48 (contrasubsetT3) =>
% 107.13/14.48 ((
% 107.13/14.48 (doubleComplementI1) =>
% 107.13/14.48 ((
% 107.13/14.48 (doubleComplementE1) =>
% 107.13/14.48 ((
% 107.13/14.48 (doubleComplementSub1) =>
% 107.13/14.48 ((
% 107.13/14.48 (doubleComplementSub2) =>
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% 107.13/14.48 (doubleComplementEq) =>
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% 107.13/14.48 (complementTnotintersectT) =>
% 107.13/14.48 ((
% 107.13/14.48 (complementImpComplementIntersect) =>
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% 107.13/14.48 (complementSubsetComplementIntersect) =>
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% 107.13/14.48 (complementInPowersetComplementIntersect) =>
% 107.13/14.48 ((
% 107.13/14.48 (contraSubsetComplement) =>
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% 107.13/14.48 (binunionTIRcontra) =>
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% 107.13/14.48 ((
% 107.13/14.48 (inIntersectImpInUnion2) =>
% 107.13/14.48 ((
% 107.13/14.48 (inIntersectImpInIntersectUnions) =>
% 107.13/14.48 ((
% 107.13/14.48 (intersectInPowersetIntersectUnions) =>
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% 107.13/14.48 (inComplementUnionImpNotIn1) =>
% 107.13/14.48 ((
% 107.13/14.48 (inComplementUnionImpInComplement1) =>
% 107.13/14.48 ((
% 107.13/14.48 (binunionTE) =>
% 107.13/14.48 ((
% 107.13/14.48 (binunionTEcontra) =>
% 107.13/14.48 ((
% 107.13/14.48 (demorgan2a1) =>
% 107.13/14.48 ((
% 107.13/14.48 (complementUnionInPowersetComplement) =>
% 107.13/14.48 ((
% 107.13/14.48 (demorgan2a2) =>
% 107.13/14.48 ((
% 107.13/14.48 (demorgan1a) =>
% 107.13/14.48 ((
% 107.13/14.48 (demorgan1b) =>
% 107.13/14.48 ((
% 107.13/14.48 (demorgan1) =>
% 107.13/14.48 ((
% 107.13/14.48 (demorgan2a) =>
% 107.13/14.48 ((
% 107.13/14.48 (demorgan2b2) =>
% 107.13/14.48 ((
% 107.13/14.48 (demorgan2b) =>
% 107.13/14.48 ((
% 107.13/14.48 (demorgan2) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz13rule0) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz13rule1) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz13rule2) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz13rule3) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz13rule4) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz1_1) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz1_2) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz1_3) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz1_4) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz1_5) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1all2) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1SetBreln1) =>
% 107.13/14.48 ((
% 107.13/14.48 (choice2fnsingleton) =>
% 107.13/14.48 ((
% 107.13/14.48 (setOfPairsIsBReln1) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1all1) =>
% 107.13/14.48 ((
% 107.13/14.48 (subbreln1) =>
% 107.13/14.48 ((
% 107.13/14.48 (eqbreln1) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1invprop) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1invI) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1invE) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1compprop) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1compI) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1compE) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1compEex) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1unionprop) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1unionIL) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1unionIR) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1unionI) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1unionE) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1unionEcases) =>
% 107.13/14.48 ((
% 107.13/14.48 (breln1unionCommutes) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz2Ex) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz2W) =>
% 107.13/14.48 ((
% 107.13/14.48 (woz2A) =>
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% 107.13/14.48 ((
% 107.13/14.48 (image1Ex1) =>
% 107.13/14.48 ((
% 107.13/14.48 (image1Equiv) =>
% 107.13/14.48 ((
% 107.13/14.48 (image1E) =>
% 107.13/14.48 ((
% 107.13/14.48 (image1I) =>
% 107.13/14.48 ((
% 107.13/14.48 (injFuncInInjFuncSet) =>
% 107.13/14.48 ((
% 107.13/14.48 (injFuncSetFuncIn) =>
% 107.13/14.48 ((
% 107.13/14.48 (injFuncSetFuncInj) =>
% 107.13/14.48 ((
% 107.13/14.48 (surjFuncSetFuncIn) =>
% 107.13/14.48 ((
% 107.13/14.48 (surjFuncSetFuncSurj) =>
% 107.13/14.48 ((
% 107.13/14.48 (leftInvIsSurj) =>
% 107.13/14.48 ((
% 107.13/14.48 (surjCantorThm) =>
% 107.13/14.48 ((
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% 107.13/14.48 (('#S') @ (
% 107.13/14.48 (
% 107.13/14.48 ('#B') @ (
% 107.13/14.48 =>) @
% 107.13/14.48 nonempty)) @
% 107.13/14.48 (
% 107.13/14.48 (
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% 107.13/14.48 ??) @
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% 107.13/14.48 (
% 107.13/14.48 (
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% 107.13/14.48 (
% 107.13/14.48 ('#B') @ (
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% 107.13/14.48 (
% 107.13/14.48 (
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% 107.13/14.48 (
% 107.13/14.48 (
% 107.13/14.48 ('#C') @ (
% 107.13/14.48 (
% 107.13/14.48 ('#B') @ (
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% 107.13/14.48 (
% 107.13/14.48 (
% 107.13/14.48 ('#B') @ (
% 107.13/14.48 (
% 107.13/14.48 ('#B') @ (
% 107.13/14.48 =))) @
% 107.13/14.48 (
% 107.13/14.48 (
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% 107.13/14.48 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 107.13/14.48 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl714])).
% 107.13/14.48 thf(zip_derived_cl749, plain,
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% 107.13/14.48 ((
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% 107.13/14.48 ((
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% 107.13/14.48 ((
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% 107.13/14.48 ((
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% 107.13/14.48 ((
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% 107.13/14.48 ((
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% 107.13/14.48 ((
% 107.13/14.48 (ubforcartprodlem3) =>
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% 107.13/14.48 ((
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% 107.13/14.48 ((
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% 107.13/14.48 ((
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% 107.13/14.48 ((
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% 107.13/14.48 ((
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% 107.13/14.48 ((
% 107.13/14.48 (kpairsurjEq) =>
% 107.13/14.48 ((
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% 107.13/14.48 ((
% 107.13/14.48 (cartprodpairmemEL) =>
% 107.13/14.48 ((
% 107.13/14.48 (cartprodpairmemER) =>
% 107.13/14.48 ((
% 107.13/14.48 (cartprodmempaircEq) =>
% 107.13/14.48 ((
% 107.13/14.48 (cartprodfstpairEq) =>
% 107.13/14.48 ((
% 107.13/14.48 (cartprodsndpairEq) =>
% 107.13/14.48 ((
% 107.13/14.48 (cartprodpairsurjEq) =>
% 107.13/14.48 ((
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% 107.13/14.48 ((
% 107.13/14.48 (dpsetconstrSub) =>
% 107.13/14.48 ((
% 107.13/14.48 (setOfPairsIsBReln) =>
% 107.13/14.48 ((
% 107.13/14.48 (dpsetconstrERa) =>
% 107.13/14.48 ((
% 107.13/14.48 (dpsetconstrEL1) =>
% 107.13/14.48 ((
% 107.13/14.48 (dpsetconstrEL2) =>
% 107.13/14.48 ((
% 107.13/14.48 (dpsetconstrER) =>
% 107.13/14.48 ((
% 107.13/14.48 (funcImageSingleton) =>
% 107.13/14.48 ((
% 107.13/14.48 (apProp) =>
% 107.13/14.48 ((
% 107.13/14.48 (app) =>
% 107.13/14.48 ((
% 107.13/14.48 (infuncsetfunc) =>
% 107.13/14.48 ((
% 107.13/14.48 (ap2p) =>
% 107.13/14.48 ((
% 107.13/14.48 (funcinfuncset) =>
% 107.13/14.48 ((
% 107.13/14.48 (lamProp) =>
% 107.13/14.48 ((
% 107.13/14.48 (lamp) =>
% 107.13/14.48 ((
% 107.13/14.48 (lam2p) =>
% 107.13/14.48 ((
% 107.13/14.48 (brelnall1) =>
% 107.13/14.48 ((
% 107.13/14.48 (brelnall2) =>
% 107.13/14.48 ((
% 107.13/14.48 (ex1E2) =>
% 107.13/14.48 ((
% 107.13/14.48 (funcGraphProp1) =>
% 107.13/14.48 ((
% 107.13/14.48 (funcGraphProp3) =>
% 107.13/14.48 ((
% 107.13/14.48 (funcGraphProp2) =>
% 107.13/14.48 ((
% 107.13/14.48 (funcextLem) =>
% 107.13/14.48 ((
% 107.13/14.48 (funcGraphProp4) =>
% 107.13/14.48 ((
% 107.13/14.48 (subbreln) =>
% 107.13/14.48 ((
% 107.13/14.48 (eqbreln) =>
% 107.13/14.48 ((
% 107.13/14.48 (funcext) =>
% 107.13/14.48 ((
% 107.13/14.48 (funcext2) =>
% 107.13/14.48 ((
% 107.13/14.48 (ap2apEq1) =>
% 107.13/14.48 ((
% 107.13/14.48 (ap2apEq2) =>
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% 107.13/14.48 (beta1) =>
% 107.13/14.48 ((
% 107.13/14.48 (eta1) =>
% 107.13/14.48 ((
% 107.13/14.48 (lam2lamEq) =>
% 107.13/14.48 ((
% 107.13/14.48 (beta2) =>
% 107.13/14.48 ((
% 107.13/14.48 (eta2) =>
% 107.13/14.49 ((
% 107.13/14.49 (iffalseProp1) =>
% 107.13/14.49 ((
% 107.13/14.49 (iffalseProp2) =>
% 107.13/14.49 ((
% 107.13/14.49 (iftrueProp1) =>
% 107.13/14.49 ((
% 107.13/14.49 (iftrueProp2) =>
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% 107.13/14.49 ((
% 107.13/14.49 (theeq) =>
% 107.13/14.49 ((
% 107.13/14.49 (iftrue) =>
% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 (powersetT_lem) =>
% 107.13/14.49 ((
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% 107.13/14.49 ((
% 107.13/14.49 (setextT) =>
% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
% 107.13/14.49 (powersetTE1) =>
% 107.13/14.49 ((
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% 107.13/14.49 ((
% 107.13/14.49 (complementTE1) =>
% 107.13/14.49 ((
% 107.13/14.49 (binintersectTELcontra) =>
% 107.13/14.49 ((
% 107.13/14.49 (binintersectTERcontra) =>
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% 107.13/14.49 ((
% 107.13/14.49 (contrasubsetT1) =>
% 107.13/14.49 ((
% 107.13/14.49 (contrasubsetT2) =>
% 107.13/14.49 ((
% 107.13/14.49 (contrasubsetT3) =>
% 107.13/14.49 ((
% 107.13/14.49 (doubleComplementI1) =>
% 107.13/14.49 ((
% 107.13/14.49 (doubleComplementE1) =>
% 107.13/14.49 ((
% 107.13/14.49 (doubleComplementSub1) =>
% 107.13/14.49 ((
% 107.13/14.49 (doubleComplementSub2) =>
% 107.13/14.49 ((
% 107.13/14.49 (doubleComplementEq) =>
% 107.13/14.49 ((
% 107.13/14.49 (complementTnotintersectT) =>
% 107.13/14.49 ((
% 107.13/14.49 (complementImpComplementIntersect) =>
% 107.13/14.49 ((
% 107.13/14.49 (complementSubsetComplementIntersect) =>
% 107.13/14.49 ((
% 107.13/14.49 (complementInPowersetComplementIntersect) =>
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% 107.13/14.49 ((
% 107.13/14.49 (complementTcontraSubset) =>
% 107.13/14.49 ((
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% 107.13/14.49 ((
% 107.13/14.49 (binunionTIRcontra) =>
% 107.13/14.49 ((
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% 107.13/14.49 ((
% 107.13/14.49 (inIntersectImpInUnion2) =>
% 107.13/14.49 ((
% 107.13/14.49 (inIntersectImpInIntersectUnions) =>
% 107.13/14.49 ((
% 107.13/14.49 (intersectInPowersetIntersectUnions) =>
% 107.13/14.49 ((
% 107.13/14.49 (inComplementUnionImpNotIn1) =>
% 107.13/14.49 ((
% 107.13/14.49 (inComplementUnionImpInComplement1) =>
% 107.13/14.49 ((
% 107.13/14.49 (binunionTE) =>
% 107.13/14.49 ((
% 107.13/14.49 (binunionTEcontra) =>
% 107.13/14.49 ((
% 107.13/14.49 (demorgan2a1) =>
% 107.13/14.49 ((
% 107.13/14.49 (complementUnionInPowersetComplement) =>
% 107.13/14.49 ((
% 107.13/14.49 (demorgan2a2) =>
% 107.13/14.49 ((
% 107.13/14.49 (demorgan1a) =>
% 107.13/14.49 ((
% 107.13/14.49 (demorgan1b) =>
% 107.13/14.49 ((
% 107.13/14.49 (demorgan1) =>
% 107.13/14.49 ((
% 107.13/14.49 (demorgan2a) =>
% 107.13/14.49 ((
% 107.13/14.49 (demorgan2b2) =>
% 107.13/14.49 ((
% 107.13/14.49 (demorgan2b) =>
% 107.13/14.49 ((
% 107.13/14.49 (demorgan2) =>
% 107.13/14.49 ((
% 107.13/14.49 (woz13rule0) =>
% 107.13/14.49 ((
% 107.13/14.49 (woz13rule1) =>
% 107.13/14.49 ((
% 107.13/14.49 (woz13rule2) =>
% 107.13/14.49 ((
% 107.13/14.49 (woz13rule3) =>
% 107.13/14.49 ((
% 107.13/14.49 (woz13rule4) =>
% 107.13/14.49 ((
% 107.13/14.49 (woz1_1) =>
% 107.13/14.49 ((
% 107.13/14.49 (woz1_2) =>
% 107.13/14.49 ((
% 107.13/14.49 (woz1_3) =>
% 107.13/14.49 ((
% 107.13/14.49 (woz1_4) =>
% 107.13/14.49 ((
% 107.13/14.49 (woz1_5) =>
% 107.13/14.49 ((
% 107.13/14.49 (breln1all2) =>
% 107.13/14.49 ((
% 107.13/14.49 (breln1SetBreln1) =>
% 107.13/14.49 ((
% 107.13/14.49 (choice2fnsingleton) =>
% 107.13/14.49 ((
% 107.13/14.49 (setOfPairsIsBReln1) =>
% 107.13/14.49 ((
% 107.13/14.49 (breln1all1) =>
% 107.13/14.49 ((
% 107.13/14.49 (subbreln1) =>
% 107.13/14.49 ((
% 107.13/14.49 (eqbreln1) =>
% 107.13/14.49 ((
% 107.13/14.49 (breln1invprop) =>
% 107.13/14.49 ((
% 107.13/14.49 (breln1invI) =>
% 107.13/14.49 ((
% 107.13/14.49 (breln1invE) =>
% 107.13/14.49 ((
% 107.13/14.49 (breln1compprop) =>
% 107.13/14.49 ((
% 107.13/14.49 (breln1compI) =>
% 107.13/14.49 ((
% 107.13/14.49 (breln1compE) =>
% 107.13/14.49 ((
% 107.13/14.49 (breln1compEex) =>
% 107.13/14.49 ((
% 107.13/14.49 (breln1unionprop) =>
% 107.13/14.49 ((
% 107.13/14.49 (breln1unionIL) =>
% 107.13/14.49 ((
% 107.13/14.49 (breln1unionIR) =>
% 107.13/14.49 ((
% 107.13/14.49 (breln1unionI) =>
% 107.13/14.49 ((
% 107.13/14.49 (breln1unionE) =>
% 107.13/14.49 ((
% 107.13/14.49 (breln1unionEcases) =>
% 107.13/14.49 ((
% 107.13/14.49 (breln1unionCommutes) =>
% 107.13/14.49 ((
% 107.13/14.49 (woz2Ex) =>
% 107.13/14.49 ((
% 107.13/14.49 (woz2W) =>
% 107.13/14.49 ((
% 107.13/14.49 (woz2A) =>
% 107.13/14.49 ((
% 107.13/14.49 (woz2B) =>
% 107.13/14.49 ((
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% 107.13/14.49 ((
% 107.13/14.49 (image1Ex1) =>
% 107.13/14.49 ((
% 107.13/14.49 (image1Equiv) =>
% 107.13/14.49 ((
% 107.13/14.49 (image1E) =>
% 107.13/14.49 ((
% 107.13/14.49 (image1I) =>
% 107.13/14.49 ((
% 107.13/14.49 (injFuncInInjFuncSet) =>
% 107.13/14.49 ((
% 107.13/14.49 (injFuncSetFuncIn) =>
% 107.13/14.49 ((
% 107.13/14.49 (injFuncSetFuncInj) =>
% 107.13/14.49 ((
% 107.13/14.49 (surjFuncSetFuncIn) =>
% 107.13/14.49 ((
% 107.13/14.49 (surjFuncSetFuncSurj) =>
% 107.13/14.49 ((
% 107.13/14.49 (leftInvIsSurj) =>
% 107.13/14.49 ((
% 107.13/14.49 (surjCantorThm) =>
% 107.13/14.49 ((
% 107.13/14.49 (!!) @ (
% 107.13/14.49 (('#S') @ (
% 107.13/14.49 (
% 107.13/14.49 ('#B') @ (
% 107.13/14.49 =>) @
% 107.13/14.49 nonempty)) @
% 107.13/14.49 (
% 107.13/14.49 (
% 107.13/14.49 ('#B') @ (
% 107.13/14.49 ??) @
% 107.13/14.49 (
% 107.13/14.49 (
% 107.13/14.49 ('#S') @ (
% 107.13/14.49 (
% 107.13/14.49 ('#B') @ (
% 107.13/14.49 '#S') @
% 107.13/14.49 (
% 107.13/14.49 (
% 107.13/14.49 ('#B') @ (
% 107.13/14.49 (
% 107.13/14.49 ('#B') @ (
% 107.13/14.49 &))) @
% 107.13/14.49 (
% 107.13/14.49 (
% 107.13/14.49 ('#C') @ in)))))) @
% 107.13/14.49 (
% 107.13/14.49 (
% 107.13/14.49 ('#C') @ (
% 107.13/14.49 (
% 107.13/14.49 ('#B') @ (
% 107.13/14.49 '#C') @
% 107.13/14.49 (
% 107.13/14.49 (
% 107.13/14.49 ('#B') @ (
% 107.13/14.49 (
% 107.13/14.49 ('#B') @ (
% 107.13/14.49 =))) @
% 107.13/14.49 (
% 107.13/14.49 (
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% 107.13/14.49 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 107.13/14.49 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl731])).
% 107.13/14.49 thf(zip_derived_cl769, plain,
% 107.13/14.49 (~ (((dsetconstr__Cong) =>
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% 107.13/14.49 (((eqimpsubset2) =>
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% 107.13/14.49 (((subsetE) =>
% 107.13/14.49 (((subsetE2) =>
% 107.13/14.49 (((notsubsetI) =>
% 107.13/14.49 (((notequalI1) =>
% 107.13/14.49 (((notequalI2) =>
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% 107.13/14.49 (((upairset2IR) =>
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% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
% 107.13/14.49 (binintersectSubset3) =>
% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
% 107.13/14.49 (setminusEL) =>
% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
% 107.13/14.49 (symdiffI2) =>
% 107.13/14.49 ((
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% 107.13/14.49 ((
% 107.13/14.49 (symdiffIneg2) =>
% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
% 107.13/14.49 (ubforcartprodlem2) =>
% 107.13/14.49 ((
% 107.13/14.49 (ubforcartprodlem3) =>
% 107.13/14.49 ((
% 107.13/14.49 (cartprodpairin) =>
% 107.13/14.49 ((
% 107.13/14.49 (cartprodmempair1) =>
% 107.13/14.49 ((
% 107.13/14.49 (cartprodmempair) =>
% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
% 107.13/14.49 (ex1I2) =>
% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 (setukpairinjR12) =>
% 107.13/14.49 ((
% 107.13/14.49 (setukpairinjR1) =>
% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
% 107.13/14.49 (setukpairinjR) =>
% 107.13/14.49 ((
% 107.13/14.49 (ksndsingleton) =>
% 107.13/14.49 ((
% 107.13/14.49 (ksndpairEq) =>
% 107.13/14.49 ((
% 107.13/14.49 (kpairsurjEq) =>
% 107.13/14.49 ((
% 107.13/14.49 (cartprodsndin) =>
% 107.13/14.49 ((
% 107.13/14.49 (cartprodpairmemEL) =>
% 107.13/14.49 ((
% 107.13/14.49 (cartprodpairmemER) =>
% 107.13/14.49 ((
% 107.13/14.49 (cartprodmempaircEq) =>
% 107.13/14.49 ((
% 107.13/14.49 (cartprodfstpairEq) =>
% 107.13/14.49 ((
% 107.13/14.49 (cartprodsndpairEq) =>
% 107.13/14.49 ((
% 107.13/14.49 (cartprodpairsurjEq) =>
% 107.13/14.49 ((
% 107.13/14.49 (dpsetconstrI) =>
% 107.13/14.49 ((
% 107.13/14.49 (dpsetconstrSub) =>
% 107.13/14.49 ((
% 107.13/14.49 (setOfPairsIsBReln) =>
% 107.13/14.49 ((
% 107.13/14.49 (dpsetconstrERa) =>
% 107.13/14.49 ((
% 107.13/14.49 (dpsetconstrEL1) =>
% 107.13/14.49 ((
% 107.13/14.49 (dpsetconstrEL2) =>
% 107.13/14.49 ((
% 107.13/14.49 (dpsetconstrER) =>
% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
% 107.13/14.49 (brelnall1) =>
% 107.13/14.49 ((
% 107.13/14.49 (brelnall2) =>
% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
% 107.13/14.49 (funcGraphProp3) =>
% 107.13/14.49 ((
% 107.13/14.49 (funcGraphProp2) =>
% 107.13/14.49 ((
% 107.13/14.49 (funcextLem) =>
% 107.13/14.49 ((
% 107.13/14.49 (funcGraphProp4) =>
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% 107.13/14.49 ((
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% 107.13/14.49 (breln1unionEcases) =>
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% 107.13/14.49 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl749])).
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% 107.13/14.49 (demorgan2) =>
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% 107.13/14.49 ((
% 107.13/14.49 (breln1compI) =>
% 107.13/14.49 ((
% 107.13/14.49 (breln1compE) =>
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% 107.13/14.49 (breln1compEex) =>
% 107.13/14.49 ((
% 107.13/14.49 (breln1unionprop) =>
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% 107.13/14.49 ((
% 107.13/14.49 (breln1unionI) =>
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% 107.13/14.49 (breln1unionEcases) =>
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% 107.13/14.49 (breln1unionCommutes) =>
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% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
% 107.13/14.49 (injFuncSetFuncInj) =>
% 107.13/14.49 ((
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% 107.13/14.49 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl769])).
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% 107.13/14.49 (kpairsurjEq) =>
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% 107.13/14.49 ((
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% 107.13/14.49 ((
% 107.13/14.49 (cartprodpairmemER) =>
% 107.13/14.49 ((
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% 107.13/14.49 ((
% 107.13/14.49 (cartprodfstpairEq) =>
% 107.13/14.49 ((
% 107.13/14.49 (cartprodsndpairEq) =>
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% 107.13/14.49 (dpsetconstrEL2) =>
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% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl789])).
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% 107.13/14.49 (woz2Ex) =>
% 107.13/14.49 ((
% 107.13/14.49 (woz2W) =>
% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
% 107.13/14.49 (image1Equiv) =>
% 107.13/14.49 ((
% 107.13/14.49 (image1E) =>
% 107.13/14.49 ((
% 107.13/14.49 (image1I) =>
% 107.13/14.49 ((
% 107.13/14.49 (injFuncInInjFuncSet) =>
% 107.13/14.49 ((
% 107.13/14.49 (injFuncSetFuncIn) =>
% 107.13/14.49 ((
% 107.13/14.49 (injFuncSetFuncInj) =>
% 107.13/14.49 ((
% 107.13/14.49 (surjFuncSetFuncIn) =>
% 107.13/14.49 ((
% 107.13/14.49 (surjFuncSetFuncSurj) =>
% 107.13/14.49 ((
% 107.13/14.49 (leftInvIsSurj) =>
% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 (
% 107.13/14.49 ('#B') @ (
% 107.13/14.49 =>) @
% 107.13/14.49 nonempty)) @
% 107.13/14.49 (
% 107.13/14.49 (
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% 107.13/14.49 (
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% 107.13/14.49 ('#B') @ (
% 107.13/14.49 (
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% 107.13/14.49 (
% 107.13/14.49 (
% 107.13/14.49 ('#C') @ (
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% 107.13/14.49 (
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% 107.13/14.49 (
% 107.13/14.49 ('#B') @ (
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% 107.13/14.49 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 107.13/14.49 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl824])).
% 107.13/14.49 thf(zip_derived_cl850, plain,
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% 107.13/14.49 (((notequalI2) =>
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% 107.13/14.49 (((powersetE1) =>
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% 107.13/14.49 (((binintersectLsub) =>
% 107.13/14.49 ((
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% 107.13/14.49 ((
% 107.13/14.49 (binintersectSubset3) =>
% 107.13/14.49 ((
% 107.13/14.49 (binintersectER) =>
% 107.13/14.49 ((
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% 107.13/14.49 ((
% 107.13/14.49 (binintersectRsub) =>
% 107.13/14.49 ((
% 107.13/14.49 (binintersectSubset4) =>
% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
% 107.13/14.49 (setminusELneg) =>
% 107.13/14.49 ((
% 107.13/14.49 (setminusILneg) =>
% 107.13/14.49 ((
% 107.13/14.49 (setminusIRneg) =>
% 107.13/14.49 ((
% 107.13/14.49 (setminusLsub) =>
% 107.13/14.49 ((
% 107.13/14.49 (setminusSubset1) =>
% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
% 107.13/14.49 (symdiffIneg2) =>
% 107.13/14.49 ((
% 107.13/14.49 (secondinupair) =>
% 107.13/14.49 ((
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% 107.13/14.49 ((
% 107.13/14.49 (setukpairIR) =>
% 107.13/14.49 ((
% 107.13/14.49 (kpairiskpair) =>
% 107.13/14.49 ((
% 107.13/14.49 (kpairp) =>
% 107.13/14.49 ((
% 107.13/14.49 (singletonsubset) =>
% 107.13/14.49 ((
% 107.13/14.49 (singletoninpowerset) =>
% 107.13/14.49 ((
% 107.13/14.49 (singletoninpowunion) =>
% 107.13/14.49 ((
% 107.13/14.49 (upairset2E) =>
% 107.13/14.49 ((
% 107.13/14.49 (upairsubunion) =>
% 107.13/14.49 ((
% 107.13/14.49 (upairinpowunion) =>
% 107.13/14.49 ((
% 107.13/14.49 (ubforcartprodlem1) =>
% 107.13/14.49 ((
% 107.13/14.49 (ubforcartprodlem2) =>
% 107.13/14.49 ((
% 107.13/14.49 (ubforcartprodlem3) =>
% 107.13/14.49 ((
% 107.13/14.49 (cartprodpairin) =>
% 107.13/14.49 ((
% 107.13/14.49 (cartprodmempair1) =>
% 107.13/14.49 ((
% 107.13/14.49 (cartprodmempair) =>
% 107.13/14.49 ((
% 107.13/14.49 (setunionE2) =>
% 107.13/14.49 ((
% 107.13/14.49 (setunionsingleton1) =>
% 107.13/14.49 ((
% 107.13/14.49 (setunionsingleton2) =>
% 107.13/14.49 ((
% 107.13/14.49 (setunionsingleton) =>
% 107.13/14.49 ((
% 107.13/14.49 (singletonprop) =>
% 107.13/14.49 ((
% 107.13/14.49 (ex1E1) =>
% 107.13/14.49 ((
% 107.13/14.49 (ex1I) =>
% 107.13/14.49 ((
% 107.13/14.49 (ex1I2) =>
% 107.13/14.49 ((
% 107.13/14.49 (singletonsuniq) =>
% 107.13/14.49 ((
% 107.13/14.49 (setukpairinjL1) =>
% 107.13/14.49 ((
% 107.13/14.49 (kfstsingleton) =>
% 107.13/14.49 ((
% 107.13/14.49 (theprop) =>
% 107.13/14.49 ((
% 107.13/14.49 (kfstpairEq) =>
% 107.13/14.49 ((
% 107.13/14.49 (cartprodfstin) =>
% 107.13/14.49 ((
% 107.13/14.49 (setukpairinjL2) =>
% 107.13/14.49 ((
% 107.13/14.49 (setukpairinjL) =>
% 107.13/14.49 ((
% 107.13/14.49 (setukpairinjR11) =>
% 107.13/14.49 ((
% 107.13/14.49 (setukpairinjR12) =>
% 107.13/14.49 ((
% 107.13/14.49 (setukpairinjR1) =>
% 107.13/14.49 ((
% 107.13/14.49 (upairequniteq) =>
% 107.13/14.49 ((
% 107.13/14.49 (setukpairinjR2) =>
% 107.13/14.49 ((
% 107.13/14.49 (setukpairinjR) =>
% 107.13/14.49 ((
% 107.13/14.49 (ksndsingleton) =>
% 107.13/14.49 ((
% 107.13/14.49 (ksndpairEq) =>
% 107.13/14.49 ((
% 107.13/14.49 (kpairsurjEq) =>
% 107.13/14.49 ((
% 107.13/14.49 (cartprodsndin) =>
% 107.13/14.49 ((
% 107.13/14.49 (cartprodpairmemEL) =>
% 107.13/14.49 ((
% 107.13/14.49 (cartprodpairmemER) =>
% 107.13/14.49 ((
% 107.13/14.49 (cartprodmempaircEq) =>
% 107.13/14.49 ((
% 107.13/14.49 (cartprodfstpairEq) =>
% 107.13/14.49 ((
% 107.13/14.49 (cartprodsndpairEq) =>
% 107.13/14.49 ((
% 107.13/14.49 (cartprodpairsurjEq) =>
% 107.13/14.49 ((
% 107.13/14.49 (dpsetconstrI) =>
% 107.13/14.49 ((
% 107.13/14.49 (dpsetconstrSub) =>
% 107.13/14.49 ((
% 107.13/14.49 (setOfPairsIsBReln) =>
% 107.13/14.49 ((
% 107.13/14.49 (dpsetconstrERa) =>
% 107.13/14.49 ((
% 107.13/14.49 (dpsetconstrEL1) =>
% 107.13/14.49 ((
% 107.13/14.49 (dpsetconstrEL2) =>
% 107.13/14.49 ((
% 107.13/14.49 (dpsetconstrER) =>
% 107.13/14.49 ((
% 107.13/14.49 (funcImageSingleton) =>
% 107.13/14.49 ((
% 107.13/14.49 (apProp) =>
% 107.13/14.49 ((
% 107.13/14.49 (app) =>
% 107.13/14.49 ((
% 107.13/14.49 (infuncsetfunc) =>
% 107.13/14.49 ((
% 107.13/14.49 (ap2p) =>
% 107.13/14.49 ((
% 107.13/14.49 (funcinfuncset) =>
% 107.13/14.49 ((
% 107.13/14.49 (lamProp) =>
% 107.13/14.49 ((
% 107.13/14.49 (lamp) =>
% 107.13/14.49 ((
% 107.13/14.49 (lam2p) =>
% 107.13/14.49 ((
% 107.13/14.49 (brelnall1) =>
% 107.13/14.49 ((
% 107.13/14.49 (brelnall2) =>
% 107.13/14.49 ((
% 107.13/14.49 (ex1E2) =>
% 107.13/14.49 ((
% 107.13/14.49 (funcGraphProp1) =>
% 107.13/14.49 ((
% 107.13/14.49 (funcGraphProp3) =>
% 107.13/14.49 ((
% 107.13/14.49 (funcGraphProp2) =>
% 107.13/14.49 ((
% 107.13/14.49 (funcextLem) =>
% 107.13/14.49 ((
% 107.13/14.49 (funcGraphProp4) =>
% 107.13/14.49 ((
% 107.13/14.49 (subbreln) =>
% 107.13/14.49 ((
% 107.13/14.49 (eqbreln) =>
% 107.13/14.49 ((
% 107.13/14.49 (funcext) =>
% 107.13/14.49 ((
% 107.13/14.49 (funcext2) =>
% 107.13/14.49 ((
% 107.13/14.49 (ap2apEq1) =>
% 107.13/14.49 ((
% 107.13/14.49 (ap2apEq2) =>
% 107.13/14.49 ((
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% 107.13/14.49 ((
% 107.13/14.49 (eta1) =>
% 107.13/14.49 ((
% 107.13/14.49 (lam2lamEq) =>
% 107.13/14.49 ((
% 107.13/14.49 (beta2) =>
% 107.13/14.49 ((
% 107.13/14.49 (eta2) =>
% 107.13/14.49 ((
% 107.13/14.49 (iffalseProp1) =>
% 107.13/14.49 ((
% 107.13/14.49 (iffalseProp2) =>
% 107.13/14.49 ((
% 107.13/14.49 (iftrueProp1) =>
% 107.13/14.49 ((
% 107.13/14.49 (iftrueProp2) =>
% 107.13/14.49 ((
% 107.13/14.49 (ifSingleton) =>
% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
% 107.13/14.49 (binunionT_lem) =>
% 107.13/14.49 ((
% 107.13/14.49 (powersetT_lem) =>
% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
% 107.13/14.49 (subsetTI) =>
% 107.13/14.49 ((
% 107.13/14.49 (powersetTI1) =>
% 107.13/14.49 ((
% 107.13/14.49 (powersetTE1) =>
% 107.13/14.49 ((
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% 107.13/14.49 ((
% 107.13/14.49 (complementTE1) =>
% 107.13/14.49 ((
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% 107.13/14.49 ((
% 107.13/14.49 (binintersectTERcontra) =>
% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
% 107.13/14.49 (contrasubsetT2) =>
% 107.13/14.49 ((
% 107.13/14.49 (contrasubsetT3) =>
% 107.13/14.49 ((
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% 107.13/14.49 ((
% 107.13/14.49 (doubleComplementE1) =>
% 107.13/14.49 ((
% 107.13/14.49 (doubleComplementSub1) =>
% 107.13/14.49 ((
% 107.13/14.49 (doubleComplementSub2) =>
% 107.13/14.49 ((
% 107.13/14.49 (doubleComplementEq) =>
% 107.13/14.49 ((
% 107.13/14.49 (complementTnotintersectT) =>
% 107.13/14.49 ((
% 107.13/14.49 (complementImpComplementIntersect) =>
% 107.13/14.49 ((
% 107.13/14.49 (complementSubsetComplementIntersect) =>
% 107.13/14.49 ((
% 107.13/14.49 (complementInPowersetComplementIntersect) =>
% 107.13/14.49 ((
% 107.13/14.49 (contraSubsetComplement) =>
% 107.13/14.49 ((
% 107.13/14.49 (complementTcontraSubset) =>
% 107.13/14.49 ((
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% 107.13/14.49 ((
% 107.13/14.49 (binunionTIRcontra) =>
% 107.13/14.49 ((
% 107.13/14.49 (inIntersectImpInUnion) =>
% 107.13/14.49 ((
% 107.13/14.49 (inIntersectImpInUnion2) =>
% 107.13/14.49 ((
% 107.13/14.49 (inIntersectImpInIntersectUnions) =>
% 107.13/14.49 ((
% 107.13/14.49 (intersectInPowersetIntersectUnions) =>
% 107.13/14.49 ((
% 107.13/14.49 (inComplementUnionImpNotIn1) =>
% 107.13/14.49 ((
% 107.13/14.49 (inComplementUnionImpInComplement1) =>
% 107.13/14.49 ((
% 107.13/14.49 (binunionTE) =>
% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
% 107.13/14.49 (complementUnionInPowersetComplement) =>
% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
% 107.13/14.49 (demorgan2a) =>
% 107.13/14.49 ((
% 107.13/14.49 (demorgan2b2) =>
% 107.13/14.49 ((
% 107.13/14.49 (demorgan2b) =>
% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.49 ((
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% 107.13/14.50 (((binintersectSubset5) =>
% 107.13/14.50 (((binintersectEL) =>
% 107.13/14.50 (((binintersectLsub) =>
% 107.13/14.50 (((binintersectSubset2) =>
% 107.13/14.50 (((binintersectSubset3) =>
% 107.13/14.50 ((
% 107.13/14.50 (binintersectER) =>
% 107.13/14.50 ((
% 107.13/14.50 (disjointsetsI1) =>
% 107.13/14.50 ((
% 107.13/14.50 (binintersectRsub) =>
% 107.13/14.50 ((
% 107.13/14.50 (binintersectSubset4) =>
% 107.13/14.50 ((
% 107.13/14.50 (binintersectSubset1) =>
% 107.13/14.50 ((
% 107.13/14.50 (bs114d) =>
% 107.13/14.50 ((
% 107.13/14.50 (setminusI) =>
% 107.13/14.50 ((
% 107.13/14.50 (setminusEL) =>
% 107.13/14.50 ((
% 107.13/14.50 (setminusER) =>
% 107.13/14.50 ((
% 107.13/14.50 (setminusSubset2) =>
% 107.13/14.50 ((
% 107.13/14.50 (setminusERneg) =>
% 107.13/14.50 ((
% 107.13/14.50 (setminusELneg) =>
% 107.13/14.50 ((
% 107.13/14.50 (setminusILneg) =>
% 107.13/14.50 ((
% 107.13/14.50 (setminusIRneg) =>
% 107.13/14.50 ((
% 107.13/14.50 (setminusLsub) =>
% 107.13/14.50 ((
% 107.13/14.50 (setminusSubset1) =>
% 107.13/14.50 ((
% 107.13/14.50 (symdiffE) =>
% 107.13/14.50 ((
% 107.13/14.50 (symdiffI1) =>
% 107.13/14.50 ((
% 107.13/14.50 (symdiffI2) =>
% 107.13/14.50 ((
% 107.13/14.50 (symdiffIneg1) =>
% 107.13/14.50 ((
% 107.13/14.50 (symdiffIneg2) =>
% 107.13/14.50 ((
% 107.13/14.50 (secondinupair) =>
% 107.13/14.50 ((
% 107.13/14.50 (setukpairIL) =>
% 107.13/14.50 ((
% 107.13/14.50 (setukpairIR) =>
% 107.13/14.50 ((
% 107.13/14.50 (kpairiskpair) =>
% 107.13/14.50 ((
% 107.13/14.50 (kpairp) =>
% 107.13/14.50 ((
% 107.13/14.50 (singletonsubset) =>
% 107.13/14.50 ((
% 107.13/14.50 (singletoninpowerset) =>
% 107.13/14.50 ((
% 107.13/14.50 (singletoninpowunion) =>
% 107.13/14.50 ((
% 107.13/14.50 (upairset2E) =>
% 107.13/14.50 ((
% 107.13/14.50 (upairsubunion) =>
% 107.13/14.50 ((
% 107.13/14.50 (upairinpowunion) =>
% 107.13/14.50 ((
% 107.13/14.50 (ubforcartprodlem1) =>
% 107.13/14.50 ((
% 107.13/14.50 (ubforcartprodlem2) =>
% 107.13/14.50 ((
% 107.13/14.50 (ubforcartprodlem3) =>
% 107.13/14.50 ((
% 107.13/14.50 (cartprodpairin) =>
% 107.13/14.50 ((
% 107.13/14.50 (cartprodmempair1) =>
% 107.13/14.50 ((
% 107.13/14.50 (cartprodmempair) =>
% 107.13/14.50 ((
% 107.13/14.50 (setunionE2) =>
% 107.13/14.50 ((
% 107.13/14.50 (setunionsingleton1) =>
% 107.13/14.50 ((
% 107.13/14.50 (setunionsingleton2) =>
% 107.13/14.50 ((
% 107.13/14.50 (setunionsingleton) =>
% 107.13/14.50 ((
% 107.13/14.50 (singletonprop) =>
% 107.13/14.50 ((
% 107.13/14.50 (ex1E1) =>
% 107.13/14.50 ((
% 107.13/14.50 (ex1I) =>
% 107.13/14.50 ((
% 107.13/14.50 (ex1I2) =>
% 107.13/14.50 ((
% 107.13/14.50 (singletonsuniq) =>
% 107.13/14.50 ((
% 107.13/14.50 (setukpairinjL1) =>
% 107.13/14.50 ((
% 107.13/14.50 (kfstsingleton) =>
% 107.13/14.50 ((
% 107.13/14.50 (theprop) =>
% 107.13/14.50 ((
% 107.13/14.50 (kfstpairEq) =>
% 107.13/14.50 ((
% 107.13/14.50 (cartprodfstin) =>
% 107.13/14.50 ((
% 107.13/14.50 (setukpairinjL2) =>
% 107.13/14.50 ((
% 107.13/14.50 (setukpairinjL) =>
% 107.13/14.50 ((
% 107.13/14.50 (setukpairinjR11) =>
% 107.13/14.50 ((
% 107.13/14.50 (setukpairinjR12) =>
% 107.13/14.50 ((
% 107.13/14.50 (setukpairinjR1) =>
% 107.13/14.50 ((
% 107.13/14.50 (upairequniteq) =>
% 107.13/14.50 ((
% 107.13/14.50 (setukpairinjR2) =>
% 107.13/14.50 ((
% 107.13/14.50 (setukpairinjR) =>
% 107.13/14.50 ((
% 107.13/14.50 (ksndsingleton) =>
% 107.13/14.50 ((
% 107.13/14.50 (ksndpairEq) =>
% 107.13/14.50 ((
% 107.13/14.50 (kpairsurjEq) =>
% 107.13/14.50 ((
% 107.13/14.50 (cartprodsndin) =>
% 107.13/14.50 ((
% 107.13/14.50 (cartprodpairmemEL) =>
% 107.13/14.50 ((
% 107.13/14.50 (cartprodpairmemER) =>
% 107.13/14.50 ((
% 107.13/14.50 (cartprodmempaircEq) =>
% 107.13/14.50 ((
% 107.13/14.50 (cartprodfstpairEq) =>
% 107.13/14.50 ((
% 107.13/14.50 (cartprodsndpairEq) =>
% 107.13/14.50 ((
% 107.13/14.50 (cartprodpairsurjEq) =>
% 107.13/14.50 ((
% 107.13/14.50 (dpsetconstrI) =>
% 107.13/14.50 ((
% 107.13/14.50 (dpsetconstrSub) =>
% 107.13/14.50 ((
% 107.13/14.50 (setOfPairsIsBReln) =>
% 107.13/14.50 ((
% 107.13/14.50 (dpsetconstrERa) =>
% 107.13/14.50 ((
% 107.13/14.50 (dpsetconstrEL1) =>
% 107.13/14.50 ((
% 107.13/14.50 (dpsetconstrEL2) =>
% 107.13/14.50 ((
% 107.13/14.50 (dpsetconstrER) =>
% 107.13/14.50 ((
% 107.13/14.50 (funcImageSingleton) =>
% 107.13/14.50 ((
% 107.13/14.50 (apProp) =>
% 107.13/14.50 ((
% 107.13/14.50 (app) =>
% 107.13/14.50 ((
% 107.13/14.50 (infuncsetfunc) =>
% 107.13/14.50 ((
% 107.13/14.50 (ap2p) =>
% 107.13/14.50 ((
% 107.13/14.50 (funcinfuncset) =>
% 107.13/14.50 ((
% 107.13/14.50 (lamProp) =>
% 107.13/14.50 ((
% 107.13/14.50 (lamp) =>
% 107.13/14.50 ((
% 107.13/14.50 (lam2p) =>
% 107.13/14.50 ((
% 107.13/14.50 (brelnall1) =>
% 107.13/14.50 ((
% 107.13/14.50 (brelnall2) =>
% 107.13/14.50 ((
% 107.13/14.50 (ex1E2) =>
% 107.13/14.50 ((
% 107.13/14.50 (funcGraphProp1) =>
% 107.13/14.50 ((
% 107.13/14.50 (funcGraphProp3) =>
% 107.13/14.50 ((
% 107.13/14.50 (funcGraphProp2) =>
% 107.13/14.50 ((
% 107.13/14.50 (funcextLem) =>
% 107.13/14.50 ((
% 107.13/14.50 (funcGraphProp4) =>
% 107.13/14.50 ((
% 107.13/14.50 (subbreln) =>
% 107.13/14.50 ((
% 107.13/14.50 (eqbreln) =>
% 107.13/14.50 ((
% 107.13/14.50 (funcext) =>
% 107.13/14.50 ((
% 107.13/14.50 (funcext2) =>
% 107.13/14.50 ((
% 107.13/14.50 (ap2apEq1) =>
% 107.13/14.50 ((
% 107.13/14.50 (ap2apEq2) =>
% 107.13/14.50 ((
% 107.13/14.50 (beta1) =>
% 107.13/14.50 ((
% 107.13/14.50 (eta1) =>
% 107.13/14.50 ((
% 107.13/14.50 (lam2lamEq) =>
% 107.13/14.50 ((
% 107.13/14.50 (beta2) =>
% 107.13/14.50 ((
% 107.13/14.50 (eta2) =>
% 107.13/14.50 ((
% 107.13/14.50 (iffalseProp1) =>
% 107.13/14.50 ((
% 107.13/14.50 (iffalseProp2) =>
% 107.13/14.50 ((
% 107.13/14.50 (iftrueProp1) =>
% 107.13/14.50 ((
% 107.13/14.50 (iftrueProp2) =>
% 107.13/14.50 ((
% 107.13/14.50 (ifSingleton) =>
% 107.13/14.50 ((
% 107.13/14.50 (ifp) =>
% 107.13/14.50 ((
% 107.13/14.50 (theeq) =>
% 107.13/14.50 ((
% 107.13/14.50 (iftrue) =>
% 107.13/14.50 ((
% 107.13/14.50 (iffalse) =>
% 107.13/14.50 ((
% 107.13/14.50 (iftrueorfalse) =>
% 107.13/14.50 ((
% 107.13/14.50 (binintersectT_lem) =>
% 107.13/14.50 ((
% 107.13/14.50 (binunionT_lem) =>
% 107.13/14.50 ((
% 107.13/14.50 (powersetT_lem) =>
% 107.13/14.50 ((
% 107.13/14.50 (setminusT_lem) =>
% 107.13/14.50 ((
% 107.13/14.50 (complementT_lem) =>
% 107.13/14.50 ((
% 107.13/14.50 (setextT) =>
% 107.13/14.50 ((
% 107.13/14.50 (subsetTI) =>
% 107.13/14.50 ((
% 107.13/14.50 (powersetTI1) =>
% 107.13/14.50 ((
% 107.13/14.50 (powersetTE1) =>
% 107.13/14.50 ((
% 107.13/14.50 (complementTI1) =>
% 107.13/14.50 ((
% 107.13/14.50 (complementTE1) =>
% 107.13/14.50 ((
% 107.13/14.50 (binintersectTELcontra) =>
% 107.13/14.50 ((
% 107.13/14.50 (binintersectTERcontra) =>
% 107.13/14.50 ((
% 107.13/14.50 (contrasubsetT) =>
% 107.13/14.50 ((
% 107.13/14.50 (contrasubsetT1) =>
% 107.13/14.50 ((
% 107.13/14.50 (contrasubsetT2) =>
% 107.13/14.50 ((
% 107.13/14.50 (contrasubsetT3) =>
% 107.13/14.50 ((
% 107.13/14.50 (doubleComplementI1) =>
% 107.13/14.50 ((
% 107.13/14.50 (doubleComplementE1) =>
% 107.13/14.50 ((
% 107.13/14.50 (doubleComplementSub1) =>
% 107.13/14.50 ((
% 107.13/14.50 (doubleComplementSub2) =>
% 107.13/14.50 ((
% 107.13/14.50 (doubleComplementEq) =>
% 107.13/14.50 ((
% 107.13/14.50 (complementTnotintersectT) =>
% 107.13/14.50 ((
% 107.13/14.50 (complementImpComplementIntersect) =>
% 107.13/14.50 ((
% 107.13/14.50 (complementSubsetComplementIntersect) =>
% 107.13/14.50 ((
% 107.13/14.50 (complementInPowersetComplementIntersect) =>
% 107.13/14.50 ((
% 107.13/14.50 (contraSubsetComplement) =>
% 107.13/14.50 ((
% 107.13/14.50 (complementTcontraSubset) =>
% 107.13/14.50 ((
% 107.13/14.50 (binunionTILcontra) =>
% 107.13/14.50 ((
% 107.13/14.50 (binunionTIRcontra) =>
% 107.13/14.50 ((
% 107.13/14.50 (inIntersectImpInUnion) =>
% 107.13/14.50 ((
% 107.13/14.50 (inIntersectImpInUnion2) =>
% 107.13/14.50 ((
% 107.13/14.50 (inIntersectImpInIntersectUnions) =>
% 107.13/14.50 ((
% 107.13/14.50 (intersectInPowersetIntersectUnions) =>
% 107.13/14.50 ((
% 107.13/14.50 (inComplementUnionImpNotIn1) =>
% 107.13/14.50 ((
% 107.13/14.50 (inComplementUnionImpInComplement1) =>
% 107.13/14.50 ((
% 107.13/14.50 (binunionTE) =>
% 107.13/14.50 ((
% 107.13/14.50 (binunionTEcontra) =>
% 107.13/14.50 ((
% 107.13/14.50 (demorgan2a1) =>
% 107.13/14.50 ((
% 107.13/14.50 (complementUnionInPowersetComplement) =>
% 107.13/14.50 ((
% 107.13/14.50 (demorgan2a2) =>
% 107.13/14.50 ((
% 107.13/14.50 (demorgan1a) =>
% 107.13/14.50 ((
% 107.13/14.50 (demorgan1b) =>
% 107.13/14.50 ((
% 107.13/14.50 (demorgan1) =>
% 107.13/14.50 ((
% 107.13/14.50 (demorgan2a) =>
% 107.13/14.50 ((
% 107.13/14.50 (demorgan2b2) =>
% 107.13/14.50 ((
% 107.13/14.50 (demorgan2b) =>
% 107.13/14.50 ((
% 107.13/14.50 (demorgan2) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz13rule0) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz13rule1) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz13rule2) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz13rule3) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz13rule4) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz1_1) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz1_2) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz1_3) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz1_4) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz1_5) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1all2) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1SetBreln1) =>
% 107.13/14.50 ((
% 107.13/14.50 (choice2fnsingleton) =>
% 107.13/14.50 ((
% 107.13/14.50 (setOfPairsIsBReln1) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1all1) =>
% 107.13/14.50 ((
% 107.13/14.50 (subbreln1) =>
% 107.13/14.50 ((
% 107.13/14.50 (eqbreln1) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1invprop) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1invI) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1invE) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1compprop) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1compI) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1compE) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1compEex) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1unionprop) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1unionIL) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1unionIR) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1unionI) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1unionE) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1unionEcases) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1unionCommutes) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz2Ex) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz2W) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz2A) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz2B) =>
% 107.13/14.50 ((
% 107.13/14.50 (image1Ex) =>
% 107.13/14.50 ((
% 107.13/14.50 (image1Ex1) =>
% 107.13/14.50 ((
% 107.13/14.50 (image1Equiv) =>
% 107.13/14.50 ((
% 107.13/14.50 (image1E) =>
% 107.13/14.50 ((
% 107.13/14.50 (image1I) =>
% 107.13/14.50 ((
% 107.13/14.50 (injFuncInInjFuncSet) =>
% 107.13/14.50 ((
% 107.13/14.50 (injFuncSetFuncIn) =>
% 107.13/14.50 ((
% 107.13/14.50 (injFuncSetFuncInj) =>
% 107.13/14.50 ((
% 107.13/14.50 (surjFuncSetFuncIn) =>
% 107.13/14.50 ((
% 107.13/14.50 (surjFuncSetFuncSurj) =>
% 107.13/14.50 ((
% 107.13/14.50 (leftInvIsSurj) =>
% 107.13/14.50 ((
% 107.13/14.50 (surjCantorThm) =>
% 107.13/14.50 ((
% 107.13/14.50 (!!) @ (
% 107.13/14.50 (('#S') @ (
% 107.13/14.50 (
% 107.13/14.50 ('#B') @ (
% 107.13/14.50 =>) @
% 107.13/14.50 nonempty)) @
% 107.13/14.50 (
% 107.13/14.50 (
% 107.13/14.50 ('#B') @ (
% 107.13/14.50 ??) @
% 107.13/14.50 (
% 107.13/14.50 (
% 107.13/14.50 ('#S') @ (
% 107.13/14.50 (
% 107.13/14.50 ('#B') @ (
% 107.13/14.50 '#S') @
% 107.13/14.50 (
% 107.13/14.50 (
% 107.13/14.50 ('#B') @ (
% 107.13/14.50 (
% 107.13/14.50 ('#B') @ (
% 107.13/14.50 &))) @
% 107.13/14.50 (
% 107.13/14.50 (
% 107.13/14.50 ('#C') @ in)))))) @
% 107.13/14.50 (
% 107.13/14.50 (
% 107.13/14.50 ('#C') @ (
% 107.13/14.50 (
% 107.13/14.50 ('#B') @ (
% 107.13/14.50 '#C') @
% 107.13/14.50 (
% 107.13/14.50 (
% 107.13/14.50 ('#B') @ (
% 107.13/14.50 (
% 107.13/14.50 ('#B') @ (
% 107.13/14.50 =))) @
% 107.13/14.50 (
% 107.13/14.50 (
% 107.13/14.50 ('#C') @ binintersect)))))) @
% 107.13/14.50 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 107.13/14.50 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl863])).
% 107.13/14.50 thf(zip_derived_cl896, plain,
% 107.13/14.50 (~ (((notsubsetI) =>
% 107.13/14.50 (((notequalI1) =>
% 107.13/14.50 (((notequalI2) =>
% 107.13/14.50 (((subsetRefl) =>
% 107.13/14.50 (((subsetTrans) =>
% 107.13/14.50 (((setadjoinSub) =>
% 107.13/14.50 (((setadjoinSub2) =>
% 107.13/14.50 (((subset2powerset) =>
% 107.13/14.50 (((setextsub) =>
% 107.13/14.50 (((subsetemptysetimpeq) =>
% 107.13/14.50 (((powersetI1) =>
% 107.13/14.50 (((powersetE1) =>
% 107.13/14.50 (((inPowerset) =>
% 107.13/14.50 (((powersetsubset) =>
% 107.13/14.50 (((sepInPowerset) =>
% 107.13/14.50 (((sepSubset) =>
% 107.13/14.50 (((binunionIL) =>
% 107.13/14.50 (((upairset2IR) =>
% 107.13/14.50 (((binunionIR) =>
% 107.13/14.50 (((binunionEcases) =>
% 107.13/14.50 (((binunionE) =>
% 107.13/14.50 (((binunionLsub) =>
% 107.13/14.50 (((binunionRsub) =>
% 107.13/14.50 (((binintersectI) =>
% 107.13/14.50 (((binintersectSubset5) =>
% 107.13/14.50 (((binintersectEL) =>
% 107.13/14.50 (((binintersectLsub) =>
% 107.13/14.50 (((binintersectSubset2) =>
% 107.13/14.50 (((binintersectSubset3) =>
% 107.13/14.50 (((binintersectER) =>
% 107.13/14.50 ((
% 107.13/14.50 (disjointsetsI1) =>
% 107.13/14.50 ((
% 107.13/14.50 (binintersectRsub) =>
% 107.13/14.50 ((
% 107.13/14.50 (binintersectSubset4) =>
% 107.13/14.50 ((
% 107.13/14.50 (binintersectSubset1) =>
% 107.13/14.50 ((
% 107.13/14.50 (bs114d) =>
% 107.13/14.50 ((
% 107.13/14.50 (setminusI) =>
% 107.13/14.50 ((
% 107.13/14.50 (setminusEL) =>
% 107.13/14.50 ((
% 107.13/14.50 (setminusER) =>
% 107.13/14.50 ((
% 107.13/14.50 (setminusSubset2) =>
% 107.13/14.50 ((
% 107.13/14.50 (setminusERneg) =>
% 107.13/14.50 ((
% 107.13/14.50 (setminusELneg) =>
% 107.13/14.50 ((
% 107.13/14.50 (setminusILneg) =>
% 107.13/14.50 ((
% 107.13/14.50 (setminusIRneg) =>
% 107.13/14.50 ((
% 107.13/14.50 (setminusLsub) =>
% 107.13/14.50 ((
% 107.13/14.50 (setminusSubset1) =>
% 107.13/14.50 ((
% 107.13/14.50 (symdiffE) =>
% 107.13/14.50 ((
% 107.13/14.50 (symdiffI1) =>
% 107.13/14.50 ((
% 107.13/14.50 (symdiffI2) =>
% 107.13/14.50 ((
% 107.13/14.50 (symdiffIneg1) =>
% 107.13/14.50 ((
% 107.13/14.50 (symdiffIneg2) =>
% 107.13/14.50 ((
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% 107.13/14.50 ((
% 107.13/14.50 (setukpairIL) =>
% 107.13/14.50 ((
% 107.13/14.50 (setukpairIR) =>
% 107.13/14.50 ((
% 107.13/14.50 (kpairiskpair) =>
% 107.13/14.50 ((
% 107.13/14.50 (kpairp) =>
% 107.13/14.50 ((
% 107.13/14.50 (singletonsubset) =>
% 107.13/14.50 ((
% 107.13/14.50 (singletoninpowerset) =>
% 107.13/14.50 ((
% 107.13/14.50 (singletoninpowunion) =>
% 107.13/14.50 ((
% 107.13/14.50 (upairset2E) =>
% 107.13/14.50 ((
% 107.13/14.50 (upairsubunion) =>
% 107.13/14.50 ((
% 107.13/14.50 (upairinpowunion) =>
% 107.13/14.50 ((
% 107.13/14.50 (ubforcartprodlem1) =>
% 107.13/14.50 ((
% 107.13/14.50 (ubforcartprodlem2) =>
% 107.13/14.50 ((
% 107.13/14.50 (ubforcartprodlem3) =>
% 107.13/14.50 ((
% 107.13/14.50 (cartprodpairin) =>
% 107.13/14.50 ((
% 107.13/14.50 (cartprodmempair1) =>
% 107.13/14.50 ((
% 107.13/14.50 (cartprodmempair) =>
% 107.13/14.50 ((
% 107.13/14.50 (setunionE2) =>
% 107.13/14.50 ((
% 107.13/14.50 (setunionsingleton1) =>
% 107.13/14.50 ((
% 107.13/14.50 (setunionsingleton2) =>
% 107.13/14.50 ((
% 107.13/14.50 (setunionsingleton) =>
% 107.13/14.50 ((
% 107.13/14.50 (singletonprop) =>
% 107.13/14.50 ((
% 107.13/14.50 (ex1E1) =>
% 107.13/14.50 ((
% 107.13/14.50 (ex1I) =>
% 107.13/14.50 ((
% 107.13/14.50 (ex1I2) =>
% 107.13/14.50 ((
% 107.13/14.50 (singletonsuniq) =>
% 107.13/14.50 ((
% 107.13/14.50 (setukpairinjL1) =>
% 107.13/14.50 ((
% 107.13/14.50 (kfstsingleton) =>
% 107.13/14.50 ((
% 107.13/14.50 (theprop) =>
% 107.13/14.50 ((
% 107.13/14.50 (kfstpairEq) =>
% 107.13/14.50 ((
% 107.13/14.50 (cartprodfstin) =>
% 107.13/14.50 ((
% 107.13/14.50 (setukpairinjL2) =>
% 107.13/14.50 ((
% 107.13/14.50 (setukpairinjL) =>
% 107.13/14.50 ((
% 107.13/14.50 (setukpairinjR11) =>
% 107.13/14.50 ((
% 107.13/14.50 (setukpairinjR12) =>
% 107.13/14.50 ((
% 107.13/14.50 (setukpairinjR1) =>
% 107.13/14.50 ((
% 107.13/14.50 (upairequniteq) =>
% 107.13/14.50 ((
% 107.13/14.50 (setukpairinjR2) =>
% 107.13/14.50 ((
% 107.13/14.50 (setukpairinjR) =>
% 107.13/14.50 ((
% 107.13/14.50 (ksndsingleton) =>
% 107.13/14.50 ((
% 107.13/14.50 (ksndpairEq) =>
% 107.13/14.50 ((
% 107.13/14.50 (kpairsurjEq) =>
% 107.13/14.50 ((
% 107.13/14.50 (cartprodsndin) =>
% 107.13/14.50 ((
% 107.13/14.50 (cartprodpairmemEL) =>
% 107.13/14.50 ((
% 107.13/14.50 (cartprodpairmemER) =>
% 107.13/14.50 ((
% 107.13/14.50 (cartprodmempaircEq) =>
% 107.13/14.50 ((
% 107.13/14.50 (cartprodfstpairEq) =>
% 107.13/14.50 ((
% 107.13/14.50 (cartprodsndpairEq) =>
% 107.13/14.50 ((
% 107.13/14.50 (cartprodpairsurjEq) =>
% 107.13/14.50 ((
% 107.13/14.50 (dpsetconstrI) =>
% 107.13/14.50 ((
% 107.13/14.50 (dpsetconstrSub) =>
% 107.13/14.50 ((
% 107.13/14.50 (setOfPairsIsBReln) =>
% 107.13/14.50 ((
% 107.13/14.50 (dpsetconstrERa) =>
% 107.13/14.50 ((
% 107.13/14.50 (dpsetconstrEL1) =>
% 107.13/14.50 ((
% 107.13/14.50 (dpsetconstrEL2) =>
% 107.13/14.50 ((
% 107.13/14.50 (dpsetconstrER) =>
% 107.13/14.50 ((
% 107.13/14.50 (funcImageSingleton) =>
% 107.13/14.50 ((
% 107.13/14.50 (apProp) =>
% 107.13/14.50 ((
% 107.13/14.50 (app) =>
% 107.13/14.50 ((
% 107.13/14.50 (infuncsetfunc) =>
% 107.13/14.50 ((
% 107.13/14.50 (ap2p) =>
% 107.13/14.50 ((
% 107.13/14.50 (funcinfuncset) =>
% 107.13/14.50 ((
% 107.13/14.50 (lamProp) =>
% 107.13/14.50 ((
% 107.13/14.50 (lamp) =>
% 107.13/14.50 ((
% 107.13/14.50 (lam2p) =>
% 107.13/14.50 ((
% 107.13/14.50 (brelnall1) =>
% 107.13/14.50 ((
% 107.13/14.50 (brelnall2) =>
% 107.13/14.50 ((
% 107.13/14.50 (ex1E2) =>
% 107.13/14.50 ((
% 107.13/14.50 (funcGraphProp1) =>
% 107.13/14.50 ((
% 107.13/14.50 (funcGraphProp3) =>
% 107.13/14.50 ((
% 107.13/14.50 (funcGraphProp2) =>
% 107.13/14.50 ((
% 107.13/14.50 (funcextLem) =>
% 107.13/14.50 ((
% 107.13/14.50 (funcGraphProp4) =>
% 107.13/14.50 ((
% 107.13/14.50 (subbreln) =>
% 107.13/14.50 ((
% 107.13/14.50 (eqbreln) =>
% 107.13/14.50 ((
% 107.13/14.50 (funcext) =>
% 107.13/14.50 ((
% 107.13/14.50 (funcext2) =>
% 107.13/14.50 ((
% 107.13/14.50 (ap2apEq1) =>
% 107.13/14.50 ((
% 107.13/14.50 (ap2apEq2) =>
% 107.13/14.50 ((
% 107.13/14.50 (beta1) =>
% 107.13/14.50 ((
% 107.13/14.50 (eta1) =>
% 107.13/14.50 ((
% 107.13/14.50 (lam2lamEq) =>
% 107.13/14.50 ((
% 107.13/14.50 (beta2) =>
% 107.13/14.50 ((
% 107.13/14.50 (eta2) =>
% 107.13/14.50 ((
% 107.13/14.50 (iffalseProp1) =>
% 107.13/14.50 ((
% 107.13/14.50 (iffalseProp2) =>
% 107.13/14.50 ((
% 107.13/14.50 (iftrueProp1) =>
% 107.13/14.50 ((
% 107.13/14.50 (iftrueProp2) =>
% 107.13/14.50 ((
% 107.13/14.50 (ifSingleton) =>
% 107.13/14.50 ((
% 107.13/14.50 (ifp) =>
% 107.13/14.50 ((
% 107.13/14.50 (theeq) =>
% 107.13/14.50 ((
% 107.13/14.50 (iftrue) =>
% 107.13/14.50 ((
% 107.13/14.50 (iffalse) =>
% 107.13/14.50 ((
% 107.13/14.50 (iftrueorfalse) =>
% 107.13/14.50 ((
% 107.13/14.50 (binintersectT_lem) =>
% 107.13/14.50 ((
% 107.13/14.50 (binunionT_lem) =>
% 107.13/14.50 ((
% 107.13/14.50 (powersetT_lem) =>
% 107.13/14.50 ((
% 107.13/14.50 (setminusT_lem) =>
% 107.13/14.50 ((
% 107.13/14.50 (complementT_lem) =>
% 107.13/14.50 ((
% 107.13/14.50 (setextT) =>
% 107.13/14.50 ((
% 107.13/14.50 (subsetTI) =>
% 107.13/14.50 ((
% 107.13/14.50 (powersetTI1) =>
% 107.13/14.50 ((
% 107.13/14.50 (powersetTE1) =>
% 107.13/14.50 ((
% 107.13/14.50 (complementTI1) =>
% 107.13/14.50 ((
% 107.13/14.50 (complementTE1) =>
% 107.13/14.50 ((
% 107.13/14.50 (binintersectTELcontra) =>
% 107.13/14.50 ((
% 107.13/14.50 (binintersectTERcontra) =>
% 107.13/14.50 ((
% 107.13/14.50 (contrasubsetT) =>
% 107.13/14.50 ((
% 107.13/14.50 (contrasubsetT1) =>
% 107.13/14.50 ((
% 107.13/14.50 (contrasubsetT2) =>
% 107.13/14.50 ((
% 107.13/14.50 (contrasubsetT3) =>
% 107.13/14.50 ((
% 107.13/14.50 (doubleComplementI1) =>
% 107.13/14.50 ((
% 107.13/14.50 (doubleComplementE1) =>
% 107.13/14.50 ((
% 107.13/14.50 (doubleComplementSub1) =>
% 107.13/14.50 ((
% 107.13/14.50 (doubleComplementSub2) =>
% 107.13/14.50 ((
% 107.13/14.50 (doubleComplementEq) =>
% 107.13/14.50 ((
% 107.13/14.50 (complementTnotintersectT) =>
% 107.13/14.50 ((
% 107.13/14.50 (complementImpComplementIntersect) =>
% 107.13/14.50 ((
% 107.13/14.50 (complementSubsetComplementIntersect) =>
% 107.13/14.50 ((
% 107.13/14.50 (complementInPowersetComplementIntersect) =>
% 107.13/14.50 ((
% 107.13/14.50 (contraSubsetComplement) =>
% 107.13/14.50 ((
% 107.13/14.50 (complementTcontraSubset) =>
% 107.13/14.50 ((
% 107.13/14.50 (binunionTILcontra) =>
% 107.13/14.50 ((
% 107.13/14.50 (binunionTIRcontra) =>
% 107.13/14.50 ((
% 107.13/14.50 (inIntersectImpInUnion) =>
% 107.13/14.50 ((
% 107.13/14.50 (inIntersectImpInUnion2) =>
% 107.13/14.50 ((
% 107.13/14.50 (inIntersectImpInIntersectUnions) =>
% 107.13/14.50 ((
% 107.13/14.50 (intersectInPowersetIntersectUnions) =>
% 107.13/14.50 ((
% 107.13/14.50 (inComplementUnionImpNotIn1) =>
% 107.13/14.50 ((
% 107.13/14.50 (inComplementUnionImpInComplement1) =>
% 107.13/14.50 ((
% 107.13/14.50 (binunionTE) =>
% 107.13/14.50 ((
% 107.13/14.50 (binunionTEcontra) =>
% 107.13/14.50 ((
% 107.13/14.50 (demorgan2a1) =>
% 107.13/14.50 ((
% 107.13/14.50 (complementUnionInPowersetComplement) =>
% 107.13/14.50 ((
% 107.13/14.50 (demorgan2a2) =>
% 107.13/14.50 ((
% 107.13/14.50 (demorgan1a) =>
% 107.13/14.50 ((
% 107.13/14.50 (demorgan1b) =>
% 107.13/14.50 ((
% 107.13/14.50 (demorgan1) =>
% 107.13/14.50 ((
% 107.13/14.50 (demorgan2a) =>
% 107.13/14.50 ((
% 107.13/14.50 (demorgan2b2) =>
% 107.13/14.50 ((
% 107.13/14.50 (demorgan2b) =>
% 107.13/14.50 ((
% 107.13/14.50 (demorgan2) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz13rule0) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz13rule1) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz13rule2) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz13rule3) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz13rule4) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz1_1) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz1_2) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz1_3) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz1_4) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz1_5) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1all2) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1SetBreln1) =>
% 107.13/14.50 ((
% 107.13/14.50 (choice2fnsingleton) =>
% 107.13/14.50 ((
% 107.13/14.50 (setOfPairsIsBReln1) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1all1) =>
% 107.13/14.50 ((
% 107.13/14.50 (subbreln1) =>
% 107.13/14.50 ((
% 107.13/14.50 (eqbreln1) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1invprop) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1invI) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1invE) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1compprop) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1compI) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1compE) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1compEex) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1unionprop) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1unionIL) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1unionIR) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1unionI) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1unionE) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1unionEcases) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1unionCommutes) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz2Ex) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz2W) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz2A) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz2B) =>
% 107.13/14.50 ((
% 107.13/14.50 (image1Ex) =>
% 107.13/14.50 ((
% 107.13/14.50 (image1Ex1) =>
% 107.13/14.50 ((
% 107.13/14.50 (image1Equiv) =>
% 107.13/14.50 ((
% 107.13/14.50 (image1E) =>
% 107.13/14.50 ((
% 107.13/14.50 (image1I) =>
% 107.13/14.50 ((
% 107.13/14.50 (injFuncInInjFuncSet) =>
% 107.13/14.50 ((
% 107.13/14.50 (injFuncSetFuncIn) =>
% 107.13/14.50 ((
% 107.13/14.50 (injFuncSetFuncInj) =>
% 107.13/14.50 ((
% 107.13/14.50 (surjFuncSetFuncIn) =>
% 107.13/14.50 ((
% 107.13/14.50 (surjFuncSetFuncSurj) =>
% 107.13/14.50 ((
% 107.13/14.50 (leftInvIsSurj) =>
% 107.13/14.50 ((
% 107.13/14.50 (surjCantorThm) =>
% 107.13/14.50 ((
% 107.13/14.50 (!!) @ (
% 107.13/14.50 (('#S') @ (
% 107.13/14.50 (
% 107.13/14.50 ('#B') @ (
% 107.13/14.50 =>) @
% 107.13/14.50 nonempty)) @
% 107.13/14.50 (
% 107.13/14.50 (
% 107.13/14.50 ('#B') @ (
% 107.13/14.50 ??) @
% 107.13/14.50 (
% 107.13/14.50 (
% 107.13/14.50 ('#S') @ (
% 107.13/14.50 (
% 107.13/14.50 ('#B') @ (
% 107.13/14.50 '#S') @
% 107.13/14.50 (
% 107.13/14.50 (
% 107.13/14.50 ('#B') @ (
% 107.13/14.50 (
% 107.13/14.50 ('#B') @ (
% 107.13/14.50 &))) @
% 107.13/14.50 (
% 107.13/14.50 (
% 107.13/14.50 ('#C') @ in)))))) @
% 107.13/14.50 (
% 107.13/14.50 (
% 107.13/14.50 ('#C') @ (
% 107.13/14.50 (
% 107.13/14.50 ('#B') @ (
% 107.13/14.50 '#C') @
% 107.13/14.50 (
% 107.13/14.50 (
% 107.13/14.50 ('#B') @ (
% 107.13/14.50 (
% 107.13/14.50 ('#B') @ (
% 107.13/14.50 =))) @
% 107.13/14.50 (
% 107.13/14.50 (
% 107.13/14.50 ('#C') @ binintersect)))))) @
% 107.13/14.50 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 107.13/14.50 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl878])).
% 107.13/14.50 thf(zip_derived_cl909, plain,
% 107.13/14.50 (~ (((notequalI1) =>
% 107.13/14.50 (((notequalI2) =>
% 107.13/14.50 (((subsetRefl) =>
% 107.13/14.50 (((subsetTrans) =>
% 107.13/14.50 (((setadjoinSub) =>
% 107.13/14.50 (((setadjoinSub2) =>
% 107.13/14.50 (((subset2powerset) =>
% 107.13/14.50 (((setextsub) =>
% 107.13/14.50 (((subsetemptysetimpeq) =>
% 107.13/14.50 (((powersetI1) =>
% 107.13/14.50 (((powersetE1) =>
% 107.13/14.50 (((inPowerset) =>
% 107.13/14.50 (((powersetsubset) =>
% 107.13/14.50 (((sepInPowerset) =>
% 107.13/14.50 (((sepSubset) =>
% 107.13/14.50 (((binunionIL) =>
% 107.13/14.50 (((upairset2IR) =>
% 107.13/14.50 (((binunionIR) =>
% 107.13/14.50 (((binunionEcases) =>
% 107.13/14.50 (((binunionE) =>
% 107.13/14.50 (((binunionLsub) =>
% 107.13/14.50 (((binunionRsub) =>
% 107.13/14.50 (((binintersectI) =>
% 107.13/14.50 (((binintersectSubset5) =>
% 107.13/14.50 (((binintersectEL) =>
% 107.13/14.50 (((binintersectLsub) =>
% 107.13/14.50 (((binintersectSubset2) =>
% 107.13/14.50 (((binintersectSubset3) =>
% 107.13/14.50 (((binintersectER) =>
% 107.13/14.50 (((disjointsetsI1) =>
% 107.13/14.50 ((
% 107.13/14.50 (binintersectRsub) =>
% 107.13/14.50 ((
% 107.13/14.50 (binintersectSubset4) =>
% 107.13/14.50 ((
% 107.13/14.50 (binintersectSubset1) =>
% 107.13/14.50 ((
% 107.13/14.50 (bs114d) =>
% 107.13/14.50 ((
% 107.13/14.50 (setminusI) =>
% 107.13/14.50 ((
% 107.13/14.50 (setminusEL) =>
% 107.13/14.50 ((
% 107.13/14.50 (setminusER) =>
% 107.13/14.50 ((
% 107.13/14.50 (setminusSubset2) =>
% 107.13/14.50 ((
% 107.13/14.50 (setminusERneg) =>
% 107.13/14.50 ((
% 107.13/14.50 (setminusELneg) =>
% 107.13/14.50 ((
% 107.13/14.50 (setminusILneg) =>
% 107.13/14.50 ((
% 107.13/14.50 (setminusIRneg) =>
% 107.13/14.50 ((
% 107.13/14.50 (setminusLsub) =>
% 107.13/14.50 ((
% 107.13/14.50 (setminusSubset1) =>
% 107.13/14.50 ((
% 107.13/14.50 (symdiffE) =>
% 107.13/14.50 ((
% 107.13/14.50 (symdiffI1) =>
% 107.13/14.50 ((
% 107.13/14.50 (symdiffI2) =>
% 107.13/14.50 ((
% 107.13/14.50 (symdiffIneg1) =>
% 107.13/14.50 ((
% 107.13/14.50 (symdiffIneg2) =>
% 107.13/14.50 ((
% 107.13/14.50 (secondinupair) =>
% 107.13/14.50 ((
% 107.13/14.50 (setukpairIL) =>
% 107.13/14.50 ((
% 107.13/14.50 (setukpairIR) =>
% 107.13/14.50 ((
% 107.13/14.50 (kpairiskpair) =>
% 107.13/14.50 ((
% 107.13/14.50 (kpairp) =>
% 107.13/14.50 ((
% 107.13/14.50 (singletonsubset) =>
% 107.13/14.50 ((
% 107.13/14.50 (singletoninpowerset) =>
% 107.13/14.50 ((
% 107.13/14.50 (singletoninpowunion) =>
% 107.13/14.50 ((
% 107.13/14.50 (upairset2E) =>
% 107.13/14.50 ((
% 107.13/14.50 (upairsubunion) =>
% 107.13/14.50 ((
% 107.13/14.50 (upairinpowunion) =>
% 107.13/14.50 ((
% 107.13/14.50 (ubforcartprodlem1) =>
% 107.13/14.50 ((
% 107.13/14.50 (ubforcartprodlem2) =>
% 107.13/14.50 ((
% 107.13/14.50 (ubforcartprodlem3) =>
% 107.13/14.50 ((
% 107.13/14.50 (cartprodpairin) =>
% 107.13/14.50 ((
% 107.13/14.50 (cartprodmempair1) =>
% 107.13/14.50 ((
% 107.13/14.50 (cartprodmempair) =>
% 107.13/14.50 ((
% 107.13/14.50 (setunionE2) =>
% 107.13/14.50 ((
% 107.13/14.50 (setunionsingleton1) =>
% 107.13/14.50 ((
% 107.13/14.50 (setunionsingleton2) =>
% 107.13/14.50 ((
% 107.13/14.50 (setunionsingleton) =>
% 107.13/14.50 ((
% 107.13/14.50 (singletonprop) =>
% 107.13/14.50 ((
% 107.13/14.50 (ex1E1) =>
% 107.13/14.50 ((
% 107.13/14.50 (ex1I) =>
% 107.13/14.50 ((
% 107.13/14.50 (ex1I2) =>
% 107.13/14.50 ((
% 107.13/14.50 (singletonsuniq) =>
% 107.13/14.50 ((
% 107.13/14.50 (setukpairinjL1) =>
% 107.13/14.50 ((
% 107.13/14.50 (kfstsingleton) =>
% 107.13/14.50 ((
% 107.13/14.50 (theprop) =>
% 107.13/14.50 ((
% 107.13/14.50 (kfstpairEq) =>
% 107.13/14.50 ((
% 107.13/14.50 (cartprodfstin) =>
% 107.13/14.50 ((
% 107.13/14.50 (setukpairinjL2) =>
% 107.13/14.50 ((
% 107.13/14.50 (setukpairinjL) =>
% 107.13/14.50 ((
% 107.13/14.50 (setukpairinjR11) =>
% 107.13/14.50 ((
% 107.13/14.50 (setukpairinjR12) =>
% 107.13/14.50 ((
% 107.13/14.50 (setukpairinjR1) =>
% 107.13/14.50 ((
% 107.13/14.50 (upairequniteq) =>
% 107.13/14.50 ((
% 107.13/14.50 (setukpairinjR2) =>
% 107.13/14.50 ((
% 107.13/14.50 (setukpairinjR) =>
% 107.13/14.50 ((
% 107.13/14.50 (ksndsingleton) =>
% 107.13/14.50 ((
% 107.13/14.50 (ksndpairEq) =>
% 107.13/14.50 ((
% 107.13/14.50 (kpairsurjEq) =>
% 107.13/14.50 ((
% 107.13/14.50 (cartprodsndin) =>
% 107.13/14.50 ((
% 107.13/14.50 (cartprodpairmemEL) =>
% 107.13/14.50 ((
% 107.13/14.50 (cartprodpairmemER) =>
% 107.13/14.50 ((
% 107.13/14.50 (cartprodmempaircEq) =>
% 107.13/14.50 ((
% 107.13/14.50 (cartprodfstpairEq) =>
% 107.13/14.50 ((
% 107.13/14.50 (cartprodsndpairEq) =>
% 107.13/14.50 ((
% 107.13/14.50 (cartprodpairsurjEq) =>
% 107.13/14.50 ((
% 107.13/14.50 (dpsetconstrI) =>
% 107.13/14.50 ((
% 107.13/14.50 (dpsetconstrSub) =>
% 107.13/14.50 ((
% 107.13/14.50 (setOfPairsIsBReln) =>
% 107.13/14.50 ((
% 107.13/14.50 (dpsetconstrERa) =>
% 107.13/14.50 ((
% 107.13/14.50 (dpsetconstrEL1) =>
% 107.13/14.50 ((
% 107.13/14.50 (dpsetconstrEL2) =>
% 107.13/14.50 ((
% 107.13/14.50 (dpsetconstrER) =>
% 107.13/14.50 ((
% 107.13/14.50 (funcImageSingleton) =>
% 107.13/14.50 ((
% 107.13/14.50 (apProp) =>
% 107.13/14.50 ((
% 107.13/14.50 (app) =>
% 107.13/14.50 ((
% 107.13/14.50 (infuncsetfunc) =>
% 107.13/14.50 ((
% 107.13/14.50 (ap2p) =>
% 107.13/14.50 ((
% 107.13/14.50 (funcinfuncset) =>
% 107.13/14.50 ((
% 107.13/14.50 (lamProp) =>
% 107.13/14.50 ((
% 107.13/14.50 (lamp) =>
% 107.13/14.50 ((
% 107.13/14.50 (lam2p) =>
% 107.13/14.50 ((
% 107.13/14.50 (brelnall1) =>
% 107.13/14.50 ((
% 107.13/14.50 (brelnall2) =>
% 107.13/14.50 ((
% 107.13/14.50 (ex1E2) =>
% 107.13/14.50 ((
% 107.13/14.50 (funcGraphProp1) =>
% 107.13/14.50 ((
% 107.13/14.50 (funcGraphProp3) =>
% 107.13/14.50 ((
% 107.13/14.50 (funcGraphProp2) =>
% 107.13/14.50 ((
% 107.13/14.50 (funcextLem) =>
% 107.13/14.50 ((
% 107.13/14.50 (funcGraphProp4) =>
% 107.13/14.50 ((
% 107.13/14.50 (subbreln) =>
% 107.13/14.50 ((
% 107.13/14.50 (eqbreln) =>
% 107.13/14.50 ((
% 107.13/14.50 (funcext) =>
% 107.13/14.50 ((
% 107.13/14.50 (funcext2) =>
% 107.13/14.50 ((
% 107.13/14.50 (ap2apEq1) =>
% 107.13/14.50 ((
% 107.13/14.50 (ap2apEq2) =>
% 107.13/14.50 ((
% 107.13/14.50 (beta1) =>
% 107.13/14.50 ((
% 107.13/14.50 (eta1) =>
% 107.13/14.50 ((
% 107.13/14.50 (lam2lamEq) =>
% 107.13/14.50 ((
% 107.13/14.50 (beta2) =>
% 107.13/14.50 ((
% 107.13/14.50 (eta2) =>
% 107.13/14.50 ((
% 107.13/14.50 (iffalseProp1) =>
% 107.13/14.50 ((
% 107.13/14.50 (iffalseProp2) =>
% 107.13/14.50 ((
% 107.13/14.50 (iftrueProp1) =>
% 107.13/14.50 ((
% 107.13/14.50 (iftrueProp2) =>
% 107.13/14.50 ((
% 107.13/14.50 (ifSingleton) =>
% 107.13/14.50 ((
% 107.13/14.50 (ifp) =>
% 107.13/14.50 ((
% 107.13/14.50 (theeq) =>
% 107.13/14.50 ((
% 107.13/14.50 (iftrue) =>
% 107.13/14.50 ((
% 107.13/14.50 (iffalse) =>
% 107.13/14.50 ((
% 107.13/14.50 (iftrueorfalse) =>
% 107.13/14.50 ((
% 107.13/14.50 (binintersectT_lem) =>
% 107.13/14.50 ((
% 107.13/14.50 (binunionT_lem) =>
% 107.13/14.50 ((
% 107.13/14.50 (powersetT_lem) =>
% 107.13/14.50 ((
% 107.13/14.50 (setminusT_lem) =>
% 107.13/14.50 ((
% 107.13/14.50 (complementT_lem) =>
% 107.13/14.50 ((
% 107.13/14.50 (setextT) =>
% 107.13/14.50 ((
% 107.13/14.50 (subsetTI) =>
% 107.13/14.50 ((
% 107.13/14.50 (powersetTI1) =>
% 107.13/14.50 ((
% 107.13/14.50 (powersetTE1) =>
% 107.13/14.50 ((
% 107.13/14.50 (complementTI1) =>
% 107.13/14.50 ((
% 107.13/14.50 (complementTE1) =>
% 107.13/14.50 ((
% 107.13/14.50 (binintersectTELcontra) =>
% 107.13/14.50 ((
% 107.13/14.50 (binintersectTERcontra) =>
% 107.13/14.50 ((
% 107.13/14.50 (contrasubsetT) =>
% 107.13/14.50 ((
% 107.13/14.50 (contrasubsetT1) =>
% 107.13/14.50 ((
% 107.13/14.50 (contrasubsetT2) =>
% 107.13/14.50 ((
% 107.13/14.50 (contrasubsetT3) =>
% 107.13/14.50 ((
% 107.13/14.50 (doubleComplementI1) =>
% 107.13/14.50 ((
% 107.13/14.50 (doubleComplementE1) =>
% 107.13/14.50 ((
% 107.13/14.50 (doubleComplementSub1) =>
% 107.13/14.50 ((
% 107.13/14.50 (doubleComplementSub2) =>
% 107.13/14.50 ((
% 107.13/14.50 (doubleComplementEq) =>
% 107.13/14.50 ((
% 107.13/14.50 (complementTnotintersectT) =>
% 107.13/14.50 ((
% 107.13/14.50 (complementImpComplementIntersect) =>
% 107.13/14.50 ((
% 107.13/14.50 (complementSubsetComplementIntersect) =>
% 107.13/14.50 ((
% 107.13/14.50 (complementInPowersetComplementIntersect) =>
% 107.13/14.50 ((
% 107.13/14.50 (contraSubsetComplement) =>
% 107.13/14.50 ((
% 107.13/14.50 (complementTcontraSubset) =>
% 107.13/14.50 ((
% 107.13/14.50 (binunionTILcontra) =>
% 107.13/14.50 ((
% 107.13/14.50 (binunionTIRcontra) =>
% 107.13/14.50 ((
% 107.13/14.50 (inIntersectImpInUnion) =>
% 107.13/14.50 ((
% 107.13/14.50 (inIntersectImpInUnion2) =>
% 107.13/14.50 ((
% 107.13/14.50 (inIntersectImpInIntersectUnions) =>
% 107.13/14.50 ((
% 107.13/14.50 (intersectInPowersetIntersectUnions) =>
% 107.13/14.50 ((
% 107.13/14.50 (inComplementUnionImpNotIn1) =>
% 107.13/14.50 ((
% 107.13/14.50 (inComplementUnionImpInComplement1) =>
% 107.13/14.50 ((
% 107.13/14.50 (binunionTE) =>
% 107.13/14.50 ((
% 107.13/14.50 (binunionTEcontra) =>
% 107.13/14.50 ((
% 107.13/14.50 (demorgan2a1) =>
% 107.13/14.50 ((
% 107.13/14.50 (complementUnionInPowersetComplement) =>
% 107.13/14.50 ((
% 107.13/14.50 (demorgan2a2) =>
% 107.13/14.50 ((
% 107.13/14.50 (demorgan1a) =>
% 107.13/14.50 ((
% 107.13/14.50 (demorgan1b) =>
% 107.13/14.50 ((
% 107.13/14.50 (demorgan1) =>
% 107.13/14.50 ((
% 107.13/14.50 (demorgan2a) =>
% 107.13/14.50 ((
% 107.13/14.50 (demorgan2b2) =>
% 107.13/14.50 ((
% 107.13/14.50 (demorgan2b) =>
% 107.13/14.50 ((
% 107.13/14.50 (demorgan2) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz13rule0) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz13rule1) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz13rule2) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz13rule3) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz13rule4) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz1_1) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz1_2) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz1_3) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz1_4) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz1_5) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1all2) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1SetBreln1) =>
% 107.13/14.50 ((
% 107.13/14.50 (choice2fnsingleton) =>
% 107.13/14.50 ((
% 107.13/14.50 (setOfPairsIsBReln1) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1all1) =>
% 107.13/14.50 ((
% 107.13/14.50 (subbreln1) =>
% 107.13/14.50 ((
% 107.13/14.50 (eqbreln1) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1invprop) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1invI) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1invE) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1compprop) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1compI) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1compE) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1compEex) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1unionprop) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1unionIL) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1unionIR) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1unionI) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1unionE) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1unionEcases) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1unionCommutes) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz2Ex) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz2W) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz2A) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz2B) =>
% 107.13/14.50 ((
% 107.13/14.50 (image1Ex) =>
% 107.13/14.50 ((
% 107.13/14.50 (image1Ex1) =>
% 107.13/14.50 ((
% 107.13/14.50 (image1Equiv) =>
% 107.13/14.50 ((
% 107.13/14.50 (image1E) =>
% 107.13/14.50 ((
% 107.13/14.50 (image1I) =>
% 107.13/14.50 ((
% 107.13/14.50 (injFuncInInjFuncSet) =>
% 107.13/14.50 ((
% 107.13/14.50 (injFuncSetFuncIn) =>
% 107.13/14.50 ((
% 107.13/14.50 (injFuncSetFuncInj) =>
% 107.13/14.50 ((
% 107.13/14.50 (surjFuncSetFuncIn) =>
% 107.13/14.50 ((
% 107.13/14.50 (surjFuncSetFuncSurj) =>
% 107.13/14.50 ((
% 107.13/14.50 (leftInvIsSurj) =>
% 107.13/14.50 ((
% 107.13/14.50 (surjCantorThm) =>
% 107.13/14.50 ((
% 107.13/14.50 (!!) @ (
% 107.13/14.50 (('#S') @ (
% 107.13/14.50 (
% 107.13/14.50 ('#B') @ (
% 107.13/14.50 =>) @
% 107.13/14.50 nonempty)) @
% 107.13/14.50 (
% 107.13/14.50 (
% 107.13/14.50 ('#B') @ (
% 107.13/14.50 ??) @
% 107.13/14.50 (
% 107.13/14.50 (
% 107.13/14.50 ('#S') @ (
% 107.13/14.50 (
% 107.13/14.50 ('#B') @ (
% 107.13/14.50 '#S') @
% 107.13/14.50 (
% 107.13/14.50 (
% 107.13/14.50 ('#B') @ (
% 107.13/14.50 (
% 107.13/14.50 ('#B') @ (
% 107.13/14.50 &))) @
% 107.13/14.50 (
% 107.13/14.50 (
% 107.13/14.50 ('#C') @ in)))))) @
% 107.13/14.50 (
% 107.13/14.50 (
% 107.13/14.50 ('#C') @ (
% 107.13/14.50 (
% 107.13/14.50 ('#B') @ (
% 107.13/14.50 '#C') @
% 107.13/14.50 (
% 107.13/14.50 (
% 107.13/14.50 ('#B') @ (
% 107.13/14.50 (
% 107.13/14.50 ('#B') @ (
% 107.13/14.50 =))) @
% 107.13/14.50 (
% 107.13/14.50 (
% 107.13/14.50 ('#C') @ binintersect)))))) @
% 107.13/14.50 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 107.13/14.50 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl896])).
% 107.13/14.50 thf(zip_derived_cl924, plain,
% 107.13/14.50 (~ (((notequalI2) =>
% 107.13/14.50 (((subsetRefl) =>
% 107.13/14.50 (((subsetTrans) =>
% 107.13/14.50 (((setadjoinSub) =>
% 107.13/14.50 (((setadjoinSub2) =>
% 107.13/14.50 (((subset2powerset) =>
% 107.13/14.50 (((setextsub) =>
% 107.13/14.50 (((subsetemptysetimpeq) =>
% 107.13/14.50 (((powersetI1) =>
% 107.13/14.50 (((powersetE1) =>
% 107.13/14.50 (((inPowerset) =>
% 107.13/14.50 (((powersetsubset) =>
% 107.13/14.50 (((sepInPowerset) =>
% 107.13/14.50 (((sepSubset) =>
% 107.13/14.50 (((binunionIL) =>
% 107.13/14.50 (((upairset2IR) =>
% 107.13/14.50 (((binunionIR) =>
% 107.13/14.50 (((binunionEcases) =>
% 107.13/14.50 (((binunionE) =>
% 107.13/14.50 (((binunionLsub) =>
% 107.13/14.50 (((binunionRsub) =>
% 107.13/14.50 (((binintersectI) =>
% 107.13/14.50 (((binintersectSubset5) =>
% 107.13/14.50 (((binintersectEL) =>
% 107.13/14.50 (((binintersectLsub) =>
% 107.13/14.50 (((binintersectSubset2) =>
% 107.13/14.50 (((binintersectSubset3) =>
% 107.13/14.50 (((binintersectER) =>
% 107.13/14.50 (((disjointsetsI1) =>
% 107.13/14.50 (((binintersectRsub) =>
% 107.13/14.50 ((
% 107.13/14.50 (binintersectSubset4) =>
% 107.13/14.50 ((
% 107.13/14.50 (binintersectSubset1) =>
% 107.13/14.50 ((
% 107.13/14.50 (bs114d) =>
% 107.13/14.50 ((
% 107.13/14.50 (setminusI) =>
% 107.13/14.50 ((
% 107.13/14.50 (setminusEL) =>
% 107.13/14.50 ((
% 107.13/14.50 (setminusER) =>
% 107.13/14.50 ((
% 107.13/14.50 (setminusSubset2) =>
% 107.13/14.50 ((
% 107.13/14.50 (setminusERneg) =>
% 107.13/14.50 ((
% 107.13/14.50 (setminusELneg) =>
% 107.13/14.50 ((
% 107.13/14.50 (setminusILneg) =>
% 107.13/14.50 ((
% 107.13/14.50 (setminusIRneg) =>
% 107.13/14.50 ((
% 107.13/14.50 (setminusLsub) =>
% 107.13/14.50 ((
% 107.13/14.50 (setminusSubset1) =>
% 107.13/14.50 ((
% 107.13/14.50 (symdiffE) =>
% 107.13/14.50 ((
% 107.13/14.50 (symdiffI1) =>
% 107.13/14.50 ((
% 107.13/14.50 (symdiffI2) =>
% 107.13/14.50 ((
% 107.13/14.50 (symdiffIneg1) =>
% 107.13/14.50 ((
% 107.13/14.50 (symdiffIneg2) =>
% 107.13/14.50 ((
% 107.13/14.50 (secondinupair) =>
% 107.13/14.50 ((
% 107.13/14.50 (setukpairIL) =>
% 107.13/14.50 ((
% 107.13/14.50 (setukpairIR) =>
% 107.13/14.50 ((
% 107.13/14.50 (kpairiskpair) =>
% 107.13/14.50 ((
% 107.13/14.50 (kpairp) =>
% 107.13/14.50 ((
% 107.13/14.50 (singletonsubset) =>
% 107.13/14.50 ((
% 107.13/14.50 (singletoninpowerset) =>
% 107.13/14.50 ((
% 107.13/14.50 (singletoninpowunion) =>
% 107.13/14.50 ((
% 107.13/14.50 (upairset2E) =>
% 107.13/14.50 ((
% 107.13/14.50 (upairsubunion) =>
% 107.13/14.50 ((
% 107.13/14.50 (upairinpowunion) =>
% 107.13/14.50 ((
% 107.13/14.50 (ubforcartprodlem1) =>
% 107.13/14.50 ((
% 107.13/14.50 (ubforcartprodlem2) =>
% 107.13/14.50 ((
% 107.13/14.50 (ubforcartprodlem3) =>
% 107.13/14.50 ((
% 107.13/14.50 (cartprodpairin) =>
% 107.13/14.50 ((
% 107.13/14.50 (cartprodmempair1) =>
% 107.13/14.50 ((
% 107.13/14.50 (cartprodmempair) =>
% 107.13/14.50 ((
% 107.13/14.50 (setunionE2) =>
% 107.13/14.50 ((
% 107.13/14.50 (setunionsingleton1) =>
% 107.13/14.50 ((
% 107.13/14.50 (setunionsingleton2) =>
% 107.13/14.50 ((
% 107.13/14.50 (setunionsingleton) =>
% 107.13/14.50 ((
% 107.13/14.50 (singletonprop) =>
% 107.13/14.50 ((
% 107.13/14.50 (ex1E1) =>
% 107.13/14.50 ((
% 107.13/14.50 (ex1I) =>
% 107.13/14.50 ((
% 107.13/14.50 (ex1I2) =>
% 107.13/14.50 ((
% 107.13/14.50 (singletonsuniq) =>
% 107.13/14.50 ((
% 107.13/14.50 (setukpairinjL1) =>
% 107.13/14.50 ((
% 107.13/14.50 (kfstsingleton) =>
% 107.13/14.50 ((
% 107.13/14.50 (theprop) =>
% 107.13/14.50 ((
% 107.13/14.50 (kfstpairEq) =>
% 107.13/14.50 ((
% 107.13/14.50 (cartprodfstin) =>
% 107.13/14.50 ((
% 107.13/14.50 (setukpairinjL2) =>
% 107.13/14.50 ((
% 107.13/14.50 (setukpairinjL) =>
% 107.13/14.50 ((
% 107.13/14.50 (setukpairinjR11) =>
% 107.13/14.50 ((
% 107.13/14.50 (setukpairinjR12) =>
% 107.13/14.50 ((
% 107.13/14.50 (setukpairinjR1) =>
% 107.13/14.50 ((
% 107.13/14.50 (upairequniteq) =>
% 107.13/14.50 ((
% 107.13/14.50 (setukpairinjR2) =>
% 107.13/14.50 ((
% 107.13/14.50 (setukpairinjR) =>
% 107.13/14.50 ((
% 107.13/14.50 (ksndsingleton) =>
% 107.13/14.50 ((
% 107.13/14.50 (ksndpairEq) =>
% 107.13/14.50 ((
% 107.13/14.50 (kpairsurjEq) =>
% 107.13/14.50 ((
% 107.13/14.50 (cartprodsndin) =>
% 107.13/14.50 ((
% 107.13/14.50 (cartprodpairmemEL) =>
% 107.13/14.50 ((
% 107.13/14.50 (cartprodpairmemER) =>
% 107.13/14.50 ((
% 107.13/14.50 (cartprodmempaircEq) =>
% 107.13/14.50 ((
% 107.13/14.50 (cartprodfstpairEq) =>
% 107.13/14.50 ((
% 107.13/14.50 (cartprodsndpairEq) =>
% 107.13/14.50 ((
% 107.13/14.50 (cartprodpairsurjEq) =>
% 107.13/14.50 ((
% 107.13/14.50 (dpsetconstrI) =>
% 107.13/14.50 ((
% 107.13/14.50 (dpsetconstrSub) =>
% 107.13/14.50 ((
% 107.13/14.50 (setOfPairsIsBReln) =>
% 107.13/14.50 ((
% 107.13/14.50 (dpsetconstrERa) =>
% 107.13/14.50 ((
% 107.13/14.50 (dpsetconstrEL1) =>
% 107.13/14.50 ((
% 107.13/14.50 (dpsetconstrEL2) =>
% 107.13/14.50 ((
% 107.13/14.50 (dpsetconstrER) =>
% 107.13/14.50 ((
% 107.13/14.50 (funcImageSingleton) =>
% 107.13/14.50 ((
% 107.13/14.50 (apProp) =>
% 107.13/14.50 ((
% 107.13/14.50 (app) =>
% 107.13/14.50 ((
% 107.13/14.50 (infuncsetfunc) =>
% 107.13/14.50 ((
% 107.13/14.50 (ap2p) =>
% 107.13/14.50 ((
% 107.13/14.50 (funcinfuncset) =>
% 107.13/14.50 ((
% 107.13/14.50 (lamProp) =>
% 107.13/14.50 ((
% 107.13/14.50 (lamp) =>
% 107.13/14.50 ((
% 107.13/14.50 (lam2p) =>
% 107.13/14.50 ((
% 107.13/14.50 (brelnall1) =>
% 107.13/14.50 ((
% 107.13/14.50 (brelnall2) =>
% 107.13/14.50 ((
% 107.13/14.50 (ex1E2) =>
% 107.13/14.50 ((
% 107.13/14.50 (funcGraphProp1) =>
% 107.13/14.50 ((
% 107.13/14.50 (funcGraphProp3) =>
% 107.13/14.50 ((
% 107.13/14.50 (funcGraphProp2) =>
% 107.13/14.50 ((
% 107.13/14.50 (funcextLem) =>
% 107.13/14.50 ((
% 107.13/14.50 (funcGraphProp4) =>
% 107.13/14.50 ((
% 107.13/14.50 (subbreln) =>
% 107.13/14.50 ((
% 107.13/14.50 (eqbreln) =>
% 107.13/14.50 ((
% 107.13/14.50 (funcext) =>
% 107.13/14.50 ((
% 107.13/14.50 (funcext2) =>
% 107.13/14.50 ((
% 107.13/14.50 (ap2apEq1) =>
% 107.13/14.50 ((
% 107.13/14.50 (ap2apEq2) =>
% 107.13/14.50 ((
% 107.13/14.50 (beta1) =>
% 107.13/14.50 ((
% 107.13/14.50 (eta1) =>
% 107.13/14.50 ((
% 107.13/14.50 (lam2lamEq) =>
% 107.13/14.50 ((
% 107.13/14.50 (beta2) =>
% 107.13/14.50 ((
% 107.13/14.50 (eta2) =>
% 107.13/14.50 ((
% 107.13/14.50 (iffalseProp1) =>
% 107.13/14.50 ((
% 107.13/14.50 (iffalseProp2) =>
% 107.13/14.50 ((
% 107.13/14.50 (iftrueProp1) =>
% 107.13/14.50 ((
% 107.13/14.50 (iftrueProp2) =>
% 107.13/14.50 ((
% 107.13/14.50 (ifSingleton) =>
% 107.13/14.50 ((
% 107.13/14.50 (ifp) =>
% 107.13/14.50 ((
% 107.13/14.50 (theeq) =>
% 107.13/14.50 ((
% 107.13/14.50 (iftrue) =>
% 107.13/14.50 ((
% 107.13/14.50 (iffalse) =>
% 107.13/14.50 ((
% 107.13/14.50 (iftrueorfalse) =>
% 107.13/14.50 ((
% 107.13/14.50 (binintersectT_lem) =>
% 107.13/14.50 ((
% 107.13/14.50 (binunionT_lem) =>
% 107.13/14.50 ((
% 107.13/14.50 (powersetT_lem) =>
% 107.13/14.50 ((
% 107.13/14.50 (setminusT_lem) =>
% 107.13/14.50 ((
% 107.13/14.50 (complementT_lem) =>
% 107.13/14.50 ((
% 107.13/14.50 (setextT) =>
% 107.13/14.50 ((
% 107.13/14.50 (subsetTI) =>
% 107.13/14.50 ((
% 107.13/14.50 (powersetTI1) =>
% 107.13/14.50 ((
% 107.13/14.50 (powersetTE1) =>
% 107.13/14.50 ((
% 107.13/14.50 (complementTI1) =>
% 107.13/14.50 ((
% 107.13/14.50 (complementTE1) =>
% 107.13/14.50 ((
% 107.13/14.50 (binintersectTELcontra) =>
% 107.13/14.50 ((
% 107.13/14.50 (binintersectTERcontra) =>
% 107.13/14.50 ((
% 107.13/14.50 (contrasubsetT) =>
% 107.13/14.50 ((
% 107.13/14.50 (contrasubsetT1) =>
% 107.13/14.50 ((
% 107.13/14.50 (contrasubsetT2) =>
% 107.13/14.50 ((
% 107.13/14.50 (contrasubsetT3) =>
% 107.13/14.50 ((
% 107.13/14.50 (doubleComplementI1) =>
% 107.13/14.50 ((
% 107.13/14.50 (doubleComplementE1) =>
% 107.13/14.50 ((
% 107.13/14.50 (doubleComplementSub1) =>
% 107.13/14.50 ((
% 107.13/14.50 (doubleComplementSub2) =>
% 107.13/14.50 ((
% 107.13/14.50 (doubleComplementEq) =>
% 107.13/14.50 ((
% 107.13/14.50 (complementTnotintersectT) =>
% 107.13/14.50 ((
% 107.13/14.50 (complementImpComplementIntersect) =>
% 107.13/14.50 ((
% 107.13/14.50 (complementSubsetComplementIntersect) =>
% 107.13/14.50 ((
% 107.13/14.50 (complementInPowersetComplementIntersect) =>
% 107.13/14.50 ((
% 107.13/14.50 (contraSubsetComplement) =>
% 107.13/14.50 ((
% 107.13/14.50 (complementTcontraSubset) =>
% 107.13/14.50 ((
% 107.13/14.50 (binunionTILcontra) =>
% 107.13/14.50 ((
% 107.13/14.50 (binunionTIRcontra) =>
% 107.13/14.50 ((
% 107.13/14.50 (inIntersectImpInUnion) =>
% 107.13/14.50 ((
% 107.13/14.50 (inIntersectImpInUnion2) =>
% 107.13/14.50 ((
% 107.13/14.50 (inIntersectImpInIntersectUnions) =>
% 107.13/14.50 ((
% 107.13/14.50 (intersectInPowersetIntersectUnions) =>
% 107.13/14.50 ((
% 107.13/14.50 (inComplementUnionImpNotIn1) =>
% 107.13/14.50 ((
% 107.13/14.50 (inComplementUnionImpInComplement1) =>
% 107.13/14.50 ((
% 107.13/14.50 (binunionTE) =>
% 107.13/14.50 ((
% 107.13/14.50 (binunionTEcontra) =>
% 107.13/14.50 ((
% 107.13/14.50 (demorgan2a1) =>
% 107.13/14.50 ((
% 107.13/14.50 (complementUnionInPowersetComplement) =>
% 107.13/14.50 ((
% 107.13/14.50 (demorgan2a2) =>
% 107.13/14.50 ((
% 107.13/14.50 (demorgan1a) =>
% 107.13/14.50 ((
% 107.13/14.50 (demorgan1b) =>
% 107.13/14.50 ((
% 107.13/14.50 (demorgan1) =>
% 107.13/14.50 ((
% 107.13/14.50 (demorgan2a) =>
% 107.13/14.50 ((
% 107.13/14.50 (demorgan2b2) =>
% 107.13/14.50 ((
% 107.13/14.50 (demorgan2b) =>
% 107.13/14.50 ((
% 107.13/14.50 (demorgan2) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz13rule0) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz13rule1) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz13rule2) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz13rule3) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz13rule4) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz1_1) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz1_2) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz1_3) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz1_4) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz1_5) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1all2) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1SetBreln1) =>
% 107.13/14.50 ((
% 107.13/14.50 (choice2fnsingleton) =>
% 107.13/14.50 ((
% 107.13/14.50 (setOfPairsIsBReln1) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1all1) =>
% 107.13/14.50 ((
% 107.13/14.50 (subbreln1) =>
% 107.13/14.50 ((
% 107.13/14.50 (eqbreln1) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1invprop) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1invI) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1invE) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1compprop) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1compI) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1compE) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1compEex) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1unionprop) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1unionIL) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1unionIR) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1unionI) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1unionE) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1unionEcases) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1unionCommutes) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz2Ex) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz2W) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz2A) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz2B) =>
% 107.13/14.50 ((
% 107.13/14.50 (image1Ex) =>
% 107.13/14.50 ((
% 107.13/14.50 (image1Ex1) =>
% 107.13/14.50 ((
% 107.13/14.50 (image1Equiv) =>
% 107.13/14.50 ((
% 107.13/14.50 (image1E) =>
% 107.13/14.50 ((
% 107.13/14.50 (image1I) =>
% 107.13/14.50 ((
% 107.13/14.50 (injFuncInInjFuncSet) =>
% 107.13/14.50 ((
% 107.13/14.50 (injFuncSetFuncIn) =>
% 107.13/14.50 ((
% 107.13/14.50 (injFuncSetFuncInj) =>
% 107.13/14.50 ((
% 107.13/14.50 (surjFuncSetFuncIn) =>
% 107.13/14.50 ((
% 107.13/14.50 (surjFuncSetFuncSurj) =>
% 107.13/14.50 ((
% 107.13/14.50 (leftInvIsSurj) =>
% 107.13/14.50 ((
% 107.13/14.50 (surjCantorThm) =>
% 107.13/14.50 ((
% 107.13/14.50 (!!) @ (
% 107.13/14.50 (('#S') @ (
% 107.13/14.50 (
% 107.13/14.50 ('#B') @ (
% 107.13/14.50 =>) @
% 107.13/14.50 nonempty)) @
% 107.13/14.50 (
% 107.13/14.50 (
% 107.13/14.50 ('#B') @ (
% 107.13/14.50 ??) @
% 107.13/14.50 (
% 107.13/14.50 (
% 107.13/14.50 ('#S') @ (
% 107.13/14.50 (
% 107.13/14.50 ('#B') @ (
% 107.13/14.50 '#S') @
% 107.13/14.50 (
% 107.13/14.50 (
% 107.13/14.50 ('#B') @ (
% 107.13/14.50 (
% 107.13/14.50 ('#B') @ (
% 107.13/14.50 &))) @
% 107.13/14.50 (
% 107.13/14.50 (
% 107.13/14.50 ('#C') @ in)))))) @
% 107.13/14.50 (
% 107.13/14.50 (
% 107.13/14.50 ('#C') @ (
% 107.13/14.50 (
% 107.13/14.50 ('#B') @ (
% 107.13/14.50 '#C') @
% 107.13/14.50 (
% 107.13/14.50 (
% 107.13/14.50 ('#B') @ (
% 107.13/14.50 (
% 107.13/14.50 ('#B') @ (
% 107.13/14.50 =))) @
% 107.13/14.50 (
% 107.13/14.50 (
% 107.13/14.50 ('#C') @ binintersect)))))) @
% 107.13/14.50 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 107.13/14.50 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl909])).
% 107.13/14.50 thf(zip_derived_cl938, plain,
% 107.13/14.50 (~ (((subsetRefl) =>
% 107.13/14.50 (((subsetTrans) =>
% 107.13/14.50 (((setadjoinSub) =>
% 107.13/14.50 (((setadjoinSub2) =>
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% 107.13/14.50 (((setextsub) =>
% 107.13/14.50 (((subsetemptysetimpeq) =>
% 107.13/14.50 (((powersetI1) =>
% 107.13/14.50 (((powersetE1) =>
% 107.13/14.50 (((inPowerset) =>
% 107.13/14.50 (((powersetsubset) =>
% 107.13/14.50 (((sepInPowerset) =>
% 107.13/14.50 (((sepSubset) =>
% 107.13/14.50 (((binunionIL) =>
% 107.13/14.50 (((upairset2IR) =>
% 107.13/14.50 (((binunionIR) =>
% 107.13/14.50 (((binunionEcases) =>
% 107.13/14.50 (((binunionE) =>
% 107.13/14.50 (((binunionLsub) =>
% 107.13/14.50 (((binunionRsub) =>
% 107.13/14.50 (((binintersectI) =>
% 107.13/14.50 (((binintersectSubset5) =>
% 107.13/14.50 (((binintersectEL) =>
% 107.13/14.50 (((binintersectLsub) =>
% 107.13/14.50 (((binintersectSubset2) =>
% 107.13/14.50 (((binintersectSubset3) =>
% 107.13/14.50 (((binintersectER) =>
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% 107.13/14.50 (((binintersectRsub) =>
% 107.13/14.50 (((binintersectSubset4) =>
% 107.13/14.50 ((
% 107.13/14.50 (binintersectSubset1) =>
% 107.13/14.50 ((
% 107.13/14.50 (bs114d) =>
% 107.13/14.50 ((
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% 107.13/14.50 ((
% 107.13/14.50 (setminusEL) =>
% 107.13/14.50 ((
% 107.13/14.50 (setminusER) =>
% 107.13/14.50 ((
% 107.13/14.50 (setminusSubset2) =>
% 107.13/14.50 ((
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% 107.13/14.50 ((
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% 107.13/14.50 ((
% 107.13/14.50 (setminusILneg) =>
% 107.13/14.50 ((
% 107.13/14.50 (setminusIRneg) =>
% 107.13/14.50 ((
% 107.13/14.50 (setminusLsub) =>
% 107.13/14.50 ((
% 107.13/14.50 (setminusSubset1) =>
% 107.13/14.50 ((
% 107.13/14.50 (symdiffE) =>
% 107.13/14.50 ((
% 107.13/14.50 (symdiffI1) =>
% 107.13/14.50 ((
% 107.13/14.50 (symdiffI2) =>
% 107.13/14.50 ((
% 107.13/14.50 (symdiffIneg1) =>
% 107.13/14.50 ((
% 107.13/14.50 (symdiffIneg2) =>
% 107.13/14.50 ((
% 107.13/14.50 (secondinupair) =>
% 107.13/14.50 ((
% 107.13/14.50 (setukpairIL) =>
% 107.13/14.50 ((
% 107.13/14.50 (setukpairIR) =>
% 107.13/14.50 ((
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% 107.13/14.50 ((
% 107.13/14.50 (kpairp) =>
% 107.13/14.50 ((
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% 107.13/14.50 ((
% 107.13/14.50 (singletoninpowerset) =>
% 107.13/14.50 ((
% 107.13/14.50 (singletoninpowunion) =>
% 107.13/14.50 ((
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% 107.13/14.50 ((
% 107.13/14.50 (upairsubunion) =>
% 107.13/14.50 ((
% 107.13/14.50 (upairinpowunion) =>
% 107.13/14.50 ((
% 107.13/14.50 (ubforcartprodlem1) =>
% 107.13/14.50 ((
% 107.13/14.50 (ubforcartprodlem2) =>
% 107.13/14.50 ((
% 107.13/14.50 (ubforcartprodlem3) =>
% 107.13/14.50 ((
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% 107.13/14.50 ((
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% 107.13/14.50 ((
% 107.13/14.50 (cartprodmempair) =>
% 107.13/14.50 ((
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% 107.13/14.50 ((
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% 107.13/14.50 ((
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% 107.13/14.50 ((
% 107.13/14.50 (ex1I2) =>
% 107.13/14.50 ((
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% 107.13/14.50 ((
% 107.13/14.50 (setukpairinjL1) =>
% 107.13/14.50 ((
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% 107.13/14.50 ((
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% 107.13/14.50 ((
% 107.13/14.50 (kfstpairEq) =>
% 107.13/14.50 ((
% 107.13/14.50 (cartprodfstin) =>
% 107.13/14.50 ((
% 107.13/14.50 (setukpairinjL2) =>
% 107.13/14.50 ((
% 107.13/14.50 (setukpairinjL) =>
% 107.13/14.50 ((
% 107.13/14.50 (setukpairinjR11) =>
% 107.13/14.50 ((
% 107.13/14.50 (setukpairinjR12) =>
% 107.13/14.50 ((
% 107.13/14.50 (setukpairinjR1) =>
% 107.13/14.50 ((
% 107.13/14.50 (upairequniteq) =>
% 107.13/14.50 ((
% 107.13/14.50 (setukpairinjR2) =>
% 107.13/14.50 ((
% 107.13/14.50 (setukpairinjR) =>
% 107.13/14.50 ((
% 107.13/14.50 (ksndsingleton) =>
% 107.13/14.50 ((
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% 107.13/14.50 ((
% 107.13/14.50 (kpairsurjEq) =>
% 107.13/14.50 ((
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% 107.13/14.50 ((
% 107.13/14.50 (cartprodpairmemEL) =>
% 107.13/14.50 ((
% 107.13/14.50 (cartprodpairmemER) =>
% 107.13/14.50 ((
% 107.13/14.50 (cartprodmempaircEq) =>
% 107.13/14.50 ((
% 107.13/14.50 (cartprodfstpairEq) =>
% 107.13/14.50 ((
% 107.13/14.50 (cartprodsndpairEq) =>
% 107.13/14.50 ((
% 107.13/14.50 (cartprodpairsurjEq) =>
% 107.13/14.50 ((
% 107.13/14.50 (dpsetconstrI) =>
% 107.13/14.50 ((
% 107.13/14.50 (dpsetconstrSub) =>
% 107.13/14.50 ((
% 107.13/14.50 (setOfPairsIsBReln) =>
% 107.13/14.50 ((
% 107.13/14.50 (dpsetconstrERa) =>
% 107.13/14.50 ((
% 107.13/14.50 (dpsetconstrEL1) =>
% 107.13/14.50 ((
% 107.13/14.50 (dpsetconstrEL2) =>
% 107.13/14.50 ((
% 107.13/14.50 (dpsetconstrER) =>
% 107.13/14.50 ((
% 107.13/14.50 (funcImageSingleton) =>
% 107.13/14.50 ((
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% 107.13/14.50 ((
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% 107.13/14.50 ((
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% 107.13/14.50 ((
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% 107.13/14.50 ((
% 107.13/14.50 (funcinfuncset) =>
% 107.13/14.50 ((
% 107.13/14.50 (lamProp) =>
% 107.13/14.50 ((
% 107.13/14.50 (lamp) =>
% 107.13/14.50 ((
% 107.13/14.50 (lam2p) =>
% 107.13/14.50 ((
% 107.13/14.50 (brelnall1) =>
% 107.13/14.50 ((
% 107.13/14.50 (brelnall2) =>
% 107.13/14.50 ((
% 107.13/14.50 (ex1E2) =>
% 107.13/14.50 ((
% 107.13/14.50 (funcGraphProp1) =>
% 107.13/14.50 ((
% 107.13/14.50 (funcGraphProp3) =>
% 107.13/14.50 ((
% 107.13/14.50 (funcGraphProp2) =>
% 107.13/14.50 ((
% 107.13/14.50 (funcextLem) =>
% 107.13/14.50 ((
% 107.13/14.50 (funcGraphProp4) =>
% 107.13/14.50 ((
% 107.13/14.50 (subbreln) =>
% 107.13/14.50 ((
% 107.13/14.50 (eqbreln) =>
% 107.13/14.50 ((
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% 107.13/14.50 ((
% 107.13/14.50 (funcext2) =>
% 107.13/14.50 ((
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% 107.13/14.50 ((
% 107.13/14.50 (ap2apEq2) =>
% 107.13/14.50 ((
% 107.13/14.50 (beta1) =>
% 107.13/14.50 ((
% 107.13/14.50 (eta1) =>
% 107.13/14.50 ((
% 107.13/14.50 (lam2lamEq) =>
% 107.13/14.50 ((
% 107.13/14.50 (beta2) =>
% 107.13/14.50 ((
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% 107.13/14.50 ((
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% 107.13/14.50 ((
% 107.13/14.50 (iffalseProp2) =>
% 107.13/14.50 ((
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% 107.13/14.50 ((
% 107.13/14.50 (iftrueProp2) =>
% 107.13/14.50 ((
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% 107.13/14.50 ((
% 107.13/14.50 (ifp) =>
% 107.13/14.50 ((
% 107.13/14.50 (theeq) =>
% 107.13/14.50 ((
% 107.13/14.50 (iftrue) =>
% 107.13/14.50 ((
% 107.13/14.50 (iffalse) =>
% 107.13/14.50 ((
% 107.13/14.50 (iftrueorfalse) =>
% 107.13/14.50 ((
% 107.13/14.50 (binintersectT_lem) =>
% 107.13/14.50 ((
% 107.13/14.50 (binunionT_lem) =>
% 107.13/14.50 ((
% 107.13/14.50 (powersetT_lem) =>
% 107.13/14.50 ((
% 107.13/14.50 (setminusT_lem) =>
% 107.13/14.50 ((
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% 107.13/14.50 ((
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% 107.13/14.50 ((
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% 107.13/14.50 ((
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% 107.13/14.50 ((
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% 107.13/14.50 ((
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% 107.13/14.50 ((
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% 107.13/14.50 ((
% 107.13/14.50 (binintersectTELcontra) =>
% 107.13/14.50 ((
% 107.13/14.50 (binintersectTERcontra) =>
% 107.13/14.50 ((
% 107.13/14.50 (contrasubsetT) =>
% 107.13/14.50 ((
% 107.13/14.50 (contrasubsetT1) =>
% 107.13/14.50 ((
% 107.13/14.50 (contrasubsetT2) =>
% 107.13/14.50 ((
% 107.13/14.50 (contrasubsetT3) =>
% 107.13/14.50 ((
% 107.13/14.50 (doubleComplementI1) =>
% 107.13/14.50 ((
% 107.13/14.50 (doubleComplementE1) =>
% 107.13/14.50 ((
% 107.13/14.50 (doubleComplementSub1) =>
% 107.13/14.50 ((
% 107.13/14.50 (doubleComplementSub2) =>
% 107.13/14.50 ((
% 107.13/14.50 (doubleComplementEq) =>
% 107.13/14.50 ((
% 107.13/14.50 (complementTnotintersectT) =>
% 107.13/14.50 ((
% 107.13/14.50 (complementImpComplementIntersect) =>
% 107.13/14.50 ((
% 107.13/14.50 (complementSubsetComplementIntersect) =>
% 107.13/14.50 ((
% 107.13/14.50 (complementInPowersetComplementIntersect) =>
% 107.13/14.50 ((
% 107.13/14.50 (contraSubsetComplement) =>
% 107.13/14.50 ((
% 107.13/14.50 (complementTcontraSubset) =>
% 107.13/14.50 ((
% 107.13/14.50 (binunionTILcontra) =>
% 107.13/14.50 ((
% 107.13/14.50 (binunionTIRcontra) =>
% 107.13/14.50 ((
% 107.13/14.50 (inIntersectImpInUnion) =>
% 107.13/14.50 ((
% 107.13/14.50 (inIntersectImpInUnion2) =>
% 107.13/14.50 ((
% 107.13/14.50 (inIntersectImpInIntersectUnions) =>
% 107.13/14.50 ((
% 107.13/14.50 (intersectInPowersetIntersectUnions) =>
% 107.13/14.50 ((
% 107.13/14.50 (inComplementUnionImpNotIn1) =>
% 107.13/14.50 ((
% 107.13/14.50 (inComplementUnionImpInComplement1) =>
% 107.13/14.50 ((
% 107.13/14.50 (binunionTE) =>
% 107.13/14.50 ((
% 107.13/14.50 (binunionTEcontra) =>
% 107.13/14.50 ((
% 107.13/14.50 (demorgan2a1) =>
% 107.13/14.50 ((
% 107.13/14.50 (complementUnionInPowersetComplement) =>
% 107.13/14.50 ((
% 107.13/14.50 (demorgan2a2) =>
% 107.13/14.50 ((
% 107.13/14.50 (demorgan1a) =>
% 107.13/14.50 ((
% 107.13/14.50 (demorgan1b) =>
% 107.13/14.50 ((
% 107.13/14.50 (demorgan1) =>
% 107.13/14.50 ((
% 107.13/14.50 (demorgan2a) =>
% 107.13/14.50 ((
% 107.13/14.50 (demorgan2b2) =>
% 107.13/14.50 ((
% 107.13/14.50 (demorgan2b) =>
% 107.13/14.50 ((
% 107.13/14.50 (demorgan2) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz13rule0) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz13rule1) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz13rule2) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz13rule3) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz13rule4) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz1_1) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz1_2) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz1_3) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz1_4) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz1_5) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1all2) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1SetBreln1) =>
% 107.13/14.50 ((
% 107.13/14.50 (choice2fnsingleton) =>
% 107.13/14.50 ((
% 107.13/14.50 (setOfPairsIsBReln1) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1all1) =>
% 107.13/14.50 ((
% 107.13/14.50 (subbreln1) =>
% 107.13/14.50 ((
% 107.13/14.50 (eqbreln1) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1invprop) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1invI) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1invE) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1compprop) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1compI) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1compE) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1compEex) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1unionprop) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1unionIL) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1unionIR) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1unionI) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1unionE) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1unionEcases) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1unionCommutes) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz2Ex) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz2W) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz2A) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz2B) =>
% 107.13/14.50 ((
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% 107.13/14.50 ((
% 107.13/14.50 (image1Ex1) =>
% 107.13/14.50 ((
% 107.13/14.50 (image1Equiv) =>
% 107.13/14.50 ((
% 107.13/14.50 (image1E) =>
% 107.13/14.50 ((
% 107.13/14.50 (image1I) =>
% 107.13/14.50 ((
% 107.13/14.50 (injFuncInInjFuncSet) =>
% 107.13/14.50 ((
% 107.13/14.50 (injFuncSetFuncIn) =>
% 107.13/14.50 ((
% 107.13/14.50 (injFuncSetFuncInj) =>
% 107.13/14.50 ((
% 107.13/14.50 (surjFuncSetFuncIn) =>
% 107.13/14.50 ((
% 107.13/14.50 (surjFuncSetFuncSurj) =>
% 107.13/14.50 ((
% 107.13/14.50 (leftInvIsSurj) =>
% 107.13/14.50 ((
% 107.13/14.50 (surjCantorThm) =>
% 107.13/14.50 ((
% 107.13/14.50 (!!) @ (
% 107.13/14.50 (('#S') @ (
% 107.13/14.50 (
% 107.13/14.50 ('#B') @ (
% 107.13/14.50 =>) @
% 107.13/14.50 nonempty)) @
% 107.13/14.50 (
% 107.13/14.50 (
% 107.13/14.50 ('#B') @ (
% 107.13/14.50 ??) @
% 107.13/14.50 (
% 107.13/14.50 (
% 107.13/14.50 ('#S') @ (
% 107.13/14.50 (
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% 107.13/14.50 (
% 107.13/14.50 (
% 107.13/14.50 ('#B') @ (
% 107.13/14.50 (
% 107.13/14.50 ('#B') @ (
% 107.13/14.50 &))) @
% 107.13/14.50 (
% 107.13/14.50 (
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% 107.13/14.50 (
% 107.13/14.50 (
% 107.13/14.50 ('#C') @ (
% 107.13/14.50 (
% 107.13/14.50 ('#B') @ (
% 107.13/14.50 '#C') @
% 107.13/14.50 (
% 107.13/14.50 (
% 107.13/14.50 ('#B') @ (
% 107.13/14.50 (
% 107.13/14.50 ('#B') @ (
% 107.13/14.50 =))) @
% 107.13/14.50 (
% 107.13/14.50 (
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% 107.13/14.50 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 107.13/14.50 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl924])).
% 107.13/14.50 thf(zip_derived_cl952, plain,
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% 107.13/14.50 (((setadjoinSub2) =>
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% 107.13/14.50 (((powersetE1) =>
% 107.13/14.50 (((inPowerset) =>
% 107.13/14.50 (((powersetsubset) =>
% 107.13/14.50 (((sepInPowerset) =>
% 107.13/14.50 (((sepSubset) =>
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% 107.13/14.50 (((upairset2IR) =>
% 107.13/14.50 (((binunionIR) =>
% 107.13/14.50 (((binunionEcases) =>
% 107.13/14.50 (((binunionE) =>
% 107.13/14.50 (((binunionLsub) =>
% 107.13/14.50 (((binunionRsub) =>
% 107.13/14.50 (((binintersectI) =>
% 107.13/14.50 (((binintersectSubset5) =>
% 107.13/14.50 (((binintersectEL) =>
% 107.13/14.50 (((binintersectLsub) =>
% 107.13/14.50 (((binintersectSubset2) =>
% 107.13/14.50 (((binintersectSubset3) =>
% 107.13/14.50 (((binintersectER) =>
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% 107.13/14.50 (((binintersectRsub) =>
% 107.13/14.50 (((binintersectSubset4) =>
% 107.13/14.50 (((binintersectSubset1) =>
% 107.13/14.50 ((
% 107.13/14.50 (bs114d) =>
% 107.13/14.50 ((
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% 107.13/14.50 ((
% 107.13/14.50 (setminusEL) =>
% 107.13/14.50 ((
% 107.13/14.50 (setminusER) =>
% 107.13/14.50 ((
% 107.13/14.50 (setminusSubset2) =>
% 107.13/14.50 ((
% 107.13/14.50 (setminusERneg) =>
% 107.13/14.50 ((
% 107.13/14.50 (setminusELneg) =>
% 107.13/14.50 ((
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% 107.13/14.50 ((
% 107.13/14.50 (setminusIRneg) =>
% 107.13/14.50 ((
% 107.13/14.50 (setminusLsub) =>
% 107.13/14.50 ((
% 107.13/14.50 (setminusSubset1) =>
% 107.13/14.50 ((
% 107.13/14.50 (symdiffE) =>
% 107.13/14.50 ((
% 107.13/14.50 (symdiffI1) =>
% 107.13/14.50 ((
% 107.13/14.50 (symdiffI2) =>
% 107.13/14.50 ((
% 107.13/14.50 (symdiffIneg1) =>
% 107.13/14.50 ((
% 107.13/14.50 (symdiffIneg2) =>
% 107.13/14.50 ((
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% 107.13/14.50 ((
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% 107.13/14.50 ((
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% 107.13/14.50 ((
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% 107.13/14.50 ((
% 107.13/14.50 (kpairp) =>
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% 107.13/14.50 ((
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% 107.13/14.50 ((
% 107.13/14.50 (singletoninpowunion) =>
% 107.13/14.50 ((
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% 107.13/14.50 ((
% 107.13/14.50 (upairsubunion) =>
% 107.13/14.50 ((
% 107.13/14.50 (upairinpowunion) =>
% 107.13/14.50 ((
% 107.13/14.50 (ubforcartprodlem1) =>
% 107.13/14.50 ((
% 107.13/14.50 (ubforcartprodlem2) =>
% 107.13/14.50 ((
% 107.13/14.50 (ubforcartprodlem3) =>
% 107.13/14.50 ((
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% 107.13/14.50 ((
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% 107.13/14.50 ((
% 107.13/14.50 (cartprodmempair) =>
% 107.13/14.50 ((
% 107.13/14.50 (setunionE2) =>
% 107.13/14.50 ((
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% 107.13/14.50 ((
% 107.13/14.50 (setunionsingleton2) =>
% 107.13/14.50 ((
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% 107.13/14.50 (ex1I2) =>
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% 107.13/14.50 ((
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% 107.13/14.50 ((
% 107.13/14.50 (theprop) =>
% 107.13/14.50 ((
% 107.13/14.50 (kfstpairEq) =>
% 107.13/14.50 ((
% 107.13/14.50 (cartprodfstin) =>
% 107.13/14.50 ((
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% 107.13/14.50 ((
% 107.13/14.50 (setukpairinjL) =>
% 107.13/14.50 ((
% 107.13/14.50 (setukpairinjR11) =>
% 107.13/14.50 ((
% 107.13/14.50 (setukpairinjR12) =>
% 107.13/14.50 ((
% 107.13/14.50 (setukpairinjR1) =>
% 107.13/14.50 ((
% 107.13/14.50 (upairequniteq) =>
% 107.13/14.50 ((
% 107.13/14.50 (setukpairinjR2) =>
% 107.13/14.50 ((
% 107.13/14.50 (setukpairinjR) =>
% 107.13/14.50 ((
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% 107.13/14.50 ((
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% 107.13/14.50 ((
% 107.13/14.50 (kpairsurjEq) =>
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% 107.13/14.50 ((
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% 107.13/14.50 ((
% 107.13/14.50 (cartprodpairmemER) =>
% 107.13/14.50 ((
% 107.13/14.50 (cartprodmempaircEq) =>
% 107.13/14.50 ((
% 107.13/14.50 (cartprodfstpairEq) =>
% 107.13/14.50 ((
% 107.13/14.50 (cartprodsndpairEq) =>
% 107.13/14.50 ((
% 107.13/14.50 (cartprodpairsurjEq) =>
% 107.13/14.50 ((
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% 107.13/14.50 ((
% 107.13/14.50 (dpsetconstrSub) =>
% 107.13/14.50 ((
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% 107.13/14.50 ((
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% 107.13/14.50 ((
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% 107.13/14.50 ((
% 107.13/14.50 (dpsetconstrEL2) =>
% 107.13/14.50 ((
% 107.13/14.50 (dpsetconstrER) =>
% 107.13/14.50 ((
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% 107.13/14.50 ((
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% 107.13/14.50 ((
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% 107.13/14.50 ((
% 107.13/14.50 (funcinfuncset) =>
% 107.13/14.50 ((
% 107.13/14.50 (lamProp) =>
% 107.13/14.50 ((
% 107.13/14.50 (lamp) =>
% 107.13/14.50 ((
% 107.13/14.50 (lam2p) =>
% 107.13/14.50 ((
% 107.13/14.50 (brelnall1) =>
% 107.13/14.50 ((
% 107.13/14.50 (brelnall2) =>
% 107.13/14.50 ((
% 107.13/14.50 (ex1E2) =>
% 107.13/14.50 ((
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% 107.13/14.50 ((
% 107.13/14.50 (funcGraphProp3) =>
% 107.13/14.50 ((
% 107.13/14.50 (funcGraphProp2) =>
% 107.13/14.50 ((
% 107.13/14.50 (funcextLem) =>
% 107.13/14.50 ((
% 107.13/14.50 (funcGraphProp4) =>
% 107.13/14.50 ((
% 107.13/14.50 (subbreln) =>
% 107.13/14.50 ((
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% 107.13/14.50 ((
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% 107.13/14.50 ((
% 107.13/14.50 (funcext2) =>
% 107.13/14.50 ((
% 107.13/14.50 (ap2apEq1) =>
% 107.13/14.50 ((
% 107.13/14.50 (ap2apEq2) =>
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% 107.13/14.50 ((
% 107.13/14.50 (eta1) =>
% 107.13/14.50 ((
% 107.13/14.50 (lam2lamEq) =>
% 107.13/14.50 ((
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% 107.13/14.50 ((
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% 107.13/14.50 ((
% 107.13/14.50 (theeq) =>
% 107.13/14.50 ((
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% 107.13/14.50 ((
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% 107.13/14.50 ((
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% 107.13/14.50 ((
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% 107.13/14.50 ((
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% 107.13/14.50 ((
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% 107.13/14.50 ((
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% 107.13/14.50 ((
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% 107.13/14.50 ((
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% 107.13/14.50 (contrasubsetT3) =>
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% 107.13/14.50 (demorgan1b) =>
% 107.13/14.50 ((
% 107.13/14.50 (demorgan1) =>
% 107.13/14.50 ((
% 107.13/14.50 (demorgan2a) =>
% 107.13/14.50 ((
% 107.13/14.50 (demorgan2b2) =>
% 107.13/14.50 ((
% 107.13/14.50 (demorgan2b) =>
% 107.13/14.50 ((
% 107.13/14.50 (demorgan2) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz13rule0) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz13rule1) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz13rule2) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz13rule3) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz13rule4) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz1_1) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz1_2) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz1_3) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz1_4) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz1_5) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1all2) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1SetBreln1) =>
% 107.13/14.50 ((
% 107.13/14.50 (choice2fnsingleton) =>
% 107.13/14.50 ((
% 107.13/14.50 (setOfPairsIsBReln1) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1all1) =>
% 107.13/14.50 ((
% 107.13/14.50 (subbreln1) =>
% 107.13/14.50 ((
% 107.13/14.50 (eqbreln1) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1invprop) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1invI) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1invE) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1compprop) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1compI) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1compE) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1compEex) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1unionprop) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1unionIL) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1unionIR) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1unionI) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1unionE) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1unionEcases) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1unionCommutes) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz2Ex) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz2W) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz2A) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz2B) =>
% 107.13/14.50 ((
% 107.13/14.50 (image1Ex) =>
% 107.13/14.50 ((
% 107.13/14.50 (image1Ex1) =>
% 107.13/14.50 ((
% 107.13/14.50 (image1Equiv) =>
% 107.13/14.50 ((
% 107.13/14.50 (image1E) =>
% 107.13/14.50 ((
% 107.13/14.50 (image1I) =>
% 107.13/14.50 ((
% 107.13/14.50 (injFuncInInjFuncSet) =>
% 107.13/14.50 ((
% 107.13/14.50 (injFuncSetFuncIn) =>
% 107.13/14.50 ((
% 107.13/14.50 (injFuncSetFuncInj) =>
% 107.13/14.50 ((
% 107.13/14.50 (surjFuncSetFuncIn) =>
% 107.13/14.50 ((
% 107.13/14.50 (surjFuncSetFuncSurj) =>
% 107.13/14.50 ((
% 107.13/14.50 (leftInvIsSurj) =>
% 107.13/14.50 ((
% 107.13/14.50 (surjCantorThm) =>
% 107.13/14.50 ((
% 107.13/14.50 (!!) @ (
% 107.13/14.50 (('#S') @ (
% 107.13/14.50 (
% 107.13/14.50 ('#B') @ (
% 107.13/14.50 =>) @
% 107.13/14.50 nonempty)) @
% 107.13/14.50 (
% 107.13/14.50 (
% 107.13/14.50 ('#B') @ (
% 107.13/14.50 ??) @
% 107.13/14.50 (
% 107.13/14.50 (
% 107.13/14.50 ('#S') @ (
% 107.13/14.50 (
% 107.13/14.50 ('#B') @ (
% 107.13/14.50 '#S') @
% 107.13/14.50 (
% 107.13/14.50 (
% 107.13/14.50 ('#B') @ (
% 107.13/14.50 (
% 107.13/14.50 ('#B') @ (
% 107.13/14.50 &))) @
% 107.13/14.50 (
% 107.13/14.50 (
% 107.13/14.50 ('#C') @ in)))))) @
% 107.13/14.50 (
% 107.13/14.50 (
% 107.13/14.50 ('#C') @ (
% 107.13/14.50 (
% 107.13/14.50 ('#B') @ (
% 107.13/14.50 '#C') @
% 107.13/14.50 (
% 107.13/14.50 (
% 107.13/14.50 ('#B') @ (
% 107.13/14.50 (
% 107.13/14.50 ('#B') @ (
% 107.13/14.50 =))) @
% 107.13/14.50 (
% 107.13/14.50 (
% 107.13/14.50 ('#C') @ binintersect)))))) @
% 107.13/14.50 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 107.13/14.50 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl938])).
% 107.13/14.50 thf(zip_derived_cl967, plain,
% 107.13/14.50 (~ (((setadjoinSub) =>
% 107.13/14.50 (((setadjoinSub2) =>
% 107.13/14.50 (((subset2powerset) =>
% 107.13/14.50 (((setextsub) =>
% 107.13/14.50 (((subsetemptysetimpeq) =>
% 107.13/14.50 (((powersetI1) =>
% 107.13/14.50 (((powersetE1) =>
% 107.13/14.50 (((inPowerset) =>
% 107.13/14.50 (((powersetsubset) =>
% 107.13/14.50 (((sepInPowerset) =>
% 107.13/14.50 (((sepSubset) =>
% 107.13/14.50 (((binunionIL) =>
% 107.13/14.50 (((upairset2IR) =>
% 107.13/14.50 (((binunionIR) =>
% 107.13/14.50 (((binunionEcases) =>
% 107.13/14.50 (((binunionE) =>
% 107.13/14.50 (((binunionLsub) =>
% 107.13/14.50 (((binunionRsub) =>
% 107.13/14.50 (((binintersectI) =>
% 107.13/14.50 (((binintersectSubset5) =>
% 107.13/14.50 (((binintersectEL) =>
% 107.13/14.50 (((binintersectLsub) =>
% 107.13/14.50 (((binintersectSubset2) =>
% 107.13/14.50 (((binintersectSubset3) =>
% 107.13/14.50 (((binintersectER) =>
% 107.13/14.50 (((disjointsetsI1) =>
% 107.13/14.50 (((binintersectRsub) =>
% 107.13/14.50 (((binintersectSubset4) =>
% 107.13/14.50 (((binintersectSubset1) =>
% 107.13/14.50 (((bs114d) =>
% 107.13/14.50 ((
% 107.13/14.50 (setminusI) =>
% 107.13/14.50 ((
% 107.13/14.50 (setminusEL) =>
% 107.13/14.50 ((
% 107.13/14.50 (setminusER) =>
% 107.13/14.50 ((
% 107.13/14.50 (setminusSubset2) =>
% 107.13/14.50 ((
% 107.13/14.50 (setminusERneg) =>
% 107.13/14.50 ((
% 107.13/14.50 (setminusELneg) =>
% 107.13/14.50 ((
% 107.13/14.50 (setminusILneg) =>
% 107.13/14.50 ((
% 107.13/14.50 (setminusIRneg) =>
% 107.13/14.50 ((
% 107.13/14.50 (setminusLsub) =>
% 107.13/14.50 ((
% 107.13/14.50 (setminusSubset1) =>
% 107.13/14.50 ((
% 107.13/14.50 (symdiffE) =>
% 107.13/14.50 ((
% 107.13/14.50 (symdiffI1) =>
% 107.13/14.50 ((
% 107.13/14.50 (symdiffI2) =>
% 107.13/14.50 ((
% 107.13/14.50 (symdiffIneg1) =>
% 107.13/14.50 ((
% 107.13/14.50 (symdiffIneg2) =>
% 107.13/14.50 ((
% 107.13/14.50 (secondinupair) =>
% 107.13/14.50 ((
% 107.13/14.50 (setukpairIL) =>
% 107.13/14.50 ((
% 107.13/14.50 (setukpairIR) =>
% 107.13/14.50 ((
% 107.13/14.50 (kpairiskpair) =>
% 107.13/14.50 ((
% 107.13/14.50 (kpairp) =>
% 107.13/14.50 ((
% 107.13/14.50 (singletonsubset) =>
% 107.13/14.50 ((
% 107.13/14.50 (singletoninpowerset) =>
% 107.13/14.50 ((
% 107.13/14.50 (singletoninpowunion) =>
% 107.13/14.50 ((
% 107.13/14.50 (upairset2E) =>
% 107.13/14.50 ((
% 107.13/14.50 (upairsubunion) =>
% 107.13/14.50 ((
% 107.13/14.50 (upairinpowunion) =>
% 107.13/14.50 ((
% 107.13/14.50 (ubforcartprodlem1) =>
% 107.13/14.50 ((
% 107.13/14.50 (ubforcartprodlem2) =>
% 107.13/14.50 ((
% 107.13/14.50 (ubforcartprodlem3) =>
% 107.13/14.50 ((
% 107.13/14.50 (cartprodpairin) =>
% 107.13/14.50 ((
% 107.13/14.50 (cartprodmempair1) =>
% 107.13/14.50 ((
% 107.13/14.50 (cartprodmempair) =>
% 107.13/14.50 ((
% 107.13/14.50 (setunionE2) =>
% 107.13/14.50 ((
% 107.13/14.50 (setunionsingleton1) =>
% 107.13/14.50 ((
% 107.13/14.50 (setunionsingleton2) =>
% 107.13/14.50 ((
% 107.13/14.50 (setunionsingleton) =>
% 107.13/14.50 ((
% 107.13/14.50 (singletonprop) =>
% 107.13/14.50 ((
% 107.13/14.50 (ex1E1) =>
% 107.13/14.50 ((
% 107.13/14.50 (ex1I) =>
% 107.13/14.50 ((
% 107.13/14.50 (ex1I2) =>
% 107.13/14.50 ((
% 107.13/14.50 (singletonsuniq) =>
% 107.13/14.50 ((
% 107.13/14.50 (setukpairinjL1) =>
% 107.13/14.50 ((
% 107.13/14.50 (kfstsingleton) =>
% 107.13/14.50 ((
% 107.13/14.50 (theprop) =>
% 107.13/14.50 ((
% 107.13/14.50 (kfstpairEq) =>
% 107.13/14.50 ((
% 107.13/14.50 (cartprodfstin) =>
% 107.13/14.50 ((
% 107.13/14.50 (setukpairinjL2) =>
% 107.13/14.50 ((
% 107.13/14.50 (setukpairinjL) =>
% 107.13/14.50 ((
% 107.13/14.50 (setukpairinjR11) =>
% 107.13/14.50 ((
% 107.13/14.50 (setukpairinjR12) =>
% 107.13/14.50 ((
% 107.13/14.50 (setukpairinjR1) =>
% 107.13/14.50 ((
% 107.13/14.50 (upairequniteq) =>
% 107.13/14.50 ((
% 107.13/14.50 (setukpairinjR2) =>
% 107.13/14.50 ((
% 107.13/14.50 (setukpairinjR) =>
% 107.13/14.50 ((
% 107.13/14.50 (ksndsingleton) =>
% 107.13/14.50 ((
% 107.13/14.50 (ksndpairEq) =>
% 107.13/14.50 ((
% 107.13/14.50 (kpairsurjEq) =>
% 107.13/14.50 ((
% 107.13/14.50 (cartprodsndin) =>
% 107.13/14.50 ((
% 107.13/14.50 (cartprodpairmemEL) =>
% 107.13/14.50 ((
% 107.13/14.50 (cartprodpairmemER) =>
% 107.13/14.50 ((
% 107.13/14.50 (cartprodmempaircEq) =>
% 107.13/14.50 ((
% 107.13/14.50 (cartprodfstpairEq) =>
% 107.13/14.50 ((
% 107.13/14.50 (cartprodsndpairEq) =>
% 107.13/14.50 ((
% 107.13/14.50 (cartprodpairsurjEq) =>
% 107.13/14.50 ((
% 107.13/14.50 (dpsetconstrI) =>
% 107.13/14.50 ((
% 107.13/14.50 (dpsetconstrSub) =>
% 107.13/14.50 ((
% 107.13/14.50 (setOfPairsIsBReln) =>
% 107.13/14.50 ((
% 107.13/14.50 (dpsetconstrERa) =>
% 107.13/14.50 ((
% 107.13/14.50 (dpsetconstrEL1) =>
% 107.13/14.50 ((
% 107.13/14.50 (dpsetconstrEL2) =>
% 107.13/14.50 ((
% 107.13/14.50 (dpsetconstrER) =>
% 107.13/14.50 ((
% 107.13/14.50 (funcImageSingleton) =>
% 107.13/14.50 ((
% 107.13/14.50 (apProp) =>
% 107.13/14.50 ((
% 107.13/14.50 (app) =>
% 107.13/14.50 ((
% 107.13/14.50 (infuncsetfunc) =>
% 107.13/14.50 ((
% 107.13/14.50 (ap2p) =>
% 107.13/14.50 ((
% 107.13/14.50 (funcinfuncset) =>
% 107.13/14.50 ((
% 107.13/14.50 (lamProp) =>
% 107.13/14.50 ((
% 107.13/14.50 (lamp) =>
% 107.13/14.50 ((
% 107.13/14.50 (lam2p) =>
% 107.13/14.50 ((
% 107.13/14.50 (brelnall1) =>
% 107.13/14.50 ((
% 107.13/14.50 (brelnall2) =>
% 107.13/14.50 ((
% 107.13/14.50 (ex1E2) =>
% 107.13/14.50 ((
% 107.13/14.50 (funcGraphProp1) =>
% 107.13/14.50 ((
% 107.13/14.50 (funcGraphProp3) =>
% 107.13/14.50 ((
% 107.13/14.50 (funcGraphProp2) =>
% 107.13/14.50 ((
% 107.13/14.50 (funcextLem) =>
% 107.13/14.50 ((
% 107.13/14.50 (funcGraphProp4) =>
% 107.13/14.50 ((
% 107.13/14.50 (subbreln) =>
% 107.13/14.50 ((
% 107.13/14.50 (eqbreln) =>
% 107.13/14.50 ((
% 107.13/14.50 (funcext) =>
% 107.13/14.50 ((
% 107.13/14.50 (funcext2) =>
% 107.13/14.50 ((
% 107.13/14.50 (ap2apEq1) =>
% 107.13/14.50 ((
% 107.13/14.50 (ap2apEq2) =>
% 107.13/14.50 ((
% 107.13/14.50 (beta1) =>
% 107.13/14.50 ((
% 107.13/14.50 (eta1) =>
% 107.13/14.50 ((
% 107.13/14.50 (lam2lamEq) =>
% 107.13/14.50 ((
% 107.13/14.50 (beta2) =>
% 107.13/14.50 ((
% 107.13/14.50 (eta2) =>
% 107.13/14.50 ((
% 107.13/14.50 (iffalseProp1) =>
% 107.13/14.50 ((
% 107.13/14.50 (iffalseProp2) =>
% 107.13/14.50 ((
% 107.13/14.50 (iftrueProp1) =>
% 107.13/14.50 ((
% 107.13/14.50 (iftrueProp2) =>
% 107.13/14.50 ((
% 107.13/14.50 (ifSingleton) =>
% 107.13/14.50 ((
% 107.13/14.50 (ifp) =>
% 107.13/14.50 ((
% 107.13/14.50 (theeq) =>
% 107.13/14.50 ((
% 107.13/14.50 (iftrue) =>
% 107.13/14.50 ((
% 107.13/14.50 (iffalse) =>
% 107.13/14.50 ((
% 107.13/14.50 (iftrueorfalse) =>
% 107.13/14.50 ((
% 107.13/14.50 (binintersectT_lem) =>
% 107.13/14.50 ((
% 107.13/14.50 (binunionT_lem) =>
% 107.13/14.50 ((
% 107.13/14.50 (powersetT_lem) =>
% 107.13/14.50 ((
% 107.13/14.50 (setminusT_lem) =>
% 107.13/14.50 ((
% 107.13/14.50 (complementT_lem) =>
% 107.13/14.50 ((
% 107.13/14.50 (setextT) =>
% 107.13/14.50 ((
% 107.13/14.50 (subsetTI) =>
% 107.13/14.50 ((
% 107.13/14.50 (powersetTI1) =>
% 107.13/14.50 ((
% 107.13/14.50 (powersetTE1) =>
% 107.13/14.50 ((
% 107.13/14.50 (complementTI1) =>
% 107.13/14.50 ((
% 107.13/14.50 (complementTE1) =>
% 107.13/14.50 ((
% 107.13/14.50 (binintersectTELcontra) =>
% 107.13/14.50 ((
% 107.13/14.50 (binintersectTERcontra) =>
% 107.13/14.50 ((
% 107.13/14.50 (contrasubsetT) =>
% 107.13/14.50 ((
% 107.13/14.50 (contrasubsetT1) =>
% 107.13/14.50 ((
% 107.13/14.50 (contrasubsetT2) =>
% 107.13/14.50 ((
% 107.13/14.50 (contrasubsetT3) =>
% 107.13/14.50 ((
% 107.13/14.50 (doubleComplementI1) =>
% 107.13/14.50 ((
% 107.13/14.50 (doubleComplementE1) =>
% 107.13/14.50 ((
% 107.13/14.50 (doubleComplementSub1) =>
% 107.13/14.50 ((
% 107.13/14.50 (doubleComplementSub2) =>
% 107.13/14.50 ((
% 107.13/14.50 (doubleComplementEq) =>
% 107.13/14.50 ((
% 107.13/14.50 (complementTnotintersectT) =>
% 107.13/14.50 ((
% 107.13/14.50 (complementImpComplementIntersect) =>
% 107.13/14.50 ((
% 107.13/14.50 (complementSubsetComplementIntersect) =>
% 107.13/14.50 ((
% 107.13/14.50 (complementInPowersetComplementIntersect) =>
% 107.13/14.50 ((
% 107.13/14.50 (contraSubsetComplement) =>
% 107.13/14.50 ((
% 107.13/14.50 (complementTcontraSubset) =>
% 107.13/14.50 ((
% 107.13/14.50 (binunionTILcontra) =>
% 107.13/14.50 ((
% 107.13/14.50 (binunionTIRcontra) =>
% 107.13/14.50 ((
% 107.13/14.50 (inIntersectImpInUnion) =>
% 107.13/14.50 ((
% 107.13/14.50 (inIntersectImpInUnion2) =>
% 107.13/14.50 ((
% 107.13/14.50 (inIntersectImpInIntersectUnions) =>
% 107.13/14.50 ((
% 107.13/14.50 (intersectInPowersetIntersectUnions) =>
% 107.13/14.50 ((
% 107.13/14.50 (inComplementUnionImpNotIn1) =>
% 107.13/14.50 ((
% 107.13/14.50 (inComplementUnionImpInComplement1) =>
% 107.13/14.50 ((
% 107.13/14.50 (binunionTE) =>
% 107.13/14.50 ((
% 107.13/14.50 (binunionTEcontra) =>
% 107.13/14.50 ((
% 107.13/14.50 (demorgan2a1) =>
% 107.13/14.50 ((
% 107.13/14.50 (complementUnionInPowersetComplement) =>
% 107.13/14.50 ((
% 107.13/14.50 (demorgan2a2) =>
% 107.13/14.50 ((
% 107.13/14.50 (demorgan1a) =>
% 107.13/14.50 ((
% 107.13/14.50 (demorgan1b) =>
% 107.13/14.50 ((
% 107.13/14.50 (demorgan1) =>
% 107.13/14.50 ((
% 107.13/14.50 (demorgan2a) =>
% 107.13/14.50 ((
% 107.13/14.50 (demorgan2b2) =>
% 107.13/14.50 ((
% 107.13/14.50 (demorgan2b) =>
% 107.13/14.50 ((
% 107.13/14.50 (demorgan2) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz13rule0) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz13rule1) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz13rule2) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz13rule3) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz13rule4) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz1_1) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz1_2) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz1_3) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz1_4) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz1_5) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1all2) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1SetBreln1) =>
% 107.13/14.50 ((
% 107.13/14.50 (choice2fnsingleton) =>
% 107.13/14.50 ((
% 107.13/14.50 (setOfPairsIsBReln1) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1all1) =>
% 107.13/14.50 ((
% 107.13/14.50 (subbreln1) =>
% 107.13/14.50 ((
% 107.13/14.50 (eqbreln1) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1invprop) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1invI) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1invE) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1compprop) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1compI) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1compE) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1compEex) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1unionprop) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1unionIL) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1unionIR) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1unionI) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1unionE) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1unionEcases) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1unionCommutes) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz2Ex) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz2W) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz2A) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz2B) =>
% 107.13/14.50 ((
% 107.13/14.50 (image1Ex) =>
% 107.13/14.50 ((
% 107.13/14.50 (image1Ex1) =>
% 107.13/14.50 ((
% 107.13/14.50 (image1Equiv) =>
% 107.13/14.50 ((
% 107.13/14.50 (image1E) =>
% 107.13/14.50 ((
% 107.13/14.50 (image1I) =>
% 107.13/14.50 ((
% 107.13/14.50 (injFuncInInjFuncSet) =>
% 107.13/14.50 ((
% 107.13/14.50 (injFuncSetFuncIn) =>
% 107.13/14.50 ((
% 107.13/14.50 (injFuncSetFuncInj) =>
% 107.13/14.50 ((
% 107.13/14.50 (surjFuncSetFuncIn) =>
% 107.13/14.50 ((
% 107.13/14.50 (surjFuncSetFuncSurj) =>
% 107.13/14.50 ((
% 107.13/14.50 (leftInvIsSurj) =>
% 107.13/14.50 ((
% 107.13/14.50 (surjCantorThm) =>
% 107.13/14.50 ((
% 107.13/14.50 (!!) @ (
% 107.13/14.50 (('#S') @ (
% 107.13/14.50 (
% 107.13/14.50 ('#B') @ (
% 107.13/14.50 =>) @
% 107.13/14.50 nonempty)) @
% 107.13/14.50 (
% 107.13/14.50 (
% 107.13/14.50 ('#B') @ (
% 107.13/14.50 ??) @
% 107.13/14.50 (
% 107.13/14.50 (
% 107.13/14.50 ('#S') @ (
% 107.13/14.50 (
% 107.13/14.50 ('#B') @ (
% 107.13/14.50 '#S') @
% 107.13/14.50 (
% 107.13/14.50 (
% 107.13/14.50 ('#B') @ (
% 107.13/14.50 (
% 107.13/14.50 ('#B') @ (
% 107.13/14.50 &))) @
% 107.13/14.50 (
% 107.13/14.50 (
% 107.13/14.50 ('#C') @ in)))))) @
% 107.13/14.50 (
% 107.13/14.50 (
% 107.13/14.50 ('#C') @ (
% 107.13/14.50 (
% 107.13/14.50 ('#B') @ (
% 107.13/14.50 '#C') @
% 107.13/14.50 (
% 107.13/14.50 (
% 107.13/14.50 ('#B') @ (
% 107.13/14.50 (
% 107.13/14.50 ('#B') @ (
% 107.13/14.50 =))) @
% 107.13/14.50 (
% 107.13/14.50 (
% 107.13/14.50 ('#C') @ binintersect)))))) @
% 107.13/14.50 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 107.13/14.50 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl952])).
% 107.13/14.50 thf(zip_derived_cl984, plain,
% 107.13/14.50 (~ (((setadjoinSub2) =>
% 107.13/14.50 (((subset2powerset) =>
% 107.13/14.50 (((setextsub) =>
% 107.13/14.50 (((subsetemptysetimpeq) =>
% 107.13/14.50 (((powersetI1) =>
% 107.13/14.50 (((powersetE1) =>
% 107.13/14.50 (((inPowerset) =>
% 107.13/14.50 (((powersetsubset) =>
% 107.13/14.50 (((sepInPowerset) =>
% 107.13/14.50 (((sepSubset) =>
% 107.13/14.50 (((binunionIL) =>
% 107.13/14.50 (((upairset2IR) =>
% 107.13/14.50 (((binunionIR) =>
% 107.13/14.50 (((binunionEcases) =>
% 107.13/14.50 (((binunionE) =>
% 107.13/14.50 (((binunionLsub) =>
% 107.13/14.50 (((binunionRsub) =>
% 107.13/14.50 (((binintersectI) =>
% 107.13/14.50 (((binintersectSubset5) =>
% 107.13/14.50 (((binintersectEL) =>
% 107.13/14.50 (((binintersectLsub) =>
% 107.13/14.50 (((binintersectSubset2) =>
% 107.13/14.50 (((binintersectSubset3) =>
% 107.13/14.50 (((binintersectER) =>
% 107.13/14.50 (((disjointsetsI1) =>
% 107.13/14.50 (((binintersectRsub) =>
% 107.13/14.50 (((binintersectSubset4) =>
% 107.13/14.50 (((binintersectSubset1) =>
% 107.13/14.50 (((bs114d) =>
% 107.13/14.50 (((setminusI) =>
% 107.13/14.50 ((
% 107.13/14.50 (setminusEL) =>
% 107.13/14.50 ((
% 107.13/14.50 (setminusER) =>
% 107.13/14.50 ((
% 107.13/14.50 (setminusSubset2) =>
% 107.13/14.50 ((
% 107.13/14.50 (setminusERneg) =>
% 107.13/14.50 ((
% 107.13/14.50 (setminusELneg) =>
% 107.13/14.50 ((
% 107.13/14.50 (setminusILneg) =>
% 107.13/14.50 ((
% 107.13/14.50 (setminusIRneg) =>
% 107.13/14.50 ((
% 107.13/14.50 (setminusLsub) =>
% 107.13/14.50 ((
% 107.13/14.50 (setminusSubset1) =>
% 107.13/14.50 ((
% 107.13/14.50 (symdiffE) =>
% 107.13/14.50 ((
% 107.13/14.50 (symdiffI1) =>
% 107.13/14.50 ((
% 107.13/14.50 (symdiffI2) =>
% 107.13/14.50 ((
% 107.13/14.50 (symdiffIneg1) =>
% 107.13/14.50 ((
% 107.13/14.50 (symdiffIneg2) =>
% 107.13/14.50 ((
% 107.13/14.50 (secondinupair) =>
% 107.13/14.50 ((
% 107.13/14.50 (setukpairIL) =>
% 107.13/14.50 ((
% 107.13/14.50 (setukpairIR) =>
% 107.13/14.50 ((
% 107.13/14.50 (kpairiskpair) =>
% 107.13/14.50 ((
% 107.13/14.50 (kpairp) =>
% 107.13/14.50 ((
% 107.13/14.50 (singletonsubset) =>
% 107.13/14.50 ((
% 107.13/14.50 (singletoninpowerset) =>
% 107.13/14.50 ((
% 107.13/14.50 (singletoninpowunion) =>
% 107.13/14.50 ((
% 107.13/14.50 (upairset2E) =>
% 107.13/14.50 ((
% 107.13/14.50 (upairsubunion) =>
% 107.13/14.50 ((
% 107.13/14.50 (upairinpowunion) =>
% 107.13/14.50 ((
% 107.13/14.50 (ubforcartprodlem1) =>
% 107.13/14.50 ((
% 107.13/14.50 (ubforcartprodlem2) =>
% 107.13/14.50 ((
% 107.13/14.50 (ubforcartprodlem3) =>
% 107.13/14.50 ((
% 107.13/14.50 (cartprodpairin) =>
% 107.13/14.50 ((
% 107.13/14.50 (cartprodmempair1) =>
% 107.13/14.50 ((
% 107.13/14.50 (cartprodmempair) =>
% 107.13/14.50 ((
% 107.13/14.50 (setunionE2) =>
% 107.13/14.50 ((
% 107.13/14.50 (setunionsingleton1) =>
% 107.13/14.50 ((
% 107.13/14.50 (setunionsingleton2) =>
% 107.13/14.50 ((
% 107.13/14.50 (setunionsingleton) =>
% 107.13/14.50 ((
% 107.13/14.50 (singletonprop) =>
% 107.13/14.50 ((
% 107.13/14.50 (ex1E1) =>
% 107.13/14.50 ((
% 107.13/14.50 (ex1I) =>
% 107.13/14.50 ((
% 107.13/14.50 (ex1I2) =>
% 107.13/14.50 ((
% 107.13/14.50 (singletonsuniq) =>
% 107.13/14.50 ((
% 107.13/14.50 (setukpairinjL1) =>
% 107.13/14.50 ((
% 107.13/14.50 (kfstsingleton) =>
% 107.13/14.50 ((
% 107.13/14.50 (theprop) =>
% 107.13/14.50 ((
% 107.13/14.50 (kfstpairEq) =>
% 107.13/14.50 ((
% 107.13/14.50 (cartprodfstin) =>
% 107.13/14.50 ((
% 107.13/14.50 (setukpairinjL2) =>
% 107.13/14.50 ((
% 107.13/14.50 (setukpairinjL) =>
% 107.13/14.50 ((
% 107.13/14.50 (setukpairinjR11) =>
% 107.13/14.50 ((
% 107.13/14.50 (setukpairinjR12) =>
% 107.13/14.50 ((
% 107.13/14.50 (setukpairinjR1) =>
% 107.13/14.50 ((
% 107.13/14.50 (upairequniteq) =>
% 107.13/14.50 ((
% 107.13/14.50 (setukpairinjR2) =>
% 107.13/14.50 ((
% 107.13/14.50 (setukpairinjR) =>
% 107.13/14.50 ((
% 107.13/14.50 (ksndsingleton) =>
% 107.13/14.50 ((
% 107.13/14.50 (ksndpairEq) =>
% 107.13/14.50 ((
% 107.13/14.50 (kpairsurjEq) =>
% 107.13/14.50 ((
% 107.13/14.50 (cartprodsndin) =>
% 107.13/14.50 ((
% 107.13/14.50 (cartprodpairmemEL) =>
% 107.13/14.50 ((
% 107.13/14.50 (cartprodpairmemER) =>
% 107.13/14.50 ((
% 107.13/14.50 (cartprodmempaircEq) =>
% 107.13/14.50 ((
% 107.13/14.50 (cartprodfstpairEq) =>
% 107.13/14.50 ((
% 107.13/14.50 (cartprodsndpairEq) =>
% 107.13/14.50 ((
% 107.13/14.50 (cartprodpairsurjEq) =>
% 107.13/14.50 ((
% 107.13/14.50 (dpsetconstrI) =>
% 107.13/14.50 ((
% 107.13/14.50 (dpsetconstrSub) =>
% 107.13/14.50 ((
% 107.13/14.50 (setOfPairsIsBReln) =>
% 107.13/14.50 ((
% 107.13/14.50 (dpsetconstrERa) =>
% 107.13/14.50 ((
% 107.13/14.50 (dpsetconstrEL1) =>
% 107.13/14.50 ((
% 107.13/14.50 (dpsetconstrEL2) =>
% 107.13/14.50 ((
% 107.13/14.50 (dpsetconstrER) =>
% 107.13/14.50 ((
% 107.13/14.50 (funcImageSingleton) =>
% 107.13/14.50 ((
% 107.13/14.50 (apProp) =>
% 107.13/14.50 ((
% 107.13/14.50 (app) =>
% 107.13/14.50 ((
% 107.13/14.50 (infuncsetfunc) =>
% 107.13/14.50 ((
% 107.13/14.50 (ap2p) =>
% 107.13/14.50 ((
% 107.13/14.50 (funcinfuncset) =>
% 107.13/14.50 ((
% 107.13/14.50 (lamProp) =>
% 107.13/14.50 ((
% 107.13/14.50 (lamp) =>
% 107.13/14.50 ((
% 107.13/14.50 (lam2p) =>
% 107.13/14.50 ((
% 107.13/14.50 (brelnall1) =>
% 107.13/14.50 ((
% 107.13/14.50 (brelnall2) =>
% 107.13/14.50 ((
% 107.13/14.50 (ex1E2) =>
% 107.13/14.50 ((
% 107.13/14.50 (funcGraphProp1) =>
% 107.13/14.50 ((
% 107.13/14.50 (funcGraphProp3) =>
% 107.13/14.50 ((
% 107.13/14.50 (funcGraphProp2) =>
% 107.13/14.50 ((
% 107.13/14.50 (funcextLem) =>
% 107.13/14.50 ((
% 107.13/14.50 (funcGraphProp4) =>
% 107.13/14.50 ((
% 107.13/14.50 (subbreln) =>
% 107.13/14.50 ((
% 107.13/14.50 (eqbreln) =>
% 107.13/14.50 ((
% 107.13/14.50 (funcext) =>
% 107.13/14.50 ((
% 107.13/14.50 (funcext2) =>
% 107.13/14.50 ((
% 107.13/14.50 (ap2apEq1) =>
% 107.13/14.50 ((
% 107.13/14.50 (ap2apEq2) =>
% 107.13/14.50 ((
% 107.13/14.50 (beta1) =>
% 107.13/14.50 ((
% 107.13/14.50 (eta1) =>
% 107.13/14.50 ((
% 107.13/14.50 (lam2lamEq) =>
% 107.13/14.50 ((
% 107.13/14.50 (beta2) =>
% 107.13/14.50 ((
% 107.13/14.50 (eta2) =>
% 107.13/14.50 ((
% 107.13/14.50 (iffalseProp1) =>
% 107.13/14.50 ((
% 107.13/14.50 (iffalseProp2) =>
% 107.13/14.50 ((
% 107.13/14.50 (iftrueProp1) =>
% 107.13/14.50 ((
% 107.13/14.50 (iftrueProp2) =>
% 107.13/14.50 ((
% 107.13/14.50 (ifSingleton) =>
% 107.13/14.50 ((
% 107.13/14.50 (ifp) =>
% 107.13/14.50 ((
% 107.13/14.50 (theeq) =>
% 107.13/14.50 ((
% 107.13/14.50 (iftrue) =>
% 107.13/14.50 ((
% 107.13/14.50 (iffalse) =>
% 107.13/14.50 ((
% 107.13/14.50 (iftrueorfalse) =>
% 107.13/14.50 ((
% 107.13/14.50 (binintersectT_lem) =>
% 107.13/14.50 ((
% 107.13/14.50 (binunionT_lem) =>
% 107.13/14.50 ((
% 107.13/14.50 (powersetT_lem) =>
% 107.13/14.50 ((
% 107.13/14.50 (setminusT_lem) =>
% 107.13/14.50 ((
% 107.13/14.50 (complementT_lem) =>
% 107.13/14.50 ((
% 107.13/14.50 (setextT) =>
% 107.13/14.50 ((
% 107.13/14.50 (subsetTI) =>
% 107.13/14.50 ((
% 107.13/14.50 (powersetTI1) =>
% 107.13/14.50 ((
% 107.13/14.50 (powersetTE1) =>
% 107.13/14.50 ((
% 107.13/14.50 (complementTI1) =>
% 107.13/14.50 ((
% 107.13/14.50 (complementTE1) =>
% 107.13/14.50 ((
% 107.13/14.50 (binintersectTELcontra) =>
% 107.13/14.50 ((
% 107.13/14.50 (binintersectTERcontra) =>
% 107.13/14.50 ((
% 107.13/14.50 (contrasubsetT) =>
% 107.13/14.50 ((
% 107.13/14.50 (contrasubsetT1) =>
% 107.13/14.50 ((
% 107.13/14.50 (contrasubsetT2) =>
% 107.13/14.50 ((
% 107.13/14.50 (contrasubsetT3) =>
% 107.13/14.50 ((
% 107.13/14.50 (doubleComplementI1) =>
% 107.13/14.50 ((
% 107.13/14.50 (doubleComplementE1) =>
% 107.13/14.50 ((
% 107.13/14.50 (doubleComplementSub1) =>
% 107.13/14.50 ((
% 107.13/14.50 (doubleComplementSub2) =>
% 107.13/14.50 ((
% 107.13/14.50 (doubleComplementEq) =>
% 107.13/14.50 ((
% 107.13/14.50 (complementTnotintersectT) =>
% 107.13/14.50 ((
% 107.13/14.50 (complementImpComplementIntersect) =>
% 107.13/14.50 ((
% 107.13/14.50 (complementSubsetComplementIntersect) =>
% 107.13/14.50 ((
% 107.13/14.50 (complementInPowersetComplementIntersect) =>
% 107.13/14.50 ((
% 107.13/14.50 (contraSubsetComplement) =>
% 107.13/14.50 ((
% 107.13/14.50 (complementTcontraSubset) =>
% 107.13/14.50 ((
% 107.13/14.50 (binunionTILcontra) =>
% 107.13/14.50 ((
% 107.13/14.50 (binunionTIRcontra) =>
% 107.13/14.50 ((
% 107.13/14.50 (inIntersectImpInUnion) =>
% 107.13/14.50 ((
% 107.13/14.50 (inIntersectImpInUnion2) =>
% 107.13/14.50 ((
% 107.13/14.50 (inIntersectImpInIntersectUnions) =>
% 107.13/14.50 ((
% 107.13/14.50 (intersectInPowersetIntersectUnions) =>
% 107.13/14.50 ((
% 107.13/14.50 (inComplementUnionImpNotIn1) =>
% 107.13/14.50 ((
% 107.13/14.50 (inComplementUnionImpInComplement1) =>
% 107.13/14.50 ((
% 107.13/14.50 (binunionTE) =>
% 107.13/14.50 ((
% 107.13/14.50 (binunionTEcontra) =>
% 107.13/14.50 ((
% 107.13/14.50 (demorgan2a1) =>
% 107.13/14.50 ((
% 107.13/14.50 (complementUnionInPowersetComplement) =>
% 107.13/14.50 ((
% 107.13/14.50 (demorgan2a2) =>
% 107.13/14.50 ((
% 107.13/14.50 (demorgan1a) =>
% 107.13/14.50 ((
% 107.13/14.50 (demorgan1b) =>
% 107.13/14.50 ((
% 107.13/14.50 (demorgan1) =>
% 107.13/14.50 ((
% 107.13/14.50 (demorgan2a) =>
% 107.13/14.50 ((
% 107.13/14.50 (demorgan2b2) =>
% 107.13/14.50 ((
% 107.13/14.50 (demorgan2b) =>
% 107.13/14.50 ((
% 107.13/14.50 (demorgan2) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz13rule0) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz13rule1) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz13rule2) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz13rule3) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz13rule4) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz1_1) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz1_2) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz1_3) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz1_4) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz1_5) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1all2) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1SetBreln1) =>
% 107.13/14.50 ((
% 107.13/14.50 (choice2fnsingleton) =>
% 107.13/14.50 ((
% 107.13/14.50 (setOfPairsIsBReln1) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1all1) =>
% 107.13/14.50 ((
% 107.13/14.50 (subbreln1) =>
% 107.13/14.50 ((
% 107.13/14.50 (eqbreln1) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1invprop) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1invI) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1invE) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1compprop) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1compI) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1compE) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1compEex) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1unionprop) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1unionIL) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1unionIR) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1unionI) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1unionE) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1unionEcases) =>
% 107.13/14.50 ((
% 107.13/14.50 (breln1unionCommutes) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz2Ex) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz2W) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz2A) =>
% 107.13/14.50 ((
% 107.13/14.50 (woz2B) =>
% 107.13/14.50 ((
% 107.13/14.50 (image1Ex) =>
% 107.13/14.50 ((
% 107.13/14.50 (image1Ex1) =>
% 107.13/14.50 ((
% 107.13/14.50 (image1Equiv) =>
% 107.13/14.50 ((
% 107.13/14.50 (image1E) =>
% 107.13/14.50 ((
% 107.13/14.50 (image1I) =>
% 107.13/14.50 ((
% 107.13/14.50 (injFuncInInjFuncSet) =>
% 107.13/14.50 ((
% 107.13/14.50 (injFuncSetFuncIn) =>
% 107.13/14.50 ((
% 107.13/14.50 (injFuncSetFuncInj) =>
% 107.13/14.50 ((
% 107.13/14.50 (surjFuncSetFuncIn) =>
% 107.13/14.50 ((
% 107.13/14.50 (surjFuncSetFuncSurj) =>
% 107.13/14.50 ((
% 107.13/14.50 (leftInvIsSurj) =>
% 107.13/14.50 ((
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% 107.13/14.50 ((
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% 107.13/14.50 (('#S') @ (
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% 107.13/14.50 ('#B') @ (
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% 107.13/14.50 (
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% 107.13/14.51 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl984])).
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% 107.13/14.51 (secondinupair) =>
% 107.13/14.51 ((
% 107.13/14.51 (setukpairIL) =>
% 107.13/14.51 ((
% 107.13/14.51 (setukpairIR) =>
% 107.13/14.51 ((
% 107.13/14.51 (kpairiskpair) =>
% 107.13/14.51 ((
% 107.13/14.51 (kpairp) =>
% 107.13/14.51 ((
% 107.13/14.51 (singletonsubset) =>
% 107.13/14.51 ((
% 107.13/14.51 (singletoninpowerset) =>
% 107.13/14.51 ((
% 107.13/14.51 (singletoninpowunion) =>
% 107.13/14.51 ((
% 107.13/14.51 (upairset2E) =>
% 107.13/14.51 ((
% 107.13/14.51 (upairsubunion) =>
% 107.13/14.51 ((
% 107.13/14.51 (upairinpowunion) =>
% 107.13/14.51 ((
% 107.13/14.51 (ubforcartprodlem1) =>
% 107.13/14.51 ((
% 107.13/14.51 (ubforcartprodlem2) =>
% 107.13/14.51 ((
% 107.13/14.51 (ubforcartprodlem3) =>
% 107.13/14.51 ((
% 107.13/14.51 (cartprodpairin) =>
% 107.13/14.51 ((
% 107.13/14.51 (cartprodmempair1) =>
% 107.13/14.51 ((
% 107.13/14.51 (cartprodmempair) =>
% 107.13/14.51 ((
% 107.13/14.51 (setunionE2) =>
% 107.13/14.51 ((
% 107.13/14.51 (setunionsingleton1) =>
% 107.13/14.51 ((
% 107.13/14.51 (setunionsingleton2) =>
% 107.13/14.51 ((
% 107.13/14.51 (setunionsingleton) =>
% 107.13/14.51 ((
% 107.13/14.51 (singletonprop) =>
% 107.13/14.51 ((
% 107.13/14.51 (ex1E1) =>
% 107.13/14.51 ((
% 107.13/14.51 (ex1I) =>
% 107.13/14.51 ((
% 107.13/14.51 (ex1I2) =>
% 107.13/14.51 ((
% 107.13/14.51 (singletonsuniq) =>
% 107.13/14.51 ((
% 107.13/14.51 (setukpairinjL1) =>
% 107.13/14.51 ((
% 107.13/14.51 (kfstsingleton) =>
% 107.13/14.51 ((
% 107.13/14.51 (theprop) =>
% 107.13/14.51 ((
% 107.13/14.51 (kfstpairEq) =>
% 107.13/14.51 ((
% 107.13/14.51 (cartprodfstin) =>
% 107.13/14.51 ((
% 107.13/14.51 (setukpairinjL2) =>
% 107.13/14.51 ((
% 107.13/14.51 (setukpairinjL) =>
% 107.13/14.51 ((
% 107.13/14.51 (setukpairinjR11) =>
% 107.13/14.51 ((
% 107.13/14.51 (setukpairinjR12) =>
% 107.13/14.51 ((
% 107.13/14.51 (setukpairinjR1) =>
% 107.13/14.51 ((
% 107.13/14.51 (upairequniteq) =>
% 107.13/14.51 ((
% 107.13/14.51 (setukpairinjR2) =>
% 107.13/14.51 ((
% 107.13/14.51 (setukpairinjR) =>
% 107.13/14.51 ((
% 107.13/14.51 (ksndsingleton) =>
% 107.13/14.51 ((
% 107.13/14.51 (ksndpairEq) =>
% 107.13/14.51 ((
% 107.13/14.51 (kpairsurjEq) =>
% 107.13/14.51 ((
% 107.13/14.51 (cartprodsndin) =>
% 107.13/14.51 ((
% 107.13/14.51 (cartprodpairmemEL) =>
% 107.13/14.51 ((
% 107.13/14.51 (cartprodpairmemER) =>
% 107.13/14.51 ((
% 107.13/14.51 (cartprodmempaircEq) =>
% 107.13/14.51 ((
% 107.13/14.51 (cartprodfstpairEq) =>
% 107.13/14.51 ((
% 107.13/14.51 (cartprodsndpairEq) =>
% 107.13/14.51 ((
% 107.13/14.51 (cartprodpairsurjEq) =>
% 107.13/14.51 ((
% 107.13/14.51 (dpsetconstrI) =>
% 107.13/14.51 ((
% 107.13/14.51 (dpsetconstrSub) =>
% 107.13/14.51 ((
% 107.13/14.51 (setOfPairsIsBReln) =>
% 107.13/14.51 ((
% 107.13/14.51 (dpsetconstrERa) =>
% 107.13/14.51 ((
% 107.13/14.51 (dpsetconstrEL1) =>
% 107.13/14.51 ((
% 107.13/14.51 (dpsetconstrEL2) =>
% 107.13/14.51 ((
% 107.13/14.51 (dpsetconstrER) =>
% 107.13/14.51 ((
% 107.13/14.51 (funcImageSingleton) =>
% 107.13/14.51 ((
% 107.13/14.51 (apProp) =>
% 107.13/14.51 ((
% 107.13/14.51 (app) =>
% 107.13/14.51 ((
% 107.13/14.51 (infuncsetfunc) =>
% 107.13/14.51 ((
% 107.13/14.51 (ap2p) =>
% 107.13/14.51 ((
% 107.13/14.51 (funcinfuncset) =>
% 107.13/14.51 ((
% 107.13/14.51 (lamProp) =>
% 107.13/14.51 ((
% 107.13/14.51 (lamp) =>
% 107.13/14.51 ((
% 107.13/14.51 (lam2p) =>
% 107.13/14.51 ((
% 107.13/14.51 (brelnall1) =>
% 107.13/14.51 ((
% 107.13/14.51 (brelnall2) =>
% 107.13/14.51 ((
% 107.13/14.51 (ex1E2) =>
% 107.13/14.51 ((
% 107.13/14.51 (funcGraphProp1) =>
% 107.13/14.51 ((
% 107.13/14.51 (funcGraphProp3) =>
% 107.13/14.51 ((
% 107.13/14.51 (funcGraphProp2) =>
% 107.13/14.51 ((
% 107.13/14.51 (funcextLem) =>
% 107.13/14.51 ((
% 107.13/14.51 (funcGraphProp4) =>
% 107.13/14.51 ((
% 107.13/14.51 (subbreln) =>
% 107.13/14.51 ((
% 107.13/14.51 (eqbreln) =>
% 107.13/14.51 ((
% 107.13/14.51 (funcext) =>
% 107.13/14.51 ((
% 107.13/14.51 (funcext2) =>
% 107.13/14.51 ((
% 107.13/14.51 (ap2apEq1) =>
% 107.13/14.51 ((
% 107.13/14.51 (ap2apEq2) =>
% 107.13/14.51 ((
% 107.13/14.51 (beta1) =>
% 107.13/14.51 ((
% 107.13/14.51 (eta1) =>
% 107.13/14.51 ((
% 107.13/14.51 (lam2lamEq) =>
% 107.13/14.51 ((
% 107.13/14.51 (beta2) =>
% 107.13/14.51 ((
% 107.13/14.51 (eta2) =>
% 107.13/14.51 ((
% 107.13/14.51 (iffalseProp1) =>
% 107.13/14.51 ((
% 107.13/14.51 (iffalseProp2) =>
% 107.13/14.51 ((
% 107.13/14.51 (iftrueProp1) =>
% 107.13/14.51 ((
% 107.13/14.51 (iftrueProp2) =>
% 107.13/14.51 ((
% 107.13/14.51 (ifSingleton) =>
% 107.13/14.51 ((
% 107.13/14.51 (ifp) =>
% 107.13/14.51 ((
% 107.13/14.51 (theeq) =>
% 107.13/14.51 ((
% 107.13/14.51 (iftrue) =>
% 107.13/14.51 ((
% 107.13/14.51 (iffalse) =>
% 107.13/14.51 ((
% 107.13/14.51 (iftrueorfalse) =>
% 107.13/14.51 ((
% 107.13/14.51 (binintersectT_lem) =>
% 107.13/14.51 ((
% 107.13/14.51 (binunionT_lem) =>
% 107.13/14.51 ((
% 107.13/14.51 (powersetT_lem) =>
% 107.13/14.51 ((
% 107.13/14.51 (setminusT_lem) =>
% 107.13/14.51 ((
% 107.13/14.51 (complementT_lem) =>
% 107.13/14.51 ((
% 107.13/14.51 (setextT) =>
% 107.13/14.51 ((
% 107.13/14.51 (subsetTI) =>
% 107.13/14.51 ((
% 107.13/14.51 (powersetTI1) =>
% 107.13/14.51 ((
% 107.13/14.51 (powersetTE1) =>
% 107.13/14.51 ((
% 107.13/14.51 (complementTI1) =>
% 107.13/14.51 ((
% 107.13/14.51 (complementTE1) =>
% 107.13/14.51 ((
% 107.13/14.51 (binintersectTELcontra) =>
% 107.13/14.51 ((
% 107.13/14.51 (binintersectTERcontra) =>
% 107.13/14.51 ((
% 107.13/14.51 (contrasubsetT) =>
% 107.13/14.51 ((
% 107.13/14.51 (contrasubsetT1) =>
% 107.13/14.51 ((
% 107.13/14.51 (contrasubsetT2) =>
% 107.13/14.51 ((
% 107.13/14.51 (contrasubsetT3) =>
% 107.13/14.51 ((
% 107.13/14.51 (doubleComplementI1) =>
% 107.13/14.51 ((
% 107.13/14.51 (doubleComplementE1) =>
% 107.13/14.51 ((
% 107.13/14.51 (doubleComplementSub1) =>
% 107.13/14.51 ((
% 107.13/14.51 (doubleComplementSub2) =>
% 107.13/14.51 ((
% 107.13/14.51 (doubleComplementEq) =>
% 107.13/14.51 ((
% 107.13/14.51 (complementTnotintersectT) =>
% 107.13/14.51 ((
% 107.13/14.51 (complementImpComplementIntersect) =>
% 107.13/14.51 ((
% 107.13/14.51 (complementSubsetComplementIntersect) =>
% 107.13/14.51 ((
% 107.13/14.51 (complementInPowersetComplementIntersect) =>
% 107.13/14.51 ((
% 107.13/14.51 (contraSubsetComplement) =>
% 107.13/14.51 ((
% 107.13/14.51 (complementTcontraSubset) =>
% 107.13/14.51 ((
% 107.13/14.51 (binunionTILcontra) =>
% 107.13/14.51 ((
% 107.13/14.51 (binunionTIRcontra) =>
% 107.13/14.51 ((
% 107.13/14.51 (inIntersectImpInUnion) =>
% 107.13/14.51 ((
% 107.13/14.51 (inIntersectImpInUnion2) =>
% 107.13/14.51 ((
% 107.13/14.51 (inIntersectImpInIntersectUnions) =>
% 107.13/14.51 ((
% 107.13/14.51 (intersectInPowersetIntersectUnions) =>
% 107.13/14.51 ((
% 107.13/14.51 (inComplementUnionImpNotIn1) =>
% 107.13/14.51 ((
% 107.13/14.51 (inComplementUnionImpInComplement1) =>
% 107.13/14.51 ((
% 107.13/14.51 (binunionTE) =>
% 107.13/14.51 ((
% 107.13/14.51 (binunionTEcontra) =>
% 107.13/14.51 ((
% 107.13/14.51 (demorgan2a1) =>
% 107.13/14.51 ((
% 107.13/14.51 (complementUnionInPowersetComplement) =>
% 107.13/14.51 ((
% 107.13/14.51 (demorgan2a2) =>
% 107.13/14.51 ((
% 107.13/14.51 (demorgan1a) =>
% 107.13/14.51 ((
% 107.13/14.51 (demorgan1b) =>
% 107.13/14.51 ((
% 107.13/14.51 (demorgan1) =>
% 107.13/14.51 ((
% 107.13/14.51 (demorgan2a) =>
% 107.13/14.51 ((
% 107.13/14.51 (demorgan2b2) =>
% 107.13/14.51 ((
% 107.13/14.51 (demorgan2b) =>
% 107.13/14.51 ((
% 107.13/14.51 (demorgan2) =>
% 107.13/14.51 ((
% 107.13/14.51 (woz13rule0) =>
% 107.13/14.51 ((
% 107.13/14.51 (woz13rule1) =>
% 107.13/14.51 ((
% 107.13/14.51 (woz13rule2) =>
% 107.13/14.51 ((
% 107.13/14.51 (woz13rule3) =>
% 107.13/14.51 ((
% 107.13/14.51 (woz13rule4) =>
% 107.13/14.51 ((
% 107.13/14.51 (woz1_1) =>
% 107.13/14.51 ((
% 107.13/14.51 (woz1_2) =>
% 107.13/14.51 ((
% 107.13/14.51 (woz1_3) =>
% 107.13/14.51 ((
% 107.13/14.51 (woz1_4) =>
% 107.13/14.51 ((
% 107.13/14.51 (woz1_5) =>
% 107.13/14.51 ((
% 107.13/14.51 (breln1all2) =>
% 107.13/14.51 ((
% 107.13/14.51 (breln1SetBreln1) =>
% 107.13/14.51 ((
% 107.13/14.51 (choice2fnsingleton) =>
% 107.13/14.51 ((
% 107.13/14.51 (setOfPairsIsBReln1) =>
% 107.13/14.51 ((
% 107.13/14.51 (breln1all1) =>
% 107.13/14.51 ((
% 107.13/14.51 (subbreln1) =>
% 107.13/14.51 ((
% 107.13/14.51 (eqbreln1) =>
% 107.13/14.51 ((
% 107.13/14.51 (breln1invprop) =>
% 107.13/14.51 ((
% 107.13/14.51 (breln1invI) =>
% 107.13/14.51 ((
% 107.13/14.51 (breln1invE) =>
% 107.13/14.51 ((
% 107.13/14.51 (breln1compprop) =>
% 107.13/14.51 ((
% 107.13/14.51 (breln1compI) =>
% 107.13/14.51 ((
% 107.13/14.51 (breln1compE) =>
% 107.13/14.51 ((
% 107.13/14.51 (breln1compEex) =>
% 107.13/14.51 ((
% 107.13/14.51 (breln1unionprop) =>
% 107.13/14.51 ((
% 107.13/14.51 (breln1unionIL) =>
% 107.13/14.51 ((
% 107.13/14.51 (breln1unionIR) =>
% 107.13/14.51 ((
% 107.13/14.51 (breln1unionI) =>
% 107.13/14.51 ((
% 107.13/14.51 (breln1unionE) =>
% 107.13/14.51 ((
% 107.13/14.51 (breln1unionEcases) =>
% 107.13/14.51 ((
% 107.13/14.51 (breln1unionCommutes) =>
% 107.13/14.51 ((
% 107.13/14.51 (woz2Ex) =>
% 107.13/14.51 ((
% 107.13/14.51 (woz2W) =>
% 107.13/14.51 ((
% 107.13/14.51 (woz2A) =>
% 107.13/14.51 ((
% 107.13/14.51 (woz2B) =>
% 107.13/14.51 ((
% 107.13/14.51 (image1Ex) =>
% 107.13/14.51 ((
% 107.13/14.51 (image1Ex1) =>
% 107.13/14.51 ((
% 107.13/14.51 (image1Equiv) =>
% 107.13/14.51 ((
% 107.13/14.51 (image1E) =>
% 107.13/14.51 ((
% 107.13/14.51 (image1I) =>
% 107.13/14.51 ((
% 107.13/14.51 (injFuncInInjFuncSet) =>
% 107.13/14.51 ((
% 107.13/14.51 (injFuncSetFuncIn) =>
% 107.13/14.51 ((
% 107.13/14.51 (injFuncSetFuncInj) =>
% 107.13/14.51 ((
% 107.13/14.51 (surjFuncSetFuncIn) =>
% 107.13/14.51 ((
% 107.13/14.51 (surjFuncSetFuncSurj) =>
% 107.13/14.51 ((
% 107.13/14.51 (leftInvIsSurj) =>
% 107.13/14.51 ((
% 107.13/14.51 (surjCantorThm) =>
% 107.13/14.51 ((
% 107.13/14.51 (!!) @ (
% 107.13/14.51 (('#S') @ (
% 107.13/14.51 (
% 107.13/14.51 ('#B') @ (
% 107.13/14.51 =>) @
% 107.13/14.51 nonempty)) @
% 107.13/14.51 (
% 107.13/14.51 (
% 107.13/14.51 ('#B') @ (
% 107.13/14.51 ??) @
% 107.13/14.51 (
% 107.13/14.51 (
% 107.13/14.51 ('#S') @ (
% 107.13/14.51 (
% 107.13/14.51 ('#B') @ (
% 107.13/14.51 '#S') @
% 107.13/14.51 (
% 107.13/14.51 (
% 107.13/14.51 ('#B') @ (
% 107.13/14.51 (
% 107.13/14.51 ('#B') @ (
% 107.13/14.51 &))) @
% 107.13/14.51 (
% 107.13/14.51 (
% 107.13/14.51 ('#C') @ in)))))) @
% 107.13/14.51 (
% 107.13/14.51 (
% 107.13/14.51 ('#C') @ (
% 107.13/14.51 (
% 107.13/14.51 ('#B') @ (
% 107.13/14.51 '#C') @
% 107.13/14.51 (
% 107.13/14.51 (
% 107.13/14.51 ('#B') @ (
% 107.13/14.51 (
% 107.13/14.51 ('#B') @ (
% 107.13/14.51 =))) @
% 107.13/14.51 (
% 107.13/14.51 (
% 107.13/14.51 ('#C') @ binintersect)))))) @
% 107.13/14.51 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 107.13/14.51 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1000])).
% 107.13/14.51 thf(zip_derived_cl1027, plain,
% 107.13/14.51 (~ (((subsetemptysetimpeq) =>
% 107.13/14.51 (((powersetI1) =>
% 107.13/14.51 (((powersetE1) =>
% 107.13/14.51 (((inPowerset) =>
% 107.13/14.51 (((powersetsubset) =>
% 107.13/14.51 (((sepInPowerset) =>
% 107.13/14.51 (((sepSubset) =>
% 107.13/14.51 (((binunionIL) =>
% 107.13/14.51 (((upairset2IR) =>
% 107.13/14.51 (((binunionIR) =>
% 107.13/14.51 (((binunionEcases) =>
% 107.13/14.51 (((binunionE) =>
% 107.13/14.51 (((binunionLsub) =>
% 107.13/14.51 (((binunionRsub) =>
% 107.13/14.51 (((binintersectI) =>
% 107.13/14.51 (((binintersectSubset5) =>
% 107.13/14.51 (((binintersectEL) =>
% 107.13/14.51 (((binintersectLsub) =>
% 107.13/14.51 (((binintersectSubset2) =>
% 107.13/14.51 (((binintersectSubset3) =>
% 107.13/14.51 (((binintersectER) =>
% 107.13/14.51 (((disjointsetsI1) =>
% 107.13/14.51 (((binintersectRsub) =>
% 107.13/14.51 (((binintersectSubset4) =>
% 107.13/14.51 (((binintersectSubset1) =>
% 107.13/14.51 (((bs114d) =>
% 107.13/14.51 (((setminusI) =>
% 107.13/14.51 (((setminusEL) =>
% 107.13/14.51 (((setminusER) =>
% 107.13/14.51 (((setminusSubset2) =>
% 107.13/14.51 ((
% 107.13/14.51 (setminusERneg) =>
% 107.13/14.51 ((
% 107.13/14.51 (setminusELneg) =>
% 107.13/14.51 ((
% 107.13/14.51 (setminusILneg) =>
% 107.13/14.51 ((
% 107.13/14.51 (setminusIRneg) =>
% 107.13/14.51 ((
% 107.13/14.51 (setminusLsub) =>
% 107.13/14.51 ((
% 107.13/14.51 (setminusSubset1) =>
% 107.13/14.51 ((
% 107.13/14.51 (symdiffE) =>
% 107.13/14.51 ((
% 107.13/14.51 (symdiffI1) =>
% 107.13/14.51 ((
% 107.13/14.51 (symdiffI2) =>
% 107.13/14.51 ((
% 107.13/14.51 (symdiffIneg1) =>
% 107.13/14.51 ((
% 107.13/14.51 (symdiffIneg2) =>
% 107.13/14.51 ((
% 107.13/14.51 (secondinupair) =>
% 107.13/14.51 ((
% 107.13/14.51 (setukpairIL) =>
% 107.13/14.51 ((
% 107.13/14.51 (setukpairIR) =>
% 107.13/14.51 ((
% 107.13/14.51 (kpairiskpair) =>
% 107.13/14.51 ((
% 107.13/14.51 (kpairp) =>
% 107.13/14.51 ((
% 107.13/14.51 (singletonsubset) =>
% 107.13/14.51 ((
% 107.13/14.51 (singletoninpowerset) =>
% 107.13/14.51 ((
% 107.13/14.51 (singletoninpowunion) =>
% 107.13/14.51 ((
% 107.13/14.51 (upairset2E) =>
% 107.13/14.51 ((
% 107.13/14.51 (upairsubunion) =>
% 107.13/14.51 ((
% 107.13/14.51 (upairinpowunion) =>
% 107.13/14.51 ((
% 107.13/14.51 (ubforcartprodlem1) =>
% 107.13/14.51 ((
% 107.13/14.51 (ubforcartprodlem2) =>
% 107.13/14.51 ((
% 107.13/14.51 (ubforcartprodlem3) =>
% 107.13/14.51 ((
% 107.13/14.51 (cartprodpairin) =>
% 107.13/14.51 ((
% 107.13/14.51 (cartprodmempair1) =>
% 107.13/14.51 ((
% 107.13/14.51 (cartprodmempair) =>
% 107.13/14.51 ((
% 107.13/14.51 (setunionE2) =>
% 107.13/14.51 ((
% 107.13/14.51 (setunionsingleton1) =>
% 107.13/14.51 ((
% 107.13/14.51 (setunionsingleton2) =>
% 107.13/14.51 ((
% 107.13/14.51 (setunionsingleton) =>
% 107.13/14.51 ((
% 107.13/14.51 (singletonprop) =>
% 107.13/14.51 ((
% 107.13/14.51 (ex1E1) =>
% 107.13/14.51 ((
% 107.13/14.51 (ex1I) =>
% 107.13/14.51 ((
% 107.13/14.51 (ex1I2) =>
% 107.13/14.51 ((
% 107.13/14.51 (singletonsuniq) =>
% 107.13/14.51 ((
% 107.13/14.51 (setukpairinjL1) =>
% 107.13/14.51 ((
% 107.13/14.51 (kfstsingleton) =>
% 107.13/14.51 ((
% 107.13/14.51 (theprop) =>
% 107.13/14.51 ((
% 107.13/14.51 (kfstpairEq) =>
% 107.13/14.51 ((
% 107.13/14.51 (cartprodfstin) =>
% 107.13/14.51 ((
% 107.13/14.51 (setukpairinjL2) =>
% 107.13/14.51 ((
% 107.13/14.51 (setukpairinjL) =>
% 107.13/14.51 ((
% 107.13/14.51 (setukpairinjR11) =>
% 107.13/14.51 ((
% 107.13/14.51 (setukpairinjR12) =>
% 107.13/14.51 ((
% 107.13/14.51 (setukpairinjR1) =>
% 107.13/14.51 ((
% 107.13/14.51 (upairequniteq) =>
% 107.13/14.51 ((
% 107.13/14.51 (setukpairinjR2) =>
% 107.13/14.51 ((
% 107.13/14.51 (setukpairinjR) =>
% 107.13/14.51 ((
% 107.13/14.51 (ksndsingleton) =>
% 107.13/14.51 ((
% 107.13/14.51 (ksndpairEq) =>
% 107.13/14.51 ((
% 107.13/14.51 (kpairsurjEq) =>
% 107.13/14.51 ((
% 107.13/14.51 (cartprodsndin) =>
% 107.13/14.51 ((
% 107.13/14.51 (cartprodpairmemEL) =>
% 107.13/14.51 ((
% 107.13/14.51 (cartprodpairmemER) =>
% 107.13/14.51 ((
% 107.13/14.51 (cartprodmempaircEq) =>
% 107.13/14.51 ((
% 107.13/14.51 (cartprodfstpairEq) =>
% 107.13/14.51 ((
% 107.13/14.51 (cartprodsndpairEq) =>
% 107.13/14.51 ((
% 107.13/14.51 (cartprodpairsurjEq) =>
% 107.13/14.51 ((
% 107.13/14.51 (dpsetconstrI) =>
% 107.13/14.51 ((
% 107.13/14.51 (dpsetconstrSub) =>
% 107.13/14.51 ((
% 107.13/14.51 (setOfPairsIsBReln) =>
% 107.13/14.51 ((
% 107.13/14.51 (dpsetconstrERa) =>
% 107.13/14.51 ((
% 107.13/14.51 (dpsetconstrEL1) =>
% 107.13/14.51 ((
% 107.13/14.51 (dpsetconstrEL2) =>
% 107.13/14.51 ((
% 107.13/14.51 (dpsetconstrER) =>
% 107.13/14.51 ((
% 107.13/14.51 (funcImageSingleton) =>
% 107.13/14.51 ((
% 107.13/14.51 (apProp) =>
% 107.13/14.51 ((
% 107.13/14.51 (app) =>
% 107.13/14.51 ((
% 107.13/14.51 (infuncsetfunc) =>
% 107.13/14.51 ((
% 107.13/14.51 (ap2p) =>
% 107.13/14.51 ((
% 107.13/14.51 (funcinfuncset) =>
% 107.13/14.51 ((
% 107.13/14.51 (lamProp) =>
% 107.13/14.51 ((
% 107.13/14.51 (lamp) =>
% 107.13/14.51 ((
% 107.13/14.51 (lam2p) =>
% 107.13/14.51 ((
% 107.13/14.51 (brelnall1) =>
% 107.13/14.51 ((
% 107.13/14.51 (brelnall2) =>
% 107.13/14.51 ((
% 107.13/14.51 (ex1E2) =>
% 107.13/14.51 ((
% 107.13/14.51 (funcGraphProp1) =>
% 107.13/14.51 ((
% 107.13/14.51 (funcGraphProp3) =>
% 107.13/14.51 ((
% 107.13/14.51 (funcGraphProp2) =>
% 107.13/14.51 ((
% 107.13/14.51 (funcextLem) =>
% 107.13/14.51 ((
% 107.13/14.51 (funcGraphProp4) =>
% 107.13/14.51 ((
% 107.13/14.51 (subbreln) =>
% 107.13/14.51 ((
% 107.13/14.51 (eqbreln) =>
% 107.13/14.51 ((
% 107.13/14.51 (funcext) =>
% 107.13/14.51 ((
% 107.13/14.51 (funcext2) =>
% 107.13/14.51 ((
% 107.13/14.51 (ap2apEq1) =>
% 107.13/14.51 ((
% 107.13/14.51 (ap2apEq2) =>
% 107.13/14.51 ((
% 107.13/14.51 (beta1) =>
% 107.13/14.51 ((
% 107.13/14.51 (eta1) =>
% 107.13/14.51 ((
% 107.13/14.51 (lam2lamEq) =>
% 107.13/14.51 ((
% 107.13/14.51 (beta2) =>
% 107.13/14.51 ((
% 107.13/14.51 (eta2) =>
% 107.13/14.51 ((
% 107.13/14.51 (iffalseProp1) =>
% 107.13/14.51 ((
% 107.13/14.51 (iffalseProp2) =>
% 107.13/14.51 ((
% 107.13/14.51 (iftrueProp1) =>
% 107.13/14.51 ((
% 107.13/14.51 (iftrueProp2) =>
% 107.13/14.51 ((
% 107.13/14.51 (ifSingleton) =>
% 107.13/14.51 ((
% 107.13/14.51 (ifp) =>
% 107.13/14.51 ((
% 107.13/14.51 (theeq) =>
% 107.13/14.51 ((
% 107.13/14.51 (iftrue) =>
% 107.13/14.51 ((
% 107.13/14.51 (iffalse) =>
% 107.13/14.51 ((
% 107.13/14.51 (iftrueorfalse) =>
% 107.13/14.51 ((
% 107.13/14.51 (binintersectT_lem) =>
% 107.13/14.51 ((
% 107.13/14.51 (binunionT_lem) =>
% 107.13/14.51 ((
% 107.13/14.51 (powersetT_lem) =>
% 107.13/14.51 ((
% 107.13/14.51 (setminusT_lem) =>
% 107.13/14.51 ((
% 107.13/14.51 (complementT_lem) =>
% 107.13/14.51 ((
% 107.13/14.51 (setextT) =>
% 107.13/14.51 ((
% 107.13/14.51 (subsetTI) =>
% 107.13/14.51 ((
% 107.13/14.51 (powersetTI1) =>
% 107.13/14.51 ((
% 107.13/14.51 (powersetTE1) =>
% 107.13/14.51 ((
% 107.13/14.51 (complementTI1) =>
% 107.13/14.51 ((
% 107.13/14.51 (complementTE1) =>
% 107.13/14.51 ((
% 107.13/14.51 (binintersectTELcontra) =>
% 107.13/14.51 ((
% 107.13/14.51 (binintersectTERcontra) =>
% 107.13/14.51 ((
% 107.13/14.51 (contrasubsetT) =>
% 107.13/14.51 ((
% 107.13/14.51 (contrasubsetT1) =>
% 107.13/14.51 ((
% 107.13/14.51 (contrasubsetT2) =>
% 107.13/14.51 ((
% 107.13/14.51 (contrasubsetT3) =>
% 107.13/14.51 ((
% 107.13/14.51 (doubleComplementI1) =>
% 107.13/14.51 ((
% 107.13/14.51 (doubleComplementE1) =>
% 107.13/14.51 ((
% 107.13/14.51 (doubleComplementSub1) =>
% 107.13/14.51 ((
% 107.13/14.51 (doubleComplementSub2) =>
% 107.13/14.51 ((
% 107.13/14.51 (doubleComplementEq) =>
% 107.13/14.51 ((
% 107.13/14.51 (complementTnotintersectT) =>
% 107.13/14.51 ((
% 107.13/14.51 (complementImpComplementIntersect) =>
% 107.13/14.51 ((
% 107.13/14.51 (complementSubsetComplementIntersect) =>
% 107.13/14.51 ((
% 107.13/14.51 (complementInPowersetComplementIntersect) =>
% 107.13/14.51 ((
% 107.13/14.51 (contraSubsetComplement) =>
% 107.13/14.51 ((
% 107.13/14.51 (complementTcontraSubset) =>
% 107.13/14.51 ((
% 107.13/14.51 (binunionTILcontra) =>
% 107.13/14.51 ((
% 107.13/14.51 (binunionTIRcontra) =>
% 107.13/14.51 ((
% 107.13/14.51 (inIntersectImpInUnion) =>
% 107.13/14.51 ((
% 107.13/14.51 (inIntersectImpInUnion2) =>
% 107.13/14.51 ((
% 107.13/14.51 (inIntersectImpInIntersectUnions) =>
% 107.13/14.51 ((
% 107.13/14.51 (intersectInPowersetIntersectUnions) =>
% 107.13/14.51 ((
% 107.13/14.51 (inComplementUnionImpNotIn1) =>
% 107.13/14.51 ((
% 107.13/14.51 (inComplementUnionImpInComplement1) =>
% 107.13/14.51 ((
% 107.13/14.51 (binunionTE) =>
% 107.13/14.51 ((
% 107.13/14.51 (binunionTEcontra) =>
% 107.13/14.51 ((
% 107.13/14.51 (demorgan2a1) =>
% 107.13/14.51 ((
% 107.13/14.51 (complementUnionInPowersetComplement) =>
% 107.13/14.51 ((
% 107.13/14.51 (demorgan2a2) =>
% 107.13/14.51 ((
% 107.13/14.51 (demorgan1a) =>
% 107.13/14.51 ((
% 107.13/14.51 (demorgan1b) =>
% 107.13/14.51 ((
% 107.13/14.51 (demorgan1) =>
% 107.13/14.51 ((
% 107.13/14.51 (demorgan2a) =>
% 107.13/14.51 ((
% 107.13/14.51 (demorgan2b2) =>
% 107.13/14.51 ((
% 107.13/14.51 (demorgan2b) =>
% 107.13/14.51 ((
% 107.13/14.51 (demorgan2) =>
% 107.13/14.51 ((
% 107.13/14.51 (woz13rule0) =>
% 107.13/14.51 ((
% 107.13/14.51 (woz13rule1) =>
% 107.13/14.51 ((
% 107.13/14.51 (woz13rule2) =>
% 107.13/14.51 ((
% 107.13/14.51 (woz13rule3) =>
% 107.13/14.51 ((
% 107.13/14.51 (woz13rule4) =>
% 107.13/14.51 ((
% 107.13/14.51 (woz1_1) =>
% 107.13/14.51 ((
% 107.13/14.51 (woz1_2) =>
% 107.13/14.51 ((
% 107.13/14.51 (woz1_3) =>
% 107.13/14.51 ((
% 107.13/14.51 (woz1_4) =>
% 107.13/14.51 ((
% 107.13/14.51 (woz1_5) =>
% 107.13/14.51 ((
% 107.13/14.51 (breln1all2) =>
% 107.13/14.51 ((
% 107.13/14.51 (breln1SetBreln1) =>
% 107.13/14.51 ((
% 107.13/14.51 (choice2fnsingleton) =>
% 107.13/14.51 ((
% 107.13/14.51 (setOfPairsIsBReln1) =>
% 107.13/14.51 ((
% 107.13/14.51 (breln1all1) =>
% 107.13/14.51 ((
% 107.13/14.51 (subbreln1) =>
% 107.13/14.51 ((
% 107.13/14.51 (eqbreln1) =>
% 107.13/14.51 ((
% 107.13/14.51 (breln1invprop) =>
% 107.13/14.51 ((
% 107.13/14.51 (breln1invI) =>
% 107.13/14.51 ((
% 107.13/14.51 (breln1invE) =>
% 107.13/14.51 ((
% 107.13/14.51 (breln1compprop) =>
% 107.13/14.51 ((
% 107.13/14.51 (breln1compI) =>
% 107.13/14.51 ((
% 107.13/14.51 (breln1compE) =>
% 107.13/14.51 ((
% 107.13/14.51 (breln1compEex) =>
% 107.13/14.51 ((
% 107.13/14.51 (breln1unionprop) =>
% 107.13/14.51 ((
% 107.13/14.51 (breln1unionIL) =>
% 107.13/14.51 ((
% 107.13/14.51 (breln1unionIR) =>
% 107.13/14.51 ((
% 107.13/14.51 (breln1unionI) =>
% 107.13/14.51 ((
% 107.13/14.51 (breln1unionE) =>
% 107.13/14.51 ((
% 107.13/14.51 (breln1unionEcases) =>
% 107.13/14.51 ((
% 107.13/14.51 (breln1unionCommutes) =>
% 107.13/14.51 ((
% 107.13/14.51 (woz2Ex) =>
% 107.13/14.51 ((
% 107.13/14.51 (woz2W) =>
% 107.13/14.51 ((
% 107.13/14.51 (woz2A) =>
% 107.13/14.51 ((
% 107.13/14.51 (woz2B) =>
% 107.13/14.51 ((
% 107.13/14.51 (image1Ex) =>
% 107.13/14.51 ((
% 107.13/14.51 (image1Ex1) =>
% 107.13/14.51 ((
% 107.13/14.51 (image1Equiv) =>
% 107.13/14.51 ((
% 107.13/14.51 (image1E) =>
% 107.13/14.51 ((
% 107.13/14.51 (image1I) =>
% 107.13/14.51 ((
% 107.13/14.51 (injFuncInInjFuncSet) =>
% 107.13/14.51 ((
% 107.13/14.51 (injFuncSetFuncIn) =>
% 107.13/14.51 ((
% 107.13/14.51 (injFuncSetFuncInj) =>
% 107.13/14.51 ((
% 107.13/14.51 (surjFuncSetFuncIn) =>
% 107.13/14.51 ((
% 107.13/14.51 (surjFuncSetFuncSurj) =>
% 107.13/14.51 ((
% 107.13/14.51 (leftInvIsSurj) =>
% 107.13/14.51 ((
% 107.13/14.51 (surjCantorThm) =>
% 107.13/14.51 ((
% 107.13/14.51 (!!) @ (
% 107.13/14.51 (('#S') @ (
% 107.13/14.51 (
% 107.13/14.51 ('#B') @ (
% 107.13/14.51 =>) @
% 107.13/14.51 nonempty)) @
% 107.13/14.51 (
% 107.13/14.51 (
% 107.13/14.51 ('#B') @ (
% 107.13/14.51 ??) @
% 107.13/14.51 (
% 107.13/14.51 (
% 107.13/14.51 ('#S') @ (
% 107.13/14.51 (
% 107.13/14.51 ('#B') @ (
% 107.13/14.51 '#S') @
% 107.13/14.51 (
% 107.13/14.51 (
% 107.13/14.51 ('#B') @ (
% 107.13/14.51 (
% 107.13/14.51 ('#B') @ (
% 107.13/14.51 &))) @
% 107.13/14.51 (
% 107.13/14.51 (
% 107.13/14.51 ('#C') @ in)))))) @
% 107.13/14.51 (
% 107.13/14.51 (
% 107.13/14.51 ('#C') @ (
% 107.13/14.51 (
% 107.13/14.51 ('#B') @ (
% 107.13/14.51 '#C') @
% 107.13/14.51 (
% 107.13/14.51 (
% 107.13/14.51 ('#B') @ (
% 107.13/14.51 (
% 107.13/14.51 ('#B') @ (
% 107.13/14.51 =))) @
% 107.13/14.51 (
% 107.13/14.51 (
% 107.13/14.51 ('#C') @ binintersect)))))) @
% 107.13/14.51 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 107.13/14.51 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1015])).
% 107.13/14.51 thf(zip_derived_cl1039, plain,
% 107.13/14.51 (~ (((powersetI1) =>
% 107.13/14.51 (((powersetE1) =>
% 107.13/14.51 (((inPowerset) =>
% 107.13/14.51 (((powersetsubset) =>
% 107.13/14.51 (((sepInPowerset) =>
% 107.13/14.51 (((sepSubset) =>
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% 107.13/14.51 (((upairset2IR) =>
% 107.13/14.51 (((binunionIR) =>
% 107.13/14.51 (((binunionEcases) =>
% 107.13/14.51 (((binunionE) =>
% 107.13/14.51 (((binunionLsub) =>
% 107.13/14.51 (((binunionRsub) =>
% 107.13/14.51 (((binintersectI) =>
% 107.13/14.51 (((binintersectSubset5) =>
% 107.13/14.51 (((binintersectEL) =>
% 107.13/14.51 (((binintersectLsub) =>
% 107.13/14.51 (((binintersectSubset2) =>
% 107.13/14.51 (((binintersectSubset3) =>
% 107.13/14.51 (((binintersectER) =>
% 107.13/14.51 (((disjointsetsI1) =>
% 107.13/14.51 (((binintersectRsub) =>
% 107.13/14.51 (((binintersectSubset4) =>
% 107.13/14.51 (((binintersectSubset1) =>
% 107.13/14.51 (((bs114d) =>
% 107.13/14.51 (((setminusI) =>
% 107.13/14.51 (((setminusEL) =>
% 107.13/14.51 (((setminusER) =>
% 107.13/14.51 (((setminusSubset2) =>
% 107.13/14.51 (((setminusERneg) =>
% 107.13/14.51 ((
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% 107.13/14.51 ((
% 107.13/14.51 (setminusILneg) =>
% 107.13/14.51 ((
% 107.13/14.51 (setminusIRneg) =>
% 107.13/14.51 ((
% 107.13/14.51 (setminusLsub) =>
% 107.13/14.51 ((
% 107.13/14.51 (setminusSubset1) =>
% 107.13/14.51 ((
% 107.13/14.51 (symdiffE) =>
% 107.13/14.51 ((
% 107.13/14.51 (symdiffI1) =>
% 107.13/14.51 ((
% 107.13/14.51 (symdiffI2) =>
% 107.13/14.51 ((
% 107.13/14.51 (symdiffIneg1) =>
% 107.13/14.51 ((
% 107.13/14.51 (symdiffIneg2) =>
% 107.13/14.51 ((
% 107.13/14.51 (secondinupair) =>
% 107.13/14.51 ((
% 107.13/14.51 (setukpairIL) =>
% 107.13/14.51 ((
% 107.13/14.51 (setukpairIR) =>
% 107.13/14.51 ((
% 107.13/14.51 (kpairiskpair) =>
% 107.13/14.51 ((
% 107.13/14.51 (kpairp) =>
% 107.13/14.51 ((
% 107.13/14.51 (singletonsubset) =>
% 107.13/14.51 ((
% 107.13/14.51 (singletoninpowerset) =>
% 107.13/14.51 ((
% 107.13/14.51 (singletoninpowunion) =>
% 107.13/14.51 ((
% 107.13/14.51 (upairset2E) =>
% 107.13/14.51 ((
% 107.13/14.51 (upairsubunion) =>
% 107.13/14.51 ((
% 107.13/14.51 (upairinpowunion) =>
% 107.13/14.51 ((
% 107.13/14.51 (ubforcartprodlem1) =>
% 107.13/14.51 ((
% 107.13/14.51 (ubforcartprodlem2) =>
% 107.13/14.51 ((
% 107.13/14.51 (ubforcartprodlem3) =>
% 107.13/14.51 ((
% 107.13/14.51 (cartprodpairin) =>
% 107.13/14.51 ((
% 107.13/14.51 (cartprodmempair1) =>
% 107.13/14.51 ((
% 107.13/14.51 (cartprodmempair) =>
% 107.13/14.51 ((
% 107.13/14.51 (setunionE2) =>
% 107.13/14.51 ((
% 107.13/14.51 (setunionsingleton1) =>
% 107.13/14.51 ((
% 107.13/14.51 (setunionsingleton2) =>
% 107.13/14.51 ((
% 107.13/14.51 (setunionsingleton) =>
% 107.13/14.51 ((
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% 107.13/14.51 ((
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% 107.13/14.51 ((
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% 107.13/14.51 ((
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% 107.13/14.51 ((
% 107.13/14.51 (singletonsuniq) =>
% 107.13/14.51 ((
% 107.13/14.51 (setukpairinjL1) =>
% 107.13/14.51 ((
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% 107.13/14.51 ((
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% 107.13/14.51 ((
% 107.13/14.51 (kfstpairEq) =>
% 107.13/14.51 ((
% 107.13/14.51 (cartprodfstin) =>
% 107.13/14.51 ((
% 107.13/14.51 (setukpairinjL2) =>
% 107.13/14.51 ((
% 107.13/14.51 (setukpairinjL) =>
% 107.13/14.51 ((
% 107.13/14.51 (setukpairinjR11) =>
% 107.13/14.51 ((
% 107.13/14.51 (setukpairinjR12) =>
% 107.13/14.51 ((
% 107.13/14.51 (setukpairinjR1) =>
% 107.13/14.51 ((
% 107.13/14.51 (upairequniteq) =>
% 107.13/14.51 ((
% 107.13/14.51 (setukpairinjR2) =>
% 107.13/14.51 ((
% 107.13/14.51 (setukpairinjR) =>
% 107.13/14.51 ((
% 107.13/14.51 (ksndsingleton) =>
% 107.13/14.51 ((
% 107.13/14.51 (ksndpairEq) =>
% 107.13/14.51 ((
% 107.13/14.51 (kpairsurjEq) =>
% 107.13/14.51 ((
% 107.13/14.51 (cartprodsndin) =>
% 107.13/14.51 ((
% 107.13/14.51 (cartprodpairmemEL) =>
% 107.13/14.51 ((
% 107.13/14.51 (cartprodpairmemER) =>
% 107.13/14.51 ((
% 107.13/14.51 (cartprodmempaircEq) =>
% 107.13/14.51 ((
% 107.13/14.51 (cartprodfstpairEq) =>
% 107.13/14.51 ((
% 107.13/14.51 (cartprodsndpairEq) =>
% 107.13/14.51 ((
% 107.13/14.51 (cartprodpairsurjEq) =>
% 107.13/14.51 ((
% 107.13/14.51 (dpsetconstrI) =>
% 107.13/14.51 ((
% 107.13/14.51 (dpsetconstrSub) =>
% 107.13/14.51 ((
% 107.13/14.51 (setOfPairsIsBReln) =>
% 107.13/14.51 ((
% 107.13/14.51 (dpsetconstrERa) =>
% 107.13/14.51 ((
% 107.13/14.51 (dpsetconstrEL1) =>
% 107.13/14.51 ((
% 107.13/14.51 (dpsetconstrEL2) =>
% 107.13/14.51 ((
% 107.13/14.51 (dpsetconstrER) =>
% 107.13/14.51 ((
% 107.13/14.51 (funcImageSingleton) =>
% 107.13/14.51 ((
% 107.13/14.51 (apProp) =>
% 107.13/14.51 ((
% 107.13/14.51 (app) =>
% 107.13/14.51 ((
% 107.13/14.51 (infuncsetfunc) =>
% 107.13/14.51 ((
% 107.13/14.51 (ap2p) =>
% 107.13/14.51 ((
% 107.13/14.51 (funcinfuncset) =>
% 107.13/14.51 ((
% 107.13/14.51 (lamProp) =>
% 107.13/14.51 ((
% 107.13/14.51 (lamp) =>
% 107.13/14.51 ((
% 107.13/14.51 (lam2p) =>
% 107.13/14.51 ((
% 107.13/14.51 (brelnall1) =>
% 107.13/14.51 ((
% 107.13/14.51 (brelnall2) =>
% 107.13/14.51 ((
% 107.13/14.51 (ex1E2) =>
% 107.13/14.51 ((
% 107.13/14.51 (funcGraphProp1) =>
% 107.13/14.51 ((
% 107.13/14.51 (funcGraphProp3) =>
% 107.13/14.51 ((
% 107.13/14.51 (funcGraphProp2) =>
% 107.13/14.51 ((
% 107.13/14.51 (funcextLem) =>
% 107.13/14.51 ((
% 107.13/14.51 (funcGraphProp4) =>
% 107.13/14.51 ((
% 107.13/14.51 (subbreln) =>
% 107.13/14.51 ((
% 107.13/14.51 (eqbreln) =>
% 107.13/14.51 ((
% 107.13/14.51 (funcext) =>
% 107.13/14.51 ((
% 107.13/14.51 (funcext2) =>
% 107.13/14.51 ((
% 107.13/14.51 (ap2apEq1) =>
% 107.13/14.51 ((
% 107.13/14.51 (ap2apEq2) =>
% 107.13/14.51 ((
% 107.13/14.51 (beta1) =>
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% 107.13/14.51 (breln1unionCommutes) =>
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% 107.13/14.51 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1027])).
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% 107.13/14.51 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1067])).
% 107.13/14.51 thf(zip_derived_cl1082, plain,
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% 107.13/14.51 ((
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% 107.13/14.51 ((
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% 107.13/14.51 ((
% 107.13/14.51 (setukpairinjR1) =>
% 107.13/14.51 ((
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% 107.13/14.51 ((
% 107.13/14.51 (kpairsurjEq) =>
% 107.13/14.51 ((
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% 107.13/14.51 ((
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% 107.13/14.51 ((
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% 107.13/14.51 ((
% 107.13/14.51 (cartprodmempaircEq) =>
% 107.13/14.51 ((
% 107.13/14.51 (cartprodfstpairEq) =>
% 107.13/14.51 ((
% 107.13/14.51 (cartprodsndpairEq) =>
% 107.13/14.51 ((
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% 107.13/14.51 ((
% 107.13/14.51 (lamp) =>
% 107.13/14.51 ((
% 107.13/14.51 (lam2p) =>
% 107.13/14.51 ((
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% 107.13/14.51 ((
% 107.13/14.51 (brelnall2) =>
% 107.13/14.51 ((
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% 107.13/14.51 ((
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% 107.13/14.51 ((
% 107.13/14.51 (funcGraphProp3) =>
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% 107.13/14.51 (funcGraphProp2) =>
% 107.13/14.51 ((
% 107.13/14.51 (funcextLem) =>
% 107.13/14.51 ((
% 107.13/14.51 (funcGraphProp4) =>
% 107.13/14.51 ((
% 107.13/14.51 (subbreln) =>
% 107.13/14.51 ((
% 107.13/14.51 (eqbreln) =>
% 107.13/14.51 ((
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% 107.13/14.51 (funcext2) =>
% 107.13/14.51 ((
% 107.13/14.51 (ap2apEq1) =>
% 107.13/14.51 ((
% 107.13/14.51 (ap2apEq2) =>
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% 107.13/14.51 ((
% 107.13/14.51 (eta1) =>
% 107.13/14.51 ((
% 107.13/14.51 (lam2lamEq) =>
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% 107.13/14.51 (beta2) =>
% 107.13/14.51 ((
% 107.13/14.51 (eta2) =>
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% 107.13/14.51 ((
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% 107.13/14.51 ((
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% 107.13/14.51 ((
% 107.13/14.51 (binintersectTERcontra) =>
% 107.13/14.51 ((
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% 107.13/14.51 ((
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% 107.13/14.51 ((
% 107.13/14.51 (contrasubsetT2) =>
% 107.13/14.51 ((
% 107.13/14.51 (contrasubsetT3) =>
% 107.13/14.51 ((
% 107.13/14.51 (doubleComplementI1) =>
% 107.13/14.51 ((
% 107.13/14.51 (doubleComplementE1) =>
% 107.13/14.51 ((
% 107.13/14.51 (doubleComplementSub1) =>
% 107.13/14.51 ((
% 107.13/14.51 (doubleComplementSub2) =>
% 107.13/14.51 ((
% 107.13/14.51 (doubleComplementEq) =>
% 107.13/14.51 ((
% 107.13/14.51 (complementTnotintersectT) =>
% 107.13/14.51 ((
% 107.13/14.51 (complementImpComplementIntersect) =>
% 107.13/14.51 ((
% 107.13/14.51 (complementSubsetComplementIntersect) =>
% 107.13/14.51 ((
% 107.13/14.51 (complementInPowersetComplementIntersect) =>
% 107.13/14.51 ((
% 107.13/14.51 (contraSubsetComplement) =>
% 107.13/14.51 ((
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% 107.13/14.51 ((
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% 107.13/14.51 ((
% 107.13/14.51 (inIntersectImpInUnion2) =>
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% 107.13/14.51 (inComplementUnionImpNotIn1) =>
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% 107.13/14.51 (inComplementUnionImpInComplement1) =>
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% 107.13/14.51 ((
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% 107.13/14.51 ((
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% 107.13/14.51 ((
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% 107.13/14.51 ((
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% 107.13/14.51 ((
% 107.13/14.51 (demorgan2b) =>
% 107.13/14.51 ((
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% 107.13/14.51 ((
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% 107.13/14.51 ((
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% 107.13/14.51 ((
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% 107.13/14.51 ((
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% 107.13/14.51 ((
% 107.13/14.51 (woz13rule4) =>
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% 107.13/14.51 ((
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% 107.13/14.51 ((
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% 107.13/14.51 ((
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% 107.13/14.51 ((
% 107.13/14.51 (woz1_5) =>
% 107.13/14.51 ((
% 107.13/14.51 (breln1all2) =>
% 107.13/14.51 ((
% 107.13/14.51 (breln1SetBreln1) =>
% 107.13/14.51 ((
% 107.13/14.51 (choice2fnsingleton) =>
% 107.13/14.51 ((
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% 107.13/14.51 ((
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% 107.13/14.51 ((
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% 107.13/14.51 ((
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% 107.13/14.51 ((
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% 107.13/14.51 ((
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% 107.13/14.52 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1074])).
% 107.13/14.52 thf(zip_derived_cl1090, plain,
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% 107.13/14.52 (ubforcartprodlem2) =>
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% 107.13/14.52 (ubforcartprodlem3) =>
% 107.13/14.52 ((
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% 107.13/14.52 ((
% 107.13/14.52 (cartprodmempair1) =>
% 107.13/14.52 ((
% 107.13/14.52 (cartprodmempair) =>
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% 107.13/14.52 (setunionsingleton2) =>
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% 107.13/14.52 ((
% 107.13/14.52 (kfstpairEq) =>
% 107.13/14.52 ((
% 107.13/14.52 (cartprodfstin) =>
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% 107.13/14.52 (setukpairinjL) =>
% 107.13/14.52 ((
% 107.13/14.52 (setukpairinjR11) =>
% 107.13/14.52 ((
% 107.13/14.52 (setukpairinjR12) =>
% 107.13/14.52 ((
% 107.13/14.52 (setukpairinjR1) =>
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% 107.13/14.52 (cartprodpairmemEL) =>
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% 107.13/14.52 (cartprodpairmemER) =>
% 107.13/14.52 ((
% 107.13/14.52 (cartprodmempaircEq) =>
% 107.13/14.52 ((
% 107.13/14.52 (cartprodfstpairEq) =>
% 107.13/14.52 ((
% 107.13/14.52 (cartprodsndpairEq) =>
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% 107.13/14.52 (cartprodpairsurjEq) =>
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% 107.13/14.52 (dpsetconstrSub) =>
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% 107.13/14.52 (dpsetconstrEL2) =>
% 107.13/14.52 ((
% 107.13/14.52 (dpsetconstrER) =>
% 107.13/14.52 ((
% 107.13/14.52 (funcImageSingleton) =>
% 107.13/14.52 ((
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% 107.13/14.52 ((
% 107.13/14.52 (app) =>
% 107.13/14.52 ((
% 107.13/14.52 (infuncsetfunc) =>
% 107.13/14.52 ((
% 107.13/14.52 (ap2p) =>
% 107.13/14.52 ((
% 107.13/14.52 (funcinfuncset) =>
% 107.13/14.52 ((
% 107.13/14.52 (lamProp) =>
% 107.13/14.52 ((
% 107.13/14.52 (lamp) =>
% 107.13/14.52 ((
% 107.13/14.52 (lam2p) =>
% 107.13/14.52 ((
% 107.13/14.52 (brelnall1) =>
% 107.13/14.52 ((
% 107.13/14.52 (brelnall2) =>
% 107.13/14.52 ((
% 107.13/14.52 (ex1E2) =>
% 107.13/14.52 ((
% 107.13/14.52 (funcGraphProp1) =>
% 107.13/14.52 ((
% 107.13/14.52 (funcGraphProp3) =>
% 107.13/14.52 ((
% 107.13/14.52 (funcGraphProp2) =>
% 107.13/14.52 ((
% 107.13/14.52 (funcextLem) =>
% 107.13/14.52 ((
% 107.13/14.52 (funcGraphProp4) =>
% 107.13/14.52 ((
% 107.13/14.52 (subbreln) =>
% 107.13/14.52 ((
% 107.13/14.52 (eqbreln) =>
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% 107.13/14.52 (funcext2) =>
% 107.13/14.52 ((
% 107.13/14.52 (ap2apEq1) =>
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% 107.13/14.52 (ap2apEq2) =>
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% 107.13/14.52 (eta1) =>
% 107.13/14.52 ((
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% 107.13/14.52 (beta2) =>
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% 107.13/14.52 (eta2) =>
% 107.13/14.52 ((
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% 107.13/14.52 (iffalseProp2) =>
% 107.13/14.52 ((
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% 107.13/14.52 (iftrueProp2) =>
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% 107.13/14.52 ((
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% 107.13/14.52 ((
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% 107.13/14.52 ((
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% 107.13/14.52 ((
% 107.13/14.52 (complementTE1) =>
% 107.13/14.52 ((
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% 107.13/14.52 ((
% 107.13/14.52 (binintersectTERcontra) =>
% 107.13/14.52 ((
% 107.13/14.52 (contrasubsetT) =>
% 107.13/14.52 ((
% 107.13/14.52 (contrasubsetT1) =>
% 107.13/14.52 ((
% 107.13/14.52 (contrasubsetT2) =>
% 107.13/14.52 ((
% 107.13/14.52 (contrasubsetT3) =>
% 107.13/14.52 ((
% 107.13/14.52 (doubleComplementI1) =>
% 107.13/14.52 ((
% 107.13/14.52 (doubleComplementE1) =>
% 107.13/14.52 ((
% 107.13/14.52 (doubleComplementSub1) =>
% 107.13/14.52 ((
% 107.13/14.52 (doubleComplementSub2) =>
% 107.13/14.52 ((
% 107.13/14.52 (doubleComplementEq) =>
% 107.13/14.52 ((
% 107.13/14.52 (complementTnotintersectT) =>
% 107.13/14.52 ((
% 107.13/14.52 (complementImpComplementIntersect) =>
% 107.13/14.52 ((
% 107.13/14.52 (complementSubsetComplementIntersect) =>
% 107.13/14.52 ((
% 107.13/14.52 (complementInPowersetComplementIntersect) =>
% 107.13/14.52 ((
% 107.13/14.52 (contraSubsetComplement) =>
% 107.13/14.52 ((
% 107.13/14.52 (complementTcontraSubset) =>
% 107.13/14.52 ((
% 107.13/14.52 (binunionTILcontra) =>
% 107.13/14.52 ((
% 107.13/14.52 (binunionTIRcontra) =>
% 107.13/14.52 ((
% 107.13/14.52 (inIntersectImpInUnion) =>
% 107.13/14.52 ((
% 107.13/14.52 (inIntersectImpInUnion2) =>
% 107.13/14.52 ((
% 107.13/14.52 (inIntersectImpInIntersectUnions) =>
% 107.13/14.52 ((
% 107.13/14.52 (intersectInPowersetIntersectUnions) =>
% 107.13/14.52 ((
% 107.13/14.52 (inComplementUnionImpNotIn1) =>
% 107.13/14.52 ((
% 107.13/14.52 (inComplementUnionImpInComplement1) =>
% 107.13/14.52 ((
% 107.13/14.52 (binunionTE) =>
% 107.13/14.52 ((
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% 107.13/14.52 ((
% 107.13/14.52 (demorgan2a1) =>
% 107.13/14.52 ((
% 107.13/14.52 (complementUnionInPowersetComplement) =>
% 107.13/14.52 ((
% 107.13/14.52 (demorgan2a2) =>
% 107.13/14.52 ((
% 107.13/14.52 (demorgan1a) =>
% 107.13/14.52 ((
% 107.13/14.52 (demorgan1b) =>
% 107.13/14.52 ((
% 107.13/14.52 (demorgan1) =>
% 107.13/14.52 ((
% 107.13/14.52 (demorgan2a) =>
% 107.13/14.52 ((
% 107.13/14.52 (demorgan2b2) =>
% 107.13/14.52 ((
% 107.13/14.52 (demorgan2b) =>
% 107.13/14.52 ((
% 107.13/14.52 (demorgan2) =>
% 107.13/14.52 ((
% 107.13/14.52 (woz13rule0) =>
% 107.13/14.52 ((
% 107.13/14.52 (woz13rule1) =>
% 107.13/14.52 ((
% 107.13/14.52 (woz13rule2) =>
% 107.13/14.52 ((
% 107.13/14.52 (woz13rule3) =>
% 107.13/14.52 ((
% 107.13/14.52 (woz13rule4) =>
% 107.13/14.52 ((
% 107.13/14.52 (woz1_1) =>
% 107.13/14.52 ((
% 107.13/14.52 (woz1_2) =>
% 107.13/14.52 ((
% 107.13/14.52 (woz1_3) =>
% 107.13/14.52 ((
% 107.13/14.52 (woz1_4) =>
% 107.13/14.52 ((
% 107.13/14.52 (woz1_5) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1all2) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1SetBreln1) =>
% 107.13/14.52 ((
% 107.13/14.52 (choice2fnsingleton) =>
% 107.13/14.52 ((
% 107.13/14.52 (setOfPairsIsBReln1) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1all1) =>
% 107.13/14.52 ((
% 107.13/14.52 (subbreln1) =>
% 107.13/14.52 ((
% 107.13/14.52 (eqbreln1) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1invprop) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1invI) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1invE) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1compprop) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1compI) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1compE) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1compEex) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1unionprop) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1unionIL) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1unionIR) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1unionI) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1unionE) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1unionEcases) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1unionCommutes) =>
% 107.13/14.52 ((
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% 107.13/14.52 ((
% 107.13/14.52 (woz2W) =>
% 107.13/14.52 ((
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% 107.13/14.52 ((
% 107.13/14.52 (image1Ex1) =>
% 107.13/14.52 ((
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% 107.13/14.52 ((
% 107.13/14.52 (image1E) =>
% 107.13/14.52 ((
% 107.13/14.52 (image1I) =>
% 107.13/14.52 ((
% 107.13/14.52 (injFuncInInjFuncSet) =>
% 107.13/14.52 ((
% 107.13/14.52 (injFuncSetFuncIn) =>
% 107.13/14.52 ((
% 107.13/14.52 (injFuncSetFuncInj) =>
% 107.13/14.52 ((
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% 107.13/14.52 ((
% 107.13/14.52 (surjFuncSetFuncSurj) =>
% 107.13/14.52 ((
% 107.13/14.52 (leftInvIsSurj) =>
% 107.13/14.52 ((
% 107.13/14.52 (surjCantorThm) =>
% 107.13/14.52 ((
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% 107.13/14.52 (('#S') @ (
% 107.13/14.52 (
% 107.13/14.52 ('#B') @ (
% 107.13/14.52 =>) @
% 107.13/14.52 nonempty)) @
% 107.13/14.52 (
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% 107.13/14.52 ('#B') @ (
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% 107.13/14.52 (
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% 107.13/14.52 ('#B') @ (
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% 107.13/14.52 (
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% 107.13/14.52 (
% 107.13/14.52 (
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% 107.13/14.52 (
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% 107.13/14.52 (
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% 107.13/14.52 =))) @
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% 107.13/14.52 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 107.13/14.52 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1082])).
% 107.13/14.52 thf(zip_derived_cl1096, plain,
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% 107.13/14.52 ((
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% 107.13/14.52 ((
% 107.13/14.52 (symdiffIneg2) =>
% 107.13/14.52 ((
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% 107.13/14.52 ((
% 107.13/14.52 (setukpairIL) =>
% 107.13/14.52 ((
% 107.13/14.52 (setukpairIR) =>
% 107.13/14.52 ((
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% 107.13/14.52 ((
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% 107.13/14.52 ((
% 107.13/14.52 (singletoninpowunion) =>
% 107.13/14.52 ((
% 107.13/14.52 (upairset2E) =>
% 107.13/14.52 ((
% 107.13/14.52 (upairsubunion) =>
% 107.13/14.52 ((
% 107.13/14.52 (upairinpowunion) =>
% 107.13/14.52 ((
% 107.13/14.52 (ubforcartprodlem1) =>
% 107.13/14.52 ((
% 107.13/14.52 (ubforcartprodlem2) =>
% 107.13/14.52 ((
% 107.13/14.52 (ubforcartprodlem3) =>
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% 107.13/14.52 (cartprodmempair) =>
% 107.13/14.52 ((
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% 107.13/14.52 ((
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% 107.13/14.52 ((
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% 107.13/14.52 ((
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% 107.13/14.52 ((
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% 107.13/14.52 ((
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% 107.13/14.52 ((
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% 107.13/14.52 ((
% 107.13/14.52 (setukpairinjR2) =>
% 107.13/14.52 ((
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% 107.13/14.52 ((
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% 107.13/14.52 ((
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% 107.13/14.52 ((
% 107.13/14.52 (kpairsurjEq) =>
% 107.13/14.52 ((
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% 107.13/14.52 ((
% 107.13/14.52 (cartprodpairmemEL) =>
% 107.13/14.52 ((
% 107.13/14.52 (cartprodpairmemER) =>
% 107.13/14.52 ((
% 107.13/14.52 (cartprodmempaircEq) =>
% 107.13/14.52 ((
% 107.13/14.52 (cartprodfstpairEq) =>
% 107.13/14.52 ((
% 107.13/14.52 (cartprodsndpairEq) =>
% 107.13/14.52 ((
% 107.13/14.52 (cartprodpairsurjEq) =>
% 107.13/14.52 ((
% 107.13/14.52 (dpsetconstrI) =>
% 107.13/14.52 ((
% 107.13/14.52 (dpsetconstrSub) =>
% 107.13/14.52 ((
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% 107.13/14.52 ((
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% 107.13/14.52 ((
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% 107.13/14.52 (funcImageSingleton) =>
% 107.13/14.52 ((
% 107.13/14.52 (apProp) =>
% 107.13/14.52 ((
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% 107.13/14.52 ((
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% 107.13/14.52 ((
% 107.13/14.52 (ap2p) =>
% 107.13/14.52 ((
% 107.13/14.52 (funcinfuncset) =>
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% 107.13/14.52 ((
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% 107.13/14.52 ((
% 107.13/14.52 (lam2p) =>
% 107.13/14.52 ((
% 107.13/14.52 (brelnall1) =>
% 107.13/14.52 ((
% 107.13/14.52 (brelnall2) =>
% 107.13/14.52 ((
% 107.13/14.52 (ex1E2) =>
% 107.13/14.52 ((
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% 107.13/14.52 ((
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% 107.13/14.52 ((
% 107.13/14.52 (funcGraphProp2) =>
% 107.13/14.52 ((
% 107.13/14.52 (funcextLem) =>
% 107.13/14.52 ((
% 107.13/14.52 (funcGraphProp4) =>
% 107.13/14.52 ((
% 107.13/14.52 (subbreln) =>
% 107.13/14.52 ((
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% 107.13/14.52 (funcext2) =>
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% 107.13/14.52 (ap2apEq1) =>
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% 107.13/14.52 (ap2apEq2) =>
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% 107.13/14.52 (beta1) =>
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% 107.13/14.52 ((
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% 107.13/14.52 ((
% 107.13/14.52 (contrasubsetT2) =>
% 107.13/14.52 ((
% 107.13/14.52 (contrasubsetT3) =>
% 107.13/14.52 ((
% 107.13/14.52 (doubleComplementI1) =>
% 107.13/14.52 ((
% 107.13/14.52 (doubleComplementE1) =>
% 107.13/14.52 ((
% 107.13/14.52 (doubleComplementSub1) =>
% 107.13/14.52 ((
% 107.13/14.52 (doubleComplementSub2) =>
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% 107.13/14.52 (doubleComplementEq) =>
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% 107.13/14.52 (complementTnotintersectT) =>
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% 107.13/14.52 (complementImpComplementIntersect) =>
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% 107.13/14.52 (complementInPowersetComplementIntersect) =>
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% 107.13/14.52 (contraSubsetComplement) =>
% 107.13/14.52 ((
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% 107.13/14.52 ((
% 107.13/14.52 (binunionTIRcontra) =>
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% 107.13/14.52 ((
% 107.13/14.52 (inIntersectImpInUnion2) =>
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% 107.13/14.52 (intersectInPowersetIntersectUnions) =>
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% 107.13/14.52 (inComplementUnionImpNotIn1) =>
% 107.13/14.52 ((
% 107.13/14.52 (inComplementUnionImpInComplement1) =>
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% 107.13/14.52 (demorgan2a2) =>
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% 107.13/14.52 (demorgan1b) =>
% 107.13/14.52 ((
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% 107.13/14.52 ((
% 107.13/14.52 (demorgan2a) =>
% 107.13/14.52 ((
% 107.13/14.52 (demorgan2b2) =>
% 107.13/14.52 ((
% 107.13/14.52 (demorgan2b) =>
% 107.13/14.52 ((
% 107.13/14.52 (demorgan2) =>
% 107.13/14.52 ((
% 107.13/14.52 (woz13rule0) =>
% 107.13/14.52 ((
% 107.13/14.52 (woz13rule1) =>
% 107.13/14.52 ((
% 107.13/14.52 (woz13rule2) =>
% 107.13/14.52 ((
% 107.13/14.52 (woz13rule3) =>
% 107.13/14.52 ((
% 107.13/14.52 (woz13rule4) =>
% 107.13/14.52 ((
% 107.13/14.52 (woz1_1) =>
% 107.13/14.52 ((
% 107.13/14.52 (woz1_2) =>
% 107.13/14.52 ((
% 107.13/14.52 (woz1_3) =>
% 107.13/14.52 ((
% 107.13/14.52 (woz1_4) =>
% 107.13/14.52 ((
% 107.13/14.52 (woz1_5) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1all2) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1SetBreln1) =>
% 107.13/14.52 ((
% 107.13/14.52 (choice2fnsingleton) =>
% 107.13/14.52 ((
% 107.13/14.52 (setOfPairsIsBReln1) =>
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% 107.13/14.52 (breln1all1) =>
% 107.13/14.52 ((
% 107.13/14.52 (subbreln1) =>
% 107.13/14.52 ((
% 107.13/14.52 (eqbreln1) =>
% 107.13/14.52 ((
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% 107.13/14.52 ((
% 107.13/14.52 (breln1invI) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1invE) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1compprop) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1compI) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1compE) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1compEex) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1unionprop) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1unionIL) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1unionIR) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1unionI) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1unionE) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1unionEcases) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1unionCommutes) =>
% 107.13/14.52 ((
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% 107.13/14.52 ((
% 107.13/14.52 (woz2W) =>
% 107.13/14.52 ((
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% 107.13/14.52 (woz2B) =>
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% 107.13/14.52 ((
% 107.13/14.52 (image1Ex1) =>
% 107.13/14.52 ((
% 107.13/14.52 (image1Equiv) =>
% 107.13/14.52 ((
% 107.13/14.52 (image1E) =>
% 107.13/14.52 ((
% 107.13/14.52 (image1I) =>
% 107.13/14.52 ((
% 107.13/14.52 (injFuncInInjFuncSet) =>
% 107.13/14.52 ((
% 107.13/14.52 (injFuncSetFuncIn) =>
% 107.13/14.52 ((
% 107.13/14.52 (injFuncSetFuncInj) =>
% 107.13/14.52 ((
% 107.13/14.52 (surjFuncSetFuncIn) =>
% 107.13/14.52 ((
% 107.13/14.52 (surjFuncSetFuncSurj) =>
% 107.13/14.52 ((
% 107.13/14.52 (leftInvIsSurj) =>
% 107.13/14.52 ((
% 107.13/14.52 (surjCantorThm) =>
% 107.13/14.52 ((
% 107.13/14.52 (!!) @ (
% 107.13/14.52 (('#S') @ (
% 107.13/14.52 (
% 107.13/14.52 ('#B') @ (
% 107.13/14.52 =>) @
% 107.13/14.52 nonempty)) @
% 107.13/14.52 (
% 107.13/14.52 (
% 107.13/14.52 ('#B') @ (
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% 107.13/14.52 (
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% 107.13/14.52 ('#B') @ (
% 107.13/14.52 &))) @
% 107.13/14.52 (
% 107.13/14.52 (
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% 107.13/14.52 (
% 107.13/14.52 (
% 107.13/14.52 ('#C') @ (
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% 107.13/14.52 (
% 107.13/14.52 ('#B') @ (
% 107.13/14.52 (
% 107.13/14.52 ('#B') @ (
% 107.13/14.52 =))) @
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% 107.13/14.52 (
% 107.13/14.52 ('#C') @ binintersect)))))) @
% 107.13/14.52 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 107.13/14.52 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1090])).
% 107.13/14.52 thf(zip_derived_cl1102, plain,
% 107.13/14.52 (~ (((upairset2IR) =>
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% 107.13/14.52 (((binintersectRsub) =>
% 107.13/14.52 (((binintersectSubset4) =>
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% 107.13/14.52 ((
% 107.13/14.52 (symdiffIneg2) =>
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% 107.13/14.52 ((
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% 107.13/14.52 ((
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% 107.13/14.52 ((
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% 107.13/14.52 ((
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% 107.13/14.52 ((
% 107.13/14.52 (ubforcartprodlem1) =>
% 107.13/14.52 ((
% 107.13/14.52 (ubforcartprodlem2) =>
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% 107.13/14.52 (ubforcartprodlem3) =>
% 107.13/14.52 ((
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% 107.13/14.52 ((
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% 107.13/14.52 ((
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% 107.13/14.52 ((
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% 107.13/14.52 ((
% 107.13/14.52 (kpairsurjEq) =>
% 107.13/14.52 ((
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% 107.13/14.52 ((
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% 107.13/14.52 ((
% 107.13/14.52 (cartprodpairmemER) =>
% 107.13/14.52 ((
% 107.13/14.52 (cartprodmempaircEq) =>
% 107.13/14.52 ((
% 107.13/14.52 (cartprodfstpairEq) =>
% 107.13/14.52 ((
% 107.13/14.52 (cartprodsndpairEq) =>
% 107.13/14.52 ((
% 107.13/14.52 (cartprodpairsurjEq) =>
% 107.13/14.52 ((
% 107.13/14.52 (dpsetconstrI) =>
% 107.13/14.52 ((
% 107.13/14.52 (dpsetconstrSub) =>
% 107.13/14.52 ((
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% 107.13/14.52 ((
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% 107.13/14.52 ((
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% 107.13/14.52 ((
% 107.13/14.52 (brelnall1) =>
% 107.13/14.52 ((
% 107.13/14.52 (brelnall2) =>
% 107.13/14.52 ((
% 107.13/14.52 (ex1E2) =>
% 107.13/14.52 ((
% 107.13/14.52 (funcGraphProp1) =>
% 107.13/14.52 ((
% 107.13/14.52 (funcGraphProp3) =>
% 107.13/14.52 ((
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% 107.13/14.52 ((
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% 107.13/14.52 ((
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% 107.13/14.52 ((
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% 107.13/14.52 ((
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% 107.13/14.52 ((
% 107.13/14.52 (funcext2) =>
% 107.13/14.52 ((
% 107.13/14.52 (ap2apEq1) =>
% 107.13/14.52 ((
% 107.13/14.52 (ap2apEq2) =>
% 107.13/14.52 ((
% 107.13/14.52 (beta1) =>
% 107.13/14.52 ((
% 107.13/14.52 (eta1) =>
% 107.13/14.52 ((
% 107.13/14.52 (lam2lamEq) =>
% 107.13/14.52 ((
% 107.13/14.52 (beta2) =>
% 107.13/14.52 ((
% 107.13/14.52 (eta2) =>
% 107.13/14.52 ((
% 107.13/14.52 (iffalseProp1) =>
% 107.13/14.52 ((
% 107.13/14.52 (iffalseProp2) =>
% 107.13/14.52 ((
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% 107.13/14.52 ((
% 107.13/14.52 (iftrueProp2) =>
% 107.13/14.52 ((
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% 107.13/14.52 ((
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% 107.13/14.52 (theeq) =>
% 107.13/14.52 ((
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% 107.13/14.52 ((
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% 107.13/14.52 ((
% 107.13/14.52 (iftrueorfalse) =>
% 107.13/14.52 ((
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% 107.13/14.52 ((
% 107.13/14.52 (binunionT_lem) =>
% 107.13/14.52 ((
% 107.13/14.52 (powersetT_lem) =>
% 107.13/14.52 ((
% 107.13/14.52 (setminusT_lem) =>
% 107.13/14.52 ((
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% 107.13/14.52 ((
% 107.13/14.52 (setextT) =>
% 107.13/14.52 ((
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% 107.13/14.52 ((
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% 107.13/14.52 ((
% 107.13/14.52 (powersetTE1) =>
% 107.13/14.52 ((
% 107.13/14.52 (complementTI1) =>
% 107.13/14.52 ((
% 107.13/14.52 (complementTE1) =>
% 107.13/14.52 ((
% 107.13/14.52 (binintersectTELcontra) =>
% 107.13/14.52 ((
% 107.13/14.52 (binintersectTERcontra) =>
% 107.13/14.52 ((
% 107.13/14.52 (contrasubsetT) =>
% 107.13/14.52 ((
% 107.13/14.52 (contrasubsetT1) =>
% 107.13/14.52 ((
% 107.13/14.52 (contrasubsetT2) =>
% 107.13/14.52 ((
% 107.13/14.52 (contrasubsetT3) =>
% 107.13/14.52 ((
% 107.13/14.52 (doubleComplementI1) =>
% 107.13/14.52 ((
% 107.13/14.52 (doubleComplementE1) =>
% 107.13/14.52 ((
% 107.13/14.52 (doubleComplementSub1) =>
% 107.13/14.52 ((
% 107.13/14.52 (doubleComplementSub2) =>
% 107.13/14.52 ((
% 107.13/14.52 (doubleComplementEq) =>
% 107.13/14.52 ((
% 107.13/14.52 (complementTnotintersectT) =>
% 107.13/14.52 ((
% 107.13/14.52 (complementImpComplementIntersect) =>
% 107.13/14.52 ((
% 107.13/14.52 (complementSubsetComplementIntersect) =>
% 107.13/14.52 ((
% 107.13/14.52 (complementInPowersetComplementIntersect) =>
% 107.13/14.52 ((
% 107.13/14.52 (contraSubsetComplement) =>
% 107.13/14.52 ((
% 107.13/14.52 (complementTcontraSubset) =>
% 107.13/14.52 ((
% 107.13/14.52 (binunionTILcontra) =>
% 107.13/14.52 ((
% 107.13/14.52 (binunionTIRcontra) =>
% 107.13/14.52 ((
% 107.13/14.52 (inIntersectImpInUnion) =>
% 107.13/14.52 ((
% 107.13/14.52 (inIntersectImpInUnion2) =>
% 107.13/14.52 ((
% 107.13/14.52 (inIntersectImpInIntersectUnions) =>
% 107.13/14.52 ((
% 107.13/14.52 (intersectInPowersetIntersectUnions) =>
% 107.13/14.52 ((
% 107.13/14.52 (inComplementUnionImpNotIn1) =>
% 107.13/14.52 ((
% 107.13/14.52 (inComplementUnionImpInComplement1) =>
% 107.13/14.52 ((
% 107.13/14.52 (binunionTE) =>
% 107.13/14.52 ((
% 107.13/14.52 (binunionTEcontra) =>
% 107.13/14.52 ((
% 107.13/14.52 (demorgan2a1) =>
% 107.13/14.52 ((
% 107.13/14.52 (complementUnionInPowersetComplement) =>
% 107.13/14.52 ((
% 107.13/14.52 (demorgan2a2) =>
% 107.13/14.52 ((
% 107.13/14.52 (demorgan1a) =>
% 107.13/14.52 ((
% 107.13/14.52 (demorgan1b) =>
% 107.13/14.52 ((
% 107.13/14.52 (demorgan1) =>
% 107.13/14.52 ((
% 107.13/14.52 (demorgan2a) =>
% 107.13/14.52 ((
% 107.13/14.52 (demorgan2b2) =>
% 107.13/14.52 ((
% 107.13/14.52 (demorgan2b) =>
% 107.13/14.52 ((
% 107.13/14.52 (demorgan2) =>
% 107.13/14.52 ((
% 107.13/14.52 (woz13rule0) =>
% 107.13/14.52 ((
% 107.13/14.52 (woz13rule1) =>
% 107.13/14.52 ((
% 107.13/14.52 (woz13rule2) =>
% 107.13/14.52 ((
% 107.13/14.52 (woz13rule3) =>
% 107.13/14.52 ((
% 107.13/14.52 (woz13rule4) =>
% 107.13/14.52 ((
% 107.13/14.52 (woz1_1) =>
% 107.13/14.52 ((
% 107.13/14.52 (woz1_2) =>
% 107.13/14.52 ((
% 107.13/14.52 (woz1_3) =>
% 107.13/14.52 ((
% 107.13/14.52 (woz1_4) =>
% 107.13/14.52 ((
% 107.13/14.52 (woz1_5) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1all2) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1SetBreln1) =>
% 107.13/14.52 ((
% 107.13/14.52 (choice2fnsingleton) =>
% 107.13/14.52 ((
% 107.13/14.52 (setOfPairsIsBReln1) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1all1) =>
% 107.13/14.52 ((
% 107.13/14.52 (subbreln1) =>
% 107.13/14.52 ((
% 107.13/14.52 (eqbreln1) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1invprop) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1invI) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1invE) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1compprop) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1compI) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1compE) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1compEex) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1unionprop) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1unionIL) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1unionIR) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1unionI) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1unionE) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1unionEcases) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1unionCommutes) =>
% 107.13/14.52 ((
% 107.13/14.52 (woz2Ex) =>
% 107.13/14.52 ((
% 107.13/14.52 (woz2W) =>
% 107.13/14.52 ((
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% 107.13/14.52 ((
% 107.13/14.52 (woz2B) =>
% 107.13/14.52 ((
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% 107.13/14.52 ((
% 107.13/14.52 (image1Ex1) =>
% 107.13/14.52 ((
% 107.13/14.52 (image1Equiv) =>
% 107.13/14.52 ((
% 107.13/14.52 (image1E) =>
% 107.13/14.52 ((
% 107.13/14.52 (image1I) =>
% 107.13/14.52 ((
% 107.13/14.52 (injFuncInInjFuncSet) =>
% 107.13/14.52 ((
% 107.13/14.52 (injFuncSetFuncIn) =>
% 107.13/14.52 ((
% 107.13/14.52 (injFuncSetFuncInj) =>
% 107.13/14.52 ((
% 107.13/14.52 (surjFuncSetFuncIn) =>
% 107.13/14.52 ((
% 107.13/14.52 (surjFuncSetFuncSurj) =>
% 107.13/14.52 ((
% 107.13/14.52 (leftInvIsSurj) =>
% 107.13/14.52 ((
% 107.13/14.52 (surjCantorThm) =>
% 107.13/14.52 ((
% 107.13/14.52 (!!) @ (
% 107.13/14.52 (('#S') @ (
% 107.13/14.52 (
% 107.13/14.52 ('#B') @ (
% 107.13/14.52 =>) @
% 107.13/14.52 nonempty)) @
% 107.13/14.52 (
% 107.13/14.52 (
% 107.13/14.52 ('#B') @ (
% 107.13/14.52 ??) @
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% 107.13/14.52 (
% 107.13/14.52 ('#S') @ (
% 107.13/14.52 (
% 107.13/14.52 ('#B') @ (
% 107.13/14.52 '#S') @
% 107.13/14.52 (
% 107.13/14.52 (
% 107.13/14.52 ('#B') @ (
% 107.13/14.52 (
% 107.13/14.52 ('#B') @ (
% 107.13/14.52 &))) @
% 107.13/14.52 (
% 107.13/14.52 (
% 107.13/14.52 ('#C') @ in)))))) @
% 107.13/14.52 (
% 107.13/14.52 (
% 107.13/14.52 ('#C') @ (
% 107.13/14.52 (
% 107.13/14.52 ('#B') @ (
% 107.13/14.52 '#C') @
% 107.13/14.52 (
% 107.13/14.52 (
% 107.13/14.52 ('#B') @ (
% 107.13/14.52 (
% 107.13/14.52 ('#B') @ (
% 107.13/14.52 =))) @
% 107.13/14.52 (
% 107.13/14.52 (
% 107.13/14.52 ('#C') @ binintersect)))))) @
% 107.13/14.52 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 107.13/14.52 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1096])).
% 107.13/14.52 thf(zip_derived_cl1109, plain,
% 107.13/14.52 (~ (((binunionIR) =>
% 107.13/14.52 (((binunionEcases) =>
% 107.13/14.52 (((binunionE) =>
% 107.13/14.52 (((binunionLsub) =>
% 107.13/14.52 (((binunionRsub) =>
% 107.13/14.52 (((binintersectI) =>
% 107.13/14.52 (((binintersectSubset5) =>
% 107.13/14.52 (((binintersectEL) =>
% 107.13/14.52 (((binintersectLsub) =>
% 107.13/14.52 (((binintersectSubset2) =>
% 107.13/14.52 (((binintersectSubset3) =>
% 107.13/14.52 (((binintersectER) =>
% 107.13/14.52 (((disjointsetsI1) =>
% 107.13/14.52 (((binintersectRsub) =>
% 107.13/14.52 (((binintersectSubset4) =>
% 107.13/14.52 (((binintersectSubset1) =>
% 107.13/14.52 (((bs114d) =>
% 107.13/14.52 (((setminusI) =>
% 107.13/14.52 (((setminusEL) =>
% 107.13/14.52 (((setminusER) =>
% 107.13/14.52 (((setminusSubset2) =>
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% 107.13/14.52 (((setminusELneg) =>
% 107.13/14.52 (((setminusILneg) =>
% 107.13/14.52 (((setminusIRneg) =>
% 107.13/14.52 (((setminusLsub) =>
% 107.13/14.52 (((setminusSubset1) =>
% 107.13/14.52 (((symdiffE) =>
% 107.13/14.52 (((symdiffI1) =>
% 107.13/14.52 (((symdiffI2) =>
% 107.13/14.52 ((
% 107.13/14.52 (symdiffIneg1) =>
% 107.13/14.52 ((
% 107.13/14.52 (symdiffIneg2) =>
% 107.13/14.52 ((
% 107.13/14.52 (secondinupair) =>
% 107.13/14.52 ((
% 107.13/14.52 (setukpairIL) =>
% 107.13/14.52 ((
% 107.13/14.52 (setukpairIR) =>
% 107.13/14.52 ((
% 107.13/14.52 (kpairiskpair) =>
% 107.13/14.52 ((
% 107.13/14.52 (kpairp) =>
% 107.13/14.52 ((
% 107.13/14.52 (singletonsubset) =>
% 107.13/14.52 ((
% 107.13/14.52 (singletoninpowerset) =>
% 107.13/14.52 ((
% 107.13/14.52 (singletoninpowunion) =>
% 107.13/14.52 ((
% 107.13/14.52 (upairset2E) =>
% 107.13/14.52 ((
% 107.13/14.52 (upairsubunion) =>
% 107.13/14.52 ((
% 107.13/14.52 (upairinpowunion) =>
% 107.13/14.52 ((
% 107.13/14.52 (ubforcartprodlem1) =>
% 107.13/14.52 ((
% 107.13/14.52 (ubforcartprodlem2) =>
% 107.13/14.52 ((
% 107.13/14.52 (ubforcartprodlem3) =>
% 107.13/14.52 ((
% 107.13/14.52 (cartprodpairin) =>
% 107.13/14.52 ((
% 107.13/14.52 (cartprodmempair1) =>
% 107.13/14.52 ((
% 107.13/14.52 (cartprodmempair) =>
% 107.13/14.52 ((
% 107.13/14.52 (setunionE2) =>
% 107.13/14.52 ((
% 107.13/14.52 (setunionsingleton1) =>
% 107.13/14.52 ((
% 107.13/14.52 (setunionsingleton2) =>
% 107.13/14.52 ((
% 107.13/14.52 (setunionsingleton) =>
% 107.13/14.52 ((
% 107.13/14.52 (singletonprop) =>
% 107.13/14.52 ((
% 107.13/14.52 (ex1E1) =>
% 107.13/14.52 ((
% 107.13/14.52 (ex1I) =>
% 107.13/14.52 ((
% 107.13/14.52 (ex1I2) =>
% 107.13/14.52 ((
% 107.13/14.52 (singletonsuniq) =>
% 107.13/14.52 ((
% 107.13/14.52 (setukpairinjL1) =>
% 107.13/14.52 ((
% 107.13/14.52 (kfstsingleton) =>
% 107.13/14.52 ((
% 107.13/14.52 (theprop) =>
% 107.13/14.52 ((
% 107.13/14.52 (kfstpairEq) =>
% 107.13/14.52 ((
% 107.13/14.52 (cartprodfstin) =>
% 107.13/14.52 ((
% 107.13/14.52 (setukpairinjL2) =>
% 107.13/14.52 ((
% 107.13/14.52 (setukpairinjL) =>
% 107.13/14.52 ((
% 107.13/14.52 (setukpairinjR11) =>
% 107.13/14.52 ((
% 107.13/14.52 (setukpairinjR12) =>
% 107.13/14.52 ((
% 107.13/14.52 (setukpairinjR1) =>
% 107.13/14.52 ((
% 107.13/14.52 (upairequniteq) =>
% 107.13/14.52 ((
% 107.13/14.52 (setukpairinjR2) =>
% 107.13/14.52 ((
% 107.13/14.52 (setukpairinjR) =>
% 107.13/14.52 ((
% 107.13/14.52 (ksndsingleton) =>
% 107.13/14.52 ((
% 107.13/14.52 (ksndpairEq) =>
% 107.13/14.52 ((
% 107.13/14.52 (kpairsurjEq) =>
% 107.13/14.52 ((
% 107.13/14.52 (cartprodsndin) =>
% 107.13/14.52 ((
% 107.13/14.52 (cartprodpairmemEL) =>
% 107.13/14.52 ((
% 107.13/14.52 (cartprodpairmemER) =>
% 107.13/14.52 ((
% 107.13/14.52 (cartprodmempaircEq) =>
% 107.13/14.52 ((
% 107.13/14.52 (cartprodfstpairEq) =>
% 107.13/14.52 ((
% 107.13/14.52 (cartprodsndpairEq) =>
% 107.13/14.52 ((
% 107.13/14.52 (cartprodpairsurjEq) =>
% 107.13/14.52 ((
% 107.13/14.52 (dpsetconstrI) =>
% 107.13/14.52 ((
% 107.13/14.52 (dpsetconstrSub) =>
% 107.13/14.52 ((
% 107.13/14.52 (setOfPairsIsBReln) =>
% 107.13/14.52 ((
% 107.13/14.52 (dpsetconstrERa) =>
% 107.13/14.52 ((
% 107.13/14.52 (dpsetconstrEL1) =>
% 107.13/14.52 ((
% 107.13/14.52 (dpsetconstrEL2) =>
% 107.13/14.52 ((
% 107.13/14.52 (dpsetconstrER) =>
% 107.13/14.52 ((
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% 107.13/14.52 ((
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% 107.13/14.52 ((
% 107.13/14.52 (app) =>
% 107.13/14.52 ((
% 107.13/14.52 (infuncsetfunc) =>
% 107.13/14.52 ((
% 107.13/14.52 (ap2p) =>
% 107.13/14.52 ((
% 107.13/14.52 (funcinfuncset) =>
% 107.13/14.52 ((
% 107.13/14.52 (lamProp) =>
% 107.13/14.52 ((
% 107.13/14.52 (lamp) =>
% 107.13/14.52 ((
% 107.13/14.52 (lam2p) =>
% 107.13/14.52 ((
% 107.13/14.52 (brelnall1) =>
% 107.13/14.52 ((
% 107.13/14.52 (brelnall2) =>
% 107.13/14.52 ((
% 107.13/14.52 (ex1E2) =>
% 107.13/14.52 ((
% 107.13/14.52 (funcGraphProp1) =>
% 107.13/14.52 ((
% 107.13/14.52 (funcGraphProp3) =>
% 107.13/14.52 ((
% 107.13/14.52 (funcGraphProp2) =>
% 107.13/14.52 ((
% 107.13/14.52 (funcextLem) =>
% 107.13/14.52 ((
% 107.13/14.52 (funcGraphProp4) =>
% 107.13/14.52 ((
% 107.13/14.52 (subbreln) =>
% 107.13/14.52 ((
% 107.13/14.52 (eqbreln) =>
% 107.13/14.52 ((
% 107.13/14.52 (funcext) =>
% 107.13/14.52 ((
% 107.13/14.52 (funcext2) =>
% 107.13/14.52 ((
% 107.13/14.52 (ap2apEq1) =>
% 107.13/14.52 ((
% 107.13/14.52 (ap2apEq2) =>
% 107.13/14.52 ((
% 107.13/14.52 (beta1) =>
% 107.13/14.52 ((
% 107.13/14.52 (eta1) =>
% 107.13/14.52 ((
% 107.13/14.52 (lam2lamEq) =>
% 107.13/14.52 ((
% 107.13/14.52 (beta2) =>
% 107.13/14.52 ((
% 107.13/14.52 (eta2) =>
% 107.13/14.52 ((
% 107.13/14.52 (iffalseProp1) =>
% 107.13/14.52 ((
% 107.13/14.52 (iffalseProp2) =>
% 107.13/14.52 ((
% 107.13/14.52 (iftrueProp1) =>
% 107.13/14.52 ((
% 107.13/14.52 (iftrueProp2) =>
% 107.13/14.52 ((
% 107.13/14.52 (ifSingleton) =>
% 107.13/14.52 ((
% 107.13/14.52 (ifp) =>
% 107.13/14.52 ((
% 107.13/14.52 (theeq) =>
% 107.13/14.52 ((
% 107.13/14.52 (iftrue) =>
% 107.13/14.52 ((
% 107.13/14.52 (iffalse) =>
% 107.13/14.52 ((
% 107.13/14.52 (iftrueorfalse) =>
% 107.13/14.52 ((
% 107.13/14.52 (binintersectT_lem) =>
% 107.13/14.52 ((
% 107.13/14.52 (binunionT_lem) =>
% 107.13/14.52 ((
% 107.13/14.52 (powersetT_lem) =>
% 107.13/14.52 ((
% 107.13/14.52 (setminusT_lem) =>
% 107.13/14.52 ((
% 107.13/14.52 (complementT_lem) =>
% 107.13/14.52 ((
% 107.13/14.52 (setextT) =>
% 107.13/14.52 ((
% 107.13/14.52 (subsetTI) =>
% 107.13/14.52 ((
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% 107.13/14.52 ((
% 107.13/14.52 (powersetTE1) =>
% 107.13/14.52 ((
% 107.13/14.52 (complementTI1) =>
% 107.13/14.52 ((
% 107.13/14.52 (complementTE1) =>
% 107.13/14.52 ((
% 107.13/14.52 (binintersectTELcontra) =>
% 107.13/14.52 ((
% 107.13/14.52 (binintersectTERcontra) =>
% 107.13/14.52 ((
% 107.13/14.52 (contrasubsetT) =>
% 107.13/14.52 ((
% 107.13/14.52 (contrasubsetT1) =>
% 107.13/14.52 ((
% 107.13/14.52 (contrasubsetT2) =>
% 107.13/14.52 ((
% 107.13/14.52 (contrasubsetT3) =>
% 107.13/14.52 ((
% 107.13/14.52 (doubleComplementI1) =>
% 107.13/14.52 ((
% 107.13/14.52 (doubleComplementE1) =>
% 107.13/14.52 ((
% 107.13/14.52 (doubleComplementSub1) =>
% 107.13/14.52 ((
% 107.13/14.52 (doubleComplementSub2) =>
% 107.13/14.52 ((
% 107.13/14.52 (doubleComplementEq) =>
% 107.13/14.52 ((
% 107.13/14.52 (complementTnotintersectT) =>
% 107.13/14.52 ((
% 107.13/14.52 (complementImpComplementIntersect) =>
% 107.13/14.52 ((
% 107.13/14.52 (complementSubsetComplementIntersect) =>
% 107.13/14.52 ((
% 107.13/14.52 (complementInPowersetComplementIntersect) =>
% 107.13/14.52 ((
% 107.13/14.52 (contraSubsetComplement) =>
% 107.13/14.52 ((
% 107.13/14.52 (complementTcontraSubset) =>
% 107.13/14.52 ((
% 107.13/14.52 (binunionTILcontra) =>
% 107.13/14.52 ((
% 107.13/14.52 (binunionTIRcontra) =>
% 107.13/14.52 ((
% 107.13/14.52 (inIntersectImpInUnion) =>
% 107.13/14.52 ((
% 107.13/14.52 (inIntersectImpInUnion2) =>
% 107.13/14.52 ((
% 107.13/14.52 (inIntersectImpInIntersectUnions) =>
% 107.13/14.52 ((
% 107.13/14.52 (intersectInPowersetIntersectUnions) =>
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% 107.13/14.52 (inComplementUnionImpNotIn1) =>
% 107.13/14.52 ((
% 107.13/14.52 (inComplementUnionImpInComplement1) =>
% 107.13/14.52 ((
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% 107.13/14.52 ((
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% 107.13/14.52 ((
% 107.13/14.52 (demorgan2a1) =>
% 107.13/14.52 ((
% 107.13/14.52 (complementUnionInPowersetComplement) =>
% 107.13/14.52 ((
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% 107.13/14.52 ((
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% 107.13/14.52 ((
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% 107.13/14.52 ((
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% 107.13/14.52 ((
% 107.13/14.52 (breln1all2) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1SetBreln1) =>
% 107.13/14.52 ((
% 107.13/14.52 (choice2fnsingleton) =>
% 107.13/14.52 ((
% 107.13/14.52 (setOfPairsIsBReln1) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1all1) =>
% 107.13/14.52 ((
% 107.13/14.52 (subbreln1) =>
% 107.13/14.52 ((
% 107.13/14.52 (eqbreln1) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1invprop) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1invI) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1invE) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1compprop) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1compI) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1compE) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1compEex) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1unionprop) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1unionIL) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1unionIR) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1unionI) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1unionE) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1unionEcases) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1unionCommutes) =>
% 107.13/14.52 ((
% 107.13/14.52 (woz2Ex) =>
% 107.13/14.52 ((
% 107.13/14.52 (woz2W) =>
% 107.13/14.52 ((
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% 107.13/14.52 ((
% 107.13/14.52 (woz2B) =>
% 107.13/14.52 ((
% 107.13/14.52 (image1Ex) =>
% 107.13/14.52 ((
% 107.13/14.52 (image1Ex1) =>
% 107.13/14.52 ((
% 107.13/14.52 (image1Equiv) =>
% 107.13/14.52 ((
% 107.13/14.52 (image1E) =>
% 107.13/14.52 ((
% 107.13/14.52 (image1I) =>
% 107.13/14.52 ((
% 107.13/14.52 (injFuncInInjFuncSet) =>
% 107.13/14.52 ((
% 107.13/14.52 (injFuncSetFuncIn) =>
% 107.13/14.52 ((
% 107.13/14.52 (injFuncSetFuncInj) =>
% 107.13/14.52 ((
% 107.13/14.52 (surjFuncSetFuncIn) =>
% 107.13/14.52 ((
% 107.13/14.52 (surjFuncSetFuncSurj) =>
% 107.13/14.52 ((
% 107.13/14.52 (leftInvIsSurj) =>
% 107.13/14.52 ((
% 107.13/14.52 (surjCantorThm) =>
% 107.13/14.52 ((
% 107.13/14.52 (!!) @ (
% 107.13/14.52 (('#S') @ (
% 107.13/14.52 (
% 107.13/14.52 ('#B') @ (
% 107.13/14.52 =>) @
% 107.13/14.52 nonempty)) @
% 107.13/14.52 (
% 107.13/14.52 (
% 107.13/14.52 ('#B') @ (
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% 107.13/14.52 ('#S') @ (
% 107.13/14.52 (
% 107.13/14.52 ('#B') @ (
% 107.13/14.52 '#S') @
% 107.13/14.52 (
% 107.13/14.52 (
% 107.13/14.52 ('#B') @ (
% 107.13/14.52 (
% 107.13/14.52 ('#B') @ (
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% 107.13/14.52 (
% 107.13/14.52 (
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% 107.13/14.52 (
% 107.13/14.52 (
% 107.13/14.52 ('#C') @ (
% 107.13/14.52 (
% 107.13/14.52 ('#B') @ (
% 107.13/14.52 '#C') @
% 107.13/14.52 (
% 107.13/14.52 (
% 107.13/14.52 ('#B') @ (
% 107.13/14.52 (
% 107.13/14.52 ('#B') @ (
% 107.13/14.52 =))) @
% 107.13/14.52 (
% 107.13/14.52 (
% 107.13/14.52 ('#C') @ binintersect)))))) @
% 107.13/14.52 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 107.13/14.52 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1102])).
% 107.13/14.52 thf(zip_derived_cl1115, plain,
% 107.13/14.52 (~ (((binunionEcases) =>
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% 107.13/14.52 (((binunionLsub) =>
% 107.13/14.52 (((binunionRsub) =>
% 107.13/14.52 (((binintersectI) =>
% 107.13/14.52 (((binintersectSubset5) =>
% 107.13/14.52 (((binintersectEL) =>
% 107.13/14.52 (((binintersectLsub) =>
% 107.13/14.52 (((binintersectSubset2) =>
% 107.13/14.52 (((binintersectSubset3) =>
% 107.13/14.52 (((binintersectER) =>
% 107.13/14.52 (((disjointsetsI1) =>
% 107.13/14.52 (((binintersectRsub) =>
% 107.13/14.52 (((binintersectSubset4) =>
% 107.13/14.52 (((binintersectSubset1) =>
% 107.13/14.52 (((bs114d) =>
% 107.13/14.52 (((setminusI) =>
% 107.13/14.52 (((setminusEL) =>
% 107.13/14.52 (((setminusER) =>
% 107.13/14.52 (((setminusSubset2) =>
% 107.13/14.52 (((setminusERneg) =>
% 107.13/14.52 (((setminusELneg) =>
% 107.13/14.52 (((setminusILneg) =>
% 107.13/14.52 (((setminusIRneg) =>
% 107.13/14.52 (((setminusLsub) =>
% 107.13/14.52 (((setminusSubset1) =>
% 107.13/14.52 (((symdiffE) =>
% 107.13/14.52 (((symdiffI1) =>
% 107.13/14.52 (((symdiffI2) =>
% 107.13/14.52 (((symdiffIneg1) =>
% 107.13/14.52 ((
% 107.13/14.52 (symdiffIneg2) =>
% 107.13/14.52 ((
% 107.13/14.52 (secondinupair) =>
% 107.13/14.52 ((
% 107.13/14.52 (setukpairIL) =>
% 107.13/14.52 ((
% 107.13/14.52 (setukpairIR) =>
% 107.13/14.52 ((
% 107.13/14.52 (kpairiskpair) =>
% 107.13/14.52 ((
% 107.13/14.52 (kpairp) =>
% 107.13/14.52 ((
% 107.13/14.52 (singletonsubset) =>
% 107.13/14.52 ((
% 107.13/14.52 (singletoninpowerset) =>
% 107.13/14.52 ((
% 107.13/14.52 (singletoninpowunion) =>
% 107.13/14.52 ((
% 107.13/14.52 (upairset2E) =>
% 107.13/14.52 ((
% 107.13/14.52 (upairsubunion) =>
% 107.13/14.52 ((
% 107.13/14.52 (upairinpowunion) =>
% 107.13/14.52 ((
% 107.13/14.52 (ubforcartprodlem1) =>
% 107.13/14.52 ((
% 107.13/14.52 (ubforcartprodlem2) =>
% 107.13/14.52 ((
% 107.13/14.52 (ubforcartprodlem3) =>
% 107.13/14.52 ((
% 107.13/14.52 (cartprodpairin) =>
% 107.13/14.52 ((
% 107.13/14.52 (cartprodmempair1) =>
% 107.13/14.52 ((
% 107.13/14.52 (cartprodmempair) =>
% 107.13/14.52 ((
% 107.13/14.52 (setunionE2) =>
% 107.13/14.52 ((
% 107.13/14.52 (setunionsingleton1) =>
% 107.13/14.52 ((
% 107.13/14.52 (setunionsingleton2) =>
% 107.13/14.52 ((
% 107.13/14.52 (setunionsingleton) =>
% 107.13/14.52 ((
% 107.13/14.52 (singletonprop) =>
% 107.13/14.52 ((
% 107.13/14.52 (ex1E1) =>
% 107.13/14.52 ((
% 107.13/14.52 (ex1I) =>
% 107.13/14.52 ((
% 107.13/14.52 (ex1I2) =>
% 107.13/14.52 ((
% 107.13/14.52 (singletonsuniq) =>
% 107.13/14.52 ((
% 107.13/14.52 (setukpairinjL1) =>
% 107.13/14.52 ((
% 107.13/14.52 (kfstsingleton) =>
% 107.13/14.52 ((
% 107.13/14.52 (theprop) =>
% 107.13/14.52 ((
% 107.13/14.52 (kfstpairEq) =>
% 107.13/14.52 ((
% 107.13/14.52 (cartprodfstin) =>
% 107.13/14.52 ((
% 107.13/14.52 (setukpairinjL2) =>
% 107.13/14.52 ((
% 107.13/14.52 (setukpairinjL) =>
% 107.13/14.52 ((
% 107.13/14.52 (setukpairinjR11) =>
% 107.13/14.52 ((
% 107.13/14.52 (setukpairinjR12) =>
% 107.13/14.52 ((
% 107.13/14.52 (setukpairinjR1) =>
% 107.13/14.52 ((
% 107.13/14.52 (upairequniteq) =>
% 107.13/14.52 ((
% 107.13/14.52 (setukpairinjR2) =>
% 107.13/14.52 ((
% 107.13/14.52 (setukpairinjR) =>
% 107.13/14.52 ((
% 107.13/14.52 (ksndsingleton) =>
% 107.13/14.52 ((
% 107.13/14.52 (ksndpairEq) =>
% 107.13/14.52 ((
% 107.13/14.52 (kpairsurjEq) =>
% 107.13/14.52 ((
% 107.13/14.52 (cartprodsndin) =>
% 107.13/14.52 ((
% 107.13/14.52 (cartprodpairmemEL) =>
% 107.13/14.52 ((
% 107.13/14.52 (cartprodpairmemER) =>
% 107.13/14.52 ((
% 107.13/14.52 (cartprodmempaircEq) =>
% 107.13/14.52 ((
% 107.13/14.52 (cartprodfstpairEq) =>
% 107.13/14.52 ((
% 107.13/14.52 (cartprodsndpairEq) =>
% 107.13/14.52 ((
% 107.13/14.52 (cartprodpairsurjEq) =>
% 107.13/14.52 ((
% 107.13/14.52 (dpsetconstrI) =>
% 107.13/14.52 ((
% 107.13/14.52 (dpsetconstrSub) =>
% 107.13/14.52 ((
% 107.13/14.52 (setOfPairsIsBReln) =>
% 107.13/14.52 ((
% 107.13/14.52 (dpsetconstrERa) =>
% 107.13/14.52 ((
% 107.13/14.52 (dpsetconstrEL1) =>
% 107.13/14.52 ((
% 107.13/14.52 (dpsetconstrEL2) =>
% 107.13/14.52 ((
% 107.13/14.52 (dpsetconstrER) =>
% 107.13/14.52 ((
% 107.13/14.52 (funcImageSingleton) =>
% 107.13/14.52 ((
% 107.13/14.52 (apProp) =>
% 107.13/14.52 ((
% 107.13/14.52 (app) =>
% 107.13/14.52 ((
% 107.13/14.52 (infuncsetfunc) =>
% 107.13/14.52 ((
% 107.13/14.52 (ap2p) =>
% 107.13/14.52 ((
% 107.13/14.52 (funcinfuncset) =>
% 107.13/14.52 ((
% 107.13/14.52 (lamProp) =>
% 107.13/14.52 ((
% 107.13/14.52 (lamp) =>
% 107.13/14.52 ((
% 107.13/14.52 (lam2p) =>
% 107.13/14.52 ((
% 107.13/14.52 (brelnall1) =>
% 107.13/14.52 ((
% 107.13/14.52 (brelnall2) =>
% 107.13/14.52 ((
% 107.13/14.52 (ex1E2) =>
% 107.13/14.52 ((
% 107.13/14.52 (funcGraphProp1) =>
% 107.13/14.52 ((
% 107.13/14.52 (funcGraphProp3) =>
% 107.13/14.52 ((
% 107.13/14.52 (funcGraphProp2) =>
% 107.13/14.52 ((
% 107.13/14.52 (funcextLem) =>
% 107.13/14.52 ((
% 107.13/14.52 (funcGraphProp4) =>
% 107.13/14.52 ((
% 107.13/14.52 (subbreln) =>
% 107.13/14.52 ((
% 107.13/14.52 (eqbreln) =>
% 107.13/14.52 ((
% 107.13/14.52 (funcext) =>
% 107.13/14.52 ((
% 107.13/14.52 (funcext2) =>
% 107.13/14.52 ((
% 107.13/14.52 (ap2apEq1) =>
% 107.13/14.52 ((
% 107.13/14.52 (ap2apEq2) =>
% 107.13/14.52 ((
% 107.13/14.52 (beta1) =>
% 107.13/14.52 ((
% 107.13/14.52 (eta1) =>
% 107.13/14.52 ((
% 107.13/14.52 (lam2lamEq) =>
% 107.13/14.52 ((
% 107.13/14.52 (beta2) =>
% 107.13/14.52 ((
% 107.13/14.52 (eta2) =>
% 107.13/14.52 ((
% 107.13/14.52 (iffalseProp1) =>
% 107.13/14.52 ((
% 107.13/14.52 (iffalseProp2) =>
% 107.13/14.52 ((
% 107.13/14.52 (iftrueProp1) =>
% 107.13/14.52 ((
% 107.13/14.52 (iftrueProp2) =>
% 107.13/14.52 ((
% 107.13/14.52 (ifSingleton) =>
% 107.13/14.52 ((
% 107.13/14.52 (ifp) =>
% 107.13/14.52 ((
% 107.13/14.52 (theeq) =>
% 107.13/14.52 ((
% 107.13/14.52 (iftrue) =>
% 107.13/14.52 ((
% 107.13/14.52 (iffalse) =>
% 107.13/14.52 ((
% 107.13/14.52 (iftrueorfalse) =>
% 107.13/14.52 ((
% 107.13/14.52 (binintersectT_lem) =>
% 107.13/14.52 ((
% 107.13/14.52 (binunionT_lem) =>
% 107.13/14.52 ((
% 107.13/14.52 (powersetT_lem) =>
% 107.13/14.52 ((
% 107.13/14.52 (setminusT_lem) =>
% 107.13/14.52 ((
% 107.13/14.52 (complementT_lem) =>
% 107.13/14.52 ((
% 107.13/14.52 (setextT) =>
% 107.13/14.52 ((
% 107.13/14.52 (subsetTI) =>
% 107.13/14.52 ((
% 107.13/14.52 (powersetTI1) =>
% 107.13/14.52 ((
% 107.13/14.52 (powersetTE1) =>
% 107.13/14.52 ((
% 107.13/14.52 (complementTI1) =>
% 107.13/14.52 ((
% 107.13/14.52 (complementTE1) =>
% 107.13/14.52 ((
% 107.13/14.52 (binintersectTELcontra) =>
% 107.13/14.52 ((
% 107.13/14.52 (binintersectTERcontra) =>
% 107.13/14.52 ((
% 107.13/14.52 (contrasubsetT) =>
% 107.13/14.52 ((
% 107.13/14.52 (contrasubsetT1) =>
% 107.13/14.52 ((
% 107.13/14.52 (contrasubsetT2) =>
% 107.13/14.52 ((
% 107.13/14.52 (contrasubsetT3) =>
% 107.13/14.52 ((
% 107.13/14.52 (doubleComplementI1) =>
% 107.13/14.52 ((
% 107.13/14.52 (doubleComplementE1) =>
% 107.13/14.52 ((
% 107.13/14.52 (doubleComplementSub1) =>
% 107.13/14.52 ((
% 107.13/14.52 (doubleComplementSub2) =>
% 107.13/14.52 ((
% 107.13/14.52 (doubleComplementEq) =>
% 107.13/14.52 ((
% 107.13/14.52 (complementTnotintersectT) =>
% 107.13/14.52 ((
% 107.13/14.52 (complementImpComplementIntersect) =>
% 107.13/14.52 ((
% 107.13/14.52 (complementSubsetComplementIntersect) =>
% 107.13/14.52 ((
% 107.13/14.52 (complementInPowersetComplementIntersect) =>
% 107.13/14.52 ((
% 107.13/14.52 (contraSubsetComplement) =>
% 107.13/14.52 ((
% 107.13/14.52 (complementTcontraSubset) =>
% 107.13/14.52 ((
% 107.13/14.52 (binunionTILcontra) =>
% 107.13/14.52 ((
% 107.13/14.52 (binunionTIRcontra) =>
% 107.13/14.52 ((
% 107.13/14.52 (inIntersectImpInUnion) =>
% 107.13/14.52 ((
% 107.13/14.52 (inIntersectImpInUnion2) =>
% 107.13/14.52 ((
% 107.13/14.52 (inIntersectImpInIntersectUnions) =>
% 107.13/14.52 ((
% 107.13/14.52 (intersectInPowersetIntersectUnions) =>
% 107.13/14.52 ((
% 107.13/14.52 (inComplementUnionImpNotIn1) =>
% 107.13/14.52 ((
% 107.13/14.52 (inComplementUnionImpInComplement1) =>
% 107.13/14.52 ((
% 107.13/14.52 (binunionTE) =>
% 107.13/14.52 ((
% 107.13/14.52 (binunionTEcontra) =>
% 107.13/14.52 ((
% 107.13/14.52 (demorgan2a1) =>
% 107.13/14.52 ((
% 107.13/14.52 (complementUnionInPowersetComplement) =>
% 107.13/14.52 ((
% 107.13/14.52 (demorgan2a2) =>
% 107.13/14.52 ((
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% 107.13/14.52 ((
% 107.13/14.52 (demorgan1b) =>
% 107.13/14.52 ((
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% 107.13/14.52 ((
% 107.13/14.52 (demorgan2a) =>
% 107.13/14.52 ((
% 107.13/14.52 (demorgan2b2) =>
% 107.13/14.52 ((
% 107.13/14.52 (demorgan2b) =>
% 107.13/14.52 ((
% 107.13/14.52 (demorgan2) =>
% 107.13/14.52 ((
% 107.13/14.52 (woz13rule0) =>
% 107.13/14.52 ((
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% 107.13/14.52 ((
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% 107.13/14.52 ((
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% 107.13/14.52 ((
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% 107.13/14.52 ((
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% 107.13/14.52 ((
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% 107.13/14.52 ((
% 107.13/14.52 (woz1_5) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1all2) =>
% 107.13/14.52 ((
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% 107.13/14.52 ((
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% 107.13/14.52 ((
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% 107.13/14.52 ((
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% 107.13/14.52 ((
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% 107.13/14.52 ((
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% 107.13/14.52 ((
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% 107.13/14.52 ((
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% 107.13/14.52 ((
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% 107.13/14.52 ((
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% 107.13/14.52 ((
% 107.13/14.52 (injFuncSetFuncIn) =>
% 107.13/14.52 ((
% 107.13/14.52 (injFuncSetFuncInj) =>
% 107.13/14.52 ((
% 107.13/14.52 (surjFuncSetFuncIn) =>
% 107.13/14.52 ((
% 107.13/14.52 (surjFuncSetFuncSurj) =>
% 107.13/14.52 ((
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% 107.13/14.52 ((
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% 107.13/14.52 (
% 107.13/14.52 (
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% 107.13/14.52 (
% 107.13/14.52 (
% 107.13/14.52 ('#C') @ (
% 107.13/14.52 (
% 107.13/14.52 ('#B') @ (
% 107.13/14.52 '#C') @
% 107.13/14.52 (
% 107.13/14.52 (
% 107.13/14.52 ('#B') @ (
% 107.13/14.52 (
% 107.13/14.52 ('#B') @ (
% 107.13/14.52 =))) @
% 107.13/14.52 (
% 107.13/14.52 (
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% 107.13/14.52 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 107.13/14.52 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1109])).
% 107.13/14.52 thf(zip_derived_cl1121, plain,
% 107.13/14.52 (~ (((binunionE) =>
% 107.13/14.52 (((binunionLsub) =>
% 107.13/14.52 (((binunionRsub) =>
% 107.13/14.52 (((binintersectI) =>
% 107.13/14.52 (((binintersectSubset5) =>
% 107.13/14.52 (((binintersectEL) =>
% 107.13/14.52 (((binintersectLsub) =>
% 107.13/14.52 (((binintersectSubset2) =>
% 107.13/14.52 (((binintersectSubset3) =>
% 107.13/14.52 (((binintersectER) =>
% 107.13/14.52 (((disjointsetsI1) =>
% 107.13/14.52 (((binintersectRsub) =>
% 107.13/14.52 (((binintersectSubset4) =>
% 107.13/14.52 (((binintersectSubset1) =>
% 107.13/14.52 (((bs114d) =>
% 107.13/14.52 (((setminusI) =>
% 107.13/14.52 (((setminusEL) =>
% 107.13/14.52 (((setminusER) =>
% 107.13/14.52 (((setminusSubset2) =>
% 107.13/14.52 (((setminusERneg) =>
% 107.13/14.52 (((setminusELneg) =>
% 107.13/14.52 (((setminusILneg) =>
% 107.13/14.52 (((setminusIRneg) =>
% 107.13/14.52 (((setminusLsub) =>
% 107.13/14.52 (((setminusSubset1) =>
% 107.13/14.52 (((symdiffE) =>
% 107.13/14.52 (((symdiffI1) =>
% 107.13/14.52 (((symdiffI2) =>
% 107.13/14.52 (((symdiffIneg1) =>
% 107.13/14.52 (((symdiffIneg2) =>
% 107.13/14.52 ((
% 107.13/14.52 (secondinupair) =>
% 107.13/14.52 ((
% 107.13/14.52 (setukpairIL) =>
% 107.13/14.52 ((
% 107.13/14.52 (setukpairIR) =>
% 107.13/14.52 ((
% 107.13/14.52 (kpairiskpair) =>
% 107.13/14.52 ((
% 107.13/14.52 (kpairp) =>
% 107.13/14.52 ((
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% 107.13/14.52 ((
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% 107.13/14.52 ((
% 107.13/14.52 (singletoninpowunion) =>
% 107.13/14.52 ((
% 107.13/14.52 (upairset2E) =>
% 107.13/14.52 ((
% 107.13/14.52 (upairsubunion) =>
% 107.13/14.52 ((
% 107.13/14.52 (upairinpowunion) =>
% 107.13/14.52 ((
% 107.13/14.52 (ubforcartprodlem1) =>
% 107.13/14.52 ((
% 107.13/14.52 (ubforcartprodlem2) =>
% 107.13/14.52 ((
% 107.13/14.52 (ubforcartprodlem3) =>
% 107.13/14.52 ((
% 107.13/14.52 (cartprodpairin) =>
% 107.13/14.52 ((
% 107.13/14.52 (cartprodmempair1) =>
% 107.13/14.52 ((
% 107.13/14.52 (cartprodmempair) =>
% 107.13/14.52 ((
% 107.13/14.52 (setunionE2) =>
% 107.13/14.52 ((
% 107.13/14.52 (setunionsingleton1) =>
% 107.13/14.52 ((
% 107.13/14.52 (setunionsingleton2) =>
% 107.13/14.52 ((
% 107.13/14.52 (setunionsingleton) =>
% 107.13/14.52 ((
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% 107.13/14.52 ((
% 107.13/14.52 (ex1E1) =>
% 107.13/14.52 ((
% 107.13/14.52 (ex1I) =>
% 107.13/14.52 ((
% 107.13/14.52 (ex1I2) =>
% 107.13/14.52 ((
% 107.13/14.52 (singletonsuniq) =>
% 107.13/14.52 ((
% 107.13/14.52 (setukpairinjL1) =>
% 107.13/14.52 ((
% 107.13/14.52 (kfstsingleton) =>
% 107.13/14.52 ((
% 107.13/14.52 (theprop) =>
% 107.13/14.52 ((
% 107.13/14.52 (kfstpairEq) =>
% 107.13/14.52 ((
% 107.13/14.52 (cartprodfstin) =>
% 107.13/14.52 ((
% 107.13/14.52 (setukpairinjL2) =>
% 107.13/14.52 ((
% 107.13/14.52 (setukpairinjL) =>
% 107.13/14.52 ((
% 107.13/14.52 (setukpairinjR11) =>
% 107.13/14.52 ((
% 107.13/14.52 (setukpairinjR12) =>
% 107.13/14.52 ((
% 107.13/14.52 (setukpairinjR1) =>
% 107.13/14.52 ((
% 107.13/14.52 (upairequniteq) =>
% 107.13/14.52 ((
% 107.13/14.52 (setukpairinjR2) =>
% 107.13/14.52 ((
% 107.13/14.52 (setukpairinjR) =>
% 107.13/14.52 ((
% 107.13/14.52 (ksndsingleton) =>
% 107.13/14.52 ((
% 107.13/14.52 (ksndpairEq) =>
% 107.13/14.52 ((
% 107.13/14.52 (kpairsurjEq) =>
% 107.13/14.52 ((
% 107.13/14.52 (cartprodsndin) =>
% 107.13/14.52 ((
% 107.13/14.52 (cartprodpairmemEL) =>
% 107.13/14.52 ((
% 107.13/14.52 (cartprodpairmemER) =>
% 107.13/14.52 ((
% 107.13/14.52 (cartprodmempaircEq) =>
% 107.13/14.52 ((
% 107.13/14.52 (cartprodfstpairEq) =>
% 107.13/14.52 ((
% 107.13/14.52 (cartprodsndpairEq) =>
% 107.13/14.52 ((
% 107.13/14.52 (cartprodpairsurjEq) =>
% 107.13/14.52 ((
% 107.13/14.52 (dpsetconstrI) =>
% 107.13/14.52 ((
% 107.13/14.52 (dpsetconstrSub) =>
% 107.13/14.52 ((
% 107.13/14.52 (setOfPairsIsBReln) =>
% 107.13/14.52 ((
% 107.13/14.52 (dpsetconstrERa) =>
% 107.13/14.52 ((
% 107.13/14.52 (dpsetconstrEL1) =>
% 107.13/14.52 ((
% 107.13/14.52 (dpsetconstrEL2) =>
% 107.13/14.52 ((
% 107.13/14.52 (dpsetconstrER) =>
% 107.13/14.52 ((
% 107.13/14.52 (funcImageSingleton) =>
% 107.13/14.52 ((
% 107.13/14.52 (apProp) =>
% 107.13/14.52 ((
% 107.13/14.52 (app) =>
% 107.13/14.52 ((
% 107.13/14.52 (infuncsetfunc) =>
% 107.13/14.52 ((
% 107.13/14.52 (ap2p) =>
% 107.13/14.52 ((
% 107.13/14.52 (funcinfuncset) =>
% 107.13/14.52 ((
% 107.13/14.52 (lamProp) =>
% 107.13/14.52 ((
% 107.13/14.52 (lamp) =>
% 107.13/14.52 ((
% 107.13/14.52 (lam2p) =>
% 107.13/14.52 ((
% 107.13/14.52 (brelnall1) =>
% 107.13/14.52 ((
% 107.13/14.52 (brelnall2) =>
% 107.13/14.52 ((
% 107.13/14.52 (ex1E2) =>
% 107.13/14.52 ((
% 107.13/14.52 (funcGraphProp1) =>
% 107.13/14.52 ((
% 107.13/14.52 (funcGraphProp3) =>
% 107.13/14.52 ((
% 107.13/14.52 (funcGraphProp2) =>
% 107.13/14.52 ((
% 107.13/14.52 (funcextLem) =>
% 107.13/14.52 ((
% 107.13/14.52 (funcGraphProp4) =>
% 107.13/14.52 ((
% 107.13/14.52 (subbreln) =>
% 107.13/14.52 ((
% 107.13/14.52 (eqbreln) =>
% 107.13/14.52 ((
% 107.13/14.52 (funcext) =>
% 107.13/14.52 ((
% 107.13/14.52 (funcext2) =>
% 107.13/14.52 ((
% 107.13/14.52 (ap2apEq1) =>
% 107.13/14.52 ((
% 107.13/14.52 (ap2apEq2) =>
% 107.13/14.52 ((
% 107.13/14.52 (beta1) =>
% 107.13/14.52 ((
% 107.13/14.52 (eta1) =>
% 107.13/14.52 ((
% 107.13/14.52 (lam2lamEq) =>
% 107.13/14.52 ((
% 107.13/14.52 (beta2) =>
% 107.13/14.52 ((
% 107.13/14.52 (eta2) =>
% 107.13/14.52 ((
% 107.13/14.52 (iffalseProp1) =>
% 107.13/14.52 ((
% 107.13/14.52 (iffalseProp2) =>
% 107.13/14.52 ((
% 107.13/14.52 (iftrueProp1) =>
% 107.13/14.52 ((
% 107.13/14.52 (iftrueProp2) =>
% 107.13/14.52 ((
% 107.13/14.52 (ifSingleton) =>
% 107.13/14.52 ((
% 107.13/14.52 (ifp) =>
% 107.13/14.52 ((
% 107.13/14.52 (theeq) =>
% 107.13/14.52 ((
% 107.13/14.52 (iftrue) =>
% 107.13/14.52 ((
% 107.13/14.52 (iffalse) =>
% 107.13/14.52 ((
% 107.13/14.52 (iftrueorfalse) =>
% 107.13/14.52 ((
% 107.13/14.52 (binintersectT_lem) =>
% 107.13/14.52 ((
% 107.13/14.52 (binunionT_lem) =>
% 107.13/14.52 ((
% 107.13/14.52 (powersetT_lem) =>
% 107.13/14.52 ((
% 107.13/14.52 (setminusT_lem) =>
% 107.13/14.52 ((
% 107.13/14.52 (complementT_lem) =>
% 107.13/14.52 ((
% 107.13/14.52 (setextT) =>
% 107.13/14.52 ((
% 107.13/14.52 (subsetTI) =>
% 107.13/14.52 ((
% 107.13/14.52 (powersetTI1) =>
% 107.13/14.52 ((
% 107.13/14.52 (powersetTE1) =>
% 107.13/14.52 ((
% 107.13/14.52 (complementTI1) =>
% 107.13/14.52 ((
% 107.13/14.52 (complementTE1) =>
% 107.13/14.52 ((
% 107.13/14.52 (binintersectTELcontra) =>
% 107.13/14.52 ((
% 107.13/14.52 (binintersectTERcontra) =>
% 107.13/14.52 ((
% 107.13/14.52 (contrasubsetT) =>
% 107.13/14.52 ((
% 107.13/14.52 (contrasubsetT1) =>
% 107.13/14.52 ((
% 107.13/14.52 (contrasubsetT2) =>
% 107.13/14.52 ((
% 107.13/14.52 (contrasubsetT3) =>
% 107.13/14.52 ((
% 107.13/14.52 (doubleComplementI1) =>
% 107.13/14.52 ((
% 107.13/14.52 (doubleComplementE1) =>
% 107.13/14.52 ((
% 107.13/14.52 (doubleComplementSub1) =>
% 107.13/14.52 ((
% 107.13/14.52 (doubleComplementSub2) =>
% 107.13/14.52 ((
% 107.13/14.52 (doubleComplementEq) =>
% 107.13/14.52 ((
% 107.13/14.52 (complementTnotintersectT) =>
% 107.13/14.52 ((
% 107.13/14.52 (complementImpComplementIntersect) =>
% 107.13/14.52 ((
% 107.13/14.52 (complementSubsetComplementIntersect) =>
% 107.13/14.52 ((
% 107.13/14.52 (complementInPowersetComplementIntersect) =>
% 107.13/14.52 ((
% 107.13/14.52 (contraSubsetComplement) =>
% 107.13/14.52 ((
% 107.13/14.52 (complementTcontraSubset) =>
% 107.13/14.52 ((
% 107.13/14.52 (binunionTILcontra) =>
% 107.13/14.52 ((
% 107.13/14.52 (binunionTIRcontra) =>
% 107.13/14.52 ((
% 107.13/14.52 (inIntersectImpInUnion) =>
% 107.13/14.52 ((
% 107.13/14.52 (inIntersectImpInUnion2) =>
% 107.13/14.52 ((
% 107.13/14.52 (inIntersectImpInIntersectUnions) =>
% 107.13/14.52 ((
% 107.13/14.52 (intersectInPowersetIntersectUnions) =>
% 107.13/14.52 ((
% 107.13/14.52 (inComplementUnionImpNotIn1) =>
% 107.13/14.52 ((
% 107.13/14.52 (inComplementUnionImpInComplement1) =>
% 107.13/14.52 ((
% 107.13/14.52 (binunionTE) =>
% 107.13/14.52 ((
% 107.13/14.52 (binunionTEcontra) =>
% 107.13/14.52 ((
% 107.13/14.52 (demorgan2a1) =>
% 107.13/14.52 ((
% 107.13/14.52 (complementUnionInPowersetComplement) =>
% 107.13/14.52 ((
% 107.13/14.52 (demorgan2a2) =>
% 107.13/14.52 ((
% 107.13/14.52 (demorgan1a) =>
% 107.13/14.52 ((
% 107.13/14.52 (demorgan1b) =>
% 107.13/14.52 ((
% 107.13/14.52 (demorgan1) =>
% 107.13/14.52 ((
% 107.13/14.52 (demorgan2a) =>
% 107.13/14.52 ((
% 107.13/14.52 (demorgan2b2) =>
% 107.13/14.52 ((
% 107.13/14.52 (demorgan2b) =>
% 107.13/14.52 ((
% 107.13/14.52 (demorgan2) =>
% 107.13/14.52 ((
% 107.13/14.52 (woz13rule0) =>
% 107.13/14.52 ((
% 107.13/14.52 (woz13rule1) =>
% 107.13/14.52 ((
% 107.13/14.52 (woz13rule2) =>
% 107.13/14.52 ((
% 107.13/14.52 (woz13rule3) =>
% 107.13/14.52 ((
% 107.13/14.52 (woz13rule4) =>
% 107.13/14.52 ((
% 107.13/14.52 (woz1_1) =>
% 107.13/14.52 ((
% 107.13/14.52 (woz1_2) =>
% 107.13/14.52 ((
% 107.13/14.52 (woz1_3) =>
% 107.13/14.52 ((
% 107.13/14.52 (woz1_4) =>
% 107.13/14.52 ((
% 107.13/14.52 (woz1_5) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1all2) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1SetBreln1) =>
% 107.13/14.52 ((
% 107.13/14.52 (choice2fnsingleton) =>
% 107.13/14.52 ((
% 107.13/14.52 (setOfPairsIsBReln1) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1all1) =>
% 107.13/14.52 ((
% 107.13/14.52 (subbreln1) =>
% 107.13/14.52 ((
% 107.13/14.52 (eqbreln1) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1invprop) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1invI) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1invE) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1compprop) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1compI) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1compE) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1compEex) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1unionprop) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1unionIL) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1unionIR) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1unionI) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1unionE) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1unionEcases) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1unionCommutes) =>
% 107.13/14.52 ((
% 107.13/14.52 (woz2Ex) =>
% 107.13/14.52 ((
% 107.13/14.52 (woz2W) =>
% 107.13/14.52 ((
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% 107.13/14.52 ((
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% 107.13/14.52 ((
% 107.13/14.52 (image1Ex1) =>
% 107.13/14.52 ((
% 107.13/14.52 (image1Equiv) =>
% 107.13/14.52 ((
% 107.13/14.52 (image1E) =>
% 107.13/14.52 ((
% 107.13/14.52 (image1I) =>
% 107.13/14.52 ((
% 107.13/14.52 (injFuncInInjFuncSet) =>
% 107.13/14.52 ((
% 107.13/14.52 (injFuncSetFuncIn) =>
% 107.13/14.52 ((
% 107.13/14.52 (injFuncSetFuncInj) =>
% 107.13/14.52 ((
% 107.13/14.52 (surjFuncSetFuncIn) =>
% 107.13/14.52 ((
% 107.13/14.52 (surjFuncSetFuncSurj) =>
% 107.13/14.52 ((
% 107.13/14.52 (leftInvIsSurj) =>
% 107.13/14.52 ((
% 107.13/14.52 (surjCantorThm) =>
% 107.13/14.52 ((
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% 107.13/14.52 (('#S') @ (
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% 107.13/14.52 ('#B') @ (
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% 107.13/14.52 nonempty)) @
% 107.13/14.52 (
% 107.13/14.52 (
% 107.13/14.52 ('#B') @ (
% 107.13/14.52 ??) @
% 107.13/14.52 (
% 107.13/14.52 (
% 107.13/14.52 ('#S') @ (
% 107.13/14.52 (
% 107.13/14.52 ('#B') @ (
% 107.13/14.52 '#S') @
% 107.13/14.52 (
% 107.13/14.52 (
% 107.13/14.52 ('#B') @ (
% 107.13/14.52 (
% 107.13/14.52 ('#B') @ (
% 107.13/14.52 &))) @
% 107.13/14.52 (
% 107.13/14.52 (
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% 107.13/14.52 (
% 107.13/14.52 (
% 107.13/14.52 ('#C') @ (
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% 107.13/14.52 ('#B') @ (
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% 107.13/14.52 (
% 107.13/14.52 (
% 107.13/14.52 ('#B') @ (
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% 107.13/14.52 ('#B') @ (
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% 107.13/14.52 (
% 107.13/14.52 (
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% 107.13/14.52 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 107.13/14.52 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1115])).
% 107.13/14.52 thf(zip_derived_cl1128, plain,
% 107.13/14.52 (~ (((binunionLsub) =>
% 107.13/14.52 (((binunionRsub) =>
% 107.13/14.52 (((binintersectI) =>
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% 107.13/14.52 (((binintersectRsub) =>
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% 107.13/14.52 (((secondinupair) =>
% 107.13/14.52 ((
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% 107.13/14.52 ((
% 107.13/14.52 (setukpairIR) =>
% 107.13/14.52 ((
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% 107.13/14.52 ((
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% 107.13/14.52 ((
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% 107.13/14.52 ((
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% 107.13/14.52 ((
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% 107.13/14.52 ((
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% 107.13/14.52 ((
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% 107.13/14.52 ((
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% 107.13/14.52 ((
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% 107.13/14.52 ((
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% 107.13/14.52 ((
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% 107.13/14.52 ((
% 107.13/14.52 (setunionsingleton1) =>
% 107.13/14.52 ((
% 107.13/14.52 (setunionsingleton2) =>
% 107.13/14.52 ((
% 107.13/14.52 (setunionsingleton) =>
% 107.13/14.52 ((
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% 107.13/14.52 ((
% 107.13/14.52 (ex1E1) =>
% 107.13/14.52 ((
% 107.13/14.52 (ex1I) =>
% 107.13/14.52 ((
% 107.13/14.52 (ex1I2) =>
% 107.13/14.52 ((
% 107.13/14.52 (singletonsuniq) =>
% 107.13/14.52 ((
% 107.13/14.52 (setukpairinjL1) =>
% 107.13/14.52 ((
% 107.13/14.52 (kfstsingleton) =>
% 107.13/14.52 ((
% 107.13/14.52 (theprop) =>
% 107.13/14.52 ((
% 107.13/14.52 (kfstpairEq) =>
% 107.13/14.52 ((
% 107.13/14.52 (cartprodfstin) =>
% 107.13/14.52 ((
% 107.13/14.52 (setukpairinjL2) =>
% 107.13/14.52 ((
% 107.13/14.52 (setukpairinjL) =>
% 107.13/14.52 ((
% 107.13/14.52 (setukpairinjR11) =>
% 107.13/14.52 ((
% 107.13/14.52 (setukpairinjR12) =>
% 107.13/14.52 ((
% 107.13/14.52 (setukpairinjR1) =>
% 107.13/14.52 ((
% 107.13/14.52 (upairequniteq) =>
% 107.13/14.52 ((
% 107.13/14.52 (setukpairinjR2) =>
% 107.13/14.52 ((
% 107.13/14.52 (setukpairinjR) =>
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% 107.13/14.52 (ksndsingleton) =>
% 107.13/14.52 ((
% 107.13/14.52 (ksndpairEq) =>
% 107.13/14.52 ((
% 107.13/14.52 (kpairsurjEq) =>
% 107.13/14.52 ((
% 107.13/14.52 (cartprodsndin) =>
% 107.13/14.52 ((
% 107.13/14.52 (cartprodpairmemEL) =>
% 107.13/14.52 ((
% 107.13/14.52 (cartprodpairmemER) =>
% 107.13/14.52 ((
% 107.13/14.52 (cartprodmempaircEq) =>
% 107.13/14.52 ((
% 107.13/14.52 (cartprodfstpairEq) =>
% 107.13/14.52 ((
% 107.13/14.52 (cartprodsndpairEq) =>
% 107.13/14.52 ((
% 107.13/14.52 (cartprodpairsurjEq) =>
% 107.13/14.52 ((
% 107.13/14.52 (dpsetconstrI) =>
% 107.13/14.52 ((
% 107.13/14.52 (dpsetconstrSub) =>
% 107.13/14.52 ((
% 107.13/14.52 (setOfPairsIsBReln) =>
% 107.13/14.52 ((
% 107.13/14.52 (dpsetconstrERa) =>
% 107.13/14.52 ((
% 107.13/14.52 (dpsetconstrEL1) =>
% 107.13/14.52 ((
% 107.13/14.52 (dpsetconstrEL2) =>
% 107.13/14.52 ((
% 107.13/14.52 (dpsetconstrER) =>
% 107.13/14.52 ((
% 107.13/14.52 (funcImageSingleton) =>
% 107.13/14.52 ((
% 107.13/14.52 (apProp) =>
% 107.13/14.52 ((
% 107.13/14.52 (app) =>
% 107.13/14.52 ((
% 107.13/14.52 (infuncsetfunc) =>
% 107.13/14.52 ((
% 107.13/14.52 (ap2p) =>
% 107.13/14.52 ((
% 107.13/14.52 (funcinfuncset) =>
% 107.13/14.52 ((
% 107.13/14.52 (lamProp) =>
% 107.13/14.52 ((
% 107.13/14.52 (lamp) =>
% 107.13/14.52 ((
% 107.13/14.52 (lam2p) =>
% 107.13/14.52 ((
% 107.13/14.52 (brelnall1) =>
% 107.13/14.52 ((
% 107.13/14.52 (brelnall2) =>
% 107.13/14.52 ((
% 107.13/14.52 (ex1E2) =>
% 107.13/14.52 ((
% 107.13/14.52 (funcGraphProp1) =>
% 107.13/14.52 ((
% 107.13/14.52 (funcGraphProp3) =>
% 107.13/14.52 ((
% 107.13/14.52 (funcGraphProp2) =>
% 107.13/14.52 ((
% 107.13/14.52 (funcextLem) =>
% 107.13/14.52 ((
% 107.13/14.52 (funcGraphProp4) =>
% 107.13/14.52 ((
% 107.13/14.52 (subbreln) =>
% 107.13/14.52 ((
% 107.13/14.52 (eqbreln) =>
% 107.13/14.52 ((
% 107.13/14.52 (funcext) =>
% 107.13/14.52 ((
% 107.13/14.52 (funcext2) =>
% 107.13/14.52 ((
% 107.13/14.52 (ap2apEq1) =>
% 107.13/14.52 ((
% 107.13/14.52 (ap2apEq2) =>
% 107.13/14.52 ((
% 107.13/14.52 (beta1) =>
% 107.13/14.52 ((
% 107.13/14.52 (eta1) =>
% 107.13/14.52 ((
% 107.13/14.52 (lam2lamEq) =>
% 107.13/14.52 ((
% 107.13/14.52 (beta2) =>
% 107.13/14.52 ((
% 107.13/14.52 (eta2) =>
% 107.13/14.52 ((
% 107.13/14.52 (iffalseProp1) =>
% 107.13/14.52 ((
% 107.13/14.52 (iffalseProp2) =>
% 107.13/14.52 ((
% 107.13/14.52 (iftrueProp1) =>
% 107.13/14.52 ((
% 107.13/14.52 (iftrueProp2) =>
% 107.13/14.52 ((
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% 107.13/14.52 ((
% 107.13/14.52 (ifp) =>
% 107.13/14.52 ((
% 107.13/14.52 (theeq) =>
% 107.13/14.52 ((
% 107.13/14.52 (iftrue) =>
% 107.13/14.52 ((
% 107.13/14.52 (iffalse) =>
% 107.13/14.52 ((
% 107.13/14.52 (iftrueorfalse) =>
% 107.13/14.52 ((
% 107.13/14.52 (binintersectT_lem) =>
% 107.13/14.52 ((
% 107.13/14.52 (binunionT_lem) =>
% 107.13/14.52 ((
% 107.13/14.52 (powersetT_lem) =>
% 107.13/14.52 ((
% 107.13/14.52 (setminusT_lem) =>
% 107.13/14.52 ((
% 107.13/14.52 (complementT_lem) =>
% 107.13/14.52 ((
% 107.13/14.52 (setextT) =>
% 107.13/14.52 ((
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% 107.13/14.52 ((
% 107.13/14.52 (powersetTI1) =>
% 107.13/14.52 ((
% 107.13/14.52 (powersetTE1) =>
% 107.13/14.52 ((
% 107.13/14.52 (complementTI1) =>
% 107.13/14.52 ((
% 107.13/14.52 (complementTE1) =>
% 107.13/14.52 ((
% 107.13/14.52 (binintersectTELcontra) =>
% 107.13/14.52 ((
% 107.13/14.52 (binintersectTERcontra) =>
% 107.13/14.52 ((
% 107.13/14.52 (contrasubsetT) =>
% 107.13/14.52 ((
% 107.13/14.52 (contrasubsetT1) =>
% 107.13/14.52 ((
% 107.13/14.52 (contrasubsetT2) =>
% 107.13/14.52 ((
% 107.13/14.52 (contrasubsetT3) =>
% 107.13/14.52 ((
% 107.13/14.52 (doubleComplementI1) =>
% 107.13/14.52 ((
% 107.13/14.52 (doubleComplementE1) =>
% 107.13/14.52 ((
% 107.13/14.52 (doubleComplementSub1) =>
% 107.13/14.52 ((
% 107.13/14.52 (doubleComplementSub2) =>
% 107.13/14.52 ((
% 107.13/14.52 (doubleComplementEq) =>
% 107.13/14.52 ((
% 107.13/14.52 (complementTnotintersectT) =>
% 107.13/14.52 ((
% 107.13/14.52 (complementImpComplementIntersect) =>
% 107.13/14.52 ((
% 107.13/14.52 (complementSubsetComplementIntersect) =>
% 107.13/14.52 ((
% 107.13/14.52 (complementInPowersetComplementIntersect) =>
% 107.13/14.52 ((
% 107.13/14.52 (contraSubsetComplement) =>
% 107.13/14.52 ((
% 107.13/14.52 (complementTcontraSubset) =>
% 107.13/14.52 ((
% 107.13/14.52 (binunionTILcontra) =>
% 107.13/14.52 ((
% 107.13/14.52 (binunionTIRcontra) =>
% 107.13/14.52 ((
% 107.13/14.52 (inIntersectImpInUnion) =>
% 107.13/14.52 ((
% 107.13/14.52 (inIntersectImpInUnion2) =>
% 107.13/14.52 ((
% 107.13/14.52 (inIntersectImpInIntersectUnions) =>
% 107.13/14.52 ((
% 107.13/14.52 (intersectInPowersetIntersectUnions) =>
% 107.13/14.52 ((
% 107.13/14.52 (inComplementUnionImpNotIn1) =>
% 107.13/14.52 ((
% 107.13/14.52 (inComplementUnionImpInComplement1) =>
% 107.13/14.52 ((
% 107.13/14.52 (binunionTE) =>
% 107.13/14.52 ((
% 107.13/14.52 (binunionTEcontra) =>
% 107.13/14.52 ((
% 107.13/14.52 (demorgan2a1) =>
% 107.13/14.52 ((
% 107.13/14.52 (complementUnionInPowersetComplement) =>
% 107.13/14.52 ((
% 107.13/14.52 (demorgan2a2) =>
% 107.13/14.52 ((
% 107.13/14.52 (demorgan1a) =>
% 107.13/14.52 ((
% 107.13/14.52 (demorgan1b) =>
% 107.13/14.52 ((
% 107.13/14.52 (demorgan1) =>
% 107.13/14.52 ((
% 107.13/14.52 (demorgan2a) =>
% 107.13/14.52 ((
% 107.13/14.52 (demorgan2b2) =>
% 107.13/14.52 ((
% 107.13/14.52 (demorgan2b) =>
% 107.13/14.52 ((
% 107.13/14.52 (demorgan2) =>
% 107.13/14.52 ((
% 107.13/14.52 (woz13rule0) =>
% 107.13/14.52 ((
% 107.13/14.52 (woz13rule1) =>
% 107.13/14.52 ((
% 107.13/14.52 (woz13rule2) =>
% 107.13/14.52 ((
% 107.13/14.52 (woz13rule3) =>
% 107.13/14.52 ((
% 107.13/14.52 (woz13rule4) =>
% 107.13/14.52 ((
% 107.13/14.52 (woz1_1) =>
% 107.13/14.52 ((
% 107.13/14.52 (woz1_2) =>
% 107.13/14.52 ((
% 107.13/14.52 (woz1_3) =>
% 107.13/14.52 ((
% 107.13/14.52 (woz1_4) =>
% 107.13/14.52 ((
% 107.13/14.52 (woz1_5) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1all2) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1SetBreln1) =>
% 107.13/14.52 ((
% 107.13/14.52 (choice2fnsingleton) =>
% 107.13/14.52 ((
% 107.13/14.52 (setOfPairsIsBReln1) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1all1) =>
% 107.13/14.52 ((
% 107.13/14.52 (subbreln1) =>
% 107.13/14.52 ((
% 107.13/14.52 (eqbreln1) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1invprop) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1invI) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1invE) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1compprop) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1compI) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1compE) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1compEex) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1unionprop) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1unionIL) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1unionIR) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1unionI) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1unionE) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1unionEcases) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1unionCommutes) =>
% 107.13/14.52 ((
% 107.13/14.52 (woz2Ex) =>
% 107.13/14.52 ((
% 107.13/14.52 (woz2W) =>
% 107.13/14.52 ((
% 107.13/14.52 (woz2A) =>
% 107.13/14.52 ((
% 107.13/14.52 (woz2B) =>
% 107.13/14.52 ((
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% 107.13/14.52 ((
% 107.13/14.52 (image1Ex1) =>
% 107.13/14.52 ((
% 107.13/14.52 (image1Equiv) =>
% 107.13/14.52 ((
% 107.13/14.52 (image1E) =>
% 107.13/14.52 ((
% 107.13/14.52 (image1I) =>
% 107.13/14.52 ((
% 107.13/14.52 (injFuncInInjFuncSet) =>
% 107.13/14.52 ((
% 107.13/14.52 (injFuncSetFuncIn) =>
% 107.13/14.52 ((
% 107.13/14.52 (injFuncSetFuncInj) =>
% 107.13/14.52 ((
% 107.13/14.52 (surjFuncSetFuncIn) =>
% 107.13/14.52 ((
% 107.13/14.52 (surjFuncSetFuncSurj) =>
% 107.13/14.52 ((
% 107.13/14.52 (leftInvIsSurj) =>
% 107.13/14.52 ((
% 107.13/14.52 (surjCantorThm) =>
% 107.13/14.52 ((
% 107.13/14.52 (!!) @ (
% 107.13/14.52 (('#S') @ (
% 107.13/14.52 (
% 107.13/14.52 ('#B') @ (
% 107.13/14.52 =>) @
% 107.13/14.52 nonempty)) @
% 107.13/14.52 (
% 107.13/14.52 (
% 107.13/14.52 ('#B') @ (
% 107.13/14.52 ??) @
% 107.13/14.52 (
% 107.13/14.52 (
% 107.13/14.52 ('#S') @ (
% 107.13/14.52 (
% 107.13/14.52 ('#B') @ (
% 107.13/14.52 '#S') @
% 107.13/14.52 (
% 107.13/14.52 (
% 107.13/14.52 ('#B') @ (
% 107.13/14.52 (
% 107.13/14.52 ('#B') @ (
% 107.13/14.52 &))) @
% 107.13/14.52 (
% 107.13/14.52 (
% 107.13/14.52 ('#C') @ in)))))) @
% 107.13/14.52 (
% 107.13/14.52 (
% 107.13/14.52 ('#C') @ (
% 107.13/14.52 (
% 107.13/14.52 ('#B') @ (
% 107.13/14.52 '#C') @
% 107.13/14.52 (
% 107.13/14.52 (
% 107.13/14.52 ('#B') @ (
% 107.13/14.52 (
% 107.13/14.52 ('#B') @ (
% 107.13/14.52 =))) @
% 107.13/14.52 (
% 107.13/14.52 (
% 107.13/14.52 ('#C') @ binintersect)))))) @
% 107.13/14.52 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 107.13/14.52 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1121])).
% 107.13/14.52 thf(zip_derived_cl1135, plain,
% 107.13/14.52 (~ (((binunionRsub) =>
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% 107.13/14.52 (((binintersectSubset5) =>
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% 107.13/14.52 (((binintersectLsub) =>
% 107.13/14.52 (((binintersectSubset2) =>
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% 107.13/14.52 (((binintersectER) =>
% 107.13/14.52 (((disjointsetsI1) =>
% 107.13/14.52 (((binintersectRsub) =>
% 107.13/14.52 (((binintersectSubset4) =>
% 107.13/14.52 (((binintersectSubset1) =>
% 107.13/14.52 (((bs114d) =>
% 107.13/14.52 (((setminusI) =>
% 107.13/14.52 (((setminusEL) =>
% 107.13/14.52 (((setminusER) =>
% 107.13/14.52 (((setminusSubset2) =>
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% 107.13/14.52 (((setminusELneg) =>
% 107.13/14.52 (((setminusILneg) =>
% 107.13/14.52 (((setminusIRneg) =>
% 107.13/14.52 (((setminusLsub) =>
% 107.13/14.52 (((setminusSubset1) =>
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% 107.13/14.52 (((symdiffI1) =>
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% 107.13/14.52 (((symdiffIneg2) =>
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% 107.13/14.52 (((setukpairIL) =>
% 107.13/14.52 ((
% 107.13/14.52 (setukpairIR) =>
% 107.13/14.52 ((
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% 107.13/14.52 ((
% 107.13/14.52 (kpairp) =>
% 107.13/14.52 ((
% 107.13/14.52 (singletonsubset) =>
% 107.13/14.52 ((
% 107.13/14.52 (singletoninpowerset) =>
% 107.13/14.52 ((
% 107.13/14.52 (singletoninpowunion) =>
% 107.13/14.52 ((
% 107.13/14.52 (upairset2E) =>
% 107.13/14.52 ((
% 107.13/14.52 (upairsubunion) =>
% 107.13/14.52 ((
% 107.13/14.52 (upairinpowunion) =>
% 107.13/14.52 ((
% 107.13/14.52 (ubforcartprodlem1) =>
% 107.13/14.52 ((
% 107.13/14.52 (ubforcartprodlem2) =>
% 107.13/14.52 ((
% 107.13/14.52 (ubforcartprodlem3) =>
% 107.13/14.52 ((
% 107.13/14.52 (cartprodpairin) =>
% 107.13/14.52 ((
% 107.13/14.52 (cartprodmempair1) =>
% 107.13/14.52 ((
% 107.13/14.52 (cartprodmempair) =>
% 107.13/14.52 ((
% 107.13/14.52 (setunionE2) =>
% 107.13/14.52 ((
% 107.13/14.52 (setunionsingleton1) =>
% 107.13/14.52 ((
% 107.13/14.52 (setunionsingleton2) =>
% 107.13/14.52 ((
% 107.13/14.52 (setunionsingleton) =>
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% 107.13/14.52 ((
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% 107.13/14.52 ((
% 107.13/14.52 (ex1I2) =>
% 107.13/14.52 ((
% 107.13/14.52 (singletonsuniq) =>
% 107.13/14.52 ((
% 107.13/14.52 (setukpairinjL1) =>
% 107.13/14.52 ((
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% 107.13/14.52 ((
% 107.13/14.52 (theprop) =>
% 107.13/14.52 ((
% 107.13/14.52 (kfstpairEq) =>
% 107.13/14.52 ((
% 107.13/14.52 (cartprodfstin) =>
% 107.13/14.52 ((
% 107.13/14.52 (setukpairinjL2) =>
% 107.13/14.52 ((
% 107.13/14.52 (setukpairinjL) =>
% 107.13/14.52 ((
% 107.13/14.52 (setukpairinjR11) =>
% 107.13/14.52 ((
% 107.13/14.52 (setukpairinjR12) =>
% 107.13/14.52 ((
% 107.13/14.52 (setukpairinjR1) =>
% 107.13/14.52 ((
% 107.13/14.52 (upairequniteq) =>
% 107.13/14.52 ((
% 107.13/14.52 (setukpairinjR2) =>
% 107.13/14.52 ((
% 107.13/14.52 (setukpairinjR) =>
% 107.13/14.52 ((
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% 107.13/14.52 ((
% 107.13/14.52 (ksndpairEq) =>
% 107.13/14.52 ((
% 107.13/14.52 (kpairsurjEq) =>
% 107.13/14.52 ((
% 107.13/14.52 (cartprodsndin) =>
% 107.13/14.52 ((
% 107.13/14.52 (cartprodpairmemEL) =>
% 107.13/14.52 ((
% 107.13/14.52 (cartprodpairmemER) =>
% 107.13/14.52 ((
% 107.13/14.52 (cartprodmempaircEq) =>
% 107.13/14.52 ((
% 107.13/14.52 (cartprodfstpairEq) =>
% 107.13/14.52 ((
% 107.13/14.52 (cartprodsndpairEq) =>
% 107.13/14.52 ((
% 107.13/14.52 (cartprodpairsurjEq) =>
% 107.13/14.52 ((
% 107.13/14.52 (dpsetconstrI) =>
% 107.13/14.52 ((
% 107.13/14.52 (dpsetconstrSub) =>
% 107.13/14.52 ((
% 107.13/14.52 (setOfPairsIsBReln) =>
% 107.13/14.52 ((
% 107.13/14.52 (dpsetconstrERa) =>
% 107.13/14.52 ((
% 107.13/14.52 (dpsetconstrEL1) =>
% 107.13/14.52 ((
% 107.13/14.52 (dpsetconstrEL2) =>
% 107.13/14.52 ((
% 107.13/14.52 (dpsetconstrER) =>
% 107.13/14.52 ((
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% 107.13/14.52 ((
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% 107.13/14.52 ((
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% 107.13/14.52 ((
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% 107.13/14.52 ((
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% 107.13/14.52 ((
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% 107.13/14.52 ((
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% 107.13/14.52 ((
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% 107.13/14.52 ((
% 107.13/14.52 (brelnall2) =>
% 107.13/14.52 ((
% 107.13/14.52 (ex1E2) =>
% 107.13/14.52 ((
% 107.13/14.52 (funcGraphProp1) =>
% 107.13/14.52 ((
% 107.13/14.52 (funcGraphProp3) =>
% 107.13/14.52 ((
% 107.13/14.52 (funcGraphProp2) =>
% 107.13/14.52 ((
% 107.13/14.52 (funcextLem) =>
% 107.13/14.52 ((
% 107.13/14.52 (funcGraphProp4) =>
% 107.13/14.52 ((
% 107.13/14.52 (subbreln) =>
% 107.13/14.52 ((
% 107.13/14.52 (eqbreln) =>
% 107.13/14.52 ((
% 107.13/14.52 (funcext) =>
% 107.13/14.52 ((
% 107.13/14.52 (funcext2) =>
% 107.13/14.52 ((
% 107.13/14.52 (ap2apEq1) =>
% 107.13/14.52 ((
% 107.13/14.52 (ap2apEq2) =>
% 107.13/14.52 ((
% 107.13/14.52 (beta1) =>
% 107.13/14.52 ((
% 107.13/14.52 (eta1) =>
% 107.13/14.52 ((
% 107.13/14.52 (lam2lamEq) =>
% 107.13/14.52 ((
% 107.13/14.52 (beta2) =>
% 107.13/14.52 ((
% 107.13/14.52 (eta2) =>
% 107.13/14.52 ((
% 107.13/14.52 (iffalseProp1) =>
% 107.13/14.52 ((
% 107.13/14.52 (iffalseProp2) =>
% 107.13/14.52 ((
% 107.13/14.52 (iftrueProp1) =>
% 107.13/14.52 ((
% 107.13/14.52 (iftrueProp2) =>
% 107.13/14.52 ((
% 107.13/14.52 (ifSingleton) =>
% 107.13/14.52 ((
% 107.13/14.52 (ifp) =>
% 107.13/14.52 ((
% 107.13/14.52 (theeq) =>
% 107.13/14.52 ((
% 107.13/14.52 (iftrue) =>
% 107.13/14.52 ((
% 107.13/14.52 (iffalse) =>
% 107.13/14.52 ((
% 107.13/14.52 (iftrueorfalse) =>
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% 107.13/14.52 ((
% 107.13/14.52 (binunionT_lem) =>
% 107.13/14.52 ((
% 107.13/14.52 (powersetT_lem) =>
% 107.13/14.52 ((
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% 107.13/14.52 (complementT_lem) =>
% 107.13/14.52 ((
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% 107.13/14.52 ((
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% 107.13/14.52 ((
% 107.13/14.52 (complementTI1) =>
% 107.13/14.52 ((
% 107.13/14.52 (complementTE1) =>
% 107.13/14.52 ((
% 107.13/14.52 (binintersectTELcontra) =>
% 107.13/14.52 ((
% 107.13/14.52 (binintersectTERcontra) =>
% 107.13/14.52 ((
% 107.13/14.52 (contrasubsetT) =>
% 107.13/14.52 ((
% 107.13/14.52 (contrasubsetT1) =>
% 107.13/14.52 ((
% 107.13/14.52 (contrasubsetT2) =>
% 107.13/14.52 ((
% 107.13/14.52 (contrasubsetT3) =>
% 107.13/14.52 ((
% 107.13/14.52 (doubleComplementI1) =>
% 107.13/14.52 ((
% 107.13/14.52 (doubleComplementE1) =>
% 107.13/14.52 ((
% 107.13/14.52 (doubleComplementSub1) =>
% 107.13/14.52 ((
% 107.13/14.52 (doubleComplementSub2) =>
% 107.13/14.52 ((
% 107.13/14.52 (doubleComplementEq) =>
% 107.13/14.52 ((
% 107.13/14.52 (complementTnotintersectT) =>
% 107.13/14.52 ((
% 107.13/14.52 (complementImpComplementIntersect) =>
% 107.13/14.52 ((
% 107.13/14.52 (complementSubsetComplementIntersect) =>
% 107.13/14.52 ((
% 107.13/14.52 (complementInPowersetComplementIntersect) =>
% 107.13/14.52 ((
% 107.13/14.52 (contraSubsetComplement) =>
% 107.13/14.52 ((
% 107.13/14.52 (complementTcontraSubset) =>
% 107.13/14.52 ((
% 107.13/14.52 (binunionTILcontra) =>
% 107.13/14.52 ((
% 107.13/14.52 (binunionTIRcontra) =>
% 107.13/14.52 ((
% 107.13/14.52 (inIntersectImpInUnion) =>
% 107.13/14.52 ((
% 107.13/14.52 (inIntersectImpInUnion2) =>
% 107.13/14.52 ((
% 107.13/14.52 (inIntersectImpInIntersectUnions) =>
% 107.13/14.52 ((
% 107.13/14.52 (intersectInPowersetIntersectUnions) =>
% 107.13/14.52 ((
% 107.13/14.52 (inComplementUnionImpNotIn1) =>
% 107.13/14.52 ((
% 107.13/14.52 (inComplementUnionImpInComplement1) =>
% 107.13/14.52 ((
% 107.13/14.52 (binunionTE) =>
% 107.13/14.52 ((
% 107.13/14.52 (binunionTEcontra) =>
% 107.13/14.52 ((
% 107.13/14.52 (demorgan2a1) =>
% 107.13/14.52 ((
% 107.13/14.52 (complementUnionInPowersetComplement) =>
% 107.13/14.52 ((
% 107.13/14.52 (demorgan2a2) =>
% 107.13/14.52 ((
% 107.13/14.52 (demorgan1a) =>
% 107.13/14.52 ((
% 107.13/14.52 (demorgan1b) =>
% 107.13/14.52 ((
% 107.13/14.52 (demorgan1) =>
% 107.13/14.52 ((
% 107.13/14.52 (demorgan2a) =>
% 107.13/14.52 ((
% 107.13/14.52 (demorgan2b2) =>
% 107.13/14.52 ((
% 107.13/14.52 (demorgan2b) =>
% 107.13/14.52 ((
% 107.13/14.52 (demorgan2) =>
% 107.13/14.52 ((
% 107.13/14.52 (woz13rule0) =>
% 107.13/14.52 ((
% 107.13/14.52 (woz13rule1) =>
% 107.13/14.52 ((
% 107.13/14.52 (woz13rule2) =>
% 107.13/14.52 ((
% 107.13/14.52 (woz13rule3) =>
% 107.13/14.52 ((
% 107.13/14.52 (woz13rule4) =>
% 107.13/14.52 ((
% 107.13/14.52 (woz1_1) =>
% 107.13/14.52 ((
% 107.13/14.52 (woz1_2) =>
% 107.13/14.52 ((
% 107.13/14.52 (woz1_3) =>
% 107.13/14.52 ((
% 107.13/14.52 (woz1_4) =>
% 107.13/14.52 ((
% 107.13/14.52 (woz1_5) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1all2) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1SetBreln1) =>
% 107.13/14.52 ((
% 107.13/14.52 (choice2fnsingleton) =>
% 107.13/14.52 ((
% 107.13/14.52 (setOfPairsIsBReln1) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1all1) =>
% 107.13/14.52 ((
% 107.13/14.52 (subbreln1) =>
% 107.13/14.52 ((
% 107.13/14.52 (eqbreln1) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1invprop) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1invI) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1invE) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1compprop) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1compI) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1compE) =>
% 107.13/14.52 ((
% 107.13/14.52 (breln1compEex) =>
% 107.13/14.53 ((
% 107.13/14.53 (breln1unionprop) =>
% 107.13/14.53 ((
% 107.13/14.53 (breln1unionIL) =>
% 107.13/14.53 ((
% 107.13/14.53 (breln1unionIR) =>
% 107.13/14.53 ((
% 107.13/14.53 (breln1unionI) =>
% 107.13/14.53 ((
% 107.13/14.53 (breln1unionE) =>
% 107.13/14.53 ((
% 107.13/14.53 (breln1unionEcases) =>
% 107.13/14.53 ((
% 107.13/14.53 (breln1unionCommutes) =>
% 107.13/14.53 ((
% 107.13/14.53 (woz2Ex) =>
% 107.13/14.53 ((
% 107.13/14.53 (woz2W) =>
% 107.13/14.53 ((
% 107.13/14.53 (woz2A) =>
% 107.13/14.53 ((
% 107.13/14.53 (woz2B) =>
% 107.13/14.53 ((
% 107.13/14.53 (image1Ex) =>
% 107.13/14.53 ((
% 107.13/14.53 (image1Ex1) =>
% 107.13/14.53 ((
% 107.13/14.53 (image1Equiv) =>
% 107.13/14.53 ((
% 107.13/14.53 (image1E) =>
% 107.13/14.53 ((
% 107.13/14.53 (image1I) =>
% 107.13/14.53 ((
% 107.13/14.53 (injFuncInInjFuncSet) =>
% 107.13/14.53 ((
% 107.13/14.53 (injFuncSetFuncIn) =>
% 107.13/14.53 ((
% 107.13/14.53 (injFuncSetFuncInj) =>
% 107.13/14.53 ((
% 107.13/14.53 (surjFuncSetFuncIn) =>
% 107.13/14.53 ((
% 107.13/14.53 (surjFuncSetFuncSurj) =>
% 107.13/14.53 ((
% 107.13/14.53 (leftInvIsSurj) =>
% 107.13/14.53 ((
% 107.13/14.53 (surjCantorThm) =>
% 107.13/14.53 ((
% 107.13/14.53 (!!) @ (
% 107.13/14.53 (('#S') @ (
% 107.13/14.53 (
% 107.13/14.53 ('#B') @ (
% 107.13/14.53 =>) @
% 107.13/14.53 nonempty)) @
% 107.13/14.53 (
% 107.13/14.53 (
% 107.13/14.53 ('#B') @ (
% 107.13/14.53 ??) @
% 107.13/14.53 (
% 107.13/14.53 (
% 107.13/14.53 ('#S') @ (
% 107.13/14.53 (
% 107.13/14.53 ('#B') @ (
% 107.13/14.53 '#S') @
% 107.13/14.53 (
% 107.13/14.53 (
% 107.13/14.53 ('#B') @ (
% 107.13/14.53 (
% 107.13/14.53 ('#B') @ (
% 107.13/14.53 &))) @
% 107.13/14.53 (
% 107.13/14.53 (
% 107.13/14.53 ('#C') @ in)))))) @
% 107.13/14.53 (
% 107.13/14.53 (
% 107.13/14.53 ('#C') @ (
% 107.13/14.53 (
% 107.13/14.53 ('#B') @ (
% 107.13/14.53 '#C') @
% 107.13/14.53 (
% 107.13/14.53 (
% 107.13/14.53 ('#B') @ (
% 107.13/14.53 (
% 107.13/14.53 ('#B') @ (
% 107.13/14.53 =))) @
% 107.13/14.53 (
% 107.13/14.53 (
% 107.13/14.53 ('#C') @ binintersect)))))) @
% 107.13/14.53 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 107.13/14.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1128])).
% 107.13/14.53 thf(zip_derived_cl1142, plain,
% 107.13/14.53 (~ (((binintersectI) =>
% 107.13/14.53 (((binintersectSubset5) =>
% 107.13/14.53 (((binintersectEL) =>
% 107.13/14.53 (((binintersectLsub) =>
% 107.13/14.53 (((binintersectSubset2) =>
% 107.13/14.53 (((binintersectSubset3) =>
% 107.13/14.53 (((binintersectER) =>
% 107.13/14.53 (((disjointsetsI1) =>
% 107.13/14.53 (((binintersectRsub) =>
% 107.13/14.53 (((binintersectSubset4) =>
% 107.13/14.53 (((binintersectSubset1) =>
% 107.13/14.53 (((bs114d) =>
% 107.13/14.53 (((setminusI) =>
% 107.13/14.53 (((setminusEL) =>
% 107.13/14.53 (((setminusER) =>
% 107.13/14.53 (((setminusSubset2) =>
% 107.13/14.53 (((setminusERneg) =>
% 107.13/14.53 (((setminusELneg) =>
% 107.13/14.53 (((setminusILneg) =>
% 107.13/14.53 (((setminusIRneg) =>
% 107.13/14.53 (((setminusLsub) =>
% 107.13/14.53 (((setminusSubset1) =>
% 107.13/14.53 (((symdiffE) =>
% 107.13/14.53 (((symdiffI1) =>
% 107.13/14.53 (((symdiffI2) =>
% 107.13/14.53 (((symdiffIneg1) =>
% 107.13/14.53 (((symdiffIneg2) =>
% 107.13/14.53 (((secondinupair) =>
% 107.13/14.53 (((setukpairIL) =>
% 107.13/14.53 (((setukpairIR) =>
% 107.13/14.53 ((
% 107.13/14.53 (kpairiskpair) =>
% 107.13/14.53 ((
% 107.13/14.53 (kpairp) =>
% 107.13/14.53 ((
% 107.13/14.53 (singletonsubset) =>
% 107.13/14.53 ((
% 107.13/14.53 (singletoninpowerset) =>
% 107.13/14.53 ((
% 107.13/14.53 (singletoninpowunion) =>
% 107.13/14.53 ((
% 107.13/14.53 (upairset2E) =>
% 107.13/14.53 ((
% 107.13/14.53 (upairsubunion) =>
% 107.13/14.53 ((
% 107.13/14.53 (upairinpowunion) =>
% 107.13/14.53 ((
% 107.13/14.53 (ubforcartprodlem1) =>
% 107.13/14.53 ((
% 107.13/14.53 (ubforcartprodlem2) =>
% 107.13/14.53 ((
% 107.13/14.53 (ubforcartprodlem3) =>
% 107.13/14.53 ((
% 107.13/14.53 (cartprodpairin) =>
% 107.13/14.53 ((
% 107.13/14.53 (cartprodmempair1) =>
% 107.13/14.53 ((
% 107.13/14.53 (cartprodmempair) =>
% 107.13/14.53 ((
% 107.13/14.53 (setunionE2) =>
% 107.13/14.53 ((
% 107.13/14.53 (setunionsingleton1) =>
% 107.13/14.53 ((
% 107.13/14.53 (setunionsingleton2) =>
% 107.13/14.53 ((
% 107.13/14.53 (setunionsingleton) =>
% 107.13/14.53 ((
% 107.13/14.53 (singletonprop) =>
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% 107.13/14.53 ((
% 107.13/14.53 (ex1I2) =>
% 107.13/14.53 ((
% 107.13/14.53 (singletonsuniq) =>
% 107.13/14.53 ((
% 107.13/14.53 (setukpairinjL1) =>
% 107.13/14.53 ((
% 107.13/14.53 (kfstsingleton) =>
% 107.13/14.53 ((
% 107.13/14.53 (theprop) =>
% 107.13/14.53 ((
% 107.13/14.53 (kfstpairEq) =>
% 107.13/14.53 ((
% 107.13/14.53 (cartprodfstin) =>
% 107.13/14.53 ((
% 107.13/14.53 (setukpairinjL2) =>
% 107.13/14.53 ((
% 107.13/14.53 (setukpairinjL) =>
% 107.13/14.53 ((
% 107.13/14.53 (setukpairinjR11) =>
% 107.13/14.53 ((
% 107.13/14.53 (setukpairinjR12) =>
% 107.13/14.53 ((
% 107.13/14.53 (setukpairinjR1) =>
% 107.13/14.53 ((
% 107.13/14.53 (upairequniteq) =>
% 107.13/14.53 ((
% 107.13/14.53 (setukpairinjR2) =>
% 107.13/14.53 ((
% 107.13/14.53 (setukpairinjR) =>
% 107.13/14.53 ((
% 107.13/14.53 (ksndsingleton) =>
% 107.13/14.53 ((
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% 107.13/14.53 ((
% 107.13/14.53 (kpairsurjEq) =>
% 107.13/14.53 ((
% 107.13/14.53 (cartprodsndin) =>
% 107.13/14.53 ((
% 107.13/14.53 (cartprodpairmemEL) =>
% 107.13/14.53 ((
% 107.13/14.53 (cartprodpairmemER) =>
% 107.13/14.53 ((
% 107.13/14.53 (cartprodmempaircEq) =>
% 107.13/14.53 ((
% 107.13/14.53 (cartprodfstpairEq) =>
% 107.13/14.53 ((
% 107.13/14.53 (cartprodsndpairEq) =>
% 107.13/14.53 ((
% 107.13/14.53 (cartprodpairsurjEq) =>
% 107.13/14.53 ((
% 107.13/14.53 (dpsetconstrI) =>
% 107.13/14.53 ((
% 107.13/14.53 (dpsetconstrSub) =>
% 107.13/14.53 ((
% 107.13/14.53 (setOfPairsIsBReln) =>
% 107.13/14.53 ((
% 107.13/14.53 (dpsetconstrERa) =>
% 107.13/14.53 ((
% 107.13/14.53 (dpsetconstrEL1) =>
% 107.13/14.53 ((
% 107.13/14.53 (dpsetconstrEL2) =>
% 107.13/14.53 ((
% 107.13/14.53 (dpsetconstrER) =>
% 107.13/14.53 ((
% 107.13/14.53 (funcImageSingleton) =>
% 107.13/14.53 ((
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% 107.13/14.53 ((
% 107.13/14.53 (app) =>
% 107.13/14.53 ((
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% 107.13/14.53 ((
% 107.13/14.53 (ap2p) =>
% 107.13/14.53 ((
% 107.13/14.53 (funcinfuncset) =>
% 107.13/14.53 ((
% 107.13/14.53 (lamProp) =>
% 107.13/14.53 ((
% 107.13/14.53 (lamp) =>
% 107.13/14.53 ((
% 107.13/14.53 (lam2p) =>
% 107.13/14.53 ((
% 107.13/14.53 (brelnall1) =>
% 107.13/14.53 ((
% 107.13/14.53 (brelnall2) =>
% 107.13/14.53 ((
% 107.13/14.53 (ex1E2) =>
% 107.13/14.53 ((
% 107.13/14.53 (funcGraphProp1) =>
% 107.13/14.53 ((
% 107.13/14.53 (funcGraphProp3) =>
% 107.13/14.53 ((
% 107.13/14.53 (funcGraphProp2) =>
% 107.13/14.53 ((
% 107.13/14.53 (funcextLem) =>
% 107.13/14.53 ((
% 107.13/14.53 (funcGraphProp4) =>
% 107.13/14.53 ((
% 107.13/14.53 (subbreln) =>
% 107.13/14.53 ((
% 107.13/14.53 (eqbreln) =>
% 107.13/14.53 ((
% 107.13/14.53 (funcext) =>
% 107.13/14.53 ((
% 107.13/14.53 (funcext2) =>
% 107.13/14.53 ((
% 107.13/14.53 (ap2apEq1) =>
% 107.13/14.53 ((
% 107.13/14.53 (ap2apEq2) =>
% 107.13/14.53 ((
% 107.13/14.53 (beta1) =>
% 107.13/14.53 ((
% 107.13/14.53 (eta1) =>
% 107.13/14.53 ((
% 107.13/14.53 (lam2lamEq) =>
% 107.13/14.53 ((
% 107.13/14.53 (beta2) =>
% 107.13/14.53 ((
% 107.13/14.53 (eta2) =>
% 107.13/14.53 ((
% 107.13/14.53 (iffalseProp1) =>
% 107.13/14.53 ((
% 107.13/14.53 (iffalseProp2) =>
% 107.13/14.53 ((
% 107.13/14.53 (iftrueProp1) =>
% 107.13/14.53 ((
% 107.13/14.53 (iftrueProp2) =>
% 107.13/14.53 ((
% 107.13/14.53 (ifSingleton) =>
% 107.13/14.53 ((
% 107.13/14.53 (ifp) =>
% 107.13/14.53 ((
% 107.13/14.53 (theeq) =>
% 107.13/14.53 ((
% 107.13/14.53 (iftrue) =>
% 107.13/14.53 ((
% 107.13/14.53 (iffalse) =>
% 107.13/14.53 ((
% 107.13/14.53 (iftrueorfalse) =>
% 107.13/14.53 ((
% 107.13/14.53 (binintersectT_lem) =>
% 107.13/14.53 ((
% 107.13/14.53 (binunionT_lem) =>
% 107.13/14.53 ((
% 107.13/14.53 (powersetT_lem) =>
% 107.13/14.53 ((
% 107.13/14.53 (setminusT_lem) =>
% 107.13/14.53 ((
% 107.13/14.53 (complementT_lem) =>
% 107.13/14.53 ((
% 107.13/14.53 (setextT) =>
% 107.13/14.53 ((
% 107.13/14.53 (subsetTI) =>
% 107.13/14.53 ((
% 107.13/14.53 (powersetTI1) =>
% 107.13/14.53 ((
% 107.13/14.53 (powersetTE1) =>
% 107.13/14.53 ((
% 107.13/14.53 (complementTI1) =>
% 107.13/14.53 ((
% 107.13/14.53 (complementTE1) =>
% 107.13/14.53 ((
% 107.13/14.53 (binintersectTELcontra) =>
% 107.13/14.53 ((
% 107.13/14.53 (binintersectTERcontra) =>
% 107.13/14.53 ((
% 107.13/14.53 (contrasubsetT) =>
% 107.13/14.53 ((
% 107.13/14.53 (contrasubsetT1) =>
% 107.13/14.53 ((
% 107.13/14.53 (contrasubsetT2) =>
% 107.13/14.53 ((
% 107.13/14.53 (contrasubsetT3) =>
% 107.13/14.53 ((
% 107.13/14.53 (doubleComplementI1) =>
% 107.13/14.53 ((
% 107.13/14.53 (doubleComplementE1) =>
% 107.13/14.53 ((
% 107.13/14.53 (doubleComplementSub1) =>
% 107.13/14.53 ((
% 107.13/14.53 (doubleComplementSub2) =>
% 107.13/14.53 ((
% 107.13/14.53 (doubleComplementEq) =>
% 107.13/14.53 ((
% 107.13/14.53 (complementTnotintersectT) =>
% 107.13/14.53 ((
% 107.13/14.53 (complementImpComplementIntersect) =>
% 107.13/14.53 ((
% 107.13/14.53 (complementSubsetComplementIntersect) =>
% 107.13/14.53 ((
% 107.13/14.53 (complementInPowersetComplementIntersect) =>
% 107.13/14.53 ((
% 107.13/14.53 (contraSubsetComplement) =>
% 107.13/14.53 ((
% 107.13/14.53 (complementTcontraSubset) =>
% 107.13/14.53 ((
% 107.13/14.53 (binunionTILcontra) =>
% 107.13/14.53 ((
% 107.13/14.53 (binunionTIRcontra) =>
% 107.13/14.53 ((
% 107.13/14.53 (inIntersectImpInUnion) =>
% 107.13/14.53 ((
% 107.13/14.53 (inIntersectImpInUnion2) =>
% 107.13/14.53 ((
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% 107.13/14.53 (intersectInPowersetIntersectUnions) =>
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% 107.13/14.53 (inComplementUnionImpNotIn1) =>
% 107.13/14.53 ((
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% 107.13/14.53 (demorgan2b) =>
% 107.13/14.53 ((
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% 107.13/14.53 ((
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% 107.13/14.53 ((
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% 107.13/14.53 ((
% 107.13/14.53 (woz13rule4) =>
% 107.13/14.53 ((
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% 107.13/14.53 (woz1_2) =>
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% 107.13/14.53 (woz1_5) =>
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% 107.13/14.53 (breln1all2) =>
% 107.13/14.53 ((
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% 107.13/14.53 ((
% 107.13/14.53 (choice2fnsingleton) =>
% 107.13/14.53 ((
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% 107.13/14.53 (breln1compI) =>
% 107.13/14.53 ((
% 107.13/14.53 (breln1compE) =>
% 107.13/14.53 ((
% 107.13/14.53 (breln1compEex) =>
% 107.13/14.53 ((
% 107.13/14.53 (breln1unionprop) =>
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% 107.13/14.53 ((
% 107.13/14.53 (breln1unionIR) =>
% 107.13/14.53 ((
% 107.13/14.53 (breln1unionI) =>
% 107.13/14.53 ((
% 107.13/14.53 (breln1unionE) =>
% 107.13/14.53 ((
% 107.13/14.53 (breln1unionEcases) =>
% 107.13/14.53 ((
% 107.13/14.53 (breln1unionCommutes) =>
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% 107.13/14.53 ((
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% 107.13/14.53 ((
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% 107.13/14.53 ((
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% 107.13/14.53 ((
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% 107.13/14.53 ((
% 107.13/14.53 (injFuncSetFuncIn) =>
% 107.13/14.53 ((
% 107.13/14.53 (injFuncSetFuncInj) =>
% 107.13/14.53 ((
% 107.13/14.53 (surjFuncSetFuncIn) =>
% 107.13/14.53 ((
% 107.13/14.53 (surjFuncSetFuncSurj) =>
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% 107.13/14.53 (surjCantorThm) =>
% 107.13/14.53 ((
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% 107.13/14.53 (('#S') @ (
% 107.13/14.53 (
% 107.13/14.53 ('#B') @ (
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% 107.13/14.53 nonempty)) @
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% 107.13/14.53 (
% 107.13/14.53 (
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% 107.13/14.53 (
% 107.13/14.53 (
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% 107.13/14.53 (
% 107.13/14.53 ('#B') @ (
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% 107.13/14.53 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 107.13/14.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1135])).
% 107.13/14.53 thf(zip_derived_cl1150, plain,
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% 107.13/14.53 ((
% 107.13/14.53 (singletoninpowunion) =>
% 107.13/14.53 ((
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% 107.13/14.53 ((
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% 107.13/14.53 ((
% 107.13/14.53 (upairinpowunion) =>
% 107.13/14.53 ((
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% 107.13/14.53 ((
% 107.13/14.53 (ubforcartprodlem2) =>
% 107.13/14.53 ((
% 107.13/14.53 (ubforcartprodlem3) =>
% 107.13/14.53 ((
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% 107.13/14.53 ((
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% 107.13/14.53 ((
% 107.13/14.53 (cartprodmempair) =>
% 107.13/14.53 ((
% 107.13/14.53 (setunionE2) =>
% 107.13/14.53 ((
% 107.13/14.53 (setunionsingleton1) =>
% 107.13/14.53 ((
% 107.13/14.53 (setunionsingleton2) =>
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% 107.13/14.53 ((
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% 107.13/14.53 ((
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% 107.13/14.53 ((
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% 107.13/14.53 ((
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% 107.13/14.53 (setukpairinjL) =>
% 107.13/14.53 ((
% 107.13/14.53 (setukpairinjR11) =>
% 107.13/14.53 ((
% 107.13/14.53 (setukpairinjR12) =>
% 107.13/14.53 ((
% 107.13/14.53 (setukpairinjR1) =>
% 107.13/14.53 ((
% 107.13/14.53 (upairequniteq) =>
% 107.13/14.53 ((
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% 107.13/14.53 ((
% 107.13/14.53 (setukpairinjR) =>
% 107.13/14.53 ((
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% 107.13/14.53 ((
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% 107.13/14.53 ((
% 107.13/14.53 (cartprodpairmemER) =>
% 107.13/14.53 ((
% 107.13/14.53 (cartprodmempaircEq) =>
% 107.13/14.53 ((
% 107.13/14.53 (cartprodfstpairEq) =>
% 107.13/14.53 ((
% 107.13/14.53 (cartprodsndpairEq) =>
% 107.13/14.53 ((
% 107.13/14.53 (cartprodpairsurjEq) =>
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% 107.13/14.53 ((
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% 107.13/14.53 ((
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% 107.13/14.53 ((
% 107.13/14.53 (funcGraphProp2) =>
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% 107.13/14.53 ((
% 107.13/14.53 (funcGraphProp4) =>
% 107.13/14.53 ((
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% 107.13/14.53 ((
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% 107.13/14.53 ((
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% 107.13/14.53 ((
% 107.13/14.53 (funcext2) =>
% 107.13/14.53 ((
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% 107.13/14.53 ((
% 107.13/14.53 (ap2apEq2) =>
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% 107.13/14.53 ((
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% 107.13/14.53 ((
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% 107.13/14.53 ((
% 107.13/14.53 (beta2) =>
% 107.13/14.53 ((
% 107.13/14.53 (eta2) =>
% 107.13/14.53 ((
% 107.13/14.53 (iffalseProp1) =>
% 107.13/14.53 ((
% 107.13/14.53 (iffalseProp2) =>
% 107.13/14.53 ((
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% 107.13/14.53 ((
% 107.13/14.53 (iftrueProp2) =>
% 107.13/14.53 ((
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% 107.13/14.53 ((
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% 107.13/14.53 ((
% 107.13/14.53 (theeq) =>
% 107.13/14.53 ((
% 107.13/14.53 (iftrue) =>
% 107.13/14.53 ((
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% 107.13/14.53 ((
% 107.13/14.53 (iftrueorfalse) =>
% 107.13/14.53 ((
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% 107.13/14.53 ((
% 107.13/14.53 (binunionT_lem) =>
% 107.13/14.53 ((
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% 107.13/14.53 ((
% 107.13/14.53 (setminusT_lem) =>
% 107.13/14.53 ((
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% 107.13/14.53 ((
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% 107.13/14.53 ((
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% 107.13/14.53 ((
% 107.13/14.53 (contrasubsetT2) =>
% 107.13/14.53 ((
% 107.13/14.53 (contrasubsetT3) =>
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% 107.13/14.53 (doubleComplementI1) =>
% 107.13/14.53 ((
% 107.13/14.53 (doubleComplementE1) =>
% 107.13/14.53 ((
% 107.13/14.53 (doubleComplementSub1) =>
% 107.13/14.53 ((
% 107.13/14.53 (doubleComplementSub2) =>
% 107.13/14.53 ((
% 107.13/14.53 (doubleComplementEq) =>
% 107.13/14.53 ((
% 107.13/14.53 (complementTnotintersectT) =>
% 107.13/14.53 ((
% 107.13/14.53 (complementImpComplementIntersect) =>
% 107.13/14.53 ((
% 107.13/14.53 (complementSubsetComplementIntersect) =>
% 107.13/14.53 ((
% 107.13/14.53 (complementInPowersetComplementIntersect) =>
% 107.13/14.53 ((
% 107.13/14.53 (contraSubsetComplement) =>
% 107.13/14.53 ((
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% 107.13/14.53 ((
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% 107.13/14.53 ((
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% 107.13/14.53 ((
% 107.13/14.53 (intersectInPowersetIntersectUnions) =>
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% 107.13/14.53 ((
% 107.13/14.53 (inComplementUnionImpInComplement1) =>
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% 107.13/14.53 ((
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% 107.13/14.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1150])).
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% 107.13/14.53 (lamp) =>
% 107.13/14.53 ((
% 107.13/14.53 (lam2p) =>
% 107.13/14.53 ((
% 107.13/14.53 (brelnall1) =>
% 107.13/14.53 ((
% 107.13/14.53 (brelnall2) =>
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% 107.13/14.53 (ex1E2) =>
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% 107.13/14.53 (funcGraphProp2) =>
% 107.13/14.53 ((
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% 107.13/14.53 (funcGraphProp4) =>
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% 107.13/14.53 (contrasubsetT3) =>
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% 107.13/14.53 (complementImpComplementIntersect) =>
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% 107.13/14.53 (inComplementUnionImpNotIn1) =>
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% 107.13/14.53 (demorgan2a) =>
% 107.13/14.53 ((
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% 107.13/14.53 (demorgan2b) =>
% 107.13/14.53 ((
% 107.13/14.53 (demorgan2) =>
% 107.13/14.53 ((
% 107.13/14.53 (woz13rule0) =>
% 107.13/14.53 ((
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% 107.13/14.53 (woz13rule2) =>
% 107.13/14.53 ((
% 107.13/14.53 (woz13rule3) =>
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% 107.13/14.53 (woz13rule4) =>
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% 107.13/14.53 (woz1_2) =>
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% 107.13/14.53 (woz1_4) =>
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% 107.13/14.53 (woz1_5) =>
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% 107.13/14.53 (breln1all2) =>
% 107.13/14.53 ((
% 107.13/14.53 (breln1SetBreln1) =>
% 107.13/14.53 ((
% 107.13/14.53 (choice2fnsingleton) =>
% 107.13/14.53 ((
% 107.13/14.53 (setOfPairsIsBReln1) =>
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% 107.13/14.53 (breln1compprop) =>
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% 107.13/14.53 (breln1compI) =>
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% 107.13/14.53 ((
% 107.13/14.53 (breln1compEex) =>
% 107.13/14.53 ((
% 107.13/14.53 (breln1unionprop) =>
% 107.13/14.53 ((
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% 107.13/14.53 ((
% 107.13/14.53 (breln1unionIR) =>
% 107.13/14.53 ((
% 107.13/14.53 (breln1unionI) =>
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% 107.13/14.53 (breln1unionE) =>
% 107.13/14.53 ((
% 107.13/14.53 (breln1unionEcases) =>
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% 107.13/14.53 ((
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% 107.13/14.53 ((
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% 107.13/14.53 ((
% 107.13/14.53 (image1I) =>
% 107.13/14.53 ((
% 107.13/14.53 (injFuncInInjFuncSet) =>
% 107.13/14.53 ((
% 107.13/14.53 (injFuncSetFuncIn) =>
% 107.13/14.53 ((
% 107.13/14.53 (injFuncSetFuncInj) =>
% 107.13/14.53 ((
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% 107.13/14.53 ((
% 107.13/14.53 (surjFuncSetFuncSurj) =>
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% 107.13/14.53 ((
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% 107.13/14.53 nonempty)) @
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% 107.13/14.53 (
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% 107.13/14.53 (
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% 107.13/14.53 (
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% 107.13/14.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1158])).
% 107.13/14.53 thf(zip_derived_cl1174, plain,
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% 107.13/14.53 ((
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% 107.13/14.53 ((
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% 107.13/14.53 ((
% 107.13/14.53 (ubforcartprodlem2) =>
% 107.13/14.53 ((
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% 107.13/14.53 ((
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% 107.13/14.53 ((
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% 107.13/14.53 ((
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% 107.13/14.53 ((
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% 107.13/14.53 (setukpairinjR1) =>
% 107.13/14.53 ((
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% 107.13/14.53 ((
% 107.13/14.53 (cartprodpairsurjEq) =>
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% 107.13/14.53 ((
% 107.13/14.53 (lamProp) =>
% 107.13/14.53 ((
% 107.13/14.53 (lamp) =>
% 107.13/14.53 ((
% 107.13/14.53 (lam2p) =>
% 107.13/14.53 ((
% 107.13/14.53 (brelnall1) =>
% 107.13/14.53 ((
% 107.13/14.53 (brelnall2) =>
% 107.13/14.53 ((
% 107.13/14.53 (ex1E2) =>
% 107.13/14.53 ((
% 107.13/14.53 (funcGraphProp1) =>
% 107.13/14.53 ((
% 107.13/14.53 (funcGraphProp3) =>
% 107.13/14.53 ((
% 107.13/14.53 (funcGraphProp2) =>
% 107.13/14.53 ((
% 107.13/14.53 (funcextLem) =>
% 107.13/14.53 ((
% 107.13/14.53 (funcGraphProp4) =>
% 107.13/14.53 ((
% 107.13/14.53 (subbreln) =>
% 107.13/14.53 ((
% 107.13/14.53 (eqbreln) =>
% 107.13/14.53 ((
% 107.13/14.53 (funcext) =>
% 107.13/14.53 ((
% 107.13/14.53 (funcext2) =>
% 107.13/14.53 ((
% 107.13/14.53 (ap2apEq1) =>
% 107.13/14.53 ((
% 107.13/14.53 (ap2apEq2) =>
% 107.13/14.53 ((
% 107.13/14.53 (beta1) =>
% 107.13/14.53 ((
% 107.13/14.53 (eta1) =>
% 107.13/14.53 ((
% 107.13/14.53 (lam2lamEq) =>
% 107.13/14.53 ((
% 107.13/14.53 (beta2) =>
% 107.13/14.53 ((
% 107.13/14.53 (eta2) =>
% 107.13/14.53 ((
% 107.13/14.53 (iffalseProp1) =>
% 107.13/14.53 ((
% 107.13/14.53 (iffalseProp2) =>
% 107.13/14.53 ((
% 107.13/14.53 (iftrueProp1) =>
% 107.13/14.53 ((
% 107.13/14.53 (iftrueProp2) =>
% 107.13/14.53 ((
% 107.13/14.53 (ifSingleton) =>
% 107.13/14.53 ((
% 107.13/14.53 (ifp) =>
% 107.13/14.53 ((
% 107.13/14.53 (theeq) =>
% 107.13/14.53 ((
% 107.13/14.53 (iftrue) =>
% 107.13/14.53 ((
% 107.13/14.53 (iffalse) =>
% 107.13/14.53 ((
% 107.13/14.53 (iftrueorfalse) =>
% 107.13/14.53 ((
% 107.13/14.53 (binintersectT_lem) =>
% 107.13/14.53 ((
% 107.13/14.53 (binunionT_lem) =>
% 107.13/14.53 ((
% 107.13/14.53 (powersetT_lem) =>
% 107.13/14.53 ((
% 107.13/14.53 (setminusT_lem) =>
% 107.13/14.53 ((
% 107.13/14.53 (complementT_lem) =>
% 107.13/14.53 ((
% 107.13/14.53 (setextT) =>
% 107.13/14.53 ((
% 107.13/14.53 (subsetTI) =>
% 107.13/14.53 ((
% 107.13/14.53 (powersetTI1) =>
% 107.13/14.53 ((
% 107.13/14.53 (powersetTE1) =>
% 107.13/14.53 ((
% 107.13/14.53 (complementTI1) =>
% 107.13/14.53 ((
% 107.13/14.53 (complementTE1) =>
% 107.13/14.53 ((
% 107.13/14.53 (binintersectTELcontra) =>
% 107.13/14.53 ((
% 107.13/14.53 (binintersectTERcontra) =>
% 107.13/14.53 ((
% 107.13/14.53 (contrasubsetT) =>
% 107.13/14.53 ((
% 107.13/14.53 (contrasubsetT1) =>
% 107.13/14.53 ((
% 107.13/14.53 (contrasubsetT2) =>
% 107.13/14.53 ((
% 107.13/14.53 (contrasubsetT3) =>
% 107.13/14.53 ((
% 107.13/14.53 (doubleComplementI1) =>
% 107.13/14.53 ((
% 107.13/14.53 (doubleComplementE1) =>
% 107.13/14.53 ((
% 107.13/14.53 (doubleComplementSub1) =>
% 107.13/14.53 ((
% 107.13/14.53 (doubleComplementSub2) =>
% 107.13/14.53 ((
% 107.13/14.53 (doubleComplementEq) =>
% 107.13/14.53 ((
% 107.13/14.53 (complementTnotintersectT) =>
% 107.13/14.53 ((
% 107.13/14.53 (complementImpComplementIntersect) =>
% 107.13/14.53 ((
% 107.13/14.53 (complementSubsetComplementIntersect) =>
% 107.13/14.53 ((
% 107.13/14.53 (complementInPowersetComplementIntersect) =>
% 107.13/14.53 ((
% 107.13/14.53 (contraSubsetComplement) =>
% 107.13/14.53 ((
% 107.13/14.53 (complementTcontraSubset) =>
% 107.13/14.53 ((
% 107.13/14.53 (binunionTILcontra) =>
% 107.13/14.53 ((
% 107.13/14.53 (binunionTIRcontra) =>
% 107.13/14.53 ((
% 107.13/14.53 (inIntersectImpInUnion) =>
% 107.13/14.53 ((
% 107.13/14.53 (inIntersectImpInUnion2) =>
% 107.13/14.53 ((
% 107.13/14.53 (inIntersectImpInIntersectUnions) =>
% 107.13/14.53 ((
% 107.13/14.53 (intersectInPowersetIntersectUnions) =>
% 107.13/14.53 ((
% 107.13/14.53 (inComplementUnionImpNotIn1) =>
% 107.13/14.53 ((
% 107.13/14.53 (inComplementUnionImpInComplement1) =>
% 107.13/14.53 ((
% 107.13/14.53 (binunionTE) =>
% 107.13/14.53 ((
% 107.13/14.53 (binunionTEcontra) =>
% 107.13/14.53 ((
% 107.13/14.53 (demorgan2a1) =>
% 107.13/14.53 ((
% 107.13/14.53 (complementUnionInPowersetComplement) =>
% 107.13/14.53 ((
% 107.13/14.53 (demorgan2a2) =>
% 107.13/14.53 ((
% 107.13/14.53 (demorgan1a) =>
% 107.13/14.53 ((
% 107.13/14.53 (demorgan1b) =>
% 107.13/14.53 ((
% 107.13/14.53 (demorgan1) =>
% 107.13/14.53 ((
% 107.13/14.53 (demorgan2a) =>
% 107.13/14.53 ((
% 107.13/14.53 (demorgan2b2) =>
% 107.13/14.53 ((
% 107.13/14.53 (demorgan2b) =>
% 107.13/14.53 ((
% 107.13/14.53 (demorgan2) =>
% 107.13/14.53 ((
% 107.13/14.53 (woz13rule0) =>
% 107.13/14.53 ((
% 107.13/14.53 (woz13rule1) =>
% 107.13/14.53 ((
% 107.13/14.53 (woz13rule2) =>
% 107.13/14.53 ((
% 107.13/14.53 (woz13rule3) =>
% 107.13/14.53 ((
% 107.13/14.53 (woz13rule4) =>
% 107.13/14.53 ((
% 107.13/14.53 (woz1_1) =>
% 107.13/14.53 ((
% 107.13/14.53 (woz1_2) =>
% 107.13/14.53 ((
% 107.13/14.53 (woz1_3) =>
% 107.13/14.53 ((
% 107.13/14.53 (woz1_4) =>
% 107.13/14.53 ((
% 107.13/14.53 (woz1_5) =>
% 107.13/14.53 ((
% 107.13/14.53 (breln1all2) =>
% 107.13/14.53 ((
% 107.13/14.53 (breln1SetBreln1) =>
% 107.13/14.53 ((
% 107.13/14.53 (choice2fnsingleton) =>
% 107.13/14.53 ((
% 107.13/14.53 (setOfPairsIsBReln1) =>
% 107.13/14.53 ((
% 107.13/14.53 (breln1all1) =>
% 107.13/14.53 ((
% 107.13/14.53 (subbreln1) =>
% 107.13/14.53 ((
% 107.13/14.53 (eqbreln1) =>
% 107.13/14.53 ((
% 107.13/14.53 (breln1invprop) =>
% 107.13/14.53 ((
% 107.13/14.53 (breln1invI) =>
% 107.13/14.53 ((
% 107.13/14.53 (breln1invE) =>
% 107.13/14.53 ((
% 107.13/14.53 (breln1compprop) =>
% 107.13/14.53 ((
% 107.13/14.53 (breln1compI) =>
% 107.13/14.53 ((
% 107.13/14.53 (breln1compE) =>
% 107.13/14.53 ((
% 107.13/14.53 (breln1compEex) =>
% 107.13/14.53 ((
% 107.13/14.53 (breln1unionprop) =>
% 107.13/14.53 ((
% 107.13/14.53 (breln1unionIL) =>
% 107.13/14.53 ((
% 107.13/14.53 (breln1unionIR) =>
% 107.13/14.53 ((
% 107.13/14.53 (breln1unionI) =>
% 107.13/14.53 ((
% 107.13/14.53 (breln1unionE) =>
% 107.13/14.53 ((
% 107.13/14.53 (breln1unionEcases) =>
% 107.13/14.53 ((
% 107.13/14.53 (breln1unionCommutes) =>
% 107.13/14.53 ((
% 107.13/14.53 (woz2Ex) =>
% 107.13/14.53 ((
% 107.13/14.53 (woz2W) =>
% 107.13/14.53 ((
% 107.13/14.53 (woz2A) =>
% 107.13/14.53 ((
% 107.13/14.53 (woz2B) =>
% 107.13/14.53 ((
% 107.13/14.53 (image1Ex) =>
% 107.13/14.53 ((
% 107.13/14.53 (image1Ex1) =>
% 107.13/14.53 ((
% 107.13/14.53 (image1Equiv) =>
% 107.13/14.53 ((
% 107.13/14.53 (image1E) =>
% 107.13/14.53 ((
% 107.13/14.53 (image1I) =>
% 107.13/14.53 ((
% 107.13/14.53 (injFuncInInjFuncSet) =>
% 107.13/14.53 ((
% 107.13/14.53 (injFuncSetFuncIn) =>
% 107.13/14.53 ((
% 107.13/14.53 (injFuncSetFuncInj) =>
% 107.13/14.53 ((
% 107.13/14.53 (surjFuncSetFuncIn) =>
% 107.13/14.53 ((
% 107.13/14.53 (surjFuncSetFuncSurj) =>
% 107.13/14.53 ((
% 107.13/14.53 (leftInvIsSurj) =>
% 107.13/14.53 ((
% 107.13/14.53 (surjCantorThm) =>
% 107.13/14.53 ((
% 107.13/14.53 (!!) @ (
% 107.13/14.53 (('#S') @ (
% 107.13/14.53 (
% 107.13/14.53 ('#B') @ (
% 107.13/14.53 =>) @
% 107.13/14.53 nonempty)) @
% 107.13/14.53 (
% 107.13/14.53 (
% 107.13/14.53 ('#B') @ (
% 107.13/14.53 ??) @
% 107.13/14.53 (
% 107.13/14.53 (
% 107.13/14.53 ('#S') @ (
% 107.13/14.53 (
% 107.13/14.53 ('#B') @ (
% 107.13/14.53 '#S') @
% 107.13/14.53 (
% 107.13/14.53 (
% 107.13/14.53 ('#B') @ (
% 107.13/14.53 (
% 107.13/14.53 ('#B') @ (
% 107.13/14.53 &))) @
% 107.13/14.53 (
% 107.13/14.53 (
% 107.13/14.53 ('#C') @ in)))))) @
% 107.13/14.53 (
% 107.13/14.53 (
% 107.13/14.53 ('#C') @ (
% 107.13/14.53 (
% 107.13/14.53 ('#B') @ (
% 107.13/14.53 '#C') @
% 107.13/14.53 (
% 107.13/14.53 (
% 107.13/14.53 ('#B') @ (
% 107.13/14.53 (
% 107.13/14.53 ('#B') @ (
% 107.13/14.53 =))) @
% 107.13/14.53 (
% 107.13/14.53 (
% 107.13/14.53 ('#C') @ binintersect)))))) @
% 107.13/14.53 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 107.13/14.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1166])).
% 107.13/14.53 thf(zip_derived_cl1183, plain,
% 107.13/14.53 (~ (((binintersectSubset3) =>
% 107.13/14.53 (((binintersectER) =>
% 107.13/14.53 (((disjointsetsI1) =>
% 107.13/14.53 (((binintersectRsub) =>
% 107.13/14.53 (((binintersectSubset4) =>
% 107.13/14.53 (((binintersectSubset1) =>
% 107.13/14.53 (((bs114d) =>
% 107.13/14.53 (((setminusI) =>
% 107.13/14.53 (((setminusEL) =>
% 107.13/14.53 (((setminusER) =>
% 107.13/14.53 (((setminusSubset2) =>
% 107.13/14.53 (((setminusERneg) =>
% 107.13/14.53 (((setminusELneg) =>
% 107.13/14.53 (((setminusILneg) =>
% 107.13/14.53 (((setminusIRneg) =>
% 107.13/14.53 (((setminusLsub) =>
% 107.13/14.53 (((setminusSubset1) =>
% 107.13/14.53 (((symdiffE) =>
% 107.13/14.53 (((symdiffI1) =>
% 107.13/14.53 (((symdiffI2) =>
% 107.13/14.53 (((symdiffIneg1) =>
% 107.13/14.53 (((symdiffIneg2) =>
% 107.13/14.53 (((secondinupair) =>
% 107.13/14.53 (((setukpairIL) =>
% 107.13/14.53 (((setukpairIR) =>
% 107.13/14.53 (((kpairiskpair) =>
% 107.13/14.53 (((kpairp) =>
% 107.13/14.53 (((singletonsubset) =>
% 107.13/14.53 (((singletoninpowerset) =>
% 107.13/14.53 (((singletoninpowunion) =>
% 107.13/14.53 ((
% 107.13/14.53 (upairset2E) =>
% 107.13/14.53 ((
% 107.13/14.53 (upairsubunion) =>
% 107.13/14.53 ((
% 107.13/14.53 (upairinpowunion) =>
% 107.13/14.53 ((
% 107.13/14.53 (ubforcartprodlem1) =>
% 107.13/14.53 ((
% 107.13/14.53 (ubforcartprodlem2) =>
% 107.13/14.53 ((
% 107.13/14.53 (ubforcartprodlem3) =>
% 107.13/14.53 ((
% 107.13/14.53 (cartprodpairin) =>
% 107.13/14.53 ((
% 107.13/14.53 (cartprodmempair1) =>
% 107.13/14.53 ((
% 107.13/14.53 (cartprodmempair) =>
% 107.13/14.53 ((
% 107.13/14.53 (setunionE2) =>
% 107.13/14.53 ((
% 107.13/14.53 (setunionsingleton1) =>
% 107.13/14.53 ((
% 107.13/14.53 (setunionsingleton2) =>
% 107.13/14.53 ((
% 107.13/14.53 (setunionsingleton) =>
% 107.13/14.53 ((
% 107.13/14.53 (singletonprop) =>
% 107.13/14.53 ((
% 107.13/14.53 (ex1E1) =>
% 107.13/14.53 ((
% 107.13/14.53 (ex1I) =>
% 107.13/14.53 ((
% 107.13/14.53 (ex1I2) =>
% 107.13/14.53 ((
% 107.13/14.53 (singletonsuniq) =>
% 107.13/14.53 ((
% 107.13/14.53 (setukpairinjL1) =>
% 107.13/14.53 ((
% 107.13/14.53 (kfstsingleton) =>
% 107.13/14.53 ((
% 107.13/14.53 (theprop) =>
% 107.13/14.53 ((
% 107.13/14.53 (kfstpairEq) =>
% 107.13/14.53 ((
% 107.13/14.53 (cartprodfstin) =>
% 107.13/14.53 ((
% 107.13/14.53 (setukpairinjL2) =>
% 107.13/14.53 ((
% 107.13/14.53 (setukpairinjL) =>
% 107.13/14.53 ((
% 107.13/14.53 (setukpairinjR11) =>
% 107.13/14.53 ((
% 107.13/14.53 (setukpairinjR12) =>
% 107.13/14.53 ((
% 107.13/14.53 (setukpairinjR1) =>
% 107.13/14.53 ((
% 107.13/14.53 (upairequniteq) =>
% 107.13/14.53 ((
% 107.13/14.53 (setukpairinjR2) =>
% 107.13/14.53 ((
% 107.13/14.53 (setukpairinjR) =>
% 107.13/14.53 ((
% 107.13/14.53 (ksndsingleton) =>
% 107.13/14.53 ((
% 107.13/14.53 (ksndpairEq) =>
% 107.13/14.53 ((
% 107.13/14.53 (kpairsurjEq) =>
% 107.13/14.53 ((
% 107.13/14.53 (cartprodsndin) =>
% 107.13/14.53 ((
% 107.13/14.53 (cartprodpairmemEL) =>
% 107.13/14.53 ((
% 107.13/14.53 (cartprodpairmemER) =>
% 107.13/14.53 ((
% 107.13/14.53 (cartprodmempaircEq) =>
% 107.13/14.53 ((
% 107.13/14.53 (cartprodfstpairEq) =>
% 107.13/14.53 ((
% 107.13/14.53 (cartprodsndpairEq) =>
% 107.13/14.53 ((
% 107.13/14.53 (cartprodpairsurjEq) =>
% 107.13/14.53 ((
% 107.13/14.53 (dpsetconstrI) =>
% 107.13/14.53 ((
% 107.13/14.53 (dpsetconstrSub) =>
% 107.13/14.53 ((
% 107.13/14.53 (setOfPairsIsBReln) =>
% 107.13/14.53 ((
% 107.13/14.53 (dpsetconstrERa) =>
% 107.13/14.53 ((
% 107.13/14.53 (dpsetconstrEL1) =>
% 107.13/14.53 ((
% 107.13/14.53 (dpsetconstrEL2) =>
% 107.13/14.53 ((
% 107.13/14.53 (dpsetconstrER) =>
% 107.13/14.53 ((
% 107.13/14.53 (funcImageSingleton) =>
% 107.13/14.53 ((
% 107.13/14.53 (apProp) =>
% 107.13/14.53 ((
% 107.13/14.53 (app) =>
% 107.13/14.53 ((
% 107.13/14.53 (infuncsetfunc) =>
% 107.13/14.53 ((
% 107.13/14.53 (ap2p) =>
% 107.13/14.53 ((
% 107.13/14.53 (funcinfuncset) =>
% 107.13/14.53 ((
% 107.13/14.53 (lamProp) =>
% 107.13/14.53 ((
% 107.13/14.53 (lamp) =>
% 107.13/14.53 ((
% 107.13/14.53 (lam2p) =>
% 107.13/14.53 ((
% 107.13/14.53 (brelnall1) =>
% 107.13/14.53 ((
% 107.13/14.53 (brelnall2) =>
% 107.13/14.53 ((
% 107.13/14.53 (ex1E2) =>
% 107.13/14.53 ((
% 107.13/14.53 (funcGraphProp1) =>
% 107.13/14.53 ((
% 107.13/14.53 (funcGraphProp3) =>
% 107.13/14.53 ((
% 107.13/14.53 (funcGraphProp2) =>
% 107.13/14.53 ((
% 107.13/14.53 (funcextLem) =>
% 107.13/14.53 ((
% 107.13/14.53 (funcGraphProp4) =>
% 107.13/14.53 ((
% 107.13/14.53 (subbreln) =>
% 107.13/14.53 ((
% 107.13/14.53 (eqbreln) =>
% 107.13/14.53 ((
% 107.13/14.53 (funcext) =>
% 107.13/14.53 ((
% 107.13/14.53 (funcext2) =>
% 107.13/14.53 ((
% 107.13/14.53 (ap2apEq1) =>
% 107.13/14.53 ((
% 107.13/14.53 (ap2apEq2) =>
% 107.13/14.53 ((
% 107.13/14.53 (beta1) =>
% 107.13/14.53 ((
% 107.13/14.53 (eta1) =>
% 107.13/14.53 ((
% 107.13/14.53 (lam2lamEq) =>
% 107.13/14.53 ((
% 107.13/14.53 (beta2) =>
% 107.13/14.53 ((
% 107.13/14.53 (eta2) =>
% 107.13/14.53 ((
% 107.13/14.53 (iffalseProp1) =>
% 107.13/14.53 ((
% 107.13/14.53 (iffalseProp2) =>
% 107.13/14.53 ((
% 107.13/14.53 (iftrueProp1) =>
% 107.13/14.53 ((
% 107.13/14.53 (iftrueProp2) =>
% 107.13/14.53 ((
% 107.13/14.53 (ifSingleton) =>
% 107.13/14.53 ((
% 107.13/14.53 (ifp) =>
% 107.13/14.53 ((
% 107.13/14.53 (theeq) =>
% 107.13/14.53 ((
% 107.13/14.53 (iftrue) =>
% 107.13/14.53 ((
% 107.13/14.53 (iffalse) =>
% 107.13/14.53 ((
% 107.13/14.53 (iftrueorfalse) =>
% 107.13/14.53 ((
% 107.13/14.53 (binintersectT_lem) =>
% 107.13/14.53 ((
% 107.13/14.53 (binunionT_lem) =>
% 107.13/14.53 ((
% 107.13/14.53 (powersetT_lem) =>
% 107.13/14.53 ((
% 107.13/14.53 (setminusT_lem) =>
% 107.13/14.53 ((
% 107.13/14.53 (complementT_lem) =>
% 107.13/14.53 ((
% 107.13/14.53 (setextT) =>
% 107.13/14.53 ((
% 107.13/14.53 (subsetTI) =>
% 107.13/14.53 ((
% 107.13/14.53 (powersetTI1) =>
% 107.13/14.53 ((
% 107.13/14.53 (powersetTE1) =>
% 107.13/14.53 ((
% 107.13/14.53 (complementTI1) =>
% 107.13/14.53 ((
% 107.13/14.53 (complementTE1) =>
% 107.13/14.53 ((
% 107.13/14.53 (binintersectTELcontra) =>
% 107.13/14.53 ((
% 107.13/14.53 (binintersectTERcontra) =>
% 107.13/14.53 ((
% 107.13/14.53 (contrasubsetT) =>
% 107.13/14.53 ((
% 107.13/14.53 (contrasubsetT1) =>
% 107.13/14.53 ((
% 107.13/14.53 (contrasubsetT2) =>
% 107.13/14.53 ((
% 107.13/14.53 (contrasubsetT3) =>
% 107.13/14.53 ((
% 107.13/14.53 (doubleComplementI1) =>
% 107.13/14.53 ((
% 107.13/14.53 (doubleComplementE1) =>
% 107.13/14.53 ((
% 107.13/14.53 (doubleComplementSub1) =>
% 107.13/14.53 ((
% 107.13/14.53 (doubleComplementSub2) =>
% 107.13/14.53 ((
% 107.13/14.53 (doubleComplementEq) =>
% 107.13/14.53 ((
% 107.13/14.53 (complementTnotintersectT) =>
% 107.13/14.53 ((
% 107.13/14.53 (complementImpComplementIntersect) =>
% 107.13/14.53 ((
% 107.13/14.53 (complementSubsetComplementIntersect) =>
% 107.13/14.53 ((
% 107.13/14.53 (complementInPowersetComplementIntersect) =>
% 107.13/14.53 ((
% 107.13/14.53 (contraSubsetComplement) =>
% 107.13/14.53 ((
% 107.13/14.53 (complementTcontraSubset) =>
% 107.13/14.53 ((
% 107.13/14.53 (binunionTILcontra) =>
% 107.13/14.53 ((
% 107.13/14.53 (binunionTIRcontra) =>
% 107.13/14.53 ((
% 107.13/14.53 (inIntersectImpInUnion) =>
% 107.13/14.53 ((
% 107.13/14.53 (inIntersectImpInUnion2) =>
% 107.13/14.53 ((
% 107.13/14.53 (inIntersectImpInIntersectUnions) =>
% 107.13/14.53 ((
% 107.13/14.53 (intersectInPowersetIntersectUnions) =>
% 107.13/14.53 ((
% 107.13/14.53 (inComplementUnionImpNotIn1) =>
% 107.13/14.53 ((
% 107.13/14.53 (inComplementUnionImpInComplement1) =>
% 107.13/14.53 ((
% 107.13/14.53 (binunionTE) =>
% 107.13/14.53 ((
% 107.13/14.53 (binunionTEcontra) =>
% 107.13/14.53 ((
% 107.13/14.53 (demorgan2a1) =>
% 107.13/14.53 ((
% 107.13/14.53 (complementUnionInPowersetComplement) =>
% 107.13/14.53 ((
% 107.13/14.53 (demorgan2a2) =>
% 107.13/14.53 ((
% 107.13/14.53 (demorgan1a) =>
% 107.13/14.53 ((
% 107.13/14.53 (demorgan1b) =>
% 107.13/14.53 ((
% 107.13/14.53 (demorgan1) =>
% 107.13/14.53 ((
% 107.13/14.53 (demorgan2a) =>
% 107.13/14.53 ((
% 107.13/14.53 (demorgan2b2) =>
% 107.13/14.53 ((
% 107.13/14.53 (demorgan2b) =>
% 107.13/14.53 ((
% 107.13/14.53 (demorgan2) =>
% 107.13/14.53 ((
% 107.13/14.53 (woz13rule0) =>
% 107.13/14.53 ((
% 107.13/14.53 (woz13rule1) =>
% 107.13/14.53 ((
% 107.13/14.53 (woz13rule2) =>
% 107.13/14.53 ((
% 107.13/14.53 (woz13rule3) =>
% 107.13/14.53 ((
% 107.13/14.53 (woz13rule4) =>
% 107.13/14.53 ((
% 107.13/14.53 (woz1_1) =>
% 107.13/14.53 ((
% 107.13/14.53 (woz1_2) =>
% 107.13/14.53 ((
% 107.13/14.53 (woz1_3) =>
% 107.13/14.53 ((
% 107.13/14.53 (woz1_4) =>
% 107.13/14.53 ((
% 107.13/14.53 (woz1_5) =>
% 107.13/14.53 ((
% 107.13/14.53 (breln1all2) =>
% 107.13/14.53 ((
% 107.13/14.53 (breln1SetBreln1) =>
% 107.13/14.53 ((
% 107.13/14.53 (choice2fnsingleton) =>
% 107.13/14.53 ((
% 107.13/14.53 (setOfPairsIsBReln1) =>
% 107.13/14.53 ((
% 107.13/14.53 (breln1all1) =>
% 107.13/14.53 ((
% 107.13/14.53 (subbreln1) =>
% 107.13/14.53 ((
% 107.13/14.53 (eqbreln1) =>
% 107.13/14.53 ((
% 107.13/14.53 (breln1invprop) =>
% 107.13/14.53 ((
% 107.13/14.53 (breln1invI) =>
% 107.13/14.53 ((
% 107.13/14.53 (breln1invE) =>
% 107.13/14.53 ((
% 107.13/14.53 (breln1compprop) =>
% 107.13/14.53 ((
% 107.13/14.53 (breln1compI) =>
% 107.13/14.53 ((
% 107.13/14.53 (breln1compE) =>
% 107.13/14.53 ((
% 107.13/14.53 (breln1compEex) =>
% 107.13/14.53 ((
% 107.13/14.53 (breln1unionprop) =>
% 107.13/14.53 ((
% 107.13/14.53 (breln1unionIL) =>
% 107.13/14.53 ((
% 107.13/14.53 (breln1unionIR) =>
% 107.13/14.53 ((
% 107.13/14.53 (breln1unionI) =>
% 107.13/14.53 ((
% 107.13/14.53 (breln1unionE) =>
% 107.13/14.53 ((
% 107.13/14.53 (breln1unionEcases) =>
% 107.13/14.53 ((
% 107.13/14.53 (breln1unionCommutes) =>
% 107.13/14.53 ((
% 107.13/14.53 (woz2Ex) =>
% 107.13/14.53 ((
% 107.13/14.53 (woz2W) =>
% 107.13/14.53 ((
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% 107.13/14.53 ((
% 107.13/14.53 (woz2B) =>
% 107.13/14.53 ((
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% 107.13/14.53 ((
% 107.13/14.53 (image1Ex1) =>
% 107.13/14.53 ((
% 107.13/14.53 (image1Equiv) =>
% 107.13/14.53 ((
% 107.13/14.53 (image1E) =>
% 107.13/14.53 ((
% 107.13/14.53 (image1I) =>
% 107.13/14.53 ((
% 107.13/14.53 (injFuncInInjFuncSet) =>
% 107.13/14.53 ((
% 107.13/14.53 (injFuncSetFuncIn) =>
% 107.13/14.53 ((
% 107.13/14.53 (injFuncSetFuncInj) =>
% 107.13/14.53 ((
% 107.13/14.53 (surjFuncSetFuncIn) =>
% 107.13/14.53 ((
% 107.13/14.53 (surjFuncSetFuncSurj) =>
% 107.13/14.53 ((
% 107.13/14.53 (leftInvIsSurj) =>
% 107.13/14.53 ((
% 107.13/14.53 (surjCantorThm) =>
% 107.13/14.53 ((
% 107.13/14.53 (!!) @ (
% 107.13/14.53 (('#S') @ (
% 107.13/14.53 (
% 107.13/14.53 ('#B') @ (
% 107.13/14.53 =>) @
% 107.13/14.53 nonempty)) @
% 107.13/14.53 (
% 107.13/14.53 (
% 107.13/14.53 ('#B') @ (
% 107.13/14.53 ??) @
% 107.13/14.53 (
% 107.13/14.53 (
% 107.13/14.53 ('#S') @ (
% 107.13/14.53 (
% 107.13/14.53 ('#B') @ (
% 107.13/14.53 '#S') @
% 107.13/14.53 (
% 107.13/14.53 (
% 107.13/14.53 ('#B') @ (
% 107.13/14.53 (
% 107.13/14.53 ('#B') @ (
% 107.13/14.53 &))) @
% 107.13/14.53 (
% 107.13/14.53 (
% 107.13/14.53 ('#C') @ in)))))) @
% 107.13/14.53 (
% 107.13/14.53 (
% 107.13/14.53 ('#C') @ (
% 107.13/14.53 (
% 107.13/14.53 ('#B') @ (
% 107.13/14.53 '#C') @
% 107.13/14.53 (
% 107.13/14.53 (
% 107.13/14.53 ('#B') @ (
% 107.13/14.53 (
% 107.13/14.53 ('#B') @ (
% 107.13/14.53 =))) @
% 107.13/14.53 (
% 107.13/14.53 (
% 107.13/14.53 ('#C') @ binintersect)))))) @
% 107.13/14.53 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 107.13/14.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1174])).
% 107.13/14.53 thf(zip_derived_cl1193, plain,
% 107.13/14.53 (~ (((binintersectER) =>
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% 107.13/14.53 (((binintersectRsub) =>
% 107.13/14.53 (((binintersectSubset4) =>
% 107.13/14.53 (((binintersectSubset1) =>
% 107.13/14.53 (((bs114d) =>
% 107.13/14.53 (((setminusI) =>
% 107.13/14.53 (((setminusEL) =>
% 107.13/14.53 (((setminusER) =>
% 107.13/14.53 (((setminusSubset2) =>
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% 107.13/14.53 (((setminusELneg) =>
% 107.13/14.53 (((setminusILneg) =>
% 107.13/14.53 (((setminusIRneg) =>
% 107.13/14.53 (((setminusLsub) =>
% 107.13/14.53 (((setminusSubset1) =>
% 107.13/14.53 (((symdiffE) =>
% 107.13/14.53 (((symdiffI1) =>
% 107.13/14.53 (((symdiffI2) =>
% 107.13/14.53 (((symdiffIneg1) =>
% 107.13/14.53 (((symdiffIneg2) =>
% 107.13/14.53 (((secondinupair) =>
% 107.13/14.53 (((setukpairIL) =>
% 107.13/14.53 (((setukpairIR) =>
% 107.13/14.53 (((kpairiskpair) =>
% 107.13/14.53 (((kpairp) =>
% 107.13/14.53 (((singletonsubset) =>
% 107.13/14.53 (((singletoninpowerset) =>
% 107.13/14.53 (((singletoninpowunion) =>
% 107.13/14.53 (((upairset2E) =>
% 107.13/14.53 ((
% 107.13/14.53 (upairsubunion) =>
% 107.13/14.53 ((
% 107.13/14.53 (upairinpowunion) =>
% 107.13/14.53 ((
% 107.13/14.53 (ubforcartprodlem1) =>
% 107.13/14.53 ((
% 107.13/14.53 (ubforcartprodlem2) =>
% 107.13/14.53 ((
% 107.13/14.53 (ubforcartprodlem3) =>
% 107.13/14.53 ((
% 107.13/14.53 (cartprodpairin) =>
% 107.13/14.53 ((
% 107.13/14.53 (cartprodmempair1) =>
% 107.13/14.53 ((
% 107.13/14.53 (cartprodmempair) =>
% 107.13/14.53 ((
% 107.13/14.53 (setunionE2) =>
% 107.13/14.53 ((
% 107.13/14.53 (setunionsingleton1) =>
% 107.13/14.53 ((
% 107.13/14.53 (setunionsingleton2) =>
% 107.13/14.53 ((
% 107.13/14.53 (setunionsingleton) =>
% 107.13/14.53 ((
% 107.13/14.53 (singletonprop) =>
% 107.13/14.53 ((
% 107.13/14.53 (ex1E1) =>
% 107.13/14.53 ((
% 107.13/14.53 (ex1I) =>
% 107.13/14.53 ((
% 107.13/14.53 (ex1I2) =>
% 107.13/14.53 ((
% 107.13/14.53 (singletonsuniq) =>
% 107.13/14.53 ((
% 107.13/14.53 (setukpairinjL1) =>
% 107.13/14.53 ((
% 107.13/14.53 (kfstsingleton) =>
% 107.13/14.53 ((
% 107.13/14.53 (theprop) =>
% 107.13/14.53 ((
% 107.13/14.53 (kfstpairEq) =>
% 107.13/14.53 ((
% 107.13/14.53 (cartprodfstin) =>
% 107.13/14.53 ((
% 107.13/14.53 (setukpairinjL2) =>
% 107.13/14.53 ((
% 107.13/14.53 (setukpairinjL) =>
% 107.13/14.53 ((
% 107.13/14.53 (setukpairinjR11) =>
% 107.13/14.53 ((
% 107.13/14.53 (setukpairinjR12) =>
% 107.13/14.53 ((
% 107.13/14.53 (setukpairinjR1) =>
% 107.13/14.53 ((
% 107.13/14.53 (upairequniteq) =>
% 107.13/14.53 ((
% 107.13/14.53 (setukpairinjR2) =>
% 107.13/14.53 ((
% 107.13/14.53 (setukpairinjR) =>
% 107.13/14.53 ((
% 107.13/14.53 (ksndsingleton) =>
% 107.13/14.53 ((
% 107.13/14.53 (ksndpairEq) =>
% 107.13/14.53 ((
% 107.13/14.53 (kpairsurjEq) =>
% 107.13/14.53 ((
% 107.13/14.53 (cartprodsndin) =>
% 107.13/14.53 ((
% 107.13/14.53 (cartprodpairmemEL) =>
% 107.13/14.53 ((
% 107.13/14.53 (cartprodpairmemER) =>
% 107.13/14.53 ((
% 107.13/14.53 (cartprodmempaircEq) =>
% 107.13/14.53 ((
% 107.13/14.53 (cartprodfstpairEq) =>
% 107.13/14.53 ((
% 107.13/14.53 (cartprodsndpairEq) =>
% 107.13/14.53 ((
% 107.13/14.53 (cartprodpairsurjEq) =>
% 107.13/14.53 ((
% 107.13/14.53 (dpsetconstrI) =>
% 107.13/14.53 ((
% 107.13/14.53 (dpsetconstrSub) =>
% 107.13/14.53 ((
% 107.13/14.53 (setOfPairsIsBReln) =>
% 107.13/14.53 ((
% 107.13/14.53 (dpsetconstrERa) =>
% 107.13/14.53 ((
% 107.13/14.53 (dpsetconstrEL1) =>
% 107.13/14.53 ((
% 107.13/14.53 (dpsetconstrEL2) =>
% 107.13/14.53 ((
% 107.13/14.53 (dpsetconstrER) =>
% 107.13/14.53 ((
% 107.13/14.53 (funcImageSingleton) =>
% 107.13/14.53 ((
% 107.13/14.53 (apProp) =>
% 107.13/14.53 ((
% 107.13/14.53 (app) =>
% 107.13/14.53 ((
% 107.13/14.53 (infuncsetfunc) =>
% 107.13/14.53 ((
% 107.13/14.53 (ap2p) =>
% 107.13/14.53 ((
% 107.13/14.53 (funcinfuncset) =>
% 107.13/14.53 ((
% 107.13/14.53 (lamProp) =>
% 107.13/14.53 ((
% 107.13/14.53 (lamp) =>
% 107.13/14.53 ((
% 107.13/14.53 (lam2p) =>
% 107.13/14.53 ((
% 107.13/14.53 (brelnall1) =>
% 107.13/14.53 ((
% 107.13/14.53 (brelnall2) =>
% 107.13/14.53 ((
% 107.13/14.53 (ex1E2) =>
% 107.13/14.53 ((
% 107.13/14.53 (funcGraphProp1) =>
% 107.13/14.53 ((
% 107.13/14.53 (funcGraphProp3) =>
% 107.13/14.53 ((
% 107.13/14.53 (funcGraphProp2) =>
% 107.13/14.53 ((
% 107.13/14.53 (funcextLem) =>
% 107.13/14.53 ((
% 107.13/14.53 (funcGraphProp4) =>
% 107.13/14.53 ((
% 107.13/14.53 (subbreln) =>
% 107.13/14.53 ((
% 107.13/14.53 (eqbreln) =>
% 107.13/14.53 ((
% 107.13/14.53 (funcext) =>
% 107.13/14.53 ((
% 107.13/14.53 (funcext2) =>
% 107.13/14.53 ((
% 107.13/14.53 (ap2apEq1) =>
% 107.13/14.53 ((
% 107.13/14.53 (ap2apEq2) =>
% 107.13/14.53 ((
% 107.13/14.53 (beta1) =>
% 107.13/14.53 ((
% 107.13/14.53 (eta1) =>
% 107.13/14.53 ((
% 107.13/14.53 (lam2lamEq) =>
% 107.13/14.53 ((
% 107.13/14.53 (beta2) =>
% 107.13/14.53 ((
% 107.13/14.53 (eta2) =>
% 107.13/14.53 ((
% 107.13/14.53 (iffalseProp1) =>
% 107.13/14.53 ((
% 107.13/14.53 (iffalseProp2) =>
% 107.13/14.53 ((
% 107.13/14.53 (iftrueProp1) =>
% 107.13/14.53 ((
% 107.13/14.53 (iftrueProp2) =>
% 107.13/14.53 ((
% 107.13/14.53 (ifSingleton) =>
% 107.13/14.53 ((
% 107.13/14.53 (ifp) =>
% 107.13/14.53 ((
% 107.13/14.53 (theeq) =>
% 107.13/14.53 ((
% 107.13/14.53 (iftrue) =>
% 107.13/14.53 ((
% 107.13/14.53 (iffalse) =>
% 107.13/14.53 ((
% 107.13/14.53 (iftrueorfalse) =>
% 107.13/14.53 ((
% 107.13/14.53 (binintersectT_lem) =>
% 107.13/14.53 ((
% 107.13/14.53 (binunionT_lem) =>
% 107.13/14.53 ((
% 107.13/14.53 (powersetT_lem) =>
% 107.13/14.53 ((
% 107.13/14.53 (setminusT_lem) =>
% 107.13/14.53 ((
% 107.13/14.53 (complementT_lem) =>
% 107.13/14.53 ((
% 107.13/14.53 (setextT) =>
% 107.13/14.53 ((
% 107.13/14.53 (subsetTI) =>
% 107.13/14.53 ((
% 107.13/14.53 (powersetTI1) =>
% 107.13/14.53 ((
% 107.13/14.53 (powersetTE1) =>
% 107.13/14.53 ((
% 107.13/14.53 (complementTI1) =>
% 107.13/14.53 ((
% 107.13/14.53 (complementTE1) =>
% 107.13/14.53 ((
% 107.13/14.53 (binintersectTELcontra) =>
% 107.13/14.53 ((
% 107.13/14.53 (binintersectTERcontra) =>
% 107.13/14.53 ((
% 107.13/14.53 (contrasubsetT) =>
% 107.13/14.53 ((
% 107.13/14.53 (contrasubsetT1) =>
% 107.13/14.53 ((
% 107.13/14.53 (contrasubsetT2) =>
% 107.13/14.53 ((
% 107.13/14.53 (contrasubsetT3) =>
% 107.13/14.53 ((
% 107.13/14.53 (doubleComplementI1) =>
% 107.13/14.53 ((
% 107.13/14.53 (doubleComplementE1) =>
% 107.13/14.53 ((
% 107.13/14.53 (doubleComplementSub1) =>
% 107.13/14.53 ((
% 107.13/14.53 (doubleComplementSub2) =>
% 107.13/14.53 ((
% 107.13/14.53 (doubleComplementEq) =>
% 107.13/14.53 ((
% 107.13/14.53 (complementTnotintersectT) =>
% 107.13/14.53 ((
% 107.13/14.53 (complementImpComplementIntersect) =>
% 107.13/14.53 ((
% 107.13/14.53 (complementSubsetComplementIntersect) =>
% 107.13/14.53 ((
% 107.13/14.53 (complementInPowersetComplementIntersect) =>
% 107.13/14.53 ((
% 107.13/14.53 (contraSubsetComplement) =>
% 107.13/14.53 ((
% 107.13/14.53 (complementTcontraSubset) =>
% 107.13/14.53 ((
% 107.13/14.53 (binunionTILcontra) =>
% 107.13/14.53 ((
% 107.13/14.53 (binunionTIRcontra) =>
% 107.13/14.53 ((
% 107.13/14.53 (inIntersectImpInUnion) =>
% 107.13/14.53 ((
% 107.13/14.53 (inIntersectImpInUnion2) =>
% 107.13/14.53 ((
% 107.13/14.53 (inIntersectImpInIntersectUnions) =>
% 107.13/14.53 ((
% 107.13/14.53 (intersectInPowersetIntersectUnions) =>
% 107.13/14.53 ((
% 107.13/14.53 (inComplementUnionImpNotIn1) =>
% 107.13/14.53 ((
% 107.13/14.53 (inComplementUnionImpInComplement1) =>
% 107.13/14.53 ((
% 107.13/14.53 (binunionTE) =>
% 107.13/14.53 ((
% 107.13/14.53 (binunionTEcontra) =>
% 107.13/14.53 ((
% 107.13/14.53 (demorgan2a1) =>
% 107.13/14.53 ((
% 107.13/14.53 (complementUnionInPowersetComplement) =>
% 107.13/14.53 ((
% 107.13/14.53 (demorgan2a2) =>
% 107.13/14.53 ((
% 107.13/14.53 (demorgan1a) =>
% 107.13/14.53 ((
% 107.13/14.53 (demorgan1b) =>
% 107.13/14.53 ((
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% 107.13/14.53 ((
% 107.13/14.53 (demorgan2a) =>
% 107.13/14.53 ((
% 107.13/14.53 (demorgan2b2) =>
% 107.13/14.53 ((
% 107.13/14.53 (demorgan2b) =>
% 107.13/14.53 ((
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% 107.13/14.53 ((
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% 107.13/14.53 ((
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% 107.13/14.53 ((
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% 107.13/14.53 (woz1_5) =>
% 107.13/14.53 ((
% 107.13/14.53 (breln1all2) =>
% 107.13/14.53 ((
% 107.13/14.53 (breln1SetBreln1) =>
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% 107.13/14.53 ((
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% 107.13/14.53 ((
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% 107.13/14.53 ((
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% 107.13/14.53 ((
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% 107.13/14.53 ((
% 107.13/14.53 (breln1unionI) =>
% 107.13/14.53 ((
% 107.13/14.53 (breln1unionE) =>
% 107.13/14.53 ((
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% 107.13/14.53 ((
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% 107.13/14.53 ((
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% 107.13/14.53 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1193])).
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% 107.13/14.53 (setunionsingleton1) =>
% 107.13/14.53 ((
% 107.13/14.53 (setunionsingleton2) =>
% 107.13/14.53 ((
% 107.13/14.53 (setunionsingleton) =>
% 107.13/14.53 ((
% 107.13/14.53 (singletonprop) =>
% 107.13/14.53 ((
% 107.13/14.53 (ex1E1) =>
% 107.13/14.53 ((
% 107.13/14.53 (ex1I) =>
% 107.13/14.53 ((
% 107.13/14.53 (ex1I2) =>
% 107.13/14.53 ((
% 107.13/14.53 (singletonsuniq) =>
% 107.13/14.53 ((
% 107.13/14.53 (setukpairinjL1) =>
% 107.13/14.53 ((
% 107.13/14.53 (kfstsingleton) =>
% 107.13/14.54 ((
% 107.13/14.54 (theprop) =>
% 107.13/14.54 ((
% 107.13/14.54 (kfstpairEq) =>
% 107.13/14.54 ((
% 107.13/14.54 (cartprodfstin) =>
% 107.13/14.54 ((
% 107.13/14.54 (setukpairinjL2) =>
% 107.13/14.54 ((
% 107.13/14.54 (setukpairinjL) =>
% 107.13/14.54 ((
% 107.13/14.54 (setukpairinjR11) =>
% 107.13/14.54 ((
% 107.13/14.54 (setukpairinjR12) =>
% 107.13/14.54 ((
% 107.13/14.54 (setukpairinjR1) =>
% 107.13/14.54 ((
% 107.13/14.54 (upairequniteq) =>
% 107.13/14.54 ((
% 107.13/14.54 (setukpairinjR2) =>
% 107.13/14.54 ((
% 107.13/14.54 (setukpairinjR) =>
% 107.13/14.54 ((
% 107.13/14.54 (ksndsingleton) =>
% 107.13/14.54 ((
% 107.13/14.54 (ksndpairEq) =>
% 107.13/14.54 ((
% 107.13/14.54 (kpairsurjEq) =>
% 107.13/14.54 ((
% 107.13/14.54 (cartprodsndin) =>
% 107.13/14.54 ((
% 107.13/14.54 (cartprodpairmemEL) =>
% 107.13/14.54 ((
% 107.13/14.54 (cartprodpairmemER) =>
% 107.13/14.54 ((
% 107.13/14.54 (cartprodmempaircEq) =>
% 107.13/14.54 ((
% 107.13/14.54 (cartprodfstpairEq) =>
% 107.13/14.54 ((
% 107.13/14.54 (cartprodsndpairEq) =>
% 107.13/14.54 ((
% 107.13/14.54 (cartprodpairsurjEq) =>
% 107.13/14.54 ((
% 107.13/14.54 (dpsetconstrI) =>
% 107.13/14.54 ((
% 107.13/14.54 (dpsetconstrSub) =>
% 107.13/14.54 ((
% 107.13/14.54 (setOfPairsIsBReln) =>
% 107.13/14.54 ((
% 107.13/14.54 (dpsetconstrERa) =>
% 107.13/14.54 ((
% 107.13/14.54 (dpsetconstrEL1) =>
% 107.13/14.54 ((
% 107.13/14.54 (dpsetconstrEL2) =>
% 107.13/14.54 ((
% 107.13/14.54 (dpsetconstrER) =>
% 107.13/14.54 ((
% 107.13/14.54 (funcImageSingleton) =>
% 107.13/14.54 ((
% 107.13/14.54 (apProp) =>
% 107.13/14.54 ((
% 107.13/14.54 (app) =>
% 107.13/14.54 ((
% 107.13/14.54 (infuncsetfunc) =>
% 107.13/14.54 ((
% 107.13/14.54 (ap2p) =>
% 107.13/14.54 ((
% 107.13/14.54 (funcinfuncset) =>
% 107.13/14.54 ((
% 107.13/14.54 (lamProp) =>
% 107.13/14.54 ((
% 107.13/14.54 (lamp) =>
% 107.13/14.54 ((
% 107.13/14.54 (lam2p) =>
% 107.13/14.54 ((
% 107.13/14.54 (brelnall1) =>
% 107.13/14.54 ((
% 107.13/14.54 (brelnall2) =>
% 107.13/14.54 ((
% 107.13/14.54 (ex1E2) =>
% 107.13/14.54 ((
% 107.13/14.54 (funcGraphProp1) =>
% 107.13/14.54 ((
% 107.13/14.54 (funcGraphProp3) =>
% 107.13/14.54 ((
% 107.13/14.54 (funcGraphProp2) =>
% 107.13/14.54 ((
% 107.13/14.54 (funcextLem) =>
% 107.13/14.54 ((
% 107.13/14.54 (funcGraphProp4) =>
% 107.13/14.54 ((
% 107.13/14.54 (subbreln) =>
% 107.13/14.54 ((
% 107.13/14.54 (eqbreln) =>
% 107.13/14.54 ((
% 107.13/14.54 (funcext) =>
% 107.13/14.54 ((
% 107.13/14.54 (funcext2) =>
% 107.13/14.54 ((
% 107.13/14.54 (ap2apEq1) =>
% 107.13/14.54 ((
% 107.13/14.54 (ap2apEq2) =>
% 107.13/14.54 ((
% 107.13/14.54 (beta1) =>
% 107.13/14.54 ((
% 107.13/14.54 (eta1) =>
% 107.13/14.54 ((
% 107.13/14.54 (lam2lamEq) =>
% 107.13/14.54 ((
% 107.13/14.54 (beta2) =>
% 107.13/14.54 ((
% 107.13/14.54 (eta2) =>
% 107.13/14.54 ((
% 107.13/14.54 (iffalseProp1) =>
% 107.13/14.54 ((
% 107.13/14.54 (iffalseProp2) =>
% 107.13/14.54 ((
% 107.13/14.54 (iftrueProp1) =>
% 107.13/14.54 ((
% 107.13/14.54 (iftrueProp2) =>
% 107.13/14.54 ((
% 107.13/14.54 (ifSingleton) =>
% 107.13/14.54 ((
% 107.13/14.54 (ifp) =>
% 107.13/14.54 ((
% 107.13/14.54 (theeq) =>
% 107.13/14.54 ((
% 107.13/14.54 (iftrue) =>
% 107.13/14.54 ((
% 107.13/14.54 (iffalse) =>
% 107.13/14.54 ((
% 107.13/14.54 (iftrueorfalse) =>
% 107.13/14.54 ((
% 107.13/14.54 (binintersectT_lem) =>
% 107.13/14.54 ((
% 107.13/14.54 (binunionT_lem) =>
% 107.13/14.54 ((
% 107.13/14.54 (powersetT_lem) =>
% 107.13/14.54 ((
% 107.13/14.54 (setminusT_lem) =>
% 107.13/14.54 ((
% 107.13/14.54 (complementT_lem) =>
% 107.13/14.54 ((
% 107.13/14.54 (setextT) =>
% 107.13/14.54 ((
% 107.13/14.54 (subsetTI) =>
% 107.13/14.54 ((
% 107.13/14.54 (powersetTI1) =>
% 107.13/14.54 ((
% 107.13/14.54 (powersetTE1) =>
% 107.13/14.54 ((
% 107.13/14.54 (complementTI1) =>
% 107.13/14.54 ((
% 107.13/14.54 (complementTE1) =>
% 107.13/14.54 ((
% 107.13/14.54 (binintersectTELcontra) =>
% 107.13/14.54 ((
% 107.13/14.54 (binintersectTERcontra) =>
% 107.13/14.54 ((
% 107.13/14.54 (contrasubsetT) =>
% 107.13/14.54 ((
% 107.13/14.54 (contrasubsetT1) =>
% 107.13/14.54 ((
% 107.13/14.54 (contrasubsetT2) =>
% 107.13/14.54 ((
% 107.13/14.54 (contrasubsetT3) =>
% 107.13/14.54 ((
% 107.13/14.54 (doubleComplementI1) =>
% 107.13/14.54 ((
% 107.13/14.54 (doubleComplementE1) =>
% 107.13/14.54 ((
% 107.13/14.54 (doubleComplementSub1) =>
% 107.13/14.54 ((
% 107.13/14.54 (doubleComplementSub2) =>
% 107.13/14.54 ((
% 107.13/14.54 (doubleComplementEq) =>
% 107.13/14.54 ((
% 107.13/14.54 (complementTnotintersectT) =>
% 107.13/14.54 ((
% 107.13/14.54 (complementImpComplementIntersect) =>
% 107.13/14.54 ((
% 107.13/14.54 (complementSubsetComplementIntersect) =>
% 107.13/14.54 ((
% 107.13/14.54 (complementInPowersetComplementIntersect) =>
% 107.13/14.54 ((
% 107.13/14.54 (contraSubsetComplement) =>
% 107.13/14.54 ((
% 107.13/14.54 (complementTcontraSubset) =>
% 107.13/14.54 ((
% 107.13/14.54 (binunionTILcontra) =>
% 107.13/14.54 ((
% 107.13/14.54 (binunionTIRcontra) =>
% 107.13/14.54 ((
% 107.13/14.54 (inIntersectImpInUnion) =>
% 107.13/14.54 ((
% 107.13/14.54 (inIntersectImpInUnion2) =>
% 107.13/14.54 ((
% 107.13/14.54 (inIntersectImpInIntersectUnions) =>
% 107.13/14.54 ((
% 107.13/14.54 (intersectInPowersetIntersectUnions) =>
% 107.13/14.54 ((
% 107.13/14.54 (inComplementUnionImpNotIn1) =>
% 107.13/14.54 ((
% 107.13/14.54 (inComplementUnionImpInComplement1) =>
% 107.13/14.54 ((
% 107.13/14.54 (binunionTE) =>
% 107.13/14.54 ((
% 107.13/14.54 (binunionTEcontra) =>
% 107.13/14.54 ((
% 107.13/14.54 (demorgan2a1) =>
% 107.13/14.54 ((
% 107.13/14.54 (complementUnionInPowersetComplement) =>
% 107.13/14.54 ((
% 107.13/14.54 (demorgan2a2) =>
% 107.13/14.54 ((
% 107.13/14.54 (demorgan1a) =>
% 107.13/14.54 ((
% 107.13/14.54 (demorgan1b) =>
% 107.13/14.54 ((
% 107.13/14.54 (demorgan1) =>
% 107.13/14.54 ((
% 107.13/14.54 (demorgan2a) =>
% 107.13/14.54 ((
% 107.13/14.54 (demorgan2b2) =>
% 107.13/14.54 ((
% 107.13/14.54 (demorgan2b) =>
% 107.13/14.54 ((
% 107.13/14.54 (demorgan2) =>
% 107.13/14.54 ((
% 107.13/14.54 (woz13rule0) =>
% 107.13/14.54 ((
% 107.13/14.54 (woz13rule1) =>
% 107.13/14.54 ((
% 107.13/14.54 (woz13rule2) =>
% 107.13/14.54 ((
% 107.13/14.54 (woz13rule3) =>
% 107.13/14.54 ((
% 107.13/14.54 (woz13rule4) =>
% 107.13/14.54 ((
% 107.13/14.54 (woz1_1) =>
% 107.13/14.54 ((
% 107.13/14.54 (woz1_2) =>
% 107.13/14.54 ((
% 107.13/14.54 (woz1_3) =>
% 107.13/14.54 ((
% 107.13/14.54 (woz1_4) =>
% 107.13/14.54 ((
% 107.13/14.54 (woz1_5) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1all2) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1SetBreln1) =>
% 107.13/14.54 ((
% 107.13/14.54 (choice2fnsingleton) =>
% 107.13/14.54 ((
% 107.13/14.54 (setOfPairsIsBReln1) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1all1) =>
% 107.13/14.54 ((
% 107.13/14.54 (subbreln1) =>
% 107.13/14.54 ((
% 107.13/14.54 (eqbreln1) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1invprop) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1invI) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1invE) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1compprop) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1compI) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1compE) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1compEex) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1unionprop) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1unionIL) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1unionIR) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1unionI) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1unionE) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1unionEcases) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1unionCommutes) =>
% 107.13/14.54 ((
% 107.13/14.54 (woz2Ex) =>
% 107.13/14.54 ((
% 107.13/14.54 (woz2W) =>
% 107.13/14.54 ((
% 107.13/14.54 (woz2A) =>
% 107.13/14.54 ((
% 107.13/14.54 (woz2B) =>
% 107.13/14.54 ((
% 107.13/14.54 (image1Ex) =>
% 107.13/14.54 ((
% 107.13/14.54 (image1Ex1) =>
% 107.13/14.54 ((
% 107.13/14.54 (image1Equiv) =>
% 107.13/14.54 ((
% 107.13/14.54 (image1E) =>
% 107.13/14.54 ((
% 107.13/14.54 (image1I) =>
% 107.13/14.54 ((
% 107.13/14.54 (injFuncInInjFuncSet) =>
% 107.13/14.54 ((
% 107.13/14.54 (injFuncSetFuncIn) =>
% 107.13/14.54 ((
% 107.13/14.54 (injFuncSetFuncInj) =>
% 107.13/14.54 ((
% 107.13/14.54 (surjFuncSetFuncIn) =>
% 107.13/14.54 ((
% 107.13/14.54 (surjFuncSetFuncSurj) =>
% 107.13/14.54 ((
% 107.13/14.54 (leftInvIsSurj) =>
% 107.13/14.54 ((
% 107.13/14.54 (surjCantorThm) =>
% 107.13/14.54 ((
% 107.13/14.54 (!!) @ (
% 107.13/14.54 (('#S') @ (
% 107.13/14.54 (
% 107.13/14.54 ('#B') @ (
% 107.13/14.54 =>) @
% 107.13/14.54 nonempty)) @
% 107.13/14.54 (
% 107.13/14.54 (
% 107.13/14.54 ('#B') @ (
% 107.13/14.54 ??) @
% 107.13/14.54 (
% 107.13/14.54 (
% 107.13/14.54 ('#S') @ (
% 107.13/14.54 (
% 107.13/14.54 ('#B') @ (
% 107.13/14.54 '#S') @
% 107.13/14.54 (
% 107.13/14.54 (
% 107.13/14.54 ('#B') @ (
% 107.13/14.54 (
% 107.13/14.54 ('#B') @ (
% 107.13/14.54 &))) @
% 107.13/14.54 (
% 107.13/14.54 (
% 107.13/14.54 ('#C') @ in)))))) @
% 107.13/14.54 (
% 107.13/14.54 (
% 107.13/14.54 ('#C') @ (
% 107.13/14.54 (
% 107.13/14.54 ('#B') @ (
% 107.13/14.54 '#C') @
% 107.13/14.54 (
% 107.13/14.54 (
% 107.13/14.54 ('#B') @ (
% 107.13/14.54 (
% 107.13/14.54 ('#B') @ (
% 107.13/14.54 =))) @
% 107.13/14.54 (
% 107.13/14.54 (
% 107.13/14.54 ('#C') @ binintersect)))))) @
% 107.13/14.54 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 107.13/14.54 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1206])).
% 107.13/14.54 thf(zip_derived_cl1223, plain,
% 107.13/14.54 (~ (((binintersectSubset4) =>
% 107.13/14.54 (((binintersectSubset1) =>
% 107.13/14.54 (((bs114d) =>
% 107.13/14.54 (((setminusI) =>
% 107.13/14.54 (((setminusEL) =>
% 107.13/14.54 (((setminusER) =>
% 107.13/14.54 (((setminusSubset2) =>
% 107.13/14.54 (((setminusERneg) =>
% 107.13/14.54 (((setminusELneg) =>
% 107.13/14.54 (((setminusILneg) =>
% 107.13/14.54 (((setminusIRneg) =>
% 107.13/14.54 (((setminusLsub) =>
% 107.13/14.54 (((setminusSubset1) =>
% 107.13/14.54 (((symdiffE) =>
% 107.13/14.54 (((symdiffI1) =>
% 107.13/14.54 (((symdiffI2) =>
% 107.13/14.54 (((symdiffIneg1) =>
% 107.13/14.54 (((symdiffIneg2) =>
% 107.13/14.54 (((secondinupair) =>
% 107.13/14.54 (((setukpairIL) =>
% 107.13/14.54 (((setukpairIR) =>
% 107.13/14.54 (((kpairiskpair) =>
% 107.13/14.54 (((kpairp) =>
% 107.13/14.54 (((singletonsubset) =>
% 107.13/14.54 (((singletoninpowerset) =>
% 107.13/14.54 (((singletoninpowunion) =>
% 107.13/14.54 (((upairset2E) =>
% 107.13/14.54 (((upairsubunion) =>
% 107.13/14.54 (((upairinpowunion) =>
% 107.13/14.54 (((ubforcartprodlem1) =>
% 107.13/14.54 ((
% 107.13/14.54 (ubforcartprodlem2) =>
% 107.13/14.54 ((
% 107.13/14.54 (ubforcartprodlem3) =>
% 107.13/14.54 ((
% 107.13/14.54 (cartprodpairin) =>
% 107.13/14.54 ((
% 107.13/14.54 (cartprodmempair1) =>
% 107.13/14.54 ((
% 107.13/14.54 (cartprodmempair) =>
% 107.13/14.54 ((
% 107.13/14.54 (setunionE2) =>
% 107.13/14.54 ((
% 107.13/14.54 (setunionsingleton1) =>
% 107.13/14.54 ((
% 107.13/14.54 (setunionsingleton2) =>
% 107.13/14.54 ((
% 107.13/14.54 (setunionsingleton) =>
% 107.13/14.54 ((
% 107.13/14.54 (singletonprop) =>
% 107.13/14.54 ((
% 107.13/14.54 (ex1E1) =>
% 107.13/14.54 ((
% 107.13/14.54 (ex1I) =>
% 107.13/14.54 ((
% 107.13/14.54 (ex1I2) =>
% 107.13/14.54 ((
% 107.13/14.54 (singletonsuniq) =>
% 107.13/14.54 ((
% 107.13/14.54 (setukpairinjL1) =>
% 107.13/14.54 ((
% 107.13/14.54 (kfstsingleton) =>
% 107.13/14.54 ((
% 107.13/14.54 (theprop) =>
% 107.13/14.54 ((
% 107.13/14.54 (kfstpairEq) =>
% 107.13/14.54 ((
% 107.13/14.54 (cartprodfstin) =>
% 107.13/14.54 ((
% 107.13/14.54 (setukpairinjL2) =>
% 107.13/14.54 ((
% 107.13/14.54 (setukpairinjL) =>
% 107.13/14.54 ((
% 107.13/14.54 (setukpairinjR11) =>
% 107.13/14.54 ((
% 107.13/14.54 (setukpairinjR12) =>
% 107.13/14.54 ((
% 107.13/14.54 (setukpairinjR1) =>
% 107.13/14.54 ((
% 107.13/14.54 (upairequniteq) =>
% 107.13/14.54 ((
% 107.13/14.54 (setukpairinjR2) =>
% 107.13/14.54 ((
% 107.13/14.54 (setukpairinjR) =>
% 107.13/14.54 ((
% 107.13/14.54 (ksndsingleton) =>
% 107.13/14.54 ((
% 107.13/14.54 (ksndpairEq) =>
% 107.13/14.54 ((
% 107.13/14.54 (kpairsurjEq) =>
% 107.13/14.54 ((
% 107.13/14.54 (cartprodsndin) =>
% 107.13/14.54 ((
% 107.13/14.54 (cartprodpairmemEL) =>
% 107.13/14.54 ((
% 107.13/14.54 (cartprodpairmemER) =>
% 107.13/14.54 ((
% 107.13/14.54 (cartprodmempaircEq) =>
% 107.13/14.54 ((
% 107.13/14.54 (cartprodfstpairEq) =>
% 107.13/14.54 ((
% 107.13/14.54 (cartprodsndpairEq) =>
% 107.13/14.54 ((
% 107.13/14.54 (cartprodpairsurjEq) =>
% 107.13/14.54 ((
% 107.13/14.54 (dpsetconstrI) =>
% 107.13/14.54 ((
% 107.13/14.54 (dpsetconstrSub) =>
% 107.13/14.54 ((
% 107.13/14.54 (setOfPairsIsBReln) =>
% 107.13/14.54 ((
% 107.13/14.54 (dpsetconstrERa) =>
% 107.13/14.54 ((
% 107.13/14.54 (dpsetconstrEL1) =>
% 107.13/14.54 ((
% 107.13/14.54 (dpsetconstrEL2) =>
% 107.13/14.54 ((
% 107.13/14.54 (dpsetconstrER) =>
% 107.13/14.54 ((
% 107.13/14.54 (funcImageSingleton) =>
% 107.13/14.54 ((
% 107.13/14.54 (apProp) =>
% 107.13/14.54 ((
% 107.13/14.54 (app) =>
% 107.13/14.54 ((
% 107.13/14.54 (infuncsetfunc) =>
% 107.13/14.54 ((
% 107.13/14.54 (ap2p) =>
% 107.13/14.54 ((
% 107.13/14.54 (funcinfuncset) =>
% 107.13/14.54 ((
% 107.13/14.54 (lamProp) =>
% 107.13/14.54 ((
% 107.13/14.54 (lamp) =>
% 107.13/14.54 ((
% 107.13/14.54 (lam2p) =>
% 107.13/14.54 ((
% 107.13/14.54 (brelnall1) =>
% 107.13/14.54 ((
% 107.13/14.54 (brelnall2) =>
% 107.13/14.54 ((
% 107.13/14.54 (ex1E2) =>
% 107.13/14.54 ((
% 107.13/14.54 (funcGraphProp1) =>
% 107.13/14.54 ((
% 107.13/14.54 (funcGraphProp3) =>
% 107.13/14.54 ((
% 107.13/14.54 (funcGraphProp2) =>
% 107.13/14.54 ((
% 107.13/14.54 (funcextLem) =>
% 107.13/14.54 ((
% 107.13/14.54 (funcGraphProp4) =>
% 107.13/14.54 ((
% 107.13/14.54 (subbreln) =>
% 107.13/14.54 ((
% 107.13/14.54 (eqbreln) =>
% 107.13/14.54 ((
% 107.13/14.54 (funcext) =>
% 107.13/14.54 ((
% 107.13/14.54 (funcext2) =>
% 107.13/14.54 ((
% 107.13/14.54 (ap2apEq1) =>
% 107.13/14.54 ((
% 107.13/14.54 (ap2apEq2) =>
% 107.13/14.54 ((
% 107.13/14.54 (beta1) =>
% 107.13/14.54 ((
% 107.13/14.54 (eta1) =>
% 107.13/14.54 ((
% 107.13/14.54 (lam2lamEq) =>
% 107.13/14.54 ((
% 107.13/14.54 (beta2) =>
% 107.13/14.54 ((
% 107.13/14.54 (eta2) =>
% 107.13/14.54 ((
% 107.13/14.54 (iffalseProp1) =>
% 107.13/14.54 ((
% 107.13/14.54 (iffalseProp2) =>
% 107.13/14.54 ((
% 107.13/14.54 (iftrueProp1) =>
% 107.13/14.54 ((
% 107.13/14.54 (iftrueProp2) =>
% 107.13/14.54 ((
% 107.13/14.54 (ifSingleton) =>
% 107.13/14.54 ((
% 107.13/14.54 (ifp) =>
% 107.13/14.54 ((
% 107.13/14.54 (theeq) =>
% 107.13/14.54 ((
% 107.13/14.54 (iftrue) =>
% 107.13/14.54 ((
% 107.13/14.54 (iffalse) =>
% 107.13/14.54 ((
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% 107.13/14.54 ((
% 107.13/14.54 (binintersectT_lem) =>
% 107.13/14.54 ((
% 107.13/14.54 (binunionT_lem) =>
% 107.13/14.54 ((
% 107.13/14.54 (powersetT_lem) =>
% 107.13/14.54 ((
% 107.13/14.54 (setminusT_lem) =>
% 107.13/14.54 ((
% 107.13/14.54 (complementT_lem) =>
% 107.13/14.54 ((
% 107.13/14.54 (setextT) =>
% 107.13/14.54 ((
% 107.13/14.54 (subsetTI) =>
% 107.13/14.54 ((
% 107.13/14.54 (powersetTI1) =>
% 107.13/14.54 ((
% 107.13/14.54 (powersetTE1) =>
% 107.13/14.54 ((
% 107.13/14.54 (complementTI1) =>
% 107.13/14.54 ((
% 107.13/14.54 (complementTE1) =>
% 107.13/14.54 ((
% 107.13/14.54 (binintersectTELcontra) =>
% 107.13/14.54 ((
% 107.13/14.54 (binintersectTERcontra) =>
% 107.13/14.54 ((
% 107.13/14.54 (contrasubsetT) =>
% 107.13/14.54 ((
% 107.13/14.54 (contrasubsetT1) =>
% 107.13/14.54 ((
% 107.13/14.54 (contrasubsetT2) =>
% 107.13/14.54 ((
% 107.13/14.54 (contrasubsetT3) =>
% 107.13/14.54 ((
% 107.13/14.54 (doubleComplementI1) =>
% 107.13/14.54 ((
% 107.13/14.54 (doubleComplementE1) =>
% 107.13/14.54 ((
% 107.13/14.54 (doubleComplementSub1) =>
% 107.13/14.54 ((
% 107.13/14.54 (doubleComplementSub2) =>
% 107.13/14.54 ((
% 107.13/14.54 (doubleComplementEq) =>
% 107.13/14.54 ((
% 107.13/14.54 (complementTnotintersectT) =>
% 107.13/14.54 ((
% 107.13/14.54 (complementImpComplementIntersect) =>
% 107.13/14.54 ((
% 107.13/14.54 (complementSubsetComplementIntersect) =>
% 107.13/14.54 ((
% 107.13/14.54 (complementInPowersetComplementIntersect) =>
% 107.13/14.54 ((
% 107.13/14.54 (contraSubsetComplement) =>
% 107.13/14.54 ((
% 107.13/14.54 (complementTcontraSubset) =>
% 107.13/14.54 ((
% 107.13/14.54 (binunionTILcontra) =>
% 107.13/14.54 ((
% 107.13/14.54 (binunionTIRcontra) =>
% 107.13/14.54 ((
% 107.13/14.54 (inIntersectImpInUnion) =>
% 107.13/14.54 ((
% 107.13/14.54 (inIntersectImpInUnion2) =>
% 107.13/14.54 ((
% 107.13/14.54 (inIntersectImpInIntersectUnions) =>
% 107.13/14.54 ((
% 107.13/14.54 (intersectInPowersetIntersectUnions) =>
% 107.13/14.54 ((
% 107.13/14.54 (inComplementUnionImpNotIn1) =>
% 107.13/14.54 ((
% 107.13/14.54 (inComplementUnionImpInComplement1) =>
% 107.13/14.54 ((
% 107.13/14.54 (binunionTE) =>
% 107.13/14.54 ((
% 107.13/14.54 (binunionTEcontra) =>
% 107.13/14.54 ((
% 107.13/14.54 (demorgan2a1) =>
% 107.13/14.54 ((
% 107.13/14.54 (complementUnionInPowersetComplement) =>
% 107.13/14.54 ((
% 107.13/14.54 (demorgan2a2) =>
% 107.13/14.54 ((
% 107.13/14.54 (demorgan1a) =>
% 107.13/14.54 ((
% 107.13/14.54 (demorgan1b) =>
% 107.13/14.54 ((
% 107.13/14.54 (demorgan1) =>
% 107.13/14.54 ((
% 107.13/14.54 (demorgan2a) =>
% 107.13/14.54 ((
% 107.13/14.54 (demorgan2b2) =>
% 107.13/14.54 ((
% 107.13/14.54 (demorgan2b) =>
% 107.13/14.54 ((
% 107.13/14.54 (demorgan2) =>
% 107.13/14.54 ((
% 107.13/14.54 (woz13rule0) =>
% 107.13/14.54 ((
% 107.13/14.54 (woz13rule1) =>
% 107.13/14.54 ((
% 107.13/14.54 (woz13rule2) =>
% 107.13/14.54 ((
% 107.13/14.54 (woz13rule3) =>
% 107.13/14.54 ((
% 107.13/14.54 (woz13rule4) =>
% 107.13/14.54 ((
% 107.13/14.54 (woz1_1) =>
% 107.13/14.54 ((
% 107.13/14.54 (woz1_2) =>
% 107.13/14.54 ((
% 107.13/14.54 (woz1_3) =>
% 107.13/14.54 ((
% 107.13/14.54 (woz1_4) =>
% 107.13/14.54 ((
% 107.13/14.54 (woz1_5) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1all2) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1SetBreln1) =>
% 107.13/14.54 ((
% 107.13/14.54 (choice2fnsingleton) =>
% 107.13/14.54 ((
% 107.13/14.54 (setOfPairsIsBReln1) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1all1) =>
% 107.13/14.54 ((
% 107.13/14.54 (subbreln1) =>
% 107.13/14.54 ((
% 107.13/14.54 (eqbreln1) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1invprop) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1invI) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1invE) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1compprop) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1compI) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1compE) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1compEex) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1unionprop) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1unionIL) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1unionIR) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1unionI) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1unionE) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1unionEcases) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1unionCommutes) =>
% 107.13/14.54 ((
% 107.13/14.54 (woz2Ex) =>
% 107.13/14.54 ((
% 107.13/14.54 (woz2W) =>
% 107.13/14.54 ((
% 107.13/14.54 (woz2A) =>
% 107.13/14.54 ((
% 107.13/14.54 (woz2B) =>
% 107.13/14.54 ((
% 107.13/14.54 (image1Ex) =>
% 107.13/14.54 ((
% 107.13/14.54 (image1Ex1) =>
% 107.13/14.54 ((
% 107.13/14.54 (image1Equiv) =>
% 107.13/14.54 ((
% 107.13/14.54 (image1E) =>
% 107.13/14.54 ((
% 107.13/14.54 (image1I) =>
% 107.13/14.54 ((
% 107.13/14.54 (injFuncInInjFuncSet) =>
% 107.13/14.54 ((
% 107.13/14.54 (injFuncSetFuncIn) =>
% 107.13/14.54 ((
% 107.13/14.54 (injFuncSetFuncInj) =>
% 107.13/14.54 ((
% 107.13/14.54 (surjFuncSetFuncIn) =>
% 107.13/14.54 ((
% 107.13/14.54 (surjFuncSetFuncSurj) =>
% 107.13/14.54 ((
% 107.13/14.54 (leftInvIsSurj) =>
% 107.13/14.54 ((
% 107.13/14.54 (surjCantorThm) =>
% 107.13/14.54 ((
% 107.13/14.54 (!!) @ (
% 107.13/14.54 (('#S') @ (
% 107.13/14.54 (
% 107.13/14.54 ('#B') @ (
% 107.13/14.54 =>) @
% 107.13/14.54 nonempty)) @
% 107.13/14.54 (
% 107.13/14.54 (
% 107.13/14.54 ('#B') @ (
% 107.13/14.54 ??) @
% 107.13/14.54 (
% 107.13/14.54 (
% 107.13/14.54 ('#S') @ (
% 107.13/14.54 (
% 107.13/14.54 ('#B') @ (
% 107.13/14.54 '#S') @
% 107.13/14.54 (
% 107.13/14.54 (
% 107.13/14.54 ('#B') @ (
% 107.13/14.54 (
% 107.13/14.54 ('#B') @ (
% 107.13/14.54 &))) @
% 107.13/14.54 (
% 107.13/14.54 (
% 107.13/14.54 ('#C') @ in)))))) @
% 107.13/14.54 (
% 107.13/14.54 (
% 107.13/14.54 ('#C') @ (
% 107.13/14.54 (
% 107.13/14.54 ('#B') @ (
% 107.13/14.54 '#C') @
% 107.13/14.54 (
% 107.13/14.54 (
% 107.13/14.54 ('#B') @ (
% 107.13/14.54 (
% 107.13/14.54 ('#B') @ (
% 107.13/14.54 =))) @
% 107.13/14.54 (
% 107.13/14.54 (
% 107.13/14.54 ('#C') @ binintersect)))))) @
% 107.13/14.54 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 107.13/14.54 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1216])).
% 107.13/14.54 thf(zip_derived_cl1231, plain,
% 107.13/14.54 (~ (((binintersectSubset1) =>
% 107.13/14.54 (((bs114d) =>
% 107.13/14.54 (((setminusI) =>
% 107.13/14.54 (((setminusEL) =>
% 107.13/14.54 (((setminusER) =>
% 107.13/14.54 (((setminusSubset2) =>
% 107.13/14.54 (((setminusERneg) =>
% 107.13/14.54 (((setminusELneg) =>
% 107.13/14.54 (((setminusILneg) =>
% 107.13/14.54 (((setminusIRneg) =>
% 107.13/14.54 (((setminusLsub) =>
% 107.13/14.54 (((setminusSubset1) =>
% 107.13/14.54 (((symdiffE) =>
% 107.13/14.54 (((symdiffI1) =>
% 107.13/14.54 (((symdiffI2) =>
% 107.13/14.54 (((symdiffIneg1) =>
% 107.13/14.54 (((symdiffIneg2) =>
% 107.13/14.54 (((secondinupair) =>
% 107.13/14.54 (((setukpairIL) =>
% 107.13/14.54 (((setukpairIR) =>
% 107.13/14.54 (((kpairiskpair) =>
% 107.13/14.54 (((kpairp) =>
% 107.13/14.54 (((singletonsubset) =>
% 107.13/14.54 (((singletoninpowerset) =>
% 107.13/14.54 (((singletoninpowunion) =>
% 107.13/14.54 (((upairset2E) =>
% 107.13/14.54 (((upairsubunion) =>
% 107.13/14.54 (((upairinpowunion) =>
% 107.13/14.54 (((ubforcartprodlem1) =>
% 107.13/14.54 (((ubforcartprodlem2) =>
% 107.13/14.54 ((
% 107.13/14.54 (ubforcartprodlem3) =>
% 107.13/14.54 ((
% 107.13/14.54 (cartprodpairin) =>
% 107.13/14.54 ((
% 107.13/14.54 (cartprodmempair1) =>
% 107.13/14.54 ((
% 107.13/14.54 (cartprodmempair) =>
% 107.13/14.54 ((
% 107.13/14.54 (setunionE2) =>
% 107.13/14.54 ((
% 107.13/14.54 (setunionsingleton1) =>
% 107.13/14.54 ((
% 107.13/14.54 (setunionsingleton2) =>
% 107.13/14.54 ((
% 107.13/14.54 (setunionsingleton) =>
% 107.13/14.54 ((
% 107.13/14.54 (singletonprop) =>
% 107.13/14.54 ((
% 107.13/14.54 (ex1E1) =>
% 107.13/14.54 ((
% 107.13/14.54 (ex1I) =>
% 107.13/14.54 ((
% 107.13/14.54 (ex1I2) =>
% 107.13/14.54 ((
% 107.13/14.54 (singletonsuniq) =>
% 107.13/14.54 ((
% 107.13/14.54 (setukpairinjL1) =>
% 107.13/14.54 ((
% 107.13/14.54 (kfstsingleton) =>
% 107.13/14.54 ((
% 107.13/14.54 (theprop) =>
% 107.13/14.54 ((
% 107.13/14.54 (kfstpairEq) =>
% 107.13/14.54 ((
% 107.13/14.54 (cartprodfstin) =>
% 107.13/14.54 ((
% 107.13/14.54 (setukpairinjL2) =>
% 107.13/14.54 ((
% 107.13/14.54 (setukpairinjL) =>
% 107.13/14.54 ((
% 107.13/14.54 (setukpairinjR11) =>
% 107.13/14.54 ((
% 107.13/14.54 (setukpairinjR12) =>
% 107.13/14.54 ((
% 107.13/14.54 (setukpairinjR1) =>
% 107.13/14.54 ((
% 107.13/14.54 (upairequniteq) =>
% 107.13/14.54 ((
% 107.13/14.54 (setukpairinjR2) =>
% 107.13/14.54 ((
% 107.13/14.54 (setukpairinjR) =>
% 107.13/14.54 ((
% 107.13/14.54 (ksndsingleton) =>
% 107.13/14.54 ((
% 107.13/14.54 (ksndpairEq) =>
% 107.13/14.54 ((
% 107.13/14.54 (kpairsurjEq) =>
% 107.13/14.54 ((
% 107.13/14.54 (cartprodsndin) =>
% 107.13/14.54 ((
% 107.13/14.54 (cartprodpairmemEL) =>
% 107.13/14.54 ((
% 107.13/14.54 (cartprodpairmemER) =>
% 107.13/14.54 ((
% 107.13/14.54 (cartprodmempaircEq) =>
% 107.13/14.54 ((
% 107.13/14.54 (cartprodfstpairEq) =>
% 107.13/14.54 ((
% 107.13/14.54 (cartprodsndpairEq) =>
% 107.13/14.54 ((
% 107.13/14.54 (cartprodpairsurjEq) =>
% 107.13/14.54 ((
% 107.13/14.54 (dpsetconstrI) =>
% 107.13/14.54 ((
% 107.13/14.54 (dpsetconstrSub) =>
% 107.13/14.54 ((
% 107.13/14.54 (setOfPairsIsBReln) =>
% 107.13/14.54 ((
% 107.13/14.54 (dpsetconstrERa) =>
% 107.13/14.54 ((
% 107.13/14.54 (dpsetconstrEL1) =>
% 107.13/14.54 ((
% 107.13/14.54 (dpsetconstrEL2) =>
% 107.13/14.54 ((
% 107.13/14.54 (dpsetconstrER) =>
% 107.13/14.54 ((
% 107.13/14.54 (funcImageSingleton) =>
% 107.13/14.54 ((
% 107.13/14.54 (apProp) =>
% 107.13/14.54 ((
% 107.13/14.54 (app) =>
% 107.13/14.54 ((
% 107.13/14.54 (infuncsetfunc) =>
% 107.13/14.54 ((
% 107.13/14.54 (ap2p) =>
% 107.13/14.54 ((
% 107.13/14.54 (funcinfuncset) =>
% 107.13/14.54 ((
% 107.13/14.54 (lamProp) =>
% 107.13/14.54 ((
% 107.13/14.54 (lamp) =>
% 107.13/14.54 ((
% 107.13/14.54 (lam2p) =>
% 107.13/14.54 ((
% 107.13/14.54 (brelnall1) =>
% 107.13/14.54 ((
% 107.13/14.54 (brelnall2) =>
% 107.13/14.54 ((
% 107.13/14.54 (ex1E2) =>
% 107.13/14.54 ((
% 107.13/14.54 (funcGraphProp1) =>
% 107.13/14.54 ((
% 107.13/14.54 (funcGraphProp3) =>
% 107.13/14.54 ((
% 107.13/14.54 (funcGraphProp2) =>
% 107.13/14.54 ((
% 107.13/14.54 (funcextLem) =>
% 107.13/14.54 ((
% 107.13/14.54 (funcGraphProp4) =>
% 107.13/14.54 ((
% 107.13/14.54 (subbreln) =>
% 107.13/14.54 ((
% 107.13/14.54 (eqbreln) =>
% 107.13/14.54 ((
% 107.13/14.54 (funcext) =>
% 107.13/14.54 ((
% 107.13/14.54 (funcext2) =>
% 107.13/14.54 ((
% 107.13/14.54 (ap2apEq1) =>
% 107.13/14.54 ((
% 107.13/14.54 (ap2apEq2) =>
% 107.13/14.54 ((
% 107.13/14.54 (beta1) =>
% 107.13/14.54 ((
% 107.13/14.54 (eta1) =>
% 107.13/14.54 ((
% 107.13/14.54 (lam2lamEq) =>
% 107.13/14.54 ((
% 107.13/14.54 (beta2) =>
% 107.13/14.54 ((
% 107.13/14.54 (eta2) =>
% 107.13/14.54 ((
% 107.13/14.54 (iffalseProp1) =>
% 107.13/14.54 ((
% 107.13/14.54 (iffalseProp2) =>
% 107.13/14.54 ((
% 107.13/14.54 (iftrueProp1) =>
% 107.13/14.54 ((
% 107.13/14.54 (iftrueProp2) =>
% 107.13/14.54 ((
% 107.13/14.54 (ifSingleton) =>
% 107.13/14.54 ((
% 107.13/14.54 (ifp) =>
% 107.13/14.54 ((
% 107.13/14.54 (theeq) =>
% 107.13/14.54 ((
% 107.13/14.54 (iftrue) =>
% 107.13/14.54 ((
% 107.13/14.54 (iffalse) =>
% 107.13/14.54 ((
% 107.13/14.54 (iftrueorfalse) =>
% 107.13/14.54 ((
% 107.13/14.54 (binintersectT_lem) =>
% 107.13/14.54 ((
% 107.13/14.54 (binunionT_lem) =>
% 107.13/14.54 ((
% 107.13/14.54 (powersetT_lem) =>
% 107.13/14.54 ((
% 107.13/14.54 (setminusT_lem) =>
% 107.13/14.54 ((
% 107.13/14.54 (complementT_lem) =>
% 107.13/14.54 ((
% 107.13/14.54 (setextT) =>
% 107.13/14.54 ((
% 107.13/14.54 (subsetTI) =>
% 107.13/14.54 ((
% 107.13/14.54 (powersetTI1) =>
% 107.13/14.54 ((
% 107.13/14.54 (powersetTE1) =>
% 107.13/14.54 ((
% 107.13/14.54 (complementTI1) =>
% 107.13/14.54 ((
% 107.13/14.54 (complementTE1) =>
% 107.13/14.54 ((
% 107.13/14.54 (binintersectTELcontra) =>
% 107.13/14.54 ((
% 107.13/14.54 (binintersectTERcontra) =>
% 107.13/14.54 ((
% 107.13/14.54 (contrasubsetT) =>
% 107.13/14.54 ((
% 107.13/14.54 (contrasubsetT1) =>
% 107.13/14.54 ((
% 107.13/14.54 (contrasubsetT2) =>
% 107.13/14.54 ((
% 107.13/14.54 (contrasubsetT3) =>
% 107.13/14.54 ((
% 107.13/14.54 (doubleComplementI1) =>
% 107.13/14.54 ((
% 107.13/14.54 (doubleComplementE1) =>
% 107.13/14.54 ((
% 107.13/14.54 (doubleComplementSub1) =>
% 107.13/14.54 ((
% 107.13/14.54 (doubleComplementSub2) =>
% 107.13/14.54 ((
% 107.13/14.54 (doubleComplementEq) =>
% 107.13/14.54 ((
% 107.13/14.54 (complementTnotintersectT) =>
% 107.13/14.54 ((
% 107.13/14.54 (complementImpComplementIntersect) =>
% 107.13/14.54 ((
% 107.13/14.54 (complementSubsetComplementIntersect) =>
% 107.13/14.54 ((
% 107.13/14.54 (complementInPowersetComplementIntersect) =>
% 107.13/14.54 ((
% 107.13/14.54 (contraSubsetComplement) =>
% 107.13/14.54 ((
% 107.13/14.54 (complementTcontraSubset) =>
% 107.13/14.54 ((
% 107.13/14.54 (binunionTILcontra) =>
% 107.13/14.54 ((
% 107.13/14.54 (binunionTIRcontra) =>
% 107.13/14.54 ((
% 107.13/14.54 (inIntersectImpInUnion) =>
% 107.13/14.54 ((
% 107.13/14.54 (inIntersectImpInUnion2) =>
% 107.13/14.54 ((
% 107.13/14.54 (inIntersectImpInIntersectUnions) =>
% 107.13/14.54 ((
% 107.13/14.54 (intersectInPowersetIntersectUnions) =>
% 107.13/14.54 ((
% 107.13/14.54 (inComplementUnionImpNotIn1) =>
% 107.13/14.54 ((
% 107.13/14.54 (inComplementUnionImpInComplement1) =>
% 107.13/14.54 ((
% 107.13/14.54 (binunionTE) =>
% 107.13/14.54 ((
% 107.13/14.54 (binunionTEcontra) =>
% 107.13/14.54 ((
% 107.13/14.54 (demorgan2a1) =>
% 107.13/14.54 ((
% 107.13/14.54 (complementUnionInPowersetComplement) =>
% 107.13/14.54 ((
% 107.13/14.54 (demorgan2a2) =>
% 107.13/14.54 ((
% 107.13/14.54 (demorgan1a) =>
% 107.13/14.54 ((
% 107.13/14.54 (demorgan1b) =>
% 107.13/14.54 ((
% 107.13/14.54 (demorgan1) =>
% 107.13/14.54 ((
% 107.13/14.54 (demorgan2a) =>
% 107.13/14.54 ((
% 107.13/14.54 (demorgan2b2) =>
% 107.13/14.54 ((
% 107.13/14.54 (demorgan2b) =>
% 107.13/14.54 ((
% 107.13/14.54 (demorgan2) =>
% 107.13/14.54 ((
% 107.13/14.54 (woz13rule0) =>
% 107.13/14.54 ((
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% 107.13/14.54 ((
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% 107.13/14.54 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1223])).
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% 107.13/14.54 (cartprodpairmemER) =>
% 107.13/14.54 ((
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% 107.13/14.54 ('#C') @ binintersect)))))) @
% 107.13/14.54 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 107.13/14.54 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1231])).
% 107.13/14.54 thf(zip_derived_cl1247, plain,
% 107.13/14.54 (~ (((setminusI) =>
% 107.13/14.54 (((setminusEL) =>
% 107.13/14.54 (((setminusER) =>
% 107.13/14.54 (((setminusSubset2) =>
% 107.13/14.54 (((setminusERneg) =>
% 107.13/14.54 (((setminusELneg) =>
% 107.13/14.54 (((setminusILneg) =>
% 107.13/14.54 (((setminusIRneg) =>
% 107.13/14.54 (((setminusLsub) =>
% 107.13/14.54 (((setminusSubset1) =>
% 107.13/14.54 (((symdiffE) =>
% 107.13/14.54 (((symdiffI1) =>
% 107.13/14.54 (((symdiffI2) =>
% 107.13/14.54 (((symdiffIneg1) =>
% 107.13/14.54 (((symdiffIneg2) =>
% 107.13/14.54 (((secondinupair) =>
% 107.13/14.54 (((setukpairIL) =>
% 107.13/14.54 (((setukpairIR) =>
% 107.13/14.54 (((kpairiskpair) =>
% 107.13/14.54 (((kpairp) =>
% 107.13/14.54 (((singletonsubset) =>
% 107.13/14.54 (((singletoninpowerset) =>
% 107.13/14.54 (((singletoninpowunion) =>
% 107.13/14.54 (((upairset2E) =>
% 107.13/14.54 (((upairsubunion) =>
% 107.13/14.54 (((upairinpowunion) =>
% 107.13/14.54 (((ubforcartprodlem1) =>
% 107.13/14.54 (((ubforcartprodlem2) =>
% 107.13/14.54 (((ubforcartprodlem3) =>
% 107.13/14.54 (((cartprodpairin) =>
% 107.13/14.54 ((
% 107.13/14.54 (cartprodmempair1) =>
% 107.13/14.54 ((
% 107.13/14.54 (cartprodmempair) =>
% 107.13/14.54 ((
% 107.13/14.54 (setunionE2) =>
% 107.13/14.54 ((
% 107.13/14.54 (setunionsingleton1) =>
% 107.13/14.54 ((
% 107.13/14.54 (setunionsingleton2) =>
% 107.13/14.54 ((
% 107.13/14.54 (setunionsingleton) =>
% 107.13/14.54 ((
% 107.13/14.54 (singletonprop) =>
% 107.13/14.54 ((
% 107.13/14.54 (ex1E1) =>
% 107.13/14.54 ((
% 107.13/14.54 (ex1I) =>
% 107.13/14.54 ((
% 107.13/14.54 (ex1I2) =>
% 107.13/14.54 ((
% 107.13/14.54 (singletonsuniq) =>
% 107.13/14.54 ((
% 107.13/14.54 (setukpairinjL1) =>
% 107.13/14.54 ((
% 107.13/14.54 (kfstsingleton) =>
% 107.13/14.54 ((
% 107.13/14.54 (theprop) =>
% 107.13/14.54 ((
% 107.13/14.54 (kfstpairEq) =>
% 107.13/14.54 ((
% 107.13/14.54 (cartprodfstin) =>
% 107.13/14.54 ((
% 107.13/14.54 (setukpairinjL2) =>
% 107.13/14.54 ((
% 107.13/14.54 (setukpairinjL) =>
% 107.13/14.54 ((
% 107.13/14.54 (setukpairinjR11) =>
% 107.13/14.54 ((
% 107.13/14.54 (setukpairinjR12) =>
% 107.13/14.54 ((
% 107.13/14.54 (setukpairinjR1) =>
% 107.13/14.54 ((
% 107.13/14.54 (upairequniteq) =>
% 107.13/14.54 ((
% 107.13/14.54 (setukpairinjR2) =>
% 107.13/14.54 ((
% 107.13/14.54 (setukpairinjR) =>
% 107.13/14.54 ((
% 107.13/14.54 (ksndsingleton) =>
% 107.13/14.54 ((
% 107.13/14.54 (ksndpairEq) =>
% 107.13/14.54 ((
% 107.13/14.54 (kpairsurjEq) =>
% 107.13/14.54 ((
% 107.13/14.54 (cartprodsndin) =>
% 107.13/14.54 ((
% 107.13/14.54 (cartprodpairmemEL) =>
% 107.13/14.54 ((
% 107.13/14.54 (cartprodpairmemER) =>
% 107.13/14.54 ((
% 107.13/14.54 (cartprodmempaircEq) =>
% 107.13/14.54 ((
% 107.13/14.54 (cartprodfstpairEq) =>
% 107.13/14.54 ((
% 107.13/14.54 (cartprodsndpairEq) =>
% 107.13/14.54 ((
% 107.13/14.54 (cartprodpairsurjEq) =>
% 107.13/14.54 ((
% 107.13/14.54 (dpsetconstrI) =>
% 107.13/14.54 ((
% 107.13/14.54 (dpsetconstrSub) =>
% 107.13/14.54 ((
% 107.13/14.54 (setOfPairsIsBReln) =>
% 107.13/14.54 ((
% 107.13/14.54 (dpsetconstrERa) =>
% 107.13/14.54 ((
% 107.13/14.54 (dpsetconstrEL1) =>
% 107.13/14.54 ((
% 107.13/14.54 (dpsetconstrEL2) =>
% 107.13/14.54 ((
% 107.13/14.54 (dpsetconstrER) =>
% 107.13/14.54 ((
% 107.13/14.54 (funcImageSingleton) =>
% 107.13/14.54 ((
% 107.13/14.54 (apProp) =>
% 107.13/14.54 ((
% 107.13/14.54 (app) =>
% 107.13/14.54 ((
% 107.13/14.54 (infuncsetfunc) =>
% 107.13/14.54 ((
% 107.13/14.54 (ap2p) =>
% 107.13/14.54 ((
% 107.13/14.54 (funcinfuncset) =>
% 107.13/14.54 ((
% 107.13/14.54 (lamProp) =>
% 107.13/14.54 ((
% 107.13/14.54 (lamp) =>
% 107.13/14.54 ((
% 107.13/14.54 (lam2p) =>
% 107.13/14.54 ((
% 107.13/14.54 (brelnall1) =>
% 107.13/14.54 ((
% 107.13/14.54 (brelnall2) =>
% 107.13/14.54 ((
% 107.13/14.54 (ex1E2) =>
% 107.13/14.54 ((
% 107.13/14.54 (funcGraphProp1) =>
% 107.13/14.54 ((
% 107.13/14.54 (funcGraphProp3) =>
% 107.13/14.54 ((
% 107.13/14.54 (funcGraphProp2) =>
% 107.13/14.54 ((
% 107.13/14.54 (funcextLem) =>
% 107.13/14.54 ((
% 107.13/14.54 (funcGraphProp4) =>
% 107.13/14.54 ((
% 107.13/14.54 (subbreln) =>
% 107.13/14.54 ((
% 107.13/14.54 (eqbreln) =>
% 107.13/14.54 ((
% 107.13/14.54 (funcext) =>
% 107.13/14.54 ((
% 107.13/14.54 (funcext2) =>
% 107.13/14.54 ((
% 107.13/14.54 (ap2apEq1) =>
% 107.13/14.54 ((
% 107.13/14.54 (ap2apEq2) =>
% 107.13/14.54 ((
% 107.13/14.54 (beta1) =>
% 107.13/14.54 ((
% 107.13/14.54 (eta1) =>
% 107.13/14.54 ((
% 107.13/14.54 (lam2lamEq) =>
% 107.13/14.54 ((
% 107.13/14.54 (beta2) =>
% 107.13/14.54 ((
% 107.13/14.54 (eta2) =>
% 107.13/14.54 ((
% 107.13/14.54 (iffalseProp1) =>
% 107.13/14.54 ((
% 107.13/14.54 (iffalseProp2) =>
% 107.13/14.54 ((
% 107.13/14.54 (iftrueProp1) =>
% 107.13/14.54 ((
% 107.13/14.54 (iftrueProp2) =>
% 107.13/14.54 ((
% 107.13/14.54 (ifSingleton) =>
% 107.13/14.54 ((
% 107.13/14.54 (ifp) =>
% 107.13/14.54 ((
% 107.13/14.54 (theeq) =>
% 107.13/14.54 ((
% 107.13/14.54 (iftrue) =>
% 107.13/14.54 ((
% 107.13/14.54 (iffalse) =>
% 107.13/14.54 ((
% 107.13/14.54 (iftrueorfalse) =>
% 107.13/14.54 ((
% 107.13/14.54 (binintersectT_lem) =>
% 107.13/14.54 ((
% 107.13/14.54 (binunionT_lem) =>
% 107.13/14.54 ((
% 107.13/14.54 (powersetT_lem) =>
% 107.13/14.54 ((
% 107.13/14.54 (setminusT_lem) =>
% 107.13/14.54 ((
% 107.13/14.54 (complementT_lem) =>
% 107.13/14.54 ((
% 107.13/14.54 (setextT) =>
% 107.13/14.54 ((
% 107.13/14.54 (subsetTI) =>
% 107.13/14.54 ((
% 107.13/14.54 (powersetTI1) =>
% 107.13/14.54 ((
% 107.13/14.54 (powersetTE1) =>
% 107.13/14.54 ((
% 107.13/14.54 (complementTI1) =>
% 107.13/14.54 ((
% 107.13/14.54 (complementTE1) =>
% 107.13/14.54 ((
% 107.13/14.54 (binintersectTELcontra) =>
% 107.13/14.54 ((
% 107.13/14.54 (binintersectTERcontra) =>
% 107.13/14.54 ((
% 107.13/14.54 (contrasubsetT) =>
% 107.13/14.54 ((
% 107.13/14.54 (contrasubsetT1) =>
% 107.13/14.54 ((
% 107.13/14.54 (contrasubsetT2) =>
% 107.13/14.54 ((
% 107.13/14.54 (contrasubsetT3) =>
% 107.13/14.54 ((
% 107.13/14.54 (doubleComplementI1) =>
% 107.13/14.54 ((
% 107.13/14.54 (doubleComplementE1) =>
% 107.13/14.54 ((
% 107.13/14.54 (doubleComplementSub1) =>
% 107.13/14.54 ((
% 107.13/14.54 (doubleComplementSub2) =>
% 107.13/14.54 ((
% 107.13/14.54 (doubleComplementEq) =>
% 107.13/14.54 ((
% 107.13/14.54 (complementTnotintersectT) =>
% 107.13/14.54 ((
% 107.13/14.54 (complementImpComplementIntersect) =>
% 107.13/14.54 ((
% 107.13/14.54 (complementSubsetComplementIntersect) =>
% 107.13/14.54 ((
% 107.13/14.54 (complementInPowersetComplementIntersect) =>
% 107.13/14.54 ((
% 107.13/14.54 (contraSubsetComplement) =>
% 107.13/14.54 ((
% 107.13/14.54 (complementTcontraSubset) =>
% 107.13/14.54 ((
% 107.13/14.54 (binunionTILcontra) =>
% 107.13/14.54 ((
% 107.13/14.54 (binunionTIRcontra) =>
% 107.13/14.54 ((
% 107.13/14.54 (inIntersectImpInUnion) =>
% 107.13/14.54 ((
% 107.13/14.54 (inIntersectImpInUnion2) =>
% 107.13/14.54 ((
% 107.13/14.54 (inIntersectImpInIntersectUnions) =>
% 107.13/14.54 ((
% 107.13/14.54 (intersectInPowersetIntersectUnions) =>
% 107.13/14.54 ((
% 107.13/14.54 (inComplementUnionImpNotIn1) =>
% 107.13/14.54 ((
% 107.13/14.54 (inComplementUnionImpInComplement1) =>
% 107.13/14.54 ((
% 107.13/14.54 (binunionTE) =>
% 107.13/14.54 ((
% 107.13/14.54 (binunionTEcontra) =>
% 107.13/14.54 ((
% 107.13/14.54 (demorgan2a1) =>
% 107.13/14.54 ((
% 107.13/14.54 (complementUnionInPowersetComplement) =>
% 107.13/14.54 ((
% 107.13/14.54 (demorgan2a2) =>
% 107.13/14.54 ((
% 107.13/14.54 (demorgan1a) =>
% 107.13/14.54 ((
% 107.13/14.54 (demorgan1b) =>
% 107.13/14.54 ((
% 107.13/14.54 (demorgan1) =>
% 107.13/14.54 ((
% 107.13/14.54 (demorgan2a) =>
% 107.13/14.54 ((
% 107.13/14.54 (demorgan2b2) =>
% 107.13/14.54 ((
% 107.13/14.54 (demorgan2b) =>
% 107.13/14.54 ((
% 107.13/14.54 (demorgan2) =>
% 107.13/14.54 ((
% 107.13/14.54 (woz13rule0) =>
% 107.13/14.54 ((
% 107.13/14.54 (woz13rule1) =>
% 107.13/14.54 ((
% 107.13/14.54 (woz13rule2) =>
% 107.13/14.54 ((
% 107.13/14.54 (woz13rule3) =>
% 107.13/14.54 ((
% 107.13/14.54 (woz13rule4) =>
% 107.13/14.54 ((
% 107.13/14.54 (woz1_1) =>
% 107.13/14.54 ((
% 107.13/14.54 (woz1_2) =>
% 107.13/14.54 ((
% 107.13/14.54 (woz1_3) =>
% 107.13/14.54 ((
% 107.13/14.54 (woz1_4) =>
% 107.13/14.54 ((
% 107.13/14.54 (woz1_5) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1all2) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1SetBreln1) =>
% 107.13/14.54 ((
% 107.13/14.54 (choice2fnsingleton) =>
% 107.13/14.54 ((
% 107.13/14.54 (setOfPairsIsBReln1) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1all1) =>
% 107.13/14.54 ((
% 107.13/14.54 (subbreln1) =>
% 107.13/14.54 ((
% 107.13/14.54 (eqbreln1) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1invprop) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1invI) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1invE) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1compprop) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1compI) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1compE) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1compEex) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1unionprop) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1unionIL) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1unionIR) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1unionI) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1unionE) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1unionEcases) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1unionCommutes) =>
% 107.13/14.54 ((
% 107.13/14.54 (woz2Ex) =>
% 107.13/14.54 ((
% 107.13/14.54 (woz2W) =>
% 107.13/14.54 ((
% 107.13/14.54 (woz2A) =>
% 107.13/14.54 ((
% 107.13/14.54 (woz2B) =>
% 107.13/14.54 ((
% 107.13/14.54 (image1Ex) =>
% 107.13/14.54 ((
% 107.13/14.54 (image1Ex1) =>
% 107.13/14.54 ((
% 107.13/14.54 (image1Equiv) =>
% 107.13/14.54 ((
% 107.13/14.54 (image1E) =>
% 107.13/14.54 ((
% 107.13/14.54 (image1I) =>
% 107.13/14.54 ((
% 107.13/14.54 (injFuncInInjFuncSet) =>
% 107.13/14.54 ((
% 107.13/14.54 (injFuncSetFuncIn) =>
% 107.13/14.54 ((
% 107.13/14.54 (injFuncSetFuncInj) =>
% 107.13/14.54 ((
% 107.13/14.54 (surjFuncSetFuncIn) =>
% 107.13/14.54 ((
% 107.13/14.54 (surjFuncSetFuncSurj) =>
% 107.13/14.54 ((
% 107.13/14.54 (leftInvIsSurj) =>
% 107.13/14.54 ((
% 107.13/14.54 (surjCantorThm) =>
% 107.13/14.54 ((
% 107.13/14.54 (!!) @ (
% 107.13/14.54 (('#S') @ (
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% 107.13/14.54 ('#B') @ (
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% 107.13/14.54 nonempty)) @
% 107.13/14.54 (
% 107.13/14.54 (
% 107.13/14.54 ('#B') @ (
% 107.13/14.54 ??) @
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% 107.13/14.54 (
% 107.13/14.54 ('#S') @ (
% 107.13/14.54 (
% 107.13/14.54 ('#B') @ (
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% 107.13/14.54 (
% 107.13/14.54 (
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% 107.13/14.54 (
% 107.13/14.54 (
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% 107.13/14.54 (
% 107.13/14.54 (
% 107.13/14.54 ('#C') @ (
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% 107.13/14.54 (
% 107.13/14.54 (
% 107.13/14.54 ('#B') @ (
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% 107.13/14.54 ('#B') @ (
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% 107.13/14.54 (
% 107.13/14.54 (
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% 107.13/14.54 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1239])).
% 107.13/14.54 thf(zip_derived_cl1255, plain,
% 107.13/14.54 (~ (((setminusEL) =>
% 107.13/14.54 (((setminusER) =>
% 107.13/14.54 (((setminusSubset2) =>
% 107.13/14.54 (((setminusERneg) =>
% 107.13/14.54 (((setminusELneg) =>
% 107.13/14.54 (((setminusILneg) =>
% 107.13/14.54 (((setminusIRneg) =>
% 107.13/14.54 (((setminusLsub) =>
% 107.13/14.54 (((setminusSubset1) =>
% 107.13/14.54 (((symdiffE) =>
% 107.13/14.54 (((symdiffI1) =>
% 107.13/14.54 (((symdiffI2) =>
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% 107.13/14.54 (((symdiffIneg2) =>
% 107.13/14.54 (((secondinupair) =>
% 107.13/14.54 (((setukpairIL) =>
% 107.13/14.54 (((setukpairIR) =>
% 107.13/14.54 (((kpairiskpair) =>
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% 107.13/14.54 (((singletoninpowunion) =>
% 107.13/14.54 (((upairset2E) =>
% 107.13/14.54 (((upairsubunion) =>
% 107.13/14.54 (((upairinpowunion) =>
% 107.13/14.54 (((ubforcartprodlem1) =>
% 107.13/14.54 (((ubforcartprodlem2) =>
% 107.13/14.54 (((ubforcartprodlem3) =>
% 107.13/14.54 (((cartprodpairin) =>
% 107.13/14.54 (((cartprodmempair1) =>
% 107.13/14.54 ((
% 107.13/14.54 (cartprodmempair) =>
% 107.13/14.54 ((
% 107.13/14.54 (setunionE2) =>
% 107.13/14.54 ((
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% 107.13/14.54 ((
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% 107.13/14.54 ((
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% 107.13/14.54 ((
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% 107.13/14.54 ((
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% 107.13/14.54 ((
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% 107.13/14.54 ((
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% 107.13/14.54 ((
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% 107.13/14.54 ((
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% 107.13/14.54 ((
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% 107.13/14.54 ((
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% 107.13/14.54 ((
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% 107.13/14.54 ((
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% 107.13/14.54 ((
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% 107.13/14.54 ((
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% 107.13/14.54 ((
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% 107.13/14.54 ((
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% 107.13/14.54 ((
% 107.13/14.54 (kpairsurjEq) =>
% 107.13/14.54 ((
% 107.13/14.54 (cartprodsndin) =>
% 107.13/14.54 ((
% 107.13/14.54 (cartprodpairmemEL) =>
% 107.13/14.54 ((
% 107.13/14.54 (cartprodpairmemER) =>
% 107.13/14.54 ((
% 107.13/14.54 (cartprodmempaircEq) =>
% 107.13/14.54 ((
% 107.13/14.54 (cartprodfstpairEq) =>
% 107.13/14.54 ((
% 107.13/14.54 (cartprodsndpairEq) =>
% 107.13/14.54 ((
% 107.13/14.54 (cartprodpairsurjEq) =>
% 107.13/14.54 ((
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% 107.13/14.54 ((
% 107.13/14.54 (dpsetconstrSub) =>
% 107.13/14.54 ((
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% 107.13/14.54 ((
% 107.13/14.54 (dpsetconstrER) =>
% 107.13/14.54 ((
% 107.13/14.54 (funcImageSingleton) =>
% 107.13/14.54 ((
% 107.13/14.54 (apProp) =>
% 107.13/14.54 ((
% 107.13/14.54 (app) =>
% 107.13/14.54 ((
% 107.13/14.54 (infuncsetfunc) =>
% 107.13/14.54 ((
% 107.13/14.54 (ap2p) =>
% 107.13/14.54 ((
% 107.13/14.54 (funcinfuncset) =>
% 107.13/14.54 ((
% 107.13/14.54 (lamProp) =>
% 107.13/14.54 ((
% 107.13/14.54 (lamp) =>
% 107.13/14.54 ((
% 107.13/14.54 (lam2p) =>
% 107.13/14.54 ((
% 107.13/14.54 (brelnall1) =>
% 107.13/14.54 ((
% 107.13/14.54 (brelnall2) =>
% 107.13/14.54 ((
% 107.13/14.54 (ex1E2) =>
% 107.13/14.54 ((
% 107.13/14.54 (funcGraphProp1) =>
% 107.13/14.54 ((
% 107.13/14.54 (funcGraphProp3) =>
% 107.13/14.54 ((
% 107.13/14.54 (funcGraphProp2) =>
% 107.13/14.54 ((
% 107.13/14.54 (funcextLem) =>
% 107.13/14.54 ((
% 107.13/14.54 (funcGraphProp4) =>
% 107.13/14.54 ((
% 107.13/14.54 (subbreln) =>
% 107.13/14.54 ((
% 107.13/14.54 (eqbreln) =>
% 107.13/14.54 ((
% 107.13/14.54 (funcext) =>
% 107.13/14.54 ((
% 107.13/14.54 (funcext2) =>
% 107.13/14.54 ((
% 107.13/14.54 (ap2apEq1) =>
% 107.13/14.54 ((
% 107.13/14.54 (ap2apEq2) =>
% 107.13/14.54 ((
% 107.13/14.54 (beta1) =>
% 107.13/14.54 ((
% 107.13/14.54 (eta1) =>
% 107.13/14.54 ((
% 107.13/14.54 (lam2lamEq) =>
% 107.13/14.54 ((
% 107.13/14.54 (beta2) =>
% 107.13/14.54 ((
% 107.13/14.54 (eta2) =>
% 107.13/14.54 ((
% 107.13/14.54 (iffalseProp1) =>
% 107.13/14.54 ((
% 107.13/14.54 (iffalseProp2) =>
% 107.13/14.54 ((
% 107.13/14.54 (iftrueProp1) =>
% 107.13/14.54 ((
% 107.13/14.54 (iftrueProp2) =>
% 107.13/14.54 ((
% 107.13/14.54 (ifSingleton) =>
% 107.13/14.54 ((
% 107.13/14.54 (ifp) =>
% 107.13/14.54 ((
% 107.13/14.54 (theeq) =>
% 107.13/14.54 ((
% 107.13/14.54 (iftrue) =>
% 107.13/14.54 ((
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% 107.13/14.54 ((
% 107.13/14.54 (binunionT_lem) =>
% 107.13/14.54 ((
% 107.13/14.54 (powersetT_lem) =>
% 107.13/14.54 ((
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% 107.13/14.54 ((
% 107.13/14.54 (complementT_lem) =>
% 107.13/14.54 ((
% 107.13/14.54 (setextT) =>
% 107.13/14.54 ((
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% 107.13/14.54 ((
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% 107.13/14.54 ((
% 107.13/14.54 (powersetTE1) =>
% 107.13/14.54 ((
% 107.13/14.54 (complementTI1) =>
% 107.13/14.54 ((
% 107.13/14.54 (complementTE1) =>
% 107.13/14.54 ((
% 107.13/14.54 (binintersectTELcontra) =>
% 107.13/14.54 ((
% 107.13/14.54 (binintersectTERcontra) =>
% 107.13/14.54 ((
% 107.13/14.54 (contrasubsetT) =>
% 107.13/14.54 ((
% 107.13/14.54 (contrasubsetT1) =>
% 107.13/14.54 ((
% 107.13/14.54 (contrasubsetT2) =>
% 107.13/14.54 ((
% 107.13/14.54 (contrasubsetT3) =>
% 107.13/14.54 ((
% 107.13/14.54 (doubleComplementI1) =>
% 107.13/14.54 ((
% 107.13/14.54 (doubleComplementE1) =>
% 107.13/14.54 ((
% 107.13/14.54 (doubleComplementSub1) =>
% 107.13/14.54 ((
% 107.13/14.54 (doubleComplementSub2) =>
% 107.13/14.54 ((
% 107.13/14.54 (doubleComplementEq) =>
% 107.13/14.54 ((
% 107.13/14.54 (complementTnotintersectT) =>
% 107.13/14.54 ((
% 107.13/14.54 (complementImpComplementIntersect) =>
% 107.13/14.54 ((
% 107.13/14.54 (complementSubsetComplementIntersect) =>
% 107.13/14.54 ((
% 107.13/14.54 (complementInPowersetComplementIntersect) =>
% 107.13/14.54 ((
% 107.13/14.54 (contraSubsetComplement) =>
% 107.13/14.54 ((
% 107.13/14.54 (complementTcontraSubset) =>
% 107.13/14.54 ((
% 107.13/14.54 (binunionTILcontra) =>
% 107.13/14.54 ((
% 107.13/14.54 (binunionTIRcontra) =>
% 107.13/14.54 ((
% 107.13/14.54 (inIntersectImpInUnion) =>
% 107.13/14.54 ((
% 107.13/14.54 (inIntersectImpInUnion2) =>
% 107.13/14.54 ((
% 107.13/14.54 (inIntersectImpInIntersectUnions) =>
% 107.13/14.54 ((
% 107.13/14.54 (intersectInPowersetIntersectUnions) =>
% 107.13/14.54 ((
% 107.13/14.54 (inComplementUnionImpNotIn1) =>
% 107.13/14.54 ((
% 107.13/14.54 (inComplementUnionImpInComplement1) =>
% 107.13/14.54 ((
% 107.13/14.54 (binunionTE) =>
% 107.13/14.54 ((
% 107.13/14.54 (binunionTEcontra) =>
% 107.13/14.54 ((
% 107.13/14.54 (demorgan2a1) =>
% 107.13/14.54 ((
% 107.13/14.54 (complementUnionInPowersetComplement) =>
% 107.13/14.54 ((
% 107.13/14.54 (demorgan2a2) =>
% 107.13/14.54 ((
% 107.13/14.54 (demorgan1a) =>
% 107.13/14.54 ((
% 107.13/14.54 (demorgan1b) =>
% 107.13/14.54 ((
% 107.13/14.54 (demorgan1) =>
% 107.13/14.54 ((
% 107.13/14.54 (demorgan2a) =>
% 107.13/14.54 ((
% 107.13/14.54 (demorgan2b2) =>
% 107.13/14.54 ((
% 107.13/14.54 (demorgan2b) =>
% 107.13/14.54 ((
% 107.13/14.54 (demorgan2) =>
% 107.13/14.54 ((
% 107.13/14.54 (woz13rule0) =>
% 107.13/14.54 ((
% 107.13/14.54 (woz13rule1) =>
% 107.13/14.54 ((
% 107.13/14.54 (woz13rule2) =>
% 107.13/14.54 ((
% 107.13/14.54 (woz13rule3) =>
% 107.13/14.54 ((
% 107.13/14.54 (woz13rule4) =>
% 107.13/14.54 ((
% 107.13/14.54 (woz1_1) =>
% 107.13/14.54 ((
% 107.13/14.54 (woz1_2) =>
% 107.13/14.54 ((
% 107.13/14.54 (woz1_3) =>
% 107.13/14.54 ((
% 107.13/14.54 (woz1_4) =>
% 107.13/14.54 ((
% 107.13/14.54 (woz1_5) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1all2) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1SetBreln1) =>
% 107.13/14.54 ((
% 107.13/14.54 (choice2fnsingleton) =>
% 107.13/14.54 ((
% 107.13/14.54 (setOfPairsIsBReln1) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1all1) =>
% 107.13/14.54 ((
% 107.13/14.54 (subbreln1) =>
% 107.13/14.54 ((
% 107.13/14.54 (eqbreln1) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1invprop) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1invI) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1invE) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1compprop) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1compI) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1compE) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1compEex) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1unionprop) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1unionIL) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1unionIR) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1unionI) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1unionE) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1unionEcases) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1unionCommutes) =>
% 107.13/14.54 ((
% 107.13/14.54 (woz2Ex) =>
% 107.13/14.54 ((
% 107.13/14.54 (woz2W) =>
% 107.13/14.54 ((
% 107.13/14.54 (woz2A) =>
% 107.13/14.54 ((
% 107.13/14.54 (woz2B) =>
% 107.13/14.54 ((
% 107.13/14.54 (image1Ex) =>
% 107.13/14.54 ((
% 107.13/14.54 (image1Ex1) =>
% 107.13/14.54 ((
% 107.13/14.54 (image1Equiv) =>
% 107.13/14.54 ((
% 107.13/14.54 (image1E) =>
% 107.13/14.54 ((
% 107.13/14.54 (image1I) =>
% 107.13/14.54 ((
% 107.13/14.54 (injFuncInInjFuncSet) =>
% 107.13/14.54 ((
% 107.13/14.54 (injFuncSetFuncIn) =>
% 107.13/14.54 ((
% 107.13/14.54 (injFuncSetFuncInj) =>
% 107.13/14.54 ((
% 107.13/14.54 (surjFuncSetFuncIn) =>
% 107.13/14.54 ((
% 107.13/14.54 (surjFuncSetFuncSurj) =>
% 107.13/14.54 ((
% 107.13/14.54 (leftInvIsSurj) =>
% 107.13/14.54 ((
% 107.13/14.54 (surjCantorThm) =>
% 107.13/14.54 ((
% 107.13/14.54 (!!) @ (
% 107.13/14.54 (('#S') @ (
% 107.13/14.54 (
% 107.13/14.54 ('#B') @ (
% 107.13/14.54 =>) @
% 107.13/14.54 nonempty)) @
% 107.13/14.54 (
% 107.13/14.54 (
% 107.13/14.54 ('#B') @ (
% 107.13/14.54 ??) @
% 107.13/14.54 (
% 107.13/14.54 (
% 107.13/14.54 ('#S') @ (
% 107.13/14.54 (
% 107.13/14.54 ('#B') @ (
% 107.13/14.54 '#S') @
% 107.13/14.54 (
% 107.13/14.54 (
% 107.13/14.54 ('#B') @ (
% 107.13/14.54 (
% 107.13/14.54 ('#B') @ (
% 107.13/14.54 &))) @
% 107.13/14.54 (
% 107.13/14.54 (
% 107.13/14.54 ('#C') @ in)))))) @
% 107.13/14.54 (
% 107.13/14.54 (
% 107.13/14.54 ('#C') @ (
% 107.13/14.54 (
% 107.13/14.54 ('#B') @ (
% 107.13/14.54 '#C') @
% 107.13/14.54 (
% 107.13/14.54 (
% 107.13/14.54 ('#B') @ (
% 107.13/14.54 (
% 107.13/14.54 ('#B') @ (
% 107.13/14.54 =))) @
% 107.13/14.54 (
% 107.13/14.54 (
% 107.13/14.54 ('#C') @ binintersect)))))) @
% 107.13/14.54 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 107.13/14.54 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1247])).
% 107.13/14.54 thf(zip_derived_cl1264, plain,
% 107.13/14.54 (~ (((setminusER) =>
% 107.13/14.54 (((setminusSubset2) =>
% 107.13/14.54 (((setminusERneg) =>
% 107.13/14.54 (((setminusELneg) =>
% 107.13/14.54 (((setminusILneg) =>
% 107.13/14.54 (((setminusIRneg) =>
% 107.13/14.54 (((setminusLsub) =>
% 107.13/14.54 (((setminusSubset1) =>
% 107.13/14.54 (((symdiffE) =>
% 107.13/14.54 (((symdiffI1) =>
% 107.13/14.54 (((symdiffI2) =>
% 107.13/14.54 (((symdiffIneg1) =>
% 107.13/14.54 (((symdiffIneg2) =>
% 107.13/14.54 (((secondinupair) =>
% 107.13/14.54 (((setukpairIL) =>
% 107.13/14.54 (((setukpairIR) =>
% 107.13/14.54 (((kpairiskpair) =>
% 107.13/14.54 (((kpairp) =>
% 107.13/14.54 (((singletonsubset) =>
% 107.13/14.54 (((singletoninpowerset) =>
% 107.13/14.54 (((singletoninpowunion) =>
% 107.13/14.54 (((upairset2E) =>
% 107.13/14.54 (((upairsubunion) =>
% 107.13/14.54 (((upairinpowunion) =>
% 107.13/14.54 (((ubforcartprodlem1) =>
% 107.13/14.54 (((ubforcartprodlem2) =>
% 107.13/14.54 (((ubforcartprodlem3) =>
% 107.13/14.54 (((cartprodpairin) =>
% 107.13/14.54 (((cartprodmempair1) =>
% 107.13/14.54 (((cartprodmempair) =>
% 107.13/14.54 ((
% 107.13/14.54 (setunionE2) =>
% 107.13/14.54 ((
% 107.13/14.54 (setunionsingleton1) =>
% 107.13/14.54 ((
% 107.13/14.54 (setunionsingleton2) =>
% 107.13/14.54 ((
% 107.13/14.54 (setunionsingleton) =>
% 107.13/14.54 ((
% 107.13/14.54 (singletonprop) =>
% 107.13/14.54 ((
% 107.13/14.54 (ex1E1) =>
% 107.13/14.54 ((
% 107.13/14.54 (ex1I) =>
% 107.13/14.54 ((
% 107.13/14.54 (ex1I2) =>
% 107.13/14.54 ((
% 107.13/14.54 (singletonsuniq) =>
% 107.13/14.54 ((
% 107.13/14.54 (setukpairinjL1) =>
% 107.13/14.54 ((
% 107.13/14.54 (kfstsingleton) =>
% 107.13/14.54 ((
% 107.13/14.54 (theprop) =>
% 107.13/14.54 ((
% 107.13/14.54 (kfstpairEq) =>
% 107.13/14.54 ((
% 107.13/14.54 (cartprodfstin) =>
% 107.13/14.54 ((
% 107.13/14.54 (setukpairinjL2) =>
% 107.13/14.54 ((
% 107.13/14.54 (setukpairinjL) =>
% 107.13/14.54 ((
% 107.13/14.54 (setukpairinjR11) =>
% 107.13/14.54 ((
% 107.13/14.54 (setukpairinjR12) =>
% 107.13/14.54 ((
% 107.13/14.54 (setukpairinjR1) =>
% 107.13/14.54 ((
% 107.13/14.54 (upairequniteq) =>
% 107.13/14.54 ((
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% 107.13/14.54 ((
% 107.13/14.54 (setukpairinjR) =>
% 107.13/14.54 ((
% 107.13/14.54 (ksndsingleton) =>
% 107.13/14.54 ((
% 107.13/14.54 (ksndpairEq) =>
% 107.13/14.54 ((
% 107.13/14.54 (kpairsurjEq) =>
% 107.13/14.54 ((
% 107.13/14.54 (cartprodsndin) =>
% 107.13/14.54 ((
% 107.13/14.54 (cartprodpairmemEL) =>
% 107.13/14.54 ((
% 107.13/14.54 (cartprodpairmemER) =>
% 107.13/14.54 ((
% 107.13/14.54 (cartprodmempaircEq) =>
% 107.13/14.54 ((
% 107.13/14.54 (cartprodfstpairEq) =>
% 107.13/14.54 ((
% 107.13/14.54 (cartprodsndpairEq) =>
% 107.13/14.54 ((
% 107.13/14.54 (cartprodpairsurjEq) =>
% 107.13/14.54 ((
% 107.13/14.54 (dpsetconstrI) =>
% 107.13/14.54 ((
% 107.13/14.54 (dpsetconstrSub) =>
% 107.13/14.54 ((
% 107.13/14.54 (setOfPairsIsBReln) =>
% 107.13/14.54 ((
% 107.13/14.54 (dpsetconstrERa) =>
% 107.13/14.54 ((
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% 107.13/14.54 ((
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% 107.13/14.54 ((
% 107.13/14.54 (dpsetconstrER) =>
% 107.13/14.54 ((
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% 107.13/14.54 ((
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% 107.13/14.54 ((
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% 107.13/14.54 ((
% 107.13/14.54 (infuncsetfunc) =>
% 107.13/14.54 ((
% 107.13/14.54 (ap2p) =>
% 107.13/14.54 ((
% 107.13/14.54 (funcinfuncset) =>
% 107.13/14.54 ((
% 107.13/14.54 (lamProp) =>
% 107.13/14.54 ((
% 107.13/14.54 (lamp) =>
% 107.13/14.54 ((
% 107.13/14.54 (lam2p) =>
% 107.13/14.54 ((
% 107.13/14.54 (brelnall1) =>
% 107.13/14.54 ((
% 107.13/14.54 (brelnall2) =>
% 107.13/14.54 ((
% 107.13/14.54 (ex1E2) =>
% 107.13/14.54 ((
% 107.13/14.54 (funcGraphProp1) =>
% 107.13/14.54 ((
% 107.13/14.54 (funcGraphProp3) =>
% 107.13/14.54 ((
% 107.13/14.54 (funcGraphProp2) =>
% 107.13/14.54 ((
% 107.13/14.54 (funcextLem) =>
% 107.13/14.54 ((
% 107.13/14.54 (funcGraphProp4) =>
% 107.13/14.54 ((
% 107.13/14.54 (subbreln) =>
% 107.13/14.54 ((
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% 107.13/14.54 ((
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% 107.13/14.54 ((
% 107.13/14.54 (funcext2) =>
% 107.13/14.54 ((
% 107.13/14.54 (ap2apEq1) =>
% 107.13/14.54 ((
% 107.13/14.54 (ap2apEq2) =>
% 107.13/14.54 ((
% 107.13/14.54 (beta1) =>
% 107.13/14.54 ((
% 107.13/14.54 (eta1) =>
% 107.13/14.54 ((
% 107.13/14.54 (lam2lamEq) =>
% 107.13/14.54 ((
% 107.13/14.54 (beta2) =>
% 107.13/14.54 ((
% 107.13/14.54 (eta2) =>
% 107.13/14.54 ((
% 107.13/14.54 (iffalseProp1) =>
% 107.13/14.54 ((
% 107.13/14.54 (iffalseProp2) =>
% 107.13/14.54 ((
% 107.13/14.54 (iftrueProp1) =>
% 107.13/14.54 ((
% 107.13/14.54 (iftrueProp2) =>
% 107.13/14.54 ((
% 107.13/14.54 (ifSingleton) =>
% 107.13/14.54 ((
% 107.13/14.54 (ifp) =>
% 107.13/14.54 ((
% 107.13/14.54 (theeq) =>
% 107.13/14.54 ((
% 107.13/14.54 (iftrue) =>
% 107.13/14.54 ((
% 107.13/14.54 (iffalse) =>
% 107.13/14.54 ((
% 107.13/14.54 (iftrueorfalse) =>
% 107.13/14.54 ((
% 107.13/14.54 (binintersectT_lem) =>
% 107.13/14.54 ((
% 107.13/14.54 (binunionT_lem) =>
% 107.13/14.54 ((
% 107.13/14.54 (powersetT_lem) =>
% 107.13/14.54 ((
% 107.13/14.54 (setminusT_lem) =>
% 107.13/14.54 ((
% 107.13/14.54 (complementT_lem) =>
% 107.13/14.54 ((
% 107.13/14.54 (setextT) =>
% 107.13/14.54 ((
% 107.13/14.54 (subsetTI) =>
% 107.13/14.54 ((
% 107.13/14.54 (powersetTI1) =>
% 107.13/14.54 ((
% 107.13/14.54 (powersetTE1) =>
% 107.13/14.54 ((
% 107.13/14.54 (complementTI1) =>
% 107.13/14.54 ((
% 107.13/14.54 (complementTE1) =>
% 107.13/14.54 ((
% 107.13/14.54 (binintersectTELcontra) =>
% 107.13/14.54 ((
% 107.13/14.54 (binintersectTERcontra) =>
% 107.13/14.54 ((
% 107.13/14.54 (contrasubsetT) =>
% 107.13/14.54 ((
% 107.13/14.54 (contrasubsetT1) =>
% 107.13/14.54 ((
% 107.13/14.54 (contrasubsetT2) =>
% 107.13/14.54 ((
% 107.13/14.54 (contrasubsetT3) =>
% 107.13/14.54 ((
% 107.13/14.54 (doubleComplementI1) =>
% 107.13/14.54 ((
% 107.13/14.54 (doubleComplementE1) =>
% 107.13/14.54 ((
% 107.13/14.54 (doubleComplementSub1) =>
% 107.13/14.54 ((
% 107.13/14.54 (doubleComplementSub2) =>
% 107.13/14.54 ((
% 107.13/14.54 (doubleComplementEq) =>
% 107.13/14.54 ((
% 107.13/14.54 (complementTnotintersectT) =>
% 107.13/14.54 ((
% 107.13/14.54 (complementImpComplementIntersect) =>
% 107.13/14.54 ((
% 107.13/14.54 (complementSubsetComplementIntersect) =>
% 107.13/14.54 ((
% 107.13/14.54 (complementInPowersetComplementIntersect) =>
% 107.13/14.54 ((
% 107.13/14.54 (contraSubsetComplement) =>
% 107.13/14.54 ((
% 107.13/14.54 (complementTcontraSubset) =>
% 107.13/14.54 ((
% 107.13/14.54 (binunionTILcontra) =>
% 107.13/14.54 ((
% 107.13/14.54 (binunionTIRcontra) =>
% 107.13/14.54 ((
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% 107.13/14.54 ((
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% 107.13/14.54 ((
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% 107.13/14.54 ((
% 107.13/14.54 (woz13rule4) =>
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% 107.13/14.54 ((
% 107.13/14.54 (breln1SetBreln1) =>
% 107.13/14.54 ((
% 107.13/14.54 (choice2fnsingleton) =>
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% 107.13/14.54 (breln1compprop) =>
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% 107.13/14.54 ((
% 107.13/14.54 (breln1compE) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1compEex) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1unionprop) =>
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% 107.13/14.54 (breln1unionIL) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1unionIR) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1unionI) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1unionE) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1unionEcases) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1unionCommutes) =>
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% 107.13/14.54 ((
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% 107.13/14.54 ((
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% 107.13/14.54 ((
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% 107.13/14.54 ((
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% 107.13/14.54 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1255])).
% 107.13/14.54 thf(zip_derived_cl1272, plain,
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% 107.13/14.54 (((upairset2E) =>
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% 107.13/14.54 (((ubforcartprodlem1) =>
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% 107.13/14.54 (kpairsurjEq) =>
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% 107.13/14.54 ((
% 107.13/14.54 (cartprodpairmemER) =>
% 107.13/14.54 ((
% 107.13/14.54 (cartprodmempaircEq) =>
% 107.13/14.54 ((
% 107.13/14.54 (cartprodfstpairEq) =>
% 107.13/14.54 ((
% 107.13/14.54 (cartprodsndpairEq) =>
% 107.13/14.54 ((
% 107.13/14.54 (cartprodpairsurjEq) =>
% 107.13/14.54 ((
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% 107.13/14.54 ((
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% 107.13/14.54 ((
% 107.13/14.54 (setminusT_lem) =>
% 107.13/14.54 ((
% 107.13/14.54 (complementT_lem) =>
% 107.13/14.54 ((
% 107.13/14.54 (setextT) =>
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% 107.13/14.54 ((
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% 107.13/14.54 ((
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% 107.13/14.54 ((
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% 107.13/14.54 ((
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% 107.13/14.54 ((
% 107.13/14.54 (binintersectTERcontra) =>
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% 107.13/14.54 ((
% 107.13/14.54 (binunionTIRcontra) =>
% 107.13/14.54 ((
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% 107.13/14.54 ((
% 107.13/14.54 (inIntersectImpInUnion2) =>
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% 107.13/14.54 ((
% 107.13/14.54 (intersectInPowersetIntersectUnions) =>
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% 107.13/14.54 ((
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% 107.13/14.54 ((
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% 107.13/14.54 (
% 107.13/14.54 ('#B') @ (
% 107.13/14.54 =>) @
% 107.13/14.54 nonempty)) @
% 107.13/14.54 (
% 107.13/14.54 (
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% 107.13/14.54 ??) @
% 107.13/14.54 (
% 107.13/14.54 (
% 107.13/14.54 ('#S') @ (
% 107.13/14.54 (
% 107.13/14.54 ('#B') @ (
% 107.13/14.54 '#S') @
% 107.13/14.54 (
% 107.13/14.54 (
% 107.13/14.54 ('#B') @ (
% 107.13/14.54 (
% 107.13/14.54 ('#B') @ (
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% 107.13/14.54 (
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% 107.13/14.54 (
% 107.13/14.54 (
% 107.13/14.54 ('#C') @ (
% 107.13/14.54 (
% 107.13/14.54 ('#B') @ (
% 107.13/14.54 '#C') @
% 107.13/14.54 (
% 107.13/14.54 (
% 107.13/14.54 ('#B') @ (
% 107.13/14.54 (
% 107.13/14.54 ('#B') @ (
% 107.13/14.54 =))) @
% 107.13/14.54 (
% 107.13/14.54 (
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% 107.13/14.54 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 107.13/14.54 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1264])).
% 107.13/14.54 thf(zip_derived_cl1280, plain,
% 107.13/14.54 (~ (((setminusERneg) =>
% 107.13/14.54 (((setminusELneg) =>
% 107.13/14.54 (((setminusILneg) =>
% 107.13/14.54 (((setminusIRneg) =>
% 107.13/14.54 (((setminusLsub) =>
% 107.13/14.54 (((setminusSubset1) =>
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% 107.13/14.54 (((symdiffI1) =>
% 107.13/14.54 (((symdiffI2) =>
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% 107.13/14.54 (((symdiffIneg2) =>
% 107.13/14.54 (((secondinupair) =>
% 107.13/14.54 (((setukpairIL) =>
% 107.13/14.54 (((setukpairIR) =>
% 107.13/14.54 (((kpairiskpair) =>
% 107.13/14.54 (((kpairp) =>
% 107.13/14.54 (((singletonsubset) =>
% 107.13/14.54 (((singletoninpowerset) =>
% 107.13/14.54 (((singletoninpowunion) =>
% 107.13/14.54 (((upairset2E) =>
% 107.13/14.54 (((upairsubunion) =>
% 107.13/14.54 (((upairinpowunion) =>
% 107.13/14.54 (((ubforcartprodlem1) =>
% 107.13/14.54 (((ubforcartprodlem2) =>
% 107.13/14.54 (((ubforcartprodlem3) =>
% 107.13/14.54 (((cartprodpairin) =>
% 107.13/14.54 (((cartprodmempair1) =>
% 107.13/14.54 (((cartprodmempair) =>
% 107.13/14.54 (((setunionE2) =>
% 107.13/14.54 (((setunionsingleton1) =>
% 107.13/14.54 ((
% 107.13/14.54 (setunionsingleton2) =>
% 107.13/14.54 ((
% 107.13/14.54 (setunionsingleton) =>
% 107.13/14.54 ((
% 107.13/14.54 (singletonprop) =>
% 107.13/14.54 ((
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% 107.13/14.54 ((
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% 107.13/14.54 ((
% 107.13/14.54 (ex1I2) =>
% 107.13/14.54 ((
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% 107.13/14.54 ((
% 107.13/14.54 (setukpairinjL1) =>
% 107.13/14.54 ((
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% 107.13/14.54 ((
% 107.13/14.54 (kfstpairEq) =>
% 107.13/14.54 ((
% 107.13/14.54 (cartprodfstin) =>
% 107.13/14.54 ((
% 107.13/14.54 (setukpairinjL2) =>
% 107.13/14.54 ((
% 107.13/14.54 (setukpairinjL) =>
% 107.13/14.54 ((
% 107.13/14.54 (setukpairinjR11) =>
% 107.13/14.54 ((
% 107.13/14.54 (setukpairinjR12) =>
% 107.13/14.54 ((
% 107.13/14.54 (setukpairinjR1) =>
% 107.13/14.54 ((
% 107.13/14.54 (upairequniteq) =>
% 107.13/14.54 ((
% 107.13/14.54 (setukpairinjR2) =>
% 107.13/14.54 ((
% 107.13/14.54 (setukpairinjR) =>
% 107.13/14.54 ((
% 107.13/14.54 (ksndsingleton) =>
% 107.13/14.54 ((
% 107.13/14.54 (ksndpairEq) =>
% 107.13/14.54 ((
% 107.13/14.54 (kpairsurjEq) =>
% 107.13/14.54 ((
% 107.13/14.54 (cartprodsndin) =>
% 107.13/14.54 ((
% 107.13/14.54 (cartprodpairmemEL) =>
% 107.13/14.54 ((
% 107.13/14.54 (cartprodpairmemER) =>
% 107.13/14.54 ((
% 107.13/14.54 (cartprodmempaircEq) =>
% 107.13/14.54 ((
% 107.13/14.54 (cartprodfstpairEq) =>
% 107.13/14.54 ((
% 107.13/14.54 (cartprodsndpairEq) =>
% 107.13/14.54 ((
% 107.13/14.54 (cartprodpairsurjEq) =>
% 107.13/14.54 ((
% 107.13/14.54 (dpsetconstrI) =>
% 107.13/14.54 ((
% 107.13/14.54 (dpsetconstrSub) =>
% 107.13/14.54 ((
% 107.13/14.54 (setOfPairsIsBReln) =>
% 107.13/14.54 ((
% 107.13/14.54 (dpsetconstrERa) =>
% 107.13/14.54 ((
% 107.13/14.54 (dpsetconstrEL1) =>
% 107.13/14.54 ((
% 107.13/14.54 (dpsetconstrEL2) =>
% 107.13/14.54 ((
% 107.13/14.54 (dpsetconstrER) =>
% 107.13/14.54 ((
% 107.13/14.54 (funcImageSingleton) =>
% 107.13/14.54 ((
% 107.13/14.54 (apProp) =>
% 107.13/14.54 ((
% 107.13/14.54 (app) =>
% 107.13/14.54 ((
% 107.13/14.54 (infuncsetfunc) =>
% 107.13/14.54 ((
% 107.13/14.54 (ap2p) =>
% 107.13/14.54 ((
% 107.13/14.54 (funcinfuncset) =>
% 107.13/14.54 ((
% 107.13/14.54 (lamProp) =>
% 107.13/14.54 ((
% 107.13/14.54 (lamp) =>
% 107.13/14.54 ((
% 107.13/14.54 (lam2p) =>
% 107.13/14.54 ((
% 107.13/14.54 (brelnall1) =>
% 107.13/14.54 ((
% 107.13/14.54 (brelnall2) =>
% 107.13/14.54 ((
% 107.13/14.54 (ex1E2) =>
% 107.13/14.54 ((
% 107.13/14.54 (funcGraphProp1) =>
% 107.13/14.54 ((
% 107.13/14.54 (funcGraphProp3) =>
% 107.13/14.54 ((
% 107.13/14.54 (funcGraphProp2) =>
% 107.13/14.54 ((
% 107.13/14.54 (funcextLem) =>
% 107.13/14.54 ((
% 107.13/14.54 (funcGraphProp4) =>
% 107.13/14.54 ((
% 107.13/14.54 (subbreln) =>
% 107.13/14.54 ((
% 107.13/14.54 (eqbreln) =>
% 107.13/14.54 ((
% 107.13/14.54 (funcext) =>
% 107.13/14.54 ((
% 107.13/14.54 (funcext2) =>
% 107.13/14.54 ((
% 107.13/14.54 (ap2apEq1) =>
% 107.13/14.54 ((
% 107.13/14.54 (ap2apEq2) =>
% 107.13/14.54 ((
% 107.13/14.54 (beta1) =>
% 107.13/14.54 ((
% 107.13/14.54 (eta1) =>
% 107.13/14.54 ((
% 107.13/14.54 (lam2lamEq) =>
% 107.13/14.54 ((
% 107.13/14.54 (beta2) =>
% 107.13/14.54 ((
% 107.13/14.54 (eta2) =>
% 107.13/14.54 ((
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% 107.13/14.54 ((
% 107.13/14.54 (iffalseProp2) =>
% 107.13/14.54 ((
% 107.13/14.54 (iftrueProp1) =>
% 107.13/14.54 ((
% 107.13/14.54 (iftrueProp2) =>
% 107.13/14.54 ((
% 107.13/14.54 (ifSingleton) =>
% 107.13/14.54 ((
% 107.13/14.54 (ifp) =>
% 107.13/14.54 ((
% 107.13/14.54 (theeq) =>
% 107.13/14.54 ((
% 107.13/14.54 (iftrue) =>
% 107.13/14.54 ((
% 107.13/14.54 (iffalse) =>
% 107.13/14.54 ((
% 107.13/14.54 (iftrueorfalse) =>
% 107.13/14.54 ((
% 107.13/14.54 (binintersectT_lem) =>
% 107.13/14.54 ((
% 107.13/14.54 (binunionT_lem) =>
% 107.13/14.54 ((
% 107.13/14.54 (powersetT_lem) =>
% 107.13/14.54 ((
% 107.13/14.54 (setminusT_lem) =>
% 107.13/14.54 ((
% 107.13/14.54 (complementT_lem) =>
% 107.13/14.54 ((
% 107.13/14.54 (setextT) =>
% 107.13/14.54 ((
% 107.13/14.54 (subsetTI) =>
% 107.13/14.54 ((
% 107.13/14.54 (powersetTI1) =>
% 107.13/14.54 ((
% 107.13/14.54 (powersetTE1) =>
% 107.13/14.54 ((
% 107.13/14.54 (complementTI1) =>
% 107.13/14.54 ((
% 107.13/14.54 (complementTE1) =>
% 107.13/14.54 ((
% 107.13/14.54 (binintersectTELcontra) =>
% 107.13/14.54 ((
% 107.13/14.54 (binintersectTERcontra) =>
% 107.13/14.54 ((
% 107.13/14.54 (contrasubsetT) =>
% 107.13/14.54 ((
% 107.13/14.54 (contrasubsetT1) =>
% 107.13/14.54 ((
% 107.13/14.54 (contrasubsetT2) =>
% 107.13/14.54 ((
% 107.13/14.54 (contrasubsetT3) =>
% 107.13/14.54 ((
% 107.13/14.54 (doubleComplementI1) =>
% 107.13/14.54 ((
% 107.13/14.54 (doubleComplementE1) =>
% 107.13/14.54 ((
% 107.13/14.54 (doubleComplementSub1) =>
% 107.13/14.54 ((
% 107.13/14.54 (doubleComplementSub2) =>
% 107.13/14.54 ((
% 107.13/14.54 (doubleComplementEq) =>
% 107.13/14.54 ((
% 107.13/14.54 (complementTnotintersectT) =>
% 107.13/14.54 ((
% 107.13/14.54 (complementImpComplementIntersect) =>
% 107.13/14.54 ((
% 107.13/14.54 (complementSubsetComplementIntersect) =>
% 107.13/14.54 ((
% 107.13/14.54 (complementInPowersetComplementIntersect) =>
% 107.13/14.54 ((
% 107.13/14.54 (contraSubsetComplement) =>
% 107.13/14.54 ((
% 107.13/14.54 (complementTcontraSubset) =>
% 107.13/14.54 ((
% 107.13/14.54 (binunionTILcontra) =>
% 107.13/14.54 ((
% 107.13/14.54 (binunionTIRcontra) =>
% 107.13/14.54 ((
% 107.13/14.54 (inIntersectImpInUnion) =>
% 107.13/14.54 ((
% 107.13/14.54 (inIntersectImpInUnion2) =>
% 107.13/14.54 ((
% 107.13/14.54 (inIntersectImpInIntersectUnions) =>
% 107.13/14.54 ((
% 107.13/14.54 (intersectInPowersetIntersectUnions) =>
% 107.13/14.54 ((
% 107.13/14.54 (inComplementUnionImpNotIn1) =>
% 107.13/14.54 ((
% 107.13/14.54 (inComplementUnionImpInComplement1) =>
% 107.13/14.54 ((
% 107.13/14.54 (binunionTE) =>
% 107.13/14.54 ((
% 107.13/14.54 (binunionTEcontra) =>
% 107.13/14.54 ((
% 107.13/14.54 (demorgan2a1) =>
% 107.13/14.54 ((
% 107.13/14.54 (complementUnionInPowersetComplement) =>
% 107.13/14.54 ((
% 107.13/14.54 (demorgan2a2) =>
% 107.13/14.54 ((
% 107.13/14.54 (demorgan1a) =>
% 107.13/14.54 ((
% 107.13/14.54 (demorgan1b) =>
% 107.13/14.54 ((
% 107.13/14.54 (demorgan1) =>
% 107.13/14.54 ((
% 107.13/14.54 (demorgan2a) =>
% 107.13/14.54 ((
% 107.13/14.54 (demorgan2b2) =>
% 107.13/14.54 ((
% 107.13/14.54 (demorgan2b) =>
% 107.13/14.54 ((
% 107.13/14.54 (demorgan2) =>
% 107.13/14.54 ((
% 107.13/14.54 (woz13rule0) =>
% 107.13/14.54 ((
% 107.13/14.54 (woz13rule1) =>
% 107.13/14.54 ((
% 107.13/14.54 (woz13rule2) =>
% 107.13/14.54 ((
% 107.13/14.54 (woz13rule3) =>
% 107.13/14.54 ((
% 107.13/14.54 (woz13rule4) =>
% 107.13/14.54 ((
% 107.13/14.54 (woz1_1) =>
% 107.13/14.54 ((
% 107.13/14.54 (woz1_2) =>
% 107.13/14.54 ((
% 107.13/14.54 (woz1_3) =>
% 107.13/14.54 ((
% 107.13/14.54 (woz1_4) =>
% 107.13/14.54 ((
% 107.13/14.54 (woz1_5) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1all2) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1SetBreln1) =>
% 107.13/14.54 ((
% 107.13/14.54 (choice2fnsingleton) =>
% 107.13/14.54 ((
% 107.13/14.54 (setOfPairsIsBReln1) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1all1) =>
% 107.13/14.54 ((
% 107.13/14.54 (subbreln1) =>
% 107.13/14.54 ((
% 107.13/14.54 (eqbreln1) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1invprop) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1invI) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1invE) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1compprop) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1compI) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1compE) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1compEex) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1unionprop) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1unionIL) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1unionIR) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1unionI) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1unionE) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1unionEcases) =>
% 107.13/14.54 ((
% 107.13/14.54 (breln1unionCommutes) =>
% 107.13/14.54 ((
% 107.13/14.54 (woz2Ex) =>
% 107.13/14.54 ((
% 107.13/14.54 (woz2W) =>
% 107.13/14.54 ((
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% 107.13/14.54 ((
% 107.13/14.54 (woz2B) =>
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% 107.13/14.54 ((
% 107.13/14.54 (image1Ex1) =>
% 107.13/14.54 ((
% 107.13/14.54 (image1Equiv) =>
% 107.13/14.54 ((
% 107.13/14.54 (image1E) =>
% 107.13/14.54 ((
% 107.13/14.54 (image1I) =>
% 107.13/14.54 ((
% 107.13/14.55 (injFuncInInjFuncSet) =>
% 107.13/14.55 ((
% 107.13/14.55 (injFuncSetFuncIn) =>
% 107.13/14.55 ((
% 107.13/14.55 (injFuncSetFuncInj) =>
% 107.13/14.55 ((
% 107.13/14.55 (surjFuncSetFuncIn) =>
% 107.13/14.55 ((
% 107.13/14.55 (surjFuncSetFuncSurj) =>
% 107.13/14.55 ((
% 107.13/14.55 (leftInvIsSurj) =>
% 107.13/14.55 ((
% 107.13/14.55 (surjCantorThm) =>
% 107.13/14.55 ((
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% 107.13/14.55 ('#B') @ (
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% 107.13/14.55 nonempty)) @
% 107.13/14.55 (
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% 107.13/14.55 (
% 107.13/14.55 (
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% 107.13/14.55 (
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% 107.13/14.55 (
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% 107.13/14.55 (
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% 107.13/14.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1272])).
% 107.13/14.55 thf(zip_derived_cl1288, plain,
% 107.13/14.55 (~ (((setminusELneg) =>
% 107.13/14.55 (((setminusILneg) =>
% 107.13/14.55 (((setminusIRneg) =>
% 107.13/14.55 (((setminusLsub) =>
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% 107.13/14.55 (((symdiffIneg2) =>
% 107.13/14.55 (((secondinupair) =>
% 107.13/14.55 (((setukpairIL) =>
% 107.13/14.55 (((setukpairIR) =>
% 107.13/14.55 (((kpairiskpair) =>
% 107.13/14.55 (((kpairp) =>
% 107.13/14.55 (((singletonsubset) =>
% 107.13/14.55 (((singletoninpowerset) =>
% 107.13/14.55 (((singletoninpowunion) =>
% 107.13/14.55 (((upairset2E) =>
% 107.13/14.55 (((upairsubunion) =>
% 107.13/14.55 (((upairinpowunion) =>
% 107.13/14.55 (((ubforcartprodlem1) =>
% 107.13/14.55 (((ubforcartprodlem2) =>
% 107.13/14.55 (((ubforcartprodlem3) =>
% 107.13/14.55 (((cartprodpairin) =>
% 107.13/14.55 (((cartprodmempair1) =>
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% 107.13/14.55 (((setunionsingleton1) =>
% 107.13/14.55 (((setunionsingleton2) =>
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% 107.13/14.55 ((
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% 107.13/14.55 ((
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% 107.13/14.55 ((
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% 107.13/14.55 ((
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% 107.13/14.55 ((
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% 107.13/14.55 ((
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% 107.13/14.55 ((
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% 107.13/14.55 ((
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% 107.13/14.55 ((
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% 107.13/14.55 ((
% 107.13/14.55 (upairequniteq) =>
% 107.13/14.55 ((
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% 107.13/14.55 ((
% 107.13/14.55 (setukpairinjR) =>
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% 107.13/14.55 ((
% 107.13/14.55 (kpairsurjEq) =>
% 107.13/14.55 ((
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% 107.13/14.55 ((
% 107.13/14.55 (cartprodpairmemEL) =>
% 107.13/14.55 ((
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% 107.13/14.55 ((
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% 107.13/14.55 ((
% 107.13/14.55 (cartprodfstpairEq) =>
% 107.13/14.55 ((
% 107.13/14.55 (cartprodsndpairEq) =>
% 107.13/14.55 ((
% 107.13/14.55 (cartprodpairsurjEq) =>
% 107.13/14.55 ((
% 107.13/14.55 (dpsetconstrI) =>
% 107.13/14.55 ((
% 107.13/14.55 (dpsetconstrSub) =>
% 107.13/14.55 ((
% 107.13/14.55 (setOfPairsIsBReln) =>
% 107.13/14.55 ((
% 107.13/14.55 (dpsetconstrERa) =>
% 107.13/14.55 ((
% 107.13/14.55 (dpsetconstrEL1) =>
% 107.13/14.55 ((
% 107.13/14.55 (dpsetconstrEL2) =>
% 107.13/14.55 ((
% 107.13/14.55 (dpsetconstrER) =>
% 107.13/14.55 ((
% 107.13/14.55 (funcImageSingleton) =>
% 107.13/14.55 ((
% 107.13/14.55 (apProp) =>
% 107.13/14.55 ((
% 107.13/14.55 (app) =>
% 107.13/14.55 ((
% 107.13/14.55 (infuncsetfunc) =>
% 107.13/14.55 ((
% 107.13/14.55 (ap2p) =>
% 107.13/14.55 ((
% 107.13/14.55 (funcinfuncset) =>
% 107.13/14.55 ((
% 107.13/14.55 (lamProp) =>
% 107.13/14.55 ((
% 107.13/14.55 (lamp) =>
% 107.13/14.55 ((
% 107.13/14.55 (lam2p) =>
% 107.13/14.55 ((
% 107.13/14.55 (brelnall1) =>
% 107.13/14.55 ((
% 107.13/14.55 (brelnall2) =>
% 107.13/14.55 ((
% 107.13/14.55 (ex1E2) =>
% 107.13/14.55 ((
% 107.13/14.55 (funcGraphProp1) =>
% 107.13/14.55 ((
% 107.13/14.55 (funcGraphProp3) =>
% 107.13/14.55 ((
% 107.13/14.55 (funcGraphProp2) =>
% 107.13/14.55 ((
% 107.13/14.55 (funcextLem) =>
% 107.13/14.55 ((
% 107.13/14.55 (funcGraphProp4) =>
% 107.13/14.55 ((
% 107.13/14.55 (subbreln) =>
% 107.13/14.55 ((
% 107.13/14.55 (eqbreln) =>
% 107.13/14.55 ((
% 107.13/14.55 (funcext) =>
% 107.13/14.55 ((
% 107.13/14.55 (funcext2) =>
% 107.13/14.55 ((
% 107.13/14.55 (ap2apEq1) =>
% 107.13/14.55 ((
% 107.13/14.55 (ap2apEq2) =>
% 107.13/14.55 ((
% 107.13/14.55 (beta1) =>
% 107.13/14.55 ((
% 107.13/14.55 (eta1) =>
% 107.13/14.55 ((
% 107.13/14.55 (lam2lamEq) =>
% 107.13/14.55 ((
% 107.13/14.55 (beta2) =>
% 107.13/14.55 ((
% 107.13/14.55 (eta2) =>
% 107.13/14.55 ((
% 107.13/14.55 (iffalseProp1) =>
% 107.13/14.55 ((
% 107.13/14.55 (iffalseProp2) =>
% 107.13/14.55 ((
% 107.13/14.55 (iftrueProp1) =>
% 107.13/14.55 ((
% 107.13/14.55 (iftrueProp2) =>
% 107.13/14.55 ((
% 107.13/14.55 (ifSingleton) =>
% 107.13/14.55 ((
% 107.13/14.55 (ifp) =>
% 107.13/14.55 ((
% 107.13/14.55 (theeq) =>
% 107.13/14.55 ((
% 107.13/14.55 (iftrue) =>
% 107.13/14.55 ((
% 107.13/14.55 (iffalse) =>
% 107.13/14.55 ((
% 107.13/14.55 (iftrueorfalse) =>
% 107.13/14.55 ((
% 107.13/14.55 (binintersectT_lem) =>
% 107.13/14.55 ((
% 107.13/14.55 (binunionT_lem) =>
% 107.13/14.55 ((
% 107.13/14.55 (powersetT_lem) =>
% 107.13/14.55 ((
% 107.13/14.55 (setminusT_lem) =>
% 107.13/14.55 ((
% 107.13/14.55 (complementT_lem) =>
% 107.13/14.55 ((
% 107.13/14.55 (setextT) =>
% 107.13/14.55 ((
% 107.13/14.55 (subsetTI) =>
% 107.13/14.55 ((
% 107.13/14.55 (powersetTI1) =>
% 107.13/14.55 ((
% 107.13/14.55 (powersetTE1) =>
% 107.13/14.55 ((
% 107.13/14.55 (complementTI1) =>
% 107.13/14.55 ((
% 107.13/14.55 (complementTE1) =>
% 107.13/14.55 ((
% 107.13/14.55 (binintersectTELcontra) =>
% 107.13/14.55 ((
% 107.13/14.55 (binintersectTERcontra) =>
% 107.13/14.55 ((
% 107.13/14.55 (contrasubsetT) =>
% 107.13/14.55 ((
% 107.13/14.55 (contrasubsetT1) =>
% 107.13/14.55 ((
% 107.13/14.55 (contrasubsetT2) =>
% 107.13/14.55 ((
% 107.13/14.55 (contrasubsetT3) =>
% 107.13/14.55 ((
% 107.13/14.55 (doubleComplementI1) =>
% 107.13/14.55 ((
% 107.13/14.55 (doubleComplementE1) =>
% 107.13/14.55 ((
% 107.13/14.55 (doubleComplementSub1) =>
% 107.13/14.55 ((
% 107.13/14.55 (doubleComplementSub2) =>
% 107.13/14.55 ((
% 107.13/14.55 (doubleComplementEq) =>
% 107.13/14.55 ((
% 107.13/14.55 (complementTnotintersectT) =>
% 107.13/14.55 ((
% 107.13/14.55 (complementImpComplementIntersect) =>
% 107.13/14.55 ((
% 107.13/14.55 (complementSubsetComplementIntersect) =>
% 107.13/14.55 ((
% 107.13/14.55 (complementInPowersetComplementIntersect) =>
% 107.13/14.55 ((
% 107.13/14.55 (contraSubsetComplement) =>
% 107.13/14.55 ((
% 107.13/14.55 (complementTcontraSubset) =>
% 107.13/14.55 ((
% 107.13/14.55 (binunionTILcontra) =>
% 107.13/14.55 ((
% 107.13/14.55 (binunionTIRcontra) =>
% 107.13/14.55 ((
% 107.13/14.55 (inIntersectImpInUnion) =>
% 107.13/14.55 ((
% 107.13/14.55 (inIntersectImpInUnion2) =>
% 107.13/14.55 ((
% 107.13/14.55 (inIntersectImpInIntersectUnions) =>
% 107.13/14.55 ((
% 107.13/14.55 (intersectInPowersetIntersectUnions) =>
% 107.13/14.55 ((
% 107.13/14.55 (inComplementUnionImpNotIn1) =>
% 107.13/14.55 ((
% 107.13/14.55 (inComplementUnionImpInComplement1) =>
% 107.13/14.55 ((
% 107.13/14.55 (binunionTE) =>
% 107.13/14.55 ((
% 107.13/14.55 (binunionTEcontra) =>
% 107.13/14.55 ((
% 107.13/14.55 (demorgan2a1) =>
% 107.13/14.55 ((
% 107.13/14.55 (complementUnionInPowersetComplement) =>
% 107.13/14.55 ((
% 107.13/14.55 (demorgan2a2) =>
% 107.13/14.55 ((
% 107.13/14.55 (demorgan1a) =>
% 107.13/14.55 ((
% 107.13/14.55 (demorgan1b) =>
% 107.13/14.55 ((
% 107.13/14.55 (demorgan1) =>
% 107.13/14.55 ((
% 107.13/14.55 (demorgan2a) =>
% 107.13/14.55 ((
% 107.13/14.55 (demorgan2b2) =>
% 107.13/14.55 ((
% 107.13/14.55 (demorgan2b) =>
% 107.13/14.55 ((
% 107.13/14.55 (demorgan2) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz13rule0) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz13rule1) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz13rule2) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz13rule3) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz13rule4) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz1_1) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz1_2) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz1_3) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz1_4) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz1_5) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1all2) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1SetBreln1) =>
% 107.13/14.55 ((
% 107.13/14.55 (choice2fnsingleton) =>
% 107.13/14.55 ((
% 107.13/14.55 (setOfPairsIsBReln1) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1all1) =>
% 107.13/14.55 ((
% 107.13/14.55 (subbreln1) =>
% 107.13/14.55 ((
% 107.13/14.55 (eqbreln1) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1invprop) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1invI) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1invE) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1compprop) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1compI) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1compE) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1compEex) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1unionprop) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1unionIL) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1unionIR) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1unionI) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1unionE) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1unionEcases) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1unionCommutes) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz2Ex) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz2W) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz2A) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz2B) =>
% 107.13/14.55 ((
% 107.13/14.55 (image1Ex) =>
% 107.13/14.55 ((
% 107.13/14.55 (image1Ex1) =>
% 107.13/14.55 ((
% 107.13/14.55 (image1Equiv) =>
% 107.13/14.55 ((
% 107.13/14.55 (image1E) =>
% 107.13/14.55 ((
% 107.13/14.55 (image1I) =>
% 107.13/14.55 ((
% 107.13/14.55 (injFuncInInjFuncSet) =>
% 107.13/14.55 ((
% 107.13/14.55 (injFuncSetFuncIn) =>
% 107.13/14.55 ((
% 107.13/14.55 (injFuncSetFuncInj) =>
% 107.13/14.55 ((
% 107.13/14.55 (surjFuncSetFuncIn) =>
% 107.13/14.55 ((
% 107.13/14.55 (surjFuncSetFuncSurj) =>
% 107.13/14.55 ((
% 107.13/14.55 (leftInvIsSurj) =>
% 107.13/14.55 ((
% 107.13/14.55 (surjCantorThm) =>
% 107.13/14.55 ((
% 107.13/14.55 (!!) @ (
% 107.13/14.55 (('#S') @ (
% 107.13/14.55 (
% 107.13/14.55 ('#B') @ (
% 107.13/14.55 =>) @
% 107.13/14.55 nonempty)) @
% 107.13/14.55 (
% 107.13/14.55 (
% 107.13/14.55 ('#B') @ (
% 107.13/14.55 ??) @
% 107.13/14.55 (
% 107.13/14.55 (
% 107.13/14.55 ('#S') @ (
% 107.13/14.55 (
% 107.13/14.55 ('#B') @ (
% 107.13/14.55 '#S') @
% 107.13/14.55 (
% 107.13/14.55 (
% 107.13/14.55 ('#B') @ (
% 107.13/14.55 (
% 107.13/14.55 ('#B') @ (
% 107.13/14.55 &))) @
% 107.13/14.55 (
% 107.13/14.55 (
% 107.13/14.55 ('#C') @ in)))))) @
% 107.13/14.55 (
% 107.13/14.55 (
% 107.13/14.55 ('#C') @ (
% 107.13/14.55 (
% 107.13/14.55 ('#B') @ (
% 107.13/14.55 '#C') @
% 107.13/14.55 (
% 107.13/14.55 (
% 107.13/14.55 ('#B') @ (
% 107.13/14.55 (
% 107.13/14.55 ('#B') @ (
% 107.13/14.55 =))) @
% 107.13/14.55 (
% 107.13/14.55 (
% 107.13/14.55 ('#C') @ binintersect)))))) @
% 107.13/14.55 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 107.13/14.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1280])).
% 107.13/14.55 thf(zip_derived_cl1296, plain,
% 107.13/14.55 (~ (((setminusILneg) =>
% 107.13/14.55 (((setminusIRneg) =>
% 107.13/14.55 (((setminusLsub) =>
% 107.13/14.55 (((setminusSubset1) =>
% 107.13/14.55 (((symdiffE) =>
% 107.13/14.55 (((symdiffI1) =>
% 107.13/14.55 (((symdiffI2) =>
% 107.13/14.55 (((symdiffIneg1) =>
% 107.13/14.55 (((symdiffIneg2) =>
% 107.13/14.55 (((secondinupair) =>
% 107.13/14.55 (((setukpairIL) =>
% 107.13/14.55 (((setukpairIR) =>
% 107.13/14.55 (((kpairiskpair) =>
% 107.13/14.55 (((kpairp) =>
% 107.13/14.55 (((singletonsubset) =>
% 107.13/14.55 (((singletoninpowerset) =>
% 107.13/14.55 (((singletoninpowunion) =>
% 107.13/14.55 (((upairset2E) =>
% 107.13/14.55 (((upairsubunion) =>
% 107.13/14.55 (((upairinpowunion) =>
% 107.13/14.55 (((ubforcartprodlem1) =>
% 107.13/14.55 (((ubforcartprodlem2) =>
% 107.13/14.55 (((ubforcartprodlem3) =>
% 107.13/14.55 (((cartprodpairin) =>
% 107.13/14.55 (((cartprodmempair1) =>
% 107.13/14.55 (((cartprodmempair) =>
% 107.13/14.55 (((setunionE2) =>
% 107.13/14.55 (((setunionsingleton1) =>
% 107.13/14.55 (((setunionsingleton2) =>
% 107.13/14.55 (((setunionsingleton) =>
% 107.13/14.55 ((
% 107.13/14.55 (singletonprop) =>
% 107.13/14.55 ((
% 107.13/14.55 (ex1E1) =>
% 107.13/14.55 ((
% 107.13/14.55 (ex1I) =>
% 107.13/14.55 ((
% 107.13/14.55 (ex1I2) =>
% 107.13/14.55 ((
% 107.13/14.55 (singletonsuniq) =>
% 107.13/14.55 ((
% 107.13/14.55 (setukpairinjL1) =>
% 107.13/14.55 ((
% 107.13/14.55 (kfstsingleton) =>
% 107.13/14.55 ((
% 107.13/14.55 (theprop) =>
% 107.13/14.55 ((
% 107.13/14.55 (kfstpairEq) =>
% 107.13/14.55 ((
% 107.13/14.55 (cartprodfstin) =>
% 107.13/14.55 ((
% 107.13/14.55 (setukpairinjL2) =>
% 107.13/14.55 ((
% 107.13/14.55 (setukpairinjL) =>
% 107.13/14.55 ((
% 107.13/14.55 (setukpairinjR11) =>
% 107.13/14.55 ((
% 107.13/14.55 (setukpairinjR12) =>
% 107.13/14.55 ((
% 107.13/14.55 (setukpairinjR1) =>
% 107.13/14.55 ((
% 107.13/14.55 (upairequniteq) =>
% 107.13/14.55 ((
% 107.13/14.55 (setukpairinjR2) =>
% 107.13/14.55 ((
% 107.13/14.55 (setukpairinjR) =>
% 107.13/14.55 ((
% 107.13/14.55 (ksndsingleton) =>
% 107.13/14.55 ((
% 107.13/14.55 (ksndpairEq) =>
% 107.13/14.55 ((
% 107.13/14.55 (kpairsurjEq) =>
% 107.13/14.55 ((
% 107.13/14.55 (cartprodsndin) =>
% 107.13/14.55 ((
% 107.13/14.55 (cartprodpairmemEL) =>
% 107.13/14.55 ((
% 107.13/14.55 (cartprodpairmemER) =>
% 107.13/14.55 ((
% 107.13/14.55 (cartprodmempaircEq) =>
% 107.13/14.55 ((
% 107.13/14.55 (cartprodfstpairEq) =>
% 107.13/14.55 ((
% 107.13/14.55 (cartprodsndpairEq) =>
% 107.13/14.55 ((
% 107.13/14.55 (cartprodpairsurjEq) =>
% 107.13/14.55 ((
% 107.13/14.55 (dpsetconstrI) =>
% 107.13/14.55 ((
% 107.13/14.55 (dpsetconstrSub) =>
% 107.13/14.55 ((
% 107.13/14.55 (setOfPairsIsBReln) =>
% 107.13/14.55 ((
% 107.13/14.55 (dpsetconstrERa) =>
% 107.13/14.55 ((
% 107.13/14.55 (dpsetconstrEL1) =>
% 107.13/14.55 ((
% 107.13/14.55 (dpsetconstrEL2) =>
% 107.13/14.55 ((
% 107.13/14.55 (dpsetconstrER) =>
% 107.13/14.55 ((
% 107.13/14.55 (funcImageSingleton) =>
% 107.13/14.55 ((
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% 107.13/14.55 ((
% 107.13/14.55 (app) =>
% 107.13/14.55 ((
% 107.13/14.55 (infuncsetfunc) =>
% 107.13/14.55 ((
% 107.13/14.55 (ap2p) =>
% 107.13/14.55 ((
% 107.13/14.55 (funcinfuncset) =>
% 107.13/14.55 ((
% 107.13/14.55 (lamProp) =>
% 107.13/14.55 ((
% 107.13/14.55 (lamp) =>
% 107.13/14.55 ((
% 107.13/14.55 (lam2p) =>
% 107.13/14.55 ((
% 107.13/14.55 (brelnall1) =>
% 107.13/14.55 ((
% 107.13/14.55 (brelnall2) =>
% 107.13/14.55 ((
% 107.13/14.55 (ex1E2) =>
% 107.13/14.55 ((
% 107.13/14.55 (funcGraphProp1) =>
% 107.13/14.55 ((
% 107.13/14.55 (funcGraphProp3) =>
% 107.13/14.55 ((
% 107.13/14.55 (funcGraphProp2) =>
% 107.13/14.55 ((
% 107.13/14.55 (funcextLem) =>
% 107.13/14.55 ((
% 107.13/14.55 (funcGraphProp4) =>
% 107.13/14.55 ((
% 107.13/14.55 (subbreln) =>
% 107.13/14.55 ((
% 107.13/14.55 (eqbreln) =>
% 107.13/14.55 ((
% 107.13/14.55 (funcext) =>
% 107.13/14.55 ((
% 107.13/14.55 (funcext2) =>
% 107.13/14.55 ((
% 107.13/14.55 (ap2apEq1) =>
% 107.13/14.55 ((
% 107.13/14.55 (ap2apEq2) =>
% 107.13/14.55 ((
% 107.13/14.55 (beta1) =>
% 107.13/14.55 ((
% 107.13/14.55 (eta1) =>
% 107.13/14.55 ((
% 107.13/14.55 (lam2lamEq) =>
% 107.13/14.55 ((
% 107.13/14.55 (beta2) =>
% 107.13/14.55 ((
% 107.13/14.55 (eta2) =>
% 107.13/14.55 ((
% 107.13/14.55 (iffalseProp1) =>
% 107.13/14.55 ((
% 107.13/14.55 (iffalseProp2) =>
% 107.13/14.55 ((
% 107.13/14.55 (iftrueProp1) =>
% 107.13/14.55 ((
% 107.13/14.55 (iftrueProp2) =>
% 107.13/14.55 ((
% 107.13/14.55 (ifSingleton) =>
% 107.13/14.55 ((
% 107.13/14.55 (ifp) =>
% 107.13/14.55 ((
% 107.13/14.55 (theeq) =>
% 107.13/14.55 ((
% 107.13/14.55 (iftrue) =>
% 107.13/14.55 ((
% 107.13/14.55 (iffalse) =>
% 107.13/14.55 ((
% 107.13/14.55 (iftrueorfalse) =>
% 107.13/14.55 ((
% 107.13/14.55 (binintersectT_lem) =>
% 107.13/14.55 ((
% 107.13/14.55 (binunionT_lem) =>
% 107.13/14.55 ((
% 107.13/14.55 (powersetT_lem) =>
% 107.13/14.55 ((
% 107.13/14.55 (setminusT_lem) =>
% 107.13/14.55 ((
% 107.13/14.55 (complementT_lem) =>
% 107.13/14.55 ((
% 107.13/14.55 (setextT) =>
% 107.13/14.55 ((
% 107.13/14.55 (subsetTI) =>
% 107.13/14.55 ((
% 107.13/14.55 (powersetTI1) =>
% 107.13/14.55 ((
% 107.13/14.55 (powersetTE1) =>
% 107.13/14.55 ((
% 107.13/14.55 (complementTI1) =>
% 107.13/14.55 ((
% 107.13/14.55 (complementTE1) =>
% 107.13/14.55 ((
% 107.13/14.55 (binintersectTELcontra) =>
% 107.13/14.55 ((
% 107.13/14.55 (binintersectTERcontra) =>
% 107.13/14.55 ((
% 107.13/14.55 (contrasubsetT) =>
% 107.13/14.55 ((
% 107.13/14.55 (contrasubsetT1) =>
% 107.13/14.55 ((
% 107.13/14.55 (contrasubsetT2) =>
% 107.13/14.55 ((
% 107.13/14.55 (contrasubsetT3) =>
% 107.13/14.55 ((
% 107.13/14.55 (doubleComplementI1) =>
% 107.13/14.55 ((
% 107.13/14.55 (doubleComplementE1) =>
% 107.13/14.55 ((
% 107.13/14.55 (doubleComplementSub1) =>
% 107.13/14.55 ((
% 107.13/14.55 (doubleComplementSub2) =>
% 107.13/14.55 ((
% 107.13/14.55 (doubleComplementEq) =>
% 107.13/14.55 ((
% 107.13/14.55 (complementTnotintersectT) =>
% 107.13/14.55 ((
% 107.13/14.55 (complementImpComplementIntersect) =>
% 107.13/14.55 ((
% 107.13/14.55 (complementSubsetComplementIntersect) =>
% 107.13/14.55 ((
% 107.13/14.55 (complementInPowersetComplementIntersect) =>
% 107.13/14.55 ((
% 107.13/14.55 (contraSubsetComplement) =>
% 107.13/14.55 ((
% 107.13/14.55 (complementTcontraSubset) =>
% 107.13/14.55 ((
% 107.13/14.55 (binunionTILcontra) =>
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% 107.13/14.55 (binunionTIRcontra) =>
% 107.13/14.55 ((
% 107.13/14.55 (inIntersectImpInUnion) =>
% 107.13/14.55 ((
% 107.13/14.55 (inIntersectImpInUnion2) =>
% 107.13/14.55 ((
% 107.13/14.55 (inIntersectImpInIntersectUnions) =>
% 107.13/14.55 ((
% 107.13/14.55 (intersectInPowersetIntersectUnions) =>
% 107.13/14.55 ((
% 107.13/14.55 (inComplementUnionImpNotIn1) =>
% 107.13/14.55 ((
% 107.13/14.55 (inComplementUnionImpInComplement1) =>
% 107.13/14.55 ((
% 107.13/14.55 (binunionTE) =>
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% 107.13/14.55 (complementUnionInPowersetComplement) =>
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% 107.13/14.55 (demorgan2a2) =>
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% 107.13/14.55 ((
% 107.13/14.55 (demorgan1b) =>
% 107.13/14.55 ((
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% 107.13/14.55 ((
% 107.13/14.55 (demorgan2a) =>
% 107.13/14.55 ((
% 107.13/14.55 (demorgan2b2) =>
% 107.13/14.55 ((
% 107.13/14.55 (demorgan2b) =>
% 107.13/14.55 ((
% 107.13/14.55 (demorgan2) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz13rule0) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz13rule1) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz13rule2) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz13rule3) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz13rule4) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz1_1) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz1_2) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz1_3) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz1_4) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz1_5) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1all2) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1SetBreln1) =>
% 107.13/14.55 ((
% 107.13/14.55 (choice2fnsingleton) =>
% 107.13/14.55 ((
% 107.13/14.55 (setOfPairsIsBReln1) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1all1) =>
% 107.13/14.55 ((
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% 107.13/14.55 ((
% 107.13/14.55 (eqbreln1) =>
% 107.13/14.55 ((
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% 107.13/14.55 ((
% 107.13/14.55 (breln1invI) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1invE) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1compprop) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1compI) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1compE) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1compEex) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1unionprop) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1unionIL) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1unionIR) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1unionI) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1unionE) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1unionEcases) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1unionCommutes) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz2Ex) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz2W) =>
% 107.13/14.55 ((
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% 107.13/14.55 ((
% 107.13/14.55 (woz2B) =>
% 107.13/14.55 ((
% 107.13/14.55 (image1Ex) =>
% 107.13/14.55 ((
% 107.13/14.55 (image1Ex1) =>
% 107.13/14.55 ((
% 107.13/14.55 (image1Equiv) =>
% 107.13/14.55 ((
% 107.13/14.55 (image1E) =>
% 107.13/14.55 ((
% 107.13/14.55 (image1I) =>
% 107.13/14.55 ((
% 107.13/14.55 (injFuncInInjFuncSet) =>
% 107.13/14.55 ((
% 107.13/14.55 (injFuncSetFuncIn) =>
% 107.13/14.55 ((
% 107.13/14.55 (injFuncSetFuncInj) =>
% 107.13/14.55 ((
% 107.13/14.55 (surjFuncSetFuncIn) =>
% 107.13/14.55 ((
% 107.13/14.55 (surjFuncSetFuncSurj) =>
% 107.13/14.55 ((
% 107.13/14.55 (leftInvIsSurj) =>
% 107.13/14.55 ((
% 107.13/14.55 (surjCantorThm) =>
% 107.13/14.55 ((
% 107.13/14.55 (!!) @ (
% 107.13/14.55 (('#S') @ (
% 107.13/14.55 (
% 107.13/14.55 ('#B') @ (
% 107.13/14.55 =>) @
% 107.13/14.55 nonempty)) @
% 107.13/14.55 (
% 107.13/14.55 (
% 107.13/14.55 ('#B') @ (
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% 107.13/14.55 (
% 107.13/14.55 (
% 107.13/14.55 ('#S') @ (
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% 107.13/14.55 ('#B') @ (
% 107.13/14.55 '#S') @
% 107.13/14.55 (
% 107.13/14.55 (
% 107.13/14.55 ('#B') @ (
% 107.13/14.55 (
% 107.13/14.55 ('#B') @ (
% 107.13/14.55 &))) @
% 107.13/14.55 (
% 107.13/14.55 (
% 107.13/14.55 ('#C') @ in)))))) @
% 107.13/14.55 (
% 107.13/14.55 (
% 107.13/14.55 ('#C') @ (
% 107.13/14.55 (
% 107.13/14.55 ('#B') @ (
% 107.13/14.55 '#C') @
% 107.13/14.55 (
% 107.13/14.55 (
% 107.13/14.55 ('#B') @ (
% 107.13/14.55 (
% 107.13/14.55 ('#B') @ (
% 107.13/14.55 =))) @
% 107.13/14.55 (
% 107.13/14.55 (
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% 107.13/14.55 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 107.13/14.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1288])).
% 107.13/14.55 thf(zip_derived_cl1305, plain,
% 107.13/14.55 (~ (((setminusIRneg) =>
% 107.13/14.55 (((setminusLsub) =>
% 107.13/14.55 (((setminusSubset1) =>
% 107.13/14.55 (((symdiffE) =>
% 107.13/14.55 (((symdiffI1) =>
% 107.13/14.55 (((symdiffI2) =>
% 107.13/14.55 (((symdiffIneg1) =>
% 107.13/14.55 (((symdiffIneg2) =>
% 107.13/14.55 (((secondinupair) =>
% 107.13/14.55 (((setukpairIL) =>
% 107.13/14.55 (((setukpairIR) =>
% 107.13/14.55 (((kpairiskpair) =>
% 107.13/14.55 (((kpairp) =>
% 107.13/14.55 (((singletonsubset) =>
% 107.13/14.55 (((singletoninpowerset) =>
% 107.13/14.55 (((singletoninpowunion) =>
% 107.13/14.55 (((upairset2E) =>
% 107.13/14.55 (((upairsubunion) =>
% 107.13/14.55 (((upairinpowunion) =>
% 107.13/14.55 (((ubforcartprodlem1) =>
% 107.13/14.55 (((ubforcartprodlem2) =>
% 107.13/14.55 (((ubforcartprodlem3) =>
% 107.13/14.55 (((cartprodpairin) =>
% 107.13/14.55 (((cartprodmempair1) =>
% 107.13/14.55 (((cartprodmempair) =>
% 107.13/14.55 (((setunionE2) =>
% 107.13/14.55 (((setunionsingleton1) =>
% 107.13/14.55 (((setunionsingleton2) =>
% 107.13/14.55 (((setunionsingleton) =>
% 107.13/14.55 (((singletonprop) =>
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% 107.13/14.55 ((
% 107.13/14.55 (ex1I) =>
% 107.13/14.55 ((
% 107.13/14.55 (ex1I2) =>
% 107.13/14.55 ((
% 107.13/14.55 (singletonsuniq) =>
% 107.13/14.55 ((
% 107.13/14.55 (setukpairinjL1) =>
% 107.13/14.55 ((
% 107.13/14.55 (kfstsingleton) =>
% 107.13/14.55 ((
% 107.13/14.55 (theprop) =>
% 107.13/14.55 ((
% 107.13/14.55 (kfstpairEq) =>
% 107.13/14.55 ((
% 107.13/14.55 (cartprodfstin) =>
% 107.13/14.55 ((
% 107.13/14.55 (setukpairinjL2) =>
% 107.13/14.55 ((
% 107.13/14.55 (setukpairinjL) =>
% 107.13/14.55 ((
% 107.13/14.55 (setukpairinjR11) =>
% 107.13/14.55 ((
% 107.13/14.55 (setukpairinjR12) =>
% 107.13/14.55 ((
% 107.13/14.55 (setukpairinjR1) =>
% 107.13/14.55 ((
% 107.13/14.55 (upairequniteq) =>
% 107.13/14.55 ((
% 107.13/14.55 (setukpairinjR2) =>
% 107.13/14.55 ((
% 107.13/14.55 (setukpairinjR) =>
% 107.13/14.55 ((
% 107.13/14.55 (ksndsingleton) =>
% 107.13/14.55 ((
% 107.13/14.55 (ksndpairEq) =>
% 107.13/14.55 ((
% 107.13/14.55 (kpairsurjEq) =>
% 107.13/14.55 ((
% 107.13/14.55 (cartprodsndin) =>
% 107.13/14.55 ((
% 107.13/14.55 (cartprodpairmemEL) =>
% 107.13/14.55 ((
% 107.13/14.55 (cartprodpairmemER) =>
% 107.13/14.55 ((
% 107.13/14.55 (cartprodmempaircEq) =>
% 107.13/14.55 ((
% 107.13/14.55 (cartprodfstpairEq) =>
% 107.13/14.55 ((
% 107.13/14.55 (cartprodsndpairEq) =>
% 107.13/14.55 ((
% 107.13/14.55 (cartprodpairsurjEq) =>
% 107.13/14.55 ((
% 107.13/14.55 (dpsetconstrI) =>
% 107.13/14.55 ((
% 107.13/14.55 (dpsetconstrSub) =>
% 107.13/14.55 ((
% 107.13/14.55 (setOfPairsIsBReln) =>
% 107.13/14.55 ((
% 107.13/14.55 (dpsetconstrERa) =>
% 107.13/14.55 ((
% 107.13/14.55 (dpsetconstrEL1) =>
% 107.13/14.55 ((
% 107.13/14.55 (dpsetconstrEL2) =>
% 107.13/14.55 ((
% 107.13/14.55 (dpsetconstrER) =>
% 107.13/14.55 ((
% 107.13/14.55 (funcImageSingleton) =>
% 107.13/14.55 ((
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% 107.13/14.55 ((
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% 107.13/14.55 ((
% 107.13/14.55 (ap2p) =>
% 107.13/14.55 ((
% 107.13/14.55 (funcinfuncset) =>
% 107.13/14.55 ((
% 107.13/14.55 (lamProp) =>
% 107.13/14.55 ((
% 107.13/14.55 (lamp) =>
% 107.13/14.55 ((
% 107.13/14.55 (lam2p) =>
% 107.13/14.55 ((
% 107.13/14.55 (brelnall1) =>
% 107.13/14.55 ((
% 107.13/14.55 (brelnall2) =>
% 107.13/14.55 ((
% 107.13/14.55 (ex1E2) =>
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% 107.13/14.55 ((
% 107.13/14.55 (funcGraphProp3) =>
% 107.13/14.55 ((
% 107.13/14.55 (funcGraphProp2) =>
% 107.13/14.55 ((
% 107.13/14.55 (funcextLem) =>
% 107.13/14.55 ((
% 107.13/14.55 (funcGraphProp4) =>
% 107.13/14.55 ((
% 107.13/14.55 (subbreln) =>
% 107.13/14.55 ((
% 107.13/14.55 (eqbreln) =>
% 107.13/14.55 ((
% 107.13/14.55 (funcext) =>
% 107.13/14.55 ((
% 107.13/14.55 (funcext2) =>
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% 107.13/14.55 (ap2apEq1) =>
% 107.13/14.55 ((
% 107.13/14.55 (ap2apEq2) =>
% 107.13/14.55 ((
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% 107.13/14.55 ((
% 107.13/14.55 (eta1) =>
% 107.13/14.55 ((
% 107.13/14.55 (lam2lamEq) =>
% 107.13/14.55 ((
% 107.13/14.55 (beta2) =>
% 107.13/14.55 ((
% 107.13/14.55 (eta2) =>
% 107.13/14.55 ((
% 107.13/14.55 (iffalseProp1) =>
% 107.13/14.55 ((
% 107.13/14.55 (iffalseProp2) =>
% 107.13/14.55 ((
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% 107.13/14.55 ((
% 107.13/14.55 (iftrueProp2) =>
% 107.13/14.55 ((
% 107.13/14.55 (ifSingleton) =>
% 107.13/14.55 ((
% 107.13/14.55 (ifp) =>
% 107.13/14.55 ((
% 107.13/14.55 (theeq) =>
% 107.13/14.55 ((
% 107.13/14.55 (iftrue) =>
% 107.13/14.55 ((
% 107.13/14.55 (iffalse) =>
% 107.13/14.55 ((
% 107.13/14.55 (iftrueorfalse) =>
% 107.13/14.55 ((
% 107.13/14.55 (binintersectT_lem) =>
% 107.13/14.55 ((
% 107.13/14.55 (binunionT_lem) =>
% 107.13/14.55 ((
% 107.13/14.55 (powersetT_lem) =>
% 107.13/14.55 ((
% 107.13/14.55 (setminusT_lem) =>
% 107.13/14.55 ((
% 107.13/14.55 (complementT_lem) =>
% 107.13/14.55 ((
% 107.13/14.55 (setextT) =>
% 107.13/14.55 ((
% 107.13/14.55 (subsetTI) =>
% 107.13/14.55 ((
% 107.13/14.55 (powersetTI1) =>
% 107.13/14.55 ((
% 107.13/14.55 (powersetTE1) =>
% 107.13/14.55 ((
% 107.13/14.55 (complementTI1) =>
% 107.13/14.55 ((
% 107.13/14.55 (complementTE1) =>
% 107.13/14.55 ((
% 107.13/14.55 (binintersectTELcontra) =>
% 107.13/14.55 ((
% 107.13/14.55 (binintersectTERcontra) =>
% 107.13/14.55 ((
% 107.13/14.55 (contrasubsetT) =>
% 107.13/14.55 ((
% 107.13/14.55 (contrasubsetT1) =>
% 107.13/14.55 ((
% 107.13/14.55 (contrasubsetT2) =>
% 107.13/14.55 ((
% 107.13/14.55 (contrasubsetT3) =>
% 107.13/14.55 ((
% 107.13/14.55 (doubleComplementI1) =>
% 107.13/14.55 ((
% 107.13/14.55 (doubleComplementE1) =>
% 107.13/14.55 ((
% 107.13/14.55 (doubleComplementSub1) =>
% 107.13/14.55 ((
% 107.13/14.55 (doubleComplementSub2) =>
% 107.13/14.55 ((
% 107.13/14.55 (doubleComplementEq) =>
% 107.13/14.55 ((
% 107.13/14.55 (complementTnotintersectT) =>
% 107.13/14.55 ((
% 107.13/14.55 (complementImpComplementIntersect) =>
% 107.13/14.55 ((
% 107.13/14.55 (complementSubsetComplementIntersect) =>
% 107.13/14.55 ((
% 107.13/14.55 (complementInPowersetComplementIntersect) =>
% 107.13/14.55 ((
% 107.13/14.55 (contraSubsetComplement) =>
% 107.13/14.55 ((
% 107.13/14.55 (complementTcontraSubset) =>
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% 107.13/14.55 ((
% 107.13/14.55 (binunionTIRcontra) =>
% 107.13/14.55 ((
% 107.13/14.55 (inIntersectImpInUnion) =>
% 107.13/14.55 ((
% 107.13/14.55 (inIntersectImpInUnion2) =>
% 107.13/14.55 ((
% 107.13/14.55 (inIntersectImpInIntersectUnions) =>
% 107.13/14.55 ((
% 107.13/14.55 (intersectInPowersetIntersectUnions) =>
% 107.13/14.55 ((
% 107.13/14.55 (inComplementUnionImpNotIn1) =>
% 107.13/14.55 ((
% 107.13/14.55 (inComplementUnionImpInComplement1) =>
% 107.13/14.55 ((
% 107.13/14.55 (binunionTE) =>
% 107.13/14.55 ((
% 107.13/14.55 (binunionTEcontra) =>
% 107.13/14.55 ((
% 107.13/14.55 (demorgan2a1) =>
% 107.13/14.55 ((
% 107.13/14.55 (complementUnionInPowersetComplement) =>
% 107.13/14.55 ((
% 107.13/14.55 (demorgan2a2) =>
% 107.13/14.55 ((
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% 107.13/14.55 ((
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% 107.13/14.55 ((
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% 107.13/14.55 ((
% 107.13/14.55 (demorgan2a) =>
% 107.13/14.55 ((
% 107.13/14.55 (demorgan2b2) =>
% 107.13/14.55 ((
% 107.13/14.55 (demorgan2b) =>
% 107.13/14.55 ((
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% 107.13/14.55 ((
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% 107.13/14.55 ((
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% 107.13/14.55 ((
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% 107.13/14.55 (leftInvIsSurj) =>
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% 107.13/14.55 (surjCantorThm) =>
% 107.13/14.55 ((
% 107.13/14.55 (!!) @ (
% 107.13/14.55 (('#S') @ (
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% 107.13/14.55 ('#B') @ (
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% 107.13/14.55 (
% 107.13/14.55 (
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% 107.13/14.55 (
% 107.13/14.55 ('#S') @ (
% 107.13/14.55 (
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% 107.13/14.55 (
% 107.13/14.55 (
% 107.13/14.55 ('#B') @ (
% 107.13/14.55 (
% 107.13/14.55 ('#B') @ (
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% 107.13/14.55 (
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% 107.13/14.55 (
% 107.13/14.55 (
% 107.13/14.55 ('#C') @ (
% 107.13/14.55 (
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% 107.13/14.55 (
% 107.13/14.55 (
% 107.13/14.55 ('#B') @ (
% 107.13/14.55 (
% 107.13/14.55 ('#B') @ (
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% 107.13/14.55 (
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% 107.13/14.55 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 107.13/14.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1296])).
% 107.13/14.55 thf(zip_derived_cl1313, plain,
% 107.13/14.55 (~ (((setminusLsub) =>
% 107.13/14.55 (((setminusSubset1) =>
% 107.13/14.55 (((symdiffE) =>
% 107.13/14.55 (((symdiffI1) =>
% 107.13/14.55 (((symdiffI2) =>
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% 107.13/14.55 (((setukpairIL) =>
% 107.13/14.55 (((setukpairIR) =>
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% 107.13/14.55 (((kpairp) =>
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% 107.13/14.55 (((singletoninpowerset) =>
% 107.13/14.55 (((singletoninpowunion) =>
% 107.13/14.55 (((upairset2E) =>
% 107.13/14.55 (((upairsubunion) =>
% 107.13/14.55 (((upairinpowunion) =>
% 107.13/14.55 (((ubforcartprodlem1) =>
% 107.13/14.55 (((ubforcartprodlem2) =>
% 107.13/14.55 (((ubforcartprodlem3) =>
% 107.13/14.55 (((cartprodpairin) =>
% 107.13/14.55 (((cartprodmempair1) =>
% 107.13/14.55 (((cartprodmempair) =>
% 107.13/14.55 (((setunionE2) =>
% 107.13/14.55 (((setunionsingleton1) =>
% 107.13/14.55 (((setunionsingleton2) =>
% 107.13/14.55 (((setunionsingleton) =>
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% 107.13/14.55 ((
% 107.13/14.55 (ex1I) =>
% 107.13/14.55 ((
% 107.13/14.55 (ex1I2) =>
% 107.13/14.55 ((
% 107.13/14.55 (singletonsuniq) =>
% 107.13/14.55 ((
% 107.13/14.55 (setukpairinjL1) =>
% 107.13/14.55 ((
% 107.13/14.55 (kfstsingleton) =>
% 107.13/14.55 ((
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% 107.13/14.55 ((
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% 107.13/14.55 ((
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% 107.13/14.55 ((
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% 107.13/14.55 ((
% 107.13/14.55 (setukpairinjL) =>
% 107.13/14.55 ((
% 107.13/14.55 (setukpairinjR11) =>
% 107.13/14.55 ((
% 107.13/14.55 (setukpairinjR12) =>
% 107.13/14.55 ((
% 107.13/14.55 (setukpairinjR1) =>
% 107.13/14.55 ((
% 107.13/14.55 (upairequniteq) =>
% 107.13/14.55 ((
% 107.13/14.55 (setukpairinjR2) =>
% 107.13/14.55 ((
% 107.13/14.55 (setukpairinjR) =>
% 107.13/14.55 ((
% 107.13/14.55 (ksndsingleton) =>
% 107.13/14.55 ((
% 107.13/14.55 (ksndpairEq) =>
% 107.13/14.55 ((
% 107.13/14.55 (kpairsurjEq) =>
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% 107.13/14.55 (cartprodsndin) =>
% 107.13/14.55 ((
% 107.13/14.55 (cartprodpairmemEL) =>
% 107.13/14.55 ((
% 107.13/14.55 (cartprodpairmemER) =>
% 107.13/14.55 ((
% 107.13/14.55 (cartprodmempaircEq) =>
% 107.13/14.55 ((
% 107.13/14.55 (cartprodfstpairEq) =>
% 107.13/14.55 ((
% 107.13/14.55 (cartprodsndpairEq) =>
% 107.13/14.55 ((
% 107.13/14.55 (cartprodpairsurjEq) =>
% 107.13/14.55 ((
% 107.13/14.55 (dpsetconstrI) =>
% 107.13/14.55 ((
% 107.13/14.55 (dpsetconstrSub) =>
% 107.13/14.55 ((
% 107.13/14.55 (setOfPairsIsBReln) =>
% 107.13/14.55 ((
% 107.13/14.55 (dpsetconstrERa) =>
% 107.13/14.55 ((
% 107.13/14.55 (dpsetconstrEL1) =>
% 107.13/14.55 ((
% 107.13/14.55 (dpsetconstrEL2) =>
% 107.13/14.55 ((
% 107.13/14.55 (dpsetconstrER) =>
% 107.13/14.55 ((
% 107.13/14.55 (funcImageSingleton) =>
% 107.13/14.55 ((
% 107.13/14.55 (apProp) =>
% 107.13/14.55 ((
% 107.13/14.55 (app) =>
% 107.13/14.55 ((
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% 107.13/14.55 ((
% 107.13/14.55 (ap2p) =>
% 107.13/14.55 ((
% 107.13/14.55 (funcinfuncset) =>
% 107.13/14.55 ((
% 107.13/14.55 (lamProp) =>
% 107.13/14.55 ((
% 107.13/14.55 (lamp) =>
% 107.13/14.55 ((
% 107.13/14.55 (lam2p) =>
% 107.13/14.55 ((
% 107.13/14.55 (brelnall1) =>
% 107.13/14.55 ((
% 107.13/14.55 (brelnall2) =>
% 107.13/14.55 ((
% 107.13/14.55 (ex1E2) =>
% 107.13/14.55 ((
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% 107.13/14.55 ((
% 107.13/14.55 (funcGraphProp3) =>
% 107.13/14.55 ((
% 107.13/14.55 (funcGraphProp2) =>
% 107.13/14.55 ((
% 107.13/14.55 (funcextLem) =>
% 107.13/14.55 ((
% 107.13/14.55 (funcGraphProp4) =>
% 107.13/14.55 ((
% 107.13/14.55 (subbreln) =>
% 107.13/14.55 ((
% 107.13/14.55 (eqbreln) =>
% 107.13/14.55 ((
% 107.13/14.55 (funcext) =>
% 107.13/14.55 ((
% 107.13/14.55 (funcext2) =>
% 107.13/14.55 ((
% 107.13/14.55 (ap2apEq1) =>
% 107.13/14.55 ((
% 107.13/14.55 (ap2apEq2) =>
% 107.13/14.55 ((
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% 107.13/14.55 ((
% 107.13/14.55 (eta1) =>
% 107.13/14.55 ((
% 107.13/14.55 (lam2lamEq) =>
% 107.13/14.55 ((
% 107.13/14.55 (beta2) =>
% 107.13/14.55 ((
% 107.13/14.55 (eta2) =>
% 107.13/14.55 ((
% 107.13/14.55 (iffalseProp1) =>
% 107.13/14.55 ((
% 107.13/14.55 (iffalseProp2) =>
% 107.13/14.55 ((
% 107.13/14.55 (iftrueProp1) =>
% 107.13/14.55 ((
% 107.13/14.55 (iftrueProp2) =>
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% 107.13/14.55 ((
% 107.13/14.55 (ifp) =>
% 107.13/14.55 ((
% 107.13/14.55 (theeq) =>
% 107.13/14.55 ((
% 107.13/14.55 (iftrue) =>
% 107.13/14.55 ((
% 107.13/14.55 (iffalse) =>
% 107.13/14.55 ((
% 107.13/14.55 (iftrueorfalse) =>
% 107.13/14.55 ((
% 107.13/14.55 (binintersectT_lem) =>
% 107.13/14.55 ((
% 107.13/14.55 (binunionT_lem) =>
% 107.13/14.55 ((
% 107.13/14.55 (powersetT_lem) =>
% 107.13/14.55 ((
% 107.13/14.55 (setminusT_lem) =>
% 107.13/14.55 ((
% 107.13/14.55 (complementT_lem) =>
% 107.13/14.55 ((
% 107.13/14.55 (setextT) =>
% 107.13/14.55 ((
% 107.13/14.55 (subsetTI) =>
% 107.13/14.55 ((
% 107.13/14.55 (powersetTI1) =>
% 107.13/14.55 ((
% 107.13/14.55 (powersetTE1) =>
% 107.13/14.55 ((
% 107.13/14.55 (complementTI1) =>
% 107.13/14.55 ((
% 107.13/14.55 (complementTE1) =>
% 107.13/14.55 ((
% 107.13/14.55 (binintersectTELcontra) =>
% 107.13/14.55 ((
% 107.13/14.55 (binintersectTERcontra) =>
% 107.13/14.55 ((
% 107.13/14.55 (contrasubsetT) =>
% 107.13/14.55 ((
% 107.13/14.55 (contrasubsetT1) =>
% 107.13/14.55 ((
% 107.13/14.55 (contrasubsetT2) =>
% 107.13/14.55 ((
% 107.13/14.55 (contrasubsetT3) =>
% 107.13/14.55 ((
% 107.13/14.55 (doubleComplementI1) =>
% 107.13/14.55 ((
% 107.13/14.55 (doubleComplementE1) =>
% 107.13/14.55 ((
% 107.13/14.55 (doubleComplementSub1) =>
% 107.13/14.55 ((
% 107.13/14.55 (doubleComplementSub2) =>
% 107.13/14.55 ((
% 107.13/14.55 (doubleComplementEq) =>
% 107.13/14.55 ((
% 107.13/14.55 (complementTnotintersectT) =>
% 107.13/14.55 ((
% 107.13/14.55 (complementImpComplementIntersect) =>
% 107.13/14.55 ((
% 107.13/14.55 (complementSubsetComplementIntersect) =>
% 107.13/14.55 ((
% 107.13/14.55 (complementInPowersetComplementIntersect) =>
% 107.13/14.55 ((
% 107.13/14.55 (contraSubsetComplement) =>
% 107.13/14.55 ((
% 107.13/14.55 (complementTcontraSubset) =>
% 107.13/14.55 ((
% 107.13/14.55 (binunionTILcontra) =>
% 107.13/14.55 ((
% 107.13/14.55 (binunionTIRcontra) =>
% 107.13/14.55 ((
% 107.13/14.55 (inIntersectImpInUnion) =>
% 107.13/14.55 ((
% 107.13/14.55 (inIntersectImpInUnion2) =>
% 107.13/14.55 ((
% 107.13/14.55 (inIntersectImpInIntersectUnions) =>
% 107.13/14.55 ((
% 107.13/14.55 (intersectInPowersetIntersectUnions) =>
% 107.13/14.55 ((
% 107.13/14.55 (inComplementUnionImpNotIn1) =>
% 107.13/14.55 ((
% 107.13/14.55 (inComplementUnionImpInComplement1) =>
% 107.13/14.55 ((
% 107.13/14.55 (binunionTE) =>
% 107.13/14.55 ((
% 107.13/14.55 (binunionTEcontra) =>
% 107.13/14.55 ((
% 107.13/14.55 (demorgan2a1) =>
% 107.13/14.55 ((
% 107.13/14.55 (complementUnionInPowersetComplement) =>
% 107.13/14.55 ((
% 107.13/14.55 (demorgan2a2) =>
% 107.13/14.55 ((
% 107.13/14.55 (demorgan1a) =>
% 107.13/14.55 ((
% 107.13/14.55 (demorgan1b) =>
% 107.13/14.55 ((
% 107.13/14.55 (demorgan1) =>
% 107.13/14.55 ((
% 107.13/14.55 (demorgan2a) =>
% 107.13/14.55 ((
% 107.13/14.55 (demorgan2b2) =>
% 107.13/14.55 ((
% 107.13/14.55 (demorgan2b) =>
% 107.13/14.55 ((
% 107.13/14.55 (demorgan2) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz13rule0) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz13rule1) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz13rule2) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz13rule3) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz13rule4) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz1_1) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz1_2) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz1_3) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz1_4) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz1_5) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1all2) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1SetBreln1) =>
% 107.13/14.55 ((
% 107.13/14.55 (choice2fnsingleton) =>
% 107.13/14.55 ((
% 107.13/14.55 (setOfPairsIsBReln1) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1all1) =>
% 107.13/14.55 ((
% 107.13/14.55 (subbreln1) =>
% 107.13/14.55 ((
% 107.13/14.55 (eqbreln1) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1invprop) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1invI) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1invE) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1compprop) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1compI) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1compE) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1compEex) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1unionprop) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1unionIL) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1unionIR) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1unionI) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1unionE) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1unionEcases) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1unionCommutes) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz2Ex) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz2W) =>
% 107.13/14.55 ((
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% 107.13/14.55 ((
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% 107.13/14.55 ((
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% 107.13/14.55 ((
% 107.13/14.55 (image1Equiv) =>
% 107.13/14.55 ((
% 107.13/14.55 (image1E) =>
% 107.13/14.55 ((
% 107.13/14.55 (image1I) =>
% 107.13/14.55 ((
% 107.13/14.55 (injFuncInInjFuncSet) =>
% 107.13/14.55 ((
% 107.13/14.55 (injFuncSetFuncIn) =>
% 107.13/14.55 ((
% 107.13/14.55 (injFuncSetFuncInj) =>
% 107.13/14.55 ((
% 107.13/14.55 (surjFuncSetFuncIn) =>
% 107.13/14.55 ((
% 107.13/14.55 (surjFuncSetFuncSurj) =>
% 107.13/14.55 ((
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% 107.13/14.55 ((
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% 107.13/14.55 ((
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% 107.13/14.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1305])).
% 107.13/14.55 thf(zip_derived_cl1321, plain,
% 107.13/14.55 (~ (((setminusSubset1) =>
% 107.13/14.55 (((symdiffE) =>
% 107.13/14.55 (((symdiffI1) =>
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% 107.13/14.55 (((singletoninpowunion) =>
% 107.13/14.55 (((upairset2E) =>
% 107.13/14.55 (((upairsubunion) =>
% 107.13/14.55 (((upairinpowunion) =>
% 107.13/14.55 (((ubforcartprodlem1) =>
% 107.13/14.55 (((ubforcartprodlem2) =>
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% 107.13/14.55 (setOfPairsIsBReln) =>
% 107.13/14.55 ((
% 107.13/14.55 (dpsetconstrERa) =>
% 107.13/14.55 ((
% 107.13/14.55 (dpsetconstrEL1) =>
% 107.13/14.55 ((
% 107.13/14.55 (dpsetconstrEL2) =>
% 107.13/14.55 ((
% 107.13/14.55 (dpsetconstrER) =>
% 107.13/14.55 ((
% 107.13/14.55 (funcImageSingleton) =>
% 107.13/14.55 ((
% 107.13/14.55 (apProp) =>
% 107.13/14.55 ((
% 107.13/14.55 (app) =>
% 107.13/14.55 ((
% 107.13/14.55 (infuncsetfunc) =>
% 107.13/14.55 ((
% 107.13/14.55 (ap2p) =>
% 107.13/14.55 ((
% 107.13/14.55 (funcinfuncset) =>
% 107.13/14.55 ((
% 107.13/14.55 (lamProp) =>
% 107.13/14.55 ((
% 107.13/14.55 (lamp) =>
% 107.13/14.55 ((
% 107.13/14.55 (lam2p) =>
% 107.13/14.55 ((
% 107.13/14.55 (brelnall1) =>
% 107.13/14.55 ((
% 107.13/14.55 (brelnall2) =>
% 107.13/14.55 ((
% 107.13/14.55 (ex1E2) =>
% 107.13/14.55 ((
% 107.13/14.55 (funcGraphProp1) =>
% 107.13/14.55 ((
% 107.13/14.55 (funcGraphProp3) =>
% 107.13/14.55 ((
% 107.13/14.55 (funcGraphProp2) =>
% 107.13/14.55 ((
% 107.13/14.55 (funcextLem) =>
% 107.13/14.55 ((
% 107.13/14.55 (funcGraphProp4) =>
% 107.13/14.55 ((
% 107.13/14.55 (subbreln) =>
% 107.13/14.55 ((
% 107.13/14.55 (eqbreln) =>
% 107.13/14.55 ((
% 107.13/14.55 (funcext) =>
% 107.13/14.55 ((
% 107.13/14.55 (funcext2) =>
% 107.13/14.55 ((
% 107.13/14.55 (ap2apEq1) =>
% 107.13/14.55 ((
% 107.13/14.55 (ap2apEq2) =>
% 107.13/14.55 ((
% 107.13/14.55 (beta1) =>
% 107.13/14.55 ((
% 107.13/14.55 (eta1) =>
% 107.13/14.55 ((
% 107.13/14.55 (lam2lamEq) =>
% 107.13/14.55 ((
% 107.13/14.55 (beta2) =>
% 107.13/14.55 ((
% 107.13/14.55 (eta2) =>
% 107.13/14.55 ((
% 107.13/14.55 (iffalseProp1) =>
% 107.13/14.55 ((
% 107.13/14.55 (iffalseProp2) =>
% 107.13/14.55 ((
% 107.13/14.55 (iftrueProp1) =>
% 107.13/14.55 ((
% 107.13/14.55 (iftrueProp2) =>
% 107.13/14.55 ((
% 107.13/14.55 (ifSingleton) =>
% 107.13/14.55 ((
% 107.13/14.55 (ifp) =>
% 107.13/14.55 ((
% 107.13/14.55 (theeq) =>
% 107.13/14.55 ((
% 107.13/14.55 (iftrue) =>
% 107.13/14.55 ((
% 107.13/14.55 (iffalse) =>
% 107.13/14.55 ((
% 107.13/14.55 (iftrueorfalse) =>
% 107.13/14.55 ((
% 107.13/14.55 (binintersectT_lem) =>
% 107.13/14.55 ((
% 107.13/14.55 (binunionT_lem) =>
% 107.13/14.55 ((
% 107.13/14.55 (powersetT_lem) =>
% 107.13/14.55 ((
% 107.13/14.55 (setminusT_lem) =>
% 107.13/14.55 ((
% 107.13/14.55 (complementT_lem) =>
% 107.13/14.55 ((
% 107.13/14.55 (setextT) =>
% 107.13/14.55 ((
% 107.13/14.55 (subsetTI) =>
% 107.13/14.55 ((
% 107.13/14.55 (powersetTI1) =>
% 107.13/14.55 ((
% 107.13/14.55 (powersetTE1) =>
% 107.13/14.55 ((
% 107.13/14.55 (complementTI1) =>
% 107.13/14.55 ((
% 107.13/14.55 (complementTE1) =>
% 107.13/14.55 ((
% 107.13/14.55 (binintersectTELcontra) =>
% 107.13/14.55 ((
% 107.13/14.55 (binintersectTERcontra) =>
% 107.13/14.55 ((
% 107.13/14.55 (contrasubsetT) =>
% 107.13/14.55 ((
% 107.13/14.55 (contrasubsetT1) =>
% 107.13/14.55 ((
% 107.13/14.55 (contrasubsetT2) =>
% 107.13/14.55 ((
% 107.13/14.55 (contrasubsetT3) =>
% 107.13/14.55 ((
% 107.13/14.55 (doubleComplementI1) =>
% 107.13/14.55 ((
% 107.13/14.55 (doubleComplementE1) =>
% 107.13/14.55 ((
% 107.13/14.55 (doubleComplementSub1) =>
% 107.13/14.55 ((
% 107.13/14.55 (doubleComplementSub2) =>
% 107.13/14.55 ((
% 107.13/14.55 (doubleComplementEq) =>
% 107.13/14.55 ((
% 107.13/14.55 (complementTnotintersectT) =>
% 107.13/14.55 ((
% 107.13/14.55 (complementImpComplementIntersect) =>
% 107.13/14.55 ((
% 107.13/14.55 (complementSubsetComplementIntersect) =>
% 107.13/14.55 ((
% 107.13/14.55 (complementInPowersetComplementIntersect) =>
% 107.13/14.55 ((
% 107.13/14.55 (contraSubsetComplement) =>
% 107.13/14.55 ((
% 107.13/14.55 (complementTcontraSubset) =>
% 107.13/14.55 ((
% 107.13/14.55 (binunionTILcontra) =>
% 107.13/14.55 ((
% 107.13/14.55 (binunionTIRcontra) =>
% 107.13/14.55 ((
% 107.13/14.55 (inIntersectImpInUnion) =>
% 107.13/14.55 ((
% 107.13/14.55 (inIntersectImpInUnion2) =>
% 107.13/14.55 ((
% 107.13/14.55 (inIntersectImpInIntersectUnions) =>
% 107.13/14.55 ((
% 107.13/14.55 (intersectInPowersetIntersectUnions) =>
% 107.13/14.55 ((
% 107.13/14.55 (inComplementUnionImpNotIn1) =>
% 107.13/14.55 ((
% 107.13/14.55 (inComplementUnionImpInComplement1) =>
% 107.13/14.55 ((
% 107.13/14.55 (binunionTE) =>
% 107.13/14.55 ((
% 107.13/14.55 (binunionTEcontra) =>
% 107.13/14.55 ((
% 107.13/14.55 (demorgan2a1) =>
% 107.13/14.55 ((
% 107.13/14.55 (complementUnionInPowersetComplement) =>
% 107.13/14.55 ((
% 107.13/14.55 (demorgan2a2) =>
% 107.13/14.55 ((
% 107.13/14.55 (demorgan1a) =>
% 107.13/14.55 ((
% 107.13/14.55 (demorgan1b) =>
% 107.13/14.55 ((
% 107.13/14.55 (demorgan1) =>
% 107.13/14.55 ((
% 107.13/14.55 (demorgan2a) =>
% 107.13/14.55 ((
% 107.13/14.55 (demorgan2b2) =>
% 107.13/14.55 ((
% 107.13/14.55 (demorgan2b) =>
% 107.13/14.55 ((
% 107.13/14.55 (demorgan2) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz13rule0) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz13rule1) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz13rule2) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz13rule3) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz13rule4) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz1_1) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz1_2) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz1_3) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz1_4) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz1_5) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1all2) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1SetBreln1) =>
% 107.13/14.55 ((
% 107.13/14.55 (choice2fnsingleton) =>
% 107.13/14.55 ((
% 107.13/14.55 (setOfPairsIsBReln1) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1all1) =>
% 107.13/14.55 ((
% 107.13/14.55 (subbreln1) =>
% 107.13/14.55 ((
% 107.13/14.55 (eqbreln1) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1invprop) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1invI) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1invE) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1compprop) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1compI) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1compE) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1compEex) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1unionprop) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1unionIL) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1unionIR) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1unionI) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1unionE) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1unionEcases) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1unionCommutes) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz2Ex) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz2W) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz2A) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz2B) =>
% 107.13/14.55 ((
% 107.13/14.55 (image1Ex) =>
% 107.13/14.55 ((
% 107.13/14.55 (image1Ex1) =>
% 107.13/14.55 ((
% 107.13/14.55 (image1Equiv) =>
% 107.13/14.55 ((
% 107.13/14.55 (image1E) =>
% 107.13/14.55 ((
% 107.13/14.55 (image1I) =>
% 107.13/14.55 ((
% 107.13/14.55 (injFuncInInjFuncSet) =>
% 107.13/14.55 ((
% 107.13/14.55 (injFuncSetFuncIn) =>
% 107.13/14.55 ((
% 107.13/14.55 (injFuncSetFuncInj) =>
% 107.13/14.55 ((
% 107.13/14.55 (surjFuncSetFuncIn) =>
% 107.13/14.55 ((
% 107.13/14.55 (surjFuncSetFuncSurj) =>
% 107.13/14.55 ((
% 107.13/14.55 (leftInvIsSurj) =>
% 107.13/14.55 ((
% 107.13/14.55 (surjCantorThm) =>
% 107.13/14.55 ((
% 107.13/14.55 (!!) @ (
% 107.13/14.55 (('#S') @ (
% 107.13/14.55 (
% 107.13/14.55 ('#B') @ (
% 107.13/14.55 =>) @
% 107.13/14.55 nonempty)) @
% 107.13/14.55 (
% 107.13/14.55 (
% 107.13/14.55 ('#B') @ (
% 107.13/14.55 ??) @
% 107.13/14.55 (
% 107.13/14.55 (
% 107.13/14.55 ('#S') @ (
% 107.13/14.55 (
% 107.13/14.55 ('#B') @ (
% 107.13/14.55 '#S') @
% 107.13/14.55 (
% 107.13/14.55 (
% 107.13/14.55 ('#B') @ (
% 107.13/14.55 (
% 107.13/14.55 ('#B') @ (
% 107.13/14.55 &))) @
% 107.13/14.55 (
% 107.13/14.55 (
% 107.13/14.55 ('#C') @ in)))))) @
% 107.13/14.55 (
% 107.13/14.55 (
% 107.13/14.55 ('#C') @ (
% 107.13/14.55 (
% 107.13/14.55 ('#B') @ (
% 107.13/14.55 '#C') @
% 107.13/14.55 (
% 107.13/14.55 (
% 107.13/14.55 ('#B') @ (
% 107.13/14.55 (
% 107.13/14.55 ('#B') @ (
% 107.13/14.55 =))) @
% 107.13/14.55 (
% 107.13/14.55 (
% 107.13/14.55 ('#C') @ binintersect)))))) @
% 107.13/14.55 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 107.13/14.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1313])).
% 107.13/14.55 thf(zip_derived_cl1329, plain,
% 107.13/14.55 (~ (((symdiffE) =>
% 107.13/14.55 (((symdiffI1) =>
% 107.13/14.55 (((symdiffI2) =>
% 107.13/14.55 (((symdiffIneg1) =>
% 107.13/14.55 (((symdiffIneg2) =>
% 107.13/14.55 (((secondinupair) =>
% 107.13/14.55 (((setukpairIL) =>
% 107.13/14.55 (((setukpairIR) =>
% 107.13/14.55 (((kpairiskpair) =>
% 107.13/14.55 (((kpairp) =>
% 107.13/14.55 (((singletonsubset) =>
% 107.13/14.55 (((singletoninpowerset) =>
% 107.13/14.55 (((singletoninpowunion) =>
% 107.13/14.55 (((upairset2E) =>
% 107.13/14.55 (((upairsubunion) =>
% 107.13/14.55 (((upairinpowunion) =>
% 107.13/14.55 (((ubforcartprodlem1) =>
% 107.13/14.55 (((ubforcartprodlem2) =>
% 107.13/14.55 (((ubforcartprodlem3) =>
% 107.13/14.55 (((cartprodpairin) =>
% 107.13/14.55 (((cartprodmempair1) =>
% 107.13/14.55 (((cartprodmempair) =>
% 107.13/14.55 (((setunionE2) =>
% 107.13/14.55 (((setunionsingleton1) =>
% 107.13/14.55 (((setunionsingleton2) =>
% 107.13/14.55 (((setunionsingleton) =>
% 107.13/14.55 (((singletonprop) =>
% 107.13/14.55 (((ex1E1) =>
% 107.13/14.55 (((ex1I) =>
% 107.13/14.55 (((ex1I2) =>
% 107.13/14.55 ((
% 107.13/14.55 (singletonsuniq) =>
% 107.13/14.55 ((
% 107.13/14.55 (setukpairinjL1) =>
% 107.13/14.55 ((
% 107.13/14.55 (kfstsingleton) =>
% 107.13/14.55 ((
% 107.13/14.55 (theprop) =>
% 107.13/14.55 ((
% 107.13/14.55 (kfstpairEq) =>
% 107.13/14.55 ((
% 107.13/14.55 (cartprodfstin) =>
% 107.13/14.55 ((
% 107.13/14.55 (setukpairinjL2) =>
% 107.13/14.55 ((
% 107.13/14.55 (setukpairinjL) =>
% 107.13/14.55 ((
% 107.13/14.55 (setukpairinjR11) =>
% 107.13/14.55 ((
% 107.13/14.55 (setukpairinjR12) =>
% 107.13/14.55 ((
% 107.13/14.55 (setukpairinjR1) =>
% 107.13/14.55 ((
% 107.13/14.55 (upairequniteq) =>
% 107.13/14.55 ((
% 107.13/14.55 (setukpairinjR2) =>
% 107.13/14.55 ((
% 107.13/14.55 (setukpairinjR) =>
% 107.13/14.55 ((
% 107.13/14.55 (ksndsingleton) =>
% 107.13/14.55 ((
% 107.13/14.55 (ksndpairEq) =>
% 107.13/14.55 ((
% 107.13/14.55 (kpairsurjEq) =>
% 107.13/14.55 ((
% 107.13/14.55 (cartprodsndin) =>
% 107.13/14.55 ((
% 107.13/14.55 (cartprodpairmemEL) =>
% 107.13/14.55 ((
% 107.13/14.55 (cartprodpairmemER) =>
% 107.13/14.55 ((
% 107.13/14.55 (cartprodmempaircEq) =>
% 107.13/14.55 ((
% 107.13/14.55 (cartprodfstpairEq) =>
% 107.13/14.55 ((
% 107.13/14.55 (cartprodsndpairEq) =>
% 107.13/14.55 ((
% 107.13/14.55 (cartprodpairsurjEq) =>
% 107.13/14.55 ((
% 107.13/14.55 (dpsetconstrI) =>
% 107.13/14.55 ((
% 107.13/14.55 (dpsetconstrSub) =>
% 107.13/14.55 ((
% 107.13/14.55 (setOfPairsIsBReln) =>
% 107.13/14.55 ((
% 107.13/14.55 (dpsetconstrERa) =>
% 107.13/14.55 ((
% 107.13/14.55 (dpsetconstrEL1) =>
% 107.13/14.55 ((
% 107.13/14.55 (dpsetconstrEL2) =>
% 107.13/14.55 ((
% 107.13/14.55 (dpsetconstrER) =>
% 107.13/14.55 ((
% 107.13/14.55 (funcImageSingleton) =>
% 107.13/14.55 ((
% 107.13/14.55 (apProp) =>
% 107.13/14.55 ((
% 107.13/14.55 (app) =>
% 107.13/14.55 ((
% 107.13/14.55 (infuncsetfunc) =>
% 107.13/14.55 ((
% 107.13/14.55 (ap2p) =>
% 107.13/14.55 ((
% 107.13/14.55 (funcinfuncset) =>
% 107.13/14.55 ((
% 107.13/14.55 (lamProp) =>
% 107.13/14.55 ((
% 107.13/14.55 (lamp) =>
% 107.13/14.55 ((
% 107.13/14.55 (lam2p) =>
% 107.13/14.55 ((
% 107.13/14.55 (brelnall1) =>
% 107.13/14.55 ((
% 107.13/14.55 (brelnall2) =>
% 107.13/14.55 ((
% 107.13/14.55 (ex1E2) =>
% 107.13/14.55 ((
% 107.13/14.55 (funcGraphProp1) =>
% 107.13/14.55 ((
% 107.13/14.55 (funcGraphProp3) =>
% 107.13/14.55 ((
% 107.13/14.55 (funcGraphProp2) =>
% 107.13/14.55 ((
% 107.13/14.55 (funcextLem) =>
% 107.13/14.55 ((
% 107.13/14.55 (funcGraphProp4) =>
% 107.13/14.55 ((
% 107.13/14.55 (subbreln) =>
% 107.13/14.55 ((
% 107.13/14.55 (eqbreln) =>
% 107.13/14.55 ((
% 107.13/14.55 (funcext) =>
% 107.13/14.55 ((
% 107.13/14.55 (funcext2) =>
% 107.13/14.55 ((
% 107.13/14.55 (ap2apEq1) =>
% 107.13/14.55 ((
% 107.13/14.55 (ap2apEq2) =>
% 107.13/14.55 ((
% 107.13/14.55 (beta1) =>
% 107.13/14.55 ((
% 107.13/14.55 (eta1) =>
% 107.13/14.55 ((
% 107.13/14.55 (lam2lamEq) =>
% 107.13/14.55 ((
% 107.13/14.55 (beta2) =>
% 107.13/14.55 ((
% 107.13/14.55 (eta2) =>
% 107.13/14.55 ((
% 107.13/14.55 (iffalseProp1) =>
% 107.13/14.55 ((
% 107.13/14.55 (iffalseProp2) =>
% 107.13/14.55 ((
% 107.13/14.55 (iftrueProp1) =>
% 107.13/14.55 ((
% 107.13/14.55 (iftrueProp2) =>
% 107.13/14.55 ((
% 107.13/14.55 (ifSingleton) =>
% 107.13/14.55 ((
% 107.13/14.55 (ifp) =>
% 107.13/14.55 ((
% 107.13/14.55 (theeq) =>
% 107.13/14.55 ((
% 107.13/14.55 (iftrue) =>
% 107.13/14.55 ((
% 107.13/14.55 (iffalse) =>
% 107.13/14.55 ((
% 107.13/14.55 (iftrueorfalse) =>
% 107.13/14.55 ((
% 107.13/14.55 (binintersectT_lem) =>
% 107.13/14.55 ((
% 107.13/14.55 (binunionT_lem) =>
% 107.13/14.55 ((
% 107.13/14.55 (powersetT_lem) =>
% 107.13/14.55 ((
% 107.13/14.55 (setminusT_lem) =>
% 107.13/14.55 ((
% 107.13/14.55 (complementT_lem) =>
% 107.13/14.55 ((
% 107.13/14.55 (setextT) =>
% 107.13/14.55 ((
% 107.13/14.55 (subsetTI) =>
% 107.13/14.55 ((
% 107.13/14.55 (powersetTI1) =>
% 107.13/14.55 ((
% 107.13/14.55 (powersetTE1) =>
% 107.13/14.55 ((
% 107.13/14.55 (complementTI1) =>
% 107.13/14.55 ((
% 107.13/14.55 (complementTE1) =>
% 107.13/14.55 ((
% 107.13/14.55 (binintersectTELcontra) =>
% 107.13/14.55 ((
% 107.13/14.55 (binintersectTERcontra) =>
% 107.13/14.55 ((
% 107.13/14.55 (contrasubsetT) =>
% 107.13/14.55 ((
% 107.13/14.55 (contrasubsetT1) =>
% 107.13/14.55 ((
% 107.13/14.55 (contrasubsetT2) =>
% 107.13/14.55 ((
% 107.13/14.55 (contrasubsetT3) =>
% 107.13/14.55 ((
% 107.13/14.55 (doubleComplementI1) =>
% 107.13/14.55 ((
% 107.13/14.55 (doubleComplementE1) =>
% 107.13/14.55 ((
% 107.13/14.55 (doubleComplementSub1) =>
% 107.13/14.55 ((
% 107.13/14.55 (doubleComplementSub2) =>
% 107.13/14.55 ((
% 107.13/14.55 (doubleComplementEq) =>
% 107.13/14.55 ((
% 107.13/14.55 (complementTnotintersectT) =>
% 107.13/14.55 ((
% 107.13/14.55 (complementImpComplementIntersect) =>
% 107.13/14.55 ((
% 107.13/14.55 (complementSubsetComplementIntersect) =>
% 107.13/14.55 ((
% 107.13/14.55 (complementInPowersetComplementIntersect) =>
% 107.13/14.55 ((
% 107.13/14.55 (contraSubsetComplement) =>
% 107.13/14.55 ((
% 107.13/14.55 (complementTcontraSubset) =>
% 107.13/14.55 ((
% 107.13/14.55 (binunionTILcontra) =>
% 107.13/14.55 ((
% 107.13/14.55 (binunionTIRcontra) =>
% 107.13/14.55 ((
% 107.13/14.55 (inIntersectImpInUnion) =>
% 107.13/14.55 ((
% 107.13/14.55 (inIntersectImpInUnion2) =>
% 107.13/14.55 ((
% 107.13/14.55 (inIntersectImpInIntersectUnions) =>
% 107.13/14.55 ((
% 107.13/14.55 (intersectInPowersetIntersectUnions) =>
% 107.13/14.55 ((
% 107.13/14.55 (inComplementUnionImpNotIn1) =>
% 107.13/14.55 ((
% 107.13/14.55 (inComplementUnionImpInComplement1) =>
% 107.13/14.55 ((
% 107.13/14.55 (binunionTE) =>
% 107.13/14.55 ((
% 107.13/14.55 (binunionTEcontra) =>
% 107.13/14.55 ((
% 107.13/14.55 (demorgan2a1) =>
% 107.13/14.55 ((
% 107.13/14.55 (complementUnionInPowersetComplement) =>
% 107.13/14.55 ((
% 107.13/14.55 (demorgan2a2) =>
% 107.13/14.55 ((
% 107.13/14.55 (demorgan1a) =>
% 107.13/14.55 ((
% 107.13/14.55 (demorgan1b) =>
% 107.13/14.55 ((
% 107.13/14.55 (demorgan1) =>
% 107.13/14.55 ((
% 107.13/14.55 (demorgan2a) =>
% 107.13/14.55 ((
% 107.13/14.55 (demorgan2b2) =>
% 107.13/14.55 ((
% 107.13/14.55 (demorgan2b) =>
% 107.13/14.55 ((
% 107.13/14.55 (demorgan2) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz13rule0) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz13rule1) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz13rule2) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz13rule3) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz13rule4) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz1_1) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz1_2) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz1_3) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz1_4) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz1_5) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1all2) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1SetBreln1) =>
% 107.13/14.55 ((
% 107.13/14.55 (choice2fnsingleton) =>
% 107.13/14.55 ((
% 107.13/14.55 (setOfPairsIsBReln1) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1all1) =>
% 107.13/14.55 ((
% 107.13/14.55 (subbreln1) =>
% 107.13/14.55 ((
% 107.13/14.55 (eqbreln1) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1invprop) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1invI) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1invE) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1compprop) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1compI) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1compE) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1compEex) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1unionprop) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1unionIL) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1unionIR) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1unionI) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1unionE) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1unionEcases) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1unionCommutes) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz2Ex) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz2W) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz2A) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz2B) =>
% 107.13/14.55 ((
% 107.13/14.55 (image1Ex) =>
% 107.13/14.55 ((
% 107.13/14.55 (image1Ex1) =>
% 107.13/14.55 ((
% 107.13/14.55 (image1Equiv) =>
% 107.13/14.55 ((
% 107.13/14.55 (image1E) =>
% 107.13/14.55 ((
% 107.13/14.55 (image1I) =>
% 107.13/14.55 ((
% 107.13/14.55 (injFuncInInjFuncSet) =>
% 107.13/14.55 ((
% 107.13/14.55 (injFuncSetFuncIn) =>
% 107.13/14.55 ((
% 107.13/14.55 (injFuncSetFuncInj) =>
% 107.13/14.55 ((
% 107.13/14.55 (surjFuncSetFuncIn) =>
% 107.13/14.55 ((
% 107.13/14.55 (surjFuncSetFuncSurj) =>
% 107.13/14.55 ((
% 107.13/14.55 (leftInvIsSurj) =>
% 107.13/14.55 ((
% 107.13/14.55 (surjCantorThm) =>
% 107.13/14.55 ((
% 107.13/14.55 (!!) @ (
% 107.13/14.55 (('#S') @ (
% 107.13/14.55 (
% 107.13/14.55 ('#B') @ (
% 107.13/14.55 =>) @
% 107.13/14.55 nonempty)) @
% 107.13/14.55 (
% 107.13/14.55 (
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% 107.13/14.55 (
% 107.13/14.55 ('#S') @ (
% 107.13/14.55 (
% 107.13/14.55 ('#B') @ (
% 107.13/14.55 '#S') @
% 107.13/14.55 (
% 107.13/14.55 (
% 107.13/14.55 ('#B') @ (
% 107.13/14.55 (
% 107.13/14.55 ('#B') @ (
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% 107.13/14.55 (
% 107.13/14.55 (
% 107.13/14.55 ('#C') @ in)))))) @
% 107.13/14.55 (
% 107.13/14.55 (
% 107.13/14.55 ('#C') @ (
% 107.13/14.55 (
% 107.13/14.55 ('#B') @ (
% 107.13/14.55 '#C') @
% 107.13/14.55 (
% 107.13/14.55 (
% 107.13/14.55 ('#B') @ (
% 107.13/14.55 (
% 107.13/14.55 ('#B') @ (
% 107.13/14.55 =))) @
% 107.13/14.55 (
% 107.13/14.55 (
% 107.13/14.55 ('#C') @ binintersect)))))) @
% 107.13/14.55 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 107.13/14.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1321])).
% 107.13/14.55 thf(zip_derived_cl1338, plain,
% 107.13/14.55 (~ (((symdiffI1) =>
% 107.13/14.55 (((symdiffI2) =>
% 107.13/14.55 (((symdiffIneg1) =>
% 107.13/14.55 (((symdiffIneg2) =>
% 107.13/14.55 (((secondinupair) =>
% 107.13/14.55 (((setukpairIL) =>
% 107.13/14.55 (((setukpairIR) =>
% 107.13/14.55 (((kpairiskpair) =>
% 107.13/14.55 (((kpairp) =>
% 107.13/14.55 (((singletonsubset) =>
% 107.13/14.55 (((singletoninpowerset) =>
% 107.13/14.55 (((singletoninpowunion) =>
% 107.13/14.55 (((upairset2E) =>
% 107.13/14.55 (((upairsubunion) =>
% 107.13/14.55 (((upairinpowunion) =>
% 107.13/14.55 (((ubforcartprodlem1) =>
% 107.13/14.55 (((ubforcartprodlem2) =>
% 107.13/14.55 (((ubforcartprodlem3) =>
% 107.13/14.55 (((cartprodpairin) =>
% 107.13/14.55 (((cartprodmempair1) =>
% 107.13/14.55 (((cartprodmempair) =>
% 107.13/14.55 (((setunionE2) =>
% 107.13/14.55 (((setunionsingleton1) =>
% 107.13/14.55 (((setunionsingleton2) =>
% 107.13/14.55 (((setunionsingleton) =>
% 107.13/14.55 (((singletonprop) =>
% 107.13/14.55 (((ex1E1) =>
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% 107.13/14.55 (((ex1I2) =>
% 107.13/14.55 (((singletonsuniq) =>
% 107.13/14.55 ((
% 107.13/14.55 (setukpairinjL1) =>
% 107.13/14.55 ((
% 107.13/14.55 (kfstsingleton) =>
% 107.13/14.55 ((
% 107.13/14.55 (theprop) =>
% 107.13/14.55 ((
% 107.13/14.55 (kfstpairEq) =>
% 107.13/14.55 ((
% 107.13/14.55 (cartprodfstin) =>
% 107.13/14.55 ((
% 107.13/14.55 (setukpairinjL2) =>
% 107.13/14.55 ((
% 107.13/14.55 (setukpairinjL) =>
% 107.13/14.55 ((
% 107.13/14.55 (setukpairinjR11) =>
% 107.13/14.55 ((
% 107.13/14.55 (setukpairinjR12) =>
% 107.13/14.55 ((
% 107.13/14.55 (setukpairinjR1) =>
% 107.13/14.55 ((
% 107.13/14.55 (upairequniteq) =>
% 107.13/14.55 ((
% 107.13/14.55 (setukpairinjR2) =>
% 107.13/14.55 ((
% 107.13/14.55 (setukpairinjR) =>
% 107.13/14.55 ((
% 107.13/14.55 (ksndsingleton) =>
% 107.13/14.55 ((
% 107.13/14.55 (ksndpairEq) =>
% 107.13/14.55 ((
% 107.13/14.55 (kpairsurjEq) =>
% 107.13/14.55 ((
% 107.13/14.55 (cartprodsndin) =>
% 107.13/14.55 ((
% 107.13/14.55 (cartprodpairmemEL) =>
% 107.13/14.55 ((
% 107.13/14.55 (cartprodpairmemER) =>
% 107.13/14.55 ((
% 107.13/14.55 (cartprodmempaircEq) =>
% 107.13/14.55 ((
% 107.13/14.55 (cartprodfstpairEq) =>
% 107.13/14.55 ((
% 107.13/14.55 (cartprodsndpairEq) =>
% 107.13/14.55 ((
% 107.13/14.55 (cartprodpairsurjEq) =>
% 107.13/14.55 ((
% 107.13/14.55 (dpsetconstrI) =>
% 107.13/14.55 ((
% 107.13/14.55 (dpsetconstrSub) =>
% 107.13/14.55 ((
% 107.13/14.55 (setOfPairsIsBReln) =>
% 107.13/14.55 ((
% 107.13/14.55 (dpsetconstrERa) =>
% 107.13/14.55 ((
% 107.13/14.55 (dpsetconstrEL1) =>
% 107.13/14.55 ((
% 107.13/14.55 (dpsetconstrEL2) =>
% 107.13/14.55 ((
% 107.13/14.55 (dpsetconstrER) =>
% 107.13/14.55 ((
% 107.13/14.55 (funcImageSingleton) =>
% 107.13/14.55 ((
% 107.13/14.55 (apProp) =>
% 107.13/14.55 ((
% 107.13/14.55 (app) =>
% 107.13/14.55 ((
% 107.13/14.55 (infuncsetfunc) =>
% 107.13/14.55 ((
% 107.13/14.55 (ap2p) =>
% 107.13/14.55 ((
% 107.13/14.55 (funcinfuncset) =>
% 107.13/14.55 ((
% 107.13/14.55 (lamProp) =>
% 107.13/14.55 ((
% 107.13/14.55 (lamp) =>
% 107.13/14.55 ((
% 107.13/14.55 (lam2p) =>
% 107.13/14.55 ((
% 107.13/14.55 (brelnall1) =>
% 107.13/14.55 ((
% 107.13/14.55 (brelnall2) =>
% 107.13/14.55 ((
% 107.13/14.55 (ex1E2) =>
% 107.13/14.55 ((
% 107.13/14.55 (funcGraphProp1) =>
% 107.13/14.55 ((
% 107.13/14.55 (funcGraphProp3) =>
% 107.13/14.55 ((
% 107.13/14.55 (funcGraphProp2) =>
% 107.13/14.55 ((
% 107.13/14.55 (funcextLem) =>
% 107.13/14.55 ((
% 107.13/14.55 (funcGraphProp4) =>
% 107.13/14.55 ((
% 107.13/14.55 (subbreln) =>
% 107.13/14.55 ((
% 107.13/14.55 (eqbreln) =>
% 107.13/14.55 ((
% 107.13/14.55 (funcext) =>
% 107.13/14.55 ((
% 107.13/14.55 (funcext2) =>
% 107.13/14.55 ((
% 107.13/14.55 (ap2apEq1) =>
% 107.13/14.55 ((
% 107.13/14.55 (ap2apEq2) =>
% 107.13/14.55 ((
% 107.13/14.55 (beta1) =>
% 107.13/14.55 ((
% 107.13/14.55 (eta1) =>
% 107.13/14.55 ((
% 107.13/14.55 (lam2lamEq) =>
% 107.13/14.55 ((
% 107.13/14.55 (beta2) =>
% 107.13/14.55 ((
% 107.13/14.55 (eta2) =>
% 107.13/14.55 ((
% 107.13/14.55 (iffalseProp1) =>
% 107.13/14.55 ((
% 107.13/14.55 (iffalseProp2) =>
% 107.13/14.55 ((
% 107.13/14.55 (iftrueProp1) =>
% 107.13/14.55 ((
% 107.13/14.55 (iftrueProp2) =>
% 107.13/14.55 ((
% 107.13/14.55 (ifSingleton) =>
% 107.13/14.55 ((
% 107.13/14.55 (ifp) =>
% 107.13/14.55 ((
% 107.13/14.55 (theeq) =>
% 107.13/14.55 ((
% 107.13/14.55 (iftrue) =>
% 107.13/14.55 ((
% 107.13/14.55 (iffalse) =>
% 107.13/14.55 ((
% 107.13/14.55 (iftrueorfalse) =>
% 107.13/14.55 ((
% 107.13/14.55 (binintersectT_lem) =>
% 107.13/14.55 ((
% 107.13/14.55 (binunionT_lem) =>
% 107.13/14.55 ((
% 107.13/14.55 (powersetT_lem) =>
% 107.13/14.55 ((
% 107.13/14.55 (setminusT_lem) =>
% 107.13/14.55 ((
% 107.13/14.55 (complementT_lem) =>
% 107.13/14.55 ((
% 107.13/14.55 (setextT) =>
% 107.13/14.55 ((
% 107.13/14.55 (subsetTI) =>
% 107.13/14.55 ((
% 107.13/14.55 (powersetTI1) =>
% 107.13/14.55 ((
% 107.13/14.55 (powersetTE1) =>
% 107.13/14.55 ((
% 107.13/14.55 (complementTI1) =>
% 107.13/14.55 ((
% 107.13/14.55 (complementTE1) =>
% 107.13/14.55 ((
% 107.13/14.55 (binintersectTELcontra) =>
% 107.13/14.55 ((
% 107.13/14.55 (binintersectTERcontra) =>
% 107.13/14.55 ((
% 107.13/14.55 (contrasubsetT) =>
% 107.13/14.55 ((
% 107.13/14.55 (contrasubsetT1) =>
% 107.13/14.55 ((
% 107.13/14.55 (contrasubsetT2) =>
% 107.13/14.55 ((
% 107.13/14.55 (contrasubsetT3) =>
% 107.13/14.55 ((
% 107.13/14.55 (doubleComplementI1) =>
% 107.13/14.55 ((
% 107.13/14.55 (doubleComplementE1) =>
% 107.13/14.55 ((
% 107.13/14.55 (doubleComplementSub1) =>
% 107.13/14.55 ((
% 107.13/14.55 (doubleComplementSub2) =>
% 107.13/14.55 ((
% 107.13/14.55 (doubleComplementEq) =>
% 107.13/14.55 ((
% 107.13/14.55 (complementTnotintersectT) =>
% 107.13/14.55 ((
% 107.13/14.55 (complementImpComplementIntersect) =>
% 107.13/14.55 ((
% 107.13/14.55 (complementSubsetComplementIntersect) =>
% 107.13/14.55 ((
% 107.13/14.55 (complementInPowersetComplementIntersect) =>
% 107.13/14.55 ((
% 107.13/14.55 (contraSubsetComplement) =>
% 107.13/14.55 ((
% 107.13/14.55 (complementTcontraSubset) =>
% 107.13/14.55 ((
% 107.13/14.55 (binunionTILcontra) =>
% 107.13/14.55 ((
% 107.13/14.55 (binunionTIRcontra) =>
% 107.13/14.55 ((
% 107.13/14.55 (inIntersectImpInUnion) =>
% 107.13/14.55 ((
% 107.13/14.55 (inIntersectImpInUnion2) =>
% 107.13/14.55 ((
% 107.13/14.55 (inIntersectImpInIntersectUnions) =>
% 107.13/14.55 ((
% 107.13/14.55 (intersectInPowersetIntersectUnions) =>
% 107.13/14.55 ((
% 107.13/14.55 (inComplementUnionImpNotIn1) =>
% 107.13/14.55 ((
% 107.13/14.55 (inComplementUnionImpInComplement1) =>
% 107.13/14.55 ((
% 107.13/14.55 (binunionTE) =>
% 107.13/14.55 ((
% 107.13/14.55 (binunionTEcontra) =>
% 107.13/14.55 ((
% 107.13/14.55 (demorgan2a1) =>
% 107.13/14.55 ((
% 107.13/14.55 (complementUnionInPowersetComplement) =>
% 107.13/14.55 ((
% 107.13/14.55 (demorgan2a2) =>
% 107.13/14.55 ((
% 107.13/14.55 (demorgan1a) =>
% 107.13/14.55 ((
% 107.13/14.55 (demorgan1b) =>
% 107.13/14.55 ((
% 107.13/14.55 (demorgan1) =>
% 107.13/14.55 ((
% 107.13/14.55 (demorgan2a) =>
% 107.13/14.55 ((
% 107.13/14.55 (demorgan2b2) =>
% 107.13/14.55 ((
% 107.13/14.55 (demorgan2b) =>
% 107.13/14.55 ((
% 107.13/14.55 (demorgan2) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz13rule0) =>
% 107.13/14.55 ((
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% 107.13/14.55 ((
% 107.13/14.55 (woz13rule2) =>
% 107.13/14.55 ((
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% 107.13/14.55 ((
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% 107.13/14.55 (woz1_2) =>
% 107.13/14.55 ((
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% 107.13/14.55 ((
% 107.13/14.55 (woz1_4) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz1_5) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1all2) =>
% 107.13/14.55 ((
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% 107.13/14.55 ((
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% 107.13/14.55 ((
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% 107.13/14.55 ((
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% 107.13/14.55 ((
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% 107.13/14.55 ((
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% 107.13/14.55 ((
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% 107.13/14.55 ((
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% 107.13/14.55 ('#C') @ in)))))) @
% 107.13/14.55 (
% 107.13/14.55 (
% 107.13/14.55 ('#C') @ (
% 107.13/14.55 (
% 107.13/14.55 ('#B') @ (
% 107.13/14.55 '#C') @
% 107.13/14.55 (
% 107.13/14.55 (
% 107.13/14.55 ('#B') @ (
% 107.13/14.55 (
% 107.13/14.55 ('#B') @ (
% 107.13/14.55 =))) @
% 107.13/14.55 (
% 107.13/14.55 (
% 107.13/14.55 ('#C') @ binintersect)))))) @
% 107.13/14.55 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 107.13/14.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1329])).
% 107.13/14.55 thf(zip_derived_cl1347, plain,
% 107.13/14.55 (~ (((symdiffI2) =>
% 107.13/14.55 (((symdiffIneg1) =>
% 107.13/14.55 (((symdiffIneg2) =>
% 107.13/14.55 (((secondinupair) =>
% 107.13/14.55 (((setukpairIL) =>
% 107.13/14.55 (((setukpairIR) =>
% 107.13/14.55 (((kpairiskpair) =>
% 107.13/14.55 (((kpairp) =>
% 107.13/14.55 (((singletonsubset) =>
% 107.13/14.55 (((singletoninpowerset) =>
% 107.13/14.55 (((singletoninpowunion) =>
% 107.13/14.55 (((upairset2E) =>
% 107.13/14.55 (((upairsubunion) =>
% 107.13/14.55 (((upairinpowunion) =>
% 107.13/14.55 (((ubforcartprodlem1) =>
% 107.13/14.55 (((ubforcartprodlem2) =>
% 107.13/14.55 (((ubforcartprodlem3) =>
% 107.13/14.55 (((cartprodpairin) =>
% 107.13/14.55 (((cartprodmempair1) =>
% 107.13/14.55 (((cartprodmempair) =>
% 107.13/14.55 (((setunionE2) =>
% 107.13/14.55 (((setunionsingleton1) =>
% 107.13/14.55 (((setunionsingleton2) =>
% 107.13/14.55 (((setunionsingleton) =>
% 107.13/14.55 (((singletonprop) =>
% 107.13/14.55 (((ex1E1) =>
% 107.13/14.55 (((ex1I) =>
% 107.13/14.55 (((ex1I2) =>
% 107.13/14.55 (((singletonsuniq) =>
% 107.13/14.55 (((setukpairinjL1) =>
% 107.13/14.55 ((
% 107.13/14.55 (kfstsingleton) =>
% 107.13/14.55 ((
% 107.13/14.55 (theprop) =>
% 107.13/14.55 ((
% 107.13/14.55 (kfstpairEq) =>
% 107.13/14.55 ((
% 107.13/14.55 (cartprodfstin) =>
% 107.13/14.55 ((
% 107.13/14.55 (setukpairinjL2) =>
% 107.13/14.55 ((
% 107.13/14.55 (setukpairinjL) =>
% 107.13/14.55 ((
% 107.13/14.55 (setukpairinjR11) =>
% 107.13/14.55 ((
% 107.13/14.55 (setukpairinjR12) =>
% 107.13/14.55 ((
% 107.13/14.55 (setukpairinjR1) =>
% 107.13/14.55 ((
% 107.13/14.55 (upairequniteq) =>
% 107.13/14.55 ((
% 107.13/14.55 (setukpairinjR2) =>
% 107.13/14.55 ((
% 107.13/14.55 (setukpairinjR) =>
% 107.13/14.55 ((
% 107.13/14.55 (ksndsingleton) =>
% 107.13/14.55 ((
% 107.13/14.55 (ksndpairEq) =>
% 107.13/14.55 ((
% 107.13/14.55 (kpairsurjEq) =>
% 107.13/14.55 ((
% 107.13/14.55 (cartprodsndin) =>
% 107.13/14.55 ((
% 107.13/14.55 (cartprodpairmemEL) =>
% 107.13/14.55 ((
% 107.13/14.55 (cartprodpairmemER) =>
% 107.13/14.55 ((
% 107.13/14.55 (cartprodmempaircEq) =>
% 107.13/14.55 ((
% 107.13/14.55 (cartprodfstpairEq) =>
% 107.13/14.55 ((
% 107.13/14.55 (cartprodsndpairEq) =>
% 107.13/14.55 ((
% 107.13/14.55 (cartprodpairsurjEq) =>
% 107.13/14.55 ((
% 107.13/14.55 (dpsetconstrI) =>
% 107.13/14.55 ((
% 107.13/14.55 (dpsetconstrSub) =>
% 107.13/14.55 ((
% 107.13/14.55 (setOfPairsIsBReln) =>
% 107.13/14.55 ((
% 107.13/14.55 (dpsetconstrERa) =>
% 107.13/14.55 ((
% 107.13/14.55 (dpsetconstrEL1) =>
% 107.13/14.55 ((
% 107.13/14.55 (dpsetconstrEL2) =>
% 107.13/14.55 ((
% 107.13/14.55 (dpsetconstrER) =>
% 107.13/14.55 ((
% 107.13/14.55 (funcImageSingleton) =>
% 107.13/14.55 ((
% 107.13/14.55 (apProp) =>
% 107.13/14.55 ((
% 107.13/14.55 (app) =>
% 107.13/14.55 ((
% 107.13/14.55 (infuncsetfunc) =>
% 107.13/14.55 ((
% 107.13/14.55 (ap2p) =>
% 107.13/14.55 ((
% 107.13/14.55 (funcinfuncset) =>
% 107.13/14.55 ((
% 107.13/14.55 (lamProp) =>
% 107.13/14.55 ((
% 107.13/14.55 (lamp) =>
% 107.13/14.55 ((
% 107.13/14.55 (lam2p) =>
% 107.13/14.55 ((
% 107.13/14.55 (brelnall1) =>
% 107.13/14.55 ((
% 107.13/14.55 (brelnall2) =>
% 107.13/14.55 ((
% 107.13/14.55 (ex1E2) =>
% 107.13/14.55 ((
% 107.13/14.55 (funcGraphProp1) =>
% 107.13/14.55 ((
% 107.13/14.55 (funcGraphProp3) =>
% 107.13/14.55 ((
% 107.13/14.55 (funcGraphProp2) =>
% 107.13/14.55 ((
% 107.13/14.55 (funcextLem) =>
% 107.13/14.55 ((
% 107.13/14.55 (funcGraphProp4) =>
% 107.13/14.55 ((
% 107.13/14.55 (subbreln) =>
% 107.13/14.55 ((
% 107.13/14.55 (eqbreln) =>
% 107.13/14.55 ((
% 107.13/14.55 (funcext) =>
% 107.13/14.55 ((
% 107.13/14.55 (funcext2) =>
% 107.13/14.55 ((
% 107.13/14.55 (ap2apEq1) =>
% 107.13/14.55 ((
% 107.13/14.55 (ap2apEq2) =>
% 107.13/14.55 ((
% 107.13/14.55 (beta1) =>
% 107.13/14.55 ((
% 107.13/14.55 (eta1) =>
% 107.13/14.55 ((
% 107.13/14.55 (lam2lamEq) =>
% 107.13/14.55 ((
% 107.13/14.55 (beta2) =>
% 107.13/14.55 ((
% 107.13/14.55 (eta2) =>
% 107.13/14.55 ((
% 107.13/14.55 (iffalseProp1) =>
% 107.13/14.55 ((
% 107.13/14.55 (iffalseProp2) =>
% 107.13/14.55 ((
% 107.13/14.55 (iftrueProp1) =>
% 107.13/14.55 ((
% 107.13/14.55 (iftrueProp2) =>
% 107.13/14.55 ((
% 107.13/14.55 (ifSingleton) =>
% 107.13/14.55 ((
% 107.13/14.55 (ifp) =>
% 107.13/14.55 ((
% 107.13/14.55 (theeq) =>
% 107.13/14.55 ((
% 107.13/14.55 (iftrue) =>
% 107.13/14.55 ((
% 107.13/14.55 (iffalse) =>
% 107.13/14.55 ((
% 107.13/14.55 (iftrueorfalse) =>
% 107.13/14.55 ((
% 107.13/14.55 (binintersectT_lem) =>
% 107.13/14.55 ((
% 107.13/14.55 (binunionT_lem) =>
% 107.13/14.55 ((
% 107.13/14.55 (powersetT_lem) =>
% 107.13/14.55 ((
% 107.13/14.55 (setminusT_lem) =>
% 107.13/14.55 ((
% 107.13/14.55 (complementT_lem) =>
% 107.13/14.55 ((
% 107.13/14.55 (setextT) =>
% 107.13/14.55 ((
% 107.13/14.55 (subsetTI) =>
% 107.13/14.55 ((
% 107.13/14.55 (powersetTI1) =>
% 107.13/14.55 ((
% 107.13/14.55 (powersetTE1) =>
% 107.13/14.55 ((
% 107.13/14.55 (complementTI1) =>
% 107.13/14.55 ((
% 107.13/14.55 (complementTE1) =>
% 107.13/14.55 ((
% 107.13/14.55 (binintersectTELcontra) =>
% 107.13/14.55 ((
% 107.13/14.55 (binintersectTERcontra) =>
% 107.13/14.55 ((
% 107.13/14.55 (contrasubsetT) =>
% 107.13/14.55 ((
% 107.13/14.55 (contrasubsetT1) =>
% 107.13/14.55 ((
% 107.13/14.55 (contrasubsetT2) =>
% 107.13/14.55 ((
% 107.13/14.55 (contrasubsetT3) =>
% 107.13/14.55 ((
% 107.13/14.55 (doubleComplementI1) =>
% 107.13/14.55 ((
% 107.13/14.55 (doubleComplementE1) =>
% 107.13/14.55 ((
% 107.13/14.55 (doubleComplementSub1) =>
% 107.13/14.55 ((
% 107.13/14.55 (doubleComplementSub2) =>
% 107.13/14.55 ((
% 107.13/14.55 (doubleComplementEq) =>
% 107.13/14.55 ((
% 107.13/14.55 (complementTnotintersectT) =>
% 107.13/14.55 ((
% 107.13/14.55 (complementImpComplementIntersect) =>
% 107.13/14.55 ((
% 107.13/14.55 (complementSubsetComplementIntersect) =>
% 107.13/14.55 ((
% 107.13/14.55 (complementInPowersetComplementIntersect) =>
% 107.13/14.55 ((
% 107.13/14.55 (contraSubsetComplement) =>
% 107.13/14.55 ((
% 107.13/14.55 (complementTcontraSubset) =>
% 107.13/14.55 ((
% 107.13/14.55 (binunionTILcontra) =>
% 107.13/14.55 ((
% 107.13/14.55 (binunionTIRcontra) =>
% 107.13/14.55 ((
% 107.13/14.55 (inIntersectImpInUnion) =>
% 107.13/14.55 ((
% 107.13/14.55 (inIntersectImpInUnion2) =>
% 107.13/14.55 ((
% 107.13/14.55 (inIntersectImpInIntersectUnions) =>
% 107.13/14.55 ((
% 107.13/14.55 (intersectInPowersetIntersectUnions) =>
% 107.13/14.55 ((
% 107.13/14.55 (inComplementUnionImpNotIn1) =>
% 107.13/14.55 ((
% 107.13/14.55 (inComplementUnionImpInComplement1) =>
% 107.13/14.55 ((
% 107.13/14.55 (binunionTE) =>
% 107.13/14.55 ((
% 107.13/14.55 (binunionTEcontra) =>
% 107.13/14.55 ((
% 107.13/14.55 (demorgan2a1) =>
% 107.13/14.55 ((
% 107.13/14.55 (complementUnionInPowersetComplement) =>
% 107.13/14.55 ((
% 107.13/14.55 (demorgan2a2) =>
% 107.13/14.55 ((
% 107.13/14.55 (demorgan1a) =>
% 107.13/14.55 ((
% 107.13/14.55 (demorgan1b) =>
% 107.13/14.55 ((
% 107.13/14.55 (demorgan1) =>
% 107.13/14.55 ((
% 107.13/14.55 (demorgan2a) =>
% 107.13/14.55 ((
% 107.13/14.55 (demorgan2b2) =>
% 107.13/14.55 ((
% 107.13/14.55 (demorgan2b) =>
% 107.13/14.55 ((
% 107.13/14.55 (demorgan2) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz13rule0) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz13rule1) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz13rule2) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz13rule3) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz13rule4) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz1_1) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz1_2) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz1_3) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz1_4) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz1_5) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1all2) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1SetBreln1) =>
% 107.13/14.55 ((
% 107.13/14.55 (choice2fnsingleton) =>
% 107.13/14.55 ((
% 107.13/14.55 (setOfPairsIsBReln1) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1all1) =>
% 107.13/14.55 ((
% 107.13/14.55 (subbreln1) =>
% 107.13/14.55 ((
% 107.13/14.55 (eqbreln1) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1invprop) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1invI) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1invE) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1compprop) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1compI) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1compE) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1compEex) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1unionprop) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1unionIL) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1unionIR) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1unionI) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1unionE) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1unionEcases) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1unionCommutes) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz2Ex) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz2W) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz2A) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz2B) =>
% 107.13/14.55 ((
% 107.13/14.55 (image1Ex) =>
% 107.13/14.55 ((
% 107.13/14.55 (image1Ex1) =>
% 107.13/14.55 ((
% 107.13/14.55 (image1Equiv) =>
% 107.13/14.55 ((
% 107.13/14.55 (image1E) =>
% 107.13/14.55 ((
% 107.13/14.55 (image1I) =>
% 107.13/14.55 ((
% 107.13/14.55 (injFuncInInjFuncSet) =>
% 107.13/14.55 ((
% 107.13/14.55 (injFuncSetFuncIn) =>
% 107.13/14.55 ((
% 107.13/14.55 (injFuncSetFuncInj) =>
% 107.13/14.55 ((
% 107.13/14.55 (surjFuncSetFuncIn) =>
% 107.13/14.55 ((
% 107.13/14.55 (surjFuncSetFuncSurj) =>
% 107.13/14.55 ((
% 107.13/14.55 (leftInvIsSurj) =>
% 107.13/14.55 ((
% 107.13/14.55 (surjCantorThm) =>
% 107.13/14.55 ((
% 107.13/14.55 (!!) @ (
% 107.13/14.55 (('#S') @ (
% 107.13/14.55 (
% 107.13/14.55 ('#B') @ (
% 107.13/14.55 =>) @
% 107.13/14.55 nonempty)) @
% 107.13/14.55 (
% 107.13/14.55 (
% 107.13/14.55 ('#B') @ (
% 107.13/14.55 ??) @
% 107.13/14.55 (
% 107.13/14.55 (
% 107.13/14.55 ('#S') @ (
% 107.13/14.55 (
% 107.13/14.55 ('#B') @ (
% 107.13/14.55 '#S') @
% 107.13/14.55 (
% 107.13/14.55 (
% 107.13/14.55 ('#B') @ (
% 107.13/14.55 (
% 107.13/14.55 ('#B') @ (
% 107.13/14.55 &))) @
% 107.13/14.55 (
% 107.13/14.55 (
% 107.13/14.55 ('#C') @ in)))))) @
% 107.13/14.55 (
% 107.13/14.55 (
% 107.13/14.55 ('#C') @ (
% 107.13/14.55 (
% 107.13/14.55 ('#B') @ (
% 107.13/14.55 '#C') @
% 107.13/14.55 (
% 107.13/14.55 (
% 107.13/14.55 ('#B') @ (
% 107.13/14.55 (
% 107.13/14.55 ('#B') @ (
% 107.13/14.55 =))) @
% 107.13/14.55 (
% 107.13/14.55 (
% 107.13/14.55 ('#C') @ binintersect)))))) @
% 107.13/14.55 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 107.13/14.55 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1338])).
% 107.13/14.55 thf(zip_derived_cl1354, plain,
% 107.13/14.55 (~ (((symdiffIneg1) =>
% 107.13/14.55 (((symdiffIneg2) =>
% 107.13/14.55 (((secondinupair) =>
% 107.13/14.55 (((setukpairIL) =>
% 107.13/14.55 (((setukpairIR) =>
% 107.13/14.55 (((kpairiskpair) =>
% 107.13/14.55 (((kpairp) =>
% 107.13/14.55 (((singletonsubset) =>
% 107.13/14.55 (((singletoninpowerset) =>
% 107.13/14.55 (((singletoninpowunion) =>
% 107.13/14.55 (((upairset2E) =>
% 107.13/14.55 (((upairsubunion) =>
% 107.13/14.55 (((upairinpowunion) =>
% 107.13/14.55 (((ubforcartprodlem1) =>
% 107.13/14.55 (((ubforcartprodlem2) =>
% 107.13/14.55 (((ubforcartprodlem3) =>
% 107.13/14.55 (((cartprodpairin) =>
% 107.13/14.55 (((cartprodmempair1) =>
% 107.13/14.55 (((cartprodmempair) =>
% 107.13/14.55 (((setunionE2) =>
% 107.13/14.55 (((setunionsingleton1) =>
% 107.13/14.55 (((setunionsingleton2) =>
% 107.13/14.55 (((setunionsingleton) =>
% 107.13/14.55 (((singletonprop) =>
% 107.13/14.55 (((ex1E1) =>
% 107.13/14.55 (((ex1I) =>
% 107.13/14.55 (((ex1I2) =>
% 107.13/14.55 (((singletonsuniq) =>
% 107.13/14.55 (((setukpairinjL1) =>
% 107.13/14.55 (((kfstsingleton) =>
% 107.13/14.55 ((
% 107.13/14.55 (theprop) =>
% 107.13/14.55 ((
% 107.13/14.55 (kfstpairEq) =>
% 107.13/14.55 ((
% 107.13/14.55 (cartprodfstin) =>
% 107.13/14.55 ((
% 107.13/14.55 (setukpairinjL2) =>
% 107.13/14.55 ((
% 107.13/14.55 (setukpairinjL) =>
% 107.13/14.55 ((
% 107.13/14.55 (setukpairinjR11) =>
% 107.13/14.55 ((
% 107.13/14.55 (setukpairinjR12) =>
% 107.13/14.55 ((
% 107.13/14.55 (setukpairinjR1) =>
% 107.13/14.55 ((
% 107.13/14.55 (upairequniteq) =>
% 107.13/14.55 ((
% 107.13/14.55 (setukpairinjR2) =>
% 107.13/14.55 ((
% 107.13/14.55 (setukpairinjR) =>
% 107.13/14.55 ((
% 107.13/14.55 (ksndsingleton) =>
% 107.13/14.55 ((
% 107.13/14.55 (ksndpairEq) =>
% 107.13/14.55 ((
% 107.13/14.55 (kpairsurjEq) =>
% 107.13/14.55 ((
% 107.13/14.55 (cartprodsndin) =>
% 107.13/14.55 ((
% 107.13/14.55 (cartprodpairmemEL) =>
% 107.13/14.55 ((
% 107.13/14.55 (cartprodpairmemER) =>
% 107.13/14.55 ((
% 107.13/14.55 (cartprodmempaircEq) =>
% 107.13/14.55 ((
% 107.13/14.55 (cartprodfstpairEq) =>
% 107.13/14.55 ((
% 107.13/14.55 (cartprodsndpairEq) =>
% 107.13/14.55 ((
% 107.13/14.55 (cartprodpairsurjEq) =>
% 107.13/14.55 ((
% 107.13/14.55 (dpsetconstrI) =>
% 107.13/14.55 ((
% 107.13/14.55 (dpsetconstrSub) =>
% 107.13/14.55 ((
% 107.13/14.55 (setOfPairsIsBReln) =>
% 107.13/14.55 ((
% 107.13/14.55 (dpsetconstrERa) =>
% 107.13/14.55 ((
% 107.13/14.55 (dpsetconstrEL1) =>
% 107.13/14.55 ((
% 107.13/14.55 (dpsetconstrEL2) =>
% 107.13/14.55 ((
% 107.13/14.55 (dpsetconstrER) =>
% 107.13/14.55 ((
% 107.13/14.55 (funcImageSingleton) =>
% 107.13/14.55 ((
% 107.13/14.55 (apProp) =>
% 107.13/14.55 ((
% 107.13/14.55 (app) =>
% 107.13/14.55 ((
% 107.13/14.55 (infuncsetfunc) =>
% 107.13/14.55 ((
% 107.13/14.55 (ap2p) =>
% 107.13/14.55 ((
% 107.13/14.55 (funcinfuncset) =>
% 107.13/14.55 ((
% 107.13/14.55 (lamProp) =>
% 107.13/14.55 ((
% 107.13/14.55 (lamp) =>
% 107.13/14.55 ((
% 107.13/14.55 (lam2p) =>
% 107.13/14.55 ((
% 107.13/14.55 (brelnall1) =>
% 107.13/14.55 ((
% 107.13/14.55 (brelnall2) =>
% 107.13/14.55 ((
% 107.13/14.55 (ex1E2) =>
% 107.13/14.55 ((
% 107.13/14.55 (funcGraphProp1) =>
% 107.13/14.55 ((
% 107.13/14.55 (funcGraphProp3) =>
% 107.13/14.55 ((
% 107.13/14.55 (funcGraphProp2) =>
% 107.13/14.55 ((
% 107.13/14.55 (funcextLem) =>
% 107.13/14.55 ((
% 107.13/14.55 (funcGraphProp4) =>
% 107.13/14.55 ((
% 107.13/14.55 (subbreln) =>
% 107.13/14.55 ((
% 107.13/14.55 (eqbreln) =>
% 107.13/14.55 ((
% 107.13/14.55 (funcext) =>
% 107.13/14.55 ((
% 107.13/14.55 (funcext2) =>
% 107.13/14.55 ((
% 107.13/14.55 (ap2apEq1) =>
% 107.13/14.55 ((
% 107.13/14.55 (ap2apEq2) =>
% 107.13/14.55 ((
% 107.13/14.55 (beta1) =>
% 107.13/14.55 ((
% 107.13/14.55 (eta1) =>
% 107.13/14.55 ((
% 107.13/14.55 (lam2lamEq) =>
% 107.13/14.55 ((
% 107.13/14.55 (beta2) =>
% 107.13/14.55 ((
% 107.13/14.55 (eta2) =>
% 107.13/14.55 ((
% 107.13/14.55 (iffalseProp1) =>
% 107.13/14.55 ((
% 107.13/14.55 (iffalseProp2) =>
% 107.13/14.55 ((
% 107.13/14.55 (iftrueProp1) =>
% 107.13/14.55 ((
% 107.13/14.55 (iftrueProp2) =>
% 107.13/14.55 ((
% 107.13/14.55 (ifSingleton) =>
% 107.13/14.55 ((
% 107.13/14.55 (ifp) =>
% 107.13/14.55 ((
% 107.13/14.55 (theeq) =>
% 107.13/14.55 ((
% 107.13/14.55 (iftrue) =>
% 107.13/14.55 ((
% 107.13/14.55 (iffalse) =>
% 107.13/14.55 ((
% 107.13/14.55 (iftrueorfalse) =>
% 107.13/14.55 ((
% 107.13/14.55 (binintersectT_lem) =>
% 107.13/14.55 ((
% 107.13/14.55 (binunionT_lem) =>
% 107.13/14.55 ((
% 107.13/14.55 (powersetT_lem) =>
% 107.13/14.55 ((
% 107.13/14.55 (setminusT_lem) =>
% 107.13/14.55 ((
% 107.13/14.55 (complementT_lem) =>
% 107.13/14.55 ((
% 107.13/14.55 (setextT) =>
% 107.13/14.55 ((
% 107.13/14.55 (subsetTI) =>
% 107.13/14.55 ((
% 107.13/14.55 (powersetTI1) =>
% 107.13/14.55 ((
% 107.13/14.55 (powersetTE1) =>
% 107.13/14.55 ((
% 107.13/14.55 (complementTI1) =>
% 107.13/14.55 ((
% 107.13/14.55 (complementTE1) =>
% 107.13/14.55 ((
% 107.13/14.55 (binintersectTELcontra) =>
% 107.13/14.55 ((
% 107.13/14.55 (binintersectTERcontra) =>
% 107.13/14.55 ((
% 107.13/14.55 (contrasubsetT) =>
% 107.13/14.55 ((
% 107.13/14.55 (contrasubsetT1) =>
% 107.13/14.55 ((
% 107.13/14.55 (contrasubsetT2) =>
% 107.13/14.55 ((
% 107.13/14.55 (contrasubsetT3) =>
% 107.13/14.55 ((
% 107.13/14.55 (doubleComplementI1) =>
% 107.13/14.55 ((
% 107.13/14.55 (doubleComplementE1) =>
% 107.13/14.55 ((
% 107.13/14.55 (doubleComplementSub1) =>
% 107.13/14.55 ((
% 107.13/14.55 (doubleComplementSub2) =>
% 107.13/14.55 ((
% 107.13/14.55 (doubleComplementEq) =>
% 107.13/14.55 ((
% 107.13/14.55 (complementTnotintersectT) =>
% 107.13/14.55 ((
% 107.13/14.55 (complementImpComplementIntersect) =>
% 107.13/14.55 ((
% 107.13/14.55 (complementSubsetComplementIntersect) =>
% 107.13/14.55 ((
% 107.13/14.55 (complementInPowersetComplementIntersect) =>
% 107.13/14.55 ((
% 107.13/14.55 (contraSubsetComplement) =>
% 107.13/14.55 ((
% 107.13/14.55 (complementTcontraSubset) =>
% 107.13/14.55 ((
% 107.13/14.55 (binunionTILcontra) =>
% 107.13/14.55 ((
% 107.13/14.55 (binunionTIRcontra) =>
% 107.13/14.55 ((
% 107.13/14.55 (inIntersectImpInUnion) =>
% 107.13/14.55 ((
% 107.13/14.55 (inIntersectImpInUnion2) =>
% 107.13/14.55 ((
% 107.13/14.55 (inIntersectImpInIntersectUnions) =>
% 107.13/14.55 ((
% 107.13/14.55 (intersectInPowersetIntersectUnions) =>
% 107.13/14.55 ((
% 107.13/14.55 (inComplementUnionImpNotIn1) =>
% 107.13/14.55 ((
% 107.13/14.55 (inComplementUnionImpInComplement1) =>
% 107.13/14.55 ((
% 107.13/14.55 (binunionTE) =>
% 107.13/14.55 ((
% 107.13/14.55 (binunionTEcontra) =>
% 107.13/14.55 ((
% 107.13/14.55 (demorgan2a1) =>
% 107.13/14.55 ((
% 107.13/14.55 (complementUnionInPowersetComplement) =>
% 107.13/14.55 ((
% 107.13/14.55 (demorgan2a2) =>
% 107.13/14.55 ((
% 107.13/14.55 (demorgan1a) =>
% 107.13/14.55 ((
% 107.13/14.55 (demorgan1b) =>
% 107.13/14.55 ((
% 107.13/14.55 (demorgan1) =>
% 107.13/14.55 ((
% 107.13/14.55 (demorgan2a) =>
% 107.13/14.55 ((
% 107.13/14.55 (demorgan2b2) =>
% 107.13/14.55 ((
% 107.13/14.55 (demorgan2b) =>
% 107.13/14.55 ((
% 107.13/14.55 (demorgan2) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz13rule0) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz13rule1) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz13rule2) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz13rule3) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz13rule4) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz1_1) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz1_2) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz1_3) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz1_4) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz1_5) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1all2) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1SetBreln1) =>
% 107.13/14.55 ((
% 107.13/14.55 (choice2fnsingleton) =>
% 107.13/14.55 ((
% 107.13/14.55 (setOfPairsIsBReln1) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1all1) =>
% 107.13/14.55 ((
% 107.13/14.55 (subbreln1) =>
% 107.13/14.55 ((
% 107.13/14.55 (eqbreln1) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1invprop) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1invI) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1invE) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1compprop) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1compI) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1compE) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1compEex) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1unionprop) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1unionIL) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1unionIR) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1unionI) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1unionE) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1unionEcases) =>
% 107.13/14.55 ((
% 107.13/14.55 (breln1unionCommutes) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz2Ex) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz2W) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz2A) =>
% 107.13/14.55 ((
% 107.13/14.55 (woz2B) =>
% 107.13/14.55 ((
% 107.13/14.55 (image1Ex) =>
% 107.13/14.55 ((
% 107.13/14.55 (image1Ex1) =>
% 107.13/14.55 ((
% 107.13/14.55 (image1Equiv) =>
% 107.13/14.55 ((
% 107.13/14.55 (image1E) =>
% 107.13/14.55 ((
% 107.13/14.55 (image1I) =>
% 107.13/14.55 ((
% 107.13/14.55 (injFuncInInjFuncSet) =>
% 107.13/14.55 ((
% 107.13/14.55 (injFuncSetFuncIn) =>
% 107.13/14.55 ((
% 107.13/14.55 (injFuncSetFuncInj) =>
% 107.13/14.55 ((
% 107.13/14.55 (surjFuncSetFuncIn) =>
% 107.13/14.55 ((
% 107.13/14.55 (surjFuncSetFuncSurj) =>
% 107.13/14.55 ((
% 107.13/14.55 (leftInvIsSurj) =>
% 107.13/14.55 ((
% 107.13/14.55 (surjCantorThm) =>
% 107.13/14.55 ((
% 107.13/14.55 (!!) @ (
% 107.13/14.55 (('#S') @ (
% 107.13/14.55 (
% 107.13/14.55 ('#B') @ (
% 107.13/14.55 =>) @
% 107.13/14.55 nonempty)) @
% 107.13/14.55 (
% 107.13/14.55 (
% 107.13/14.55 ('#B') @ (
% 107.13/14.55 ??) @
% 107.13/14.55 (
% 107.13/14.55 (
% 107.13/14.55 ('#S') @ (
% 107.13/14.55 (
% 107.13/14.55 ('#B') @ (
% 107.13/14.55 '#S') @
% 107.13/14.55 (
% 107.13/14.55 (
% 107.13/14.55 ('#B') @ (
% 107.13/14.55 (
% 107.13/14.55 ('#B') @ (
% 107.13/14.56 &))) @
% 107.13/14.56 (
% 107.13/14.56 (
% 107.13/14.56 ('#C') @ in)))))) @
% 107.13/14.56 (
% 107.13/14.56 (
% 107.13/14.56 ('#C') @ (
% 107.13/14.56 (
% 107.13/14.56 ('#B') @ (
% 107.13/14.56 '#C') @
% 107.13/14.56 (
% 107.13/14.56 (
% 107.13/14.56 ('#B') @ (
% 107.13/14.56 (
% 107.13/14.56 ('#B') @ (
% 107.13/14.56 =))) @
% 107.13/14.56 (
% 107.13/14.56 (
% 107.13/14.56 ('#C') @ binintersect)))))) @
% 107.13/14.56 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 107.13/14.56 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1347])).
% 107.13/14.56 thf(zip_derived_cl1361, plain,
% 107.13/14.56 (~ (((symdiffIneg2) =>
% 107.13/14.56 (((secondinupair) =>
% 107.13/14.56 (((setukpairIL) =>
% 107.13/14.56 (((setukpairIR) =>
% 107.13/14.56 (((kpairiskpair) =>
% 107.13/14.56 (((kpairp) =>
% 107.13/14.56 (((singletonsubset) =>
% 107.13/14.56 (((singletoninpowerset) =>
% 107.13/14.56 (((singletoninpowunion) =>
% 107.13/14.56 (((upairset2E) =>
% 107.13/14.56 (((upairsubunion) =>
% 107.13/14.56 (((upairinpowunion) =>
% 107.13/14.56 (((ubforcartprodlem1) =>
% 107.13/14.56 (((ubforcartprodlem2) =>
% 107.13/14.56 (((ubforcartprodlem3) =>
% 107.13/14.56 (((cartprodpairin) =>
% 107.13/14.56 (((cartprodmempair1) =>
% 107.13/14.56 (((cartprodmempair) =>
% 107.13/14.56 (((setunionE2) =>
% 107.13/14.56 (((setunionsingleton1) =>
% 107.13/14.56 (((setunionsingleton2) =>
% 107.13/14.56 (((setunionsingleton) =>
% 107.13/14.56 (((singletonprop) =>
% 107.13/14.56 (((ex1E1) =>
% 107.13/14.56 (((ex1I) =>
% 107.13/14.56 (((ex1I2) =>
% 107.13/14.56 (((singletonsuniq) =>
% 107.13/14.56 (((setukpairinjL1) =>
% 107.13/14.56 (((kfstsingleton) =>
% 107.13/14.56 (((theprop) =>
% 107.13/14.56 ((
% 107.13/14.56 (kfstpairEq) =>
% 107.13/14.56 ((
% 107.13/14.56 (cartprodfstin) =>
% 107.13/14.56 ((
% 107.13/14.56 (setukpairinjL2) =>
% 107.13/14.56 ((
% 107.13/14.56 (setukpairinjL) =>
% 107.13/14.56 ((
% 107.13/14.56 (setukpairinjR11) =>
% 107.13/14.56 ((
% 107.13/14.56 (setukpairinjR12) =>
% 107.13/14.56 ((
% 107.13/14.56 (setukpairinjR1) =>
% 107.13/14.56 ((
% 107.13/14.56 (upairequniteq) =>
% 107.13/14.56 ((
% 107.13/14.56 (setukpairinjR2) =>
% 107.13/14.56 ((
% 107.13/14.56 (setukpairinjR) =>
% 107.13/14.56 ((
% 107.13/14.56 (ksndsingleton) =>
% 107.13/14.56 ((
% 107.13/14.56 (ksndpairEq) =>
% 107.13/14.56 ((
% 107.13/14.56 (kpairsurjEq) =>
% 107.13/14.56 ((
% 107.13/14.56 (cartprodsndin) =>
% 107.13/14.56 ((
% 107.13/14.56 (cartprodpairmemEL) =>
% 107.13/14.56 ((
% 107.13/14.56 (cartprodpairmemER) =>
% 107.13/14.56 ((
% 107.13/14.56 (cartprodmempaircEq) =>
% 107.13/14.56 ((
% 107.13/14.56 (cartprodfstpairEq) =>
% 107.13/14.56 ((
% 107.13/14.56 (cartprodsndpairEq) =>
% 107.13/14.56 ((
% 107.13/14.56 (cartprodpairsurjEq) =>
% 107.13/14.56 ((
% 107.13/14.56 (dpsetconstrI) =>
% 107.13/14.56 ((
% 107.13/14.56 (dpsetconstrSub) =>
% 107.13/14.56 ((
% 107.13/14.56 (setOfPairsIsBReln) =>
% 107.13/14.56 ((
% 107.13/14.56 (dpsetconstrERa) =>
% 107.13/14.56 ((
% 107.13/14.56 (dpsetconstrEL1) =>
% 107.13/14.56 ((
% 107.13/14.56 (dpsetconstrEL2) =>
% 107.13/14.56 ((
% 107.13/14.56 (dpsetconstrER) =>
% 107.13/14.56 ((
% 107.13/14.56 (funcImageSingleton) =>
% 107.13/14.56 ((
% 107.13/14.56 (apProp) =>
% 107.13/14.56 ((
% 107.13/14.56 (app) =>
% 107.13/14.56 ((
% 107.13/14.56 (infuncsetfunc) =>
% 107.13/14.56 ((
% 107.13/14.56 (ap2p) =>
% 107.13/14.56 ((
% 107.13/14.56 (funcinfuncset) =>
% 107.13/14.56 ((
% 107.13/14.56 (lamProp) =>
% 107.13/14.56 ((
% 107.13/14.56 (lamp) =>
% 107.13/14.56 ((
% 107.13/14.56 (lam2p) =>
% 107.13/14.56 ((
% 107.13/14.56 (brelnall1) =>
% 107.13/14.56 ((
% 107.13/14.56 (brelnall2) =>
% 107.13/14.56 ((
% 107.13/14.56 (ex1E2) =>
% 107.13/14.56 ((
% 107.13/14.56 (funcGraphProp1) =>
% 107.13/14.56 ((
% 107.13/14.56 (funcGraphProp3) =>
% 107.13/14.56 ((
% 107.13/14.56 (funcGraphProp2) =>
% 107.13/14.56 ((
% 107.13/14.56 (funcextLem) =>
% 107.13/14.56 ((
% 107.13/14.56 (funcGraphProp4) =>
% 107.13/14.56 ((
% 107.13/14.56 (subbreln) =>
% 107.13/14.56 ((
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% 107.13/14.56 ((
% 107.13/14.56 (funcext) =>
% 107.13/14.56 ((
% 107.13/14.56 (funcext2) =>
% 107.13/14.56 ((
% 107.13/14.56 (ap2apEq1) =>
% 107.13/14.56 ((
% 107.13/14.56 (ap2apEq2) =>
% 107.13/14.56 ((
% 107.13/14.56 (beta1) =>
% 107.13/14.56 ((
% 107.13/14.56 (eta1) =>
% 107.13/14.56 ((
% 107.13/14.56 (lam2lamEq) =>
% 107.13/14.56 ((
% 107.13/14.56 (beta2) =>
% 107.13/14.56 ((
% 107.13/14.56 (eta2) =>
% 107.13/14.56 ((
% 107.13/14.56 (iffalseProp1) =>
% 107.13/14.56 ((
% 107.13/14.56 (iffalseProp2) =>
% 107.13/14.56 ((
% 107.13/14.56 (iftrueProp1) =>
% 107.13/14.56 ((
% 107.13/14.56 (iftrueProp2) =>
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% 107.13/14.56 ((
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% 107.13/14.56 ((
% 107.13/14.56 (theeq) =>
% 107.13/14.56 ((
% 107.13/14.56 (iftrue) =>
% 107.13/14.56 ((
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% 107.13/14.56 ((
% 107.13/14.56 (iftrueorfalse) =>
% 107.13/14.56 ((
% 107.13/14.56 (binintersectT_lem) =>
% 107.13/14.56 ((
% 107.13/14.56 (binunionT_lem) =>
% 107.13/14.56 ((
% 107.13/14.56 (powersetT_lem) =>
% 107.13/14.56 ((
% 107.13/14.56 (setminusT_lem) =>
% 107.13/14.56 ((
% 107.13/14.56 (complementT_lem) =>
% 107.13/14.56 ((
% 107.13/14.56 (setextT) =>
% 107.13/14.56 ((
% 107.13/14.56 (subsetTI) =>
% 107.13/14.56 ((
% 107.13/14.56 (powersetTI1) =>
% 107.13/14.56 ((
% 107.13/14.56 (powersetTE1) =>
% 107.13/14.56 ((
% 107.13/14.56 (complementTI1) =>
% 107.13/14.56 ((
% 107.13/14.56 (complementTE1) =>
% 107.13/14.56 ((
% 107.13/14.56 (binintersectTELcontra) =>
% 107.13/14.56 ((
% 107.13/14.56 (binintersectTERcontra) =>
% 107.13/14.56 ((
% 107.13/14.56 (contrasubsetT) =>
% 107.13/14.56 ((
% 107.13/14.56 (contrasubsetT1) =>
% 107.13/14.56 ((
% 107.13/14.56 (contrasubsetT2) =>
% 107.13/14.56 ((
% 107.13/14.56 (contrasubsetT3) =>
% 107.13/14.56 ((
% 107.13/14.56 (doubleComplementI1) =>
% 107.13/14.56 ((
% 107.13/14.56 (doubleComplementE1) =>
% 107.13/14.56 ((
% 107.13/14.56 (doubleComplementSub1) =>
% 107.13/14.56 ((
% 107.13/14.56 (doubleComplementSub2) =>
% 107.13/14.56 ((
% 107.13/14.56 (doubleComplementEq) =>
% 107.13/14.56 ((
% 107.13/14.56 (complementTnotintersectT) =>
% 107.13/14.56 ((
% 107.13/14.56 (complementImpComplementIntersect) =>
% 107.13/14.56 ((
% 107.13/14.56 (complementSubsetComplementIntersect) =>
% 107.13/14.56 ((
% 107.13/14.56 (complementInPowersetComplementIntersect) =>
% 107.13/14.56 ((
% 107.13/14.56 (contraSubsetComplement) =>
% 107.13/14.56 ((
% 107.13/14.56 (complementTcontraSubset) =>
% 107.13/14.56 ((
% 107.13/14.56 (binunionTILcontra) =>
% 107.13/14.56 ((
% 107.13/14.56 (binunionTIRcontra) =>
% 107.13/14.56 ((
% 107.13/14.56 (inIntersectImpInUnion) =>
% 107.13/14.56 ((
% 107.13/14.56 (inIntersectImpInUnion2) =>
% 107.13/14.56 ((
% 107.13/14.56 (inIntersectImpInIntersectUnions) =>
% 107.13/14.56 ((
% 107.13/14.56 (intersectInPowersetIntersectUnions) =>
% 107.13/14.56 ((
% 107.13/14.56 (inComplementUnionImpNotIn1) =>
% 107.13/14.56 ((
% 107.13/14.56 (inComplementUnionImpInComplement1) =>
% 107.13/14.56 ((
% 107.13/14.56 (binunionTE) =>
% 107.13/14.56 ((
% 107.13/14.56 (binunionTEcontra) =>
% 107.13/14.56 ((
% 107.13/14.56 (demorgan2a1) =>
% 107.13/14.56 ((
% 107.13/14.56 (complementUnionInPowersetComplement) =>
% 107.13/14.56 ((
% 107.13/14.56 (demorgan2a2) =>
% 107.13/14.56 ((
% 107.13/14.56 (demorgan1a) =>
% 107.13/14.56 ((
% 107.13/14.56 (demorgan1b) =>
% 107.13/14.56 ((
% 107.13/14.56 (demorgan1) =>
% 107.13/14.56 ((
% 107.13/14.56 (demorgan2a) =>
% 107.13/14.56 ((
% 107.13/14.56 (demorgan2b2) =>
% 107.13/14.56 ((
% 107.13/14.56 (demorgan2b) =>
% 107.13/14.56 ((
% 107.13/14.56 (demorgan2) =>
% 107.13/14.56 ((
% 107.13/14.56 (woz13rule0) =>
% 107.13/14.56 ((
% 107.13/14.56 (woz13rule1) =>
% 107.13/14.56 ((
% 107.13/14.56 (woz13rule2) =>
% 107.13/14.56 ((
% 107.13/14.56 (woz13rule3) =>
% 107.13/14.56 ((
% 107.13/14.56 (woz13rule4) =>
% 107.13/14.56 ((
% 107.13/14.56 (woz1_1) =>
% 107.13/14.56 ((
% 107.13/14.56 (woz1_2) =>
% 107.13/14.56 ((
% 107.13/14.56 (woz1_3) =>
% 107.13/14.56 ((
% 107.13/14.56 (woz1_4) =>
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% 107.13/14.56 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1354])).
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% 107.13/14.56 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1361])).
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% 107.13/14.56 (((theprop) =>
% 107.13/14.56 (((kfstpairEq) =>
% 107.13/14.56 (((cartprodfstin) =>
% 107.13/14.56 ((
% 107.13/14.56 (setukpairinjL2) =>
% 107.13/14.56 ((
% 107.13/14.56 (setukpairinjL) =>
% 107.13/14.56 ((
% 107.13/14.56 (setukpairinjR11) =>
% 107.13/14.56 ((
% 107.13/14.56 (setukpairinjR12) =>
% 107.13/14.56 ((
% 107.13/14.56 (setukpairinjR1) =>
% 107.13/14.56 ((
% 107.13/14.56 (upairequniteq) =>
% 107.13/14.56 ((
% 107.13/14.56 (setukpairinjR2) =>
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% 107.13/14.56 (setukpairinjR) =>
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% 107.13/14.56 ((
% 107.13/14.56 (ksndpairEq) =>
% 107.13/14.56 ((
% 107.13/14.56 (kpairsurjEq) =>
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% 107.13/14.56 (cartprodsndin) =>
% 107.13/14.56 ((
% 107.13/14.56 (cartprodpairmemEL) =>
% 107.13/14.56 ((
% 107.13/14.56 (cartprodpairmemER) =>
% 107.13/14.56 ((
% 107.13/14.56 (cartprodmempaircEq) =>
% 107.13/14.56 ((
% 107.13/14.56 (cartprodfstpairEq) =>
% 107.13/14.56 ((
% 107.13/14.56 (cartprodsndpairEq) =>
% 107.13/14.56 ((
% 107.13/14.56 (cartprodpairsurjEq) =>
% 107.13/14.56 ((
% 107.13/14.56 (dpsetconstrI) =>
% 107.13/14.56 ((
% 107.13/14.56 (dpsetconstrSub) =>
% 107.13/14.56 ((
% 107.13/14.56 (setOfPairsIsBReln) =>
% 107.13/14.56 ((
% 107.13/14.56 (dpsetconstrERa) =>
% 107.13/14.56 ((
% 107.13/14.56 (dpsetconstrEL1) =>
% 107.13/14.56 ((
% 107.13/14.56 (dpsetconstrEL2) =>
% 107.13/14.56 ((
% 107.13/14.56 (dpsetconstrER) =>
% 107.13/14.56 ((
% 107.13/14.56 (funcImageSingleton) =>
% 107.13/14.56 ((
% 107.13/14.56 (apProp) =>
% 107.13/14.56 ((
% 107.13/14.56 (app) =>
% 107.13/14.56 ((
% 107.13/14.56 (infuncsetfunc) =>
% 107.13/14.56 ((
% 107.13/14.56 (ap2p) =>
% 107.13/14.56 ((
% 107.13/14.56 (funcinfuncset) =>
% 107.13/14.56 ((
% 107.13/14.56 (lamProp) =>
% 107.13/14.56 ((
% 107.13/14.56 (lamp) =>
% 107.13/14.56 ((
% 107.13/14.56 (lam2p) =>
% 107.13/14.56 ((
% 107.13/14.56 (brelnall1) =>
% 107.13/14.56 ((
% 107.13/14.56 (brelnall2) =>
% 107.13/14.56 ((
% 107.13/14.56 (ex1E2) =>
% 107.13/14.56 ((
% 107.13/14.56 (funcGraphProp1) =>
% 107.13/14.56 ((
% 107.13/14.56 (funcGraphProp3) =>
% 107.13/14.56 ((
% 107.13/14.56 (funcGraphProp2) =>
% 107.13/14.56 ((
% 107.13/14.56 (funcextLem) =>
% 107.13/14.56 ((
% 107.13/14.56 (funcGraphProp4) =>
% 107.13/14.56 ((
% 107.13/14.56 (subbreln) =>
% 107.13/14.56 ((
% 107.13/14.56 (eqbreln) =>
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% 107.13/14.56 (funcext) =>
% 107.13/14.56 ((
% 107.13/14.56 (funcext2) =>
% 107.13/14.56 ((
% 107.13/14.56 (ap2apEq1) =>
% 107.13/14.56 ((
% 107.13/14.56 (ap2apEq2) =>
% 107.13/14.56 ((
% 107.13/14.56 (beta1) =>
% 107.13/14.56 ((
% 107.13/14.56 (eta1) =>
% 107.13/14.56 ((
% 107.13/14.56 (lam2lamEq) =>
% 107.13/14.56 ((
% 107.13/14.56 (beta2) =>
% 107.13/14.56 ((
% 107.13/14.56 (eta2) =>
% 107.13/14.56 ((
% 107.13/14.56 (iffalseProp1) =>
% 107.13/14.56 ((
% 107.13/14.56 (iffalseProp2) =>
% 107.13/14.56 ((
% 107.13/14.56 (iftrueProp1) =>
% 107.13/14.56 ((
% 107.13/14.56 (iftrueProp2) =>
% 107.13/14.56 ((
% 107.13/14.56 (ifSingleton) =>
% 107.13/14.56 ((
% 107.13/14.56 (ifp) =>
% 107.13/14.56 ((
% 107.13/14.56 (theeq) =>
% 107.13/14.56 ((
% 107.13/14.56 (iftrue) =>
% 107.13/14.56 ((
% 107.13/14.56 (iffalse) =>
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% 107.13/14.56 ((
% 107.13/14.56 (binunionT_lem) =>
% 107.13/14.56 ((
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% 107.13/14.56 ((
% 107.13/14.56 (complementT_lem) =>
% 107.13/14.56 ((
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% 107.13/14.56 ((
% 107.13/14.56 (powersetTI1) =>
% 107.13/14.56 ((
% 107.13/14.56 (powersetTE1) =>
% 107.13/14.56 ((
% 107.13/14.56 (complementTI1) =>
% 107.13/14.56 ((
% 107.13/14.56 (complementTE1) =>
% 107.13/14.56 ((
% 107.13/14.56 (binintersectTELcontra) =>
% 107.13/14.56 ((
% 107.13/14.56 (binintersectTERcontra) =>
% 107.13/14.56 ((
% 107.13/14.56 (contrasubsetT) =>
% 107.13/14.56 ((
% 107.13/14.56 (contrasubsetT1) =>
% 107.13/14.56 ((
% 107.13/14.56 (contrasubsetT2) =>
% 107.13/14.56 ((
% 107.13/14.56 (contrasubsetT3) =>
% 107.13/14.56 ((
% 107.13/14.56 (doubleComplementI1) =>
% 107.13/14.56 ((
% 107.13/14.56 (doubleComplementE1) =>
% 107.13/14.56 ((
% 107.13/14.56 (doubleComplementSub1) =>
% 107.13/14.56 ((
% 107.13/14.56 (doubleComplementSub2) =>
% 107.13/14.56 ((
% 107.13/14.56 (doubleComplementEq) =>
% 107.13/14.56 ((
% 107.13/14.56 (complementTnotintersectT) =>
% 107.13/14.56 ((
% 107.13/14.56 (complementImpComplementIntersect) =>
% 107.13/14.56 ((
% 107.13/14.56 (complementSubsetComplementIntersect) =>
% 107.13/14.56 ((
% 107.13/14.56 (complementInPowersetComplementIntersect) =>
% 107.13/14.56 ((
% 107.13/14.56 (contraSubsetComplement) =>
% 107.13/14.56 ((
% 107.13/14.56 (complementTcontraSubset) =>
% 107.13/14.56 ((
% 107.13/14.56 (binunionTILcontra) =>
% 107.13/14.56 ((
% 107.13/14.56 (binunionTIRcontra) =>
% 107.13/14.56 ((
% 107.13/14.56 (inIntersectImpInUnion) =>
% 107.13/14.56 ((
% 107.13/14.56 (inIntersectImpInUnion2) =>
% 107.13/14.56 ((
% 107.13/14.56 (inIntersectImpInIntersectUnions) =>
% 107.13/14.56 ((
% 107.13/14.56 (intersectInPowersetIntersectUnions) =>
% 107.13/14.56 ((
% 107.13/14.56 (inComplementUnionImpNotIn1) =>
% 107.13/14.56 ((
% 107.13/14.56 (inComplementUnionImpInComplement1) =>
% 107.13/14.56 ((
% 107.13/14.56 (binunionTE) =>
% 107.13/14.56 ((
% 107.13/14.56 (binunionTEcontra) =>
% 107.13/14.56 ((
% 107.13/14.56 (demorgan2a1) =>
% 107.13/14.56 ((
% 107.13/14.56 (complementUnionInPowersetComplement) =>
% 107.13/14.56 ((
% 107.13/14.56 (demorgan2a2) =>
% 107.13/14.56 ((
% 107.13/14.56 (demorgan1a) =>
% 107.13/14.56 ((
% 107.13/14.56 (demorgan1b) =>
% 107.13/14.56 ((
% 107.13/14.56 (demorgan1) =>
% 107.13/14.56 ((
% 107.13/14.56 (demorgan2a) =>
% 107.13/14.56 ((
% 107.13/14.56 (demorgan2b2) =>
% 107.13/14.56 ((
% 107.13/14.56 (demorgan2b) =>
% 107.13/14.56 ((
% 107.13/14.56 (demorgan2) =>
% 107.13/14.56 ((
% 107.13/14.56 (woz13rule0) =>
% 107.13/14.56 ((
% 107.13/14.56 (woz13rule1) =>
% 107.13/14.56 ((
% 107.13/14.56 (woz13rule2) =>
% 107.13/14.56 ((
% 107.13/14.56 (woz13rule3) =>
% 107.13/14.56 ((
% 107.13/14.56 (woz13rule4) =>
% 107.13/14.56 ((
% 107.13/14.56 (woz1_1) =>
% 107.13/14.56 ((
% 107.13/14.56 (woz1_2) =>
% 107.13/14.56 ((
% 107.13/14.56 (woz1_3) =>
% 107.13/14.56 ((
% 107.13/14.56 (woz1_4) =>
% 107.13/14.56 ((
% 107.13/14.56 (woz1_5) =>
% 107.13/14.56 ((
% 107.13/14.56 (breln1all2) =>
% 107.13/14.56 ((
% 107.13/14.56 (breln1SetBreln1) =>
% 107.13/14.56 ((
% 107.13/14.56 (choice2fnsingleton) =>
% 107.13/14.56 ((
% 107.13/14.56 (setOfPairsIsBReln1) =>
% 107.13/14.56 ((
% 107.13/14.56 (breln1all1) =>
% 107.13/14.56 ((
% 107.13/14.56 (subbreln1) =>
% 107.13/14.56 ((
% 107.13/14.56 (eqbreln1) =>
% 107.13/14.56 ((
% 107.13/14.56 (breln1invprop) =>
% 107.13/14.56 ((
% 107.13/14.56 (breln1invI) =>
% 107.13/14.56 ((
% 107.13/14.56 (breln1invE) =>
% 107.13/14.56 ((
% 107.13/14.56 (breln1compprop) =>
% 107.13/14.56 ((
% 107.13/14.56 (breln1compI) =>
% 107.13/14.56 ((
% 107.13/14.56 (breln1compE) =>
% 107.13/14.56 ((
% 107.13/14.56 (breln1compEex) =>
% 107.13/14.56 ((
% 107.13/14.56 (breln1unionprop) =>
% 107.13/14.56 ((
% 107.13/14.56 (breln1unionIL) =>
% 107.13/14.56 ((
% 107.13/14.56 (breln1unionIR) =>
% 107.13/14.56 ((
% 107.13/14.56 (breln1unionI) =>
% 107.13/14.56 ((
% 107.13/14.56 (breln1unionE) =>
% 107.13/14.56 ((
% 107.13/14.56 (breln1unionEcases) =>
% 107.13/14.56 ((
% 107.13/14.56 (breln1unionCommutes) =>
% 107.13/14.56 ((
% 107.13/14.56 (woz2Ex) =>
% 107.13/14.56 ((
% 107.13/14.56 (woz2W) =>
% 107.13/14.56 ((
% 107.13/14.56 (woz2A) =>
% 107.13/14.56 ((
% 107.13/14.56 (woz2B) =>
% 107.13/14.56 ((
% 107.13/14.56 (image1Ex) =>
% 107.13/14.56 ((
% 107.13/14.56 (image1Ex1) =>
% 107.13/14.56 ((
% 107.13/14.56 (image1Equiv) =>
% 107.13/14.56 ((
% 107.13/14.56 (image1E) =>
% 107.13/14.56 ((
% 107.13/14.56 (image1I) =>
% 107.13/14.56 ((
% 107.13/14.56 (injFuncInInjFuncSet) =>
% 107.13/14.56 ((
% 107.13/14.56 (injFuncSetFuncIn) =>
% 107.13/14.56 ((
% 107.13/14.56 (injFuncSetFuncInj) =>
% 107.13/14.56 ((
% 107.13/14.56 (surjFuncSetFuncIn) =>
% 107.13/14.56 ((
% 107.13/14.56 (surjFuncSetFuncSurj) =>
% 107.13/14.56 ((
% 107.13/14.56 (leftInvIsSurj) =>
% 107.13/14.56 ((
% 107.13/14.56 (surjCantorThm) =>
% 107.13/14.56 ((
% 107.13/14.56 (!!) @ (
% 107.13/14.56 (('#S') @ (
% 107.13/14.56 (
% 107.13/14.56 ('#B') @ (
% 107.13/14.56 =>) @
% 107.13/14.56 nonempty)) @
% 107.13/14.56 (
% 107.13/14.56 (
% 107.13/14.56 ('#B') @ (
% 107.13/14.56 ??) @
% 107.13/14.56 (
% 107.13/14.56 (
% 107.13/14.56 ('#S') @ (
% 107.13/14.56 (
% 107.13/14.56 ('#B') @ (
% 107.13/14.56 '#S') @
% 107.13/14.56 (
% 107.13/14.56 (
% 107.13/14.56 ('#B') @ (
% 107.13/14.56 (
% 107.13/14.56 ('#B') @ (
% 107.13/14.56 &))) @
% 107.13/14.56 (
% 107.13/14.56 (
% 107.13/14.56 ('#C') @ in)))))) @
% 107.13/14.56 (
% 107.13/14.56 (
% 107.13/14.56 ('#C') @ (
% 107.13/14.56 (
% 107.13/14.56 ('#B') @ (
% 107.13/14.56 '#C') @
% 107.13/14.56 (
% 107.13/14.56 (
% 107.13/14.56 ('#B') @ (
% 107.13/14.56 (
% 107.13/14.56 ('#B') @ (
% 107.13/14.56 =))) @
% 107.13/14.56 (
% 107.13/14.56 (
% 107.13/14.56 ('#C') @ binintersect)))))) @
% 107.13/14.56 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 107.13/14.56 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1369])).
% 107.13/14.56 thf(zip_derived_cl1386, plain,
% 107.13/14.56 (~ (((setukpairIR) =>
% 107.13/14.56 (((kpairiskpair) =>
% 107.13/14.56 (((kpairp) =>
% 107.13/14.56 (((singletonsubset) =>
% 107.13/14.56 (((singletoninpowerset) =>
% 107.13/14.56 (((singletoninpowunion) =>
% 107.13/14.56 (((upairset2E) =>
% 107.13/14.56 (((upairsubunion) =>
% 107.13/14.56 (((upairinpowunion) =>
% 107.13/14.56 (((ubforcartprodlem1) =>
% 107.13/14.56 (((ubforcartprodlem2) =>
% 107.13/14.56 (((ubforcartprodlem3) =>
% 107.13/14.56 (((cartprodpairin) =>
% 107.13/14.56 (((cartprodmempair1) =>
% 107.13/14.56 (((cartprodmempair) =>
% 107.13/14.56 (((setunionE2) =>
% 107.13/14.56 (((setunionsingleton1) =>
% 107.13/14.56 (((setunionsingleton2) =>
% 107.13/14.56 (((setunionsingleton) =>
% 107.13/14.56 (((singletonprop) =>
% 107.13/14.56 (((ex1E1) =>
% 107.13/14.56 (((ex1I) =>
% 107.13/14.56 (((ex1I2) =>
% 107.13/14.56 (((singletonsuniq) =>
% 107.13/14.56 (((setukpairinjL1) =>
% 107.13/14.56 (((kfstsingleton) =>
% 107.13/14.56 (((theprop) =>
% 107.13/14.56 (((kfstpairEq) =>
% 107.13/14.56 (((cartprodfstin) =>
% 107.13/14.56 (((setukpairinjL2) =>
% 107.13/14.56 ((
% 107.13/14.56 (setukpairinjL) =>
% 107.13/14.56 ((
% 107.13/14.56 (setukpairinjR11) =>
% 107.13/14.56 ((
% 107.13/14.56 (setukpairinjR12) =>
% 107.13/14.56 ((
% 107.13/14.56 (setukpairinjR1) =>
% 107.13/14.56 ((
% 107.13/14.56 (upairequniteq) =>
% 107.13/14.56 ((
% 107.13/14.56 (setukpairinjR2) =>
% 107.13/14.56 ((
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% 107.13/14.56 ((
% 107.13/14.56 (ksndsingleton) =>
% 107.13/14.56 ((
% 107.13/14.56 (ksndpairEq) =>
% 107.13/14.56 ((
% 107.13/14.56 (kpairsurjEq) =>
% 107.13/14.56 ((
% 107.13/14.56 (cartprodsndin) =>
% 107.13/14.56 ((
% 107.13/14.56 (cartprodpairmemEL) =>
% 107.13/14.56 ((
% 107.13/14.56 (cartprodpairmemER) =>
% 107.13/14.56 ((
% 107.13/14.56 (cartprodmempaircEq) =>
% 107.13/14.56 ((
% 107.13/14.56 (cartprodfstpairEq) =>
% 107.13/14.56 ((
% 107.13/14.56 (cartprodsndpairEq) =>
% 107.13/14.56 ((
% 107.13/14.56 (cartprodpairsurjEq) =>
% 107.13/14.56 ((
% 107.13/14.56 (dpsetconstrI) =>
% 107.13/14.56 ((
% 107.13/14.56 (dpsetconstrSub) =>
% 107.13/14.56 ((
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% 107.13/14.56 ((
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% 107.13/14.56 ((
% 107.13/14.56 (dpsetconstrEL2) =>
% 107.13/14.56 ((
% 107.13/14.56 (dpsetconstrER) =>
% 107.13/14.56 ((
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% 107.13/14.56 ((
% 107.13/14.56 (apProp) =>
% 107.13/14.56 ((
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% 107.13/14.56 ((
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% 107.13/14.56 ((
% 107.13/14.56 (ap2p) =>
% 107.13/14.56 ((
% 107.13/14.56 (funcinfuncset) =>
% 107.13/14.56 ((
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% 107.13/14.56 ((
% 107.13/14.56 (lamp) =>
% 107.13/14.56 ((
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% 107.13/14.56 ((
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% 107.13/14.56 ((
% 107.13/14.56 (brelnall2) =>
% 107.13/14.56 ((
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% 107.13/14.56 ((
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% 107.13/14.56 ((
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% 107.13/14.56 ((
% 107.13/14.56 (funcGraphProp2) =>
% 107.13/14.56 ((
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% 107.13/14.56 ((
% 107.13/14.56 (funcGraphProp4) =>
% 107.13/14.56 ((
% 107.13/14.56 (subbreln) =>
% 107.13/14.56 ((
% 107.13/14.56 (eqbreln) =>
% 107.13/14.56 ((
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% 107.13/14.56 ((
% 107.13/14.56 (funcext2) =>
% 107.13/14.56 ((
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% 107.13/14.56 ((
% 107.13/14.56 (ap2apEq2) =>
% 107.13/14.56 ((
% 107.13/14.56 (beta1) =>
% 107.13/14.56 ((
% 107.13/14.56 (eta1) =>
% 107.13/14.56 ((
% 107.13/14.56 (lam2lamEq) =>
% 107.13/14.56 ((
% 107.13/14.56 (beta2) =>
% 107.13/14.56 ((
% 107.13/14.56 (eta2) =>
% 107.13/14.56 ((
% 107.13/14.56 (iffalseProp1) =>
% 107.13/14.56 ((
% 107.13/14.56 (iffalseProp2) =>
% 107.13/14.56 ((
% 107.13/14.56 (iftrueProp1) =>
% 107.13/14.56 ((
% 107.13/14.56 (iftrueProp2) =>
% 107.13/14.56 ((
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% 107.13/14.56 ((
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% 107.13/14.56 ((
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% 107.13/14.56 ((
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% 107.13/14.56 ((
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% 107.13/14.56 (binintersectT_lem) =>
% 107.13/14.56 ((
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% 107.13/14.56 ((
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% 107.13/14.56 ((
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% 107.13/14.56 ((
% 107.13/14.56 (complementT_lem) =>
% 107.13/14.56 ((
% 107.13/14.56 (setextT) =>
% 107.13/14.56 ((
% 107.13/14.56 (subsetTI) =>
% 107.13/14.56 ((
% 107.13/14.56 (powersetTI1) =>
% 107.13/14.56 ((
% 107.13/14.56 (powersetTE1) =>
% 107.13/14.56 ((
% 107.13/14.56 (complementTI1) =>
% 107.13/14.56 ((
% 107.13/14.56 (complementTE1) =>
% 107.13/14.56 ((
% 107.13/14.56 (binintersectTELcontra) =>
% 107.13/14.56 ((
% 107.13/14.56 (binintersectTERcontra) =>
% 107.13/14.56 ((
% 107.13/14.56 (contrasubsetT) =>
% 107.13/14.56 ((
% 107.13/14.56 (contrasubsetT1) =>
% 107.13/14.56 ((
% 107.13/14.56 (contrasubsetT2) =>
% 107.13/14.56 ((
% 107.13/14.56 (contrasubsetT3) =>
% 107.13/14.56 ((
% 107.13/14.56 (doubleComplementI1) =>
% 107.13/14.56 ((
% 107.13/14.56 (doubleComplementE1) =>
% 107.13/14.56 ((
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% 107.13/14.56 ((
% 107.13/14.56 (doubleComplementSub2) =>
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% 107.13/14.56 (doubleComplementEq) =>
% 107.13/14.56 ((
% 107.13/14.56 (complementTnotintersectT) =>
% 107.13/14.56 ((
% 107.13/14.56 (complementImpComplementIntersect) =>
% 107.13/14.56 ((
% 107.13/14.56 (complementSubsetComplementIntersect) =>
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% 107.13/14.56 (complementInPowersetComplementIntersect) =>
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% 107.13/14.56 ((
% 107.13/14.56 (inIntersectImpInUnion2) =>
% 107.13/14.56 ((
% 107.13/14.56 (inIntersectImpInIntersectUnions) =>
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% 107.13/14.56 (intersectInPowersetIntersectUnions) =>
% 107.13/14.56 ((
% 107.13/14.56 (inComplementUnionImpNotIn1) =>
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% 107.13/14.56 (inComplementUnionImpInComplement1) =>
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% 107.13/14.56 ((
% 107.13/14.56 (complementUnionInPowersetComplement) =>
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% 107.13/14.56 ((
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% 107.13/14.56 ((
% 107.13/14.56 (demorgan1b) =>
% 107.13/14.56 ((
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% 107.13/14.56 ((
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% 107.13/14.56 ((
% 107.13/14.56 (demorgan2b2) =>
% 107.13/14.56 ((
% 107.13/14.56 (demorgan2b) =>
% 107.13/14.56 ((
% 107.13/14.56 (demorgan2) =>
% 107.13/14.56 ((
% 107.13/14.56 (woz13rule0) =>
% 107.13/14.56 ((
% 107.13/14.56 (woz13rule1) =>
% 107.13/14.56 ((
% 107.13/14.56 (woz13rule2) =>
% 107.13/14.56 ((
% 107.13/14.56 (woz13rule3) =>
% 107.13/14.56 ((
% 107.13/14.56 (woz13rule4) =>
% 107.13/14.56 ((
% 107.13/14.56 (woz1_1) =>
% 107.13/14.56 ((
% 107.13/14.56 (woz1_2) =>
% 107.13/14.56 ((
% 107.13/14.56 (woz1_3) =>
% 107.13/14.56 ((
% 107.13/14.56 (woz1_4) =>
% 107.13/14.56 ((
% 107.13/14.56 (woz1_5) =>
% 107.13/14.56 ((
% 107.13/14.56 (breln1all2) =>
% 107.13/14.56 ((
% 107.13/14.56 (breln1SetBreln1) =>
% 107.13/14.56 ((
% 107.13/14.56 (choice2fnsingleton) =>
% 107.13/14.56 ((
% 107.13/14.56 (setOfPairsIsBReln1) =>
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% 107.13/14.56 (breln1all1) =>
% 107.13/14.56 ((
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% 107.13/14.56 ((
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% 107.13/14.56 ((
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% 107.13/14.56 ((
% 107.13/14.56 (breln1invE) =>
% 107.13/14.56 ((
% 107.13/14.56 (breln1compprop) =>
% 107.13/14.56 ((
% 107.13/14.56 (breln1compI) =>
% 107.13/14.56 ((
% 107.13/14.56 (breln1compE) =>
% 107.13/14.56 ((
% 107.13/14.56 (breln1compEex) =>
% 107.13/14.56 ((
% 107.13/14.56 (breln1unionprop) =>
% 107.13/14.56 ((
% 107.13/14.56 (breln1unionIL) =>
% 107.13/14.56 ((
% 107.13/14.56 (breln1unionIR) =>
% 107.13/14.56 ((
% 107.13/14.56 (breln1unionI) =>
% 107.13/14.56 ((
% 107.13/14.56 (breln1unionE) =>
% 107.13/14.56 ((
% 107.13/14.56 (breln1unionEcases) =>
% 107.13/14.56 ((
% 107.13/14.56 (breln1unionCommutes) =>
% 107.13/14.56 ((
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% 107.13/14.56 ((
% 107.13/14.56 (woz2W) =>
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% 107.13/14.56 ((
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% 107.13/14.56 ((
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% 107.13/14.56 ((
% 107.13/14.56 (image1E) =>
% 107.13/14.56 ((
% 107.13/14.56 (image1I) =>
% 107.13/14.56 ((
% 107.13/14.56 (injFuncInInjFuncSet) =>
% 107.13/14.56 ((
% 107.13/14.56 (injFuncSetFuncIn) =>
% 107.13/14.56 ((
% 107.13/14.56 (injFuncSetFuncInj) =>
% 107.13/14.56 ((
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% 107.13/14.56 ((
% 107.13/14.56 (surjFuncSetFuncSurj) =>
% 107.13/14.56 ((
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% 107.13/14.56 (surjCantorThm) =>
% 107.13/14.56 ((
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% 107.13/14.56 (
% 107.13/14.56 (
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% 107.13/14.56 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1377])).
% 107.13/14.56 thf(zip_derived_cl1396, plain,
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% 107.13/14.56 (((singletoninpowunion) =>
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% 107.13/14.56 (((upairinpowunion) =>
% 107.13/14.56 (((ubforcartprodlem1) =>
% 107.13/14.56 (((ubforcartprodlem2) =>
% 107.13/14.56 (((ubforcartprodlem3) =>
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% 107.13/14.56 (((cartprodmempair1) =>
% 107.13/14.56 (((cartprodmempair) =>
% 107.13/14.56 (((setunionE2) =>
% 107.13/14.56 (((setunionsingleton1) =>
% 107.13/14.56 (((setunionsingleton2) =>
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% 107.13/14.56 ((
% 107.13/14.56 (setukpairinjR12) =>
% 107.13/14.56 ((
% 107.13/14.56 (setukpairinjR1) =>
% 107.13/14.56 ((
% 107.13/14.56 (upairequniteq) =>
% 107.13/14.56 ((
% 107.13/14.56 (setukpairinjR2) =>
% 107.13/14.56 ((
% 107.13/14.56 (setukpairinjR) =>
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% 107.13/14.56 ((
% 107.13/14.56 (ksndpairEq) =>
% 107.13/14.56 ((
% 107.13/14.56 (kpairsurjEq) =>
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% 107.13/14.56 (cartprodsndin) =>
% 107.13/14.56 ((
% 107.13/14.56 (cartprodpairmemEL) =>
% 107.13/14.56 ((
% 107.13/14.56 (cartprodpairmemER) =>
% 107.13/14.56 ((
% 107.13/14.56 (cartprodmempaircEq) =>
% 107.13/14.56 ((
% 107.13/14.56 (cartprodfstpairEq) =>
% 107.13/14.56 ((
% 107.13/14.56 (cartprodsndpairEq) =>
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% 107.13/14.56 (cartprodpairsurjEq) =>
% 107.13/14.56 ((
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% 107.13/14.56 ((
% 107.13/14.56 (dpsetconstrSub) =>
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% 107.13/14.56 ((
% 107.13/14.56 (app) =>
% 107.13/14.56 ((
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% 107.13/14.56 ((
% 107.13/14.56 (ap2p) =>
% 107.13/14.56 ((
% 107.13/14.56 (funcinfuncset) =>
% 107.13/14.56 ((
% 107.13/14.56 (lamProp) =>
% 107.13/14.56 ((
% 107.13/14.56 (lamp) =>
% 107.13/14.56 ((
% 107.13/14.56 (lam2p) =>
% 107.13/14.56 ((
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% 107.13/14.56 ((
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% 107.13/14.56 ((
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% 107.13/14.56 ((
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% 107.13/14.56 ((
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% 107.13/14.56 ((
% 107.13/14.56 (setextT) =>
% 107.13/14.56 ((
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% 107.13/14.56 ((
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% 107.13/14.56 ((
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% 107.13/14.56 ((
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% 107.13/14.56 ((
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% 107.13/14.56 ((
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% 107.13/14.56 ((
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% 107.13/14.56 ((
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% 107.13/14.56 ((
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% 107.13/14.56 ((
% 107.13/14.56 (doubleComplementI1) =>
% 107.13/14.56 ((
% 107.13/14.56 (doubleComplementE1) =>
% 107.13/14.56 ((
% 107.13/14.56 (doubleComplementSub1) =>
% 107.13/14.56 ((
% 107.13/14.56 (doubleComplementSub2) =>
% 107.13/14.56 ((
% 107.13/14.56 (doubleComplementEq) =>
% 107.13/14.56 ((
% 107.13/14.56 (complementTnotintersectT) =>
% 107.13/14.56 ((
% 107.13/14.56 (complementImpComplementIntersect) =>
% 107.13/14.56 ((
% 107.13/14.56 (complementSubsetComplementIntersect) =>
% 107.13/14.56 ((
% 107.13/14.56 (complementInPowersetComplementIntersect) =>
% 107.13/14.56 ((
% 107.13/14.56 (contraSubsetComplement) =>
% 107.13/14.56 ((
% 107.13/14.56 (complementTcontraSubset) =>
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% 107.13/14.56 ((
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% 107.13/14.56 ((
% 107.13/14.56 (inIntersectImpInUnion2) =>
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% 107.13/14.56 (intersectInPowersetIntersectUnions) =>
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% 107.13/14.56 ((
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% 107.13/14.56 ((
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% 107.13/14.56 ((
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% 107.13/14.56 ((
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% 107.13/14.56 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1386])).
% 107.13/14.56 thf(zip_derived_cl1407, plain,
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% 107.13/14.56 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1396])).
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% 107.13/14.56 ((
% 107.13/14.56 (ap2apEq2) =>
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% 107.13/14.56 (beta1) =>
% 107.13/14.56 ((
% 107.13/14.56 (eta1) =>
% 107.13/14.56 ((
% 107.13/14.56 (lam2lamEq) =>
% 107.13/14.56 ((
% 107.13/14.56 (beta2) =>
% 107.13/14.56 ((
% 107.13/14.56 (eta2) =>
% 107.13/14.56 ((
% 107.13/14.56 (iffalseProp1) =>
% 107.13/14.56 ((
% 107.13/14.56 (iffalseProp2) =>
% 107.13/14.56 ((
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% 107.13/14.56 (iftrueProp2) =>
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% 107.13/14.56 ((
% 107.13/14.56 (ifp) =>
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% 107.13/14.56 ((
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% 107.13/14.56 ((
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% 107.13/14.56 ((
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% 107.13/14.56 ((
% 107.13/14.56 (complementTE1) =>
% 107.13/14.56 ((
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% 107.13/14.56 ((
% 107.13/14.56 (binintersectTERcontra) =>
% 107.13/14.56 ((
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% 107.13/14.56 ((
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% 107.13/14.56 ((
% 107.13/14.56 (contrasubsetT2) =>
% 107.13/14.56 ((
% 107.13/14.56 (contrasubsetT3) =>
% 107.13/14.56 ((
% 107.13/14.56 (doubleComplementI1) =>
% 107.13/14.56 ((
% 107.13/14.56 (doubleComplementE1) =>
% 107.13/14.56 ((
% 107.13/14.56 (doubleComplementSub1) =>
% 107.13/14.56 ((
% 107.13/14.56 (doubleComplementSub2) =>
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% 107.13/14.56 (doubleComplementEq) =>
% 107.13/14.56 ((
% 107.13/14.56 (complementTnotintersectT) =>
% 107.13/14.56 ((
% 107.13/14.56 (complementImpComplementIntersect) =>
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% 107.13/14.56 (inIntersectImpInUnion) =>
% 107.13/14.56 ((
% 107.13/14.56 (inIntersectImpInUnion2) =>
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% 107.13/14.56 (inIntersectImpInIntersectUnions) =>
% 107.13/14.56 ((
% 107.13/14.56 (intersectInPowersetIntersectUnions) =>
% 107.13/14.56 ((
% 107.13/14.56 (inComplementUnionImpNotIn1) =>
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% 107.13/14.56 (inComplementUnionImpInComplement1) =>
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% 107.13/14.56 ((
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% 107.13/14.56 ((
% 107.13/14.56 (demorgan1b) =>
% 107.13/14.56 ((
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% 107.13/14.56 ((
% 107.13/14.56 (demorgan2a) =>
% 107.13/14.56 ((
% 107.13/14.56 (demorgan2b2) =>
% 107.13/14.56 ((
% 107.13/14.56 (demorgan2b) =>
% 107.13/14.56 ((
% 107.13/14.56 (demorgan2) =>
% 107.13/14.56 ((
% 107.13/14.56 (woz13rule0) =>
% 107.13/14.56 ((
% 107.13/14.56 (woz13rule1) =>
% 107.13/14.56 ((
% 107.13/14.56 (woz13rule2) =>
% 107.13/14.56 ((
% 107.13/14.56 (woz13rule3) =>
% 107.13/14.56 ((
% 107.13/14.56 (woz13rule4) =>
% 107.13/14.56 ((
% 107.13/14.56 (woz1_1) =>
% 107.13/14.56 ((
% 107.13/14.56 (woz1_2) =>
% 107.13/14.56 ((
% 107.13/14.56 (woz1_3) =>
% 107.13/14.56 ((
% 107.13/14.56 (woz1_4) =>
% 107.13/14.56 ((
% 107.13/14.56 (woz1_5) =>
% 107.13/14.56 ((
% 107.13/14.56 (breln1all2) =>
% 107.13/14.56 ((
% 107.13/14.56 (breln1SetBreln1) =>
% 107.13/14.56 ((
% 107.13/14.56 (choice2fnsingleton) =>
% 107.13/14.56 ((
% 107.13/14.56 (setOfPairsIsBReln1) =>
% 107.13/14.56 ((
% 107.13/14.56 (breln1all1) =>
% 107.13/14.56 ((
% 107.13/14.56 (subbreln1) =>
% 107.13/14.56 ((
% 107.13/14.56 (eqbreln1) =>
% 107.13/14.56 ((
% 107.13/14.56 (breln1invprop) =>
% 107.13/14.56 ((
% 107.13/14.56 (breln1invI) =>
% 107.13/14.56 ((
% 107.13/14.56 (breln1invE) =>
% 107.13/14.56 ((
% 107.13/14.56 (breln1compprop) =>
% 107.13/14.56 ((
% 107.13/14.56 (breln1compI) =>
% 107.13/14.56 ((
% 107.13/14.56 (breln1compE) =>
% 107.13/14.56 ((
% 107.13/14.56 (breln1compEex) =>
% 107.13/14.56 ((
% 107.13/14.56 (breln1unionprop) =>
% 107.13/14.56 ((
% 107.13/14.56 (breln1unionIL) =>
% 107.13/14.56 ((
% 107.13/14.56 (breln1unionIR) =>
% 107.13/14.56 ((
% 107.13/14.56 (breln1unionI) =>
% 107.13/14.56 ((
% 107.13/14.56 (breln1unionE) =>
% 107.13/14.56 ((
% 107.13/14.56 (breln1unionEcases) =>
% 107.13/14.56 ((
% 107.13/14.56 (breln1unionCommutes) =>
% 107.13/14.56 ((
% 107.13/14.56 (woz2Ex) =>
% 107.13/14.56 ((
% 107.13/14.56 (woz2W) =>
% 107.13/14.56 ((
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% 107.13/14.56 ((
% 107.13/14.56 (woz2B) =>
% 107.13/14.56 ((
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% 107.13/14.56 ((
% 107.13/14.56 (image1Ex1) =>
% 107.13/14.56 ((
% 107.13/14.56 (image1Equiv) =>
% 107.13/14.56 ((
% 107.13/14.56 (image1E) =>
% 107.13/14.56 ((
% 107.13/14.56 (image1I) =>
% 107.13/14.56 ((
% 107.13/14.56 (injFuncInInjFuncSet) =>
% 107.13/14.56 ((
% 107.13/14.56 (injFuncSetFuncIn) =>
% 107.13/14.56 ((
% 107.13/14.56 (injFuncSetFuncInj) =>
% 107.13/14.56 ((
% 107.13/14.56 (surjFuncSetFuncIn) =>
% 107.13/14.56 ((
% 107.13/14.56 (surjFuncSetFuncSurj) =>
% 107.13/14.56 ((
% 107.13/14.56 (leftInvIsSurj) =>
% 107.13/14.56 ((
% 107.13/14.56 (surjCantorThm) =>
% 107.13/14.56 ((
% 107.13/14.56 (!!) @ (
% 107.13/14.56 (('#S') @ (
% 107.13/14.56 (
% 107.13/14.56 ('#B') @ (
% 107.13/14.56 =>) @
% 107.13/14.56 nonempty)) @
% 107.13/14.56 (
% 107.13/14.56 (
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% 107.13/14.56 '#S') @
% 107.13/14.56 (
% 107.13/14.56 (
% 107.13/14.56 ('#B') @ (
% 107.13/14.56 (
% 107.13/14.56 ('#B') @ (
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% 107.13/14.56 (
% 107.13/14.56 (
% 107.13/14.56 ('#C') @ in)))))) @
% 107.13/14.56 (
% 107.13/14.56 (
% 107.13/14.56 ('#C') @ (
% 107.13/14.56 (
% 107.13/14.56 ('#B') @ (
% 107.13/14.56 '#C') @
% 107.13/14.56 (
% 107.13/14.56 (
% 107.13/14.56 ('#B') @ (
% 107.13/14.56 (
% 107.13/14.56 ('#B') @ (
% 107.13/14.56 =))) @
% 107.13/14.56 (
% 107.13/14.56 (
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% 107.13/14.56 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 107.13/14.56 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1407])).
% 107.13/14.56 thf(zip_derived_cl1433, plain,
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% 107.13/14.56 (((upairinpowunion) =>
% 107.13/14.56 (((ubforcartprodlem1) =>
% 107.13/14.56 (((ubforcartprodlem2) =>
% 107.13/14.56 (((ubforcartprodlem3) =>
% 107.13/14.56 (((cartprodpairin) =>
% 107.13/14.56 (((cartprodmempair1) =>
% 107.13/14.56 (((cartprodmempair) =>
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% 107.13/14.56 (((setunionsingleton1) =>
% 107.13/14.56 (((setunionsingleton2) =>
% 107.13/14.56 (((setunionsingleton) =>
% 107.13/14.56 (((singletonprop) =>
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% 107.13/14.56 (((ex1I2) =>
% 107.13/14.56 (((singletonsuniq) =>
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% 107.13/14.56 (((kfstsingleton) =>
% 107.13/14.56 (((theprop) =>
% 107.13/14.56 (((kfstpairEq) =>
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% 107.13/14.56 (((setukpairinjR12) =>
% 107.13/14.56 (((setukpairinjR1) =>
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% 107.13/14.56 (upairequniteq) =>
% 107.13/14.56 ((
% 107.13/14.56 (setukpairinjR2) =>
% 107.13/14.56 ((
% 107.13/14.56 (setukpairinjR) =>
% 107.13/14.56 ((
% 107.13/14.56 (ksndsingleton) =>
% 107.13/14.56 ((
% 107.13/14.56 (ksndpairEq) =>
% 107.13/14.56 ((
% 107.13/14.56 (kpairsurjEq) =>
% 107.13/14.56 ((
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% 107.13/14.56 ((
% 107.13/14.56 (cartprodpairmemEL) =>
% 107.13/14.56 ((
% 107.13/14.56 (cartprodpairmemER) =>
% 107.13/14.56 ((
% 107.13/14.56 (cartprodmempaircEq) =>
% 107.13/14.56 ((
% 107.13/14.56 (cartprodfstpairEq) =>
% 107.13/14.56 ((
% 107.13/14.56 (cartprodsndpairEq) =>
% 107.13/14.56 ((
% 107.13/14.56 (cartprodpairsurjEq) =>
% 107.13/14.56 ((
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% 107.13/14.56 ((
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% 107.13/14.56 ((
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% 107.13/14.56 ((
% 107.13/14.56 (funcinfuncset) =>
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% 107.13/14.56 ((
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% 107.13/14.56 ((
% 107.13/14.56 (lam2p) =>
% 107.13/14.56 ((
% 107.13/14.56 (brelnall1) =>
% 107.13/14.56 ((
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% 107.13/14.56 ((
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% 107.13/14.56 ((
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% 107.13/14.56 ((
% 107.13/14.56 (funcext2) =>
% 107.13/14.56 ((
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% 107.13/14.56 ((
% 107.13/14.56 (ap2apEq2) =>
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% 107.13/14.56 ((
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% 107.13/14.56 ((
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% 107.13/14.56 ((
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% 107.13/14.56 ((
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% 107.13/14.56 ((
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% 107.13/14.56 ((
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% 107.13/14.56 ((
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% 107.13/14.56 ((
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% 107.13/14.56 ((
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% 107.13/14.56 ((
% 107.13/14.56 (complementTE1) =>
% 107.13/14.56 ((
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% 107.13/14.56 ((
% 107.13/14.56 (binintersectTERcontra) =>
% 107.13/14.56 ((
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% 107.13/14.56 ((
% 107.13/14.56 (contrasubsetT1) =>
% 107.13/14.56 ((
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% 107.13/14.56 ((
% 107.13/14.56 (contrasubsetT3) =>
% 107.13/14.56 ((
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% 107.13/14.56 ((
% 107.13/14.56 (doubleComplementE1) =>
% 107.13/14.56 ((
% 107.13/14.56 (doubleComplementSub1) =>
% 107.13/14.56 ((
% 107.13/14.56 (doubleComplementSub2) =>
% 107.13/14.56 ((
% 107.13/14.56 (doubleComplementEq) =>
% 107.13/14.56 ((
% 107.13/14.56 (complementTnotintersectT) =>
% 107.13/14.56 ((
% 107.13/14.56 (complementImpComplementIntersect) =>
% 107.13/14.56 ((
% 107.13/14.56 (complementSubsetComplementIntersect) =>
% 107.13/14.56 ((
% 107.13/14.56 (complementInPowersetComplementIntersect) =>
% 107.13/14.56 ((
% 107.13/14.56 (contraSubsetComplement) =>
% 107.13/14.56 ((
% 107.13/14.56 (complementTcontraSubset) =>
% 107.13/14.56 ((
% 107.13/14.56 (binunionTILcontra) =>
% 107.13/14.56 ((
% 107.13/14.56 (binunionTIRcontra) =>
% 107.13/14.56 ((
% 107.13/14.56 (inIntersectImpInUnion) =>
% 107.13/14.56 ((
% 107.13/14.56 (inIntersectImpInUnion2) =>
% 107.13/14.56 ((
% 107.13/14.56 (inIntersectImpInIntersectUnions) =>
% 107.13/14.56 ((
% 107.13/14.56 (intersectInPowersetIntersectUnions) =>
% 107.13/14.56 ((
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% 107.13/14.56 ((
% 107.13/14.56 (inComplementUnionImpInComplement1) =>
% 107.13/14.56 ((
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% 107.13/14.56 ((
% 107.13/14.56 (binunionTEcontra) =>
% 107.13/14.56 ((
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% 107.13/14.56 ((
% 107.13/14.56 (complementUnionInPowersetComplement) =>
% 107.13/14.56 ((
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% 107.13/14.56 ((
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% 107.13/14.56 ((
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% 107.13/14.56 ((
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% 107.13/14.56 ((
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% 107.13/14.56 ((
% 107.13/14.56 (demorgan2b2) =>
% 107.13/14.56 ((
% 107.13/14.56 (demorgan2b) =>
% 107.13/14.56 ((
% 107.13/14.56 (demorgan2) =>
% 107.13/14.56 ((
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% 107.13/14.56 ((
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% 107.13/14.56 ((
% 107.13/14.56 (woz13rule2) =>
% 107.13/14.56 ((
% 107.13/14.56 (woz13rule3) =>
% 107.13/14.56 ((
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% 107.13/14.56 ((
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% 107.13/14.56 (woz1_5) =>
% 107.13/14.56 ((
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% 107.13/14.56 ((
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% 107.13/14.56 (breln1all1) =>
% 107.13/14.56 ((
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% 107.13/14.56 ((
% 107.13/14.56 (eqbreln1) =>
% 107.13/14.56 ((
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% 107.13/14.56 ((
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% 107.13/14.56 ((
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% 107.77/14.56 (dpsetconstrEL1) =>
% 107.77/14.56 ((
% 107.77/14.56 (dpsetconstrEL2) =>
% 107.77/14.56 ((
% 107.77/14.56 (dpsetconstrER) =>
% 107.77/14.56 ((
% 107.77/14.56 (funcImageSingleton) =>
% 107.77/14.56 ((
% 107.77/14.56 (apProp) =>
% 107.77/14.56 ((
% 107.77/14.56 (app) =>
% 107.77/14.56 ((
% 107.77/14.56 (infuncsetfunc) =>
% 107.77/14.56 ((
% 107.77/14.56 (ap2p) =>
% 107.77/14.56 ((
% 107.77/14.56 (funcinfuncset) =>
% 107.77/14.56 ((
% 107.77/14.56 (lamProp) =>
% 107.77/14.56 ((
% 107.77/14.56 (lamp) =>
% 107.77/14.56 ((
% 107.77/14.56 (lam2p) =>
% 107.77/14.56 ((
% 107.77/14.56 (brelnall1) =>
% 107.77/14.56 ((
% 107.77/14.56 (brelnall2) =>
% 107.77/14.56 ((
% 107.77/14.56 (ex1E2) =>
% 107.77/14.56 ((
% 107.77/14.56 (funcGraphProp1) =>
% 107.77/14.56 ((
% 107.77/14.56 (funcGraphProp3) =>
% 107.77/14.56 ((
% 107.77/14.56 (funcGraphProp2) =>
% 107.77/14.56 ((
% 107.77/14.56 (funcextLem) =>
% 107.77/14.56 ((
% 107.77/14.56 (funcGraphProp4) =>
% 107.77/14.56 ((
% 107.77/14.56 (subbreln) =>
% 107.77/14.56 ((
% 107.77/14.56 (eqbreln) =>
% 107.77/14.56 ((
% 107.77/14.56 (funcext) =>
% 107.77/14.56 ((
% 107.77/14.56 (funcext2) =>
% 107.77/14.56 ((
% 107.77/14.56 (ap2apEq1) =>
% 107.77/14.56 ((
% 107.77/14.56 (ap2apEq2) =>
% 107.77/14.56 ((
% 107.77/14.56 (beta1) =>
% 107.77/14.56 ((
% 107.77/14.56 (eta1) =>
% 107.77/14.56 ((
% 107.77/14.56 (lam2lamEq) =>
% 107.77/14.56 ((
% 107.77/14.56 (beta2) =>
% 107.77/14.56 ((
% 107.77/14.56 (eta2) =>
% 107.77/14.56 ((
% 107.77/14.56 (iffalseProp1) =>
% 107.77/14.56 ((
% 107.77/14.56 (iffalseProp2) =>
% 107.77/14.56 ((
% 107.77/14.56 (iftrueProp1) =>
% 107.77/14.56 ((
% 107.77/14.56 (iftrueProp2) =>
% 107.77/14.56 ((
% 107.77/14.56 (ifSingleton) =>
% 107.77/14.56 ((
% 107.77/14.56 (ifp) =>
% 107.77/14.56 ((
% 107.77/14.56 (theeq) =>
% 107.77/14.56 ((
% 107.77/14.56 (iftrue) =>
% 107.77/14.56 ((
% 107.77/14.56 (iffalse) =>
% 107.77/14.56 ((
% 107.77/14.56 (iftrueorfalse) =>
% 107.77/14.56 ((
% 107.77/14.56 (binintersectT_lem) =>
% 107.77/14.56 ((
% 107.77/14.56 (binunionT_lem) =>
% 107.77/14.56 ((
% 107.77/14.56 (powersetT_lem) =>
% 107.77/14.56 ((
% 107.77/14.56 (setminusT_lem) =>
% 107.77/14.56 ((
% 107.77/14.56 (complementT_lem) =>
% 107.77/14.56 ((
% 107.77/14.56 (setextT) =>
% 107.77/14.56 ((
% 107.77/14.56 (subsetTI) =>
% 107.77/14.56 ((
% 107.77/14.56 (powersetTI1) =>
% 107.77/14.56 ((
% 107.77/14.56 (powersetTE1) =>
% 107.77/14.56 ((
% 107.77/14.56 (complementTI1) =>
% 107.77/14.56 ((
% 107.77/14.56 (complementTE1) =>
% 107.77/14.56 ((
% 107.77/14.56 (binintersectTELcontra) =>
% 107.77/14.56 ((
% 107.77/14.56 (binintersectTERcontra) =>
% 107.77/14.56 ((
% 107.77/14.56 (contrasubsetT) =>
% 107.77/14.56 ((
% 107.77/14.56 (contrasubsetT1) =>
% 107.77/14.56 ((
% 107.77/14.56 (contrasubsetT2) =>
% 107.77/14.56 ((
% 107.77/14.56 (contrasubsetT3) =>
% 107.77/14.56 ((
% 107.77/14.56 (doubleComplementI1) =>
% 107.77/14.56 ((
% 107.77/14.56 (doubleComplementE1) =>
% 107.77/14.56 ((
% 107.77/14.56 (doubleComplementSub1) =>
% 107.77/14.56 ((
% 107.77/14.56 (doubleComplementSub2) =>
% 107.77/14.56 ((
% 107.77/14.56 (doubleComplementEq) =>
% 107.77/14.56 ((
% 107.77/14.56 (complementTnotintersectT) =>
% 107.77/14.56 ((
% 107.77/14.56 (complementImpComplementIntersect) =>
% 107.77/14.56 ((
% 107.77/14.56 (complementSubsetComplementIntersect) =>
% 107.77/14.56 ((
% 107.77/14.56 (complementInPowersetComplementIntersect) =>
% 107.77/14.56 ((
% 107.77/14.56 (contraSubsetComplement) =>
% 107.77/14.56 ((
% 107.77/14.56 (complementTcontraSubset) =>
% 107.77/14.56 ((
% 107.77/14.56 (binunionTILcontra) =>
% 107.77/14.56 ((
% 107.77/14.56 (binunionTIRcontra) =>
% 107.77/14.56 ((
% 107.77/14.56 (inIntersectImpInUnion) =>
% 107.77/14.56 ((
% 107.77/14.56 (inIntersectImpInUnion2) =>
% 107.77/14.57 ((
% 107.77/14.57 (inIntersectImpInIntersectUnions) =>
% 107.77/14.57 ((
% 107.77/14.57 (intersectInPowersetIntersectUnions) =>
% 107.77/14.57 ((
% 107.77/14.57 (inComplementUnionImpNotIn1) =>
% 107.77/14.57 ((
% 107.77/14.57 (inComplementUnionImpInComplement1) =>
% 107.77/14.57 ((
% 107.77/14.57 (binunionTE) =>
% 107.77/14.57 ((
% 107.77/14.57 (binunionTEcontra) =>
% 107.77/14.57 ((
% 107.77/14.57 (demorgan2a1) =>
% 107.77/14.57 ((
% 107.77/14.57 (complementUnionInPowersetComplement) =>
% 107.77/14.57 ((
% 107.77/14.57 (demorgan2a2) =>
% 107.77/14.57 ((
% 107.77/14.57 (demorgan1a) =>
% 107.77/14.57 ((
% 107.77/14.57 (demorgan1b) =>
% 107.77/14.57 ((
% 107.77/14.57 (demorgan1) =>
% 107.77/14.57 ((
% 107.77/14.57 (demorgan2a) =>
% 107.77/14.57 ((
% 107.77/14.57 (demorgan2b2) =>
% 107.77/14.57 ((
% 107.77/14.57 (demorgan2b) =>
% 107.77/14.57 ((
% 107.77/14.57 (demorgan2) =>
% 107.77/14.57 ((
% 107.77/14.57 (woz13rule0) =>
% 107.77/14.57 ((
% 107.77/14.57 (woz13rule1) =>
% 107.77/14.57 ((
% 107.77/14.57 (woz13rule2) =>
% 107.77/14.57 ((
% 107.77/14.57 (woz13rule3) =>
% 107.77/14.57 ((
% 107.77/14.57 (woz13rule4) =>
% 107.77/14.57 ((
% 107.77/14.57 (woz1_1) =>
% 107.77/14.57 ((
% 107.77/14.57 (woz1_2) =>
% 107.77/14.57 ((
% 107.77/14.57 (woz1_3) =>
% 107.77/14.57 ((
% 107.77/14.57 (woz1_4) =>
% 107.77/14.57 ((
% 107.77/14.57 (woz1_5) =>
% 107.77/14.57 ((
% 107.77/14.57 (breln1all2) =>
% 107.77/14.57 ((
% 107.77/14.57 (breln1SetBreln1) =>
% 107.77/14.57 ((
% 107.77/14.57 (choice2fnsingleton) =>
% 107.77/14.57 ((
% 107.77/14.57 (setOfPairsIsBReln1) =>
% 107.77/14.57 ((
% 107.77/14.57 (breln1all1) =>
% 107.77/14.57 ((
% 107.77/14.57 (subbreln1) =>
% 107.77/14.57 ((
% 107.77/14.57 (eqbreln1) =>
% 107.77/14.57 ((
% 107.77/14.57 (breln1invprop) =>
% 107.77/14.57 ((
% 107.77/14.57 (breln1invI) =>
% 107.77/14.57 ((
% 107.77/14.57 (breln1invE) =>
% 107.77/14.57 ((
% 107.77/14.57 (breln1compprop) =>
% 107.77/14.57 ((
% 107.77/14.57 (breln1compI) =>
% 107.77/14.57 ((
% 107.77/14.57 (breln1compE) =>
% 107.77/14.57 ((
% 107.77/14.57 (breln1compEex) =>
% 107.77/14.57 ((
% 107.77/14.57 (breln1unionprop) =>
% 107.77/14.57 ((
% 107.77/14.57 (breln1unionIL) =>
% 107.77/14.57 ((
% 107.77/14.57 (breln1unionIR) =>
% 107.77/14.57 ((
% 107.77/14.57 (breln1unionI) =>
% 107.77/14.57 ((
% 107.77/14.57 (breln1unionE) =>
% 107.77/14.57 ((
% 107.77/14.57 (breln1unionEcases) =>
% 107.77/14.57 ((
% 107.77/14.57 (breln1unionCommutes) =>
% 107.77/14.57 ((
% 107.77/14.57 (woz2Ex) =>
% 107.77/14.57 ((
% 107.77/14.57 (woz2W) =>
% 107.77/14.57 ((
% 107.77/14.57 (woz2A) =>
% 107.77/14.57 ((
% 107.77/14.57 (woz2B) =>
% 107.77/14.57 ((
% 107.77/14.57 (image1Ex) =>
% 107.77/14.57 ((
% 107.77/14.57 (image1Ex1) =>
% 107.77/14.57 ((
% 107.77/14.57 (image1Equiv) =>
% 107.77/14.57 ((
% 107.77/14.57 (image1E) =>
% 107.77/14.57 ((
% 107.77/14.57 (image1I) =>
% 107.77/14.57 ((
% 107.77/14.57 (injFuncInInjFuncSet) =>
% 107.77/14.57 ((
% 107.77/14.57 (injFuncSetFuncIn) =>
% 107.77/14.57 ((
% 107.77/14.57 (injFuncSetFuncInj) =>
% 107.77/14.57 ((
% 107.77/14.57 (surjFuncSetFuncIn) =>
% 107.77/14.57 ((
% 107.77/14.57 (surjFuncSetFuncSurj) =>
% 107.77/14.57 ((
% 107.77/14.57 (leftInvIsSurj) =>
% 107.77/14.57 ((
% 107.77/14.57 (surjCantorThm) =>
% 107.77/14.57 ((
% 107.77/14.57 (!!) @ (
% 107.77/14.57 (('#S') @ (
% 107.77/14.57 (
% 107.77/14.57 ('#B') @ (
% 107.77/14.57 =>) @
% 107.77/14.57 nonempty)) @
% 107.77/14.57 (
% 107.77/14.57 (
% 107.77/14.57 ('#B') @ (
% 107.77/14.57 ??) @
% 107.77/14.57 (
% 107.77/14.57 (
% 107.77/14.57 ('#S') @ (
% 107.77/14.57 (
% 107.77/14.57 ('#B') @ (
% 107.77/14.57 '#S') @
% 107.77/14.57 (
% 107.77/14.57 (
% 107.77/14.57 ('#B') @ (
% 107.77/14.57 (
% 107.77/14.57 ('#B') @ (
% 107.77/14.57 &))) @
% 107.77/14.57 (
% 107.77/14.57 (
% 107.77/14.57 ('#C') @ in)))))) @
% 107.77/14.57 (
% 107.77/14.57 (
% 107.77/14.57 ('#C') @ (
% 107.77/14.57 (
% 107.77/14.57 ('#B') @ (
% 107.77/14.57 '#C') @
% 107.77/14.57 (
% 107.77/14.57 (
% 107.77/14.57 ('#B') @ (
% 107.77/14.57 (
% 107.77/14.57 ('#B') @ (
% 107.77/14.57 =))) @
% 107.77/14.57 (
% 107.77/14.57 (
% 107.77/14.57 ('#C') @ binintersect)))))) @
% 107.77/14.57 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 107.77/14.57 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1444])).
% 107.77/14.57 thf(zip_derived_cl1459, plain,
% 107.77/14.57 (~ (((upairsubunion) =>
% 107.77/14.57 (((upairinpowunion) =>
% 107.77/14.57 (((ubforcartprodlem1) =>
% 107.77/14.57 (((ubforcartprodlem2) =>
% 107.77/14.57 (((ubforcartprodlem3) =>
% 107.77/14.57 (((cartprodpairin) =>
% 107.77/14.57 (((cartprodmempair1) =>
% 107.77/14.57 (((cartprodmempair) =>
% 107.77/14.57 (((setunionE2) =>
% 107.77/14.57 (((setunionsingleton1) =>
% 107.77/14.57 (((setunionsingleton2) =>
% 107.77/14.57 (((setunionsingleton) =>
% 107.77/14.57 (((singletonprop) =>
% 107.77/14.57 (((ex1E1) =>
% 107.77/14.57 (((ex1I) =>
% 107.77/14.57 (((ex1I2) =>
% 107.77/14.57 (((singletonsuniq) =>
% 107.77/14.57 (((setukpairinjL1) =>
% 107.77/14.57 (((kfstsingleton) =>
% 107.77/14.57 (((theprop) =>
% 107.77/14.57 (((kfstpairEq) =>
% 107.77/14.57 (((cartprodfstin) =>
% 107.77/14.57 (((setukpairinjL2) =>
% 107.77/14.57 (((setukpairinjL) =>
% 107.77/14.57 (((setukpairinjR11) =>
% 107.77/14.57 (((setukpairinjR12) =>
% 107.77/14.57 (((setukpairinjR1) =>
% 107.77/14.57 (((upairequniteq) =>
% 107.77/14.57 (((setukpairinjR2) =>
% 107.77/14.57 (((setukpairinjR) =>
% 107.77/14.57 ((
% 107.77/14.57 (ksndsingleton) =>
% 107.77/14.57 ((
% 107.77/14.57 (ksndpairEq) =>
% 107.77/14.57 ((
% 107.77/14.57 (kpairsurjEq) =>
% 107.77/14.57 ((
% 107.77/14.57 (cartprodsndin) =>
% 107.77/14.57 ((
% 107.77/14.57 (cartprodpairmemEL) =>
% 107.77/14.57 ((
% 107.77/14.57 (cartprodpairmemER) =>
% 107.77/14.57 ((
% 107.77/14.57 (cartprodmempaircEq) =>
% 107.77/14.57 ((
% 107.77/14.57 (cartprodfstpairEq) =>
% 107.77/14.57 ((
% 107.77/14.57 (cartprodsndpairEq) =>
% 107.77/14.57 ((
% 107.77/14.57 (cartprodpairsurjEq) =>
% 107.77/14.57 ((
% 107.77/14.57 (dpsetconstrI) =>
% 107.77/14.57 ((
% 107.77/14.57 (dpsetconstrSub) =>
% 107.77/14.57 ((
% 107.77/14.57 (setOfPairsIsBReln) =>
% 107.77/14.57 ((
% 107.77/14.57 (dpsetconstrERa) =>
% 107.77/14.57 ((
% 107.77/14.57 (dpsetconstrEL1) =>
% 107.77/14.57 ((
% 107.77/14.57 (dpsetconstrEL2) =>
% 107.77/14.57 ((
% 107.77/14.57 (dpsetconstrER) =>
% 107.77/14.57 ((
% 107.77/14.57 (funcImageSingleton) =>
% 107.77/14.57 ((
% 107.77/14.57 (apProp) =>
% 107.77/14.57 ((
% 107.77/14.57 (app) =>
% 107.77/14.57 ((
% 107.77/14.57 (infuncsetfunc) =>
% 107.77/14.57 ((
% 107.77/14.57 (ap2p) =>
% 107.77/14.57 ((
% 107.77/14.57 (funcinfuncset) =>
% 107.77/14.57 ((
% 107.77/14.57 (lamProp) =>
% 107.77/14.57 ((
% 107.77/14.57 (lamp) =>
% 107.77/14.57 ((
% 107.77/14.57 (lam2p) =>
% 107.77/14.57 ((
% 107.77/14.57 (brelnall1) =>
% 107.77/14.57 ((
% 107.77/14.57 (brelnall2) =>
% 107.77/14.57 ((
% 107.77/14.57 (ex1E2) =>
% 107.77/14.57 ((
% 107.77/14.57 (funcGraphProp1) =>
% 107.77/14.57 ((
% 107.77/14.57 (funcGraphProp3) =>
% 107.77/14.57 ((
% 107.77/14.57 (funcGraphProp2) =>
% 107.77/14.57 ((
% 107.77/14.57 (funcextLem) =>
% 107.77/14.57 ((
% 107.77/14.57 (funcGraphProp4) =>
% 107.77/14.57 ((
% 107.77/14.57 (subbreln) =>
% 107.77/14.57 ((
% 107.77/14.57 (eqbreln) =>
% 107.77/14.57 ((
% 107.77/14.57 (funcext) =>
% 107.77/14.57 ((
% 107.77/14.57 (funcext2) =>
% 107.77/14.57 ((
% 107.77/14.57 (ap2apEq1) =>
% 107.77/14.57 ((
% 107.77/14.57 (ap2apEq2) =>
% 107.77/14.57 ((
% 107.77/14.57 (beta1) =>
% 107.77/14.57 ((
% 107.77/14.57 (eta1) =>
% 107.77/14.57 ((
% 107.77/14.57 (lam2lamEq) =>
% 107.77/14.57 ((
% 107.77/14.57 (beta2) =>
% 107.77/14.57 ((
% 107.77/14.57 (eta2) =>
% 107.77/14.57 ((
% 107.77/14.57 (iffalseProp1) =>
% 107.77/14.57 ((
% 107.77/14.57 (iffalseProp2) =>
% 107.77/14.57 ((
% 107.77/14.57 (iftrueProp1) =>
% 107.77/14.57 ((
% 107.77/14.57 (iftrueProp2) =>
% 107.77/14.57 ((
% 107.77/14.57 (ifSingleton) =>
% 107.77/14.57 ((
% 107.77/14.57 (ifp) =>
% 107.77/14.57 ((
% 107.77/14.57 (theeq) =>
% 107.77/14.57 ((
% 107.77/14.57 (iftrue) =>
% 107.77/14.57 ((
% 107.77/14.57 (iffalse) =>
% 107.77/14.57 ((
% 107.77/14.57 (iftrueorfalse) =>
% 107.77/14.57 ((
% 107.77/14.57 (binintersectT_lem) =>
% 107.77/14.57 ((
% 107.77/14.57 (binunionT_lem) =>
% 107.77/14.57 ((
% 107.77/14.57 (powersetT_lem) =>
% 107.77/14.57 ((
% 107.77/14.57 (setminusT_lem) =>
% 107.77/14.57 ((
% 107.77/14.57 (complementT_lem) =>
% 107.77/14.57 ((
% 107.77/14.57 (setextT) =>
% 107.77/14.57 ((
% 107.77/14.57 (subsetTI) =>
% 107.77/14.57 ((
% 107.77/14.57 (powersetTI1) =>
% 107.77/14.57 ((
% 107.77/14.57 (powersetTE1) =>
% 107.77/14.57 ((
% 107.77/14.57 (complementTI1) =>
% 107.77/14.57 ((
% 107.77/14.57 (complementTE1) =>
% 107.77/14.57 ((
% 107.77/14.57 (binintersectTELcontra) =>
% 107.77/14.57 ((
% 107.77/14.57 (binintersectTERcontra) =>
% 107.77/14.57 ((
% 107.77/14.57 (contrasubsetT) =>
% 107.77/14.57 ((
% 107.77/14.57 (contrasubsetT1) =>
% 107.77/14.57 ((
% 107.77/14.57 (contrasubsetT2) =>
% 107.77/14.57 ((
% 107.77/14.57 (contrasubsetT3) =>
% 107.77/14.57 ((
% 107.77/14.57 (doubleComplementI1) =>
% 107.77/14.57 ((
% 107.77/14.57 (doubleComplementE1) =>
% 107.77/14.57 ((
% 107.77/14.57 (doubleComplementSub1) =>
% 107.77/14.57 ((
% 107.77/14.57 (doubleComplementSub2) =>
% 107.77/14.57 ((
% 107.77/14.57 (doubleComplementEq) =>
% 107.77/14.57 ((
% 107.77/14.57 (complementTnotintersectT) =>
% 107.77/14.57 ((
% 107.77/14.57 (complementImpComplementIntersect) =>
% 107.77/14.57 ((
% 107.77/14.57 (complementSubsetComplementIntersect) =>
% 107.77/14.57 ((
% 107.77/14.57 (complementInPowersetComplementIntersect) =>
% 107.77/14.57 ((
% 107.77/14.57 (contraSubsetComplement) =>
% 107.77/14.57 ((
% 107.77/14.57 (complementTcontraSubset) =>
% 107.77/14.57 ((
% 107.77/14.57 (binunionTILcontra) =>
% 107.77/14.57 ((
% 107.77/14.57 (binunionTIRcontra) =>
% 107.77/14.57 ((
% 107.77/14.57 (inIntersectImpInUnion) =>
% 107.77/14.57 ((
% 107.77/14.57 (inIntersectImpInUnion2) =>
% 107.77/14.57 ((
% 107.77/14.57 (inIntersectImpInIntersectUnions) =>
% 107.77/14.57 ((
% 107.77/14.57 (intersectInPowersetIntersectUnions) =>
% 107.77/14.57 ((
% 107.77/14.57 (inComplementUnionImpNotIn1) =>
% 107.77/14.57 ((
% 107.77/14.57 (inComplementUnionImpInComplement1) =>
% 107.77/14.57 ((
% 107.77/14.57 (binunionTE) =>
% 107.77/14.57 ((
% 107.77/14.57 (binunionTEcontra) =>
% 107.77/14.57 ((
% 107.77/14.57 (demorgan2a1) =>
% 107.77/14.57 ((
% 107.77/14.57 (complementUnionInPowersetComplement) =>
% 107.77/14.57 ((
% 107.77/14.57 (demorgan2a2) =>
% 107.77/14.57 ((
% 107.77/14.57 (demorgan1a) =>
% 107.77/14.57 ((
% 107.77/14.57 (demorgan1b) =>
% 107.77/14.57 ((
% 107.77/14.57 (demorgan1) =>
% 107.77/14.57 ((
% 107.77/14.57 (demorgan2a) =>
% 107.77/14.57 ((
% 107.77/14.57 (demorgan2b2) =>
% 107.77/14.57 ((
% 107.77/14.57 (demorgan2b) =>
% 107.77/14.57 ((
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% 107.77/14.57 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1452])).
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% 107.77/14.57 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1459])).
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% 107.77/14.57 (breln1compEex) =>
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% 107.77/14.57 (breln1unionprop) =>
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% 107.77/14.57 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1466])).
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% 107.77/14.57 ((
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% 107.77/14.57 ((
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% 107.77/14.57 ((
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% 107.77/14.57 (intersectInPowersetIntersectUnions) =>
% 107.77/14.57 ((
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% 107.77/14.57 (((theprop) =>
% 107.77/14.57 (((kfstpairEq) =>
% 107.77/14.57 (((cartprodfstin) =>
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% 107.77/14.57 (((setukpairinjL) =>
% 107.77/14.57 (((setukpairinjR11) =>
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% 107.77/14.57 (cartprodpairmemER) =>
% 107.77/14.57 ((
% 107.77/14.57 (cartprodmempaircEq) =>
% 107.77/14.57 ((
% 107.77/14.57 (cartprodfstpairEq) =>
% 107.77/14.57 ((
% 107.77/14.57 (cartprodsndpairEq) =>
% 107.77/14.57 ((
% 107.77/14.57 (cartprodpairsurjEq) =>
% 107.77/14.57 ((
% 107.77/14.57 (dpsetconstrI) =>
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% 107.77/14.57 (dpsetconstrSub) =>
% 107.77/14.57 ((
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% 107.77/14.57 ((
% 107.77/14.57 (dpsetconstrEL2) =>
% 107.77/14.57 ((
% 107.77/14.57 (dpsetconstrER) =>
% 107.77/14.57 ((
% 107.77/14.57 (funcImageSingleton) =>
% 107.77/14.57 ((
% 107.77/14.57 (apProp) =>
% 107.77/14.57 ((
% 107.77/14.57 (app) =>
% 107.77/14.57 ((
% 107.77/14.57 (infuncsetfunc) =>
% 107.77/14.57 ((
% 107.77/14.57 (ap2p) =>
% 107.77/14.57 ((
% 107.77/14.57 (funcinfuncset) =>
% 107.77/14.57 ((
% 107.77/14.57 (lamProp) =>
% 107.77/14.57 ((
% 107.77/14.57 (lamp) =>
% 107.77/14.57 ((
% 107.77/14.57 (lam2p) =>
% 107.77/14.57 ((
% 107.77/14.57 (brelnall1) =>
% 107.77/14.57 ((
% 107.77/14.57 (brelnall2) =>
% 107.77/14.57 ((
% 107.77/14.57 (ex1E2) =>
% 107.77/14.57 ((
% 107.77/14.57 (funcGraphProp1) =>
% 107.77/14.57 ((
% 107.77/14.57 (funcGraphProp3) =>
% 107.77/14.57 ((
% 107.77/14.57 (funcGraphProp2) =>
% 107.77/14.57 ((
% 107.77/14.57 (funcextLem) =>
% 107.77/14.57 ((
% 107.77/14.57 (funcGraphProp4) =>
% 107.77/14.57 ((
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% 107.77/14.57 ((
% 107.77/14.57 (funcext2) =>
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% 107.77/14.57 (ap2apEq2) =>
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% 107.77/14.57 (beta1) =>
% 107.77/14.57 ((
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% 107.77/14.57 (lam2lamEq) =>
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% 107.77/14.57 (beta2) =>
% 107.77/14.57 ((
% 107.77/14.57 (eta2) =>
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% 107.77/14.57 (iffalseProp1) =>
% 107.77/14.57 ((
% 107.77/14.57 (iffalseProp2) =>
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% 107.77/14.57 (ifp) =>
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% 107.77/14.57 (iftrue) =>
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% 107.77/14.57 ((
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% 107.77/14.57 ((
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% 107.77/14.57 ((
% 107.77/14.57 (binintersectTERcontra) =>
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% 107.77/14.57 (contrasubsetT) =>
% 107.77/14.57 ((
% 107.77/14.57 (contrasubsetT1) =>
% 107.77/14.57 ((
% 107.77/14.57 (contrasubsetT2) =>
% 107.77/14.57 ((
% 107.77/14.57 (contrasubsetT3) =>
% 107.77/14.57 ((
% 107.77/14.57 (doubleComplementI1) =>
% 107.77/14.57 ((
% 107.77/14.57 (doubleComplementE1) =>
% 107.77/14.57 ((
% 107.77/14.57 (doubleComplementSub1) =>
% 107.77/14.57 ((
% 107.77/14.57 (doubleComplementSub2) =>
% 107.77/14.57 ((
% 107.77/14.57 (doubleComplementEq) =>
% 107.77/14.57 ((
% 107.77/14.57 (complementTnotintersectT) =>
% 107.77/14.57 ((
% 107.77/14.57 (complementImpComplementIntersect) =>
% 107.77/14.57 ((
% 107.77/14.57 (complementSubsetComplementIntersect) =>
% 107.77/14.57 ((
% 107.77/14.57 (complementInPowersetComplementIntersect) =>
% 107.77/14.57 ((
% 107.77/14.57 (contraSubsetComplement) =>
% 107.77/14.57 ((
% 107.77/14.57 (complementTcontraSubset) =>
% 107.77/14.57 ((
% 107.77/14.57 (binunionTILcontra) =>
% 107.77/14.57 ((
% 107.77/14.57 (binunionTIRcontra) =>
% 107.77/14.57 ((
% 107.77/14.57 (inIntersectImpInUnion) =>
% 107.77/14.57 ((
% 107.77/14.57 (inIntersectImpInUnion2) =>
% 107.77/14.57 ((
% 107.77/14.57 (inIntersectImpInIntersectUnions) =>
% 107.77/14.57 ((
% 107.77/14.57 (intersectInPowersetIntersectUnions) =>
% 107.77/14.57 ((
% 107.77/14.57 (inComplementUnionImpNotIn1) =>
% 107.77/14.57 ((
% 107.77/14.57 (inComplementUnionImpInComplement1) =>
% 107.77/14.57 ((
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% 107.77/14.57 ((
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% 107.77/14.57 ((
% 107.77/14.57 (demorgan1a) =>
% 107.77/14.57 ((
% 107.77/14.57 (demorgan1b) =>
% 107.77/14.57 ((
% 107.77/14.57 (demorgan1) =>
% 107.77/14.57 ((
% 107.77/14.57 (demorgan2a) =>
% 107.77/14.57 ((
% 107.77/14.57 (demorgan2b2) =>
% 107.77/14.57 ((
% 107.77/14.57 (demorgan2b) =>
% 107.77/14.57 ((
% 107.77/14.57 (demorgan2) =>
% 107.77/14.57 ((
% 107.77/14.57 (woz13rule0) =>
% 107.77/14.57 ((
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% 107.77/14.57 ((
% 107.77/14.57 (woz13rule2) =>
% 107.77/14.57 ((
% 107.77/14.57 (woz13rule3) =>
% 107.77/14.57 ((
% 107.77/14.57 (woz13rule4) =>
% 107.77/14.57 ((
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% 107.77/14.57 ((
% 107.77/14.57 (woz1_2) =>
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% 107.77/14.57 ((
% 107.77/14.57 (woz1_4) =>
% 107.77/14.57 ((
% 107.77/14.57 (woz1_5) =>
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% 107.77/14.57 (breln1all2) =>
% 107.77/14.57 ((
% 107.77/14.57 (breln1SetBreln1) =>
% 107.77/14.57 ((
% 107.77/14.57 (choice2fnsingleton) =>
% 107.77/14.57 ((
% 107.77/14.57 (setOfPairsIsBReln1) =>
% 107.77/14.57 ((
% 107.77/14.57 (breln1all1) =>
% 107.77/14.57 ((
% 107.77/14.57 (subbreln1) =>
% 107.77/14.57 ((
% 107.77/14.57 (eqbreln1) =>
% 107.77/14.57 ((
% 107.77/14.57 (breln1invprop) =>
% 107.77/14.57 ((
% 107.77/14.57 (breln1invI) =>
% 107.77/14.57 ((
% 107.77/14.57 (breln1invE) =>
% 107.77/14.57 ((
% 107.77/14.57 (breln1compprop) =>
% 107.77/14.57 ((
% 107.77/14.57 (breln1compI) =>
% 107.77/14.57 ((
% 107.77/14.57 (breln1compE) =>
% 107.77/14.57 ((
% 107.77/14.57 (breln1compEex) =>
% 107.77/14.57 ((
% 107.77/14.57 (breln1unionprop) =>
% 107.77/14.57 ((
% 107.77/14.57 (breln1unionIL) =>
% 107.77/14.57 ((
% 107.77/14.57 (breln1unionIR) =>
% 107.77/14.57 ((
% 107.77/14.57 (breln1unionI) =>
% 107.77/14.57 ((
% 107.77/14.57 (breln1unionE) =>
% 107.77/14.57 ((
% 107.77/14.57 (breln1unionEcases) =>
% 107.77/14.57 ((
% 107.77/14.57 (breln1unionCommutes) =>
% 107.77/14.57 ((
% 107.77/14.57 (woz2Ex) =>
% 107.77/14.57 ((
% 107.77/14.57 (woz2W) =>
% 107.77/14.57 ((
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% 107.77/14.57 ((
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% 107.77/14.57 ((
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% 107.77/14.57 ((
% 107.77/14.57 (image1E) =>
% 107.77/14.57 ((
% 107.77/14.57 (image1I) =>
% 107.77/14.57 ((
% 107.77/14.57 (injFuncInInjFuncSet) =>
% 107.77/14.57 ((
% 107.77/14.57 (injFuncSetFuncIn) =>
% 107.77/14.57 ((
% 107.77/14.57 (injFuncSetFuncInj) =>
% 107.77/14.57 ((
% 107.77/14.57 (surjFuncSetFuncIn) =>
% 107.77/14.57 ((
% 107.77/14.57 (surjFuncSetFuncSurj) =>
% 107.77/14.57 ((
% 107.77/14.57 (leftInvIsSurj) =>
% 107.77/14.57 ((
% 107.77/14.57 (surjCantorThm) =>
% 107.77/14.57 ((
% 107.77/14.57 (!!) @ (
% 107.77/14.57 (('#S') @ (
% 107.77/14.57 (
% 107.77/14.57 ('#B') @ (
% 107.77/14.57 =>) @
% 107.77/14.57 nonempty)) @
% 107.77/14.57 (
% 107.77/14.57 (
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% 107.77/14.57 (
% 107.77/14.57 ('#S') @ (
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% 107.77/14.57 (
% 107.77/14.57 (
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% 107.77/14.57 (
% 107.77/14.57 ('#B') @ (
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% 107.77/14.57 (
% 107.77/14.57 (
% 107.77/14.57 ('#C') @ in)))))) @
% 107.77/14.57 (
% 107.77/14.57 (
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% 107.77/14.57 (
% 107.77/14.57 ('#B') @ (
% 107.77/14.57 '#C') @
% 107.77/14.57 (
% 107.77/14.57 (
% 107.77/14.57 ('#B') @ (
% 107.77/14.57 (
% 107.77/14.57 ('#B') @ (
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% 107.77/14.57 (
% 107.77/14.57 (
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% 107.77/14.57 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 107.77/14.57 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1488])).
% 107.77/14.57 thf(zip_derived_cl1505, plain,
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% 107.77/14.57 (((kfstpairEq) =>
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% 107.77/14.57 (((cartprodpairmemER) =>
% 107.77/14.57 ((
% 107.77/14.57 (cartprodmempaircEq) =>
% 107.77/14.57 ((
% 107.77/14.57 (cartprodfstpairEq) =>
% 107.77/14.57 ((
% 107.77/14.57 (cartprodsndpairEq) =>
% 107.77/14.57 ((
% 107.77/14.57 (cartprodpairsurjEq) =>
% 107.77/14.57 ((
% 107.77/14.57 (dpsetconstrI) =>
% 107.77/14.57 ((
% 107.77/14.57 (dpsetconstrSub) =>
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% 107.77/14.57 (dpsetconstrER) =>
% 107.77/14.57 ((
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% 107.77/14.57 ((
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% 107.77/14.57 ((
% 107.77/14.57 (app) =>
% 107.77/14.57 ((
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% 107.77/14.57 ((
% 107.77/14.57 (ap2p) =>
% 107.77/14.57 ((
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% 107.77/14.57 ((
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% 107.77/14.57 ((
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% 107.77/14.57 ((
% 107.77/14.57 (funcGraphProp2) =>
% 107.77/14.57 ((
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% 107.77/14.57 ((
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% 107.77/14.57 ((
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% 107.77/14.57 ((
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% 107.77/14.57 ((
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% 107.77/14.57 ((
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% 107.77/14.57 ((
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% 107.77/14.57 ((
% 107.77/14.57 (iftrueProp2) =>
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% 107.77/14.57 (iffalse) =>
% 107.77/14.57 ((
% 107.77/14.57 (iftrueorfalse) =>
% 107.77/14.57 ((
% 107.77/14.57 (binintersectT_lem) =>
% 107.77/14.57 ((
% 107.77/14.57 (binunionT_lem) =>
% 107.77/14.57 ((
% 107.77/14.57 (powersetT_lem) =>
% 107.77/14.57 ((
% 107.77/14.57 (setminusT_lem) =>
% 107.77/14.57 ((
% 107.77/14.57 (complementT_lem) =>
% 107.77/14.57 ((
% 107.77/14.57 (setextT) =>
% 107.77/14.57 ((
% 107.77/14.57 (subsetTI) =>
% 107.77/14.57 ((
% 107.77/14.57 (powersetTI1) =>
% 107.77/14.57 ((
% 107.77/14.57 (powersetTE1) =>
% 107.77/14.57 ((
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% 107.77/14.57 ((
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% 107.77/14.57 ((
% 107.77/14.57 (binintersectTELcontra) =>
% 107.77/14.57 ((
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% 107.77/14.57 ((
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% 107.77/14.57 ((
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% 107.77/14.57 ((
% 107.77/14.57 (contrasubsetT2) =>
% 107.77/14.57 ((
% 107.77/14.57 (contrasubsetT3) =>
% 107.77/14.57 ((
% 107.77/14.57 (doubleComplementI1) =>
% 107.77/14.57 ((
% 107.77/14.57 (doubleComplementE1) =>
% 107.77/14.57 ((
% 107.77/14.57 (doubleComplementSub1) =>
% 107.77/14.57 ((
% 107.77/14.57 (doubleComplementSub2) =>
% 107.77/14.57 ((
% 107.77/14.57 (doubleComplementEq) =>
% 107.77/14.57 ((
% 107.77/14.57 (complementTnotintersectT) =>
% 107.77/14.57 ((
% 107.77/14.57 (complementImpComplementIntersect) =>
% 107.77/14.57 ((
% 107.77/14.57 (complementSubsetComplementIntersect) =>
% 107.77/14.57 ((
% 107.77/14.57 (complementInPowersetComplementIntersect) =>
% 107.77/14.57 ((
% 107.77/14.57 (contraSubsetComplement) =>
% 107.77/14.57 ((
% 107.77/14.57 (complementTcontraSubset) =>
% 107.77/14.57 ((
% 107.77/14.57 (binunionTILcontra) =>
% 107.77/14.57 ((
% 107.77/14.57 (binunionTIRcontra) =>
% 107.77/14.57 ((
% 107.77/14.57 (inIntersectImpInUnion) =>
% 107.77/14.57 ((
% 107.77/14.57 (inIntersectImpInUnion2) =>
% 107.77/14.57 ((
% 107.77/14.57 (inIntersectImpInIntersectUnions) =>
% 107.77/14.57 ((
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% 107.77/14.57 (((cartprodpairmemER) =>
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% 107.77/14.57 (ap2p) =>
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% 107.77/14.57 (lamp) =>
% 107.77/14.57 ((
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% 107.77/14.57 ((
% 107.77/14.57 (brelnall2) =>
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% 107.77/14.57 (ex1E2) =>
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% 107.77/14.57 (funcGraphProp2) =>
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% 107.77/14.57 ((
% 107.77/14.57 (funcGraphProp4) =>
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% 107.77/14.57 (contrasubsetT2) =>
% 107.77/14.57 ((
% 107.77/14.57 (contrasubsetT3) =>
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% 107.77/14.57 ((
% 107.77/14.57 (doubleComplementE1) =>
% 107.77/14.57 ((
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% 107.77/14.57 ((
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% 107.77/14.57 ((
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% 107.77/14.57 ((
% 107.77/14.57 (inIntersectImpInUnion2) =>
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% 107.77/14.57 ((
% 107.77/14.57 (intersectInPowersetIntersectUnions) =>
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% 107.77/14.57 ((
% 107.77/14.57 (demorgan2a) =>
% 107.77/14.57 ((
% 107.77/14.57 (demorgan2b2) =>
% 107.77/14.57 ((
% 107.77/14.57 (demorgan2b) =>
% 107.77/14.57 ((
% 107.77/14.57 (demorgan2) =>
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% 107.77/14.57 ((
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% 107.77/14.57 (woz13rule2) =>
% 107.77/14.57 ((
% 107.77/14.57 (woz13rule3) =>
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% 107.77/14.57 (woz1_2) =>
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% 107.77/14.57 (breln1all2) =>
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% 107.77/14.57 (breln1SetBreln1) =>
% 107.77/14.57 ((
% 107.77/14.57 (choice2fnsingleton) =>
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% 107.77/14.57 (setOfPairsIsBReln1) =>
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% 107.77/14.57 ((
% 107.77/14.57 (breln1invI) =>
% 107.77/14.57 ((
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% 107.77/14.57 ((
% 107.77/14.57 (breln1compprop) =>
% 107.77/14.57 ((
% 107.77/14.57 (breln1compI) =>
% 107.77/14.57 ((
% 107.77/14.57 (breln1compE) =>
% 107.77/14.57 ((
% 107.77/14.57 (breln1compEex) =>
% 107.77/14.57 ((
% 107.77/14.57 (breln1unionprop) =>
% 107.77/14.57 ((
% 107.77/14.57 (breln1unionIL) =>
% 107.77/14.57 ((
% 107.77/14.57 (breln1unionIR) =>
% 107.77/14.57 ((
% 107.77/14.57 (breln1unionI) =>
% 107.77/14.57 ((
% 107.77/14.57 (breln1unionE) =>
% 107.77/14.57 ((
% 107.77/14.57 (breln1unionEcases) =>
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% 107.77/14.57 (breln1unionCommutes) =>
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% 107.77/14.57 ((
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% 107.77/14.57 ((
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% 107.77/14.57 ((
% 107.77/14.57 (injFuncSetFuncIn) =>
% 107.77/14.57 ((
% 107.77/14.57 (injFuncSetFuncInj) =>
% 107.77/14.57 ((
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% 107.77/14.57 ((
% 107.77/14.57 (surjFuncSetFuncSurj) =>
% 107.77/14.57 ((
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% 107.77/14.57 ((
% 107.77/14.57 (surjCantorThm) =>
% 107.77/14.57 ((
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% 107.77/14.57 (
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% 107.77/14.57 nonempty)) @
% 107.77/14.57 (
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% 107.77/14.57 (
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% 107.77/14.57 (
% 107.77/14.57 (
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% 107.77/14.57 (
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% 107.77/14.57 (
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% 107.77/14.57 (
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% 107.77/14.57 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 107.77/14.57 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1515])).
% 107.77/14.57 thf(zip_derived_cl1535, plain,
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% 107.77/14.57 ((
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% 107.77/14.57 (doubleComplementSub2) =>
% 107.77/14.57 ((
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% 107.77/14.57 (complementTnotintersectT) =>
% 107.77/14.57 ((
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% 107.77/14.57 ((
% 107.77/14.57 (complementSubsetComplementIntersect) =>
% 107.77/14.57 ((
% 107.77/14.57 (complementInPowersetComplementIntersect) =>
% 107.77/14.57 ((
% 107.77/14.57 (contraSubsetComplement) =>
% 107.77/14.57 ((
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% 107.77/14.57 ((
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% 107.77/14.57 ((
% 107.77/14.57 (inIntersectImpInUnion2) =>
% 107.77/14.57 ((
% 107.77/14.57 (inIntersectImpInIntersectUnions) =>
% 107.77/14.57 ((
% 107.77/14.57 (intersectInPowersetIntersectUnions) =>
% 107.77/14.57 ((
% 107.77/14.57 (inComplementUnionImpNotIn1) =>
% 107.77/14.57 ((
% 107.77/14.57 (inComplementUnionImpInComplement1) =>
% 107.77/14.57 ((
% 107.77/14.57 (binunionTE) =>
% 107.77/14.57 ((
% 107.77/14.57 (binunionTEcontra) =>
% 107.77/14.57 ((
% 107.77/14.57 (demorgan2a1) =>
% 107.77/14.57 ((
% 107.77/14.57 (complementUnionInPowersetComplement) =>
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% 107.77/14.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1545])).
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% 107.77/14.58 ((
% 107.77/14.58 (breln1unionI) =>
% 107.77/14.58 ((
% 107.77/14.58 (breln1unionE) =>
% 107.77/14.58 ((
% 107.77/14.58 (breln1unionEcases) =>
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% 107.77/14.58 ((
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% 107.77/14.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1555])).
% 107.77/14.58 thf(zip_derived_cl1574, plain,
% 107.77/14.58 (~ (((ex1E1) =>
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% 107.77/14.58 (((setukpairinjR1) =>
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% 107.77/14.58 (((setukpairinjR2) =>
% 107.77/14.58 (((setukpairinjR) =>
% 107.77/14.58 (((ksndsingleton) =>
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% 107.77/14.58 (((kpairsurjEq) =>
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% 107.77/14.58 (((cartprodpairmemEL) =>
% 107.77/14.58 (((cartprodpairmemER) =>
% 107.77/14.58 (((cartprodmempaircEq) =>
% 107.77/14.58 (((cartprodfstpairEq) =>
% 107.77/14.58 (((cartprodsndpairEq) =>
% 107.77/14.58 (((cartprodpairsurjEq) =>
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% 107.77/14.58 (((setOfPairsIsBReln) =>
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% 107.77/14.58 ((
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% 107.77/14.58 ((
% 107.77/14.58 (dpsetconstrEL2) =>
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% 107.77/14.58 (dpsetconstrER) =>
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% 107.77/14.58 ((
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% 107.77/14.58 (inComplementUnionImpInComplement1) =>
% 107.77/14.58 ((
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% 107.77/14.58 ((
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% 107.77/14.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1565])).
% 107.77/14.58 thf(zip_derived_cl1582, plain,
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% 107.77/14.58 (subbreln) =>
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% 107.77/14.58 (eqbreln) =>
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% 107.77/14.58 (funcext2) =>
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% 107.77/14.58 ((
% 107.77/14.58 (eta1) =>
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% 107.77/14.58 (lam2lamEq) =>
% 107.77/14.58 ((
% 107.77/14.58 (beta2) =>
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% 107.77/14.58 (eta2) =>
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% 107.77/14.58 ((
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% 107.77/14.58 (binintersectTERcontra) =>
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% 107.77/14.58 ((
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% 107.77/14.58 ((
% 107.77/14.58 (contrasubsetT2) =>
% 107.77/14.58 ((
% 107.77/14.58 (contrasubsetT3) =>
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% 107.77/14.58 (doubleComplementSub2) =>
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% 107.77/14.58 ((
% 107.77/14.58 (intersectInPowersetIntersectUnions) =>
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% 107.77/14.58 (inComplementUnionImpInComplement1) =>
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% 107.77/14.58 ((
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% 107.77/14.58 (demorgan2b2) =>
% 107.77/14.58 ((
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% 107.77/14.58 ((
% 107.77/14.58 (demorgan2) =>
% 107.77/14.58 ((
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% 107.77/14.58 ((
% 107.77/14.58 (woz13rule2) =>
% 107.77/14.58 ((
% 107.77/14.58 (woz13rule3) =>
% 107.77/14.58 ((
% 107.77/14.58 (woz13rule4) =>
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% 107.77/14.58 ((
% 107.77/14.58 (woz1_2) =>
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% 107.77/14.58 (woz1_3) =>
% 107.77/14.58 ((
% 107.77/14.58 (woz1_4) =>
% 107.77/14.58 ((
% 107.77/14.58 (woz1_5) =>
% 107.77/14.58 ((
% 107.77/14.58 (breln1all2) =>
% 107.77/14.58 ((
% 107.77/14.58 (breln1SetBreln1) =>
% 107.77/14.58 ((
% 107.77/14.58 (choice2fnsingleton) =>
% 107.77/14.58 ((
% 107.77/14.58 (setOfPairsIsBReln1) =>
% 107.77/14.58 ((
% 107.77/14.58 (breln1all1) =>
% 107.77/14.58 ((
% 107.77/14.58 (subbreln1) =>
% 107.77/14.58 ((
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% 107.77/14.58 (breln1invprop) =>
% 107.77/14.58 ((
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% 107.77/14.58 ((
% 107.77/14.58 (breln1invE) =>
% 107.77/14.58 ((
% 107.77/14.58 (breln1compprop) =>
% 107.77/14.58 ((
% 107.77/14.58 (breln1compI) =>
% 107.77/14.58 ((
% 107.77/14.58 (breln1compE) =>
% 107.77/14.58 ((
% 107.77/14.58 (breln1compEex) =>
% 107.77/14.58 ((
% 107.77/14.58 (breln1unionprop) =>
% 107.77/14.58 ((
% 107.77/14.58 (breln1unionIL) =>
% 107.77/14.58 ((
% 107.77/14.58 (breln1unionIR) =>
% 107.77/14.58 ((
% 107.77/14.58 (breln1unionI) =>
% 107.77/14.58 ((
% 107.77/14.58 (breln1unionE) =>
% 107.77/14.58 ((
% 107.77/14.58 (breln1unionEcases) =>
% 107.77/14.58 ((
% 107.77/14.58 (breln1unionCommutes) =>
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% 107.77/14.58 ((
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% 107.77/14.58 ((
% 107.77/14.58 (image1Ex1) =>
% 107.77/14.58 ((
% 107.77/14.58 (image1Equiv) =>
% 107.77/14.58 ((
% 107.77/14.58 (image1E) =>
% 107.77/14.58 ((
% 107.77/14.58 (image1I) =>
% 107.77/14.58 ((
% 107.77/14.58 (injFuncInInjFuncSet) =>
% 107.77/14.58 ((
% 107.77/14.58 (injFuncSetFuncIn) =>
% 107.77/14.58 ((
% 107.77/14.58 (injFuncSetFuncInj) =>
% 107.77/14.58 ((
% 107.77/14.58 (surjFuncSetFuncIn) =>
% 107.77/14.58 ((
% 107.77/14.58 (surjFuncSetFuncSurj) =>
% 107.77/14.58 ((
% 107.77/14.58 (leftInvIsSurj) =>
% 107.77/14.58 ((
% 107.77/14.58 (surjCantorThm) =>
% 107.77/14.58 ((
% 107.77/14.58 (!!) @ (
% 107.77/14.58 (('#S') @ (
% 107.77/14.58 (
% 107.77/14.58 ('#B') @ (
% 107.77/14.58 =>) @
% 107.77/14.58 nonempty)) @
% 107.77/14.58 (
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% 107.77/14.58 (
% 107.77/14.58 (
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% 107.77/14.58 (
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% 107.77/14.58 (
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% 107.77/14.58 (
% 107.77/14.58 (
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% 107.77/14.58 (
% 107.77/14.58 ('#B') @ (
% 107.77/14.58 (
% 107.77/14.58 ('#B') @ (
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% 107.77/14.58 (
% 107.77/14.58 (
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% 107.77/14.58 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 107.77/14.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1574])).
% 107.77/14.58 thf(zip_derived_cl1591, plain,
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% 107.77/14.58 (dpsetconstrER) =>
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% 107.77/14.58 ((
% 107.77/14.58 (funcinfuncset) =>
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% 107.77/14.58 ((
% 107.77/14.58 (lam2p) =>
% 107.77/14.58 ((
% 107.77/14.58 (brelnall1) =>
% 107.77/14.58 ((
% 107.77/14.58 (brelnall2) =>
% 107.77/14.58 ((
% 107.77/14.58 (ex1E2) =>
% 107.77/14.58 ((
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% 107.77/14.58 ((
% 107.77/14.58 (eta1) =>
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% 107.77/14.58 (eta2) =>
% 107.77/14.58 ((
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% 107.77/14.58 ((
% 107.77/14.58 (iffalseProp2) =>
% 107.77/14.58 ((
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% 107.77/14.58 (complementTE1) =>
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% 107.77/14.58 (contrasubsetT3) =>
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% 107.77/14.58 ((
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% 107.77/14.58 ((
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% 107.77/14.58 ((
% 107.77/14.58 (complementInPowersetComplementIntersect) =>
% 107.77/14.58 ((
% 107.77/14.58 (contraSubsetComplement) =>
% 107.77/14.58 ((
% 107.77/14.58 (complementTcontraSubset) =>
% 107.77/14.58 ((
% 107.77/14.58 (binunionTILcontra) =>
% 107.77/14.58 ((
% 107.77/14.58 (binunionTIRcontra) =>
% 107.77/14.58 ((
% 107.77/14.58 (inIntersectImpInUnion) =>
% 107.77/14.58 ((
% 107.77/14.58 (inIntersectImpInUnion2) =>
% 107.77/14.58 ((
% 107.77/14.58 (inIntersectImpInIntersectUnions) =>
% 107.77/14.58 ((
% 107.77/14.58 (intersectInPowersetIntersectUnions) =>
% 107.77/14.58 ((
% 107.77/14.58 (inComplementUnionImpNotIn1) =>
% 107.77/14.58 ((
% 107.77/14.58 (inComplementUnionImpInComplement1) =>
% 107.77/14.58 ((
% 107.77/14.58 (binunionTE) =>
% 107.77/14.58 ((
% 107.77/14.58 (binunionTEcontra) =>
% 107.77/14.58 ((
% 107.77/14.58 (demorgan2a1) =>
% 107.77/14.58 ((
% 107.77/14.58 (complementUnionInPowersetComplement) =>
% 107.77/14.58 ((
% 107.77/14.58 (demorgan2a2) =>
% 107.77/14.58 ((
% 107.77/14.58 (demorgan1a) =>
% 107.77/14.58 ((
% 107.77/14.58 (demorgan1b) =>
% 107.77/14.58 ((
% 107.77/14.58 (demorgan1) =>
% 107.77/14.58 ((
% 107.77/14.58 (demorgan2a) =>
% 107.77/14.58 ((
% 107.77/14.58 (demorgan2b2) =>
% 107.77/14.58 ((
% 107.77/14.58 (demorgan2b) =>
% 107.77/14.58 ((
% 107.77/14.58 (demorgan2) =>
% 107.77/14.58 ((
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% 107.77/14.58 ((
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% 107.77/14.58 ((
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% 107.77/14.58 ((
% 107.77/14.58 (subbreln1) =>
% 107.77/14.58 ((
% 107.77/14.58 (eqbreln1) =>
% 107.77/14.58 ((
% 107.77/14.58 (breln1invprop) =>
% 107.77/14.58 ((
% 107.77/14.58 (breln1invI) =>
% 107.77/14.58 ((
% 107.77/14.58 (breln1invE) =>
% 107.77/14.58 ((
% 107.77/14.58 (breln1compprop) =>
% 107.77/14.58 ((
% 107.77/14.58 (breln1compI) =>
% 107.77/14.58 ((
% 107.77/14.58 (breln1compE) =>
% 107.77/14.58 ((
% 107.77/14.58 (breln1compEex) =>
% 107.77/14.58 ((
% 107.77/14.58 (breln1unionprop) =>
% 107.77/14.58 ((
% 107.77/14.58 (breln1unionIL) =>
% 107.77/14.58 ((
% 107.77/14.58 (breln1unionIR) =>
% 107.77/14.58 ((
% 107.77/14.58 (breln1unionI) =>
% 107.77/14.58 ((
% 107.77/14.58 (breln1unionE) =>
% 107.77/14.58 ((
% 107.77/14.58 (breln1unionEcases) =>
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% 107.77/14.58 (breln1unionCommutes) =>
% 107.77/14.58 ((
% 107.77/14.58 (woz2Ex) =>
% 107.77/14.58 ((
% 107.77/14.58 (woz2W) =>
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% 107.77/14.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1582])).
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% 107.77/14.58 ((
% 107.77/14.58 (contrasubsetT3) =>
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% 107.77/14.58 ((
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% 107.77/14.58 (demorgan2) =>
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% 107.77/14.58 (woz13rule2) =>
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% 107.77/14.58 ((
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% 107.77/14.58 ((
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% 107.77/14.58 ((
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% 107.77/14.58 (breln1compI) =>
% 107.77/14.58 ((
% 107.77/14.58 (breln1compE) =>
% 107.77/14.58 ((
% 107.77/14.58 (breln1compEex) =>
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% 107.77/14.58 ((
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% 107.77/14.58 ((
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% 107.77/14.58 (breln1unionI) =>
% 107.77/14.58 ((
% 107.77/14.58 (breln1unionE) =>
% 107.77/14.58 ((
% 107.77/14.58 (breln1unionEcases) =>
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% 107.77/14.58 ((
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% 107.77/14.58 ((
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% 107.77/14.58 ((
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% 107.77/14.58 ((
% 107.77/14.58 (injFuncSetFuncInj) =>
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% 107.77/14.58 (surjFuncSetFuncSurj) =>
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% 107.77/14.58 (
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% 107.77/14.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1599])).
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% 107.77/14.58 ((
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% 107.77/14.58 ((
% 107.77/14.58 (lam2p) =>
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% 107.77/14.58 (funcGraphProp2) =>
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% 107.77/14.58 ((
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% 107.77/14.58 ((
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% 107.77/14.58 ((
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% 107.77/14.58 ((
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% 107.77/14.58 ((
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% 107.77/14.58 ((
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% 107.77/14.58 ((
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% 107.77/14.58 (
% 107.77/14.58 ('#C') @ binintersect)))))) @
% 107.77/14.58 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 107.77/14.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1607])).
% 107.77/14.58 thf(zip_derived_cl1625, plain,
% 107.77/14.58 (~ (((theprop) =>
% 107.77/14.58 (((kfstpairEq) =>
% 107.77/14.58 (((cartprodfstin) =>
% 107.77/14.58 (((setukpairinjL2) =>
% 107.77/14.58 (((setukpairinjL) =>
% 107.77/14.58 (((setukpairinjR11) =>
% 107.77/14.58 (((setukpairinjR12) =>
% 107.77/14.58 (((setukpairinjR1) =>
% 107.77/14.58 (((upairequniteq) =>
% 107.77/14.58 (((setukpairinjR2) =>
% 107.77/14.58 (((setukpairinjR) =>
% 107.77/14.58 (((ksndsingleton) =>
% 107.77/14.58 (((ksndpairEq) =>
% 107.77/14.58 (((kpairsurjEq) =>
% 107.77/14.58 (((cartprodsndin) =>
% 107.77/14.58 (((cartprodpairmemEL) =>
% 107.77/14.58 (((cartprodpairmemER) =>
% 107.77/14.58 (((cartprodmempaircEq) =>
% 107.77/14.58 (((cartprodfstpairEq) =>
% 107.77/14.58 (((cartprodsndpairEq) =>
% 107.77/14.58 (((cartprodpairsurjEq) =>
% 107.77/14.58 (((dpsetconstrI) =>
% 107.77/14.58 (((dpsetconstrSub) =>
% 107.77/14.58 (((setOfPairsIsBReln) =>
% 107.77/14.58 (((dpsetconstrERa) =>
% 107.77/14.58 (((dpsetconstrEL1) =>
% 107.77/14.58 (((dpsetconstrEL2) =>
% 107.77/14.58 (((dpsetconstrER) =>
% 107.77/14.58 (((funcImageSingleton) =>
% 107.77/14.58 (((apProp) =>
% 107.77/14.58 ((
% 107.77/14.58 (app) =>
% 107.77/14.58 ((
% 107.77/14.58 (infuncsetfunc) =>
% 107.77/14.58 ((
% 107.77/14.58 (ap2p) =>
% 107.77/14.58 ((
% 107.77/14.58 (funcinfuncset) =>
% 107.77/14.58 ((
% 107.77/14.58 (lamProp) =>
% 107.77/14.58 ((
% 107.77/14.58 (lamp) =>
% 107.77/14.58 ((
% 107.77/14.58 (lam2p) =>
% 107.77/14.58 ((
% 107.77/14.58 (brelnall1) =>
% 107.77/14.58 ((
% 107.77/14.58 (brelnall2) =>
% 107.77/14.58 ((
% 107.77/14.58 (ex1E2) =>
% 107.77/14.58 ((
% 107.77/14.58 (funcGraphProp1) =>
% 107.77/14.58 ((
% 107.77/14.58 (funcGraphProp3) =>
% 107.77/14.58 ((
% 107.77/14.58 (funcGraphProp2) =>
% 107.77/14.58 ((
% 107.77/14.58 (funcextLem) =>
% 107.77/14.58 ((
% 107.77/14.58 (funcGraphProp4) =>
% 107.77/14.58 ((
% 107.77/14.58 (subbreln) =>
% 107.77/14.58 ((
% 107.77/14.58 (eqbreln) =>
% 107.77/14.58 ((
% 107.77/14.58 (funcext) =>
% 107.77/14.58 ((
% 107.77/14.58 (funcext2) =>
% 107.77/14.58 ((
% 107.77/14.58 (ap2apEq1) =>
% 107.77/14.58 ((
% 107.77/14.58 (ap2apEq2) =>
% 107.77/14.58 ((
% 107.77/14.58 (beta1) =>
% 107.77/14.58 ((
% 107.77/14.58 (eta1) =>
% 107.77/14.58 ((
% 107.77/14.58 (lam2lamEq) =>
% 107.77/14.58 ((
% 107.77/14.58 (beta2) =>
% 107.77/14.58 ((
% 107.77/14.58 (eta2) =>
% 107.77/14.58 ((
% 107.77/14.58 (iffalseProp1) =>
% 107.77/14.58 ((
% 107.77/14.58 (iffalseProp2) =>
% 107.77/14.58 ((
% 107.77/14.58 (iftrueProp1) =>
% 107.77/14.58 ((
% 107.77/14.58 (iftrueProp2) =>
% 107.77/14.58 ((
% 107.77/14.58 (ifSingleton) =>
% 107.77/14.58 ((
% 107.77/14.58 (ifp) =>
% 107.77/14.58 ((
% 107.77/14.58 (theeq) =>
% 107.77/14.58 ((
% 107.77/14.58 (iftrue) =>
% 107.77/14.58 ((
% 107.77/14.58 (iffalse) =>
% 107.77/14.58 ((
% 107.77/14.58 (iftrueorfalse) =>
% 107.77/14.58 ((
% 107.77/14.58 (binintersectT_lem) =>
% 107.77/14.58 ((
% 107.77/14.58 (binunionT_lem) =>
% 107.77/14.58 ((
% 107.77/14.58 (powersetT_lem) =>
% 107.77/14.58 ((
% 107.77/14.58 (setminusT_lem) =>
% 107.77/14.58 ((
% 107.77/14.58 (complementT_lem) =>
% 107.77/14.58 ((
% 107.77/14.58 (setextT) =>
% 107.77/14.58 ((
% 107.77/14.58 (subsetTI) =>
% 107.77/14.58 ((
% 107.77/14.58 (powersetTI1) =>
% 107.77/14.58 ((
% 107.77/14.58 (powersetTE1) =>
% 107.77/14.58 ((
% 107.77/14.58 (complementTI1) =>
% 107.77/14.58 ((
% 107.77/14.58 (complementTE1) =>
% 107.77/14.58 ((
% 107.77/14.58 (binintersectTELcontra) =>
% 107.77/14.58 ((
% 107.77/14.58 (binintersectTERcontra) =>
% 107.77/14.58 ((
% 107.77/14.58 (contrasubsetT) =>
% 107.77/14.58 ((
% 107.77/14.58 (contrasubsetT1) =>
% 107.77/14.58 ((
% 107.77/14.58 (contrasubsetT2) =>
% 107.77/14.58 ((
% 107.77/14.58 (contrasubsetT3) =>
% 107.77/14.58 ((
% 107.77/14.58 (doubleComplementI1) =>
% 107.77/14.58 ((
% 107.77/14.58 (doubleComplementE1) =>
% 107.77/14.58 ((
% 107.77/14.58 (doubleComplementSub1) =>
% 107.77/14.58 ((
% 107.77/14.58 (doubleComplementSub2) =>
% 107.77/14.58 ((
% 107.77/14.58 (doubleComplementEq) =>
% 107.77/14.58 ((
% 107.77/14.58 (complementTnotintersectT) =>
% 107.77/14.58 ((
% 107.77/14.58 (complementImpComplementIntersect) =>
% 107.77/14.58 ((
% 107.77/14.58 (complementSubsetComplementIntersect) =>
% 107.77/14.58 ((
% 107.77/14.58 (complementInPowersetComplementIntersect) =>
% 107.77/14.58 ((
% 107.77/14.58 (contraSubsetComplement) =>
% 107.77/14.58 ((
% 107.77/14.58 (complementTcontraSubset) =>
% 107.77/14.58 ((
% 107.77/14.58 (binunionTILcontra) =>
% 107.77/14.58 ((
% 107.77/14.58 (binunionTIRcontra) =>
% 107.77/14.58 ((
% 107.77/14.58 (inIntersectImpInUnion) =>
% 107.77/14.58 ((
% 107.77/14.58 (inIntersectImpInUnion2) =>
% 107.77/14.58 ((
% 107.77/14.58 (inIntersectImpInIntersectUnions) =>
% 107.77/14.58 ((
% 107.77/14.58 (intersectInPowersetIntersectUnions) =>
% 107.77/14.58 ((
% 107.77/14.58 (inComplementUnionImpNotIn1) =>
% 107.77/14.58 ((
% 107.77/14.58 (inComplementUnionImpInComplement1) =>
% 107.77/14.58 ((
% 107.77/14.58 (binunionTE) =>
% 107.77/14.58 ((
% 107.77/14.58 (binunionTEcontra) =>
% 107.77/14.58 ((
% 107.77/14.58 (demorgan2a1) =>
% 107.77/14.58 ((
% 107.77/14.58 (complementUnionInPowersetComplement) =>
% 107.77/14.58 ((
% 107.77/14.58 (demorgan2a2) =>
% 107.77/14.58 ((
% 107.77/14.58 (demorgan1a) =>
% 107.77/14.58 ((
% 107.77/14.58 (demorgan1b) =>
% 107.77/14.58 ((
% 107.77/14.58 (demorgan1) =>
% 107.77/14.58 ((
% 107.77/14.58 (demorgan2a) =>
% 107.77/14.58 ((
% 107.77/14.58 (demorgan2b2) =>
% 107.77/14.58 ((
% 107.77/14.58 (demorgan2b) =>
% 107.77/14.58 ((
% 107.77/14.58 (demorgan2) =>
% 107.77/14.58 ((
% 107.77/14.58 (woz13rule0) =>
% 107.77/14.58 ((
% 107.77/14.58 (woz13rule1) =>
% 107.77/14.58 ((
% 107.77/14.58 (woz13rule2) =>
% 107.77/14.58 ((
% 107.77/14.58 (woz13rule3) =>
% 107.77/14.58 ((
% 107.77/14.58 (woz13rule4) =>
% 107.77/14.58 ((
% 107.77/14.58 (woz1_1) =>
% 107.77/14.58 ((
% 107.77/14.58 (woz1_2) =>
% 107.77/14.58 ((
% 107.77/14.58 (woz1_3) =>
% 107.77/14.58 ((
% 107.77/14.58 (woz1_4) =>
% 107.77/14.58 ((
% 107.77/14.58 (woz1_5) =>
% 107.77/14.58 ((
% 107.77/14.58 (breln1all2) =>
% 107.77/14.58 ((
% 107.77/14.58 (breln1SetBreln1) =>
% 107.77/14.58 ((
% 107.77/14.58 (choice2fnsingleton) =>
% 107.77/14.58 ((
% 107.77/14.58 (setOfPairsIsBReln1) =>
% 107.77/14.58 ((
% 107.77/14.58 (breln1all1) =>
% 107.77/14.58 ((
% 107.77/14.58 (subbreln1) =>
% 107.77/14.58 ((
% 107.77/14.58 (eqbreln1) =>
% 107.77/14.58 ((
% 107.77/14.58 (breln1invprop) =>
% 107.77/14.58 ((
% 107.77/14.58 (breln1invI) =>
% 107.77/14.58 ((
% 107.77/14.58 (breln1invE) =>
% 107.77/14.58 ((
% 107.77/14.58 (breln1compprop) =>
% 107.77/14.58 ((
% 107.77/14.58 (breln1compI) =>
% 107.77/14.58 ((
% 107.77/14.58 (breln1compE) =>
% 107.77/14.58 ((
% 107.77/14.58 (breln1compEex) =>
% 107.77/14.58 ((
% 107.77/14.58 (breln1unionprop) =>
% 107.77/14.58 ((
% 107.77/14.58 (breln1unionIL) =>
% 107.77/14.58 ((
% 107.77/14.58 (breln1unionIR) =>
% 107.77/14.58 ((
% 107.77/14.58 (breln1unionI) =>
% 107.77/14.58 ((
% 107.77/14.58 (breln1unionE) =>
% 107.77/14.58 ((
% 107.77/14.58 (breln1unionEcases) =>
% 107.77/14.58 ((
% 107.77/14.58 (breln1unionCommutes) =>
% 107.77/14.58 ((
% 107.77/14.58 (woz2Ex) =>
% 107.77/14.58 ((
% 107.77/14.58 (woz2W) =>
% 107.77/14.58 ((
% 107.77/14.58 (woz2A) =>
% 107.77/14.58 ((
% 107.77/14.58 (woz2B) =>
% 107.77/14.58 ((
% 107.77/14.58 (image1Ex) =>
% 107.77/14.58 ((
% 107.77/14.58 (image1Ex1) =>
% 107.77/14.58 ((
% 107.77/14.58 (image1Equiv) =>
% 107.77/14.58 ((
% 107.77/14.58 (image1E) =>
% 107.77/14.58 ((
% 107.77/14.58 (image1I) =>
% 107.77/14.58 ((
% 107.77/14.58 (injFuncInInjFuncSet) =>
% 107.77/14.58 ((
% 107.77/14.58 (injFuncSetFuncIn) =>
% 107.77/14.58 ((
% 107.77/14.58 (injFuncSetFuncInj) =>
% 107.77/14.58 ((
% 107.77/14.58 (surjFuncSetFuncIn) =>
% 107.77/14.58 ((
% 107.77/14.58 (surjFuncSetFuncSurj) =>
% 107.77/14.58 ((
% 107.77/14.58 (leftInvIsSurj) =>
% 107.77/14.58 ((
% 107.77/14.58 (surjCantorThm) =>
% 107.77/14.58 ((
% 107.77/14.58 (!!) @ (
% 107.77/14.58 (('#S') @ (
% 107.77/14.58 (
% 107.77/14.58 ('#B') @ (
% 107.77/14.58 =>) @
% 107.77/14.58 nonempty)) @
% 107.77/14.58 (
% 107.77/14.58 (
% 107.77/14.58 ('#B') @ (
% 107.77/14.58 ??) @
% 107.77/14.58 (
% 107.77/14.58 (
% 107.77/14.58 ('#S') @ (
% 107.77/14.58 (
% 107.77/14.58 ('#B') @ (
% 107.77/14.58 '#S') @
% 107.77/14.58 (
% 107.77/14.58 (
% 107.77/14.58 ('#B') @ (
% 107.77/14.58 (
% 107.77/14.58 ('#B') @ (
% 107.77/14.58 &))) @
% 107.77/14.58 (
% 107.77/14.58 (
% 107.77/14.58 ('#C') @ in)))))) @
% 107.77/14.58 (
% 107.77/14.58 (
% 107.77/14.58 ('#C') @ (
% 107.77/14.58 (
% 107.77/14.58 ('#B') @ (
% 107.77/14.58 '#C') @
% 107.77/14.58 (
% 107.77/14.58 (
% 107.77/14.58 ('#B') @ (
% 107.77/14.58 (
% 107.77/14.58 ('#B') @ (
% 107.77/14.58 =))) @
% 107.77/14.58 (
% 107.77/14.58 (
% 107.77/14.58 ('#C') @ binintersect)))))) @
% 107.77/14.58 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 107.77/14.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1615])).
% 107.77/14.58 thf(zip_derived_cl1637, plain,
% 107.77/14.58 (~ (((kfstpairEq) =>
% 107.77/14.58 (((cartprodfstin) =>
% 107.77/14.58 (((setukpairinjL2) =>
% 107.77/14.58 (((setukpairinjL) =>
% 107.77/14.58 (((setukpairinjR11) =>
% 107.77/14.58 (((setukpairinjR12) =>
% 107.77/14.58 (((setukpairinjR1) =>
% 107.77/14.58 (((upairequniteq) =>
% 107.77/14.58 (((setukpairinjR2) =>
% 107.77/14.58 (((setukpairinjR) =>
% 107.77/14.58 (((ksndsingleton) =>
% 107.77/14.58 (((ksndpairEq) =>
% 107.77/14.58 (((kpairsurjEq) =>
% 107.77/14.58 (((cartprodsndin) =>
% 107.77/14.58 (((cartprodpairmemEL) =>
% 107.77/14.58 (((cartprodpairmemER) =>
% 107.77/14.58 (((cartprodmempaircEq) =>
% 107.77/14.58 (((cartprodfstpairEq) =>
% 107.77/14.58 (((cartprodsndpairEq) =>
% 107.77/14.58 (((cartprodpairsurjEq) =>
% 107.77/14.58 (((dpsetconstrI) =>
% 107.77/14.58 (((dpsetconstrSub) =>
% 107.77/14.58 (((setOfPairsIsBReln) =>
% 107.77/14.58 (((dpsetconstrERa) =>
% 107.77/14.58 (((dpsetconstrEL1) =>
% 107.77/14.58 (((dpsetconstrEL2) =>
% 107.77/14.58 (((dpsetconstrER) =>
% 107.77/14.58 (((funcImageSingleton) =>
% 107.77/14.58 (((apProp) =>
% 107.77/14.58 (((app) =>
% 107.77/14.58 ((
% 107.77/14.58 (infuncsetfunc) =>
% 107.77/14.58 ((
% 107.77/14.58 (ap2p) =>
% 107.77/14.58 ((
% 107.77/14.58 (funcinfuncset) =>
% 107.77/14.58 ((
% 107.77/14.58 (lamProp) =>
% 107.77/14.58 ((
% 107.77/14.58 (lamp) =>
% 107.77/14.58 ((
% 107.77/14.58 (lam2p) =>
% 107.77/14.58 ((
% 107.77/14.58 (brelnall1) =>
% 107.77/14.58 ((
% 107.77/14.58 (brelnall2) =>
% 107.77/14.58 ((
% 107.77/14.58 (ex1E2) =>
% 107.77/14.58 ((
% 107.77/14.58 (funcGraphProp1) =>
% 107.77/14.58 ((
% 107.77/14.58 (funcGraphProp3) =>
% 107.77/14.58 ((
% 107.77/14.58 (funcGraphProp2) =>
% 107.77/14.58 ((
% 107.77/14.58 (funcextLem) =>
% 107.77/14.58 ((
% 107.77/14.58 (funcGraphProp4) =>
% 107.77/14.58 ((
% 107.77/14.58 (subbreln) =>
% 107.77/14.58 ((
% 107.77/14.58 (eqbreln) =>
% 107.77/14.58 ((
% 107.77/14.58 (funcext) =>
% 107.77/14.58 ((
% 107.77/14.58 (funcext2) =>
% 107.77/14.58 ((
% 107.77/14.58 (ap2apEq1) =>
% 107.77/14.58 ((
% 107.77/14.58 (ap2apEq2) =>
% 107.77/14.58 ((
% 107.77/14.58 (beta1) =>
% 107.77/14.58 ((
% 107.77/14.58 (eta1) =>
% 107.77/14.58 ((
% 107.77/14.58 (lam2lamEq) =>
% 107.77/14.58 ((
% 107.77/14.58 (beta2) =>
% 107.77/14.58 ((
% 107.77/14.58 (eta2) =>
% 107.77/14.58 ((
% 107.77/14.58 (iffalseProp1) =>
% 107.77/14.58 ((
% 107.77/14.58 (iffalseProp2) =>
% 107.77/14.58 ((
% 107.77/14.58 (iftrueProp1) =>
% 107.77/14.58 ((
% 107.77/14.58 (iftrueProp2) =>
% 107.77/14.58 ((
% 107.77/14.58 (ifSingleton) =>
% 107.77/14.58 ((
% 107.77/14.58 (ifp) =>
% 107.77/14.58 ((
% 107.77/14.58 (theeq) =>
% 107.77/14.58 ((
% 107.77/14.58 (iftrue) =>
% 107.77/14.58 ((
% 107.77/14.58 (iffalse) =>
% 107.77/14.58 ((
% 107.77/14.58 (iftrueorfalse) =>
% 107.77/14.58 ((
% 107.77/14.58 (binintersectT_lem) =>
% 107.77/14.58 ((
% 107.77/14.58 (binunionT_lem) =>
% 107.77/14.58 ((
% 107.77/14.58 (powersetT_lem) =>
% 107.77/14.58 ((
% 107.77/14.58 (setminusT_lem) =>
% 107.77/14.58 ((
% 107.77/14.58 (complementT_lem) =>
% 107.77/14.58 ((
% 107.77/14.58 (setextT) =>
% 107.77/14.58 ((
% 107.77/14.58 (subsetTI) =>
% 107.77/14.58 ((
% 107.77/14.58 (powersetTI1) =>
% 107.77/14.58 ((
% 107.77/14.58 (powersetTE1) =>
% 107.77/14.58 ((
% 107.77/14.58 (complementTI1) =>
% 107.77/14.58 ((
% 107.77/14.58 (complementTE1) =>
% 107.77/14.58 ((
% 107.77/14.58 (binintersectTELcontra) =>
% 107.77/14.58 ((
% 107.77/14.58 (binintersectTERcontra) =>
% 107.77/14.58 ((
% 107.77/14.58 (contrasubsetT) =>
% 107.77/14.58 ((
% 107.77/14.58 (contrasubsetT1) =>
% 107.77/14.58 ((
% 107.77/14.58 (contrasubsetT2) =>
% 107.77/14.58 ((
% 107.77/14.58 (contrasubsetT3) =>
% 107.77/14.58 ((
% 107.77/14.58 (doubleComplementI1) =>
% 107.77/14.58 ((
% 107.77/14.58 (doubleComplementE1) =>
% 107.77/14.58 ((
% 107.77/14.58 (doubleComplementSub1) =>
% 107.77/14.58 ((
% 107.77/14.58 (doubleComplementSub2) =>
% 107.77/14.58 ((
% 107.77/14.58 (doubleComplementEq) =>
% 107.77/14.58 ((
% 107.77/14.58 (complementTnotintersectT) =>
% 107.77/14.58 ((
% 107.77/14.58 (complementImpComplementIntersect) =>
% 107.77/14.58 ((
% 107.77/14.58 (complementSubsetComplementIntersect) =>
% 107.77/14.58 ((
% 107.77/14.58 (complementInPowersetComplementIntersect) =>
% 107.77/14.58 ((
% 107.77/14.58 (contraSubsetComplement) =>
% 107.77/14.58 ((
% 107.77/14.58 (complementTcontraSubset) =>
% 107.77/14.58 ((
% 107.77/14.58 (binunionTILcontra) =>
% 107.77/14.58 ((
% 107.77/14.58 (binunionTIRcontra) =>
% 107.77/14.58 ((
% 107.77/14.58 (inIntersectImpInUnion) =>
% 107.77/14.58 ((
% 107.77/14.58 (inIntersectImpInUnion2) =>
% 107.77/14.58 ((
% 107.77/14.58 (inIntersectImpInIntersectUnions) =>
% 107.77/14.58 ((
% 107.77/14.58 (intersectInPowersetIntersectUnions) =>
% 107.77/14.58 ((
% 107.77/14.58 (inComplementUnionImpNotIn1) =>
% 107.77/14.58 ((
% 107.77/14.58 (inComplementUnionImpInComplement1) =>
% 107.77/14.58 ((
% 107.77/14.58 (binunionTE) =>
% 107.77/14.58 ((
% 107.77/14.58 (binunionTEcontra) =>
% 107.77/14.58 ((
% 107.77/14.58 (demorgan2a1) =>
% 107.77/14.58 ((
% 107.77/14.58 (complementUnionInPowersetComplement) =>
% 107.77/14.58 ((
% 107.77/14.58 (demorgan2a2) =>
% 107.77/14.58 ((
% 107.77/14.58 (demorgan1a) =>
% 107.77/14.58 ((
% 107.77/14.58 (demorgan1b) =>
% 107.77/14.58 ((
% 107.77/14.58 (demorgan1) =>
% 107.77/14.58 ((
% 107.77/14.58 (demorgan2a) =>
% 107.77/14.58 ((
% 107.77/14.58 (demorgan2b2) =>
% 107.77/14.58 ((
% 107.77/14.58 (demorgan2b) =>
% 107.77/14.58 ((
% 107.77/14.58 (demorgan2) =>
% 107.77/14.58 ((
% 107.77/14.58 (woz13rule0) =>
% 107.77/14.58 ((
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% 107.77/14.58 ((
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% 107.77/14.59 ((
% 107.77/14.59 (woz1_2) =>
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% 107.77/14.59 (woz1_3) =>
% 107.77/14.59 ((
% 107.77/14.59 (woz1_4) =>
% 107.77/14.59 ((
% 107.77/14.59 (woz1_5) =>
% 107.77/14.59 ((
% 107.77/14.59 (breln1all2) =>
% 107.77/14.59 ((
% 107.77/14.59 (breln1SetBreln1) =>
% 107.77/14.59 ((
% 107.77/14.59 (choice2fnsingleton) =>
% 107.77/14.59 ((
% 107.77/14.59 (setOfPairsIsBReln1) =>
% 107.77/14.59 ((
% 107.77/14.59 (breln1all1) =>
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% 107.77/14.59 ((
% 107.77/14.59 (breln1invI) =>
% 107.77/14.59 ((
% 107.77/14.59 (breln1invE) =>
% 107.77/14.59 ((
% 107.77/14.59 (breln1compprop) =>
% 107.77/14.59 ((
% 107.77/14.59 (breln1compI) =>
% 107.77/14.59 ((
% 107.77/14.59 (breln1compE) =>
% 107.77/14.59 ((
% 107.77/14.59 (breln1compEex) =>
% 107.77/14.59 ((
% 107.77/14.59 (breln1unionprop) =>
% 107.77/14.59 ((
% 107.77/14.59 (breln1unionIL) =>
% 107.77/14.59 ((
% 107.77/14.59 (breln1unionIR) =>
% 107.77/14.59 ((
% 107.77/14.59 (breln1unionI) =>
% 107.77/14.59 ((
% 107.77/14.59 (breln1unionE) =>
% 107.77/14.59 ((
% 107.77/14.59 (breln1unionEcases) =>
% 107.77/14.59 ((
% 107.77/14.59 (breln1unionCommutes) =>
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% 107.77/14.59 ((
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% 107.77/14.59 ((
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% 107.77/14.59 ((
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% 107.77/14.59 ((
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% 107.77/14.59 ((
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% 107.77/14.59 ((
% 107.77/14.59 (injFuncSetFuncInj) =>
% 107.77/14.59 ((
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% 107.77/14.59 ((
% 107.77/14.59 (surjFuncSetFuncSurj) =>
% 107.77/14.59 ((
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% 107.77/14.59 (surjCantorThm) =>
% 107.77/14.59 ((
% 107.77/14.59 (!!) @ (
% 107.77/14.59 (('#S') @ (
% 107.77/14.59 (
% 107.77/14.59 ('#B') @ (
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% 107.77/14.59 nonempty)) @
% 107.77/14.59 (
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% 107.77/14.59 (
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% 107.77/14.59 (
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% 107.77/14.59 (
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% 107.77/14.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1625])).
% 107.77/14.59 thf(zip_derived_cl1649, plain,
% 107.77/14.59 (~ (((cartprodfstin) =>
% 107.77/14.59 (((setukpairinjL2) =>
% 107.77/14.59 (((setukpairinjL) =>
% 107.77/14.59 (((setukpairinjR11) =>
% 107.77/14.59 (((setukpairinjR12) =>
% 107.77/14.59 (((setukpairinjR1) =>
% 107.77/14.59 (((upairequniteq) =>
% 107.77/14.59 (((setukpairinjR2) =>
% 107.77/14.59 (((setukpairinjR) =>
% 107.77/14.59 (((ksndsingleton) =>
% 107.77/14.59 (((ksndpairEq) =>
% 107.77/14.59 (((kpairsurjEq) =>
% 107.77/14.59 (((cartprodsndin) =>
% 107.77/14.59 (((cartprodpairmemEL) =>
% 107.77/14.59 (((cartprodpairmemER) =>
% 107.77/14.59 (((cartprodmempaircEq) =>
% 107.77/14.59 (((cartprodfstpairEq) =>
% 107.77/14.59 (((cartprodsndpairEq) =>
% 107.77/14.59 (((cartprodpairsurjEq) =>
% 107.77/14.59 (((dpsetconstrI) =>
% 107.77/14.59 (((dpsetconstrSub) =>
% 107.77/14.59 (((setOfPairsIsBReln) =>
% 107.77/14.59 (((dpsetconstrERa) =>
% 107.77/14.59 (((dpsetconstrEL1) =>
% 107.77/14.59 (((dpsetconstrEL2) =>
% 107.77/14.59 (((dpsetconstrER) =>
% 107.77/14.59 (((funcImageSingleton) =>
% 107.77/14.59 (((apProp) =>
% 107.77/14.59 (((app) =>
% 107.77/14.59 (((infuncsetfunc) =>
% 107.77/14.59 ((
% 107.77/14.59 (ap2p) =>
% 107.77/14.59 ((
% 107.77/14.59 (funcinfuncset) =>
% 107.77/14.59 ((
% 107.77/14.59 (lamProp) =>
% 107.77/14.59 ((
% 107.77/14.59 (lamp) =>
% 107.77/14.59 ((
% 107.77/14.59 (lam2p) =>
% 107.77/14.59 ((
% 107.77/14.59 (brelnall1) =>
% 107.77/14.59 ((
% 107.77/14.59 (brelnall2) =>
% 107.77/14.59 ((
% 107.77/14.59 (ex1E2) =>
% 107.77/14.59 ((
% 107.77/14.59 (funcGraphProp1) =>
% 107.77/14.59 ((
% 107.77/14.59 (funcGraphProp3) =>
% 107.77/14.59 ((
% 107.77/14.59 (funcGraphProp2) =>
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% 107.77/14.59 (funcextLem) =>
% 107.77/14.59 ((
% 107.77/14.59 (funcGraphProp4) =>
% 107.77/14.59 ((
% 107.77/14.59 (subbreln) =>
% 107.77/14.59 ((
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% 107.77/14.59 ((
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% 107.77/14.59 ((
% 107.77/14.59 (funcext2) =>
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% 107.77/14.59 (beta2) =>
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% 107.77/14.59 (setextT) =>
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% 107.77/14.59 (powersetTE1) =>
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% 107.77/14.59 ((
% 107.77/14.59 (complementTE1) =>
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% 107.77/14.59 ((
% 107.77/14.59 (binintersectTERcontra) =>
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% 107.77/14.59 (contrasubsetT2) =>
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% 107.77/14.59 (contrasubsetT3) =>
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% 107.77/14.59 ((
% 107.77/14.59 (doubleComplementE1) =>
% 107.77/14.59 ((
% 107.77/14.59 (doubleComplementSub1) =>
% 107.77/14.59 ((
% 107.77/14.59 (doubleComplementSub2) =>
% 107.77/14.59 ((
% 107.77/14.59 (doubleComplementEq) =>
% 107.77/14.59 ((
% 107.77/14.59 (complementTnotintersectT) =>
% 107.77/14.59 ((
% 107.77/14.59 (complementImpComplementIntersect) =>
% 107.77/14.59 ((
% 107.77/14.59 (complementSubsetComplementIntersect) =>
% 107.77/14.59 ((
% 107.77/14.59 (complementInPowersetComplementIntersect) =>
% 107.77/14.59 ((
% 107.77/14.59 (contraSubsetComplement) =>
% 107.77/14.59 ((
% 107.77/14.59 (complementTcontraSubset) =>
% 107.77/14.59 ((
% 107.77/14.59 (binunionTILcontra) =>
% 107.77/14.59 ((
% 107.77/14.59 (binunionTIRcontra) =>
% 107.77/14.59 ((
% 107.77/14.59 (inIntersectImpInUnion) =>
% 107.77/14.59 ((
% 107.77/14.59 (inIntersectImpInUnion2) =>
% 107.77/14.59 ((
% 107.77/14.59 (inIntersectImpInIntersectUnions) =>
% 107.77/14.59 ((
% 107.77/14.59 (intersectInPowersetIntersectUnions) =>
% 107.77/14.59 ((
% 107.77/14.59 (inComplementUnionImpNotIn1) =>
% 107.77/14.59 ((
% 107.77/14.59 (inComplementUnionImpInComplement1) =>
% 107.77/14.59 ((
% 107.77/14.59 (binunionTE) =>
% 107.77/14.59 ((
% 107.77/14.59 (binunionTEcontra) =>
% 107.77/14.59 ((
% 107.77/14.59 (demorgan2a1) =>
% 107.77/14.59 ((
% 107.77/14.59 (complementUnionInPowersetComplement) =>
% 107.77/14.59 ((
% 107.77/14.59 (demorgan2a2) =>
% 107.77/14.59 ((
% 107.77/14.59 (demorgan1a) =>
% 107.77/14.59 ((
% 107.77/14.59 (demorgan1b) =>
% 107.77/14.59 ((
% 107.77/14.59 (demorgan1) =>
% 107.77/14.59 ((
% 107.77/14.59 (demorgan2a) =>
% 107.77/14.59 ((
% 107.77/14.59 (demorgan2b2) =>
% 107.77/14.59 ((
% 107.77/14.59 (demorgan2b) =>
% 107.77/14.59 ((
% 107.77/14.59 (demorgan2) =>
% 107.77/14.59 ((
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% 107.77/14.59 ((
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% 107.77/14.59 ((
% 107.77/14.59 (woz13rule2) =>
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% 107.77/14.59 (woz13rule3) =>
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% 107.77/14.59 (woz13rule4) =>
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% 107.77/14.59 (woz1_5) =>
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% 107.77/14.59 ((
% 107.77/14.59 (breln1SetBreln1) =>
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% 107.77/14.59 ((
% 107.77/14.59 (breln1all1) =>
% 107.77/14.59 ((
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% 107.77/14.59 ((
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% 107.77/14.59 ((
% 107.77/14.59 (breln1compE) =>
% 107.77/14.59 ((
% 107.77/14.59 (breln1compEex) =>
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% 107.77/14.59 (breln1unionprop) =>
% 107.77/14.59 ((
% 107.77/14.59 (breln1unionIL) =>
% 107.77/14.59 ((
% 107.77/14.59 (breln1unionIR) =>
% 107.77/14.59 ((
% 107.77/14.59 (breln1unionI) =>
% 107.77/14.59 ((
% 107.77/14.59 (breln1unionE) =>
% 107.77/14.59 ((
% 107.77/14.59 (breln1unionEcases) =>
% 107.77/14.59 ((
% 107.77/14.59 (breln1unionCommutes) =>
% 107.77/14.59 ((
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% 107.77/14.59 ((
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% 107.77/14.59 ((
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% 107.77/14.59 ((
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% 107.77/14.59 (image1E) =>
% 107.77/14.59 ((
% 107.77/14.59 (image1I) =>
% 107.77/14.59 ((
% 107.77/14.59 (injFuncInInjFuncSet) =>
% 107.77/14.59 ((
% 107.77/14.59 (injFuncSetFuncIn) =>
% 107.77/14.59 ((
% 107.77/14.59 (injFuncSetFuncInj) =>
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% 107.77/14.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1637])).
% 107.77/14.59 thf(zip_derived_cl1664, plain,
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% 107.92/14.59 (((cartprodpairmemER) =>
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% 107.92/14.59 ((
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% 107.92/14.59 ((
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% 107.92/14.59 (beta1) =>
% 107.92/14.59 ((
% 107.92/14.59 (eta1) =>
% 107.92/14.59 ((
% 107.92/14.59 (lam2lamEq) =>
% 107.92/14.59 ((
% 107.92/14.59 (beta2) =>
% 107.92/14.59 ((
% 107.92/14.59 (eta2) =>
% 107.92/14.59 ((
% 107.92/14.59 (iffalseProp1) =>
% 107.92/14.59 ((
% 107.92/14.59 (iffalseProp2) =>
% 107.92/14.59 ((
% 107.92/14.59 (iftrueProp1) =>
% 107.92/14.59 ((
% 107.92/14.59 (iftrueProp2) =>
% 107.92/14.59 ((
% 107.92/14.59 (ifSingleton) =>
% 107.92/14.59 ((
% 107.92/14.59 (ifp) =>
% 107.92/14.59 ((
% 107.92/14.59 (theeq) =>
% 107.92/14.59 ((
% 107.92/14.59 (iftrue) =>
% 107.92/14.59 ((
% 107.92/14.59 (iffalse) =>
% 107.92/14.59 ((
% 107.92/14.59 (iftrueorfalse) =>
% 107.92/14.59 ((
% 107.92/14.59 (binintersectT_lem) =>
% 107.92/14.59 ((
% 107.92/14.59 (binunionT_lem) =>
% 107.92/14.59 ((
% 107.92/14.59 (powersetT_lem) =>
% 107.92/14.59 ((
% 107.92/14.59 (setminusT_lem) =>
% 107.92/14.59 ((
% 107.92/14.59 (complementT_lem) =>
% 107.92/14.59 ((
% 107.92/14.59 (setextT) =>
% 107.92/14.59 ((
% 107.92/14.59 (subsetTI) =>
% 107.92/14.59 ((
% 107.92/14.59 (powersetTI1) =>
% 107.92/14.59 ((
% 107.92/14.59 (powersetTE1) =>
% 107.92/14.59 ((
% 107.92/14.59 (complementTI1) =>
% 107.92/14.59 ((
% 107.92/14.59 (complementTE1) =>
% 107.92/14.59 ((
% 107.92/14.59 (binintersectTELcontra) =>
% 107.92/14.59 ((
% 107.92/14.59 (binintersectTERcontra) =>
% 107.92/14.59 ((
% 107.92/14.59 (contrasubsetT) =>
% 107.92/14.59 ((
% 107.92/14.59 (contrasubsetT1) =>
% 107.92/14.59 ((
% 107.92/14.59 (contrasubsetT2) =>
% 107.92/14.59 ((
% 107.92/14.59 (contrasubsetT3) =>
% 107.92/14.59 ((
% 107.92/14.59 (doubleComplementI1) =>
% 107.92/14.59 ((
% 107.92/14.59 (doubleComplementE1) =>
% 107.92/14.59 ((
% 107.92/14.59 (doubleComplementSub1) =>
% 107.92/14.59 ((
% 107.92/14.59 (doubleComplementSub2) =>
% 107.92/14.59 ((
% 107.92/14.59 (doubleComplementEq) =>
% 107.92/14.59 ((
% 107.92/14.59 (complementTnotintersectT) =>
% 107.92/14.59 ((
% 107.92/14.59 (complementImpComplementIntersect) =>
% 107.92/14.59 ((
% 107.92/14.59 (complementSubsetComplementIntersect) =>
% 107.92/14.59 ((
% 107.92/14.59 (complementInPowersetComplementIntersect) =>
% 107.92/14.59 ((
% 107.92/14.59 (contraSubsetComplement) =>
% 107.92/14.59 ((
% 107.92/14.59 (complementTcontraSubset) =>
% 107.92/14.59 ((
% 107.92/14.59 (binunionTILcontra) =>
% 107.92/14.59 ((
% 107.92/14.59 (binunionTIRcontra) =>
% 107.92/14.59 ((
% 107.92/14.59 (inIntersectImpInUnion) =>
% 107.92/14.59 ((
% 107.92/14.59 (inIntersectImpInUnion2) =>
% 107.92/14.59 ((
% 107.92/14.59 (inIntersectImpInIntersectUnions) =>
% 107.92/14.59 ((
% 107.92/14.59 (intersectInPowersetIntersectUnions) =>
% 107.92/14.59 ((
% 107.92/14.59 (inComplementUnionImpNotIn1) =>
% 107.92/14.59 ((
% 107.92/14.59 (inComplementUnionImpInComplement1) =>
% 107.92/14.59 ((
% 107.92/14.59 (binunionTE) =>
% 107.92/14.59 ((
% 107.92/14.59 (binunionTEcontra) =>
% 107.92/14.59 ((
% 107.92/14.59 (demorgan2a1) =>
% 107.92/14.59 ((
% 107.92/14.59 (complementUnionInPowersetComplement) =>
% 107.92/14.59 ((
% 107.92/14.59 (demorgan2a2) =>
% 107.92/14.59 ((
% 107.92/14.59 (demorgan1a) =>
% 107.92/14.59 ((
% 107.92/14.59 (demorgan1b) =>
% 107.92/14.59 ((
% 107.92/14.59 (demorgan1) =>
% 107.92/14.59 ((
% 107.92/14.59 (demorgan2a) =>
% 107.92/14.59 ((
% 107.92/14.59 (demorgan2b2) =>
% 107.92/14.59 ((
% 107.92/14.59 (demorgan2b) =>
% 107.92/14.59 ((
% 107.92/14.59 (demorgan2) =>
% 107.92/14.59 ((
% 107.92/14.59 (woz13rule0) =>
% 107.92/14.59 ((
% 107.92/14.59 (woz13rule1) =>
% 107.92/14.59 ((
% 107.92/14.59 (woz13rule2) =>
% 107.92/14.59 ((
% 107.92/14.59 (woz13rule3) =>
% 107.92/14.59 ((
% 107.92/14.59 (woz13rule4) =>
% 107.92/14.59 ((
% 107.92/14.59 (woz1_1) =>
% 107.92/14.59 ((
% 107.92/14.59 (woz1_2) =>
% 107.92/14.59 ((
% 107.92/14.59 (woz1_3) =>
% 107.92/14.59 ((
% 107.92/14.59 (woz1_4) =>
% 107.92/14.59 ((
% 107.92/14.59 (woz1_5) =>
% 107.92/14.59 ((
% 107.92/14.59 (breln1all2) =>
% 107.92/14.59 ((
% 107.92/14.59 (breln1SetBreln1) =>
% 107.92/14.59 ((
% 107.92/14.59 (choice2fnsingleton) =>
% 107.92/14.59 ((
% 107.92/14.59 (setOfPairsIsBReln1) =>
% 107.92/14.59 ((
% 107.92/14.59 (breln1all1) =>
% 107.92/14.59 ((
% 107.92/14.59 (subbreln1) =>
% 107.92/14.59 ((
% 107.92/14.59 (eqbreln1) =>
% 107.92/14.59 ((
% 107.92/14.59 (breln1invprop) =>
% 107.92/14.59 ((
% 107.92/14.59 (breln1invI) =>
% 107.92/14.59 ((
% 107.92/14.59 (breln1invE) =>
% 107.92/14.59 ((
% 107.92/14.59 (breln1compprop) =>
% 107.92/14.59 ((
% 107.92/14.59 (breln1compI) =>
% 107.92/14.59 ((
% 107.92/14.59 (breln1compE) =>
% 107.92/14.59 ((
% 107.92/14.59 (breln1compEex) =>
% 107.92/14.59 ((
% 107.92/14.59 (breln1unionprop) =>
% 107.92/14.59 ((
% 107.92/14.59 (breln1unionIL) =>
% 107.92/14.59 ((
% 107.92/14.59 (breln1unionIR) =>
% 107.92/14.59 ((
% 107.92/14.59 (breln1unionI) =>
% 107.92/14.59 ((
% 107.92/14.59 (breln1unionE) =>
% 107.92/14.59 ((
% 107.92/14.59 (breln1unionEcases) =>
% 107.92/14.59 ((
% 107.92/14.59 (breln1unionCommutes) =>
% 107.92/14.59 ((
% 107.92/14.59 (woz2Ex) =>
% 107.92/14.59 ((
% 107.92/14.59 (woz2W) =>
% 107.92/14.59 ((
% 107.92/14.59 (woz2A) =>
% 107.92/14.59 ((
% 107.92/14.59 (woz2B) =>
% 107.92/14.59 ((
% 107.92/14.59 (image1Ex) =>
% 107.92/14.59 ((
% 107.92/14.59 (image1Ex1) =>
% 107.92/14.59 ((
% 107.92/14.59 (image1Equiv) =>
% 107.92/14.59 ((
% 107.92/14.59 (image1E) =>
% 107.92/14.59 ((
% 107.92/14.59 (image1I) =>
% 107.92/14.59 ((
% 107.92/14.59 (injFuncInInjFuncSet) =>
% 107.92/14.59 ((
% 107.92/14.59 (injFuncSetFuncIn) =>
% 107.92/14.59 ((
% 107.92/14.59 (injFuncSetFuncInj) =>
% 107.92/14.59 ((
% 107.92/14.59 (surjFuncSetFuncIn) =>
% 107.92/14.59 ((
% 107.92/14.59 (surjFuncSetFuncSurj) =>
% 107.92/14.59 ((
% 107.92/14.59 (leftInvIsSurj) =>
% 107.92/14.59 ((
% 107.92/14.59 (surjCantorThm) =>
% 107.92/14.59 ((
% 107.92/14.59 (!!) @ (
% 107.92/14.59 (('#S') @ (
% 107.92/14.59 (
% 107.92/14.59 ('#B') @ (
% 107.92/14.59 =>) @
% 107.92/14.59 nonempty)) @
% 107.92/14.59 (
% 107.92/14.59 (
% 107.92/14.59 ('#B') @ (
% 107.92/14.59 ??) @
% 107.92/14.59 (
% 107.92/14.59 (
% 107.92/14.59 ('#S') @ (
% 107.92/14.59 (
% 107.92/14.59 ('#B') @ (
% 107.92/14.59 '#S') @
% 107.92/14.59 (
% 107.92/14.59 (
% 107.92/14.59 ('#B') @ (
% 107.92/14.59 (
% 107.92/14.59 ('#B') @ (
% 107.92/14.59 &))) @
% 107.92/14.59 (
% 107.92/14.59 (
% 107.92/14.59 ('#C') @ in)))))) @
% 107.92/14.59 (
% 107.92/14.59 (
% 107.92/14.59 ('#C') @ (
% 107.92/14.59 (
% 107.92/14.59 ('#B') @ (
% 107.92/14.59 '#C') @
% 107.92/14.59 (
% 107.92/14.59 (
% 107.92/14.59 ('#B') @ (
% 107.92/14.59 (
% 107.92/14.59 ('#B') @ (
% 107.92/14.59 =))) @
% 107.92/14.59 (
% 107.92/14.59 (
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% 107.92/14.59 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 107.92/14.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1649])).
% 107.92/14.59 thf(zip_derived_cl1678, plain,
% 107.92/14.59 (~ (((setukpairinjL) =>
% 107.92/14.59 (((setukpairinjR11) =>
% 107.92/14.59 (((setukpairinjR12) =>
% 107.92/14.59 (((setukpairinjR1) =>
% 107.92/14.59 (((upairequniteq) =>
% 107.92/14.59 (((setukpairinjR2) =>
% 107.92/14.59 (((setukpairinjR) =>
% 107.92/14.59 (((ksndsingleton) =>
% 107.92/14.59 (((ksndpairEq) =>
% 107.92/14.59 (((kpairsurjEq) =>
% 107.92/14.59 (((cartprodsndin) =>
% 107.92/14.59 (((cartprodpairmemEL) =>
% 107.92/14.59 (((cartprodpairmemER) =>
% 107.92/14.59 (((cartprodmempaircEq) =>
% 107.92/14.59 (((cartprodfstpairEq) =>
% 107.92/14.59 (((cartprodsndpairEq) =>
% 107.92/14.59 (((cartprodpairsurjEq) =>
% 107.92/14.59 (((dpsetconstrI) =>
% 107.92/14.59 (((dpsetconstrSub) =>
% 107.92/14.59 (((setOfPairsIsBReln) =>
% 107.92/14.59 (((dpsetconstrERa) =>
% 107.92/14.59 (((dpsetconstrEL1) =>
% 107.92/14.59 (((dpsetconstrEL2) =>
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% 107.92/14.59 (((app) =>
% 107.92/14.59 (((infuncsetfunc) =>
% 107.92/14.59 (((ap2p) =>
% 107.92/14.59 (((funcinfuncset) =>
% 107.92/14.59 ((
% 107.92/14.59 (lamProp) =>
% 107.92/14.59 ((
% 107.92/14.59 (lamp) =>
% 107.92/14.59 ((
% 107.92/14.59 (lam2p) =>
% 107.92/14.59 ((
% 107.92/14.59 (brelnall1) =>
% 107.92/14.59 ((
% 107.92/14.59 (brelnall2) =>
% 107.92/14.59 ((
% 107.92/14.59 (ex1E2) =>
% 107.92/14.59 ((
% 107.92/14.59 (funcGraphProp1) =>
% 107.92/14.59 ((
% 107.92/14.59 (funcGraphProp3) =>
% 107.92/14.59 ((
% 107.92/14.59 (funcGraphProp2) =>
% 107.92/14.59 ((
% 107.92/14.59 (funcextLem) =>
% 107.92/14.59 ((
% 107.92/14.59 (funcGraphProp4) =>
% 107.92/14.59 ((
% 107.92/14.59 (subbreln) =>
% 107.92/14.59 ((
% 107.92/14.59 (eqbreln) =>
% 107.92/14.59 ((
% 107.92/14.59 (funcext) =>
% 107.92/14.59 ((
% 107.92/14.59 (funcext2) =>
% 107.92/14.59 ((
% 107.92/14.59 (ap2apEq1) =>
% 107.92/14.59 ((
% 107.92/14.59 (ap2apEq2) =>
% 107.92/14.59 ((
% 107.92/14.59 (beta1) =>
% 107.92/14.59 ((
% 107.92/14.59 (eta1) =>
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% 107.92/14.59 (beta2) =>
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% 107.92/14.59 (eta2) =>
% 107.92/14.59 ((
% 107.92/14.59 (iffalseProp1) =>
% 107.92/14.59 ((
% 107.92/14.59 (iffalseProp2) =>
% 107.92/14.59 ((
% 107.92/14.59 (iftrueProp1) =>
% 107.92/14.59 ((
% 107.92/14.59 (iftrueProp2) =>
% 107.92/14.59 ((
% 107.92/14.59 (ifSingleton) =>
% 107.92/14.59 ((
% 107.92/14.59 (ifp) =>
% 107.92/14.59 ((
% 107.92/14.59 (theeq) =>
% 107.92/14.59 ((
% 107.92/14.59 (iftrue) =>
% 107.92/14.59 ((
% 107.92/14.59 (iffalse) =>
% 107.92/14.59 ((
% 107.92/14.59 (iftrueorfalse) =>
% 107.92/14.59 ((
% 107.92/14.59 (binintersectT_lem) =>
% 107.92/14.59 ((
% 107.92/14.59 (binunionT_lem) =>
% 107.92/14.59 ((
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% 107.92/14.59 ((
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% 107.92/14.59 ((
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% 107.92/14.59 ((
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% 107.92/14.59 ((
% 107.92/14.59 (complementTE1) =>
% 107.92/14.59 ((
% 107.92/14.59 (binintersectTELcontra) =>
% 107.92/14.59 ((
% 107.92/14.59 (binintersectTERcontra) =>
% 107.92/14.59 ((
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% 107.92/14.59 ((
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% 107.92/14.59 ((
% 107.92/14.59 (contrasubsetT2) =>
% 107.92/14.59 ((
% 107.92/14.59 (contrasubsetT3) =>
% 107.92/14.59 ((
% 107.92/14.59 (doubleComplementI1) =>
% 107.92/14.59 ((
% 107.92/14.59 (doubleComplementE1) =>
% 107.92/14.59 ((
% 107.92/14.59 (doubleComplementSub1) =>
% 107.92/14.59 ((
% 107.92/14.59 (doubleComplementSub2) =>
% 107.92/14.59 ((
% 107.92/14.59 (doubleComplementEq) =>
% 107.92/14.59 ((
% 107.92/14.59 (complementTnotintersectT) =>
% 107.92/14.59 ((
% 107.92/14.59 (complementImpComplementIntersect) =>
% 107.92/14.59 ((
% 107.92/14.59 (complementSubsetComplementIntersect) =>
% 107.92/14.59 ((
% 107.92/14.59 (complementInPowersetComplementIntersect) =>
% 107.92/14.59 ((
% 107.92/14.59 (contraSubsetComplement) =>
% 107.92/14.59 ((
% 107.92/14.59 (complementTcontraSubset) =>
% 107.92/14.59 ((
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% 107.92/14.59 ((
% 107.92/14.59 (binunionTIRcontra) =>
% 107.92/14.59 ((
% 107.92/14.59 (inIntersectImpInUnion) =>
% 107.92/14.59 ((
% 107.92/14.59 (inIntersectImpInUnion2) =>
% 107.92/14.59 ((
% 107.92/14.59 (inIntersectImpInIntersectUnions) =>
% 107.92/14.59 ((
% 107.92/14.59 (intersectInPowersetIntersectUnions) =>
% 107.92/14.59 ((
% 107.92/14.59 (inComplementUnionImpNotIn1) =>
% 107.92/14.59 ((
% 107.92/14.59 (inComplementUnionImpInComplement1) =>
% 107.92/14.59 ((
% 107.92/14.59 (binunionTE) =>
% 107.92/14.59 ((
% 107.92/14.59 (binunionTEcontra) =>
% 107.92/14.59 ((
% 107.92/14.59 (demorgan2a1) =>
% 107.92/14.59 ((
% 107.92/14.59 (complementUnionInPowersetComplement) =>
% 107.92/14.59 ((
% 107.92/14.59 (demorgan2a2) =>
% 107.92/14.59 ((
% 107.92/14.59 (demorgan1a) =>
% 107.92/14.59 ((
% 107.92/14.59 (demorgan1b) =>
% 107.92/14.59 ((
% 107.92/14.59 (demorgan1) =>
% 107.92/14.59 ((
% 107.92/14.59 (demorgan2a) =>
% 107.92/14.59 ((
% 107.92/14.59 (demorgan2b2) =>
% 107.92/14.59 ((
% 107.92/14.59 (demorgan2b) =>
% 107.92/14.59 ((
% 107.92/14.59 (demorgan2) =>
% 107.92/14.59 ((
% 107.92/14.59 (woz13rule0) =>
% 107.92/14.59 ((
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% 107.92/14.59 ((
% 107.92/14.59 (woz13rule2) =>
% 107.92/14.59 ((
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% 107.92/14.59 ((
% 107.92/14.59 (woz13rule4) =>
% 107.92/14.59 ((
% 107.92/14.59 (woz1_1) =>
% 107.92/14.59 ((
% 107.92/14.59 (woz1_2) =>
% 107.92/14.59 ((
% 107.92/14.59 (woz1_3) =>
% 107.92/14.59 ((
% 107.92/14.59 (woz1_4) =>
% 107.92/14.59 ((
% 107.92/14.59 (woz1_5) =>
% 107.92/14.59 ((
% 107.92/14.59 (breln1all2) =>
% 107.92/14.59 ((
% 107.92/14.59 (breln1SetBreln1) =>
% 107.92/14.59 ((
% 107.92/14.59 (choice2fnsingleton) =>
% 107.92/14.59 ((
% 107.92/14.59 (setOfPairsIsBReln1) =>
% 107.92/14.59 ((
% 107.92/14.59 (breln1all1) =>
% 107.92/14.59 ((
% 107.92/14.59 (subbreln1) =>
% 107.92/14.59 ((
% 107.92/14.59 (eqbreln1) =>
% 107.92/14.59 ((
% 107.92/14.59 (breln1invprop) =>
% 107.92/14.59 ((
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% 107.92/14.59 ((
% 107.92/14.59 (breln1invE) =>
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% 107.92/14.59 ((
% 107.92/14.59 (breln1compE) =>
% 107.92/14.59 ((
% 107.92/14.59 (breln1compEex) =>
% 107.92/14.59 ((
% 107.92/14.59 (breln1unionprop) =>
% 107.92/14.59 ((
% 107.92/14.59 (breln1unionIL) =>
% 107.92/14.59 ((
% 107.92/14.59 (breln1unionIR) =>
% 107.92/14.59 ((
% 107.92/14.59 (breln1unionI) =>
% 107.92/14.59 ((
% 107.92/14.59 (breln1unionE) =>
% 107.92/14.59 ((
% 107.92/14.59 (breln1unionEcases) =>
% 107.92/14.59 ((
% 107.92/14.59 (breln1unionCommutes) =>
% 107.92/14.59 ((
% 107.92/14.59 (woz2Ex) =>
% 107.92/14.59 ((
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% 107.92/14.59 ((
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% 107.92/14.59 (image1I) =>
% 107.92/14.59 ((
% 107.92/14.59 (injFuncInInjFuncSet) =>
% 107.92/14.59 ((
% 107.92/14.59 (injFuncSetFuncIn) =>
% 107.92/14.59 ((
% 107.92/14.59 (injFuncSetFuncInj) =>
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% 107.92/14.59 ((
% 107.92/14.59 (surjFuncSetFuncSurj) =>
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% 107.92/14.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1664])).
% 107.92/14.59 thf(zip_derived_cl1695, plain,
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% 107.92/14.59 ((
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% 107.92/14.59 ((
% 107.92/14.59 (demorgan2b2) =>
% 107.92/14.59 ((
% 107.92/14.59 (demorgan2b) =>
% 107.92/14.59 ((
% 107.92/14.59 (demorgan2) =>
% 107.92/14.59 ((
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% 107.92/14.59 ((
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% 107.92/14.59 ((
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% 107.92/14.59 ((
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% 107.92/14.59 ((
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% 107.92/14.59 ((
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% 107.92/14.59 (breln1unionEcases) =>
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% 107.92/14.59 (breln1unionCommutes) =>
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% 107.92/14.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1678])).
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% 107.92/14.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1695])).
% 107.92/14.59 thf(zip_derived_cl1725, plain,
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% 107.92/14.59 ((
% 107.92/14.59 (iffalseProp2) =>
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% 107.92/14.59 ((
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% 107.92/14.59 ((
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% 107.92/14.59 ((
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% 107.92/14.59 ((
% 107.92/14.59 (complementTE1) =>
% 107.92/14.59 ((
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% 107.92/14.59 ((
% 107.92/14.59 (binintersectTERcontra) =>
% 107.92/14.59 ((
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% 107.92/14.59 ((
% 107.92/14.59 (contrasubsetT1) =>
% 107.92/14.59 ((
% 107.92/14.59 (contrasubsetT2) =>
% 107.92/14.59 ((
% 107.92/14.59 (contrasubsetT3) =>
% 107.92/14.59 ((
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% 107.92/14.59 ((
% 107.92/14.59 (doubleComplementE1) =>
% 107.92/14.59 ((
% 107.92/14.59 (doubleComplementSub1) =>
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% 107.92/14.59 (doubleComplementSub2) =>
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% 107.92/14.59 (doubleComplementEq) =>
% 107.92/14.59 ((
% 107.92/14.59 (complementTnotintersectT) =>
% 107.92/14.59 ((
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% 107.92/14.59 ((
% 107.92/14.59 (complementSubsetComplementIntersect) =>
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% 107.92/14.59 (complementInPowersetComplementIntersect) =>
% 107.92/14.59 ((
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% 107.92/14.59 ((
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% 107.92/14.59 ((
% 107.92/14.59 (binunionTIRcontra) =>
% 107.92/14.59 ((
% 107.92/14.59 (inIntersectImpInUnion) =>
% 107.92/14.59 ((
% 107.92/14.59 (inIntersectImpInUnion2) =>
% 107.92/14.59 ((
% 107.92/14.59 (inIntersectImpInIntersectUnions) =>
% 107.92/14.59 ((
% 107.92/14.59 (intersectInPowersetIntersectUnions) =>
% 107.92/14.59 ((
% 107.92/14.59 (inComplementUnionImpNotIn1) =>
% 107.92/14.59 ((
% 107.92/14.59 (inComplementUnionImpInComplement1) =>
% 107.92/14.59 ((
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% 107.92/14.59 ((
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% 107.92/14.59 ((
% 107.92/14.59 (demorgan2a1) =>
% 107.92/14.59 ((
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% 107.92/14.59 ((
% 107.92/14.59 (demorgan2a2) =>
% 107.92/14.59 ((
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% 107.92/14.59 ((
% 107.92/14.59 (demorgan1b) =>
% 107.92/14.59 ((
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% 107.92/14.59 ((
% 107.92/14.59 (demorgan2a) =>
% 107.92/14.59 ((
% 107.92/14.59 (demorgan2b2) =>
% 107.92/14.59 ((
% 107.92/14.59 (demorgan2b) =>
% 107.92/14.59 ((
% 107.92/14.59 (demorgan2) =>
% 107.92/14.59 ((
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% 107.92/14.59 ((
% 107.92/14.59 (woz13rule1) =>
% 107.92/14.59 ((
% 107.92/14.59 (woz13rule2) =>
% 107.92/14.59 ((
% 107.92/14.59 (woz13rule3) =>
% 107.92/14.59 ((
% 107.92/14.59 (woz13rule4) =>
% 107.92/14.59 ((
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% 107.92/14.59 ((
% 107.92/14.59 (woz1_2) =>
% 107.92/14.59 ((
% 107.92/14.59 (woz1_3) =>
% 107.92/14.59 ((
% 107.92/14.59 (woz1_4) =>
% 107.92/14.59 ((
% 107.92/14.59 (woz1_5) =>
% 107.92/14.59 ((
% 107.92/14.59 (breln1all2) =>
% 107.92/14.59 ((
% 107.92/14.59 (breln1SetBreln1) =>
% 107.92/14.59 ((
% 107.92/14.59 (choice2fnsingleton) =>
% 107.92/14.59 ((
% 107.92/14.59 (setOfPairsIsBReln1) =>
% 107.92/14.59 ((
% 107.92/14.59 (breln1all1) =>
% 107.92/14.59 ((
% 107.92/14.59 (subbreln1) =>
% 107.92/14.59 ((
% 107.92/14.59 (eqbreln1) =>
% 107.92/14.59 ((
% 107.92/14.59 (breln1invprop) =>
% 107.92/14.59 ((
% 107.92/14.59 (breln1invI) =>
% 107.92/14.59 ((
% 107.92/14.59 (breln1invE) =>
% 107.92/14.59 ((
% 107.92/14.59 (breln1compprop) =>
% 107.92/14.59 ((
% 107.92/14.59 (breln1compI) =>
% 107.92/14.59 ((
% 107.92/14.59 (breln1compE) =>
% 107.92/14.59 ((
% 107.92/14.59 (breln1compEex) =>
% 107.92/14.59 ((
% 107.92/14.59 (breln1unionprop) =>
% 107.92/14.59 ((
% 107.92/14.59 (breln1unionIL) =>
% 107.92/14.59 ((
% 107.92/14.59 (breln1unionIR) =>
% 107.92/14.59 ((
% 107.92/14.59 (breln1unionI) =>
% 107.92/14.59 ((
% 107.92/14.59 (breln1unionE) =>
% 107.92/14.59 ((
% 107.92/14.59 (breln1unionEcases) =>
% 107.92/14.59 ((
% 107.92/14.59 (breln1unionCommutes) =>
% 107.92/14.59 ((
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% 107.92/14.59 ((
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% 107.92/14.59 ((
% 107.92/14.59 (image1Ex1) =>
% 107.92/14.59 ((
% 107.92/14.59 (image1Equiv) =>
% 107.92/14.59 ((
% 107.92/14.59 (image1E) =>
% 107.92/14.59 ((
% 107.92/14.59 (image1I) =>
% 107.92/14.59 ((
% 107.92/14.59 (injFuncInInjFuncSet) =>
% 107.92/14.59 ((
% 107.92/14.59 (injFuncSetFuncIn) =>
% 107.92/14.59 ((
% 107.92/14.59 (injFuncSetFuncInj) =>
% 107.92/14.59 ((
% 107.92/14.59 (surjFuncSetFuncIn) =>
% 107.92/14.59 ((
% 107.92/14.59 (surjFuncSetFuncSurj) =>
% 107.92/14.59 ((
% 107.92/14.59 (leftInvIsSurj) =>
% 107.92/14.59 ((
% 107.92/14.59 (surjCantorThm) =>
% 107.92/14.59 ((
% 107.92/14.59 (!!) @ (
% 107.92/14.59 (('#S') @ (
% 107.92/14.59 (
% 107.92/14.59 ('#B') @ (
% 107.92/14.59 =>) @
% 107.92/14.59 nonempty)) @
% 107.92/14.59 (
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% 107.92/14.59 ('#B') @ (
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% 107.92/14.59 (
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% 107.92/14.59 (
% 107.92/14.59 (
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% 107.92/14.59 (
% 107.92/14.59 (
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% 107.92/14.59 (
% 107.92/14.59 (
% 107.92/14.59 ('#B') @ (
% 107.92/14.59 (
% 107.92/14.59 ('#B') @ (
% 107.92/14.59 =))) @
% 107.92/14.59 (
% 107.92/14.59 (
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% 107.92/14.59 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 107.92/14.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1725])).
% 107.92/14.59 thf(zip_derived_cl1749, plain,
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% 107.92/14.59 (((setukpairinjR) =>
% 107.92/14.59 (((ksndsingleton) =>
% 107.92/14.59 (((ksndpairEq) =>
% 107.92/14.59 (((kpairsurjEq) =>
% 107.92/14.59 (((cartprodsndin) =>
% 107.92/14.59 (((cartprodpairmemEL) =>
% 107.92/14.59 (((cartprodpairmemER) =>
% 107.92/14.59 (((cartprodmempaircEq) =>
% 107.92/14.59 (((cartprodfstpairEq) =>
% 107.92/14.59 (((cartprodsndpairEq) =>
% 107.92/14.59 (((cartprodpairsurjEq) =>
% 107.92/14.59 (((dpsetconstrI) =>
% 107.92/14.59 (((dpsetconstrSub) =>
% 107.92/14.59 (((setOfPairsIsBReln) =>
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% 107.92/14.59 (((dpsetconstrER) =>
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% 107.92/14.59 (((infuncsetfunc) =>
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% 107.92/14.59 (ex1E2) =>
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% 107.92/14.59 ((
% 107.92/14.59 (funcGraphProp3) =>
% 107.92/14.59 ((
% 107.92/14.59 (funcGraphProp2) =>
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% 107.92/14.59 (funcextLem) =>
% 107.92/14.59 ((
% 107.92/14.59 (funcGraphProp4) =>
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% 107.92/14.59 ((
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% 107.92/14.59 ((
% 107.92/14.59 (ap2apEq2) =>
% 107.92/14.59 ((
% 107.92/14.59 (beta1) =>
% 107.92/14.59 ((
% 107.92/14.59 (eta1) =>
% 107.92/14.59 ((
% 107.92/14.59 (lam2lamEq) =>
% 107.92/14.59 ((
% 107.92/14.59 (beta2) =>
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% 107.92/14.59 (eta2) =>
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% 107.92/14.59 (iffalseProp1) =>
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% 107.92/14.59 ((
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% 107.92/14.59 ((
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% 107.92/14.59 ((
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% 107.92/14.59 ((
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% 107.92/14.59 ((
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% 107.92/14.59 ((
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% 107.92/14.59 (breln1all2) =>
% 107.92/14.59 ((
% 107.92/14.59 (breln1SetBreln1) =>
% 107.92/14.59 ((
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% 107.92/14.59 ((
% 107.92/14.59 (breln1unionE) =>
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% 107.92/14.59 (breln1unionEcases) =>
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% 107.92/14.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1738])).
% 107.92/14.59 thf(zip_derived_cl1760, plain,
% 107.92/14.59 (~ (((setukpairinjR) =>
% 107.92/14.59 (((ksndsingleton) =>
% 107.92/14.59 (((ksndpairEq) =>
% 107.92/14.59 (((kpairsurjEq) =>
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% 107.92/14.59 (((cartprodmempaircEq) =>
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% 107.92/14.59 (((setOfPairsIsBReln) =>
% 107.92/14.59 (((dpsetconstrERa) =>
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% 107.92/14.59 (((dpsetconstrEL2) =>
% 107.92/14.59 (((dpsetconstrER) =>
% 107.92/14.59 (((funcImageSingleton) =>
% 107.92/14.59 (((apProp) =>
% 107.92/14.59 (((app) =>
% 107.92/14.59 (((infuncsetfunc) =>
% 107.92/14.59 (((ap2p) =>
% 107.92/14.59 (((funcinfuncset) =>
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% 107.92/14.59 (((lam2p) =>
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% 107.92/14.59 (((brelnall2) =>
% 107.92/14.59 (((ex1E2) =>
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% 107.92/14.59 ((
% 107.92/14.59 (funcGraphProp3) =>
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% 107.92/14.59 ((
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% 107.92/14.59 ((
% 107.92/14.59 (demorgan2a) =>
% 107.92/14.59 ((
% 107.92/14.59 (demorgan2b2) =>
% 107.92/14.59 ((
% 107.92/14.59 (demorgan2b) =>
% 107.92/14.59 ((
% 107.92/14.59 (demorgan2) =>
% 107.92/14.59 ((
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% 107.92/14.59 ((
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% 107.92/14.59 ((
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% 107.92/14.59 ((
% 107.92/14.59 (woz1_1) =>
% 107.92/14.59 ((
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% 107.92/14.59 ((
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% 107.92/14.59 (woz1_5) =>
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% 107.92/14.59 ((
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% 107.92/14.59 ((
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% 107.92/14.59 (breln1unionEcases) =>
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% 107.92/14.59 (breln1unionCommutes) =>
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% 107.92/14.59 ((
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% 107.92/14.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1749])).
% 107.92/14.59 thf(zip_derived_cl1770, plain,
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% 107.92/14.59 (choice2fnsingleton) =>
% 107.92/14.59 ((
% 107.92/14.59 (setOfPairsIsBReln1) =>
% 107.92/14.59 ((
% 107.92/14.59 (breln1all1) =>
% 107.92/14.59 ((
% 107.92/14.59 (subbreln1) =>
% 107.92/14.59 ((
% 107.92/14.59 (eqbreln1) =>
% 107.92/14.59 ((
% 107.92/14.59 (breln1invprop) =>
% 107.92/14.59 ((
% 107.92/14.59 (breln1invI) =>
% 107.92/14.59 ((
% 107.92/14.59 (breln1invE) =>
% 107.92/14.59 ((
% 107.92/14.59 (breln1compprop) =>
% 107.92/14.59 ((
% 107.92/14.59 (breln1compI) =>
% 107.92/14.59 ((
% 107.92/14.59 (breln1compE) =>
% 107.92/14.59 ((
% 107.92/14.59 (breln1compEex) =>
% 107.92/14.59 ((
% 107.92/14.59 (breln1unionprop) =>
% 107.92/14.59 ((
% 107.92/14.59 (breln1unionIL) =>
% 107.92/14.59 ((
% 107.92/14.59 (breln1unionIR) =>
% 107.92/14.59 ((
% 107.92/14.59 (breln1unionI) =>
% 107.92/14.59 ((
% 107.92/14.59 (breln1unionE) =>
% 107.92/14.59 ((
% 107.92/14.59 (breln1unionEcases) =>
% 107.92/14.59 ((
% 107.92/14.59 (breln1unionCommutes) =>
% 107.92/14.59 ((
% 107.92/14.59 (woz2Ex) =>
% 107.92/14.59 ((
% 107.92/14.59 (woz2W) =>
% 107.92/14.59 ((
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% 107.92/14.59 ((
% 107.92/14.59 (woz2B) =>
% 107.92/14.59 ((
% 107.92/14.59 (image1Ex) =>
% 107.92/14.59 ((
% 107.92/14.59 (image1Ex1) =>
% 107.92/14.59 ((
% 107.92/14.59 (image1Equiv) =>
% 107.92/14.59 ((
% 107.92/14.59 (image1E) =>
% 107.92/14.59 ((
% 107.92/14.59 (image1I) =>
% 107.92/14.59 ((
% 107.92/14.59 (injFuncInInjFuncSet) =>
% 107.92/14.59 ((
% 107.92/14.59 (injFuncSetFuncIn) =>
% 107.92/14.59 ((
% 107.92/14.59 (injFuncSetFuncInj) =>
% 107.92/14.59 ((
% 107.92/14.59 (surjFuncSetFuncIn) =>
% 107.92/14.59 ((
% 107.92/14.59 (surjFuncSetFuncSurj) =>
% 107.92/14.59 ((
% 107.92/14.59 (leftInvIsSurj) =>
% 107.92/14.59 ((
% 107.92/14.59 (surjCantorThm) =>
% 107.92/14.59 ((
% 107.92/14.59 (!!) @ (
% 107.92/14.59 (('#S') @ (
% 107.92/14.59 (
% 107.92/14.59 ('#B') @ (
% 107.92/14.59 =>) @
% 107.92/14.59 nonempty)) @
% 107.92/14.59 (
% 107.92/14.59 (
% 107.92/14.59 ('#B') @ (
% 107.92/14.59 ??) @
% 107.92/14.59 (
% 107.92/14.59 (
% 107.92/14.59 ('#S') @ (
% 107.92/14.59 (
% 107.92/14.59 ('#B') @ (
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% 107.92/14.59 (
% 107.92/14.59 (
% 107.92/14.59 ('#B') @ (
% 107.92/14.59 (
% 107.92/14.59 ('#B') @ (
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% 107.92/14.59 (
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% 107.92/14.59 (
% 107.92/14.59 (
% 107.92/14.59 ('#C') @ (
% 107.92/14.59 (
% 107.92/14.59 ('#B') @ (
% 107.92/14.59 '#C') @
% 107.92/14.59 (
% 107.92/14.59 (
% 107.92/14.59 ('#B') @ (
% 107.92/14.59 (
% 107.92/14.59 ('#B') @ (
% 107.92/14.59 =))) @
% 107.92/14.59 (
% 107.92/14.59 (
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% 107.92/14.59 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 107.92/14.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1760])).
% 107.92/14.59 thf(zip_derived_cl1779, plain,
% 107.92/14.59 (~ (((ksndpairEq) =>
% 107.92/14.59 (((kpairsurjEq) =>
% 107.92/14.59 (((cartprodsndin) =>
% 107.92/14.59 (((cartprodpairmemEL) =>
% 107.92/14.59 (((cartprodpairmemER) =>
% 107.92/14.59 (((cartprodmempaircEq) =>
% 107.92/14.59 (((cartprodfstpairEq) =>
% 107.92/14.59 (((cartprodsndpairEq) =>
% 107.92/14.59 (((cartprodpairsurjEq) =>
% 107.92/14.59 (((dpsetconstrI) =>
% 107.92/14.59 (((dpsetconstrSub) =>
% 107.92/14.59 (((setOfPairsIsBReln) =>
% 107.92/14.59 (((dpsetconstrERa) =>
% 107.92/14.59 (((dpsetconstrEL1) =>
% 107.92/14.59 (((dpsetconstrEL2) =>
% 107.92/14.59 (((dpsetconstrER) =>
% 107.92/14.59 (((funcImageSingleton) =>
% 107.92/14.59 (((apProp) =>
% 107.92/14.59 (((app) =>
% 107.92/14.59 (((infuncsetfunc) =>
% 107.92/14.59 (((ap2p) =>
% 107.92/14.59 (((funcinfuncset) =>
% 107.92/14.59 (((lamProp) =>
% 107.92/14.59 (((lamp) =>
% 107.92/14.59 (((lam2p) =>
% 107.92/14.59 (((brelnall1) =>
% 107.92/14.59 (((brelnall2) =>
% 107.92/14.59 (((ex1E2) =>
% 107.92/14.59 (((funcGraphProp1) =>
% 107.92/14.59 (((funcGraphProp3) =>
% 107.92/14.59 ((
% 107.92/14.59 (funcGraphProp2) =>
% 107.92/14.59 ((
% 107.92/14.59 (funcextLem) =>
% 107.92/14.59 ((
% 107.92/14.59 (funcGraphProp4) =>
% 107.92/14.59 ((
% 107.92/14.59 (subbreln) =>
% 107.92/14.59 ((
% 107.92/14.59 (eqbreln) =>
% 107.92/14.59 ((
% 107.92/14.59 (funcext) =>
% 107.92/14.59 ((
% 107.92/14.59 (funcext2) =>
% 107.92/14.59 ((
% 107.92/14.59 (ap2apEq1) =>
% 107.92/14.59 ((
% 107.92/14.59 (ap2apEq2) =>
% 107.92/14.59 ((
% 107.92/14.59 (beta1) =>
% 107.92/14.59 ((
% 107.92/14.59 (eta1) =>
% 107.92/14.59 ((
% 107.92/14.59 (lam2lamEq) =>
% 107.92/14.59 ((
% 107.92/14.59 (beta2) =>
% 107.92/14.59 ((
% 107.92/14.59 (eta2) =>
% 107.92/14.59 ((
% 107.92/14.59 (iffalseProp1) =>
% 107.92/14.59 ((
% 107.92/14.59 (iffalseProp2) =>
% 107.92/14.59 ((
% 107.92/14.59 (iftrueProp1) =>
% 107.92/14.59 ((
% 107.92/14.59 (iftrueProp2) =>
% 107.92/14.59 ((
% 107.92/14.59 (ifSingleton) =>
% 107.92/14.59 ((
% 107.92/14.59 (ifp) =>
% 107.92/14.59 ((
% 107.92/14.59 (theeq) =>
% 107.92/14.59 ((
% 107.92/14.59 (iftrue) =>
% 107.92/14.59 ((
% 107.92/14.59 (iffalse) =>
% 107.92/14.59 ((
% 107.92/14.59 (iftrueorfalse) =>
% 107.92/14.59 ((
% 107.92/14.59 (binintersectT_lem) =>
% 107.92/14.59 ((
% 107.92/14.59 (binunionT_lem) =>
% 107.92/14.59 ((
% 107.92/14.59 (powersetT_lem) =>
% 107.92/14.59 ((
% 107.92/14.59 (setminusT_lem) =>
% 107.92/14.59 ((
% 107.92/14.59 (complementT_lem) =>
% 107.92/14.59 ((
% 107.92/14.59 (setextT) =>
% 107.92/14.59 ((
% 107.92/14.59 (subsetTI) =>
% 107.92/14.59 ((
% 107.92/14.59 (powersetTI1) =>
% 107.92/14.59 ((
% 107.92/14.59 (powersetTE1) =>
% 107.92/14.59 ((
% 107.92/14.59 (complementTI1) =>
% 107.92/14.59 ((
% 107.92/14.59 (complementTE1) =>
% 107.92/14.59 ((
% 107.92/14.59 (binintersectTELcontra) =>
% 107.92/14.59 ((
% 107.92/14.59 (binintersectTERcontra) =>
% 107.92/14.59 ((
% 107.92/14.59 (contrasubsetT) =>
% 107.92/14.59 ((
% 107.92/14.59 (contrasubsetT1) =>
% 107.92/14.59 ((
% 107.92/14.59 (contrasubsetT2) =>
% 107.92/14.59 ((
% 107.92/14.59 (contrasubsetT3) =>
% 107.92/14.59 ((
% 107.92/14.59 (doubleComplementI1) =>
% 107.92/14.59 ((
% 107.92/14.59 (doubleComplementE1) =>
% 107.92/14.59 ((
% 107.92/14.59 (doubleComplementSub1) =>
% 107.92/14.59 ((
% 107.92/14.59 (doubleComplementSub2) =>
% 107.92/14.59 ((
% 107.92/14.59 (doubleComplementEq) =>
% 107.92/14.59 ((
% 107.92/14.59 (complementTnotintersectT) =>
% 107.92/14.59 ((
% 107.92/14.59 (complementImpComplementIntersect) =>
% 107.92/14.59 ((
% 107.92/14.59 (complementSubsetComplementIntersect) =>
% 107.92/14.59 ((
% 107.92/14.59 (complementInPowersetComplementIntersect) =>
% 107.92/14.59 ((
% 107.92/14.59 (contraSubsetComplement) =>
% 107.92/14.59 ((
% 107.92/14.59 (complementTcontraSubset) =>
% 107.92/14.59 ((
% 107.92/14.59 (binunionTILcontra) =>
% 107.92/14.59 ((
% 107.92/14.59 (binunionTIRcontra) =>
% 107.92/14.59 ((
% 107.92/14.59 (inIntersectImpInUnion) =>
% 107.92/14.59 ((
% 107.92/14.59 (inIntersectImpInUnion2) =>
% 107.92/14.59 ((
% 107.92/14.59 (inIntersectImpInIntersectUnions) =>
% 107.92/14.59 ((
% 107.92/14.59 (intersectInPowersetIntersectUnions) =>
% 107.92/14.59 ((
% 107.92/14.59 (inComplementUnionImpNotIn1) =>
% 107.92/14.59 ((
% 107.92/14.59 (inComplementUnionImpInComplement1) =>
% 107.92/14.59 ((
% 107.92/14.59 (binunionTE) =>
% 107.92/14.59 ((
% 107.92/14.59 (binunionTEcontra) =>
% 107.92/14.59 ((
% 107.92/14.59 (demorgan2a1) =>
% 107.92/14.59 ((
% 107.92/14.59 (complementUnionInPowersetComplement) =>
% 107.92/14.59 ((
% 107.92/14.59 (demorgan2a2) =>
% 107.92/14.59 ((
% 107.92/14.59 (demorgan1a) =>
% 107.92/14.59 ((
% 107.92/14.59 (demorgan1b) =>
% 107.92/14.59 ((
% 107.92/14.59 (demorgan1) =>
% 107.92/14.59 ((
% 107.92/14.59 (demorgan2a) =>
% 107.92/14.59 ((
% 107.92/14.59 (demorgan2b2) =>
% 107.92/14.59 ((
% 107.92/14.59 (demorgan2b) =>
% 107.92/14.59 ((
% 107.92/14.59 (demorgan2) =>
% 107.92/14.59 ((
% 107.92/14.59 (woz13rule0) =>
% 107.92/14.59 ((
% 107.92/14.59 (woz13rule1) =>
% 107.92/14.59 ((
% 107.92/14.59 (woz13rule2) =>
% 107.92/14.59 ((
% 107.92/14.59 (woz13rule3) =>
% 107.92/14.59 ((
% 107.92/14.59 (woz13rule4) =>
% 107.92/14.59 ((
% 107.92/14.59 (woz1_1) =>
% 107.92/14.59 ((
% 107.92/14.59 (woz1_2) =>
% 107.92/14.59 ((
% 107.92/14.59 (woz1_3) =>
% 107.92/14.59 ((
% 107.92/14.59 (woz1_4) =>
% 107.92/14.59 ((
% 107.92/14.59 (woz1_5) =>
% 107.92/14.59 ((
% 107.92/14.59 (breln1all2) =>
% 107.92/14.59 ((
% 107.92/14.59 (breln1SetBreln1) =>
% 107.92/14.59 ((
% 107.92/14.59 (choice2fnsingleton) =>
% 107.92/14.59 ((
% 107.92/14.59 (setOfPairsIsBReln1) =>
% 107.92/14.59 ((
% 107.92/14.59 (breln1all1) =>
% 107.92/14.59 ((
% 107.92/14.59 (subbreln1) =>
% 107.92/14.59 ((
% 107.92/14.59 (eqbreln1) =>
% 107.92/14.59 ((
% 107.92/14.59 (breln1invprop) =>
% 107.92/14.59 ((
% 107.92/14.59 (breln1invI) =>
% 107.92/14.59 ((
% 107.92/14.59 (breln1invE) =>
% 107.92/14.59 ((
% 107.92/14.59 (breln1compprop) =>
% 107.92/14.59 ((
% 107.92/14.59 (breln1compI) =>
% 107.92/14.59 ((
% 107.92/14.59 (breln1compE) =>
% 107.92/14.59 ((
% 107.92/14.59 (breln1compEex) =>
% 107.92/14.59 ((
% 107.92/14.59 (breln1unionprop) =>
% 107.92/14.59 ((
% 107.92/14.59 (breln1unionIL) =>
% 107.92/14.59 ((
% 107.92/14.59 (breln1unionIR) =>
% 107.92/14.59 ((
% 107.92/14.59 (breln1unionI) =>
% 107.92/14.59 ((
% 107.92/14.59 (breln1unionE) =>
% 107.92/14.59 ((
% 107.92/14.59 (breln1unionEcases) =>
% 107.92/14.59 ((
% 107.92/14.59 (breln1unionCommutes) =>
% 107.92/14.59 ((
% 107.92/14.59 (woz2Ex) =>
% 107.92/14.59 ((
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% 107.92/14.60 (woz2B) =>
% 107.92/14.60 ((
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% 107.92/14.60 ((
% 107.92/14.60 (image1Ex1) =>
% 107.92/14.60 ((
% 107.92/14.60 (image1Equiv) =>
% 107.92/14.60 ((
% 107.92/14.60 (image1E) =>
% 107.92/14.60 ((
% 107.92/14.60 (image1I) =>
% 107.92/14.60 ((
% 107.92/14.60 (injFuncInInjFuncSet) =>
% 107.92/14.60 ((
% 107.92/14.60 (injFuncSetFuncIn) =>
% 107.92/14.60 ((
% 107.92/14.60 (injFuncSetFuncInj) =>
% 107.92/14.60 ((
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% 107.92/14.60 ((
% 107.92/14.60 (surjFuncSetFuncSurj) =>
% 107.92/14.60 ((
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% 107.92/14.60 ((
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% 107.92/14.60 ((
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% 107.92/14.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1770])).
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% 107.92/14.60 (((dpsetconstrSub) =>
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% 107.92/14.60 (((dpsetconstrERa) =>
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% 107.92/14.60 (((infuncsetfunc) =>
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% 107.92/14.60 ((
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% 107.92/14.60 ((
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% 107.92/14.60 ((
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% 107.92/14.60 ((
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% 107.92/14.60 ((
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% 107.92/14.60 ((
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% 107.92/14.60 ((
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% 107.92/14.60 ((
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% 107.92/14.60 ((
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% 107.92/14.60 ((
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% 107.92/14.60 ((
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% 107.92/14.60 ((
% 107.92/14.60 (breln1unionE) =>
% 107.92/14.60 ((
% 107.92/14.60 (breln1unionEcases) =>
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% 107.92/14.60 (breln1unionCommutes) =>
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% 107.92/14.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1779])).
% 107.92/14.60 thf(zip_derived_cl1796, plain,
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% 107.92/14.60 (((cartprodpairmemEL) =>
% 107.92/14.60 (((cartprodpairmemER) =>
% 107.92/14.60 (((cartprodmempaircEq) =>
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% 107.92/14.60 (((cartprodsndpairEq) =>
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% 107.92/14.60 (((infuncsetfunc) =>
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% 107.92/14.60 (ap2apEq2) =>
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% 107.92/14.60 (eta1) =>
% 107.92/14.60 ((
% 107.92/14.60 (lam2lamEq) =>
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% 107.92/14.60 (beta2) =>
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% 107.92/14.60 (iffalseProp2) =>
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% 107.92/14.60 (iftrueProp2) =>
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% 107.92/14.60 ((
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% 107.92/14.60 (theeq) =>
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% 107.92/14.60 ((
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% 107.92/14.60 ((
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% 107.92/14.60 ((
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% 107.92/14.60 ((
% 107.92/14.60 (contrasubsetT2) =>
% 107.92/14.60 ((
% 107.92/14.60 (contrasubsetT3) =>
% 107.92/14.60 ((
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% 107.92/14.60 ((
% 107.92/14.60 (doubleComplementE1) =>
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% 107.92/14.60 (doubleComplementEq) =>
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% 107.92/14.60 ((
% 107.92/14.60 (inIntersectImpInUnion2) =>
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% 107.92/14.60 (inIntersectImpInIntersectUnions) =>
% 107.92/14.60 ((
% 107.92/14.60 (intersectInPowersetIntersectUnions) =>
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% 107.92/14.60 (demorgan2a) =>
% 107.92/14.60 ((
% 107.92/14.60 (demorgan2b2) =>
% 107.92/14.60 ((
% 107.92/14.60 (demorgan2b) =>
% 107.92/14.60 ((
% 107.92/14.60 (demorgan2) =>
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% 107.92/14.60 ((
% 107.92/14.60 (woz13rule3) =>
% 107.92/14.60 ((
% 107.92/14.60 (woz13rule4) =>
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% 107.92/14.60 ((
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% 107.92/14.60 (woz1_3) =>
% 107.92/14.60 ((
% 107.92/14.60 (woz1_4) =>
% 107.92/14.60 ((
% 107.92/14.60 (woz1_5) =>
% 107.92/14.60 ((
% 107.92/14.60 (breln1all2) =>
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% 107.92/14.60 (breln1SetBreln1) =>
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% 107.92/14.60 (breln1all1) =>
% 107.92/14.60 ((
% 107.92/14.60 (subbreln1) =>
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% 107.92/14.60 ((
% 107.92/14.60 (breln1invI) =>
% 107.92/14.60 ((
% 107.92/14.60 (breln1invE) =>
% 107.92/14.60 ((
% 107.92/14.60 (breln1compprop) =>
% 107.92/14.60 ((
% 107.92/14.60 (breln1compI) =>
% 107.92/14.60 ((
% 107.92/14.60 (breln1compE) =>
% 107.92/14.60 ((
% 107.92/14.60 (breln1compEex) =>
% 107.92/14.60 ((
% 107.92/14.60 (breln1unionprop) =>
% 107.92/14.60 ((
% 107.92/14.60 (breln1unionIL) =>
% 107.92/14.60 ((
% 107.92/14.60 (breln1unionIR) =>
% 107.92/14.60 ((
% 107.92/14.60 (breln1unionI) =>
% 107.92/14.60 ((
% 107.92/14.60 (breln1unionE) =>
% 107.92/14.60 ((
% 107.92/14.60 (breln1unionEcases) =>
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% 107.92/14.60 (breln1unionCommutes) =>
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% 107.92/14.60 ((
% 107.92/14.60 (image1Ex1) =>
% 107.92/14.60 ((
% 107.92/14.60 (image1Equiv) =>
% 107.92/14.60 ((
% 107.92/14.60 (image1E) =>
% 107.92/14.60 ((
% 107.92/14.60 (image1I) =>
% 107.92/14.60 ((
% 107.92/14.60 (injFuncInInjFuncSet) =>
% 107.92/14.60 ((
% 107.92/14.60 (injFuncSetFuncIn) =>
% 107.92/14.60 ((
% 107.92/14.60 (injFuncSetFuncInj) =>
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% 107.92/14.60 (surjFuncSetFuncIn) =>
% 107.92/14.60 ((
% 107.92/14.60 (surjFuncSetFuncSurj) =>
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% 107.92/14.60 ((
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% 107.92/14.60 ((
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% 107.92/14.60 (
% 107.92/14.60 (
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% 107.92/14.60 (
% 107.92/14.60 (
% 107.92/14.60 ('#B') @ (
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% 107.92/14.60 ('#B') @ (
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% 107.92/14.60 (
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% 107.92/14.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1796])).
% 107.92/14.60 thf(zip_derived_cl1816, plain,
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% 107.92/14.60 (((setOfPairsIsBReln) =>
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% 107.92/14.60 ((
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% 107.92/14.60 (
% 107.92/14.60 (
% 107.92/14.60 ('#C') @ (
% 107.92/14.60 (
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% 107.92/14.60 (
% 107.92/14.60 (
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% 107.92/14.60 (
% 107.92/14.60 ('#B') @ (
% 107.92/14.60 =))) @
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% 107.92/14.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1807])).
% 107.92/14.60 thf(zip_derived_cl1825, plain,
% 107.92/14.60 (~ (((cartprodmempaircEq) =>
% 107.92/14.60 (((cartprodfstpairEq) =>
% 107.92/14.60 (((cartprodsndpairEq) =>
% 107.92/14.60 (((cartprodpairsurjEq) =>
% 107.92/14.60 (((dpsetconstrI) =>
% 107.92/14.60 (((dpsetconstrSub) =>
% 107.92/14.60 (((setOfPairsIsBReln) =>
% 107.92/14.60 (((dpsetconstrERa) =>
% 107.92/14.60 (((dpsetconstrEL1) =>
% 107.92/14.60 (((dpsetconstrEL2) =>
% 107.92/14.60 (((dpsetconstrER) =>
% 107.92/14.60 (((funcImageSingleton) =>
% 107.92/14.60 (((apProp) =>
% 107.92/14.60 (((app) =>
% 107.92/14.60 (((infuncsetfunc) =>
% 107.92/14.60 (((ap2p) =>
% 107.92/14.60 (((funcinfuncset) =>
% 107.92/14.60 (((lamProp) =>
% 107.92/14.60 (((lamp) =>
% 107.92/14.60 (((lam2p) =>
% 107.92/14.60 (((brelnall1) =>
% 107.92/14.60 (((brelnall2) =>
% 107.92/14.60 (((ex1E2) =>
% 107.92/14.60 (((funcGraphProp1) =>
% 107.92/14.60 (((funcGraphProp3) =>
% 107.92/14.60 (((funcGraphProp2) =>
% 107.92/14.60 (((funcextLem) =>
% 107.92/14.60 (((funcGraphProp4) =>
% 107.92/14.60 (((subbreln) =>
% 107.92/14.60 (((eqbreln) =>
% 107.92/14.60 ((
% 107.92/14.60 (funcext) =>
% 107.92/14.60 ((
% 107.92/14.60 (funcext2) =>
% 107.92/14.60 ((
% 107.92/14.60 (ap2apEq1) =>
% 107.92/14.60 ((
% 107.92/14.60 (ap2apEq2) =>
% 107.92/14.60 ((
% 107.92/14.60 (beta1) =>
% 107.92/14.60 ((
% 107.92/14.60 (eta1) =>
% 107.92/14.60 ((
% 107.92/14.60 (lam2lamEq) =>
% 107.92/14.60 ((
% 107.92/14.60 (beta2) =>
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% 107.92/14.60 ((
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% 107.92/14.60 ((
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% 107.92/14.60 ((
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% 107.92/14.60 ((
% 107.92/14.60 (ifSingleton) =>
% 107.92/14.60 ((
% 107.92/14.60 (ifp) =>
% 107.92/14.60 ((
% 107.92/14.60 (theeq) =>
% 107.92/14.60 ((
% 107.92/14.60 (iftrue) =>
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% 107.92/14.60 ((
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% 107.92/14.60 ((
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% 107.92/14.60 ((
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% 107.92/14.60 ((
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% 107.92/14.60 ((
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% 107.92/14.60 ((
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% 107.92/14.60 ((
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% 107.92/14.60 ((
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% 107.92/14.60 ((
% 107.92/14.60 (complementTE1) =>
% 107.92/14.60 ((
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% 107.92/14.60 ((
% 107.92/14.60 (binintersectTERcontra) =>
% 107.92/14.60 ((
% 107.92/14.60 (contrasubsetT) =>
% 107.92/14.60 ((
% 107.92/14.60 (contrasubsetT1) =>
% 107.92/14.60 ((
% 107.92/14.60 (contrasubsetT2) =>
% 107.92/14.60 ((
% 107.92/14.60 (contrasubsetT3) =>
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% 107.92/14.60 ((
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% 107.92/14.60 ((
% 107.92/14.60 (complementImpComplementIntersect) =>
% 107.92/14.60 ((
% 107.92/14.60 (complementSubsetComplementIntersect) =>
% 107.92/14.60 ((
% 107.92/14.60 (complementInPowersetComplementIntersect) =>
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% 107.92/14.60 ((
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% 107.92/14.60 ((
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% 107.92/14.60 ((
% 107.92/14.60 (complementUnionInPowersetComplement) =>
% 107.92/14.60 ((
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% 107.92/14.60 ((
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% 107.92/14.60 ((
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% 107.92/14.60 ((
% 107.92/14.60 (demorgan1) =>
% 107.92/14.60 ((
% 107.92/14.60 (demorgan2a) =>
% 107.92/14.60 ((
% 107.92/14.60 (demorgan2b2) =>
% 107.92/14.60 ((
% 107.92/14.60 (demorgan2b) =>
% 107.92/14.60 ((
% 107.92/14.60 (demorgan2) =>
% 107.92/14.60 ((
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% 107.92/14.60 ((
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% 107.92/14.60 ((
% 107.92/14.60 (woz13rule2) =>
% 107.92/14.60 ((
% 107.92/14.60 (woz13rule3) =>
% 107.92/14.60 ((
% 107.92/14.60 (woz13rule4) =>
% 107.92/14.60 ((
% 107.92/14.60 (woz1_1) =>
% 107.92/14.60 ((
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% 107.92/14.60 ((
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% 107.92/14.60 ((
% 107.92/14.60 (woz1_4) =>
% 107.92/14.60 ((
% 107.92/14.60 (woz1_5) =>
% 107.92/14.60 ((
% 107.92/14.60 (breln1all2) =>
% 107.92/14.60 ((
% 107.92/14.60 (breln1SetBreln1) =>
% 107.92/14.60 ((
% 107.92/14.60 (choice2fnsingleton) =>
% 107.92/14.60 ((
% 107.92/14.60 (setOfPairsIsBReln1) =>
% 107.92/14.60 ((
% 107.92/14.60 (breln1all1) =>
% 107.92/14.60 ((
% 107.92/14.60 (subbreln1) =>
% 107.92/14.60 ((
% 107.92/14.60 (eqbreln1) =>
% 107.92/14.60 ((
% 107.92/14.60 (breln1invprop) =>
% 107.92/14.60 ((
% 107.92/14.60 (breln1invI) =>
% 107.92/14.60 ((
% 107.92/14.60 (breln1invE) =>
% 107.92/14.60 ((
% 107.92/14.60 (breln1compprop) =>
% 107.92/14.60 ((
% 107.92/14.60 (breln1compI) =>
% 107.92/14.60 ((
% 107.92/14.60 (breln1compE) =>
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% 107.92/14.60 (breln1compEex) =>
% 107.92/14.60 ((
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% 107.92/14.60 ((
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% 107.92/14.60 ((
% 107.92/14.60 (breln1unionI) =>
% 107.92/14.60 ((
% 107.92/14.60 (breln1unionE) =>
% 107.92/14.60 ((
% 107.92/14.60 (breln1unionEcases) =>
% 107.92/14.60 ((
% 107.92/14.60 (breln1unionCommutes) =>
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% 107.92/14.60 ((
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% 107.92/14.60 ((
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% 107.92/14.60 ((
% 107.92/14.60 (image1E) =>
% 107.92/14.60 ((
% 107.92/14.60 (image1I) =>
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% 107.92/14.60 (injFuncInInjFuncSet) =>
% 107.92/14.60 ((
% 107.92/14.60 (injFuncSetFuncIn) =>
% 107.92/14.60 ((
% 107.92/14.60 (injFuncSetFuncInj) =>
% 107.92/14.60 ((
% 107.92/14.60 (surjFuncSetFuncIn) =>
% 107.92/14.60 ((
% 107.92/14.60 (surjFuncSetFuncSurj) =>
% 107.92/14.60 ((
% 107.92/14.60 (leftInvIsSurj) =>
% 107.92/14.60 ((
% 107.92/14.60 (surjCantorThm) =>
% 107.92/14.60 ((
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% 107.92/14.60 (('#S') @ (
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% 107.92/14.60 ('#B') @ (
% 107.92/14.60 =>) @
% 107.92/14.60 nonempty)) @
% 107.92/14.60 (
% 107.92/14.60 (
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% 107.92/14.60 (
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% 107.92/14.60 ('#B') @ (
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% 107.92/14.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1816])).
% 107.92/14.60 thf(zip_derived_cl1833, plain,
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% 107.92/14.60 (((app) =>
% 107.92/14.60 (((infuncsetfunc) =>
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% 107.92/14.60 (((funcGraphProp3) =>
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% 107.92/14.60 ((
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% 107.92/14.60 ((
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% 107.92/14.60 ((
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% 107.92/14.60 ((
% 107.92/14.60 (inIntersectImpInUnion2) =>
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% 107.92/14.60 ((
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% 107.92/14.60 ((
% 107.92/14.60 (setOfPairsIsBReln1) =>
% 107.92/14.60 ((
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% 107.92/14.60 ((
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% 107.92/14.60 ((
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% 107.92/14.60 ((
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% 107.92/14.60 ((
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% 107.92/14.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1825])).
% 107.92/14.60 thf(zip_derived_cl1840, plain,
% 107.92/14.60 (~ (((cartprodsndpairEq) =>
% 107.92/14.60 (((cartprodpairsurjEq) =>
% 107.92/14.60 (((dpsetconstrI) =>
% 107.92/14.60 (((dpsetconstrSub) =>
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% 107.92/14.60 (((infuncsetfunc) =>
% 107.92/14.60 (((ap2p) =>
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% 107.92/14.60 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1833])).
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% 107.92/14.61 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1914])).
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% 107.92/14.61 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1923])).
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% 107.92/14.61 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1950])).
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% 107.92/14.62 (demorgan2a1) =>
% 107.92/14.62 ((
% 107.92/14.62 (complementUnionInPowersetComplement) =>
% 107.92/14.62 ((
% 107.92/14.62 (demorgan2a2) =>
% 107.92/14.62 ((
% 107.92/14.62 (demorgan1a) =>
% 107.92/14.62 ((
% 107.92/14.62 (demorgan1b) =>
% 107.92/14.62 ((
% 107.92/14.62 (demorgan1) =>
% 107.92/14.62 ((
% 107.92/14.62 (demorgan2a) =>
% 107.92/14.62 ((
% 107.92/14.62 (demorgan2b2) =>
% 107.92/14.62 ((
% 107.92/14.62 (demorgan2b) =>
% 107.92/14.62 ((
% 107.92/14.62 (demorgan2) =>
% 107.92/14.62 ((
% 107.92/14.62 (woz13rule0) =>
% 107.92/14.62 ((
% 107.92/14.62 (woz13rule1) =>
% 107.92/14.62 ((
% 107.92/14.62 (woz13rule2) =>
% 107.92/14.62 ((
% 107.92/14.62 (woz13rule3) =>
% 107.92/14.62 ((
% 107.92/14.62 (woz13rule4) =>
% 107.92/14.62 ((
% 107.92/14.62 (woz1_1) =>
% 107.92/14.62 ((
% 107.92/14.62 (woz1_2) =>
% 107.92/14.62 ((
% 107.92/14.62 (woz1_3) =>
% 107.92/14.62 ((
% 107.92/14.62 (woz1_4) =>
% 107.92/14.62 ((
% 107.92/14.62 (woz1_5) =>
% 107.92/14.62 ((
% 107.92/14.62 (breln1all2) =>
% 107.92/14.62 ((
% 107.92/14.62 (breln1SetBreln1) =>
% 107.92/14.62 ((
% 107.92/14.62 (choice2fnsingleton) =>
% 107.92/14.62 ((
% 107.92/14.62 (setOfPairsIsBReln1) =>
% 107.92/14.62 ((
% 107.92/14.62 (breln1all1) =>
% 107.92/14.62 ((
% 107.92/14.62 (subbreln1) =>
% 107.92/14.62 ((
% 107.92/14.62 (eqbreln1) =>
% 107.92/14.62 ((
% 107.92/14.62 (breln1invprop) =>
% 107.92/14.62 ((
% 107.92/14.62 (breln1invI) =>
% 107.92/14.62 ((
% 107.92/14.62 (breln1invE) =>
% 107.92/14.62 ((
% 107.92/14.62 (breln1compprop) =>
% 107.92/14.62 ((
% 107.92/14.62 (breln1compI) =>
% 107.92/14.62 ((
% 107.92/14.62 (breln1compE) =>
% 107.92/14.62 ((
% 107.92/14.62 (breln1compEex) =>
% 107.92/14.62 ((
% 107.92/14.62 (breln1unionprop) =>
% 107.92/14.62 ((
% 107.92/14.62 (breln1unionIL) =>
% 107.92/14.62 ((
% 107.92/14.62 (breln1unionIR) =>
% 107.92/14.62 ((
% 107.92/14.62 (breln1unionI) =>
% 107.92/14.62 ((
% 107.92/14.62 (breln1unionE) =>
% 107.92/14.62 ((
% 107.92/14.62 (breln1unionEcases) =>
% 107.92/14.62 ((
% 107.92/14.62 (breln1unionCommutes) =>
% 107.92/14.62 ((
% 107.92/14.62 (woz2Ex) =>
% 107.92/14.62 ((
% 107.92/14.62 (woz2W) =>
% 107.92/14.62 ((
% 107.92/14.62 (woz2A) =>
% 107.92/14.62 ((
% 107.92/14.62 (woz2B) =>
% 107.92/14.62 ((
% 107.92/14.62 (image1Ex) =>
% 107.92/14.62 ((
% 107.92/14.62 (image1Ex1) =>
% 107.92/14.62 ((
% 107.92/14.62 (image1Equiv) =>
% 107.92/14.62 ((
% 107.92/14.62 (image1E) =>
% 107.92/14.62 ((
% 107.92/14.62 (image1I) =>
% 107.92/14.62 ((
% 107.92/14.62 (injFuncInInjFuncSet) =>
% 107.92/14.62 ((
% 107.92/14.62 (injFuncSetFuncIn) =>
% 107.92/14.62 ((
% 107.92/14.62 (injFuncSetFuncInj) =>
% 107.92/14.62 ((
% 107.92/14.62 (surjFuncSetFuncIn) =>
% 107.92/14.62 ((
% 107.92/14.62 (surjFuncSetFuncSurj) =>
% 107.92/14.62 ((
% 107.92/14.62 (leftInvIsSurj) =>
% 107.92/14.62 ((
% 107.92/14.62 (surjCantorThm) =>
% 107.92/14.62 ((
% 107.92/14.62 (!!) @ (
% 107.92/14.62 (('#S') @ (
% 107.92/14.62 (
% 107.92/14.62 ('#B') @ (
% 107.92/14.62 =>) @
% 107.92/14.62 nonempty)) @
% 107.92/14.62 (
% 107.92/14.62 (
% 107.92/14.62 ('#B') @ (
% 107.92/14.62 ??) @
% 107.92/14.62 (
% 107.92/14.62 (
% 107.92/14.62 ('#S') @ (
% 107.92/14.62 (
% 107.92/14.62 ('#B') @ (
% 107.92/14.62 '#S') @
% 107.92/14.62 (
% 107.92/14.62 (
% 107.92/14.62 ('#B') @ (
% 107.92/14.62 (
% 107.92/14.62 ('#B') @ (
% 107.92/14.62 &))) @
% 107.92/14.62 (
% 107.92/14.62 (
% 107.92/14.62 ('#C') @ in)))))) @
% 107.92/14.62 (
% 107.92/14.62 (
% 107.92/14.62 ('#C') @ (
% 107.92/14.62 (
% 107.92/14.62 ('#B') @ (
% 107.92/14.62 '#C') @
% 107.92/14.62 (
% 107.92/14.62 (
% 107.92/14.62 ('#B') @ (
% 107.92/14.62 (
% 107.92/14.62 ('#B') @ (
% 107.92/14.62 =))) @
% 107.92/14.62 (
% 107.92/14.62 (
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% 107.92/14.62 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 107.92/14.62 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2070])).
% 107.92/14.62 thf(zip_derived_cl2091, plain,
% 107.92/14.62 (~ (((subbreln) =>
% 107.92/14.62 (((eqbreln) =>
% 107.92/14.62 (((funcext) =>
% 107.92/14.62 (((funcext2) =>
% 107.92/14.62 (((ap2apEq1) =>
% 107.92/14.62 (((ap2apEq2) =>
% 107.92/14.62 (((beta1) =>
% 107.92/14.62 (((eta1) =>
% 107.92/14.62 (((lam2lamEq) =>
% 107.92/14.62 (((beta2) =>
% 107.92/14.62 (((eta2) =>
% 107.92/14.62 (((iffalseProp1) =>
% 107.92/14.62 (((iffalseProp2) =>
% 107.92/14.62 (((iftrueProp1) =>
% 107.92/14.62 (((iftrueProp2) =>
% 107.92/14.62 (((ifSingleton) =>
% 107.92/14.62 (((ifp) =>
% 107.92/14.62 (((theeq) =>
% 107.92/14.62 (((iftrue) =>
% 107.92/14.62 (((iffalse) =>
% 107.92/14.62 (((iftrueorfalse) =>
% 107.92/14.62 (((binintersectT_lem) =>
% 107.92/14.62 (((binunionT_lem) =>
% 107.92/14.62 (((powersetT_lem) =>
% 107.92/14.62 (((setminusT_lem) =>
% 107.92/14.62 (((complementT_lem) =>
% 107.92/14.62 (((setextT) =>
% 107.92/14.62 (((subsetTI) =>
% 107.92/14.62 (((powersetTI1) =>
% 107.92/14.62 (((powersetTE1) =>
% 107.92/14.62 ((
% 107.92/14.62 (complementTI1) =>
% 107.92/14.62 ((
% 107.92/14.62 (complementTE1) =>
% 107.92/14.62 ((
% 107.92/14.62 (binintersectTELcontra) =>
% 107.92/14.62 ((
% 107.92/14.62 (binintersectTERcontra) =>
% 107.92/14.62 ((
% 107.92/14.62 (contrasubsetT) =>
% 107.92/14.62 ((
% 107.92/14.62 (contrasubsetT1) =>
% 107.92/14.62 ((
% 107.92/14.62 (contrasubsetT2) =>
% 107.92/14.62 ((
% 107.92/14.62 (contrasubsetT3) =>
% 107.92/14.62 ((
% 107.92/14.62 (doubleComplementI1) =>
% 107.92/14.62 ((
% 107.92/14.62 (doubleComplementE1) =>
% 107.92/14.62 ((
% 107.92/14.62 (doubleComplementSub1) =>
% 107.92/14.62 ((
% 107.92/14.62 (doubleComplementSub2) =>
% 107.92/14.62 ((
% 107.92/14.62 (doubleComplementEq) =>
% 107.92/14.62 ((
% 107.92/14.62 (complementTnotintersectT) =>
% 107.92/14.62 ((
% 107.92/14.62 (complementImpComplementIntersect) =>
% 107.92/14.62 ((
% 107.92/14.62 (complementSubsetComplementIntersect) =>
% 107.92/14.62 ((
% 107.92/14.62 (complementInPowersetComplementIntersect) =>
% 107.92/14.62 ((
% 107.92/14.62 (contraSubsetComplement) =>
% 107.92/14.62 ((
% 107.92/14.62 (complementTcontraSubset) =>
% 107.92/14.62 ((
% 107.92/14.62 (binunionTILcontra) =>
% 107.92/14.62 ((
% 107.92/14.62 (binunionTIRcontra) =>
% 107.92/14.62 ((
% 107.92/14.62 (inIntersectImpInUnion) =>
% 107.92/14.62 ((
% 107.92/14.62 (inIntersectImpInUnion2) =>
% 107.92/14.62 ((
% 107.92/14.62 (inIntersectImpInIntersectUnions) =>
% 107.92/14.62 ((
% 107.92/14.62 (intersectInPowersetIntersectUnions) =>
% 107.92/14.62 ((
% 107.92/14.62 (inComplementUnionImpNotIn1) =>
% 107.92/14.62 ((
% 107.92/14.62 (inComplementUnionImpInComplement1) =>
% 107.92/14.62 ((
% 107.92/14.62 (binunionTE) =>
% 107.92/14.62 ((
% 107.92/14.62 (binunionTEcontra) =>
% 107.92/14.62 ((
% 107.92/14.62 (demorgan2a1) =>
% 107.92/14.62 ((
% 107.92/14.62 (complementUnionInPowersetComplement) =>
% 107.92/14.62 ((
% 107.92/14.62 (demorgan2a2) =>
% 107.92/14.62 ((
% 107.92/14.62 (demorgan1a) =>
% 107.92/14.62 ((
% 107.92/14.62 (demorgan1b) =>
% 107.92/14.62 ((
% 107.92/14.62 (demorgan1) =>
% 107.92/14.62 ((
% 107.92/14.62 (demorgan2a) =>
% 107.92/14.62 ((
% 107.92/14.62 (demorgan2b2) =>
% 107.92/14.62 ((
% 107.92/14.62 (demorgan2b) =>
% 107.92/14.62 ((
% 107.92/14.62 (demorgan2) =>
% 107.92/14.62 ((
% 107.92/14.62 (woz13rule0) =>
% 107.92/14.62 ((
% 107.92/14.62 (woz13rule1) =>
% 107.92/14.62 ((
% 107.92/14.62 (woz13rule2) =>
% 107.92/14.62 ((
% 107.92/14.62 (woz13rule3) =>
% 107.92/14.62 ((
% 107.92/14.62 (woz13rule4) =>
% 107.92/14.62 ((
% 107.92/14.62 (woz1_1) =>
% 107.92/14.62 ((
% 107.92/14.62 (woz1_2) =>
% 107.92/14.62 ((
% 107.92/14.62 (woz1_3) =>
% 107.92/14.62 ((
% 107.92/14.62 (woz1_4) =>
% 107.92/14.62 ((
% 107.92/14.62 (woz1_5) =>
% 107.92/14.62 ((
% 107.92/14.62 (breln1all2) =>
% 107.92/14.62 ((
% 107.92/14.62 (breln1SetBreln1) =>
% 107.92/14.62 ((
% 107.92/14.62 (choice2fnsingleton) =>
% 107.92/14.62 ((
% 107.92/14.62 (setOfPairsIsBReln1) =>
% 107.92/14.62 ((
% 107.92/14.62 (breln1all1) =>
% 107.92/14.62 ((
% 107.92/14.62 (subbreln1) =>
% 107.92/14.62 ((
% 107.92/14.62 (eqbreln1) =>
% 107.92/14.62 ((
% 107.92/14.62 (breln1invprop) =>
% 107.92/14.62 ((
% 107.92/14.62 (breln1invI) =>
% 107.92/14.62 ((
% 107.92/14.62 (breln1invE) =>
% 107.92/14.62 ((
% 107.92/14.62 (breln1compprop) =>
% 107.92/14.62 ((
% 107.92/14.62 (breln1compI) =>
% 107.92/14.62 ((
% 107.92/14.62 (breln1compE) =>
% 107.92/14.62 ((
% 107.92/14.62 (breln1compEex) =>
% 107.92/14.62 ((
% 107.92/14.62 (breln1unionprop) =>
% 107.92/14.62 ((
% 107.92/14.62 (breln1unionIL) =>
% 107.92/14.62 ((
% 107.92/14.62 (breln1unionIR) =>
% 107.92/14.62 ((
% 107.92/14.62 (breln1unionI) =>
% 107.92/14.62 ((
% 107.92/14.62 (breln1unionE) =>
% 107.92/14.62 ((
% 107.92/14.62 (breln1unionEcases) =>
% 107.92/14.62 ((
% 107.92/14.62 (breln1unionCommutes) =>
% 107.92/14.62 ((
% 107.92/14.62 (woz2Ex) =>
% 107.92/14.62 ((
% 107.92/14.62 (woz2W) =>
% 107.92/14.62 ((
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% 107.92/14.62 ((
% 107.92/14.62 (woz2B) =>
% 108.14/14.62 ((
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% 108.14/14.62 ((
% 108.14/14.62 (image1Ex1) =>
% 108.14/14.62 ((
% 108.14/14.62 (image1Equiv) =>
% 108.14/14.62 ((
% 108.14/14.62 (image1E) =>
% 108.14/14.62 ((
% 108.14/14.62 (image1I) =>
% 108.14/14.62 ((
% 108.14/14.62 (injFuncInInjFuncSet) =>
% 108.14/14.62 ((
% 108.14/14.62 (injFuncSetFuncIn) =>
% 108.14/14.62 ((
% 108.14/14.62 (injFuncSetFuncInj) =>
% 108.14/14.62 ((
% 108.14/14.62 (surjFuncSetFuncIn) =>
% 108.14/14.62 ((
% 108.14/14.62 (surjFuncSetFuncSurj) =>
% 108.14/14.62 ((
% 108.14/14.62 (leftInvIsSurj) =>
% 108.14/14.62 ((
% 108.14/14.62 (surjCantorThm) =>
% 108.14/14.62 ((
% 108.14/14.62 (!!) @ (
% 108.14/14.62 (('#S') @ (
% 108.14/14.62 (
% 108.14/14.62 ('#B') @ (
% 108.14/14.62 =>) @
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% 108.14/14.62 (
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% 108.14/14.62 (
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% 108.14/14.62 ('#B') @ (
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% 108.14/14.62 (
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% 108.14/14.62 (
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% 108.14/14.62 (
% 108.14/14.62 (
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% 108.14/14.62 (
% 108.14/14.62 (
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% 108.14/14.62 (
% 108.14/14.62 (
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% 108.14/14.62 (
% 108.14/14.62 ('#B') @ (
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% 108.14/14.62 (
% 108.14/14.62 (
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% 108.14/14.62 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 108.14/14.62 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2081])).
% 108.14/14.62 thf(zip_derived_cl2102, plain,
% 108.14/14.62 (~ (((eqbreln) =>
% 108.14/14.62 (((funcext) =>
% 108.14/14.62 (((funcext2) =>
% 108.14/14.62 (((ap2apEq1) =>
% 108.14/14.62 (((ap2apEq2) =>
% 108.14/14.62 (((beta1) =>
% 108.14/14.62 (((eta1) =>
% 108.14/14.62 (((lam2lamEq) =>
% 108.14/14.62 (((beta2) =>
% 108.14/14.62 (((eta2) =>
% 108.14/14.62 (((iffalseProp1) =>
% 108.14/14.62 (((iffalseProp2) =>
% 108.14/14.62 (((iftrueProp1) =>
% 108.14/14.62 (((iftrueProp2) =>
% 108.14/14.62 (((ifSingleton) =>
% 108.14/14.62 (((ifp) =>
% 108.14/14.62 (((theeq) =>
% 108.14/14.62 (((iftrue) =>
% 108.14/14.62 (((iffalse) =>
% 108.14/14.62 (((iftrueorfalse) =>
% 108.14/14.62 (((binintersectT_lem) =>
% 108.14/14.62 (((binunionT_lem) =>
% 108.14/14.62 (((powersetT_lem) =>
% 108.14/14.62 (((setminusT_lem) =>
% 108.14/14.62 (((complementT_lem) =>
% 108.14/14.62 (((setextT) =>
% 108.14/14.62 (((subsetTI) =>
% 108.14/14.62 (((powersetTI1) =>
% 108.14/14.62 (((powersetTE1) =>
% 108.14/14.62 (((complementTI1) =>
% 108.14/14.62 ((
% 108.14/14.62 (complementTE1) =>
% 108.14/14.62 ((
% 108.14/14.62 (binintersectTELcontra) =>
% 108.14/14.62 ((
% 108.14/14.62 (binintersectTERcontra) =>
% 108.14/14.62 ((
% 108.14/14.62 (contrasubsetT) =>
% 108.14/14.62 ((
% 108.14/14.62 (contrasubsetT1) =>
% 108.14/14.62 ((
% 108.14/14.62 (contrasubsetT2) =>
% 108.14/14.62 ((
% 108.14/14.62 (contrasubsetT3) =>
% 108.14/14.62 ((
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% 108.14/14.62 ((
% 108.14/14.62 (doubleComplementE1) =>
% 108.14/14.62 ((
% 108.14/14.62 (doubleComplementSub1) =>
% 108.14/14.62 ((
% 108.14/14.62 (doubleComplementSub2) =>
% 108.14/14.62 ((
% 108.14/14.62 (doubleComplementEq) =>
% 108.14/14.62 ((
% 108.14/14.62 (complementTnotintersectT) =>
% 108.14/14.62 ((
% 108.14/14.62 (complementImpComplementIntersect) =>
% 108.14/14.62 ((
% 108.14/14.62 (complementSubsetComplementIntersect) =>
% 108.14/14.62 ((
% 108.14/14.62 (complementInPowersetComplementIntersect) =>
% 108.14/14.62 ((
% 108.14/14.62 (contraSubsetComplement) =>
% 108.14/14.62 ((
% 108.14/14.62 (complementTcontraSubset) =>
% 108.14/14.62 ((
% 108.14/14.62 (binunionTILcontra) =>
% 108.14/14.62 ((
% 108.14/14.62 (binunionTIRcontra) =>
% 108.14/14.62 ((
% 108.14/14.62 (inIntersectImpInUnion) =>
% 108.14/14.62 ((
% 108.14/14.62 (inIntersectImpInUnion2) =>
% 108.14/14.62 ((
% 108.14/14.62 (inIntersectImpInIntersectUnions) =>
% 108.14/14.62 ((
% 108.14/14.62 (intersectInPowersetIntersectUnions) =>
% 108.14/14.62 ((
% 108.14/14.62 (inComplementUnionImpNotIn1) =>
% 108.14/14.62 ((
% 108.14/14.62 (inComplementUnionImpInComplement1) =>
% 108.14/14.62 ((
% 108.14/14.62 (binunionTE) =>
% 108.14/14.62 ((
% 108.14/14.62 (binunionTEcontra) =>
% 108.14/14.62 ((
% 108.14/14.62 (demorgan2a1) =>
% 108.14/14.62 ((
% 108.14/14.62 (complementUnionInPowersetComplement) =>
% 108.14/14.62 ((
% 108.14/14.62 (demorgan2a2) =>
% 108.14/14.62 ((
% 108.14/14.62 (demorgan1a) =>
% 108.14/14.62 ((
% 108.14/14.62 (demorgan1b) =>
% 108.14/14.62 ((
% 108.14/14.62 (demorgan1) =>
% 108.14/14.62 ((
% 108.14/14.62 (demorgan2a) =>
% 108.14/14.62 ((
% 108.14/14.62 (demorgan2b2) =>
% 108.14/14.62 ((
% 108.14/14.62 (demorgan2b) =>
% 108.14/14.62 ((
% 108.14/14.62 (demorgan2) =>
% 108.14/14.62 ((
% 108.14/14.62 (woz13rule0) =>
% 108.14/14.62 ((
% 108.14/14.62 (woz13rule1) =>
% 108.14/14.62 ((
% 108.14/14.62 (woz13rule2) =>
% 108.14/14.62 ((
% 108.14/14.62 (woz13rule3) =>
% 108.14/14.62 ((
% 108.14/14.62 (woz13rule4) =>
% 108.14/14.62 ((
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% 108.14/14.62 ((
% 108.14/14.62 (woz1_2) =>
% 108.14/14.62 ((
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% 108.14/14.62 ((
% 108.14/14.62 (woz1_4) =>
% 108.14/14.62 ((
% 108.14/14.62 (woz1_5) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1all2) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1SetBreln1) =>
% 108.14/14.62 ((
% 108.14/14.62 (choice2fnsingleton) =>
% 108.14/14.62 ((
% 108.14/14.62 (setOfPairsIsBReln1) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1all1) =>
% 108.14/14.62 ((
% 108.14/14.62 (subbreln1) =>
% 108.14/14.62 ((
% 108.14/14.62 (eqbreln1) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1invprop) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1invI) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1invE) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1compprop) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1compI) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1compE) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1compEex) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1unionprop) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1unionIL) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1unionIR) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1unionI) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1unionE) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1unionEcases) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1unionCommutes) =>
% 108.14/14.62 ((
% 108.14/14.62 (woz2Ex) =>
% 108.14/14.62 ((
% 108.14/14.62 (woz2W) =>
% 108.14/14.62 ((
% 108.14/14.62 (woz2A) =>
% 108.14/14.62 ((
% 108.14/14.62 (woz2B) =>
% 108.14/14.62 ((
% 108.14/14.62 (image1Ex) =>
% 108.14/14.62 ((
% 108.14/14.62 (image1Ex1) =>
% 108.14/14.62 ((
% 108.14/14.62 (image1Equiv) =>
% 108.14/14.62 ((
% 108.14/14.62 (image1E) =>
% 108.14/14.62 ((
% 108.14/14.62 (image1I) =>
% 108.14/14.62 ((
% 108.14/14.62 (injFuncInInjFuncSet) =>
% 108.14/14.62 ((
% 108.14/14.62 (injFuncSetFuncIn) =>
% 108.14/14.62 ((
% 108.14/14.62 (injFuncSetFuncInj) =>
% 108.14/14.62 ((
% 108.14/14.62 (surjFuncSetFuncIn) =>
% 108.14/14.62 ((
% 108.14/14.62 (surjFuncSetFuncSurj) =>
% 108.14/14.62 ((
% 108.14/14.62 (leftInvIsSurj) =>
% 108.14/14.62 ((
% 108.14/14.62 (surjCantorThm) =>
% 108.14/14.62 ((
% 108.14/14.62 (!!) @ (
% 108.14/14.62 (('#S') @ (
% 108.14/14.62 (
% 108.14/14.62 ('#B') @ (
% 108.14/14.62 =>) @
% 108.14/14.62 nonempty)) @
% 108.14/14.62 (
% 108.14/14.62 (
% 108.14/14.62 ('#B') @ (
% 108.14/14.62 ??) @
% 108.14/14.62 (
% 108.14/14.62 (
% 108.14/14.62 ('#S') @ (
% 108.14/14.62 (
% 108.14/14.62 ('#B') @ (
% 108.14/14.62 '#S') @
% 108.14/14.62 (
% 108.14/14.62 (
% 108.14/14.62 ('#B') @ (
% 108.14/14.62 (
% 108.14/14.62 ('#B') @ (
% 108.14/14.62 &))) @
% 108.14/14.62 (
% 108.14/14.62 (
% 108.14/14.62 ('#C') @ in)))))) @
% 108.14/14.62 (
% 108.14/14.62 (
% 108.14/14.62 ('#C') @ (
% 108.14/14.62 (
% 108.14/14.62 ('#B') @ (
% 108.14/14.62 '#C') @
% 108.14/14.62 (
% 108.14/14.62 (
% 108.14/14.62 ('#B') @ (
% 108.14/14.62 (
% 108.14/14.62 ('#B') @ (
% 108.14/14.62 =))) @
% 108.14/14.62 (
% 108.14/14.62 (
% 108.14/14.62 ('#C') @ binintersect)))))) @
% 108.14/14.62 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 108.14/14.62 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2091])).
% 108.14/14.62 thf(zip_derived_cl2115, plain,
% 108.14/14.62 (~ (((funcext) =>
% 108.14/14.62 (((funcext2) =>
% 108.14/14.62 (((ap2apEq1) =>
% 108.14/14.62 (((ap2apEq2) =>
% 108.14/14.62 (((beta1) =>
% 108.14/14.62 (((eta1) =>
% 108.14/14.62 (((lam2lamEq) =>
% 108.14/14.62 (((beta2) =>
% 108.14/14.62 (((eta2) =>
% 108.14/14.62 (((iffalseProp1) =>
% 108.14/14.62 (((iffalseProp2) =>
% 108.14/14.62 (((iftrueProp1) =>
% 108.14/14.62 (((iftrueProp2) =>
% 108.14/14.62 (((ifSingleton) =>
% 108.14/14.62 (((ifp) =>
% 108.14/14.62 (((theeq) =>
% 108.14/14.62 (((iftrue) =>
% 108.14/14.62 (((iffalse) =>
% 108.14/14.62 (((iftrueorfalse) =>
% 108.14/14.62 (((binintersectT_lem) =>
% 108.14/14.62 (((binunionT_lem) =>
% 108.14/14.62 (((powersetT_lem) =>
% 108.14/14.62 (((setminusT_lem) =>
% 108.14/14.62 (((complementT_lem) =>
% 108.14/14.62 (((setextT) =>
% 108.14/14.62 (((subsetTI) =>
% 108.14/14.62 (((powersetTI1) =>
% 108.14/14.62 (((powersetTE1) =>
% 108.14/14.62 (((complementTI1) =>
% 108.14/14.62 (((complementTE1) =>
% 108.14/14.62 ((
% 108.14/14.62 (binintersectTELcontra) =>
% 108.14/14.62 ((
% 108.14/14.62 (binintersectTERcontra) =>
% 108.14/14.62 ((
% 108.14/14.62 (contrasubsetT) =>
% 108.14/14.62 ((
% 108.14/14.62 (contrasubsetT1) =>
% 108.14/14.62 ((
% 108.14/14.62 (contrasubsetT2) =>
% 108.14/14.62 ((
% 108.14/14.62 (contrasubsetT3) =>
% 108.14/14.62 ((
% 108.14/14.62 (doubleComplementI1) =>
% 108.14/14.62 ((
% 108.14/14.62 (doubleComplementE1) =>
% 108.14/14.62 ((
% 108.14/14.62 (doubleComplementSub1) =>
% 108.14/14.62 ((
% 108.14/14.62 (doubleComplementSub2) =>
% 108.14/14.62 ((
% 108.14/14.62 (doubleComplementEq) =>
% 108.14/14.62 ((
% 108.14/14.62 (complementTnotintersectT) =>
% 108.14/14.62 ((
% 108.14/14.62 (complementImpComplementIntersect) =>
% 108.14/14.62 ((
% 108.14/14.62 (complementSubsetComplementIntersect) =>
% 108.14/14.62 ((
% 108.14/14.62 (complementInPowersetComplementIntersect) =>
% 108.14/14.62 ((
% 108.14/14.62 (contraSubsetComplement) =>
% 108.14/14.62 ((
% 108.14/14.62 (complementTcontraSubset) =>
% 108.14/14.62 ((
% 108.14/14.62 (binunionTILcontra) =>
% 108.14/14.62 ((
% 108.14/14.62 (binunionTIRcontra) =>
% 108.14/14.62 ((
% 108.14/14.62 (inIntersectImpInUnion) =>
% 108.14/14.62 ((
% 108.14/14.62 (inIntersectImpInUnion2) =>
% 108.14/14.62 ((
% 108.14/14.62 (inIntersectImpInIntersectUnions) =>
% 108.14/14.62 ((
% 108.14/14.62 (intersectInPowersetIntersectUnions) =>
% 108.14/14.62 ((
% 108.14/14.62 (inComplementUnionImpNotIn1) =>
% 108.14/14.62 ((
% 108.14/14.62 (inComplementUnionImpInComplement1) =>
% 108.14/14.62 ((
% 108.14/14.62 (binunionTE) =>
% 108.14/14.62 ((
% 108.14/14.62 (binunionTEcontra) =>
% 108.14/14.62 ((
% 108.14/14.62 (demorgan2a1) =>
% 108.14/14.62 ((
% 108.14/14.62 (complementUnionInPowersetComplement) =>
% 108.14/14.62 ((
% 108.14/14.62 (demorgan2a2) =>
% 108.14/14.62 ((
% 108.14/14.62 (demorgan1a) =>
% 108.14/14.62 ((
% 108.14/14.62 (demorgan1b) =>
% 108.14/14.62 ((
% 108.14/14.62 (demorgan1) =>
% 108.14/14.62 ((
% 108.14/14.62 (demorgan2a) =>
% 108.14/14.62 ((
% 108.14/14.62 (demorgan2b2) =>
% 108.14/14.62 ((
% 108.14/14.62 (demorgan2b) =>
% 108.14/14.62 ((
% 108.14/14.62 (demorgan2) =>
% 108.14/14.62 ((
% 108.14/14.62 (woz13rule0) =>
% 108.14/14.62 ((
% 108.14/14.62 (woz13rule1) =>
% 108.14/14.62 ((
% 108.14/14.62 (woz13rule2) =>
% 108.14/14.62 ((
% 108.14/14.62 (woz13rule3) =>
% 108.14/14.62 ((
% 108.14/14.62 (woz13rule4) =>
% 108.14/14.62 ((
% 108.14/14.62 (woz1_1) =>
% 108.14/14.62 ((
% 108.14/14.62 (woz1_2) =>
% 108.14/14.62 ((
% 108.14/14.62 (woz1_3) =>
% 108.14/14.62 ((
% 108.14/14.62 (woz1_4) =>
% 108.14/14.62 ((
% 108.14/14.62 (woz1_5) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1all2) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1SetBreln1) =>
% 108.14/14.62 ((
% 108.14/14.62 (choice2fnsingleton) =>
% 108.14/14.62 ((
% 108.14/14.62 (setOfPairsIsBReln1) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1all1) =>
% 108.14/14.62 ((
% 108.14/14.62 (subbreln1) =>
% 108.14/14.62 ((
% 108.14/14.62 (eqbreln1) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1invprop) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1invI) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1invE) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1compprop) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1compI) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1compE) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1compEex) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1unionprop) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1unionIL) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1unionIR) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1unionI) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1unionE) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1unionEcases) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1unionCommutes) =>
% 108.14/14.62 ((
% 108.14/14.62 (woz2Ex) =>
% 108.14/14.62 ((
% 108.14/14.62 (woz2W) =>
% 108.14/14.62 ((
% 108.14/14.62 (woz2A) =>
% 108.14/14.62 ((
% 108.14/14.62 (woz2B) =>
% 108.14/14.62 ((
% 108.14/14.62 (image1Ex) =>
% 108.14/14.62 ((
% 108.14/14.62 (image1Ex1) =>
% 108.14/14.62 ((
% 108.14/14.62 (image1Equiv) =>
% 108.14/14.62 ((
% 108.14/14.62 (image1E) =>
% 108.14/14.62 ((
% 108.14/14.62 (image1I) =>
% 108.14/14.62 ((
% 108.14/14.62 (injFuncInInjFuncSet) =>
% 108.14/14.62 ((
% 108.14/14.62 (injFuncSetFuncIn) =>
% 108.14/14.62 ((
% 108.14/14.62 (injFuncSetFuncInj) =>
% 108.14/14.62 ((
% 108.14/14.62 (surjFuncSetFuncIn) =>
% 108.14/14.62 ((
% 108.14/14.62 (surjFuncSetFuncSurj) =>
% 108.14/14.62 ((
% 108.14/14.62 (leftInvIsSurj) =>
% 108.14/14.62 ((
% 108.14/14.62 (surjCantorThm) =>
% 108.14/14.62 ((
% 108.14/14.62 (!!) @ (
% 108.14/14.62 (('#S') @ (
% 108.14/14.62 (
% 108.14/14.62 ('#B') @ (
% 108.14/14.62 =>) @
% 108.14/14.62 nonempty)) @
% 108.14/14.62 (
% 108.14/14.62 (
% 108.14/14.62 ('#B') @ (
% 108.14/14.62 ??) @
% 108.14/14.62 (
% 108.14/14.62 (
% 108.14/14.62 ('#S') @ (
% 108.14/14.62 (
% 108.14/14.62 ('#B') @ (
% 108.14/14.62 '#S') @
% 108.14/14.62 (
% 108.14/14.62 (
% 108.14/14.62 ('#B') @ (
% 108.14/14.62 (
% 108.14/14.62 ('#B') @ (
% 108.14/14.62 &))) @
% 108.14/14.62 (
% 108.14/14.62 (
% 108.14/14.62 ('#C') @ in)))))) @
% 108.14/14.62 (
% 108.14/14.62 (
% 108.14/14.62 ('#C') @ (
% 108.14/14.62 (
% 108.14/14.62 ('#B') @ (
% 108.14/14.62 '#C') @
% 108.14/14.62 (
% 108.14/14.62 (
% 108.14/14.62 ('#B') @ (
% 108.14/14.62 (
% 108.14/14.62 ('#B') @ (
% 108.14/14.62 =))) @
% 108.14/14.62 (
% 108.14/14.62 (
% 108.14/14.62 ('#C') @ binintersect)))))) @
% 108.14/14.62 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 108.14/14.62 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2102])).
% 108.14/14.62 thf(zip_derived_cl2130, plain,
% 108.14/14.62 (~ (((funcext2) =>
% 108.14/14.62 (((ap2apEq1) =>
% 108.14/14.62 (((ap2apEq2) =>
% 108.14/14.62 (((beta1) =>
% 108.14/14.62 (((eta1) =>
% 108.14/14.62 (((lam2lamEq) =>
% 108.14/14.62 (((beta2) =>
% 108.14/14.62 (((eta2) =>
% 108.14/14.62 (((iffalseProp1) =>
% 108.14/14.62 (((iffalseProp2) =>
% 108.14/14.62 (((iftrueProp1) =>
% 108.14/14.62 (((iftrueProp2) =>
% 108.14/14.62 (((ifSingleton) =>
% 108.14/14.62 (((ifp) =>
% 108.14/14.62 (((theeq) =>
% 108.14/14.62 (((iftrue) =>
% 108.14/14.62 (((iffalse) =>
% 108.14/14.62 (((iftrueorfalse) =>
% 108.14/14.62 (((binintersectT_lem) =>
% 108.14/14.62 (((binunionT_lem) =>
% 108.14/14.62 (((powersetT_lem) =>
% 108.14/14.62 (((setminusT_lem) =>
% 108.14/14.62 (((complementT_lem) =>
% 108.14/14.62 (((setextT) =>
% 108.14/14.62 (((subsetTI) =>
% 108.14/14.62 (((powersetTI1) =>
% 108.14/14.62 (((powersetTE1) =>
% 108.14/14.62 (((complementTI1) =>
% 108.14/14.62 (((complementTE1) =>
% 108.14/14.62 (((binintersectTELcontra) =>
% 108.14/14.62 ((
% 108.14/14.62 (binintersectTERcontra) =>
% 108.14/14.62 ((
% 108.14/14.62 (contrasubsetT) =>
% 108.14/14.62 ((
% 108.14/14.62 (contrasubsetT1) =>
% 108.14/14.62 ((
% 108.14/14.62 (contrasubsetT2) =>
% 108.14/14.62 ((
% 108.14/14.62 (contrasubsetT3) =>
% 108.14/14.62 ((
% 108.14/14.62 (doubleComplementI1) =>
% 108.14/14.62 ((
% 108.14/14.62 (doubleComplementE1) =>
% 108.14/14.62 ((
% 108.14/14.62 (doubleComplementSub1) =>
% 108.14/14.62 ((
% 108.14/14.62 (doubleComplementSub2) =>
% 108.14/14.62 ((
% 108.14/14.62 (doubleComplementEq) =>
% 108.14/14.62 ((
% 108.14/14.62 (complementTnotintersectT) =>
% 108.14/14.62 ((
% 108.14/14.62 (complementImpComplementIntersect) =>
% 108.14/14.62 ((
% 108.14/14.62 (complementSubsetComplementIntersect) =>
% 108.14/14.62 ((
% 108.14/14.62 (complementInPowersetComplementIntersect) =>
% 108.14/14.62 ((
% 108.14/14.62 (contraSubsetComplement) =>
% 108.14/14.62 ((
% 108.14/14.62 (complementTcontraSubset) =>
% 108.14/14.62 ((
% 108.14/14.62 (binunionTILcontra) =>
% 108.14/14.62 ((
% 108.14/14.62 (binunionTIRcontra) =>
% 108.14/14.62 ((
% 108.14/14.62 (inIntersectImpInUnion) =>
% 108.14/14.62 ((
% 108.14/14.62 (inIntersectImpInUnion2) =>
% 108.14/14.62 ((
% 108.14/14.62 (inIntersectImpInIntersectUnions) =>
% 108.14/14.62 ((
% 108.14/14.62 (intersectInPowersetIntersectUnions) =>
% 108.14/14.62 ((
% 108.14/14.62 (inComplementUnionImpNotIn1) =>
% 108.14/14.62 ((
% 108.14/14.62 (inComplementUnionImpInComplement1) =>
% 108.14/14.62 ((
% 108.14/14.62 (binunionTE) =>
% 108.14/14.62 ((
% 108.14/14.62 (binunionTEcontra) =>
% 108.14/14.62 ((
% 108.14/14.62 (demorgan2a1) =>
% 108.14/14.62 ((
% 108.14/14.62 (complementUnionInPowersetComplement) =>
% 108.14/14.62 ((
% 108.14/14.62 (demorgan2a2) =>
% 108.14/14.62 ((
% 108.14/14.62 (demorgan1a) =>
% 108.14/14.62 ((
% 108.14/14.62 (demorgan1b) =>
% 108.14/14.62 ((
% 108.14/14.62 (demorgan1) =>
% 108.14/14.62 ((
% 108.14/14.62 (demorgan2a) =>
% 108.14/14.62 ((
% 108.14/14.62 (demorgan2b2) =>
% 108.14/14.62 ((
% 108.14/14.62 (demorgan2b) =>
% 108.14/14.62 ((
% 108.14/14.62 (demorgan2) =>
% 108.14/14.62 ((
% 108.14/14.62 (woz13rule0) =>
% 108.14/14.62 ((
% 108.14/14.62 (woz13rule1) =>
% 108.14/14.62 ((
% 108.14/14.62 (woz13rule2) =>
% 108.14/14.62 ((
% 108.14/14.62 (woz13rule3) =>
% 108.14/14.62 ((
% 108.14/14.62 (woz13rule4) =>
% 108.14/14.62 ((
% 108.14/14.62 (woz1_1) =>
% 108.14/14.62 ((
% 108.14/14.62 (woz1_2) =>
% 108.14/14.62 ((
% 108.14/14.62 (woz1_3) =>
% 108.14/14.62 ((
% 108.14/14.62 (woz1_4) =>
% 108.14/14.62 ((
% 108.14/14.62 (woz1_5) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1all2) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1SetBreln1) =>
% 108.14/14.62 ((
% 108.14/14.62 (choice2fnsingleton) =>
% 108.14/14.62 ((
% 108.14/14.62 (setOfPairsIsBReln1) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1all1) =>
% 108.14/14.62 ((
% 108.14/14.62 (subbreln1) =>
% 108.14/14.62 ((
% 108.14/14.62 (eqbreln1) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1invprop) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1invI) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1invE) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1compprop) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1compI) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1compE) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1compEex) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1unionprop) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1unionIL) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1unionIR) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1unionI) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1unionE) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1unionEcases) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1unionCommutes) =>
% 108.14/14.62 ((
% 108.14/14.62 (woz2Ex) =>
% 108.14/14.62 ((
% 108.14/14.62 (woz2W) =>
% 108.14/14.62 ((
% 108.14/14.62 (woz2A) =>
% 108.14/14.62 ((
% 108.14/14.62 (woz2B) =>
% 108.14/14.62 ((
% 108.14/14.62 (image1Ex) =>
% 108.14/14.62 ((
% 108.14/14.62 (image1Ex1) =>
% 108.14/14.62 ((
% 108.14/14.62 (image1Equiv) =>
% 108.14/14.62 ((
% 108.14/14.62 (image1E) =>
% 108.14/14.62 ((
% 108.14/14.62 (image1I) =>
% 108.14/14.62 ((
% 108.14/14.62 (injFuncInInjFuncSet) =>
% 108.14/14.62 ((
% 108.14/14.62 (injFuncSetFuncIn) =>
% 108.14/14.62 ((
% 108.14/14.62 (injFuncSetFuncInj) =>
% 108.14/14.62 ((
% 108.14/14.62 (surjFuncSetFuncIn) =>
% 108.14/14.62 ((
% 108.14/14.62 (surjFuncSetFuncSurj) =>
% 108.14/14.62 ((
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% 108.14/14.62 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2115])).
% 108.14/14.62 thf(zip_derived_cl2146, plain,
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% 108.14/14.62 ((
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% 108.14/14.62 ((
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% 108.14/14.62 ((
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% 108.14/14.62 ((
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% 108.14/14.62 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2130])).
% 108.14/14.62 thf(zip_derived_cl2163, plain,
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% 108.14/14.62 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2146])).
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% 108.14/14.62 (((ifp) =>
% 108.14/14.62 (((theeq) =>
% 108.14/14.62 (((iftrue) =>
% 108.14/14.62 (((iffalse) =>
% 108.14/14.62 (((iftrueorfalse) =>
% 108.14/14.62 (((binintersectT_lem) =>
% 108.14/14.62 (((binunionT_lem) =>
% 108.14/14.62 (((powersetT_lem) =>
% 108.14/14.62 (((setminusT_lem) =>
% 108.14/14.62 (((complementT_lem) =>
% 108.14/14.62 (((setextT) =>
% 108.14/14.62 (((subsetTI) =>
% 108.14/14.62 (((powersetTI1) =>
% 108.14/14.62 (((powersetTE1) =>
% 108.14/14.62 (((complementTI1) =>
% 108.14/14.62 (((complementTE1) =>
% 108.14/14.62 (((binintersectTELcontra) =>
% 108.14/14.62 (((binintersectTERcontra) =>
% 108.14/14.62 (((contrasubsetT) =>
% 108.14/14.62 (((contrasubsetT1) =>
% 108.14/14.62 ((
% 108.14/14.62 (contrasubsetT2) =>
% 108.14/14.62 ((
% 108.14/14.62 (contrasubsetT3) =>
% 108.14/14.62 ((
% 108.14/14.62 (doubleComplementI1) =>
% 108.14/14.62 ((
% 108.14/14.62 (doubleComplementE1) =>
% 108.14/14.62 ((
% 108.14/14.62 (doubleComplementSub1) =>
% 108.14/14.62 ((
% 108.14/14.62 (doubleComplementSub2) =>
% 108.14/14.62 ((
% 108.14/14.62 (doubleComplementEq) =>
% 108.14/14.62 ((
% 108.14/14.62 (complementTnotintersectT) =>
% 108.14/14.62 ((
% 108.14/14.62 (complementImpComplementIntersect) =>
% 108.14/14.62 ((
% 108.14/14.62 (complementSubsetComplementIntersect) =>
% 108.14/14.62 ((
% 108.14/14.62 (complementInPowersetComplementIntersect) =>
% 108.14/14.62 ((
% 108.14/14.62 (contraSubsetComplement) =>
% 108.14/14.62 ((
% 108.14/14.62 (complementTcontraSubset) =>
% 108.14/14.62 ((
% 108.14/14.62 (binunionTILcontra) =>
% 108.14/14.62 ((
% 108.14/14.62 (binunionTIRcontra) =>
% 108.14/14.62 ((
% 108.14/14.62 (inIntersectImpInUnion) =>
% 108.14/14.62 ((
% 108.14/14.62 (inIntersectImpInUnion2) =>
% 108.14/14.62 ((
% 108.14/14.62 (inIntersectImpInIntersectUnions) =>
% 108.14/14.62 ((
% 108.14/14.62 (intersectInPowersetIntersectUnions) =>
% 108.14/14.62 ((
% 108.14/14.62 (inComplementUnionImpNotIn1) =>
% 108.14/14.62 ((
% 108.14/14.62 (inComplementUnionImpInComplement1) =>
% 108.14/14.62 ((
% 108.14/14.62 (binunionTE) =>
% 108.14/14.62 ((
% 108.14/14.62 (binunionTEcontra) =>
% 108.14/14.62 ((
% 108.14/14.62 (demorgan2a1) =>
% 108.14/14.62 ((
% 108.14/14.62 (complementUnionInPowersetComplement) =>
% 108.14/14.62 ((
% 108.14/14.62 (demorgan2a2) =>
% 108.14/14.62 ((
% 108.14/14.62 (demorgan1a) =>
% 108.14/14.62 ((
% 108.14/14.62 (demorgan1b) =>
% 108.14/14.62 ((
% 108.14/14.62 (demorgan1) =>
% 108.14/14.62 ((
% 108.14/14.62 (demorgan2a) =>
% 108.14/14.62 ((
% 108.14/14.62 (demorgan2b2) =>
% 108.14/14.62 ((
% 108.14/14.62 (demorgan2b) =>
% 108.14/14.62 ((
% 108.14/14.62 (demorgan2) =>
% 108.14/14.62 ((
% 108.14/14.62 (woz13rule0) =>
% 108.14/14.62 ((
% 108.14/14.62 (woz13rule1) =>
% 108.14/14.62 ((
% 108.14/14.62 (woz13rule2) =>
% 108.14/14.62 ((
% 108.14/14.62 (woz13rule3) =>
% 108.14/14.62 ((
% 108.14/14.62 (woz13rule4) =>
% 108.14/14.62 ((
% 108.14/14.62 (woz1_1) =>
% 108.14/14.62 ((
% 108.14/14.62 (woz1_2) =>
% 108.14/14.62 ((
% 108.14/14.62 (woz1_3) =>
% 108.14/14.62 ((
% 108.14/14.62 (woz1_4) =>
% 108.14/14.62 ((
% 108.14/14.62 (woz1_5) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1all2) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1SetBreln1) =>
% 108.14/14.62 ((
% 108.14/14.62 (choice2fnsingleton) =>
% 108.14/14.62 ((
% 108.14/14.62 (setOfPairsIsBReln1) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1all1) =>
% 108.14/14.62 ((
% 108.14/14.62 (subbreln1) =>
% 108.14/14.62 ((
% 108.14/14.62 (eqbreln1) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1invprop) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1invI) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1invE) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1compprop) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1compI) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1compE) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1compEex) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1unionprop) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1unionIL) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1unionIR) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1unionI) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1unionE) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1unionEcases) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1unionCommutes) =>
% 108.14/14.62 ((
% 108.14/14.62 (woz2Ex) =>
% 108.14/14.62 ((
% 108.14/14.62 (woz2W) =>
% 108.14/14.62 ((
% 108.14/14.62 (woz2A) =>
% 108.14/14.62 ((
% 108.14/14.62 (woz2B) =>
% 108.14/14.62 ((
% 108.14/14.62 (image1Ex) =>
% 108.14/14.62 ((
% 108.14/14.62 (image1Ex1) =>
% 108.14/14.62 ((
% 108.14/14.62 (image1Equiv) =>
% 108.14/14.62 ((
% 108.14/14.62 (image1E) =>
% 108.14/14.62 ((
% 108.14/14.62 (image1I) =>
% 108.14/14.62 ((
% 108.14/14.62 (injFuncInInjFuncSet) =>
% 108.14/14.62 ((
% 108.14/14.62 (injFuncSetFuncIn) =>
% 108.14/14.62 ((
% 108.14/14.62 (injFuncSetFuncInj) =>
% 108.14/14.62 ((
% 108.14/14.62 (surjFuncSetFuncIn) =>
% 108.14/14.62 ((
% 108.14/14.62 (surjFuncSetFuncSurj) =>
% 108.14/14.62 ((
% 108.14/14.62 (leftInvIsSurj) =>
% 108.14/14.62 ((
% 108.14/14.62 (surjCantorThm) =>
% 108.14/14.62 ((
% 108.14/14.62 (!!) @ (
% 108.14/14.62 (('#S') @ (
% 108.14/14.62 (
% 108.14/14.62 ('#B') @ (
% 108.14/14.62 =>) @
% 108.14/14.62 nonempty)) @
% 108.14/14.62 (
% 108.14/14.62 (
% 108.14/14.62 ('#B') @ (
% 108.14/14.62 ??) @
% 108.14/14.62 (
% 108.14/14.62 (
% 108.14/14.62 ('#S') @ (
% 108.14/14.62 (
% 108.14/14.62 ('#B') @ (
% 108.14/14.62 '#S') @
% 108.14/14.62 (
% 108.14/14.62 (
% 108.14/14.62 ('#B') @ (
% 108.14/14.62 (
% 108.14/14.62 ('#B') @ (
% 108.14/14.62 &))) @
% 108.14/14.62 (
% 108.14/14.62 (
% 108.14/14.62 ('#C') @ in)))))) @
% 108.14/14.62 (
% 108.14/14.62 (
% 108.14/14.62 ('#C') @ (
% 108.14/14.62 (
% 108.14/14.62 ('#B') @ (
% 108.14/14.62 '#C') @
% 108.14/14.62 (
% 108.14/14.62 (
% 108.14/14.62 ('#B') @ (
% 108.14/14.62 (
% 108.14/14.62 ('#B') @ (
% 108.14/14.62 =))) @
% 108.14/14.62 (
% 108.14/14.62 (
% 108.14/14.62 ('#C') @ binintersect)))))) @
% 108.14/14.62 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 108.14/14.62 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2163])).
% 108.14/14.62 thf(zip_derived_cl2198, plain,
% 108.14/14.62 (~ (((eta1) =>
% 108.14/14.62 (((lam2lamEq) =>
% 108.14/14.62 (((beta2) =>
% 108.14/14.62 (((eta2) =>
% 108.14/14.62 (((iffalseProp1) =>
% 108.14/14.62 (((iffalseProp2) =>
% 108.14/14.62 (((iftrueProp1) =>
% 108.14/14.62 (((iftrueProp2) =>
% 108.14/14.62 (((ifSingleton) =>
% 108.14/14.62 (((ifp) =>
% 108.14/14.62 (((theeq) =>
% 108.14/14.62 (((iftrue) =>
% 108.14/14.62 (((iffalse) =>
% 108.14/14.62 (((iftrueorfalse) =>
% 108.14/14.62 (((binintersectT_lem) =>
% 108.14/14.62 (((binunionT_lem) =>
% 108.14/14.62 (((powersetT_lem) =>
% 108.14/14.62 (((setminusT_lem) =>
% 108.14/14.62 (((complementT_lem) =>
% 108.14/14.62 (((setextT) =>
% 108.14/14.62 (((subsetTI) =>
% 108.14/14.62 (((powersetTI1) =>
% 108.14/14.62 (((powersetTE1) =>
% 108.14/14.62 (((complementTI1) =>
% 108.14/14.62 (((complementTE1) =>
% 108.14/14.62 (((binintersectTELcontra) =>
% 108.14/14.62 (((binintersectTERcontra) =>
% 108.14/14.62 (((contrasubsetT) =>
% 108.14/14.62 (((contrasubsetT1) =>
% 108.14/14.62 (((contrasubsetT2) =>
% 108.14/14.62 ((
% 108.14/14.62 (contrasubsetT3) =>
% 108.14/14.62 ((
% 108.14/14.62 (doubleComplementI1) =>
% 108.14/14.62 ((
% 108.14/14.62 (doubleComplementE1) =>
% 108.14/14.62 ((
% 108.14/14.62 (doubleComplementSub1) =>
% 108.14/14.62 ((
% 108.14/14.62 (doubleComplementSub2) =>
% 108.14/14.62 ((
% 108.14/14.62 (doubleComplementEq) =>
% 108.14/14.62 ((
% 108.14/14.62 (complementTnotintersectT) =>
% 108.14/14.62 ((
% 108.14/14.62 (complementImpComplementIntersect) =>
% 108.14/14.62 ((
% 108.14/14.62 (complementSubsetComplementIntersect) =>
% 108.14/14.62 ((
% 108.14/14.62 (complementInPowersetComplementIntersect) =>
% 108.14/14.62 ((
% 108.14/14.62 (contraSubsetComplement) =>
% 108.14/14.62 ((
% 108.14/14.62 (complementTcontraSubset) =>
% 108.14/14.62 ((
% 108.14/14.62 (binunionTILcontra) =>
% 108.14/14.62 ((
% 108.14/14.62 (binunionTIRcontra) =>
% 108.14/14.62 ((
% 108.14/14.62 (inIntersectImpInUnion) =>
% 108.14/14.62 ((
% 108.14/14.62 (inIntersectImpInUnion2) =>
% 108.14/14.62 ((
% 108.14/14.62 (inIntersectImpInIntersectUnions) =>
% 108.14/14.62 ((
% 108.14/14.62 (intersectInPowersetIntersectUnions) =>
% 108.14/14.62 ((
% 108.14/14.62 (inComplementUnionImpNotIn1) =>
% 108.14/14.62 ((
% 108.14/14.62 (inComplementUnionImpInComplement1) =>
% 108.14/14.62 ((
% 108.14/14.62 (binunionTE) =>
% 108.14/14.62 ((
% 108.14/14.62 (binunionTEcontra) =>
% 108.14/14.62 ((
% 108.14/14.62 (demorgan2a1) =>
% 108.14/14.62 ((
% 108.14/14.62 (complementUnionInPowersetComplement) =>
% 108.14/14.62 ((
% 108.14/14.62 (demorgan2a2) =>
% 108.14/14.62 ((
% 108.14/14.62 (demorgan1a) =>
% 108.14/14.62 ((
% 108.14/14.62 (demorgan1b) =>
% 108.14/14.62 ((
% 108.14/14.62 (demorgan1) =>
% 108.14/14.62 ((
% 108.14/14.62 (demorgan2a) =>
% 108.14/14.62 ((
% 108.14/14.62 (demorgan2b2) =>
% 108.14/14.62 ((
% 108.14/14.62 (demorgan2b) =>
% 108.14/14.62 ((
% 108.14/14.62 (demorgan2) =>
% 108.14/14.62 ((
% 108.14/14.62 (woz13rule0) =>
% 108.14/14.62 ((
% 108.14/14.62 (woz13rule1) =>
% 108.14/14.62 ((
% 108.14/14.62 (woz13rule2) =>
% 108.14/14.62 ((
% 108.14/14.62 (woz13rule3) =>
% 108.14/14.62 ((
% 108.14/14.62 (woz13rule4) =>
% 108.14/14.62 ((
% 108.14/14.62 (woz1_1) =>
% 108.14/14.62 ((
% 108.14/14.62 (woz1_2) =>
% 108.14/14.62 ((
% 108.14/14.62 (woz1_3) =>
% 108.14/14.62 ((
% 108.14/14.62 (woz1_4) =>
% 108.14/14.62 ((
% 108.14/14.62 (woz1_5) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1all2) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1SetBreln1) =>
% 108.14/14.62 ((
% 108.14/14.62 (choice2fnsingleton) =>
% 108.14/14.62 ((
% 108.14/14.62 (setOfPairsIsBReln1) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1all1) =>
% 108.14/14.62 ((
% 108.14/14.62 (subbreln1) =>
% 108.14/14.62 ((
% 108.14/14.62 (eqbreln1) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1invprop) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1invI) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1invE) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1compprop) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1compI) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1compE) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1compEex) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1unionprop) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1unionIL) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1unionIR) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1unionI) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1unionE) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1unionEcases) =>
% 108.14/14.62 ((
% 108.14/14.62 (breln1unionCommutes) =>
% 108.14/14.62 ((
% 108.14/14.62 (woz2Ex) =>
% 108.14/14.62 ((
% 108.14/14.62 (woz2W) =>
% 108.14/14.62 ((
% 108.14/14.62 (woz2A) =>
% 108.14/14.62 ((
% 108.14/14.62 (woz2B) =>
% 108.14/14.62 ((
% 108.14/14.62 (image1Ex) =>
% 108.14/14.62 ((
% 108.14/14.62 (image1Ex1) =>
% 108.14/14.62 ((
% 108.14/14.62 (image1Equiv) =>
% 108.14/14.62 ((
% 108.14/14.62 (image1E) =>
% 108.14/14.62 ((
% 108.14/14.62 (image1I) =>
% 108.14/14.62 ((
% 108.14/14.62 (injFuncInInjFuncSet) =>
% 108.14/14.62 ((
% 108.14/14.62 (injFuncSetFuncIn) =>
% 108.14/14.62 ((
% 108.14/14.62 (injFuncSetFuncInj) =>
% 108.14/14.62 ((
% 108.14/14.62 (surjFuncSetFuncIn) =>
% 108.14/14.62 ((
% 108.14/14.62 (surjFuncSetFuncSurj) =>
% 108.14/14.62 ((
% 108.14/14.62 (leftInvIsSurj) =>
% 108.14/14.62 ((
% 108.14/14.62 (surjCantorThm) =>
% 108.14/14.62 ((
% 108.14/14.62 (!!) @ (
% 108.14/14.62 (('#S') @ (
% 108.14/14.62 (
% 108.14/14.62 ('#B') @ (
% 108.14/14.62 =>) @
% 108.14/14.62 nonempty)) @
% 108.14/14.62 (
% 108.14/14.62 (
% 108.14/14.62 ('#B') @ (
% 108.14/14.62 ??) @
% 108.14/14.62 (
% 108.14/14.62 (
% 108.14/14.62 ('#S') @ (
% 108.14/14.62 (
% 108.14/14.62 ('#B') @ (
% 108.14/14.62 '#S') @
% 108.14/14.62 (
% 108.14/14.62 (
% 108.14/14.62 ('#B') @ (
% 108.14/14.62 (
% 108.14/14.62 ('#B') @ (
% 108.14/14.62 &))) @
% 108.14/14.62 (
% 108.14/14.62 (
% 108.14/14.62 ('#C') @ in)))))) @
% 108.14/14.62 (
% 108.14/14.62 (
% 108.14/14.62 ('#C') @ (
% 108.14/14.62 (
% 108.14/14.62 ('#B') @ (
% 108.14/14.62 '#C') @
% 108.14/14.62 (
% 108.14/14.62 (
% 108.14/14.62 ('#B') @ (
% 108.14/14.62 (
% 108.14/14.62 ('#B') @ (
% 108.14/14.62 =))) @
% 108.14/14.62 (
% 108.14/14.62 (
% 108.14/14.62 ('#C') @ binintersect)))))) @
% 108.14/14.62 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 108.14/14.62 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2181])).
% 108.14/14.62 thf(zip_derived_cl2213, plain,
% 108.14/14.62 (~ (((lam2lamEq) =>
% 108.14/14.62 (((beta2) =>
% 108.14/14.62 (((eta2) =>
% 108.14/14.62 (((iffalseProp1) =>
% 108.14/14.62 (((iffalseProp2) =>
% 108.14/14.62 (((iftrueProp1) =>
% 108.14/14.62 (((iftrueProp2) =>
% 108.14/14.62 (((ifSingleton) =>
% 108.14/14.62 (((ifp) =>
% 108.14/14.62 (((theeq) =>
% 108.14/14.62 (((iftrue) =>
% 108.14/14.62 (((iffalse) =>
% 108.14/14.63 (((iftrueorfalse) =>
% 108.14/14.63 (((binintersectT_lem) =>
% 108.14/14.63 (((binunionT_lem) =>
% 108.14/14.63 (((powersetT_lem) =>
% 108.14/14.63 (((setminusT_lem) =>
% 108.14/14.63 (((complementT_lem) =>
% 108.14/14.63 (((setextT) =>
% 108.14/14.63 (((subsetTI) =>
% 108.14/14.63 (((powersetTI1) =>
% 108.14/14.63 (((powersetTE1) =>
% 108.14/14.63 (((complementTI1) =>
% 108.14/14.63 (((complementTE1) =>
% 108.14/14.63 (((binintersectTELcontra) =>
% 108.14/14.63 (((binintersectTERcontra) =>
% 108.14/14.63 (((contrasubsetT) =>
% 108.14/14.63 (((contrasubsetT1) =>
% 108.14/14.63 (((contrasubsetT2) =>
% 108.14/14.63 (((contrasubsetT3) =>
% 108.14/14.63 ((
% 108.14/14.63 (doubleComplementI1) =>
% 108.14/14.63 ((
% 108.14/14.63 (doubleComplementE1) =>
% 108.14/14.63 ((
% 108.14/14.63 (doubleComplementSub1) =>
% 108.14/14.63 ((
% 108.14/14.63 (doubleComplementSub2) =>
% 108.14/14.63 ((
% 108.14/14.63 (doubleComplementEq) =>
% 108.14/14.63 ((
% 108.14/14.63 (complementTnotintersectT) =>
% 108.14/14.63 ((
% 108.14/14.63 (complementImpComplementIntersect) =>
% 108.14/14.63 ((
% 108.14/14.63 (complementSubsetComplementIntersect) =>
% 108.14/14.63 ((
% 108.14/14.63 (complementInPowersetComplementIntersect) =>
% 108.14/14.63 ((
% 108.14/14.63 (contraSubsetComplement) =>
% 108.14/14.63 ((
% 108.14/14.63 (complementTcontraSubset) =>
% 108.14/14.63 ((
% 108.14/14.63 (binunionTILcontra) =>
% 108.14/14.63 ((
% 108.14/14.63 (binunionTIRcontra) =>
% 108.14/14.63 ((
% 108.14/14.63 (inIntersectImpInUnion) =>
% 108.14/14.63 ((
% 108.14/14.63 (inIntersectImpInUnion2) =>
% 108.14/14.63 ((
% 108.14/14.63 (inIntersectImpInIntersectUnions) =>
% 108.14/14.63 ((
% 108.14/14.63 (intersectInPowersetIntersectUnions) =>
% 108.14/14.63 ((
% 108.14/14.63 (inComplementUnionImpNotIn1) =>
% 108.14/14.63 ((
% 108.14/14.63 (inComplementUnionImpInComplement1) =>
% 108.14/14.63 ((
% 108.14/14.63 (binunionTE) =>
% 108.14/14.63 ((
% 108.14/14.63 (binunionTEcontra) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan2a1) =>
% 108.14/14.63 ((
% 108.14/14.63 (complementUnionInPowersetComplement) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan2a2) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan1a) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan1b) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan1) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan2a) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan2b2) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan2b) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan2) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz13rule0) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz13rule1) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz13rule2) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz13rule3) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz13rule4) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz1_1) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz1_2) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz1_3) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz1_4) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz1_5) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1all2) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1SetBreln1) =>
% 108.14/14.63 ((
% 108.14/14.63 (choice2fnsingleton) =>
% 108.14/14.63 ((
% 108.14/14.63 (setOfPairsIsBReln1) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1all1) =>
% 108.14/14.63 ((
% 108.14/14.63 (subbreln1) =>
% 108.14/14.63 ((
% 108.14/14.63 (eqbreln1) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1invprop) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1invI) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1invE) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1compprop) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1compI) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1compE) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1compEex) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1unionprop) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1unionIL) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1unionIR) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1unionI) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1unionE) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1unionEcases) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1unionCommutes) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz2Ex) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz2W) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz2A) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz2B) =>
% 108.14/14.63 ((
% 108.14/14.63 (image1Ex) =>
% 108.14/14.63 ((
% 108.14/14.63 (image1Ex1) =>
% 108.14/14.63 ((
% 108.14/14.63 (image1Equiv) =>
% 108.14/14.63 ((
% 108.14/14.63 (image1E) =>
% 108.14/14.63 ((
% 108.14/14.63 (image1I) =>
% 108.14/14.63 ((
% 108.14/14.63 (injFuncInInjFuncSet) =>
% 108.14/14.63 ((
% 108.14/14.63 (injFuncSetFuncIn) =>
% 108.14/14.63 ((
% 108.14/14.63 (injFuncSetFuncInj) =>
% 108.14/14.63 ((
% 108.14/14.63 (surjFuncSetFuncIn) =>
% 108.14/14.63 ((
% 108.14/14.63 (surjFuncSetFuncSurj) =>
% 108.14/14.63 ((
% 108.14/14.63 (leftInvIsSurj) =>
% 108.14/14.63 ((
% 108.14/14.63 (surjCantorThm) =>
% 108.14/14.63 ((
% 108.14/14.63 (!!) @ (
% 108.14/14.63 (('#S') @ (
% 108.14/14.63 (
% 108.14/14.63 ('#B') @ (
% 108.14/14.63 =>) @
% 108.14/14.63 nonempty)) @
% 108.14/14.63 (
% 108.14/14.63 (
% 108.14/14.63 ('#B') @ (
% 108.14/14.63 ??) @
% 108.14/14.63 (
% 108.14/14.63 (
% 108.14/14.63 ('#S') @ (
% 108.14/14.63 (
% 108.14/14.63 ('#B') @ (
% 108.14/14.63 '#S') @
% 108.14/14.63 (
% 108.14/14.63 (
% 108.14/14.63 ('#B') @ (
% 108.14/14.63 (
% 108.14/14.63 ('#B') @ (
% 108.14/14.63 &))) @
% 108.14/14.63 (
% 108.14/14.63 (
% 108.14/14.63 ('#C') @ in)))))) @
% 108.14/14.63 (
% 108.14/14.63 (
% 108.14/14.63 ('#C') @ (
% 108.14/14.63 (
% 108.14/14.63 ('#B') @ (
% 108.14/14.63 '#C') @
% 108.14/14.63 (
% 108.14/14.63 (
% 108.14/14.63 ('#B') @ (
% 108.14/14.63 (
% 108.14/14.63 ('#B') @ (
% 108.14/14.63 =))) @
% 108.14/14.63 (
% 108.14/14.63 (
% 108.14/14.63 ('#C') @ binintersect)))))) @
% 108.14/14.63 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 108.14/14.63 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2198])).
% 108.14/14.63 thf(zip_derived_cl2228, plain,
% 108.14/14.63 (~ (((beta2) =>
% 108.14/14.63 (((eta2) =>
% 108.14/14.63 (((iffalseProp1) =>
% 108.14/14.63 (((iffalseProp2) =>
% 108.14/14.63 (((iftrueProp1) =>
% 108.14/14.63 (((iftrueProp2) =>
% 108.14/14.63 (((ifSingleton) =>
% 108.14/14.63 (((ifp) =>
% 108.14/14.63 (((theeq) =>
% 108.14/14.63 (((iftrue) =>
% 108.14/14.63 (((iffalse) =>
% 108.14/14.63 (((iftrueorfalse) =>
% 108.14/14.63 (((binintersectT_lem) =>
% 108.14/14.63 (((binunionT_lem) =>
% 108.14/14.63 (((powersetT_lem) =>
% 108.14/14.63 (((setminusT_lem) =>
% 108.14/14.63 (((complementT_lem) =>
% 108.14/14.63 (((setextT) =>
% 108.14/14.63 (((subsetTI) =>
% 108.14/14.63 (((powersetTI1) =>
% 108.14/14.63 (((powersetTE1) =>
% 108.14/14.63 (((complementTI1) =>
% 108.14/14.63 (((complementTE1) =>
% 108.14/14.63 (((binintersectTELcontra) =>
% 108.14/14.63 (((binintersectTERcontra) =>
% 108.14/14.63 (((contrasubsetT) =>
% 108.14/14.63 (((contrasubsetT1) =>
% 108.14/14.63 (((contrasubsetT2) =>
% 108.14/14.63 (((contrasubsetT3) =>
% 108.14/14.63 (((doubleComplementI1) =>
% 108.14/14.63 ((
% 108.14/14.63 (doubleComplementE1) =>
% 108.14/14.63 ((
% 108.14/14.63 (doubleComplementSub1) =>
% 108.14/14.63 ((
% 108.14/14.63 (doubleComplementSub2) =>
% 108.14/14.63 ((
% 108.14/14.63 (doubleComplementEq) =>
% 108.14/14.63 ((
% 108.14/14.63 (complementTnotintersectT) =>
% 108.14/14.63 ((
% 108.14/14.63 (complementImpComplementIntersect) =>
% 108.14/14.63 ((
% 108.14/14.63 (complementSubsetComplementIntersect) =>
% 108.14/14.63 ((
% 108.14/14.63 (complementInPowersetComplementIntersect) =>
% 108.14/14.63 ((
% 108.14/14.63 (contraSubsetComplement) =>
% 108.14/14.63 ((
% 108.14/14.63 (complementTcontraSubset) =>
% 108.14/14.63 ((
% 108.14/14.63 (binunionTILcontra) =>
% 108.14/14.63 ((
% 108.14/14.63 (binunionTIRcontra) =>
% 108.14/14.63 ((
% 108.14/14.63 (inIntersectImpInUnion) =>
% 108.14/14.63 ((
% 108.14/14.63 (inIntersectImpInUnion2) =>
% 108.14/14.63 ((
% 108.14/14.63 (inIntersectImpInIntersectUnions) =>
% 108.14/14.63 ((
% 108.14/14.63 (intersectInPowersetIntersectUnions) =>
% 108.14/14.63 ((
% 108.14/14.63 (inComplementUnionImpNotIn1) =>
% 108.14/14.63 ((
% 108.14/14.63 (inComplementUnionImpInComplement1) =>
% 108.14/14.63 ((
% 108.14/14.63 (binunionTE) =>
% 108.14/14.63 ((
% 108.14/14.63 (binunionTEcontra) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan2a1) =>
% 108.14/14.63 ((
% 108.14/14.63 (complementUnionInPowersetComplement) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan2a2) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan1a) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan1b) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan1) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan2a) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan2b2) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan2b) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan2) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz13rule0) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz13rule1) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz13rule2) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz13rule3) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz13rule4) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz1_1) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz1_2) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz1_3) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz1_4) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz1_5) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1all2) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1SetBreln1) =>
% 108.14/14.63 ((
% 108.14/14.63 (choice2fnsingleton) =>
% 108.14/14.63 ((
% 108.14/14.63 (setOfPairsIsBReln1) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1all1) =>
% 108.14/14.63 ((
% 108.14/14.63 (subbreln1) =>
% 108.14/14.63 ((
% 108.14/14.63 (eqbreln1) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1invprop) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1invI) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1invE) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1compprop) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1compI) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1compE) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1compEex) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1unionprop) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1unionIL) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1unionIR) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1unionI) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1unionE) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1unionEcases) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1unionCommutes) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz2Ex) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz2W) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz2A) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz2B) =>
% 108.14/14.63 ((
% 108.14/14.63 (image1Ex) =>
% 108.14/14.63 ((
% 108.14/14.63 (image1Ex1) =>
% 108.14/14.63 ((
% 108.14/14.63 (image1Equiv) =>
% 108.14/14.63 ((
% 108.14/14.63 (image1E) =>
% 108.14/14.63 ((
% 108.14/14.63 (image1I) =>
% 108.14/14.63 ((
% 108.14/14.63 (injFuncInInjFuncSet) =>
% 108.14/14.63 ((
% 108.14/14.63 (injFuncSetFuncIn) =>
% 108.14/14.63 ((
% 108.14/14.63 (injFuncSetFuncInj) =>
% 108.14/14.63 ((
% 108.14/14.63 (surjFuncSetFuncIn) =>
% 108.14/14.63 ((
% 108.14/14.63 (surjFuncSetFuncSurj) =>
% 108.14/14.63 ((
% 108.14/14.63 (leftInvIsSurj) =>
% 108.14/14.63 ((
% 108.14/14.63 (surjCantorThm) =>
% 108.14/14.63 ((
% 108.14/14.63 (!!) @ (
% 108.14/14.63 (('#S') @ (
% 108.14/14.63 (
% 108.14/14.63 ('#B') @ (
% 108.14/14.63 =>) @
% 108.14/14.63 nonempty)) @
% 108.14/14.63 (
% 108.14/14.63 (
% 108.14/14.63 ('#B') @ (
% 108.14/14.63 ??) @
% 108.14/14.63 (
% 108.14/14.63 (
% 108.14/14.63 ('#S') @ (
% 108.14/14.63 (
% 108.14/14.63 ('#B') @ (
% 108.14/14.63 '#S') @
% 108.14/14.63 (
% 108.14/14.63 (
% 108.14/14.63 ('#B') @ (
% 108.14/14.63 (
% 108.14/14.63 ('#B') @ (
% 108.14/14.63 &))) @
% 108.14/14.63 (
% 108.14/14.63 (
% 108.14/14.63 ('#C') @ in)))))) @
% 108.14/14.63 (
% 108.14/14.63 (
% 108.14/14.63 ('#C') @ (
% 108.14/14.63 (
% 108.14/14.63 ('#B') @ (
% 108.14/14.63 '#C') @
% 108.14/14.63 (
% 108.14/14.63 (
% 108.14/14.63 ('#B') @ (
% 108.14/14.63 (
% 108.14/14.63 ('#B') @ (
% 108.14/14.63 =))) @
% 108.14/14.63 (
% 108.14/14.63 (
% 108.14/14.63 ('#C') @ binintersect)))))) @
% 108.14/14.63 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 108.14/14.63 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2213])).
% 108.14/14.63 thf(zip_derived_cl2244, plain,
% 108.14/14.63 (~ (((eta2) =>
% 108.14/14.63 (((iffalseProp1) =>
% 108.14/14.63 (((iffalseProp2) =>
% 108.14/14.63 (((iftrueProp1) =>
% 108.14/14.63 (((iftrueProp2) =>
% 108.14/14.63 (((ifSingleton) =>
% 108.14/14.63 (((ifp) =>
% 108.14/14.63 (((theeq) =>
% 108.14/14.63 (((iftrue) =>
% 108.14/14.63 (((iffalse) =>
% 108.14/14.63 (((iftrueorfalse) =>
% 108.14/14.63 (((binintersectT_lem) =>
% 108.14/14.63 (((binunionT_lem) =>
% 108.14/14.63 (((powersetT_lem) =>
% 108.14/14.63 (((setminusT_lem) =>
% 108.14/14.63 (((complementT_lem) =>
% 108.14/14.63 (((setextT) =>
% 108.14/14.63 (((subsetTI) =>
% 108.14/14.63 (((powersetTI1) =>
% 108.14/14.63 (((powersetTE1) =>
% 108.14/14.63 (((complementTI1) =>
% 108.14/14.63 (((complementTE1) =>
% 108.14/14.63 (((binintersectTELcontra) =>
% 108.14/14.63 (((binintersectTERcontra) =>
% 108.14/14.63 (((contrasubsetT) =>
% 108.14/14.63 (((contrasubsetT1) =>
% 108.14/14.63 (((contrasubsetT2) =>
% 108.14/14.63 (((contrasubsetT3) =>
% 108.14/14.63 (((doubleComplementI1) =>
% 108.14/14.63 (((doubleComplementE1) =>
% 108.14/14.63 ((
% 108.14/14.63 (doubleComplementSub1) =>
% 108.14/14.63 ((
% 108.14/14.63 (doubleComplementSub2) =>
% 108.14/14.63 ((
% 108.14/14.63 (doubleComplementEq) =>
% 108.14/14.63 ((
% 108.14/14.63 (complementTnotintersectT) =>
% 108.14/14.63 ((
% 108.14/14.63 (complementImpComplementIntersect) =>
% 108.14/14.63 ((
% 108.14/14.63 (complementSubsetComplementIntersect) =>
% 108.14/14.63 ((
% 108.14/14.63 (complementInPowersetComplementIntersect) =>
% 108.14/14.63 ((
% 108.14/14.63 (contraSubsetComplement) =>
% 108.14/14.63 ((
% 108.14/14.63 (complementTcontraSubset) =>
% 108.14/14.63 ((
% 108.14/14.63 (binunionTILcontra) =>
% 108.14/14.63 ((
% 108.14/14.63 (binunionTIRcontra) =>
% 108.14/14.63 ((
% 108.14/14.63 (inIntersectImpInUnion) =>
% 108.14/14.63 ((
% 108.14/14.63 (inIntersectImpInUnion2) =>
% 108.14/14.63 ((
% 108.14/14.63 (inIntersectImpInIntersectUnions) =>
% 108.14/14.63 ((
% 108.14/14.63 (intersectInPowersetIntersectUnions) =>
% 108.14/14.63 ((
% 108.14/14.63 (inComplementUnionImpNotIn1) =>
% 108.14/14.63 ((
% 108.14/14.63 (inComplementUnionImpInComplement1) =>
% 108.14/14.63 ((
% 108.14/14.63 (binunionTE) =>
% 108.14/14.63 ((
% 108.14/14.63 (binunionTEcontra) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan2a1) =>
% 108.14/14.63 ((
% 108.14/14.63 (complementUnionInPowersetComplement) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan2a2) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan1a) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan1b) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan1) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan2a) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan2b2) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan2b) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan2) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz13rule0) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz13rule1) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz13rule2) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz13rule3) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz13rule4) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz1_1) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz1_2) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz1_3) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz1_4) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz1_5) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1all2) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1SetBreln1) =>
% 108.14/14.63 ((
% 108.14/14.63 (choice2fnsingleton) =>
% 108.14/14.63 ((
% 108.14/14.63 (setOfPairsIsBReln1) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1all1) =>
% 108.14/14.63 ((
% 108.14/14.63 (subbreln1) =>
% 108.14/14.63 ((
% 108.14/14.63 (eqbreln1) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1invprop) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1invI) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1invE) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1compprop) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1compI) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1compE) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1compEex) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1unionprop) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1unionIL) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1unionIR) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1unionI) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1unionE) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1unionEcases) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1unionCommutes) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz2Ex) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz2W) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz2A) =>
% 108.14/14.63 ((
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% 108.14/14.63 (((complementTE1) =>
% 108.14/14.63 (((binintersectTELcontra) =>
% 108.14/14.63 (((binintersectTERcontra) =>
% 108.14/14.63 (((contrasubsetT) =>
% 108.14/14.63 (((contrasubsetT1) =>
% 108.14/14.63 (((contrasubsetT2) =>
% 108.14/14.63 (((contrasubsetT3) =>
% 108.14/14.63 (((doubleComplementI1) =>
% 108.14/14.63 (((doubleComplementE1) =>
% 108.14/14.63 (((doubleComplementSub1) =>
% 108.14/14.63 (((doubleComplementSub2) =>
% 108.14/14.63 (((doubleComplementEq) =>
% 108.14/14.63 ((
% 108.14/14.63 (complementTnotintersectT) =>
% 108.14/14.63 ((
% 108.14/14.63 (complementImpComplementIntersect) =>
% 108.14/14.63 ((
% 108.14/14.63 (complementSubsetComplementIntersect) =>
% 108.14/14.63 ((
% 108.14/14.63 (complementInPowersetComplementIntersect) =>
% 108.14/14.63 ((
% 108.14/14.63 (contraSubsetComplement) =>
% 108.14/14.63 ((
% 108.14/14.63 (complementTcontraSubset) =>
% 108.14/14.63 ((
% 108.14/14.63 (binunionTILcontra) =>
% 108.14/14.63 ((
% 108.14/14.63 (binunionTIRcontra) =>
% 108.14/14.63 ((
% 108.14/14.63 (inIntersectImpInUnion) =>
% 108.14/14.63 ((
% 108.14/14.63 (inIntersectImpInUnion2) =>
% 108.14/14.63 ((
% 108.14/14.63 (inIntersectImpInIntersectUnions) =>
% 108.14/14.63 ((
% 108.14/14.63 (intersectInPowersetIntersectUnions) =>
% 108.14/14.63 ((
% 108.14/14.63 (inComplementUnionImpNotIn1) =>
% 108.14/14.63 ((
% 108.14/14.63 (inComplementUnionImpInComplement1) =>
% 108.14/14.63 ((
% 108.14/14.63 (binunionTE) =>
% 108.14/14.63 ((
% 108.14/14.63 (binunionTEcontra) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan2a1) =>
% 108.14/14.63 ((
% 108.14/14.63 (complementUnionInPowersetComplement) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan2a2) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan1a) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan1b) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan1) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan2a) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan2b2) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan2b) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan2) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz13rule0) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz13rule1) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz13rule2) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz13rule3) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz13rule4) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz1_1) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz1_2) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz1_3) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz1_4) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz1_5) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1all2) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1SetBreln1) =>
% 108.14/14.63 ((
% 108.14/14.63 (choice2fnsingleton) =>
% 108.14/14.63 ((
% 108.14/14.63 (setOfPairsIsBReln1) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1all1) =>
% 108.14/14.63 ((
% 108.14/14.63 (subbreln1) =>
% 108.14/14.63 ((
% 108.14/14.63 (eqbreln1) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1invprop) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1invI) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1invE) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1compprop) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1compI) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1compE) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1compEex) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1unionprop) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1unionIL) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1unionIR) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1unionI) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1unionE) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1unionEcases) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1unionCommutes) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz2Ex) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz2W) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz2A) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz2B) =>
% 108.14/14.63 ((
% 108.14/14.63 (image1Ex) =>
% 108.14/14.63 ((
% 108.14/14.63 (image1Ex1) =>
% 108.14/14.63 ((
% 108.14/14.63 (image1Equiv) =>
% 108.14/14.63 ((
% 108.14/14.63 (image1E) =>
% 108.14/14.63 ((
% 108.14/14.63 (image1I) =>
% 108.14/14.63 ((
% 108.14/14.63 (injFuncInInjFuncSet) =>
% 108.14/14.63 ((
% 108.14/14.63 (injFuncSetFuncIn) =>
% 108.14/14.63 ((
% 108.14/14.63 (injFuncSetFuncInj) =>
% 108.14/14.63 ((
% 108.14/14.63 (surjFuncSetFuncIn) =>
% 108.14/14.63 ((
% 108.14/14.63 (surjFuncSetFuncSurj) =>
% 108.14/14.63 ((
% 108.14/14.63 (leftInvIsSurj) =>
% 108.14/14.63 ((
% 108.14/14.63 (surjCantorThm) =>
% 108.14/14.63 ((
% 108.14/14.63 (!!) @ (
% 108.14/14.63 (('#S') @ (
% 108.14/14.63 (
% 108.14/14.63 ('#B') @ (
% 108.14/14.63 =>) @
% 108.14/14.63 nonempty)) @
% 108.14/14.63 (
% 108.14/14.63 (
% 108.14/14.63 ('#B') @ (
% 108.14/14.63 ??) @
% 108.14/14.63 (
% 108.14/14.63 (
% 108.14/14.63 ('#S') @ (
% 108.14/14.63 (
% 108.14/14.63 ('#B') @ (
% 108.14/14.63 '#S') @
% 108.14/14.63 (
% 108.14/14.63 (
% 108.14/14.63 ('#B') @ (
% 108.14/14.63 (
% 108.14/14.63 ('#B') @ (
% 108.14/14.63 &))) @
% 108.14/14.63 (
% 108.14/14.63 (
% 108.14/14.63 ('#C') @ in)))))) @
% 108.14/14.63 (
% 108.14/14.63 (
% 108.14/14.63 ('#C') @ (
% 108.14/14.63 (
% 108.14/14.63 ('#B') @ (
% 108.14/14.63 '#C') @
% 108.14/14.63 (
% 108.14/14.63 (
% 108.14/14.63 ('#B') @ (
% 108.14/14.63 (
% 108.14/14.63 ('#B') @ (
% 108.14/14.63 =))) @
% 108.14/14.63 (
% 108.14/14.63 (
% 108.14/14.63 ('#C') @ binintersect)))))) @
% 108.14/14.63 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 108.14/14.63 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2279])).
% 108.14/14.63 thf(zip_derived_cl2321, plain,
% 108.14/14.63 (~ (((iftrueProp2) =>
% 108.14/14.63 (((ifSingleton) =>
% 108.14/14.63 (((ifp) =>
% 108.14/14.63 (((theeq) =>
% 108.14/14.63 (((iftrue) =>
% 108.14/14.63 (((iffalse) =>
% 108.14/14.63 (((iftrueorfalse) =>
% 108.14/14.63 (((binintersectT_lem) =>
% 108.14/14.63 (((binunionT_lem) =>
% 108.14/14.63 (((powersetT_lem) =>
% 108.14/14.63 (((setminusT_lem) =>
% 108.14/14.63 (((complementT_lem) =>
% 108.14/14.63 (((setextT) =>
% 108.14/14.63 (((subsetTI) =>
% 108.14/14.63 (((powersetTI1) =>
% 108.14/14.63 (((powersetTE1) =>
% 108.14/14.63 (((complementTI1) =>
% 108.14/14.63 (((complementTE1) =>
% 108.14/14.63 (((binintersectTELcontra) =>
% 108.14/14.63 (((binintersectTERcontra) =>
% 108.14/14.63 (((contrasubsetT) =>
% 108.14/14.63 (((contrasubsetT1) =>
% 108.14/14.63 (((contrasubsetT2) =>
% 108.14/14.63 (((contrasubsetT3) =>
% 108.14/14.63 (((doubleComplementI1) =>
% 108.14/14.63 (((doubleComplementE1) =>
% 108.14/14.63 (((doubleComplementSub1) =>
% 108.14/14.63 (((doubleComplementSub2) =>
% 108.14/14.63 (((doubleComplementEq) =>
% 108.14/14.63 (((complementTnotintersectT) =>
% 108.14/14.63 ((
% 108.14/14.63 (complementImpComplementIntersect) =>
% 108.14/14.63 ((
% 108.14/14.63 (complementSubsetComplementIntersect) =>
% 108.14/14.63 ((
% 108.14/14.63 (complementInPowersetComplementIntersect) =>
% 108.14/14.63 ((
% 108.14/14.63 (contraSubsetComplement) =>
% 108.14/14.63 ((
% 108.14/14.63 (complementTcontraSubset) =>
% 108.14/14.63 ((
% 108.14/14.63 (binunionTILcontra) =>
% 108.14/14.63 ((
% 108.14/14.63 (binunionTIRcontra) =>
% 108.14/14.63 ((
% 108.14/14.63 (inIntersectImpInUnion) =>
% 108.14/14.63 ((
% 108.14/14.63 (inIntersectImpInUnion2) =>
% 108.14/14.63 ((
% 108.14/14.63 (inIntersectImpInIntersectUnions) =>
% 108.14/14.63 ((
% 108.14/14.63 (intersectInPowersetIntersectUnions) =>
% 108.14/14.63 ((
% 108.14/14.63 (inComplementUnionImpNotIn1) =>
% 108.14/14.63 ((
% 108.14/14.63 (inComplementUnionImpInComplement1) =>
% 108.14/14.63 ((
% 108.14/14.63 (binunionTE) =>
% 108.14/14.63 ((
% 108.14/14.63 (binunionTEcontra) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan2a1) =>
% 108.14/14.63 ((
% 108.14/14.63 (complementUnionInPowersetComplement) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan2a2) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan1a) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan1b) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan1) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan2a) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan2b2) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan2b) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan2) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz13rule0) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz13rule1) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz13rule2) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz13rule3) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz13rule4) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz1_1) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz1_2) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz1_3) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz1_4) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz1_5) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1all2) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1SetBreln1) =>
% 108.14/14.63 ((
% 108.14/14.63 (choice2fnsingleton) =>
% 108.14/14.63 ((
% 108.14/14.63 (setOfPairsIsBReln1) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1all1) =>
% 108.14/14.63 ((
% 108.14/14.63 (subbreln1) =>
% 108.14/14.63 ((
% 108.14/14.63 (eqbreln1) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1invprop) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1invI) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1invE) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1compprop) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1compI) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1compE) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1compEex) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1unionprop) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1unionIL) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1unionIR) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1unionI) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1unionE) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1unionEcases) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1unionCommutes) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz2Ex) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz2W) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz2A) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz2B) =>
% 108.14/14.63 ((
% 108.14/14.63 (image1Ex) =>
% 108.14/14.63 ((
% 108.14/14.63 (image1Ex1) =>
% 108.14/14.63 ((
% 108.14/14.63 (image1Equiv) =>
% 108.14/14.63 ((
% 108.14/14.63 (image1E) =>
% 108.14/14.63 ((
% 108.14/14.63 (image1I) =>
% 108.14/14.63 ((
% 108.14/14.63 (injFuncInInjFuncSet) =>
% 108.14/14.63 ((
% 108.14/14.63 (injFuncSetFuncIn) =>
% 108.14/14.63 ((
% 108.14/14.63 (injFuncSetFuncInj) =>
% 108.14/14.63 ((
% 108.14/14.63 (surjFuncSetFuncIn) =>
% 108.14/14.63 ((
% 108.14/14.63 (surjFuncSetFuncSurj) =>
% 108.14/14.63 ((
% 108.14/14.63 (leftInvIsSurj) =>
% 108.14/14.63 ((
% 108.14/14.63 (surjCantorThm) =>
% 108.14/14.63 ((
% 108.14/14.63 (!!) @ (
% 108.14/14.63 (('#S') @ (
% 108.14/14.63 (
% 108.14/14.63 ('#B') @ (
% 108.14/14.63 =>) @
% 108.14/14.63 nonempty)) @
% 108.14/14.63 (
% 108.14/14.63 (
% 108.14/14.63 ('#B') @ (
% 108.14/14.63 ??) @
% 108.14/14.63 (
% 108.14/14.63 (
% 108.14/14.63 ('#S') @ (
% 108.14/14.63 (
% 108.14/14.63 ('#B') @ (
% 108.14/14.63 '#S') @
% 108.14/14.63 (
% 108.14/14.63 (
% 108.14/14.63 ('#B') @ (
% 108.14/14.63 (
% 108.14/14.63 ('#B') @ (
% 108.14/14.63 &))) @
% 108.14/14.63 (
% 108.14/14.63 (
% 108.14/14.63 ('#C') @ in)))))) @
% 108.14/14.63 (
% 108.14/14.63 (
% 108.14/14.63 ('#C') @ (
% 108.14/14.63 (
% 108.14/14.63 ('#B') @ (
% 108.14/14.63 '#C') @
% 108.14/14.63 (
% 108.14/14.63 (
% 108.14/14.63 ('#B') @ (
% 108.14/14.63 (
% 108.14/14.63 ('#B') @ (
% 108.14/14.63 =))) @
% 108.14/14.63 (
% 108.14/14.63 (
% 108.14/14.63 ('#C') @ binintersect)))))) @
% 108.14/14.63 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 108.14/14.63 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2299])).
% 108.14/14.63 thf(zip_derived_cl2337, plain,
% 108.14/14.63 (~ (((ifSingleton) =>
% 108.14/14.63 (((ifp) =>
% 108.14/14.63 (((theeq) =>
% 108.14/14.63 (((iftrue) =>
% 108.14/14.63 (((iffalse) =>
% 108.14/14.63 (((iftrueorfalse) =>
% 108.14/14.63 (((binintersectT_lem) =>
% 108.14/14.63 (((binunionT_lem) =>
% 108.14/14.63 (((powersetT_lem) =>
% 108.14/14.63 (((setminusT_lem) =>
% 108.14/14.63 (((complementT_lem) =>
% 108.14/14.63 (((setextT) =>
% 108.14/14.63 (((subsetTI) =>
% 108.14/14.63 (((powersetTI1) =>
% 108.14/14.63 (((powersetTE1) =>
% 108.14/14.63 (((complementTI1) =>
% 108.14/14.63 (((complementTE1) =>
% 108.14/14.63 (((binintersectTELcontra) =>
% 108.14/14.63 (((binintersectTERcontra) =>
% 108.14/14.63 (((contrasubsetT) =>
% 108.14/14.63 (((contrasubsetT1) =>
% 108.14/14.63 (((contrasubsetT2) =>
% 108.14/14.63 (((contrasubsetT3) =>
% 108.14/14.63 (((doubleComplementI1) =>
% 108.14/14.63 (((doubleComplementE1) =>
% 108.14/14.63 (((doubleComplementSub1) =>
% 108.14/14.63 (((doubleComplementSub2) =>
% 108.14/14.63 (((doubleComplementEq) =>
% 108.14/14.63 (((complementTnotintersectT) =>
% 108.14/14.63 (((complementImpComplementIntersect) =>
% 108.14/14.63 ((
% 108.14/14.63 (complementSubsetComplementIntersect) =>
% 108.14/14.63 ((
% 108.14/14.63 (complementInPowersetComplementIntersect) =>
% 108.14/14.63 ((
% 108.14/14.63 (contraSubsetComplement) =>
% 108.14/14.63 ((
% 108.14/14.63 (complementTcontraSubset) =>
% 108.14/14.63 ((
% 108.14/14.63 (binunionTILcontra) =>
% 108.14/14.63 ((
% 108.14/14.63 (binunionTIRcontra) =>
% 108.14/14.63 ((
% 108.14/14.63 (inIntersectImpInUnion) =>
% 108.14/14.63 ((
% 108.14/14.63 (inIntersectImpInUnion2) =>
% 108.14/14.63 ((
% 108.14/14.63 (inIntersectImpInIntersectUnions) =>
% 108.14/14.63 ((
% 108.14/14.63 (intersectInPowersetIntersectUnions) =>
% 108.14/14.63 ((
% 108.14/14.63 (inComplementUnionImpNotIn1) =>
% 108.14/14.63 ((
% 108.14/14.63 (inComplementUnionImpInComplement1) =>
% 108.14/14.63 ((
% 108.14/14.63 (binunionTE) =>
% 108.14/14.63 ((
% 108.14/14.63 (binunionTEcontra) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan2a1) =>
% 108.14/14.63 ((
% 108.14/14.63 (complementUnionInPowersetComplement) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan2a2) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan1a) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan1b) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan1) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan2a) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan2b2) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan2b) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan2) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz13rule0) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz13rule1) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz13rule2) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz13rule3) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz13rule4) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz1_1) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz1_2) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz1_3) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz1_4) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz1_5) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1all2) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1SetBreln1) =>
% 108.14/14.63 ((
% 108.14/14.63 (choice2fnsingleton) =>
% 108.14/14.63 ((
% 108.14/14.63 (setOfPairsIsBReln1) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1all1) =>
% 108.14/14.63 ((
% 108.14/14.63 (subbreln1) =>
% 108.14/14.63 ((
% 108.14/14.63 (eqbreln1) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1invprop) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1invI) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1invE) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1compprop) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1compI) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1compE) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1compEex) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1unionprop) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1unionIL) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1unionIR) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1unionI) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1unionE) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1unionEcases) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1unionCommutes) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz2Ex) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz2W) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz2A) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz2B) =>
% 108.14/14.63 ((
% 108.14/14.63 (image1Ex) =>
% 108.14/14.63 ((
% 108.14/14.63 (image1Ex1) =>
% 108.14/14.63 ((
% 108.14/14.63 (image1Equiv) =>
% 108.14/14.63 ((
% 108.14/14.63 (image1E) =>
% 108.14/14.63 ((
% 108.14/14.63 (image1I) =>
% 108.14/14.63 ((
% 108.14/14.63 (injFuncInInjFuncSet) =>
% 108.14/14.63 ((
% 108.14/14.63 (injFuncSetFuncIn) =>
% 108.14/14.63 ((
% 108.14/14.63 (injFuncSetFuncInj) =>
% 108.14/14.63 ((
% 108.14/14.63 (surjFuncSetFuncIn) =>
% 108.14/14.63 ((
% 108.14/14.63 (surjFuncSetFuncSurj) =>
% 108.14/14.63 ((
% 108.14/14.63 (leftInvIsSurj) =>
% 108.14/14.63 ((
% 108.14/14.63 (surjCantorThm) =>
% 108.14/14.63 ((
% 108.14/14.63 (!!) @ (
% 108.14/14.63 (('#S') @ (
% 108.14/14.63 (
% 108.14/14.63 ('#B') @ (
% 108.14/14.63 =>) @
% 108.14/14.63 nonempty)) @
% 108.14/14.63 (
% 108.14/14.63 (
% 108.14/14.63 ('#B') @ (
% 108.14/14.63 ??) @
% 108.14/14.63 (
% 108.14/14.63 (
% 108.14/14.63 ('#S') @ (
% 108.14/14.63 (
% 108.14/14.63 ('#B') @ (
% 108.14/14.63 '#S') @
% 108.14/14.63 (
% 108.14/14.63 (
% 108.14/14.63 ('#B') @ (
% 108.14/14.63 (
% 108.14/14.63 ('#B') @ (
% 108.14/14.63 &))) @
% 108.14/14.63 (
% 108.14/14.63 (
% 108.14/14.63 ('#C') @ in)))))) @
% 108.14/14.63 (
% 108.14/14.63 (
% 108.14/14.63 ('#C') @ (
% 108.14/14.63 (
% 108.14/14.63 ('#B') @ (
% 108.14/14.63 '#C') @
% 108.14/14.63 (
% 108.14/14.63 (
% 108.14/14.63 ('#B') @ (
% 108.14/14.63 (
% 108.14/14.63 ('#B') @ (
% 108.14/14.63 =))) @
% 108.14/14.63 (
% 108.14/14.63 (
% 108.14/14.63 ('#C') @ binintersect)))))) @
% 108.14/14.63 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 108.14/14.63 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2321])).
% 108.14/14.63 thf(zip_derived_cl2353, plain,
% 108.14/14.63 (~ (((ifp) =>
% 108.14/14.63 (((theeq) =>
% 108.14/14.63 (((iftrue) =>
% 108.14/14.63 (((iffalse) =>
% 108.14/14.63 (((iftrueorfalse) =>
% 108.14/14.63 (((binintersectT_lem) =>
% 108.14/14.63 (((binunionT_lem) =>
% 108.14/14.63 (((powersetT_lem) =>
% 108.14/14.63 (((setminusT_lem) =>
% 108.14/14.63 (((complementT_lem) =>
% 108.14/14.63 (((setextT) =>
% 108.14/14.63 (((subsetTI) =>
% 108.14/14.63 (((powersetTI1) =>
% 108.14/14.63 (((powersetTE1) =>
% 108.14/14.63 (((complementTI1) =>
% 108.14/14.63 (((complementTE1) =>
% 108.14/14.63 (((binintersectTELcontra) =>
% 108.14/14.63 (((binintersectTERcontra) =>
% 108.14/14.63 (((contrasubsetT) =>
% 108.14/14.63 (((contrasubsetT1) =>
% 108.14/14.63 (((contrasubsetT2) =>
% 108.14/14.63 (((contrasubsetT3) =>
% 108.14/14.63 (((doubleComplementI1) =>
% 108.14/14.63 (((doubleComplementE1) =>
% 108.14/14.63 (((doubleComplementSub1) =>
% 108.14/14.63 (((doubleComplementSub2) =>
% 108.14/14.63 (((doubleComplementEq) =>
% 108.14/14.63 (((complementTnotintersectT) =>
% 108.14/14.63 (((complementImpComplementIntersect) =>
% 108.14/14.63 (((complementSubsetComplementIntersect) =>
% 108.14/14.63 ((
% 108.14/14.63 (complementInPowersetComplementIntersect) =>
% 108.14/14.63 ((
% 108.14/14.63 (contraSubsetComplement) =>
% 108.14/14.63 ((
% 108.14/14.63 (complementTcontraSubset) =>
% 108.14/14.63 ((
% 108.14/14.63 (binunionTILcontra) =>
% 108.14/14.63 ((
% 108.14/14.63 (binunionTIRcontra) =>
% 108.14/14.63 ((
% 108.14/14.63 (inIntersectImpInUnion) =>
% 108.14/14.63 ((
% 108.14/14.63 (inIntersectImpInUnion2) =>
% 108.14/14.63 ((
% 108.14/14.63 (inIntersectImpInIntersectUnions) =>
% 108.14/14.63 ((
% 108.14/14.63 (intersectInPowersetIntersectUnions) =>
% 108.14/14.63 ((
% 108.14/14.63 (inComplementUnionImpNotIn1) =>
% 108.14/14.63 ((
% 108.14/14.63 (inComplementUnionImpInComplement1) =>
% 108.14/14.63 ((
% 108.14/14.63 (binunionTE) =>
% 108.14/14.63 ((
% 108.14/14.63 (binunionTEcontra) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan2a1) =>
% 108.14/14.63 ((
% 108.14/14.63 (complementUnionInPowersetComplement) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan2a2) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan1a) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan1b) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan1) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan2a) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan2b2) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan2b) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan2) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz13rule0) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz13rule1) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz13rule2) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz13rule3) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz13rule4) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz1_1) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz1_2) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz1_3) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz1_4) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz1_5) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1all2) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1SetBreln1) =>
% 108.14/14.63 ((
% 108.14/14.63 (choice2fnsingleton) =>
% 108.14/14.63 ((
% 108.14/14.63 (setOfPairsIsBReln1) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1all1) =>
% 108.14/14.63 ((
% 108.14/14.63 (subbreln1) =>
% 108.14/14.63 ((
% 108.14/14.63 (eqbreln1) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1invprop) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1invI) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1invE) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1compprop) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1compI) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1compE) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1compEex) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1unionprop) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1unionIL) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1unionIR) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1unionI) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1unionE) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1unionEcases) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1unionCommutes) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz2Ex) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz2W) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz2A) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz2B) =>
% 108.14/14.63 ((
% 108.14/14.63 (image1Ex) =>
% 108.14/14.63 ((
% 108.14/14.63 (image1Ex1) =>
% 108.14/14.63 ((
% 108.14/14.63 (image1Equiv) =>
% 108.14/14.63 ((
% 108.14/14.63 (image1E) =>
% 108.14/14.63 ((
% 108.14/14.63 (image1I) =>
% 108.14/14.63 ((
% 108.14/14.63 (injFuncInInjFuncSet) =>
% 108.14/14.63 ((
% 108.14/14.63 (injFuncSetFuncIn) =>
% 108.14/14.63 ((
% 108.14/14.63 (injFuncSetFuncInj) =>
% 108.14/14.63 ((
% 108.14/14.63 (surjFuncSetFuncIn) =>
% 108.14/14.63 ((
% 108.14/14.63 (surjFuncSetFuncSurj) =>
% 108.14/14.63 ((
% 108.14/14.63 (leftInvIsSurj) =>
% 108.14/14.63 ((
% 108.14/14.63 (surjCantorThm) =>
% 108.14/14.63 ((
% 108.14/14.63 (!!) @ (
% 108.14/14.63 (('#S') @ (
% 108.14/14.63 (
% 108.14/14.63 ('#B') @ (
% 108.14/14.63 =>) @
% 108.14/14.63 nonempty)) @
% 108.14/14.63 (
% 108.14/14.63 (
% 108.14/14.63 ('#B') @ (
% 108.14/14.63 ??) @
% 108.14/14.63 (
% 108.14/14.63 (
% 108.14/14.63 ('#S') @ (
% 108.14/14.63 (
% 108.14/14.63 ('#B') @ (
% 108.14/14.63 '#S') @
% 108.14/14.63 (
% 108.14/14.63 (
% 108.14/14.63 ('#B') @ (
% 108.14/14.63 (
% 108.14/14.63 ('#B') @ (
% 108.14/14.63 &))) @
% 108.14/14.63 (
% 108.14/14.63 (
% 108.14/14.63 ('#C') @ in)))))) @
% 108.14/14.63 (
% 108.14/14.63 (
% 108.14/14.63 ('#C') @ (
% 108.14/14.63 (
% 108.14/14.63 ('#B') @ (
% 108.14/14.63 '#C') @
% 108.14/14.63 (
% 108.14/14.63 (
% 108.14/14.63 ('#B') @ (
% 108.14/14.63 (
% 108.14/14.63 ('#B') @ (
% 108.14/14.63 =))) @
% 108.14/14.63 (
% 108.14/14.63 (
% 108.14/14.63 ('#C') @ binintersect)))))) @
% 108.14/14.63 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 108.14/14.63 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2337])).
% 108.14/14.63 thf(zip_derived_cl2374, plain,
% 108.14/14.63 (~ (((theeq) =>
% 108.14/14.63 (((iftrue) =>
% 108.14/14.63 (((iffalse) =>
% 108.14/14.63 (((iftrueorfalse) =>
% 108.14/14.63 (((binintersectT_lem) =>
% 108.14/14.63 (((binunionT_lem) =>
% 108.14/14.63 (((powersetT_lem) =>
% 108.14/14.63 (((setminusT_lem) =>
% 108.14/14.63 (((complementT_lem) =>
% 108.14/14.63 (((setextT) =>
% 108.14/14.63 (((subsetTI) =>
% 108.14/14.63 (((powersetTI1) =>
% 108.14/14.63 (((powersetTE1) =>
% 108.14/14.63 (((complementTI1) =>
% 108.14/14.63 (((complementTE1) =>
% 108.14/14.63 (((binintersectTELcontra) =>
% 108.14/14.63 (((binintersectTERcontra) =>
% 108.14/14.63 (((contrasubsetT) =>
% 108.14/14.63 (((contrasubsetT1) =>
% 108.14/14.63 (((contrasubsetT2) =>
% 108.14/14.63 (((contrasubsetT3) =>
% 108.14/14.63 (((doubleComplementI1) =>
% 108.14/14.63 (((doubleComplementE1) =>
% 108.14/14.63 (((doubleComplementSub1) =>
% 108.14/14.63 (((doubleComplementSub2) =>
% 108.14/14.63 (((doubleComplementEq) =>
% 108.14/14.63 (((complementTnotintersectT) =>
% 108.14/14.63 (((complementImpComplementIntersect) =>
% 108.14/14.63 (((complementSubsetComplementIntersect) =>
% 108.14/14.63 (((complementInPowersetComplementIntersect) =>
% 108.14/14.63 ((
% 108.14/14.63 (contraSubsetComplement) =>
% 108.14/14.63 ((
% 108.14/14.63 (complementTcontraSubset) =>
% 108.14/14.63 ((
% 108.14/14.63 (binunionTILcontra) =>
% 108.14/14.63 ((
% 108.14/14.63 (binunionTIRcontra) =>
% 108.14/14.63 ((
% 108.14/14.63 (inIntersectImpInUnion) =>
% 108.14/14.63 ((
% 108.14/14.63 (inIntersectImpInUnion2) =>
% 108.14/14.63 ((
% 108.14/14.63 (inIntersectImpInIntersectUnions) =>
% 108.14/14.63 ((
% 108.14/14.63 (intersectInPowersetIntersectUnions) =>
% 108.14/14.63 ((
% 108.14/14.63 (inComplementUnionImpNotIn1) =>
% 108.14/14.63 ((
% 108.14/14.63 (inComplementUnionImpInComplement1) =>
% 108.14/14.63 ((
% 108.14/14.63 (binunionTE) =>
% 108.14/14.63 ((
% 108.14/14.63 (binunionTEcontra) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan2a1) =>
% 108.14/14.63 ((
% 108.14/14.63 (complementUnionInPowersetComplement) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan2a2) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan1a) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan1b) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan1) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan2a) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan2b2) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan2b) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan2) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz13rule0) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz13rule1) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz13rule2) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz13rule3) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz13rule4) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz1_1) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz1_2) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz1_3) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz1_4) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz1_5) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1all2) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1SetBreln1) =>
% 108.14/14.63 ((
% 108.14/14.63 (choice2fnsingleton) =>
% 108.14/14.63 ((
% 108.14/14.63 (setOfPairsIsBReln1) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1all1) =>
% 108.14/14.63 ((
% 108.14/14.63 (subbreln1) =>
% 108.14/14.63 ((
% 108.14/14.63 (eqbreln1) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1invprop) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1invI) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1invE) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1compprop) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1compI) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1compE) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1compEex) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1unionprop) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1unionIL) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1unionIR) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1unionI) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1unionE) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1unionEcases) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1unionCommutes) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz2Ex) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz2W) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz2A) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz2B) =>
% 108.14/14.63 ((
% 108.14/14.63 (image1Ex) =>
% 108.14/14.63 ((
% 108.14/14.63 (image1Ex1) =>
% 108.14/14.63 ((
% 108.14/14.63 (image1Equiv) =>
% 108.14/14.63 ((
% 108.14/14.63 (image1E) =>
% 108.14/14.63 ((
% 108.14/14.63 (image1I) =>
% 108.14/14.63 ((
% 108.14/14.63 (injFuncInInjFuncSet) =>
% 108.14/14.63 ((
% 108.14/14.63 (injFuncSetFuncIn) =>
% 108.14/14.63 ((
% 108.14/14.63 (injFuncSetFuncInj) =>
% 108.14/14.63 ((
% 108.14/14.63 (surjFuncSetFuncIn) =>
% 108.14/14.63 ((
% 108.14/14.63 (surjFuncSetFuncSurj) =>
% 108.14/14.63 ((
% 108.14/14.63 (leftInvIsSurj) =>
% 108.14/14.63 ((
% 108.14/14.63 (surjCantorThm) =>
% 108.14/14.63 ((
% 108.14/14.63 (!!) @ (
% 108.14/14.63 (('#S') @ (
% 108.14/14.63 (
% 108.14/14.63 ('#B') @ (
% 108.14/14.63 =>) @
% 108.14/14.63 nonempty)) @
% 108.14/14.63 (
% 108.14/14.63 (
% 108.14/14.63 ('#B') @ (
% 108.14/14.63 ??) @
% 108.14/14.63 (
% 108.14/14.63 (
% 108.14/14.63 ('#S') @ (
% 108.14/14.63 (
% 108.14/14.63 ('#B') @ (
% 108.14/14.63 '#S') @
% 108.14/14.63 (
% 108.14/14.63 (
% 108.14/14.63 ('#B') @ (
% 108.14/14.63 (
% 108.14/14.63 ('#B') @ (
% 108.14/14.63 &))) @
% 108.14/14.63 (
% 108.14/14.63 (
% 108.14/14.63 ('#C') @ in)))))) @
% 108.14/14.63 (
% 108.14/14.63 (
% 108.14/14.63 ('#C') @ (
% 108.14/14.63 (
% 108.14/14.63 ('#B') @ (
% 108.14/14.63 '#C') @
% 108.14/14.63 (
% 108.14/14.63 (
% 108.14/14.63 ('#B') @ (
% 108.14/14.63 (
% 108.14/14.63 ('#B') @ (
% 108.14/14.63 =))) @
% 108.14/14.63 (
% 108.14/14.63 (
% 108.14/14.63 ('#C') @ binintersect)))))) @
% 108.14/14.63 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 108.14/14.63 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2353])).
% 108.14/14.63 thf(zip_derived_cl2392, plain,
% 108.14/14.63 (~ (((iftrue) =>
% 108.14/14.63 (((iffalse) =>
% 108.14/14.63 (((iftrueorfalse) =>
% 108.14/14.63 (((binintersectT_lem) =>
% 108.14/14.63 (((binunionT_lem) =>
% 108.14/14.63 (((powersetT_lem) =>
% 108.14/14.63 (((setminusT_lem) =>
% 108.14/14.63 (((complementT_lem) =>
% 108.14/14.63 (((setextT) =>
% 108.14/14.63 (((subsetTI) =>
% 108.14/14.63 (((powersetTI1) =>
% 108.14/14.63 (((powersetTE1) =>
% 108.14/14.63 (((complementTI1) =>
% 108.14/14.63 (((complementTE1) =>
% 108.14/14.63 (((binintersectTELcontra) =>
% 108.14/14.63 (((binintersectTERcontra) =>
% 108.14/14.63 (((contrasubsetT) =>
% 108.14/14.63 (((contrasubsetT1) =>
% 108.14/14.63 (((contrasubsetT2) =>
% 108.14/14.63 (((contrasubsetT3) =>
% 108.14/14.63 (((doubleComplementI1) =>
% 108.14/14.63 (((doubleComplementE1) =>
% 108.14/14.63 (((doubleComplementSub1) =>
% 108.14/14.63 (((doubleComplementSub2) =>
% 108.14/14.63 (((doubleComplementEq) =>
% 108.14/14.63 (((complementTnotintersectT) =>
% 108.14/14.63 (((complementImpComplementIntersect) =>
% 108.14/14.63 (((complementSubsetComplementIntersect) =>
% 108.14/14.63 (((complementInPowersetComplementIntersect) =>
% 108.14/14.63 (((contraSubsetComplement) =>
% 108.14/14.63 ((
% 108.14/14.63 (complementTcontraSubset) =>
% 108.14/14.63 ((
% 108.14/14.63 (binunionTILcontra) =>
% 108.14/14.63 ((
% 108.14/14.63 (binunionTIRcontra) =>
% 108.14/14.63 ((
% 108.14/14.63 (inIntersectImpInUnion) =>
% 108.14/14.63 ((
% 108.14/14.63 (inIntersectImpInUnion2) =>
% 108.14/14.63 ((
% 108.14/14.63 (inIntersectImpInIntersectUnions) =>
% 108.14/14.63 ((
% 108.14/14.63 (intersectInPowersetIntersectUnions) =>
% 108.14/14.63 ((
% 108.14/14.63 (inComplementUnionImpNotIn1) =>
% 108.14/14.63 ((
% 108.14/14.63 (inComplementUnionImpInComplement1) =>
% 108.14/14.63 ((
% 108.14/14.63 (binunionTE) =>
% 108.14/14.63 ((
% 108.14/14.63 (binunionTEcontra) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan2a1) =>
% 108.14/14.63 ((
% 108.14/14.63 (complementUnionInPowersetComplement) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan2a2) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan1a) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan1b) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan1) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan2a) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan2b2) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan2b) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan2) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz13rule0) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz13rule1) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz13rule2) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz13rule3) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz13rule4) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz1_1) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz1_2) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz1_3) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz1_4) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz1_5) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1all2) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1SetBreln1) =>
% 108.14/14.63 ((
% 108.14/14.63 (choice2fnsingleton) =>
% 108.14/14.63 ((
% 108.14/14.63 (setOfPairsIsBReln1) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1all1) =>
% 108.14/14.63 ((
% 108.14/14.63 (subbreln1) =>
% 108.14/14.63 ((
% 108.14/14.63 (eqbreln1) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1invprop) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1invI) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1invE) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1compprop) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1compI) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1compE) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1compEex) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1unionprop) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1unionIL) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1unionIR) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1unionI) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1unionE) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1unionEcases) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1unionCommutes) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz2Ex) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz2W) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz2A) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz2B) =>
% 108.14/14.63 ((
% 108.14/14.63 (image1Ex) =>
% 108.14/14.63 ((
% 108.14/14.63 (image1Ex1) =>
% 108.14/14.63 ((
% 108.14/14.63 (image1Equiv) =>
% 108.14/14.63 ((
% 108.14/14.63 (image1E) =>
% 108.14/14.63 ((
% 108.14/14.63 (image1I) =>
% 108.14/14.63 ((
% 108.14/14.63 (injFuncInInjFuncSet) =>
% 108.14/14.63 ((
% 108.14/14.63 (injFuncSetFuncIn) =>
% 108.14/14.63 ((
% 108.14/14.63 (injFuncSetFuncInj) =>
% 108.14/14.63 ((
% 108.14/14.63 (surjFuncSetFuncIn) =>
% 108.14/14.63 ((
% 108.14/14.63 (surjFuncSetFuncSurj) =>
% 108.14/14.63 ((
% 108.14/14.63 (leftInvIsSurj) =>
% 108.14/14.63 ((
% 108.14/14.63 (surjCantorThm) =>
% 108.14/14.63 ((
% 108.14/14.63 (!!) @ (
% 108.14/14.63 (('#S') @ (
% 108.14/14.63 (
% 108.14/14.63 ('#B') @ (
% 108.14/14.63 =>) @
% 108.14/14.63 nonempty)) @
% 108.14/14.63 (
% 108.14/14.63 (
% 108.14/14.63 ('#B') @ (
% 108.14/14.63 ??) @
% 108.14/14.63 (
% 108.14/14.63 (
% 108.14/14.63 ('#S') @ (
% 108.14/14.63 (
% 108.14/14.63 ('#B') @ (
% 108.14/14.63 '#S') @
% 108.14/14.63 (
% 108.14/14.63 (
% 108.14/14.63 ('#B') @ (
% 108.14/14.63 (
% 108.14/14.63 ('#B') @ (
% 108.14/14.63 &))) @
% 108.14/14.63 (
% 108.14/14.63 (
% 108.14/14.63 ('#C') @ in)))))) @
% 108.14/14.63 (
% 108.14/14.63 (
% 108.14/14.63 ('#C') @ (
% 108.14/14.63 (
% 108.14/14.63 ('#B') @ (
% 108.14/14.63 '#C') @
% 108.14/14.63 (
% 108.14/14.63 (
% 108.14/14.63 ('#B') @ (
% 108.14/14.63 (
% 108.14/14.63 ('#B') @ (
% 108.14/14.63 =))) @
% 108.14/14.63 (
% 108.14/14.63 (
% 108.14/14.63 ('#C') @ binintersect)))))) @
% 108.14/14.63 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 108.14/14.63 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2374])).
% 108.14/14.63 thf(zip_derived_cl2408, plain,
% 108.14/14.63 (~ (((iffalse) =>
% 108.14/14.63 (((iftrueorfalse) =>
% 108.14/14.63 (((binintersectT_lem) =>
% 108.14/14.63 (((binunionT_lem) =>
% 108.14/14.63 (((powersetT_lem) =>
% 108.14/14.63 (((setminusT_lem) =>
% 108.14/14.63 (((complementT_lem) =>
% 108.14/14.63 (((setextT) =>
% 108.14/14.63 (((subsetTI) =>
% 108.14/14.63 (((powersetTI1) =>
% 108.14/14.63 (((powersetTE1) =>
% 108.14/14.63 (((complementTI1) =>
% 108.14/14.63 (((complementTE1) =>
% 108.14/14.63 (((binintersectTELcontra) =>
% 108.14/14.63 (((binintersectTERcontra) =>
% 108.14/14.63 (((contrasubsetT) =>
% 108.14/14.63 (((contrasubsetT1) =>
% 108.14/14.63 (((contrasubsetT2) =>
% 108.14/14.63 (((contrasubsetT3) =>
% 108.14/14.63 (((doubleComplementI1) =>
% 108.14/14.63 (((doubleComplementE1) =>
% 108.14/14.63 (((doubleComplementSub1) =>
% 108.14/14.63 (((doubleComplementSub2) =>
% 108.14/14.63 (((doubleComplementEq) =>
% 108.14/14.63 (((complementTnotintersectT) =>
% 108.14/14.63 (((complementImpComplementIntersect) =>
% 108.14/14.63 (((complementSubsetComplementIntersect) =>
% 108.14/14.63 (((complementInPowersetComplementIntersect) =>
% 108.14/14.63 (((contraSubsetComplement) =>
% 108.14/14.63 (((complementTcontraSubset) =>
% 108.14/14.63 ((
% 108.14/14.63 (binunionTILcontra) =>
% 108.14/14.63 ((
% 108.14/14.63 (binunionTIRcontra) =>
% 108.14/14.63 ((
% 108.14/14.63 (inIntersectImpInUnion) =>
% 108.14/14.63 ((
% 108.14/14.63 (inIntersectImpInUnion2) =>
% 108.14/14.63 ((
% 108.14/14.63 (inIntersectImpInIntersectUnions) =>
% 108.14/14.63 ((
% 108.14/14.63 (intersectInPowersetIntersectUnions) =>
% 108.14/14.63 ((
% 108.14/14.63 (inComplementUnionImpNotIn1) =>
% 108.14/14.63 ((
% 108.14/14.63 (inComplementUnionImpInComplement1) =>
% 108.14/14.63 ((
% 108.14/14.63 (binunionTE) =>
% 108.14/14.63 ((
% 108.14/14.63 (binunionTEcontra) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan2a1) =>
% 108.14/14.63 ((
% 108.14/14.63 (complementUnionInPowersetComplement) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan2a2) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan1a) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan1b) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan1) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan2a) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan2b2) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan2b) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan2) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz13rule0) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz13rule1) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz13rule2) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz13rule3) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz13rule4) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz1_1) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz1_2) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz1_3) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz1_4) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz1_5) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1all2) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1SetBreln1) =>
% 108.14/14.63 ((
% 108.14/14.63 (choice2fnsingleton) =>
% 108.14/14.63 ((
% 108.14/14.63 (setOfPairsIsBReln1) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1all1) =>
% 108.14/14.63 ((
% 108.14/14.63 (subbreln1) =>
% 108.14/14.63 ((
% 108.14/14.63 (eqbreln1) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1invprop) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1invI) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1invE) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1compprop) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1compI) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1compE) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1compEex) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1unionprop) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1unionIL) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1unionIR) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1unionI) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1unionE) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1unionEcases) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1unionCommutes) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz2Ex) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz2W) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz2A) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz2B) =>
% 108.14/14.63 ((
% 108.14/14.63 (image1Ex) =>
% 108.14/14.63 ((
% 108.14/14.63 (image1Ex1) =>
% 108.14/14.63 ((
% 108.14/14.63 (image1Equiv) =>
% 108.14/14.63 ((
% 108.14/14.63 (image1E) =>
% 108.14/14.63 ((
% 108.14/14.63 (image1I) =>
% 108.14/14.63 ((
% 108.14/14.63 (injFuncInInjFuncSet) =>
% 108.14/14.63 ((
% 108.14/14.63 (injFuncSetFuncIn) =>
% 108.14/14.63 ((
% 108.14/14.63 (injFuncSetFuncInj) =>
% 108.14/14.63 ((
% 108.14/14.63 (surjFuncSetFuncIn) =>
% 108.14/14.63 ((
% 108.14/14.63 (surjFuncSetFuncSurj) =>
% 108.14/14.63 ((
% 108.14/14.63 (leftInvIsSurj) =>
% 108.14/14.63 ((
% 108.14/14.63 (surjCantorThm) =>
% 108.14/14.63 ((
% 108.14/14.63 (!!) @ (
% 108.14/14.63 (('#S') @ (
% 108.14/14.63 (
% 108.14/14.63 ('#B') @ (
% 108.14/14.63 =>) @
% 108.14/14.63 nonempty)) @
% 108.14/14.63 (
% 108.14/14.63 (
% 108.14/14.63 ('#B') @ (
% 108.14/14.63 ??) @
% 108.14/14.63 (
% 108.14/14.63 (
% 108.14/14.63 ('#S') @ (
% 108.14/14.63 (
% 108.14/14.63 ('#B') @ (
% 108.14/14.63 '#S') @
% 108.14/14.63 (
% 108.14/14.63 (
% 108.14/14.63 ('#B') @ (
% 108.14/14.63 (
% 108.14/14.63 ('#B') @ (
% 108.14/14.63 &))) @
% 108.14/14.63 (
% 108.14/14.63 (
% 108.14/14.63 ('#C') @ in)))))) @
% 108.14/14.63 (
% 108.14/14.63 (
% 108.14/14.63 ('#C') @ (
% 108.14/14.63 (
% 108.14/14.63 ('#B') @ (
% 108.14/14.63 '#C') @
% 108.14/14.63 (
% 108.14/14.63 (
% 108.14/14.63 ('#B') @ (
% 108.14/14.63 (
% 108.14/14.63 ('#B') @ (
% 108.14/14.63 =))) @
% 108.14/14.63 (
% 108.14/14.63 (
% 108.14/14.63 ('#C') @ binintersect)))))) @
% 108.14/14.63 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 108.14/14.63 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2392])).
% 108.14/14.63 thf(zip_derived_cl2427, plain,
% 108.14/14.63 (~ (((iftrueorfalse) =>
% 108.14/14.63 (((binintersectT_lem) =>
% 108.14/14.63 (((binunionT_lem) =>
% 108.14/14.63 (((powersetT_lem) =>
% 108.14/14.63 (((setminusT_lem) =>
% 108.14/14.63 (((complementT_lem) =>
% 108.14/14.63 (((setextT) =>
% 108.14/14.63 (((subsetTI) =>
% 108.14/14.63 (((powersetTI1) =>
% 108.14/14.63 (((powersetTE1) =>
% 108.14/14.63 (((complementTI1) =>
% 108.14/14.63 (((complementTE1) =>
% 108.14/14.63 (((binintersectTELcontra) =>
% 108.14/14.63 (((binintersectTERcontra) =>
% 108.14/14.63 (((contrasubsetT) =>
% 108.14/14.63 (((contrasubsetT1) =>
% 108.14/14.63 (((contrasubsetT2) =>
% 108.14/14.63 (((contrasubsetT3) =>
% 108.14/14.63 (((doubleComplementI1) =>
% 108.14/14.63 (((doubleComplementE1) =>
% 108.14/14.63 (((doubleComplementSub1) =>
% 108.14/14.63 (((doubleComplementSub2) =>
% 108.14/14.63 (((doubleComplementEq) =>
% 108.14/14.63 (((complementTnotintersectT) =>
% 108.14/14.63 (((complementImpComplementIntersect) =>
% 108.14/14.63 (((complementSubsetComplementIntersect) =>
% 108.14/14.63 (((complementInPowersetComplementIntersect) =>
% 108.14/14.63 (((contraSubsetComplement) =>
% 108.14/14.63 (((complementTcontraSubset) =>
% 108.14/14.63 (((binunionTILcontra) =>
% 108.14/14.63 ((
% 108.14/14.63 (binunionTIRcontra) =>
% 108.14/14.63 ((
% 108.14/14.63 (inIntersectImpInUnion) =>
% 108.14/14.63 ((
% 108.14/14.63 (inIntersectImpInUnion2) =>
% 108.14/14.63 ((
% 108.14/14.63 (inIntersectImpInIntersectUnions) =>
% 108.14/14.63 ((
% 108.14/14.63 (intersectInPowersetIntersectUnions) =>
% 108.14/14.63 ((
% 108.14/14.63 (inComplementUnionImpNotIn1) =>
% 108.14/14.63 ((
% 108.14/14.63 (inComplementUnionImpInComplement1) =>
% 108.14/14.63 ((
% 108.14/14.63 (binunionTE) =>
% 108.14/14.63 ((
% 108.14/14.63 (binunionTEcontra) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan2a1) =>
% 108.14/14.63 ((
% 108.14/14.63 (complementUnionInPowersetComplement) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan2a2) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan1a) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan1b) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan1) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan2a) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan2b2) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan2b) =>
% 108.14/14.63 ((
% 108.14/14.63 (demorgan2) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz13rule0) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz13rule1) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz13rule2) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz13rule3) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz13rule4) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz1_1) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz1_2) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz1_3) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz1_4) =>
% 108.14/14.63 ((
% 108.14/14.63 (woz1_5) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1all2) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1SetBreln1) =>
% 108.14/14.63 ((
% 108.14/14.63 (choice2fnsingleton) =>
% 108.14/14.63 ((
% 108.14/14.63 (setOfPairsIsBReln1) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1all1) =>
% 108.14/14.63 ((
% 108.14/14.63 (subbreln1) =>
% 108.14/14.63 ((
% 108.14/14.63 (eqbreln1) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1invprop) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1invI) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1invE) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1compprop) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1compI) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1compE) =>
% 108.14/14.63 ((
% 108.14/14.63 (breln1compEex) =>
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% 108.14/14.63 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2408])).
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% 108.14/14.63 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2427])).
% 108.14/14.63 thf(zip_derived_cl2454, plain,
% 108.14/14.63 (~ (((binunionT_lem) =>
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% 108.14/14.63 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2442])).
% 108.14/14.63 thf(zip_derived_cl2465, plain,
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% 108.14/14.64 (breln1all1) =>
% 108.14/14.64 ((
% 108.14/14.64 (subbreln1) =>
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% 108.14/14.64 ((
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% 108.14/14.64 ((
% 108.14/14.64 (breln1compEex) =>
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% 108.14/14.64 ((
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% 108.14/14.64 ((
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% 108.14/14.64 ((
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% 108.14/14.64 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2648])).
% 108.14/14.64 thf(zip_derived_cl2680, plain,
% 108.14/14.64 (~ (((doubleComplementSub2) =>
% 108.14/14.64 (((doubleComplementEq) =>
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% 108.14/14.64 (((binunionTEcontra) =>
% 108.14/14.64 (((demorgan2a1) =>
% 108.14/14.64 (((complementUnionInPowersetComplement) =>
% 108.14/14.64 (((demorgan2a2) =>
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% 108.14/14.64 (((demorgan1b) =>
% 108.14/14.64 (((demorgan1) =>
% 108.14/14.64 (((demorgan2a) =>
% 108.14/14.64 (((demorgan2b2) =>
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% 108.14/14.64 (((demorgan2) =>
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% 108.14/14.64 ((
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% 108.14/14.64 ((
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% 108.14/14.64 ((
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% 108.14/14.64 ((
% 108.14/14.64 (setOfPairsIsBReln1) =>
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% 108.14/14.64 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2665])).
% 108.14/14.64 thf(zip_derived_cl2692, plain,
% 108.14/14.64 (~ (((doubleComplementEq) =>
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% 108.14/14.64 (((inIntersectImpInIntersectUnions) =>
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% 108.14/14.64 (((inComplementUnionImpNotIn1) =>
% 108.14/14.64 (((inComplementUnionImpInComplement1) =>
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% 108.14/14.64 (((binunionTEcontra) =>
% 108.14/14.64 (((demorgan2a1) =>
% 108.14/14.64 (((complementUnionInPowersetComplement) =>
% 108.14/14.64 (((demorgan2a2) =>
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% 108.14/14.64 (((demorgan1) =>
% 108.14/14.64 (((demorgan2a) =>
% 108.14/14.64 (((demorgan2b2) =>
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% 108.14/14.64 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2680])).
% 108.14/14.64 thf(zip_derived_cl2704, plain,
% 108.14/14.64 (~ (((complementTnotintersectT) =>
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% 108.14/14.64 (((intersectInPowersetIntersectUnions) =>
% 108.14/14.64 (((inComplementUnionImpNotIn1) =>
% 108.14/14.64 (((inComplementUnionImpInComplement1) =>
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% 108.14/14.64 (((binunionTEcontra) =>
% 108.14/14.64 (((demorgan2a1) =>
% 108.14/14.64 (((complementUnionInPowersetComplement) =>
% 108.14/14.64 (((demorgan2a2) =>
% 108.14/14.64 (((demorgan1a) =>
% 108.14/14.64 (((demorgan1b) =>
% 108.14/14.64 (((demorgan1) =>
% 108.14/14.64 (((demorgan2a) =>
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% 108.14/14.64 ((
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% 108.14/14.64 ((
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% 108.14/14.64 ((
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% 108.14/14.64 ((
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% 108.14/14.64 ((
% 108.14/14.64 (breln1unionEcases) =>
% 108.14/14.64 ((
% 108.14/14.64 (breln1unionCommutes) =>
% 108.14/14.64 ((
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% 108.14/14.64 ((
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% 108.14/14.64 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2704])).
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% 108.14/14.65 ('#B') @ (
% 108.14/14.65 (
% 108.14/14.65 ('#B') @ (
% 108.14/14.65 =))) @
% 108.14/14.65 (
% 108.14/14.65 (
% 108.14/14.65 ('#C') @ binintersect)))))) @
% 108.14/14.65 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 108.14/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2728])).
% 108.14/14.65 thf(zip_derived_cl2746, plain,
% 108.14/14.65 (~ (((contraSubsetComplement) =>
% 108.14/14.65 (((complementTcontraSubset) =>
% 108.14/14.65 (((binunionTILcontra) =>
% 108.14/14.65 (((binunionTIRcontra) =>
% 108.14/14.65 (((inIntersectImpInUnion) =>
% 108.14/14.65 (((inIntersectImpInUnion2) =>
% 108.14/14.65 (((inIntersectImpInIntersectUnions) =>
% 108.14/14.65 (((intersectInPowersetIntersectUnions) =>
% 108.14/14.65 (((inComplementUnionImpNotIn1) =>
% 108.14/14.65 (((inComplementUnionImpInComplement1) =>
% 108.14/14.65 (((binunionTE) =>
% 108.14/14.65 (((binunionTEcontra) =>
% 108.14/14.65 (((demorgan2a1) =>
% 108.14/14.65 (((complementUnionInPowersetComplement) =>
% 108.14/14.65 (((demorgan2a2) =>
% 108.14/14.65 (((demorgan1a) =>
% 108.14/14.65 (((demorgan1b) =>
% 108.14/14.65 (((demorgan1) =>
% 108.14/14.65 (((demorgan2a) =>
% 108.14/14.65 (((demorgan2b2) =>
% 108.14/14.65 (((demorgan2b) =>
% 108.14/14.65 (((demorgan2) =>
% 108.14/14.65 (((woz13rule0) =>
% 108.14/14.65 (((woz13rule1) =>
% 108.14/14.65 (((woz13rule2) =>
% 108.14/14.65 (((woz13rule3) =>
% 108.14/14.65 (((woz13rule4) =>
% 108.14/14.65 (((woz1_1) =>
% 108.14/14.65 (((woz1_2) =>
% 108.14/14.65 (((woz1_3) =>
% 108.14/14.65 ((
% 108.14/14.65 (woz1_4) =>
% 108.14/14.65 ((
% 108.14/14.65 (woz1_5) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1all2) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1SetBreln1) =>
% 108.14/14.65 ((
% 108.14/14.65 (choice2fnsingleton) =>
% 108.14/14.65 ((
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% 108.14/14.65 ((
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% 108.14/14.65 ((
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% 108.14/14.65 ((
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% 108.14/14.65 (breln1compprop) =>
% 108.14/14.65 ((
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% 108.14/14.65 ((
% 108.14/14.65 (breln1compE) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1compEex) =>
% 108.14/14.65 ((
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% 108.14/14.65 ((
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% 108.14/14.65 ((
% 108.14/14.65 (breln1unionIR) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionI) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionE) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionEcases) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionCommutes) =>
% 108.14/14.65 ((
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% 108.14/14.65 ((
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% 108.14/14.65 ((
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% 108.14/14.65 ((
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% 108.14/14.65 ((
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% 108.14/14.65 ((
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% 108.14/14.65 ((
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% 108.14/14.65 ((
% 108.14/14.65 (image1E) =>
% 108.14/14.65 ((
% 108.14/14.65 (image1I) =>
% 108.14/14.65 ((
% 108.14/14.65 (injFuncInInjFuncSet) =>
% 108.14/14.65 ((
% 108.14/14.65 (injFuncSetFuncIn) =>
% 108.14/14.65 ((
% 108.14/14.65 (injFuncSetFuncInj) =>
% 108.14/14.65 ((
% 108.14/14.65 (surjFuncSetFuncIn) =>
% 108.14/14.65 ((
% 108.14/14.65 (surjFuncSetFuncSurj) =>
% 108.14/14.65 ((
% 108.14/14.65 (leftInvIsSurj) =>
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% 108.14/14.65 ((
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% 108.14/14.65 (
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% 108.14/14.65 (
% 108.14/14.65 (
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% 108.14/14.65 (
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% 108.14/14.65 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 108.14/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2738])).
% 108.14/14.65 thf(zip_derived_cl2754, plain,
% 108.14/14.65 (~ (((complementTcontraSubset) =>
% 108.14/14.65 (((binunionTILcontra) =>
% 108.14/14.65 (((binunionTIRcontra) =>
% 108.14/14.65 (((inIntersectImpInUnion) =>
% 108.14/14.65 (((inIntersectImpInUnion2) =>
% 108.14/14.65 (((inIntersectImpInIntersectUnions) =>
% 108.14/14.65 (((intersectInPowersetIntersectUnions) =>
% 108.14/14.65 (((inComplementUnionImpNotIn1) =>
% 108.14/14.65 (((inComplementUnionImpInComplement1) =>
% 108.14/14.65 (((binunionTE) =>
% 108.14/14.65 (((binunionTEcontra) =>
% 108.14/14.65 (((demorgan2a1) =>
% 108.14/14.65 (((complementUnionInPowersetComplement) =>
% 108.14/14.65 (((demorgan2a2) =>
% 108.14/14.65 (((demorgan1a) =>
% 108.14/14.65 (((demorgan1b) =>
% 108.14/14.65 (((demorgan1) =>
% 108.14/14.65 (((demorgan2a) =>
% 108.14/14.65 (((demorgan2b2) =>
% 108.14/14.65 (((demorgan2b) =>
% 108.14/14.65 (((demorgan2) =>
% 108.14/14.65 (((woz13rule0) =>
% 108.14/14.65 (((woz13rule1) =>
% 108.14/14.65 (((woz13rule2) =>
% 108.14/14.65 (((woz13rule3) =>
% 108.14/14.65 (((woz13rule4) =>
% 108.14/14.65 (((woz1_1) =>
% 108.14/14.65 (((woz1_2) =>
% 108.14/14.65 (((woz1_3) =>
% 108.14/14.65 (((woz1_4) =>
% 108.14/14.65 ((
% 108.14/14.65 (woz1_5) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1all2) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1SetBreln1) =>
% 108.14/14.65 ((
% 108.14/14.65 (choice2fnsingleton) =>
% 108.14/14.65 ((
% 108.14/14.65 (setOfPairsIsBReln1) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1all1) =>
% 108.14/14.65 ((
% 108.14/14.65 (subbreln1) =>
% 108.14/14.65 ((
% 108.14/14.65 (eqbreln1) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1invprop) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1invI) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1invE) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1compprop) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1compI) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1compE) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1compEex) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionprop) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionIL) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionIR) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionI) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionE) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionEcases) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionCommutes) =>
% 108.14/14.65 ((
% 108.14/14.65 (woz2Ex) =>
% 108.14/14.65 ((
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% 108.14/14.65 ((
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% 108.14/14.65 ((
% 108.14/14.65 (woz2B) =>
% 108.14/14.65 ((
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% 108.14/14.65 ((
% 108.14/14.65 (image1Ex1) =>
% 108.14/14.65 ((
% 108.14/14.65 (image1Equiv) =>
% 108.14/14.65 ((
% 108.14/14.65 (image1E) =>
% 108.14/14.65 ((
% 108.14/14.65 (image1I) =>
% 108.14/14.65 ((
% 108.14/14.65 (injFuncInInjFuncSet) =>
% 108.14/14.65 ((
% 108.14/14.65 (injFuncSetFuncIn) =>
% 108.14/14.65 ((
% 108.14/14.65 (injFuncSetFuncInj) =>
% 108.14/14.65 ((
% 108.14/14.65 (surjFuncSetFuncIn) =>
% 108.14/14.65 ((
% 108.14/14.65 (surjFuncSetFuncSurj) =>
% 108.14/14.65 ((
% 108.14/14.65 (leftInvIsSurj) =>
% 108.14/14.65 ((
% 108.14/14.65 (surjCantorThm) =>
% 108.14/14.65 ((
% 108.14/14.65 (!!) @ (
% 108.14/14.65 (('#S') @ (
% 108.14/14.65 (
% 108.14/14.65 ('#B') @ (
% 108.14/14.65 =>) @
% 108.14/14.65 nonempty)) @
% 108.14/14.65 (
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% 108.14/14.65 ??) @
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% 108.14/14.65 (
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% 108.14/14.65 (
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% 108.14/14.65 (
% 108.14/14.65 ('#B') @ (
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% 108.14/14.65 (
% 108.14/14.65 (
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% 108.14/14.65 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 108.14/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2746])).
% 108.14/14.65 thf(zip_derived_cl2762, plain,
% 108.14/14.65 (~ (((binunionTILcontra) =>
% 108.14/14.65 (((binunionTIRcontra) =>
% 108.14/14.65 (((inIntersectImpInUnion) =>
% 108.14/14.65 (((inIntersectImpInUnion2) =>
% 108.14/14.65 (((inIntersectImpInIntersectUnions) =>
% 108.14/14.65 (((intersectInPowersetIntersectUnions) =>
% 108.14/14.65 (((inComplementUnionImpNotIn1) =>
% 108.14/14.65 (((inComplementUnionImpInComplement1) =>
% 108.14/14.65 (((binunionTE) =>
% 108.14/14.65 (((binunionTEcontra) =>
% 108.14/14.65 (((demorgan2a1) =>
% 108.14/14.65 (((complementUnionInPowersetComplement) =>
% 108.14/14.65 (((demorgan2a2) =>
% 108.14/14.65 (((demorgan1a) =>
% 108.14/14.65 (((demorgan1b) =>
% 108.14/14.65 (((demorgan1) =>
% 108.14/14.65 (((demorgan2a) =>
% 108.14/14.65 (((demorgan2b2) =>
% 108.14/14.65 (((demorgan2b) =>
% 108.14/14.65 (((demorgan2) =>
% 108.14/14.65 (((woz13rule0) =>
% 108.14/14.65 (((woz13rule1) =>
% 108.14/14.65 (((woz13rule2) =>
% 108.14/14.65 (((woz13rule3) =>
% 108.14/14.65 (((woz13rule4) =>
% 108.14/14.65 (((woz1_1) =>
% 108.14/14.65 (((woz1_2) =>
% 108.14/14.65 (((woz1_3) =>
% 108.14/14.65 (((woz1_4) =>
% 108.14/14.65 (((woz1_5) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1all2) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1SetBreln1) =>
% 108.14/14.65 ((
% 108.14/14.65 (choice2fnsingleton) =>
% 108.14/14.65 ((
% 108.14/14.65 (setOfPairsIsBReln1) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1all1) =>
% 108.14/14.65 ((
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% 108.14/14.65 ((
% 108.14/14.65 (eqbreln1) =>
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% 108.14/14.65 ((
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% 108.14/14.65 ((
% 108.14/14.65 (breln1invE) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1compprop) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1compI) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1compE) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1compEex) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionprop) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionIL) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionIR) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionI) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionE) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionEcases) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionCommutes) =>
% 108.14/14.65 ((
% 108.14/14.65 (woz2Ex) =>
% 108.14/14.65 ((
% 108.14/14.65 (woz2W) =>
% 108.14/14.65 ((
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% 108.14/14.65 ((
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% 108.14/14.65 ((
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% 108.14/14.65 ((
% 108.14/14.65 (image1Ex1) =>
% 108.14/14.65 ((
% 108.14/14.65 (image1Equiv) =>
% 108.14/14.65 ((
% 108.14/14.65 (image1E) =>
% 108.14/14.65 ((
% 108.14/14.65 (image1I) =>
% 108.14/14.65 ((
% 108.14/14.65 (injFuncInInjFuncSet) =>
% 108.14/14.65 ((
% 108.14/14.65 (injFuncSetFuncIn) =>
% 108.14/14.65 ((
% 108.14/14.65 (injFuncSetFuncInj) =>
% 108.14/14.65 ((
% 108.14/14.65 (surjFuncSetFuncIn) =>
% 108.14/14.65 ((
% 108.14/14.65 (surjFuncSetFuncSurj) =>
% 108.14/14.65 ((
% 108.14/14.65 (leftInvIsSurj) =>
% 108.14/14.65 ((
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% 108.14/14.65 ((
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% 108.14/14.65 (('#S') @ (
% 108.14/14.65 (
% 108.14/14.65 ('#B') @ (
% 108.14/14.65 =>) @
% 108.14/14.65 nonempty)) @
% 108.14/14.65 (
% 108.14/14.65 (
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% 108.14/14.65 (
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% 108.14/14.65 (
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% 108.14/14.65 (
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% 108.14/14.65 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 108.14/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2754])).
% 108.14/14.65 thf(zip_derived_cl2771, plain,
% 108.14/14.65 (~ (((binunionTIRcontra) =>
% 108.14/14.65 (((inIntersectImpInUnion) =>
% 108.14/14.65 (((inIntersectImpInUnion2) =>
% 108.14/14.65 (((inIntersectImpInIntersectUnions) =>
% 108.14/14.65 (((intersectInPowersetIntersectUnions) =>
% 108.14/14.65 (((inComplementUnionImpNotIn1) =>
% 108.14/14.65 (((inComplementUnionImpInComplement1) =>
% 108.14/14.65 (((binunionTE) =>
% 108.14/14.65 (((binunionTEcontra) =>
% 108.14/14.65 (((demorgan2a1) =>
% 108.14/14.65 (((complementUnionInPowersetComplement) =>
% 108.14/14.65 (((demorgan2a2) =>
% 108.14/14.65 (((demorgan1a) =>
% 108.14/14.65 (((demorgan1b) =>
% 108.14/14.65 (((demorgan1) =>
% 108.14/14.65 (((demorgan2a) =>
% 108.14/14.65 (((demorgan2b2) =>
% 108.14/14.65 (((demorgan2b) =>
% 108.14/14.65 (((demorgan2) =>
% 108.14/14.65 (((woz13rule0) =>
% 108.14/14.65 (((woz13rule1) =>
% 108.14/14.65 (((woz13rule2) =>
% 108.14/14.65 (((woz13rule3) =>
% 108.14/14.65 (((woz13rule4) =>
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% 108.14/14.65 (((woz1_2) =>
% 108.14/14.65 (((woz1_3) =>
% 108.14/14.65 (((woz1_4) =>
% 108.14/14.65 (((woz1_5) =>
% 108.14/14.65 (((breln1all2) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1SetBreln1) =>
% 108.14/14.65 ((
% 108.14/14.65 (choice2fnsingleton) =>
% 108.14/14.65 ((
% 108.14/14.65 (setOfPairsIsBReln1) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1all1) =>
% 108.14/14.65 ((
% 108.14/14.65 (subbreln1) =>
% 108.14/14.65 ((
% 108.14/14.65 (eqbreln1) =>
% 108.14/14.65 ((
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% 108.14/14.65 ((
% 108.14/14.65 (breln1invI) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1invE) =>
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% 108.14/14.65 ((
% 108.14/14.65 (breln1compE) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1compEex) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionprop) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionIL) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionIR) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionI) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionE) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionEcases) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionCommutes) =>
% 108.14/14.65 ((
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% 108.14/14.65 ((
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% 108.14/14.65 ((
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% 108.14/14.65 ((
% 108.14/14.65 (image1E) =>
% 108.14/14.65 ((
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% 108.14/14.65 ((
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% 108.14/14.65 ((
% 108.14/14.65 (injFuncSetFuncIn) =>
% 108.14/14.65 ((
% 108.14/14.65 (injFuncSetFuncInj) =>
% 108.14/14.65 ((
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% 108.14/14.65 ((
% 108.14/14.65 (surjFuncSetFuncSurj) =>
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% 108.14/14.65 (
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% 108.14/14.65 (
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% 108.14/14.65 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 108.14/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2762])).
% 108.14/14.65 thf(zip_derived_cl2781, plain,
% 108.14/14.65 (~ (((inIntersectImpInUnion) =>
% 108.14/14.65 (((inIntersectImpInUnion2) =>
% 108.14/14.65 (((inIntersectImpInIntersectUnions) =>
% 108.14/14.65 (((intersectInPowersetIntersectUnions) =>
% 108.14/14.65 (((inComplementUnionImpNotIn1) =>
% 108.14/14.65 (((inComplementUnionImpInComplement1) =>
% 108.14/14.65 (((binunionTE) =>
% 108.14/14.65 (((binunionTEcontra) =>
% 108.14/14.65 (((demorgan2a1) =>
% 108.14/14.65 (((complementUnionInPowersetComplement) =>
% 108.14/14.65 (((demorgan2a2) =>
% 108.14/14.65 (((demorgan1a) =>
% 108.14/14.65 (((demorgan1b) =>
% 108.14/14.65 (((demorgan1) =>
% 108.14/14.65 (((demorgan2a) =>
% 108.14/14.65 (((demorgan2b2) =>
% 108.14/14.65 (((demorgan2b) =>
% 108.14/14.65 (((demorgan2) =>
% 108.14/14.65 (((woz13rule0) =>
% 108.14/14.65 (((woz13rule1) =>
% 108.14/14.65 (((woz13rule2) =>
% 108.14/14.65 (((woz13rule3) =>
% 108.14/14.65 (((woz13rule4) =>
% 108.14/14.65 (((woz1_1) =>
% 108.14/14.65 (((woz1_2) =>
% 108.14/14.65 (((woz1_3) =>
% 108.14/14.65 (((woz1_4) =>
% 108.14/14.65 (((woz1_5) =>
% 108.14/14.65 (((breln1all2) =>
% 108.14/14.65 (((breln1SetBreln1) =>
% 108.14/14.65 ((
% 108.14/14.65 (choice2fnsingleton) =>
% 108.14/14.65 ((
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% 108.14/14.65 ((
% 108.14/14.65 (breln1all1) =>
% 108.14/14.65 ((
% 108.14/14.65 (subbreln1) =>
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% 108.14/14.65 ((
% 108.14/14.65 (breln1invI) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1invE) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1compprop) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1compI) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1compE) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1compEex) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionprop) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionIL) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionIR) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionI) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionE) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionEcases) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionCommutes) =>
% 108.14/14.65 ((
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% 108.14/14.65 ((
% 108.14/14.65 (woz2W) =>
% 108.14/14.65 ((
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% 108.14/14.65 ((
% 108.14/14.65 (woz2B) =>
% 108.14/14.65 ((
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% 108.14/14.65 ((
% 108.14/14.65 (image1Ex1) =>
% 108.14/14.65 ((
% 108.14/14.65 (image1Equiv) =>
% 108.14/14.65 ((
% 108.14/14.65 (image1E) =>
% 108.14/14.65 ((
% 108.14/14.65 (image1I) =>
% 108.14/14.65 ((
% 108.14/14.65 (injFuncInInjFuncSet) =>
% 108.14/14.65 ((
% 108.14/14.65 (injFuncSetFuncIn) =>
% 108.14/14.65 ((
% 108.14/14.65 (injFuncSetFuncInj) =>
% 108.14/14.65 ((
% 108.14/14.65 (surjFuncSetFuncIn) =>
% 108.14/14.65 ((
% 108.14/14.65 (surjFuncSetFuncSurj) =>
% 108.14/14.65 ((
% 108.14/14.65 (leftInvIsSurj) =>
% 108.14/14.65 ((
% 108.14/14.65 (surjCantorThm) =>
% 108.14/14.65 ((
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% 108.14/14.65 (
% 108.14/14.65 (
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% 108.14/14.65 (
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% 108.14/14.65 (
% 108.14/14.65 (
% 108.14/14.65 ('#B') @ (
% 108.14/14.65 (
% 108.14/14.65 ('#B') @ (
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% 108.14/14.65 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 108.14/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2771])).
% 108.14/14.65 thf(zip_derived_cl2792, plain,
% 108.14/14.65 (~ (((inIntersectImpInUnion2) =>
% 108.14/14.65 (((inIntersectImpInIntersectUnions) =>
% 108.14/14.65 (((intersectInPowersetIntersectUnions) =>
% 108.14/14.65 (((inComplementUnionImpNotIn1) =>
% 108.14/14.65 (((inComplementUnionImpInComplement1) =>
% 108.14/14.65 (((binunionTE) =>
% 108.14/14.65 (((binunionTEcontra) =>
% 108.14/14.65 (((demorgan2a1) =>
% 108.14/14.65 (((complementUnionInPowersetComplement) =>
% 108.14/14.65 (((demorgan2a2) =>
% 108.14/14.65 (((demorgan1a) =>
% 108.14/14.65 (((demorgan1b) =>
% 108.14/14.65 (((demorgan1) =>
% 108.14/14.65 (((demorgan2a) =>
% 108.14/14.65 (((demorgan2b2) =>
% 108.14/14.65 (((demorgan2b) =>
% 108.14/14.65 (((demorgan2) =>
% 108.14/14.65 (((woz13rule0) =>
% 108.14/14.65 (((woz13rule1) =>
% 108.14/14.65 (((woz13rule2) =>
% 108.14/14.65 (((woz13rule3) =>
% 108.14/14.65 (((woz13rule4) =>
% 108.14/14.65 (((woz1_1) =>
% 108.14/14.65 (((woz1_2) =>
% 108.14/14.65 (((woz1_3) =>
% 108.14/14.65 (((woz1_4) =>
% 108.14/14.65 (((woz1_5) =>
% 108.14/14.65 (((breln1all2) =>
% 108.14/14.65 (((breln1SetBreln1) =>
% 108.14/14.65 (((choice2fnsingleton) =>
% 108.14/14.65 ((
% 108.14/14.65 (setOfPairsIsBReln1) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1all1) =>
% 108.14/14.65 ((
% 108.14/14.65 (subbreln1) =>
% 108.14/14.65 ((
% 108.14/14.65 (eqbreln1) =>
% 108.14/14.65 ((
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% 108.14/14.65 ((
% 108.14/14.65 (breln1invI) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1invE) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1compprop) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1compI) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1compE) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1compEex) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionprop) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionIL) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionIR) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionI) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionE) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionEcases) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionCommutes) =>
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% 108.14/14.65 ((
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% 108.14/14.65 ((
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% 108.14/14.65 ((
% 108.14/14.65 (image1E) =>
% 108.14/14.65 ((
% 108.14/14.65 (image1I) =>
% 108.14/14.65 ((
% 108.14/14.65 (injFuncInInjFuncSet) =>
% 108.14/14.65 ((
% 108.14/14.65 (injFuncSetFuncIn) =>
% 108.14/14.65 ((
% 108.14/14.65 (injFuncSetFuncInj) =>
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% 108.14/14.65 ((
% 108.14/14.65 (surjFuncSetFuncSurj) =>
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% 108.14/14.65 (leftInvIsSurj) =>
% 108.14/14.65 ((
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% 108.14/14.65 ((
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% 108.14/14.65 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 108.14/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2781])).
% 108.14/14.65 thf(zip_derived_cl2803, plain,
% 108.14/14.65 (~ (((inIntersectImpInIntersectUnions) =>
% 108.14/14.65 (((intersectInPowersetIntersectUnions) =>
% 108.14/14.65 (((inComplementUnionImpNotIn1) =>
% 108.14/14.65 (((inComplementUnionImpInComplement1) =>
% 108.14/14.65 (((binunionTE) =>
% 108.14/14.65 (((binunionTEcontra) =>
% 108.14/14.65 (((demorgan2a1) =>
% 108.14/14.65 (((complementUnionInPowersetComplement) =>
% 108.14/14.65 (((demorgan2a2) =>
% 108.14/14.65 (((demorgan1a) =>
% 108.14/14.65 (((demorgan1b) =>
% 108.14/14.65 (((demorgan1) =>
% 108.14/14.65 (((demorgan2a) =>
% 108.14/14.65 (((demorgan2b2) =>
% 108.14/14.65 (((demorgan2b) =>
% 108.14/14.65 (((demorgan2) =>
% 108.14/14.65 (((woz13rule0) =>
% 108.14/14.65 (((woz13rule1) =>
% 108.14/14.65 (((woz13rule2) =>
% 108.14/14.65 (((woz13rule3) =>
% 108.14/14.65 (((woz13rule4) =>
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% 108.14/14.65 (((woz1_2) =>
% 108.14/14.65 (((woz1_3) =>
% 108.14/14.65 (((woz1_4) =>
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% 108.14/14.65 ((
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% 108.14/14.65 ((
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% 108.14/14.65 ((
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% 108.14/14.65 ((
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% 108.14/14.65 ((
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% 108.14/14.65 ((
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% 108.14/14.65 ((
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% 108.14/14.65 ((
% 108.14/14.65 (breln1unionIL) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionIR) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionI) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionE) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionEcases) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionCommutes) =>
% 108.14/14.65 ((
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% 108.14/14.65 ((
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% 108.14/14.65 ((
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% 108.14/14.65 ((
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% 108.14/14.65 ((
% 108.14/14.65 (image1E) =>
% 108.14/14.65 ((
% 108.14/14.65 (image1I) =>
% 108.14/14.65 ((
% 108.14/14.65 (injFuncInInjFuncSet) =>
% 108.14/14.65 ((
% 108.14/14.65 (injFuncSetFuncIn) =>
% 108.14/14.65 ((
% 108.14/14.65 (injFuncSetFuncInj) =>
% 108.14/14.65 ((
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% 108.14/14.65 ((
% 108.14/14.65 (surjFuncSetFuncSurj) =>
% 108.14/14.65 ((
% 108.14/14.65 (leftInvIsSurj) =>
% 108.14/14.65 ((
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% 108.14/14.65 (('#S') @ (
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% 108.14/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2792])).
% 108.14/14.65 thf(zip_derived_cl2813, plain,
% 108.14/14.65 (~ (((intersectInPowersetIntersectUnions) =>
% 108.14/14.65 (((inComplementUnionImpNotIn1) =>
% 108.14/14.65 (((inComplementUnionImpInComplement1) =>
% 108.14/14.65 (((binunionTE) =>
% 108.14/14.65 (((binunionTEcontra) =>
% 108.14/14.65 (((demorgan2a1) =>
% 108.14/14.65 (((complementUnionInPowersetComplement) =>
% 108.14/14.65 (((demorgan2a2) =>
% 108.14/14.65 (((demorgan1a) =>
% 108.14/14.65 (((demorgan1b) =>
% 108.14/14.65 (((demorgan1) =>
% 108.14/14.65 (((demorgan2a) =>
% 108.14/14.65 (((demorgan2b2) =>
% 108.14/14.65 (((demorgan2b) =>
% 108.14/14.65 (((demorgan2) =>
% 108.14/14.65 (((woz13rule0) =>
% 108.14/14.65 (((woz13rule1) =>
% 108.14/14.65 (((woz13rule2) =>
% 108.14/14.65 (((woz13rule3) =>
% 108.14/14.65 (((woz13rule4) =>
% 108.14/14.65 (((woz1_1) =>
% 108.14/14.65 (((woz1_2) =>
% 108.14/14.65 (((woz1_3) =>
% 108.14/14.65 (((woz1_4) =>
% 108.14/14.65 (((woz1_5) =>
% 108.14/14.65 (((breln1all2) =>
% 108.14/14.65 (((breln1SetBreln1) =>
% 108.14/14.65 (((choice2fnsingleton) =>
% 108.14/14.65 (((setOfPairsIsBReln1) =>
% 108.14/14.65 (((breln1all1) =>
% 108.14/14.65 ((
% 108.14/14.65 (subbreln1) =>
% 108.14/14.65 ((
% 108.14/14.65 (eqbreln1) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1invprop) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1invI) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1invE) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1compprop) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1compI) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1compE) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1compEex) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionprop) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionIL) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionIR) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionI) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionE) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionEcases) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionCommutes) =>
% 108.14/14.65 ((
% 108.14/14.65 (woz2Ex) =>
% 108.14/14.65 ((
% 108.14/14.65 (woz2W) =>
% 108.14/14.65 ((
% 108.14/14.65 (woz2A) =>
% 108.14/14.65 ((
% 108.14/14.65 (woz2B) =>
% 108.14/14.65 ((
% 108.14/14.65 (image1Ex) =>
% 108.14/14.65 ((
% 108.14/14.65 (image1Ex1) =>
% 108.14/14.65 ((
% 108.14/14.65 (image1Equiv) =>
% 108.14/14.65 ((
% 108.14/14.65 (image1E) =>
% 108.14/14.65 ((
% 108.14/14.65 (image1I) =>
% 108.14/14.65 ((
% 108.14/14.65 (injFuncInInjFuncSet) =>
% 108.14/14.65 ((
% 108.14/14.65 (injFuncSetFuncIn) =>
% 108.14/14.65 ((
% 108.14/14.65 (injFuncSetFuncInj) =>
% 108.14/14.65 ((
% 108.14/14.65 (surjFuncSetFuncIn) =>
% 108.14/14.65 ((
% 108.14/14.65 (surjFuncSetFuncSurj) =>
% 108.14/14.65 ((
% 108.14/14.65 (leftInvIsSurj) =>
% 108.14/14.65 ((
% 108.14/14.65 (surjCantorThm) =>
% 108.14/14.65 ((
% 108.14/14.65 (!!) @ (
% 108.14/14.65 (('#S') @ (
% 108.14/14.65 (
% 108.14/14.65 ('#B') @ (
% 108.14/14.65 =>) @
% 108.14/14.65 nonempty)) @
% 108.14/14.65 (
% 108.14/14.65 (
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% 108.14/14.65 ??) @
% 108.14/14.65 (
% 108.14/14.65 (
% 108.14/14.65 ('#S') @ (
% 108.14/14.65 (
% 108.14/14.65 ('#B') @ (
% 108.14/14.65 '#S') @
% 108.14/14.65 (
% 108.14/14.65 (
% 108.14/14.65 ('#B') @ (
% 108.14/14.65 (
% 108.14/14.65 ('#B') @ (
% 108.14/14.65 &))) @
% 108.14/14.65 (
% 108.14/14.65 (
% 108.14/14.65 ('#C') @ in)))))) @
% 108.14/14.65 (
% 108.14/14.65 (
% 108.14/14.65 ('#C') @ (
% 108.14/14.65 (
% 108.14/14.65 ('#B') @ (
% 108.14/14.65 '#C') @
% 108.14/14.65 (
% 108.14/14.65 (
% 108.14/14.65 ('#B') @ (
% 108.14/14.65 (
% 108.14/14.65 ('#B') @ (
% 108.14/14.65 =))) @
% 108.14/14.65 (
% 108.14/14.65 (
% 108.14/14.65 ('#C') @ binintersect)))))) @
% 108.14/14.65 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 108.14/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2803])).
% 108.14/14.65 thf(zip_derived_cl2823, plain,
% 108.14/14.65 (~ (((inComplementUnionImpNotIn1) =>
% 108.14/14.65 (((inComplementUnionImpInComplement1) =>
% 108.14/14.65 (((binunionTE) =>
% 108.14/14.65 (((binunionTEcontra) =>
% 108.14/14.65 (((demorgan2a1) =>
% 108.14/14.65 (((complementUnionInPowersetComplement) =>
% 108.14/14.65 (((demorgan2a2) =>
% 108.14/14.65 (((demorgan1a) =>
% 108.14/14.65 (((demorgan1b) =>
% 108.14/14.65 (((demorgan1) =>
% 108.14/14.65 (((demorgan2a) =>
% 108.14/14.65 (((demorgan2b2) =>
% 108.14/14.65 (((demorgan2b) =>
% 108.14/14.65 (((demorgan2) =>
% 108.14/14.65 (((woz13rule0) =>
% 108.14/14.65 (((woz13rule1) =>
% 108.14/14.65 (((woz13rule2) =>
% 108.14/14.65 (((woz13rule3) =>
% 108.14/14.65 (((woz13rule4) =>
% 108.14/14.65 (((woz1_1) =>
% 108.14/14.65 (((woz1_2) =>
% 108.14/14.65 (((woz1_3) =>
% 108.14/14.65 (((woz1_4) =>
% 108.14/14.65 (((woz1_5) =>
% 108.14/14.65 (((breln1all2) =>
% 108.14/14.65 (((breln1SetBreln1) =>
% 108.14/14.65 (((choice2fnsingleton) =>
% 108.14/14.65 (((setOfPairsIsBReln1) =>
% 108.14/14.65 (((breln1all1) =>
% 108.14/14.65 (((subbreln1) =>
% 108.14/14.65 ((
% 108.14/14.65 (eqbreln1) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1invprop) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1invI) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1invE) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1compprop) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1compI) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1compE) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1compEex) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionprop) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionIL) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionIR) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionI) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionE) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionEcases) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionCommutes) =>
% 108.14/14.65 ((
% 108.14/14.65 (woz2Ex) =>
% 108.14/14.65 ((
% 108.14/14.65 (woz2W) =>
% 108.14/14.65 ((
% 108.14/14.65 (woz2A) =>
% 108.14/14.65 ((
% 108.14/14.65 (woz2B) =>
% 108.14/14.65 ((
% 108.14/14.65 (image1Ex) =>
% 108.14/14.65 ((
% 108.14/14.65 (image1Ex1) =>
% 108.14/14.65 ((
% 108.14/14.65 (image1Equiv) =>
% 108.14/14.65 ((
% 108.14/14.65 (image1E) =>
% 108.14/14.65 ((
% 108.14/14.65 (image1I) =>
% 108.14/14.65 ((
% 108.14/14.65 (injFuncInInjFuncSet) =>
% 108.14/14.65 ((
% 108.14/14.65 (injFuncSetFuncIn) =>
% 108.14/14.65 ((
% 108.14/14.65 (injFuncSetFuncInj) =>
% 108.14/14.65 ((
% 108.14/14.65 (surjFuncSetFuncIn) =>
% 108.14/14.65 ((
% 108.14/14.65 (surjFuncSetFuncSurj) =>
% 108.14/14.65 ((
% 108.14/14.65 (leftInvIsSurj) =>
% 108.14/14.65 ((
% 108.14/14.65 (surjCantorThm) =>
% 108.14/14.65 ((
% 108.14/14.65 (!!) @ (
% 108.14/14.65 (('#S') @ (
% 108.14/14.65 (
% 108.14/14.65 ('#B') @ (
% 108.14/14.65 =>) @
% 108.14/14.65 nonempty)) @
% 108.14/14.65 (
% 108.14/14.65 (
% 108.14/14.65 ('#B') @ (
% 108.14/14.65 ??) @
% 108.14/14.65 (
% 108.14/14.65 (
% 108.14/14.65 ('#S') @ (
% 108.14/14.65 (
% 108.14/14.65 ('#B') @ (
% 108.14/14.65 '#S') @
% 108.14/14.65 (
% 108.14/14.65 (
% 108.14/14.65 ('#B') @ (
% 108.14/14.65 (
% 108.14/14.65 ('#B') @ (
% 108.14/14.65 &))) @
% 108.14/14.65 (
% 108.14/14.65 (
% 108.14/14.65 ('#C') @ in)))))) @
% 108.14/14.65 (
% 108.14/14.65 (
% 108.14/14.65 ('#C') @ (
% 108.14/14.65 (
% 108.14/14.65 ('#B') @ (
% 108.14/14.65 '#C') @
% 108.14/14.65 (
% 108.14/14.65 (
% 108.14/14.65 ('#B') @ (
% 108.14/14.65 (
% 108.14/14.65 ('#B') @ (
% 108.14/14.65 =))) @
% 108.14/14.65 (
% 108.14/14.65 (
% 108.14/14.65 ('#C') @ binintersect)))))) @
% 108.14/14.65 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 108.14/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2813])).
% 108.14/14.65 thf(zip_derived_cl2834, plain,
% 108.14/14.65 (~ (((inComplementUnionImpInComplement1) =>
% 108.14/14.65 (((binunionTE) =>
% 108.14/14.65 (((binunionTEcontra) =>
% 108.14/14.65 (((demorgan2a1) =>
% 108.14/14.65 (((complementUnionInPowersetComplement) =>
% 108.14/14.65 (((demorgan2a2) =>
% 108.14/14.65 (((demorgan1a) =>
% 108.14/14.65 (((demorgan1b) =>
% 108.14/14.65 (((demorgan1) =>
% 108.14/14.65 (((demorgan2a) =>
% 108.14/14.65 (((demorgan2b2) =>
% 108.14/14.65 (((demorgan2b) =>
% 108.14/14.65 (((demorgan2) =>
% 108.14/14.65 (((woz13rule0) =>
% 108.14/14.65 (((woz13rule1) =>
% 108.14/14.65 (((woz13rule2) =>
% 108.14/14.65 (((woz13rule3) =>
% 108.14/14.65 (((woz13rule4) =>
% 108.14/14.65 (((woz1_1) =>
% 108.14/14.65 (((woz1_2) =>
% 108.14/14.65 (((woz1_3) =>
% 108.14/14.65 (((woz1_4) =>
% 108.14/14.65 (((woz1_5) =>
% 108.14/14.65 (((breln1all2) =>
% 108.14/14.65 (((breln1SetBreln1) =>
% 108.14/14.65 (((choice2fnsingleton) =>
% 108.14/14.65 (((setOfPairsIsBReln1) =>
% 108.14/14.65 (((breln1all1) =>
% 108.14/14.65 (((subbreln1) =>
% 108.14/14.65 (((eqbreln1) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1invprop) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1invI) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1invE) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1compprop) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1compI) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1compE) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1compEex) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionprop) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionIL) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionIR) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionI) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionE) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionEcases) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionCommutes) =>
% 108.14/14.65 ((
% 108.14/14.65 (woz2Ex) =>
% 108.14/14.65 ((
% 108.14/14.65 (woz2W) =>
% 108.14/14.65 ((
% 108.14/14.65 (woz2A) =>
% 108.14/14.65 ((
% 108.14/14.65 (woz2B) =>
% 108.14/14.65 ((
% 108.14/14.65 (image1Ex) =>
% 108.14/14.65 ((
% 108.14/14.65 (image1Ex1) =>
% 108.14/14.65 ((
% 108.14/14.65 (image1Equiv) =>
% 108.14/14.65 ((
% 108.14/14.65 (image1E) =>
% 108.14/14.65 ((
% 108.14/14.65 (image1I) =>
% 108.14/14.65 ((
% 108.14/14.65 (injFuncInInjFuncSet) =>
% 108.14/14.65 ((
% 108.14/14.65 (injFuncSetFuncIn) =>
% 108.14/14.65 ((
% 108.14/14.65 (injFuncSetFuncInj) =>
% 108.14/14.65 ((
% 108.14/14.65 (surjFuncSetFuncIn) =>
% 108.14/14.65 ((
% 108.14/14.65 (surjFuncSetFuncSurj) =>
% 108.14/14.65 ((
% 108.14/14.65 (leftInvIsSurj) =>
% 108.14/14.65 ((
% 108.14/14.65 (surjCantorThm) =>
% 108.14/14.65 ((
% 108.14/14.65 (!!) @ (
% 108.14/14.65 (('#S') @ (
% 108.14/14.65 (
% 108.14/14.65 ('#B') @ (
% 108.14/14.65 =>) @
% 108.14/14.65 nonempty)) @
% 108.14/14.65 (
% 108.14/14.65 (
% 108.14/14.65 ('#B') @ (
% 108.14/14.65 ??) @
% 108.14/14.65 (
% 108.14/14.65 (
% 108.14/14.65 ('#S') @ (
% 108.14/14.65 (
% 108.14/14.65 ('#B') @ (
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% 108.14/14.65 (
% 108.14/14.65 (
% 108.14/14.65 ('#B') @ (
% 108.14/14.65 (
% 108.14/14.65 ('#B') @ (
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% 108.14/14.65 (
% 108.14/14.65 (
% 108.14/14.65 ('#C') @ in)))))) @
% 108.14/14.65 (
% 108.14/14.65 (
% 108.14/14.65 ('#C') @ (
% 108.14/14.65 (
% 108.14/14.65 ('#B') @ (
% 108.14/14.65 '#C') @
% 108.14/14.65 (
% 108.14/14.65 (
% 108.14/14.65 ('#B') @ (
% 108.14/14.65 (
% 108.14/14.65 ('#B') @ (
% 108.14/14.65 =))) @
% 108.14/14.65 (
% 108.14/14.65 (
% 108.14/14.65 ('#C') @ binintersect)))))) @
% 108.14/14.65 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 108.14/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2823])).
% 108.14/14.65 thf(zip_derived_cl2845, plain,
% 108.14/14.65 (~ (((binunionTE) =>
% 108.14/14.65 (((binunionTEcontra) =>
% 108.14/14.65 (((demorgan2a1) =>
% 108.14/14.65 (((complementUnionInPowersetComplement) =>
% 108.14/14.65 (((demorgan2a2) =>
% 108.14/14.65 (((demorgan1a) =>
% 108.14/14.65 (((demorgan1b) =>
% 108.14/14.65 (((demorgan1) =>
% 108.14/14.65 (((demorgan2a) =>
% 108.14/14.65 (((demorgan2b2) =>
% 108.14/14.65 (((demorgan2b) =>
% 108.14/14.65 (((demorgan2) =>
% 108.14/14.65 (((woz13rule0) =>
% 108.14/14.65 (((woz13rule1) =>
% 108.14/14.65 (((woz13rule2) =>
% 108.14/14.65 (((woz13rule3) =>
% 108.14/14.65 (((woz13rule4) =>
% 108.14/14.65 (((woz1_1) =>
% 108.14/14.65 (((woz1_2) =>
% 108.14/14.65 (((woz1_3) =>
% 108.14/14.65 (((woz1_4) =>
% 108.14/14.65 (((woz1_5) =>
% 108.14/14.65 (((breln1all2) =>
% 108.14/14.65 (((breln1SetBreln1) =>
% 108.14/14.65 (((choice2fnsingleton) =>
% 108.14/14.65 (((setOfPairsIsBReln1) =>
% 108.14/14.65 (((breln1all1) =>
% 108.14/14.65 (((subbreln1) =>
% 108.14/14.65 (((eqbreln1) =>
% 108.14/14.65 (((breln1invprop) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1invI) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1invE) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1compprop) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1compI) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1compE) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1compEex) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionprop) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionIL) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionIR) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionI) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionE) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionEcases) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionCommutes) =>
% 108.14/14.65 ((
% 108.14/14.65 (woz2Ex) =>
% 108.14/14.65 ((
% 108.14/14.65 (woz2W) =>
% 108.14/14.65 ((
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% 108.14/14.65 ((
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% 108.14/14.65 ((
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% 108.14/14.65 ((
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% 108.14/14.65 ((
% 108.14/14.65 (image1E) =>
% 108.14/14.65 ((
% 108.14/14.65 (image1I) =>
% 108.14/14.65 ((
% 108.14/14.65 (injFuncInInjFuncSet) =>
% 108.14/14.65 ((
% 108.14/14.65 (injFuncSetFuncIn) =>
% 108.14/14.65 ((
% 108.14/14.65 (injFuncSetFuncInj) =>
% 108.14/14.65 ((
% 108.14/14.65 (surjFuncSetFuncIn) =>
% 108.14/14.65 ((
% 108.14/14.65 (surjFuncSetFuncSurj) =>
% 108.14/14.65 ((
% 108.14/14.65 (leftInvIsSurj) =>
% 108.14/14.65 ((
% 108.14/14.65 (surjCantorThm) =>
% 108.14/14.65 ((
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% 108.14/14.65 (('#S') @ (
% 108.14/14.65 (
% 108.14/14.65 ('#B') @ (
% 108.14/14.65 =>) @
% 108.14/14.65 nonempty)) @
% 108.14/14.65 (
% 108.14/14.65 (
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% 108.14/14.65 ('#B') @ (
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% 108.14/14.65 (
% 108.14/14.65 (
% 108.14/14.65 ('#C') @ in)))))) @
% 108.14/14.65 (
% 108.14/14.65 (
% 108.14/14.65 ('#C') @ (
% 108.14/14.65 (
% 108.14/14.65 ('#B') @ (
% 108.14/14.65 '#C') @
% 108.14/14.65 (
% 108.14/14.65 (
% 108.14/14.65 ('#B') @ (
% 108.14/14.65 (
% 108.14/14.65 ('#B') @ (
% 108.14/14.65 =))) @
% 108.14/14.65 (
% 108.14/14.65 (
% 108.14/14.65 ('#C') @ binintersect)))))) @
% 108.14/14.65 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 108.14/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2834])).
% 108.14/14.65 thf(zip_derived_cl2857, plain,
% 108.14/14.65 (~ (((binunionTEcontra) =>
% 108.14/14.65 (((demorgan2a1) =>
% 108.14/14.65 (((complementUnionInPowersetComplement) =>
% 108.14/14.65 (((demorgan2a2) =>
% 108.14/14.65 (((demorgan1a) =>
% 108.14/14.65 (((demorgan1b) =>
% 108.14/14.65 (((demorgan1) =>
% 108.14/14.65 (((demorgan2a) =>
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% 108.14/14.65 (((woz1_2) =>
% 108.14/14.65 (((woz1_3) =>
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% 108.14/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2845])).
% 108.14/14.65 thf(zip_derived_cl2869, plain,
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% 108.14/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2857])).
% 108.14/14.65 thf(zip_derived_cl2881, plain,
% 108.14/14.65 (~ (((complementUnionInPowersetComplement) =>
% 108.14/14.65 (((demorgan2a2) =>
% 108.14/14.65 (((demorgan1a) =>
% 108.14/14.65 (((demorgan1b) =>
% 108.14/14.65 (((demorgan1) =>
% 108.14/14.65 (((demorgan2a) =>
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% 108.14/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2869])).
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% 108.14/14.65 (((demorgan2) =>
% 108.14/14.65 (((woz13rule0) =>
% 108.14/14.65 (((woz13rule1) =>
% 108.14/14.65 (((woz13rule2) =>
% 108.14/14.65 (((woz13rule3) =>
% 108.14/14.65 (((woz13rule4) =>
% 108.14/14.65 (((woz1_1) =>
% 108.14/14.65 (((woz1_2) =>
% 108.14/14.65 (((woz1_3) =>
% 108.14/14.65 (((woz1_4) =>
% 108.14/14.65 (((woz1_5) =>
% 108.14/14.65 (((breln1all2) =>
% 108.14/14.65 (((breln1SetBreln1) =>
% 108.14/14.65 (((choice2fnsingleton) =>
% 108.14/14.65 (((setOfPairsIsBReln1) =>
% 108.14/14.65 (((breln1all1) =>
% 108.14/14.65 (((subbreln1) =>
% 108.14/14.65 (((eqbreln1) =>
% 108.14/14.65 (((breln1invprop) =>
% 108.14/14.65 (((breln1invI) =>
% 108.14/14.65 (((breln1invE) =>
% 108.14/14.65 (((breln1compprop) =>
% 108.14/14.65 (((breln1compI) =>
% 108.14/14.65 (((breln1compE) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1compEex) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionprop) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionIL) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionIR) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionI) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionE) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionEcases) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionCommutes) =>
% 108.14/14.65 ((
% 108.14/14.65 (woz2Ex) =>
% 108.14/14.65 ((
% 108.14/14.65 (woz2W) =>
% 108.14/14.65 ((
% 108.14/14.65 (woz2A) =>
% 108.14/14.65 ((
% 108.14/14.65 (woz2B) =>
% 108.14/14.65 ((
% 108.14/14.65 (image1Ex) =>
% 108.14/14.65 ((
% 108.14/14.65 (image1Ex1) =>
% 108.14/14.65 ((
% 108.14/14.65 (image1Equiv) =>
% 108.14/14.65 ((
% 108.14/14.65 (image1E) =>
% 108.14/14.65 ((
% 108.14/14.65 (image1I) =>
% 108.14/14.65 ((
% 108.14/14.65 (injFuncInInjFuncSet) =>
% 108.14/14.65 ((
% 108.14/14.65 (injFuncSetFuncIn) =>
% 108.14/14.65 ((
% 108.14/14.65 (injFuncSetFuncInj) =>
% 108.14/14.65 ((
% 108.14/14.65 (surjFuncSetFuncIn) =>
% 108.14/14.65 ((
% 108.14/14.65 (surjFuncSetFuncSurj) =>
% 108.14/14.65 ((
% 108.14/14.65 (leftInvIsSurj) =>
% 108.14/14.65 ((
% 108.14/14.65 (surjCantorThm) =>
% 108.14/14.65 ((
% 108.14/14.65 (!!) @ (
% 108.14/14.65 (('#S') @ (
% 108.14/14.65 (
% 108.14/14.65 ('#B') @ (
% 108.14/14.65 =>) @
% 108.14/14.65 nonempty)) @
% 108.14/14.65 (
% 108.14/14.65 (
% 108.14/14.65 ('#B') @ (
% 108.14/14.65 ??) @
% 108.14/14.65 (
% 108.14/14.65 (
% 108.14/14.65 ('#S') @ (
% 108.14/14.65 (
% 108.14/14.65 ('#B') @ (
% 108.14/14.65 '#S') @
% 108.14/14.65 (
% 108.14/14.65 (
% 108.14/14.65 ('#B') @ (
% 108.14/14.65 (
% 108.14/14.65 ('#B') @ (
% 108.14/14.65 &))) @
% 108.14/14.65 (
% 108.14/14.65 (
% 108.14/14.65 ('#C') @ in)))))) @
% 108.14/14.65 (
% 108.14/14.65 (
% 108.14/14.65 ('#C') @ (
% 108.14/14.65 (
% 108.14/14.65 ('#B') @ (
% 108.14/14.65 '#C') @
% 108.14/14.65 (
% 108.14/14.65 (
% 108.14/14.65 ('#B') @ (
% 108.14/14.65 (
% 108.14/14.65 ('#B') @ (
% 108.14/14.65 =))) @
% 108.14/14.65 (
% 108.14/14.65 (
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% 108.14/14.65 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 108.14/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2893])).
% 108.14/14.65 thf(zip_derived_cl2920, plain,
% 108.14/14.65 (~ (((demorgan1b) =>
% 108.14/14.65 (((demorgan1) =>
% 108.14/14.65 (((demorgan2a) =>
% 108.14/14.65 (((demorgan2b2) =>
% 108.14/14.65 (((demorgan2b) =>
% 108.14/14.65 (((demorgan2) =>
% 108.14/14.65 (((woz13rule0) =>
% 108.14/14.65 (((woz13rule1) =>
% 108.14/14.65 (((woz13rule2) =>
% 108.14/14.65 (((woz13rule3) =>
% 108.14/14.65 (((woz13rule4) =>
% 108.14/14.65 (((woz1_1) =>
% 108.14/14.65 (((woz1_2) =>
% 108.14/14.65 (((woz1_3) =>
% 108.14/14.65 (((woz1_4) =>
% 108.14/14.65 (((woz1_5) =>
% 108.14/14.65 (((breln1all2) =>
% 108.14/14.65 (((breln1SetBreln1) =>
% 108.14/14.65 (((choice2fnsingleton) =>
% 108.14/14.65 (((setOfPairsIsBReln1) =>
% 108.14/14.65 (((breln1all1) =>
% 108.14/14.65 (((subbreln1) =>
% 108.14/14.65 (((eqbreln1) =>
% 108.14/14.65 (((breln1invprop) =>
% 108.14/14.65 (((breln1invI) =>
% 108.14/14.65 (((breln1invE) =>
% 108.14/14.65 (((breln1compprop) =>
% 108.14/14.65 (((breln1compI) =>
% 108.14/14.65 (((breln1compE) =>
% 108.14/14.65 (((breln1compEex) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionprop) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionIL) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionIR) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionI) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionE) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionEcases) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionCommutes) =>
% 108.14/14.65 ((
% 108.14/14.65 (woz2Ex) =>
% 108.14/14.65 ((
% 108.14/14.65 (woz2W) =>
% 108.14/14.65 ((
% 108.14/14.65 (woz2A) =>
% 108.14/14.65 ((
% 108.14/14.65 (woz2B) =>
% 108.14/14.65 ((
% 108.14/14.65 (image1Ex) =>
% 108.14/14.65 ((
% 108.14/14.65 (image1Ex1) =>
% 108.14/14.65 ((
% 108.14/14.65 (image1Equiv) =>
% 108.14/14.65 ((
% 108.14/14.65 (image1E) =>
% 108.14/14.65 ((
% 108.14/14.65 (image1I) =>
% 108.14/14.65 ((
% 108.14/14.65 (injFuncInInjFuncSet) =>
% 108.14/14.65 ((
% 108.14/14.65 (injFuncSetFuncIn) =>
% 108.14/14.65 ((
% 108.14/14.65 (injFuncSetFuncInj) =>
% 108.14/14.65 ((
% 108.14/14.65 (surjFuncSetFuncIn) =>
% 108.14/14.65 ((
% 108.14/14.65 (surjFuncSetFuncSurj) =>
% 108.14/14.65 ((
% 108.14/14.65 (leftInvIsSurj) =>
% 108.14/14.65 ((
% 108.14/14.65 (surjCantorThm) =>
% 108.14/14.65 ((
% 108.14/14.65 (!!) @ (
% 108.14/14.65 (('#S') @ (
% 108.14/14.65 (
% 108.14/14.65 ('#B') @ (
% 108.14/14.65 =>) @
% 108.14/14.65 nonempty)) @
% 108.14/14.65 (
% 108.14/14.65 (
% 108.14/14.65 ('#B') @ (
% 108.14/14.65 ??) @
% 108.14/14.65 (
% 108.14/14.65 (
% 108.14/14.65 ('#S') @ (
% 108.14/14.65 (
% 108.14/14.65 ('#B') @ (
% 108.14/14.65 '#S') @
% 108.14/14.65 (
% 108.14/14.65 (
% 108.14/14.65 ('#B') @ (
% 108.14/14.65 (
% 108.14/14.65 ('#B') @ (
% 108.14/14.65 &))) @
% 108.14/14.65 (
% 108.14/14.65 (
% 108.14/14.65 ('#C') @ in)))))) @
% 108.14/14.65 (
% 108.14/14.65 (
% 108.14/14.65 ('#C') @ (
% 108.14/14.65 (
% 108.14/14.65 ('#B') @ (
% 108.14/14.65 '#C') @
% 108.14/14.65 (
% 108.14/14.65 (
% 108.14/14.65 ('#B') @ (
% 108.14/14.65 (
% 108.14/14.65 ('#B') @ (
% 108.14/14.65 =))) @
% 108.14/14.65 (
% 108.14/14.65 (
% 108.14/14.65 ('#C') @ binintersect)))))) @
% 108.14/14.65 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 108.14/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2906])).
% 108.14/14.65 thf(zip_derived_cl2933, plain,
% 108.14/14.65 (~ (((demorgan1) =>
% 108.14/14.65 (((demorgan2a) =>
% 108.14/14.65 (((demorgan2b2) =>
% 108.14/14.65 (((demorgan2b) =>
% 108.14/14.65 (((demorgan2) =>
% 108.14/14.65 (((woz13rule0) =>
% 108.14/14.65 (((woz13rule1) =>
% 108.14/14.65 (((woz13rule2) =>
% 108.14/14.65 (((woz13rule3) =>
% 108.14/14.65 (((woz13rule4) =>
% 108.14/14.65 (((woz1_1) =>
% 108.14/14.65 (((woz1_2) =>
% 108.14/14.65 (((woz1_3) =>
% 108.14/14.65 (((woz1_4) =>
% 108.14/14.65 (((woz1_5) =>
% 108.14/14.65 (((breln1all2) =>
% 108.14/14.65 (((breln1SetBreln1) =>
% 108.14/14.65 (((choice2fnsingleton) =>
% 108.14/14.65 (((setOfPairsIsBReln1) =>
% 108.14/14.65 (((breln1all1) =>
% 108.14/14.65 (((subbreln1) =>
% 108.14/14.65 (((eqbreln1) =>
% 108.14/14.65 (((breln1invprop) =>
% 108.14/14.65 (((breln1invI) =>
% 108.14/14.65 (((breln1invE) =>
% 108.14/14.65 (((breln1compprop) =>
% 108.14/14.65 (((breln1compI) =>
% 108.14/14.65 (((breln1compE) =>
% 108.14/14.65 (((breln1compEex) =>
% 108.14/14.65 (((breln1unionprop) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionIL) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionIR) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionI) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionE) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionEcases) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionCommutes) =>
% 108.14/14.65 ((
% 108.14/14.65 (woz2Ex) =>
% 108.14/14.65 ((
% 108.14/14.65 (woz2W) =>
% 108.14/14.65 ((
% 108.14/14.65 (woz2A) =>
% 108.14/14.65 ((
% 108.14/14.65 (woz2B) =>
% 108.14/14.65 ((
% 108.14/14.65 (image1Ex) =>
% 108.14/14.65 ((
% 108.14/14.65 (image1Ex1) =>
% 108.14/14.65 ((
% 108.14/14.65 (image1Equiv) =>
% 108.14/14.65 ((
% 108.14/14.65 (image1E) =>
% 108.14/14.65 ((
% 108.14/14.65 (image1I) =>
% 108.14/14.65 ((
% 108.14/14.65 (injFuncInInjFuncSet) =>
% 108.14/14.65 ((
% 108.14/14.65 (injFuncSetFuncIn) =>
% 108.14/14.65 ((
% 108.14/14.65 (injFuncSetFuncInj) =>
% 108.14/14.65 ((
% 108.14/14.65 (surjFuncSetFuncIn) =>
% 108.14/14.65 ((
% 108.14/14.65 (surjFuncSetFuncSurj) =>
% 108.14/14.65 ((
% 108.14/14.65 (leftInvIsSurj) =>
% 108.14/14.65 ((
% 108.14/14.65 (surjCantorThm) =>
% 108.14/14.65 ((
% 108.14/14.65 (!!) @ (
% 108.14/14.65 (('#S') @ (
% 108.14/14.65 (
% 108.14/14.65 ('#B') @ (
% 108.14/14.65 =>) @
% 108.14/14.65 nonempty)) @
% 108.14/14.65 (
% 108.14/14.65 (
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% 108.14/14.65 (
% 108.14/14.65 (
% 108.14/14.65 ('#S') @ (
% 108.14/14.65 (
% 108.14/14.65 ('#B') @ (
% 108.14/14.65 '#S') @
% 108.14/14.65 (
% 108.14/14.65 (
% 108.14/14.65 ('#B') @ (
% 108.14/14.65 (
% 108.14/14.65 ('#B') @ (
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% 108.14/14.65 (
% 108.14/14.65 (
% 108.14/14.65 ('#C') @ in)))))) @
% 108.14/14.65 (
% 108.14/14.65 (
% 108.14/14.65 ('#C') @ (
% 108.14/14.65 (
% 108.14/14.65 ('#B') @ (
% 108.14/14.65 '#C') @
% 108.14/14.65 (
% 108.14/14.65 (
% 108.14/14.65 ('#B') @ (
% 108.14/14.65 (
% 108.14/14.65 ('#B') @ (
% 108.14/14.65 =))) @
% 108.14/14.65 (
% 108.14/14.65 (
% 108.14/14.65 ('#C') @ binintersect)))))) @
% 108.14/14.65 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 108.14/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2920])).
% 108.14/14.65 thf(zip_derived_cl2946, plain,
% 108.14/14.65 (~ (((demorgan2a) =>
% 108.14/14.65 (((demorgan2b2) =>
% 108.14/14.65 (((demorgan2b) =>
% 108.14/14.65 (((demorgan2) =>
% 108.14/14.65 (((woz13rule0) =>
% 108.14/14.65 (((woz13rule1) =>
% 108.14/14.65 (((woz13rule2) =>
% 108.14/14.65 (((woz13rule3) =>
% 108.14/14.65 (((woz13rule4) =>
% 108.14/14.65 (((woz1_1) =>
% 108.14/14.65 (((woz1_2) =>
% 108.14/14.65 (((woz1_3) =>
% 108.14/14.65 (((woz1_4) =>
% 108.14/14.65 (((woz1_5) =>
% 108.14/14.65 (((breln1all2) =>
% 108.14/14.65 (((breln1SetBreln1) =>
% 108.14/14.65 (((choice2fnsingleton) =>
% 108.14/14.65 (((setOfPairsIsBReln1) =>
% 108.14/14.65 (((breln1all1) =>
% 108.14/14.65 (((subbreln1) =>
% 108.14/14.65 (((eqbreln1) =>
% 108.14/14.65 (((breln1invprop) =>
% 108.14/14.65 (((breln1invI) =>
% 108.14/14.65 (((breln1invE) =>
% 108.14/14.65 (((breln1compprop) =>
% 108.14/14.65 (((breln1compI) =>
% 108.14/14.65 (((breln1compE) =>
% 108.14/14.65 (((breln1compEex) =>
% 108.14/14.65 (((breln1unionprop) =>
% 108.14/14.65 (((breln1unionIL) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionIR) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionI) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionE) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionEcases) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionCommutes) =>
% 108.14/14.65 ((
% 108.14/14.65 (woz2Ex) =>
% 108.14/14.65 ((
% 108.14/14.65 (woz2W) =>
% 108.14/14.65 ((
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% 108.14/14.65 ((
% 108.14/14.65 (woz2B) =>
% 108.14/14.65 ((
% 108.14/14.65 (image1Ex) =>
% 108.14/14.65 ((
% 108.14/14.65 (image1Ex1) =>
% 108.14/14.65 ((
% 108.14/14.65 (image1Equiv) =>
% 108.14/14.65 ((
% 108.14/14.65 (image1E) =>
% 108.14/14.65 ((
% 108.14/14.65 (image1I) =>
% 108.14/14.65 ((
% 108.14/14.65 (injFuncInInjFuncSet) =>
% 108.14/14.65 ((
% 108.14/14.65 (injFuncSetFuncIn) =>
% 108.14/14.65 ((
% 108.14/14.65 (injFuncSetFuncInj) =>
% 108.14/14.65 ((
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% 108.14/14.65 ((
% 108.14/14.65 (surjFuncSetFuncSurj) =>
% 108.14/14.65 ((
% 108.14/14.65 (leftInvIsSurj) =>
% 108.14/14.65 ((
% 108.14/14.65 (surjCantorThm) =>
% 108.14/14.65 ((
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% 108.14/14.65 (('#S') @ (
% 108.14/14.65 (
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% 108.14/14.65 (
% 108.14/14.65 ('#S') @ (
% 108.14/14.65 (
% 108.14/14.65 ('#B') @ (
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% 108.14/14.65 (
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% 108.14/14.65 (
% 108.14/14.65 ('#B') @ (
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% 108.14/14.65 (
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% 108.14/14.65 (
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% 108.14/14.65 (
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% 108.14/14.65 (
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% 108.14/14.65 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 108.14/14.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2933])).
% 108.14/14.65 thf(zip_derived_cl2958, plain,
% 108.14/14.65 (~ (((demorgan2b2) =>
% 108.14/14.65 (((demorgan2b) =>
% 108.14/14.65 (((demorgan2) =>
% 108.14/14.65 (((woz13rule0) =>
% 108.14/14.65 (((woz13rule1) =>
% 108.14/14.65 (((woz13rule2) =>
% 108.14/14.65 (((woz13rule3) =>
% 108.14/14.65 (((woz13rule4) =>
% 108.14/14.65 (((woz1_1) =>
% 108.14/14.65 (((woz1_2) =>
% 108.14/14.65 (((woz1_3) =>
% 108.14/14.65 (((woz1_4) =>
% 108.14/14.65 (((woz1_5) =>
% 108.14/14.65 (((breln1all2) =>
% 108.14/14.65 (((breln1SetBreln1) =>
% 108.14/14.65 (((choice2fnsingleton) =>
% 108.14/14.65 (((setOfPairsIsBReln1) =>
% 108.14/14.65 (((breln1all1) =>
% 108.14/14.65 (((subbreln1) =>
% 108.14/14.65 (((eqbreln1) =>
% 108.14/14.65 (((breln1invprop) =>
% 108.14/14.65 (((breln1invI) =>
% 108.14/14.65 (((breln1invE) =>
% 108.14/14.65 (((breln1compprop) =>
% 108.14/14.65 (((breln1compI) =>
% 108.14/14.65 (((breln1compE) =>
% 108.14/14.65 (((breln1compEex) =>
% 108.14/14.65 (((breln1unionprop) =>
% 108.14/14.65 (((breln1unionIL) =>
% 108.14/14.65 (((breln1unionIR) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionI) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionE) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionEcases) =>
% 108.14/14.65 ((
% 108.14/14.65 (breln1unionCommutes) =>
% 108.14/14.65 ((
% 108.14/14.65 (woz2Ex) =>
% 108.14/14.65 ((
% 108.14/14.65 (woz2W) =>
% 108.14/14.65 ((
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% 108.14/14.65 ((
% 108.14/14.65 (woz2B) =>
% 108.14/14.65 ((
% 108.14/14.65 (image1Ex) =>
% 108.14/14.65 ((
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