%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU820^1 : TPTP v9.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.7lSARJU8zh true
% Computer : n006.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 Oct 2 04:56:39 PM UTC 2025
% Result : Theorem 130.98s 22.71s
% Output : Refutation 132.79s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14 % Problem : SEU820^1 : TPTP v9.2.0. Released v3.7.0.
% 0.07/0.15 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.7lSARJU8zh true
% 0.15/0.37 % Computer : n006.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Wed Oct 1 16:12:38 EDT 2025
% 0.15/0.37 % CPUTime :
% 0.15/0.37 % Running portfolio for 300 s
% 0.15/0.37 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.37 % Number of cores: 8
% 0.15/0.37 % Python version: Python 3.6.8
% 0.15/0.37 % Running in HO mode
% 0.56/0.70 % Total configuration time : 828
% 0.56/0.70 % Estimated wc time : 1656
% 0.56/0.70 % Estimated cpu time (8 cpus) : 207.0
% 0.58/0.77 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.58/0.77 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.59/0.78 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.59/0.79 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.59/0.79 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.59/0.82 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.59/0.86 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.59/0.91 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 0.60/1.03 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s
% 130.98/22.71 % Solved by lams/30_b.l.sh.
% 130.98/22.71 % done 398 iterations in 21.141s
% 130.98/22.71 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 130.98/22.71 % SZS output start Refutation
% 130.98/22.71 thf(setadjoinAx_type, type, setadjoinAx: $o).
% 130.98/22.71 thf(cartprodfstpairEq_type, type, cartprodfstpairEq: $o).
% 130.98/22.71 thf(notdexE_type, type, notdexE: $o).
% 130.98/22.71 thf(setunionAx_type, type, setunionAx: $o).
% 130.98/22.71 thf(setminusELneg_type, type, setminusELneg: $o).
% 130.98/22.71 thf(breln1unionEcases_type, type, breln1unionEcases: $o).
% 130.98/22.71 thf(omegaSp_type, type, omegaSp: $o).
% 130.98/22.71 thf(powersetE_type, type, powersetE: $o).
% 130.98/22.71 thf(woz1_1_type, type, woz1_1: $o).
% 130.98/22.71 thf('#sk290_type', type, '#sk290': $i > ($i > $o) > $i).
% 130.98/22.71 thf(omegaSAx_type, type, omegaSAx: $o).
% 130.98/22.71 thf(breln1unionI_type, type, breln1unionI: $o).
% 130.98/22.71 thf(complementSubsetComplementIntersect_type, type, complementSubsetComplementIntersect:
% 130.98/22.71 $o).
% 130.98/22.71 thf(surjCantorThm_type, type, surjCantorThm: $o).
% 130.98/22.71 thf(exuI1_type, type, exuI1: $o).
% 130.98/22.71 thf(exuI2_type, type, exuI2: $o).
% 130.98/22.71 thf(notequalI2_type, type, notequalI2: $o).
% 130.98/22.71 thf(kfstsingleton_type, type, kfstsingleton: $o).
% 130.98/22.71 thf(kpairiskpair_type, type, kpairiskpair: $o).
% 130.98/22.71 thf(upairsubunion_type, type, upairsubunion: $o).
% 130.98/22.71 thf(binunionTE_type, type, binunionTE: $o).
% 130.98/22.71 thf(binunionTEcontra_type, type, binunionTEcontra: $o).
% 130.98/22.71 thf(powerset__Cong_type, type, powerset__Cong: $o).
% 130.98/22.71 thf(ordinalTransSet1_type, type, ordinalTransSet1: $o).
% 130.98/22.71 thf(setukpairinjR2_type, type, setukpairinjR2: $o).
% 130.98/22.71 thf(singletonsuniq_type, type, singletonsuniq: $o).
% 130.98/22.71 thf(setminusILneg_type, type, setminusILneg: $o).
% 130.98/22.71 thf(wellorderingAx_type, type, wellorderingAx: $o).
% 130.98/22.71 thf(kpairsurjEq_type, type, kpairsurjEq: $o).
% 130.98/22.71 thf(funcextLem_type, type, funcextLem: $o).
% 130.98/22.71 thf(setadjoinSub2_type, type, setadjoinSub2: $o).
% 130.98/22.71 thf(binintersectSubset5_type, type, binintersectSubset5: $o).
% 130.98/22.71 thf(upairinpowunion_type, type, upairinpowunion: $o).
% 130.98/22.71 thf(eta1_type, type, eta1: $o).
% 130.98/22.71 thf(complementTnotintersectT_type, type, complementTnotintersectT: $o).
% 130.98/22.71 thf(setoftrueEq_type, type, setoftrueEq: $o).
% 130.98/22.71 thf(notinself_type, type, notinself: $o).
% 130.98/22.71 thf(apProp_type, type, apProp: $o).
% 130.98/22.71 thf(setextT_type, type, setextT: $o).
% 130.98/22.71 thf(inIntersectImpInIntersectUnions_type, type, inIntersectImpInIntersectUnions:
% 130.98/22.71 $o).
% 130.98/22.71 thf(emptyset__Cong_type, type, emptyset__Cong: $o).
% 130.98/22.71 thf(cartprodmempaircEq_type, type, cartprodmempaircEq: $o).
% 130.98/22.71 thf(breln1invprop_type, type, breln1invprop: $o).
% 130.98/22.71 thf(lamProp_type, type, lamProp: $o).
% 130.98/22.71 thf(dpsetconstrSub_type, type, dpsetconstrSub: $o).
% 130.98/22.71 thf(setunionTransitive_type, type, setunionTransitive: $o).
% 130.98/22.71 thf(ex1E1_type, type, ex1E1: $o).
% 130.98/22.71 thf(sepInPowerset_type, type, sepInPowerset: $o).
% 130.98/22.71 thf(setukpairIR_type, type, setukpairIR: $o).
% 130.98/22.71 thf(brelnall1_type, type, brelnall1: $o).
% 130.98/22.71 thf(binunionE_type, type, binunionE: $o).
% 130.98/22.71 thf(setext_type, type, setext: $o).
% 130.98/22.71 thf(complementTcontraSubset_type, type, complementTcontraSubset: $o).
% 130.98/22.71 thf(emptyinPowerset_type, type, emptyinPowerset: $o).
% 130.98/22.71 thf(binintersectTELcontra_type, type, binintersectTELcontra: $o).
% 130.98/22.71 thf('#sk134_type', type, '#sk134': $i > $i > $i).
% 130.98/22.71 thf(ubforcartprodlem1_type, type, ubforcartprodlem1: $o).
% 130.98/22.71 thf(iftrue_type, type, iftrue: $o).
% 130.98/22.71 thf(woz13rule4_type, type, woz13rule4: $o).
% 130.98/22.71 thf(descr__Cong_type, type, descr__Cong: $o).
% 130.98/22.71 thf(funcGraphProp2_type, type, funcGraphProp2: $o).
% 130.98/22.71 thf('#form1597_type', type, '#form1597': $i > $o).
% 130.98/22.71 thf(theprop_type, type, theprop: $o).
% 130.98/22.71 thf(image1I_type, type, image1I: $o).
% 130.98/22.71 thf(binintersectSubset1_type, type, binintersectSubset1: $o).
% 130.98/22.71 thf(in_type, type, in: $i > $i > $o).
% 130.98/22.71 thf(cartprodsndpairEq_type, type, cartprodsndpairEq: $o).
% 130.98/22.71 thf(quantDeMorgan1_type, type, quantDeMorgan1: $o).
% 130.98/22.71 thf(setukpairinjL2_type, type, setukpairinjL2: $o).
% 130.98/22.71 thf(demorgan1_type, type, demorgan1: $o).
% 130.98/22.71 thf(setadjoinIR_type, type, setadjoinIR: $o).
% 130.98/22.71 thf(complementInPowersetComplementIntersect_type, type, complementInPowersetComplementIntersect:
% 130.98/22.71 $o).
% 130.98/22.71 thf(inIntersectImpInUnion_type, type, inIntersectImpInUnion: $o).
% 130.98/22.71 thf(breln1SetBreln1_type, type, breln1SetBreln1: $o).
% 130.98/22.71 thf('#form1598_type', type, '#form1598': $i > $o).
% 130.98/22.71 thf(setadjoin__Cong_type, type, setadjoin__Cong: $o).
% 130.98/22.71 thf(ksndpairEq_type, type, ksndpairEq: $o).
% 130.98/22.71 thf(ex1I2_type, type, ex1I2: $o).
% 130.98/22.71 thf(foundation2_type, type, foundation2: $o).
% 130.98/22.71 thf(symdiffI2_type, type, symdiffI2: $o).
% 130.98/22.71 thf(ap2apEq2_type, type, ap2apEq2: $o).
% 130.98/22.71 thf(ifSingleton_type, type, ifSingleton: $o).
% 130.98/22.71 thf('#sk337_type', type, '#sk337': $i > ($i > $o) > $i).
% 130.98/22.71 thf(upairset2IR_type, type, upairset2IR: $o).
% 130.98/22.71 thf(iftrueProp1_type, type, iftrueProp1: $o).
% 130.98/22.71 thf(complementTI1_type, type, complementTI1: $o).
% 130.98/22.71 thf('#sk1599_type', type, '#sk1599': $i > $i).
% 130.98/22.71 thf(subsetE_type, type, subsetE: $o).
% 130.98/22.71 thf(wellorderedByIn_type, type, wellorderedByIn: $i > $o).
% 130.98/22.71 thf(prop2set2propI_type, type, prop2set2propI: $o).
% 130.98/22.71 thf(doubleComplementSub2_type, type, doubleComplementSub2: $o).
% 130.98/22.71 thf(complementUnionInPowersetComplement_type, type, complementUnionInPowersetComplement:
% 130.98/22.71 $o).
% 130.98/22.71 thf(iffalse_type, type, iffalse: $o).
% 130.98/22.71 thf(dsetconstrEL_type, type, dsetconstrEL: $o).
% 130.98/22.71 thf(setbeta_type, type, setbeta: $o).
% 130.98/22.71 thf(eqinunit_type, type, eqinunit: $o).
% 130.98/22.71 thf(upairsetIL_type, type, upairsetIL: $o).
% 130.98/22.71 thf(powersetI1_type, type, powersetI1: $o).
% 130.98/22.71 thf(cartprodfstin_type, type, cartprodfstin: $o).
% 130.98/22.71 thf(lamp_type, type, lamp: $o).
% 130.98/22.71 thf('#form172_type', type, '#form172': $i > $i > $o).
% 130.98/22.71 thf(iffalseProp1_type, type, iffalseProp1: $o).
% 130.98/22.71 thf(breln1invI_type, type, breln1invI: $o).
% 130.98/22.71 thf(binintersectSubset3_type, type, binintersectSubset3: $o).
% 130.98/22.71 thf(breln1unionE_type, type, breln1unionE: $o).
% 130.98/22.71 thf(ksndsingleton_type, type, ksndsingleton: $o).
% 130.98/22.71 thf(setminusIRneg_type, type, setminusIRneg: $o).
% 130.98/22.71 thf(lam2lamEq_type, type, lam2lamEq: $o).
% 130.98/22.71 thf(powersetAx_type, type, powersetAx: $o).
% 130.98/22.71 thf(woz2Ex_type, type, woz2Ex: $o).
% 130.98/22.71 thf(eta2_type, type, eta2: $o).
% 130.98/22.71 thf(binintersectSubset4_type, type, binintersectSubset4: $o).
% 130.98/22.71 thf(singletoninpowunion_type, type, singletoninpowunion: $o).
% 130.98/22.71 thf(image1Ex_type, type, image1Ex: $o).
% 130.98/22.71 thf(powersetI_type, type, powersetI: $o).
% 130.98/22.71 thf(cartprodmempair_type, type, cartprodmempair: $o).
% 130.98/22.71 thf(powersetTE1_type, type, powersetTE1: $o).
% 130.98/22.71 thf(upairsetIR_type, type, upairsetIR: $o).
% 130.98/22.71 thf(cartprodpairsurjEq_type, type, cartprodpairsurjEq: $o).
% 130.98/22.71 thf(lam2p_type, type, lam2p: $o).
% 130.98/22.71 thf(contraSubsetComplement_type, type, contraSubsetComplement: $o).
% 130.98/22.71 thf(doubleComplementSub1_type, type, doubleComplementSub1: $o).
% 130.98/22.71 thf(cartprodpairmemEL_type, type, cartprodpairmemEL: $o).
% 130.98/22.71 thf(setOfPairsIsBReln1_type, type, setOfPairsIsBReln1: $o).
% 130.98/22.71 thf(inCongP_type, type, inCongP: $o).
% 130.98/22.71 thf(setukpairinjR11_type, type, setukpairinjR11: $o).
% 130.98/22.71 thf(setadjoinSub_type, type, setadjoinSub: $o).
% 130.98/22.71 thf(exuE3e_type, type, exuE3e: $o).
% 130.98/22.71 thf(emptysetE_type, type, emptysetE: $o).
% 130.98/22.71 thf(woz13rule2_type, type, woz13rule2: $o).
% 130.98/22.71 thf(binintersectSubset2_type, type, binintersectSubset2: $o).
% 130.98/22.71 thf(peano0notS_type, type, peano0notS: $o).
% 130.98/22.71 thf(image1E_type, type, image1E: $o).
% 130.98/22.71 thf(setunionI_type, type, setunionI: $o).
% 130.98/22.71 thf(breln1unionIR_type, type, breln1unionIR: $o).
% 130.98/22.71 thf(binintersectTERcontra_type, type, binintersectTERcontra: $o).
% 130.98/22.71 thf(setunion__Cong_type, type, setunion__Cong: $o).
% 130.98/22.71 thf(injFuncSetFuncInj_type, type, injFuncSetFuncInj: $o).
% 130.98/22.71 thf(prop2setI_type, type, prop2setI: $o).
% 130.98/22.71 thf(nonemptyImpWitness_type, type, nonemptyImpWitness: $o).
% 130.98/22.71 thf(setminusER_type, type, setminusER: $o).
% 130.98/22.72 thf(peanoSinj_type, type, peanoSinj: $o).
% 130.98/22.72 thf(exuE2_type, type, exuE2: $o).
% 130.98/22.72 thf(woz1_2_type, type, woz1_2: $o).
% 130.98/22.72 thf(emptyset_type, type, emptyset: $i).
% 130.98/22.72 thf(setukpairinjR12_type, type, setukpairinjR12: $o).
% 130.98/22.72 thf(funcGraphProp1_type, type, funcGraphProp1: $o).
% 130.98/22.72 thf(powersetsubset_type, type, powersetsubset: $o).
% 130.98/22.72 thf(upairequniteq_type, type, upairequniteq: $o).
% 130.98/22.72 thf('#form1602_type', type, '#form1602': $o).
% 130.98/22.72 thf(dpsetconstrEL1_type, type, dpsetconstrEL1: $o).
% 130.98/22.72 thf(ordinal_type, type, ordinal: $i > $o).
% 130.98/22.72 thf(injFuncInInjFuncSet_type, type, injFuncInInjFuncSet: $o).
% 130.98/22.72 thf(subPowSU_type, type, subPowSU: $o).
% 130.98/22.72 thf(breln1compprop_type, type, breln1compprop: $o).
% 130.98/22.72 thf(woz2B_type, type, woz2B: $o).
% 130.98/22.72 thf(notequalI1_type, type, notequalI1: $o).
% 130.98/22.72 thf(demorgan2b_type, type, demorgan2b: $o).
% 130.98/22.72 thf(notinemptyset_type, type, notinemptyset: $o).
% 130.98/22.72 thf(nonemptyI1_type, type, nonemptyI1: $o).
% 130.98/22.72 thf(breln1unionIL_type, type, breln1unionIL: $o).
% 130.98/22.72 thf(subsetTrans_type, type, subsetTrans: $o).
% 130.98/22.72 thf(setukpairinjR_type, type, setukpairinjR: $o).
% 130.98/22.72 thf(infuncsetfunc_type, type, infuncsetfunc: $o).
% 130.98/22.72 thf(kpairp_type, type, kpairp: $o).
% 130.98/22.72 thf(setukpairinjR1_type, type, setukpairinjR1: $o).
% 130.98/22.72 thf(setminusI_type, type, setminusI: $o).
% 130.98/22.72 thf(notinself2_type, type, notinself2: $o).
% 130.98/22.72 thf(binunionIL_type, type, binunionIL: $o).
% 130.98/22.72 thf(setOfPairsIsBReln_type, type, setOfPairsIsBReln: $o).
% 130.98/22.72 thf(setukpairinjL1_type, type, setukpairinjL1: $o).
% 130.98/22.72 thf(setunionsingleton_type, type, setunionsingleton: $o).
% 130.98/22.72 thf(powersetTI1_type, type, powersetTI1: $o).
% 130.98/22.72 thf(subsetE2_type, type, subsetE2: $o).
% 130.98/22.72 thf(image1Ex1_type, type, image1Ex1: $o).
% 130.98/22.72 thf(singletonsswitch_type, type, singletonsswitch: $o).
% 130.98/22.72 thf(ubforcartprodlem3_type, type, ubforcartprodlem3: $o).
% 130.98/22.72 thf(setextsub_type, type, setextsub: $o).
% 130.98/22.72 thf('#form1607_type', type, '#form1607': $o).
% 130.98/22.72 thf(binunionLsub_type, type, binunionLsub: $o).
% 130.98/22.72 thf(contrasubsetT1_type, type, contrasubsetT1: $o).
% 130.98/22.72 thf(setunionsingleton1_type, type, setunionsingleton1: $o).
% 130.98/22.72 thf(breln1compE_type, type, breln1compE: $o).
% 130.98/22.72 thf(binintersect_type, type, binintersect: $i > $i > $i).
% 130.98/22.72 thf('#sk111_type', type, '#sk111': $i > $i > $i).
% 130.98/22.72 thf(emptysetsubset_type, type, emptysetsubset: $o).
% 130.98/22.72 thf(quantDeMorgan3_type, type, quantDeMorgan3: $o).
% 130.98/22.72 thf('#sk173_type', type, '#sk173': $i > $i > $i).
% 130.98/22.72 thf(dpsetconstrERa_type, type, dpsetconstrERa: $o).
% 130.98/22.72 thf(setunionE_type, type, setunionE: $o).
% 130.98/22.72 thf(setminusSubset1_type, type, setminusSubset1: $o).
% 130.98/22.72 thf(complementT_lem_type, type, complementT_lem: $o).
% 130.98/22.72 thf(binintersectT_lem_type, type, binintersectT_lem: $o).
% 130.98/22.72 thf(ordinalTransSet_type, type, ordinalTransSet: $o).
% 130.98/22.72 thf(emptyinunitempty_type, type, emptyinunitempty: $o).
% 130.98/22.72 thf(binunionIR_type, type, binunionIR: $o).
% 130.98/22.72 thf(injFuncSetFuncIn_type, type, injFuncSetFuncIn: $o).
% 130.98/22.72 thf(setadjoinE_type, type, setadjoinE: $o).
% 130.98/22.72 thf(doubleComplementEq_type, type, doubleComplementEq: $o).
% 130.98/22.72 thf(eqbreln1_type, type, eqbreln1: $o).
% 130.98/22.72 thf(cartprodpairmemER_type, type, cartprodpairmemER: $o).
% 130.98/22.72 thf(dpsetconstrER_type, type, dpsetconstrER: $o).
% 130.98/22.72 thf(leftInvIsSurj_type, type, leftInvIsSurj: $o).
% 130.98/22.72 thf(doubleComplementE1_type, type, doubleComplementE1: $o).
% 130.98/22.72 thf(setadjoinIL_type, type, setadjoinIL: $o).
% 130.98/22.72 thf(exuE1_type, type, exuE1: $o).
% 130.98/22.72 thf(ubforcartprodlem2_type, type, ubforcartprodlem2: $o).
% 130.98/22.72 thf(binintersectRsub_type, type, binintersectRsub: $o).
% 130.98/22.72 thf(setminusLsub_type, type, setminusLsub: $o).
% 130.98/22.72 thf(prop2set_type, type, prop2set: $o > $i).
% 130.98/22.72 thf(notinsingleton_type, type, notinsingleton: $o).
% 130.98/22.72 thf(intersectInPowersetIntersectUnions_type, type, intersectInPowersetIntersectUnions:
% 130.98/22.72 $o).
% 130.98/22.72 thf(dpsetconstrEL2_type, type, dpsetconstrEL2: $o).
% 130.98/22.72 thf(eqimpsubset2_type, type, eqimpsubset2: $o).
% 130.98/22.72 thf(exuEu_type, type, exuEu: $o).
% 130.98/22.72 thf(emptysetimpfalse_type, type, emptysetimpfalse: $o).
% 130.98/22.72 thf(upairsetE_type, type, upairsetE: $o).
% 130.98/22.72 thf(omega0Ax_type, type, omega0Ax: $o).
% 130.98/22.72 thf(breln1invE_type, type, breln1invE: $o).
% 130.98/22.72 thf(breln1unionCommutes_type, type, breln1unionCommutes: $o).
% 130.98/22.72 thf(funcGraphProp3_type, type, funcGraphProp3: $o).
% 130.98/22.72 thf(app_type, type, app: $o).
% 130.98/22.72 thf(transitiveset_type, type, transitiveset: $i > $o).
% 130.98/22.72 thf(funcImageSingleton_type, type, funcImageSingleton: $o).
% 130.98/22.72 thf(dpsetconstrI_type, type, dpsetconstrI: $o).
% 130.98/22.72 thf(notsubsetI_type, type, notsubsetI: $o).
% 130.98/22.72 thf(powersetT_lem_type, type, powersetT_lem: $o).
% 130.98/22.72 thf(binintTransitive_type, type, binintTransitive: $o).
% 130.98/22.72 thf(woz2W_type, type, woz2W: $o).
% 130.98/22.72 thf(iffalseProp2_type, type, iffalseProp2: $o).
% 130.98/22.72 thf(quantDeMorgan4_type, type, quantDeMorgan4: $o).
% 130.98/22.72 thf(setextAx_type, type, setextAx: $o).
% 130.98/22.72 thf(breln1all1_type, type, breln1all1: $o).
% 130.98/22.72 thf(setunionOrdinalLem1_type, type, setunionOrdinalLem1: $o).
% 130.98/22.72 thf(choice2fnsingleton_type, type, choice2fnsingleton: $o).
% 130.98/22.72 thf(breln1compI_type, type, breln1compI: $o).
% 130.98/22.72 thf(demorgan2a1_type, type, demorgan2a1: $o).
% 130.98/22.72 thf('#sk16_type', type, '#sk16': $i > $i).
% 130.98/22.72 thf(powersetE1_type, type, powersetE1: $o).
% 130.98/22.72 thf(bs114d_type, type, bs114d: $o).
% 130.98/22.72 thf(complementTE1_type, type, complementTE1: $o).
% 130.98/22.72 thf(noeltsimpempty_type, type, noeltsimpempty: $o).
% 130.98/22.72 thf(setunion_type, type, setunion: $i > $i).
% 130.98/22.72 thf(breln1all2_type, type, breln1all2: $o).
% 130.98/22.72 thf(contrasubsetT2_type, type, contrasubsetT2: $o).
% 130.98/22.72 thf(inIntersectImpInUnion2_type, type, inIntersectImpInUnion2: $o).
% 130.98/22.72 thf(demorgan2b2_type, type, demorgan2b2: $o).
% 130.98/22.72 thf(binintersectLsub_type, type, binintersectLsub: $o).
% 130.98/22.72 thf(subsetI1_type, type, subsetI1: $o).
% 130.98/22.72 thf(symdiffE_type, type, symdiffE: $o).
% 130.98/22.72 thf(woz13rule1_type, type, woz13rule1: $o).
% 130.98/22.72 thf(breln1unionprop_type, type, breln1unionprop: $o).
% 130.98/22.72 thf(descrp_type, type, descrp: $o).
% 130.98/22.72 thf(dsetconstr__Cong_type, type, dsetconstr__Cong: $o).
% 130.98/22.72 thf(foundationAx_type, type, foundationAx: $o).
% 130.98/22.72 thf(brelnall2_type, type, brelnall2: $o).
% 130.98/22.72 thf(emptysetAx_type, type, emptysetAx: $o).
% 130.98/22.72 thf(emptyI_type, type, emptyI: $o).
% 130.98/22.72 thf(setadjoinOr_type, type, setadjoinOr: $o).
% 130.98/22.72 thf(stricttotalorderedByIn_type, type, stricttotalorderedByIn: $i > $o).
% 130.98/22.72 thf(binintersectEL_type, type, binintersectEL: $o).
% 130.98/22.72 thf(emptyE1_type, type, emptyE1: $o).
% 130.98/22.72 thf(demorgan2a_type, type, demorgan2a: $o).
% 130.98/22.72 thf(woz1_3_type, type, woz1_3: $o).
% 130.98/22.72 thf(emptyInPowerset_type, type, emptyInPowerset: $o).
% 130.98/22.72 thf(vacuousDall_type, type, vacuousDall: $o).
% 130.98/22.72 thf(dsetconstrER_type, type, dsetconstrER: $o).
% 130.98/22.72 thf(demorgan1a_type, type, demorgan1a: $o).
% 130.98/22.72 thf(ifp_type, type, ifp: $o).
% 130.98/22.72 thf(binintersectI_type, type, binintersectI: $o).
% 130.98/22.72 thf(beta1_type, type, beta1: $o).
% 130.98/22.72 thf(funcext2_type, type, funcext2: $o).
% 130.98/22.72 thf(subbreln_type, type, subbreln: $o).
% 130.98/22.72 thf('#sk218_type', type, '#sk218': ($i > $o) > $i).
% 130.98/22.72 thf(cartprodpairin_type, type, cartprodpairin: $o).
% 130.98/22.72 thf(ordinalMinLem1_type, type, ordinalMinLem1: $o).
% 130.98/22.72 thf('#sk1603_type', type, '#sk1603': $i).
% 130.98/22.72 thf('#sk1600_type', type, '#sk1600': $i).
% 130.98/22.72 thf(cartprodmempair1_type, type, cartprodmempair1: $o).
% 130.98/22.72 thf(subbreln1_type, type, subbreln1: $o).
% 130.98/22.72 thf(demorgan2a2_type, type, demorgan2a2: $o).
% 130.98/22.72 thf(image1Equiv_type, type, image1Equiv: $o).
% 130.98/22.72 thf(subsetTI_type, type, subsetTI: $o).
% 130.98/22.72 thf(setminusT_lem_type, type, setminusT_lem: $o).
% 130.98/22.72 thf(ap2p_type, type, ap2p: $o).
% 130.98/22.72 thf(doubleComplementI1_type, type, doubleComplementI1: $o).
% 130.98/22.72 thf(binunionT_lem_type, type, binunionT_lem: $o).
% 130.98/22.72 thf(symdiffI1_type, type, symdiffI1: $o).
% 130.98/22.72 thf(woz1_4_type, type, woz1_4: $o).
% 130.98/22.72 thf('#sk256_type', type, '#sk256': $i > $i > $o > $i).
% 130.98/22.72 thf(kfstpairEq_type, type, kfstpairEq: $o).
% 130.98/22.72 thf(subsetI2_type, type, subsetI2: $o).
% 130.98/22.72 thf(symdiffIneg1_type, type, symdiffIneg1: $o).
% 130.98/22.72 thf(theeq_type, type, theeq: $o).
% 130.98/22.72 thf(setminusERneg_type, type, setminusERneg: $o).
% 130.98/22.72 thf(symdiffIneg2_type, type, symdiffIneg2: $o).
% 130.98/22.72 thf(binunionTIRcontra_type, type, binunionTIRcontra: $o).
% 130.98/22.72 thf(omega__Cong_type, type, omega__Cong: $o).
% 130.98/22.72 thf(demorgan1b_type, type, demorgan1b: $o).
% 130.98/22.72 thf(subsetRefl_type, type, subsetRefl: $o).
% 130.98/22.72 thf(uniqinunit_type, type, uniqinunit: $o).
% 130.98/22.72 thf(eqbreln_type, type, eqbreln: $o).
% 130.98/22.72 thf(inComplementUnionImpNotIn1_type, type, inComplementUnionImpNotIn1: $o).
% 130.98/22.72 thf(funcinfuncset_type, type, funcinfuncset: $o).
% 130.98/22.72 thf(breln1compEex_type, type, breln1compEex: $o).
% 130.98/22.72 thf(contrasubsetT_type, type, contrasubsetT: $o).
% 130.98/22.72 thf(setminusSubset2_type, type, setminusSubset2: $o).
% 130.98/22.72 thf(prop2setE_type, type, prop2setE: $o).
% 130.98/22.72 thf(omegaSclos_type, type, omegaSclos: $o).
% 130.98/22.72 thf(binunionEcases_type, type, binunionEcases: $o).
% 130.98/22.72 thf(omega_type, type, omega: $i).
% 130.98/22.72 thf(nonemptyI_type, type, nonemptyI: $o).
% 130.98/22.72 thf(disjointsetsI1_type, type, disjointsetsI1: $o).
% 130.98/22.72 thf(woz2A_type, type, woz2A: $o).
% 130.98/22.72 thf(transitivesetOp1_type, type, transitivesetOp1: $o).
% 130.98/22.72 thf(exuE3u_type, type, exuE3u: $o).
% 130.98/22.72 thf(setminusEL_type, type, setminusEL: $o).
% 130.98/22.72 thf(funcGraphProp4_type, type, funcGraphProp4: $o).
% 130.98/22.72 thf(woz1_5_type, type, woz1_5: $o).
% 130.98/22.72 thf(demorgan2_type, type, demorgan2: $o).
% 130.98/22.72 thf(setunionsingleton2_type, type, setunionsingleton2: $o).
% 130.98/22.72 thf(sepSubset_type, type, sepSubset: $o).
% 130.98/22.72 thf(inComplementUnionImpInComplement1_type, type, inComplementUnionImpInComplement1:
% 130.98/22.72 $o).
% 130.98/22.72 thf(transitivesetOp2_type, type, transitivesetOp2: $o).
% 130.98/22.72 thf(funcext_type, type, funcext: $o).
% 130.98/22.72 thf(surjFuncSetFuncSurj_type, type, surjFuncSetFuncSurj: $o).
% 130.98/22.72 thf(upairset2E_type, type, upairset2E: $o).
% 130.98/22.72 thf(eqimpsubset1_type, type, eqimpsubset1: $o).
% 130.98/22.72 thf(exuI3_type, type, exuI3: $o).
% 130.98/22.72 thf(notdallE_type, type, notdallE: $o).
% 130.98/22.72 thf(iftrueProp2_type, type, iftrueProp2: $o).
% 130.98/22.72 thf(binintersectER_type, type, binintersectER: $o).
% 130.98/22.72 thf(powerset_type, type, powerset: $i > $i).
% 130.98/22.72 thf(woz13rule0_type, type, woz13rule0: $o).
% 130.98/22.72 thf(dsetconstrI_type, type, dsetconstrI: $o).
% 130.98/22.72 thf(nonempty_type, type, nonempty: $i > $o).
% 130.98/22.72 thf(beta2_type, type, beta2: $o).
% 130.98/22.72 thf(setadjoin_type, type, setadjoin: $i > $i > $i).
% 130.98/22.72 thf(exu__Cong_type, type, exu__Cong: $o).
% 130.98/22.72 thf(cartprodsndin_type, type, cartprodsndin: $o).
% 130.98/22.72 thf(iftrueorfalse_type, type, iftrueorfalse: $o).
% 130.98/22.72 thf(surjFuncSetFuncIn_type, type, surjFuncSetFuncIn: $o).
% 130.98/22.72 thf(quantDeMorgan2_type, type, quantDeMorgan2: $o).
% 130.98/22.72 thf(ex1I_type, type, ex1I: $o).
% 130.98/22.72 thf(secondinupair_type, type, secondinupair: $o).
% 130.98/22.72 thf(singletonprop_type, type, singletonprop: $o).
% 130.98/22.72 thf(singletonsubset_type, type, singletonsubset: $o).
% 130.98/22.72 thf(singletoninpowerset_type, type, singletoninpowerset: $o).
% 130.98/22.72 thf(subsetemptysetimpeq_type, type, subsetemptysetimpeq: $o).
% 130.98/22.72 thf(ex1E2_type, type, ex1E2: $o).
% 130.98/22.72 thf(replAx_type, type, replAx: $o).
% 130.98/22.72 thf('#sk1571_type', type, '#sk1571': $i > $i).
% 130.98/22.72 thf(nonemptyE1_type, type, nonemptyE1: $o).
% 130.98/22.72 thf(omegaIndAx_type, type, omegaIndAx: $o).
% 130.98/22.72 thf(setukpairIL_type, type, setukpairIL: $o).
% 130.98/22.72 thf(setunionE2_type, type, setunionE2: $o).
% 130.98/22.72 thf(inPowerset_type, type, inPowerset: $o).
% 130.98/22.72 thf(binunionTILcontra_type, type, binunionTILcontra: $o).
% 130.98/22.72 thf(ap2apEq1_type, type, ap2apEq1: $o).
% 130.98/22.72 thf(contrasubsetT3_type, type, contrasubsetT3: $o).
% 130.98/22.72 thf(subset_type, type, subset: $i > $i > $o).
% 130.98/22.72 thf(woz13rule3_type, type, woz13rule3: $o).
% 130.98/22.72 thf(complementImpComplementIntersect_type, type, complementImpComplementIntersect:
% 130.98/22.72 $o).
% 130.98/22.72 thf(in__Cong_type, type, in__Cong: $o).
% 130.98/22.72 thf(setukpairinjL_type, type, setukpairinjL: $o).
% 130.98/22.72 thf(binunionRsub_type, type, binunionRsub: $o).
% 130.98/22.72 thf(subset2powerset_type, type, subset2powerset: $o).
% 130.98/22.72 thf(emptysetOrdinal, conjecture,
% 130.98/22.72 (( setextAx ) =>
% 130.98/22.72 ( ( emptysetAx ) =>
% 130.98/22.72 ( ( setadjoinAx ) =>
% 130.98/22.72 ( ( powersetAx ) =>
% 130.98/22.72 ( ( setunionAx ) =>
% 130.98/22.72 ( ( omega0Ax ) =>
% 130.98/22.72 ( ( omegaSAx ) =>
% 130.98/22.72 ( ( omegaIndAx ) =>
% 130.98/22.72 ( ( replAx ) =>
% 130.98/22.72 ( ( foundationAx ) =>
% 130.98/22.72 ( ( wellorderingAx ) =>
% 130.98/22.72 ( ( descrp ) =>
% 130.98/22.72 ( ( dsetconstrI ) =>
% 130.98/22.72 ( ( dsetconstrEL ) =>
% 130.98/22.72 ( ( dsetconstrER ) =>
% 130.98/22.72 ( ( exuE1 ) =>
% 130.98/22.72 ( ( prop2setE ) =>
% 130.98/22.72 ( ( emptysetE ) =>
% 130.98/22.72 ( ( emptysetimpfalse ) =>
% 130.98/22.72 ( ( notinemptyset ) =>
% 130.98/22.72 ( ( exuE3e ) =>
% 130.98/22.72 ( ( setext ) =>
% 130.98/22.72 ( ( emptyI ) =>
% 130.98/22.72 ( ( noeltsimpempty ) =>
% 130.98/22.72 ( ( setbeta ) =>
% 130.98/22.72 ( ( nonemptyE1 ) =>
% 130.98/22.72 ( ( nonemptyI ) =>
% 130.98/22.72 ( ( nonemptyI1 ) =>
% 130.98/22.72 ( ( setadjoinIL ) =>
% 130.98/22.72 ( ( emptyinunitempty ) =>
% 130.98/22.72 ( ( setadjoinIR ) =>
% 130.98/22.72 ( ( setadjoinE ) =>
% 130.98/22.72 ( (
% 130.98/22.72 setadjoinOr ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 setoftrueEq ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 powersetI ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 emptyinPowerset ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 emptyInPowerset ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 powersetE ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 setunionI ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 setunionE ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 subPowSU ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 exuE2 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 nonemptyImpWitness ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 uniqinunit ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 notinsingleton ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 eqinunit ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 singletonsswitch ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 upairsetE ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 upairsetIL ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 upairsetIR ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 emptyE1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 vacuousDall ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 quantDeMorgan1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 quantDeMorgan2 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 quantDeMorgan3 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 quantDeMorgan4 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 prop2setI ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 prop2set2propI ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 notdexE ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 notdallE ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 exuI1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 exuI3 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 exuI2 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 inCongP ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 in__Cong ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 exuE3u ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 exu__Cong ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 emptyset__Cong ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 setadjoin__Cong ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 powerset__Cong ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 setunion__Cong ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 omega__Cong ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 exuEu ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 descr__Cong ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 dsetconstr__Cong ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 subsetI1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 eqimpsubset2 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 eqimpsubset1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 subsetI2 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 emptysetsubset ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 subsetE ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 subsetE2 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 notsubsetI ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 notequalI1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 notequalI2 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 subsetRefl ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 subsetTrans ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 setadjoinSub ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 setadjoinSub2 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 subset2powerset ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 setextsub ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 subsetemptysetimpeq ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 powersetI1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 powersetE1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 inPowerset ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 powersetsubset ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 sepInPowerset ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 sepSubset ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 binunionIL ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 upairset2IR ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 binunionIR ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 binunionEcases ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 binunionE ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 binunionLsub ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 binunionRsub ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 binintersectI ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 binintersectSubset5 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 binintersectEL ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 binintersectLsub ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 binintersectSubset2 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 binintersectSubset3 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 binintersectER ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 disjointsetsI1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 binintersectRsub ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 binintersectSubset4 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 binintersectSubset1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 bs114d ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 setminusI ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 setminusEL ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 setminusER ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 setminusSubset2 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 setminusERneg ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 setminusELneg ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 setminusILneg ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 setminusIRneg ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 setminusLsub ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 setminusSubset1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 symdiffE ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 symdiffI1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 symdiffI2 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 symdiffIneg1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 symdiffIneg2 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 secondinupair ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 setukpairIL ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 setukpairIR ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 kpairiskpair ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 kpairp ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 singletonsubset ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 singletoninpowerset ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 singletoninpowunion ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 upairset2E ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 upairsubunion ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 upairinpowunion ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 ubforcartprodlem1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 ubforcartprodlem2 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 ubforcartprodlem3 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 cartprodpairin ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 cartprodmempair1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 cartprodmempair ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 setunionE2 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 setunionsingleton1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 setunionsingleton2 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 setunionsingleton ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 singletonprop ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 ex1E1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 ex1I ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 ex1I2 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 singletonsuniq ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 setukpairinjL1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 kfstsingleton ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 theprop ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 kfstpairEq ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 cartprodfstin ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 setukpairinjL2 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 setukpairinjL ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 setukpairinjR11 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 setukpairinjR12 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 setukpairinjR1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 upairequniteq ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 setukpairinjR2 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 setukpairinjR ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 ksndsingleton ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 ksndpairEq ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 kpairsurjEq ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 cartprodsndin ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 cartprodpairmemEL ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 cartprodpairmemER ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 cartprodmempaircEq ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 cartprodfstpairEq ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 cartprodsndpairEq ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 cartprodpairsurjEq ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 dpsetconstrI ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 dpsetconstrSub ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 setOfPairsIsBReln ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 dpsetconstrERa ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 dpsetconstrEL1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 dpsetconstrEL2 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 dpsetconstrER ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 funcImageSingleton ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 apProp ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 app ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 infuncsetfunc ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 ap2p ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 funcinfuncset ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 lamProp ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 lamp ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 lam2p ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 brelnall1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 brelnall2 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 ex1E2 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 funcGraphProp1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 funcGraphProp3 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 funcGraphProp2 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 funcextLem ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 funcGraphProp4 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 subbreln ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 eqbreln ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 funcext ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 funcext2 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 ap2apEq1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 ap2apEq2 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 beta1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 eta1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 lam2lamEq ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 beta2 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 eta2 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 iffalseProp1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 iffalseProp2 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 iftrueProp1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 iftrueProp2 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 ifSingleton ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 ifp ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 theeq ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 iftrue ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 iffalse ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 iftrueorfalse ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 binintersectT_lem ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 binunionT_lem ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 powersetT_lem ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 setminusT_lem ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 complementT_lem ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 setextT ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 subsetTI ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 powersetTI1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 powersetTE1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 complementTI1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 complementTE1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 binintersectTELcontra ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 binintersectTERcontra ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 contrasubsetT ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 contrasubsetT1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 contrasubsetT2 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 contrasubsetT3 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 doubleComplementI1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 doubleComplementE1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 doubleComplementSub1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 doubleComplementSub2 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 doubleComplementEq ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 complementTnotintersectT ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 complementImpComplementIntersect ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 complementSubsetComplementIntersect ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 complementInPowersetComplementIntersect ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 contraSubsetComplement ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 complementTcontraSubset ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 binunionTILcontra ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 binunionTIRcontra ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 inIntersectImpInUnion ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 inIntersectImpInUnion2 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 inIntersectImpInIntersectUnions ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 intersectInPowersetIntersectUnions ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 inComplementUnionImpNotIn1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 inComplementUnionImpInComplement1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 binunionTE ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 binunionTEcontra ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 demorgan2a1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 complementUnionInPowersetComplement ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 demorgan2a2 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 demorgan1a ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 demorgan1b ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 demorgan1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 demorgan2a ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 demorgan2b2 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 demorgan2b ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 demorgan2 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 woz13rule0 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 woz13rule1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 woz13rule2 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 woz13rule3 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 woz13rule4 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 woz1_1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 woz1_2 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 woz1_3 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 woz1_4 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 woz1_5 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 breln1all2 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 breln1SetBreln1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 choice2fnsingleton ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 setOfPairsIsBReln1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 breln1all1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 subbreln1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 eqbreln1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 breln1invprop ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 breln1invI ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 breln1invE ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 breln1compprop ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 breln1compI ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 breln1compE ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 breln1compEex ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 breln1unionprop ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 breln1unionIL ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 breln1unionIR ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 breln1unionI ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 breln1unionE ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 breln1unionEcases ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 breln1unionCommutes ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 woz2Ex ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 woz2W ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 woz2A ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 woz2B ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 image1Ex ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 image1Ex1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 image1Equiv ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 image1E ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 image1I ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 injFuncInInjFuncSet ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 injFuncSetFuncIn ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 injFuncSetFuncInj ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 surjFuncSetFuncIn ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 surjFuncSetFuncSurj ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 leftInvIsSurj ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 surjCantorThm ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 foundation2 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 notinself ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 notinself2 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 omegaSp ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 omegaSclos ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 peano0notS ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 peanoSinj ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 transitivesetOp1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 binintTransitive ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 transitivesetOp2 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 setunionTransitive ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 ordinalMinLem1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 ordinalTransSet ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 ordinalTransSet1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 setunionOrdinalLem1 ) =>
% 130.98/22.72 (
% 130.98/22.72 ordinal @
% 130.98/22.72 emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 130.98/22.72 thf(zf_stmt_0, negated_conjecture,
% 130.98/22.72 (~( ( setextAx ) =>
% 130.98/22.72 ( ( emptysetAx ) =>
% 130.98/22.72 ( ( setadjoinAx ) =>
% 130.98/22.72 ( ( powersetAx ) =>
% 130.98/22.72 ( ( setunionAx ) =>
% 130.98/22.72 ( ( omega0Ax ) =>
% 130.98/22.72 ( ( omegaSAx ) =>
% 130.98/22.72 ( ( omegaIndAx ) =>
% 130.98/22.72 ( ( replAx ) =>
% 130.98/22.72 ( ( foundationAx ) =>
% 130.98/22.72 ( ( wellorderingAx ) =>
% 130.98/22.72 ( ( descrp ) =>
% 130.98/22.72 ( ( dsetconstrI ) =>
% 130.98/22.72 ( ( dsetconstrEL ) =>
% 130.98/22.72 ( ( dsetconstrER ) =>
% 130.98/22.72 ( ( exuE1 ) =>
% 130.98/22.72 ( ( prop2setE ) =>
% 130.98/22.72 ( ( emptysetE ) =>
% 130.98/22.72 ( ( emptysetimpfalse ) =>
% 130.98/22.72 ( ( notinemptyset ) =>
% 130.98/22.72 ( ( exuE3e ) =>
% 130.98/22.72 ( ( setext ) =>
% 130.98/22.72 ( ( emptyI ) =>
% 130.98/22.72 ( ( noeltsimpempty ) =>
% 130.98/22.72 ( ( setbeta ) =>
% 130.98/22.72 ( ( nonemptyE1 ) =>
% 130.98/22.72 ( ( nonemptyI ) =>
% 130.98/22.72 ( ( nonemptyI1 ) =>
% 130.98/22.72 ( ( setadjoinIL ) =>
% 130.98/22.72 ( ( emptyinunitempty ) =>
% 130.98/22.72 ( ( setadjoinIR ) =>
% 130.98/22.72 ( (
% 130.98/22.72 setadjoinE ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 setadjoinOr ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 setoftrueEq ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 powersetI ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 emptyinPowerset ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 emptyInPowerset ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 powersetE ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 setunionI ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 setunionE ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 subPowSU ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 exuE2 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 nonemptyImpWitness ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 uniqinunit ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 notinsingleton ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 eqinunit ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 singletonsswitch ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 upairsetE ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 upairsetIL ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 upairsetIR ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 emptyE1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 vacuousDall ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 quantDeMorgan1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 quantDeMorgan2 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 quantDeMorgan3 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 quantDeMorgan4 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 prop2setI ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 prop2set2propI ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 notdexE ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 notdallE ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 exuI1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 exuI3 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 exuI2 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 inCongP ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 in__Cong ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 exuE3u ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 exu__Cong ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 emptyset__Cong ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 setadjoin__Cong ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 powerset__Cong ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 setunion__Cong ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 omega__Cong ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 exuEu ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 descr__Cong ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 dsetconstr__Cong ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 subsetI1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 eqimpsubset2 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 eqimpsubset1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 subsetI2 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 emptysetsubset ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 subsetE ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 subsetE2 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 notsubsetI ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 notequalI1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 notequalI2 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 subsetRefl ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 subsetTrans ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 setadjoinSub ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 setadjoinSub2 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 subset2powerset ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 setextsub ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 subsetemptysetimpeq ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 powersetI1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 powersetE1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 inPowerset ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 powersetsubset ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 sepInPowerset ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 sepSubset ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 binunionIL ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 upairset2IR ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 binunionIR ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 binunionEcases ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 binunionE ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 binunionLsub ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 binunionRsub ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 binintersectI ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 binintersectSubset5 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 binintersectEL ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 binintersectLsub ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 binintersectSubset2 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 binintersectSubset3 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 binintersectER ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 disjointsetsI1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 binintersectRsub ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 binintersectSubset4 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 binintersectSubset1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 bs114d ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 setminusI ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 setminusEL ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 setminusER ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 setminusSubset2 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 setminusERneg ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 setminusELneg ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 setminusILneg ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 setminusIRneg ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 setminusLsub ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 setminusSubset1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 symdiffE ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 symdiffI1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 symdiffI2 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 symdiffIneg1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 symdiffIneg2 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 secondinupair ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 setukpairIL ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 setukpairIR ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 kpairiskpair ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 kpairp ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 singletonsubset ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 singletoninpowerset ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 singletoninpowunion ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 upairset2E ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 upairsubunion ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 upairinpowunion ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 ubforcartprodlem1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 ubforcartprodlem2 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 ubforcartprodlem3 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 cartprodpairin ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 cartprodmempair1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 cartprodmempair ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 setunionE2 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 setunionsingleton1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 setunionsingleton2 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 setunionsingleton ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 singletonprop ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 ex1E1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 ex1I ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 ex1I2 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 singletonsuniq ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 setukpairinjL1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 kfstsingleton ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 theprop ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 kfstpairEq ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 cartprodfstin ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 setukpairinjL2 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 setukpairinjL ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 setukpairinjR11 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 setukpairinjR12 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 setukpairinjR1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 upairequniteq ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 setukpairinjR2 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 setukpairinjR ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 ksndsingleton ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 ksndpairEq ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 kpairsurjEq ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 cartprodsndin ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 cartprodpairmemEL ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 cartprodpairmemER ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 cartprodmempaircEq ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 cartprodfstpairEq ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 cartprodsndpairEq ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 cartprodpairsurjEq ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 dpsetconstrI ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 dpsetconstrSub ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 setOfPairsIsBReln ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 dpsetconstrERa ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 dpsetconstrEL1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 dpsetconstrEL2 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 dpsetconstrER ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 funcImageSingleton ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 apProp ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 app ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 infuncsetfunc ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 ap2p ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 funcinfuncset ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 lamProp ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 lamp ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 lam2p ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 brelnall1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 brelnall2 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 ex1E2 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 funcGraphProp1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 funcGraphProp3 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 funcGraphProp2 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 funcextLem ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 funcGraphProp4 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 subbreln ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 eqbreln ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 funcext ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 funcext2 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 ap2apEq1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 ap2apEq2 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 beta1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 eta1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 lam2lamEq ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 beta2 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 eta2 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 iffalseProp1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 iffalseProp2 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 iftrueProp1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 iftrueProp2 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 ifSingleton ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 ifp ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 theeq ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 iftrue ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 iffalse ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 iftrueorfalse ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 binintersectT_lem ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 binunionT_lem ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 powersetT_lem ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 setminusT_lem ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 complementT_lem ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 setextT ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 subsetTI ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 powersetTI1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 powersetTE1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 complementTI1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 complementTE1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 binintersectTELcontra ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 binintersectTERcontra ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 contrasubsetT ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 contrasubsetT1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 contrasubsetT2 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 contrasubsetT3 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 doubleComplementI1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 doubleComplementE1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 doubleComplementSub1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 doubleComplementSub2 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 doubleComplementEq ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 complementTnotintersectT ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 complementImpComplementIntersect ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 complementSubsetComplementIntersect ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 complementInPowersetComplementIntersect ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 contraSubsetComplement ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 complementTcontraSubset ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 binunionTILcontra ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 binunionTIRcontra ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 inIntersectImpInUnion ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 inIntersectImpInUnion2 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 inIntersectImpInIntersectUnions ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 intersectInPowersetIntersectUnions ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 inComplementUnionImpNotIn1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 inComplementUnionImpInComplement1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 binunionTE ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 binunionTEcontra ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 demorgan2a1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 complementUnionInPowersetComplement ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 demorgan2a2 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 demorgan1a ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 demorgan1b ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 demorgan1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 demorgan2a ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 demorgan2b2 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 demorgan2b ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 demorgan2 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 woz13rule0 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 woz13rule1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 woz13rule2 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 woz13rule3 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 woz13rule4 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 woz1_1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 woz1_2 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 woz1_3 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 woz1_4 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 woz1_5 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 breln1all2 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 breln1SetBreln1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 choice2fnsingleton ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 setOfPairsIsBReln1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 breln1all1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 subbreln1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 eqbreln1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 breln1invprop ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 breln1invI ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 breln1invE ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 breln1compprop ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 breln1compI ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 breln1compE ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 breln1compEex ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 breln1unionprop ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 breln1unionIL ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 breln1unionIR ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 breln1unionI ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 breln1unionE ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 breln1unionEcases ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 breln1unionCommutes ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 woz2Ex ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 woz2W ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 woz2A ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 woz2B ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 image1Ex ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 image1Ex1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 image1Equiv ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 image1E ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 image1I ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 injFuncInInjFuncSet ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 injFuncSetFuncIn ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 injFuncSetFuncInj ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 surjFuncSetFuncIn ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 surjFuncSetFuncSurj ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 leftInvIsSurj ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 surjCantorThm ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 foundation2 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 notinself ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 notinself2 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 omegaSp ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 omegaSclos ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 peano0notS ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 peanoSinj ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 transitivesetOp1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 binintTransitive ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 transitivesetOp2 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 setunionTransitive ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 ordinalMinLem1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 ordinalTransSet ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 ordinalTransSet1 ) =>
% 130.98/22.72 (
% 130.98/22.72 (
% 130.98/22.72 setunionOrdinalLem1 ) =>
% 130.98/22.72 (
% 130.98/22.72 ordinal @
% 130.98/22.72 emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )),
% 130.98/22.72 inference('cnf.neg', [status(esa)], [emptysetOrdinal])).
% 130.98/22.72 thf(zip_derived_cl0, plain,
% 130.98/22.72 (~ (((setextAx) =>
% 130.98/22.72 (((emptysetAx) =>
% 130.98/22.72 (((setadjoinAx) =>
% 130.98/22.72 (((powersetAx) =>
% 130.98/22.72 (((setunionAx) =>
% 130.98/22.72 (((omega0Ax) =>
% 130.98/22.72 (((omegaSAx) =>
% 130.98/22.72 (((omegaIndAx) =>
% 130.98/22.72 (((replAx) =>
% 130.98/22.72 (((foundationAx) =>
% 130.98/22.72 (((wellorderingAx) =>
% 130.98/22.72 (((descrp) =>
% 130.98/22.72 (((dsetconstrI) =>
% 130.98/22.72 (((dsetconstrEL) =>
% 130.98/22.72 (((dsetconstrER) =>
% 130.98/22.72 (((exuE1) =>
% 130.98/22.72 (((prop2setE) =>
% 130.98/22.72 (((emptysetE) =>
% 130.98/22.72 (((emptysetimpfalse) =>
% 130.98/22.72 (((notinemptyset) =>
% 130.98/22.72 (((exuE3e) =>
% 130.98/22.72 (((setext) =>
% 130.98/22.72 (((emptyI) =>
% 130.98/22.72 (((noeltsimpempty) =>
% 130.98/22.72 (((setbeta) =>
% 130.98/22.72 (((nonemptyE1) =>
% 130.98/22.72 (((nonemptyI) =>
% 130.98/22.72 (((nonemptyI1) =>
% 130.98/22.72 (((setadjoinIL) =>
% 130.98/22.72 (((emptyinunitempty) =>
% 130.98/22.72 ((
% 130.98/22.72 (setadjoinIR) =>
% 130.98/22.72 ((
% 130.98/22.72 (setadjoinE) =>
% 130.98/22.72 ((
% 130.98/22.72 (setadjoinOr) =>
% 130.98/22.72 ((
% 130.98/22.72 (setoftrueEq) =>
% 130.98/22.72 ((
% 130.98/22.72 (powersetI) =>
% 130.98/22.72 ((
% 130.98/22.72 (emptyinPowerset) =>
% 130.98/22.72 ((
% 130.98/22.72 (emptyInPowerset) =>
% 130.98/22.72 ((
% 130.98/22.72 (powersetE) =>
% 130.98/22.72 ((
% 130.98/22.72 (setunionI) =>
% 130.98/22.72 ((
% 130.98/22.72 (setunionE) =>
% 130.98/22.72 ((
% 130.98/22.72 (subPowSU) =>
% 130.98/22.72 ((
% 130.98/22.72 (exuE2) =>
% 130.98/22.72 ((
% 130.98/22.72 (nonemptyImpWitness) =>
% 130.98/22.72 ((
% 130.98/22.72 (uniqinunit) =>
% 130.98/22.72 ((
% 130.98/22.72 (notinsingleton) =>
% 130.98/22.72 ((
% 130.98/22.72 (eqinunit) =>
% 130.98/22.72 ((
% 130.98/22.72 (singletonsswitch) =>
% 130.98/22.72 ((
% 130.98/22.72 (upairsetE) =>
% 130.98/22.72 ((
% 130.98/22.72 (upairsetIL) =>
% 130.98/22.72 ((
% 130.98/22.72 (upairsetIR) =>
% 130.98/22.72 ((
% 130.98/22.72 (emptyE1) =>
% 130.98/22.72 ((
% 130.98/22.72 (vacuousDall) =>
% 130.98/22.72 ((
% 130.98/22.72 (quantDeMorgan1) =>
% 130.98/22.72 ((
% 130.98/22.72 (quantDeMorgan2) =>
% 130.98/22.72 ((
% 130.98/22.72 (quantDeMorgan3) =>
% 130.98/22.72 ((
% 130.98/22.72 (quantDeMorgan4) =>
% 130.98/22.72 ((
% 130.98/22.72 (prop2setI) =>
% 130.98/22.72 ((
% 130.98/22.72 (prop2set2propI) =>
% 130.98/22.72 ((
% 130.98/22.72 (notdexE) =>
% 130.98/22.72 ((
% 130.98/22.72 (notdallE) =>
% 130.98/22.72 ((
% 130.98/22.72 (exuI1) =>
% 130.98/22.72 ((
% 130.98/22.72 (exuI3) =>
% 130.98/22.72 ((
% 130.98/22.72 (exuI2) =>
% 130.98/22.72 ((
% 130.98/22.72 (inCongP) =>
% 130.98/22.72 ((
% 130.98/22.72 (in__Cong) =>
% 130.98/22.72 ((
% 130.98/22.72 (exuE3u) =>
% 130.98/22.72 ((
% 130.98/22.72 (exu__Cong) =>
% 130.98/22.72 ((
% 130.98/22.72 (emptyset__Cong) =>
% 130.98/22.72 ((
% 130.98/22.72 (setadjoin__Cong) =>
% 130.98/22.72 ((
% 130.98/22.72 (powerset__Cong) =>
% 130.98/22.72 ((
% 130.98/22.72 (setunion__Cong) =>
% 130.98/22.72 ((
% 130.98/22.72 (omega__Cong) =>
% 130.98/22.72 ((
% 130.98/22.72 (exuEu) =>
% 130.98/22.72 ((
% 130.98/22.72 (descr__Cong) =>
% 130.98/22.72 ((
% 130.98/22.72 (dsetconstr__Cong) =>
% 130.98/22.72 ((
% 130.98/22.72 (subsetI1) =>
% 130.98/22.72 ((
% 130.98/22.72 (eqimpsubset2) =>
% 130.98/22.72 ((
% 130.98/22.72 (eqimpsubset1) =>
% 130.98/22.72 ((
% 130.98/22.72 (subsetI2) =>
% 130.98/22.72 ((
% 130.98/22.72 (emptysetsubset) =>
% 130.98/22.72 ((
% 130.98/22.72 (subsetE) =>
% 130.98/22.72 ((
% 130.98/22.72 (subsetE2) =>
% 130.98/22.72 ((
% 130.98/22.72 (notsubsetI) =>
% 130.98/22.72 ((
% 130.98/22.72 (notequalI1) =>
% 130.98/22.72 ((
% 130.98/22.72 (notequalI2) =>
% 130.98/22.72 ((
% 130.98/22.72 (subsetRefl) =>
% 130.98/22.72 ((
% 130.98/22.72 (subsetTrans) =>
% 130.98/22.72 ((
% 130.98/22.72 (setadjoinSub) =>
% 130.98/22.72 ((
% 130.98/22.72 (setadjoinSub2) =>
% 130.98/22.72 ((
% 130.98/22.72 (subset2powerset) =>
% 130.98/22.72 ((
% 130.98/22.72 (setextsub) =>
% 130.98/22.72 ((
% 130.98/22.72 (subsetemptysetimpeq) =>
% 130.98/22.72 ((
% 130.98/22.72 (powersetI1) =>
% 130.98/22.72 ((
% 130.98/22.72 (powersetE1) =>
% 130.98/22.72 ((
% 130.98/22.72 (inPowerset) =>
% 130.98/22.72 ((
% 130.98/22.72 (powersetsubset) =>
% 130.98/22.72 ((
% 130.98/22.72 (sepInPowerset) =>
% 130.98/22.72 ((
% 130.98/22.72 (sepSubset) =>
% 130.98/22.72 ((
% 130.98/22.72 (binunionIL) =>
% 130.98/22.72 ((
% 130.98/22.72 (upairset2IR) =>
% 130.98/22.72 ((
% 130.98/22.72 (binunionIR) =>
% 130.98/22.72 ((
% 130.98/22.72 (binunionEcases) =>
% 130.98/22.72 ((
% 130.98/22.72 (binunionE) =>
% 130.98/22.72 ((
% 130.98/22.72 (binunionLsub) =>
% 130.98/22.72 ((
% 130.98/22.72 (binunionRsub) =>
% 130.98/22.72 ((
% 130.98/22.72 (binintersectI) =>
% 130.98/22.72 ((
% 130.98/22.72 (binintersectSubset5) =>
% 130.98/22.72 ((
% 130.98/22.72 (binintersectEL) =>
% 130.98/22.72 ((
% 130.98/22.72 (binintersectLsub) =>
% 130.98/22.72 ((
% 130.98/22.72 (binintersectSubset2) =>
% 130.98/22.72 ((
% 130.98/22.72 (binintersectSubset3) =>
% 130.98/22.72 ((
% 130.98/22.72 (binintersectER) =>
% 130.98/22.72 ((
% 130.98/22.72 (disjointsetsI1) =>
% 130.98/22.72 ((
% 130.98/22.72 (binintersectRsub) =>
% 130.98/22.72 ((
% 130.98/22.72 (binintersectSubset4) =>
% 130.98/22.72 ((
% 130.98/22.72 (binintersectSubset1) =>
% 130.98/22.72 ((
% 130.98/22.72 (bs114d) =>
% 130.98/22.72 ((
% 130.98/22.72 (setminusI) =>
% 130.98/22.72 ((
% 130.98/22.72 (setminusEL) =>
% 130.98/22.72 ((
% 130.98/22.72 (setminusER) =>
% 130.98/22.72 ((
% 130.98/22.72 (setminusSubset2) =>
% 130.98/22.72 ((
% 130.98/22.72 (setminusERneg) =>
% 130.98/22.72 ((
% 130.98/22.72 (setminusELneg) =>
% 130.98/22.72 ((
% 130.98/22.72 (setminusILneg) =>
% 130.98/22.72 ((
% 130.98/22.72 (setminusIRneg) =>
% 130.98/22.72 ((
% 130.98/22.72 (setminusLsub) =>
% 130.98/22.72 ((
% 130.98/22.72 (setminusSubset1) =>
% 130.98/22.72 ((
% 130.98/22.72 (symdiffE) =>
% 130.98/22.72 ((
% 130.98/22.72 (symdiffI1) =>
% 130.98/22.72 ((
% 130.98/22.72 (symdiffI2) =>
% 130.98/22.72 ((
% 130.98/22.72 (symdiffIneg1) =>
% 130.98/22.72 ((
% 130.98/22.72 (symdiffIneg2) =>
% 130.98/22.72 ((
% 130.98/22.72 (secondinupair) =>
% 130.98/22.72 ((
% 130.98/22.72 (setukpairIL) =>
% 130.98/22.72 ((
% 130.98/22.72 (setukpairIR) =>
% 130.98/22.72 ((
% 130.98/22.72 (kpairiskpair) =>
% 130.98/22.72 ((
% 130.98/22.72 (kpairp) =>
% 130.98/22.72 ((
% 130.98/22.72 (singletonsubset) =>
% 130.98/22.72 ((
% 130.98/22.72 (singletoninpowerset) =>
% 130.98/22.72 ((
% 130.98/22.72 (singletoninpowunion) =>
% 130.98/22.72 ((
% 130.98/22.72 (upairset2E) =>
% 130.98/22.72 ((
% 130.98/22.72 (upairsubunion) =>
% 130.98/22.72 ((
% 130.98/22.72 (upairinpowunion) =>
% 130.98/22.72 ((
% 130.98/22.72 (ubforcartprodlem1) =>
% 130.98/22.72 ((
% 130.98/22.72 (ubforcartprodlem2) =>
% 130.98/22.72 ((
% 130.98/22.72 (ubforcartprodlem3) =>
% 130.98/22.72 ((
% 130.98/22.72 (cartprodpairin) =>
% 130.98/22.72 ((
% 130.98/22.72 (cartprodmempair1) =>
% 130.98/22.72 ((
% 130.98/22.72 (cartprodmempair) =>
% 130.98/22.72 ((
% 130.98/22.72 (setunionE2) =>
% 130.98/22.72 ((
% 130.98/22.72 (setunionsingleton1) =>
% 130.98/22.72 ((
% 130.98/22.72 (setunionsingleton2) =>
% 130.98/22.72 ((
% 130.98/22.72 (setunionsingleton) =>
% 130.98/22.72 ((
% 130.98/22.72 (singletonprop) =>
% 130.98/22.72 ((
% 130.98/22.72 (ex1E1) =>
% 130.98/22.72 ((
% 130.98/22.72 (ex1I) =>
% 130.98/22.72 ((
% 130.98/22.72 (ex1I2) =>
% 130.98/22.72 ((
% 130.98/22.72 (singletonsuniq) =>
% 130.98/22.72 ((
% 130.98/22.72 (setukpairinjL1) =>
% 130.98/22.72 ((
% 130.98/22.72 (kfstsingleton) =>
% 130.98/22.72 ((
% 130.98/22.72 (theprop) =>
% 130.98/22.72 ((
% 130.98/22.72 (kfstpairEq) =>
% 130.98/22.72 ((
% 130.98/22.72 (cartprodfstin) =>
% 130.98/22.72 ((
% 130.98/22.72 (setukpairinjL2) =>
% 130.98/22.72 ((
% 130.98/22.72 (setukpairinjL) =>
% 130.98/22.72 ((
% 130.98/22.72 (setukpairinjR11) =>
% 130.98/22.72 ((
% 130.98/22.72 (setukpairinjR12) =>
% 130.98/22.72 ((
% 130.98/22.72 (setukpairinjR1) =>
% 130.98/22.72 ((
% 130.98/22.72 (upairequniteq) =>
% 130.98/22.72 ((
% 130.98/22.72 (setukpairinjR2) =>
% 130.98/22.72 ((
% 130.98/22.72 (setukpairinjR) =>
% 130.98/22.72 ((
% 130.98/22.72 (ksndsingleton) =>
% 130.98/22.72 ((
% 130.98/22.72 (ksndpairEq) =>
% 130.98/22.72 ((
% 130.98/22.72 (kpairsurjEq) =>
% 130.98/22.72 ((
% 130.98/22.72 (cartprodsndin) =>
% 130.98/22.72 ((
% 130.98/22.72 (cartprodpairmemEL) =>
% 130.98/22.72 ((
% 130.98/22.72 (cartprodpairmemER) =>
% 130.98/22.72 ((
% 130.98/22.72 (cartprodmempaircEq) =>
% 130.98/22.72 ((
% 130.98/22.72 (cartprodfstpairEq) =>
% 130.98/22.72 ((
% 130.98/22.72 (cartprodsndpairEq) =>
% 130.98/22.72 ((
% 130.98/22.72 (cartprodpairsurjEq) =>
% 130.98/22.72 ((
% 130.98/22.72 (dpsetconstrI) =>
% 130.98/22.72 ((
% 130.98/22.72 (dpsetconstrSub) =>
% 130.98/22.72 ((
% 130.98/22.72 (setOfPairsIsBReln) =>
% 130.98/22.72 ((
% 130.98/22.72 (dpsetconstrERa) =>
% 130.98/22.72 ((
% 130.98/22.72 (dpsetconstrEL1) =>
% 130.98/22.72 ((
% 130.98/22.72 (dpsetconstrEL2) =>
% 130.98/22.72 ((
% 130.98/22.72 (dpsetconstrER) =>
% 130.98/22.72 ((
% 130.98/22.72 (funcImageSingleton) =>
% 130.98/22.72 ((
% 130.98/22.72 (apProp) =>
% 130.98/22.72 ((
% 130.98/22.72 (app) =>
% 130.98/22.72 ((
% 130.98/22.72 (infuncsetfunc) =>
% 130.98/22.72 ((
% 130.98/22.72 (ap2p) =>
% 130.98/22.72 ((
% 130.98/22.72 (funcinfuncset) =>
% 130.98/22.72 ((
% 130.98/22.72 (lamProp) =>
% 130.98/22.72 ((
% 130.98/22.72 (lamp) =>
% 130.98/22.72 ((
% 130.98/22.72 (lam2p) =>
% 130.98/22.72 ((
% 130.98/22.72 (brelnall1) =>
% 130.98/22.72 ((
% 130.98/22.72 (brelnall2) =>
% 130.98/22.72 ((
% 130.98/22.72 (ex1E2) =>
% 130.98/22.72 ((
% 130.98/22.72 (funcGraphProp1) =>
% 130.98/22.72 ((
% 130.98/22.72 (funcGraphProp3) =>
% 130.98/22.72 ((
% 130.98/22.72 (funcGraphProp2) =>
% 130.98/22.72 ((
% 130.98/22.72 (funcextLem) =>
% 130.98/22.72 ((
% 130.98/22.72 (funcGraphProp4) =>
% 130.98/22.72 ((
% 130.98/22.72 (subbreln) =>
% 130.98/22.72 ((
% 130.98/22.72 (eqbreln) =>
% 130.98/22.72 ((
% 130.98/22.72 (funcext) =>
% 130.98/22.72 ((
% 130.98/22.72 (funcext2) =>
% 130.98/22.72 ((
% 130.98/22.72 (ap2apEq1) =>
% 130.98/22.72 ((
% 130.98/22.72 (ap2apEq2) =>
% 130.98/22.72 ((
% 130.98/22.72 (beta1) =>
% 130.98/22.72 ((
% 130.98/22.72 (eta1) =>
% 130.98/22.72 ((
% 130.98/22.72 (lam2lamEq) =>
% 130.98/22.72 ((
% 130.98/22.72 (beta2) =>
% 130.98/22.72 ((
% 130.98/22.72 (eta2) =>
% 130.98/22.72 ((
% 130.98/22.72 (iffalseProp1) =>
% 130.98/22.72 ((
% 130.98/22.72 (iffalseProp2) =>
% 130.98/22.72 ((
% 130.98/22.72 (iftrueProp1) =>
% 130.98/22.72 ((
% 130.98/22.72 (iftrueProp2) =>
% 130.98/22.72 ((
% 130.98/22.72 (ifSingleton) =>
% 130.98/22.72 ((
% 130.98/22.72 (ifp) =>
% 130.98/22.72 ((
% 130.98/22.72 (theeq) =>
% 130.98/22.72 ((
% 130.98/22.72 (iftrue) =>
% 130.98/22.72 ((
% 130.98/22.72 (iffalse) =>
% 130.98/22.72 ((
% 130.98/22.72 (iftrueorfalse) =>
% 130.98/22.72 ((
% 130.98/22.72 (binintersectT_lem) =>
% 130.98/22.72 ((
% 130.98/22.72 (binunionT_lem) =>
% 130.98/22.72 ((
% 130.98/22.72 (powersetT_lem) =>
% 130.98/22.72 ((
% 130.98/22.72 (setminusT_lem) =>
% 130.98/22.72 ((
% 130.98/22.72 (complementT_lem) =>
% 130.98/22.72 ((
% 130.98/22.72 (setextT) =>
% 130.98/22.72 ((
% 130.98/22.72 (subsetTI) =>
% 130.98/22.72 ((
% 130.98/22.72 (powersetTI1) =>
% 130.98/22.72 ((
% 130.98/22.72 (powersetTE1) =>
% 130.98/22.72 ((
% 130.98/22.72 (complementTI1) =>
% 130.98/22.72 ((
% 130.98/22.72 (complementTE1) =>
% 130.98/22.72 ((
% 130.98/22.72 (binintersectTELcontra) =>
% 130.98/22.72 ((
% 130.98/22.72 (binintersectTERcontra) =>
% 130.98/22.72 ((
% 130.98/22.72 (contrasubsetT) =>
% 130.98/22.72 ((
% 130.98/22.72 (contrasubsetT1) =>
% 130.98/22.72 ((
% 130.98/22.72 (contrasubsetT2) =>
% 130.98/22.72 ((
% 130.98/22.72 (contrasubsetT3) =>
% 130.98/22.72 ((
% 130.98/22.72 (doubleComplementI1) =>
% 130.98/22.72 ((
% 130.98/22.72 (doubleComplementE1) =>
% 130.98/22.72 ((
% 130.98/22.72 (doubleComplementSub1) =>
% 130.98/22.72 ((
% 130.98/22.72 (doubleComplementSub2) =>
% 130.98/22.72 ((
% 130.98/22.72 (doubleComplementEq) =>
% 130.98/22.72 ((
% 130.98/22.72 (complementTnotintersectT) =>
% 130.98/22.72 ((
% 130.98/22.72 (complementImpComplementIntersect) =>
% 130.98/22.72 ((
% 130.98/22.72 (complementSubsetComplementIntersect) =>
% 130.98/22.72 ((
% 130.98/22.72 (complementInPowersetComplementIntersect) =>
% 130.98/22.72 ((
% 130.98/22.72 (contraSubsetComplement) =>
% 130.98/22.72 ((
% 130.98/22.72 (complementTcontraSubset) =>
% 130.98/22.72 ((
% 130.98/22.72 (binunionTILcontra) =>
% 130.98/22.72 ((
% 130.98/22.72 (binunionTIRcontra) =>
% 130.98/22.72 ((
% 130.98/22.72 (inIntersectImpInUnion) =>
% 130.98/22.72 ((
% 130.98/22.72 (inIntersectImpInUnion2) =>
% 130.98/22.72 ((
% 130.98/22.72 (inIntersectImpInIntersectUnions) =>
% 130.98/22.72 ((
% 130.98/22.72 (intersectInPowersetIntersectUnions) =>
% 130.98/22.72 ((
% 130.98/22.72 (inComplementUnionImpNotIn1) =>
% 130.98/22.72 ((
% 130.98/22.72 (inComplementUnionImpInComplement1) =>
% 130.98/22.72 ((
% 130.98/22.72 (binunionTE) =>
% 130.98/22.72 ((
% 130.98/22.72 (binunionTEcontra) =>
% 130.98/22.72 ((
% 130.98/22.72 (demorgan2a1) =>
% 130.98/22.72 ((
% 130.98/22.72 (complementUnionInPowersetComplement) =>
% 130.98/22.72 ((
% 130.98/22.72 (demorgan2a2) =>
% 130.98/22.72 ((
% 130.98/22.72 (demorgan1a) =>
% 130.98/22.72 ((
% 130.98/22.72 (demorgan1b) =>
% 130.98/22.72 ((
% 130.98/22.72 (demorgan1) =>
% 130.98/22.72 ((
% 130.98/22.72 (demorgan2a) =>
% 130.98/22.72 ((
% 130.98/22.72 (demorgan2b2) =>
% 130.98/22.72 ((
% 130.98/22.72 (demorgan2b) =>
% 130.98/22.72 ((
% 130.98/22.72 (demorgan2) =>
% 130.98/22.72 ((
% 130.98/22.72 (woz13rule0) =>
% 130.98/22.72 ((
% 130.98/22.72 (woz13rule1) =>
% 130.98/22.72 ((
% 130.98/22.72 (woz13rule2) =>
% 130.98/22.72 ((
% 130.98/22.72 (woz13rule3) =>
% 130.98/22.72 ((
% 130.98/22.72 (woz13rule4) =>
% 130.98/22.72 ((
% 130.98/22.72 (woz1_1) =>
% 130.98/22.72 ((
% 130.98/22.72 (woz1_2) =>
% 130.98/22.72 ((
% 130.98/22.72 (woz1_3) =>
% 130.98/22.72 ((
% 130.98/22.72 (woz1_4) =>
% 130.98/22.72 ((
% 130.98/22.72 (woz1_5) =>
% 130.98/22.72 ((
% 130.98/22.72 (breln1all2) =>
% 130.98/22.72 ((
% 130.98/22.72 (breln1SetBreln1) =>
% 130.98/22.72 ((
% 130.98/22.72 (choice2fnsingleton) =>
% 130.98/22.72 ((
% 130.98/22.72 (setOfPairsIsBReln1) =>
% 130.98/22.72 ((
% 130.98/22.72 (breln1all1) =>
% 130.98/22.72 ((
% 130.98/22.72 (subbreln1) =>
% 130.98/22.72 ((
% 130.98/22.72 (eqbreln1) =>
% 130.98/22.72 ((
% 130.98/22.72 (breln1invprop) =>
% 130.98/22.72 ((
% 130.98/22.72 (breln1invI) =>
% 130.98/22.72 ((
% 130.98/22.72 (breln1invE) =>
% 130.98/22.72 ((
% 130.98/22.72 (breln1compprop) =>
% 130.98/22.72 ((
% 130.98/22.72 (breln1compI) =>
% 130.98/22.72 ((
% 130.98/22.72 (breln1compE) =>
% 130.98/22.72 ((
% 130.98/22.72 (breln1compEex) =>
% 130.98/22.72 ((
% 130.98/22.72 (breln1unionprop) =>
% 130.98/22.72 ((
% 130.98/22.72 (breln1unionIL) =>
% 130.98/22.72 ((
% 130.98/22.72 (breln1unionIR) =>
% 130.98/22.72 ((
% 130.98/22.72 (breln1unionI) =>
% 130.98/22.72 ((
% 130.98/22.72 (breln1unionE) =>
% 130.98/22.72 ((
% 130.98/22.72 (breln1unionEcases) =>
% 130.98/22.72 ((
% 130.98/22.72 (breln1unionCommutes) =>
% 130.98/22.72 ((
% 130.98/22.72 (woz2Ex) =>
% 130.98/22.72 ((
% 130.98/22.72 (woz2W) =>
% 130.98/22.72 ((
% 130.98/22.72 (woz2A) =>
% 130.98/22.72 ((
% 130.98/22.72 (woz2B) =>
% 130.98/22.72 ((
% 130.98/22.72 (image1Ex) =>
% 130.98/22.72 ((
% 130.98/22.72 (image1Ex1) =>
% 130.98/22.72 ((
% 130.98/22.72 (image1Equiv) =>
% 130.98/22.72 ((
% 130.98/22.72 (image1E) =>
% 130.98/22.72 ((
% 130.98/22.72 (image1I) =>
% 130.98/22.72 ((
% 130.98/22.72 (injFuncInInjFuncSet) =>
% 130.98/22.72 ((
% 130.98/22.72 (injFuncSetFuncIn) =>
% 130.98/22.72 ((
% 130.98/22.72 (injFuncSetFuncInj) =>
% 130.98/22.72 ((
% 130.98/22.72 (surjFuncSetFuncIn) =>
% 130.98/22.72 ((
% 130.98/22.72 (surjFuncSetFuncSurj) =>
% 130.98/22.72 ((
% 130.98/22.72 (leftInvIsSurj) =>
% 130.98/22.72 ((
% 130.98/22.72 (surjCantorThm) =>
% 130.98/22.72 ((
% 130.98/22.72 (foundation2) =>
% 130.98/22.72 ((
% 130.98/22.72 (notinself) =>
% 130.98/22.72 ((
% 130.98/22.72 (notinself2) =>
% 130.98/22.72 ((
% 130.98/22.72 (omegaSp) =>
% 130.98/22.72 ((
% 130.98/22.72 (omegaSclos) =>
% 130.98/22.72 ((
% 130.98/22.72 (peano0notS) =>
% 130.98/22.72 ((
% 130.98/22.72 (peanoSinj) =>
% 130.98/22.72 ((
% 130.98/22.72 (transitivesetOp1) =>
% 130.98/22.72 ((
% 130.98/22.72 (binintTransitive) =>
% 130.98/22.72 ((
% 130.98/22.72 (transitivesetOp2) =>
% 130.98/22.72 ((
% 130.98/22.72 (setunionTransitive) =>
% 130.98/22.72 ((
% 130.98/22.72 (ordinalMinLem1) =>
% 130.98/22.72 ((
% 130.98/22.72 (ordinalTransSet) =>
% 130.98/22.72 ((
% 130.98/22.72 (ordinalTransSet1) =>
% 130.98/22.72 ((
% 130.98/22.72 (setunionOrdinalLem1) =>
% 130.98/22.72 (ordinal @
% 130.98/22.72 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 130.98/22.72 inference('cnf', [status(esa)], [zf_stmt_0])).
% 130.98/22.72 thf(omega0Ax, axiom,(( omega0Ax ) = ((in @ emptyset @ omega)))).
% 130.98/22.72 thf('0', plain, (( omega0Ax ) = ( in @ emptyset @ omega )),
% 130.98/22.72 define([status(thm)])).
% 130.98/22.72 thf(emptyinunitempty, axiom,(( emptyinunitempty ) =
% 130.98/22.72 ((in @ emptyset @ (setadjoin @ emptyset @ emptyset))))).
% 130.98/22.72 thf('1', plain,
% 130.98/22.72 (( emptyinunitempty ) =
% 130.98/22.72 ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )),
% 130.98/22.72 define([status(thm)])).
% 130.98/22.72 thf(emptyset__Cong, axiom,(( emptyset__Cong ) =
% 130.98/22.72 ((((emptyset) = (emptyset)))))).
% 130.98/22.72 thf('2', plain, (( emptyset__Cong ) = ( ( emptyset ) = ( emptyset ) )),
% 130.98/22.72 define([status(thm)])).
% 130.98/22.72 thf(omega__Cong, axiom,(( omega__Cong ) = ((((omega) = (omega)))))).
% 130.98/22.72 thf('3', plain, (( omega__Cong ) = ( ( omega ) = ( omega ) )),
% 130.98/22.72 define([status(thm)])).
% 130.98/22.72 thf(zip_derived_cl1, plain,
% 130.98/22.72 (~ (((setextAx) =>
% 130.98/22.72 (((emptysetAx) =>
% 130.98/22.72 (((setadjoinAx) =>
% 130.98/22.72 (((powersetAx) =>
% 130.98/22.72 (((setunionAx) =>
% 130.98/22.72 (((in @ emptyset @ omega) =>
% 130.98/22.72 (((omegaSAx) =>
% 130.98/22.72 (((omegaIndAx) =>
% 130.98/22.72 (((replAx) =>
% 130.98/22.72 (((foundationAx) =>
% 130.98/22.72 (((wellorderingAx) =>
% 130.98/22.72 (((descrp) =>
% 130.98/22.72 (((dsetconstrI) =>
% 130.98/22.72 (((dsetconstrEL) =>
% 130.98/22.72 (((dsetconstrER) =>
% 130.98/22.72 (((exuE1) =>
% 130.98/22.72 (((prop2setE) =>
% 130.98/22.72 (((emptysetE) =>
% 130.98/22.72 (((emptysetimpfalse) =>
% 130.98/22.72 (((notinemptyset) =>
% 130.98/22.72 (((exuE3e) =>
% 130.98/22.72 (((setext) =>
% 130.98/22.72 (((emptyI) =>
% 130.98/22.72 (((noeltsimpempty) =>
% 130.98/22.72 (((setbeta) =>
% 130.98/22.72 (((nonemptyE1) =>
% 130.98/22.72 (((nonemptyI) =>
% 130.98/22.72 (((nonemptyI1) =>
% 130.98/22.72 (((setadjoinIL) =>
% 130.98/22.72 (((in @
% 130.98/22.72 emptyset @
% 130.98/22.72 (setadjoin @
% 130.98/22.72 emptyset @
% 130.98/22.72 emptyset)) =>
% 130.98/22.72 ((
% 130.98/22.72 (setadjoinIR) =>
% 130.98/22.72 ((
% 130.98/22.72 (setadjoinE) =>
% 130.98/22.72 ((
% 130.98/22.72 (setadjoinOr) =>
% 130.98/22.72 ((
% 130.98/22.72 (setoftrueEq) =>
% 130.98/22.72 ((
% 130.98/22.72 (powersetI) =>
% 130.98/22.72 ((
% 130.98/22.72 (emptyinPowerset) =>
% 130.98/22.72 ((
% 130.98/22.72 (emptyInPowerset) =>
% 130.98/22.72 ((
% 130.98/22.72 (powersetE) =>
% 130.98/22.72 ((
% 130.98/22.72 (setunionI) =>
% 130.98/22.72 ((
% 130.98/22.72 (setunionE) =>
% 130.98/22.72 ((
% 130.98/22.72 (subPowSU) =>
% 130.98/22.72 ((
% 130.98/22.72 (exuE2) =>
% 130.98/22.72 ((
% 130.98/22.72 (nonemptyImpWitness) =>
% 130.98/22.72 ((
% 130.98/22.72 (uniqinunit) =>
% 130.98/22.72 ((
% 130.98/22.72 (notinsingleton) =>
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% 130.98/22.72 ((
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% 130.98/22.72 (woz1_4) =>
% 130.98/22.72 ((
% 130.98/22.72 (woz1_5) =>
% 130.98/22.72 ((
% 130.98/22.72 (breln1all2) =>
% 130.98/22.72 ((
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% 130.98/22.72 ((
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% 130.98/22.72 ((
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% 130.98/22.72 ((
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% 130.98/22.72 ((
% 130.98/22.72 (breln1invI) =>
% 130.98/22.72 ((
% 130.98/22.72 (breln1invE) =>
% 130.98/22.72 ((
% 130.98/22.72 (breln1compprop) =>
% 130.98/22.72 ((
% 130.98/22.72 (breln1compI) =>
% 130.98/22.72 ((
% 130.98/22.72 (breln1compE) =>
% 130.98/22.72 ((
% 130.98/22.72 (breln1compEex) =>
% 130.98/22.72 ((
% 130.98/22.72 (breln1unionprop) =>
% 130.98/22.72 ((
% 130.98/22.72 (breln1unionIL) =>
% 130.98/22.72 ((
% 130.98/22.72 (breln1unionIR) =>
% 130.98/22.72 ((
% 130.98/22.72 (breln1unionI) =>
% 130.98/22.72 ((
% 130.98/22.72 (breln1unionE) =>
% 130.98/22.72 ((
% 130.98/22.72 (breln1unionEcases) =>
% 130.98/22.72 ((
% 130.98/22.72 (breln1unionCommutes) =>
% 130.98/22.72 ((
% 130.98/22.72 (woz2Ex) =>
% 130.98/22.72 ((
% 130.98/22.72 (woz2W) =>
% 130.98/22.72 ((
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% 130.98/22.72 ((
% 130.98/22.72 (woz2B) =>
% 130.98/22.72 ((
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% 130.98/22.72 ((
% 130.98/22.72 (image1Ex1) =>
% 130.98/22.72 ((
% 130.98/22.72 (image1Equiv) =>
% 130.98/22.72 ((
% 130.98/22.72 (image1E) =>
% 130.98/22.72 ((
% 130.98/22.72 (image1I) =>
% 130.98/22.72 ((
% 130.98/22.72 (injFuncInInjFuncSet) =>
% 130.98/22.72 ((
% 130.98/22.72 (injFuncSetFuncIn) =>
% 130.98/22.72 ((
% 130.98/22.72 (injFuncSetFuncInj) =>
% 130.98/22.72 ((
% 130.98/22.72 (surjFuncSetFuncIn) =>
% 130.98/22.72 ((
% 130.98/22.72 (surjFuncSetFuncSurj) =>
% 130.98/22.72 ((
% 130.98/22.72 (leftInvIsSurj) =>
% 130.98/22.72 ((
% 130.98/22.72 (surjCantorThm) =>
% 130.98/22.72 ((
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% 130.98/22.72 ((
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% 130.98/22.72 ((
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% 130.98/22.72 ((
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% 130.98/22.72 ((
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% 130.98/22.72 ((
% 130.98/22.72 (peano0notS) =>
% 130.98/22.72 ((
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% 130.98/22.72 ((
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% 130.98/22.72 ((
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% 130.98/22.72 ((
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% 130.98/22.72 ((
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% 130.98/22.72 ((
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% 130.98/22.72 ((
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% 130.98/22.72 ((
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% 130.98/22.72 ((
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% 130.98/22.72 ((
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% 130.98/22.72 ((
% 130.98/22.72 (exu__Cong) =>
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% 130.98/22.72 ((
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% 130.98/22.72 ((
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% 130.98/22.72 ((
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% 130.98/22.72 ((
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% 130.98/22.72 ((
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% 130.98/22.72 ((
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% 130.98/22.72 ((
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% 130.98/22.72 ((
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% 130.98/22.72 ((
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% 130.98/22.72 ((
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% 130.98/22.72 ((
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% 130.98/22.72 ((
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% 130.98/22.72 ((
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% 130.98/22.72 ((
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% 130.98/22.72 ((
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% 130.98/22.72 ((
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% 130.98/22.72 ((
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% 130.98/22.72 ((
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% 130.98/22.72 (binintersectTERcontra) =>
% 130.98/22.72 ((
% 130.98/22.72 (contrasubsetT) =>
% 130.98/22.72 ((
% 130.98/22.72 (contrasubsetT1) =>
% 130.98/22.72 ((
% 130.98/22.72 (contrasubsetT2) =>
% 130.98/22.72 ((
% 130.98/22.72 (contrasubsetT3) =>
% 130.98/22.72 ((
% 130.98/22.72 (doubleComplementI1) =>
% 130.98/22.72 ((
% 130.98/22.72 (doubleComplementE1) =>
% 130.98/22.72 ((
% 130.98/22.72 (doubleComplementSub1) =>
% 130.98/22.72 ((
% 130.98/22.72 (doubleComplementSub2) =>
% 130.98/22.72 ((
% 130.98/22.72 (doubleComplementEq) =>
% 130.98/22.72 ((
% 130.98/22.72 (complementTnotintersectT) =>
% 130.98/22.72 ((
% 130.98/22.72 (complementImpComplementIntersect) =>
% 130.98/22.72 ((
% 130.98/22.72 (complementSubsetComplementIntersect) =>
% 130.98/22.72 ((
% 130.98/22.72 (complementInPowersetComplementIntersect) =>
% 130.98/22.72 ((
% 130.98/22.72 (contraSubsetComplement) =>
% 130.98/22.72 ((
% 130.98/22.72 (complementTcontraSubset) =>
% 130.98/22.72 ((
% 130.98/22.72 (binunionTILcontra) =>
% 130.98/22.72 ((
% 130.98/22.72 (binunionTIRcontra) =>
% 130.98/22.72 ((
% 130.98/22.72 (inIntersectImpInUnion) =>
% 130.98/22.72 ((
% 130.98/22.72 (inIntersectImpInUnion2) =>
% 130.98/22.72 ((
% 130.98/22.72 (inIntersectImpInIntersectUnions) =>
% 130.98/22.72 ((
% 130.98/22.72 (intersectInPowersetIntersectUnions) =>
% 130.98/22.72 ((
% 130.98/22.72 (inComplementUnionImpNotIn1) =>
% 130.98/22.72 ((
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% 130.98/22.72 ((
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% 130.98/22.72 ((
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% 130.98/22.72 ((
% 130.98/22.72 (demorgan2a1) =>
% 130.98/22.72 ((
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% 130.98/22.72 ((
% 130.98/22.72 (demorgan2a2) =>
% 130.98/22.72 ((
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% 130.98/22.72 ((
% 130.98/22.72 (demorgan1b) =>
% 130.98/22.72 ((
% 130.98/22.72 (demorgan1) =>
% 130.98/22.72 ((
% 130.98/22.72 (demorgan2a) =>
% 130.98/22.72 ((
% 130.98/22.72 (demorgan2b2) =>
% 130.98/22.72 ((
% 130.98/22.72 (demorgan2b) =>
% 130.98/22.72 ((
% 130.98/22.72 (demorgan2) =>
% 130.98/22.72 ((
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% 130.98/22.72 ((
% 130.98/22.72 (woz13rule1) =>
% 130.98/22.72 ((
% 130.98/22.72 (woz13rule2) =>
% 130.98/22.72 ((
% 130.98/22.72 (woz13rule3) =>
% 130.98/22.72 ((
% 130.98/22.72 (woz13rule4) =>
% 130.98/22.72 ((
% 130.98/22.72 (woz1_1) =>
% 130.98/22.72 ((
% 130.98/22.72 (woz1_2) =>
% 130.98/22.72 ((
% 130.98/22.72 (woz1_3) =>
% 130.98/22.72 ((
% 130.98/22.72 (woz1_4) =>
% 130.98/22.72 ((
% 130.98/22.72 (woz1_5) =>
% 130.98/22.72 ((
% 130.98/22.72 (breln1all2) =>
% 130.98/22.72 ((
% 130.98/22.72 (breln1SetBreln1) =>
% 130.98/22.72 ((
% 130.98/22.72 (choice2fnsingleton) =>
% 130.98/22.72 ((
% 130.98/22.72 (setOfPairsIsBReln1) =>
% 130.98/22.72 ((
% 130.98/22.72 (breln1all1) =>
% 130.98/22.72 ((
% 130.98/22.72 (subbreln1) =>
% 130.98/22.72 ((
% 130.98/22.72 (eqbreln1) =>
% 130.98/22.72 ((
% 130.98/22.72 (breln1invprop) =>
% 130.98/22.72 ((
% 130.98/22.72 (breln1invI) =>
% 130.98/22.72 ((
% 130.98/22.72 (breln1invE) =>
% 130.98/22.72 ((
% 130.98/22.72 (breln1compprop) =>
% 130.98/22.72 ((
% 130.98/22.72 (breln1compI) =>
% 130.98/22.72 ((
% 130.98/22.72 (breln1compE) =>
% 130.98/22.72 ((
% 130.98/22.72 (breln1compEex) =>
% 130.98/22.72 ((
% 130.98/22.72 (breln1unionprop) =>
% 130.98/22.72 ((
% 130.98/22.72 (breln1unionIL) =>
% 130.98/22.72 ((
% 130.98/22.72 (breln1unionIR) =>
% 130.98/22.72 ((
% 130.98/22.72 (breln1unionI) =>
% 130.98/22.72 ((
% 130.98/22.72 (breln1unionE) =>
% 130.98/22.72 ((
% 130.98/22.72 (breln1unionEcases) =>
% 130.98/22.72 ((
% 130.98/22.72 (breln1unionCommutes) =>
% 130.98/22.72 ((
% 130.98/22.72 (woz2Ex) =>
% 130.98/22.72 ((
% 130.98/22.72 (woz2W) =>
% 130.98/22.72 ((
% 130.98/22.72 (woz2A) =>
% 130.98/22.72 ((
% 130.98/22.72 (woz2B) =>
% 130.98/22.72 ((
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% 130.98/22.72 ((
% 130.98/22.72 (image1Ex1) =>
% 130.98/22.72 ((
% 130.98/22.72 (image1Equiv) =>
% 130.98/22.72 ((
% 130.98/22.72 (image1E) =>
% 130.98/22.72 ((
% 130.98/22.72 (image1I) =>
% 130.98/22.72 ((
% 130.98/22.72 (injFuncInInjFuncSet) =>
% 130.98/22.72 ((
% 130.98/22.72 (injFuncSetFuncIn) =>
% 130.98/22.72 ((
% 130.98/22.72 (injFuncSetFuncInj) =>
% 130.98/22.72 ((
% 130.98/22.72 (surjFuncSetFuncIn) =>
% 130.98/22.72 ((
% 130.98/22.72 (surjFuncSetFuncSurj) =>
% 130.98/22.72 ((
% 130.98/22.72 (leftInvIsSurj) =>
% 130.98/22.72 ((
% 130.98/22.72 (surjCantorThm) =>
% 130.98/22.72 ((
% 130.98/22.72 (foundation2) =>
% 130.98/22.72 ((
% 130.98/22.72 (notinself) =>
% 130.98/22.72 ((
% 130.98/22.72 (notinself2) =>
% 130.98/22.72 ((
% 130.98/22.72 (omegaSp) =>
% 130.98/22.72 ((
% 130.98/22.72 (omegaSclos) =>
% 130.98/22.72 ((
% 130.98/22.72 (peano0notS) =>
% 130.98/22.72 ((
% 130.98/22.72 (peanoSinj) =>
% 130.98/22.72 ((
% 130.98/22.72 (transitivesetOp1) =>
% 130.98/22.72 ((
% 130.98/22.72 (binintTransitive) =>
% 130.98/22.72 ((
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% 130.98/22.72 ((
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% 130.98/22.72 ((
% 130.98/22.72 (ordinalMinLem1) =>
% 130.98/22.72 ((
% 130.98/22.72 (ordinalTransSet) =>
% 130.98/22.72 ((
% 130.98/22.72 (ordinalTransSet1) =>
% 130.98/22.72 ((
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% 130.98/22.72 (ordinal @
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% 130.98/22.72 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2])).
% 130.98/22.72 thf(zip_derived_cl7, plain,
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% 130.98/22.72 (((replAx) =>
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% 130.98/22.72 ((
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% 130.98/22.72 ((
% 130.98/22.72 (emptyInPowerset) =>
% 130.98/22.72 ((
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% 130.98/22.72 ((
% 130.98/22.72 (setunionE) =>
% 130.98/22.72 ((
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% 130.98/22.72 ((
% 130.98/22.72 (exuE2) =>
% 130.98/22.72 ((
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% 130.98/22.72 ((
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% 130.98/22.72 ((
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% 130.98/22.72 ((
% 130.98/22.72 (eqinunit) =>
% 130.98/22.72 ((
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% 130.98/22.72 ((
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% 130.98/22.72 ((
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% 130.98/22.72 ((
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% 130.98/22.72 ((
% 130.98/22.72 (quantDeMorgan3) =>
% 130.98/22.72 ((
% 130.98/22.72 (quantDeMorgan4) =>
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% 130.98/22.72 ((
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% 130.98/22.72 ((
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% 130.98/22.72 ((
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% 130.98/22.72 ((
% 130.98/22.72 (exuI2) =>
% 130.98/22.72 ((
% 130.98/22.72 (inCongP) =>
% 130.98/22.72 ((
% 130.98/22.72 (in__Cong) =>
% 130.98/22.72 ((
% 130.98/22.72 (exuE3u) =>
% 130.98/22.72 ((
% 130.98/22.72 (exu__Cong) =>
% 130.98/22.72 ((
% 130.98/22.72 (setadjoin__Cong) =>
% 130.98/22.72 ((
% 130.98/22.72 (powerset__Cong) =>
% 130.98/22.72 ((
% 130.98/22.72 (setunion__Cong) =>
% 130.98/22.72 ((
% 130.98/22.72 (exuEu) =>
% 130.98/22.72 ((
% 130.98/22.72 (descr__Cong) =>
% 130.98/22.72 ((
% 130.98/22.72 (dsetconstr__Cong) =>
% 130.98/22.72 ((
% 130.98/22.72 (subsetI1) =>
% 130.98/22.72 ((
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% 130.98/22.72 ((
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% 130.98/22.72 ((
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% 130.98/22.72 ((
% 130.98/22.72 (subsetE2) =>
% 130.98/22.72 ((
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% 130.98/22.72 ((
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% 130.98/22.72 ((
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% 130.98/22.72 ((
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% 130.98/22.72 ((
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% 130.98/22.72 ((
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% 130.98/22.72 ((
% 130.98/22.72 (binunionRsub) =>
% 130.98/22.72 ((
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% 130.98/22.72 ((
% 130.98/22.72 (binintersectSubset5) =>
% 130.98/22.72 ((
% 130.98/22.72 (binintersectEL) =>
% 130.98/22.72 ((
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% 130.98/22.72 ((
% 130.98/22.72 (binintersectSubset2) =>
% 130.98/22.72 ((
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% 130.98/22.72 ((
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% 130.98/22.72 ((
% 130.98/22.72 (binintersectSubset1) =>
% 130.98/22.72 ((
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% 130.98/22.72 ((
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% 130.98/22.72 ((
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% 130.98/22.72 ((
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% 130.98/22.72 ((
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% 130.98/22.72 ((
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% 130.98/22.72 ((
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% 130.98/22.72 ((
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% 130.98/22.72 ((
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% 130.98/22.72 ((
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% 130.98/22.72 ((
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% 130.98/22.72 ((
% 130.98/22.72 (ap2p) =>
% 130.98/22.72 ((
% 130.98/22.72 (funcinfuncset) =>
% 130.98/22.72 ((
% 130.98/22.72 (lamProp) =>
% 130.98/22.72 ((
% 130.98/22.72 (lamp) =>
% 130.98/22.72 ((
% 130.98/22.72 (lam2p) =>
% 130.98/22.72 ((
% 130.98/22.72 (brelnall1) =>
% 130.98/22.72 ((
% 130.98/22.72 (brelnall2) =>
% 130.98/22.72 ((
% 130.98/22.72 (ex1E2) =>
% 130.98/22.72 ((
% 130.98/22.72 (funcGraphProp1) =>
% 130.98/22.72 ((
% 130.98/22.72 (funcGraphProp3) =>
% 130.98/22.72 ((
% 130.98/22.72 (funcGraphProp2) =>
% 130.98/22.72 ((
% 130.98/22.72 (funcextLem) =>
% 130.98/22.72 ((
% 130.98/22.72 (funcGraphProp4) =>
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% 130.98/22.72 ((
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% 130.98/22.72 ((
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% 130.98/22.72 ((
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% 130.98/22.72 ((
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% 130.98/22.72 ((
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% 130.98/22.72 ((
% 130.98/22.72 (binintersectTERcontra) =>
% 130.98/22.72 ((
% 130.98/22.72 (contrasubsetT) =>
% 130.98/22.72 ((
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% 130.98/22.72 ((
% 130.98/22.72 (contrasubsetT2) =>
% 130.98/22.72 ((
% 130.98/22.72 (contrasubsetT3) =>
% 130.98/22.72 ((
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% 130.98/22.72 ((
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% 130.98/22.72 ((
% 130.98/22.72 (doubleComplementSub2) =>
% 130.98/22.72 ((
% 130.98/22.72 (doubleComplementEq) =>
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% 130.98/22.72 ((
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% 130.98/22.72 ((
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% 130.98/22.72 ((
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% 130.98/22.72 ((
% 130.98/22.72 (binunionTIRcontra) =>
% 130.98/22.72 ((
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% 130.98/22.72 ((
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% 130.98/22.72 ((
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% 130.98/22.72 ((
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% 130.98/22.72 ((
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% 130.98/22.72 ((
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% 130.98/22.72 ((
% 130.98/22.72 (demorgan2a) =>
% 130.98/22.72 ((
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% 130.98/22.72 ((
% 130.98/22.72 (demorgan2b) =>
% 130.98/22.72 ((
% 130.98/22.72 (demorgan2) =>
% 130.98/22.72 ((
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% 130.98/22.72 ((
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% 130.98/22.72 ((
% 130.98/22.72 (woz13rule2) =>
% 130.98/22.72 ((
% 130.98/22.72 (woz13rule3) =>
% 130.98/22.72 ((
% 130.98/22.72 (woz13rule4) =>
% 130.98/22.72 ((
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% 130.98/22.72 ((
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% 130.98/22.72 ((
% 130.98/22.72 (woz1_3) =>
% 130.98/22.72 ((
% 130.98/22.72 (woz1_4) =>
% 130.98/22.72 ((
% 130.98/22.72 (woz1_5) =>
% 130.98/22.72 ((
% 130.98/22.72 (breln1all2) =>
% 130.98/22.72 ((
% 130.98/22.72 (breln1SetBreln1) =>
% 130.98/22.72 ((
% 130.98/22.72 (choice2fnsingleton) =>
% 130.98/22.72 ((
% 130.98/22.72 (setOfPairsIsBReln1) =>
% 130.98/22.72 ((
% 130.98/22.72 (breln1all1) =>
% 130.98/22.72 ((
% 130.98/22.72 (subbreln1) =>
% 130.98/22.72 ((
% 130.98/22.72 (eqbreln1) =>
% 130.98/22.72 ((
% 130.98/22.72 (breln1invprop) =>
% 130.98/22.72 ((
% 130.98/22.72 (breln1invI) =>
% 130.98/22.72 ((
% 130.98/22.72 (breln1invE) =>
% 130.98/22.72 ((
% 130.98/22.72 (breln1compprop) =>
% 130.98/22.72 ((
% 130.98/22.72 (breln1compI) =>
% 130.98/22.72 ((
% 130.98/22.72 (breln1compE) =>
% 130.98/22.72 ((
% 130.98/22.72 (breln1compEex) =>
% 130.98/22.72 ((
% 130.98/22.72 (breln1unionprop) =>
% 130.98/22.72 ((
% 130.98/22.72 (breln1unionIL) =>
% 130.98/22.72 ((
% 130.98/22.72 (breln1unionIR) =>
% 130.98/22.72 ((
% 130.98/22.72 (breln1unionI) =>
% 130.98/22.72 ((
% 130.98/22.72 (breln1unionE) =>
% 130.98/22.72 ((
% 130.98/22.72 (breln1unionEcases) =>
% 130.98/22.72 ((
% 130.98/22.72 (breln1unionCommutes) =>
% 130.98/22.72 ((
% 130.98/22.72 (woz2Ex) =>
% 130.98/22.72 ((
% 130.98/22.72 (woz2W) =>
% 130.98/22.72 ((
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% 130.98/22.72 ((
% 130.98/22.72 (woz2B) =>
% 130.98/22.72 ((
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% 130.98/22.72 ((
% 130.98/22.72 (image1Ex1) =>
% 130.98/22.72 ((
% 130.98/22.72 (image1Equiv) =>
% 130.98/22.72 ((
% 130.98/22.72 (image1E) =>
% 130.98/22.72 ((
% 130.98/22.72 (image1I) =>
% 130.98/22.72 ((
% 130.98/22.72 (injFuncInInjFuncSet) =>
% 130.98/22.72 ((
% 130.98/22.72 (injFuncSetFuncIn) =>
% 130.98/22.72 ((
% 130.98/22.72 (injFuncSetFuncInj) =>
% 130.98/22.72 ((
% 130.98/22.72 (surjFuncSetFuncIn) =>
% 130.98/22.72 ((
% 130.98/22.72 (surjFuncSetFuncSurj) =>
% 130.98/22.72 ((
% 130.98/22.72 (leftInvIsSurj) =>
% 130.98/22.72 ((
% 130.98/22.72 (surjCantorThm) =>
% 130.98/22.72 ((
% 130.98/22.72 (foundation2) =>
% 130.98/22.72 ((
% 130.98/22.72 (notinself) =>
% 130.98/22.72 ((
% 130.98/22.72 (notinself2) =>
% 130.98/22.72 ((
% 130.98/22.72 (omegaSp) =>
% 130.98/22.72 ((
% 130.98/22.72 (omegaSclos) =>
% 130.98/22.72 ((
% 130.98/22.72 (peano0notS) =>
% 130.98/22.72 ((
% 130.98/22.72 (peanoSinj) =>
% 130.98/22.72 ((
% 130.98/22.72 (transitivesetOp1) =>
% 130.98/22.72 ((
% 130.98/22.72 (binintTransitive) =>
% 130.98/22.72 ((
% 130.98/22.72 (transitivesetOp2) =>
% 130.98/22.72 ((
% 130.98/22.72 (setunionTransitive) =>
% 130.98/22.72 ((
% 130.98/22.72 (ordinalMinLem1) =>
% 130.98/22.72 ((
% 130.98/22.72 (ordinalTransSet) =>
% 130.98/22.72 ((
% 130.98/22.72 (ordinalTransSet1) =>
% 130.98/22.72 ((
% 130.98/22.72 (setunionOrdinalLem1) =>
% 130.98/22.72 (ordinal @
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% 130.98/22.72 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl4])).
% 130.98/22.72 thf(zip_derived_cl11, plain,
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% 130.98/22.73 ((
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% 130.98/22.73 ((
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% 130.98/22.73 ((
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% 130.98/22.73 ((
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% 130.98/22.73 ((
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% 130.98/22.73 ((
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% 130.98/22.73 ((
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% 130.98/22.73 ((
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% 130.98/22.73 ((
% 130.98/22.73 (exu__Cong) =>
% 130.98/22.73 ((
% 130.98/22.73 (setadjoin__Cong) =>
% 130.98/22.73 ((
% 130.98/22.73 (powerset__Cong) =>
% 130.98/22.73 ((
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% 130.98/22.73 ((
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% 130.98/22.73 ((
% 130.98/22.73 (descr__Cong) =>
% 130.98/22.73 ((
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% 130.98/22.73 ((
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% 130.98/22.73 ((
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% 130.98/22.73 ((
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% 130.98/22.73 ((
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% 130.98/22.73 ((
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% 130.98/22.73 ((
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% 130.98/22.73 ((
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% 130.98/22.73 (setunionE2) =>
% 130.98/22.73 ((
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% 130.98/22.73 (setunionsingleton2) =>
% 130.98/22.73 ((
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% 130.98/22.73 ((
% 130.98/22.73 (ex1I2) =>
% 130.98/22.73 ((
% 130.98/22.73 (singletonsuniq) =>
% 130.98/22.73 ((
% 130.98/22.73 (setukpairinjL1) =>
% 130.98/22.73 ((
% 130.98/22.73 (kfstsingleton) =>
% 130.98/22.73 ((
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% 130.98/22.73 ((
% 130.98/22.73 (kfstpairEq) =>
% 130.98/22.73 ((
% 130.98/22.73 (cartprodfstin) =>
% 130.98/22.73 ((
% 130.98/22.73 (setukpairinjL2) =>
% 130.98/22.73 ((
% 130.98/22.73 (setukpairinjL) =>
% 130.98/22.73 ((
% 130.98/22.73 (setukpairinjR11) =>
% 130.98/22.73 ((
% 130.98/22.73 (setukpairinjR12) =>
% 130.98/22.73 ((
% 130.98/22.73 (setukpairinjR1) =>
% 130.98/22.73 ((
% 130.98/22.73 (upairequniteq) =>
% 130.98/22.73 ((
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% 130.98/22.73 ((
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% 130.98/22.73 ((
% 130.98/22.73 (kpairsurjEq) =>
% 130.98/22.73 ((
% 130.98/22.73 (cartprodsndin) =>
% 130.98/22.73 ((
% 130.98/22.73 (cartprodpairmemEL) =>
% 130.98/22.73 ((
% 130.98/22.73 (cartprodpairmemER) =>
% 130.98/22.73 ((
% 130.98/22.73 (cartprodmempaircEq) =>
% 130.98/22.73 ((
% 130.98/22.73 (cartprodfstpairEq) =>
% 130.98/22.73 ((
% 130.98/22.73 (cartprodsndpairEq) =>
% 130.98/22.73 ((
% 130.98/22.73 (cartprodpairsurjEq) =>
% 130.98/22.73 ((
% 130.98/22.73 (dpsetconstrI) =>
% 130.98/22.73 ((
% 130.98/22.73 (dpsetconstrSub) =>
% 130.98/22.73 ((
% 130.98/22.73 (setOfPairsIsBReln) =>
% 130.98/22.73 ((
% 130.98/22.73 (dpsetconstrERa) =>
% 130.98/22.73 ((
% 130.98/22.73 (dpsetconstrEL1) =>
% 130.98/22.73 ((
% 130.98/22.73 (dpsetconstrEL2) =>
% 130.98/22.73 ((
% 130.98/22.73 (dpsetconstrER) =>
% 130.98/22.73 ((
% 130.98/22.73 (funcImageSingleton) =>
% 130.98/22.73 ((
% 130.98/22.73 (apProp) =>
% 130.98/22.73 ((
% 130.98/22.73 (app) =>
% 130.98/22.73 ((
% 130.98/22.73 (infuncsetfunc) =>
% 130.98/22.73 ((
% 130.98/22.73 (ap2p) =>
% 130.98/22.73 ((
% 130.98/22.73 (funcinfuncset) =>
% 130.98/22.73 ((
% 130.98/22.73 (lamProp) =>
% 130.98/22.73 ((
% 130.98/22.73 (lamp) =>
% 130.98/22.73 ((
% 130.98/22.73 (lam2p) =>
% 130.98/22.73 ((
% 130.98/22.73 (brelnall1) =>
% 130.98/22.73 ((
% 130.98/22.73 (brelnall2) =>
% 130.98/22.73 ((
% 130.98/22.73 (ex1E2) =>
% 130.98/22.73 ((
% 130.98/22.73 (funcGraphProp1) =>
% 130.98/22.73 ((
% 130.98/22.73 (funcGraphProp3) =>
% 130.98/22.73 ((
% 130.98/22.73 (funcGraphProp2) =>
% 130.98/22.73 ((
% 130.98/22.73 (funcextLem) =>
% 130.98/22.73 ((
% 130.98/22.73 (funcGraphProp4) =>
% 130.98/22.73 ((
% 130.98/22.73 (subbreln) =>
% 130.98/22.73 ((
% 130.98/22.73 (eqbreln) =>
% 130.98/22.73 ((
% 130.98/22.73 (funcext) =>
% 130.98/22.73 ((
% 130.98/22.73 (funcext2) =>
% 130.98/22.73 ((
% 130.98/22.73 (ap2apEq1) =>
% 130.98/22.73 ((
% 130.98/22.73 (ap2apEq2) =>
% 130.98/22.73 ((
% 130.98/22.73 (beta1) =>
% 130.98/22.73 ((
% 130.98/22.73 (eta1) =>
% 130.98/22.73 ((
% 130.98/22.73 (lam2lamEq) =>
% 130.98/22.73 ((
% 130.98/22.73 (beta2) =>
% 130.98/22.73 ((
% 130.98/22.73 (eta2) =>
% 130.98/22.73 ((
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% 130.98/22.73 ((
% 130.98/22.73 (iffalseProp2) =>
% 130.98/22.73 ((
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% 130.98/22.73 (iftrueProp2) =>
% 130.98/22.73 ((
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% 130.98/22.73 ((
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% 130.98/22.73 ((
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% 130.98/22.73 ((
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% 130.98/22.73 (powersetT_lem) =>
% 130.98/22.73 ((
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% 130.98/22.73 ((
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% 130.98/22.73 ((
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% 130.98/22.73 ((
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% 130.98/22.73 ((
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% 130.98/22.73 ((
% 130.98/22.73 (powersetTE1) =>
% 130.98/22.73 ((
% 130.98/22.73 (complementTI1) =>
% 130.98/22.73 ((
% 130.98/22.73 (complementTE1) =>
% 130.98/22.73 ((
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% 130.98/22.73 ((
% 130.98/22.73 (binintersectTERcontra) =>
% 130.98/22.73 ((
% 130.98/22.73 (contrasubsetT) =>
% 130.98/22.73 ((
% 130.98/22.73 (contrasubsetT1) =>
% 130.98/22.73 ((
% 130.98/22.73 (contrasubsetT2) =>
% 130.98/22.73 ((
% 130.98/22.73 (contrasubsetT3) =>
% 130.98/22.73 ((
% 130.98/22.73 (doubleComplementI1) =>
% 130.98/22.73 ((
% 130.98/22.73 (doubleComplementE1) =>
% 130.98/22.73 ((
% 130.98/22.73 (doubleComplementSub1) =>
% 130.98/22.73 ((
% 130.98/22.73 (doubleComplementSub2) =>
% 130.98/22.73 ((
% 130.98/22.73 (doubleComplementEq) =>
% 130.98/22.73 ((
% 130.98/22.73 (complementTnotintersectT) =>
% 130.98/22.73 ((
% 130.98/22.73 (complementImpComplementIntersect) =>
% 130.98/22.73 ((
% 130.98/22.73 (complementSubsetComplementIntersect) =>
% 130.98/22.73 ((
% 130.98/22.73 (complementInPowersetComplementIntersect) =>
% 130.98/22.73 ((
% 130.98/22.73 (contraSubsetComplement) =>
% 130.98/22.73 ((
% 130.98/22.73 (complementTcontraSubset) =>
% 130.98/22.73 ((
% 130.98/22.73 (binunionTILcontra) =>
% 130.98/22.73 ((
% 130.98/22.73 (binunionTIRcontra) =>
% 130.98/22.73 ((
% 130.98/22.73 (inIntersectImpInUnion) =>
% 130.98/22.73 ((
% 130.98/22.73 (inIntersectImpInUnion2) =>
% 130.98/22.73 ((
% 130.98/22.73 (inIntersectImpInIntersectUnions) =>
% 130.98/22.73 ((
% 130.98/22.73 (intersectInPowersetIntersectUnions) =>
% 130.98/22.73 ((
% 130.98/22.73 (inComplementUnionImpNotIn1) =>
% 130.98/22.73 ((
% 130.98/22.73 (inComplementUnionImpInComplement1) =>
% 130.98/22.73 ((
% 130.98/22.73 (binunionTE) =>
% 130.98/22.73 ((
% 130.98/22.73 (binunionTEcontra) =>
% 130.98/22.73 ((
% 130.98/22.73 (demorgan2a1) =>
% 130.98/22.73 ((
% 130.98/22.73 (complementUnionInPowersetComplement) =>
% 130.98/22.73 ((
% 130.98/22.73 (demorgan2a2) =>
% 130.98/22.73 ((
% 130.98/22.73 (demorgan1a) =>
% 130.98/22.73 ((
% 130.98/22.73 (demorgan1b) =>
% 130.98/22.73 ((
% 130.98/22.73 (demorgan1) =>
% 130.98/22.73 ((
% 130.98/22.73 (demorgan2a) =>
% 130.98/22.73 ((
% 130.98/22.73 (demorgan2b2) =>
% 130.98/22.73 ((
% 130.98/22.73 (demorgan2b) =>
% 130.98/22.73 ((
% 130.98/22.73 (demorgan2) =>
% 130.98/22.73 ((
% 130.98/22.73 (woz13rule0) =>
% 130.98/22.73 ((
% 130.98/22.73 (woz13rule1) =>
% 130.98/22.73 ((
% 130.98/22.73 (woz13rule2) =>
% 130.98/22.73 ((
% 130.98/22.73 (woz13rule3) =>
% 130.98/22.73 ((
% 130.98/22.73 (woz13rule4) =>
% 130.98/22.73 ((
% 130.98/22.73 (woz1_1) =>
% 130.98/22.73 ((
% 130.98/22.73 (woz1_2) =>
% 130.98/22.73 ((
% 130.98/22.73 (woz1_3) =>
% 130.98/22.73 ((
% 130.98/22.73 (woz1_4) =>
% 130.98/22.73 ((
% 130.98/22.73 (woz1_5) =>
% 130.98/22.73 ((
% 130.98/22.73 (breln1all2) =>
% 130.98/22.73 ((
% 130.98/22.73 (breln1SetBreln1) =>
% 130.98/22.73 ((
% 130.98/22.73 (choice2fnsingleton) =>
% 130.98/22.73 ((
% 130.98/22.73 (setOfPairsIsBReln1) =>
% 130.98/22.73 ((
% 130.98/22.73 (breln1all1) =>
% 130.98/22.73 ((
% 130.98/22.73 (subbreln1) =>
% 130.98/22.73 ((
% 130.98/22.73 (eqbreln1) =>
% 130.98/22.73 ((
% 130.98/22.73 (breln1invprop) =>
% 130.98/22.73 ((
% 130.98/22.73 (breln1invI) =>
% 130.98/22.73 ((
% 130.98/22.73 (breln1invE) =>
% 130.98/22.73 ((
% 130.98/22.73 (breln1compprop) =>
% 130.98/22.73 ((
% 130.98/22.73 (breln1compI) =>
% 130.98/22.73 ((
% 130.98/22.73 (breln1compE) =>
% 130.98/22.73 ((
% 130.98/22.73 (breln1compEex) =>
% 130.98/22.73 ((
% 130.98/22.73 (breln1unionprop) =>
% 130.98/22.73 ((
% 130.98/22.73 (breln1unionIL) =>
% 130.98/22.73 ((
% 130.98/22.73 (breln1unionIR) =>
% 130.98/22.73 ((
% 130.98/22.73 (breln1unionI) =>
% 130.98/22.73 ((
% 130.98/22.73 (breln1unionE) =>
% 130.98/22.73 ((
% 130.98/22.73 (breln1unionEcases) =>
% 130.98/22.73 ((
% 130.98/22.73 (breln1unionCommutes) =>
% 130.98/22.73 ((
% 130.98/22.73 (woz2Ex) =>
% 130.98/22.73 ((
% 130.98/22.73 (woz2W) =>
% 130.98/22.73 ((
% 130.98/22.73 (woz2A) =>
% 130.98/22.73 ((
% 130.98/22.73 (woz2B) =>
% 130.98/22.73 ((
% 130.98/22.73 (image1Ex) =>
% 130.98/22.73 ((
% 130.98/22.73 (image1Ex1) =>
% 130.98/22.73 ((
% 130.98/22.73 (image1Equiv) =>
% 130.98/22.73 ((
% 130.98/22.73 (image1E) =>
% 130.98/22.73 ((
% 130.98/22.73 (image1I) =>
% 130.98/22.73 ((
% 130.98/22.73 (injFuncInInjFuncSet) =>
% 130.98/22.73 ((
% 130.98/22.73 (injFuncSetFuncIn) =>
% 130.98/22.73 ((
% 130.98/22.73 (injFuncSetFuncInj) =>
% 130.98/22.73 ((
% 130.98/22.73 (surjFuncSetFuncIn) =>
% 130.98/22.73 ((
% 130.98/22.73 (surjFuncSetFuncSurj) =>
% 130.98/22.73 ((
% 130.98/22.73 (leftInvIsSurj) =>
% 130.98/22.73 ((
% 130.98/22.73 (surjCantorThm) =>
% 130.98/22.73 ((
% 130.98/22.73 (foundation2) =>
% 130.98/22.73 ((
% 130.98/22.73 (notinself) =>
% 130.98/22.73 ((
% 130.98/22.73 (notinself2) =>
% 130.98/22.73 ((
% 130.98/22.73 (omegaSp) =>
% 130.98/22.73 ((
% 130.98/22.73 (omegaSclos) =>
% 130.98/22.73 ((
% 130.98/22.73 (peano0notS) =>
% 130.98/22.73 ((
% 130.98/22.73 (peanoSinj) =>
% 130.98/22.73 ((
% 130.98/22.73 (transitivesetOp1) =>
% 130.98/22.73 ((
% 130.98/22.73 (binintTransitive) =>
% 130.98/22.73 ((
% 130.98/22.73 (transitivesetOp2) =>
% 130.98/22.73 ((
% 130.98/22.73 (setunionTransitive) =>
% 130.98/22.73 ((
% 130.98/22.73 (ordinalMinLem1) =>
% 130.98/22.73 ((
% 130.98/22.73 (ordinalTransSet) =>
% 130.98/22.73 ((
% 130.98/22.73 (ordinalTransSet1) =>
% 130.98/22.73 ((
% 130.98/22.73 (setunionOrdinalLem1) =>
% 130.98/22.73 (ordinal @
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% 130.98/22.73 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl7])).
% 130.98/22.73 thf(zip_derived_cl16, plain,
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% 130.98/22.73 ((
% 130.98/22.73 (emptyinPowerset) =>
% 130.98/22.73 ((
% 130.98/22.73 (emptyInPowerset) =>
% 130.98/22.73 ((
% 130.98/22.73 (powersetE) =>
% 130.98/22.73 ((
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% 130.98/22.73 ((
% 130.98/22.73 (setunionE) =>
% 130.98/22.73 ((
% 130.98/22.73 (subPowSU) =>
% 130.98/22.73 ((
% 130.98/22.73 (exuE2) =>
% 130.98/22.73 ((
% 130.98/22.73 (nonemptyImpWitness) =>
% 130.98/22.73 ((
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% 130.98/22.73 ((
% 130.98/22.73 (notinsingleton) =>
% 130.98/22.73 ((
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% 130.98/22.73 ((
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% 130.98/22.73 ((
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% 130.98/22.73 ((
% 130.98/22.73 (upairsetIL) =>
% 130.98/22.73 ((
% 130.98/22.73 (upairsetIR) =>
% 130.98/22.73 ((
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% 130.98/22.73 ((
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% 130.98/22.73 ((
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% 130.98/22.73 ((
% 130.98/22.73 (quantDeMorgan3) =>
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% 130.98/22.73 (quantDeMorgan4) =>
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% 130.98/22.73 ((
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% 130.98/22.73 ((
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% 130.98/22.73 ((
% 130.98/22.73 (exuI3) =>
% 130.98/22.73 ((
% 130.98/22.73 (exuI2) =>
% 130.98/22.73 ((
% 130.98/22.73 (inCongP) =>
% 130.98/22.73 ((
% 130.98/22.73 (in__Cong) =>
% 130.98/22.73 ((
% 130.98/22.73 (exuE3u) =>
% 130.98/22.73 ((
% 130.98/22.73 (exu__Cong) =>
% 130.98/22.73 ((
% 130.98/22.73 (setadjoin__Cong) =>
% 130.98/22.73 ((
% 130.98/22.73 (powerset__Cong) =>
% 130.98/22.73 ((
% 130.98/22.73 (setunion__Cong) =>
% 130.98/22.73 ((
% 130.98/22.73 (exuEu) =>
% 130.98/22.73 ((
% 130.98/22.73 (descr__Cong) =>
% 130.98/22.73 ((
% 130.98/22.73 (dsetconstr__Cong) =>
% 130.98/22.73 ((
% 130.98/22.73 (subsetI1) =>
% 130.98/22.73 ((
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% 130.98/22.73 ((
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% 130.98/22.73 (subsetI2) =>
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% 130.98/22.73 ((
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% 130.98/22.73 ((
% 130.98/22.73 (subsetE2) =>
% 130.98/22.73 ((
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% 130.98/22.73 ((
% 130.98/22.73 (notequalI1) =>
% 130.98/22.73 ((
% 130.98/22.73 (notequalI2) =>
% 130.98/22.73 ((
% 130.98/22.73 (subsetRefl) =>
% 130.98/22.73 ((
% 130.98/22.73 (subsetTrans) =>
% 130.98/22.73 ((
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% 130.98/22.73 ((
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% 130.98/22.73 ((
% 130.98/22.73 (setextsub) =>
% 130.98/22.73 ((
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% 130.98/22.73 (sepSubset) =>
% 130.98/22.73 ((
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% 130.98/22.73 ((
% 130.98/22.73 (upairset2IR) =>
% 130.98/22.73 ((
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% 130.98/22.73 ((
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% 130.98/22.73 (binunionE) =>
% 130.98/22.73 ((
% 130.98/22.73 (binunionLsub) =>
% 130.98/22.73 ((
% 130.98/22.73 (binunionRsub) =>
% 130.98/22.73 ((
% 130.98/22.73 (binintersectI) =>
% 130.98/22.73 ((
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% 130.98/22.73 ((
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% 130.98/22.73 ((
% 130.98/22.73 (setminusSubset2) =>
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% 130.98/22.73 (setminusLsub) =>
% 130.98/22.73 ((
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% 130.98/22.73 ((
% 130.98/22.73 (symdiffI2) =>
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% 130.98/22.73 ((
% 130.98/22.73 (singletoninpowerset) =>
% 130.98/22.73 ((
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% 130.98/22.73 (ubforcartprodlem3) =>
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% 130.98/22.73 ((
% 130.98/22.73 (kfstsingleton) =>
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% 130.98/22.73 ((
% 130.98/22.73 (kfstpairEq) =>
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% 130.98/22.73 (cartprodfstin) =>
% 130.98/22.73 ((
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% 130.98/22.73 (setukpairinjL) =>
% 130.98/22.73 ((
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% 130.98/22.73 ((
% 130.98/22.73 (kpairsurjEq) =>
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% 130.98/22.73 ((
% 130.98/22.73 (cartprodpairmemEL) =>
% 130.98/22.73 ((
% 130.98/22.73 (cartprodpairmemER) =>
% 130.98/22.73 ((
% 130.98/22.73 (cartprodmempaircEq) =>
% 130.98/22.73 ((
% 130.98/22.73 (cartprodfstpairEq) =>
% 130.98/22.73 ((
% 130.98/22.73 (cartprodsndpairEq) =>
% 130.98/22.73 ((
% 130.98/22.73 (cartprodpairsurjEq) =>
% 130.98/22.73 ((
% 130.98/22.73 (dpsetconstrI) =>
% 130.98/22.73 ((
% 130.98/22.73 (dpsetconstrSub) =>
% 130.98/22.73 ((
% 130.98/22.73 (setOfPairsIsBReln) =>
% 130.98/22.73 ((
% 130.98/22.73 (dpsetconstrERa) =>
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% 130.98/22.73 ((
% 130.98/22.73 (dpsetconstrEL2) =>
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% 130.98/22.73 (funcImageSingleton) =>
% 130.98/22.73 ((
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% 130.98/22.73 ((
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% 130.98/22.73 ((
% 130.98/22.73 (infuncsetfunc) =>
% 130.98/22.73 ((
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% 130.98/22.73 ((
% 130.98/22.73 (funcinfuncset) =>
% 130.98/22.73 ((
% 130.98/22.73 (lamProp) =>
% 130.98/22.73 ((
% 130.98/22.73 (lamp) =>
% 130.98/22.73 ((
% 130.98/22.73 (lam2p) =>
% 130.98/22.73 ((
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% 130.98/22.73 ((
% 130.98/22.73 (brelnall2) =>
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% 130.98/22.73 (funcGraphProp1) =>
% 130.98/22.73 ((
% 130.98/22.73 (funcGraphProp3) =>
% 130.98/22.73 ((
% 130.98/22.73 (funcGraphProp2) =>
% 130.98/22.73 ((
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% 130.98/22.73 ((
% 130.98/22.73 (funcGraphProp4) =>
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% 130.98/22.73 ((
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% 130.98/22.73 (complementTE1) =>
% 130.98/22.73 ((
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% 130.98/22.73 ((
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% 130.98/22.73 ((
% 130.98/22.73 (contrasubsetT) =>
% 130.98/22.73 ((
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% 130.98/22.73 ((
% 130.98/22.73 (contrasubsetT2) =>
% 130.98/22.73 ((
% 130.98/22.73 (contrasubsetT3) =>
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% 130.98/22.73 (doubleComplementI1) =>
% 130.98/22.73 ((
% 130.98/22.73 (doubleComplementE1) =>
% 130.98/22.73 ((
% 130.98/22.73 (doubleComplementSub1) =>
% 130.98/22.73 ((
% 130.98/22.73 (doubleComplementSub2) =>
% 130.98/22.73 ((
% 130.98/22.73 (doubleComplementEq) =>
% 130.98/22.73 ((
% 130.98/22.73 (complementTnotintersectT) =>
% 130.98/22.73 ((
% 130.98/22.73 (complementImpComplementIntersect) =>
% 130.98/22.73 ((
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% 130.98/22.73 ((
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% 130.98/22.73 (binunionTIRcontra) =>
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% 130.98/22.73 ((
% 130.98/22.73 (inIntersectImpInUnion2) =>
% 130.98/22.73 ((
% 130.98/22.73 (inIntersectImpInIntersectUnions) =>
% 130.98/22.73 ((
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% 130.98/22.73 (inComplementUnionImpNotIn1) =>
% 130.98/22.73 ((
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% 130.98/22.73 ((
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% 130.98/22.73 ((
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% 130.98/22.73 ((
% 130.98/22.73 (demorgan2a) =>
% 130.98/22.73 ((
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% 130.98/22.73 (demorgan2b) =>
% 130.98/22.73 ((
% 130.98/22.73 (demorgan2) =>
% 130.98/22.73 ((
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% 130.98/22.73 ((
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% 130.98/22.73 ((
% 130.98/22.73 (woz13rule2) =>
% 130.98/22.73 ((
% 130.98/22.73 (woz13rule3) =>
% 130.98/22.73 ((
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% 130.98/22.73 ((
% 130.98/22.73 (woz1_4) =>
% 130.98/22.73 ((
% 130.98/22.73 (woz1_5) =>
% 130.98/22.73 ((
% 130.98/22.73 (breln1all2) =>
% 130.98/22.73 ((
% 130.98/22.73 (breln1SetBreln1) =>
% 130.98/22.73 ((
% 130.98/22.73 (choice2fnsingleton) =>
% 130.98/22.73 ((
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% 130.98/22.73 (breln1all1) =>
% 130.98/22.73 ((
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% 130.98/22.73 ((
% 130.98/22.73 (eqbreln1) =>
% 130.98/22.73 ((
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% 130.98/22.73 ((
% 130.98/22.73 (breln1invI) =>
% 130.98/22.73 ((
% 130.98/22.73 (breln1invE) =>
% 130.98/22.73 ((
% 130.98/22.73 (breln1compprop) =>
% 130.98/22.73 ((
% 130.98/22.73 (breln1compI) =>
% 130.98/22.73 ((
% 130.98/22.73 (breln1compE) =>
% 130.98/22.73 ((
% 130.98/22.73 (breln1compEex) =>
% 130.98/22.73 ((
% 130.98/22.73 (breln1unionprop) =>
% 130.98/22.73 ((
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% 130.98/22.73 ((
% 130.98/22.73 (breln1unionIR) =>
% 130.98/22.73 ((
% 130.98/22.73 (breln1unionI) =>
% 131.56/22.74 ((
% 131.56/22.74 (breln1unionE) =>
% 131.56/22.74 ((
% 131.56/22.74 (breln1unionEcases) =>
% 131.56/22.74 ((
% 131.56/22.74 (breln1unionCommutes) =>
% 131.56/22.74 ((
% 131.56/22.74 (woz2Ex) =>
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% 131.56/22.74 ((
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% 131.56/22.74 ((
% 131.56/22.74 (woz2B) =>
% 131.56/22.74 ((
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% 131.56/22.74 ((
% 131.56/22.74 (image1Ex1) =>
% 131.56/22.74 ((
% 131.56/22.74 (image1Equiv) =>
% 131.56/22.74 ((
% 131.56/22.74 (image1E) =>
% 131.56/22.74 ((
% 131.56/22.74 (image1I) =>
% 131.56/22.74 ((
% 131.56/22.74 (injFuncInInjFuncSet) =>
% 131.56/22.74 ((
% 131.56/22.74 (injFuncSetFuncIn) =>
% 131.56/22.74 ((
% 131.56/22.74 (injFuncSetFuncInj) =>
% 131.56/22.74 ((
% 131.56/22.74 (surjFuncSetFuncIn) =>
% 131.56/22.74 ((
% 131.56/22.74 (surjFuncSetFuncSurj) =>
% 131.56/22.74 ((
% 131.56/22.74 (leftInvIsSurj) =>
% 131.56/22.74 ((
% 131.56/22.74 (surjCantorThm) =>
% 131.56/22.74 ((
% 131.56/22.74 (foundation2) =>
% 131.56/22.74 ((
% 131.56/22.74 (notinself) =>
% 131.56/22.74 ((
% 131.56/22.74 (notinself2) =>
% 131.56/22.74 ((
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% 131.56/22.74 ((
% 131.56/22.74 (omegaSclos) =>
% 131.56/22.74 ((
% 131.56/22.74 (peano0notS) =>
% 131.56/22.74 ((
% 131.56/22.74 (peanoSinj) =>
% 131.56/22.74 ((
% 131.56/22.74 (transitivesetOp1) =>
% 131.56/22.74 ((
% 131.56/22.74 (binintTransitive) =>
% 131.56/22.74 ((
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% 131.56/22.74 ((
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% 131.56/22.74 ((
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% 131.56/22.74 ((
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% 131.56/22.74 ((
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% 131.56/22.74 ((
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% 131.56/22.74 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl11])).
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% 131.56/22.74 (exuI1) =>
% 131.56/22.74 ((
% 131.56/22.74 (exuI3) =>
% 131.56/22.74 ((
% 131.56/22.74 (exuI2) =>
% 131.56/22.74 ((
% 131.56/22.74 (inCongP) =>
% 131.56/22.74 ((
% 131.56/22.74 (in__Cong) =>
% 131.56/22.74 ((
% 131.56/22.74 (exuE3u) =>
% 131.56/22.74 ((
% 131.56/22.74 (exu__Cong) =>
% 131.56/22.74 ((
% 131.56/22.74 (setadjoin__Cong) =>
% 131.56/22.74 ((
% 131.56/22.74 (powerset__Cong) =>
% 131.56/22.74 ((
% 131.56/22.74 (setunion__Cong) =>
% 131.56/22.74 ((
% 131.56/22.74 (exuEu) =>
% 131.56/22.74 ((
% 131.56/22.74 (descr__Cong) =>
% 131.56/22.74 ((
% 131.56/22.74 (dsetconstr__Cong) =>
% 131.56/22.74 ((
% 131.56/22.74 (subsetI1) =>
% 131.56/22.74 ((
% 131.56/22.74 (eqimpsubset2) =>
% 131.56/22.74 ((
% 131.56/22.74 (eqimpsubset1) =>
% 131.56/22.74 ((
% 131.56/22.74 (subsetI2) =>
% 131.56/22.74 ((
% 131.56/22.74 (emptysetsubset) =>
% 131.56/22.74 ((
% 131.56/22.74 (subsetE) =>
% 131.56/22.74 ((
% 131.56/22.74 (subsetE2) =>
% 131.56/22.74 ((
% 131.56/22.74 (notsubsetI) =>
% 131.56/22.74 ((
% 131.56/22.74 (notequalI1) =>
% 131.56/22.74 ((
% 131.56/22.74 (notequalI2) =>
% 131.56/22.74 ((
% 131.56/22.74 (subsetRefl) =>
% 131.56/22.74 ((
% 131.56/22.74 (subsetTrans) =>
% 131.56/22.74 ((
% 131.56/22.74 (setadjoinSub) =>
% 131.56/22.74 ((
% 131.56/22.74 (setadjoinSub2) =>
% 131.56/22.74 ((
% 131.56/22.74 (subset2powerset) =>
% 131.56/22.74 ((
% 131.56/22.74 (setextsub) =>
% 131.56/22.74 ((
% 131.56/22.74 (subsetemptysetimpeq) =>
% 131.56/22.74 ((
% 131.56/22.74 (powersetI1) =>
% 131.56/22.74 ((
% 131.56/22.74 (powersetE1) =>
% 131.56/22.74 ((
% 131.56/22.74 (inPowerset) =>
% 131.56/22.74 ((
% 131.56/22.74 (powersetsubset) =>
% 131.56/22.74 ((
% 131.56/22.74 (sepInPowerset) =>
% 131.56/22.74 ((
% 131.56/22.74 (sepSubset) =>
% 131.56/22.74 ((
% 131.56/22.74 (binunionIL) =>
% 131.56/22.74 ((
% 131.56/22.74 (upairset2IR) =>
% 131.56/22.74 ((
% 131.56/22.74 (binunionIR) =>
% 131.56/22.74 ((
% 131.56/22.74 (binunionEcases) =>
% 131.56/22.74 ((
% 131.56/22.74 (binunionE) =>
% 131.56/22.74 ((
% 131.56/22.74 (binunionLsub) =>
% 131.56/22.74 ((
% 131.56/22.74 (binunionRsub) =>
% 131.56/22.74 ((
% 131.56/22.74 (binintersectI) =>
% 131.56/22.74 ((
% 131.56/22.74 (binintersectSubset5) =>
% 131.56/22.74 ((
% 131.56/22.74 (binintersectEL) =>
% 131.56/22.74 ((
% 131.56/22.74 (binintersectLsub) =>
% 131.56/22.74 ((
% 131.56/22.74 (binintersectSubset2) =>
% 131.56/22.74 ((
% 131.56/22.74 (binintersectSubset3) =>
% 131.56/22.74 ((
% 131.56/22.74 (binintersectER) =>
% 131.56/22.74 ((
% 131.56/22.74 (disjointsetsI1) =>
% 131.56/22.74 ((
% 131.56/22.74 (binintersectRsub) =>
% 131.56/22.74 ((
% 131.56/22.74 (binintersectSubset4) =>
% 131.56/22.74 ((
% 131.56/22.74 (binintersectSubset1) =>
% 131.56/22.74 ((
% 131.56/22.74 (bs114d) =>
% 131.56/22.74 ((
% 131.56/22.74 (setminusI) =>
% 131.56/22.74 ((
% 131.56/22.74 (setminusEL) =>
% 131.56/22.74 ((
% 131.56/22.74 (setminusER) =>
% 131.56/22.74 ((
% 131.56/22.74 (setminusSubset2) =>
% 131.56/22.74 ((
% 131.56/22.74 (setminusERneg) =>
% 131.56/22.74 ((
% 131.56/22.74 (setminusELneg) =>
% 131.56/22.74 ((
% 131.56/22.74 (setminusILneg) =>
% 131.56/22.74 ((
% 131.56/22.74 (setminusIRneg) =>
% 131.56/22.74 ((
% 131.56/22.74 (setminusLsub) =>
% 131.56/22.74 ((
% 131.56/22.74 (setminusSubset1) =>
% 131.56/22.74 ((
% 131.56/22.74 (symdiffE) =>
% 131.56/22.74 ((
% 131.56/22.74 (symdiffI1) =>
% 131.56/22.74 ((
% 131.56/22.74 (symdiffI2) =>
% 131.56/22.74 ((
% 131.56/22.74 (symdiffIneg1) =>
% 131.56/22.74 ((
% 131.56/22.74 (symdiffIneg2) =>
% 131.56/22.74 ((
% 131.56/22.74 (secondinupair) =>
% 131.56/22.74 ((
% 131.56/22.74 (setukpairIL) =>
% 131.56/22.74 ((
% 131.56/22.74 (setukpairIR) =>
% 131.56/22.74 ((
% 131.56/22.74 (kpairiskpair) =>
% 131.56/22.74 ((
% 131.56/22.74 (kpairp) =>
% 131.56/22.74 ((
% 131.56/22.74 (singletonsubset) =>
% 131.56/22.74 ((
% 131.56/22.74 (singletoninpowerset) =>
% 131.56/22.74 ((
% 131.56/22.74 (singletoninpowunion) =>
% 131.56/22.74 ((
% 131.56/22.74 (upairset2E) =>
% 131.56/22.74 ((
% 131.56/22.74 (upairsubunion) =>
% 131.56/22.74 ((
% 131.56/22.74 (upairinpowunion) =>
% 131.56/22.74 ((
% 131.56/22.74 (ubforcartprodlem1) =>
% 131.56/22.74 ((
% 131.56/22.74 (ubforcartprodlem2) =>
% 131.56/22.74 ((
% 131.56/22.74 (ubforcartprodlem3) =>
% 131.56/22.74 ((
% 131.56/22.74 (cartprodpairin) =>
% 131.56/22.74 ((
% 131.56/22.74 (cartprodmempair1) =>
% 131.56/22.74 ((
% 131.56/22.74 (cartprodmempair) =>
% 131.56/22.74 ((
% 131.56/22.74 (setunionE2) =>
% 131.56/22.74 ((
% 131.56/22.74 (setunionsingleton1) =>
% 131.56/22.74 ((
% 131.56/22.74 (setunionsingleton2) =>
% 131.56/22.74 ((
% 131.56/22.74 (setunionsingleton) =>
% 131.56/22.74 ((
% 131.56/22.74 (singletonprop) =>
% 131.56/22.74 ((
% 131.56/22.74 (ex1E1) =>
% 131.56/22.74 ((
% 131.56/22.74 (ex1I) =>
% 131.56/22.74 ((
% 131.56/22.74 (ex1I2) =>
% 131.56/22.74 ((
% 131.56/22.74 (singletonsuniq) =>
% 131.56/22.74 ((
% 131.56/22.74 (setukpairinjL1) =>
% 131.56/22.74 ((
% 131.56/22.74 (kfstsingleton) =>
% 131.56/22.74 ((
% 131.56/22.74 (theprop) =>
% 131.56/22.74 ((
% 131.56/22.74 (kfstpairEq) =>
% 131.56/22.74 ((
% 131.56/22.74 (cartprodfstin) =>
% 131.56/22.74 ((
% 131.56/22.74 (setukpairinjL2) =>
% 131.56/22.74 ((
% 131.56/22.74 (setukpairinjL) =>
% 131.56/22.74 ((
% 131.56/22.74 (setukpairinjR11) =>
% 131.56/22.74 ((
% 131.56/22.74 (setukpairinjR12) =>
% 131.56/22.74 ((
% 131.56/22.74 (setukpairinjR1) =>
% 131.56/22.74 ((
% 131.56/22.74 (upairequniteq) =>
% 131.56/22.74 ((
% 131.56/22.74 (setukpairinjR2) =>
% 131.56/22.74 ((
% 131.56/22.74 (setukpairinjR) =>
% 131.56/22.74 ((
% 131.56/22.74 (ksndsingleton) =>
% 131.56/22.74 ((
% 131.56/22.74 (ksndpairEq) =>
% 131.56/22.74 ((
% 131.56/22.74 (kpairsurjEq) =>
% 131.56/22.74 ((
% 131.56/22.74 (cartprodsndin) =>
% 131.56/22.74 ((
% 131.56/22.74 (cartprodpairmemEL) =>
% 131.56/22.74 ((
% 131.56/22.74 (cartprodpairmemER) =>
% 131.56/22.74 ((
% 131.56/22.74 (cartprodmempaircEq) =>
% 131.56/22.74 ((
% 131.56/22.74 (cartprodfstpairEq) =>
% 131.56/22.74 ((
% 131.56/22.74 (cartprodsndpairEq) =>
% 131.56/22.74 ((
% 131.56/22.74 (cartprodpairsurjEq) =>
% 131.56/22.74 ((
% 131.56/22.74 (dpsetconstrI) =>
% 131.56/22.74 ((
% 131.56/22.74 (dpsetconstrSub) =>
% 131.56/22.74 ((
% 131.56/22.74 (setOfPairsIsBReln) =>
% 131.56/22.74 ((
% 131.56/22.74 (dpsetconstrERa) =>
% 131.56/22.74 ((
% 131.56/22.74 (dpsetconstrEL1) =>
% 131.56/22.74 ((
% 131.56/22.74 (dpsetconstrEL2) =>
% 131.56/22.74 ((
% 131.56/22.74 (dpsetconstrER) =>
% 131.56/22.74 ((
% 131.56/22.74 (funcImageSingleton) =>
% 131.56/22.74 ((
% 131.56/22.74 (apProp) =>
% 131.56/22.74 ((
% 131.56/22.74 (app) =>
% 131.56/22.74 ((
% 131.56/22.74 (infuncsetfunc) =>
% 131.56/22.74 ((
% 131.56/22.74 (ap2p) =>
% 131.56/22.74 ((
% 131.56/22.74 (funcinfuncset) =>
% 131.56/22.74 ((
% 131.56/22.74 (lamProp) =>
% 131.56/22.74 ((
% 131.56/22.74 (lamp) =>
% 131.56/22.74 ((
% 131.56/22.74 (lam2p) =>
% 131.56/22.74 ((
% 131.56/22.74 (brelnall1) =>
% 131.56/22.74 ((
% 131.56/22.74 (brelnall2) =>
% 131.56/22.74 ((
% 131.56/22.74 (ex1E2) =>
% 131.56/22.74 ((
% 131.56/22.74 (funcGraphProp1) =>
% 131.56/22.74 ((
% 131.56/22.74 (funcGraphProp3) =>
% 131.56/22.74 ((
% 131.56/22.74 (funcGraphProp2) =>
% 131.56/22.74 ((
% 131.56/22.74 (funcextLem) =>
% 131.56/22.74 ((
% 131.56/22.74 (funcGraphProp4) =>
% 131.56/22.74 ((
% 131.56/22.74 (subbreln) =>
% 131.56/22.74 ((
% 131.56/22.74 (eqbreln) =>
% 131.56/22.74 ((
% 131.56/22.74 (funcext) =>
% 131.56/22.74 ((
% 131.56/22.74 (funcext2) =>
% 131.56/22.74 ((
% 131.56/22.74 (ap2apEq1) =>
% 131.56/22.74 ((
% 131.56/22.74 (ap2apEq2) =>
% 131.56/22.74 ((
% 131.56/22.74 (beta1) =>
% 131.56/22.74 ((
% 131.56/22.74 (eta1) =>
% 131.56/22.74 ((
% 131.56/22.74 (lam2lamEq) =>
% 131.56/22.74 ((
% 131.56/22.74 (beta2) =>
% 131.56/22.74 ((
% 131.56/22.74 (eta2) =>
% 131.56/22.74 ((
% 131.56/22.74 (iffalseProp1) =>
% 131.56/22.74 ((
% 131.56/22.74 (iffalseProp2) =>
% 131.56/22.74 ((
% 131.56/22.74 (iftrueProp1) =>
% 131.56/22.74 ((
% 131.56/22.74 (iftrueProp2) =>
% 131.56/22.74 ((
% 131.56/22.74 (ifSingleton) =>
% 131.56/22.74 ((
% 131.56/22.74 (ifp) =>
% 131.56/22.74 ((
% 131.56/22.74 (theeq) =>
% 131.56/22.74 ((
% 131.56/22.74 (iftrue) =>
% 131.56/22.74 ((
% 131.56/22.74 (iffalse) =>
% 131.56/22.74 ((
% 131.56/22.74 (iftrueorfalse) =>
% 131.56/22.74 ((
% 131.56/22.74 (binintersectT_lem) =>
% 131.56/22.74 ((
% 131.56/22.74 (binunionT_lem) =>
% 131.56/22.74 ((
% 131.56/22.74 (powersetT_lem) =>
% 131.56/22.74 ((
% 131.56/22.74 (setminusT_lem) =>
% 131.56/22.74 ((
% 131.56/22.74 (complementT_lem) =>
% 131.56/22.74 ((
% 131.56/22.74 (setextT) =>
% 131.56/22.74 ((
% 131.56/22.74 (subsetTI) =>
% 131.56/22.74 ((
% 131.56/22.74 (powersetTI1) =>
% 131.56/22.74 ((
% 131.56/22.74 (powersetTE1) =>
% 131.56/22.74 ((
% 131.56/22.74 (complementTI1) =>
% 131.56/22.74 ((
% 131.56/22.74 (complementTE1) =>
% 131.56/22.74 ((
% 131.56/22.74 (binintersectTELcontra) =>
% 131.56/22.74 ((
% 131.56/22.74 (binintersectTERcontra) =>
% 131.56/22.74 ((
% 131.56/22.74 (contrasubsetT) =>
% 131.56/22.74 ((
% 131.56/22.74 (contrasubsetT1) =>
% 131.56/22.74 ((
% 131.56/22.74 (contrasubsetT2) =>
% 131.56/22.74 ((
% 131.56/22.74 (contrasubsetT3) =>
% 131.56/22.74 ((
% 131.56/22.74 (doubleComplementI1) =>
% 131.56/22.74 ((
% 131.56/22.74 (doubleComplementE1) =>
% 131.56/22.74 ((
% 131.56/22.74 (doubleComplementSub1) =>
% 131.56/22.74 ((
% 131.56/22.74 (doubleComplementSub2) =>
% 131.56/22.74 ((
% 131.56/22.74 (doubleComplementEq) =>
% 131.56/22.74 ((
% 131.56/22.74 (complementTnotintersectT) =>
% 131.56/22.74 ((
% 131.56/22.74 (complementImpComplementIntersect) =>
% 131.56/22.74 ((
% 131.56/22.74 (complementSubsetComplementIntersect) =>
% 131.56/22.74 ((
% 131.56/22.74 (complementInPowersetComplementIntersect) =>
% 131.56/22.74 ((
% 131.56/22.74 (contraSubsetComplement) =>
% 131.56/22.74 ((
% 131.56/22.74 (complementTcontraSubset) =>
% 131.56/22.74 ((
% 131.56/22.74 (binunionTILcontra) =>
% 131.56/22.74 ((
% 131.56/22.74 (binunionTIRcontra) =>
% 131.56/22.74 ((
% 131.56/22.74 (inIntersectImpInUnion) =>
% 131.56/22.74 ((
% 131.56/22.74 (inIntersectImpInUnion2) =>
% 131.56/22.74 ((
% 131.56/22.74 (inIntersectImpInIntersectUnions) =>
% 131.56/22.74 ((
% 131.56/22.74 (intersectInPowersetIntersectUnions) =>
% 131.56/22.74 ((
% 131.56/22.74 (inComplementUnionImpNotIn1) =>
% 131.56/22.74 ((
% 131.56/22.74 (inComplementUnionImpInComplement1) =>
% 131.56/22.74 ((
% 131.56/22.74 (binunionTE) =>
% 131.56/22.74 ((
% 131.56/22.74 (binunionTEcontra) =>
% 131.56/22.74 ((
% 131.56/22.74 (demorgan2a1) =>
% 131.56/22.74 ((
% 131.56/22.74 (complementUnionInPowersetComplement) =>
% 131.56/22.74 ((
% 131.56/22.74 (demorgan2a2) =>
% 131.56/22.74 ((
% 131.56/22.74 (demorgan1a) =>
% 131.56/22.74 ((
% 131.56/22.74 (demorgan1b) =>
% 131.56/22.74 ((
% 131.56/22.74 (demorgan1) =>
% 131.56/22.74 ((
% 131.56/22.74 (demorgan2a) =>
% 131.56/22.74 ((
% 131.56/22.74 (demorgan2b2) =>
% 131.56/22.74 ((
% 131.56/22.74 (demorgan2b) =>
% 131.56/22.74 ((
% 131.56/22.74 (demorgan2) =>
% 131.56/22.74 ((
% 131.56/22.74 (woz13rule0) =>
% 131.56/22.74 ((
% 131.56/22.74 (woz13rule1) =>
% 131.56/22.74 ((
% 131.56/22.74 (woz13rule2) =>
% 131.56/22.74 ((
% 131.56/22.74 (woz13rule3) =>
% 131.56/22.74 ((
% 131.56/22.74 (woz13rule4) =>
% 131.56/22.74 ((
% 131.56/22.74 (woz1_1) =>
% 131.56/22.74 ((
% 131.56/22.74 (woz1_2) =>
% 131.56/22.74 ((
% 131.56/22.74 (woz1_3) =>
% 131.56/22.74 ((
% 131.56/22.74 (woz1_4) =>
% 131.56/22.74 ((
% 131.56/22.74 (woz1_5) =>
% 131.56/22.74 ((
% 131.56/22.74 (breln1all2) =>
% 131.56/22.74 ((
% 131.56/22.74 (breln1SetBreln1) =>
% 131.56/22.74 ((
% 131.56/22.74 (choice2fnsingleton) =>
% 131.56/22.74 ((
% 131.56/22.74 (setOfPairsIsBReln1) =>
% 131.56/22.74 ((
% 131.56/22.74 (breln1all1) =>
% 131.56/22.74 ((
% 131.56/22.74 (subbreln1) =>
% 131.56/22.74 ((
% 131.56/22.74 (eqbreln1) =>
% 131.56/22.74 ((
% 131.56/22.74 (breln1invprop) =>
% 131.56/22.74 ((
% 131.56/22.74 (breln1invI) =>
% 131.56/22.74 ((
% 131.56/22.74 (breln1invE) =>
% 131.56/22.74 ((
% 131.56/22.74 (breln1compprop) =>
% 131.56/22.74 ((
% 131.56/22.74 (breln1compI) =>
% 131.56/22.74 ((
% 131.56/22.74 (breln1compE) =>
% 131.56/22.74 ((
% 131.56/22.74 (breln1compEex) =>
% 131.56/22.74 ((
% 131.56/22.74 (breln1unionprop) =>
% 131.56/22.74 ((
% 131.56/22.74 (breln1unionIL) =>
% 131.56/22.74 ((
% 131.56/22.74 (breln1unionIR) =>
% 131.56/22.74 ((
% 131.56/22.74 (breln1unionI) =>
% 131.56/22.74 ((
% 131.56/22.74 (breln1unionE) =>
% 131.56/22.74 ((
% 131.56/22.74 (breln1unionEcases) =>
% 131.56/22.74 ((
% 131.56/22.74 (breln1unionCommutes) =>
% 131.56/22.74 ((
% 131.56/22.74 (woz2Ex) =>
% 131.56/22.74 ((
% 131.56/22.74 (woz2W) =>
% 131.56/22.74 ((
% 131.56/22.74 (woz2A) =>
% 131.56/22.74 ((
% 131.56/22.74 (woz2B) =>
% 131.56/22.74 ((
% 131.56/22.74 (image1Ex) =>
% 131.56/22.74 ((
% 131.56/22.74 (image1Ex1) =>
% 131.56/22.74 ((
% 131.56/22.74 (image1Equiv) =>
% 131.56/22.74 ((
% 131.56/22.74 (image1E) =>
% 131.56/22.74 ((
% 131.56/22.74 (image1I) =>
% 131.56/22.74 ((
% 131.56/22.74 (injFuncInInjFuncSet) =>
% 131.56/22.74 ((
% 131.56/22.74 (injFuncSetFuncIn) =>
% 131.56/22.74 ((
% 131.56/22.74 (injFuncSetFuncInj) =>
% 131.56/22.74 ((
% 131.56/22.74 (surjFuncSetFuncIn) =>
% 131.56/22.74 ((
% 131.56/22.74 (surjFuncSetFuncSurj) =>
% 131.56/22.74 ((
% 131.56/22.74 (leftInvIsSurj) =>
% 131.56/22.74 ((
% 131.56/22.74 (surjCantorThm) =>
% 131.56/22.74 ((
% 131.56/22.74 (foundation2) =>
% 131.56/22.74 ((
% 131.56/22.74 (notinself) =>
% 131.56/22.74 ((
% 131.56/22.74 (notinself2) =>
% 131.56/22.74 ((
% 131.56/22.74 (omegaSp) =>
% 131.56/22.74 ((
% 131.56/22.74 (omegaSclos) =>
% 131.56/22.74 ((
% 131.56/22.74 (peano0notS) =>
% 131.56/22.74 ((
% 131.56/22.74 (peanoSinj) =>
% 131.56/22.74 ((
% 131.56/22.74 (transitivesetOp1) =>
% 131.56/22.74 ((
% 131.56/22.74 (binintTransitive) =>
% 131.56/22.74 ((
% 131.56/22.74 (transitivesetOp2) =>
% 131.56/22.74 ((
% 131.56/22.74 (setunionTransitive) =>
% 131.56/22.74 ((
% 131.56/22.74 (ordinalMinLem1) =>
% 131.56/22.74 ((
% 131.56/22.74 (ordinalTransSet) =>
% 131.56/22.74 ((
% 131.56/22.74 (ordinalTransSet1) =>
% 131.56/22.74 ((
% 131.56/22.74 (setunionOrdinalLem1) =>
% 131.56/22.74 (ordinal @
% 131.56/22.74 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 131.56/22.74 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl16])).
% 131.56/22.74 thf(zip_derived_cl28, plain,
% 131.56/22.74 (~ (((omegaSAx) =>
% 131.56/22.74 (((omegaIndAx) =>
% 131.56/22.74 (((replAx) =>
% 131.56/22.74 (((foundationAx) =>
% 131.56/22.74 (((wellorderingAx) =>
% 131.56/22.74 (((descrp) =>
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% 131.56/22.74 ((
% 131.56/22.74 (woz2B) =>
% 131.56/22.74 ((
% 131.56/22.74 (image1Ex) =>
% 131.56/22.74 ((
% 131.56/22.74 (image1Ex1) =>
% 131.56/22.74 ((
% 131.56/22.74 (image1Equiv) =>
% 131.56/22.74 ((
% 131.56/22.74 (image1E) =>
% 131.56/22.74 ((
% 131.56/22.74 (image1I) =>
% 131.56/22.74 ((
% 131.56/22.74 (injFuncInInjFuncSet) =>
% 131.56/22.74 ((
% 131.56/22.74 (injFuncSetFuncIn) =>
% 131.56/22.74 ((
% 131.56/22.74 (injFuncSetFuncInj) =>
% 131.56/22.74 ((
% 131.56/22.74 (surjFuncSetFuncIn) =>
% 131.56/22.74 ((
% 131.56/22.74 (surjFuncSetFuncSurj) =>
% 131.56/22.74 ((
% 131.56/22.74 (leftInvIsSurj) =>
% 131.56/22.74 ((
% 131.56/22.74 (surjCantorThm) =>
% 131.56/22.74 ((
% 131.56/22.74 (foundation2) =>
% 131.56/22.74 ((
% 131.56/22.74 (notinself) =>
% 131.56/22.74 ((
% 131.56/22.74 (notinself2) =>
% 131.56/22.74 ((
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% 131.56/22.74 ((
% 131.56/22.74 (omegaSclos) =>
% 131.56/22.74 ((
% 131.56/22.74 (peano0notS) =>
% 131.56/22.74 ((
% 131.56/22.74 (peanoSinj) =>
% 131.56/22.74 ((
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% 131.56/22.74 ((
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% 131.56/22.74 ((
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% 131.56/22.74 ((
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% 131.56/22.74 ((
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% 131.56/22.74 ((
% 131.56/22.74 (ordinalTransSet) =>
% 131.56/22.74 ((
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% 131.56/22.74 ((
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% 131.56/22.74 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl21])).
% 131.56/22.74 thf(zip_derived_cl34, plain,
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% 131.56/22.74 ((
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% 131.56/22.74 (quantDeMorgan3) =>
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% 131.56/22.74 ((
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% 131.56/22.74 ((
% 131.56/22.74 (exuE3u) =>
% 131.56/22.74 ((
% 131.56/22.74 (exu__Cong) =>
% 131.56/22.74 ((
% 131.56/22.74 (setadjoin__Cong) =>
% 131.56/22.74 ((
% 131.56/22.74 (powerset__Cong) =>
% 131.56/22.74 ((
% 131.56/22.74 (setunion__Cong) =>
% 131.56/22.74 ((
% 131.56/22.74 (exuEu) =>
% 131.56/22.74 ((
% 131.56/22.74 (descr__Cong) =>
% 131.56/22.74 ((
% 131.56/22.74 (dsetconstr__Cong) =>
% 131.56/22.74 ((
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% 131.56/22.74 ((
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% 131.56/22.74 ((
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% 131.56/22.74 ((
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% 131.56/22.74 ((
% 131.56/22.74 (binunionRsub) =>
% 131.56/22.74 ((
% 131.56/22.74 (binintersectI) =>
% 131.56/22.74 ((
% 131.56/22.74 (binintersectSubset5) =>
% 131.56/22.74 ((
% 131.56/22.74 (binintersectEL) =>
% 131.56/22.74 ((
% 131.56/22.74 (binintersectLsub) =>
% 131.56/22.74 ((
% 131.56/22.74 (binintersectSubset2) =>
% 131.56/22.74 ((
% 131.56/22.74 (binintersectSubset3) =>
% 131.56/22.74 ((
% 131.56/22.74 (binintersectER) =>
% 131.56/22.74 ((
% 131.56/22.74 (disjointsetsI1) =>
% 131.56/22.74 ((
% 131.56/22.74 (binintersectRsub) =>
% 131.56/22.74 ((
% 131.56/22.74 (binintersectSubset4) =>
% 131.56/22.74 ((
% 131.56/22.74 (binintersectSubset1) =>
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% 131.56/22.74 (bs114d) =>
% 131.56/22.74 ((
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% 131.56/22.74 ((
% 131.56/22.74 (setminusEL) =>
% 131.56/22.74 ((
% 131.56/22.74 (setminusER) =>
% 131.56/22.74 ((
% 131.56/22.74 (setminusSubset2) =>
% 131.56/22.74 ((
% 131.56/22.74 (setminusERneg) =>
% 131.56/22.74 ((
% 131.56/22.74 (setminusELneg) =>
% 131.56/22.74 ((
% 131.56/22.74 (setminusILneg) =>
% 131.56/22.74 ((
% 131.56/22.74 (setminusIRneg) =>
% 131.56/22.74 ((
% 131.56/22.74 (setminusLsub) =>
% 131.56/22.74 ((
% 131.56/22.74 (setminusSubset1) =>
% 131.56/22.74 ((
% 131.56/22.74 (symdiffE) =>
% 131.56/22.74 ((
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% 131.56/22.74 ((
% 131.56/22.74 (symdiffI2) =>
% 131.56/22.74 ((
% 131.56/22.74 (symdiffIneg1) =>
% 131.56/22.74 ((
% 131.56/22.74 (symdiffIneg2) =>
% 131.56/22.74 ((
% 131.56/22.74 (secondinupair) =>
% 131.56/22.74 ((
% 131.56/22.74 (setukpairIL) =>
% 131.56/22.74 ((
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% 131.56/22.74 (kpairiskpair) =>
% 131.56/22.74 ((
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% 131.56/22.74 ((
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% 131.56/22.74 ((
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% 131.56/22.74 ((
% 131.56/22.74 (upairinpowunion) =>
% 131.56/22.74 ((
% 131.56/22.74 (ubforcartprodlem1) =>
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% 131.56/22.74 (ubforcartprodlem3) =>
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% 131.56/22.74 ((
% 131.56/22.74 (cartprodmempair) =>
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% 131.56/22.74 ((
% 131.56/22.74 (demorgan2a) =>
% 131.56/22.74 ((
% 131.56/22.74 (demorgan2b2) =>
% 131.56/22.74 ((
% 131.56/22.74 (demorgan2b) =>
% 131.56/22.74 ((
% 131.56/22.74 (demorgan2) =>
% 131.56/22.74 ((
% 131.56/22.74 (woz13rule0) =>
% 131.56/22.74 ((
% 131.56/22.74 (woz13rule1) =>
% 131.56/22.74 ((
% 131.56/22.74 (woz13rule2) =>
% 131.56/22.74 ((
% 131.56/22.74 (woz13rule3) =>
% 131.56/22.74 ((
% 131.56/22.74 (woz13rule4) =>
% 131.56/22.74 ((
% 131.56/22.74 (woz1_1) =>
% 131.56/22.74 ((
% 131.56/22.74 (woz1_2) =>
% 131.56/22.74 ((
% 131.56/22.74 (woz1_3) =>
% 131.56/22.74 ((
% 131.56/22.74 (woz1_4) =>
% 131.56/22.74 ((
% 131.56/22.74 (woz1_5) =>
% 131.56/22.74 ((
% 131.56/22.74 (breln1all2) =>
% 131.56/22.74 ((
% 131.56/22.74 (breln1SetBreln1) =>
% 131.56/22.74 ((
% 131.56/22.74 (choice2fnsingleton) =>
% 131.56/22.74 ((
% 131.56/22.74 (setOfPairsIsBReln1) =>
% 131.56/22.74 ((
% 131.56/22.74 (breln1all1) =>
% 131.56/22.74 ((
% 131.56/22.74 (subbreln1) =>
% 131.56/22.74 ((
% 131.56/22.74 (eqbreln1) =>
% 131.56/22.74 ((
% 131.56/22.74 (breln1invprop) =>
% 131.56/22.74 ((
% 131.56/22.74 (breln1invI) =>
% 131.56/22.74 ((
% 131.56/22.74 (breln1invE) =>
% 131.56/22.74 ((
% 131.56/22.74 (breln1compprop) =>
% 131.56/22.74 ((
% 131.56/22.74 (breln1compI) =>
% 131.56/22.74 ((
% 131.56/22.74 (breln1compE) =>
% 131.56/22.74 ((
% 131.56/22.74 (breln1compEex) =>
% 131.56/22.74 ((
% 131.56/22.74 (breln1unionprop) =>
% 131.56/22.74 ((
% 131.56/22.74 (breln1unionIL) =>
% 131.56/22.74 ((
% 131.56/22.74 (breln1unionIR) =>
% 131.56/22.74 ((
% 131.56/22.74 (breln1unionI) =>
% 131.56/22.74 ((
% 131.56/22.74 (breln1unionE) =>
% 131.56/22.74 ((
% 131.56/22.74 (breln1unionEcases) =>
% 131.56/22.74 ((
% 131.56/22.74 (breln1unionCommutes) =>
% 131.56/22.74 ((
% 131.56/22.74 (woz2Ex) =>
% 131.56/22.74 ((
% 131.56/22.74 (woz2W) =>
% 131.56/22.74 ((
% 131.56/22.74 (woz2A) =>
% 131.56/22.74 ((
% 131.56/22.74 (woz2B) =>
% 131.56/22.74 ((
% 131.56/22.74 (image1Ex) =>
% 131.56/22.74 ((
% 131.56/22.74 (image1Ex1) =>
% 131.56/22.74 ((
% 131.56/22.74 (image1Equiv) =>
% 131.56/22.74 ((
% 131.56/22.74 (image1E) =>
% 131.56/22.74 ((
% 131.56/22.74 (image1I) =>
% 131.56/22.74 ((
% 131.56/22.74 (injFuncInInjFuncSet) =>
% 131.56/22.74 ((
% 131.56/22.74 (injFuncSetFuncIn) =>
% 131.56/22.74 ((
% 131.56/22.74 (injFuncSetFuncInj) =>
% 131.56/22.74 ((
% 131.56/22.74 (surjFuncSetFuncIn) =>
% 131.56/22.74 ((
% 131.56/22.74 (surjFuncSetFuncSurj) =>
% 131.56/22.74 ((
% 131.56/22.74 (leftInvIsSurj) =>
% 131.56/22.74 ((
% 131.56/22.74 (surjCantorThm) =>
% 131.56/22.74 ((
% 131.56/22.74 (foundation2) =>
% 131.56/22.74 ((
% 131.56/22.74 (notinself) =>
% 131.56/22.74 ((
% 131.56/22.74 (notinself2) =>
% 131.56/22.74 ((
% 131.56/22.74 (omegaSp) =>
% 131.56/22.74 ((
% 131.56/22.74 (omegaSclos) =>
% 131.56/22.74 ((
% 131.56/22.74 (peano0notS) =>
% 131.56/22.74 ((
% 131.56/22.74 (peanoSinj) =>
% 131.56/22.74 ((
% 131.56/22.74 (transitivesetOp1) =>
% 131.56/22.74 ((
% 131.56/22.74 (binintTransitive) =>
% 131.56/22.74 ((
% 131.56/22.74 (transitivesetOp2) =>
% 131.56/22.74 ((
% 131.56/22.74 (setunionTransitive) =>
% 131.56/22.74 ((
% 131.56/22.74 (ordinalMinLem1) =>
% 131.56/22.74 ((
% 131.56/22.74 (ordinalTransSet) =>
% 131.56/22.74 ((
% 131.56/22.74 (ordinalTransSet1) =>
% 131.56/22.74 ((
% 131.56/22.74 (setunionOrdinalLem1) =>
% 131.56/22.74 (ordinal @
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% 131.56/22.74 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl28])).
% 131.56/22.74 thf(zip_derived_cl40, plain,
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% 131.56/22.74 ((
% 131.56/22.74 (setunionE) =>
% 131.56/22.74 ((
% 131.56/22.74 (subPowSU) =>
% 131.56/22.74 ((
% 131.56/22.74 (exuE2) =>
% 131.56/22.74 ((
% 131.56/22.74 (nonemptyImpWitness) =>
% 131.56/22.74 ((
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% 131.56/22.74 ((
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% 131.56/22.74 ((
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% 131.56/22.74 ((
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% 131.56/22.74 ((
% 131.56/22.74 (upairsetIL) =>
% 131.56/22.74 ((
% 131.56/22.74 (upairsetIR) =>
% 131.56/22.74 ((
% 131.56/22.74 (emptyE1) =>
% 131.56/22.74 ((
% 131.56/22.74 (vacuousDall) =>
% 131.56/22.74 ((
% 131.56/22.74 (quantDeMorgan1) =>
% 131.56/22.74 ((
% 131.56/22.74 (quantDeMorgan2) =>
% 131.56/22.74 ((
% 131.56/22.74 (quantDeMorgan3) =>
% 131.56/22.74 ((
% 131.56/22.74 (quantDeMorgan4) =>
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% 131.56/22.74 ((
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% 131.56/22.74 ((
% 131.56/22.74 (exuI2) =>
% 131.56/22.74 ((
% 131.56/22.74 (inCongP) =>
% 131.56/22.74 ((
% 131.56/22.74 (in__Cong) =>
% 131.56/22.74 ((
% 131.56/22.74 (exuE3u) =>
% 131.56/22.74 ((
% 131.56/22.74 (exu__Cong) =>
% 131.56/22.74 ((
% 131.56/22.74 (setadjoin__Cong) =>
% 131.56/22.74 ((
% 131.56/22.74 (powerset__Cong) =>
% 131.56/22.74 ((
% 131.56/22.74 (setunion__Cong) =>
% 131.56/22.74 ((
% 131.56/22.74 (exuEu) =>
% 131.56/22.74 ((
% 131.56/22.74 (descr__Cong) =>
% 131.56/22.74 ((
% 131.56/22.74 (dsetconstr__Cong) =>
% 131.56/22.74 ((
% 131.56/22.74 (subsetI1) =>
% 131.56/22.74 ((
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% 131.56/22.74 ((
% 131.56/22.74 (subsetE2) =>
% 131.56/22.74 ((
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% 131.56/22.74 ((
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% 131.56/22.74 ((
% 131.56/22.74 (notequalI2) =>
% 131.56/22.74 ((
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% 131.56/22.74 ((
% 131.56/22.74 (subsetTrans) =>
% 131.56/22.74 ((
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% 131.56/22.74 ((
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% 131.56/22.74 ((
% 131.56/22.74 (powersetE1) =>
% 131.56/22.74 ((
% 131.56/22.74 (inPowerset) =>
% 131.56/22.74 ((
% 131.56/22.74 (powersetsubset) =>
% 131.56/22.74 ((
% 131.56/22.74 (sepInPowerset) =>
% 131.56/22.74 ((
% 131.56/22.74 (sepSubset) =>
% 131.56/22.74 ((
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% 131.56/22.74 ((
% 131.56/22.74 (upairset2IR) =>
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% 131.56/22.74 ((
% 131.56/22.74 (binunionEcases) =>
% 131.56/22.74 ((
% 131.56/22.74 (binunionE) =>
% 131.56/22.74 ((
% 131.56/22.74 (binunionLsub) =>
% 131.56/22.74 ((
% 131.56/22.74 (binunionRsub) =>
% 131.56/22.74 ((
% 131.56/22.74 (binintersectI) =>
% 131.56/22.74 ((
% 131.56/22.74 (binintersectSubset5) =>
% 131.56/22.74 ((
% 131.56/22.74 (binintersectEL) =>
% 131.56/22.74 ((
% 131.56/22.74 (binintersectLsub) =>
% 131.56/22.74 ((
% 131.56/22.74 (binintersectSubset2) =>
% 131.56/22.74 ((
% 131.56/22.74 (binintersectSubset3) =>
% 131.56/22.74 ((
% 131.56/22.74 (binintersectER) =>
% 131.56/22.74 ((
% 131.56/22.74 (disjointsetsI1) =>
% 131.56/22.74 ((
% 131.56/22.74 (binintersectRsub) =>
% 131.56/22.74 ((
% 131.56/22.74 (binintersectSubset4) =>
% 131.56/22.74 ((
% 131.56/22.74 (binintersectSubset1) =>
% 131.56/22.74 ((
% 131.56/22.74 (bs114d) =>
% 131.56/22.74 ((
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% 131.56/22.74 ((
% 131.56/22.74 (setminusEL) =>
% 131.56/22.74 ((
% 131.56/22.74 (setminusER) =>
% 131.56/22.74 ((
% 131.56/22.74 (setminusSubset2) =>
% 131.56/22.74 ((
% 131.56/22.74 (setminusERneg) =>
% 131.56/22.74 ((
% 131.56/22.74 (setminusELneg) =>
% 131.56/22.74 ((
% 131.56/22.74 (setminusILneg) =>
% 131.56/22.74 ((
% 131.56/22.74 (setminusIRneg) =>
% 131.56/22.74 ((
% 131.56/22.74 (setminusLsub) =>
% 131.56/22.74 ((
% 131.56/22.74 (setminusSubset1) =>
% 131.56/22.74 ((
% 131.56/22.74 (symdiffE) =>
% 131.56/22.74 ((
% 131.56/22.74 (symdiffI1) =>
% 131.56/22.74 ((
% 131.56/22.74 (symdiffI2) =>
% 131.56/22.74 ((
% 131.56/22.74 (symdiffIneg1) =>
% 131.56/22.74 ((
% 131.56/22.74 (symdiffIneg2) =>
% 131.56/22.74 ((
% 131.56/22.74 (secondinupair) =>
% 131.56/22.74 ((
% 131.56/22.74 (setukpairIL) =>
% 131.56/22.74 ((
% 131.56/22.74 (setukpairIR) =>
% 131.56/22.74 ((
% 131.56/22.74 (kpairiskpair) =>
% 131.56/22.74 ((
% 131.56/22.74 (kpairp) =>
% 131.56/22.74 ((
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% 131.56/22.74 ((
% 131.56/22.74 (singletoninpowunion) =>
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% 131.56/22.74 (upairset2E) =>
% 131.56/22.74 ((
% 131.56/22.74 (upairsubunion) =>
% 131.56/22.74 ((
% 131.56/22.74 (upairinpowunion) =>
% 131.56/22.74 ((
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% 131.56/22.74 (ubforcartprodlem3) =>
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% 131.56/22.74 ((
% 131.56/22.74 (cartprodmempair) =>
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% 131.56/22.74 (setukpairinjR1) =>
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% 131.56/22.74 (kpairsurjEq) =>
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% 131.56/22.74 (subsetTI) =>
% 131.56/22.74 ((
% 131.56/22.74 (powersetTI1) =>
% 131.56/22.74 ((
% 131.56/22.74 (powersetTE1) =>
% 131.56/22.74 ((
% 131.56/22.74 (complementTI1) =>
% 131.56/22.74 ((
% 131.56/22.74 (complementTE1) =>
% 131.56/22.74 ((
% 131.56/22.74 (binintersectTELcontra) =>
% 131.56/22.74 ((
% 131.56/22.74 (binintersectTERcontra) =>
% 131.56/22.74 ((
% 131.56/22.74 (contrasubsetT) =>
% 131.56/22.74 ((
% 131.56/22.74 (contrasubsetT1) =>
% 131.56/22.74 ((
% 131.56/22.74 (contrasubsetT2) =>
% 131.56/22.74 ((
% 131.56/22.74 (contrasubsetT3) =>
% 131.56/22.74 ((
% 131.56/22.74 (doubleComplementI1) =>
% 131.56/22.74 ((
% 131.56/22.74 (doubleComplementE1) =>
% 131.56/22.74 ((
% 131.56/22.74 (doubleComplementSub1) =>
% 131.56/22.74 ((
% 131.56/22.74 (doubleComplementSub2) =>
% 131.56/22.74 ((
% 131.56/22.74 (doubleComplementEq) =>
% 131.56/22.74 ((
% 131.56/22.74 (complementTnotintersectT) =>
% 131.56/22.74 ((
% 131.56/22.74 (complementImpComplementIntersect) =>
% 131.56/22.74 ((
% 131.56/22.74 (complementSubsetComplementIntersect) =>
% 131.56/22.74 ((
% 131.56/22.74 (complementInPowersetComplementIntersect) =>
% 131.56/22.74 ((
% 131.56/22.74 (contraSubsetComplement) =>
% 131.56/22.74 ((
% 131.56/22.74 (complementTcontraSubset) =>
% 131.56/22.74 ((
% 131.56/22.74 (binunionTILcontra) =>
% 131.56/22.74 ((
% 131.56/22.74 (binunionTIRcontra) =>
% 131.56/22.74 ((
% 131.56/22.74 (inIntersectImpInUnion) =>
% 131.56/22.74 ((
% 131.56/22.74 (inIntersectImpInUnion2) =>
% 131.56/22.74 ((
% 131.56/22.74 (inIntersectImpInIntersectUnions) =>
% 131.56/22.74 ((
% 131.56/22.74 (intersectInPowersetIntersectUnions) =>
% 131.56/22.74 ((
% 131.56/22.74 (inComplementUnionImpNotIn1) =>
% 131.56/22.74 ((
% 131.56/22.74 (inComplementUnionImpInComplement1) =>
% 131.56/22.74 ((
% 131.56/22.74 (binunionTE) =>
% 131.56/22.74 ((
% 131.56/22.74 (binunionTEcontra) =>
% 131.56/22.74 ((
% 131.56/22.74 (demorgan2a1) =>
% 131.56/22.74 ((
% 131.56/22.74 (complementUnionInPowersetComplement) =>
% 131.56/22.74 ((
% 131.56/22.74 (demorgan2a2) =>
% 131.56/22.74 ((
% 131.56/22.74 (demorgan1a) =>
% 131.56/22.74 ((
% 131.56/22.74 (demorgan1b) =>
% 131.56/22.74 ((
% 131.56/22.74 (demorgan1) =>
% 131.56/22.74 ((
% 131.56/22.74 (demorgan2a) =>
% 131.56/22.74 ((
% 131.56/22.74 (demorgan2b2) =>
% 131.56/22.74 ((
% 131.56/22.74 (demorgan2b) =>
% 131.56/22.74 ((
% 131.56/22.74 (demorgan2) =>
% 131.56/22.74 ((
% 131.56/22.74 (woz13rule0) =>
% 131.56/22.74 ((
% 131.56/22.74 (woz13rule1) =>
% 131.56/22.74 ((
% 131.56/22.74 (woz13rule2) =>
% 131.56/22.74 ((
% 131.56/22.74 (woz13rule3) =>
% 131.56/22.74 ((
% 131.56/22.74 (woz13rule4) =>
% 131.56/22.74 ((
% 131.56/22.74 (woz1_1) =>
% 131.56/22.74 ((
% 131.56/22.74 (woz1_2) =>
% 131.56/22.74 ((
% 131.56/22.74 (woz1_3) =>
% 131.56/22.74 ((
% 131.56/22.74 (woz1_4) =>
% 131.56/22.74 ((
% 131.56/22.74 (woz1_5) =>
% 131.56/22.74 ((
% 131.56/22.74 (breln1all2) =>
% 131.56/22.74 ((
% 131.56/22.74 (breln1SetBreln1) =>
% 131.56/22.74 ((
% 131.56/22.74 (choice2fnsingleton) =>
% 131.56/22.74 ((
% 131.56/22.74 (setOfPairsIsBReln1) =>
% 131.56/22.74 ((
% 131.56/22.74 (breln1all1) =>
% 131.56/22.74 ((
% 131.56/22.74 (subbreln1) =>
% 131.56/22.74 ((
% 131.56/22.74 (eqbreln1) =>
% 131.56/22.74 ((
% 131.56/22.74 (breln1invprop) =>
% 131.56/22.74 ((
% 131.56/22.74 (breln1invI) =>
% 131.56/22.74 ((
% 131.56/22.74 (breln1invE) =>
% 131.56/22.74 ((
% 131.56/22.74 (breln1compprop) =>
% 131.56/22.74 ((
% 131.56/22.74 (breln1compI) =>
% 131.56/22.74 ((
% 131.56/22.74 (breln1compE) =>
% 131.56/22.74 ((
% 131.56/22.74 (breln1compEex) =>
% 131.56/22.74 ((
% 131.56/22.74 (breln1unionprop) =>
% 131.56/22.74 ((
% 131.56/22.74 (breln1unionIL) =>
% 131.56/22.74 ((
% 131.56/22.75 (breln1unionIR) =>
% 131.56/22.75 ((
% 131.56/22.75 (breln1unionI) =>
% 131.56/22.75 ((
% 131.56/22.75 (breln1unionE) =>
% 131.56/22.75 ((
% 131.56/22.75 (breln1unionEcases) =>
% 131.56/22.75 ((
% 131.56/22.75 (breln1unionCommutes) =>
% 131.56/22.75 ((
% 131.56/22.75 (woz2Ex) =>
% 131.56/22.75 ((
% 131.56/22.75 (woz2W) =>
% 131.56/22.75 ((
% 131.56/22.75 (woz2A) =>
% 131.56/22.75 ((
% 131.56/22.75 (woz2B) =>
% 131.56/22.75 ((
% 131.56/22.75 (image1Ex) =>
% 131.56/22.75 ((
% 131.56/22.75 (image1Ex1) =>
% 131.56/22.75 ((
% 131.56/22.75 (image1Equiv) =>
% 131.56/22.75 ((
% 131.56/22.75 (image1E) =>
% 131.56/22.75 ((
% 131.56/22.75 (image1I) =>
% 131.56/22.75 ((
% 131.56/22.75 (injFuncInInjFuncSet) =>
% 131.56/22.75 ((
% 131.56/22.75 (injFuncSetFuncIn) =>
% 131.56/22.75 ((
% 131.56/22.75 (injFuncSetFuncInj) =>
% 131.56/22.75 ((
% 131.56/22.75 (surjFuncSetFuncIn) =>
% 131.56/22.75 ((
% 131.56/22.75 (surjFuncSetFuncSurj) =>
% 131.56/22.75 ((
% 131.56/22.75 (leftInvIsSurj) =>
% 131.56/22.75 ((
% 131.56/22.75 (surjCantorThm) =>
% 131.56/22.75 ((
% 131.56/22.75 (foundation2) =>
% 131.56/22.75 ((
% 131.56/22.75 (notinself) =>
% 131.56/22.75 ((
% 131.56/22.75 (notinself2) =>
% 131.56/22.75 ((
% 131.56/22.75 (omegaSp) =>
% 131.56/22.75 ((
% 131.56/22.75 (omegaSclos) =>
% 131.56/22.75 ((
% 131.56/22.75 (peano0notS) =>
% 131.56/22.75 ((
% 131.56/22.75 (peanoSinj) =>
% 131.56/22.75 ((
% 131.56/22.75 (transitivesetOp1) =>
% 131.56/22.75 ((
% 131.56/22.75 (binintTransitive) =>
% 131.56/22.75 ((
% 131.56/22.75 (transitivesetOp2) =>
% 131.56/22.75 ((
% 131.56/22.75 (setunionTransitive) =>
% 131.56/22.75 ((
% 131.56/22.75 (ordinalMinLem1) =>
% 131.56/22.75 ((
% 131.56/22.75 (ordinalTransSet) =>
% 131.56/22.75 ((
% 131.56/22.75 (ordinalTransSet1) =>
% 131.56/22.75 ((
% 131.56/22.75 (setunionOrdinalLem1) =>
% 131.56/22.75 (ordinal @
% 131.56/22.75 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 131.56/22.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl34])).
% 131.56/22.75 thf(zip_derived_cl45, plain,
% 131.56/22.75 (~ (((foundationAx) =>
% 131.56/22.75 (((wellorderingAx) =>
% 131.56/22.75 (((descrp) =>
% 131.56/22.75 (((dsetconstrI) =>
% 131.56/22.75 (((dsetconstrEL) =>
% 131.56/22.75 (((dsetconstrER) =>
% 131.56/22.75 (((exuE1) =>
% 131.56/22.75 (((prop2setE) =>
% 131.56/22.75 (((emptysetE) =>
% 131.56/22.75 (((emptysetimpfalse) =>
% 131.56/22.75 (((notinemptyset) =>
% 131.56/22.75 (((exuE3e) =>
% 131.56/22.75 (((setext) =>
% 131.56/22.75 (((emptyI) =>
% 131.56/22.75 (((noeltsimpempty) =>
% 131.56/22.75 (((setbeta) =>
% 131.56/22.75 (((nonemptyE1) =>
% 131.56/22.75 (((nonemptyI) =>
% 131.56/22.75 (((nonemptyI1) =>
% 131.56/22.75 (((setadjoinIL) =>
% 131.56/22.75 (((in @ emptyset @
% 131.56/22.75 (setadjoin @ emptyset @
% 131.56/22.75 emptyset)) =>
% 131.56/22.75 (((setadjoinIR) =>
% 131.56/22.75 (((setadjoinE) =>
% 131.56/22.75 (((setadjoinOr) =>
% 131.56/22.75 (((setoftrueEq) =>
% 131.56/22.75 (((powersetI) =>
% 131.56/22.75 (((emptyinPowerset) =>
% 131.56/22.75 (((emptyInPowerset) =>
% 131.56/22.75 (((powersetE) =>
% 131.56/22.75 (((setunionI) =>
% 131.56/22.75 ((
% 131.56/22.75 (setunionE) =>
% 131.56/22.75 ((
% 131.56/22.75 (subPowSU) =>
% 131.56/22.75 ((
% 131.56/22.75 (exuE2) =>
% 131.56/22.75 ((
% 131.56/22.75 (nonemptyImpWitness) =>
% 131.56/22.75 ((
% 131.56/22.75 (uniqinunit) =>
% 131.56/22.75 ((
% 131.56/22.75 (notinsingleton) =>
% 131.56/22.75 ((
% 131.56/22.75 (eqinunit) =>
% 131.56/22.75 ((
% 131.56/22.75 (singletonsswitch) =>
% 131.56/22.75 ((
% 131.56/22.75 (upairsetE) =>
% 131.56/22.75 ((
% 131.56/22.75 (upairsetIL) =>
% 131.56/22.75 ((
% 131.56/22.75 (upairsetIR) =>
% 131.56/22.75 ((
% 131.56/22.75 (emptyE1) =>
% 131.56/22.75 ((
% 131.56/22.75 (vacuousDall) =>
% 131.56/22.75 ((
% 131.56/22.75 (quantDeMorgan1) =>
% 131.56/22.75 ((
% 131.56/22.75 (quantDeMorgan2) =>
% 131.56/22.75 ((
% 131.56/22.75 (quantDeMorgan3) =>
% 131.56/22.75 ((
% 131.56/22.75 (quantDeMorgan4) =>
% 131.56/22.75 ((
% 131.56/22.75 (prop2setI) =>
% 131.56/22.75 ((
% 131.56/22.75 (prop2set2propI) =>
% 131.56/22.75 ((
% 131.56/22.75 (notdexE) =>
% 131.56/22.75 ((
% 131.56/22.75 (notdallE) =>
% 131.56/22.75 ((
% 131.56/22.75 (exuI1) =>
% 131.56/22.75 ((
% 131.56/22.75 (exuI3) =>
% 131.56/22.75 ((
% 131.56/22.75 (exuI2) =>
% 131.56/22.75 ((
% 131.56/22.75 (inCongP) =>
% 131.56/22.75 ((
% 131.56/22.75 (in__Cong) =>
% 131.56/22.75 ((
% 131.56/22.75 (exuE3u) =>
% 131.56/22.75 ((
% 131.56/22.75 (exu__Cong) =>
% 131.56/22.75 ((
% 131.56/22.75 (setadjoin__Cong) =>
% 131.56/22.75 ((
% 131.56/22.75 (powerset__Cong) =>
% 131.56/22.75 ((
% 131.56/22.75 (setunion__Cong) =>
% 131.56/22.75 ((
% 131.56/22.75 (exuEu) =>
% 131.56/22.75 ((
% 131.56/22.75 (descr__Cong) =>
% 131.56/22.75 ((
% 131.56/22.75 (dsetconstr__Cong) =>
% 131.56/22.75 ((
% 131.56/22.75 (subsetI1) =>
% 131.56/22.75 ((
% 131.56/22.75 (eqimpsubset2) =>
% 131.56/22.75 ((
% 131.56/22.75 (eqimpsubset1) =>
% 131.56/22.75 ((
% 131.56/22.75 (subsetI2) =>
% 131.56/22.75 ((
% 131.56/22.75 (emptysetsubset) =>
% 131.56/22.75 ((
% 131.56/22.75 (subsetE) =>
% 131.56/22.75 ((
% 131.56/22.75 (subsetE2) =>
% 131.56/22.75 ((
% 131.56/22.75 (notsubsetI) =>
% 131.56/22.75 ((
% 131.56/22.75 (notequalI1) =>
% 131.56/22.75 ((
% 131.56/22.75 (notequalI2) =>
% 131.56/22.75 ((
% 131.56/22.75 (subsetRefl) =>
% 131.56/22.75 ((
% 131.56/22.75 (subsetTrans) =>
% 131.56/22.75 ((
% 131.56/22.75 (setadjoinSub) =>
% 131.56/22.75 ((
% 131.56/22.75 (setadjoinSub2) =>
% 131.56/22.75 ((
% 131.56/22.75 (subset2powerset) =>
% 131.56/22.75 ((
% 131.56/22.75 (setextsub) =>
% 131.56/22.75 ((
% 131.56/22.75 (subsetemptysetimpeq) =>
% 131.56/22.75 ((
% 131.56/22.75 (powersetI1) =>
% 131.56/22.75 ((
% 131.56/22.75 (powersetE1) =>
% 131.56/22.75 ((
% 131.56/22.75 (inPowerset) =>
% 131.56/22.75 ((
% 131.56/22.75 (powersetsubset) =>
% 131.56/22.75 ((
% 131.56/22.75 (sepInPowerset) =>
% 131.56/22.75 ((
% 131.56/22.75 (sepSubset) =>
% 131.56/22.75 ((
% 131.56/22.75 (binunionIL) =>
% 131.56/22.75 ((
% 131.56/22.75 (upairset2IR) =>
% 131.56/22.75 ((
% 131.56/22.75 (binunionIR) =>
% 131.56/22.75 ((
% 131.56/22.75 (binunionEcases) =>
% 131.56/22.75 ((
% 131.56/22.75 (binunionE) =>
% 131.56/22.75 ((
% 131.56/22.75 (binunionLsub) =>
% 131.56/22.75 ((
% 131.56/22.75 (binunionRsub) =>
% 131.56/22.75 ((
% 131.56/22.75 (binintersectI) =>
% 131.56/22.75 ((
% 131.56/22.75 (binintersectSubset5) =>
% 131.56/22.75 ((
% 131.56/22.75 (binintersectEL) =>
% 131.56/22.75 ((
% 131.56/22.75 (binintersectLsub) =>
% 131.56/22.75 ((
% 131.56/22.75 (binintersectSubset2) =>
% 131.56/22.75 ((
% 131.56/22.75 (binintersectSubset3) =>
% 131.56/22.75 ((
% 131.56/22.75 (binintersectER) =>
% 131.56/22.75 ((
% 131.56/22.75 (disjointsetsI1) =>
% 131.56/22.75 ((
% 131.56/22.75 (binintersectRsub) =>
% 131.56/22.75 ((
% 131.56/22.75 (binintersectSubset4) =>
% 131.56/22.75 ((
% 131.56/22.75 (binintersectSubset1) =>
% 131.56/22.75 ((
% 131.56/22.75 (bs114d) =>
% 131.56/22.75 ((
% 131.56/22.75 (setminusI) =>
% 131.56/22.75 ((
% 131.56/22.75 (setminusEL) =>
% 131.56/22.75 ((
% 131.56/22.75 (setminusER) =>
% 131.56/22.75 ((
% 131.56/22.75 (setminusSubset2) =>
% 131.56/22.75 ((
% 131.56/22.75 (setminusERneg) =>
% 131.56/22.75 ((
% 131.56/22.75 (setminusELneg) =>
% 131.56/22.75 ((
% 131.56/22.75 (setminusILneg) =>
% 131.56/22.75 ((
% 131.56/22.75 (setminusIRneg) =>
% 131.56/22.75 ((
% 131.56/22.75 (setminusLsub) =>
% 131.56/22.75 ((
% 131.56/22.75 (setminusSubset1) =>
% 131.56/22.75 ((
% 131.56/22.75 (symdiffE) =>
% 131.56/22.75 ((
% 131.56/22.75 (symdiffI1) =>
% 131.56/22.75 ((
% 131.56/22.75 (symdiffI2) =>
% 131.56/22.75 ((
% 131.56/22.75 (symdiffIneg1) =>
% 131.56/22.75 ((
% 131.56/22.75 (symdiffIneg2) =>
% 131.56/22.75 ((
% 131.56/22.75 (secondinupair) =>
% 131.56/22.75 ((
% 131.56/22.75 (setukpairIL) =>
% 131.56/22.75 ((
% 131.56/22.75 (setukpairIR) =>
% 131.56/22.75 ((
% 131.56/22.75 (kpairiskpair) =>
% 131.56/22.75 ((
% 131.56/22.75 (kpairp) =>
% 131.56/22.75 ((
% 131.56/22.75 (singletonsubset) =>
% 131.56/22.75 ((
% 131.56/22.75 (singletoninpowerset) =>
% 131.56/22.75 ((
% 131.56/22.75 (singletoninpowunion) =>
% 131.56/22.75 ((
% 131.56/22.75 (upairset2E) =>
% 131.56/22.75 ((
% 131.56/22.75 (upairsubunion) =>
% 131.56/22.75 ((
% 131.56/22.75 (upairinpowunion) =>
% 131.56/22.75 ((
% 131.56/22.75 (ubforcartprodlem1) =>
% 131.56/22.75 ((
% 131.56/22.75 (ubforcartprodlem2) =>
% 131.56/22.75 ((
% 131.56/22.75 (ubforcartprodlem3) =>
% 131.56/22.75 ((
% 131.56/22.75 (cartprodpairin) =>
% 131.56/22.75 ((
% 131.56/22.75 (cartprodmempair1) =>
% 131.56/22.75 ((
% 131.56/22.75 (cartprodmempair) =>
% 131.56/22.75 ((
% 131.56/22.75 (setunionE2) =>
% 131.56/22.75 ((
% 131.56/22.75 (setunionsingleton1) =>
% 131.56/22.75 ((
% 131.56/22.75 (setunionsingleton2) =>
% 131.56/22.75 ((
% 131.56/22.75 (setunionsingleton) =>
% 131.56/22.75 ((
% 131.56/22.75 (singletonprop) =>
% 131.56/22.75 ((
% 131.56/22.75 (ex1E1) =>
% 131.56/22.75 ((
% 131.56/22.75 (ex1I) =>
% 131.56/22.75 ((
% 131.56/22.75 (ex1I2) =>
% 131.56/22.75 ((
% 131.56/22.75 (singletonsuniq) =>
% 131.56/22.75 ((
% 131.56/22.75 (setukpairinjL1) =>
% 131.56/22.75 ((
% 131.56/22.75 (kfstsingleton) =>
% 131.56/22.75 ((
% 131.56/22.75 (theprop) =>
% 131.56/22.75 ((
% 131.56/22.75 (kfstpairEq) =>
% 131.56/22.75 ((
% 131.56/22.75 (cartprodfstin) =>
% 131.56/22.75 ((
% 131.56/22.75 (setukpairinjL2) =>
% 131.56/22.75 ((
% 131.56/22.75 (setukpairinjL) =>
% 131.56/22.75 ((
% 131.56/22.75 (setukpairinjR11) =>
% 131.56/22.75 ((
% 131.56/22.75 (setukpairinjR12) =>
% 131.56/22.75 ((
% 131.56/22.75 (setukpairinjR1) =>
% 131.56/22.75 ((
% 131.56/22.75 (upairequniteq) =>
% 131.56/22.75 ((
% 131.56/22.75 (setukpairinjR2) =>
% 131.56/22.75 ((
% 131.56/22.75 (setukpairinjR) =>
% 131.56/22.75 ((
% 131.56/22.75 (ksndsingleton) =>
% 131.56/22.75 ((
% 131.56/22.75 (ksndpairEq) =>
% 131.56/22.75 ((
% 131.56/22.75 (kpairsurjEq) =>
% 131.56/22.75 ((
% 131.56/22.75 (cartprodsndin) =>
% 131.56/22.75 ((
% 131.56/22.75 (cartprodpairmemEL) =>
% 131.56/22.75 ((
% 131.56/22.75 (cartprodpairmemER) =>
% 131.56/22.75 ((
% 131.56/22.75 (cartprodmempaircEq) =>
% 131.56/22.75 ((
% 131.56/22.75 (cartprodfstpairEq) =>
% 131.56/22.75 ((
% 131.56/22.75 (cartprodsndpairEq) =>
% 131.56/22.75 ((
% 131.56/22.75 (cartprodpairsurjEq) =>
% 131.56/22.75 ((
% 131.56/22.75 (dpsetconstrI) =>
% 131.56/22.75 ((
% 131.56/22.75 (dpsetconstrSub) =>
% 131.56/22.75 ((
% 131.56/22.75 (setOfPairsIsBReln) =>
% 131.56/22.75 ((
% 131.56/22.75 (dpsetconstrERa) =>
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% 131.56/22.75 (dpsetconstrEL1) =>
% 131.56/22.75 ((
% 131.56/22.75 (dpsetconstrEL2) =>
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% 131.56/22.75 (dpsetconstrER) =>
% 131.56/22.75 ((
% 131.56/22.75 (funcImageSingleton) =>
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% 131.56/22.75 (apProp) =>
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% 131.56/22.75 (app) =>
% 131.56/22.75 ((
% 131.56/22.75 (infuncsetfunc) =>
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% 131.56/22.75 (ap2p) =>
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% 131.56/22.75 ((
% 131.56/22.75 (lamProp) =>
% 131.56/22.75 ((
% 131.56/22.75 (lamp) =>
% 131.56/22.75 ((
% 131.56/22.75 (lam2p) =>
% 131.56/22.75 ((
% 131.56/22.75 (brelnall1) =>
% 131.56/22.75 ((
% 131.56/22.75 (brelnall2) =>
% 131.56/22.75 ((
% 131.56/22.75 (ex1E2) =>
% 131.56/22.75 ((
% 131.56/22.75 (funcGraphProp1) =>
% 131.56/22.75 ((
% 131.56/22.75 (funcGraphProp3) =>
% 131.56/22.75 ((
% 131.56/22.75 (funcGraphProp2) =>
% 131.56/22.75 ((
% 131.56/22.75 (funcextLem) =>
% 131.56/22.75 ((
% 131.56/22.75 (funcGraphProp4) =>
% 131.56/22.75 ((
% 131.56/22.75 (subbreln) =>
% 131.56/22.75 ((
% 131.56/22.75 (eqbreln) =>
% 131.56/22.75 ((
% 131.56/22.75 (funcext) =>
% 131.56/22.75 ((
% 131.56/22.75 (funcext2) =>
% 131.56/22.75 ((
% 131.56/22.75 (ap2apEq1) =>
% 131.56/22.75 ((
% 131.56/22.75 (ap2apEq2) =>
% 131.56/22.75 ((
% 131.56/22.75 (beta1) =>
% 131.56/22.75 ((
% 131.56/22.75 (eta1) =>
% 131.56/22.75 ((
% 131.56/22.75 (lam2lamEq) =>
% 131.56/22.75 ((
% 131.56/22.75 (beta2) =>
% 131.56/22.75 ((
% 131.56/22.75 (eta2) =>
% 131.56/22.75 ((
% 131.56/22.75 (iffalseProp1) =>
% 131.56/22.75 ((
% 131.56/22.75 (iffalseProp2) =>
% 131.56/22.75 ((
% 131.56/22.75 (iftrueProp1) =>
% 131.56/22.75 ((
% 131.56/22.75 (iftrueProp2) =>
% 131.56/22.75 ((
% 131.56/22.75 (ifSingleton) =>
% 131.56/22.75 ((
% 131.56/22.75 (ifp) =>
% 131.56/22.75 ((
% 131.56/22.75 (theeq) =>
% 131.56/22.75 ((
% 131.56/22.75 (iftrue) =>
% 131.56/22.75 ((
% 131.56/22.75 (iffalse) =>
% 131.56/22.75 ((
% 131.56/22.75 (iftrueorfalse) =>
% 131.56/22.75 ((
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% 131.56/22.75 ((
% 131.56/22.75 (binunionT_lem) =>
% 131.56/22.75 ((
% 131.56/22.75 (powersetT_lem) =>
% 131.56/22.75 ((
% 131.56/22.75 (setminusT_lem) =>
% 131.56/22.75 ((
% 131.56/22.75 (complementT_lem) =>
% 131.56/22.75 ((
% 131.56/22.75 (setextT) =>
% 131.56/22.75 ((
% 131.56/22.75 (subsetTI) =>
% 131.56/22.75 ((
% 131.56/22.75 (powersetTI1) =>
% 131.56/22.75 ((
% 131.56/22.75 (powersetTE1) =>
% 131.56/22.75 ((
% 131.56/22.75 (complementTI1) =>
% 131.56/22.75 ((
% 131.56/22.75 (complementTE1) =>
% 131.56/22.75 ((
% 131.56/22.75 (binintersectTELcontra) =>
% 131.56/22.75 ((
% 131.56/22.75 (binintersectTERcontra) =>
% 131.56/22.75 ((
% 131.56/22.75 (contrasubsetT) =>
% 131.56/22.75 ((
% 131.56/22.75 (contrasubsetT1) =>
% 131.56/22.75 ((
% 131.56/22.75 (contrasubsetT2) =>
% 131.56/22.75 ((
% 131.56/22.75 (contrasubsetT3) =>
% 131.56/22.75 ((
% 131.56/22.75 (doubleComplementI1) =>
% 131.56/22.75 ((
% 131.56/22.75 (doubleComplementE1) =>
% 131.56/22.75 ((
% 131.56/22.75 (doubleComplementSub1) =>
% 131.56/22.75 ((
% 131.56/22.75 (doubleComplementSub2) =>
% 131.56/22.75 ((
% 131.56/22.75 (doubleComplementEq) =>
% 131.56/22.75 ((
% 131.56/22.75 (complementTnotintersectT) =>
% 131.56/22.75 ((
% 131.56/22.75 (complementImpComplementIntersect) =>
% 131.56/22.75 ((
% 131.56/22.75 (complementSubsetComplementIntersect) =>
% 131.56/22.75 ((
% 131.56/22.75 (complementInPowersetComplementIntersect) =>
% 131.56/22.75 ((
% 131.56/22.75 (contraSubsetComplement) =>
% 131.56/22.75 ((
% 131.56/22.75 (complementTcontraSubset) =>
% 131.56/22.75 ((
% 131.56/22.75 (binunionTILcontra) =>
% 131.56/22.75 ((
% 131.56/22.75 (binunionTIRcontra) =>
% 131.56/22.75 ((
% 131.56/22.75 (inIntersectImpInUnion) =>
% 131.56/22.75 ((
% 131.56/22.75 (inIntersectImpInUnion2) =>
% 131.56/22.75 ((
% 131.56/22.75 (inIntersectImpInIntersectUnions) =>
% 131.56/22.75 ((
% 131.56/22.75 (intersectInPowersetIntersectUnions) =>
% 131.56/22.75 ((
% 131.56/22.75 (inComplementUnionImpNotIn1) =>
% 131.56/22.75 ((
% 131.56/22.75 (inComplementUnionImpInComplement1) =>
% 131.56/22.75 ((
% 131.56/22.75 (binunionTE) =>
% 131.56/22.75 ((
% 131.56/22.75 (binunionTEcontra) =>
% 131.56/22.75 ((
% 131.56/22.75 (demorgan2a1) =>
% 131.56/22.75 ((
% 131.56/22.75 (complementUnionInPowersetComplement) =>
% 131.56/22.75 ((
% 131.56/22.75 (demorgan2a2) =>
% 131.56/22.75 ((
% 131.56/22.75 (demorgan1a) =>
% 131.56/22.75 ((
% 131.56/22.75 (demorgan1b) =>
% 131.56/22.75 ((
% 131.56/22.75 (demorgan1) =>
% 131.56/22.75 ((
% 131.56/22.75 (demorgan2a) =>
% 131.56/22.75 ((
% 131.56/22.75 (demorgan2b2) =>
% 131.56/22.75 ((
% 131.56/22.75 (demorgan2b) =>
% 131.56/22.75 ((
% 131.56/22.75 (demorgan2) =>
% 131.56/22.75 ((
% 131.56/22.75 (woz13rule0) =>
% 131.56/22.75 ((
% 131.56/22.75 (woz13rule1) =>
% 131.56/22.75 ((
% 131.56/22.75 (woz13rule2) =>
% 131.56/22.75 ((
% 131.56/22.75 (woz13rule3) =>
% 131.56/22.75 ((
% 131.56/22.75 (woz13rule4) =>
% 131.56/22.75 ((
% 131.56/22.75 (woz1_1) =>
% 131.56/22.75 ((
% 131.56/22.75 (woz1_2) =>
% 131.56/22.75 ((
% 131.56/22.75 (woz1_3) =>
% 131.56/22.75 ((
% 131.56/22.75 (woz1_4) =>
% 131.56/22.75 ((
% 131.56/22.75 (woz1_5) =>
% 131.56/22.75 ((
% 131.56/22.75 (breln1all2) =>
% 131.56/22.75 ((
% 131.56/22.75 (breln1SetBreln1) =>
% 131.56/22.75 ((
% 131.56/22.75 (choice2fnsingleton) =>
% 131.56/22.75 ((
% 131.56/22.75 (setOfPairsIsBReln1) =>
% 131.56/22.75 ((
% 131.56/22.75 (breln1all1) =>
% 131.56/22.75 ((
% 131.56/22.75 (subbreln1) =>
% 131.56/22.75 ((
% 131.56/22.75 (eqbreln1) =>
% 131.56/22.75 ((
% 131.56/22.75 (breln1invprop) =>
% 131.56/22.75 ((
% 131.56/22.75 (breln1invI) =>
% 131.56/22.75 ((
% 131.56/22.75 (breln1invE) =>
% 131.56/22.75 ((
% 131.56/22.75 (breln1compprop) =>
% 131.56/22.75 ((
% 131.56/22.75 (breln1compI) =>
% 131.56/22.75 ((
% 131.56/22.75 (breln1compE) =>
% 131.56/22.75 ((
% 131.56/22.75 (breln1compEex) =>
% 131.56/22.75 ((
% 131.56/22.75 (breln1unionprop) =>
% 131.56/22.75 ((
% 131.56/22.75 (breln1unionIL) =>
% 131.56/22.75 ((
% 131.56/22.75 (breln1unionIR) =>
% 131.56/22.75 ((
% 131.56/22.75 (breln1unionI) =>
% 131.56/22.75 ((
% 131.56/22.75 (breln1unionE) =>
% 131.56/22.75 ((
% 131.56/22.75 (breln1unionEcases) =>
% 131.56/22.75 ((
% 131.56/22.75 (breln1unionCommutes) =>
% 131.56/22.75 ((
% 131.56/22.75 (woz2Ex) =>
% 131.56/22.75 ((
% 131.56/22.75 (woz2W) =>
% 131.56/22.75 ((
% 131.56/22.75 (woz2A) =>
% 131.56/22.75 ((
% 131.56/22.75 (woz2B) =>
% 131.56/22.75 ((
% 131.56/22.75 (image1Ex) =>
% 131.56/22.75 ((
% 131.56/22.75 (image1Ex1) =>
% 131.56/22.75 ((
% 131.56/22.75 (image1Equiv) =>
% 131.56/22.75 ((
% 131.56/22.75 (image1E) =>
% 131.56/22.75 ((
% 131.56/22.75 (image1I) =>
% 131.56/22.75 ((
% 131.56/22.75 (injFuncInInjFuncSet) =>
% 131.56/22.75 ((
% 131.56/22.75 (injFuncSetFuncIn) =>
% 131.56/22.75 ((
% 131.56/22.75 (injFuncSetFuncInj) =>
% 131.56/22.75 ((
% 131.56/22.75 (surjFuncSetFuncIn) =>
% 131.56/22.75 ((
% 131.56/22.75 (surjFuncSetFuncSurj) =>
% 131.56/22.75 ((
% 131.56/22.75 (leftInvIsSurj) =>
% 131.56/22.75 ((
% 131.56/22.75 (surjCantorThm) =>
% 131.56/22.75 ((
% 131.56/22.75 (foundation2) =>
% 131.56/22.75 ((
% 131.56/22.75 (notinself) =>
% 131.56/22.75 ((
% 131.56/22.75 (notinself2) =>
% 131.56/22.75 ((
% 131.56/22.75 (omegaSp) =>
% 131.56/22.75 ((
% 131.56/22.75 (omegaSclos) =>
% 131.56/22.75 ((
% 131.56/22.75 (peano0notS) =>
% 131.56/22.75 ((
% 131.56/22.75 (peanoSinj) =>
% 131.56/22.75 ((
% 131.56/22.75 (transitivesetOp1) =>
% 131.56/22.75 ((
% 131.56/22.75 (binintTransitive) =>
% 131.56/22.75 ((
% 131.56/22.75 (transitivesetOp2) =>
% 131.56/22.75 ((
% 131.56/22.75 (setunionTransitive) =>
% 131.56/22.75 ((
% 131.56/22.75 (ordinalMinLem1) =>
% 131.56/22.75 ((
% 131.56/22.75 (ordinalTransSet) =>
% 131.56/22.75 ((
% 131.56/22.75 (ordinalTransSet1) =>
% 131.56/22.75 ((
% 131.56/22.75 (setunionOrdinalLem1) =>
% 131.56/22.75 (ordinal @
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% 131.56/22.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl40])).
% 131.56/22.75 thf(zip_derived_cl50, plain,
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% 131.56/22.75 (((dsetconstrEL) =>
% 131.56/22.75 (((dsetconstrER) =>
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% 131.56/22.75 (((notinemptyset) =>
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% 131.56/22.75 (((noeltsimpempty) =>
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% 131.56/22.75 (((nonemptyI1) =>
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% 131.56/22.75 (((setadjoinIR) =>
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% 131.56/22.75 (((setoftrueEq) =>
% 131.56/22.75 (((powersetI) =>
% 131.56/22.75 (((emptyinPowerset) =>
% 131.56/22.75 (((emptyInPowerset) =>
% 131.56/22.75 (((powersetE) =>
% 131.56/22.75 (((setunionI) =>
% 131.56/22.75 (((setunionE) =>
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% 131.56/22.75 (subPowSU) =>
% 131.56/22.75 ((
% 131.56/22.75 (exuE2) =>
% 131.56/22.75 ((
% 131.56/22.75 (nonemptyImpWitness) =>
% 131.56/22.75 ((
% 131.56/22.75 (uniqinunit) =>
% 131.56/22.75 ((
% 131.56/22.75 (notinsingleton) =>
% 131.56/22.75 ((
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% 131.56/22.75 ((
% 131.56/22.75 (singletonsswitch) =>
% 131.56/22.75 ((
% 131.56/22.75 (upairsetE) =>
% 131.56/22.75 ((
% 131.56/22.75 (upairsetIL) =>
% 131.56/22.75 ((
% 131.56/22.75 (upairsetIR) =>
% 131.56/22.75 ((
% 131.56/22.75 (emptyE1) =>
% 131.56/22.75 ((
% 131.56/22.75 (vacuousDall) =>
% 131.56/22.75 ((
% 131.56/22.75 (quantDeMorgan1) =>
% 131.56/22.75 ((
% 131.56/22.75 (quantDeMorgan2) =>
% 131.56/22.75 ((
% 131.56/22.75 (quantDeMorgan3) =>
% 131.56/22.75 ((
% 131.56/22.75 (quantDeMorgan4) =>
% 131.56/22.75 ((
% 131.56/22.75 (prop2setI) =>
% 131.56/22.75 ((
% 131.56/22.75 (prop2set2propI) =>
% 131.56/22.75 ((
% 131.56/22.75 (notdexE) =>
% 131.56/22.75 ((
% 131.56/22.75 (notdallE) =>
% 131.56/22.75 ((
% 131.56/22.75 (exuI1) =>
% 131.56/22.75 ((
% 131.56/22.75 (exuI3) =>
% 131.56/22.75 ((
% 131.56/22.75 (exuI2) =>
% 131.56/22.75 ((
% 131.56/22.75 (inCongP) =>
% 131.56/22.75 ((
% 131.56/22.75 (in__Cong) =>
% 131.56/22.75 ((
% 131.56/22.75 (exuE3u) =>
% 131.56/22.75 ((
% 131.56/22.75 (exu__Cong) =>
% 131.56/22.75 ((
% 131.56/22.75 (setadjoin__Cong) =>
% 131.56/22.75 ((
% 131.56/22.75 (powerset__Cong) =>
% 131.56/22.75 ((
% 131.56/22.75 (setunion__Cong) =>
% 131.56/22.75 ((
% 131.56/22.75 (exuEu) =>
% 131.56/22.75 ((
% 131.56/22.75 (descr__Cong) =>
% 131.56/22.75 ((
% 131.56/22.75 (dsetconstr__Cong) =>
% 131.56/22.75 ((
% 131.56/22.75 (subsetI1) =>
% 131.56/22.75 ((
% 131.56/22.75 (eqimpsubset2) =>
% 131.56/22.75 ((
% 131.56/22.75 (eqimpsubset1) =>
% 131.56/22.75 ((
% 131.56/22.75 (subsetI2) =>
% 131.56/22.75 ((
% 131.56/22.75 (emptysetsubset) =>
% 131.56/22.75 ((
% 131.56/22.75 (subsetE) =>
% 131.56/22.75 ((
% 131.56/22.75 (subsetE2) =>
% 131.56/22.75 ((
% 131.56/22.75 (notsubsetI) =>
% 131.56/22.75 ((
% 131.56/22.75 (notequalI1) =>
% 131.56/22.75 ((
% 131.56/22.75 (notequalI2) =>
% 131.56/22.75 ((
% 131.56/22.75 (subsetRefl) =>
% 131.56/22.75 ((
% 131.56/22.75 (subsetTrans) =>
% 131.56/22.75 ((
% 131.56/22.75 (setadjoinSub) =>
% 131.56/22.75 ((
% 131.56/22.75 (setadjoinSub2) =>
% 131.56/22.75 ((
% 131.56/22.75 (subset2powerset) =>
% 131.56/22.75 ((
% 131.56/22.75 (setextsub) =>
% 131.56/22.75 ((
% 131.56/22.75 (subsetemptysetimpeq) =>
% 131.56/22.75 ((
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% 131.56/22.75 ((
% 131.56/22.75 (powersetE1) =>
% 131.56/22.75 ((
% 131.56/22.75 (inPowerset) =>
% 131.56/22.75 ((
% 131.56/22.75 (powersetsubset) =>
% 131.56/22.75 ((
% 131.56/22.75 (sepInPowerset) =>
% 131.56/22.75 ((
% 131.56/22.75 (sepSubset) =>
% 131.56/22.75 ((
% 131.56/22.75 (binunionIL) =>
% 131.56/22.75 ((
% 131.56/22.75 (upairset2IR) =>
% 131.56/22.75 ((
% 131.56/22.75 (binunionIR) =>
% 131.56/22.75 ((
% 131.56/22.75 (binunionEcases) =>
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% 131.56/22.75 (binunionE) =>
% 131.56/22.75 ((
% 131.56/22.75 (binunionLsub) =>
% 131.56/22.75 ((
% 131.56/22.75 (binunionRsub) =>
% 131.56/22.75 ((
% 131.56/22.75 (binintersectI) =>
% 131.56/22.75 ((
% 131.56/22.75 (binintersectSubset5) =>
% 131.56/22.75 ((
% 131.56/22.75 (binintersectEL) =>
% 131.56/22.75 ((
% 131.56/22.75 (binintersectLsub) =>
% 131.56/22.75 ((
% 131.56/22.75 (binintersectSubset2) =>
% 131.56/22.75 ((
% 131.56/22.75 (binintersectSubset3) =>
% 131.56/22.75 ((
% 131.56/22.75 (binintersectER) =>
% 131.56/22.75 ((
% 131.56/22.75 (disjointsetsI1) =>
% 131.56/22.75 ((
% 131.56/22.75 (binintersectRsub) =>
% 131.56/22.75 ((
% 131.56/22.75 (binintersectSubset4) =>
% 131.56/22.75 ((
% 131.56/22.75 (binintersectSubset1) =>
% 131.56/22.75 ((
% 131.56/22.75 (bs114d) =>
% 131.56/22.75 ((
% 131.56/22.75 (setminusI) =>
% 131.56/22.75 ((
% 131.56/22.75 (setminusEL) =>
% 131.56/22.75 ((
% 131.56/22.75 (setminusER) =>
% 131.56/22.75 ((
% 131.56/22.75 (setminusSubset2) =>
% 131.56/22.75 ((
% 131.56/22.75 (setminusERneg) =>
% 131.56/22.75 ((
% 131.56/22.75 (setminusELneg) =>
% 131.56/22.75 ((
% 131.56/22.75 (setminusILneg) =>
% 131.56/22.75 ((
% 131.56/22.75 (setminusIRneg) =>
% 131.56/22.75 ((
% 131.56/22.75 (setminusLsub) =>
% 131.56/22.75 ((
% 131.56/22.75 (setminusSubset1) =>
% 131.56/22.75 ((
% 131.56/22.75 (symdiffE) =>
% 131.56/22.75 ((
% 131.56/22.75 (symdiffI1) =>
% 131.56/22.75 ((
% 131.56/22.75 (symdiffI2) =>
% 131.56/22.75 ((
% 131.56/22.75 (symdiffIneg1) =>
% 131.56/22.75 ((
% 131.56/22.75 (symdiffIneg2) =>
% 131.56/22.75 ((
% 131.56/22.75 (secondinupair) =>
% 131.56/22.75 ((
% 131.56/22.75 (setukpairIL) =>
% 131.56/22.75 ((
% 131.56/22.75 (setukpairIR) =>
% 131.56/22.75 ((
% 131.56/22.75 (kpairiskpair) =>
% 131.56/22.75 ((
% 131.56/22.75 (kpairp) =>
% 131.56/22.75 ((
% 131.56/22.75 (singletonsubset) =>
% 131.56/22.75 ((
% 131.56/22.75 (singletoninpowerset) =>
% 131.56/22.75 ((
% 131.56/22.75 (singletoninpowunion) =>
% 131.56/22.75 ((
% 131.56/22.75 (upairset2E) =>
% 131.56/22.75 ((
% 131.56/22.75 (upairsubunion) =>
% 131.56/22.75 ((
% 131.56/22.75 (upairinpowunion) =>
% 131.56/22.75 ((
% 131.56/22.75 (ubforcartprodlem1) =>
% 131.56/22.75 ((
% 131.56/22.75 (ubforcartprodlem2) =>
% 131.56/22.75 ((
% 131.56/22.75 (ubforcartprodlem3) =>
% 131.56/22.75 ((
% 131.56/22.75 (cartprodpairin) =>
% 131.56/22.75 ((
% 131.56/22.75 (cartprodmempair1) =>
% 131.56/22.75 ((
% 131.56/22.75 (cartprodmempair) =>
% 131.56/22.75 ((
% 131.56/22.75 (setunionE2) =>
% 131.56/22.75 ((
% 131.56/22.75 (setunionsingleton1) =>
% 131.56/22.75 ((
% 131.56/22.75 (setunionsingleton2) =>
% 131.56/22.75 ((
% 131.56/22.75 (setunionsingleton) =>
% 131.56/22.75 ((
% 131.56/22.75 (singletonprop) =>
% 131.56/22.75 ((
% 131.56/22.75 (ex1E1) =>
% 131.56/22.75 ((
% 131.56/22.75 (ex1I) =>
% 131.56/22.75 ((
% 131.56/22.75 (ex1I2) =>
% 131.56/22.75 ((
% 131.56/22.75 (singletonsuniq) =>
% 131.56/22.75 ((
% 131.56/22.75 (setukpairinjL1) =>
% 131.56/22.75 ((
% 131.56/22.75 (kfstsingleton) =>
% 131.56/22.75 ((
% 131.56/22.75 (theprop) =>
% 131.56/22.75 ((
% 131.56/22.75 (kfstpairEq) =>
% 131.56/22.75 ((
% 131.56/22.75 (cartprodfstin) =>
% 131.56/22.75 ((
% 131.56/22.75 (setukpairinjL2) =>
% 131.56/22.75 ((
% 131.56/22.75 (setukpairinjL) =>
% 131.56/22.75 ((
% 131.56/22.75 (setukpairinjR11) =>
% 131.56/22.75 ((
% 131.56/22.75 (setukpairinjR12) =>
% 131.56/22.75 ((
% 131.56/22.75 (setukpairinjR1) =>
% 131.56/22.75 ((
% 131.56/22.75 (upairequniteq) =>
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% 131.56/22.75 (setukpairinjR2) =>
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% 131.56/22.75 (setukpairinjR) =>
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% 131.56/22.75 (ksndsingleton) =>
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% 131.56/22.75 (ksndpairEq) =>
% 131.56/22.75 ((
% 131.56/22.75 (kpairsurjEq) =>
% 131.56/22.75 ((
% 131.56/22.75 (cartprodsndin) =>
% 131.56/22.75 ((
% 131.56/22.75 (cartprodpairmemEL) =>
% 131.56/22.75 ((
% 131.56/22.75 (cartprodpairmemER) =>
% 131.56/22.75 ((
% 131.56/22.75 (cartprodmempaircEq) =>
% 131.56/22.75 ((
% 131.56/22.75 (cartprodfstpairEq) =>
% 131.56/22.75 ((
% 131.56/22.75 (cartprodsndpairEq) =>
% 131.56/22.75 ((
% 131.56/22.75 (cartprodpairsurjEq) =>
% 131.56/22.75 ((
% 131.56/22.75 (dpsetconstrI) =>
% 131.56/22.75 ((
% 131.56/22.75 (dpsetconstrSub) =>
% 131.56/22.75 ((
% 131.56/22.75 (setOfPairsIsBReln) =>
% 131.56/22.75 ((
% 131.56/22.75 (dpsetconstrERa) =>
% 131.56/22.75 ((
% 131.56/22.75 (dpsetconstrEL1) =>
% 131.56/22.75 ((
% 131.56/22.75 (dpsetconstrEL2) =>
% 131.56/22.75 ((
% 131.56/22.75 (dpsetconstrER) =>
% 131.56/22.75 ((
% 131.56/22.75 (funcImageSingleton) =>
% 131.56/22.75 ((
% 131.56/22.75 (apProp) =>
% 131.56/22.75 ((
% 131.56/22.75 (app) =>
% 131.56/22.75 ((
% 131.56/22.75 (infuncsetfunc) =>
% 131.56/22.75 ((
% 131.56/22.75 (ap2p) =>
% 131.56/22.75 ((
% 131.56/22.75 (funcinfuncset) =>
% 131.56/22.75 ((
% 131.56/22.75 (lamProp) =>
% 131.56/22.75 ((
% 131.56/22.75 (lamp) =>
% 131.56/22.75 ((
% 131.56/22.75 (lam2p) =>
% 131.56/22.75 ((
% 131.56/22.75 (brelnall1) =>
% 131.56/22.75 ((
% 131.56/22.75 (brelnall2) =>
% 131.56/22.75 ((
% 131.56/22.75 (ex1E2) =>
% 131.56/22.75 ((
% 131.56/22.75 (funcGraphProp1) =>
% 131.56/22.75 ((
% 131.56/22.75 (funcGraphProp3) =>
% 131.56/22.75 ((
% 131.56/22.75 (funcGraphProp2) =>
% 131.56/22.75 ((
% 131.56/22.75 (funcextLem) =>
% 131.56/22.75 ((
% 131.56/22.75 (funcGraphProp4) =>
% 131.56/22.75 ((
% 131.56/22.75 (subbreln) =>
% 131.56/22.75 ((
% 131.56/22.75 (eqbreln) =>
% 131.56/22.75 ((
% 131.56/22.75 (funcext) =>
% 131.56/22.75 ((
% 131.56/22.75 (funcext2) =>
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% 131.56/22.75 (ap2apEq1) =>
% 131.56/22.75 ((
% 131.56/22.75 (ap2apEq2) =>
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% 131.56/22.75 (beta1) =>
% 131.56/22.75 ((
% 131.56/22.75 (eta1) =>
% 131.56/22.75 ((
% 131.56/22.75 (lam2lamEq) =>
% 131.56/22.75 ((
% 131.56/22.75 (beta2) =>
% 131.56/22.75 ((
% 131.56/22.75 (eta2) =>
% 131.56/22.75 ((
% 131.56/22.75 (iffalseProp1) =>
% 131.56/22.75 ((
% 131.56/22.75 (iffalseProp2) =>
% 131.56/22.75 ((
% 131.56/22.75 (iftrueProp1) =>
% 131.56/22.75 ((
% 131.56/22.75 (iftrueProp2) =>
% 131.56/22.75 ((
% 131.56/22.75 (ifSingleton) =>
% 131.56/22.75 ((
% 131.56/22.75 (ifp) =>
% 131.56/22.75 ((
% 131.56/22.75 (theeq) =>
% 131.56/22.75 ((
% 131.56/22.75 (iftrue) =>
% 131.56/22.75 ((
% 131.56/22.75 (iffalse) =>
% 131.56/22.75 ((
% 131.56/22.75 (iftrueorfalse) =>
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% 131.56/22.75 (powersetT_lem) =>
% 131.56/22.75 ((
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% 131.56/22.75 ((
% 131.56/22.75 (complementT_lem) =>
% 131.56/22.75 ((
% 131.56/22.75 (setextT) =>
% 131.56/22.75 ((
% 131.56/22.75 (subsetTI) =>
% 131.56/22.75 ((
% 131.56/22.75 (powersetTI1) =>
% 131.56/22.75 ((
% 131.56/22.75 (powersetTE1) =>
% 131.56/22.75 ((
% 131.56/22.75 (complementTI1) =>
% 131.56/22.75 ((
% 131.56/22.75 (complementTE1) =>
% 131.56/22.75 ((
% 131.56/22.75 (binintersectTELcontra) =>
% 131.56/22.75 ((
% 131.56/22.75 (binintersectTERcontra) =>
% 131.56/22.75 ((
% 131.56/22.75 (contrasubsetT) =>
% 131.56/22.75 ((
% 131.56/22.75 (contrasubsetT1) =>
% 131.56/22.75 ((
% 131.56/22.75 (contrasubsetT2) =>
% 131.56/22.75 ((
% 131.56/22.75 (contrasubsetT3) =>
% 131.56/22.75 ((
% 131.56/22.75 (doubleComplementI1) =>
% 131.56/22.75 ((
% 131.56/22.75 (doubleComplementE1) =>
% 131.56/22.75 ((
% 131.56/22.75 (doubleComplementSub1) =>
% 131.56/22.75 ((
% 131.56/22.75 (doubleComplementSub2) =>
% 131.56/22.75 ((
% 131.56/22.75 (doubleComplementEq) =>
% 131.56/22.75 ((
% 131.56/22.75 (complementTnotintersectT) =>
% 131.56/22.75 ((
% 131.56/22.75 (complementImpComplementIntersect) =>
% 131.56/22.75 ((
% 131.56/22.75 (complementSubsetComplementIntersect) =>
% 131.56/22.75 ((
% 131.56/22.75 (complementInPowersetComplementIntersect) =>
% 131.56/22.75 ((
% 131.56/22.75 (contraSubsetComplement) =>
% 131.56/22.75 ((
% 131.56/22.75 (complementTcontraSubset) =>
% 131.56/22.75 ((
% 131.56/22.75 (binunionTILcontra) =>
% 131.56/22.75 ((
% 131.56/22.75 (binunionTIRcontra) =>
% 131.56/22.75 ((
% 131.56/22.75 (inIntersectImpInUnion) =>
% 131.56/22.75 ((
% 131.56/22.75 (inIntersectImpInUnion2) =>
% 131.56/22.75 ((
% 131.56/22.75 (inIntersectImpInIntersectUnions) =>
% 131.56/22.75 ((
% 131.56/22.75 (intersectInPowersetIntersectUnions) =>
% 131.56/22.75 ((
% 131.56/22.75 (inComplementUnionImpNotIn1) =>
% 131.56/22.75 ((
% 131.56/22.75 (inComplementUnionImpInComplement1) =>
% 131.56/22.75 ((
% 131.56/22.75 (binunionTE) =>
% 131.56/22.75 ((
% 131.56/22.75 (binunionTEcontra) =>
% 131.56/22.75 ((
% 131.56/22.75 (demorgan2a1) =>
% 131.56/22.75 ((
% 131.56/22.75 (complementUnionInPowersetComplement) =>
% 131.56/22.75 ((
% 131.56/22.75 (demorgan2a2) =>
% 131.56/22.75 ((
% 131.56/22.75 (demorgan1a) =>
% 131.56/22.75 ((
% 131.56/22.75 (demorgan1b) =>
% 131.56/22.75 ((
% 131.56/22.75 (demorgan1) =>
% 131.56/22.75 ((
% 131.56/22.75 (demorgan2a) =>
% 131.56/22.75 ((
% 131.56/22.75 (demorgan2b2) =>
% 131.56/22.75 ((
% 131.56/22.75 (demorgan2b) =>
% 131.56/22.75 ((
% 131.56/22.75 (demorgan2) =>
% 131.56/22.75 ((
% 131.56/22.75 (woz13rule0) =>
% 131.56/22.75 ((
% 131.56/22.75 (woz13rule1) =>
% 131.56/22.75 ((
% 131.56/22.75 (woz13rule2) =>
% 131.56/22.75 ((
% 131.56/22.75 (woz13rule3) =>
% 131.56/22.75 ((
% 131.56/22.75 (woz13rule4) =>
% 131.56/22.75 ((
% 131.56/22.75 (woz1_1) =>
% 131.56/22.75 ((
% 131.56/22.75 (woz1_2) =>
% 131.56/22.75 ((
% 131.56/22.75 (woz1_3) =>
% 131.56/22.75 ((
% 131.56/22.75 (woz1_4) =>
% 131.56/22.75 ((
% 131.56/22.75 (woz1_5) =>
% 131.56/22.75 ((
% 131.56/22.75 (breln1all2) =>
% 131.56/22.75 ((
% 131.56/22.75 (breln1SetBreln1) =>
% 131.56/22.75 ((
% 131.56/22.75 (choice2fnsingleton) =>
% 131.56/22.75 ((
% 131.56/22.75 (setOfPairsIsBReln1) =>
% 131.56/22.75 ((
% 131.56/22.75 (breln1all1) =>
% 131.56/22.75 ((
% 131.56/22.75 (subbreln1) =>
% 131.56/22.75 ((
% 131.56/22.75 (eqbreln1) =>
% 131.56/22.75 ((
% 131.56/22.75 (breln1invprop) =>
% 131.56/22.75 ((
% 131.56/22.75 (breln1invI) =>
% 131.56/22.75 ((
% 131.56/22.75 (breln1invE) =>
% 131.56/22.75 ((
% 131.56/22.75 (breln1compprop) =>
% 131.56/22.75 ((
% 131.56/22.75 (breln1compI) =>
% 131.56/22.75 ((
% 131.56/22.75 (breln1compE) =>
% 131.56/22.75 ((
% 131.56/22.75 (breln1compEex) =>
% 131.56/22.75 ((
% 131.56/22.75 (breln1unionprop) =>
% 131.56/22.75 ((
% 131.56/22.75 (breln1unionIL) =>
% 131.56/22.75 ((
% 131.56/22.75 (breln1unionIR) =>
% 131.56/22.75 ((
% 131.56/22.75 (breln1unionI) =>
% 131.56/22.75 ((
% 131.56/22.75 (breln1unionE) =>
% 131.56/22.75 ((
% 131.56/22.75 (breln1unionEcases) =>
% 131.56/22.75 ((
% 131.56/22.75 (breln1unionCommutes) =>
% 131.56/22.75 ((
% 131.56/22.75 (woz2Ex) =>
% 131.56/22.75 ((
% 131.56/22.75 (woz2W) =>
% 131.56/22.75 ((
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% 131.56/22.75 ((
% 131.56/22.75 (woz2B) =>
% 131.56/22.75 ((
% 131.56/22.75 (image1Ex) =>
% 131.56/22.75 ((
% 131.56/22.75 (image1Ex1) =>
% 131.56/22.75 ((
% 131.56/22.75 (image1Equiv) =>
% 131.56/22.75 ((
% 131.56/22.75 (image1E) =>
% 131.56/22.75 ((
% 131.56/22.75 (image1I) =>
% 131.56/22.75 ((
% 131.56/22.75 (injFuncInInjFuncSet) =>
% 131.56/22.75 ((
% 131.56/22.75 (injFuncSetFuncIn) =>
% 131.56/22.75 ((
% 131.56/22.75 (injFuncSetFuncInj) =>
% 131.56/22.75 ((
% 131.56/22.75 (surjFuncSetFuncIn) =>
% 131.56/22.75 ((
% 131.56/22.75 (surjFuncSetFuncSurj) =>
% 131.56/22.75 ((
% 131.56/22.75 (leftInvIsSurj) =>
% 131.56/22.75 ((
% 131.56/22.75 (surjCantorThm) =>
% 131.56/22.75 ((
% 131.56/22.75 (foundation2) =>
% 131.56/22.75 ((
% 131.56/22.75 (notinself) =>
% 131.56/22.75 ((
% 131.56/22.75 (notinself2) =>
% 131.56/22.75 ((
% 131.56/22.75 (omegaSp) =>
% 131.56/22.75 ((
% 131.56/22.75 (omegaSclos) =>
% 131.56/22.75 ((
% 131.56/22.75 (peano0notS) =>
% 131.56/22.75 ((
% 131.56/22.75 (peanoSinj) =>
% 131.56/22.75 ((
% 131.56/22.75 (transitivesetOp1) =>
% 131.56/22.75 ((
% 131.56/22.75 (binintTransitive) =>
% 131.56/22.75 ((
% 131.56/22.75 (transitivesetOp2) =>
% 131.56/22.75 ((
% 131.56/22.75 (setunionTransitive) =>
% 131.56/22.75 ((
% 131.56/22.75 (ordinalMinLem1) =>
% 131.56/22.75 ((
% 131.56/22.75 (ordinalTransSet) =>
% 131.56/22.75 ((
% 131.56/22.75 (ordinalTransSet1) =>
% 131.56/22.75 ((
% 131.56/22.75 (setunionOrdinalLem1) =>
% 131.56/22.75 (ordinal @
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% 131.56/22.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl45])).
% 131.56/22.75 thf(zip_derived_cl56, plain,
% 131.56/22.75 (~ (((descrp) =>
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% 131.56/22.75 (((powersetI) =>
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% 131.56/22.75 (((subPowSU) =>
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% 131.56/22.75 ((
% 131.56/22.75 (nonemptyImpWitness) =>
% 131.56/22.75 ((
% 131.56/22.75 (uniqinunit) =>
% 131.56/22.75 ((
% 131.56/22.75 (notinsingleton) =>
% 131.56/22.75 ((
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% 131.56/22.75 ((
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% 131.56/22.75 ((
% 131.56/22.75 (upairsetE) =>
% 131.56/22.75 ((
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% 131.56/22.75 ((
% 131.56/22.75 (upairsetIR) =>
% 131.56/22.75 ((
% 131.56/22.75 (emptyE1) =>
% 131.56/22.75 ((
% 131.56/22.75 (vacuousDall) =>
% 131.56/22.75 ((
% 131.56/22.75 (quantDeMorgan1) =>
% 131.56/22.75 ((
% 131.56/22.75 (quantDeMorgan2) =>
% 131.56/22.75 ((
% 131.56/22.75 (quantDeMorgan3) =>
% 131.56/22.75 ((
% 131.56/22.75 (quantDeMorgan4) =>
% 131.56/22.75 ((
% 131.56/22.75 (prop2setI) =>
% 131.56/22.75 ((
% 131.56/22.75 (prop2set2propI) =>
% 131.56/22.75 ((
% 131.56/22.75 (notdexE) =>
% 131.56/22.75 ((
% 131.56/22.75 (notdallE) =>
% 131.56/22.75 ((
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% 131.56/22.75 ((
% 131.56/22.75 (exuI3) =>
% 131.56/22.75 ((
% 131.56/22.75 (exuI2) =>
% 131.56/22.75 ((
% 131.56/22.75 (inCongP) =>
% 131.56/22.75 ((
% 131.56/22.75 (in__Cong) =>
% 131.56/22.75 ((
% 131.56/22.75 (exuE3u) =>
% 131.56/22.75 ((
% 131.56/22.75 (exu__Cong) =>
% 131.56/22.75 ((
% 131.56/22.75 (setadjoin__Cong) =>
% 131.56/22.75 ((
% 131.56/22.75 (powerset__Cong) =>
% 131.56/22.75 ((
% 131.56/22.75 (setunion__Cong) =>
% 131.56/22.75 ((
% 131.56/22.75 (exuEu) =>
% 131.56/22.75 ((
% 131.56/22.75 (descr__Cong) =>
% 131.56/22.75 ((
% 131.56/22.75 (dsetconstr__Cong) =>
% 131.56/22.75 ((
% 131.56/22.75 (subsetI1) =>
% 131.56/22.75 ((
% 131.56/22.75 (eqimpsubset2) =>
% 131.56/22.75 ((
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% 131.56/22.75 ((
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% 131.56/22.75 ((
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% 131.56/22.75 ((
% 131.56/22.75 (notequalI1) =>
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% 131.56/22.75 ((
% 131.56/22.75 (subsetRefl) =>
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% 131.56/22.75 (subsetTrans) =>
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% 131.56/22.75 (sepSubset) =>
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% 131.56/22.75 ((
% 131.56/22.75 (upairset2IR) =>
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% 131.56/22.75 ((
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% 131.56/22.75 ((
% 131.56/22.75 (binintersectSubset5) =>
% 131.56/22.75 ((
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% 131.56/22.75 ((
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% 131.56/22.75 ((
% 131.56/22.75 (binintersectSubset3) =>
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% 131.56/22.75 (disjointsetsI1) =>
% 131.56/22.75 ((
% 131.56/22.75 (binintersectRsub) =>
% 131.56/22.75 ((
% 131.56/22.75 (binintersectSubset4) =>
% 131.56/22.75 ((
% 131.56/22.75 (binintersectSubset1) =>
% 131.56/22.75 ((
% 131.56/22.75 (bs114d) =>
% 131.56/22.75 ((
% 131.56/22.75 (setminusI) =>
% 131.56/22.75 ((
% 131.56/22.75 (setminusEL) =>
% 131.56/22.75 ((
% 131.56/22.75 (setminusER) =>
% 131.56/22.75 ((
% 131.56/22.75 (setminusSubset2) =>
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% 131.56/22.75 (setminusERneg) =>
% 131.56/22.75 ((
% 131.56/22.75 (setminusELneg) =>
% 131.56/22.75 ((
% 131.56/22.75 (setminusILneg) =>
% 131.56/22.75 ((
% 131.56/22.75 (setminusIRneg) =>
% 131.56/22.75 ((
% 131.56/22.75 (setminusLsub) =>
% 131.56/22.75 ((
% 131.56/22.75 (setminusSubset1) =>
% 131.56/22.75 ((
% 131.56/22.75 (symdiffE) =>
% 131.56/22.75 ((
% 131.56/22.75 (symdiffI1) =>
% 131.56/22.75 ((
% 131.56/22.75 (symdiffI2) =>
% 131.56/22.75 ((
% 131.56/22.75 (symdiffIneg1) =>
% 131.56/22.75 ((
% 131.56/22.75 (symdiffIneg2) =>
% 131.56/22.75 ((
% 131.56/22.75 (secondinupair) =>
% 131.56/22.75 ((
% 131.56/22.75 (setukpairIL) =>
% 131.56/22.75 ((
% 131.56/22.75 (setukpairIR) =>
% 131.56/22.75 ((
% 131.56/22.75 (kpairiskpair) =>
% 131.56/22.75 ((
% 131.56/22.75 (kpairp) =>
% 131.56/22.75 ((
% 131.56/22.75 (singletonsubset) =>
% 131.56/22.75 ((
% 131.56/22.75 (singletoninpowerset) =>
% 131.56/22.75 ((
% 131.56/22.75 (singletoninpowunion) =>
% 131.56/22.75 ((
% 131.56/22.75 (upairset2E) =>
% 131.56/22.75 ((
% 131.56/22.75 (upairsubunion) =>
% 131.56/22.75 ((
% 131.56/22.75 (upairinpowunion) =>
% 131.56/22.75 ((
% 131.56/22.75 (ubforcartprodlem1) =>
% 131.56/22.75 ((
% 131.56/22.75 (ubforcartprodlem2) =>
% 131.56/22.75 ((
% 131.56/22.75 (ubforcartprodlem3) =>
% 131.56/22.75 ((
% 131.56/22.75 (cartprodpairin) =>
% 131.56/22.75 ((
% 131.56/22.75 (cartprodmempair1) =>
% 131.56/22.75 ((
% 131.56/22.75 (cartprodmempair) =>
% 131.56/22.75 ((
% 131.56/22.75 (setunionE2) =>
% 131.56/22.75 ((
% 131.56/22.75 (setunionsingleton1) =>
% 131.56/22.75 ((
% 131.56/22.75 (setunionsingleton2) =>
% 131.56/22.75 ((
% 131.56/22.75 (setunionsingleton) =>
% 131.56/22.75 ((
% 131.56/22.75 (singletonprop) =>
% 131.56/22.75 ((
% 131.56/22.75 (ex1E1) =>
% 131.56/22.75 ((
% 131.56/22.75 (ex1I) =>
% 131.56/22.75 ((
% 131.56/22.75 (ex1I2) =>
% 131.56/22.75 ((
% 131.56/22.75 (singletonsuniq) =>
% 131.56/22.75 ((
% 131.56/22.75 (setukpairinjL1) =>
% 131.56/22.75 ((
% 131.56/22.75 (kfstsingleton) =>
% 131.56/22.75 ((
% 131.56/22.75 (theprop) =>
% 131.56/22.75 ((
% 131.56/22.75 (kfstpairEq) =>
% 131.56/22.75 ((
% 131.56/22.75 (cartprodfstin) =>
% 131.56/22.75 ((
% 131.56/22.75 (setukpairinjL2) =>
% 131.56/22.75 ((
% 131.56/22.75 (setukpairinjL) =>
% 131.56/22.75 ((
% 131.56/22.75 (setukpairinjR11) =>
% 131.56/22.75 ((
% 131.56/22.75 (setukpairinjR12) =>
% 131.56/22.75 ((
% 131.56/22.75 (setukpairinjR1) =>
% 131.56/22.75 ((
% 131.56/22.75 (upairequniteq) =>
% 131.56/22.75 ((
% 131.56/22.75 (setukpairinjR2) =>
% 131.56/22.75 ((
% 131.56/22.75 (setukpairinjR) =>
% 131.56/22.75 ((
% 131.56/22.75 (ksndsingleton) =>
% 131.56/22.75 ((
% 131.56/22.75 (ksndpairEq) =>
% 131.56/22.75 ((
% 131.56/22.75 (kpairsurjEq) =>
% 131.56/22.75 ((
% 131.56/22.75 (cartprodsndin) =>
% 131.56/22.75 ((
% 131.56/22.75 (cartprodpairmemEL) =>
% 131.56/22.75 ((
% 131.56/22.75 (cartprodpairmemER) =>
% 131.56/22.75 ((
% 131.56/22.75 (cartprodmempaircEq) =>
% 131.56/22.75 ((
% 131.56/22.75 (cartprodfstpairEq) =>
% 131.56/22.75 ((
% 131.56/22.75 (cartprodsndpairEq) =>
% 131.56/22.75 ((
% 131.56/22.75 (cartprodpairsurjEq) =>
% 131.56/22.75 ((
% 131.56/22.75 (dpsetconstrI) =>
% 131.56/22.75 ((
% 131.56/22.75 (dpsetconstrSub) =>
% 131.56/22.75 ((
% 131.56/22.75 (setOfPairsIsBReln) =>
% 131.56/22.75 ((
% 131.56/22.75 (dpsetconstrERa) =>
% 131.56/22.75 ((
% 131.56/22.75 (dpsetconstrEL1) =>
% 131.56/22.75 ((
% 131.56/22.75 (dpsetconstrEL2) =>
% 131.56/22.75 ((
% 131.56/22.75 (dpsetconstrER) =>
% 131.56/22.75 ((
% 131.56/22.75 (funcImageSingleton) =>
% 131.56/22.75 ((
% 131.56/22.75 (apProp) =>
% 131.56/22.75 ((
% 131.56/22.75 (app) =>
% 131.56/22.75 ((
% 131.56/22.75 (infuncsetfunc) =>
% 131.56/22.75 ((
% 131.56/22.75 (ap2p) =>
% 131.56/22.75 ((
% 131.56/22.75 (funcinfuncset) =>
% 131.56/22.75 ((
% 131.56/22.75 (lamProp) =>
% 131.56/22.75 ((
% 131.56/22.75 (lamp) =>
% 131.56/22.75 ((
% 131.56/22.75 (lam2p) =>
% 131.56/22.75 ((
% 131.56/22.75 (brelnall1) =>
% 131.56/22.75 ((
% 131.56/22.75 (brelnall2) =>
% 131.56/22.75 ((
% 131.56/22.75 (ex1E2) =>
% 131.56/22.75 ((
% 131.56/22.75 (funcGraphProp1) =>
% 131.56/22.75 ((
% 131.56/22.75 (funcGraphProp3) =>
% 131.56/22.75 ((
% 131.56/22.75 (funcGraphProp2) =>
% 131.56/22.75 ((
% 131.56/22.75 (funcextLem) =>
% 131.56/22.75 ((
% 131.56/22.75 (funcGraphProp4) =>
% 131.56/22.75 ((
% 131.56/22.75 (subbreln) =>
% 131.56/22.75 ((
% 131.56/22.75 (eqbreln) =>
% 131.56/22.75 ((
% 131.56/22.75 (funcext) =>
% 131.56/22.75 ((
% 131.56/22.75 (funcext2) =>
% 131.56/22.75 ((
% 131.56/22.75 (ap2apEq1) =>
% 131.56/22.75 ((
% 131.56/22.75 (ap2apEq2) =>
% 131.56/22.75 ((
% 131.56/22.75 (beta1) =>
% 131.56/22.75 ((
% 131.56/22.75 (eta1) =>
% 131.56/22.75 ((
% 131.56/22.75 (lam2lamEq) =>
% 131.56/22.75 ((
% 131.56/22.75 (beta2) =>
% 131.56/22.75 ((
% 131.56/22.75 (eta2) =>
% 131.56/22.75 ((
% 131.56/22.75 (iffalseProp1) =>
% 131.56/22.75 ((
% 131.56/22.75 (iffalseProp2) =>
% 131.56/22.75 ((
% 131.56/22.75 (iftrueProp1) =>
% 131.56/22.75 ((
% 131.56/22.75 (iftrueProp2) =>
% 131.56/22.75 ((
% 131.56/22.75 (ifSingleton) =>
% 131.56/22.75 ((
% 131.56/22.75 (ifp) =>
% 131.56/22.75 ((
% 131.56/22.75 (theeq) =>
% 131.56/22.75 ((
% 131.56/22.75 (iftrue) =>
% 131.56/22.75 ((
% 131.56/22.75 (iffalse) =>
% 131.56/22.75 ((
% 131.56/22.75 (iftrueorfalse) =>
% 131.56/22.75 ((
% 131.56/22.75 (binintersectT_lem) =>
% 131.56/22.75 ((
% 131.56/22.75 (binunionT_lem) =>
% 131.56/22.75 ((
% 131.56/22.75 (powersetT_lem) =>
% 131.56/22.75 ((
% 131.56/22.75 (setminusT_lem) =>
% 131.56/22.75 ((
% 131.56/22.75 (complementT_lem) =>
% 131.56/22.75 ((
% 131.56/22.75 (setextT) =>
% 131.56/22.75 ((
% 131.56/22.75 (subsetTI) =>
% 131.56/22.75 ((
% 131.56/22.75 (powersetTI1) =>
% 131.56/22.75 ((
% 131.56/22.75 (powersetTE1) =>
% 131.56/22.75 ((
% 131.56/22.75 (complementTI1) =>
% 131.56/22.75 ((
% 131.56/22.75 (complementTE1) =>
% 131.56/22.75 ((
% 131.56/22.75 (binintersectTELcontra) =>
% 131.56/22.75 ((
% 131.56/22.75 (binintersectTERcontra) =>
% 131.56/22.75 ((
% 131.56/22.75 (contrasubsetT) =>
% 131.56/22.75 ((
% 131.56/22.75 (contrasubsetT1) =>
% 131.56/22.75 ((
% 131.56/22.75 (contrasubsetT2) =>
% 131.56/22.75 ((
% 131.56/22.75 (contrasubsetT3) =>
% 131.56/22.75 ((
% 131.56/22.75 (doubleComplementI1) =>
% 131.56/22.75 ((
% 131.56/22.75 (doubleComplementE1) =>
% 131.56/22.75 ((
% 131.56/22.75 (doubleComplementSub1) =>
% 131.56/22.75 ((
% 131.56/22.75 (doubleComplementSub2) =>
% 131.56/22.75 ((
% 131.56/22.75 (doubleComplementEq) =>
% 131.56/22.75 ((
% 131.56/22.75 (complementTnotintersectT) =>
% 131.56/22.75 ((
% 131.56/22.75 (complementImpComplementIntersect) =>
% 131.56/22.75 ((
% 131.56/22.75 (complementSubsetComplementIntersect) =>
% 131.56/22.75 ((
% 131.56/22.75 (complementInPowersetComplementIntersect) =>
% 131.56/22.75 ((
% 131.56/22.75 (contraSubsetComplement) =>
% 131.56/22.75 ((
% 131.56/22.75 (complementTcontraSubset) =>
% 131.56/22.75 ((
% 131.56/22.75 (binunionTILcontra) =>
% 131.56/22.75 ((
% 131.56/22.75 (binunionTIRcontra) =>
% 131.56/22.75 ((
% 131.56/22.75 (inIntersectImpInUnion) =>
% 131.56/22.75 ((
% 131.56/22.75 (inIntersectImpInUnion2) =>
% 131.56/22.75 ((
% 131.56/22.75 (inIntersectImpInIntersectUnions) =>
% 131.56/22.75 ((
% 131.56/22.75 (intersectInPowersetIntersectUnions) =>
% 131.56/22.75 ((
% 131.56/22.75 (inComplementUnionImpNotIn1) =>
% 131.56/22.75 ((
% 131.56/22.75 (inComplementUnionImpInComplement1) =>
% 131.56/22.75 ((
% 131.56/22.75 (binunionTE) =>
% 131.56/22.75 ((
% 131.56/22.75 (binunionTEcontra) =>
% 131.56/22.75 ((
% 131.56/22.75 (demorgan2a1) =>
% 131.56/22.75 ((
% 131.56/22.75 (complementUnionInPowersetComplement) =>
% 131.56/22.75 ((
% 131.56/22.75 (demorgan2a2) =>
% 131.56/22.75 ((
% 131.56/22.75 (demorgan1a) =>
% 131.56/22.75 ((
% 131.56/22.75 (demorgan1b) =>
% 131.56/22.75 ((
% 131.56/22.75 (demorgan1) =>
% 131.56/22.75 ((
% 131.56/22.75 (demorgan2a) =>
% 131.56/22.75 ((
% 131.56/22.75 (demorgan2b2) =>
% 131.56/22.75 ((
% 131.56/22.75 (demorgan2b) =>
% 131.56/22.75 ((
% 131.56/22.75 (demorgan2) =>
% 131.56/22.75 ((
% 131.56/22.75 (woz13rule0) =>
% 131.56/22.75 ((
% 131.56/22.75 (woz13rule1) =>
% 131.56/22.75 ((
% 131.56/22.75 (woz13rule2) =>
% 131.56/22.75 ((
% 131.56/22.75 (woz13rule3) =>
% 131.56/22.75 ((
% 131.56/22.75 (woz13rule4) =>
% 131.56/22.75 ((
% 131.56/22.75 (woz1_1) =>
% 131.56/22.75 ((
% 131.56/22.75 (woz1_2) =>
% 131.56/22.75 ((
% 131.56/22.75 (woz1_3) =>
% 131.56/22.75 ((
% 131.56/22.75 (woz1_4) =>
% 131.56/22.75 ((
% 131.56/22.75 (woz1_5) =>
% 131.56/22.75 ((
% 131.56/22.75 (breln1all2) =>
% 131.56/22.75 ((
% 131.56/22.75 (breln1SetBreln1) =>
% 131.56/22.75 ((
% 131.56/22.75 (choice2fnsingleton) =>
% 131.56/22.75 ((
% 131.56/22.75 (setOfPairsIsBReln1) =>
% 131.56/22.75 ((
% 131.56/22.75 (breln1all1) =>
% 131.56/22.75 ((
% 131.56/22.75 (subbreln1) =>
% 131.56/22.75 ((
% 131.56/22.75 (eqbreln1) =>
% 131.56/22.75 ((
% 131.56/22.75 (breln1invprop) =>
% 131.56/22.75 ((
% 131.56/22.75 (breln1invI) =>
% 131.56/22.75 ((
% 131.56/22.75 (breln1invE) =>
% 131.56/22.75 ((
% 131.56/22.75 (breln1compprop) =>
% 131.56/22.75 ((
% 131.56/22.75 (breln1compI) =>
% 131.56/22.75 ((
% 131.56/22.75 (breln1compE) =>
% 131.56/22.75 ((
% 131.56/22.75 (breln1compEex) =>
% 131.56/22.75 ((
% 131.56/22.75 (breln1unionprop) =>
% 131.56/22.75 ((
% 131.56/22.75 (breln1unionIL) =>
% 131.56/22.75 ((
% 131.56/22.75 (breln1unionIR) =>
% 131.56/22.75 ((
% 131.56/22.75 (breln1unionI) =>
% 131.56/22.75 ((
% 131.56/22.75 (breln1unionE) =>
% 131.56/22.75 ((
% 131.56/22.75 (breln1unionEcases) =>
% 131.56/22.75 ((
% 131.56/22.75 (breln1unionCommutes) =>
% 131.56/22.75 ((
% 131.56/22.75 (woz2Ex) =>
% 131.56/22.75 ((
% 131.56/22.75 (woz2W) =>
% 131.56/22.75 ((
% 131.56/22.75 (woz2A) =>
% 131.56/22.75 ((
% 131.56/22.75 (woz2B) =>
% 131.56/22.75 ((
% 131.56/22.75 (image1Ex) =>
% 131.56/22.75 ((
% 131.56/22.75 (image1Ex1) =>
% 131.56/22.75 ((
% 131.56/22.75 (image1Equiv) =>
% 131.56/22.75 ((
% 131.56/22.75 (image1E) =>
% 131.56/22.75 ((
% 131.56/22.75 (image1I) =>
% 131.56/22.75 ((
% 131.56/22.75 (injFuncInInjFuncSet) =>
% 131.56/22.75 ((
% 131.56/22.75 (injFuncSetFuncIn) =>
% 131.56/22.75 ((
% 131.56/22.75 (injFuncSetFuncInj) =>
% 131.56/22.75 ((
% 131.56/22.75 (surjFuncSetFuncIn) =>
% 131.56/22.75 ((
% 131.56/22.75 (surjFuncSetFuncSurj) =>
% 131.56/22.75 ((
% 131.56/22.75 (leftInvIsSurj) =>
% 131.56/22.75 ((
% 131.56/22.75 (surjCantorThm) =>
% 131.56/22.75 ((
% 131.56/22.75 (foundation2) =>
% 131.56/22.75 ((
% 131.56/22.75 (notinself) =>
% 131.56/22.75 ((
% 131.56/22.75 (notinself2) =>
% 131.56/22.75 ((
% 131.56/22.75 (omegaSp) =>
% 131.56/22.75 ((
% 131.56/22.75 (omegaSclos) =>
% 131.56/22.75 ((
% 131.56/22.75 (peano0notS) =>
% 131.56/22.75 ((
% 131.56/22.75 (peanoSinj) =>
% 131.56/22.75 ((
% 131.56/22.75 (transitivesetOp1) =>
% 131.56/22.75 ((
% 131.56/22.75 (binintTransitive) =>
% 131.56/22.75 ((
% 131.56/22.75 (transitivesetOp2) =>
% 131.56/22.75 ((
% 131.56/22.75 (setunionTransitive) =>
% 131.56/22.75 ((
% 131.56/22.75 (ordinalMinLem1) =>
% 131.56/22.75 ((
% 131.56/22.75 (ordinalTransSet) =>
% 131.56/22.75 ((
% 131.56/22.75 (ordinalTransSet1) =>
% 131.56/22.75 ((
% 131.56/22.75 (setunionOrdinalLem1) =>
% 131.56/22.75 (ordinal @
% 131.56/22.75 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 131.56/22.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl50])).
% 131.56/22.75 thf(zip_derived_cl62, plain,
% 131.56/22.75 (~ (((dsetconstrI) =>
% 131.56/22.75 (((dsetconstrEL) =>
% 131.56/22.75 (((dsetconstrER) =>
% 131.56/22.75 (((exuE1) =>
% 131.56/22.75 (((prop2setE) =>
% 131.56/22.75 (((emptysetE) =>
% 131.56/22.75 (((emptysetimpfalse) =>
% 131.56/22.75 (((notinemptyset) =>
% 131.56/22.75 (((exuE3e) =>
% 131.56/22.75 (((setext) =>
% 131.56/22.75 (((emptyI) =>
% 131.56/22.75 (((noeltsimpempty) =>
% 131.56/22.75 (((setbeta) =>
% 131.56/22.75 (((nonemptyE1) =>
% 131.56/22.75 (((nonemptyI) =>
% 131.56/22.75 (((nonemptyI1) =>
% 131.56/22.75 (((setadjoinIL) =>
% 131.56/22.75 (((in @ emptyset @
% 131.56/22.75 (setadjoin @ emptyset @ emptyset)) =>
% 131.56/22.75 (((setadjoinIR) =>
% 131.56/22.75 (((setadjoinE) =>
% 131.56/22.75 (((setadjoinOr) =>
% 131.56/22.75 (((setoftrueEq) =>
% 131.56/22.75 (((powersetI) =>
% 131.56/22.75 (((emptyinPowerset) =>
% 131.56/22.75 (((emptyInPowerset) =>
% 131.56/22.75 (((powersetE) =>
% 131.56/22.75 (((setunionI) =>
% 131.56/22.75 (((setunionE) =>
% 131.56/22.75 (((subPowSU) =>
% 131.56/22.75 (((exuE2) =>
% 131.56/22.75 ((
% 131.56/22.75 (nonemptyImpWitness) =>
% 131.56/22.75 ((
% 131.56/22.75 (uniqinunit) =>
% 131.56/22.75 ((
% 131.56/22.75 (notinsingleton) =>
% 131.56/22.75 ((
% 131.56/22.75 (eqinunit) =>
% 131.56/22.75 ((
% 131.56/22.75 (singletonsswitch) =>
% 131.56/22.75 ((
% 131.56/22.75 (upairsetE) =>
% 131.56/22.75 ((
% 131.56/22.75 (upairsetIL) =>
% 131.56/22.75 ((
% 131.56/22.75 (upairsetIR) =>
% 131.56/22.75 ((
% 131.56/22.75 (emptyE1) =>
% 131.56/22.75 ((
% 131.56/22.75 (vacuousDall) =>
% 131.56/22.75 ((
% 131.56/22.75 (quantDeMorgan1) =>
% 131.56/22.75 ((
% 131.56/22.75 (quantDeMorgan2) =>
% 131.56/22.75 ((
% 131.56/22.75 (quantDeMorgan3) =>
% 131.56/22.75 ((
% 131.56/22.75 (quantDeMorgan4) =>
% 131.56/22.75 ((
% 131.56/22.75 (prop2setI) =>
% 131.56/22.75 ((
% 131.56/22.75 (prop2set2propI) =>
% 131.56/22.75 ((
% 131.56/22.75 (notdexE) =>
% 131.56/22.75 ((
% 131.56/22.75 (notdallE) =>
% 131.56/22.75 ((
% 131.56/22.75 (exuI1) =>
% 131.56/22.75 ((
% 131.56/22.75 (exuI3) =>
% 131.56/22.75 ((
% 131.56/22.75 (exuI2) =>
% 131.56/22.75 ((
% 131.56/22.75 (inCongP) =>
% 131.56/22.75 ((
% 131.56/22.75 (in__Cong) =>
% 131.56/22.75 ((
% 131.56/22.75 (exuE3u) =>
% 131.56/22.75 ((
% 131.56/22.75 (exu__Cong) =>
% 131.56/22.75 ((
% 131.56/22.75 (setadjoin__Cong) =>
% 131.56/22.75 ((
% 131.56/22.75 (powerset__Cong) =>
% 131.56/22.75 ((
% 131.56/22.75 (setunion__Cong) =>
% 131.56/22.75 ((
% 131.56/22.75 (exuEu) =>
% 131.56/22.75 ((
% 131.56/22.75 (descr__Cong) =>
% 131.56/22.75 ((
% 131.56/22.75 (dsetconstr__Cong) =>
% 131.56/22.75 ((
% 131.56/22.75 (subsetI1) =>
% 131.56/22.75 ((
% 131.56/22.75 (eqimpsubset2) =>
% 131.56/22.75 ((
% 131.56/22.75 (eqimpsubset1) =>
% 131.56/22.75 ((
% 131.56/22.75 (subsetI2) =>
% 131.56/22.75 ((
% 131.56/22.75 (emptysetsubset) =>
% 131.56/22.75 ((
% 131.56/22.75 (subsetE) =>
% 131.56/22.75 ((
% 131.56/22.75 (subsetE2) =>
% 131.56/22.75 ((
% 131.56/22.75 (notsubsetI) =>
% 131.56/22.75 ((
% 131.56/22.75 (notequalI1) =>
% 131.56/22.75 ((
% 131.56/22.75 (notequalI2) =>
% 131.56/22.75 ((
% 131.56/22.75 (subsetRefl) =>
% 131.56/22.75 ((
% 131.56/22.75 (subsetTrans) =>
% 131.56/22.75 ((
% 131.56/22.75 (setadjoinSub) =>
% 131.56/22.75 ((
% 131.56/22.75 (setadjoinSub2) =>
% 131.56/22.75 ((
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% 131.56/22.75 (quantDeMorgan1) =>
% 131.56/22.75 ((
% 131.56/22.75 (quantDeMorgan2) =>
% 131.56/22.75 ((
% 131.56/22.75 (quantDeMorgan3) =>
% 131.56/22.75 ((
% 131.56/22.75 (quantDeMorgan4) =>
% 131.56/22.75 ((
% 131.56/22.75 (prop2setI) =>
% 131.56/22.75 ((
% 131.56/22.75 (prop2set2propI) =>
% 131.56/22.75 ((
% 131.56/22.75 (notdexE) =>
% 131.56/22.75 ((
% 131.56/22.75 (notdallE) =>
% 131.56/22.75 ((
% 131.56/22.75 (exuI1) =>
% 131.56/22.75 ((
% 131.56/22.75 (exuI3) =>
% 131.56/22.75 ((
% 131.56/22.75 (exuI2) =>
% 131.56/22.75 ((
% 131.56/22.75 (inCongP) =>
% 131.56/22.75 ((
% 131.56/22.75 (in__Cong) =>
% 131.56/22.75 ((
% 131.56/22.75 (exuE3u) =>
% 131.56/22.75 ((
% 131.56/22.75 (exu__Cong) =>
% 131.56/22.75 ((
% 131.56/22.75 (setadjoin__Cong) =>
% 131.56/22.75 ((
% 131.56/22.75 (powerset__Cong) =>
% 131.56/22.75 ((
% 131.56/22.75 (setunion__Cong) =>
% 131.56/22.75 ((
% 131.56/22.75 (exuEu) =>
% 131.56/22.75 ((
% 131.56/22.75 (descr__Cong) =>
% 131.56/22.75 ((
% 131.56/22.75 (dsetconstr__Cong) =>
% 131.56/22.75 ((
% 131.56/22.75 (subsetI1) =>
% 131.56/22.75 ((
% 131.56/22.75 (eqimpsubset2) =>
% 131.56/22.75 ((
% 131.56/22.75 (eqimpsubset1) =>
% 131.56/22.75 ((
% 131.56/22.75 (subsetI2) =>
% 131.56/22.75 ((
% 131.56/22.75 (emptysetsubset) =>
% 131.56/22.75 ((
% 131.56/22.75 (subsetE) =>
% 131.56/22.75 ((
% 131.56/22.75 (subsetE2) =>
% 131.56/22.75 ((
% 131.56/22.75 (notsubsetI) =>
% 131.56/22.75 ((
% 131.56/22.75 (notequalI1) =>
% 131.56/22.75 ((
% 131.56/22.75 (notequalI2) =>
% 131.56/22.75 ((
% 131.56/22.75 (subsetRefl) =>
% 131.56/22.75 ((
% 131.56/22.75 (subsetTrans) =>
% 131.56/22.75 ((
% 131.56/22.75 (setadjoinSub) =>
% 131.56/22.75 ((
% 131.56/22.75 (setadjoinSub2) =>
% 131.56/22.75 ((
% 131.56/22.75 (subset2powerset) =>
% 131.56/22.75 ((
% 131.56/22.75 (setextsub) =>
% 131.56/22.75 ((
% 131.56/22.75 (subsetemptysetimpeq) =>
% 131.56/22.75 ((
% 131.56/22.75 (powersetI1) =>
% 131.56/22.75 ((
% 131.56/22.75 (powersetE1) =>
% 131.56/22.75 ((
% 131.56/22.75 (inPowerset) =>
% 131.56/22.75 ((
% 131.56/22.75 (powersetsubset) =>
% 131.56/22.75 ((
% 131.56/22.75 (sepInPowerset) =>
% 131.56/22.75 ((
% 131.56/22.75 (sepSubset) =>
% 131.56/22.75 ((
% 131.56/22.75 (binunionIL) =>
% 131.56/22.75 ((
% 131.56/22.75 (upairset2IR) =>
% 131.56/22.75 ((
% 131.56/22.75 (binunionIR) =>
% 131.56/22.75 ((
% 131.56/22.75 (binunionEcases) =>
% 131.56/22.75 ((
% 131.56/22.75 (binunionE) =>
% 131.56/22.75 ((
% 131.56/22.75 (binunionLsub) =>
% 131.56/22.75 ((
% 131.56/22.75 (binunionRsub) =>
% 131.56/22.75 ((
% 131.56/22.75 (binintersectI) =>
% 131.56/22.75 ((
% 131.56/22.75 (binintersectSubset5) =>
% 131.56/22.75 ((
% 131.56/22.75 (binintersectEL) =>
% 131.56/22.75 ((
% 131.56/22.75 (binintersectLsub) =>
% 131.56/22.75 ((
% 131.56/22.75 (binintersectSubset2) =>
% 131.56/22.75 ((
% 131.56/22.75 (binintersectSubset3) =>
% 131.56/22.75 ((
% 131.56/22.75 (binintersectER) =>
% 131.56/22.75 ((
% 131.56/22.75 (disjointsetsI1) =>
% 131.56/22.75 ((
% 131.56/22.75 (binintersectRsub) =>
% 131.56/22.75 ((
% 131.56/22.75 (binintersectSubset4) =>
% 131.56/22.75 ((
% 131.56/22.75 (binintersectSubset1) =>
% 131.56/22.75 ((
% 131.56/22.75 (bs114d) =>
% 131.56/22.75 ((
% 131.56/22.75 (setminusI) =>
% 131.56/22.75 ((
% 131.56/22.75 (setminusEL) =>
% 131.56/22.75 ((
% 131.56/22.75 (setminusER) =>
% 131.56/22.75 ((
% 131.56/22.75 (setminusSubset2) =>
% 131.56/22.75 ((
% 131.56/22.75 (setminusERneg) =>
% 131.56/22.75 ((
% 131.56/22.75 (setminusELneg) =>
% 131.56/22.75 ((
% 131.56/22.75 (setminusILneg) =>
% 131.56/22.75 ((
% 131.56/22.75 (setminusIRneg) =>
% 131.56/22.75 ((
% 131.56/22.75 (setminusLsub) =>
% 131.56/22.75 ((
% 131.56/22.75 (setminusSubset1) =>
% 131.56/22.75 ((
% 131.56/22.75 (symdiffE) =>
% 131.56/22.75 ((
% 131.56/22.75 (symdiffI1) =>
% 131.56/22.75 ((
% 131.56/22.75 (symdiffI2) =>
% 131.56/22.75 ((
% 131.56/22.75 (symdiffIneg1) =>
% 131.56/22.75 ((
% 131.56/22.75 (symdiffIneg2) =>
% 131.56/22.75 ((
% 131.56/22.75 (secondinupair) =>
% 131.56/22.75 ((
% 131.56/22.75 (setukpairIL) =>
% 131.56/22.75 ((
% 131.56/22.75 (setukpairIR) =>
% 131.56/22.75 ((
% 131.56/22.75 (kpairiskpair) =>
% 131.56/22.75 ((
% 131.56/22.75 (kpairp) =>
% 131.56/22.75 ((
% 131.56/22.75 (singletonsubset) =>
% 131.56/22.75 ((
% 131.56/22.75 (singletoninpowerset) =>
% 131.56/22.75 ((
% 131.56/22.75 (singletoninpowunion) =>
% 131.56/22.75 ((
% 131.56/22.75 (upairset2E) =>
% 131.56/22.75 ((
% 131.56/22.75 (upairsubunion) =>
% 131.56/22.75 ((
% 131.56/22.75 (upairinpowunion) =>
% 131.56/22.75 ((
% 131.56/22.75 (ubforcartprodlem1) =>
% 131.56/22.75 ((
% 131.56/22.75 (ubforcartprodlem2) =>
% 131.56/22.75 ((
% 131.56/22.75 (ubforcartprodlem3) =>
% 131.56/22.75 ((
% 131.56/22.75 (cartprodpairin) =>
% 131.56/22.75 ((
% 131.56/22.75 (cartprodmempair1) =>
% 131.56/22.75 ((
% 131.56/22.75 (cartprodmempair) =>
% 131.56/22.75 ((
% 131.56/22.75 (setunionE2) =>
% 131.56/22.75 ((
% 131.56/22.75 (setunionsingleton1) =>
% 131.56/22.75 ((
% 131.56/22.75 (setunionsingleton2) =>
% 131.56/22.75 ((
% 131.56/22.75 (setunionsingleton) =>
% 131.56/22.75 ((
% 131.56/22.75 (singletonprop) =>
% 131.56/22.75 ((
% 131.56/22.75 (ex1E1) =>
% 131.56/22.75 ((
% 131.56/22.75 (ex1I) =>
% 131.56/22.75 ((
% 131.56/22.75 (ex1I2) =>
% 131.56/22.75 ((
% 131.56/22.75 (singletonsuniq) =>
% 131.56/22.75 ((
% 131.56/22.75 (setukpairinjL1) =>
% 131.56/22.75 ((
% 131.56/22.75 (kfstsingleton) =>
% 131.56/22.75 ((
% 131.56/22.75 (theprop) =>
% 131.56/22.75 ((
% 131.56/22.75 (kfstpairEq) =>
% 131.56/22.75 ((
% 131.56/22.75 (cartprodfstin) =>
% 131.56/22.75 ((
% 131.56/22.75 (setukpairinjL2) =>
% 131.56/22.75 ((
% 131.56/22.75 (setukpairinjL) =>
% 131.56/22.75 ((
% 131.56/22.75 (setukpairinjR11) =>
% 131.56/22.75 ((
% 131.56/22.75 (setukpairinjR12) =>
% 131.56/22.75 ((
% 131.56/22.75 (setukpairinjR1) =>
% 131.56/22.75 ((
% 131.56/22.75 (upairequniteq) =>
% 131.56/22.75 ((
% 131.56/22.75 (setukpairinjR2) =>
% 131.56/22.75 ((
% 131.56/22.75 (setukpairinjR) =>
% 131.56/22.75 ((
% 131.56/22.75 (ksndsingleton) =>
% 131.56/22.75 ((
% 131.56/22.75 (ksndpairEq) =>
% 131.56/22.75 ((
% 131.56/22.75 (kpairsurjEq) =>
% 131.56/22.75 ((
% 131.56/22.75 (cartprodsndin) =>
% 131.56/22.75 ((
% 131.56/22.75 (cartprodpairmemEL) =>
% 131.56/22.75 ((
% 131.56/22.75 (cartprodpairmemER) =>
% 131.56/22.75 ((
% 131.56/22.75 (cartprodmempaircEq) =>
% 131.56/22.75 ((
% 131.56/22.75 (cartprodfstpairEq) =>
% 131.56/22.75 ((
% 131.56/22.75 (cartprodsndpairEq) =>
% 131.56/22.75 ((
% 131.56/22.75 (cartprodpairsurjEq) =>
% 131.56/22.75 ((
% 131.56/22.75 (dpsetconstrI) =>
% 131.56/22.75 ((
% 131.56/22.75 (dpsetconstrSub) =>
% 131.56/22.75 ((
% 131.56/22.75 (setOfPairsIsBReln) =>
% 131.56/22.75 ((
% 131.56/22.75 (dpsetconstrERa) =>
% 131.56/22.75 ((
% 131.56/22.75 (dpsetconstrEL1) =>
% 131.56/22.75 ((
% 131.56/22.75 (dpsetconstrEL2) =>
% 131.56/22.75 ((
% 131.56/22.75 (dpsetconstrER) =>
% 131.56/22.75 ((
% 131.56/22.75 (funcImageSingleton) =>
% 131.56/22.75 ((
% 131.56/22.75 (apProp) =>
% 131.56/22.75 ((
% 131.56/22.75 (app) =>
% 131.56/22.75 ((
% 131.56/22.75 (infuncsetfunc) =>
% 131.56/22.75 ((
% 131.56/22.75 (ap2p) =>
% 131.56/22.75 ((
% 131.56/22.75 (funcinfuncset) =>
% 131.56/22.75 ((
% 131.56/22.75 (lamProp) =>
% 131.56/22.75 ((
% 131.56/22.75 (lamp) =>
% 131.56/22.75 ((
% 131.56/22.75 (lam2p) =>
% 131.56/22.75 ((
% 131.56/22.75 (brelnall1) =>
% 131.56/22.75 ((
% 131.56/22.75 (brelnall2) =>
% 131.56/22.75 ((
% 131.56/22.75 (ex1E2) =>
% 131.56/22.75 ((
% 131.56/22.75 (funcGraphProp1) =>
% 131.56/22.75 ((
% 131.56/22.75 (funcGraphProp3) =>
% 131.56/22.75 ((
% 131.56/22.75 (funcGraphProp2) =>
% 131.56/22.75 ((
% 131.56/22.75 (funcextLem) =>
% 131.56/22.75 ((
% 131.56/22.75 (funcGraphProp4) =>
% 131.56/22.75 ((
% 131.56/22.75 (subbreln) =>
% 131.56/22.75 ((
% 131.56/22.75 (eqbreln) =>
% 131.56/22.75 ((
% 131.56/22.75 (funcext) =>
% 131.56/22.75 ((
% 131.56/22.75 (funcext2) =>
% 131.56/22.75 ((
% 131.56/22.75 (ap2apEq1) =>
% 131.56/22.75 ((
% 131.56/22.75 (ap2apEq2) =>
% 131.56/22.75 ((
% 131.56/22.75 (beta1) =>
% 131.56/22.75 ((
% 131.56/22.75 (eta1) =>
% 131.56/22.75 ((
% 131.56/22.75 (lam2lamEq) =>
% 131.56/22.75 ((
% 131.56/22.75 (beta2) =>
% 131.56/22.75 ((
% 131.56/22.75 (eta2) =>
% 131.56/22.75 ((
% 131.56/22.75 (iffalseProp1) =>
% 131.56/22.75 ((
% 131.56/22.75 (iffalseProp2) =>
% 131.56/22.75 ((
% 131.56/22.75 (iftrueProp1) =>
% 131.56/22.75 ((
% 131.56/22.75 (iftrueProp2) =>
% 131.56/22.75 ((
% 131.56/22.75 (ifSingleton) =>
% 131.56/22.75 ((
% 131.56/22.75 (ifp) =>
% 131.56/22.75 ((
% 131.56/22.75 (theeq) =>
% 131.56/22.75 ((
% 131.56/22.75 (iftrue) =>
% 131.56/22.75 ((
% 131.56/22.75 (iffalse) =>
% 131.56/22.75 ((
% 131.56/22.75 (iftrueorfalse) =>
% 131.56/22.75 ((
% 131.56/22.75 (binintersectT_lem) =>
% 131.56/22.75 ((
% 131.56/22.75 (binunionT_lem) =>
% 131.56/22.75 ((
% 131.56/22.75 (powersetT_lem) =>
% 131.56/22.75 ((
% 131.56/22.75 (setminusT_lem) =>
% 131.56/22.75 ((
% 131.56/22.75 (complementT_lem) =>
% 131.56/22.75 ((
% 131.56/22.75 (setextT) =>
% 131.56/22.75 ((
% 131.56/22.75 (subsetTI) =>
% 131.56/22.75 ((
% 131.56/22.75 (powersetTI1) =>
% 131.56/22.75 ((
% 131.56/22.75 (powersetTE1) =>
% 131.56/22.75 ((
% 131.56/22.75 (complementTI1) =>
% 131.56/22.75 ((
% 131.56/22.75 (complementTE1) =>
% 131.56/22.75 ((
% 131.56/22.75 (binintersectTELcontra) =>
% 131.56/22.75 ((
% 131.56/22.75 (binintersectTERcontra) =>
% 131.56/22.75 ((
% 131.56/22.75 (contrasubsetT) =>
% 131.56/22.75 ((
% 131.56/22.75 (contrasubsetT1) =>
% 131.56/22.75 ((
% 131.56/22.75 (contrasubsetT2) =>
% 131.56/22.75 ((
% 131.56/22.75 (contrasubsetT3) =>
% 131.56/22.75 ((
% 131.56/22.75 (doubleComplementI1) =>
% 131.56/22.75 ((
% 131.56/22.75 (doubleComplementE1) =>
% 131.56/22.75 ((
% 131.56/22.75 (doubleComplementSub1) =>
% 131.56/22.75 ((
% 131.56/22.75 (doubleComplementSub2) =>
% 131.56/22.75 ((
% 131.56/22.75 (doubleComplementEq) =>
% 131.56/22.75 ((
% 131.56/22.75 (complementTnotintersectT) =>
% 131.56/22.75 ((
% 131.56/22.75 (complementImpComplementIntersect) =>
% 131.56/22.75 ((
% 131.56/22.75 (complementSubsetComplementIntersect) =>
% 131.56/22.75 ((
% 131.56/22.75 (complementInPowersetComplementIntersect) =>
% 131.56/22.75 ((
% 131.56/22.75 (contraSubsetComplement) =>
% 131.56/22.75 ((
% 131.56/22.75 (complementTcontraSubset) =>
% 131.56/22.75 ((
% 131.56/22.75 (binunionTILcontra) =>
% 131.56/22.75 ((
% 131.56/22.75 (binunionTIRcontra) =>
% 131.56/22.75 ((
% 131.56/22.75 (inIntersectImpInUnion) =>
% 131.56/22.75 ((
% 131.56/22.75 (inIntersectImpInUnion2) =>
% 131.56/22.75 ((
% 131.56/22.75 (inIntersectImpInIntersectUnions) =>
% 131.56/22.75 ((
% 131.56/22.75 (intersectInPowersetIntersectUnions) =>
% 131.56/22.75 ((
% 131.56/22.75 (inComplementUnionImpNotIn1) =>
% 131.56/22.75 ((
% 131.56/22.75 (inComplementUnionImpInComplement1) =>
% 131.56/22.75 ((
% 131.56/22.75 (binunionTE) =>
% 131.56/22.75 ((
% 131.56/22.75 (binunionTEcontra) =>
% 131.56/22.75 ((
% 131.56/22.75 (demorgan2a1) =>
% 131.56/22.75 ((
% 131.56/22.75 (complementUnionInPowersetComplement) =>
% 131.56/22.75 ((
% 131.56/22.75 (demorgan2a2) =>
% 131.56/22.75 ((
% 131.56/22.75 (demorgan1a) =>
% 131.56/22.75 ((
% 131.56/22.75 (demorgan1b) =>
% 131.56/22.75 ((
% 131.56/22.75 (demorgan1) =>
% 131.56/22.75 ((
% 131.56/22.75 (demorgan2a) =>
% 131.56/22.75 ((
% 131.56/22.75 (demorgan2b2) =>
% 131.56/22.75 ((
% 131.56/22.75 (demorgan2b) =>
% 131.56/22.75 ((
% 131.56/22.75 (demorgan2) =>
% 131.56/22.75 ((
% 131.56/22.75 (woz13rule0) =>
% 131.56/22.75 ((
% 131.56/22.75 (woz13rule1) =>
% 131.56/22.75 ((
% 131.56/22.75 (woz13rule2) =>
% 131.56/22.75 ((
% 131.56/22.75 (woz13rule3) =>
% 131.56/22.75 ((
% 131.56/22.75 (woz13rule4) =>
% 131.56/22.75 ((
% 131.56/22.75 (woz1_1) =>
% 131.56/22.75 ((
% 131.56/22.75 (woz1_2) =>
% 131.56/22.75 ((
% 131.56/22.75 (woz1_3) =>
% 131.56/22.75 ((
% 131.56/22.75 (woz1_4) =>
% 131.56/22.75 ((
% 131.56/22.75 (woz1_5) =>
% 131.56/22.75 ((
% 131.56/22.75 (breln1all2) =>
% 131.56/22.75 ((
% 131.56/22.75 (breln1SetBreln1) =>
% 131.56/22.75 ((
% 131.56/22.75 (choice2fnsingleton) =>
% 131.56/22.75 ((
% 131.56/22.75 (setOfPairsIsBReln1) =>
% 131.56/22.75 ((
% 131.56/22.75 (breln1all1) =>
% 131.56/22.75 ((
% 131.56/22.75 (subbreln1) =>
% 131.56/22.75 ((
% 131.56/22.75 (eqbreln1) =>
% 131.56/22.75 ((
% 131.56/22.75 (breln1invprop) =>
% 131.56/22.75 ((
% 131.56/22.75 (breln1invI) =>
% 131.56/22.75 ((
% 131.56/22.75 (breln1invE) =>
% 131.56/22.75 ((
% 131.56/22.75 (breln1compprop) =>
% 131.56/22.75 ((
% 131.56/22.75 (breln1compI) =>
% 131.56/22.75 ((
% 131.56/22.75 (breln1compE) =>
% 131.56/22.75 ((
% 131.56/22.75 (breln1compEex) =>
% 131.56/22.75 ((
% 131.56/22.75 (breln1unionprop) =>
% 131.56/22.75 ((
% 131.56/22.75 (breln1unionIL) =>
% 131.56/22.75 ((
% 131.56/22.75 (breln1unionIR) =>
% 131.56/22.75 ((
% 131.56/22.75 (breln1unionI) =>
% 131.56/22.75 ((
% 131.56/22.75 (breln1unionE) =>
% 131.56/22.75 ((
% 131.56/22.75 (breln1unionEcases) =>
% 131.56/22.75 ((
% 131.56/22.75 (breln1unionCommutes) =>
% 131.56/22.75 ((
% 131.56/22.75 (woz2Ex) =>
% 131.56/22.75 ((
% 131.56/22.75 (woz2W) =>
% 131.56/22.75 ((
% 131.56/22.75 (woz2A) =>
% 131.56/22.75 ((
% 131.56/22.75 (woz2B) =>
% 131.56/22.75 ((
% 131.56/22.75 (image1Ex) =>
% 131.56/22.75 ((
% 131.56/22.75 (image1Ex1) =>
% 131.56/22.75 ((
% 131.56/22.75 (image1Equiv) =>
% 131.56/22.75 ((
% 131.56/22.75 (image1E) =>
% 131.56/22.75 ((
% 131.56/22.75 (image1I) =>
% 131.56/22.75 ((
% 131.56/22.75 (injFuncInInjFuncSet) =>
% 131.56/22.75 ((
% 131.56/22.75 (injFuncSetFuncIn) =>
% 131.56/22.75 ((
% 131.56/22.75 (injFuncSetFuncInj) =>
% 131.56/22.75 ((
% 131.56/22.75 (surjFuncSetFuncIn) =>
% 131.56/22.75 ((
% 131.56/22.75 (surjFuncSetFuncSurj) =>
% 131.56/22.75 ((
% 131.56/22.75 (leftInvIsSurj) =>
% 131.56/22.75 ((
% 131.56/22.75 (surjCantorThm) =>
% 131.56/22.75 ((
% 131.56/22.75 (foundation2) =>
% 131.56/22.75 ((
% 131.56/22.75 (notinself) =>
% 131.56/22.75 ((
% 131.56/22.75 (notinself2) =>
% 131.56/22.75 ((
% 131.56/22.75 (omegaSp) =>
% 131.56/22.75 ((
% 131.56/22.75 (omegaSclos) =>
% 131.56/22.75 ((
% 131.56/22.75 (peano0notS) =>
% 131.56/22.75 ((
% 131.56/22.75 (peanoSinj) =>
% 131.56/22.75 ((
% 131.56/22.75 (transitivesetOp1) =>
% 131.56/22.75 ((
% 131.56/22.75 (binintTransitive) =>
% 131.56/22.75 ((
% 131.56/22.75 (transitivesetOp2) =>
% 131.56/22.75 ((
% 131.56/22.75 (setunionTransitive) =>
% 131.56/22.75 ((
% 131.56/22.75 (ordinalMinLem1) =>
% 131.56/22.75 ((
% 131.56/22.75 (ordinalTransSet) =>
% 131.56/22.75 ((
% 131.56/22.75 (ordinalTransSet1) =>
% 131.56/22.75 ((
% 131.56/22.75 (setunionOrdinalLem1) =>
% 131.56/22.75 (ordinal @
% 131.56/22.75 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 131.56/22.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl62])).
% 131.56/22.75 thf(zip_derived_cl79, plain,
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% 131.56/22.75 ((
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% 131.56/22.75 ((
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% 131.56/22.75 ((
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% 131.56/22.75 ((
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% 131.56/22.75 ((
% 131.56/22.75 (quantDeMorgan3) =>
% 131.56/22.75 ((
% 131.56/22.75 (quantDeMorgan4) =>
% 131.56/22.75 ((
% 131.56/22.75 (prop2setI) =>
% 131.56/22.75 ((
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% 131.56/22.75 ((
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% 131.56/22.75 ((
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% 131.56/22.75 ((
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% 131.56/22.75 ((
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% 131.56/22.75 ((
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% 131.56/22.75 ((
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% 131.56/22.75 ((
% 131.56/22.75 (exuE3u) =>
% 131.56/22.75 ((
% 131.56/22.75 (exu__Cong) =>
% 131.56/22.75 ((
% 131.56/22.75 (setadjoin__Cong) =>
% 131.56/22.75 ((
% 131.56/22.75 (powerset__Cong) =>
% 131.56/22.75 ((
% 131.56/22.75 (setunion__Cong) =>
% 131.56/22.75 ((
% 131.56/22.75 (exuEu) =>
% 131.56/22.75 ((
% 131.56/22.75 (descr__Cong) =>
% 131.56/22.75 ((
% 131.56/22.75 (dsetconstr__Cong) =>
% 131.56/22.75 ((
% 131.56/22.75 (subsetI1) =>
% 131.56/22.75 ((
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% 131.56/22.75 ((
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% 131.56/22.75 ((
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% 131.56/22.75 ((
% 131.56/22.75 (subsetE2) =>
% 131.56/22.75 ((
% 131.56/22.75 (notsubsetI) =>
% 131.56/22.75 ((
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% 131.56/22.75 ((
% 131.56/22.75 (notequalI2) =>
% 131.56/22.75 ((
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% 131.56/22.75 ((
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% 131.56/22.75 ((
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% 131.56/22.75 ((
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% 131.56/22.75 ((
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% 131.56/22.75 ((
% 131.56/22.75 (powersetE1) =>
% 131.56/22.75 ((
% 131.56/22.75 (inPowerset) =>
% 131.56/22.75 ((
% 131.56/22.75 (powersetsubset) =>
% 131.56/22.75 ((
% 131.56/22.75 (sepInPowerset) =>
% 131.56/22.75 ((
% 131.56/22.75 (sepSubset) =>
% 131.56/22.75 ((
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% 131.56/22.75 ((
% 131.56/22.75 (upairset2IR) =>
% 131.56/22.75 ((
% 131.56/22.75 (binunionIR) =>
% 131.56/22.75 ((
% 131.56/22.75 (binunionEcases) =>
% 131.56/22.75 ((
% 131.56/22.75 (binunionE) =>
% 131.56/22.75 ((
% 131.56/22.75 (binunionLsub) =>
% 131.56/22.75 ((
% 131.56/22.75 (binunionRsub) =>
% 131.56/22.75 ((
% 131.56/22.75 (binintersectI) =>
% 131.56/22.75 ((
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% 131.56/22.75 ((
% 131.56/22.75 (binintersectEL) =>
% 131.56/22.75 ((
% 131.56/22.75 (binintersectLsub) =>
% 131.56/22.75 ((
% 131.56/22.75 (binintersectSubset2) =>
% 131.56/22.75 ((
% 131.56/22.75 (binintersectSubset3) =>
% 131.56/22.75 ((
% 131.56/22.75 (binintersectER) =>
% 131.56/22.75 ((
% 131.56/22.75 (disjointsetsI1) =>
% 131.56/22.75 ((
% 131.56/22.75 (binintersectRsub) =>
% 131.56/22.75 ((
% 131.56/22.75 (binintersectSubset4) =>
% 131.56/22.75 ((
% 131.56/22.75 (binintersectSubset1) =>
% 131.56/22.75 ((
% 131.56/22.75 (bs114d) =>
% 131.56/22.75 ((
% 131.56/22.75 (setminusI) =>
% 131.56/22.75 ((
% 131.56/22.75 (setminusEL) =>
% 131.56/22.75 ((
% 131.56/22.75 (setminusER) =>
% 131.56/22.75 ((
% 131.56/22.75 (setminusSubset2) =>
% 131.56/22.75 ((
% 131.56/22.75 (setminusERneg) =>
% 131.56/22.75 ((
% 131.56/22.75 (setminusELneg) =>
% 131.56/22.75 ((
% 131.56/22.75 (setminusILneg) =>
% 131.56/22.75 ((
% 131.56/22.75 (setminusIRneg) =>
% 131.56/22.75 ((
% 131.56/22.75 (setminusLsub) =>
% 131.56/22.75 ((
% 131.56/22.75 (setminusSubset1) =>
% 131.56/22.75 ((
% 131.56/22.75 (symdiffE) =>
% 131.56/22.75 ((
% 131.56/22.75 (symdiffI1) =>
% 131.56/22.75 ((
% 131.56/22.75 (symdiffI2) =>
% 131.56/22.75 ((
% 131.56/22.75 (symdiffIneg1) =>
% 131.56/22.75 ((
% 131.56/22.75 (symdiffIneg2) =>
% 131.56/22.75 ((
% 131.56/22.75 (secondinupair) =>
% 131.56/22.75 ((
% 131.56/22.75 (setukpairIL) =>
% 131.56/22.75 ((
% 131.56/22.75 (setukpairIR) =>
% 131.56/22.75 ((
% 131.56/22.75 (kpairiskpair) =>
% 131.56/22.75 ((
% 131.56/22.75 (kpairp) =>
% 131.56/22.75 ((
% 131.56/22.75 (singletonsubset) =>
% 131.56/22.75 ((
% 131.56/22.75 (singletoninpowerset) =>
% 131.56/22.75 ((
% 131.56/22.75 (singletoninpowunion) =>
% 131.56/22.75 ((
% 131.56/22.75 (upairset2E) =>
% 131.56/22.75 ((
% 131.56/22.75 (upairsubunion) =>
% 131.56/22.75 ((
% 131.56/22.75 (upairinpowunion) =>
% 131.56/22.75 ((
% 131.56/22.75 (ubforcartprodlem1) =>
% 131.56/22.75 ((
% 131.56/22.75 (ubforcartprodlem2) =>
% 131.56/22.75 ((
% 131.56/22.75 (ubforcartprodlem3) =>
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% 131.56/22.75 (cartprodpairin) =>
% 131.56/22.75 ((
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% 131.56/22.75 ((
% 131.56/22.75 (cartprodmempair) =>
% 131.56/22.75 ((
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% 131.56/22.75 ((
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% 131.56/22.75 ((
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% 131.56/22.75 ((
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% 131.56/22.75 ((
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% 131.56/22.75 ((
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% 131.56/22.75 ((
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% 131.56/22.75 (kfstsingleton) =>
% 131.56/22.75 ((
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% 131.56/22.75 ((
% 131.56/22.75 (kfstpairEq) =>
% 131.56/22.75 ((
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% 131.56/22.75 ((
% 131.56/22.75 (setukpairinjL2) =>
% 131.56/22.75 ((
% 131.56/22.75 (setukpairinjL) =>
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% 131.56/22.75 (setukpairinjR12) =>
% 131.56/22.75 ((
% 131.56/22.75 (setukpairinjR1) =>
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% 131.56/22.75 (setukpairinjR) =>
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% 131.56/22.75 (ksndsingleton) =>
% 131.56/22.75 ((
% 131.56/22.75 (ksndpairEq) =>
% 131.56/22.75 ((
% 131.56/22.75 (kpairsurjEq) =>
% 131.56/22.75 ((
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% 131.56/22.75 ((
% 131.56/22.75 (cartprodpairmemER) =>
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% 131.56/22.75 (cartprodmempaircEq) =>
% 131.56/22.75 ((
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% 131.56/22.75 ((
% 131.56/22.75 (cartprodsndpairEq) =>
% 131.56/22.75 ((
% 131.56/22.75 (cartprodpairsurjEq) =>
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% 131.56/22.75 (breln1unionCommutes) =>
% 131.56/22.75 ((
% 131.56/22.75 (woz2Ex) =>
% 131.56/22.75 ((
% 131.56/22.75 (woz2W) =>
% 131.56/22.75 ((
% 131.56/22.75 (woz2A) =>
% 131.56/22.75 ((
% 131.56/22.75 (woz2B) =>
% 131.56/22.75 ((
% 131.56/22.75 (image1Ex) =>
% 131.56/22.75 ((
% 131.56/22.75 (image1Ex1) =>
% 131.56/22.75 ((
% 131.56/22.75 (image1Equiv) =>
% 131.56/22.75 ((
% 131.56/22.75 (image1E) =>
% 131.56/22.75 ((
% 131.56/22.75 (image1I) =>
% 131.56/22.75 ((
% 131.56/22.75 (injFuncInInjFuncSet) =>
% 131.56/22.75 ((
% 131.56/22.75 (injFuncSetFuncIn) =>
% 131.56/22.75 ((
% 131.56/22.75 (injFuncSetFuncInj) =>
% 131.56/22.75 ((
% 131.56/22.75 (surjFuncSetFuncIn) =>
% 131.56/22.75 ((
% 131.56/22.75 (surjFuncSetFuncSurj) =>
% 131.56/22.75 ((
% 131.56/22.75 (leftInvIsSurj) =>
% 131.56/22.75 ((
% 131.56/22.75 (surjCantorThm) =>
% 131.56/22.75 ((
% 131.56/22.75 (foundation2) =>
% 131.56/22.75 ((
% 131.56/22.75 (notinself) =>
% 131.56/22.75 ((
% 131.56/22.75 (notinself2) =>
% 131.56/22.75 ((
% 131.56/22.75 (omegaSp) =>
% 131.56/22.75 ((
% 131.56/22.75 (omegaSclos) =>
% 131.56/22.75 ((
% 131.56/22.75 (peano0notS) =>
% 131.56/22.75 ((
% 131.56/22.75 (peanoSinj) =>
% 131.56/22.75 ((
% 131.56/22.75 (transitivesetOp1) =>
% 131.56/22.75 ((
% 131.56/22.75 (binintTransitive) =>
% 131.56/22.75 ((
% 131.56/22.75 (transitivesetOp2) =>
% 131.56/22.75 ((
% 131.56/22.75 (setunionTransitive) =>
% 131.56/22.75 ((
% 131.56/22.75 (ordinalMinLem1) =>
% 131.56/22.75 ((
% 131.56/22.75 (ordinalTransSet) =>
% 131.56/22.75 ((
% 131.56/22.75 (ordinalTransSet1) =>
% 131.56/22.75 ((
% 131.56/22.75 (setunionOrdinalLem1) =>
% 131.56/22.75 (ordinal @
% 131.56/22.75 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 131.56/22.75 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl69])).
% 131.56/22.75 thf(zip_derived_cl95, plain,
% 131.56/22.75 (~ (((exuE1) =>
% 131.56/22.75 (((prop2setE) =>
% 131.56/22.75 (((emptysetE) =>
% 131.56/22.75 (((emptysetimpfalse) =>
% 131.56/22.75 (((notinemptyset) =>
% 131.56/22.75 (((exuE3e) =>
% 131.56/22.75 (((setext) =>
% 131.56/22.75 (((emptyI) =>
% 131.56/22.75 (((noeltsimpempty) =>
% 131.56/22.75 (((setbeta) =>
% 131.56/22.75 (((nonemptyE1) =>
% 131.56/22.75 (((nonemptyI) =>
% 131.56/22.75 (((nonemptyI1) =>
% 131.56/22.75 (((setadjoinIL) =>
% 131.56/22.75 (((in @ emptyset @
% 131.56/22.75 (setadjoin @ emptyset @ emptyset)) =>
% 131.56/22.75 (((setadjoinIR) =>
% 131.56/22.75 (((setadjoinE) =>
% 131.56/22.75 (((setadjoinOr) =>
% 131.56/22.75 (((setoftrueEq) =>
% 131.56/22.75 (((powersetI) =>
% 131.56/22.75 (((emptyinPowerset) =>
% 131.56/22.75 (((emptyInPowerset) =>
% 131.56/22.75 (((powersetE) =>
% 131.56/22.75 (((setunionI) =>
% 131.56/22.75 (((setunionE) =>
% 131.56/22.75 (((subPowSU) =>
% 131.56/22.75 (((exuE2) =>
% 131.56/22.75 (((nonemptyImpWitness) =>
% 131.56/22.75 (((uniqinunit) =>
% 131.56/22.75 (((notinsingleton) =>
% 131.56/22.75 ((
% 131.56/22.75 (eqinunit) =>
% 131.56/22.75 ((
% 131.56/22.75 (singletonsswitch) =>
% 131.56/22.75 ((
% 131.56/22.75 (upairsetE) =>
% 131.56/22.75 ((
% 131.56/22.75 (upairsetIL) =>
% 131.56/22.75 ((
% 131.56/22.75 (upairsetIR) =>
% 131.56/22.75 ((
% 131.56/22.75 (emptyE1) =>
% 131.56/22.75 ((
% 131.56/22.75 (vacuousDall) =>
% 131.56/22.75 ((
% 131.56/22.75 (quantDeMorgan1) =>
% 131.56/22.75 ((
% 131.56/22.75 (quantDeMorgan2) =>
% 131.56/22.75 ((
% 131.56/22.75 (quantDeMorgan3) =>
% 131.56/22.75 ((
% 131.56/22.75 (quantDeMorgan4) =>
% 131.56/22.75 ((
% 131.56/22.75 (prop2setI) =>
% 131.56/22.75 ((
% 131.56/22.75 (prop2set2propI) =>
% 131.56/22.75 ((
% 131.56/22.75 (notdexE) =>
% 131.56/22.75 ((
% 131.56/22.75 (notdallE) =>
% 131.56/22.75 ((
% 131.56/22.75 (exuI1) =>
% 131.56/22.75 ((
% 131.56/22.75 (exuI3) =>
% 131.56/22.75 ((
% 131.56/22.75 (exuI2) =>
% 131.56/22.75 ((
% 131.56/22.75 (inCongP) =>
% 131.56/22.75 ((
% 131.56/22.75 (in__Cong) =>
% 131.56/22.75 ((
% 131.56/22.75 (exuE3u) =>
% 131.56/22.75 ((
% 131.56/22.75 (exu__Cong) =>
% 131.56/22.75 ((
% 131.56/22.75 (setadjoin__Cong) =>
% 131.56/22.75 ((
% 131.56/22.75 (powerset__Cong) =>
% 131.56/22.75 ((
% 131.56/22.75 (setunion__Cong) =>
% 131.56/22.75 ((
% 131.56/22.75 (exuEu) =>
% 131.56/22.75 ((
% 131.56/22.75 (descr__Cong) =>
% 131.56/22.75 ((
% 131.56/22.75 (dsetconstr__Cong) =>
% 131.56/22.75 ((
% 131.56/22.75 (subsetI1) =>
% 131.56/22.75 ((
% 131.56/22.75 (eqimpsubset2) =>
% 131.56/22.75 ((
% 131.56/22.75 (eqimpsubset1) =>
% 131.56/22.75 ((
% 131.56/22.75 (subsetI2) =>
% 131.56/22.75 ((
% 131.56/22.75 (emptysetsubset) =>
% 131.56/22.75 ((
% 131.56/22.75 (subsetE) =>
% 131.56/22.75 ((
% 131.56/22.75 (subsetE2) =>
% 131.56/22.75 ((
% 131.56/22.75 (notsubsetI) =>
% 131.56/22.75 ((
% 131.56/22.75 (notequalI1) =>
% 131.56/22.75 ((
% 131.56/22.75 (notequalI2) =>
% 131.56/22.75 ((
% 131.56/22.75 (subsetRefl) =>
% 131.56/22.75 ((
% 131.56/22.75 (subsetTrans) =>
% 131.56/22.75 ((
% 131.56/22.75 (setadjoinSub) =>
% 131.56/22.75 ((
% 131.56/22.75 (setadjoinSub2) =>
% 131.56/22.75 ((
% 131.56/22.75 (subset2powerset) =>
% 131.56/22.75 ((
% 131.56/22.75 (setextsub) =>
% 131.56/22.75 ((
% 131.56/22.75 (subsetemptysetimpeq) =>
% 131.56/22.75 ((
% 131.56/22.75 (powersetI1) =>
% 131.56/22.75 ((
% 131.56/22.75 (powersetE1) =>
% 131.56/22.75 ((
% 131.56/22.75 (inPowerset) =>
% 131.56/22.75 ((
% 131.56/22.75 (powersetsubset) =>
% 131.56/22.75 ((
% 131.56/22.75 (sepInPowerset) =>
% 131.56/22.75 ((
% 131.56/22.75 (sepSubset) =>
% 131.56/22.75 ((
% 131.56/22.75 (binunionIL) =>
% 131.56/22.75 ((
% 131.56/22.75 (upairset2IR) =>
% 131.56/22.75 ((
% 131.56/22.75 (binunionIR) =>
% 131.56/22.75 ((
% 131.56/22.75 (binunionEcases) =>
% 131.56/22.75 ((
% 131.56/22.75 (binunionE) =>
% 131.56/22.75 ((
% 131.56/22.75 (binunionLsub) =>
% 131.56/22.75 ((
% 131.56/22.75 (binunionRsub) =>
% 131.56/22.75 ((
% 131.56/22.75 (binintersectI) =>
% 131.56/22.75 ((
% 131.56/22.75 (binintersectSubset5) =>
% 131.56/22.75 ((
% 131.56/22.75 (binintersectEL) =>
% 131.56/22.75 ((
% 131.56/22.75 (binintersectLsub) =>
% 131.56/22.75 ((
% 131.56/22.75 (binintersectSubset2) =>
% 131.56/22.75 ((
% 131.56/22.75 (binintersectSubset3) =>
% 131.56/22.75 ((
% 131.56/22.75 (binintersectER) =>
% 131.56/22.75 ((
% 131.56/22.75 (disjointsetsI1) =>
% 131.56/22.75 ((
% 131.56/22.75 (binintersectRsub) =>
% 131.56/22.75 ((
% 131.56/22.75 (binintersectSubset4) =>
% 131.56/22.75 ((
% 131.56/22.75 (binintersectSubset1) =>
% 131.56/22.75 ((
% 131.56/22.75 (bs114d) =>
% 131.56/22.75 ((
% 131.56/22.75 (setminusI) =>
% 131.56/22.75 ((
% 131.56/22.75 (setminusEL) =>
% 131.56/22.75 ((
% 131.56/22.75 (setminusER) =>
% 131.56/22.75 ((
% 131.56/22.75 (setminusSubset2) =>
% 131.56/22.75 ((
% 131.56/22.75 (setminusERneg) =>
% 131.56/22.75 ((
% 131.56/22.75 (setminusELneg) =>
% 131.56/22.75 ((
% 131.56/22.75 (setminusILneg) =>
% 131.56/22.75 ((
% 131.56/22.75 (setminusIRneg) =>
% 131.56/22.75 ((
% 131.56/22.75 (setminusLsub) =>
% 131.56/22.75 ((
% 131.56/22.75 (setminusSubset1) =>
% 131.56/22.75 ((
% 131.56/22.75 (symdiffE) =>
% 131.56/22.75 ((
% 131.56/22.75 (symdiffI1) =>
% 131.56/22.75 ((
% 131.56/22.75 (symdiffI2) =>
% 131.56/22.75 ((
% 131.56/22.75 (symdiffIneg1) =>
% 131.56/22.75 ((
% 131.56/22.75 (symdiffIneg2) =>
% 131.56/22.75 ((
% 131.56/22.75 (secondinupair) =>
% 131.56/22.75 ((
% 131.56/22.75 (setukpairIL) =>
% 131.56/22.75 ((
% 131.56/22.75 (setukpairIR) =>
% 131.56/22.75 ((
% 131.56/22.75 (kpairiskpair) =>
% 131.56/22.75 ((
% 131.56/22.75 (kpairp) =>
% 131.56/22.75 ((
% 131.56/22.75 (singletonsubset) =>
% 131.56/22.75 ((
% 131.56/22.75 (singletoninpowerset) =>
% 131.56/22.75 ((
% 131.56/22.75 (singletoninpowunion) =>
% 131.56/22.75 ((
% 131.56/22.75 (upairset2E) =>
% 131.56/22.75 ((
% 131.56/22.75 (upairsubunion) =>
% 131.56/22.75 ((
% 131.56/22.75 (upairinpowunion) =>
% 131.56/22.75 ((
% 131.56/22.75 (ubforcartprodlem1) =>
% 131.56/22.75 ((
% 131.56/22.75 (ubforcartprodlem2) =>
% 131.56/22.75 ((
% 131.56/22.75 (ubforcartprodlem3) =>
% 131.56/22.75 ((
% 131.56/22.75 (cartprodpairin) =>
% 131.56/22.75 ((
% 131.56/22.75 (cartprodmempair1) =>
% 131.56/22.75 ((
% 131.56/22.75 (cartprodmempair) =>
% 131.56/22.75 ((
% 131.56/22.75 (setunionE2) =>
% 131.56/22.75 ((
% 131.56/22.75 (setunionsingleton1) =>
% 131.56/22.75 ((
% 131.56/22.75 (setunionsingleton2) =>
% 131.56/22.75 ((
% 131.56/22.75 (setunionsingleton) =>
% 131.56/22.75 ((
% 131.56/22.75 (singletonprop) =>
% 131.56/22.75 ((
% 131.56/22.75 (ex1E1) =>
% 131.56/22.75 ((
% 131.56/22.75 (ex1I) =>
% 131.56/22.75 ((
% 131.56/22.75 (ex1I2) =>
% 131.56/22.75 ((
% 131.56/22.75 (singletonsuniq) =>
% 131.56/22.75 ((
% 131.56/22.75 (setukpairinjL1) =>
% 131.56/22.75 ((
% 131.56/22.75 (kfstsingleton) =>
% 131.56/22.75 ((
% 131.56/22.75 (theprop) =>
% 131.56/22.75 ((
% 131.56/22.75 (kfstpairEq) =>
% 131.56/22.75 ((
% 131.56/22.75 (cartprodfstin) =>
% 131.56/22.75 ((
% 131.56/22.75 (setukpairinjL2) =>
% 131.56/22.75 ((
% 131.56/22.75 (setukpairinjL) =>
% 131.56/22.75 ((
% 131.56/22.75 (setukpairinjR11) =>
% 131.56/22.75 ((
% 131.56/22.75 (setukpairinjR12) =>
% 131.56/22.75 ((
% 131.56/22.75 (setukpairinjR1) =>
% 131.56/22.75 ((
% 131.56/22.75 (upairequniteq) =>
% 131.56/22.75 ((
% 131.56/22.75 (setukpairinjR2) =>
% 131.56/22.75 ((
% 131.56/22.75 (setukpairinjR) =>
% 131.56/22.75 ((
% 131.56/22.75 (ksndsingleton) =>
% 131.56/22.75 ((
% 131.56/22.75 (ksndpairEq) =>
% 131.56/22.75 ((
% 131.56/22.75 (kpairsurjEq) =>
% 131.56/22.75 ((
% 131.56/22.75 (cartprodsndin) =>
% 131.56/22.75 ((
% 131.56/22.75 (cartprodpairmemEL) =>
% 131.56/22.75 ((
% 131.56/22.75 (cartprodpairmemER) =>
% 131.56/22.75 ((
% 131.56/22.75 (cartprodmempaircEq) =>
% 131.56/22.75 ((
% 131.56/22.75 (cartprodfstpairEq) =>
% 131.56/22.75 ((
% 131.56/22.75 (cartprodsndpairEq) =>
% 131.56/22.75 ((
% 131.56/22.75 (cartprodpairsurjEq) =>
% 131.56/22.75 ((
% 131.56/22.75 (dpsetconstrI) =>
% 131.56/22.75 ((
% 131.56/22.75 (dpsetconstrSub) =>
% 131.56/22.75 ((
% 131.56/22.75 (setOfPairsIsBReln) =>
% 131.56/22.75 ((
% 131.56/22.75 (dpsetconstrERa) =>
% 131.56/22.75 ((
% 131.56/22.75 (dpsetconstrEL1) =>
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% 131.56/22.75 (dpsetconstrEL2) =>
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% 131.56/22.75 ((
% 131.56/22.75 (lamp) =>
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% 131.56/22.75 (brelnall1) =>
% 131.56/22.75 ((
% 131.56/22.75 (brelnall2) =>
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% 131.56/22.75 (ex1E2) =>
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% 131.56/22.75 ((
% 131.56/22.75 (beta1) =>
% 131.56/22.75 ((
% 131.56/22.75 (eta1) =>
% 131.56/22.75 ((
% 131.56/22.75 (lam2lamEq) =>
% 131.56/22.75 ((
% 131.56/22.75 (beta2) =>
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% 131.56/22.75 (iffalseProp2) =>
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% 131.56/22.75 ((
% 131.56/22.75 (iftrueProp2) =>
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% 131.56/22.75 (iftrueorfalse) =>
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% 131.56/22.75 (binintersectTERcontra) =>
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% 131.56/22.75 (complementInPowersetComplementIntersect) =>
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% 131.56/22.75 (inIntersectImpInUnion2) =>
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% 131.56/22.77 (demorgan2) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz13rule0) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz13rule1) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz13rule2) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz13rule3) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz13rule4) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz1_1) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz1_2) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz1_3) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz1_4) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz1_5) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1all2) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1SetBreln1) =>
% 131.56/22.77 ((
% 131.56/22.77 (choice2fnsingleton) =>
% 131.56/22.77 ((
% 131.56/22.77 (setOfPairsIsBReln1) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1all1) =>
% 131.56/22.77 ((
% 131.56/22.77 (subbreln1) =>
% 131.56/22.77 ((
% 131.56/22.77 (eqbreln1) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1invprop) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1invI) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1invE) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1compprop) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1compI) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1compE) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1compEex) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1unionprop) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1unionIL) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1unionIR) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1unionI) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1unionE) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1unionEcases) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1unionCommutes) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz2Ex) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz2W) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz2A) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz2B) =>
% 131.56/22.77 ((
% 131.56/22.77 (image1Ex) =>
% 131.56/22.77 ((
% 131.56/22.77 (image1Ex1) =>
% 131.56/22.77 ((
% 131.56/22.77 (image1Equiv) =>
% 131.56/22.77 ((
% 131.56/22.77 (image1E) =>
% 131.56/22.77 ((
% 131.56/22.77 (image1I) =>
% 131.56/22.77 ((
% 131.56/22.77 (injFuncInInjFuncSet) =>
% 131.56/22.77 ((
% 131.56/22.77 (injFuncSetFuncIn) =>
% 131.56/22.77 ((
% 131.56/22.77 (injFuncSetFuncInj) =>
% 131.56/22.77 ((
% 131.56/22.77 (surjFuncSetFuncIn) =>
% 131.56/22.77 ((
% 131.56/22.77 (surjFuncSetFuncSurj) =>
% 131.56/22.77 ((
% 131.56/22.77 (leftInvIsSurj) =>
% 131.56/22.77 ((
% 131.56/22.77 (surjCantorThm) =>
% 131.56/22.77 ((
% 131.56/22.77 (foundation2) =>
% 131.56/22.77 ((
% 131.56/22.77 (notinself) =>
% 131.56/22.77 ((
% 131.56/22.77 (notinself2) =>
% 131.56/22.77 ((
% 131.56/22.77 (omegaSp) =>
% 131.56/22.77 ((
% 131.56/22.77 (omegaSclos) =>
% 131.56/22.77 ((
% 131.56/22.77 (peano0notS) =>
% 131.56/22.77 ((
% 131.56/22.77 (peanoSinj) =>
% 131.56/22.77 ((
% 131.56/22.77 (transitivesetOp1) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintTransitive) =>
% 131.56/22.77 ((
% 131.56/22.77 (transitivesetOp2) =>
% 131.56/22.77 ((
% 131.56/22.77 (setunionTransitive) =>
% 131.56/22.77 ((
% 131.56/22.77 (ordinalMinLem1) =>
% 131.56/22.77 ((
% 131.56/22.77 (ordinalTransSet) =>
% 131.56/22.77 ((
% 131.56/22.77 (ordinalTransSet1) =>
% 131.56/22.77 ((
% 131.56/22.77 (setunionOrdinalLem1) =>
% 131.56/22.77 (ordinal @
% 131.56/22.77 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 131.56/22.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl79])).
% 131.56/22.77 thf(zip_derived_cl115, plain,
% 131.56/22.77 (~ (((prop2setE) =>
% 131.56/22.77 (((emptysetE) =>
% 131.56/22.77 (((emptysetimpfalse) =>
% 131.56/22.77 (((notinemptyset) =>
% 131.56/22.77 (((exuE3e) =>
% 131.56/22.77 (((setext) =>
% 131.56/22.77 (((emptyI) =>
% 131.56/22.77 (((noeltsimpempty) =>
% 131.56/22.77 (((setbeta) =>
% 131.56/22.77 (((nonemptyE1) =>
% 131.56/22.77 (((nonemptyI) =>
% 131.56/22.77 (((nonemptyI1) =>
% 131.56/22.77 (((setadjoinIL) =>
% 131.56/22.77 (((in @ emptyset @
% 131.56/22.77 (setadjoin @ emptyset @ emptyset)) =>
% 131.56/22.77 (((setadjoinIR) =>
% 131.56/22.77 (((setadjoinE) =>
% 131.56/22.77 (((setadjoinOr) =>
% 131.56/22.77 (((setoftrueEq) =>
% 131.56/22.77 (((powersetI) =>
% 131.56/22.77 (((emptyinPowerset) =>
% 131.56/22.77 (((emptyInPowerset) =>
% 131.56/22.77 (((powersetE) =>
% 131.56/22.77 (((setunionI) =>
% 131.56/22.77 (((setunionE) =>
% 131.56/22.77 (((subPowSU) =>
% 131.56/22.77 (((exuE2) =>
% 131.56/22.77 (((nonemptyImpWitness) =>
% 131.56/22.77 (((uniqinunit) =>
% 131.56/22.77 (((notinsingleton) =>
% 131.56/22.77 (((eqinunit) =>
% 131.56/22.77 ((
% 131.56/22.77 (singletonsswitch) =>
% 131.56/22.77 ((
% 131.56/22.77 (upairsetE) =>
% 131.56/22.77 ((
% 131.56/22.77 (upairsetIL) =>
% 131.56/22.77 ((
% 131.56/22.77 (upairsetIR) =>
% 131.56/22.77 ((
% 131.56/22.77 (emptyE1) =>
% 131.56/22.77 ((
% 131.56/22.77 (vacuousDall) =>
% 131.56/22.77 ((
% 131.56/22.77 (quantDeMorgan1) =>
% 131.56/22.77 ((
% 131.56/22.77 (quantDeMorgan2) =>
% 131.56/22.77 ((
% 131.56/22.77 (quantDeMorgan3) =>
% 131.56/22.77 ((
% 131.56/22.77 (quantDeMorgan4) =>
% 131.56/22.77 ((
% 131.56/22.77 (prop2setI) =>
% 131.56/22.77 ((
% 131.56/22.77 (prop2set2propI) =>
% 131.56/22.77 ((
% 131.56/22.77 (notdexE) =>
% 131.56/22.77 ((
% 131.56/22.77 (notdallE) =>
% 131.56/22.77 ((
% 131.56/22.77 (exuI1) =>
% 131.56/22.77 ((
% 131.56/22.77 (exuI3) =>
% 131.56/22.77 ((
% 131.56/22.77 (exuI2) =>
% 131.56/22.77 ((
% 131.56/22.77 (inCongP) =>
% 131.56/22.77 ((
% 131.56/22.77 (in__Cong) =>
% 131.56/22.77 ((
% 131.56/22.77 (exuE3u) =>
% 131.56/22.77 ((
% 131.56/22.77 (exu__Cong) =>
% 131.56/22.77 ((
% 131.56/22.77 (setadjoin__Cong) =>
% 131.56/22.77 ((
% 131.56/22.77 (powerset__Cong) =>
% 131.56/22.77 ((
% 131.56/22.77 (setunion__Cong) =>
% 131.56/22.77 ((
% 131.56/22.77 (exuEu) =>
% 131.56/22.77 ((
% 131.56/22.77 (descr__Cong) =>
% 131.56/22.77 ((
% 131.56/22.77 (dsetconstr__Cong) =>
% 131.56/22.77 ((
% 131.56/22.77 (subsetI1) =>
% 131.56/22.77 ((
% 131.56/22.77 (eqimpsubset2) =>
% 131.56/22.77 ((
% 131.56/22.77 (eqimpsubset1) =>
% 131.56/22.77 ((
% 131.56/22.77 (subsetI2) =>
% 131.56/22.77 ((
% 131.56/22.77 (emptysetsubset) =>
% 131.56/22.77 ((
% 131.56/22.77 (subsetE) =>
% 131.56/22.77 ((
% 131.56/22.77 (subsetE2) =>
% 131.56/22.77 ((
% 131.56/22.77 (notsubsetI) =>
% 131.56/22.77 ((
% 131.56/22.77 (notequalI1) =>
% 131.56/22.77 ((
% 131.56/22.77 (notequalI2) =>
% 131.56/22.77 ((
% 131.56/22.77 (subsetRefl) =>
% 131.56/22.77 ((
% 131.56/22.77 (subsetTrans) =>
% 131.56/22.77 ((
% 131.56/22.77 (setadjoinSub) =>
% 131.56/22.77 ((
% 131.56/22.77 (setadjoinSub2) =>
% 131.56/22.77 ((
% 131.56/22.77 (subset2powerset) =>
% 131.56/22.77 ((
% 131.56/22.77 (setextsub) =>
% 131.56/22.77 ((
% 131.56/22.77 (subsetemptysetimpeq) =>
% 131.56/22.77 ((
% 131.56/22.77 (powersetI1) =>
% 131.56/22.77 ((
% 131.56/22.77 (powersetE1) =>
% 131.56/22.77 ((
% 131.56/22.77 (inPowerset) =>
% 131.56/22.77 ((
% 131.56/22.77 (powersetsubset) =>
% 131.56/22.77 ((
% 131.56/22.77 (sepInPowerset) =>
% 131.56/22.77 ((
% 131.56/22.77 (sepSubset) =>
% 131.56/22.77 ((
% 131.56/22.77 (binunionIL) =>
% 131.56/22.77 ((
% 131.56/22.77 (upairset2IR) =>
% 131.56/22.77 ((
% 131.56/22.77 (binunionIR) =>
% 131.56/22.77 ((
% 131.56/22.77 (binunionEcases) =>
% 131.56/22.77 ((
% 131.56/22.77 (binunionE) =>
% 131.56/22.77 ((
% 131.56/22.77 (binunionLsub) =>
% 131.56/22.77 ((
% 131.56/22.77 (binunionRsub) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectI) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectSubset5) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectEL) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectLsub) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectSubset2) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectSubset3) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectER) =>
% 131.56/22.77 ((
% 131.56/22.77 (disjointsetsI1) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectRsub) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectSubset4) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectSubset1) =>
% 131.56/22.77 ((
% 131.56/22.77 (bs114d) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusI) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusEL) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusER) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusSubset2) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusERneg) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusELneg) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusILneg) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusIRneg) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusLsub) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusSubset1) =>
% 131.56/22.77 ((
% 131.56/22.77 (symdiffE) =>
% 131.56/22.77 ((
% 131.56/22.77 (symdiffI1) =>
% 131.56/22.77 ((
% 131.56/22.77 (symdiffI2) =>
% 131.56/22.77 ((
% 131.56/22.77 (symdiffIneg1) =>
% 131.56/22.77 ((
% 131.56/22.77 (symdiffIneg2) =>
% 131.56/22.77 ((
% 131.56/22.77 (secondinupair) =>
% 131.56/22.77 ((
% 131.56/22.77 (setukpairIL) =>
% 131.56/22.77 ((
% 131.56/22.77 (setukpairIR) =>
% 131.56/22.77 ((
% 131.56/22.77 (kpairiskpair) =>
% 131.56/22.77 ((
% 131.56/22.77 (kpairp) =>
% 131.56/22.77 ((
% 131.56/22.77 (singletonsubset) =>
% 131.56/22.77 ((
% 131.56/22.77 (singletoninpowerset) =>
% 131.56/22.77 ((
% 131.56/22.77 (singletoninpowunion) =>
% 131.56/22.77 ((
% 131.56/22.77 (upairset2E) =>
% 131.56/22.77 ((
% 131.56/22.77 (upairsubunion) =>
% 131.56/22.77 ((
% 131.56/22.77 (upairinpowunion) =>
% 131.56/22.77 ((
% 131.56/22.77 (ubforcartprodlem1) =>
% 131.56/22.77 ((
% 131.56/22.77 (ubforcartprodlem2) =>
% 131.56/22.77 ((
% 131.56/22.77 (ubforcartprodlem3) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodpairin) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodmempair1) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodmempair) =>
% 131.56/22.77 ((
% 131.56/22.77 (setunionE2) =>
% 131.56/22.77 ((
% 131.56/22.77 (setunionsingleton1) =>
% 131.56/22.77 ((
% 131.56/22.77 (setunionsingleton2) =>
% 131.56/22.77 ((
% 131.56/22.77 (setunionsingleton) =>
% 131.56/22.77 ((
% 131.56/22.77 (singletonprop) =>
% 131.56/22.77 ((
% 131.56/22.77 (ex1E1) =>
% 131.56/22.77 ((
% 131.56/22.77 (ex1I) =>
% 131.56/22.77 ((
% 131.56/22.77 (ex1I2) =>
% 131.56/22.77 ((
% 131.56/22.77 (singletonsuniq) =>
% 131.56/22.77 ((
% 131.56/22.77 (setukpairinjL1) =>
% 131.56/22.77 ((
% 131.56/22.77 (kfstsingleton) =>
% 131.56/22.77 ((
% 131.56/22.77 (theprop) =>
% 131.56/22.77 ((
% 131.56/22.77 (kfstpairEq) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodfstin) =>
% 131.56/22.77 ((
% 131.56/22.77 (setukpairinjL2) =>
% 131.56/22.77 ((
% 131.56/22.77 (setukpairinjL) =>
% 131.56/22.77 ((
% 131.56/22.77 (setukpairinjR11) =>
% 131.56/22.77 ((
% 131.56/22.77 (setukpairinjR12) =>
% 131.56/22.77 ((
% 131.56/22.77 (setukpairinjR1) =>
% 131.56/22.77 ((
% 131.56/22.77 (upairequniteq) =>
% 131.56/22.77 ((
% 131.56/22.77 (setukpairinjR2) =>
% 131.56/22.77 ((
% 131.56/22.77 (setukpairinjR) =>
% 131.56/22.77 ((
% 131.56/22.77 (ksndsingleton) =>
% 131.56/22.77 ((
% 131.56/22.77 (ksndpairEq) =>
% 131.56/22.77 ((
% 131.56/22.77 (kpairsurjEq) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodsndin) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodpairmemEL) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodpairmemER) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodmempaircEq) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodfstpairEq) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodsndpairEq) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodpairsurjEq) =>
% 131.56/22.77 ((
% 131.56/22.77 (dpsetconstrI) =>
% 131.56/22.77 ((
% 131.56/22.77 (dpsetconstrSub) =>
% 131.56/22.77 ((
% 131.56/22.77 (setOfPairsIsBReln) =>
% 131.56/22.77 ((
% 131.56/22.77 (dpsetconstrERa) =>
% 131.56/22.77 ((
% 131.56/22.77 (dpsetconstrEL1) =>
% 131.56/22.77 ((
% 131.56/22.77 (dpsetconstrEL2) =>
% 131.56/22.77 ((
% 131.56/22.77 (dpsetconstrER) =>
% 131.56/22.77 ((
% 131.56/22.77 (funcImageSingleton) =>
% 131.56/22.77 ((
% 131.56/22.77 (apProp) =>
% 131.56/22.77 ((
% 131.56/22.77 (app) =>
% 131.56/22.77 ((
% 131.56/22.77 (infuncsetfunc) =>
% 131.56/22.77 ((
% 131.56/22.77 (ap2p) =>
% 131.56/22.77 ((
% 131.56/22.77 (funcinfuncset) =>
% 131.56/22.77 ((
% 131.56/22.77 (lamProp) =>
% 131.56/22.77 ((
% 131.56/22.77 (lamp) =>
% 131.56/22.77 ((
% 131.56/22.77 (lam2p) =>
% 131.56/22.77 ((
% 131.56/22.77 (brelnall1) =>
% 131.56/22.77 ((
% 131.56/22.77 (brelnall2) =>
% 131.56/22.77 ((
% 131.56/22.77 (ex1E2) =>
% 131.56/22.77 ((
% 131.56/22.77 (funcGraphProp1) =>
% 131.56/22.77 ((
% 131.56/22.77 (funcGraphProp3) =>
% 131.56/22.77 ((
% 131.56/22.77 (funcGraphProp2) =>
% 131.56/22.77 ((
% 131.56/22.77 (funcextLem) =>
% 131.56/22.77 ((
% 131.56/22.77 (funcGraphProp4) =>
% 131.56/22.77 ((
% 131.56/22.77 (subbreln) =>
% 131.56/22.77 ((
% 131.56/22.77 (eqbreln) =>
% 131.56/22.77 ((
% 131.56/22.77 (funcext) =>
% 131.56/22.77 ((
% 131.56/22.77 (funcext2) =>
% 131.56/22.77 ((
% 131.56/22.77 (ap2apEq1) =>
% 131.56/22.77 ((
% 131.56/22.77 (ap2apEq2) =>
% 131.56/22.77 ((
% 131.56/22.77 (beta1) =>
% 131.56/22.77 ((
% 131.56/22.77 (eta1) =>
% 131.56/22.77 ((
% 131.56/22.77 (lam2lamEq) =>
% 131.56/22.77 ((
% 131.56/22.77 (beta2) =>
% 131.56/22.77 ((
% 131.56/22.77 (eta2) =>
% 131.56/22.77 ((
% 131.56/22.77 (iffalseProp1) =>
% 131.56/22.77 ((
% 131.56/22.77 (iffalseProp2) =>
% 131.56/22.77 ((
% 131.56/22.77 (iftrueProp1) =>
% 131.56/22.77 ((
% 131.56/22.77 (iftrueProp2) =>
% 131.56/22.77 ((
% 131.56/22.77 (ifSingleton) =>
% 131.56/22.77 ((
% 131.56/22.77 (ifp) =>
% 131.56/22.77 ((
% 131.56/22.77 (theeq) =>
% 131.56/22.77 ((
% 131.56/22.77 (iftrue) =>
% 131.56/22.77 ((
% 131.56/22.77 (iffalse) =>
% 131.56/22.77 ((
% 131.56/22.77 (iftrueorfalse) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectT_lem) =>
% 131.56/22.77 ((
% 131.56/22.77 (binunionT_lem) =>
% 131.56/22.77 ((
% 131.56/22.77 (powersetT_lem) =>
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% 131.56/22.77 (setminusT_lem) =>
% 131.56/22.77 ((
% 131.56/22.77 (complementT_lem) =>
% 131.56/22.77 ((
% 131.56/22.77 (setextT) =>
% 131.56/22.77 ((
% 131.56/22.77 (subsetTI) =>
% 131.56/22.77 ((
% 131.56/22.77 (powersetTI1) =>
% 131.56/22.77 ((
% 131.56/22.77 (powersetTE1) =>
% 131.56/22.77 ((
% 131.56/22.77 (complementTI1) =>
% 131.56/22.77 ((
% 131.56/22.77 (complementTE1) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectTELcontra) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectTERcontra) =>
% 131.56/22.77 ((
% 131.56/22.77 (contrasubsetT) =>
% 131.56/22.77 ((
% 131.56/22.77 (contrasubsetT1) =>
% 131.56/22.77 ((
% 131.56/22.77 (contrasubsetT2) =>
% 131.56/22.77 ((
% 131.56/22.77 (contrasubsetT3) =>
% 131.56/22.77 ((
% 131.56/22.77 (doubleComplementI1) =>
% 131.56/22.77 ((
% 131.56/22.77 (doubleComplementE1) =>
% 131.56/22.77 ((
% 131.56/22.77 (doubleComplementSub1) =>
% 131.56/22.77 ((
% 131.56/22.77 (doubleComplementSub2) =>
% 131.56/22.77 ((
% 131.56/22.77 (doubleComplementEq) =>
% 131.56/22.77 ((
% 131.56/22.77 (complementTnotintersectT) =>
% 131.56/22.77 ((
% 131.56/22.77 (complementImpComplementIntersect) =>
% 131.56/22.77 ((
% 131.56/22.77 (complementSubsetComplementIntersect) =>
% 131.56/22.77 ((
% 131.56/22.77 (complementInPowersetComplementIntersect) =>
% 131.56/22.77 ((
% 131.56/22.77 (contraSubsetComplement) =>
% 131.56/22.77 ((
% 131.56/22.77 (complementTcontraSubset) =>
% 131.56/22.77 ((
% 131.56/22.77 (binunionTILcontra) =>
% 131.56/22.77 ((
% 131.56/22.77 (binunionTIRcontra) =>
% 131.56/22.77 ((
% 131.56/22.77 (inIntersectImpInUnion) =>
% 131.56/22.77 ((
% 131.56/22.77 (inIntersectImpInUnion2) =>
% 131.56/22.77 ((
% 131.56/22.77 (inIntersectImpInIntersectUnions) =>
% 131.56/22.77 ((
% 131.56/22.77 (intersectInPowersetIntersectUnions) =>
% 131.56/22.77 ((
% 131.56/22.77 (inComplementUnionImpNotIn1) =>
% 131.56/22.77 ((
% 131.56/22.77 (inComplementUnionImpInComplement1) =>
% 131.56/22.77 ((
% 131.56/22.77 (binunionTE) =>
% 131.56/22.77 ((
% 131.56/22.77 (binunionTEcontra) =>
% 131.56/22.77 ((
% 131.56/22.77 (demorgan2a1) =>
% 131.56/22.77 ((
% 131.56/22.77 (complementUnionInPowersetComplement) =>
% 131.56/22.77 ((
% 131.56/22.77 (demorgan2a2) =>
% 131.56/22.77 ((
% 131.56/22.77 (demorgan1a) =>
% 131.56/22.77 ((
% 131.56/22.77 (demorgan1b) =>
% 131.56/22.77 ((
% 131.56/22.77 (demorgan1) =>
% 131.56/22.77 ((
% 131.56/22.77 (demorgan2a) =>
% 131.56/22.77 ((
% 131.56/22.77 (demorgan2b2) =>
% 131.56/22.77 ((
% 131.56/22.77 (demorgan2b) =>
% 131.56/22.77 ((
% 131.56/22.77 (demorgan2) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz13rule0) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz13rule1) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz13rule2) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz13rule3) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz13rule4) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz1_1) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz1_2) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz1_3) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz1_4) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz1_5) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1all2) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1SetBreln1) =>
% 131.56/22.77 ((
% 131.56/22.77 (choice2fnsingleton) =>
% 131.56/22.77 ((
% 131.56/22.77 (setOfPairsIsBReln1) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1all1) =>
% 131.56/22.77 ((
% 131.56/22.77 (subbreln1) =>
% 131.56/22.77 ((
% 131.56/22.77 (eqbreln1) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1invprop) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1invI) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1invE) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1compprop) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1compI) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1compE) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1compEex) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1unionprop) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1unionIL) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1unionIR) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1unionI) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1unionE) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1unionEcases) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1unionCommutes) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz2Ex) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz2W) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz2A) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz2B) =>
% 131.56/22.77 ((
% 131.56/22.77 (image1Ex) =>
% 131.56/22.77 ((
% 131.56/22.77 (image1Ex1) =>
% 131.56/22.77 ((
% 131.56/22.77 (image1Equiv) =>
% 131.56/22.77 ((
% 131.56/22.77 (image1E) =>
% 131.56/22.77 ((
% 131.56/22.77 (image1I) =>
% 131.56/22.77 ((
% 131.56/22.77 (injFuncInInjFuncSet) =>
% 131.56/22.77 ((
% 131.56/22.77 (injFuncSetFuncIn) =>
% 131.56/22.77 ((
% 131.56/22.77 (injFuncSetFuncInj) =>
% 131.56/22.77 ((
% 131.56/22.77 (surjFuncSetFuncIn) =>
% 131.56/22.77 ((
% 131.56/22.77 (surjFuncSetFuncSurj) =>
% 131.56/22.77 ((
% 131.56/22.77 (leftInvIsSurj) =>
% 131.56/22.77 ((
% 131.56/22.77 (surjCantorThm) =>
% 131.56/22.77 ((
% 131.56/22.77 (foundation2) =>
% 131.56/22.77 ((
% 131.56/22.77 (notinself) =>
% 131.56/22.77 ((
% 131.56/22.77 (notinself2) =>
% 131.56/22.77 ((
% 131.56/22.77 (omegaSp) =>
% 131.56/22.77 ((
% 131.56/22.77 (omegaSclos) =>
% 131.56/22.77 ((
% 131.56/22.77 (peano0notS) =>
% 131.56/22.77 ((
% 131.56/22.77 (peanoSinj) =>
% 131.56/22.77 ((
% 131.56/22.77 (transitivesetOp1) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintTransitive) =>
% 131.56/22.77 ((
% 131.56/22.77 (transitivesetOp2) =>
% 131.56/22.77 ((
% 131.56/22.77 (setunionTransitive) =>
% 131.56/22.77 ((
% 131.56/22.77 (ordinalMinLem1) =>
% 131.56/22.77 ((
% 131.56/22.77 (ordinalTransSet) =>
% 131.56/22.77 ((
% 131.56/22.77 (ordinalTransSet1) =>
% 131.56/22.77 ((
% 131.56/22.77 (setunionOrdinalLem1) =>
% 131.56/22.77 (ordinal @
% 131.56/22.77 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 131.56/22.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl95])).
% 131.56/22.77 thf(zip_derived_cl133, plain,
% 131.56/22.77 (~ (((emptysetE) =>
% 131.56/22.77 (((emptysetimpfalse) =>
% 131.56/22.77 (((notinemptyset) =>
% 131.56/22.77 (((exuE3e) =>
% 131.56/22.77 (((setext) =>
% 131.56/22.77 (((emptyI) =>
% 131.56/22.77 (((noeltsimpempty) =>
% 131.56/22.77 (((setbeta) =>
% 131.56/22.77 (((nonemptyE1) =>
% 131.56/22.77 (((nonemptyI) =>
% 131.56/22.77 (((nonemptyI1) =>
% 131.56/22.77 (((setadjoinIL) =>
% 131.56/22.77 (((in @ emptyset @
% 131.56/22.77 (setadjoin @ emptyset @ emptyset)) =>
% 131.56/22.77 (((setadjoinIR) =>
% 131.56/22.77 (((setadjoinE) =>
% 131.56/22.77 (((setadjoinOr) =>
% 131.56/22.77 (((setoftrueEq) =>
% 131.56/22.77 (((powersetI) =>
% 131.56/22.77 (((emptyinPowerset) =>
% 131.56/22.77 (((emptyInPowerset) =>
% 131.56/22.77 (((powersetE) =>
% 131.56/22.77 (((setunionI) =>
% 131.56/22.77 (((setunionE) =>
% 131.56/22.77 (((subPowSU) =>
% 131.56/22.77 (((exuE2) =>
% 131.56/22.77 (((nonemptyImpWitness) =>
% 131.56/22.77 (((uniqinunit) =>
% 131.56/22.77 (((notinsingleton) =>
% 131.56/22.77 (((eqinunit) =>
% 131.56/22.77 (((singletonsswitch) =>
% 131.56/22.77 ((
% 131.56/22.77 (upairsetE) =>
% 131.56/22.77 ((
% 131.56/22.77 (upairsetIL) =>
% 131.56/22.77 ((
% 131.56/22.77 (upairsetIR) =>
% 131.56/22.77 ((
% 131.56/22.77 (emptyE1) =>
% 131.56/22.77 ((
% 131.56/22.77 (vacuousDall) =>
% 131.56/22.77 ((
% 131.56/22.77 (quantDeMorgan1) =>
% 131.56/22.77 ((
% 131.56/22.77 (quantDeMorgan2) =>
% 131.56/22.77 ((
% 131.56/22.77 (quantDeMorgan3) =>
% 131.56/22.77 ((
% 131.56/22.77 (quantDeMorgan4) =>
% 131.56/22.77 ((
% 131.56/22.77 (prop2setI) =>
% 131.56/22.77 ((
% 131.56/22.77 (prop2set2propI) =>
% 131.56/22.77 ((
% 131.56/22.77 (notdexE) =>
% 131.56/22.77 ((
% 131.56/22.77 (notdallE) =>
% 131.56/22.77 ((
% 131.56/22.77 (exuI1) =>
% 131.56/22.77 ((
% 131.56/22.77 (exuI3) =>
% 131.56/22.77 ((
% 131.56/22.77 (exuI2) =>
% 131.56/22.77 ((
% 131.56/22.77 (inCongP) =>
% 131.56/22.77 ((
% 131.56/22.77 (in__Cong) =>
% 131.56/22.77 ((
% 131.56/22.77 (exuE3u) =>
% 131.56/22.77 ((
% 131.56/22.77 (exu__Cong) =>
% 131.56/22.77 ((
% 131.56/22.77 (setadjoin__Cong) =>
% 131.56/22.77 ((
% 131.56/22.77 (powerset__Cong) =>
% 131.56/22.77 ((
% 131.56/22.77 (setunion__Cong) =>
% 131.56/22.77 ((
% 131.56/22.77 (exuEu) =>
% 131.56/22.77 ((
% 131.56/22.77 (descr__Cong) =>
% 131.56/22.77 ((
% 131.56/22.77 (dsetconstr__Cong) =>
% 131.56/22.77 ((
% 131.56/22.77 (subsetI1) =>
% 131.56/22.77 ((
% 131.56/22.77 (eqimpsubset2) =>
% 131.56/22.77 ((
% 131.56/22.77 (eqimpsubset1) =>
% 131.56/22.77 ((
% 131.56/22.77 (subsetI2) =>
% 131.56/22.77 ((
% 131.56/22.77 (emptysetsubset) =>
% 131.56/22.77 ((
% 131.56/22.77 (subsetE) =>
% 131.56/22.77 ((
% 131.56/22.77 (subsetE2) =>
% 131.56/22.77 ((
% 131.56/22.77 (notsubsetI) =>
% 131.56/22.77 ((
% 131.56/22.77 (notequalI1) =>
% 131.56/22.77 ((
% 131.56/22.77 (notequalI2) =>
% 131.56/22.77 ((
% 131.56/22.77 (subsetRefl) =>
% 131.56/22.77 ((
% 131.56/22.77 (subsetTrans) =>
% 131.56/22.77 ((
% 131.56/22.77 (setadjoinSub) =>
% 131.56/22.77 ((
% 131.56/22.77 (setadjoinSub2) =>
% 131.56/22.77 ((
% 131.56/22.77 (subset2powerset) =>
% 131.56/22.77 ((
% 131.56/22.77 (setextsub) =>
% 131.56/22.77 ((
% 131.56/22.77 (subsetemptysetimpeq) =>
% 131.56/22.77 ((
% 131.56/22.77 (powersetI1) =>
% 131.56/22.77 ((
% 131.56/22.77 (powersetE1) =>
% 131.56/22.77 ((
% 131.56/22.77 (inPowerset) =>
% 131.56/22.77 ((
% 131.56/22.77 (powersetsubset) =>
% 131.56/22.77 ((
% 131.56/22.77 (sepInPowerset) =>
% 131.56/22.77 ((
% 131.56/22.77 (sepSubset) =>
% 131.56/22.77 ((
% 131.56/22.77 (binunionIL) =>
% 131.56/22.77 ((
% 131.56/22.77 (upairset2IR) =>
% 131.56/22.77 ((
% 131.56/22.77 (binunionIR) =>
% 131.56/22.77 ((
% 131.56/22.77 (binunionEcases) =>
% 131.56/22.77 ((
% 131.56/22.77 (binunionE) =>
% 131.56/22.77 ((
% 131.56/22.77 (binunionLsub) =>
% 131.56/22.77 ((
% 131.56/22.77 (binunionRsub) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectI) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectSubset5) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectEL) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectLsub) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectSubset2) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectSubset3) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectER) =>
% 131.56/22.77 ((
% 131.56/22.77 (disjointsetsI1) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectRsub) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectSubset4) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectSubset1) =>
% 131.56/22.77 ((
% 131.56/22.77 (bs114d) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusI) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusEL) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusER) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusSubset2) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusERneg) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusELneg) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusILneg) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusIRneg) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusLsub) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusSubset1) =>
% 131.56/22.77 ((
% 131.56/22.77 (symdiffE) =>
% 131.56/22.77 ((
% 131.56/22.77 (symdiffI1) =>
% 131.56/22.77 ((
% 131.56/22.77 (symdiffI2) =>
% 131.56/22.77 ((
% 131.56/22.77 (symdiffIneg1) =>
% 131.56/22.77 ((
% 131.56/22.77 (symdiffIneg2) =>
% 131.56/22.77 ((
% 131.56/22.77 (secondinupair) =>
% 131.56/22.77 ((
% 131.56/22.77 (setukpairIL) =>
% 131.56/22.77 ((
% 131.56/22.77 (setukpairIR) =>
% 131.56/22.77 ((
% 131.56/22.77 (kpairiskpair) =>
% 131.56/22.77 ((
% 131.56/22.77 (kpairp) =>
% 131.56/22.77 ((
% 131.56/22.77 (singletonsubset) =>
% 131.56/22.77 ((
% 131.56/22.77 (singletoninpowerset) =>
% 131.56/22.77 ((
% 131.56/22.77 (singletoninpowunion) =>
% 131.56/22.77 ((
% 131.56/22.77 (upairset2E) =>
% 131.56/22.77 ((
% 131.56/22.77 (upairsubunion) =>
% 131.56/22.77 ((
% 131.56/22.77 (upairinpowunion) =>
% 131.56/22.77 ((
% 131.56/22.77 (ubforcartprodlem1) =>
% 131.56/22.77 ((
% 131.56/22.77 (ubforcartprodlem2) =>
% 131.56/22.77 ((
% 131.56/22.77 (ubforcartprodlem3) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodpairin) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodmempair1) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodmempair) =>
% 131.56/22.77 ((
% 131.56/22.77 (setunionE2) =>
% 131.56/22.77 ((
% 131.56/22.77 (setunionsingleton1) =>
% 131.56/22.77 ((
% 131.56/22.77 (setunionsingleton2) =>
% 131.56/22.77 ((
% 131.56/22.77 (setunionsingleton) =>
% 131.56/22.77 ((
% 131.56/22.77 (singletonprop) =>
% 131.56/22.77 ((
% 131.56/22.77 (ex1E1) =>
% 131.56/22.77 ((
% 131.56/22.77 (ex1I) =>
% 131.56/22.77 ((
% 131.56/22.77 (ex1I2) =>
% 131.56/22.77 ((
% 131.56/22.77 (singletonsuniq) =>
% 131.56/22.77 ((
% 131.56/22.77 (setukpairinjL1) =>
% 131.56/22.77 ((
% 131.56/22.77 (kfstsingleton) =>
% 131.56/22.77 ((
% 131.56/22.77 (theprop) =>
% 131.56/22.77 ((
% 131.56/22.77 (kfstpairEq) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodfstin) =>
% 131.56/22.77 ((
% 131.56/22.77 (setukpairinjL2) =>
% 131.56/22.77 ((
% 131.56/22.77 (setukpairinjL) =>
% 131.56/22.77 ((
% 131.56/22.77 (setukpairinjR11) =>
% 131.56/22.77 ((
% 131.56/22.77 (setukpairinjR12) =>
% 131.56/22.77 ((
% 131.56/22.77 (setukpairinjR1) =>
% 131.56/22.77 ((
% 131.56/22.77 (upairequniteq) =>
% 131.56/22.77 ((
% 131.56/22.77 (setukpairinjR2) =>
% 131.56/22.77 ((
% 131.56/22.77 (setukpairinjR) =>
% 131.56/22.77 ((
% 131.56/22.77 (ksndsingleton) =>
% 131.56/22.77 ((
% 131.56/22.77 (ksndpairEq) =>
% 131.56/22.77 ((
% 131.56/22.77 (kpairsurjEq) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodsndin) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodpairmemEL) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodpairmemER) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodmempaircEq) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodfstpairEq) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodsndpairEq) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodpairsurjEq) =>
% 131.56/22.77 ((
% 131.56/22.77 (dpsetconstrI) =>
% 131.56/22.77 ((
% 131.56/22.77 (dpsetconstrSub) =>
% 131.56/22.77 ((
% 131.56/22.77 (setOfPairsIsBReln) =>
% 131.56/22.77 ((
% 131.56/22.77 (dpsetconstrERa) =>
% 131.56/22.77 ((
% 131.56/22.77 (dpsetconstrEL1) =>
% 131.56/22.77 ((
% 131.56/22.77 (dpsetconstrEL2) =>
% 131.56/22.77 ((
% 131.56/22.77 (dpsetconstrER) =>
% 131.56/22.77 ((
% 131.56/22.77 (funcImageSingleton) =>
% 131.56/22.77 ((
% 131.56/22.77 (apProp) =>
% 131.56/22.77 ((
% 131.56/22.77 (app) =>
% 131.56/22.77 ((
% 131.56/22.77 (infuncsetfunc) =>
% 131.56/22.77 ((
% 131.56/22.77 (ap2p) =>
% 131.56/22.77 ((
% 131.56/22.77 (funcinfuncset) =>
% 131.56/22.77 ((
% 131.56/22.77 (lamProp) =>
% 131.56/22.77 ((
% 131.56/22.77 (lamp) =>
% 131.56/22.77 ((
% 131.56/22.77 (lam2p) =>
% 131.56/22.77 ((
% 131.56/22.77 (brelnall1) =>
% 131.56/22.77 ((
% 131.56/22.77 (brelnall2) =>
% 131.56/22.77 ((
% 131.56/22.77 (ex1E2) =>
% 131.56/22.77 ((
% 131.56/22.77 (funcGraphProp1) =>
% 131.56/22.77 ((
% 131.56/22.77 (funcGraphProp3) =>
% 131.56/22.77 ((
% 131.56/22.77 (funcGraphProp2) =>
% 131.56/22.77 ((
% 131.56/22.77 (funcextLem) =>
% 131.56/22.77 ((
% 131.56/22.77 (funcGraphProp4) =>
% 131.56/22.77 ((
% 131.56/22.77 (subbreln) =>
% 131.56/22.77 ((
% 131.56/22.77 (eqbreln) =>
% 131.56/22.77 ((
% 131.56/22.77 (funcext) =>
% 131.56/22.77 ((
% 131.56/22.77 (funcext2) =>
% 131.56/22.77 ((
% 131.56/22.77 (ap2apEq1) =>
% 131.56/22.77 ((
% 131.56/22.77 (ap2apEq2) =>
% 131.56/22.77 ((
% 131.56/22.77 (beta1) =>
% 131.56/22.77 ((
% 131.56/22.77 (eta1) =>
% 131.56/22.77 ((
% 131.56/22.77 (lam2lamEq) =>
% 131.56/22.77 ((
% 131.56/22.77 (beta2) =>
% 131.56/22.77 ((
% 131.56/22.77 (eta2) =>
% 131.56/22.77 ((
% 131.56/22.77 (iffalseProp1) =>
% 131.56/22.77 ((
% 131.56/22.77 (iffalseProp2) =>
% 131.56/22.77 ((
% 131.56/22.77 (iftrueProp1) =>
% 131.56/22.77 ((
% 131.56/22.77 (iftrueProp2) =>
% 131.56/22.77 ((
% 131.56/22.77 (ifSingleton) =>
% 131.56/22.77 ((
% 131.56/22.77 (ifp) =>
% 131.56/22.77 ((
% 131.56/22.77 (theeq) =>
% 131.56/22.77 ((
% 131.56/22.77 (iftrue) =>
% 131.56/22.77 ((
% 131.56/22.77 (iffalse) =>
% 131.56/22.77 ((
% 131.56/22.77 (iftrueorfalse) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectT_lem) =>
% 131.56/22.77 ((
% 131.56/22.77 (binunionT_lem) =>
% 131.56/22.77 ((
% 131.56/22.77 (powersetT_lem) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusT_lem) =>
% 131.56/22.77 ((
% 131.56/22.77 (complementT_lem) =>
% 131.56/22.77 ((
% 131.56/22.77 (setextT) =>
% 131.56/22.77 ((
% 131.56/22.77 (subsetTI) =>
% 131.56/22.77 ((
% 131.56/22.77 (powersetTI1) =>
% 131.56/22.77 ((
% 131.56/22.77 (powersetTE1) =>
% 131.56/22.77 ((
% 131.56/22.77 (complementTI1) =>
% 131.56/22.77 ((
% 131.56/22.77 (complementTE1) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectTELcontra) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectTERcontra) =>
% 131.56/22.77 ((
% 131.56/22.77 (contrasubsetT) =>
% 131.56/22.77 ((
% 131.56/22.77 (contrasubsetT1) =>
% 131.56/22.77 ((
% 131.56/22.77 (contrasubsetT2) =>
% 131.56/22.77 ((
% 131.56/22.77 (contrasubsetT3) =>
% 131.56/22.77 ((
% 131.56/22.77 (doubleComplementI1) =>
% 131.56/22.77 ((
% 131.56/22.77 (doubleComplementE1) =>
% 131.56/22.77 ((
% 131.56/22.77 (doubleComplementSub1) =>
% 131.56/22.77 ((
% 131.56/22.77 (doubleComplementSub2) =>
% 131.56/22.77 ((
% 131.56/22.77 (doubleComplementEq) =>
% 131.56/22.77 ((
% 131.56/22.77 (complementTnotintersectT) =>
% 131.56/22.77 ((
% 131.56/22.77 (complementImpComplementIntersect) =>
% 131.56/22.77 ((
% 131.56/22.77 (complementSubsetComplementIntersect) =>
% 131.56/22.77 ((
% 131.56/22.77 (complementInPowersetComplementIntersect) =>
% 131.56/22.77 ((
% 131.56/22.77 (contraSubsetComplement) =>
% 131.56/22.77 ((
% 131.56/22.77 (complementTcontraSubset) =>
% 131.56/22.77 ((
% 131.56/22.77 (binunionTILcontra) =>
% 131.56/22.77 ((
% 131.56/22.77 (binunionTIRcontra) =>
% 131.56/22.77 ((
% 131.56/22.77 (inIntersectImpInUnion) =>
% 131.56/22.77 ((
% 131.56/22.77 (inIntersectImpInUnion2) =>
% 131.56/22.77 ((
% 131.56/22.77 (inIntersectImpInIntersectUnions) =>
% 131.56/22.77 ((
% 131.56/22.77 (intersectInPowersetIntersectUnions) =>
% 131.56/22.77 ((
% 131.56/22.77 (inComplementUnionImpNotIn1) =>
% 131.56/22.77 ((
% 131.56/22.77 (inComplementUnionImpInComplement1) =>
% 131.56/22.77 ((
% 131.56/22.77 (binunionTE) =>
% 131.56/22.77 ((
% 131.56/22.77 (binunionTEcontra) =>
% 131.56/22.77 ((
% 131.56/22.77 (demorgan2a1) =>
% 131.56/22.77 ((
% 131.56/22.77 (complementUnionInPowersetComplement) =>
% 131.56/22.77 ((
% 131.56/22.77 (demorgan2a2) =>
% 131.56/22.77 ((
% 131.56/22.77 (demorgan1a) =>
% 131.56/22.77 ((
% 131.56/22.77 (demorgan1b) =>
% 131.56/22.77 ((
% 131.56/22.77 (demorgan1) =>
% 131.56/22.77 ((
% 131.56/22.77 (demorgan2a) =>
% 131.56/22.77 ((
% 131.56/22.77 (demorgan2b2) =>
% 131.56/22.77 ((
% 131.56/22.77 (demorgan2b) =>
% 131.56/22.77 ((
% 131.56/22.77 (demorgan2) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz13rule0) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz13rule1) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz13rule2) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz13rule3) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz13rule4) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz1_1) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz1_2) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz1_3) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz1_4) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz1_5) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1all2) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1SetBreln1) =>
% 131.56/22.77 ((
% 131.56/22.77 (choice2fnsingleton) =>
% 131.56/22.77 ((
% 131.56/22.77 (setOfPairsIsBReln1) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1all1) =>
% 131.56/22.77 ((
% 131.56/22.77 (subbreln1) =>
% 131.56/22.77 ((
% 131.56/22.77 (eqbreln1) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1invprop) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1invI) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1invE) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1compprop) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1compI) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1compE) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1compEex) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1unionprop) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1unionIL) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1unionIR) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1unionI) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1unionE) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1unionEcases) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1unionCommutes) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz2Ex) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz2W) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz2A) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz2B) =>
% 131.56/22.77 ((
% 131.56/22.77 (image1Ex) =>
% 131.56/22.77 ((
% 131.56/22.77 (image1Ex1) =>
% 131.56/22.77 ((
% 131.56/22.77 (image1Equiv) =>
% 131.56/22.77 ((
% 131.56/22.77 (image1E) =>
% 131.56/22.77 ((
% 131.56/22.77 (image1I) =>
% 131.56/22.77 ((
% 131.56/22.77 (injFuncInInjFuncSet) =>
% 131.56/22.77 ((
% 131.56/22.77 (injFuncSetFuncIn) =>
% 131.56/22.77 ((
% 131.56/22.77 (injFuncSetFuncInj) =>
% 131.56/22.77 ((
% 131.56/22.77 (surjFuncSetFuncIn) =>
% 131.56/22.77 ((
% 131.56/22.77 (surjFuncSetFuncSurj) =>
% 131.56/22.77 ((
% 131.56/22.77 (leftInvIsSurj) =>
% 131.56/22.77 ((
% 131.56/22.77 (surjCantorThm) =>
% 131.56/22.77 ((
% 131.56/22.77 (foundation2) =>
% 131.56/22.77 ((
% 131.56/22.77 (notinself) =>
% 131.56/22.77 ((
% 131.56/22.77 (notinself2) =>
% 131.56/22.77 ((
% 131.56/22.77 (omegaSp) =>
% 131.56/22.77 ((
% 131.56/22.77 (omegaSclos) =>
% 131.56/22.77 ((
% 131.56/22.77 (peano0notS) =>
% 131.56/22.77 ((
% 131.56/22.77 (peanoSinj) =>
% 131.56/22.77 ((
% 131.56/22.77 (transitivesetOp1) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintTransitive) =>
% 131.56/22.77 ((
% 131.56/22.77 (transitivesetOp2) =>
% 131.56/22.77 ((
% 131.56/22.77 (setunionTransitive) =>
% 131.56/22.77 ((
% 131.56/22.77 (ordinalMinLem1) =>
% 131.56/22.77 ((
% 131.56/22.77 (ordinalTransSet) =>
% 131.56/22.77 ((
% 131.56/22.77 (ordinalTransSet1) =>
% 131.56/22.77 ((
% 131.56/22.77 (setunionOrdinalLem1) =>
% 131.56/22.77 (ordinal @
% 131.56/22.77 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 131.56/22.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl115])).
% 131.56/22.77 thf(zip_derived_cl149, plain,
% 131.56/22.77 (~ (((emptysetimpfalse) =>
% 131.56/22.77 (((notinemptyset) =>
% 131.56/22.77 (((exuE3e) =>
% 131.56/22.77 (((setext) =>
% 131.56/22.77 (((emptyI) =>
% 131.56/22.77 (((noeltsimpempty) =>
% 131.56/22.77 (((setbeta) =>
% 131.56/22.77 (((nonemptyE1) =>
% 131.56/22.77 (((nonemptyI) =>
% 131.56/22.77 (((nonemptyI1) =>
% 131.56/22.77 (((setadjoinIL) =>
% 131.56/22.77 (((in @ emptyset @
% 131.56/22.77 (setadjoin @ emptyset @ emptyset)) =>
% 131.56/22.77 (((setadjoinIR) =>
% 131.56/22.77 (((setadjoinE) =>
% 131.56/22.77 (((setadjoinOr) =>
% 131.56/22.77 (((setoftrueEq) =>
% 131.56/22.77 (((powersetI) =>
% 131.56/22.77 (((emptyinPowerset) =>
% 131.56/22.77 (((emptyInPowerset) =>
% 131.56/22.77 (((powersetE) =>
% 131.56/22.77 (((setunionI) =>
% 131.56/22.77 (((setunionE) =>
% 131.56/22.77 (((subPowSU) =>
% 131.56/22.77 (((exuE2) =>
% 131.56/22.77 (((nonemptyImpWitness) =>
% 131.56/22.77 (((uniqinunit) =>
% 131.56/22.77 (((notinsingleton) =>
% 131.56/22.77 (((eqinunit) =>
% 131.56/22.77 (((singletonsswitch) =>
% 131.56/22.77 (((upairsetE) =>
% 131.56/22.77 ((
% 131.56/22.77 (upairsetIL) =>
% 131.56/22.77 ((
% 131.56/22.77 (upairsetIR) =>
% 131.56/22.77 ((
% 131.56/22.77 (emptyE1) =>
% 131.56/22.77 ((
% 131.56/22.77 (vacuousDall) =>
% 131.56/22.77 ((
% 131.56/22.77 (quantDeMorgan1) =>
% 131.56/22.77 ((
% 131.56/22.77 (quantDeMorgan2) =>
% 131.56/22.77 ((
% 131.56/22.77 (quantDeMorgan3) =>
% 131.56/22.77 ((
% 131.56/22.77 (quantDeMorgan4) =>
% 131.56/22.77 ((
% 131.56/22.77 (prop2setI) =>
% 131.56/22.77 ((
% 131.56/22.77 (prop2set2propI) =>
% 131.56/22.77 ((
% 131.56/22.77 (notdexE) =>
% 131.56/22.77 ((
% 131.56/22.77 (notdallE) =>
% 131.56/22.77 ((
% 131.56/22.77 (exuI1) =>
% 131.56/22.77 ((
% 131.56/22.77 (exuI3) =>
% 131.56/22.77 ((
% 131.56/22.77 (exuI2) =>
% 131.56/22.77 ((
% 131.56/22.77 (inCongP) =>
% 131.56/22.77 ((
% 131.56/22.77 (in__Cong) =>
% 131.56/22.77 ((
% 131.56/22.77 (exuE3u) =>
% 131.56/22.77 ((
% 131.56/22.77 (exu__Cong) =>
% 131.56/22.77 ((
% 131.56/22.77 (setadjoin__Cong) =>
% 131.56/22.77 ((
% 131.56/22.77 (powerset__Cong) =>
% 131.56/22.77 ((
% 131.56/22.77 (setunion__Cong) =>
% 131.56/22.77 ((
% 131.56/22.77 (exuEu) =>
% 131.56/22.77 ((
% 131.56/22.77 (descr__Cong) =>
% 131.56/22.77 ((
% 131.56/22.77 (dsetconstr__Cong) =>
% 131.56/22.77 ((
% 131.56/22.77 (subsetI1) =>
% 131.56/22.77 ((
% 131.56/22.77 (eqimpsubset2) =>
% 131.56/22.77 ((
% 131.56/22.77 (eqimpsubset1) =>
% 131.56/22.77 ((
% 131.56/22.77 (subsetI2) =>
% 131.56/22.77 ((
% 131.56/22.77 (emptysetsubset) =>
% 131.56/22.77 ((
% 131.56/22.77 (subsetE) =>
% 131.56/22.77 ((
% 131.56/22.77 (subsetE2) =>
% 131.56/22.77 ((
% 131.56/22.77 (notsubsetI) =>
% 131.56/22.77 ((
% 131.56/22.77 (notequalI1) =>
% 131.56/22.77 ((
% 131.56/22.77 (notequalI2) =>
% 131.56/22.77 ((
% 131.56/22.77 (subsetRefl) =>
% 131.56/22.77 ((
% 131.56/22.77 (subsetTrans) =>
% 131.56/22.77 ((
% 131.56/22.77 (setadjoinSub) =>
% 131.56/22.77 ((
% 131.56/22.77 (setadjoinSub2) =>
% 131.56/22.77 ((
% 131.56/22.77 (subset2powerset) =>
% 131.56/22.77 ((
% 131.56/22.77 (setextsub) =>
% 131.56/22.77 ((
% 131.56/22.77 (subsetemptysetimpeq) =>
% 131.56/22.77 ((
% 131.56/22.77 (powersetI1) =>
% 131.56/22.77 ((
% 131.56/22.77 (powersetE1) =>
% 131.56/22.77 ((
% 131.56/22.77 (inPowerset) =>
% 131.56/22.77 ((
% 131.56/22.77 (powersetsubset) =>
% 131.56/22.77 ((
% 131.56/22.77 (sepInPowerset) =>
% 131.56/22.77 ((
% 131.56/22.77 (sepSubset) =>
% 131.56/22.77 ((
% 131.56/22.77 (binunionIL) =>
% 131.56/22.77 ((
% 131.56/22.77 (upairset2IR) =>
% 131.56/22.77 ((
% 131.56/22.77 (binunionIR) =>
% 131.56/22.77 ((
% 131.56/22.77 (binunionEcases) =>
% 131.56/22.77 ((
% 131.56/22.77 (binunionE) =>
% 131.56/22.77 ((
% 131.56/22.77 (binunionLsub) =>
% 131.56/22.77 ((
% 131.56/22.77 (binunionRsub) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectI) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectSubset5) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectEL) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectLsub) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectSubset2) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectSubset3) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectER) =>
% 131.56/22.77 ((
% 131.56/22.77 (disjointsetsI1) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectRsub) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectSubset4) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectSubset1) =>
% 131.56/22.77 ((
% 131.56/22.77 (bs114d) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusI) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusEL) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusER) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusSubset2) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusERneg) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusELneg) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusILneg) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusIRneg) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusLsub) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusSubset1) =>
% 131.56/22.77 ((
% 131.56/22.77 (symdiffE) =>
% 131.56/22.77 ((
% 131.56/22.77 (symdiffI1) =>
% 131.56/22.77 ((
% 131.56/22.77 (symdiffI2) =>
% 131.56/22.77 ((
% 131.56/22.77 (symdiffIneg1) =>
% 131.56/22.77 ((
% 131.56/22.77 (symdiffIneg2) =>
% 131.56/22.77 ((
% 131.56/22.77 (secondinupair) =>
% 131.56/22.77 ((
% 131.56/22.77 (setukpairIL) =>
% 131.56/22.77 ((
% 131.56/22.77 (setukpairIR) =>
% 131.56/22.77 ((
% 131.56/22.77 (kpairiskpair) =>
% 131.56/22.77 ((
% 131.56/22.77 (kpairp) =>
% 131.56/22.77 ((
% 131.56/22.77 (singletonsubset) =>
% 131.56/22.77 ((
% 131.56/22.77 (singletoninpowerset) =>
% 131.56/22.77 ((
% 131.56/22.77 (singletoninpowunion) =>
% 131.56/22.77 ((
% 131.56/22.77 (upairset2E) =>
% 131.56/22.77 ((
% 131.56/22.77 (upairsubunion) =>
% 131.56/22.77 ((
% 131.56/22.77 (upairinpowunion) =>
% 131.56/22.77 ((
% 131.56/22.77 (ubforcartprodlem1) =>
% 131.56/22.77 ((
% 131.56/22.77 (ubforcartprodlem2) =>
% 131.56/22.77 ((
% 131.56/22.77 (ubforcartprodlem3) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodpairin) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodmempair1) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodmempair) =>
% 131.56/22.77 ((
% 131.56/22.77 (setunionE2) =>
% 131.56/22.77 ((
% 131.56/22.77 (setunionsingleton1) =>
% 131.56/22.77 ((
% 131.56/22.77 (setunionsingleton2) =>
% 131.56/22.77 ((
% 131.56/22.77 (setunionsingleton) =>
% 131.56/22.77 ((
% 131.56/22.77 (singletonprop) =>
% 131.56/22.77 ((
% 131.56/22.77 (ex1E1) =>
% 131.56/22.77 ((
% 131.56/22.77 (ex1I) =>
% 131.56/22.77 ((
% 131.56/22.77 (ex1I2) =>
% 131.56/22.77 ((
% 131.56/22.77 (singletonsuniq) =>
% 131.56/22.77 ((
% 131.56/22.77 (setukpairinjL1) =>
% 131.56/22.77 ((
% 131.56/22.77 (kfstsingleton) =>
% 131.56/22.77 ((
% 131.56/22.77 (theprop) =>
% 131.56/22.77 ((
% 131.56/22.77 (kfstpairEq) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodfstin) =>
% 131.56/22.77 ((
% 131.56/22.77 (setukpairinjL2) =>
% 131.56/22.77 ((
% 131.56/22.77 (setukpairinjL) =>
% 131.56/22.77 ((
% 131.56/22.77 (setukpairinjR11) =>
% 131.56/22.77 ((
% 131.56/22.77 (setukpairinjR12) =>
% 131.56/22.77 ((
% 131.56/22.77 (setukpairinjR1) =>
% 131.56/22.77 ((
% 131.56/22.77 (upairequniteq) =>
% 131.56/22.77 ((
% 131.56/22.77 (setukpairinjR2) =>
% 131.56/22.77 ((
% 131.56/22.77 (setukpairinjR) =>
% 131.56/22.77 ((
% 131.56/22.77 (ksndsingleton) =>
% 131.56/22.77 ((
% 131.56/22.77 (ksndpairEq) =>
% 131.56/22.77 ((
% 131.56/22.77 (kpairsurjEq) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodsndin) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodpairmemEL) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodpairmemER) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodmempaircEq) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodfstpairEq) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodsndpairEq) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodpairsurjEq) =>
% 131.56/22.77 ((
% 131.56/22.77 (dpsetconstrI) =>
% 131.56/22.77 ((
% 131.56/22.77 (dpsetconstrSub) =>
% 131.56/22.77 ((
% 131.56/22.77 (setOfPairsIsBReln) =>
% 131.56/22.77 ((
% 131.56/22.77 (dpsetconstrERa) =>
% 131.56/22.77 ((
% 131.56/22.77 (dpsetconstrEL1) =>
% 131.56/22.77 ((
% 131.56/22.77 (dpsetconstrEL2) =>
% 131.56/22.77 ((
% 131.56/22.77 (dpsetconstrER) =>
% 131.56/22.77 ((
% 131.56/22.77 (funcImageSingleton) =>
% 131.56/22.77 ((
% 131.56/22.77 (apProp) =>
% 131.56/22.77 ((
% 131.56/22.77 (app) =>
% 131.56/22.77 ((
% 131.56/22.77 (infuncsetfunc) =>
% 131.56/22.77 ((
% 131.56/22.77 (ap2p) =>
% 131.56/22.77 ((
% 131.56/22.77 (funcinfuncset) =>
% 131.56/22.77 ((
% 131.56/22.77 (lamProp) =>
% 131.56/22.77 ((
% 131.56/22.77 (lamp) =>
% 131.56/22.77 ((
% 131.56/22.77 (lam2p) =>
% 131.56/22.77 ((
% 131.56/22.77 (brelnall1) =>
% 131.56/22.77 ((
% 131.56/22.77 (brelnall2) =>
% 131.56/22.77 ((
% 131.56/22.77 (ex1E2) =>
% 131.56/22.77 ((
% 131.56/22.77 (funcGraphProp1) =>
% 131.56/22.77 ((
% 131.56/22.77 (funcGraphProp3) =>
% 131.56/22.77 ((
% 131.56/22.77 (funcGraphProp2) =>
% 131.56/22.77 ((
% 131.56/22.77 (funcextLem) =>
% 131.56/22.77 ((
% 131.56/22.77 (funcGraphProp4) =>
% 131.56/22.77 ((
% 131.56/22.77 (subbreln) =>
% 131.56/22.77 ((
% 131.56/22.77 (eqbreln) =>
% 131.56/22.77 ((
% 131.56/22.77 (funcext) =>
% 131.56/22.77 ((
% 131.56/22.77 (funcext2) =>
% 131.56/22.77 ((
% 131.56/22.77 (ap2apEq1) =>
% 131.56/22.77 ((
% 131.56/22.77 (ap2apEq2) =>
% 131.56/22.77 ((
% 131.56/22.77 (beta1) =>
% 131.56/22.77 ((
% 131.56/22.77 (eta1) =>
% 131.56/22.77 ((
% 131.56/22.77 (lam2lamEq) =>
% 131.56/22.77 ((
% 131.56/22.77 (beta2) =>
% 131.56/22.77 ((
% 131.56/22.77 (eta2) =>
% 131.56/22.77 ((
% 131.56/22.77 (iffalseProp1) =>
% 131.56/22.77 ((
% 131.56/22.77 (iffalseProp2) =>
% 131.56/22.77 ((
% 131.56/22.77 (iftrueProp1) =>
% 131.56/22.77 ((
% 131.56/22.77 (iftrueProp2) =>
% 131.56/22.77 ((
% 131.56/22.77 (ifSingleton) =>
% 131.56/22.77 ((
% 131.56/22.77 (ifp) =>
% 131.56/22.77 ((
% 131.56/22.77 (theeq) =>
% 131.56/22.77 ((
% 131.56/22.77 (iftrue) =>
% 131.56/22.77 ((
% 131.56/22.77 (iffalse) =>
% 131.56/22.77 ((
% 131.56/22.77 (iftrueorfalse) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectT_lem) =>
% 131.56/22.77 ((
% 131.56/22.77 (binunionT_lem) =>
% 131.56/22.77 ((
% 131.56/22.77 (powersetT_lem) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusT_lem) =>
% 131.56/22.77 ((
% 131.56/22.77 (complementT_lem) =>
% 131.56/22.77 ((
% 131.56/22.77 (setextT) =>
% 131.56/22.77 ((
% 131.56/22.77 (subsetTI) =>
% 131.56/22.77 ((
% 131.56/22.77 (powersetTI1) =>
% 131.56/22.77 ((
% 131.56/22.77 (powersetTE1) =>
% 131.56/22.77 ((
% 131.56/22.77 (complementTI1) =>
% 131.56/22.77 ((
% 131.56/22.77 (complementTE1) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectTELcontra) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectTERcontra) =>
% 131.56/22.77 ((
% 131.56/22.77 (contrasubsetT) =>
% 131.56/22.77 ((
% 131.56/22.77 (contrasubsetT1) =>
% 131.56/22.77 ((
% 131.56/22.77 (contrasubsetT2) =>
% 131.56/22.77 ((
% 131.56/22.77 (contrasubsetT3) =>
% 131.56/22.77 ((
% 131.56/22.77 (doubleComplementI1) =>
% 131.56/22.77 ((
% 131.56/22.77 (doubleComplementE1) =>
% 131.56/22.77 ((
% 131.56/22.77 (doubleComplementSub1) =>
% 131.56/22.77 ((
% 131.56/22.77 (doubleComplementSub2) =>
% 131.56/22.77 ((
% 131.56/22.77 (doubleComplementEq) =>
% 131.56/22.77 ((
% 131.56/22.77 (complementTnotintersectT) =>
% 131.56/22.77 ((
% 131.56/22.77 (complementImpComplementIntersect) =>
% 131.56/22.77 ((
% 131.56/22.77 (complementSubsetComplementIntersect) =>
% 131.56/22.77 ((
% 131.56/22.77 (complementInPowersetComplementIntersect) =>
% 131.56/22.77 ((
% 131.56/22.77 (contraSubsetComplement) =>
% 131.56/22.77 ((
% 131.56/22.77 (complementTcontraSubset) =>
% 131.56/22.77 ((
% 131.56/22.77 (binunionTILcontra) =>
% 131.56/22.77 ((
% 131.56/22.77 (binunionTIRcontra) =>
% 131.56/22.77 ((
% 131.56/22.77 (inIntersectImpInUnion) =>
% 131.56/22.77 ((
% 131.56/22.77 (inIntersectImpInUnion2) =>
% 131.56/22.77 ((
% 131.56/22.77 (inIntersectImpInIntersectUnions) =>
% 131.56/22.77 ((
% 131.56/22.77 (intersectInPowersetIntersectUnions) =>
% 131.56/22.77 ((
% 131.56/22.77 (inComplementUnionImpNotIn1) =>
% 131.56/22.77 ((
% 131.56/22.77 (inComplementUnionImpInComplement1) =>
% 131.56/22.77 ((
% 131.56/22.77 (binunionTE) =>
% 131.56/22.77 ((
% 131.56/22.77 (binunionTEcontra) =>
% 131.56/22.77 ((
% 131.56/22.77 (demorgan2a1) =>
% 131.56/22.77 ((
% 131.56/22.77 (complementUnionInPowersetComplement) =>
% 131.56/22.77 ((
% 131.56/22.77 (demorgan2a2) =>
% 131.56/22.77 ((
% 131.56/22.77 (demorgan1a) =>
% 131.56/22.77 ((
% 131.56/22.77 (demorgan1b) =>
% 131.56/22.77 ((
% 131.56/22.77 (demorgan1) =>
% 131.56/22.77 ((
% 131.56/22.77 (demorgan2a) =>
% 131.56/22.77 ((
% 131.56/22.77 (demorgan2b2) =>
% 131.56/22.77 ((
% 131.56/22.77 (demorgan2b) =>
% 131.56/22.77 ((
% 131.56/22.77 (demorgan2) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz13rule0) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz13rule1) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz13rule2) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz13rule3) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz13rule4) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz1_1) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz1_2) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz1_3) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz1_4) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz1_5) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1all2) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1SetBreln1) =>
% 131.56/22.77 ((
% 131.56/22.77 (choice2fnsingleton) =>
% 131.56/22.77 ((
% 131.56/22.77 (setOfPairsIsBReln1) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1all1) =>
% 131.56/22.77 ((
% 131.56/22.77 (subbreln1) =>
% 131.56/22.77 ((
% 131.56/22.77 (eqbreln1) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1invprop) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1invI) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1invE) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1compprop) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1compI) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1compE) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1compEex) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1unionprop) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1unionIL) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1unionIR) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1unionI) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1unionE) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1unionEcases) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1unionCommutes) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz2Ex) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz2W) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz2A) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz2B) =>
% 131.56/22.77 ((
% 131.56/22.77 (image1Ex) =>
% 131.56/22.77 ((
% 131.56/22.77 (image1Ex1) =>
% 131.56/22.77 ((
% 131.56/22.77 (image1Equiv) =>
% 131.56/22.77 ((
% 131.56/22.77 (image1E) =>
% 131.56/22.77 ((
% 131.56/22.77 (image1I) =>
% 131.56/22.77 ((
% 131.56/22.77 (injFuncInInjFuncSet) =>
% 131.56/22.77 ((
% 131.56/22.77 (injFuncSetFuncIn) =>
% 131.56/22.77 ((
% 131.56/22.77 (injFuncSetFuncInj) =>
% 131.56/22.77 ((
% 131.56/22.77 (surjFuncSetFuncIn) =>
% 131.56/22.77 ((
% 131.56/22.77 (surjFuncSetFuncSurj) =>
% 131.56/22.77 ((
% 131.56/22.77 (leftInvIsSurj) =>
% 131.56/22.77 ((
% 131.56/22.77 (surjCantorThm) =>
% 131.56/22.77 ((
% 131.56/22.77 (foundation2) =>
% 131.56/22.77 ((
% 131.56/22.77 (notinself) =>
% 131.56/22.77 ((
% 131.56/22.77 (notinself2) =>
% 131.56/22.77 ((
% 131.56/22.77 (omegaSp) =>
% 131.56/22.77 ((
% 131.56/22.77 (omegaSclos) =>
% 131.56/22.77 ((
% 131.56/22.77 (peano0notS) =>
% 131.56/22.77 ((
% 131.56/22.77 (peanoSinj) =>
% 131.56/22.77 ((
% 131.56/22.77 (transitivesetOp1) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintTransitive) =>
% 131.56/22.77 ((
% 131.56/22.77 (transitivesetOp2) =>
% 131.56/22.77 ((
% 131.56/22.77 (setunionTransitive) =>
% 131.56/22.77 ((
% 131.56/22.77 (ordinalMinLem1) =>
% 131.56/22.77 ((
% 131.56/22.77 (ordinalTransSet) =>
% 131.56/22.77 ((
% 131.56/22.77 (ordinalTransSet1) =>
% 131.56/22.77 ((
% 131.56/22.77 (setunionOrdinalLem1) =>
% 131.56/22.77 (ordinal @
% 131.56/22.77 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 131.56/22.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl133])).
% 131.56/22.77 thf(zip_derived_cl164, plain,
% 131.56/22.77 (~ (((notinemptyset) =>
% 131.56/22.77 (((exuE3e) =>
% 131.56/22.77 (((setext) =>
% 131.56/22.77 (((emptyI) =>
% 131.56/22.77 (((noeltsimpempty) =>
% 131.56/22.77 (((setbeta) =>
% 131.56/22.77 (((nonemptyE1) =>
% 131.56/22.77 (((nonemptyI) =>
% 131.56/22.77 (((nonemptyI1) =>
% 131.56/22.77 (((setadjoinIL) =>
% 131.56/22.77 (((in @ emptyset @
% 131.56/22.77 (setadjoin @ emptyset @ emptyset)) =>
% 131.56/22.77 (((setadjoinIR) =>
% 131.56/22.77 (((setadjoinE) =>
% 131.56/22.77 (((setadjoinOr) =>
% 131.56/22.77 (((setoftrueEq) =>
% 131.56/22.77 (((powersetI) =>
% 131.56/22.77 (((emptyinPowerset) =>
% 131.56/22.77 (((emptyInPowerset) =>
% 131.56/22.77 (((powersetE) =>
% 131.56/22.77 (((setunionI) =>
% 131.56/22.77 (((setunionE) =>
% 131.56/22.77 (((subPowSU) =>
% 131.56/22.77 (((exuE2) =>
% 131.56/22.77 (((nonemptyImpWitness) =>
% 131.56/22.77 (((uniqinunit) =>
% 131.56/22.77 (((notinsingleton) =>
% 131.56/22.77 (((eqinunit) =>
% 131.56/22.77 (((singletonsswitch) =>
% 131.56/22.77 (((upairsetE) =>
% 131.56/22.77 (((upairsetIL) =>
% 131.56/22.77 ((
% 131.56/22.77 (upairsetIR) =>
% 131.56/22.77 ((
% 131.56/22.77 (emptyE1) =>
% 131.56/22.77 ((
% 131.56/22.77 (vacuousDall) =>
% 131.56/22.77 ((
% 131.56/22.77 (quantDeMorgan1) =>
% 131.56/22.77 ((
% 131.56/22.77 (quantDeMorgan2) =>
% 131.56/22.77 ((
% 131.56/22.77 (quantDeMorgan3) =>
% 131.56/22.77 ((
% 131.56/22.77 (quantDeMorgan4) =>
% 131.56/22.77 ((
% 131.56/22.77 (prop2setI) =>
% 131.56/22.77 ((
% 131.56/22.77 (prop2set2propI) =>
% 131.56/22.77 ((
% 131.56/22.77 (notdexE) =>
% 131.56/22.77 ((
% 131.56/22.77 (notdallE) =>
% 131.56/22.77 ((
% 131.56/22.77 (exuI1) =>
% 131.56/22.77 ((
% 131.56/22.77 (exuI3) =>
% 131.56/22.77 ((
% 131.56/22.77 (exuI2) =>
% 131.56/22.77 ((
% 131.56/22.77 (inCongP) =>
% 131.56/22.77 ((
% 131.56/22.77 (in__Cong) =>
% 131.56/22.77 ((
% 131.56/22.77 (exuE3u) =>
% 131.56/22.77 ((
% 131.56/22.77 (exu__Cong) =>
% 131.56/22.77 ((
% 131.56/22.77 (setadjoin__Cong) =>
% 131.56/22.77 ((
% 131.56/22.77 (powerset__Cong) =>
% 131.56/22.77 ((
% 131.56/22.77 (setunion__Cong) =>
% 131.56/22.77 ((
% 131.56/22.77 (exuEu) =>
% 131.56/22.77 ((
% 131.56/22.77 (descr__Cong) =>
% 131.56/22.77 ((
% 131.56/22.77 (dsetconstr__Cong) =>
% 131.56/22.77 ((
% 131.56/22.77 (subsetI1) =>
% 131.56/22.77 ((
% 131.56/22.77 (eqimpsubset2) =>
% 131.56/22.77 ((
% 131.56/22.77 (eqimpsubset1) =>
% 131.56/22.77 ((
% 131.56/22.77 (subsetI2) =>
% 131.56/22.77 ((
% 131.56/22.77 (emptysetsubset) =>
% 131.56/22.77 ((
% 131.56/22.77 (subsetE) =>
% 131.56/22.77 ((
% 131.56/22.77 (subsetE2) =>
% 131.56/22.77 ((
% 131.56/22.77 (notsubsetI) =>
% 131.56/22.77 ((
% 131.56/22.77 (notequalI1) =>
% 131.56/22.77 ((
% 131.56/22.77 (notequalI2) =>
% 131.56/22.77 ((
% 131.56/22.77 (subsetRefl) =>
% 131.56/22.77 ((
% 131.56/22.77 (subsetTrans) =>
% 131.56/22.77 ((
% 131.56/22.77 (setadjoinSub) =>
% 131.56/22.77 ((
% 131.56/22.77 (setadjoinSub2) =>
% 131.56/22.77 ((
% 131.56/22.77 (subset2powerset) =>
% 131.56/22.77 ((
% 131.56/22.77 (setextsub) =>
% 131.56/22.77 ((
% 131.56/22.77 (subsetemptysetimpeq) =>
% 131.56/22.77 ((
% 131.56/22.77 (powersetI1) =>
% 131.56/22.77 ((
% 131.56/22.77 (powersetE1) =>
% 131.56/22.77 ((
% 131.56/22.77 (inPowerset) =>
% 131.56/22.77 ((
% 131.56/22.77 (powersetsubset) =>
% 131.56/22.77 ((
% 131.56/22.77 (sepInPowerset) =>
% 131.56/22.77 ((
% 131.56/22.77 (sepSubset) =>
% 131.56/22.77 ((
% 131.56/22.77 (binunionIL) =>
% 131.56/22.77 ((
% 131.56/22.77 (upairset2IR) =>
% 131.56/22.77 ((
% 131.56/22.77 (binunionIR) =>
% 131.56/22.77 ((
% 131.56/22.77 (binunionEcases) =>
% 131.56/22.77 ((
% 131.56/22.77 (binunionE) =>
% 131.56/22.77 ((
% 131.56/22.77 (binunionLsub) =>
% 131.56/22.77 ((
% 131.56/22.77 (binunionRsub) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectI) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectSubset5) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectEL) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectLsub) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectSubset2) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectSubset3) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectER) =>
% 131.56/22.77 ((
% 131.56/22.77 (disjointsetsI1) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectRsub) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectSubset4) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectSubset1) =>
% 131.56/22.77 ((
% 131.56/22.77 (bs114d) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusI) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusEL) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusER) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusSubset2) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusERneg) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusELneg) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusILneg) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusIRneg) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusLsub) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusSubset1) =>
% 131.56/22.77 ((
% 131.56/22.77 (symdiffE) =>
% 131.56/22.77 ((
% 131.56/22.77 (symdiffI1) =>
% 131.56/22.77 ((
% 131.56/22.77 (symdiffI2) =>
% 131.56/22.77 ((
% 131.56/22.77 (symdiffIneg1) =>
% 131.56/22.77 ((
% 131.56/22.77 (symdiffIneg2) =>
% 131.56/22.77 ((
% 131.56/22.77 (secondinupair) =>
% 131.56/22.77 ((
% 131.56/22.77 (setukpairIL) =>
% 131.56/22.77 ((
% 131.56/22.77 (setukpairIR) =>
% 131.56/22.77 ((
% 131.56/22.77 (kpairiskpair) =>
% 131.56/22.77 ((
% 131.56/22.77 (kpairp) =>
% 131.56/22.77 ((
% 131.56/22.77 (singletonsubset) =>
% 131.56/22.77 ((
% 131.56/22.77 (singletoninpowerset) =>
% 131.56/22.77 ((
% 131.56/22.77 (singletoninpowunion) =>
% 131.56/22.77 ((
% 131.56/22.77 (upairset2E) =>
% 131.56/22.77 ((
% 131.56/22.77 (upairsubunion) =>
% 131.56/22.77 ((
% 131.56/22.77 (upairinpowunion) =>
% 131.56/22.77 ((
% 131.56/22.77 (ubforcartprodlem1) =>
% 131.56/22.77 ((
% 131.56/22.77 (ubforcartprodlem2) =>
% 131.56/22.77 ((
% 131.56/22.77 (ubforcartprodlem3) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodpairin) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodmempair1) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodmempair) =>
% 131.56/22.77 ((
% 131.56/22.77 (setunionE2) =>
% 131.56/22.77 ((
% 131.56/22.77 (setunionsingleton1) =>
% 131.56/22.77 ((
% 131.56/22.77 (setunionsingleton2) =>
% 131.56/22.77 ((
% 131.56/22.77 (setunionsingleton) =>
% 131.56/22.77 ((
% 131.56/22.77 (singletonprop) =>
% 131.56/22.77 ((
% 131.56/22.77 (ex1E1) =>
% 131.56/22.77 ((
% 131.56/22.77 (ex1I) =>
% 131.56/22.77 ((
% 131.56/22.77 (ex1I2) =>
% 131.56/22.77 ((
% 131.56/22.77 (singletonsuniq) =>
% 131.56/22.77 ((
% 131.56/22.77 (setukpairinjL1) =>
% 131.56/22.77 ((
% 131.56/22.77 (kfstsingleton) =>
% 131.56/22.77 ((
% 131.56/22.77 (theprop) =>
% 131.56/22.77 ((
% 131.56/22.77 (kfstpairEq) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodfstin) =>
% 131.56/22.77 ((
% 131.56/22.77 (setukpairinjL2) =>
% 131.56/22.77 ((
% 131.56/22.77 (setukpairinjL) =>
% 131.56/22.77 ((
% 131.56/22.77 (setukpairinjR11) =>
% 131.56/22.77 ((
% 131.56/22.77 (setukpairinjR12) =>
% 131.56/22.77 ((
% 131.56/22.77 (setukpairinjR1) =>
% 131.56/22.77 ((
% 131.56/22.77 (upairequniteq) =>
% 131.56/22.77 ((
% 131.56/22.77 (setukpairinjR2) =>
% 131.56/22.77 ((
% 131.56/22.77 (setukpairinjR) =>
% 131.56/22.77 ((
% 131.56/22.77 (ksndsingleton) =>
% 131.56/22.77 ((
% 131.56/22.77 (ksndpairEq) =>
% 131.56/22.77 ((
% 131.56/22.77 (kpairsurjEq) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodsndin) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodpairmemEL) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodpairmemER) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodmempaircEq) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodfstpairEq) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodsndpairEq) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodpairsurjEq) =>
% 131.56/22.77 ((
% 131.56/22.77 (dpsetconstrI) =>
% 131.56/22.77 ((
% 131.56/22.77 (dpsetconstrSub) =>
% 131.56/22.77 ((
% 131.56/22.77 (setOfPairsIsBReln) =>
% 131.56/22.77 ((
% 131.56/22.77 (dpsetconstrERa) =>
% 131.56/22.77 ((
% 131.56/22.77 (dpsetconstrEL1) =>
% 131.56/22.77 ((
% 131.56/22.77 (dpsetconstrEL2) =>
% 131.56/22.77 ((
% 131.56/22.77 (dpsetconstrER) =>
% 131.56/22.77 ((
% 131.56/22.77 (funcImageSingleton) =>
% 131.56/22.77 ((
% 131.56/22.77 (apProp) =>
% 131.56/22.77 ((
% 131.56/22.77 (app) =>
% 131.56/22.77 ((
% 131.56/22.77 (infuncsetfunc) =>
% 131.56/22.77 ((
% 131.56/22.77 (ap2p) =>
% 131.56/22.77 ((
% 131.56/22.77 (funcinfuncset) =>
% 131.56/22.77 ((
% 131.56/22.77 (lamProp) =>
% 131.56/22.77 ((
% 131.56/22.77 (lamp) =>
% 131.56/22.77 ((
% 131.56/22.77 (lam2p) =>
% 131.56/22.77 ((
% 131.56/22.77 (brelnall1) =>
% 131.56/22.77 ((
% 131.56/22.77 (brelnall2) =>
% 131.56/22.77 ((
% 131.56/22.77 (ex1E2) =>
% 131.56/22.77 ((
% 131.56/22.77 (funcGraphProp1) =>
% 131.56/22.77 ((
% 131.56/22.77 (funcGraphProp3) =>
% 131.56/22.77 ((
% 131.56/22.77 (funcGraphProp2) =>
% 131.56/22.77 ((
% 131.56/22.77 (funcextLem) =>
% 131.56/22.77 ((
% 131.56/22.77 (funcGraphProp4) =>
% 131.56/22.77 ((
% 131.56/22.77 (subbreln) =>
% 131.56/22.77 ((
% 131.56/22.77 (eqbreln) =>
% 131.56/22.77 ((
% 131.56/22.77 (funcext) =>
% 131.56/22.77 ((
% 131.56/22.77 (funcext2) =>
% 131.56/22.77 ((
% 131.56/22.77 (ap2apEq1) =>
% 131.56/22.77 ((
% 131.56/22.77 (ap2apEq2) =>
% 131.56/22.77 ((
% 131.56/22.77 (beta1) =>
% 131.56/22.77 ((
% 131.56/22.77 (eta1) =>
% 131.56/22.77 ((
% 131.56/22.77 (lam2lamEq) =>
% 131.56/22.77 ((
% 131.56/22.77 (beta2) =>
% 131.56/22.77 ((
% 131.56/22.77 (eta2) =>
% 131.56/22.77 ((
% 131.56/22.77 (iffalseProp1) =>
% 131.56/22.77 ((
% 131.56/22.77 (iffalseProp2) =>
% 131.56/22.77 ((
% 131.56/22.77 (iftrueProp1) =>
% 131.56/22.77 ((
% 131.56/22.77 (iftrueProp2) =>
% 131.56/22.77 ((
% 131.56/22.77 (ifSingleton) =>
% 131.56/22.77 ((
% 131.56/22.77 (ifp) =>
% 131.56/22.77 ((
% 131.56/22.77 (theeq) =>
% 131.56/22.77 ((
% 131.56/22.77 (iftrue) =>
% 131.56/22.77 ((
% 131.56/22.77 (iffalse) =>
% 131.56/22.77 ((
% 131.56/22.77 (iftrueorfalse) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectT_lem) =>
% 131.56/22.77 ((
% 131.56/22.77 (binunionT_lem) =>
% 131.56/22.77 ((
% 131.56/22.77 (powersetT_lem) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusT_lem) =>
% 131.56/22.77 ((
% 131.56/22.77 (complementT_lem) =>
% 131.56/22.77 ((
% 131.56/22.77 (setextT) =>
% 131.56/22.77 ((
% 131.56/22.77 (subsetTI) =>
% 131.56/22.77 ((
% 131.56/22.77 (powersetTI1) =>
% 131.56/22.77 ((
% 131.56/22.77 (powersetTE1) =>
% 131.56/22.77 ((
% 131.56/22.77 (complementTI1) =>
% 131.56/22.77 ((
% 131.56/22.77 (complementTE1) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectTELcontra) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectTERcontra) =>
% 131.56/22.77 ((
% 131.56/22.77 (contrasubsetT) =>
% 131.56/22.77 ((
% 131.56/22.77 (contrasubsetT1) =>
% 131.56/22.77 ((
% 131.56/22.77 (contrasubsetT2) =>
% 131.56/22.77 ((
% 131.56/22.77 (contrasubsetT3) =>
% 131.56/22.77 ((
% 131.56/22.77 (doubleComplementI1) =>
% 131.56/22.77 ((
% 131.56/22.77 (doubleComplementE1) =>
% 131.56/22.77 ((
% 131.56/22.77 (doubleComplementSub1) =>
% 131.56/22.77 ((
% 131.56/22.77 (doubleComplementSub2) =>
% 131.56/22.77 ((
% 131.56/22.77 (doubleComplementEq) =>
% 131.56/22.77 ((
% 131.56/22.77 (complementTnotintersectT) =>
% 131.56/22.77 ((
% 131.56/22.77 (complementImpComplementIntersect) =>
% 131.56/22.77 ((
% 131.56/22.77 (complementSubsetComplementIntersect) =>
% 131.56/22.77 ((
% 131.56/22.77 (complementInPowersetComplementIntersect) =>
% 131.56/22.77 ((
% 131.56/22.77 (contraSubsetComplement) =>
% 131.56/22.77 ((
% 131.56/22.77 (complementTcontraSubset) =>
% 131.56/22.77 ((
% 131.56/22.77 (binunionTILcontra) =>
% 131.56/22.77 ((
% 131.56/22.77 (binunionTIRcontra) =>
% 131.56/22.77 ((
% 131.56/22.77 (inIntersectImpInUnion) =>
% 131.56/22.77 ((
% 131.56/22.77 (inIntersectImpInUnion2) =>
% 131.56/22.77 ((
% 131.56/22.77 (inIntersectImpInIntersectUnions) =>
% 131.56/22.77 ((
% 131.56/22.77 (intersectInPowersetIntersectUnions) =>
% 131.56/22.77 ((
% 131.56/22.77 (inComplementUnionImpNotIn1) =>
% 131.56/22.77 ((
% 131.56/22.77 (inComplementUnionImpInComplement1) =>
% 131.56/22.77 ((
% 131.56/22.77 (binunionTE) =>
% 131.56/22.77 ((
% 131.56/22.77 (binunionTEcontra) =>
% 131.56/22.77 ((
% 131.56/22.77 (demorgan2a1) =>
% 131.56/22.77 ((
% 131.56/22.77 (complementUnionInPowersetComplement) =>
% 131.56/22.77 ((
% 131.56/22.77 (demorgan2a2) =>
% 131.56/22.77 ((
% 131.56/22.77 (demorgan1a) =>
% 131.56/22.77 ((
% 131.56/22.77 (demorgan1b) =>
% 131.56/22.77 ((
% 131.56/22.77 (demorgan1) =>
% 131.56/22.77 ((
% 131.56/22.77 (demorgan2a) =>
% 131.56/22.77 ((
% 131.56/22.77 (demorgan2b2) =>
% 131.56/22.77 ((
% 131.56/22.77 (demorgan2b) =>
% 131.56/22.77 ((
% 131.56/22.77 (demorgan2) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz13rule0) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz13rule1) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz13rule2) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz13rule3) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz13rule4) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz1_1) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz1_2) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz1_3) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz1_4) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz1_5) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1all2) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1SetBreln1) =>
% 131.56/22.77 ((
% 131.56/22.77 (choice2fnsingleton) =>
% 131.56/22.77 ((
% 131.56/22.77 (setOfPairsIsBReln1) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1all1) =>
% 131.56/22.77 ((
% 131.56/22.77 (subbreln1) =>
% 131.56/22.77 ((
% 131.56/22.77 (eqbreln1) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1invprop) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1invI) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1invE) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1compprop) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1compI) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1compE) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1compEex) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1unionprop) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1unionIL) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1unionIR) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1unionI) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1unionE) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1unionEcases) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1unionCommutes) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz2Ex) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz2W) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz2A) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz2B) =>
% 131.56/22.77 ((
% 131.56/22.77 (image1Ex) =>
% 131.56/22.77 ((
% 131.56/22.77 (image1Ex1) =>
% 131.56/22.77 ((
% 131.56/22.77 (image1Equiv) =>
% 131.56/22.77 ((
% 131.56/22.77 (image1E) =>
% 131.56/22.77 ((
% 131.56/22.77 (image1I) =>
% 131.56/22.77 ((
% 131.56/22.77 (injFuncInInjFuncSet) =>
% 131.56/22.77 ((
% 131.56/22.77 (injFuncSetFuncIn) =>
% 131.56/22.77 ((
% 131.56/22.77 (injFuncSetFuncInj) =>
% 131.56/22.77 ((
% 131.56/22.77 (surjFuncSetFuncIn) =>
% 131.56/22.77 ((
% 131.56/22.77 (surjFuncSetFuncSurj) =>
% 131.56/22.77 ((
% 131.56/22.77 (leftInvIsSurj) =>
% 131.56/22.77 ((
% 131.56/22.77 (surjCantorThm) =>
% 131.56/22.77 ((
% 131.56/22.77 (foundation2) =>
% 131.56/22.77 ((
% 131.56/22.77 (notinself) =>
% 131.56/22.77 ((
% 131.56/22.77 (notinself2) =>
% 131.56/22.77 ((
% 131.56/22.77 (omegaSp) =>
% 131.56/22.77 ((
% 131.56/22.77 (omegaSclos) =>
% 131.56/22.77 ((
% 131.56/22.77 (peano0notS) =>
% 131.56/22.77 ((
% 131.56/22.77 (peanoSinj) =>
% 131.56/22.77 ((
% 131.56/22.77 (transitivesetOp1) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintTransitive) =>
% 131.56/22.77 ((
% 131.56/22.77 (transitivesetOp2) =>
% 131.56/22.77 ((
% 131.56/22.77 (setunionTransitive) =>
% 131.56/22.77 ((
% 131.56/22.77 (ordinalMinLem1) =>
% 131.56/22.77 ((
% 131.56/22.77 (ordinalTransSet) =>
% 131.56/22.77 ((
% 131.56/22.77 (ordinalTransSet1) =>
% 131.56/22.77 ((
% 131.56/22.77 (setunionOrdinalLem1) =>
% 131.56/22.77 (ordinal @
% 131.56/22.77 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 131.56/22.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl149])).
% 131.56/22.77 thf(zip_derived_cl177, plain,
% 131.56/22.77 (~ (((exuE3e) =>
% 131.56/22.77 (((setext) =>
% 131.56/22.77 (((emptyI) =>
% 131.56/22.77 (((noeltsimpempty) =>
% 131.56/22.77 (((setbeta) =>
% 131.56/22.77 (((nonemptyE1) =>
% 131.56/22.77 (((nonemptyI) =>
% 131.56/22.77 (((nonemptyI1) =>
% 131.56/22.77 (((setadjoinIL) =>
% 131.56/22.77 (((in @ emptyset @
% 131.56/22.77 (setadjoin @ emptyset @ emptyset)) =>
% 131.56/22.77 (((setadjoinIR) =>
% 131.56/22.77 (((setadjoinE) =>
% 131.56/22.77 (((setadjoinOr) =>
% 131.56/22.77 (((setoftrueEq) =>
% 131.56/22.77 (((powersetI) =>
% 131.56/22.77 (((emptyinPowerset) =>
% 131.56/22.77 (((emptyInPowerset) =>
% 131.56/22.77 (((powersetE) =>
% 131.56/22.77 (((setunionI) =>
% 131.56/22.77 (((setunionE) =>
% 131.56/22.77 (((subPowSU) =>
% 131.56/22.77 (((exuE2) =>
% 131.56/22.77 (((nonemptyImpWitness) =>
% 131.56/22.77 (((uniqinunit) =>
% 131.56/22.77 (((notinsingleton) =>
% 131.56/22.77 (((eqinunit) =>
% 131.56/22.77 (((singletonsswitch) =>
% 131.56/22.77 (((upairsetE) =>
% 131.56/22.77 (((upairsetIL) =>
% 131.56/22.77 (((upairsetIR) =>
% 131.56/22.77 ((
% 131.56/22.77 (emptyE1) =>
% 131.56/22.77 ((
% 131.56/22.77 (vacuousDall) =>
% 131.56/22.77 ((
% 131.56/22.77 (quantDeMorgan1) =>
% 131.56/22.77 ((
% 131.56/22.77 (quantDeMorgan2) =>
% 131.56/22.77 ((
% 131.56/22.77 (quantDeMorgan3) =>
% 131.56/22.77 ((
% 131.56/22.77 (quantDeMorgan4) =>
% 131.56/22.77 ((
% 131.56/22.77 (prop2setI) =>
% 131.56/22.77 ((
% 131.56/22.77 (prop2set2propI) =>
% 131.56/22.77 ((
% 131.56/22.77 (notdexE) =>
% 131.56/22.77 ((
% 131.56/22.77 (notdallE) =>
% 131.56/22.77 ((
% 131.56/22.77 (exuI1) =>
% 131.56/22.77 ((
% 131.56/22.77 (exuI3) =>
% 131.56/22.77 ((
% 131.56/22.77 (exuI2) =>
% 131.56/22.77 ((
% 131.56/22.77 (inCongP) =>
% 131.56/22.77 ((
% 131.56/22.77 (in__Cong) =>
% 131.56/22.77 ((
% 131.56/22.77 (exuE3u) =>
% 131.56/22.77 ((
% 131.56/22.77 (exu__Cong) =>
% 131.56/22.77 ((
% 131.56/22.77 (setadjoin__Cong) =>
% 131.56/22.77 ((
% 131.56/22.77 (powerset__Cong) =>
% 131.56/22.77 ((
% 131.56/22.77 (setunion__Cong) =>
% 131.56/22.77 ((
% 131.56/22.77 (exuEu) =>
% 131.56/22.77 ((
% 131.56/22.77 (descr__Cong) =>
% 131.56/22.77 ((
% 131.56/22.77 (dsetconstr__Cong) =>
% 131.56/22.77 ((
% 131.56/22.77 (subsetI1) =>
% 131.56/22.77 ((
% 131.56/22.77 (eqimpsubset2) =>
% 131.56/22.77 ((
% 131.56/22.77 (eqimpsubset1) =>
% 131.56/22.77 ((
% 131.56/22.77 (subsetI2) =>
% 131.56/22.77 ((
% 131.56/22.77 (emptysetsubset) =>
% 131.56/22.77 ((
% 131.56/22.77 (subsetE) =>
% 131.56/22.77 ((
% 131.56/22.77 (subsetE2) =>
% 131.56/22.77 ((
% 131.56/22.77 (notsubsetI) =>
% 131.56/22.77 ((
% 131.56/22.77 (notequalI1) =>
% 131.56/22.77 ((
% 131.56/22.77 (notequalI2) =>
% 131.56/22.77 ((
% 131.56/22.77 (subsetRefl) =>
% 131.56/22.77 ((
% 131.56/22.77 (subsetTrans) =>
% 131.56/22.77 ((
% 131.56/22.77 (setadjoinSub) =>
% 131.56/22.77 ((
% 131.56/22.77 (setadjoinSub2) =>
% 131.56/22.77 ((
% 131.56/22.77 (subset2powerset) =>
% 131.56/22.77 ((
% 131.56/22.77 (setextsub) =>
% 131.56/22.77 ((
% 131.56/22.77 (subsetemptysetimpeq) =>
% 131.56/22.77 ((
% 131.56/22.77 (powersetI1) =>
% 131.56/22.77 ((
% 131.56/22.77 (powersetE1) =>
% 131.56/22.77 ((
% 131.56/22.77 (inPowerset) =>
% 131.56/22.77 ((
% 131.56/22.77 (powersetsubset) =>
% 131.56/22.77 ((
% 131.56/22.77 (sepInPowerset) =>
% 131.56/22.77 ((
% 131.56/22.77 (sepSubset) =>
% 131.56/22.77 ((
% 131.56/22.77 (binunionIL) =>
% 131.56/22.77 ((
% 131.56/22.77 (upairset2IR) =>
% 131.56/22.77 ((
% 131.56/22.77 (binunionIR) =>
% 131.56/22.77 ((
% 131.56/22.77 (binunionEcases) =>
% 131.56/22.77 ((
% 131.56/22.77 (binunionE) =>
% 131.56/22.77 ((
% 131.56/22.77 (binunionLsub) =>
% 131.56/22.77 ((
% 131.56/22.77 (binunionRsub) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectI) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectSubset5) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectEL) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectLsub) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectSubset2) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectSubset3) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectER) =>
% 131.56/22.77 ((
% 131.56/22.77 (disjointsetsI1) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectRsub) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectSubset4) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectSubset1) =>
% 131.56/22.77 ((
% 131.56/22.77 (bs114d) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusI) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusEL) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusER) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusSubset2) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusERneg) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusELneg) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusILneg) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusIRneg) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusLsub) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusSubset1) =>
% 131.56/22.77 ((
% 131.56/22.77 (symdiffE) =>
% 131.56/22.77 ((
% 131.56/22.77 (symdiffI1) =>
% 131.56/22.77 ((
% 131.56/22.77 (symdiffI2) =>
% 131.56/22.77 ((
% 131.56/22.77 (symdiffIneg1) =>
% 131.56/22.77 ((
% 131.56/22.77 (symdiffIneg2) =>
% 131.56/22.77 ((
% 131.56/22.77 (secondinupair) =>
% 131.56/22.77 ((
% 131.56/22.77 (setukpairIL) =>
% 131.56/22.77 ((
% 131.56/22.77 (setukpairIR) =>
% 131.56/22.77 ((
% 131.56/22.77 (kpairiskpair) =>
% 131.56/22.77 ((
% 131.56/22.77 (kpairp) =>
% 131.56/22.77 ((
% 131.56/22.77 (singletonsubset) =>
% 131.56/22.77 ((
% 131.56/22.77 (singletoninpowerset) =>
% 131.56/22.77 ((
% 131.56/22.77 (singletoninpowunion) =>
% 131.56/22.77 ((
% 131.56/22.77 (upairset2E) =>
% 131.56/22.77 ((
% 131.56/22.77 (upairsubunion) =>
% 131.56/22.77 ((
% 131.56/22.77 (upairinpowunion) =>
% 131.56/22.77 ((
% 131.56/22.77 (ubforcartprodlem1) =>
% 131.56/22.77 ((
% 131.56/22.77 (ubforcartprodlem2) =>
% 131.56/22.77 ((
% 131.56/22.77 (ubforcartprodlem3) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodpairin) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodmempair1) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodmempair) =>
% 131.56/22.77 ((
% 131.56/22.77 (setunionE2) =>
% 131.56/22.77 ((
% 131.56/22.77 (setunionsingleton1) =>
% 131.56/22.77 ((
% 131.56/22.77 (setunionsingleton2) =>
% 131.56/22.77 ((
% 131.56/22.77 (setunionsingleton) =>
% 131.56/22.77 ((
% 131.56/22.77 (singletonprop) =>
% 131.56/22.77 ((
% 131.56/22.77 (ex1E1) =>
% 131.56/22.77 ((
% 131.56/22.77 (ex1I) =>
% 131.56/22.77 ((
% 131.56/22.77 (ex1I2) =>
% 131.56/22.77 ((
% 131.56/22.77 (singletonsuniq) =>
% 131.56/22.77 ((
% 131.56/22.77 (setukpairinjL1) =>
% 131.56/22.77 ((
% 131.56/22.77 (kfstsingleton) =>
% 131.56/22.77 ((
% 131.56/22.77 (theprop) =>
% 131.56/22.77 ((
% 131.56/22.77 (kfstpairEq) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodfstin) =>
% 131.56/22.77 ((
% 131.56/22.77 (setukpairinjL2) =>
% 131.56/22.77 ((
% 131.56/22.77 (setukpairinjL) =>
% 131.56/22.77 ((
% 131.56/22.77 (setukpairinjR11) =>
% 131.56/22.77 ((
% 131.56/22.77 (setukpairinjR12) =>
% 131.56/22.77 ((
% 131.56/22.77 (setukpairinjR1) =>
% 131.56/22.77 ((
% 131.56/22.77 (upairequniteq) =>
% 131.56/22.77 ((
% 131.56/22.77 (setukpairinjR2) =>
% 131.56/22.77 ((
% 131.56/22.77 (setukpairinjR) =>
% 131.56/22.77 ((
% 131.56/22.77 (ksndsingleton) =>
% 131.56/22.77 ((
% 131.56/22.77 (ksndpairEq) =>
% 131.56/22.77 ((
% 131.56/22.77 (kpairsurjEq) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodsndin) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodpairmemEL) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodpairmemER) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodmempaircEq) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodfstpairEq) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodsndpairEq) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodpairsurjEq) =>
% 131.56/22.77 ((
% 131.56/22.77 (dpsetconstrI) =>
% 131.56/22.77 ((
% 131.56/22.77 (dpsetconstrSub) =>
% 131.56/22.77 ((
% 131.56/22.77 (setOfPairsIsBReln) =>
% 131.56/22.77 ((
% 131.56/22.77 (dpsetconstrERa) =>
% 131.56/22.77 ((
% 131.56/22.77 (dpsetconstrEL1) =>
% 131.56/22.77 ((
% 131.56/22.77 (dpsetconstrEL2) =>
% 131.56/22.77 ((
% 131.56/22.77 (dpsetconstrER) =>
% 131.56/22.77 ((
% 131.56/22.77 (funcImageSingleton) =>
% 131.56/22.77 ((
% 131.56/22.77 (apProp) =>
% 131.56/22.77 ((
% 131.56/22.77 (app) =>
% 131.56/22.77 ((
% 131.56/22.77 (infuncsetfunc) =>
% 131.56/22.77 ((
% 131.56/22.77 (ap2p) =>
% 131.56/22.77 ((
% 131.56/22.77 (funcinfuncset) =>
% 131.56/22.77 ((
% 131.56/22.77 (lamProp) =>
% 131.56/22.77 ((
% 131.56/22.77 (lamp) =>
% 131.56/22.77 ((
% 131.56/22.77 (lam2p) =>
% 131.56/22.77 ((
% 131.56/22.77 (brelnall1) =>
% 131.56/22.77 ((
% 131.56/22.77 (brelnall2) =>
% 131.56/22.77 ((
% 131.56/22.77 (ex1E2) =>
% 131.56/22.77 ((
% 131.56/22.77 (funcGraphProp1) =>
% 131.56/22.77 ((
% 131.56/22.77 (funcGraphProp3) =>
% 131.56/22.77 ((
% 131.56/22.77 (funcGraphProp2) =>
% 131.56/22.77 ((
% 131.56/22.77 (funcextLem) =>
% 131.56/22.77 ((
% 131.56/22.77 (funcGraphProp4) =>
% 131.56/22.77 ((
% 131.56/22.77 (subbreln) =>
% 131.56/22.77 ((
% 131.56/22.77 (eqbreln) =>
% 131.56/22.77 ((
% 131.56/22.77 (funcext) =>
% 131.56/22.77 ((
% 131.56/22.77 (funcext2) =>
% 131.56/22.77 ((
% 131.56/22.77 (ap2apEq1) =>
% 131.56/22.77 ((
% 131.56/22.77 (ap2apEq2) =>
% 131.56/22.77 ((
% 131.56/22.77 (beta1) =>
% 131.56/22.77 ((
% 131.56/22.77 (eta1) =>
% 131.56/22.77 ((
% 131.56/22.77 (lam2lamEq) =>
% 131.56/22.77 ((
% 131.56/22.77 (beta2) =>
% 131.56/22.77 ((
% 131.56/22.77 (eta2) =>
% 131.56/22.77 ((
% 131.56/22.77 (iffalseProp1) =>
% 131.56/22.77 ((
% 131.56/22.77 (iffalseProp2) =>
% 131.56/22.77 ((
% 131.56/22.77 (iftrueProp1) =>
% 131.56/22.77 ((
% 131.56/22.77 (iftrueProp2) =>
% 131.56/22.77 ((
% 131.56/22.77 (ifSingleton) =>
% 131.56/22.77 ((
% 131.56/22.77 (ifp) =>
% 131.56/22.77 ((
% 131.56/22.77 (theeq) =>
% 131.56/22.77 ((
% 131.56/22.77 (iftrue) =>
% 131.56/22.77 ((
% 131.56/22.77 (iffalse) =>
% 131.56/22.77 ((
% 131.56/22.77 (iftrueorfalse) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectT_lem) =>
% 131.56/22.77 ((
% 131.56/22.77 (binunionT_lem) =>
% 131.56/22.77 ((
% 131.56/22.77 (powersetT_lem) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusT_lem) =>
% 131.56/22.77 ((
% 131.56/22.77 (complementT_lem) =>
% 131.56/22.77 ((
% 131.56/22.77 (setextT) =>
% 131.56/22.77 ((
% 131.56/22.77 (subsetTI) =>
% 131.56/22.77 ((
% 131.56/22.77 (powersetTI1) =>
% 131.56/22.77 ((
% 131.56/22.77 (powersetTE1) =>
% 131.56/22.77 ((
% 131.56/22.77 (complementTI1) =>
% 131.56/22.77 ((
% 131.56/22.77 (complementTE1) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectTELcontra) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectTERcontra) =>
% 131.56/22.77 ((
% 131.56/22.77 (contrasubsetT) =>
% 131.56/22.77 ((
% 131.56/22.77 (contrasubsetT1) =>
% 131.56/22.77 ((
% 131.56/22.77 (contrasubsetT2) =>
% 131.56/22.77 ((
% 131.56/22.77 (contrasubsetT3) =>
% 131.56/22.77 ((
% 131.56/22.77 (doubleComplementI1) =>
% 131.56/22.77 ((
% 131.56/22.77 (doubleComplementE1) =>
% 131.56/22.77 ((
% 131.56/22.77 (doubleComplementSub1) =>
% 131.56/22.77 ((
% 131.56/22.77 (doubleComplementSub2) =>
% 131.56/22.77 ((
% 131.56/22.77 (doubleComplementEq) =>
% 131.56/22.77 ((
% 131.56/22.77 (complementTnotintersectT) =>
% 131.56/22.77 ((
% 131.56/22.77 (complementImpComplementIntersect) =>
% 131.56/22.77 ((
% 131.56/22.77 (complementSubsetComplementIntersect) =>
% 131.56/22.77 ((
% 131.56/22.77 (complementInPowersetComplementIntersect) =>
% 131.56/22.77 ((
% 131.56/22.77 (contraSubsetComplement) =>
% 131.56/22.77 ((
% 131.56/22.77 (complementTcontraSubset) =>
% 131.56/22.77 ((
% 131.56/22.77 (binunionTILcontra) =>
% 131.56/22.77 ((
% 131.56/22.77 (binunionTIRcontra) =>
% 131.56/22.77 ((
% 131.56/22.77 (inIntersectImpInUnion) =>
% 131.56/22.77 ((
% 131.56/22.77 (inIntersectImpInUnion2) =>
% 131.56/22.77 ((
% 131.56/22.77 (inIntersectImpInIntersectUnions) =>
% 131.56/22.77 ((
% 131.56/22.77 (intersectInPowersetIntersectUnions) =>
% 131.56/22.77 ((
% 131.56/22.77 (inComplementUnionImpNotIn1) =>
% 131.56/22.77 ((
% 131.56/22.77 (inComplementUnionImpInComplement1) =>
% 131.56/22.77 ((
% 131.56/22.77 (binunionTE) =>
% 131.56/22.77 ((
% 131.56/22.77 (binunionTEcontra) =>
% 131.56/22.77 ((
% 131.56/22.77 (demorgan2a1) =>
% 131.56/22.77 ((
% 131.56/22.77 (complementUnionInPowersetComplement) =>
% 131.56/22.77 ((
% 131.56/22.77 (demorgan2a2) =>
% 131.56/22.77 ((
% 131.56/22.77 (demorgan1a) =>
% 131.56/22.77 ((
% 131.56/22.77 (demorgan1b) =>
% 131.56/22.77 ((
% 131.56/22.77 (demorgan1) =>
% 131.56/22.77 ((
% 131.56/22.77 (demorgan2a) =>
% 131.56/22.77 ((
% 131.56/22.77 (demorgan2b2) =>
% 131.56/22.77 ((
% 131.56/22.77 (demorgan2b) =>
% 131.56/22.77 ((
% 131.56/22.77 (demorgan2) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz13rule0) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz13rule1) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz13rule2) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz13rule3) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz13rule4) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz1_1) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz1_2) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz1_3) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz1_4) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz1_5) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1all2) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1SetBreln1) =>
% 131.56/22.77 ((
% 131.56/22.77 (choice2fnsingleton) =>
% 131.56/22.77 ((
% 131.56/22.77 (setOfPairsIsBReln1) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1all1) =>
% 131.56/22.77 ((
% 131.56/22.77 (subbreln1) =>
% 131.56/22.77 ((
% 131.56/22.77 (eqbreln1) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1invprop) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1invI) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1invE) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1compprop) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1compI) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1compE) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1compEex) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1unionprop) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1unionIL) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1unionIR) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1unionI) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1unionE) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1unionEcases) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1unionCommutes) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz2Ex) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz2W) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz2A) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz2B) =>
% 131.56/22.77 ((
% 131.56/22.77 (image1Ex) =>
% 131.56/22.77 ((
% 131.56/22.77 (image1Ex1) =>
% 131.56/22.77 ((
% 131.56/22.77 (image1Equiv) =>
% 131.56/22.77 ((
% 131.56/22.77 (image1E) =>
% 131.56/22.77 ((
% 131.56/22.77 (image1I) =>
% 131.56/22.77 ((
% 131.56/22.77 (injFuncInInjFuncSet) =>
% 131.56/22.77 ((
% 131.56/22.77 (injFuncSetFuncIn) =>
% 131.56/22.77 ((
% 131.56/22.77 (injFuncSetFuncInj) =>
% 131.56/22.77 ((
% 131.56/22.77 (surjFuncSetFuncIn) =>
% 131.56/22.77 ((
% 131.56/22.77 (surjFuncSetFuncSurj) =>
% 131.56/22.77 ((
% 131.56/22.77 (leftInvIsSurj) =>
% 131.56/22.77 ((
% 131.56/22.77 (surjCantorThm) =>
% 131.56/22.77 ((
% 131.56/22.77 (foundation2) =>
% 131.56/22.77 ((
% 131.56/22.77 (notinself) =>
% 131.56/22.77 ((
% 131.56/22.77 (notinself2) =>
% 131.56/22.77 ((
% 131.56/22.77 (omegaSp) =>
% 131.56/22.77 ((
% 131.56/22.77 (omegaSclos) =>
% 131.56/22.77 ((
% 131.56/22.77 (peano0notS) =>
% 131.56/22.77 ((
% 131.56/22.77 (peanoSinj) =>
% 131.56/22.77 ((
% 131.56/22.77 (transitivesetOp1) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintTransitive) =>
% 131.56/22.77 ((
% 131.56/22.77 (transitivesetOp2) =>
% 131.56/22.77 ((
% 131.56/22.77 (setunionTransitive) =>
% 131.56/22.77 ((
% 131.56/22.77 (ordinalMinLem1) =>
% 131.56/22.77 ((
% 131.56/22.77 (ordinalTransSet) =>
% 131.56/22.77 ((
% 131.56/22.77 (ordinalTransSet1) =>
% 131.56/22.77 ((
% 131.56/22.77 (setunionOrdinalLem1) =>
% 131.56/22.77 (ordinal @
% 131.56/22.77 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 131.56/22.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl164])).
% 131.56/22.77 thf(zip_derived_cl191, plain,
% 131.56/22.77 (~ (((setext) =>
% 131.56/22.77 (((emptyI) =>
% 131.56/22.77 (((noeltsimpempty) =>
% 131.56/22.77 (((setbeta) =>
% 131.56/22.77 (((nonemptyE1) =>
% 131.56/22.77 (((nonemptyI) =>
% 131.56/22.77 (((nonemptyI1) =>
% 131.56/22.77 (((setadjoinIL) =>
% 131.56/22.77 (((in @ emptyset @
% 131.56/22.77 (setadjoin @ emptyset @ emptyset)) =>
% 131.56/22.77 (((setadjoinIR) =>
% 131.56/22.77 (((setadjoinE) =>
% 131.56/22.77 (((setadjoinOr) =>
% 131.56/22.77 (((setoftrueEq) =>
% 131.56/22.77 (((powersetI) =>
% 131.56/22.77 (((emptyinPowerset) =>
% 131.56/22.77 (((emptyInPowerset) =>
% 131.56/22.77 (((powersetE) =>
% 131.56/22.77 (((setunionI) =>
% 131.56/22.77 (((setunionE) =>
% 131.56/22.77 (((subPowSU) =>
% 131.56/22.77 (((exuE2) =>
% 131.56/22.77 (((nonemptyImpWitness) =>
% 131.56/22.77 (((uniqinunit) =>
% 131.56/22.77 (((notinsingleton) =>
% 131.56/22.77 (((eqinunit) =>
% 131.56/22.77 (((singletonsswitch) =>
% 131.56/22.77 (((upairsetE) =>
% 131.56/22.77 (((upairsetIL) =>
% 131.56/22.77 (((upairsetIR) =>
% 131.56/22.77 (((emptyE1) =>
% 131.56/22.77 ((
% 131.56/22.77 (vacuousDall) =>
% 131.56/22.77 ((
% 131.56/22.77 (quantDeMorgan1) =>
% 131.56/22.77 ((
% 131.56/22.77 (quantDeMorgan2) =>
% 131.56/22.77 ((
% 131.56/22.77 (quantDeMorgan3) =>
% 131.56/22.77 ((
% 131.56/22.77 (quantDeMorgan4) =>
% 131.56/22.77 ((
% 131.56/22.77 (prop2setI) =>
% 131.56/22.77 ((
% 131.56/22.77 (prop2set2propI) =>
% 131.56/22.77 ((
% 131.56/22.77 (notdexE) =>
% 131.56/22.77 ((
% 131.56/22.77 (notdallE) =>
% 131.56/22.77 ((
% 131.56/22.77 (exuI1) =>
% 131.56/22.77 ((
% 131.56/22.77 (exuI3) =>
% 131.56/22.77 ((
% 131.56/22.77 (exuI2) =>
% 131.56/22.77 ((
% 131.56/22.77 (inCongP) =>
% 131.56/22.77 ((
% 131.56/22.77 (in__Cong) =>
% 131.56/22.77 ((
% 131.56/22.77 (exuE3u) =>
% 131.56/22.77 ((
% 131.56/22.77 (exu__Cong) =>
% 131.56/22.77 ((
% 131.56/22.77 (setadjoin__Cong) =>
% 131.56/22.77 ((
% 131.56/22.77 (powerset__Cong) =>
% 131.56/22.77 ((
% 131.56/22.77 (setunion__Cong) =>
% 131.56/22.77 ((
% 131.56/22.77 (exuEu) =>
% 131.56/22.77 ((
% 131.56/22.77 (descr__Cong) =>
% 131.56/22.77 ((
% 131.56/22.77 (dsetconstr__Cong) =>
% 131.56/22.77 ((
% 131.56/22.77 (subsetI1) =>
% 131.56/22.77 ((
% 131.56/22.77 (eqimpsubset2) =>
% 131.56/22.77 ((
% 131.56/22.77 (eqimpsubset1) =>
% 131.56/22.77 ((
% 131.56/22.77 (subsetI2) =>
% 131.56/22.77 ((
% 131.56/22.77 (emptysetsubset) =>
% 131.56/22.77 ((
% 131.56/22.77 (subsetE) =>
% 131.56/22.77 ((
% 131.56/22.77 (subsetE2) =>
% 131.56/22.77 ((
% 131.56/22.77 (notsubsetI) =>
% 131.56/22.77 ((
% 131.56/22.77 (notequalI1) =>
% 131.56/22.77 ((
% 131.56/22.77 (notequalI2) =>
% 131.56/22.77 ((
% 131.56/22.77 (subsetRefl) =>
% 131.56/22.77 ((
% 131.56/22.77 (subsetTrans) =>
% 131.56/22.77 ((
% 131.56/22.77 (setadjoinSub) =>
% 131.56/22.77 ((
% 131.56/22.77 (setadjoinSub2) =>
% 131.56/22.77 ((
% 131.56/22.77 (subset2powerset) =>
% 131.56/22.77 ((
% 131.56/22.77 (setextsub) =>
% 131.56/22.77 ((
% 131.56/22.77 (subsetemptysetimpeq) =>
% 131.56/22.77 ((
% 131.56/22.77 (powersetI1) =>
% 131.56/22.77 ((
% 131.56/22.77 (powersetE1) =>
% 131.56/22.77 ((
% 131.56/22.77 (inPowerset) =>
% 131.56/22.77 ((
% 131.56/22.77 (powersetsubset) =>
% 131.56/22.77 ((
% 131.56/22.77 (sepInPowerset) =>
% 131.56/22.77 ((
% 131.56/22.77 (sepSubset) =>
% 131.56/22.77 ((
% 131.56/22.77 (binunionIL) =>
% 131.56/22.77 ((
% 131.56/22.77 (upairset2IR) =>
% 131.56/22.77 ((
% 131.56/22.77 (binunionIR) =>
% 131.56/22.77 ((
% 131.56/22.77 (binunionEcases) =>
% 131.56/22.77 ((
% 131.56/22.77 (binunionE) =>
% 131.56/22.77 ((
% 131.56/22.77 (binunionLsub) =>
% 131.56/22.77 ((
% 131.56/22.77 (binunionRsub) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectI) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectSubset5) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectEL) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectLsub) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectSubset2) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectSubset3) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectER) =>
% 131.56/22.77 ((
% 131.56/22.77 (disjointsetsI1) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectRsub) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectSubset4) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectSubset1) =>
% 131.56/22.77 ((
% 131.56/22.77 (bs114d) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusI) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusEL) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusER) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusSubset2) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusERneg) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusELneg) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusILneg) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusIRneg) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusLsub) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusSubset1) =>
% 131.56/22.77 ((
% 131.56/22.77 (symdiffE) =>
% 131.56/22.77 ((
% 131.56/22.77 (symdiffI1) =>
% 131.56/22.77 ((
% 131.56/22.77 (symdiffI2) =>
% 131.56/22.77 ((
% 131.56/22.77 (symdiffIneg1) =>
% 131.56/22.77 ((
% 131.56/22.77 (symdiffIneg2) =>
% 131.56/22.77 ((
% 131.56/22.77 (secondinupair) =>
% 131.56/22.77 ((
% 131.56/22.77 (setukpairIL) =>
% 131.56/22.77 ((
% 131.56/22.77 (setukpairIR) =>
% 131.56/22.77 ((
% 131.56/22.77 (kpairiskpair) =>
% 131.56/22.77 ((
% 131.56/22.77 (kpairp) =>
% 131.56/22.77 ((
% 131.56/22.77 (singletonsubset) =>
% 131.56/22.77 ((
% 131.56/22.77 (singletoninpowerset) =>
% 131.56/22.77 ((
% 131.56/22.77 (singletoninpowunion) =>
% 131.56/22.77 ((
% 131.56/22.77 (upairset2E) =>
% 131.56/22.77 ((
% 131.56/22.77 (upairsubunion) =>
% 131.56/22.77 ((
% 131.56/22.77 (upairinpowunion) =>
% 131.56/22.77 ((
% 131.56/22.77 (ubforcartprodlem1) =>
% 131.56/22.77 ((
% 131.56/22.77 (ubforcartprodlem2) =>
% 131.56/22.77 ((
% 131.56/22.77 (ubforcartprodlem3) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodpairin) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodmempair1) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodmempair) =>
% 131.56/22.77 ((
% 131.56/22.77 (setunionE2) =>
% 131.56/22.77 ((
% 131.56/22.77 (setunionsingleton1) =>
% 131.56/22.77 ((
% 131.56/22.77 (setunionsingleton2) =>
% 131.56/22.77 ((
% 131.56/22.77 (setunionsingleton) =>
% 131.56/22.77 ((
% 131.56/22.77 (singletonprop) =>
% 131.56/22.77 ((
% 131.56/22.77 (ex1E1) =>
% 131.56/22.77 ((
% 131.56/22.77 (ex1I) =>
% 131.56/22.77 ((
% 131.56/22.77 (ex1I2) =>
% 131.56/22.77 ((
% 131.56/22.77 (singletonsuniq) =>
% 131.56/22.77 ((
% 131.56/22.77 (setukpairinjL1) =>
% 131.56/22.77 ((
% 131.56/22.77 (kfstsingleton) =>
% 131.56/22.77 ((
% 131.56/22.77 (theprop) =>
% 131.56/22.77 ((
% 131.56/22.77 (kfstpairEq) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodfstin) =>
% 131.56/22.77 ((
% 131.56/22.77 (setukpairinjL2) =>
% 131.56/22.77 ((
% 131.56/22.77 (setukpairinjL) =>
% 131.56/22.77 ((
% 131.56/22.77 (setukpairinjR11) =>
% 131.56/22.77 ((
% 131.56/22.77 (setukpairinjR12) =>
% 131.56/22.77 ((
% 131.56/22.77 (setukpairinjR1) =>
% 131.56/22.77 ((
% 131.56/22.77 (upairequniteq) =>
% 131.56/22.77 ((
% 131.56/22.77 (setukpairinjR2) =>
% 131.56/22.77 ((
% 131.56/22.77 (setukpairinjR) =>
% 131.56/22.77 ((
% 131.56/22.77 (ksndsingleton) =>
% 131.56/22.77 ((
% 131.56/22.77 (ksndpairEq) =>
% 131.56/22.77 ((
% 131.56/22.77 (kpairsurjEq) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodsndin) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodpairmemEL) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodpairmemER) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodmempaircEq) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodfstpairEq) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodsndpairEq) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodpairsurjEq) =>
% 131.56/22.77 ((
% 131.56/22.77 (dpsetconstrI) =>
% 131.56/22.77 ((
% 131.56/22.77 (dpsetconstrSub) =>
% 131.56/22.77 ((
% 131.56/22.77 (setOfPairsIsBReln) =>
% 131.56/22.77 ((
% 131.56/22.77 (dpsetconstrERa) =>
% 131.56/22.77 ((
% 131.56/22.77 (dpsetconstrEL1) =>
% 131.56/22.77 ((
% 131.56/22.77 (dpsetconstrEL2) =>
% 131.56/22.77 ((
% 131.56/22.77 (dpsetconstrER) =>
% 131.56/22.77 ((
% 131.56/22.77 (funcImageSingleton) =>
% 131.56/22.77 ((
% 131.56/22.77 (apProp) =>
% 131.56/22.77 ((
% 131.56/22.77 (app) =>
% 131.56/22.77 ((
% 131.56/22.77 (infuncsetfunc) =>
% 131.56/22.77 ((
% 131.56/22.77 (ap2p) =>
% 131.56/22.77 ((
% 131.56/22.77 (funcinfuncset) =>
% 131.56/22.77 ((
% 131.56/22.77 (lamProp) =>
% 131.56/22.77 ((
% 131.56/22.77 (lamp) =>
% 131.56/22.77 ((
% 131.56/22.77 (lam2p) =>
% 131.56/22.77 ((
% 131.56/22.77 (brelnall1) =>
% 131.56/22.77 ((
% 131.56/22.77 (brelnall2) =>
% 131.56/22.77 ((
% 131.56/22.77 (ex1E2) =>
% 131.56/22.77 ((
% 131.56/22.77 (funcGraphProp1) =>
% 131.56/22.77 ((
% 131.56/22.77 (funcGraphProp3) =>
% 131.56/22.77 ((
% 131.56/22.77 (funcGraphProp2) =>
% 131.56/22.77 ((
% 131.56/22.77 (funcextLem) =>
% 131.56/22.77 ((
% 131.56/22.77 (funcGraphProp4) =>
% 131.56/22.77 ((
% 131.56/22.77 (subbreln) =>
% 131.56/22.77 ((
% 131.56/22.77 (eqbreln) =>
% 131.56/22.77 ((
% 131.56/22.77 (funcext) =>
% 131.56/22.77 ((
% 131.56/22.77 (funcext2) =>
% 131.56/22.77 ((
% 131.56/22.77 (ap2apEq1) =>
% 131.56/22.77 ((
% 131.56/22.77 (ap2apEq2) =>
% 131.56/22.77 ((
% 131.56/22.77 (beta1) =>
% 131.56/22.77 ((
% 131.56/22.77 (eta1) =>
% 131.56/22.77 ((
% 131.56/22.77 (lam2lamEq) =>
% 131.56/22.77 ((
% 131.56/22.77 (beta2) =>
% 131.56/22.77 ((
% 131.56/22.77 (eta2) =>
% 131.56/22.77 ((
% 131.56/22.77 (iffalseProp1) =>
% 131.56/22.77 ((
% 131.56/22.77 (iffalseProp2) =>
% 131.56/22.77 ((
% 131.56/22.77 (iftrueProp1) =>
% 131.56/22.77 ((
% 131.56/22.77 (iftrueProp2) =>
% 131.56/22.77 ((
% 131.56/22.77 (ifSingleton) =>
% 131.56/22.77 ((
% 131.56/22.77 (ifp) =>
% 131.56/22.77 ((
% 131.56/22.77 (theeq) =>
% 131.56/22.77 ((
% 131.56/22.77 (iftrue) =>
% 131.56/22.77 ((
% 131.56/22.77 (iffalse) =>
% 131.56/22.77 ((
% 131.56/22.77 (iftrueorfalse) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectT_lem) =>
% 131.56/22.77 ((
% 131.56/22.77 (binunionT_lem) =>
% 131.56/22.77 ((
% 131.56/22.77 (powersetT_lem) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusT_lem) =>
% 131.56/22.77 ((
% 131.56/22.77 (complementT_lem) =>
% 131.56/22.77 ((
% 131.56/22.77 (setextT) =>
% 131.56/22.77 ((
% 131.56/22.77 (subsetTI) =>
% 131.56/22.77 ((
% 131.56/22.77 (powersetTI1) =>
% 131.56/22.77 ((
% 131.56/22.77 (powersetTE1) =>
% 131.56/22.77 ((
% 131.56/22.77 (complementTI1) =>
% 131.56/22.77 ((
% 131.56/22.77 (complementTE1) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectTELcontra) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectTERcontra) =>
% 131.56/22.77 ((
% 131.56/22.77 (contrasubsetT) =>
% 131.56/22.77 ((
% 131.56/22.77 (contrasubsetT1) =>
% 131.56/22.77 ((
% 131.56/22.77 (contrasubsetT2) =>
% 131.56/22.77 ((
% 131.56/22.77 (contrasubsetT3) =>
% 131.56/22.77 ((
% 131.56/22.77 (doubleComplementI1) =>
% 131.56/22.77 ((
% 131.56/22.77 (doubleComplementE1) =>
% 131.56/22.77 ((
% 131.56/22.77 (doubleComplementSub1) =>
% 131.56/22.77 ((
% 131.56/22.77 (doubleComplementSub2) =>
% 131.56/22.77 ((
% 131.56/22.77 (doubleComplementEq) =>
% 131.56/22.77 ((
% 131.56/22.77 (complementTnotintersectT) =>
% 131.56/22.77 ((
% 131.56/22.77 (complementImpComplementIntersect) =>
% 131.56/22.77 ((
% 131.56/22.77 (complementSubsetComplementIntersect) =>
% 131.56/22.77 ((
% 131.56/22.77 (complementInPowersetComplementIntersect) =>
% 131.56/22.77 ((
% 131.56/22.77 (contraSubsetComplement) =>
% 131.56/22.77 ((
% 131.56/22.77 (complementTcontraSubset) =>
% 131.56/22.77 ((
% 131.56/22.77 (binunionTILcontra) =>
% 131.56/22.77 ((
% 131.56/22.77 (binunionTIRcontra) =>
% 131.56/22.77 ((
% 131.56/22.77 (inIntersectImpInUnion) =>
% 131.56/22.77 ((
% 131.56/22.77 (inIntersectImpInUnion2) =>
% 131.56/22.77 ((
% 131.56/22.77 (inIntersectImpInIntersectUnions) =>
% 131.56/22.77 ((
% 131.56/22.77 (intersectInPowersetIntersectUnions) =>
% 131.56/22.77 ((
% 131.56/22.77 (inComplementUnionImpNotIn1) =>
% 131.56/22.77 ((
% 131.56/22.77 (inComplementUnionImpInComplement1) =>
% 131.56/22.77 ((
% 131.56/22.77 (binunionTE) =>
% 131.56/22.77 ((
% 131.56/22.77 (binunionTEcontra) =>
% 131.56/22.77 ((
% 131.56/22.77 (demorgan2a1) =>
% 131.56/22.77 ((
% 131.56/22.77 (complementUnionInPowersetComplement) =>
% 131.56/22.77 ((
% 131.56/22.77 (demorgan2a2) =>
% 131.56/22.77 ((
% 131.56/22.77 (demorgan1a) =>
% 131.56/22.77 ((
% 131.56/22.77 (demorgan1b) =>
% 131.56/22.77 ((
% 131.56/22.77 (demorgan1) =>
% 131.56/22.77 ((
% 131.56/22.77 (demorgan2a) =>
% 131.56/22.77 ((
% 131.56/22.77 (demorgan2b2) =>
% 131.56/22.77 ((
% 131.56/22.77 (demorgan2b) =>
% 131.56/22.77 ((
% 131.56/22.77 (demorgan2) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz13rule0) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz13rule1) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz13rule2) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz13rule3) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz13rule4) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz1_1) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz1_2) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz1_3) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz1_4) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz1_5) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1all2) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1SetBreln1) =>
% 131.56/22.77 ((
% 131.56/22.77 (choice2fnsingleton) =>
% 131.56/22.77 ((
% 131.56/22.77 (setOfPairsIsBReln1) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1all1) =>
% 131.56/22.77 ((
% 131.56/22.77 (subbreln1) =>
% 131.56/22.77 ((
% 131.56/22.77 (eqbreln1) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1invprop) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1invI) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1invE) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1compprop) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1compI) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1compE) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1compEex) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1unionprop) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1unionIL) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1unionIR) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1unionI) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1unionE) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1unionEcases) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1unionCommutes) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz2Ex) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz2W) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz2A) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz2B) =>
% 131.56/22.77 ((
% 131.56/22.77 (image1Ex) =>
% 131.56/22.77 ((
% 131.56/22.77 (image1Ex1) =>
% 131.56/22.77 ((
% 131.56/22.77 (image1Equiv) =>
% 131.56/22.77 ((
% 131.56/22.77 (image1E) =>
% 131.56/22.77 ((
% 131.56/22.77 (image1I) =>
% 131.56/22.77 ((
% 131.56/22.77 (injFuncInInjFuncSet) =>
% 131.56/22.77 ((
% 131.56/22.77 (injFuncSetFuncIn) =>
% 131.56/22.77 ((
% 131.56/22.77 (injFuncSetFuncInj) =>
% 131.56/22.77 ((
% 131.56/22.77 (surjFuncSetFuncIn) =>
% 131.56/22.77 ((
% 131.56/22.77 (surjFuncSetFuncSurj) =>
% 131.56/22.77 ((
% 131.56/22.77 (leftInvIsSurj) =>
% 131.56/22.77 ((
% 131.56/22.77 (surjCantorThm) =>
% 131.56/22.77 ((
% 131.56/22.77 (foundation2) =>
% 131.56/22.77 ((
% 131.56/22.77 (notinself) =>
% 131.56/22.77 ((
% 131.56/22.77 (notinself2) =>
% 131.56/22.77 ((
% 131.56/22.77 (omegaSp) =>
% 131.56/22.77 ((
% 131.56/22.77 (omegaSclos) =>
% 131.56/22.77 ((
% 131.56/22.77 (peano0notS) =>
% 131.56/22.77 ((
% 131.56/22.77 (peanoSinj) =>
% 131.56/22.77 ((
% 131.56/22.77 (transitivesetOp1) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintTransitive) =>
% 131.56/22.77 ((
% 131.56/22.77 (transitivesetOp2) =>
% 131.56/22.77 ((
% 131.56/22.77 (setunionTransitive) =>
% 131.56/22.77 ((
% 131.56/22.77 (ordinalMinLem1) =>
% 131.56/22.77 ((
% 131.56/22.77 (ordinalTransSet) =>
% 131.56/22.77 ((
% 131.56/22.77 (ordinalTransSet1) =>
% 131.56/22.77 ((
% 131.56/22.77 (setunionOrdinalLem1) =>
% 131.56/22.77 (ordinal @
% 131.56/22.77 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 131.56/22.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl177])).
% 131.56/22.77 thf(zip_derived_cl205, plain,
% 131.56/22.77 (~ (((emptyI) =>
% 131.56/22.77 (((noeltsimpempty) =>
% 131.56/22.77 (((setbeta) =>
% 131.56/22.77 (((nonemptyE1) =>
% 131.56/22.77 (((nonemptyI) =>
% 131.56/22.77 (((nonemptyI1) =>
% 131.56/22.77 (((setadjoinIL) =>
% 131.56/22.77 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 131.56/22.77 (((setadjoinIR) =>
% 131.56/22.77 (((setadjoinE) =>
% 131.56/22.77 (((setadjoinOr) =>
% 131.56/22.77 (((setoftrueEq) =>
% 131.56/22.77 (((powersetI) =>
% 131.56/22.77 (((emptyinPowerset) =>
% 131.56/22.77 (((emptyInPowerset) =>
% 131.56/22.77 (((powersetE) =>
% 131.56/22.77 (((setunionI) =>
% 131.56/22.77 (((setunionE) =>
% 131.56/22.77 (((subPowSU) =>
% 131.56/22.77 (((exuE2) =>
% 131.56/22.77 (((nonemptyImpWitness) =>
% 131.56/22.77 (((uniqinunit) =>
% 131.56/22.77 (((notinsingleton) =>
% 131.56/22.77 (((eqinunit) =>
% 131.56/22.77 (((singletonsswitch) =>
% 131.56/22.77 (((upairsetE) =>
% 131.56/22.77 (((upairsetIL) =>
% 131.56/22.77 (((upairsetIR) =>
% 131.56/22.77 (((emptyE1) =>
% 131.56/22.77 (((vacuousDall) =>
% 131.56/22.77 ((
% 131.56/22.77 (quantDeMorgan1) =>
% 131.56/22.77 ((
% 131.56/22.77 (quantDeMorgan2) =>
% 131.56/22.77 ((
% 131.56/22.77 (quantDeMorgan3) =>
% 131.56/22.77 ((
% 131.56/22.77 (quantDeMorgan4) =>
% 131.56/22.77 ((
% 131.56/22.77 (prop2setI) =>
% 131.56/22.77 ((
% 131.56/22.77 (prop2set2propI) =>
% 131.56/22.77 ((
% 131.56/22.77 (notdexE) =>
% 131.56/22.77 ((
% 131.56/22.77 (notdallE) =>
% 131.56/22.77 ((
% 131.56/22.77 (exuI1) =>
% 131.56/22.77 ((
% 131.56/22.77 (exuI3) =>
% 131.56/22.77 ((
% 131.56/22.77 (exuI2) =>
% 131.56/22.77 ((
% 131.56/22.77 (inCongP) =>
% 131.56/22.77 ((
% 131.56/22.77 (in__Cong) =>
% 131.56/22.77 ((
% 131.56/22.77 (exuE3u) =>
% 131.56/22.77 ((
% 131.56/22.77 (exu__Cong) =>
% 131.56/22.77 ((
% 131.56/22.77 (setadjoin__Cong) =>
% 131.56/22.77 ((
% 131.56/22.77 (powerset__Cong) =>
% 131.56/22.77 ((
% 131.56/22.77 (setunion__Cong) =>
% 131.56/22.77 ((
% 131.56/22.77 (exuEu) =>
% 131.56/22.77 ((
% 131.56/22.77 (descr__Cong) =>
% 131.56/22.77 ((
% 131.56/22.77 (dsetconstr__Cong) =>
% 131.56/22.77 ((
% 131.56/22.77 (subsetI1) =>
% 131.56/22.77 ((
% 131.56/22.77 (eqimpsubset2) =>
% 131.56/22.77 ((
% 131.56/22.77 (eqimpsubset1) =>
% 131.56/22.77 ((
% 131.56/22.77 (subsetI2) =>
% 131.56/22.77 ((
% 131.56/22.77 (emptysetsubset) =>
% 131.56/22.77 ((
% 131.56/22.77 (subsetE) =>
% 131.56/22.77 ((
% 131.56/22.77 (subsetE2) =>
% 131.56/22.77 ((
% 131.56/22.77 (notsubsetI) =>
% 131.56/22.77 ((
% 131.56/22.77 (notequalI1) =>
% 131.56/22.77 ((
% 131.56/22.77 (notequalI2) =>
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% 131.56/22.77 ((
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% 131.56/22.77 ((
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% 131.56/22.77 (binunionRsub) =>
% 131.56/22.77 ((
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% 131.56/22.77 ((
% 131.56/22.77 (binintersectSubset5) =>
% 131.56/22.77 ((
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% 131.56/22.77 ((
% 131.56/22.77 (binintersectSubset3) =>
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% 131.56/22.77 ((
% 131.56/22.77 (disjointsetsI1) =>
% 131.56/22.77 ((
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% 131.56/22.77 (binintersectSubset4) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectSubset1) =>
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% 131.56/22.77 (bs114d) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusI) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusEL) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusER) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusSubset2) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusERneg) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusELneg) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusILneg) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusIRneg) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusLsub) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusSubset1) =>
% 131.56/22.77 ((
% 131.56/22.77 (symdiffE) =>
% 131.56/22.77 ((
% 131.56/22.77 (symdiffI1) =>
% 131.56/22.77 ((
% 131.56/22.77 (symdiffI2) =>
% 131.56/22.77 ((
% 131.56/22.77 (symdiffIneg1) =>
% 131.56/22.77 ((
% 131.56/22.77 (symdiffIneg2) =>
% 131.56/22.77 ((
% 131.56/22.77 (secondinupair) =>
% 131.56/22.77 ((
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% 131.56/22.77 ((
% 131.56/22.77 (setukpairIR) =>
% 131.56/22.77 ((
% 131.56/22.77 (kpairiskpair) =>
% 131.56/22.77 ((
% 131.56/22.77 (kpairp) =>
% 131.56/22.77 ((
% 131.56/22.77 (singletonsubset) =>
% 131.56/22.77 ((
% 131.56/22.77 (singletoninpowerset) =>
% 131.56/22.77 ((
% 131.56/22.77 (singletoninpowunion) =>
% 131.56/22.77 ((
% 131.56/22.77 (upairset2E) =>
% 131.56/22.77 ((
% 131.56/22.77 (upairsubunion) =>
% 131.56/22.77 ((
% 131.56/22.77 (upairinpowunion) =>
% 131.56/22.77 ((
% 131.56/22.77 (ubforcartprodlem1) =>
% 131.56/22.77 ((
% 131.56/22.77 (ubforcartprodlem2) =>
% 131.56/22.77 ((
% 131.56/22.77 (ubforcartprodlem3) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodpairin) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodmempair1) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodmempair) =>
% 131.56/22.77 ((
% 131.56/22.77 (setunionE2) =>
% 131.56/22.77 ((
% 131.56/22.77 (setunionsingleton1) =>
% 131.56/22.77 ((
% 131.56/22.77 (setunionsingleton2) =>
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% 131.56/22.77 ((
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% 131.56/22.77 ((
% 131.56/22.77 (ex1I2) =>
% 131.56/22.77 ((
% 131.56/22.77 (singletonsuniq) =>
% 131.56/22.77 ((
% 131.56/22.77 (setukpairinjL1) =>
% 131.56/22.77 ((
% 131.56/22.77 (kfstsingleton) =>
% 131.56/22.77 ((
% 131.56/22.77 (theprop) =>
% 131.56/22.77 ((
% 131.56/22.77 (kfstpairEq) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodfstin) =>
% 131.56/22.77 ((
% 131.56/22.77 (setukpairinjL2) =>
% 131.56/22.77 ((
% 131.56/22.77 (setukpairinjL) =>
% 131.56/22.77 ((
% 131.56/22.77 (setukpairinjR11) =>
% 131.56/22.77 ((
% 131.56/22.77 (setukpairinjR12) =>
% 131.56/22.77 ((
% 131.56/22.77 (setukpairinjR1) =>
% 131.56/22.77 ((
% 131.56/22.77 (upairequniteq) =>
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% 131.56/22.77 (setukpairinjR2) =>
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% 131.56/22.77 (setukpairinjR) =>
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% 131.56/22.77 (ksndsingleton) =>
% 131.56/22.77 ((
% 131.56/22.77 (ksndpairEq) =>
% 131.56/22.77 ((
% 131.56/22.77 (kpairsurjEq) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodsndin) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodpairmemEL) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodpairmemER) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodmempaircEq) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodfstpairEq) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodsndpairEq) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodpairsurjEq) =>
% 131.56/22.77 ((
% 131.56/22.77 (dpsetconstrI) =>
% 131.56/22.77 ((
% 131.56/22.77 (dpsetconstrSub) =>
% 131.56/22.77 ((
% 131.56/22.77 (setOfPairsIsBReln) =>
% 131.56/22.77 ((
% 131.56/22.77 (dpsetconstrERa) =>
% 131.56/22.77 ((
% 131.56/22.77 (dpsetconstrEL1) =>
% 131.56/22.77 ((
% 131.56/22.77 (dpsetconstrEL2) =>
% 131.56/22.77 ((
% 131.56/22.77 (dpsetconstrER) =>
% 131.56/22.77 ((
% 131.56/22.77 (funcImageSingleton) =>
% 131.56/22.77 ((
% 131.56/22.77 (apProp) =>
% 131.56/22.77 ((
% 131.56/22.77 (app) =>
% 131.56/22.77 ((
% 131.56/22.77 (infuncsetfunc) =>
% 131.56/22.77 ((
% 131.56/22.77 (ap2p) =>
% 131.56/22.77 ((
% 131.56/22.77 (funcinfuncset) =>
% 131.56/22.77 ((
% 131.56/22.77 (lamProp) =>
% 131.56/22.77 ((
% 131.56/22.77 (lamp) =>
% 131.56/22.77 ((
% 131.56/22.77 (lam2p) =>
% 131.56/22.77 ((
% 131.56/22.77 (brelnall1) =>
% 131.56/22.77 ((
% 131.56/22.77 (brelnall2) =>
% 131.56/22.77 ((
% 131.56/22.77 (ex1E2) =>
% 131.56/22.77 ((
% 131.56/22.77 (funcGraphProp1) =>
% 131.56/22.77 ((
% 131.56/22.77 (funcGraphProp3) =>
% 131.56/22.77 ((
% 131.56/22.77 (funcGraphProp2) =>
% 131.56/22.77 ((
% 131.56/22.77 (funcextLem) =>
% 131.56/22.77 ((
% 131.56/22.77 (funcGraphProp4) =>
% 131.56/22.77 ((
% 131.56/22.77 (subbreln) =>
% 131.56/22.77 ((
% 131.56/22.77 (eqbreln) =>
% 131.56/22.77 ((
% 131.56/22.77 (funcext) =>
% 131.56/22.77 ((
% 131.56/22.77 (funcext2) =>
% 131.56/22.77 ((
% 131.56/22.77 (ap2apEq1) =>
% 131.56/22.77 ((
% 131.56/22.77 (ap2apEq2) =>
% 131.56/22.77 ((
% 131.56/22.77 (beta1) =>
% 131.56/22.77 ((
% 131.56/22.77 (eta1) =>
% 131.56/22.77 ((
% 131.56/22.77 (lam2lamEq) =>
% 131.56/22.77 ((
% 131.56/22.77 (beta2) =>
% 131.56/22.77 ((
% 131.56/22.77 (eta2) =>
% 131.56/22.77 ((
% 131.56/22.77 (iffalseProp1) =>
% 131.56/22.77 ((
% 131.56/22.77 (iffalseProp2) =>
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% 131.56/22.77 (iftrueProp1) =>
% 131.56/22.77 ((
% 131.56/22.77 (iftrueProp2) =>
% 131.56/22.77 ((
% 131.56/22.77 (ifSingleton) =>
% 131.56/22.77 ((
% 131.56/22.77 (ifp) =>
% 131.56/22.77 ((
% 131.56/22.77 (theeq) =>
% 131.56/22.77 ((
% 131.56/22.77 (iftrue) =>
% 131.56/22.77 ((
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% 131.56/22.77 ((
% 131.56/22.77 (setextT) =>
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% 131.56/22.77 (subsetTI) =>
% 131.56/22.77 ((
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% 131.56/22.77 ((
% 131.56/22.77 (powersetTE1) =>
% 131.56/22.77 ((
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% 131.56/22.77 ((
% 131.56/22.77 (complementTE1) =>
% 131.56/22.77 ((
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% 131.56/22.77 ((
% 131.56/22.77 (binintersectTERcontra) =>
% 131.56/22.77 ((
% 131.56/22.77 (contrasubsetT) =>
% 131.56/22.77 ((
% 131.56/22.77 (contrasubsetT1) =>
% 131.56/22.77 ((
% 131.56/22.77 (contrasubsetT2) =>
% 131.56/22.77 ((
% 131.56/22.77 (contrasubsetT3) =>
% 131.56/22.77 ((
% 131.56/22.77 (doubleComplementI1) =>
% 131.56/22.77 ((
% 131.56/22.77 (doubleComplementE1) =>
% 131.56/22.77 ((
% 131.56/22.77 (doubleComplementSub1) =>
% 131.56/22.77 ((
% 131.56/22.77 (doubleComplementSub2) =>
% 131.56/22.77 ((
% 131.56/22.77 (doubleComplementEq) =>
% 131.56/22.77 ((
% 131.56/22.77 (complementTnotintersectT) =>
% 131.56/22.77 ((
% 131.56/22.77 (complementImpComplementIntersect) =>
% 131.56/22.77 ((
% 131.56/22.77 (complementSubsetComplementIntersect) =>
% 131.56/22.77 ((
% 131.56/22.77 (complementInPowersetComplementIntersect) =>
% 131.56/22.77 ((
% 131.56/22.77 (contraSubsetComplement) =>
% 131.56/22.77 ((
% 131.56/22.77 (complementTcontraSubset) =>
% 131.56/22.77 ((
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% 131.56/22.77 ((
% 131.56/22.77 (binunionTIRcontra) =>
% 131.56/22.77 ((
% 131.56/22.77 (inIntersectImpInUnion) =>
% 131.56/22.77 ((
% 131.56/22.77 (inIntersectImpInUnion2) =>
% 131.56/22.77 ((
% 131.56/22.77 (inIntersectImpInIntersectUnions) =>
% 131.56/22.77 ((
% 131.56/22.77 (intersectInPowersetIntersectUnions) =>
% 131.56/22.77 ((
% 131.56/22.77 (inComplementUnionImpNotIn1) =>
% 131.56/22.77 ((
% 131.56/22.77 (inComplementUnionImpInComplement1) =>
% 131.56/22.77 ((
% 131.56/22.77 (binunionTE) =>
% 131.56/22.77 ((
% 131.56/22.77 (binunionTEcontra) =>
% 131.56/22.77 ((
% 131.56/22.77 (demorgan2a1) =>
% 131.56/22.77 ((
% 131.56/22.77 (complementUnionInPowersetComplement) =>
% 131.56/22.77 ((
% 131.56/22.77 (demorgan2a2) =>
% 131.56/22.77 ((
% 131.56/22.77 (demorgan1a) =>
% 131.56/22.77 ((
% 131.56/22.77 (demorgan1b) =>
% 131.56/22.77 ((
% 131.56/22.77 (demorgan1) =>
% 131.56/22.77 ((
% 131.56/22.77 (demorgan2a) =>
% 131.56/22.77 ((
% 131.56/22.77 (demorgan2b2) =>
% 131.56/22.77 ((
% 131.56/22.77 (demorgan2b) =>
% 131.56/22.77 ((
% 131.56/22.77 (demorgan2) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz13rule0) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz13rule1) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz13rule2) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz13rule3) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz13rule4) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz1_1) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz1_2) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz1_3) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz1_4) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz1_5) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1all2) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1SetBreln1) =>
% 131.56/22.77 ((
% 131.56/22.77 (choice2fnsingleton) =>
% 131.56/22.77 ((
% 131.56/22.77 (setOfPairsIsBReln1) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1all1) =>
% 131.56/22.77 ((
% 131.56/22.77 (subbreln1) =>
% 131.56/22.77 ((
% 131.56/22.77 (eqbreln1) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1invprop) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1invI) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1invE) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1compprop) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1compI) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1compE) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1compEex) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1unionprop) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1unionIL) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1unionIR) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1unionI) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1unionE) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1unionEcases) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1unionCommutes) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz2Ex) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz2W) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz2A) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz2B) =>
% 131.56/22.77 ((
% 131.56/22.77 (image1Ex) =>
% 131.56/22.77 ((
% 131.56/22.77 (image1Ex1) =>
% 131.56/22.77 ((
% 131.56/22.77 (image1Equiv) =>
% 131.56/22.77 ((
% 131.56/22.77 (image1E) =>
% 131.56/22.77 ((
% 131.56/22.77 (image1I) =>
% 131.56/22.77 ((
% 131.56/22.77 (injFuncInInjFuncSet) =>
% 131.56/22.77 ((
% 131.56/22.77 (injFuncSetFuncIn) =>
% 131.56/22.77 ((
% 131.56/22.77 (injFuncSetFuncInj) =>
% 131.56/22.77 ((
% 131.56/22.77 (surjFuncSetFuncIn) =>
% 131.56/22.77 ((
% 131.56/22.77 (surjFuncSetFuncSurj) =>
% 131.56/22.77 ((
% 131.56/22.77 (leftInvIsSurj) =>
% 131.56/22.77 ((
% 131.56/22.77 (surjCantorThm) =>
% 131.56/22.77 ((
% 131.56/22.77 (foundation2) =>
% 131.56/22.77 ((
% 131.56/22.77 (notinself) =>
% 131.56/22.77 ((
% 131.56/22.77 (notinself2) =>
% 131.56/22.77 ((
% 131.56/22.77 (omegaSp) =>
% 131.56/22.77 ((
% 131.56/22.77 (omegaSclos) =>
% 131.56/22.77 ((
% 131.56/22.77 (peano0notS) =>
% 131.56/22.77 ((
% 131.56/22.77 (peanoSinj) =>
% 131.56/22.77 ((
% 131.56/22.77 (transitivesetOp1) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintTransitive) =>
% 131.56/22.77 ((
% 131.56/22.77 (transitivesetOp2) =>
% 131.56/22.77 ((
% 131.56/22.77 (setunionTransitive) =>
% 131.56/22.77 ((
% 131.56/22.77 (ordinalMinLem1) =>
% 131.56/22.77 ((
% 131.56/22.77 (ordinalTransSet) =>
% 131.56/22.77 ((
% 131.56/22.77 (ordinalTransSet1) =>
% 131.56/22.77 ((
% 131.56/22.77 (setunionOrdinalLem1) =>
% 131.56/22.77 (ordinal @
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% 131.56/22.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl191])).
% 131.56/22.77 thf(zip_derived_cl219, plain,
% 131.56/22.77 (~ (((noeltsimpempty) =>
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% 131.56/22.77 (((setadjoinE) =>
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% 131.56/22.77 (((emptyInPowerset) =>
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% 131.56/22.77 (((setunionE) =>
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% 131.56/22.77 (((quantDeMorgan1) =>
% 131.56/22.77 ((
% 131.56/22.77 (quantDeMorgan2) =>
% 131.56/22.77 ((
% 131.56/22.77 (quantDeMorgan3) =>
% 131.56/22.77 ((
% 131.56/22.77 (quantDeMorgan4) =>
% 131.56/22.77 ((
% 131.56/22.77 (prop2setI) =>
% 131.56/22.77 ((
% 131.56/22.77 (prop2set2propI) =>
% 131.56/22.77 ((
% 131.56/22.77 (notdexE) =>
% 131.56/22.77 ((
% 131.56/22.77 (notdallE) =>
% 131.56/22.77 ((
% 131.56/22.77 (exuI1) =>
% 131.56/22.77 ((
% 131.56/22.77 (exuI3) =>
% 131.56/22.77 ((
% 131.56/22.77 (exuI2) =>
% 131.56/22.77 ((
% 131.56/22.77 (inCongP) =>
% 131.56/22.77 ((
% 131.56/22.77 (in__Cong) =>
% 131.56/22.77 ((
% 131.56/22.77 (exuE3u) =>
% 131.56/22.77 ((
% 131.56/22.77 (exu__Cong) =>
% 131.56/22.77 ((
% 131.56/22.77 (setadjoin__Cong) =>
% 131.56/22.77 ((
% 131.56/22.77 (powerset__Cong) =>
% 131.56/22.77 ((
% 131.56/22.77 (setunion__Cong) =>
% 131.56/22.77 ((
% 131.56/22.77 (exuEu) =>
% 131.56/22.77 ((
% 131.56/22.77 (descr__Cong) =>
% 131.56/22.77 ((
% 131.56/22.77 (dsetconstr__Cong) =>
% 131.56/22.77 ((
% 131.56/22.77 (subsetI1) =>
% 131.56/22.77 ((
% 131.56/22.77 (eqimpsubset2) =>
% 131.56/22.77 ((
% 131.56/22.77 (eqimpsubset1) =>
% 131.56/22.77 ((
% 131.56/22.77 (subsetI2) =>
% 131.56/22.77 ((
% 131.56/22.77 (emptysetsubset) =>
% 131.56/22.77 ((
% 131.56/22.77 (subsetE) =>
% 131.56/22.77 ((
% 131.56/22.77 (subsetE2) =>
% 131.56/22.77 ((
% 131.56/22.77 (notsubsetI) =>
% 131.56/22.77 ((
% 131.56/22.77 (notequalI1) =>
% 131.56/22.77 ((
% 131.56/22.77 (notequalI2) =>
% 131.56/22.77 ((
% 131.56/22.77 (subsetRefl) =>
% 131.56/22.77 ((
% 131.56/22.77 (subsetTrans) =>
% 131.56/22.77 ((
% 131.56/22.77 (setadjoinSub) =>
% 131.56/22.77 ((
% 131.56/22.77 (setadjoinSub2) =>
% 131.56/22.77 ((
% 131.56/22.77 (subset2powerset) =>
% 131.56/22.77 ((
% 131.56/22.77 (setextsub) =>
% 131.56/22.77 ((
% 131.56/22.77 (subsetemptysetimpeq) =>
% 131.56/22.77 ((
% 131.56/22.77 (powersetI1) =>
% 131.56/22.77 ((
% 131.56/22.77 (powersetE1) =>
% 131.56/22.77 ((
% 131.56/22.77 (inPowerset) =>
% 131.56/22.77 ((
% 131.56/22.77 (powersetsubset) =>
% 131.56/22.77 ((
% 131.56/22.77 (sepInPowerset) =>
% 131.56/22.77 ((
% 131.56/22.77 (sepSubset) =>
% 131.56/22.77 ((
% 131.56/22.77 (binunionIL) =>
% 131.56/22.77 ((
% 131.56/22.77 (upairset2IR) =>
% 131.56/22.77 ((
% 131.56/22.77 (binunionIR) =>
% 131.56/22.77 ((
% 131.56/22.77 (binunionEcases) =>
% 131.56/22.77 ((
% 131.56/22.77 (binunionE) =>
% 131.56/22.77 ((
% 131.56/22.77 (binunionLsub) =>
% 131.56/22.77 ((
% 131.56/22.77 (binunionRsub) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectI) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectSubset5) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectEL) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectLsub) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectSubset2) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectSubset3) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectER) =>
% 131.56/22.77 ((
% 131.56/22.77 (disjointsetsI1) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectRsub) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectSubset4) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectSubset1) =>
% 131.56/22.77 ((
% 131.56/22.77 (bs114d) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusI) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusEL) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusER) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusSubset2) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusERneg) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusELneg) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusILneg) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusIRneg) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusLsub) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusSubset1) =>
% 131.56/22.77 ((
% 131.56/22.77 (symdiffE) =>
% 131.56/22.77 ((
% 131.56/22.77 (symdiffI1) =>
% 131.56/22.77 ((
% 131.56/22.77 (symdiffI2) =>
% 131.56/22.77 ((
% 131.56/22.77 (symdiffIneg1) =>
% 131.56/22.77 ((
% 131.56/22.77 (symdiffIneg2) =>
% 131.56/22.77 ((
% 131.56/22.77 (secondinupair) =>
% 131.56/22.77 ((
% 131.56/22.77 (setukpairIL) =>
% 131.56/22.77 ((
% 131.56/22.77 (setukpairIR) =>
% 131.56/22.77 ((
% 131.56/22.77 (kpairiskpair) =>
% 131.56/22.77 ((
% 131.56/22.77 (kpairp) =>
% 131.56/22.77 ((
% 131.56/22.77 (singletonsubset) =>
% 131.56/22.77 ((
% 131.56/22.77 (singletoninpowerset) =>
% 131.56/22.77 ((
% 131.56/22.77 (singletoninpowunion) =>
% 131.56/22.77 ((
% 131.56/22.77 (upairset2E) =>
% 131.56/22.77 ((
% 131.56/22.77 (upairsubunion) =>
% 131.56/22.77 ((
% 131.56/22.77 (upairinpowunion) =>
% 131.56/22.77 ((
% 131.56/22.77 (ubforcartprodlem1) =>
% 131.56/22.77 ((
% 131.56/22.77 (ubforcartprodlem2) =>
% 131.56/22.77 ((
% 131.56/22.77 (ubforcartprodlem3) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodpairin) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodmempair1) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodmempair) =>
% 131.56/22.77 ((
% 131.56/22.77 (setunionE2) =>
% 131.56/22.77 ((
% 131.56/22.77 (setunionsingleton1) =>
% 131.56/22.77 ((
% 131.56/22.77 (setunionsingleton2) =>
% 131.56/22.77 ((
% 131.56/22.77 (setunionsingleton) =>
% 131.56/22.77 ((
% 131.56/22.77 (singletonprop) =>
% 131.56/22.77 ((
% 131.56/22.77 (ex1E1) =>
% 131.56/22.77 ((
% 131.56/22.77 (ex1I) =>
% 131.56/22.77 ((
% 131.56/22.77 (ex1I2) =>
% 131.56/22.77 ((
% 131.56/22.77 (singletonsuniq) =>
% 131.56/22.77 ((
% 131.56/22.77 (setukpairinjL1) =>
% 131.56/22.77 ((
% 131.56/22.77 (kfstsingleton) =>
% 131.56/22.77 ((
% 131.56/22.77 (theprop) =>
% 131.56/22.77 ((
% 131.56/22.77 (kfstpairEq) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodfstin) =>
% 131.56/22.77 ((
% 131.56/22.77 (setukpairinjL2) =>
% 131.56/22.77 ((
% 131.56/22.77 (setukpairinjL) =>
% 131.56/22.77 ((
% 131.56/22.77 (setukpairinjR11) =>
% 131.56/22.77 ((
% 131.56/22.77 (setukpairinjR12) =>
% 131.56/22.77 ((
% 131.56/22.77 (setukpairinjR1) =>
% 131.56/22.77 ((
% 131.56/22.77 (upairequniteq) =>
% 131.56/22.77 ((
% 131.56/22.77 (setukpairinjR2) =>
% 131.56/22.77 ((
% 131.56/22.77 (setukpairinjR) =>
% 131.56/22.77 ((
% 131.56/22.77 (ksndsingleton) =>
% 131.56/22.77 ((
% 131.56/22.77 (ksndpairEq) =>
% 131.56/22.77 ((
% 131.56/22.77 (kpairsurjEq) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodsndin) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodpairmemEL) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodpairmemER) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodmempaircEq) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodfstpairEq) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodsndpairEq) =>
% 131.56/22.77 ((
% 131.56/22.77 (cartprodpairsurjEq) =>
% 131.56/22.77 ((
% 131.56/22.77 (dpsetconstrI) =>
% 131.56/22.77 ((
% 131.56/22.77 (dpsetconstrSub) =>
% 131.56/22.77 ((
% 131.56/22.77 (setOfPairsIsBReln) =>
% 131.56/22.77 ((
% 131.56/22.77 (dpsetconstrERa) =>
% 131.56/22.77 ((
% 131.56/22.77 (dpsetconstrEL1) =>
% 131.56/22.77 ((
% 131.56/22.77 (dpsetconstrEL2) =>
% 131.56/22.77 ((
% 131.56/22.77 (dpsetconstrER) =>
% 131.56/22.77 ((
% 131.56/22.77 (funcImageSingleton) =>
% 131.56/22.77 ((
% 131.56/22.77 (apProp) =>
% 131.56/22.77 ((
% 131.56/22.77 (app) =>
% 131.56/22.77 ((
% 131.56/22.77 (infuncsetfunc) =>
% 131.56/22.77 ((
% 131.56/22.77 (ap2p) =>
% 131.56/22.77 ((
% 131.56/22.77 (funcinfuncset) =>
% 131.56/22.77 ((
% 131.56/22.77 (lamProp) =>
% 131.56/22.77 ((
% 131.56/22.77 (lamp) =>
% 131.56/22.77 ((
% 131.56/22.77 (lam2p) =>
% 131.56/22.77 ((
% 131.56/22.77 (brelnall1) =>
% 131.56/22.77 ((
% 131.56/22.77 (brelnall2) =>
% 131.56/22.77 ((
% 131.56/22.77 (ex1E2) =>
% 131.56/22.77 ((
% 131.56/22.77 (funcGraphProp1) =>
% 131.56/22.77 ((
% 131.56/22.77 (funcGraphProp3) =>
% 131.56/22.77 ((
% 131.56/22.77 (funcGraphProp2) =>
% 131.56/22.77 ((
% 131.56/22.77 (funcextLem) =>
% 131.56/22.77 ((
% 131.56/22.77 (funcGraphProp4) =>
% 131.56/22.77 ((
% 131.56/22.77 (subbreln) =>
% 131.56/22.77 ((
% 131.56/22.77 (eqbreln) =>
% 131.56/22.77 ((
% 131.56/22.77 (funcext) =>
% 131.56/22.77 ((
% 131.56/22.77 (funcext2) =>
% 131.56/22.77 ((
% 131.56/22.77 (ap2apEq1) =>
% 131.56/22.77 ((
% 131.56/22.77 (ap2apEq2) =>
% 131.56/22.77 ((
% 131.56/22.77 (beta1) =>
% 131.56/22.77 ((
% 131.56/22.77 (eta1) =>
% 131.56/22.77 ((
% 131.56/22.77 (lam2lamEq) =>
% 131.56/22.77 ((
% 131.56/22.77 (beta2) =>
% 131.56/22.77 ((
% 131.56/22.77 (eta2) =>
% 131.56/22.77 ((
% 131.56/22.77 (iffalseProp1) =>
% 131.56/22.77 ((
% 131.56/22.77 (iffalseProp2) =>
% 131.56/22.77 ((
% 131.56/22.77 (iftrueProp1) =>
% 131.56/22.77 ((
% 131.56/22.77 (iftrueProp2) =>
% 131.56/22.77 ((
% 131.56/22.77 (ifSingleton) =>
% 131.56/22.77 ((
% 131.56/22.77 (ifp) =>
% 131.56/22.77 ((
% 131.56/22.77 (theeq) =>
% 131.56/22.77 ((
% 131.56/22.77 (iftrue) =>
% 131.56/22.77 ((
% 131.56/22.77 (iffalse) =>
% 131.56/22.77 ((
% 131.56/22.77 (iftrueorfalse) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectT_lem) =>
% 131.56/22.77 ((
% 131.56/22.77 (binunionT_lem) =>
% 131.56/22.77 ((
% 131.56/22.77 (powersetT_lem) =>
% 131.56/22.77 ((
% 131.56/22.77 (setminusT_lem) =>
% 131.56/22.77 ((
% 131.56/22.77 (complementT_lem) =>
% 131.56/22.77 ((
% 131.56/22.77 (setextT) =>
% 131.56/22.77 ((
% 131.56/22.77 (subsetTI) =>
% 131.56/22.77 ((
% 131.56/22.77 (powersetTI1) =>
% 131.56/22.77 ((
% 131.56/22.77 (powersetTE1) =>
% 131.56/22.77 ((
% 131.56/22.77 (complementTI1) =>
% 131.56/22.77 ((
% 131.56/22.77 (complementTE1) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectTELcontra) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintersectTERcontra) =>
% 131.56/22.77 ((
% 131.56/22.77 (contrasubsetT) =>
% 131.56/22.77 ((
% 131.56/22.77 (contrasubsetT1) =>
% 131.56/22.77 ((
% 131.56/22.77 (contrasubsetT2) =>
% 131.56/22.77 ((
% 131.56/22.77 (contrasubsetT3) =>
% 131.56/22.77 ((
% 131.56/22.77 (doubleComplementI1) =>
% 131.56/22.77 ((
% 131.56/22.77 (doubleComplementE1) =>
% 131.56/22.77 ((
% 131.56/22.77 (doubleComplementSub1) =>
% 131.56/22.77 ((
% 131.56/22.77 (doubleComplementSub2) =>
% 131.56/22.77 ((
% 131.56/22.77 (doubleComplementEq) =>
% 131.56/22.77 ((
% 131.56/22.77 (complementTnotintersectT) =>
% 131.56/22.77 ((
% 131.56/22.77 (complementImpComplementIntersect) =>
% 131.56/22.77 ((
% 131.56/22.77 (complementSubsetComplementIntersect) =>
% 131.56/22.77 ((
% 131.56/22.77 (complementInPowersetComplementIntersect) =>
% 131.56/22.77 ((
% 131.56/22.77 (contraSubsetComplement) =>
% 131.56/22.77 ((
% 131.56/22.77 (complementTcontraSubset) =>
% 131.56/22.77 ((
% 131.56/22.77 (binunionTILcontra) =>
% 131.56/22.77 ((
% 131.56/22.77 (binunionTIRcontra) =>
% 131.56/22.77 ((
% 131.56/22.77 (inIntersectImpInUnion) =>
% 131.56/22.77 ((
% 131.56/22.77 (inIntersectImpInUnion2) =>
% 131.56/22.77 ((
% 131.56/22.77 (inIntersectImpInIntersectUnions) =>
% 131.56/22.77 ((
% 131.56/22.77 (intersectInPowersetIntersectUnions) =>
% 131.56/22.77 ((
% 131.56/22.77 (inComplementUnionImpNotIn1) =>
% 131.56/22.77 ((
% 131.56/22.77 (inComplementUnionImpInComplement1) =>
% 131.56/22.77 ((
% 131.56/22.77 (binunionTE) =>
% 131.56/22.77 ((
% 131.56/22.77 (binunionTEcontra) =>
% 131.56/22.77 ((
% 131.56/22.77 (demorgan2a1) =>
% 131.56/22.77 ((
% 131.56/22.77 (complementUnionInPowersetComplement) =>
% 131.56/22.77 ((
% 131.56/22.77 (demorgan2a2) =>
% 131.56/22.77 ((
% 131.56/22.77 (demorgan1a) =>
% 131.56/22.77 ((
% 131.56/22.77 (demorgan1b) =>
% 131.56/22.77 ((
% 131.56/22.77 (demorgan1) =>
% 131.56/22.77 ((
% 131.56/22.77 (demorgan2a) =>
% 131.56/22.77 ((
% 131.56/22.77 (demorgan2b2) =>
% 131.56/22.77 ((
% 131.56/22.77 (demorgan2b) =>
% 131.56/22.77 ((
% 131.56/22.77 (demorgan2) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz13rule0) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz13rule1) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz13rule2) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz13rule3) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz13rule4) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz1_1) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz1_2) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz1_3) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz1_4) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz1_5) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1all2) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1SetBreln1) =>
% 131.56/22.77 ((
% 131.56/22.77 (choice2fnsingleton) =>
% 131.56/22.77 ((
% 131.56/22.77 (setOfPairsIsBReln1) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1all1) =>
% 131.56/22.77 ((
% 131.56/22.77 (subbreln1) =>
% 131.56/22.77 ((
% 131.56/22.77 (eqbreln1) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1invprop) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1invI) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1invE) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1compprop) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1compI) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1compE) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1compEex) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1unionprop) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1unionIL) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1unionIR) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1unionI) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1unionE) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1unionEcases) =>
% 131.56/22.77 ((
% 131.56/22.77 (breln1unionCommutes) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz2Ex) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz2W) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz2A) =>
% 131.56/22.77 ((
% 131.56/22.77 (woz2B) =>
% 131.56/22.77 ((
% 131.56/22.77 (image1Ex) =>
% 131.56/22.77 ((
% 131.56/22.77 (image1Ex1) =>
% 131.56/22.77 ((
% 131.56/22.77 (image1Equiv) =>
% 131.56/22.77 ((
% 131.56/22.77 (image1E) =>
% 131.56/22.77 ((
% 131.56/22.77 (image1I) =>
% 131.56/22.77 ((
% 131.56/22.77 (injFuncInInjFuncSet) =>
% 131.56/22.77 ((
% 131.56/22.77 (injFuncSetFuncIn) =>
% 131.56/22.77 ((
% 131.56/22.77 (injFuncSetFuncInj) =>
% 131.56/22.77 ((
% 131.56/22.77 (surjFuncSetFuncIn) =>
% 131.56/22.77 ((
% 131.56/22.77 (surjFuncSetFuncSurj) =>
% 131.56/22.77 ((
% 131.56/22.77 (leftInvIsSurj) =>
% 131.56/22.77 ((
% 131.56/22.77 (surjCantorThm) =>
% 131.56/22.77 ((
% 131.56/22.77 (foundation2) =>
% 131.56/22.77 ((
% 131.56/22.77 (notinself) =>
% 131.56/22.77 ((
% 131.56/22.77 (notinself2) =>
% 131.56/22.77 ((
% 131.56/22.77 (omegaSp) =>
% 131.56/22.77 ((
% 131.56/22.77 (omegaSclos) =>
% 131.56/22.77 ((
% 131.56/22.77 (peano0notS) =>
% 131.56/22.77 ((
% 131.56/22.77 (peanoSinj) =>
% 131.56/22.77 ((
% 131.56/22.77 (transitivesetOp1) =>
% 131.56/22.77 ((
% 131.56/22.77 (binintTransitive) =>
% 131.56/22.77 ((
% 131.56/22.77 (transitivesetOp2) =>
% 131.56/22.77 ((
% 131.56/22.77 (setunionTransitive) =>
% 131.56/22.77 ((
% 131.56/22.77 (ordinalMinLem1) =>
% 131.56/22.77 ((
% 131.56/22.77 (ordinalTransSet) =>
% 131.56/22.77 ((
% 131.56/22.77 (ordinalTransSet1) =>
% 131.56/22.77 ((
% 131.56/22.77 (setunionOrdinalLem1) =>
% 131.56/22.77 (ordinal @
% 131.56/22.77 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 131.56/22.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl205])).
% 131.56/22.77 thf(zip_derived_cl231, plain,
% 131.56/22.77 (~ (((setbeta) =>
% 131.56/22.77 (((nonemptyE1) =>
% 131.56/22.77 (((nonemptyI) =>
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% 131.56/22.78 ((
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% 131.56/22.78 ((
% 131.56/22.78 (omegaSp) =>
% 131.56/22.78 ((
% 131.56/22.78 (omegaSclos) =>
% 131.56/22.78 ((
% 131.56/22.78 (peano0notS) =>
% 131.56/22.78 ((
% 131.56/22.78 (peanoSinj) =>
% 131.56/22.78 ((
% 131.56/22.78 (transitivesetOp1) =>
% 131.56/22.78 ((
% 131.56/22.78 (binintTransitive) =>
% 131.56/22.78 ((
% 131.56/22.78 (transitivesetOp2) =>
% 131.56/22.78 ((
% 131.56/22.78 (setunionTransitive) =>
% 131.56/22.78 ((
% 131.56/22.78 (ordinalMinLem1) =>
% 131.56/22.78 ((
% 131.56/22.78 (ordinalTransSet) =>
% 131.56/22.78 ((
% 131.56/22.78 (ordinalTransSet1) =>
% 131.56/22.78 ((
% 131.56/22.78 (setunionOrdinalLem1) =>
% 131.56/22.78 (ordinal @
% 131.56/22.78 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 131.56/22.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl219])).
% 131.56/22.78 thf(zip_derived_cl244, plain,
% 131.56/22.78 (~ (((nonemptyE1) =>
% 131.56/22.78 (((nonemptyI) =>
% 131.56/22.78 (((nonemptyI1) =>
% 131.56/22.78 (((setadjoinIL) =>
% 131.56/22.78 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 131.56/22.78 (((setadjoinIR) =>
% 131.56/22.78 (((setadjoinE) =>
% 131.56/22.78 (((setadjoinOr) =>
% 131.56/22.78 (((setoftrueEq) =>
% 131.56/22.78 (((powersetI) =>
% 131.56/22.78 (((emptyinPowerset) =>
% 131.56/22.78 (((emptyInPowerset) =>
% 131.56/22.78 (((powersetE) =>
% 131.56/22.78 (((setunionI) =>
% 131.56/22.78 (((setunionE) =>
% 131.56/22.78 (((subPowSU) =>
% 131.56/22.78 (((exuE2) =>
% 131.56/22.78 (((nonemptyImpWitness) =>
% 131.56/22.78 (((uniqinunit) =>
% 131.56/22.78 (((notinsingleton) =>
% 131.56/22.78 (((eqinunit) =>
% 131.56/22.78 (((singletonsswitch) =>
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% 131.56/22.78 (((upairsetIL) =>
% 131.56/22.78 (((upairsetIR) =>
% 131.56/22.78 (((emptyE1) =>
% 131.56/22.78 (((vacuousDall) =>
% 131.56/22.78 (((quantDeMorgan1) =>
% 131.56/22.78 (((quantDeMorgan2) =>
% 131.56/22.78 (((quantDeMorgan3) =>
% 131.56/22.78 ((
% 131.56/22.78 (quantDeMorgan4) =>
% 131.56/22.78 ((
% 131.56/22.78 (prop2setI) =>
% 131.56/22.78 ((
% 131.56/22.78 (prop2set2propI) =>
% 131.56/22.78 ((
% 131.56/22.78 (notdexE) =>
% 131.56/22.78 ((
% 131.56/22.78 (notdallE) =>
% 131.56/22.78 ((
% 131.56/22.78 (exuI1) =>
% 131.56/22.78 ((
% 131.56/22.78 (exuI3) =>
% 131.56/22.78 ((
% 131.56/22.78 (exuI2) =>
% 131.56/22.78 ((
% 131.56/22.78 (inCongP) =>
% 131.56/22.78 ((
% 131.56/22.78 (in__Cong) =>
% 131.56/22.78 ((
% 131.56/22.78 (exuE3u) =>
% 131.56/22.78 ((
% 131.56/22.78 (exu__Cong) =>
% 131.56/22.78 ((
% 131.56/22.78 (setadjoin__Cong) =>
% 131.56/22.78 ((
% 131.56/22.78 (powerset__Cong) =>
% 131.56/22.78 ((
% 131.56/22.78 (setunion__Cong) =>
% 131.56/22.78 ((
% 131.56/22.78 (exuEu) =>
% 131.56/22.78 ((
% 131.56/22.78 (descr__Cong) =>
% 131.56/22.78 ((
% 131.56/22.78 (dsetconstr__Cong) =>
% 131.56/22.78 ((
% 131.56/22.78 (subsetI1) =>
% 131.56/22.78 ((
% 131.56/22.78 (eqimpsubset2) =>
% 131.56/22.78 ((
% 131.56/22.78 (eqimpsubset1) =>
% 131.56/22.78 ((
% 131.56/22.78 (subsetI2) =>
% 131.56/22.78 ((
% 131.56/22.78 (emptysetsubset) =>
% 131.56/22.78 ((
% 131.56/22.78 (subsetE) =>
% 131.56/22.78 ((
% 131.56/22.78 (subsetE2) =>
% 131.56/22.78 ((
% 131.56/22.78 (notsubsetI) =>
% 131.56/22.78 ((
% 131.56/22.78 (notequalI1) =>
% 131.56/22.78 ((
% 131.56/22.78 (notequalI2) =>
% 131.56/22.78 ((
% 131.56/22.78 (subsetRefl) =>
% 131.56/22.78 ((
% 131.56/22.78 (subsetTrans) =>
% 131.56/22.78 ((
% 131.56/22.78 (setadjoinSub) =>
% 131.56/22.78 ((
% 131.56/22.78 (setadjoinSub2) =>
% 131.56/22.78 ((
% 131.56/22.78 (subset2powerset) =>
% 131.56/22.78 ((
% 131.56/22.78 (setextsub) =>
% 131.56/22.78 ((
% 131.56/22.78 (subsetemptysetimpeq) =>
% 131.56/22.78 ((
% 131.56/22.78 (powersetI1) =>
% 131.56/22.78 ((
% 131.56/22.78 (powersetE1) =>
% 131.56/22.78 ((
% 131.56/22.78 (inPowerset) =>
% 131.56/22.78 ((
% 131.56/22.78 (powersetsubset) =>
% 131.56/22.78 ((
% 131.56/22.78 (sepInPowerset) =>
% 131.56/22.78 ((
% 131.56/22.78 (sepSubset) =>
% 131.56/22.78 ((
% 131.56/22.78 (binunionIL) =>
% 131.56/22.78 ((
% 131.56/22.78 (upairset2IR) =>
% 131.56/22.78 ((
% 131.56/22.78 (binunionIR) =>
% 131.56/22.78 ((
% 131.56/22.78 (binunionEcases) =>
% 131.56/22.78 ((
% 131.56/22.78 (binunionE) =>
% 131.56/22.78 ((
% 131.56/22.78 (binunionLsub) =>
% 131.56/22.78 ((
% 131.56/22.78 (binunionRsub) =>
% 131.56/22.78 ((
% 131.56/22.78 (binintersectI) =>
% 131.56/22.78 ((
% 131.56/22.78 (binintersectSubset5) =>
% 131.56/22.78 ((
% 131.56/22.78 (binintersectEL) =>
% 131.56/22.78 ((
% 131.56/22.78 (binintersectLsub) =>
% 131.56/22.78 ((
% 131.56/22.78 (binintersectSubset2) =>
% 131.56/22.78 ((
% 131.56/22.78 (binintersectSubset3) =>
% 131.56/22.78 ((
% 131.56/22.78 (binintersectER) =>
% 131.56/22.78 ((
% 131.56/22.78 (disjointsetsI1) =>
% 131.56/22.78 ((
% 131.56/22.78 (binintersectRsub) =>
% 131.56/22.78 ((
% 131.56/22.78 (binintersectSubset4) =>
% 131.56/22.78 ((
% 131.56/22.78 (binintersectSubset1) =>
% 131.56/22.78 ((
% 131.56/22.78 (bs114d) =>
% 131.56/22.78 ((
% 131.56/22.78 (setminusI) =>
% 131.56/22.78 ((
% 131.56/22.78 (setminusEL) =>
% 131.56/22.78 ((
% 131.56/22.78 (setminusER) =>
% 131.56/22.78 ((
% 131.56/22.78 (setminusSubset2) =>
% 131.56/22.78 ((
% 131.56/22.78 (setminusERneg) =>
% 131.56/22.78 ((
% 131.56/22.78 (setminusELneg) =>
% 131.56/22.78 ((
% 131.56/22.78 (setminusILneg) =>
% 131.56/22.78 ((
% 131.56/22.78 (setminusIRneg) =>
% 131.56/22.78 ((
% 131.56/22.78 (setminusLsub) =>
% 131.56/22.78 ((
% 131.56/22.78 (setminusSubset1) =>
% 131.56/22.78 ((
% 131.56/22.78 (symdiffE) =>
% 131.56/22.78 ((
% 131.56/22.78 (symdiffI1) =>
% 131.56/22.78 ((
% 131.56/22.78 (symdiffI2) =>
% 131.56/22.78 ((
% 131.56/22.78 (symdiffIneg1) =>
% 131.56/22.78 ((
% 131.56/22.78 (symdiffIneg2) =>
% 131.56/22.78 ((
% 131.56/22.78 (secondinupair) =>
% 131.56/22.78 ((
% 131.56/22.78 (setukpairIL) =>
% 131.56/22.78 ((
% 131.56/22.78 (setukpairIR) =>
% 131.56/22.78 ((
% 131.56/22.78 (kpairiskpair) =>
% 131.56/22.78 ((
% 131.56/22.78 (kpairp) =>
% 131.56/22.78 ((
% 131.56/22.78 (singletonsubset) =>
% 131.56/22.78 ((
% 131.56/22.78 (singletoninpowerset) =>
% 131.56/22.78 ((
% 131.56/22.78 (singletoninpowunion) =>
% 131.56/22.78 ((
% 131.56/22.78 (upairset2E) =>
% 131.56/22.78 ((
% 131.56/22.78 (upairsubunion) =>
% 131.56/22.78 ((
% 131.56/22.78 (upairinpowunion) =>
% 131.56/22.78 ((
% 131.56/22.78 (ubforcartprodlem1) =>
% 131.56/22.78 ((
% 131.56/22.78 (ubforcartprodlem2) =>
% 131.56/22.78 ((
% 131.56/22.78 (ubforcartprodlem3) =>
% 131.56/22.78 ((
% 131.56/22.78 (cartprodpairin) =>
% 131.56/22.78 ((
% 131.56/22.78 (cartprodmempair1) =>
% 131.56/22.78 ((
% 131.56/22.78 (cartprodmempair) =>
% 131.56/22.78 ((
% 131.56/22.78 (setunionE2) =>
% 131.56/22.78 ((
% 131.56/22.78 (setunionsingleton1) =>
% 131.56/22.78 ((
% 131.56/22.78 (setunionsingleton2) =>
% 131.56/22.78 ((
% 131.56/22.78 (setunionsingleton) =>
% 131.56/22.78 ((
% 131.56/22.78 (singletonprop) =>
% 131.56/22.78 ((
% 131.56/22.78 (ex1E1) =>
% 131.56/22.78 ((
% 131.56/22.78 (ex1I) =>
% 131.56/22.78 ((
% 131.56/22.78 (ex1I2) =>
% 131.56/22.78 ((
% 131.56/22.78 (singletonsuniq) =>
% 131.56/22.78 ((
% 131.56/22.78 (setukpairinjL1) =>
% 131.56/22.78 ((
% 131.56/22.78 (kfstsingleton) =>
% 131.56/22.78 ((
% 131.56/22.78 (theprop) =>
% 131.56/22.78 ((
% 131.56/22.78 (kfstpairEq) =>
% 131.56/22.78 ((
% 131.56/22.78 (cartprodfstin) =>
% 131.56/22.78 ((
% 131.56/22.78 (setukpairinjL2) =>
% 131.56/22.78 ((
% 131.56/22.78 (setukpairinjL) =>
% 131.56/22.78 ((
% 131.56/22.78 (setukpairinjR11) =>
% 131.56/22.78 ((
% 131.56/22.78 (setukpairinjR12) =>
% 131.56/22.78 ((
% 131.56/22.78 (setukpairinjR1) =>
% 131.56/22.78 ((
% 131.56/22.78 (upairequniteq) =>
% 131.56/22.78 ((
% 131.56/22.78 (setukpairinjR2) =>
% 131.56/22.78 ((
% 131.56/22.78 (setukpairinjR) =>
% 131.56/22.78 ((
% 131.56/22.78 (ksndsingleton) =>
% 131.56/22.78 ((
% 131.56/22.78 (ksndpairEq) =>
% 131.56/22.78 ((
% 131.56/22.78 (kpairsurjEq) =>
% 131.56/22.78 ((
% 131.56/22.78 (cartprodsndin) =>
% 131.56/22.78 ((
% 131.56/22.78 (cartprodpairmemEL) =>
% 131.56/22.78 ((
% 131.56/22.78 (cartprodpairmemER) =>
% 131.56/22.78 ((
% 131.56/22.78 (cartprodmempaircEq) =>
% 131.56/22.78 ((
% 131.56/22.78 (cartprodfstpairEq) =>
% 131.56/22.78 ((
% 131.56/22.78 (cartprodsndpairEq) =>
% 131.56/22.78 ((
% 131.56/22.78 (cartprodpairsurjEq) =>
% 131.56/22.78 ((
% 131.56/22.78 (dpsetconstrI) =>
% 131.56/22.78 ((
% 131.56/22.78 (dpsetconstrSub) =>
% 131.56/22.78 ((
% 131.56/22.78 (setOfPairsIsBReln) =>
% 131.56/22.78 ((
% 131.56/22.78 (dpsetconstrERa) =>
% 131.56/22.78 ((
% 131.56/22.78 (dpsetconstrEL1) =>
% 131.56/22.78 ((
% 131.56/22.78 (dpsetconstrEL2) =>
% 131.56/22.78 ((
% 131.56/22.78 (dpsetconstrER) =>
% 131.56/22.78 ((
% 131.56/22.78 (funcImageSingleton) =>
% 131.56/22.78 ((
% 131.56/22.78 (apProp) =>
% 131.56/22.78 ((
% 131.56/22.78 (app) =>
% 131.56/22.78 ((
% 131.56/22.78 (infuncsetfunc) =>
% 131.56/22.78 ((
% 131.56/22.78 (ap2p) =>
% 131.56/22.78 ((
% 131.56/22.78 (funcinfuncset) =>
% 131.56/22.78 ((
% 131.56/22.78 (lamProp) =>
% 131.56/22.78 ((
% 131.56/22.78 (lamp) =>
% 131.56/22.78 ((
% 131.56/22.78 (lam2p) =>
% 131.56/22.78 ((
% 131.56/22.78 (brelnall1) =>
% 131.56/22.78 ((
% 131.56/22.78 (brelnall2) =>
% 131.56/22.78 ((
% 131.56/22.78 (ex1E2) =>
% 131.56/22.78 ((
% 131.56/22.78 (funcGraphProp1) =>
% 131.56/22.78 ((
% 131.56/22.78 (funcGraphProp3) =>
% 131.56/22.78 ((
% 131.56/22.78 (funcGraphProp2) =>
% 131.56/22.78 ((
% 131.56/22.78 (funcextLem) =>
% 131.56/22.78 ((
% 131.56/22.78 (funcGraphProp4) =>
% 131.56/22.78 ((
% 131.56/22.78 (subbreln) =>
% 131.56/22.78 ((
% 131.56/22.78 (eqbreln) =>
% 131.56/22.78 ((
% 131.56/22.78 (funcext) =>
% 131.56/22.78 ((
% 131.56/22.78 (funcext2) =>
% 131.56/22.78 ((
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% 131.56/22.78 ((
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% 131.56/22.78 ((
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% 131.56/22.78 ((
% 131.56/22.78 (eta1) =>
% 131.56/22.78 ((
% 131.56/22.78 (lam2lamEq) =>
% 131.56/22.78 ((
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% 131.56/22.78 ((
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% 131.56/22.78 ((
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% 131.56/22.78 (iftrueProp1) =>
% 131.56/22.78 ((
% 131.56/22.78 (iftrueProp2) =>
% 131.56/22.78 ((
% 131.56/22.78 (ifSingleton) =>
% 131.56/22.78 ((
% 131.56/22.78 (ifp) =>
% 131.56/22.78 ((
% 131.56/22.78 (theeq) =>
% 131.56/22.78 ((
% 131.56/22.78 (iftrue) =>
% 131.56/22.78 ((
% 131.56/22.78 (iffalse) =>
% 131.56/22.78 ((
% 131.56/22.78 (iftrueorfalse) =>
% 131.56/22.78 ((
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% 131.56/22.78 ((
% 131.56/22.78 (binunionT_lem) =>
% 131.56/22.78 ((
% 131.56/22.78 (powersetT_lem) =>
% 131.56/22.78 ((
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% 131.56/22.78 ((
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% 131.56/22.78 ((
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% 131.56/22.78 ((
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% 131.56/22.78 ((
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% 131.56/22.78 ((
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% 131.56/22.78 ((
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% 131.56/22.78 ((
% 131.56/22.78 (doubleComplementE1) =>
% 131.56/22.78 ((
% 131.56/22.78 (doubleComplementSub1) =>
% 131.56/22.78 ((
% 131.56/22.78 (doubleComplementSub2) =>
% 131.56/22.78 ((
% 131.56/22.78 (doubleComplementEq) =>
% 131.56/22.78 ((
% 131.56/22.78 (complementTnotintersectT) =>
% 131.56/22.78 ((
% 131.56/22.78 (complementImpComplementIntersect) =>
% 131.56/22.78 ((
% 131.56/22.78 (complementSubsetComplementIntersect) =>
% 131.56/22.78 ((
% 131.56/22.78 (complementInPowersetComplementIntersect) =>
% 131.56/22.78 ((
% 131.56/22.78 (contraSubsetComplement) =>
% 131.56/22.78 ((
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% 131.56/22.78 ((
% 131.56/22.78 (inIntersectImpInUnion2) =>
% 131.56/22.78 ((
% 131.56/22.78 (inIntersectImpInIntersectUnions) =>
% 131.56/22.78 ((
% 131.56/22.78 (intersectInPowersetIntersectUnions) =>
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% 131.56/22.78 (inComplementUnionImpNotIn1) =>
% 131.56/22.78 ((
% 131.56/22.78 (inComplementUnionImpInComplement1) =>
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% 131.56/22.78 ((
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% 131.56/22.78 ((
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% 131.56/22.78 (breln1unionE) =>
% 131.56/22.78 ((
% 131.56/22.78 (breln1unionEcases) =>
% 131.56/22.78 ((
% 131.56/22.78 (breln1unionCommutes) =>
% 131.56/22.78 ((
% 131.56/22.78 (woz2Ex) =>
% 131.56/22.78 ((
% 131.56/22.78 (woz2W) =>
% 131.56/22.78 ((
% 131.56/22.78 (woz2A) =>
% 131.56/22.78 ((
% 131.56/22.78 (woz2B) =>
% 131.56/22.78 ((
% 131.56/22.78 (image1Ex) =>
% 131.56/22.78 ((
% 131.56/22.78 (image1Ex1) =>
% 131.56/22.78 ((
% 131.56/22.78 (image1Equiv) =>
% 131.56/22.78 ((
% 131.56/22.78 (image1E) =>
% 131.56/22.78 ((
% 131.56/22.78 (image1I) =>
% 131.56/22.78 ((
% 131.56/22.78 (injFuncInInjFuncSet) =>
% 131.56/22.78 ((
% 131.56/22.78 (injFuncSetFuncIn) =>
% 131.56/22.78 ((
% 131.56/22.78 (injFuncSetFuncInj) =>
% 131.56/22.78 ((
% 131.56/22.78 (surjFuncSetFuncIn) =>
% 131.56/22.78 ((
% 131.56/22.78 (surjFuncSetFuncSurj) =>
% 131.56/22.78 ((
% 131.56/22.78 (leftInvIsSurj) =>
% 131.56/22.78 ((
% 131.56/22.78 (surjCantorThm) =>
% 131.56/22.78 ((
% 131.56/22.78 (foundation2) =>
% 131.56/22.78 ((
% 131.56/22.78 (notinself) =>
% 131.56/22.78 ((
% 131.56/22.78 (notinself2) =>
% 131.56/22.78 ((
% 131.56/22.78 (omegaSp) =>
% 131.56/22.78 ((
% 131.56/22.78 (omegaSclos) =>
% 131.56/22.78 ((
% 131.56/22.78 (peano0notS) =>
% 131.56/22.78 ((
% 131.56/22.78 (peanoSinj) =>
% 131.56/22.78 ((
% 131.56/22.78 (transitivesetOp1) =>
% 131.56/22.78 ((
% 131.56/22.78 (binintTransitive) =>
% 131.56/22.78 ((
% 131.56/22.78 (transitivesetOp2) =>
% 131.56/22.78 ((
% 131.56/22.78 (setunionTransitive) =>
% 131.56/22.78 ((
% 131.56/22.78 (ordinalMinLem1) =>
% 131.56/22.78 ((
% 131.56/22.78 (ordinalTransSet) =>
% 131.56/22.78 ((
% 131.56/22.78 (ordinalTransSet1) =>
% 131.56/22.78 ((
% 131.56/22.78 (setunionOrdinalLem1) =>
% 131.56/22.78 (ordinal @
% 131.56/22.78 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 131.56/22.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl231])).
% 131.56/22.78 thf(zip_derived_cl258, plain,
% 131.56/22.78 (~ (((nonemptyI) =>
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% 131.56/22.78 (((setadjoinE) =>
% 131.56/22.78 (((setadjoinOr) =>
% 131.56/22.78 (((setoftrueEq) =>
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% 131.56/22.78 (((emptyinPowerset) =>
% 131.56/22.78 (((emptyInPowerset) =>
% 131.56/22.78 (((powersetE) =>
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% 131.56/22.78 (((setunionE) =>
% 131.56/22.78 (((subPowSU) =>
% 131.56/22.78 (((exuE2) =>
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% 131.56/22.78 (((upairsetIR) =>
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% 131.56/22.78 (((quantDeMorgan1) =>
% 131.56/22.78 (((quantDeMorgan2) =>
% 131.56/22.78 (((quantDeMorgan3) =>
% 131.56/22.78 (((quantDeMorgan4) =>
% 131.56/22.78 ((
% 131.56/22.78 (prop2setI) =>
% 131.56/22.78 ((
% 131.56/22.78 (prop2set2propI) =>
% 131.56/22.78 ((
% 131.56/22.78 (notdexE) =>
% 131.56/22.78 ((
% 131.56/22.78 (notdallE) =>
% 131.56/22.78 ((
% 131.56/22.78 (exuI1) =>
% 131.56/22.78 ((
% 131.56/22.78 (exuI3) =>
% 131.56/22.78 ((
% 131.56/22.78 (exuI2) =>
% 131.56/22.78 ((
% 131.56/22.78 (inCongP) =>
% 131.56/22.78 ((
% 131.56/22.78 (in__Cong) =>
% 131.56/22.78 ((
% 131.56/22.78 (exuE3u) =>
% 131.56/22.78 ((
% 131.56/22.78 (exu__Cong) =>
% 131.56/22.78 ((
% 131.56/22.78 (setadjoin__Cong) =>
% 131.56/22.78 ((
% 131.56/22.78 (powerset__Cong) =>
% 131.56/22.78 ((
% 131.56/22.78 (setunion__Cong) =>
% 131.56/22.78 ((
% 131.56/22.78 (exuEu) =>
% 131.56/22.78 ((
% 131.56/22.78 (descr__Cong) =>
% 131.56/22.78 ((
% 131.56/22.78 (dsetconstr__Cong) =>
% 131.56/22.78 ((
% 131.56/22.78 (subsetI1) =>
% 131.56/22.78 ((
% 131.56/22.78 (eqimpsubset2) =>
% 131.56/22.78 ((
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% 131.56/22.78 ((
% 131.56/22.78 (subsetI2) =>
% 131.56/22.78 ((
% 131.56/22.78 (emptysetsubset) =>
% 131.56/22.78 ((
% 131.56/22.78 (subsetE) =>
% 131.56/22.78 ((
% 131.56/22.78 (subsetE2) =>
% 131.56/22.78 ((
% 131.56/22.78 (notsubsetI) =>
% 131.56/22.78 ((
% 131.56/22.78 (notequalI1) =>
% 131.56/22.78 ((
% 131.56/22.78 (notequalI2) =>
% 131.56/22.78 ((
% 131.56/22.78 (subsetRefl) =>
% 131.56/22.78 ((
% 131.56/22.78 (subsetTrans) =>
% 131.56/22.78 ((
% 131.56/22.78 (setadjoinSub) =>
% 131.56/22.78 ((
% 131.56/22.78 (setadjoinSub2) =>
% 131.56/22.78 ((
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% 131.56/22.78 ((
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% 131.56/22.78 ((
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% 131.56/22.78 ((
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% 131.56/22.78 ((
% 131.56/22.78 (powersetE1) =>
% 131.56/22.78 ((
% 131.56/22.78 (inPowerset) =>
% 131.56/22.78 ((
% 131.56/22.78 (powersetsubset) =>
% 131.56/22.78 ((
% 131.56/22.78 (sepInPowerset) =>
% 131.56/22.78 ((
% 131.56/22.78 (sepSubset) =>
% 131.56/22.78 ((
% 131.56/22.78 (binunionIL) =>
% 131.56/22.78 ((
% 131.56/22.78 (upairset2IR) =>
% 131.56/22.78 ((
% 131.56/22.78 (binunionIR) =>
% 131.56/22.78 ((
% 131.56/22.78 (binunionEcases) =>
% 131.56/22.78 ((
% 131.56/22.78 (binunionE) =>
% 131.56/22.78 ((
% 131.56/22.78 (binunionLsub) =>
% 131.56/22.78 ((
% 131.56/22.78 (binunionRsub) =>
% 131.56/22.78 ((
% 131.56/22.78 (binintersectI) =>
% 131.56/22.78 ((
% 131.56/22.78 (binintersectSubset5) =>
% 131.56/22.78 ((
% 131.56/22.78 (binintersectEL) =>
% 131.56/22.78 ((
% 131.56/22.78 (binintersectLsub) =>
% 131.56/22.78 ((
% 131.56/22.78 (binintersectSubset2) =>
% 131.56/22.78 ((
% 131.56/22.78 (binintersectSubset3) =>
% 131.56/22.78 ((
% 131.56/22.78 (binintersectER) =>
% 131.56/22.78 ((
% 131.56/22.78 (disjointsetsI1) =>
% 131.56/22.78 ((
% 131.56/22.78 (binintersectRsub) =>
% 131.56/22.78 ((
% 131.56/22.78 (binintersectSubset4) =>
% 131.56/22.78 ((
% 131.56/22.78 (binintersectSubset1) =>
% 131.56/22.78 ((
% 131.56/22.78 (bs114d) =>
% 131.56/22.78 ((
% 131.56/22.78 (setminusI) =>
% 131.56/22.78 ((
% 131.56/22.78 (setminusEL) =>
% 131.56/22.78 ((
% 131.56/22.78 (setminusER) =>
% 131.56/22.78 ((
% 131.56/22.78 (setminusSubset2) =>
% 131.56/22.78 ((
% 131.56/22.78 (setminusERneg) =>
% 131.56/22.78 ((
% 131.56/22.78 (setminusELneg) =>
% 131.56/22.78 ((
% 131.56/22.78 (setminusILneg) =>
% 131.56/22.78 ((
% 131.56/22.78 (setminusIRneg) =>
% 131.56/22.78 ((
% 131.56/22.78 (setminusLsub) =>
% 131.56/22.78 ((
% 131.56/22.78 (setminusSubset1) =>
% 131.56/22.78 ((
% 131.56/22.78 (symdiffE) =>
% 131.56/22.78 ((
% 131.56/22.78 (symdiffI1) =>
% 131.56/22.78 ((
% 131.56/22.78 (symdiffI2) =>
% 131.56/22.78 ((
% 131.56/22.78 (symdiffIneg1) =>
% 131.56/22.78 ((
% 131.56/22.78 (symdiffIneg2) =>
% 131.56/22.78 ((
% 131.56/22.78 (secondinupair) =>
% 131.56/22.78 ((
% 131.56/22.78 (setukpairIL) =>
% 131.56/22.78 ((
% 131.56/22.78 (setukpairIR) =>
% 131.56/22.78 ((
% 131.56/22.78 (kpairiskpair) =>
% 131.56/22.78 ((
% 131.56/22.78 (kpairp) =>
% 131.56/22.78 ((
% 131.56/22.78 (singletonsubset) =>
% 131.56/22.78 ((
% 131.56/22.78 (singletoninpowerset) =>
% 131.56/22.78 ((
% 131.56/22.78 (singletoninpowunion) =>
% 131.56/22.78 ((
% 131.56/22.78 (upairset2E) =>
% 131.56/22.78 ((
% 131.56/22.78 (upairsubunion) =>
% 131.56/22.78 ((
% 131.56/22.78 (upairinpowunion) =>
% 131.56/22.78 ((
% 131.56/22.78 (ubforcartprodlem1) =>
% 131.56/22.78 ((
% 131.56/22.78 (ubforcartprodlem2) =>
% 131.56/22.78 ((
% 131.56/22.78 (ubforcartprodlem3) =>
% 131.56/22.78 ((
% 131.56/22.78 (cartprodpairin) =>
% 131.56/22.78 ((
% 131.56/22.78 (cartprodmempair1) =>
% 131.56/22.78 ((
% 131.56/22.78 (cartprodmempair) =>
% 131.56/22.78 ((
% 131.56/22.78 (setunionE2) =>
% 131.56/22.78 ((
% 131.56/22.78 (setunionsingleton1) =>
% 131.56/22.78 ((
% 131.56/22.78 (setunionsingleton2) =>
% 131.56/22.78 ((
% 131.56/22.78 (setunionsingleton) =>
% 131.56/22.78 ((
% 131.56/22.78 (singletonprop) =>
% 131.56/22.78 ((
% 131.56/22.78 (ex1E1) =>
% 131.56/22.78 ((
% 131.56/22.78 (ex1I) =>
% 131.56/22.78 ((
% 131.56/22.78 (ex1I2) =>
% 131.56/22.78 ((
% 131.56/22.78 (singletonsuniq) =>
% 131.56/22.78 ((
% 131.56/22.78 (setukpairinjL1) =>
% 131.56/22.78 ((
% 131.56/22.78 (kfstsingleton) =>
% 131.56/22.78 ((
% 131.56/22.78 (theprop) =>
% 131.56/22.78 ((
% 131.56/22.78 (kfstpairEq) =>
% 131.56/22.78 ((
% 131.56/22.78 (cartprodfstin) =>
% 131.56/22.78 ((
% 131.56/22.78 (setukpairinjL2) =>
% 131.56/22.78 ((
% 131.56/22.78 (setukpairinjL) =>
% 131.56/22.78 ((
% 131.56/22.78 (setukpairinjR11) =>
% 131.56/22.78 ((
% 131.56/22.78 (setukpairinjR12) =>
% 131.56/22.78 ((
% 131.56/22.78 (setukpairinjR1) =>
% 131.56/22.78 ((
% 131.56/22.78 (upairequniteq) =>
% 131.56/22.78 ((
% 131.56/22.78 (setukpairinjR2) =>
% 131.56/22.78 ((
% 131.56/22.78 (setukpairinjR) =>
% 131.56/22.78 ((
% 131.56/22.78 (ksndsingleton) =>
% 131.56/22.78 ((
% 131.56/22.78 (ksndpairEq) =>
% 131.56/22.78 ((
% 131.56/22.78 (kpairsurjEq) =>
% 131.56/22.78 ((
% 131.56/22.78 (cartprodsndin) =>
% 131.56/22.78 ((
% 131.56/22.78 (cartprodpairmemEL) =>
% 131.56/22.78 ((
% 131.56/22.78 (cartprodpairmemER) =>
% 131.56/22.78 ((
% 131.56/22.78 (cartprodmempaircEq) =>
% 131.56/22.78 ((
% 131.56/22.78 (cartprodfstpairEq) =>
% 131.56/22.78 ((
% 131.56/22.78 (cartprodsndpairEq) =>
% 131.56/22.78 ((
% 131.56/22.78 (cartprodpairsurjEq) =>
% 131.56/22.78 ((
% 131.56/22.78 (dpsetconstrI) =>
% 131.56/22.78 ((
% 131.56/22.78 (dpsetconstrSub) =>
% 131.56/22.78 ((
% 131.56/22.78 (setOfPairsIsBReln) =>
% 131.56/22.78 ((
% 131.56/22.78 (dpsetconstrERa) =>
% 131.56/22.78 ((
% 131.56/22.78 (dpsetconstrEL1) =>
% 131.56/22.78 ((
% 131.56/22.78 (dpsetconstrEL2) =>
% 131.56/22.78 ((
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% 131.56/22.78 ((
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% 131.56/22.78 ((
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% 131.56/22.78 ((
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% 131.56/22.79 (woz1_5) =>
% 131.56/22.79 ((
% 131.56/22.79 (breln1all2) =>
% 131.56/22.79 ((
% 131.56/22.79 (breln1SetBreln1) =>
% 131.56/22.79 ((
% 131.56/22.79 (choice2fnsingleton) =>
% 131.56/22.79 ((
% 131.56/22.79 (setOfPairsIsBReln1) =>
% 131.56/22.79 ((
% 131.56/22.79 (breln1all1) =>
% 131.56/22.79 ((
% 131.56/22.79 (subbreln1) =>
% 131.56/22.79 ((
% 131.56/22.79 (eqbreln1) =>
% 131.56/22.79 ((
% 131.56/22.79 (breln1invprop) =>
% 131.56/22.79 ((
% 131.56/22.79 (breln1invI) =>
% 131.56/22.79 ((
% 131.56/22.79 (breln1invE) =>
% 131.56/22.79 ((
% 131.56/22.79 (breln1compprop) =>
% 131.56/22.79 ((
% 131.56/22.79 (breln1compI) =>
% 131.56/22.79 ((
% 131.56/22.79 (breln1compE) =>
% 131.56/22.79 ((
% 131.56/22.79 (breln1compEex) =>
% 131.56/22.79 ((
% 131.56/22.79 (breln1unionprop) =>
% 131.56/22.79 ((
% 131.56/22.79 (breln1unionIL) =>
% 131.56/22.79 ((
% 131.56/22.79 (breln1unionIR) =>
% 131.56/22.79 ((
% 131.56/22.79 (breln1unionI) =>
% 131.56/22.79 ((
% 131.56/22.79 (breln1unionE) =>
% 131.56/22.79 ((
% 131.56/22.79 (breln1unionEcases) =>
% 131.56/22.79 ((
% 131.56/22.79 (breln1unionCommutes) =>
% 131.56/22.79 ((
% 131.56/22.79 (woz2Ex) =>
% 131.56/22.79 ((
% 131.56/22.79 (woz2W) =>
% 131.56/22.79 ((
% 131.56/22.79 (woz2A) =>
% 131.56/22.79 ((
% 131.56/22.79 (woz2B) =>
% 131.56/22.79 ((
% 131.56/22.79 (image1Ex) =>
% 131.56/22.79 ((
% 131.56/22.79 (image1Ex1) =>
% 131.56/22.79 ((
% 131.56/22.79 (image1Equiv) =>
% 131.56/22.79 ((
% 131.56/22.79 (image1E) =>
% 131.56/22.79 ((
% 131.56/22.79 (image1I) =>
% 131.56/22.79 ((
% 131.56/22.79 (injFuncInInjFuncSet) =>
% 131.56/22.79 ((
% 131.56/22.79 (injFuncSetFuncIn) =>
% 131.56/22.79 ((
% 131.56/22.79 (injFuncSetFuncInj) =>
% 131.56/22.79 ((
% 131.56/22.79 (surjFuncSetFuncIn) =>
% 131.56/22.79 ((
% 131.56/22.79 (surjFuncSetFuncSurj) =>
% 131.56/22.79 ((
% 131.56/22.79 (leftInvIsSurj) =>
% 131.56/22.79 ((
% 131.56/22.79 (surjCantorThm) =>
% 131.56/22.79 ((
% 131.56/22.79 (foundation2) =>
% 131.56/22.79 ((
% 131.56/22.79 (notinself) =>
% 131.56/22.79 ((
% 131.56/22.79 (notinself2) =>
% 131.56/22.79 ((
% 131.56/22.79 (omegaSp) =>
% 131.56/22.79 ((
% 131.56/22.79 (omegaSclos) =>
% 131.56/22.79 ((
% 131.56/22.79 (peano0notS) =>
% 131.56/22.79 ((
% 131.56/22.79 (peanoSinj) =>
% 131.56/22.79 ((
% 131.56/22.79 (transitivesetOp1) =>
% 131.56/22.79 ((
% 131.56/22.79 (binintTransitive) =>
% 131.56/22.79 ((
% 131.56/22.79 (transitivesetOp2) =>
% 131.56/22.79 ((
% 131.56/22.79 (setunionTransitive) =>
% 131.56/22.79 ((
% 131.56/22.79 (ordinalMinLem1) =>
% 131.56/22.79 ((
% 131.56/22.79 (ordinalTransSet) =>
% 131.56/22.79 ((
% 131.56/22.79 (ordinalTransSet1) =>
% 131.56/22.79 ((
% 131.56/22.79 (setunionOrdinalLem1) =>
% 131.56/22.79 (ordinal @
% 131.56/22.79 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 131.56/22.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl244])).
% 131.56/22.79 thf(zip_derived_cl274, plain,
% 131.56/22.79 (~ (((nonemptyI1) =>
% 131.56/22.79 (((setadjoinIL) =>
% 131.56/22.79 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 131.56/22.79 (((setadjoinIR) =>
% 131.56/22.79 (((setadjoinE) =>
% 131.56/22.79 (((setadjoinOr) =>
% 131.56/22.79 (((setoftrueEq) =>
% 131.56/22.79 (((powersetI) =>
% 131.56/22.79 (((emptyinPowerset) =>
% 131.56/22.79 (((emptyInPowerset) =>
% 131.56/22.79 (((powersetE) =>
% 131.56/22.79 (((setunionI) =>
% 131.56/22.79 (((setunionE) =>
% 131.56/22.79 (((subPowSU) =>
% 131.56/22.79 (((exuE2) =>
% 131.56/22.79 (((nonemptyImpWitness) =>
% 131.56/22.79 (((uniqinunit) =>
% 131.56/22.79 (((notinsingleton) =>
% 131.56/22.79 (((eqinunit) =>
% 131.56/22.79 (((singletonsswitch) =>
% 131.56/22.79 (((upairsetE) =>
% 131.56/22.79 (((upairsetIL) =>
% 131.56/22.79 (((upairsetIR) =>
% 131.56/22.79 (((emptyE1) =>
% 131.56/22.79 (((vacuousDall) =>
% 131.56/22.79 (((quantDeMorgan1) =>
% 131.56/22.79 (((quantDeMorgan2) =>
% 131.56/22.79 (((quantDeMorgan3) =>
% 131.56/22.79 (((quantDeMorgan4) =>
% 131.56/22.79 (((prop2setI) =>
% 131.56/22.79 ((
% 131.56/22.79 (prop2set2propI) =>
% 131.56/22.79 ((
% 131.56/22.79 (notdexE) =>
% 131.56/22.79 ((
% 131.56/22.79 (notdallE) =>
% 131.56/22.79 ((
% 131.56/22.79 (exuI1) =>
% 131.56/22.79 ((
% 131.56/22.79 (exuI3) =>
% 131.56/22.79 ((
% 131.56/22.79 (exuI2) =>
% 131.56/22.79 ((
% 131.56/22.79 (inCongP) =>
% 131.56/22.79 ((
% 131.56/22.79 (in__Cong) =>
% 131.56/22.79 ((
% 131.56/22.79 (exuE3u) =>
% 131.56/22.79 ((
% 131.56/22.79 (exu__Cong) =>
% 131.56/22.79 ((
% 131.56/22.79 (setadjoin__Cong) =>
% 131.56/22.79 ((
% 131.56/22.79 (powerset__Cong) =>
% 131.56/22.79 ((
% 131.56/22.79 (setunion__Cong) =>
% 131.56/22.79 ((
% 131.56/22.79 (exuEu) =>
% 131.56/22.79 ((
% 131.56/22.79 (descr__Cong) =>
% 131.56/22.79 ((
% 131.56/22.79 (dsetconstr__Cong) =>
% 131.56/22.79 ((
% 131.56/22.79 (subsetI1) =>
% 131.56/22.79 ((
% 131.56/22.79 (eqimpsubset2) =>
% 131.56/22.79 ((
% 131.56/22.79 (eqimpsubset1) =>
% 131.56/22.79 ((
% 131.56/22.79 (subsetI2) =>
% 131.56/22.79 ((
% 131.56/22.79 (emptysetsubset) =>
% 131.56/22.79 ((
% 131.56/22.79 (subsetE) =>
% 131.56/22.79 ((
% 131.56/22.79 (subsetE2) =>
% 131.56/22.79 ((
% 131.56/22.79 (notsubsetI) =>
% 131.56/22.79 ((
% 131.56/22.79 (notequalI1) =>
% 131.56/22.79 ((
% 131.56/22.79 (notequalI2) =>
% 131.56/22.79 ((
% 131.56/22.79 (subsetRefl) =>
% 131.56/22.79 ((
% 131.56/22.79 (subsetTrans) =>
% 131.56/22.79 ((
% 131.56/22.79 (setadjoinSub) =>
% 131.56/22.79 ((
% 131.56/22.79 (setadjoinSub2) =>
% 131.56/22.79 ((
% 131.56/22.79 (subset2powerset) =>
% 131.56/22.79 ((
% 131.56/22.79 (setextsub) =>
% 131.56/22.79 ((
% 131.56/22.79 (subsetemptysetimpeq) =>
% 131.56/22.79 ((
% 131.56/22.79 (powersetI1) =>
% 131.56/22.79 ((
% 131.56/22.79 (powersetE1) =>
% 131.56/22.79 ((
% 131.56/22.79 (inPowerset) =>
% 131.56/22.79 ((
% 131.56/22.79 (powersetsubset) =>
% 131.56/22.79 ((
% 131.56/22.79 (sepInPowerset) =>
% 131.56/22.79 ((
% 131.56/22.79 (sepSubset) =>
% 131.56/22.79 ((
% 131.56/22.79 (binunionIL) =>
% 131.56/22.79 ((
% 131.56/22.79 (upairset2IR) =>
% 131.56/22.79 ((
% 131.56/22.79 (binunionIR) =>
% 131.56/22.79 ((
% 131.56/22.79 (binunionEcases) =>
% 131.56/22.79 ((
% 131.56/22.79 (binunionE) =>
% 131.56/22.79 ((
% 131.56/22.79 (binunionLsub) =>
% 131.56/22.79 ((
% 131.56/22.79 (binunionRsub) =>
% 131.56/22.79 ((
% 131.56/22.79 (binintersectI) =>
% 131.56/22.79 ((
% 131.56/22.79 (binintersectSubset5) =>
% 131.56/22.79 ((
% 131.56/22.79 (binintersectEL) =>
% 131.56/22.79 ((
% 131.56/22.79 (binintersectLsub) =>
% 131.56/22.79 ((
% 131.56/22.79 (binintersectSubset2) =>
% 131.56/22.79 ((
% 131.56/22.79 (binintersectSubset3) =>
% 131.56/22.79 ((
% 131.56/22.79 (binintersectER) =>
% 131.56/22.79 ((
% 131.56/22.79 (disjointsetsI1) =>
% 131.56/22.79 ((
% 131.56/22.79 (binintersectRsub) =>
% 131.56/22.79 ((
% 131.56/22.79 (binintersectSubset4) =>
% 131.56/22.79 ((
% 131.56/22.79 (binintersectSubset1) =>
% 131.56/22.79 ((
% 131.56/22.79 (bs114d) =>
% 131.56/22.79 ((
% 131.56/22.79 (setminusI) =>
% 131.56/22.79 ((
% 131.56/22.79 (setminusEL) =>
% 131.56/22.79 ((
% 131.56/22.79 (setminusER) =>
% 131.56/22.79 ((
% 131.56/22.79 (setminusSubset2) =>
% 131.56/22.79 ((
% 131.56/22.79 (setminusERneg) =>
% 131.56/22.79 ((
% 131.56/22.79 (setminusELneg) =>
% 131.56/22.79 ((
% 131.56/22.79 (setminusILneg) =>
% 131.56/22.79 ((
% 131.56/22.79 (setminusIRneg) =>
% 131.56/22.79 ((
% 131.56/22.79 (setminusLsub) =>
% 131.56/22.79 ((
% 131.56/22.79 (setminusSubset1) =>
% 131.56/22.79 ((
% 131.56/22.79 (symdiffE) =>
% 131.56/22.79 ((
% 131.56/22.79 (symdiffI1) =>
% 131.56/22.79 ((
% 131.56/22.79 (symdiffI2) =>
% 131.56/22.79 ((
% 131.56/22.79 (symdiffIneg1) =>
% 131.56/22.79 ((
% 131.56/22.79 (symdiffIneg2) =>
% 131.56/22.79 ((
% 131.56/22.79 (secondinupair) =>
% 131.56/22.79 ((
% 131.56/22.79 (setukpairIL) =>
% 131.56/22.79 ((
% 131.56/22.79 (setukpairIR) =>
% 131.56/22.79 ((
% 131.56/22.79 (kpairiskpair) =>
% 131.56/22.79 ((
% 131.56/22.79 (kpairp) =>
% 131.56/22.79 ((
% 131.56/22.79 (singletonsubset) =>
% 131.56/22.79 ((
% 131.56/22.79 (singletoninpowerset) =>
% 131.56/22.79 ((
% 131.56/22.79 (singletoninpowunion) =>
% 131.56/22.79 ((
% 131.56/22.79 (upairset2E) =>
% 131.56/22.79 ((
% 131.56/22.79 (upairsubunion) =>
% 131.56/22.79 ((
% 131.56/22.79 (upairinpowunion) =>
% 131.56/22.79 ((
% 131.56/22.79 (ubforcartprodlem1) =>
% 131.56/22.79 ((
% 131.56/22.79 (ubforcartprodlem2) =>
% 131.56/22.79 ((
% 131.56/22.79 (ubforcartprodlem3) =>
% 131.56/22.79 ((
% 131.56/22.79 (cartprodpairin) =>
% 131.56/22.79 ((
% 131.56/22.79 (cartprodmempair1) =>
% 131.56/22.79 ((
% 131.56/22.79 (cartprodmempair) =>
% 131.56/22.79 ((
% 131.56/22.79 (setunionE2) =>
% 131.89/22.79 ((
% 131.89/22.79 (setunionsingleton1) =>
% 131.89/22.79 ((
% 131.89/22.79 (setunionsingleton2) =>
% 131.89/22.79 ((
% 131.89/22.79 (setunionsingleton) =>
% 131.89/22.79 ((
% 131.89/22.79 (singletonprop) =>
% 131.89/22.79 ((
% 131.89/22.79 (ex1E1) =>
% 131.89/22.79 ((
% 131.89/22.79 (ex1I) =>
% 131.89/22.79 ((
% 131.89/22.79 (ex1I2) =>
% 131.89/22.79 ((
% 131.89/22.79 (singletonsuniq) =>
% 131.89/22.79 ((
% 131.89/22.79 (setukpairinjL1) =>
% 131.89/22.79 ((
% 131.89/22.79 (kfstsingleton) =>
% 131.89/22.79 ((
% 131.89/22.79 (theprop) =>
% 131.89/22.79 ((
% 131.89/22.79 (kfstpairEq) =>
% 131.89/22.79 ((
% 131.89/22.79 (cartprodfstin) =>
% 131.89/22.79 ((
% 131.89/22.79 (setukpairinjL2) =>
% 131.89/22.79 ((
% 131.89/22.79 (setukpairinjL) =>
% 131.89/22.79 ((
% 131.89/22.79 (setukpairinjR11) =>
% 131.89/22.79 ((
% 131.89/22.79 (setukpairinjR12) =>
% 131.89/22.79 ((
% 131.89/22.79 (setukpairinjR1) =>
% 131.89/22.79 ((
% 131.89/22.79 (upairequniteq) =>
% 131.89/22.79 ((
% 131.89/22.79 (setukpairinjR2) =>
% 131.89/22.79 ((
% 131.89/22.79 (setukpairinjR) =>
% 131.89/22.79 ((
% 131.89/22.79 (ksndsingleton) =>
% 131.89/22.79 ((
% 131.89/22.79 (ksndpairEq) =>
% 131.89/22.79 ((
% 131.89/22.79 (kpairsurjEq) =>
% 131.89/22.79 ((
% 131.89/22.79 (cartprodsndin) =>
% 131.89/22.79 ((
% 131.89/22.79 (cartprodpairmemEL) =>
% 131.89/22.79 ((
% 131.89/22.79 (cartprodpairmemER) =>
% 131.89/22.79 ((
% 131.89/22.79 (cartprodmempaircEq) =>
% 131.89/22.79 ((
% 131.89/22.79 (cartprodfstpairEq) =>
% 131.89/22.79 ((
% 131.89/22.79 (cartprodsndpairEq) =>
% 131.89/22.79 ((
% 131.89/22.79 (cartprodpairsurjEq) =>
% 131.89/22.79 ((
% 131.89/22.79 (dpsetconstrI) =>
% 131.89/22.79 ((
% 131.89/22.79 (dpsetconstrSub) =>
% 131.89/22.79 ((
% 131.89/22.79 (setOfPairsIsBReln) =>
% 131.89/22.79 ((
% 131.89/22.79 (dpsetconstrERa) =>
% 131.89/22.79 ((
% 131.89/22.79 (dpsetconstrEL1) =>
% 131.89/22.79 ((
% 131.89/22.79 (dpsetconstrEL2) =>
% 131.89/22.79 ((
% 131.89/22.79 (dpsetconstrER) =>
% 131.89/22.79 ((
% 131.89/22.79 (funcImageSingleton) =>
% 131.89/22.79 ((
% 131.89/22.79 (apProp) =>
% 131.89/22.79 ((
% 131.89/22.79 (app) =>
% 131.89/22.79 ((
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% 131.89/22.79 ((
% 131.89/22.79 (ap2p) =>
% 131.89/22.79 ((
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% 131.89/22.79 ((
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% 131.89/22.79 ((
% 131.89/22.79 (lam2p) =>
% 131.89/22.79 ((
% 131.89/22.79 (brelnall1) =>
% 131.89/22.79 ((
% 131.89/22.79 (brelnall2) =>
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% 131.89/22.79 ((
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% 131.89/22.79 ((
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% 131.89/22.79 ((
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% 131.89/22.79 ((
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% 131.89/22.79 ((
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% 131.89/22.79 ((
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% 131.89/22.79 ((
% 131.89/22.79 (lam2lamEq) =>
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% 131.89/22.79 ((
% 131.89/22.79 (iftrueProp2) =>
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% 131.89/22.79 ((
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% 131.89/22.79 ((
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% 131.89/22.79 ((
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% 131.89/22.79 (iftrueorfalse) =>
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% 131.89/22.79 ((
% 131.89/22.79 (binunionT_lem) =>
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% 131.89/22.79 (powersetT_lem) =>
% 131.89/22.79 ((
% 131.89/22.79 (setminusT_lem) =>
% 131.89/22.79 ((
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% 131.89/22.79 ((
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% 131.89/22.79 ((
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% 131.89/22.79 ((
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% 131.89/22.79 (doubleComplementEq) =>
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% 131.89/22.79 ((
% 131.89/22.79 (complementSubsetComplementIntersect) =>
% 131.89/22.79 ((
% 131.89/22.79 (complementInPowersetComplementIntersect) =>
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% 131.89/22.79 ((
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% 131.89/22.79 (intersectInPowersetIntersectUnions) =>
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% 131.89/22.79 (inComplementUnionImpNotIn1) =>
% 131.89/22.79 ((
% 131.89/22.79 (inComplementUnionImpInComplement1) =>
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% 131.89/22.79 (demorgan2a1) =>
% 131.89/22.79 ((
% 131.89/22.79 (complementUnionInPowersetComplement) =>
% 131.89/22.79 ((
% 131.89/22.79 (demorgan2a2) =>
% 131.89/22.79 ((
% 131.89/22.79 (demorgan1a) =>
% 131.89/22.79 ((
% 131.89/22.79 (demorgan1b) =>
% 131.89/22.79 ((
% 131.89/22.79 (demorgan1) =>
% 131.89/22.79 ((
% 131.89/22.79 (demorgan2a) =>
% 131.89/22.79 ((
% 131.89/22.79 (demorgan2b2) =>
% 131.89/22.79 ((
% 131.89/22.79 (demorgan2b) =>
% 131.89/22.79 ((
% 131.89/22.79 (demorgan2) =>
% 131.89/22.79 ((
% 131.89/22.79 (woz13rule0) =>
% 131.89/22.79 ((
% 131.89/22.79 (woz13rule1) =>
% 131.89/22.79 ((
% 131.89/22.79 (woz13rule2) =>
% 131.89/22.79 ((
% 131.89/22.79 (woz13rule3) =>
% 131.89/22.79 ((
% 131.89/22.79 (woz13rule4) =>
% 131.89/22.79 ((
% 131.89/22.79 (woz1_1) =>
% 131.89/22.79 ((
% 131.89/22.79 (woz1_2) =>
% 131.89/22.79 ((
% 131.89/22.79 (woz1_3) =>
% 131.89/22.79 ((
% 131.89/22.79 (woz1_4) =>
% 131.89/22.79 ((
% 131.89/22.79 (woz1_5) =>
% 131.89/22.79 ((
% 131.89/22.79 (breln1all2) =>
% 131.89/22.79 ((
% 131.89/22.79 (breln1SetBreln1) =>
% 131.89/22.79 ((
% 131.89/22.79 (choice2fnsingleton) =>
% 131.89/22.79 ((
% 131.89/22.79 (setOfPairsIsBReln1) =>
% 131.89/22.79 ((
% 131.89/22.79 (breln1all1) =>
% 131.89/22.79 ((
% 131.89/22.79 (subbreln1) =>
% 131.89/22.79 ((
% 131.89/22.79 (eqbreln1) =>
% 131.89/22.79 ((
% 131.89/22.79 (breln1invprop) =>
% 131.89/22.79 ((
% 131.89/22.79 (breln1invI) =>
% 131.89/22.79 ((
% 131.89/22.79 (breln1invE) =>
% 131.89/22.79 ((
% 131.89/22.79 (breln1compprop) =>
% 131.89/22.79 ((
% 131.89/22.79 (breln1compI) =>
% 131.89/22.79 ((
% 131.89/22.79 (breln1compE) =>
% 131.89/22.79 ((
% 131.89/22.79 (breln1compEex) =>
% 131.89/22.79 ((
% 131.89/22.79 (breln1unionprop) =>
% 131.89/22.79 ((
% 131.89/22.79 (breln1unionIL) =>
% 131.89/22.79 ((
% 131.89/22.79 (breln1unionIR) =>
% 131.89/22.79 ((
% 131.89/22.79 (breln1unionI) =>
% 131.89/22.79 ((
% 131.89/22.79 (breln1unionE) =>
% 131.89/22.79 ((
% 131.89/22.79 (breln1unionEcases) =>
% 131.89/22.79 ((
% 131.89/22.79 (breln1unionCommutes) =>
% 131.89/22.79 ((
% 131.89/22.79 (woz2Ex) =>
% 131.89/22.79 ((
% 131.89/22.79 (woz2W) =>
% 131.89/22.79 ((
% 131.89/22.79 (woz2A) =>
% 131.89/22.79 ((
% 131.89/22.79 (woz2B) =>
% 131.89/22.79 ((
% 131.89/22.79 (image1Ex) =>
% 131.89/22.79 ((
% 131.89/22.79 (image1Ex1) =>
% 131.89/22.79 ((
% 131.89/22.79 (image1Equiv) =>
% 131.89/22.79 ((
% 131.89/22.79 (image1E) =>
% 131.89/22.79 ((
% 131.89/22.79 (image1I) =>
% 131.89/22.79 ((
% 131.89/22.79 (injFuncInInjFuncSet) =>
% 131.89/22.79 ((
% 131.89/22.79 (injFuncSetFuncIn) =>
% 131.89/22.79 ((
% 131.89/22.79 (injFuncSetFuncInj) =>
% 131.89/22.79 ((
% 131.89/22.79 (surjFuncSetFuncIn) =>
% 131.89/22.79 ((
% 131.89/22.79 (surjFuncSetFuncSurj) =>
% 131.89/22.79 ((
% 131.89/22.79 (leftInvIsSurj) =>
% 131.89/22.79 ((
% 131.89/22.79 (surjCantorThm) =>
% 131.89/22.79 ((
% 131.89/22.79 (foundation2) =>
% 131.89/22.79 ((
% 131.89/22.79 (notinself) =>
% 131.89/22.79 ((
% 131.89/22.79 (notinself2) =>
% 131.89/22.79 ((
% 131.89/22.79 (omegaSp) =>
% 131.89/22.79 ((
% 131.89/22.79 (omegaSclos) =>
% 131.89/22.79 ((
% 131.89/22.79 (peano0notS) =>
% 131.89/22.79 ((
% 131.89/22.79 (peanoSinj) =>
% 131.89/22.79 ((
% 131.89/22.79 (transitivesetOp1) =>
% 131.89/22.79 ((
% 131.89/22.79 (binintTransitive) =>
% 131.89/22.79 ((
% 131.89/22.79 (transitivesetOp2) =>
% 131.89/22.79 ((
% 131.89/22.79 (setunionTransitive) =>
% 131.89/22.79 ((
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% 131.89/22.79 ((
% 131.89/22.79 (ordinalTransSet) =>
% 131.89/22.79 ((
% 131.89/22.79 (ordinalTransSet1) =>
% 131.89/22.79 ((
% 131.89/22.79 (setunionOrdinalLem1) =>
% 131.89/22.79 (ordinal @
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% 131.89/22.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl258])).
% 131.89/22.79 thf(zip_derived_cl285, plain,
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% 131.89/22.79 (((emptyInPowerset) =>
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% 131.89/22.79 (((quantDeMorgan1) =>
% 131.89/22.79 (((quantDeMorgan2) =>
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% 131.89/22.79 (((prop2set2propI) =>
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% 131.89/22.79 ((
% 131.89/22.79 (notdallE) =>
% 131.89/22.79 ((
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% 131.89/22.79 ((
% 131.89/22.79 (exuI3) =>
% 131.89/22.79 ((
% 131.89/22.79 (exuI2) =>
% 131.89/22.79 ((
% 131.89/22.79 (inCongP) =>
% 131.89/22.79 ((
% 131.89/22.79 (in__Cong) =>
% 131.89/22.79 ((
% 131.89/22.79 (exuE3u) =>
% 131.89/22.79 ((
% 131.89/22.79 (exu__Cong) =>
% 131.89/22.79 ((
% 131.89/22.79 (setadjoin__Cong) =>
% 131.89/22.79 ((
% 131.89/22.79 (powerset__Cong) =>
% 131.89/22.79 ((
% 131.89/22.79 (setunion__Cong) =>
% 131.89/22.79 ((
% 131.89/22.79 (exuEu) =>
% 131.89/22.79 ((
% 131.89/22.79 (descr__Cong) =>
% 131.89/22.79 ((
% 131.89/22.79 (dsetconstr__Cong) =>
% 131.89/22.79 ((
% 131.89/22.79 (subsetI1) =>
% 131.89/22.79 ((
% 131.89/22.79 (eqimpsubset2) =>
% 131.89/22.79 ((
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% 131.89/22.79 ((
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% 131.89/22.79 ((
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% 131.89/22.79 ((
% 131.89/22.79 (notequalI1) =>
% 131.89/22.79 ((
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% 131.89/22.79 ((
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% 131.89/22.79 ((
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% 131.89/22.79 ((
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% 131.89/22.79 ((
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% 131.89/22.79 ((
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% 131.89/22.79 ((
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% 131.89/22.79 ((
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% 131.89/22.79 ((
% 131.89/22.79 (binunionE) =>
% 131.89/22.79 ((
% 131.89/22.79 (binunionLsub) =>
% 131.89/22.79 ((
% 131.89/22.79 (binunionRsub) =>
% 131.89/22.79 ((
% 131.89/22.79 (binintersectI) =>
% 131.89/22.79 ((
% 131.89/22.79 (binintersectSubset5) =>
% 131.89/22.79 ((
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% 131.89/22.79 ((
% 131.89/22.79 (binintersectLsub) =>
% 131.89/22.79 ((
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% 131.89/22.79 ((
% 131.89/22.79 (binintersectSubset3) =>
% 131.89/22.79 ((
% 131.89/22.79 (binintersectER) =>
% 131.89/22.79 ((
% 131.89/22.79 (disjointsetsI1) =>
% 131.89/22.79 ((
% 131.89/22.79 (binintersectRsub) =>
% 131.89/22.79 ((
% 131.89/22.79 (binintersectSubset4) =>
% 131.89/22.79 ((
% 131.89/22.79 (binintersectSubset1) =>
% 131.89/22.79 ((
% 131.89/22.79 (bs114d) =>
% 131.89/22.79 ((
% 131.89/22.79 (setminusI) =>
% 131.89/22.79 ((
% 131.89/22.79 (setminusEL) =>
% 131.89/22.79 ((
% 131.89/22.79 (setminusER) =>
% 131.89/22.79 ((
% 131.89/22.79 (setminusSubset2) =>
% 131.89/22.79 ((
% 131.89/22.79 (setminusERneg) =>
% 131.89/22.79 ((
% 131.89/22.79 (setminusELneg) =>
% 131.89/22.79 ((
% 131.89/22.79 (setminusILneg) =>
% 131.89/22.79 ((
% 131.89/22.79 (setminusIRneg) =>
% 131.89/22.79 ((
% 131.89/22.79 (setminusLsub) =>
% 131.89/22.79 ((
% 131.89/22.79 (setminusSubset1) =>
% 131.89/22.79 ((
% 131.89/22.79 (symdiffE) =>
% 131.89/22.79 ((
% 131.89/22.79 (symdiffI1) =>
% 131.89/22.79 ((
% 131.89/22.79 (symdiffI2) =>
% 131.89/22.79 ((
% 131.89/22.79 (symdiffIneg1) =>
% 131.89/22.79 ((
% 131.89/22.79 (symdiffIneg2) =>
% 131.89/22.79 ((
% 131.89/22.79 (secondinupair) =>
% 131.89/22.79 ((
% 131.89/22.79 (setukpairIL) =>
% 131.89/22.79 ((
% 131.89/22.79 (setukpairIR) =>
% 131.89/22.79 ((
% 131.89/22.79 (kpairiskpair) =>
% 131.89/22.79 ((
% 131.89/22.79 (kpairp) =>
% 131.89/22.79 ((
% 131.89/22.79 (singletonsubset) =>
% 131.89/22.79 ((
% 131.89/22.79 (singletoninpowerset) =>
% 131.89/22.79 ((
% 131.89/22.79 (singletoninpowunion) =>
% 131.89/22.79 ((
% 131.89/22.79 (upairset2E) =>
% 131.89/22.79 ((
% 131.89/22.79 (upairsubunion) =>
% 131.89/22.79 ((
% 131.89/22.79 (upairinpowunion) =>
% 131.89/22.79 ((
% 131.89/22.79 (ubforcartprodlem1) =>
% 131.89/22.79 ((
% 131.89/22.79 (ubforcartprodlem2) =>
% 131.89/22.79 ((
% 131.89/22.79 (ubforcartprodlem3) =>
% 131.89/22.79 ((
% 131.89/22.79 (cartprodpairin) =>
% 131.89/22.79 ((
% 131.89/22.79 (cartprodmempair1) =>
% 131.89/22.79 ((
% 131.89/22.79 (cartprodmempair) =>
% 131.89/22.79 ((
% 131.89/22.79 (setunionE2) =>
% 131.89/22.79 ((
% 131.89/22.79 (setunionsingleton1) =>
% 131.89/22.79 ((
% 131.89/22.79 (setunionsingleton2) =>
% 131.89/22.79 ((
% 131.89/22.79 (setunionsingleton) =>
% 131.89/22.79 ((
% 131.89/22.79 (singletonprop) =>
% 131.89/22.79 ((
% 131.89/22.79 (ex1E1) =>
% 131.89/22.79 ((
% 131.89/22.79 (ex1I) =>
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% 131.89/22.79 ((
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% 131.89/22.79 ((
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% 131.89/22.79 (theprop) =>
% 131.89/22.79 ((
% 131.89/22.79 (kfstpairEq) =>
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% 131.89/22.79 (cartprodfstin) =>
% 131.89/22.79 ((
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% 131.89/22.79 (setukpairinjR12) =>
% 131.89/22.79 ((
% 131.89/22.79 (setukpairinjR1) =>
% 131.89/22.79 ((
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% 131.89/22.79 ((
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% 131.89/22.79 ((
% 131.89/22.79 (ksndsingleton) =>
% 131.89/22.79 ((
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% 131.89/22.79 ((
% 131.89/22.79 (kpairsurjEq) =>
% 131.89/22.79 ((
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% 131.89/22.79 ((
% 131.89/22.79 (cartprodpairmemEL) =>
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% 131.89/22.79 (cartprodpairmemER) =>
% 131.89/22.79 ((
% 131.89/22.79 (cartprodmempaircEq) =>
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% 131.89/22.79 (cartprodfstpairEq) =>
% 131.89/22.79 ((
% 131.89/22.79 (cartprodsndpairEq) =>
% 131.89/22.79 ((
% 131.89/22.79 (cartprodpairsurjEq) =>
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% 131.89/22.79 (complementTnotintersectT) =>
% 131.89/22.79 ((
% 131.89/22.79 (complementImpComplementIntersect) =>
% 131.89/22.79 ((
% 131.89/22.79 (complementSubsetComplementIntersect) =>
% 131.89/22.79 ((
% 131.89/22.79 (complementInPowersetComplementIntersect) =>
% 131.89/22.79 ((
% 131.89/22.79 (contraSubsetComplement) =>
% 131.89/22.79 ((
% 131.89/22.79 (complementTcontraSubset) =>
% 131.89/22.79 ((
% 131.89/22.79 (binunionTILcontra) =>
% 131.89/22.79 ((
% 131.89/22.79 (binunionTIRcontra) =>
% 131.89/22.79 ((
% 131.89/22.79 (inIntersectImpInUnion) =>
% 131.89/22.79 ((
% 131.89/22.79 (inIntersectImpInUnion2) =>
% 131.89/22.79 ((
% 131.89/22.79 (inIntersectImpInIntersectUnions) =>
% 131.89/22.79 ((
% 131.89/22.79 (intersectInPowersetIntersectUnions) =>
% 131.89/22.79 ((
% 131.89/22.79 (inComplementUnionImpNotIn1) =>
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% 131.89/22.79 (inComplementUnionImpInComplement1) =>
% 131.89/22.79 ((
% 131.89/22.79 (binunionTE) =>
% 131.89/22.79 ((
% 131.89/22.79 (binunionTEcontra) =>
% 131.89/22.79 ((
% 131.89/22.79 (demorgan2a1) =>
% 131.89/22.79 ((
% 131.89/22.79 (complementUnionInPowersetComplement) =>
% 131.89/22.79 ((
% 131.89/22.79 (demorgan2a2) =>
% 131.89/22.79 ((
% 131.89/22.79 (demorgan1a) =>
% 131.89/22.79 ((
% 131.89/22.79 (demorgan1b) =>
% 131.89/22.79 ((
% 131.89/22.79 (demorgan1) =>
% 131.89/22.79 ((
% 131.89/22.79 (demorgan2a) =>
% 131.89/22.79 ((
% 131.89/22.79 (demorgan2b2) =>
% 131.89/22.79 ((
% 131.89/22.79 (demorgan2b) =>
% 131.89/22.79 ((
% 131.89/22.79 (demorgan2) =>
% 131.89/22.79 ((
% 131.89/22.79 (woz13rule0) =>
% 131.89/22.79 ((
% 131.89/22.79 (woz13rule1) =>
% 131.89/22.79 ((
% 131.89/22.79 (woz13rule2) =>
% 131.89/22.79 ((
% 131.89/22.79 (woz13rule3) =>
% 131.89/22.79 ((
% 131.89/22.79 (woz13rule4) =>
% 131.89/22.79 ((
% 131.89/22.79 (woz1_1) =>
% 131.89/22.79 ((
% 131.89/22.79 (woz1_2) =>
% 131.89/22.79 ((
% 131.89/22.79 (woz1_3) =>
% 131.89/22.79 ((
% 131.89/22.79 (woz1_4) =>
% 131.89/22.79 ((
% 131.89/22.79 (woz1_5) =>
% 131.89/22.79 ((
% 131.89/22.79 (breln1all2) =>
% 131.89/22.79 ((
% 131.89/22.79 (breln1SetBreln1) =>
% 131.89/22.79 ((
% 131.89/22.79 (choice2fnsingleton) =>
% 131.89/22.79 ((
% 131.89/22.79 (setOfPairsIsBReln1) =>
% 131.89/22.79 ((
% 131.89/22.79 (breln1all1) =>
% 131.89/22.79 ((
% 131.89/22.79 (subbreln1) =>
% 131.89/22.79 ((
% 131.89/22.79 (eqbreln1) =>
% 131.89/22.79 ((
% 131.89/22.79 (breln1invprop) =>
% 131.89/22.79 ((
% 131.89/22.79 (breln1invI) =>
% 131.89/22.79 ((
% 131.89/22.79 (breln1invE) =>
% 131.89/22.79 ((
% 131.89/22.79 (breln1compprop) =>
% 131.89/22.79 ((
% 131.89/22.79 (breln1compI) =>
% 131.89/22.79 ((
% 131.89/22.79 (breln1compE) =>
% 131.89/22.79 ((
% 131.89/22.79 (breln1compEex) =>
% 131.89/22.79 ((
% 131.89/22.79 (breln1unionprop) =>
% 131.89/22.79 ((
% 131.89/22.79 (breln1unionIL) =>
% 131.89/22.79 ((
% 131.89/22.79 (breln1unionIR) =>
% 131.89/22.79 ((
% 131.89/22.79 (breln1unionI) =>
% 131.89/22.79 ((
% 131.89/22.79 (breln1unionE) =>
% 131.89/22.79 ((
% 131.89/22.79 (breln1unionEcases) =>
% 131.89/22.79 ((
% 131.89/22.79 (breln1unionCommutes) =>
% 131.89/22.79 ((
% 131.89/22.79 (woz2Ex) =>
% 131.89/22.79 ((
% 131.89/22.79 (woz2W) =>
% 131.89/22.79 ((
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% 131.89/22.79 ((
% 131.89/22.79 (woz2B) =>
% 131.89/22.79 ((
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% 131.89/22.79 ((
% 131.89/22.79 (image1Ex1) =>
% 131.89/22.79 ((
% 131.89/22.79 (image1Equiv) =>
% 131.89/22.79 ((
% 131.89/22.79 (image1E) =>
% 131.89/22.79 ((
% 131.89/22.79 (image1I) =>
% 131.89/22.79 ((
% 131.89/22.79 (injFuncInInjFuncSet) =>
% 131.89/22.79 ((
% 131.89/22.79 (injFuncSetFuncIn) =>
% 131.89/22.79 ((
% 131.89/22.79 (injFuncSetFuncInj) =>
% 131.89/22.79 ((
% 131.89/22.79 (surjFuncSetFuncIn) =>
% 131.89/22.79 ((
% 131.89/22.79 (surjFuncSetFuncSurj) =>
% 131.89/22.79 ((
% 131.89/22.79 (leftInvIsSurj) =>
% 131.89/22.79 ((
% 131.89/22.79 (surjCantorThm) =>
% 131.89/22.79 ((
% 131.89/22.79 (foundation2) =>
% 131.89/22.79 ((
% 131.89/22.79 (notinself) =>
% 131.89/22.79 ((
% 131.89/22.79 (notinself2) =>
% 131.89/22.79 ((
% 131.89/22.79 (omegaSp) =>
% 131.89/22.79 ((
% 131.89/22.79 (omegaSclos) =>
% 131.89/22.79 ((
% 131.89/22.79 (peano0notS) =>
% 131.89/22.79 ((
% 131.89/22.79 (peanoSinj) =>
% 131.89/22.79 ((
% 131.89/22.79 (transitivesetOp1) =>
% 131.89/22.79 ((
% 131.89/22.79 (binintTransitive) =>
% 131.89/22.79 ((
% 131.89/22.79 (transitivesetOp2) =>
% 131.89/22.79 ((
% 131.89/22.79 (setunionTransitive) =>
% 131.89/22.79 ((
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% 131.89/22.79 ((
% 131.89/22.79 (ordinalTransSet) =>
% 131.89/22.79 ((
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% 131.89/22.79 ((
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% 131.89/22.79 (ordinal @
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% 131.89/22.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl274])).
% 131.89/22.79 thf(zip_derived_cl297, plain,
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% 131.89/22.79 (((setadjoinIR) =>
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% 131.89/22.79 (((emptyinPowerset) =>
% 131.89/22.79 (((emptyInPowerset) =>
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% 131.89/22.79 (((setunionE) =>
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% 131.89/22.79 (((quantDeMorgan2) =>
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% 131.89/22.79 ((
% 131.89/22.79 (exuI3) =>
% 131.89/22.79 ((
% 131.89/22.79 (exuI2) =>
% 131.89/22.79 ((
% 131.89/22.79 (inCongP) =>
% 131.89/22.79 ((
% 131.89/22.79 (in__Cong) =>
% 131.89/22.79 ((
% 131.89/22.79 (exuE3u) =>
% 131.89/22.79 ((
% 131.89/22.79 (exu__Cong) =>
% 131.89/22.79 ((
% 131.89/22.79 (setadjoin__Cong) =>
% 131.89/22.79 ((
% 131.89/22.79 (powerset__Cong) =>
% 131.89/22.79 ((
% 131.89/22.79 (setunion__Cong) =>
% 131.89/22.79 ((
% 131.89/22.79 (exuEu) =>
% 131.89/22.79 ((
% 131.89/22.79 (descr__Cong) =>
% 131.89/22.79 ((
% 131.89/22.79 (dsetconstr__Cong) =>
% 131.89/22.79 ((
% 131.89/22.79 (subsetI1) =>
% 131.89/22.79 ((
% 131.89/22.79 (eqimpsubset2) =>
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% 131.89/22.79 (subsetE2) =>
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% 131.89/22.79 ((
% 131.89/22.79 (notequalI2) =>
% 131.89/22.79 ((
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% 131.89/22.79 ((
% 131.89/22.79 (binintersectI) =>
% 131.89/22.79 ((
% 131.89/22.79 (binintersectSubset5) =>
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% 131.89/22.79 (bs114d) =>
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% 131.89/22.79 (setminusIRneg) =>
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% 131.89/22.79 ((
% 131.89/22.79 (symdiffIneg2) =>
% 131.89/22.79 ((
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% 131.89/22.79 ((
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% 131.89/22.79 (kpairiskpair) =>
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% 131.89/22.79 ((
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% 131.89/22.79 (upairinpowunion) =>
% 131.89/22.79 ((
% 131.89/22.79 (ubforcartprodlem1) =>
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% 131.89/22.79 (ubforcartprodlem2) =>
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% 131.89/22.79 (setextT) =>
% 131.89/22.79 ((
% 131.89/22.79 (subsetTI) =>
% 131.89/22.79 ((
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% 131.89/22.79 ((
% 131.89/22.79 (powersetTE1) =>
% 131.89/22.79 ((
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% 131.89/22.79 ((
% 131.89/22.79 (complementTE1) =>
% 131.89/22.79 ((
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% 131.89/22.79 ((
% 131.89/22.79 (binintersectTERcontra) =>
% 131.89/22.79 ((
% 131.89/22.79 (contrasubsetT) =>
% 131.89/22.79 ((
% 131.89/22.79 (contrasubsetT1) =>
% 131.89/22.79 ((
% 131.89/22.79 (contrasubsetT2) =>
% 131.89/22.79 ((
% 131.89/22.79 (contrasubsetT3) =>
% 131.89/22.79 ((
% 131.89/22.79 (doubleComplementI1) =>
% 131.89/22.79 ((
% 131.89/22.79 (doubleComplementE1) =>
% 131.89/22.79 ((
% 131.89/22.79 (doubleComplementSub1) =>
% 131.89/22.79 ((
% 131.89/22.79 (doubleComplementSub2) =>
% 131.89/22.79 ((
% 131.89/22.79 (doubleComplementEq) =>
% 131.89/22.79 ((
% 131.89/22.79 (complementTnotintersectT) =>
% 131.89/22.79 ((
% 131.89/22.79 (complementImpComplementIntersect) =>
% 131.89/22.79 ((
% 131.89/22.79 (complementSubsetComplementIntersect) =>
% 131.89/22.79 ((
% 131.89/22.79 (complementInPowersetComplementIntersect) =>
% 131.89/22.79 ((
% 131.89/22.79 (contraSubsetComplement) =>
% 131.89/22.79 ((
% 131.89/22.79 (complementTcontraSubset) =>
% 131.89/22.79 ((
% 131.89/22.79 (binunionTILcontra) =>
% 131.89/22.79 ((
% 131.89/22.79 (binunionTIRcontra) =>
% 131.89/22.79 ((
% 131.89/22.79 (inIntersectImpInUnion) =>
% 131.89/22.79 ((
% 131.89/22.79 (inIntersectImpInUnion2) =>
% 131.89/22.79 ((
% 131.89/22.79 (inIntersectImpInIntersectUnions) =>
% 131.89/22.79 ((
% 131.89/22.79 (intersectInPowersetIntersectUnions) =>
% 131.89/22.79 ((
% 131.89/22.79 (inComplementUnionImpNotIn1) =>
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% 131.89/22.79 (inComplementUnionImpInComplement1) =>
% 131.89/22.79 ((
% 131.89/22.79 (binunionTE) =>
% 131.89/22.79 ((
% 131.89/22.79 (binunionTEcontra) =>
% 131.89/22.79 ((
% 131.89/22.79 (demorgan2a1) =>
% 131.89/22.79 ((
% 131.89/22.79 (complementUnionInPowersetComplement) =>
% 131.89/22.79 ((
% 131.89/22.79 (demorgan2a2) =>
% 131.89/22.79 ((
% 131.89/22.79 (demorgan1a) =>
% 131.89/22.79 ((
% 131.89/22.79 (demorgan1b) =>
% 131.89/22.79 ((
% 131.89/22.79 (demorgan1) =>
% 131.89/22.79 ((
% 131.89/22.79 (demorgan2a) =>
% 131.89/22.79 ((
% 131.89/22.79 (demorgan2b2) =>
% 131.89/22.79 ((
% 131.89/22.79 (demorgan2b) =>
% 131.89/22.79 ((
% 131.89/22.79 (demorgan2) =>
% 131.89/22.79 ((
% 131.89/22.79 (woz13rule0) =>
% 131.89/22.79 ((
% 131.89/22.79 (woz13rule1) =>
% 131.89/22.79 ((
% 131.89/22.79 (woz13rule2) =>
% 131.89/22.79 ((
% 131.89/22.79 (woz13rule3) =>
% 131.89/22.79 ((
% 131.89/22.79 (woz13rule4) =>
% 131.89/22.79 ((
% 131.89/22.79 (woz1_1) =>
% 131.89/22.79 ((
% 131.89/22.79 (woz1_2) =>
% 131.89/22.79 ((
% 131.89/22.79 (woz1_3) =>
% 131.89/22.79 ((
% 131.89/22.79 (woz1_4) =>
% 131.89/22.79 ((
% 131.89/22.79 (woz1_5) =>
% 131.89/22.79 ((
% 131.89/22.79 (breln1all2) =>
% 131.89/22.79 ((
% 131.89/22.79 (breln1SetBreln1) =>
% 131.89/22.79 ((
% 131.89/22.79 (choice2fnsingleton) =>
% 131.89/22.79 ((
% 131.89/22.79 (setOfPairsIsBReln1) =>
% 131.89/22.79 ((
% 131.89/22.79 (breln1all1) =>
% 131.89/22.79 ((
% 131.89/22.79 (subbreln1) =>
% 131.89/22.79 ((
% 131.89/22.79 (eqbreln1) =>
% 131.89/22.79 ((
% 131.89/22.79 (breln1invprop) =>
% 131.89/22.79 ((
% 131.89/22.79 (breln1invI) =>
% 131.89/22.79 ((
% 131.89/22.79 (breln1invE) =>
% 131.89/22.79 ((
% 131.89/22.79 (breln1compprop) =>
% 131.89/22.79 ((
% 131.89/22.79 (breln1compI) =>
% 131.89/22.79 ((
% 131.89/22.79 (breln1compE) =>
% 131.89/22.79 ((
% 131.89/22.79 (breln1compEex) =>
% 131.89/22.79 ((
% 131.89/22.79 (breln1unionprop) =>
% 131.89/22.79 ((
% 131.89/22.79 (breln1unionIL) =>
% 131.89/22.79 ((
% 131.89/22.79 (breln1unionIR) =>
% 131.89/22.79 ((
% 131.89/22.79 (breln1unionI) =>
% 131.89/22.79 ((
% 131.89/22.79 (breln1unionE) =>
% 131.89/22.79 ((
% 131.89/22.79 (breln1unionEcases) =>
% 131.89/22.79 ((
% 131.89/22.79 (breln1unionCommutes) =>
% 131.89/22.79 ((
% 131.89/22.79 (woz2Ex) =>
% 131.89/22.79 ((
% 131.89/22.79 (woz2W) =>
% 131.89/22.79 ((
% 131.89/22.79 (woz2A) =>
% 131.89/22.79 ((
% 131.89/22.79 (woz2B) =>
% 131.89/22.79 ((
% 131.89/22.79 (image1Ex) =>
% 131.89/22.79 ((
% 131.89/22.79 (image1Ex1) =>
% 131.89/22.79 ((
% 131.89/22.79 (image1Equiv) =>
% 131.89/22.79 ((
% 131.89/22.79 (image1E) =>
% 131.89/22.79 ((
% 131.89/22.79 (image1I) =>
% 131.89/22.79 ((
% 131.89/22.79 (injFuncInInjFuncSet) =>
% 131.89/22.79 ((
% 131.89/22.79 (injFuncSetFuncIn) =>
% 131.89/22.79 ((
% 131.89/22.79 (injFuncSetFuncInj) =>
% 131.89/22.79 ((
% 131.89/22.79 (surjFuncSetFuncIn) =>
% 131.89/22.79 ((
% 131.89/22.79 (surjFuncSetFuncSurj) =>
% 131.89/22.79 ((
% 131.89/22.79 (leftInvIsSurj) =>
% 131.89/22.79 ((
% 131.89/22.79 (surjCantorThm) =>
% 131.89/22.79 ((
% 131.89/22.79 (foundation2) =>
% 131.89/22.79 ((
% 131.89/22.79 (notinself) =>
% 131.89/22.79 ((
% 131.89/22.79 (notinself2) =>
% 131.89/22.79 ((
% 131.89/22.79 (omegaSp) =>
% 131.89/22.79 ((
% 131.89/22.79 (omegaSclos) =>
% 131.89/22.79 ((
% 131.89/22.79 (peano0notS) =>
% 131.89/22.79 ((
% 131.89/22.79 (peanoSinj) =>
% 131.89/22.79 ((
% 131.89/22.79 (transitivesetOp1) =>
% 131.89/22.79 ((
% 131.89/22.79 (binintTransitive) =>
% 131.89/22.79 ((
% 131.89/22.79 (transitivesetOp2) =>
% 131.89/22.79 ((
% 131.89/22.79 (setunionTransitive) =>
% 131.89/22.79 ((
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% 131.89/22.79 ((
% 131.89/22.79 (ordinalTransSet) =>
% 131.89/22.79 ((
% 131.89/22.79 (ordinalTransSet1) =>
% 131.89/22.79 ((
% 131.89/22.79 (setunionOrdinalLem1) =>
% 131.89/22.79 (ordinal @
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% 131.89/22.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl285])).
% 131.89/22.79 thf(zip_derived_cl305, plain,
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% 131.89/22.79 (((setunionE) =>
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% 131.89/22.79 (((quantDeMorgan2) =>
% 131.89/22.79 (((quantDeMorgan3) =>
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% 131.89/22.79 (((prop2set2propI) =>
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% 131.89/22.79 ((
% 131.89/22.79 (exuI3) =>
% 131.89/22.79 ((
% 131.89/22.79 (exuI2) =>
% 131.89/22.79 ((
% 131.89/22.79 (inCongP) =>
% 131.89/22.79 ((
% 131.89/22.79 (in__Cong) =>
% 131.89/22.79 ((
% 131.89/22.79 (exuE3u) =>
% 131.89/22.79 ((
% 131.89/22.79 (exu__Cong) =>
% 131.89/22.79 ((
% 131.89/22.79 (setadjoin__Cong) =>
% 131.89/22.79 ((
% 131.89/22.79 (powerset__Cong) =>
% 131.89/22.79 ((
% 131.89/22.79 (setunion__Cong) =>
% 131.89/22.79 ((
% 131.89/22.79 (exuEu) =>
% 131.89/22.79 ((
% 131.89/22.79 (descr__Cong) =>
% 131.89/22.79 ((
% 131.89/22.79 (dsetconstr__Cong) =>
% 131.89/22.79 ((
% 131.89/22.79 (subsetI1) =>
% 131.89/22.79 ((
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% 131.89/22.79 ((
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% 131.89/22.79 ((
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% 131.89/22.79 ((
% 131.89/22.79 (emptysetsubset) =>
% 131.89/22.79 ((
% 131.89/22.79 (subsetE) =>
% 131.89/22.79 ((
% 131.89/22.79 (subsetE2) =>
% 131.89/22.79 ((
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% 131.89/22.79 ((
% 131.89/22.79 (notequalI1) =>
% 131.89/22.79 ((
% 131.89/22.79 (notequalI2) =>
% 131.89/22.79 ((
% 131.89/22.79 (subsetRefl) =>
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% 131.89/22.79 ((
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% 131.89/22.79 ((
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% 131.89/22.79 ((
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% 131.89/22.79 ((
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% 131.89/22.79 (binunionRsub) =>
% 131.89/22.79 ((
% 131.89/22.79 (binintersectI) =>
% 131.89/22.79 ((
% 131.89/22.79 (binintersectSubset5) =>
% 131.89/22.79 ((
% 131.89/22.79 (binintersectEL) =>
% 131.89/22.79 ((
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% 131.89/22.79 ((
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% 131.89/22.79 ((
% 131.89/22.79 (binintersectSubset3) =>
% 131.89/22.79 ((
% 131.89/22.79 (binintersectER) =>
% 131.89/22.79 ((
% 131.89/22.79 (disjointsetsI1) =>
% 131.89/22.79 ((
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% 131.89/22.79 ((
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% 131.89/22.79 ((
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% 131.89/22.79 (bs114d) =>
% 131.89/22.79 ((
% 131.89/22.79 (setminusI) =>
% 131.89/22.79 ((
% 131.89/22.79 (setminusEL) =>
% 131.89/22.79 ((
% 131.89/22.79 (setminusER) =>
% 131.89/22.79 ((
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% 131.89/22.79 ((
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% 131.89/22.79 ((
% 131.89/22.79 (setminusILneg) =>
% 131.89/22.79 ((
% 131.89/22.79 (setminusIRneg) =>
% 131.89/22.79 ((
% 131.89/22.79 (setminusLsub) =>
% 131.89/22.79 ((
% 131.89/22.79 (setminusSubset1) =>
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% 131.89/22.79 ((
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% 131.89/22.79 (symdiffI2) =>
% 131.89/22.79 ((
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% 131.89/22.79 ((
% 131.89/22.79 (secondinupair) =>
% 131.89/22.79 ((
% 131.89/22.79 (setukpairIL) =>
% 131.89/22.79 ((
% 131.89/22.79 (setukpairIR) =>
% 131.89/22.79 ((
% 131.89/22.79 (kpairiskpair) =>
% 131.89/22.79 ((
% 131.89/22.79 (kpairp) =>
% 131.89/22.79 ((
% 131.89/22.79 (singletonsubset) =>
% 131.89/22.79 ((
% 131.89/22.79 (singletoninpowerset) =>
% 131.89/22.79 ((
% 131.89/22.79 (singletoninpowunion) =>
% 131.89/22.79 ((
% 131.89/22.79 (upairset2E) =>
% 131.89/22.79 ((
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% 131.89/22.79 (upairinpowunion) =>
% 131.89/22.79 ((
% 131.89/22.79 (ubforcartprodlem1) =>
% 131.89/22.79 ((
% 131.89/22.79 (ubforcartprodlem2) =>
% 131.89/22.79 ((
% 131.89/22.79 (ubforcartprodlem3) =>
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% 131.89/22.79 (cartprodpairin) =>
% 131.89/22.79 ((
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% 131.89/22.79 (cartprodmempair) =>
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% 131.89/22.79 (setunionsingleton1) =>
% 131.89/22.79 ((
% 131.89/22.79 (setunionsingleton2) =>
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% 131.89/22.79 (setunionsingleton) =>
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% 131.89/22.79 ((
% 131.89/22.79 (kpairsurjEq) =>
% 131.89/22.79 ((
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% 131.89/22.79 ((
% 131.89/22.79 (cartprodpairmemEL) =>
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% 131.89/22.79 (cartprodpairmemER) =>
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% 131.89/22.79 (cartprodmempaircEq) =>
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% 131.89/22.79 (cartprodsndpairEq) =>
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% 131.89/22.79 (eta2) =>
% 131.89/22.79 ((
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% 131.89/22.79 ((
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% 131.89/22.79 ((
% 131.89/22.79 (iftrueProp2) =>
% 131.89/22.79 ((
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% 131.89/22.79 ((
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% 131.89/22.79 ((
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% 131.89/22.79 ((
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% 131.89/22.79 ((
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% 131.89/22.79 ((
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% 131.89/22.79 ((
% 131.89/22.79 (complementTE1) =>
% 131.89/22.79 ((
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% 131.89/22.79 ((
% 131.89/22.79 (binintersectTERcontra) =>
% 131.89/22.79 ((
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% 131.89/22.79 ((
% 131.89/22.79 (contrasubsetT1) =>
% 131.89/22.79 ((
% 131.89/22.79 (contrasubsetT2) =>
% 131.89/22.79 ((
% 131.89/22.79 (contrasubsetT3) =>
% 131.89/22.79 ((
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% 131.89/22.79 ((
% 131.89/22.79 (doubleComplementE1) =>
% 131.89/22.79 ((
% 131.89/22.79 (doubleComplementSub1) =>
% 131.89/22.79 ((
% 131.89/22.79 (doubleComplementSub2) =>
% 131.89/22.79 ((
% 131.89/22.79 (doubleComplementEq) =>
% 131.89/22.79 ((
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% 131.89/22.79 ((
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% 131.89/22.79 ((
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% 131.89/22.79 ((
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% 131.89/22.79 ((
% 131.89/22.79 (contraSubsetComplement) =>
% 131.89/22.79 ((
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% 131.89/22.79 ((
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% 131.89/22.79 ((
% 131.89/22.79 (binunionTIRcontra) =>
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% 131.89/22.79 ((
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% 131.89/22.79 ((
% 131.89/22.79 (inIntersectImpInIntersectUnions) =>
% 131.89/22.79 ((
% 131.89/22.79 (intersectInPowersetIntersectUnions) =>
% 131.89/22.79 ((
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% 131.89/22.79 ((
% 131.89/22.79 (demorgan2a1) =>
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% 131.89/22.79 ((
% 131.89/22.79 (demorgan2a2) =>
% 131.89/22.79 ((
% 131.89/22.79 (demorgan1a) =>
% 131.89/22.79 ((
% 131.89/22.79 (demorgan1b) =>
% 131.89/22.79 ((
% 131.89/22.79 (demorgan1) =>
% 131.89/22.79 ((
% 131.89/22.79 (demorgan2a) =>
% 131.89/22.79 ((
% 131.89/22.79 (demorgan2b2) =>
% 131.89/22.79 ((
% 131.89/22.79 (demorgan2b) =>
% 131.89/22.79 ((
% 131.89/22.79 (demorgan2) =>
% 131.89/22.79 ((
% 131.89/22.79 (woz13rule0) =>
% 131.89/22.79 ((
% 131.89/22.79 (woz13rule1) =>
% 131.89/22.79 ((
% 131.89/22.79 (woz13rule2) =>
% 131.89/22.79 ((
% 131.89/22.79 (woz13rule3) =>
% 131.89/22.79 ((
% 131.89/22.79 (woz13rule4) =>
% 131.89/22.79 ((
% 131.89/22.79 (woz1_1) =>
% 131.89/22.79 ((
% 131.89/22.79 (woz1_2) =>
% 131.89/22.79 ((
% 131.89/22.79 (woz1_3) =>
% 131.89/22.79 ((
% 131.89/22.79 (woz1_4) =>
% 131.89/22.79 ((
% 131.89/22.79 (woz1_5) =>
% 131.89/22.79 ((
% 131.89/22.79 (breln1all2) =>
% 131.89/22.79 ((
% 131.89/22.79 (breln1SetBreln1) =>
% 131.89/22.79 ((
% 131.89/22.79 (choice2fnsingleton) =>
% 131.89/22.79 ((
% 131.89/22.79 (setOfPairsIsBReln1) =>
% 131.89/22.79 ((
% 131.89/22.79 (breln1all1) =>
% 131.89/22.79 ((
% 131.89/22.79 (subbreln1) =>
% 131.89/22.79 ((
% 131.89/22.79 (eqbreln1) =>
% 131.89/22.79 ((
% 131.89/22.79 (breln1invprop) =>
% 131.89/22.79 ((
% 131.89/22.79 (breln1invI) =>
% 131.89/22.79 ((
% 131.89/22.79 (breln1invE) =>
% 131.89/22.79 ((
% 131.89/22.79 (breln1compprop) =>
% 131.89/22.79 ((
% 131.89/22.79 (breln1compI) =>
% 131.89/22.79 ((
% 131.89/22.79 (breln1compE) =>
% 131.89/22.79 ((
% 131.89/22.79 (breln1compEex) =>
% 131.89/22.79 ((
% 131.89/22.79 (breln1unionprop) =>
% 131.89/22.79 ((
% 131.89/22.79 (breln1unionIL) =>
% 131.89/22.79 ((
% 131.89/22.79 (breln1unionIR) =>
% 131.89/22.79 ((
% 131.89/22.79 (breln1unionI) =>
% 131.89/22.79 ((
% 131.89/22.79 (breln1unionE) =>
% 131.89/22.79 ((
% 131.89/22.79 (breln1unionEcases) =>
% 131.89/22.79 ((
% 131.89/22.79 (breln1unionCommutes) =>
% 131.89/22.79 ((
% 131.89/22.79 (woz2Ex) =>
% 131.89/22.79 ((
% 131.89/22.79 (woz2W) =>
% 131.89/22.79 ((
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% 131.89/22.79 ((
% 131.89/22.79 (woz2B) =>
% 131.89/22.79 ((
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% 131.89/22.79 ((
% 131.89/22.79 (image1Ex1) =>
% 131.89/22.79 ((
% 131.89/22.79 (image1Equiv) =>
% 131.89/22.79 ((
% 131.89/22.79 (image1E) =>
% 131.89/22.79 ((
% 131.89/22.79 (image1I) =>
% 131.89/22.79 ((
% 131.89/22.79 (injFuncInInjFuncSet) =>
% 131.89/22.79 ((
% 131.89/22.79 (injFuncSetFuncIn) =>
% 131.89/22.79 ((
% 131.89/22.79 (injFuncSetFuncInj) =>
% 131.89/22.79 ((
% 131.89/22.79 (surjFuncSetFuncIn) =>
% 131.89/22.79 ((
% 131.89/22.79 (surjFuncSetFuncSurj) =>
% 131.89/22.79 ((
% 131.89/22.79 (leftInvIsSurj) =>
% 131.89/22.79 ((
% 131.89/22.79 (surjCantorThm) =>
% 131.89/22.79 ((
% 131.89/22.80 (foundation2) =>
% 131.89/22.80 ((
% 131.89/22.80 (notinself) =>
% 131.89/22.80 ((
% 131.89/22.80 (notinself2) =>
% 131.89/22.80 ((
% 131.89/22.80 (omegaSp) =>
% 131.89/22.80 ((
% 131.89/22.80 (omegaSclos) =>
% 131.89/22.80 ((
% 131.89/22.80 (peano0notS) =>
% 131.89/22.80 ((
% 131.89/22.80 (peanoSinj) =>
% 131.89/22.80 ((
% 131.89/22.80 (transitivesetOp1) =>
% 131.89/22.80 ((
% 131.89/22.80 (binintTransitive) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (setunionTransitive) =>
% 131.89/22.80 ((
% 131.89/22.80 (ordinalMinLem1) =>
% 131.89/22.80 ((
% 131.89/22.80 (ordinalTransSet) =>
% 131.89/22.80 ((
% 131.89/22.80 (ordinalTransSet1) =>
% 131.89/22.80 ((
% 131.89/22.80 (setunionOrdinalLem1) =>
% 131.89/22.80 (ordinal @
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% 131.89/22.80 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl297])).
% 131.89/22.80 thf(zip_derived_cl312, plain,
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% 131.89/22.80 (((setunionE) =>
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% 131.89/22.80 (((exuE2) =>
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% 131.89/22.80 ((
% 131.89/22.80 (exuI2) =>
% 131.89/22.80 ((
% 131.89/22.80 (inCongP) =>
% 131.89/22.80 ((
% 131.89/22.80 (in__Cong) =>
% 131.89/22.80 ((
% 131.89/22.80 (exuE3u) =>
% 131.89/22.80 ((
% 131.89/22.80 (exu__Cong) =>
% 131.89/22.80 ((
% 131.89/22.80 (setadjoin__Cong) =>
% 131.89/22.80 ((
% 131.89/22.80 (powerset__Cong) =>
% 131.89/22.80 ((
% 131.89/22.80 (setunion__Cong) =>
% 131.89/22.80 ((
% 131.89/22.80 (exuEu) =>
% 131.89/22.80 ((
% 131.89/22.80 (descr__Cong) =>
% 131.89/22.80 ((
% 131.89/22.80 (dsetconstr__Cong) =>
% 131.89/22.80 ((
% 131.89/22.80 (subsetI1) =>
% 131.89/22.80 ((
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% 131.89/22.80 (ubforcartprodlem3) =>
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% 131.89/22.80 (funcGraphProp1) =>
% 131.89/22.80 ((
% 131.89/22.80 (funcGraphProp3) =>
% 131.89/22.80 ((
% 131.89/22.80 (funcGraphProp2) =>
% 131.89/22.80 ((
% 131.89/22.80 (funcextLem) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (iftrueProp2) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (ifp) =>
% 131.89/22.80 ((
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% 131.89/22.80 (complementTE1) =>
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% 131.89/22.80 ((
% 131.89/22.80 (binintersectTERcontra) =>
% 131.89/22.80 ((
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% 131.89/22.80 (contrasubsetT1) =>
% 131.89/22.80 ((
% 131.89/22.80 (contrasubsetT2) =>
% 131.89/22.80 ((
% 131.89/22.80 (contrasubsetT3) =>
% 131.89/22.80 ((
% 131.89/22.80 (doubleComplementI1) =>
% 131.89/22.80 ((
% 131.89/22.80 (doubleComplementE1) =>
% 131.89/22.80 ((
% 131.89/22.80 (doubleComplementSub1) =>
% 131.89/22.80 ((
% 131.89/22.80 (doubleComplementSub2) =>
% 131.89/22.80 ((
% 131.89/22.80 (doubleComplementEq) =>
% 131.89/22.80 ((
% 131.89/22.80 (complementTnotintersectT) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (binunionTIRcontra) =>
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% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (inIntersectImpInIntersectUnions) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
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% 131.89/22.80 ((
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% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (demorgan1b) =>
% 131.89/22.80 ((
% 131.89/22.80 (demorgan1) =>
% 131.89/22.80 ((
% 131.89/22.80 (demorgan2a) =>
% 131.89/22.80 ((
% 131.89/22.80 (demorgan2b2) =>
% 131.89/22.80 ((
% 131.89/22.80 (demorgan2b) =>
% 131.89/22.80 ((
% 131.89/22.80 (demorgan2) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz13rule0) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz13rule1) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz13rule2) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz13rule3) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz13rule4) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz1_1) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz1_2) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz1_3) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz1_4) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz1_5) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1all2) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1SetBreln1) =>
% 131.89/22.80 ((
% 131.89/22.80 (choice2fnsingleton) =>
% 131.89/22.80 ((
% 131.89/22.80 (setOfPairsIsBReln1) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1all1) =>
% 131.89/22.80 ((
% 131.89/22.80 (subbreln1) =>
% 131.89/22.80 ((
% 131.89/22.80 (eqbreln1) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1invprop) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1invI) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1invE) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1compprop) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1compI) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1compE) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1compEex) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1unionprop) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1unionIL) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1unionIR) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1unionI) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1unionE) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1unionEcases) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1unionCommutes) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz2Ex) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz2W) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz2A) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz2B) =>
% 131.89/22.80 ((
% 131.89/22.80 (image1Ex) =>
% 131.89/22.80 ((
% 131.89/22.80 (image1Ex1) =>
% 131.89/22.80 ((
% 131.89/22.80 (image1Equiv) =>
% 131.89/22.80 ((
% 131.89/22.80 (image1E) =>
% 131.89/22.80 ((
% 131.89/22.80 (image1I) =>
% 131.89/22.80 ((
% 131.89/22.80 (injFuncInInjFuncSet) =>
% 131.89/22.80 ((
% 131.89/22.80 (injFuncSetFuncIn) =>
% 131.89/22.80 ((
% 131.89/22.80 (injFuncSetFuncInj) =>
% 131.89/22.80 ((
% 131.89/22.80 (surjFuncSetFuncIn) =>
% 131.89/22.80 ((
% 131.89/22.80 (surjFuncSetFuncSurj) =>
% 131.89/22.80 ((
% 131.89/22.80 (leftInvIsSurj) =>
% 131.89/22.80 ((
% 131.89/22.80 (surjCantorThm) =>
% 131.89/22.80 ((
% 131.89/22.80 (foundation2) =>
% 131.89/22.80 ((
% 131.89/22.80 (notinself) =>
% 131.89/22.80 ((
% 131.89/22.80 (notinself2) =>
% 131.89/22.80 ((
% 131.89/22.80 (omegaSp) =>
% 131.89/22.80 ((
% 131.89/22.80 (omegaSclos) =>
% 131.89/22.80 ((
% 131.89/22.80 (peano0notS) =>
% 131.89/22.80 ((
% 131.89/22.80 (peanoSinj) =>
% 131.89/22.80 ((
% 131.89/22.80 (transitivesetOp1) =>
% 131.89/22.80 ((
% 131.89/22.80 (binintTransitive) =>
% 131.89/22.80 ((
% 131.89/22.80 (transitivesetOp2) =>
% 131.89/22.80 ((
% 131.89/22.80 (setunionTransitive) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (ordinalTransSet) =>
% 131.89/22.80 ((
% 131.89/22.80 (ordinalTransSet1) =>
% 131.89/22.80 ((
% 131.89/22.80 (setunionOrdinalLem1) =>
% 131.89/22.80 (ordinal @
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% 131.89/22.80 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl305])).
% 131.89/22.80 thf(zip_derived_cl318, plain,
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% 131.89/22.80 (((emptyInPowerset) =>
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% 131.89/22.80 (((setunionE) =>
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% 131.89/22.80 (exuI2) =>
% 131.89/22.80 ((
% 131.89/22.80 (inCongP) =>
% 131.89/22.80 ((
% 131.89/22.80 (in__Cong) =>
% 131.89/22.80 ((
% 131.89/22.80 (exuE3u) =>
% 131.89/22.80 ((
% 131.89/22.80 (exu__Cong) =>
% 131.89/22.80 ((
% 131.89/22.80 (setadjoin__Cong) =>
% 131.89/22.80 ((
% 131.89/22.80 (powerset__Cong) =>
% 131.89/22.80 ((
% 131.89/22.80 (setunion__Cong) =>
% 131.89/22.80 ((
% 131.89/22.80 (exuEu) =>
% 131.89/22.80 ((
% 131.89/22.80 (descr__Cong) =>
% 131.89/22.80 ((
% 131.89/22.80 (dsetconstr__Cong) =>
% 131.89/22.80 ((
% 131.89/22.80 (subsetI1) =>
% 131.89/22.80 ((
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% 131.89/22.80 (subsetE2) =>
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% 131.89/22.80 ((
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% 131.89/22.80 (bs114d) =>
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% 131.89/22.80 (setukpairIR) =>
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% 131.89/22.80 (kpairiskpair) =>
% 131.89/22.80 ((
% 131.89/22.80 (kpairp) =>
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% 131.89/22.80 (singletoninpowerset) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (upairset2E) =>
% 131.89/22.80 ((
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% 131.89/22.80 (ubforcartprodlem2) =>
% 131.89/22.80 ((
% 131.89/22.80 (ubforcartprodlem3) =>
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% 131.89/22.80 (cartprodpairin) =>
% 131.89/22.80 ((
% 131.89/22.80 (cartprodmempair1) =>
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% 131.89/22.80 (cartprodmempair) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (setunionsingleton2) =>
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% 131.89/22.80 (setunionsingleton) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (kpairsurjEq) =>
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% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (cartprodpairmemER) =>
% 131.89/22.80 ((
% 131.89/22.80 (cartprodmempaircEq) =>
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% 131.89/22.80 ((
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% 131.89/22.80 (dpsetconstrEL2) =>
% 131.89/22.80 ((
% 131.89/22.80 (dpsetconstrER) =>
% 131.89/22.80 ((
% 131.89/22.80 (funcImageSingleton) =>
% 131.89/22.80 ((
% 131.89/22.80 (apProp) =>
% 131.89/22.80 ((
% 131.89/22.80 (app) =>
% 131.89/22.80 ((
% 131.89/22.80 (infuncsetfunc) =>
% 131.89/22.80 ((
% 131.89/22.80 (ap2p) =>
% 131.89/22.80 ((
% 131.89/22.80 (funcinfuncset) =>
% 131.89/22.80 ((
% 131.89/22.80 (lamProp) =>
% 131.89/22.80 ((
% 131.89/22.80 (lamp) =>
% 131.89/22.80 ((
% 131.89/22.80 (lam2p) =>
% 131.89/22.80 ((
% 131.89/22.80 (brelnall1) =>
% 131.89/22.80 ((
% 131.89/22.80 (brelnall2) =>
% 131.89/22.80 ((
% 131.89/22.80 (ex1E2) =>
% 131.89/22.80 ((
% 131.89/22.80 (funcGraphProp1) =>
% 131.89/22.80 ((
% 131.89/22.80 (funcGraphProp3) =>
% 131.89/22.80 ((
% 131.89/22.80 (funcGraphProp2) =>
% 131.89/22.80 ((
% 131.89/22.80 (funcextLem) =>
% 131.89/22.80 ((
% 131.89/22.80 (funcGraphProp4) =>
% 131.89/22.80 ((
% 131.89/22.80 (subbreln) =>
% 131.89/22.80 ((
% 131.89/22.80 (eqbreln) =>
% 131.89/22.80 ((
% 131.89/22.80 (funcext) =>
% 131.89/22.80 ((
% 131.89/22.80 (funcext2) =>
% 131.89/22.80 ((
% 131.89/22.80 (ap2apEq1) =>
% 131.89/22.80 ((
% 131.89/22.80 (ap2apEq2) =>
% 131.89/22.80 ((
% 131.89/22.80 (beta1) =>
% 131.89/22.80 ((
% 131.89/22.80 (eta1) =>
% 131.89/22.80 ((
% 131.89/22.80 (lam2lamEq) =>
% 131.89/22.80 ((
% 131.89/22.80 (beta2) =>
% 131.89/22.80 ((
% 131.89/22.80 (eta2) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (iffalseProp2) =>
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% 131.89/22.80 ((
% 131.89/22.80 (iftrueProp2) =>
% 131.89/22.80 ((
% 131.89/22.80 (ifSingleton) =>
% 131.89/22.80 ((
% 131.89/22.80 (ifp) =>
% 131.89/22.80 ((
% 131.89/22.80 (theeq) =>
% 131.89/22.80 ((
% 131.89/22.80 (iftrue) =>
% 131.89/22.80 ((
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% 131.89/22.80 (iftrueorfalse) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
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% 131.89/22.80 ((
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% 131.89/22.80 ((
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% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (powersetTE1) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (complementTE1) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (binintersectTERcontra) =>
% 131.89/22.80 ((
% 131.89/22.80 (contrasubsetT) =>
% 131.89/22.80 ((
% 131.89/22.80 (contrasubsetT1) =>
% 131.89/22.80 ((
% 131.89/22.80 (contrasubsetT2) =>
% 131.89/22.80 ((
% 131.89/22.80 (contrasubsetT3) =>
% 131.89/22.80 ((
% 131.89/22.80 (doubleComplementI1) =>
% 131.89/22.80 ((
% 131.89/22.80 (doubleComplementE1) =>
% 131.89/22.80 ((
% 131.89/22.80 (doubleComplementSub1) =>
% 131.89/22.80 ((
% 131.89/22.80 (doubleComplementSub2) =>
% 131.89/22.80 ((
% 131.89/22.80 (doubleComplementEq) =>
% 131.89/22.80 ((
% 131.89/22.80 (complementTnotintersectT) =>
% 131.89/22.80 ((
% 131.89/22.80 (complementImpComplementIntersect) =>
% 131.89/22.80 ((
% 131.89/22.80 (complementSubsetComplementIntersect) =>
% 131.89/22.80 ((
% 131.89/22.80 (complementInPowersetComplementIntersect) =>
% 131.89/22.80 ((
% 131.89/22.80 (contraSubsetComplement) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (binunionTILcontra) =>
% 131.89/22.80 ((
% 131.89/22.80 (binunionTIRcontra) =>
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% 131.89/22.80 (inIntersectImpInUnion) =>
% 131.89/22.80 ((
% 131.89/22.80 (inIntersectImpInUnion2) =>
% 131.89/22.80 ((
% 131.89/22.80 (inIntersectImpInIntersectUnions) =>
% 131.89/22.80 ((
% 131.89/22.80 (intersectInPowersetIntersectUnions) =>
% 131.89/22.80 ((
% 131.89/22.80 (inComplementUnionImpNotIn1) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (binunionTEcontra) =>
% 131.89/22.80 ((
% 131.89/22.80 (demorgan2a1) =>
% 131.89/22.80 ((
% 131.89/22.80 (complementUnionInPowersetComplement) =>
% 131.89/22.80 ((
% 131.89/22.80 (demorgan2a2) =>
% 131.89/22.80 ((
% 131.89/22.80 (demorgan1a) =>
% 131.89/22.80 ((
% 131.89/22.80 (demorgan1b) =>
% 131.89/22.80 ((
% 131.89/22.80 (demorgan1) =>
% 131.89/22.80 ((
% 131.89/22.80 (demorgan2a) =>
% 131.89/22.80 ((
% 131.89/22.80 (demorgan2b2) =>
% 131.89/22.80 ((
% 131.89/22.80 (demorgan2b) =>
% 131.89/22.80 ((
% 131.89/22.80 (demorgan2) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz13rule0) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz13rule1) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz13rule2) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz13rule3) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz13rule4) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz1_1) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz1_2) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz1_3) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz1_4) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz1_5) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1all2) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1SetBreln1) =>
% 131.89/22.80 ((
% 131.89/22.80 (choice2fnsingleton) =>
% 131.89/22.80 ((
% 131.89/22.80 (setOfPairsIsBReln1) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1all1) =>
% 131.89/22.80 ((
% 131.89/22.80 (subbreln1) =>
% 131.89/22.80 ((
% 131.89/22.80 (eqbreln1) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1invprop) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1invI) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1invE) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1compprop) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1compI) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1compE) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1compEex) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1unionprop) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1unionIL) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1unionIR) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1unionI) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1unionE) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1unionEcases) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1unionCommutes) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz2Ex) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz2W) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz2A) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz2B) =>
% 131.89/22.80 ((
% 131.89/22.80 (image1Ex) =>
% 131.89/22.80 ((
% 131.89/22.80 (image1Ex1) =>
% 131.89/22.80 ((
% 131.89/22.80 (image1Equiv) =>
% 131.89/22.80 ((
% 131.89/22.80 (image1E) =>
% 131.89/22.80 ((
% 131.89/22.80 (image1I) =>
% 131.89/22.80 ((
% 131.89/22.80 (injFuncInInjFuncSet) =>
% 131.89/22.80 ((
% 131.89/22.80 (injFuncSetFuncIn) =>
% 131.89/22.80 ((
% 131.89/22.80 (injFuncSetFuncInj) =>
% 131.89/22.80 ((
% 131.89/22.80 (surjFuncSetFuncIn) =>
% 131.89/22.80 ((
% 131.89/22.80 (surjFuncSetFuncSurj) =>
% 131.89/22.80 ((
% 131.89/22.80 (leftInvIsSurj) =>
% 131.89/22.80 ((
% 131.89/22.80 (surjCantorThm) =>
% 131.89/22.80 ((
% 131.89/22.80 (foundation2) =>
% 131.89/22.80 ((
% 131.89/22.80 (notinself) =>
% 131.89/22.80 ((
% 131.89/22.80 (notinself2) =>
% 131.89/22.80 ((
% 131.89/22.80 (omegaSp) =>
% 131.89/22.80 ((
% 131.89/22.80 (omegaSclos) =>
% 131.89/22.80 ((
% 131.89/22.80 (peano0notS) =>
% 131.89/22.80 ((
% 131.89/22.80 (peanoSinj) =>
% 131.89/22.80 ((
% 131.89/22.80 (transitivesetOp1) =>
% 131.89/22.80 ((
% 131.89/22.80 (binintTransitive) =>
% 131.89/22.80 ((
% 131.89/22.80 (transitivesetOp2) =>
% 131.89/22.80 ((
% 131.89/22.80 (setunionTransitive) =>
% 131.89/22.80 ((
% 131.89/22.80 (ordinalMinLem1) =>
% 131.89/22.80 ((
% 131.89/22.80 (ordinalTransSet) =>
% 131.89/22.80 ((
% 131.89/22.80 (ordinalTransSet1) =>
% 131.89/22.80 ((
% 131.89/22.80 (setunionOrdinalLem1) =>
% 131.89/22.80 (ordinal @
% 131.89/22.80 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 131.89/22.80 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl312])).
% 131.89/22.80 thf(zip_derived_cl325, plain,
% 131.89/22.80 (~ (((setoftrueEq) =>
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% 131.89/22.80 (((emptyinPowerset) =>
% 131.89/22.80 (((emptyInPowerset) =>
% 131.89/22.80 (((powersetE) =>
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% 131.89/22.80 (((setunionE) =>
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% 131.89/22.80 (((quantDeMorgan2) =>
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% 131.89/22.80 (((quantDeMorgan4) =>
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% 131.89/22.80 ((
% 131.89/22.80 (inCongP) =>
% 131.89/22.80 ((
% 131.89/22.80 (in__Cong) =>
% 131.89/22.80 ((
% 131.89/22.80 (exuE3u) =>
% 131.89/22.80 ((
% 131.89/22.80 (exu__Cong) =>
% 131.89/22.80 ((
% 131.89/22.80 (setadjoin__Cong) =>
% 131.89/22.80 ((
% 131.89/22.80 (powerset__Cong) =>
% 131.89/22.80 ((
% 131.89/22.80 (setunion__Cong) =>
% 131.89/22.80 ((
% 131.89/22.80 (exuEu) =>
% 131.89/22.80 ((
% 131.89/22.80 (descr__Cong) =>
% 131.89/22.80 ((
% 131.89/22.80 (dsetconstr__Cong) =>
% 131.89/22.80 ((
% 131.89/22.80 (subsetI1) =>
% 131.89/22.80 ((
% 131.89/22.80 (eqimpsubset2) =>
% 131.89/22.80 ((
% 131.89/22.80 (eqimpsubset1) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (emptysetsubset) =>
% 131.89/22.80 ((
% 131.89/22.80 (subsetE) =>
% 131.89/22.80 ((
% 131.89/22.80 (subsetE2) =>
% 131.89/22.80 ((
% 131.89/22.80 (notsubsetI) =>
% 131.89/22.80 ((
% 131.89/22.80 (notequalI1) =>
% 131.89/22.80 ((
% 131.89/22.80 (notequalI2) =>
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% 131.89/22.80 (subsetTrans) =>
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% 131.89/22.80 ((
% 131.89/22.80 (powersetsubset) =>
% 131.89/22.80 ((
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% 131.89/22.80 (sepSubset) =>
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% 131.89/22.80 ((
% 131.89/22.80 (upairset2IR) =>
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% 131.89/22.80 ((
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% 131.89/22.80 (binintersectEL) =>
% 131.89/22.80 ((
% 131.89/22.80 (binintersectLsub) =>
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% 131.89/22.80 ((
% 131.89/22.80 (binintersectSubset3) =>
% 131.89/22.80 ((
% 131.89/22.80 (binintersectER) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (binintersectRsub) =>
% 131.89/22.80 ((
% 131.89/22.80 (binintersectSubset4) =>
% 131.89/22.80 ((
% 131.89/22.80 (binintersectSubset1) =>
% 131.89/22.80 ((
% 131.89/22.80 (bs114d) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (setminusEL) =>
% 131.89/22.80 ((
% 131.89/22.80 (setminusER) =>
% 131.89/22.80 ((
% 131.89/22.80 (setminusSubset2) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (setminusELneg) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (symdiffI2) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
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% 131.89/22.80 (secondinupair) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (setukpairIR) =>
% 131.89/22.80 ((
% 131.89/22.80 (kpairiskpair) =>
% 131.89/22.80 ((
% 131.89/22.80 (kpairp) =>
% 131.89/22.80 ((
% 131.89/22.80 (singletonsubset) =>
% 131.89/22.80 ((
% 131.89/22.80 (singletoninpowerset) =>
% 131.89/22.80 ((
% 131.89/22.80 (singletoninpowunion) =>
% 131.89/22.80 ((
% 131.89/22.80 (upairset2E) =>
% 131.89/22.80 ((
% 131.89/22.80 (upairsubunion) =>
% 131.89/22.80 ((
% 131.89/22.80 (upairinpowunion) =>
% 131.89/22.80 ((
% 131.89/22.80 (ubforcartprodlem1) =>
% 131.89/22.80 ((
% 131.89/22.80 (ubforcartprodlem2) =>
% 131.89/22.80 ((
% 131.89/22.80 (ubforcartprodlem3) =>
% 131.89/22.80 ((
% 131.89/22.80 (cartprodpairin) =>
% 131.89/22.80 ((
% 131.89/22.80 (cartprodmempair1) =>
% 131.89/22.80 ((
% 131.89/22.80 (cartprodmempair) =>
% 131.89/22.80 ((
% 131.89/22.80 (setunionE2) =>
% 131.89/22.80 ((
% 131.89/22.80 (setunionsingleton1) =>
% 131.89/22.80 ((
% 131.89/22.80 (setunionsingleton2) =>
% 131.89/22.80 ((
% 131.89/22.80 (setunionsingleton) =>
% 131.89/22.80 ((
% 131.89/22.80 (singletonprop) =>
% 131.89/22.80 ((
% 131.89/22.80 (ex1E1) =>
% 131.89/22.80 ((
% 131.89/22.80 (ex1I) =>
% 131.89/22.80 ((
% 131.89/22.80 (ex1I2) =>
% 131.89/22.80 ((
% 131.89/22.80 (singletonsuniq) =>
% 131.89/22.80 ((
% 131.89/22.80 (setukpairinjL1) =>
% 131.89/22.80 ((
% 131.89/22.80 (kfstsingleton) =>
% 131.89/22.80 ((
% 131.89/22.80 (theprop) =>
% 131.89/22.80 ((
% 131.89/22.80 (kfstpairEq) =>
% 131.89/22.80 ((
% 131.89/22.80 (cartprodfstin) =>
% 131.89/22.80 ((
% 131.89/22.80 (setukpairinjL2) =>
% 131.89/22.80 ((
% 131.89/22.80 (setukpairinjL) =>
% 131.89/22.80 ((
% 131.89/22.80 (setukpairinjR11) =>
% 131.89/22.80 ((
% 131.89/22.80 (setukpairinjR12) =>
% 131.89/22.80 ((
% 131.89/22.80 (setukpairinjR1) =>
% 131.89/22.80 ((
% 131.89/22.80 (upairequniteq) =>
% 131.89/22.80 ((
% 131.89/22.80 (setukpairinjR2) =>
% 131.89/22.80 ((
% 131.89/22.80 (setukpairinjR) =>
% 131.89/22.80 ((
% 131.89/22.80 (ksndsingleton) =>
% 131.89/22.80 ((
% 131.89/22.80 (ksndpairEq) =>
% 131.89/22.80 ((
% 131.89/22.80 (kpairsurjEq) =>
% 131.89/22.80 ((
% 131.89/22.80 (cartprodsndin) =>
% 131.89/22.80 ((
% 131.89/22.80 (cartprodpairmemEL) =>
% 131.89/22.80 ((
% 131.89/22.80 (cartprodpairmemER) =>
% 131.89/22.80 ((
% 131.89/22.80 (cartprodmempaircEq) =>
% 131.89/22.80 ((
% 131.89/22.80 (cartprodfstpairEq) =>
% 131.89/22.80 ((
% 131.89/22.80 (cartprodsndpairEq) =>
% 131.89/22.80 ((
% 131.89/22.80 (cartprodpairsurjEq) =>
% 131.89/22.80 ((
% 131.89/22.80 (dpsetconstrI) =>
% 131.89/22.80 ((
% 131.89/22.80 (dpsetconstrSub) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (funcImageSingleton) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
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% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (ap2p) =>
% 131.89/22.80 ((
% 131.89/22.80 (funcinfuncset) =>
% 131.89/22.80 ((
% 131.89/22.80 (lamProp) =>
% 131.89/22.80 ((
% 131.89/22.80 (lamp) =>
% 131.89/22.80 ((
% 131.89/22.80 (lam2p) =>
% 131.89/22.80 ((
% 131.89/22.80 (brelnall1) =>
% 131.89/22.80 ((
% 131.89/22.80 (brelnall2) =>
% 131.89/22.80 ((
% 131.89/22.80 (ex1E2) =>
% 131.89/22.80 ((
% 131.89/22.80 (funcGraphProp1) =>
% 131.89/22.80 ((
% 131.89/22.80 (funcGraphProp3) =>
% 131.89/22.80 ((
% 131.89/22.80 (funcGraphProp2) =>
% 131.89/22.80 ((
% 131.89/22.80 (funcextLem) =>
% 131.89/22.80 ((
% 131.89/22.80 (funcGraphProp4) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
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% 131.89/22.80 ((
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% 131.89/22.80 ((
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% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (eta2) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (iftrueProp2) =>
% 131.89/22.80 ((
% 131.89/22.80 (ifSingleton) =>
% 131.89/22.80 ((
% 131.89/22.80 (ifp) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
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% 131.89/22.80 ((
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% 131.89/22.80 (powersetTE1) =>
% 131.89/22.80 ((
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% 131.89/22.80 (complementTE1) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (binintersectTERcontra) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (contrasubsetT1) =>
% 131.89/22.80 ((
% 131.89/22.80 (contrasubsetT2) =>
% 131.89/22.80 ((
% 131.89/22.80 (contrasubsetT3) =>
% 131.89/22.80 ((
% 131.89/22.80 (doubleComplementI1) =>
% 131.89/22.80 ((
% 131.89/22.80 (doubleComplementE1) =>
% 131.89/22.80 ((
% 131.89/22.80 (doubleComplementSub1) =>
% 131.89/22.80 ((
% 131.89/22.80 (doubleComplementSub2) =>
% 131.89/22.80 ((
% 131.89/22.80 (doubleComplementEq) =>
% 131.89/22.80 ((
% 131.89/22.80 (complementTnotintersectT) =>
% 131.89/22.80 ((
% 131.89/22.80 (complementImpComplementIntersect) =>
% 131.89/22.80 ((
% 131.89/22.80 (complementSubsetComplementIntersect) =>
% 131.89/22.80 ((
% 131.89/22.80 (complementInPowersetComplementIntersect) =>
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% 131.89/22.80 (contraSubsetComplement) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (binunionTILcontra) =>
% 131.89/22.80 ((
% 131.89/22.80 (binunionTIRcontra) =>
% 131.89/22.80 ((
% 131.89/22.80 (inIntersectImpInUnion) =>
% 131.89/22.80 ((
% 131.89/22.80 (inIntersectImpInUnion2) =>
% 131.89/22.80 ((
% 131.89/22.80 (inIntersectImpInIntersectUnions) =>
% 131.89/22.80 ((
% 131.89/22.80 (intersectInPowersetIntersectUnions) =>
% 131.89/22.80 ((
% 131.89/22.80 (inComplementUnionImpNotIn1) =>
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% 131.89/22.80 (binunionTEcontra) =>
% 131.89/22.80 ((
% 131.89/22.80 (demorgan2a1) =>
% 131.89/22.80 ((
% 131.89/22.80 (complementUnionInPowersetComplement) =>
% 131.89/22.80 ((
% 131.89/22.80 (demorgan2a2) =>
% 131.89/22.80 ((
% 131.89/22.80 (demorgan1a) =>
% 131.89/22.80 ((
% 131.89/22.80 (demorgan1b) =>
% 131.89/22.80 ((
% 131.89/22.80 (demorgan1) =>
% 131.89/22.80 ((
% 131.89/22.80 (demorgan2a) =>
% 131.89/22.80 ((
% 131.89/22.80 (demorgan2b2) =>
% 131.89/22.80 ((
% 131.89/22.80 (demorgan2b) =>
% 131.89/22.80 ((
% 131.89/22.80 (demorgan2) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz13rule0) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz13rule1) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz13rule2) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz13rule3) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz13rule4) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz1_1) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz1_2) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz1_3) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz1_4) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz1_5) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1all2) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1SetBreln1) =>
% 131.89/22.80 ((
% 131.89/22.80 (choice2fnsingleton) =>
% 131.89/22.80 ((
% 131.89/22.80 (setOfPairsIsBReln1) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1all1) =>
% 131.89/22.80 ((
% 131.89/22.80 (subbreln1) =>
% 131.89/22.80 ((
% 131.89/22.80 (eqbreln1) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1invprop) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1invI) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1invE) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1compprop) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1compI) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1compE) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1compEex) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1unionprop) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1unionIL) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1unionIR) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1unionI) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1unionE) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1unionEcases) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1unionCommutes) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz2Ex) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz2W) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz2A) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz2B) =>
% 131.89/22.80 ((
% 131.89/22.80 (image1Ex) =>
% 131.89/22.80 ((
% 131.89/22.80 (image1Ex1) =>
% 131.89/22.80 ((
% 131.89/22.80 (image1Equiv) =>
% 131.89/22.80 ((
% 131.89/22.80 (image1E) =>
% 131.89/22.80 ((
% 131.89/22.80 (image1I) =>
% 131.89/22.80 ((
% 131.89/22.80 (injFuncInInjFuncSet) =>
% 131.89/22.80 ((
% 131.89/22.80 (injFuncSetFuncIn) =>
% 131.89/22.80 ((
% 131.89/22.80 (injFuncSetFuncInj) =>
% 131.89/22.80 ((
% 131.89/22.80 (surjFuncSetFuncIn) =>
% 131.89/22.80 ((
% 131.89/22.80 (surjFuncSetFuncSurj) =>
% 131.89/22.80 ((
% 131.89/22.80 (leftInvIsSurj) =>
% 131.89/22.80 ((
% 131.89/22.80 (surjCantorThm) =>
% 131.89/22.80 ((
% 131.89/22.80 (foundation2) =>
% 131.89/22.80 ((
% 131.89/22.80 (notinself) =>
% 131.89/22.80 ((
% 131.89/22.80 (notinself2) =>
% 131.89/22.80 ((
% 131.89/22.80 (omegaSp) =>
% 131.89/22.80 ((
% 131.89/22.80 (omegaSclos) =>
% 131.89/22.80 ((
% 131.89/22.80 (peano0notS) =>
% 131.89/22.80 ((
% 131.89/22.80 (peanoSinj) =>
% 131.89/22.80 ((
% 131.89/22.80 (transitivesetOp1) =>
% 131.89/22.80 ((
% 131.89/22.80 (binintTransitive) =>
% 131.89/22.80 ((
% 131.89/22.80 (transitivesetOp2) =>
% 131.89/22.80 ((
% 131.89/22.80 (setunionTransitive) =>
% 131.89/22.80 ((
% 131.89/22.80 (ordinalMinLem1) =>
% 131.89/22.80 ((
% 131.89/22.80 (ordinalTransSet) =>
% 131.89/22.80 ((
% 131.89/22.80 (ordinalTransSet1) =>
% 131.89/22.80 ((
% 131.89/22.80 (setunionOrdinalLem1) =>
% 131.89/22.80 (ordinal @
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% 131.89/22.80 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl318])).
% 131.89/22.80 thf(zip_derived_cl331, plain,
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% 131.89/22.80 (in__Cong) =>
% 131.89/22.80 ((
% 131.89/22.80 (exuE3u) =>
% 131.89/22.80 ((
% 131.89/22.80 (exu__Cong) =>
% 131.89/22.80 ((
% 131.89/22.80 (setadjoin__Cong) =>
% 131.89/22.80 ((
% 131.89/22.80 (powerset__Cong) =>
% 131.89/22.80 ((
% 131.89/22.80 (setunion__Cong) =>
% 131.89/22.80 ((
% 131.89/22.80 (exuEu) =>
% 131.89/22.80 ((
% 131.89/22.80 (descr__Cong) =>
% 131.89/22.80 ((
% 131.89/22.80 (dsetconstr__Cong) =>
% 131.89/22.80 ((
% 131.89/22.80 (subsetI1) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (subsetE2) =>
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% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (notequalI2) =>
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% 131.89/22.80 ((
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% 131.89/22.80 ((
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% 131.89/22.80 ((
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% 131.89/22.80 (bs114d) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
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% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (setminusERneg) =>
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% 131.89/22.80 ((
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% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (kpairp) =>
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% 131.89/22.80 ((
% 131.89/22.80 (singletoninpowerset) =>
% 131.89/22.80 ((
% 131.89/22.80 (singletoninpowunion) =>
% 131.89/22.80 ((
% 131.89/22.80 (upairset2E) =>
% 131.89/22.80 ((
% 131.89/22.80 (upairsubunion) =>
% 131.89/22.80 ((
% 131.89/22.80 (upairinpowunion) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (ubforcartprodlem2) =>
% 131.89/22.80 ((
% 131.89/22.80 (ubforcartprodlem3) =>
% 131.89/22.80 ((
% 131.89/22.80 (cartprodpairin) =>
% 131.89/22.80 ((
% 131.89/22.80 (cartprodmempair1) =>
% 131.89/22.80 ((
% 131.89/22.80 (cartprodmempair) =>
% 131.89/22.80 ((
% 131.89/22.80 (setunionE2) =>
% 131.89/22.80 ((
% 131.89/22.80 (setunionsingleton1) =>
% 131.89/22.80 ((
% 131.89/22.80 (setunionsingleton2) =>
% 131.89/22.80 ((
% 131.89/22.80 (setunionsingleton) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (ex1E1) =>
% 131.89/22.80 ((
% 131.89/22.80 (ex1I) =>
% 131.89/22.80 ((
% 131.89/22.80 (ex1I2) =>
% 131.89/22.80 ((
% 131.89/22.80 (singletonsuniq) =>
% 131.89/22.80 ((
% 131.89/22.80 (setukpairinjL1) =>
% 131.89/22.80 ((
% 131.89/22.80 (kfstsingleton) =>
% 131.89/22.80 ((
% 131.89/22.80 (theprop) =>
% 131.89/22.80 ((
% 131.89/22.80 (kfstpairEq) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
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% 131.89/22.80 (cartprodsndpairEq) =>
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% 131.89/22.80 ((
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% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (brelnall2) =>
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% 131.89/22.80 ((
% 131.89/22.80 (funcGraphProp1) =>
% 131.89/22.80 ((
% 131.89/22.80 (funcGraphProp3) =>
% 131.89/22.80 ((
% 131.89/22.80 (funcGraphProp2) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (contrasubsetT2) =>
% 131.89/22.80 ((
% 131.89/22.80 (contrasubsetT3) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (doubleComplementE1) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (doubleComplementSub2) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (inIntersectImpInIntersectUnions) =>
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% 131.89/22.80 ((
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% 131.89/22.80 (demorgan1b) =>
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% 131.89/22.80 ((
% 131.89/22.80 (demorgan2a) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (demorgan2b) =>
% 131.89/22.80 ((
% 131.89/22.80 (demorgan2) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (woz13rule1) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz13rule2) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz13rule3) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz13rule4) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (woz1_2) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz1_3) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz1_4) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz1_5) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1all2) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1SetBreln1) =>
% 131.89/22.80 ((
% 131.89/22.80 (choice2fnsingleton) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (breln1all1) =>
% 131.89/22.80 ((
% 131.89/22.80 (subbreln1) =>
% 131.89/22.80 ((
% 131.89/22.80 (eqbreln1) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (breln1invI) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1invE) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1compprop) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1compI) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1compE) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1compEex) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1unionprop) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1unionIL) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1unionIR) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1unionI) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1unionE) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1unionEcases) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1unionCommutes) =>
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% 131.89/22.80 ((
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% 131.89/22.80 ((
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% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (image1Ex1) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (image1E) =>
% 131.89/22.80 ((
% 131.89/22.80 (image1I) =>
% 131.89/22.80 ((
% 131.89/22.80 (injFuncInInjFuncSet) =>
% 131.89/22.80 ((
% 131.89/22.80 (injFuncSetFuncIn) =>
% 131.89/22.80 ((
% 131.89/22.80 (injFuncSetFuncInj) =>
% 131.89/22.80 ((
% 131.89/22.80 (surjFuncSetFuncIn) =>
% 131.89/22.80 ((
% 131.89/22.80 (surjFuncSetFuncSurj) =>
% 131.89/22.80 ((
% 131.89/22.80 (leftInvIsSurj) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (notinself) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (omegaSclos) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
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% 131.89/22.80 ((
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% 131.89/22.80 ((
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% 131.89/22.80 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl325])).
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% 131.89/22.80 (descr__Cong) =>
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% 131.89/22.80 ((
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% 131.89/22.80 ((
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% 131.89/22.80 ((
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% 131.89/22.80 ((
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% 131.89/22.80 ((
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% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (cartprodmempair) =>
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% 131.89/22.80 ((
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% 131.89/22.80 (ex1I2) =>
% 131.89/22.80 ((
% 131.89/22.80 (singletonsuniq) =>
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% 131.89/22.80 (setukpairinjL1) =>
% 131.89/22.80 ((
% 131.89/22.80 (kfstsingleton) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (kfstpairEq) =>
% 131.89/22.80 ((
% 131.89/22.80 (cartprodfstin) =>
% 131.89/22.80 ((
% 131.89/22.80 (setukpairinjL2) =>
% 131.89/22.80 ((
% 131.89/22.80 (setukpairinjL) =>
% 131.89/22.80 ((
% 131.89/22.80 (setukpairinjR11) =>
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% 131.89/22.80 (setukpairinjR12) =>
% 131.89/22.80 ((
% 131.89/22.80 (setukpairinjR1) =>
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% 131.89/22.80 (upairequniteq) =>
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% 131.89/22.80 (setukpairinjR) =>
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% 131.89/22.80 (ksndsingleton) =>
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% 131.89/22.80 ((
% 131.89/22.80 (kpairsurjEq) =>
% 131.89/22.80 ((
% 131.89/22.80 (cartprodsndin) =>
% 131.89/22.80 ((
% 131.89/22.80 (cartprodpairmemEL) =>
% 131.89/22.80 ((
% 131.89/22.80 (cartprodpairmemER) =>
% 131.89/22.80 ((
% 131.89/22.80 (cartprodmempaircEq) =>
% 131.89/22.80 ((
% 131.89/22.80 (cartprodfstpairEq) =>
% 131.89/22.80 ((
% 131.89/22.80 (cartprodsndpairEq) =>
% 131.89/22.80 ((
% 131.89/22.80 (cartprodpairsurjEq) =>
% 131.89/22.80 ((
% 131.89/22.80 (dpsetconstrI) =>
% 131.89/22.80 ((
% 131.89/22.80 (dpsetconstrSub) =>
% 131.89/22.80 ((
% 131.89/22.80 (setOfPairsIsBReln) =>
% 131.89/22.80 ((
% 131.89/22.80 (dpsetconstrERa) =>
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% 131.89/22.80 (dpsetconstrEL1) =>
% 131.89/22.80 ((
% 131.89/22.80 (dpsetconstrEL2) =>
% 131.89/22.80 ((
% 131.89/22.80 (dpsetconstrER) =>
% 131.89/22.80 ((
% 131.89/22.80 (funcImageSingleton) =>
% 131.89/22.80 ((
% 131.89/22.80 (apProp) =>
% 131.89/22.80 ((
% 131.89/22.80 (app) =>
% 131.89/22.80 ((
% 131.89/22.80 (infuncsetfunc) =>
% 131.89/22.80 ((
% 131.89/22.80 (ap2p) =>
% 131.89/22.80 ((
% 131.89/22.80 (funcinfuncset) =>
% 131.89/22.80 ((
% 131.89/22.80 (lamProp) =>
% 131.89/22.80 ((
% 131.89/22.80 (lamp) =>
% 131.89/22.80 ((
% 131.89/22.80 (lam2p) =>
% 131.89/22.80 ((
% 131.89/22.80 (brelnall1) =>
% 131.89/22.80 ((
% 131.89/22.80 (brelnall2) =>
% 131.89/22.80 ((
% 131.89/22.80 (ex1E2) =>
% 131.89/22.80 ((
% 131.89/22.80 (funcGraphProp1) =>
% 131.89/22.80 ((
% 131.89/22.80 (funcGraphProp3) =>
% 131.89/22.80 ((
% 131.89/22.80 (funcGraphProp2) =>
% 131.89/22.80 ((
% 131.89/22.80 (funcextLem) =>
% 131.89/22.80 ((
% 131.89/22.80 (funcGraphProp4) =>
% 131.89/22.80 ((
% 131.89/22.80 (subbreln) =>
% 131.89/22.80 ((
% 131.89/22.80 (eqbreln) =>
% 131.89/22.80 ((
% 131.89/22.80 (funcext) =>
% 131.89/22.80 ((
% 131.89/22.80 (funcext2) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (ap2apEq2) =>
% 131.89/22.80 ((
% 131.89/22.80 (beta1) =>
% 131.89/22.80 ((
% 131.89/22.80 (eta1) =>
% 131.89/22.80 ((
% 131.89/22.80 (lam2lamEq) =>
% 131.89/22.80 ((
% 131.89/22.80 (beta2) =>
% 131.89/22.80 ((
% 131.89/22.80 (eta2) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (iffalseProp2) =>
% 131.89/22.80 ((
% 131.89/22.80 (iftrueProp1) =>
% 131.89/22.80 ((
% 131.89/22.80 (iftrueProp2) =>
% 131.89/22.80 ((
% 131.89/22.80 (ifSingleton) =>
% 131.89/22.80 ((
% 131.89/22.80 (ifp) =>
% 131.89/22.80 ((
% 131.89/22.80 (theeq) =>
% 131.89/22.80 ((
% 131.89/22.80 (iftrue) =>
% 131.89/22.80 ((
% 131.89/22.80 (iffalse) =>
% 131.89/22.80 ((
% 131.89/22.80 (iftrueorfalse) =>
% 131.89/22.80 ((
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% 131.89/22.80 (powersetT_lem) =>
% 131.89/22.80 ((
% 131.89/22.80 (setminusT_lem) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (setextT) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (powersetTE1) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (complementTE1) =>
% 131.89/22.80 ((
% 131.89/22.80 (binintersectTELcontra) =>
% 131.89/22.80 ((
% 131.89/22.80 (binintersectTERcontra) =>
% 131.89/22.80 ((
% 131.89/22.80 (contrasubsetT) =>
% 131.89/22.80 ((
% 131.89/22.80 (contrasubsetT1) =>
% 131.89/22.80 ((
% 131.89/22.80 (contrasubsetT2) =>
% 131.89/22.80 ((
% 131.89/22.80 (contrasubsetT3) =>
% 131.89/22.80 ((
% 131.89/22.80 (doubleComplementI1) =>
% 131.89/22.80 ((
% 131.89/22.80 (doubleComplementE1) =>
% 131.89/22.80 ((
% 131.89/22.80 (doubleComplementSub1) =>
% 131.89/22.80 ((
% 131.89/22.80 (doubleComplementSub2) =>
% 131.89/22.80 ((
% 131.89/22.80 (doubleComplementEq) =>
% 131.89/22.80 ((
% 131.89/22.80 (complementTnotintersectT) =>
% 131.89/22.80 ((
% 131.89/22.80 (complementImpComplementIntersect) =>
% 131.89/22.80 ((
% 131.89/22.80 (complementSubsetComplementIntersect) =>
% 131.89/22.80 ((
% 131.89/22.80 (complementInPowersetComplementIntersect) =>
% 131.89/22.80 ((
% 131.89/22.80 (contraSubsetComplement) =>
% 131.89/22.80 ((
% 131.89/22.80 (complementTcontraSubset) =>
% 131.89/22.80 ((
% 131.89/22.80 (binunionTILcontra) =>
% 131.89/22.80 ((
% 131.89/22.80 (binunionTIRcontra) =>
% 131.89/22.80 ((
% 131.89/22.80 (inIntersectImpInUnion) =>
% 131.89/22.80 ((
% 131.89/22.80 (inIntersectImpInUnion2) =>
% 131.89/22.80 ((
% 131.89/22.80 (inIntersectImpInIntersectUnions) =>
% 131.89/22.80 ((
% 131.89/22.80 (intersectInPowersetIntersectUnions) =>
% 131.89/22.80 ((
% 131.89/22.80 (inComplementUnionImpNotIn1) =>
% 131.89/22.80 ((
% 131.89/22.80 (inComplementUnionImpInComplement1) =>
% 131.89/22.80 ((
% 131.89/22.80 (binunionTE) =>
% 131.89/22.80 ((
% 131.89/22.80 (binunionTEcontra) =>
% 131.89/22.80 ((
% 131.89/22.80 (demorgan2a1) =>
% 131.89/22.80 ((
% 131.89/22.80 (complementUnionInPowersetComplement) =>
% 131.89/22.80 ((
% 131.89/22.80 (demorgan2a2) =>
% 131.89/22.80 ((
% 131.89/22.80 (demorgan1a) =>
% 131.89/22.80 ((
% 131.89/22.80 (demorgan1b) =>
% 131.89/22.80 ((
% 131.89/22.80 (demorgan1) =>
% 131.89/22.80 ((
% 131.89/22.80 (demorgan2a) =>
% 131.89/22.80 ((
% 131.89/22.80 (demorgan2b2) =>
% 131.89/22.80 ((
% 131.89/22.80 (demorgan2b) =>
% 131.89/22.80 ((
% 131.89/22.80 (demorgan2) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz13rule0) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz13rule1) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz13rule2) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz13rule3) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz13rule4) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz1_1) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz1_2) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz1_3) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz1_4) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz1_5) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1all2) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1SetBreln1) =>
% 131.89/22.80 ((
% 131.89/22.80 (choice2fnsingleton) =>
% 131.89/22.80 ((
% 131.89/22.80 (setOfPairsIsBReln1) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1all1) =>
% 131.89/22.80 ((
% 131.89/22.80 (subbreln1) =>
% 131.89/22.80 ((
% 131.89/22.80 (eqbreln1) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1invprop) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1invI) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1invE) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1compprop) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1compI) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1compE) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1compEex) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1unionprop) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1unionIL) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1unionIR) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1unionI) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1unionE) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1unionEcases) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1unionCommutes) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz2Ex) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz2W) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz2A) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz2B) =>
% 131.89/22.80 ((
% 131.89/22.80 (image1Ex) =>
% 131.89/22.80 ((
% 131.89/22.80 (image1Ex1) =>
% 131.89/22.80 ((
% 131.89/22.80 (image1Equiv) =>
% 131.89/22.80 ((
% 131.89/22.80 (image1E) =>
% 131.89/22.80 ((
% 131.89/22.80 (image1I) =>
% 131.89/22.80 ((
% 131.89/22.80 (injFuncInInjFuncSet) =>
% 131.89/22.80 ((
% 131.89/22.80 (injFuncSetFuncIn) =>
% 131.89/22.80 ((
% 131.89/22.80 (injFuncSetFuncInj) =>
% 131.89/22.80 ((
% 131.89/22.80 (surjFuncSetFuncIn) =>
% 131.89/22.80 ((
% 131.89/22.80 (surjFuncSetFuncSurj) =>
% 131.89/22.80 ((
% 131.89/22.80 (leftInvIsSurj) =>
% 131.89/22.80 ((
% 131.89/22.80 (surjCantorThm) =>
% 131.89/22.80 ((
% 131.89/22.80 (foundation2) =>
% 131.89/22.80 ((
% 131.89/22.80 (notinself) =>
% 131.89/22.80 ((
% 131.89/22.80 (notinself2) =>
% 131.89/22.80 ((
% 131.89/22.80 (omegaSp) =>
% 131.89/22.80 ((
% 131.89/22.80 (omegaSclos) =>
% 131.89/22.80 ((
% 131.89/22.80 (peano0notS) =>
% 131.89/22.80 ((
% 131.89/22.80 (peanoSinj) =>
% 131.89/22.80 ((
% 131.89/22.80 (transitivesetOp1) =>
% 131.89/22.80 ((
% 131.89/22.80 (binintTransitive) =>
% 131.89/22.80 ((
% 131.89/22.80 (transitivesetOp2) =>
% 131.89/22.80 ((
% 131.89/22.80 (setunionTransitive) =>
% 131.89/22.80 ((
% 131.89/22.80 (ordinalMinLem1) =>
% 131.89/22.80 ((
% 131.89/22.80 (ordinalTransSet) =>
% 131.89/22.80 ((
% 131.89/22.80 (ordinalTransSet1) =>
% 131.89/22.80 ((
% 131.89/22.80 (setunionOrdinalLem1) =>
% 131.89/22.80 (ordinal @
% 131.89/22.80 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 131.89/22.80 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl331])).
% 131.89/22.80 thf(zip_derived_cl343, plain,
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% 131.89/22.80 (((setunionE) =>
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% 131.89/22.80 (((upairsetIR) =>
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% 131.89/22.80 (((quantDeMorgan2) =>
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% 131.89/22.80 (((quantDeMorgan4) =>
% 131.89/22.80 (((prop2setI) =>
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% 131.89/22.80 ((
% 131.89/22.80 (exu__Cong) =>
% 131.89/22.80 ((
% 131.89/22.80 (setadjoin__Cong) =>
% 131.89/22.80 ((
% 131.89/22.80 (powerset__Cong) =>
% 131.89/22.80 ((
% 131.89/22.80 (setunion__Cong) =>
% 131.89/22.80 ((
% 131.89/22.80 (exuEu) =>
% 131.89/22.80 ((
% 131.89/22.80 (descr__Cong) =>
% 131.89/22.80 ((
% 131.89/22.80 (dsetconstr__Cong) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
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% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (subsetI2) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (subsetE2) =>
% 131.89/22.80 ((
% 131.89/22.80 (notsubsetI) =>
% 131.89/22.80 ((
% 131.89/22.80 (notequalI1) =>
% 131.89/22.80 ((
% 131.89/22.80 (notequalI2) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (subsetTrans) =>
% 131.89/22.80 ((
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% 131.89/22.80 (powersetE1) =>
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% 131.89/22.80 ((
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% 131.89/22.80 (sepSubset) =>
% 131.89/22.80 ((
% 131.89/22.80 (binunionIL) =>
% 131.89/22.80 ((
% 131.89/22.80 (upairset2IR) =>
% 131.89/22.80 ((
% 131.89/22.80 (binunionIR) =>
% 131.89/22.80 ((
% 131.89/22.80 (binunionEcases) =>
% 131.89/22.80 ((
% 131.89/22.80 (binunionE) =>
% 131.89/22.80 ((
% 131.89/22.80 (binunionLsub) =>
% 131.89/22.80 ((
% 131.89/22.80 (binunionRsub) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (binintersectSubset3) =>
% 131.89/22.80 ((
% 131.89/22.80 (binintersectER) =>
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% 131.89/22.80 ((
% 131.89/22.80 (binintersectRsub) =>
% 131.89/22.80 ((
% 131.89/22.80 (binintersectSubset4) =>
% 131.89/22.80 ((
% 131.89/22.80 (binintersectSubset1) =>
% 131.89/22.80 ((
% 131.89/22.80 (bs114d) =>
% 131.89/22.80 ((
% 131.89/22.80 (setminusI) =>
% 131.89/22.80 ((
% 131.89/22.80 (setminusEL) =>
% 131.89/22.80 ((
% 131.89/22.80 (setminusER) =>
% 131.89/22.80 ((
% 131.89/22.80 (setminusSubset2) =>
% 131.89/22.80 ((
% 131.89/22.80 (setminusERneg) =>
% 131.89/22.80 ((
% 131.89/22.80 (setminusELneg) =>
% 131.89/22.80 ((
% 131.89/22.80 (setminusILneg) =>
% 131.89/22.80 ((
% 131.89/22.80 (setminusIRneg) =>
% 131.89/22.80 ((
% 131.89/22.80 (setminusLsub) =>
% 131.89/22.80 ((
% 131.89/22.80 (setminusSubset1) =>
% 131.89/22.80 ((
% 131.89/22.80 (symdiffE) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (symdiffI2) =>
% 131.89/22.80 ((
% 131.89/22.80 (symdiffIneg1) =>
% 131.89/22.80 ((
% 131.89/22.80 (symdiffIneg2) =>
% 131.89/22.80 ((
% 131.89/22.80 (secondinupair) =>
% 131.89/22.80 ((
% 131.89/22.80 (setukpairIL) =>
% 131.89/22.80 ((
% 131.89/22.80 (setukpairIR) =>
% 131.89/22.80 ((
% 131.89/22.80 (kpairiskpair) =>
% 131.89/22.80 ((
% 131.89/22.80 (kpairp) =>
% 131.89/22.80 ((
% 131.89/22.80 (singletonsubset) =>
% 131.89/22.80 ((
% 131.89/22.80 (singletoninpowerset) =>
% 131.89/22.80 ((
% 131.89/22.80 (singletoninpowunion) =>
% 131.89/22.80 ((
% 131.89/22.80 (upairset2E) =>
% 131.89/22.80 ((
% 131.89/22.80 (upairsubunion) =>
% 131.89/22.80 ((
% 131.89/22.80 (upairinpowunion) =>
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% 131.89/22.80 ((
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% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (kfstpairEq) =>
% 131.89/22.80 ((
% 131.89/22.80 (cartprodfstin) =>
% 131.89/22.80 ((
% 131.89/22.80 (setukpairinjL2) =>
% 131.89/22.80 ((
% 131.89/22.80 (setukpairinjL) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (setukpairinjR1) =>
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% 131.89/22.80 ((
% 131.89/22.80 (kpairsurjEq) =>
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% 131.89/22.80 (cartprodsndin) =>
% 131.89/22.80 ((
% 131.89/22.80 (cartprodpairmemEL) =>
% 131.89/22.80 ((
% 131.89/22.80 (cartprodpairmemER) =>
% 131.89/22.80 ((
% 131.89/22.80 (cartprodmempaircEq) =>
% 131.89/22.80 ((
% 131.89/22.80 (cartprodfstpairEq) =>
% 131.89/22.80 ((
% 131.89/22.80 (cartprodsndpairEq) =>
% 131.89/22.80 ((
% 131.89/22.80 (cartprodpairsurjEq) =>
% 131.89/22.80 ((
% 131.89/22.80 (dpsetconstrI) =>
% 131.89/22.80 ((
% 131.89/22.80 (dpsetconstrSub) =>
% 131.89/22.80 ((
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% 131.89/22.80 (dpsetconstrEL2) =>
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% 131.89/22.80 (funcImageSingleton) =>
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% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (infuncsetfunc) =>
% 131.89/22.80 ((
% 131.89/22.80 (ap2p) =>
% 131.89/22.80 ((
% 131.89/22.80 (funcinfuncset) =>
% 131.89/22.80 ((
% 131.89/22.80 (lamProp) =>
% 131.89/22.80 ((
% 131.89/22.80 (lamp) =>
% 131.89/22.80 ((
% 131.89/22.80 (lam2p) =>
% 131.89/22.80 ((
% 131.89/22.80 (brelnall1) =>
% 131.89/22.80 ((
% 131.89/22.80 (brelnall2) =>
% 131.89/22.80 ((
% 131.89/22.80 (ex1E2) =>
% 131.89/22.80 ((
% 131.89/22.80 (funcGraphProp1) =>
% 131.89/22.80 ((
% 131.89/22.80 (funcGraphProp3) =>
% 131.89/22.80 ((
% 131.89/22.80 (funcGraphProp2) =>
% 131.89/22.80 ((
% 131.89/22.80 (funcextLem) =>
% 131.89/22.80 ((
% 131.89/22.80 (funcGraphProp4) =>
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% 131.89/22.80 ((
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% 131.89/22.80 (ap2apEq2) =>
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% 131.89/22.80 ((
% 131.89/22.80 (eta1) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (eta2) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (iffalseProp2) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (iftrueProp2) =>
% 131.89/22.80 ((
% 131.89/22.80 (ifSingleton) =>
% 131.89/22.80 ((
% 131.89/22.80 (ifp) =>
% 131.89/22.80 ((
% 131.89/22.80 (theeq) =>
% 131.89/22.80 ((
% 131.89/22.80 (iftrue) =>
% 131.89/22.80 ((
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% 131.89/22.80 (powersetTE1) =>
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% 131.89/22.80 (complementTE1) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (binintersectTERcontra) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (contrasubsetT1) =>
% 131.89/22.80 ((
% 131.89/22.80 (contrasubsetT2) =>
% 131.89/22.80 ((
% 131.89/22.80 (contrasubsetT3) =>
% 131.89/22.80 ((
% 131.89/22.80 (doubleComplementI1) =>
% 131.89/22.80 ((
% 131.89/22.80 (doubleComplementE1) =>
% 131.89/22.80 ((
% 131.89/22.80 (doubleComplementSub1) =>
% 131.89/22.80 ((
% 131.89/22.80 (doubleComplementSub2) =>
% 131.89/22.80 ((
% 131.89/22.80 (doubleComplementEq) =>
% 131.89/22.80 ((
% 131.89/22.80 (complementTnotintersectT) =>
% 131.89/22.80 ((
% 131.89/22.80 (complementImpComplementIntersect) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (complementInPowersetComplementIntersect) =>
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% 131.89/22.80 (contraSubsetComplement) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (binunionTILcontra) =>
% 131.89/22.80 ((
% 131.89/22.80 (binunionTIRcontra) =>
% 131.89/22.80 ((
% 131.89/22.80 (inIntersectImpInUnion) =>
% 131.89/22.80 ((
% 131.89/22.80 (inIntersectImpInUnion2) =>
% 131.89/22.80 ((
% 131.89/22.80 (inIntersectImpInIntersectUnions) =>
% 131.89/22.80 ((
% 131.89/22.80 (intersectInPowersetIntersectUnions) =>
% 131.89/22.80 ((
% 131.89/22.80 (inComplementUnionImpNotIn1) =>
% 131.89/22.80 ((
% 131.89/22.80 (inComplementUnionImpInComplement1) =>
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% 131.89/22.80 ((
% 131.89/22.80 (binunionTEcontra) =>
% 131.89/22.80 ((
% 131.89/22.80 (demorgan2a1) =>
% 131.89/22.80 ((
% 131.89/22.80 (complementUnionInPowersetComplement) =>
% 131.89/22.80 ((
% 131.89/22.80 (demorgan2a2) =>
% 131.89/22.80 ((
% 131.89/22.80 (demorgan1a) =>
% 131.89/22.80 ((
% 131.89/22.80 (demorgan1b) =>
% 131.89/22.80 ((
% 131.89/22.80 (demorgan1) =>
% 131.89/22.80 ((
% 131.89/22.80 (demorgan2a) =>
% 131.89/22.80 ((
% 131.89/22.80 (demorgan2b2) =>
% 131.89/22.80 ((
% 131.89/22.80 (demorgan2b) =>
% 131.89/22.80 ((
% 131.89/22.80 (demorgan2) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz13rule0) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz13rule1) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz13rule2) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz13rule3) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz13rule4) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz1_1) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz1_2) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz1_3) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz1_4) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz1_5) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1all2) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1SetBreln1) =>
% 131.89/22.80 ((
% 131.89/22.80 (choice2fnsingleton) =>
% 131.89/22.80 ((
% 131.89/22.80 (setOfPairsIsBReln1) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1all1) =>
% 131.89/22.80 ((
% 131.89/22.80 (subbreln1) =>
% 131.89/22.80 ((
% 131.89/22.80 (eqbreln1) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1invprop) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1invI) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1invE) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1compprop) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1compI) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1compE) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1compEex) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1unionprop) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1unionIL) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1unionIR) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1unionI) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1unionE) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1unionEcases) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1unionCommutes) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz2Ex) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz2W) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (woz2B) =>
% 131.89/22.80 ((
% 131.89/22.80 (image1Ex) =>
% 131.89/22.80 ((
% 131.89/22.80 (image1Ex1) =>
% 131.89/22.80 ((
% 131.89/22.80 (image1Equiv) =>
% 131.89/22.80 ((
% 131.89/22.80 (image1E) =>
% 131.89/22.80 ((
% 131.89/22.80 (image1I) =>
% 131.89/22.80 ((
% 131.89/22.80 (injFuncInInjFuncSet) =>
% 131.89/22.80 ((
% 131.89/22.80 (injFuncSetFuncIn) =>
% 131.89/22.80 ((
% 131.89/22.80 (injFuncSetFuncInj) =>
% 131.89/22.80 ((
% 131.89/22.80 (surjFuncSetFuncIn) =>
% 131.89/22.80 ((
% 131.89/22.80 (surjFuncSetFuncSurj) =>
% 131.89/22.80 ((
% 131.89/22.80 (leftInvIsSurj) =>
% 131.89/22.80 ((
% 131.89/22.80 (surjCantorThm) =>
% 131.89/22.80 ((
% 131.89/22.80 (foundation2) =>
% 131.89/22.80 ((
% 131.89/22.80 (notinself) =>
% 131.89/22.80 ((
% 131.89/22.80 (notinself2) =>
% 131.89/22.80 ((
% 131.89/22.80 (omegaSp) =>
% 131.89/22.80 ((
% 131.89/22.80 (omegaSclos) =>
% 131.89/22.80 ((
% 131.89/22.80 (peano0notS) =>
% 131.89/22.80 ((
% 131.89/22.80 (peanoSinj) =>
% 131.89/22.80 ((
% 131.89/22.80 (transitivesetOp1) =>
% 131.89/22.80 ((
% 131.89/22.80 (binintTransitive) =>
% 131.89/22.80 ((
% 131.89/22.80 (transitivesetOp2) =>
% 131.89/22.80 ((
% 131.89/22.80 (setunionTransitive) =>
% 131.89/22.80 ((
% 131.89/22.80 (ordinalMinLem1) =>
% 131.89/22.80 ((
% 131.89/22.80 (ordinalTransSet) =>
% 131.89/22.80 ((
% 131.89/22.80 (ordinalTransSet1) =>
% 131.89/22.80 ((
% 131.89/22.80 (setunionOrdinalLem1) =>
% 131.89/22.80 (ordinal @
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% 131.89/22.80 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl337])).
% 131.89/22.80 thf(zip_derived_cl350, plain,
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% 131.89/22.80 ((
% 131.89/22.80 (setunion__Cong) =>
% 131.89/22.80 ((
% 131.89/22.80 (exuEu) =>
% 131.89/22.80 ((
% 131.89/22.80 (descr__Cong) =>
% 131.89/22.80 ((
% 131.89/22.80 (dsetconstr__Cong) =>
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% 131.89/22.80 ((
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% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (notequalI2) =>
% 131.89/22.80 ((
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% 131.89/22.80 (binintersectER) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
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% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (binintersectSubset1) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (setminusEL) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (setminusSubset2) =>
% 131.89/22.80 ((
% 131.89/22.80 (setminusERneg) =>
% 131.89/22.80 ((
% 131.89/22.80 (setminusELneg) =>
% 131.89/22.80 ((
% 131.89/22.80 (setminusILneg) =>
% 131.89/22.80 ((
% 131.89/22.80 (setminusIRneg) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (setminusSubset1) =>
% 131.89/22.80 ((
% 131.89/22.80 (symdiffE) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (symdiffI2) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (symdiffIneg2) =>
% 131.89/22.80 ((
% 131.89/22.80 (secondinupair) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (setukpairIR) =>
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% 131.89/22.80 ((
% 131.89/22.80 (kpairp) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (singletoninpowerset) =>
% 131.89/22.80 ((
% 131.89/22.80 (singletoninpowunion) =>
% 131.89/22.80 ((
% 131.89/22.80 (upairset2E) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (upairinpowunion) =>
% 131.89/22.80 ((
% 131.89/22.80 (ubforcartprodlem1) =>
% 131.89/22.80 ((
% 131.89/22.80 (ubforcartprodlem2) =>
% 131.89/22.80 ((
% 131.89/22.80 (ubforcartprodlem3) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
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% 131.89/22.80 (cartprodmempair) =>
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% 131.89/22.80 (ex1I2) =>
% 131.89/22.80 ((
% 131.89/22.80 (singletonsuniq) =>
% 131.89/22.80 ((
% 131.89/22.80 (setukpairinjL1) =>
% 131.89/22.80 ((
% 131.89/22.80 (kfstsingleton) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (kfstpairEq) =>
% 131.89/22.80 ((
% 131.89/22.80 (cartprodfstin) =>
% 131.89/22.80 ((
% 131.89/22.80 (setukpairinjL2) =>
% 131.89/22.80 ((
% 131.89/22.80 (setukpairinjL) =>
% 131.89/22.80 ((
% 131.89/22.80 (setukpairinjR11) =>
% 131.89/22.80 ((
% 131.89/22.80 (setukpairinjR12) =>
% 131.89/22.80 ((
% 131.89/22.80 (setukpairinjR1) =>
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% 131.89/22.80 (setukpairinjR) =>
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% 131.89/22.80 (ksndsingleton) =>
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% 131.89/22.80 ((
% 131.89/22.80 (kpairsurjEq) =>
% 131.89/22.80 ((
% 131.89/22.80 (cartprodsndin) =>
% 131.89/22.80 ((
% 131.89/22.80 (cartprodpairmemEL) =>
% 131.89/22.80 ((
% 131.89/22.80 (cartprodpairmemER) =>
% 131.89/22.80 ((
% 131.89/22.80 (cartprodmempaircEq) =>
% 131.89/22.80 ((
% 131.89/22.80 (cartprodfstpairEq) =>
% 131.89/22.80 ((
% 131.89/22.80 (cartprodsndpairEq) =>
% 131.89/22.80 ((
% 131.89/22.80 (cartprodpairsurjEq) =>
% 131.89/22.80 ((
% 131.89/22.80 (dpsetconstrI) =>
% 131.89/22.80 ((
% 131.89/22.80 (dpsetconstrSub) =>
% 131.89/22.80 ((
% 131.89/22.80 (setOfPairsIsBReln) =>
% 131.89/22.80 ((
% 131.89/22.80 (dpsetconstrERa) =>
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% 131.89/22.80 (dpsetconstrEL1) =>
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% 131.89/22.80 (dpsetconstrEL2) =>
% 131.89/22.80 ((
% 131.89/22.80 (dpsetconstrER) =>
% 131.89/22.80 ((
% 131.89/22.80 (funcImageSingleton) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (infuncsetfunc) =>
% 131.89/22.80 ((
% 131.89/22.80 (ap2p) =>
% 131.89/22.80 ((
% 131.89/22.80 (funcinfuncset) =>
% 131.89/22.80 ((
% 131.89/22.80 (lamProp) =>
% 131.89/22.80 ((
% 131.89/22.80 (lamp) =>
% 131.89/22.80 ((
% 131.89/22.80 (lam2p) =>
% 131.89/22.80 ((
% 131.89/22.80 (brelnall1) =>
% 131.89/22.80 ((
% 131.89/22.80 (brelnall2) =>
% 131.89/22.80 ((
% 131.89/22.80 (ex1E2) =>
% 131.89/22.80 ((
% 131.89/22.80 (funcGraphProp1) =>
% 131.89/22.80 ((
% 131.89/22.80 (funcGraphProp3) =>
% 131.89/22.80 ((
% 131.89/22.80 (funcGraphProp2) =>
% 131.89/22.80 ((
% 131.89/22.80 (funcextLem) =>
% 131.89/22.80 ((
% 131.89/22.80 (funcGraphProp4) =>
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% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (funcext2) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (ap2apEq2) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (eta1) =>
% 131.89/22.80 ((
% 131.89/22.80 (lam2lamEq) =>
% 131.89/22.80 ((
% 131.89/22.80 (beta2) =>
% 131.89/22.80 ((
% 131.89/22.80 (eta2) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (iffalseProp2) =>
% 131.89/22.80 ((
% 131.89/22.80 (iftrueProp1) =>
% 131.89/22.80 ((
% 131.89/22.80 (iftrueProp2) =>
% 131.89/22.80 ((
% 131.89/22.80 (ifSingleton) =>
% 131.89/22.80 ((
% 131.89/22.80 (ifp) =>
% 131.89/22.80 ((
% 131.89/22.80 (theeq) =>
% 131.89/22.80 ((
% 131.89/22.80 (iftrue) =>
% 131.89/22.80 ((
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% 131.89/22.80 (iftrueorfalse) =>
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% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (setextT) =>
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% 131.89/22.80 (powersetTE1) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (complementTE1) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (binintersectTERcontra) =>
% 131.89/22.80 ((
% 131.89/22.80 (contrasubsetT) =>
% 131.89/22.80 ((
% 131.89/22.80 (contrasubsetT1) =>
% 131.89/22.80 ((
% 131.89/22.80 (contrasubsetT2) =>
% 131.89/22.80 ((
% 131.89/22.80 (contrasubsetT3) =>
% 131.89/22.80 ((
% 131.89/22.80 (doubleComplementI1) =>
% 131.89/22.80 ((
% 131.89/22.80 (doubleComplementE1) =>
% 131.89/22.80 ((
% 131.89/22.80 (doubleComplementSub1) =>
% 131.89/22.80 ((
% 131.89/22.80 (doubleComplementSub2) =>
% 131.89/22.80 ((
% 131.89/22.80 (doubleComplementEq) =>
% 131.89/22.80 ((
% 131.89/22.80 (complementTnotintersectT) =>
% 131.89/22.80 ((
% 131.89/22.80 (complementImpComplementIntersect) =>
% 131.89/22.80 ((
% 131.89/22.80 (complementSubsetComplementIntersect) =>
% 131.89/22.80 ((
% 131.89/22.80 (complementInPowersetComplementIntersect) =>
% 131.89/22.80 ((
% 131.89/22.80 (contraSubsetComplement) =>
% 131.89/22.80 ((
% 131.89/22.80 (complementTcontraSubset) =>
% 131.89/22.80 ((
% 131.89/22.80 (binunionTILcontra) =>
% 131.89/22.80 ((
% 131.89/22.80 (binunionTIRcontra) =>
% 131.89/22.80 ((
% 131.89/22.80 (inIntersectImpInUnion) =>
% 131.89/22.80 ((
% 131.89/22.80 (inIntersectImpInUnion2) =>
% 131.89/22.80 ((
% 131.89/22.80 (inIntersectImpInIntersectUnions) =>
% 131.89/22.80 ((
% 131.89/22.80 (intersectInPowersetIntersectUnions) =>
% 131.89/22.80 ((
% 131.89/22.80 (inComplementUnionImpNotIn1) =>
% 131.89/22.80 ((
% 131.89/22.80 (inComplementUnionImpInComplement1) =>
% 131.89/22.80 ((
% 131.89/22.80 (binunionTE) =>
% 131.89/22.80 ((
% 131.89/22.80 (binunionTEcontra) =>
% 131.89/22.80 ((
% 131.89/22.80 (demorgan2a1) =>
% 131.89/22.80 ((
% 131.89/22.80 (complementUnionInPowersetComplement) =>
% 131.89/22.80 ((
% 131.89/22.80 (demorgan2a2) =>
% 131.89/22.80 ((
% 131.89/22.80 (demorgan1a) =>
% 131.89/22.80 ((
% 131.89/22.80 (demorgan1b) =>
% 131.89/22.80 ((
% 131.89/22.80 (demorgan1) =>
% 131.89/22.80 ((
% 131.89/22.80 (demorgan2a) =>
% 131.89/22.80 ((
% 131.89/22.80 (demorgan2b2) =>
% 131.89/22.80 ((
% 131.89/22.80 (demorgan2b) =>
% 131.89/22.80 ((
% 131.89/22.80 (demorgan2) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz13rule0) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz13rule1) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz13rule2) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz13rule3) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz13rule4) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz1_1) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz1_2) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz1_3) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz1_4) =>
% 131.89/22.80 ((
% 131.89/22.80 (woz1_5) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1all2) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1SetBreln1) =>
% 131.89/22.80 ((
% 131.89/22.80 (choice2fnsingleton) =>
% 131.89/22.80 ((
% 131.89/22.80 (setOfPairsIsBReln1) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1all1) =>
% 131.89/22.80 ((
% 131.89/22.80 (subbreln1) =>
% 131.89/22.80 ((
% 131.89/22.80 (eqbreln1) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1invprop) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1invI) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1invE) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1compprop) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1compI) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1compE) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1compEex) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1unionprop) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1unionIL) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1unionIR) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1unionI) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1unionE) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1unionEcases) =>
% 131.89/22.80 ((
% 131.89/22.80 (breln1unionCommutes) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
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% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (woz2B) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (image1Ex1) =>
% 131.89/22.80 ((
% 131.89/22.80 (image1Equiv) =>
% 131.89/22.80 ((
% 131.89/22.80 (image1E) =>
% 131.89/22.80 ((
% 131.89/22.80 (image1I) =>
% 131.89/22.80 ((
% 131.89/22.80 (injFuncInInjFuncSet) =>
% 131.89/22.80 ((
% 131.89/22.80 (injFuncSetFuncIn) =>
% 131.89/22.80 ((
% 131.89/22.80 (injFuncSetFuncInj) =>
% 131.89/22.80 ((
% 131.89/22.80 (surjFuncSetFuncIn) =>
% 131.89/22.80 ((
% 131.89/22.80 (surjFuncSetFuncSurj) =>
% 131.89/22.80 ((
% 131.89/22.80 (leftInvIsSurj) =>
% 131.89/22.80 ((
% 131.89/22.80 (surjCantorThm) =>
% 131.89/22.80 ((
% 131.89/22.80 (foundation2) =>
% 131.89/22.80 ((
% 131.89/22.80 (notinself) =>
% 131.89/22.80 ((
% 131.89/22.80 (notinself2) =>
% 131.89/22.80 ((
% 131.89/22.80 (omegaSp) =>
% 131.89/22.80 ((
% 131.89/22.80 (omegaSclos) =>
% 131.89/22.80 ((
% 131.89/22.80 (peano0notS) =>
% 131.89/22.80 ((
% 131.89/22.80 (peanoSinj) =>
% 131.89/22.80 ((
% 131.89/22.80 (transitivesetOp1) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (setunionTransitive) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
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% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (setunionOrdinalLem1) =>
% 131.89/22.80 (ordinal @
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% 131.89/22.80 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl343])).
% 131.89/22.80 thf(zip_derived_cl357, plain,
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% 131.89/22.80 (exuEu) =>
% 131.89/22.80 ((
% 131.89/22.80 (descr__Cong) =>
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% 131.89/22.80 ((
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% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (bs114d) =>
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% 131.89/22.80 (setminusEL) =>
% 131.89/22.80 ((
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% 131.89/22.80 ((
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% 131.89/22.80 ((
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% 131.89/22.80 ((
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% 131.89/22.80 ((
% 131.89/22.80 (setminusLsub) =>
% 131.89/22.80 ((
% 131.89/22.80 (setminusSubset1) =>
% 131.89/22.80 ((
% 131.89/22.80 (symdiffE) =>
% 131.89/22.80 ((
% 131.89/22.80 (symdiffI1) =>
% 131.89/22.80 ((
% 131.89/22.80 (symdiffI2) =>
% 131.89/22.80 ((
% 131.89/22.80 (symdiffIneg1) =>
% 131.89/22.80 ((
% 131.89/22.80 (symdiffIneg2) =>
% 131.89/22.80 ((
% 131.89/22.80 (secondinupair) =>
% 131.89/22.80 ((
% 131.89/22.80 (setukpairIL) =>
% 131.89/22.80 ((
% 131.89/22.80 (setukpairIR) =>
% 131.89/22.80 ((
% 131.89/22.80 (kpairiskpair) =>
% 131.89/22.80 ((
% 131.89/22.80 (kpairp) =>
% 131.89/22.80 ((
% 131.89/22.80 (singletonsubset) =>
% 131.89/22.80 ((
% 131.89/22.80 (singletoninpowerset) =>
% 131.89/22.80 ((
% 131.89/22.80 (singletoninpowunion) =>
% 131.89/22.80 ((
% 131.89/22.80 (upairset2E) =>
% 131.89/22.80 ((
% 131.89/22.82 (upairsubunion) =>
% 131.89/22.82 ((
% 131.89/22.82 (upairinpowunion) =>
% 131.89/22.82 ((
% 131.89/22.82 (ubforcartprodlem1) =>
% 131.89/22.82 ((
% 131.89/22.82 (ubforcartprodlem2) =>
% 131.89/22.82 ((
% 131.89/22.82 (ubforcartprodlem3) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodpairin) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodmempair1) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodmempair) =>
% 131.89/22.82 ((
% 131.89/22.82 (setunionE2) =>
% 131.89/22.82 ((
% 131.89/22.82 (setunionsingleton1) =>
% 131.89/22.82 ((
% 131.89/22.82 (setunionsingleton2) =>
% 131.89/22.82 ((
% 131.89/22.82 (setunionsingleton) =>
% 131.89/22.82 ((
% 131.89/22.82 (singletonprop) =>
% 131.89/22.82 ((
% 131.89/22.82 (ex1E1) =>
% 131.89/22.82 ((
% 131.89/22.82 (ex1I) =>
% 131.89/22.82 ((
% 131.89/22.82 (ex1I2) =>
% 131.89/22.82 ((
% 131.89/22.82 (singletonsuniq) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairinjL1) =>
% 131.89/22.82 ((
% 131.89/22.82 (kfstsingleton) =>
% 131.89/22.82 ((
% 131.89/22.82 (theprop) =>
% 131.89/22.82 ((
% 131.89/22.82 (kfstpairEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodfstin) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairinjL2) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairinjL) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairinjR11) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairinjR12) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairinjR1) =>
% 131.89/22.82 ((
% 131.89/22.82 (upairequniteq) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairinjR2) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairinjR) =>
% 131.89/22.82 ((
% 131.89/22.82 (ksndsingleton) =>
% 131.89/22.82 ((
% 131.89/22.82 (ksndpairEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (kpairsurjEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodsndin) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodpairmemEL) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodpairmemER) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodmempaircEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodfstpairEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodsndpairEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodpairsurjEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (dpsetconstrI) =>
% 131.89/22.82 ((
% 131.89/22.82 (dpsetconstrSub) =>
% 131.89/22.82 ((
% 131.89/22.82 (setOfPairsIsBReln) =>
% 131.89/22.82 ((
% 131.89/22.82 (dpsetconstrERa) =>
% 131.89/22.82 ((
% 131.89/22.82 (dpsetconstrEL1) =>
% 131.89/22.82 ((
% 131.89/22.82 (dpsetconstrEL2) =>
% 131.89/22.82 ((
% 131.89/22.82 (dpsetconstrER) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcImageSingleton) =>
% 131.89/22.82 ((
% 131.89/22.82 (apProp) =>
% 131.89/22.82 ((
% 131.89/22.82 (app) =>
% 131.89/22.82 ((
% 131.89/22.82 (infuncsetfunc) =>
% 131.89/22.82 ((
% 131.89/22.82 (ap2p) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcinfuncset) =>
% 131.89/22.82 ((
% 131.89/22.82 (lamProp) =>
% 131.89/22.82 ((
% 131.89/22.82 (lamp) =>
% 131.89/22.82 ((
% 131.89/22.82 (lam2p) =>
% 131.89/22.82 ((
% 131.89/22.82 (brelnall1) =>
% 131.89/22.82 ((
% 131.89/22.82 (brelnall2) =>
% 131.89/22.82 ((
% 131.89/22.82 (ex1E2) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcGraphProp1) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcGraphProp3) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcGraphProp2) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcextLem) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcGraphProp4) =>
% 131.89/22.82 ((
% 131.89/22.82 (subbreln) =>
% 131.89/22.82 ((
% 131.89/22.82 (eqbreln) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcext) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcext2) =>
% 131.89/22.82 ((
% 131.89/22.82 (ap2apEq1) =>
% 131.89/22.82 ((
% 131.89/22.82 (ap2apEq2) =>
% 131.89/22.82 ((
% 131.89/22.82 (beta1) =>
% 131.89/22.82 ((
% 131.89/22.82 (eta1) =>
% 131.89/22.82 ((
% 131.89/22.82 (lam2lamEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (beta2) =>
% 131.89/22.82 ((
% 131.89/22.82 (eta2) =>
% 131.89/22.82 ((
% 131.89/22.82 (iffalseProp1) =>
% 131.89/22.82 ((
% 131.89/22.82 (iffalseProp2) =>
% 131.89/22.82 ((
% 131.89/22.82 (iftrueProp1) =>
% 131.89/22.82 ((
% 131.89/22.82 (iftrueProp2) =>
% 131.89/22.82 ((
% 131.89/22.82 (ifSingleton) =>
% 131.89/22.82 ((
% 131.89/22.82 (ifp) =>
% 131.89/22.82 ((
% 131.89/22.82 (theeq) =>
% 131.89/22.82 ((
% 131.89/22.82 (iftrue) =>
% 131.89/22.82 ((
% 131.89/22.82 (iffalse) =>
% 131.89/22.82 ((
% 131.89/22.82 (iftrueorfalse) =>
% 131.89/22.82 ((
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% 131.89/22.82 ((
% 131.89/22.82 (binunionT_lem) =>
% 131.89/22.82 ((
% 131.89/22.82 (powersetT_lem) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusT_lem) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementT_lem) =>
% 131.89/22.82 ((
% 131.89/22.82 (setextT) =>
% 131.89/22.82 ((
% 131.89/22.82 (subsetTI) =>
% 131.89/22.82 ((
% 131.89/22.82 (powersetTI1) =>
% 131.89/22.82 ((
% 131.89/22.82 (powersetTE1) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementTI1) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementTE1) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectTELcontra) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectTERcontra) =>
% 131.89/22.82 ((
% 131.89/22.82 (contrasubsetT) =>
% 131.89/22.82 ((
% 131.89/22.82 (contrasubsetT1) =>
% 131.89/22.82 ((
% 131.89/22.82 (contrasubsetT2) =>
% 131.89/22.82 ((
% 131.89/22.82 (contrasubsetT3) =>
% 131.89/22.82 ((
% 131.89/22.82 (doubleComplementI1) =>
% 131.89/22.82 ((
% 131.89/22.82 (doubleComplementE1) =>
% 131.89/22.82 ((
% 131.89/22.82 (doubleComplementSub1) =>
% 131.89/22.82 ((
% 131.89/22.82 (doubleComplementSub2) =>
% 131.89/22.82 ((
% 131.89/22.82 (doubleComplementEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementTnotintersectT) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementImpComplementIntersect) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementSubsetComplementIntersect) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementInPowersetComplementIntersect) =>
% 131.89/22.82 ((
% 131.89/22.82 (contraSubsetComplement) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementTcontraSubset) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionTILcontra) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionTIRcontra) =>
% 131.89/22.82 ((
% 131.89/22.82 (inIntersectImpInUnion) =>
% 131.89/22.82 ((
% 131.89/22.82 (inIntersectImpInUnion2) =>
% 131.89/22.82 ((
% 131.89/22.82 (inIntersectImpInIntersectUnions) =>
% 131.89/22.82 ((
% 131.89/22.82 (intersectInPowersetIntersectUnions) =>
% 131.89/22.82 ((
% 131.89/22.82 (inComplementUnionImpNotIn1) =>
% 131.89/22.82 ((
% 131.89/22.82 (inComplementUnionImpInComplement1) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionTE) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionTEcontra) =>
% 131.89/22.82 ((
% 131.89/22.82 (demorgan2a1) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementUnionInPowersetComplement) =>
% 131.89/22.82 ((
% 131.89/22.82 (demorgan2a2) =>
% 131.89/22.82 ((
% 131.89/22.82 (demorgan1a) =>
% 131.89/22.82 ((
% 131.89/22.82 (demorgan1b) =>
% 131.89/22.82 ((
% 131.89/22.82 (demorgan1) =>
% 131.89/22.82 ((
% 131.89/22.82 (demorgan2a) =>
% 131.89/22.82 ((
% 131.89/22.82 (demorgan2b2) =>
% 131.89/22.82 ((
% 131.89/22.82 (demorgan2b) =>
% 131.89/22.82 ((
% 131.89/22.82 (demorgan2) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz13rule0) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz13rule1) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz13rule2) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz13rule3) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz13rule4) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz1_1) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz1_2) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz1_3) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz1_4) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz1_5) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1all2) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1SetBreln1) =>
% 131.89/22.82 ((
% 131.89/22.82 (choice2fnsingleton) =>
% 131.89/22.82 ((
% 131.89/22.82 (setOfPairsIsBReln1) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1all1) =>
% 131.89/22.82 ((
% 131.89/22.82 (subbreln1) =>
% 131.89/22.82 ((
% 131.89/22.82 (eqbreln1) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1invprop) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1invI) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1invE) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1compprop) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1compI) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1compE) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1compEex) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1unionprop) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1unionIL) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1unionIR) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1unionI) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1unionE) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1unionEcases) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1unionCommutes) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz2Ex) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz2W) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz2A) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz2B) =>
% 131.89/22.82 ((
% 131.89/22.82 (image1Ex) =>
% 131.89/22.82 ((
% 131.89/22.82 (image1Ex1) =>
% 131.89/22.82 ((
% 131.89/22.82 (image1Equiv) =>
% 131.89/22.82 ((
% 131.89/22.82 (image1E) =>
% 131.89/22.82 ((
% 131.89/22.82 (image1I) =>
% 131.89/22.82 ((
% 131.89/22.82 (injFuncInInjFuncSet) =>
% 131.89/22.82 ((
% 131.89/22.82 (injFuncSetFuncIn) =>
% 131.89/22.82 ((
% 131.89/22.82 (injFuncSetFuncInj) =>
% 131.89/22.82 ((
% 131.89/22.82 (surjFuncSetFuncIn) =>
% 131.89/22.82 ((
% 131.89/22.82 (surjFuncSetFuncSurj) =>
% 131.89/22.82 ((
% 131.89/22.82 (leftInvIsSurj) =>
% 131.89/22.82 ((
% 131.89/22.82 (surjCantorThm) =>
% 131.89/22.82 ((
% 131.89/22.82 (foundation2) =>
% 131.89/22.82 ((
% 131.89/22.82 (notinself) =>
% 131.89/22.82 ((
% 131.89/22.82 (notinself2) =>
% 131.89/22.82 ((
% 131.89/22.82 (omegaSp) =>
% 131.89/22.82 ((
% 131.89/22.82 (omegaSclos) =>
% 131.89/22.82 ((
% 131.89/22.82 (peano0notS) =>
% 131.89/22.82 ((
% 131.89/22.82 (peanoSinj) =>
% 131.89/22.82 ((
% 131.89/22.82 (transitivesetOp1) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintTransitive) =>
% 131.89/22.82 ((
% 131.89/22.82 (transitivesetOp2) =>
% 131.89/22.82 ((
% 131.89/22.82 (setunionTransitive) =>
% 131.89/22.82 ((
% 131.89/22.82 (ordinalMinLem1) =>
% 131.89/22.82 ((
% 131.89/22.82 (ordinalTransSet) =>
% 131.89/22.82 ((
% 131.89/22.82 (ordinalTransSet1) =>
% 131.89/22.82 ((
% 131.89/22.82 (setunionOrdinalLem1) =>
% 131.89/22.82 (ordinal @
% 131.89/22.82 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 131.89/22.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl350])).
% 131.89/22.82 thf(zip_derived_cl364, plain,
% 131.89/22.82 (~ (((setunionE) =>
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% 131.89/22.82 (((upairsetIR) =>
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% 131.89/22.82 (((vacuousDall) =>
% 131.89/22.82 (((quantDeMorgan1) =>
% 131.89/22.82 (((quantDeMorgan2) =>
% 131.89/22.82 (((quantDeMorgan3) =>
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% 131.89/22.82 (((prop2setI) =>
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% 131.89/22.82 (((in__Cong) =>
% 131.89/22.82 (((exuE3u) =>
% 131.89/22.82 (((exu__Cong) =>
% 131.89/22.82 (((setadjoin__Cong) =>
% 131.89/22.82 (((powerset__Cong) =>
% 131.89/22.82 ((
% 131.89/22.82 (setunion__Cong) =>
% 131.89/22.82 ((
% 131.89/22.82 (exuEu) =>
% 131.89/22.82 ((
% 131.89/22.82 (descr__Cong) =>
% 131.89/22.82 ((
% 131.89/22.82 (dsetconstr__Cong) =>
% 131.89/22.82 ((
% 131.89/22.82 (subsetI1) =>
% 131.89/22.82 ((
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% 131.89/22.82 ((
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% 131.89/22.82 ((
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% 131.89/22.82 ((
% 131.89/22.82 (subsetE2) =>
% 131.89/22.82 ((
% 131.89/22.82 (notsubsetI) =>
% 131.89/22.82 ((
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% 131.89/22.82 ((
% 131.89/22.82 (notequalI2) =>
% 131.89/22.82 ((
% 131.89/22.82 (subsetRefl) =>
% 131.89/22.82 ((
% 131.89/22.82 (subsetTrans) =>
% 131.89/22.82 ((
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% 131.89/22.82 ((
% 131.89/22.82 (setadjoinSub2) =>
% 131.89/22.82 ((
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% 131.89/22.82 ((
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% 131.89/22.82 ((
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% 131.89/22.82 ((
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% 131.89/22.82 ((
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% 131.89/22.82 ((
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% 131.89/22.82 ((
% 131.89/22.82 (upairset2IR) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionIR) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionEcases) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionE) =>
% 131.89/22.82 ((
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% 131.89/22.82 ((
% 131.89/22.82 (binunionRsub) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectI) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectSubset5) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectEL) =>
% 131.89/22.82 ((
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% 131.89/22.82 ((
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% 131.89/22.82 ((
% 131.89/22.82 (binintersectSubset3) =>
% 131.89/22.82 ((
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% 131.89/22.82 ((
% 131.89/22.82 (disjointsetsI1) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectRsub) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectSubset4) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectSubset1) =>
% 131.89/22.82 ((
% 131.89/22.82 (bs114d) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusI) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusEL) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusER) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusSubset2) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusERneg) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusELneg) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusILneg) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusIRneg) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusLsub) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusSubset1) =>
% 131.89/22.82 ((
% 131.89/22.82 (symdiffE) =>
% 131.89/22.82 ((
% 131.89/22.82 (symdiffI1) =>
% 131.89/22.82 ((
% 131.89/22.82 (symdiffI2) =>
% 131.89/22.82 ((
% 131.89/22.82 (symdiffIneg1) =>
% 131.89/22.82 ((
% 131.89/22.82 (symdiffIneg2) =>
% 131.89/22.82 ((
% 131.89/22.82 (secondinupair) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairIL) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairIR) =>
% 131.89/22.82 ((
% 131.89/22.82 (kpairiskpair) =>
% 131.89/22.82 ((
% 131.89/22.82 (kpairp) =>
% 131.89/22.82 ((
% 131.89/22.82 (singletonsubset) =>
% 131.89/22.82 ((
% 131.89/22.82 (singletoninpowerset) =>
% 131.89/22.82 ((
% 131.89/22.82 (singletoninpowunion) =>
% 131.89/22.82 ((
% 131.89/22.82 (upairset2E) =>
% 131.89/22.82 ((
% 131.89/22.82 (upairsubunion) =>
% 131.89/22.82 ((
% 131.89/22.82 (upairinpowunion) =>
% 131.89/22.82 ((
% 131.89/22.82 (ubforcartprodlem1) =>
% 131.89/22.82 ((
% 131.89/22.82 (ubforcartprodlem2) =>
% 131.89/22.82 ((
% 131.89/22.82 (ubforcartprodlem3) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodpairin) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodmempair1) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodmempair) =>
% 131.89/22.82 ((
% 131.89/22.82 (setunionE2) =>
% 131.89/22.82 ((
% 131.89/22.82 (setunionsingleton1) =>
% 131.89/22.82 ((
% 131.89/22.82 (setunionsingleton2) =>
% 131.89/22.82 ((
% 131.89/22.82 (setunionsingleton) =>
% 131.89/22.82 ((
% 131.89/22.82 (singletonprop) =>
% 131.89/22.82 ((
% 131.89/22.82 (ex1E1) =>
% 131.89/22.82 ((
% 131.89/22.82 (ex1I) =>
% 131.89/22.82 ((
% 131.89/22.82 (ex1I2) =>
% 131.89/22.82 ((
% 131.89/22.82 (singletonsuniq) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairinjL1) =>
% 131.89/22.82 ((
% 131.89/22.82 (kfstsingleton) =>
% 131.89/22.82 ((
% 131.89/22.82 (theprop) =>
% 131.89/22.82 ((
% 131.89/22.82 (kfstpairEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodfstin) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairinjL2) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairinjL) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairinjR11) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairinjR12) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairinjR1) =>
% 131.89/22.82 ((
% 131.89/22.82 (upairequniteq) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairinjR2) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairinjR) =>
% 131.89/22.82 ((
% 131.89/22.82 (ksndsingleton) =>
% 131.89/22.82 ((
% 131.89/22.82 (ksndpairEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (kpairsurjEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodsndin) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodpairmemEL) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodpairmemER) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodmempaircEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodfstpairEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodsndpairEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodpairsurjEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (dpsetconstrI) =>
% 131.89/22.82 ((
% 131.89/22.82 (dpsetconstrSub) =>
% 131.89/22.82 ((
% 131.89/22.82 (setOfPairsIsBReln) =>
% 131.89/22.82 ((
% 131.89/22.82 (dpsetconstrERa) =>
% 131.89/22.82 ((
% 131.89/22.82 (dpsetconstrEL1) =>
% 131.89/22.82 ((
% 131.89/22.82 (dpsetconstrEL2) =>
% 131.89/22.82 ((
% 131.89/22.82 (dpsetconstrER) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcImageSingleton) =>
% 131.89/22.82 ((
% 131.89/22.82 (apProp) =>
% 131.89/22.82 ((
% 131.89/22.82 (app) =>
% 131.89/22.82 ((
% 131.89/22.82 (infuncsetfunc) =>
% 131.89/22.82 ((
% 131.89/22.82 (ap2p) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcinfuncset) =>
% 131.89/22.82 ((
% 131.89/22.82 (lamProp) =>
% 131.89/22.82 ((
% 131.89/22.82 (lamp) =>
% 131.89/22.82 ((
% 131.89/22.82 (lam2p) =>
% 131.89/22.82 ((
% 131.89/22.82 (brelnall1) =>
% 131.89/22.82 ((
% 131.89/22.82 (brelnall2) =>
% 131.89/22.82 ((
% 131.89/22.82 (ex1E2) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcGraphProp1) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcGraphProp3) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcGraphProp2) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcextLem) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcGraphProp4) =>
% 131.89/22.82 ((
% 131.89/22.82 (subbreln) =>
% 131.89/22.82 ((
% 131.89/22.82 (eqbreln) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcext) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcext2) =>
% 131.89/22.82 ((
% 131.89/22.82 (ap2apEq1) =>
% 131.89/22.82 ((
% 131.89/22.82 (ap2apEq2) =>
% 131.89/22.82 ((
% 131.89/22.82 (beta1) =>
% 131.89/22.82 ((
% 131.89/22.82 (eta1) =>
% 131.89/22.82 ((
% 131.89/22.82 (lam2lamEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (beta2) =>
% 131.89/22.82 ((
% 131.89/22.82 (eta2) =>
% 131.89/22.82 ((
% 131.89/22.82 (iffalseProp1) =>
% 131.89/22.82 ((
% 131.89/22.82 (iffalseProp2) =>
% 131.89/22.82 ((
% 131.89/22.82 (iftrueProp1) =>
% 131.89/22.82 ((
% 131.89/22.82 (iftrueProp2) =>
% 131.89/22.82 ((
% 131.89/22.82 (ifSingleton) =>
% 131.89/22.82 ((
% 131.89/22.82 (ifp) =>
% 131.89/22.82 ((
% 131.89/22.82 (theeq) =>
% 131.89/22.82 ((
% 131.89/22.82 (iftrue) =>
% 131.89/22.82 ((
% 131.89/22.82 (iffalse) =>
% 131.89/22.82 ((
% 131.89/22.82 (iftrueorfalse) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectT_lem) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionT_lem) =>
% 131.89/22.82 ((
% 131.89/22.82 (powersetT_lem) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusT_lem) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementT_lem) =>
% 131.89/22.82 ((
% 131.89/22.82 (setextT) =>
% 131.89/22.82 ((
% 131.89/22.82 (subsetTI) =>
% 131.89/22.82 ((
% 131.89/22.82 (powersetTI1) =>
% 131.89/22.82 ((
% 131.89/22.82 (powersetTE1) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementTI1) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementTE1) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectTELcontra) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectTERcontra) =>
% 131.89/22.82 ((
% 131.89/22.82 (contrasubsetT) =>
% 131.89/22.82 ((
% 131.89/22.82 (contrasubsetT1) =>
% 131.89/22.82 ((
% 131.89/22.82 (contrasubsetT2) =>
% 131.89/22.82 ((
% 131.89/22.82 (contrasubsetT3) =>
% 131.89/22.82 ((
% 131.89/22.82 (doubleComplementI1) =>
% 131.89/22.82 ((
% 131.89/22.82 (doubleComplementE1) =>
% 131.89/22.82 ((
% 131.89/22.82 (doubleComplementSub1) =>
% 131.89/22.82 ((
% 131.89/22.82 (doubleComplementSub2) =>
% 131.89/22.82 ((
% 131.89/22.82 (doubleComplementEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementTnotintersectT) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementImpComplementIntersect) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementSubsetComplementIntersect) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementInPowersetComplementIntersect) =>
% 131.89/22.82 ((
% 131.89/22.82 (contraSubsetComplement) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementTcontraSubset) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionTILcontra) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionTIRcontra) =>
% 131.89/22.82 ((
% 131.89/22.82 (inIntersectImpInUnion) =>
% 131.89/22.82 ((
% 131.89/22.82 (inIntersectImpInUnion2) =>
% 131.89/22.82 ((
% 131.89/22.82 (inIntersectImpInIntersectUnions) =>
% 131.89/22.82 ((
% 131.89/22.82 (intersectInPowersetIntersectUnions) =>
% 131.89/22.82 ((
% 131.89/22.82 (inComplementUnionImpNotIn1) =>
% 131.89/22.82 ((
% 131.89/22.82 (inComplementUnionImpInComplement1) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionTE) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionTEcontra) =>
% 131.89/22.82 ((
% 131.89/22.82 (demorgan2a1) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementUnionInPowersetComplement) =>
% 131.89/22.82 ((
% 131.89/22.82 (demorgan2a2) =>
% 131.89/22.82 ((
% 131.89/22.82 (demorgan1a) =>
% 131.89/22.82 ((
% 131.89/22.82 (demorgan1b) =>
% 131.89/22.82 ((
% 131.89/22.82 (demorgan1) =>
% 131.89/22.82 ((
% 131.89/22.82 (demorgan2a) =>
% 131.89/22.82 ((
% 131.89/22.82 (demorgan2b2) =>
% 131.89/22.82 ((
% 131.89/22.82 (demorgan2b) =>
% 131.89/22.82 ((
% 131.89/22.82 (demorgan2) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz13rule0) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz13rule1) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz13rule2) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz13rule3) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz13rule4) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz1_1) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz1_2) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz1_3) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz1_4) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz1_5) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1all2) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1SetBreln1) =>
% 131.89/22.82 ((
% 131.89/22.82 (choice2fnsingleton) =>
% 131.89/22.82 ((
% 131.89/22.82 (setOfPairsIsBReln1) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1all1) =>
% 131.89/22.82 ((
% 131.89/22.82 (subbreln1) =>
% 131.89/22.82 ((
% 131.89/22.82 (eqbreln1) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1invprop) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1invI) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1invE) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1compprop) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1compI) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1compE) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1compEex) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1unionprop) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1unionIL) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1unionIR) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1unionI) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1unionE) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1unionEcases) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1unionCommutes) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz2Ex) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz2W) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz2A) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz2B) =>
% 131.89/22.82 ((
% 131.89/22.82 (image1Ex) =>
% 131.89/22.82 ((
% 131.89/22.82 (image1Ex1) =>
% 131.89/22.82 ((
% 131.89/22.82 (image1Equiv) =>
% 131.89/22.82 ((
% 131.89/22.82 (image1E) =>
% 131.89/22.82 ((
% 131.89/22.82 (image1I) =>
% 131.89/22.82 ((
% 131.89/22.82 (injFuncInInjFuncSet) =>
% 131.89/22.82 ((
% 131.89/22.82 (injFuncSetFuncIn) =>
% 131.89/22.82 ((
% 131.89/22.82 (injFuncSetFuncInj) =>
% 131.89/22.82 ((
% 131.89/22.82 (surjFuncSetFuncIn) =>
% 131.89/22.82 ((
% 131.89/22.82 (surjFuncSetFuncSurj) =>
% 131.89/22.82 ((
% 131.89/22.82 (leftInvIsSurj) =>
% 131.89/22.82 ((
% 131.89/22.82 (surjCantorThm) =>
% 131.89/22.82 ((
% 131.89/22.82 (foundation2) =>
% 131.89/22.82 ((
% 131.89/22.82 (notinself) =>
% 131.89/22.82 ((
% 131.89/22.82 (notinself2) =>
% 131.89/22.82 ((
% 131.89/22.82 (omegaSp) =>
% 131.89/22.82 ((
% 131.89/22.82 (omegaSclos) =>
% 131.89/22.82 ((
% 131.89/22.82 (peano0notS) =>
% 131.89/22.82 ((
% 131.89/22.82 (peanoSinj) =>
% 131.89/22.82 ((
% 131.89/22.82 (transitivesetOp1) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintTransitive) =>
% 131.89/22.82 ((
% 131.89/22.82 (transitivesetOp2) =>
% 131.89/22.82 ((
% 131.89/22.82 (setunionTransitive) =>
% 131.89/22.82 ((
% 131.89/22.82 (ordinalMinLem1) =>
% 131.89/22.82 ((
% 131.89/22.82 (ordinalTransSet) =>
% 131.89/22.82 ((
% 131.89/22.82 (ordinalTransSet1) =>
% 131.89/22.82 ((
% 131.89/22.82 (setunionOrdinalLem1) =>
% 131.89/22.82 (ordinal @
% 131.89/22.82 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 131.89/22.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl357])).
% 131.89/22.82 thf(zip_derived_cl372, plain,
% 131.89/22.82 (~ (((subPowSU) =>
% 131.89/22.82 (((exuE2) =>
% 131.89/22.82 (((nonemptyImpWitness) =>
% 131.89/22.82 (((uniqinunit) =>
% 131.89/22.82 (((notinsingleton) =>
% 131.89/22.82 (((eqinunit) =>
% 131.89/22.82 (((singletonsswitch) =>
% 131.89/22.82 (((upairsetE) =>
% 131.89/22.82 (((upairsetIL) =>
% 131.89/22.82 (((upairsetIR) =>
% 131.89/22.82 (((emptyE1) =>
% 131.89/22.82 (((vacuousDall) =>
% 131.89/22.82 (((quantDeMorgan1) =>
% 131.89/22.82 (((quantDeMorgan2) =>
% 131.89/22.82 (((quantDeMorgan3) =>
% 131.89/22.82 (((quantDeMorgan4) =>
% 131.89/22.82 (((prop2setI) =>
% 131.89/22.82 (((prop2set2propI) =>
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% 131.89/22.82 (((notdallE) =>
% 131.89/22.82 (((exuI1) =>
% 131.89/22.82 (((exuI3) =>
% 131.89/22.82 (((exuI2) =>
% 131.89/22.82 (((inCongP) =>
% 131.89/22.82 (((in__Cong) =>
% 131.89/22.82 (((exuE3u) =>
% 131.89/22.82 (((exu__Cong) =>
% 131.89/22.82 (((setadjoin__Cong) =>
% 131.89/22.82 (((powerset__Cong) =>
% 131.89/22.82 (((setunion__Cong) =>
% 131.89/22.82 ((
% 131.89/22.82 (exuEu) =>
% 131.89/22.82 ((
% 131.89/22.82 (descr__Cong) =>
% 131.89/22.82 ((
% 131.89/22.82 (dsetconstr__Cong) =>
% 131.89/22.82 ((
% 131.89/22.82 (subsetI1) =>
% 131.89/22.82 ((
% 131.89/22.82 (eqimpsubset2) =>
% 131.89/22.82 ((
% 131.89/22.82 (eqimpsubset1) =>
% 131.89/22.82 ((
% 131.89/22.82 (subsetI2) =>
% 131.89/22.82 ((
% 131.89/22.82 (emptysetsubset) =>
% 131.89/22.82 ((
% 131.89/22.82 (subsetE) =>
% 131.89/22.82 ((
% 131.89/22.82 (subsetE2) =>
% 131.89/22.82 ((
% 131.89/22.82 (notsubsetI) =>
% 131.89/22.82 ((
% 131.89/22.82 (notequalI1) =>
% 131.89/22.82 ((
% 131.89/22.82 (notequalI2) =>
% 131.89/22.82 ((
% 131.89/22.82 (subsetRefl) =>
% 131.89/22.82 ((
% 131.89/22.82 (subsetTrans) =>
% 131.89/22.82 ((
% 131.89/22.82 (setadjoinSub) =>
% 131.89/22.82 ((
% 131.89/22.82 (setadjoinSub2) =>
% 131.89/22.82 ((
% 131.89/22.82 (subset2powerset) =>
% 131.89/22.82 ((
% 131.89/22.82 (setextsub) =>
% 131.89/22.82 ((
% 131.89/22.82 (subsetemptysetimpeq) =>
% 131.89/22.82 ((
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% 131.89/22.82 ((
% 131.89/22.82 (powersetE1) =>
% 131.89/22.82 ((
% 131.89/22.82 (inPowerset) =>
% 131.89/22.82 ((
% 131.89/22.82 (powersetsubset) =>
% 131.89/22.82 ((
% 131.89/22.82 (sepInPowerset) =>
% 131.89/22.82 ((
% 131.89/22.82 (sepSubset) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionIL) =>
% 131.89/22.82 ((
% 131.89/22.82 (upairset2IR) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionIR) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionEcases) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionE) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionLsub) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionRsub) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectI) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectSubset5) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectEL) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectLsub) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectSubset2) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectSubset3) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectER) =>
% 131.89/22.82 ((
% 131.89/22.82 (disjointsetsI1) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectRsub) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectSubset4) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectSubset1) =>
% 131.89/22.82 ((
% 131.89/22.82 (bs114d) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusI) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusEL) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusER) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusSubset2) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusERneg) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusELneg) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusILneg) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusIRneg) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusLsub) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusSubset1) =>
% 131.89/22.82 ((
% 131.89/22.82 (symdiffE) =>
% 131.89/22.82 ((
% 131.89/22.82 (symdiffI1) =>
% 131.89/22.82 ((
% 131.89/22.82 (symdiffI2) =>
% 131.89/22.82 ((
% 131.89/22.82 (symdiffIneg1) =>
% 131.89/22.82 ((
% 131.89/22.82 (symdiffIneg2) =>
% 131.89/22.82 ((
% 131.89/22.82 (secondinupair) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairIL) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairIR) =>
% 131.89/22.82 ((
% 131.89/22.82 (kpairiskpair) =>
% 131.89/22.82 ((
% 131.89/22.82 (kpairp) =>
% 131.89/22.82 ((
% 131.89/22.82 (singletonsubset) =>
% 131.89/22.82 ((
% 131.89/22.82 (singletoninpowerset) =>
% 131.89/22.82 ((
% 131.89/22.82 (singletoninpowunion) =>
% 131.89/22.82 ((
% 131.89/22.82 (upairset2E) =>
% 131.89/22.82 ((
% 131.89/22.82 (upairsubunion) =>
% 131.89/22.82 ((
% 131.89/22.82 (upairinpowunion) =>
% 131.89/22.82 ((
% 131.89/22.82 (ubforcartprodlem1) =>
% 131.89/22.82 ((
% 131.89/22.82 (ubforcartprodlem2) =>
% 131.89/22.82 ((
% 131.89/22.82 (ubforcartprodlem3) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodpairin) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodmempair1) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodmempair) =>
% 131.89/22.82 ((
% 131.89/22.82 (setunionE2) =>
% 131.89/22.82 ((
% 131.89/22.82 (setunionsingleton1) =>
% 131.89/22.82 ((
% 131.89/22.82 (setunionsingleton2) =>
% 131.89/22.82 ((
% 131.89/22.82 (setunionsingleton) =>
% 131.89/22.82 ((
% 131.89/22.82 (singletonprop) =>
% 131.89/22.82 ((
% 131.89/22.82 (ex1E1) =>
% 131.89/22.82 ((
% 131.89/22.82 (ex1I) =>
% 131.89/22.82 ((
% 131.89/22.82 (ex1I2) =>
% 131.89/22.82 ((
% 131.89/22.82 (singletonsuniq) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairinjL1) =>
% 131.89/22.82 ((
% 131.89/22.82 (kfstsingleton) =>
% 131.89/22.82 ((
% 131.89/22.82 (theprop) =>
% 131.89/22.82 ((
% 131.89/22.82 (kfstpairEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodfstin) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairinjL2) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairinjL) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairinjR11) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairinjR12) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairinjR1) =>
% 131.89/22.82 ((
% 131.89/22.82 (upairequniteq) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairinjR2) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairinjR) =>
% 131.89/22.82 ((
% 131.89/22.82 (ksndsingleton) =>
% 131.89/22.82 ((
% 131.89/22.82 (ksndpairEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (kpairsurjEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodsndin) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodpairmemEL) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodpairmemER) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodmempaircEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodfstpairEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodsndpairEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodpairsurjEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (dpsetconstrI) =>
% 131.89/22.82 ((
% 131.89/22.82 (dpsetconstrSub) =>
% 131.89/22.82 ((
% 131.89/22.82 (setOfPairsIsBReln) =>
% 131.89/22.82 ((
% 131.89/22.82 (dpsetconstrERa) =>
% 131.89/22.82 ((
% 131.89/22.82 (dpsetconstrEL1) =>
% 131.89/22.82 ((
% 131.89/22.82 (dpsetconstrEL2) =>
% 131.89/22.82 ((
% 131.89/22.82 (dpsetconstrER) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcImageSingleton) =>
% 131.89/22.82 ((
% 131.89/22.82 (apProp) =>
% 131.89/22.82 ((
% 131.89/22.82 (app) =>
% 131.89/22.82 ((
% 131.89/22.82 (infuncsetfunc) =>
% 131.89/22.82 ((
% 131.89/22.82 (ap2p) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcinfuncset) =>
% 131.89/22.82 ((
% 131.89/22.82 (lamProp) =>
% 131.89/22.82 ((
% 131.89/22.82 (lamp) =>
% 131.89/22.82 ((
% 131.89/22.82 (lam2p) =>
% 131.89/22.82 ((
% 131.89/22.82 (brelnall1) =>
% 131.89/22.82 ((
% 131.89/22.82 (brelnall2) =>
% 131.89/22.82 ((
% 131.89/22.82 (ex1E2) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcGraphProp1) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcGraphProp3) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcGraphProp2) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcextLem) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcGraphProp4) =>
% 131.89/22.82 ((
% 131.89/22.82 (subbreln) =>
% 131.89/22.82 ((
% 131.89/22.82 (eqbreln) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcext) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcext2) =>
% 131.89/22.82 ((
% 131.89/22.82 (ap2apEq1) =>
% 131.89/22.82 ((
% 131.89/22.82 (ap2apEq2) =>
% 131.89/22.82 ((
% 131.89/22.82 (beta1) =>
% 131.89/22.82 ((
% 131.89/22.82 (eta1) =>
% 131.89/22.82 ((
% 131.89/22.82 (lam2lamEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (beta2) =>
% 131.89/22.82 ((
% 131.89/22.82 (eta2) =>
% 131.89/22.82 ((
% 131.89/22.82 (iffalseProp1) =>
% 131.89/22.82 ((
% 131.89/22.82 (iffalseProp2) =>
% 131.89/22.82 ((
% 131.89/22.82 (iftrueProp1) =>
% 131.89/22.82 ((
% 131.89/22.82 (iftrueProp2) =>
% 131.89/22.82 ((
% 131.89/22.82 (ifSingleton) =>
% 131.89/22.82 ((
% 131.89/22.82 (ifp) =>
% 131.89/22.82 ((
% 131.89/22.82 (theeq) =>
% 131.89/22.82 ((
% 131.89/22.82 (iftrue) =>
% 131.89/22.82 ((
% 131.89/22.82 (iffalse) =>
% 131.89/22.82 ((
% 131.89/22.82 (iftrueorfalse) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectT_lem) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionT_lem) =>
% 131.89/22.82 ((
% 131.89/22.82 (powersetT_lem) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusT_lem) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementT_lem) =>
% 131.89/22.82 ((
% 131.89/22.82 (setextT) =>
% 131.89/22.82 ((
% 131.89/22.82 (subsetTI) =>
% 131.89/22.82 ((
% 131.89/22.82 (powersetTI1) =>
% 131.89/22.82 ((
% 131.89/22.82 (powersetTE1) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementTI1) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementTE1) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectTELcontra) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectTERcontra) =>
% 131.89/22.82 ((
% 131.89/22.82 (contrasubsetT) =>
% 131.89/22.82 ((
% 131.89/22.82 (contrasubsetT1) =>
% 131.89/22.82 ((
% 131.89/22.82 (contrasubsetT2) =>
% 131.89/22.82 ((
% 131.89/22.82 (contrasubsetT3) =>
% 131.89/22.82 ((
% 131.89/22.82 (doubleComplementI1) =>
% 131.89/22.82 ((
% 131.89/22.82 (doubleComplementE1) =>
% 131.89/22.82 ((
% 131.89/22.82 (doubleComplementSub1) =>
% 131.89/22.82 ((
% 131.89/22.82 (doubleComplementSub2) =>
% 131.89/22.82 ((
% 131.89/22.82 (doubleComplementEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementTnotintersectT) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementImpComplementIntersect) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementSubsetComplementIntersect) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementInPowersetComplementIntersect) =>
% 131.89/22.82 ((
% 131.89/22.82 (contraSubsetComplement) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementTcontraSubset) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionTILcontra) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionTIRcontra) =>
% 131.89/22.82 ((
% 131.89/22.82 (inIntersectImpInUnion) =>
% 131.89/22.82 ((
% 131.89/22.82 (inIntersectImpInUnion2) =>
% 131.89/22.82 ((
% 131.89/22.82 (inIntersectImpInIntersectUnions) =>
% 131.89/22.82 ((
% 131.89/22.82 (intersectInPowersetIntersectUnions) =>
% 131.89/22.82 ((
% 131.89/22.82 (inComplementUnionImpNotIn1) =>
% 131.89/22.82 ((
% 131.89/22.82 (inComplementUnionImpInComplement1) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionTE) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionTEcontra) =>
% 131.89/22.82 ((
% 131.89/22.82 (demorgan2a1) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementUnionInPowersetComplement) =>
% 131.89/22.82 ((
% 131.89/22.82 (demorgan2a2) =>
% 131.89/22.82 ((
% 131.89/22.82 (demorgan1a) =>
% 131.89/22.82 ((
% 131.89/22.82 (demorgan1b) =>
% 131.89/22.82 ((
% 131.89/22.82 (demorgan1) =>
% 131.89/22.82 ((
% 131.89/22.82 (demorgan2a) =>
% 131.89/22.82 ((
% 131.89/22.82 (demorgan2b2) =>
% 131.89/22.82 ((
% 131.89/22.82 (demorgan2b) =>
% 131.89/22.82 ((
% 131.89/22.82 (demorgan2) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz13rule0) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz13rule1) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz13rule2) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz13rule3) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz13rule4) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz1_1) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz1_2) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz1_3) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz1_4) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz1_5) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1all2) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1SetBreln1) =>
% 131.89/22.82 ((
% 131.89/22.82 (choice2fnsingleton) =>
% 131.89/22.82 ((
% 131.89/22.82 (setOfPairsIsBReln1) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1all1) =>
% 131.89/22.82 ((
% 131.89/22.82 (subbreln1) =>
% 131.89/22.82 ((
% 131.89/22.82 (eqbreln1) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1invprop) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1invI) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1invE) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1compprop) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1compI) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1compE) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1compEex) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1unionprop) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1unionIL) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1unionIR) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1unionI) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1unionE) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1unionEcases) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1unionCommutes) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz2Ex) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz2W) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz2A) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz2B) =>
% 131.89/22.82 ((
% 131.89/22.82 (image1Ex) =>
% 131.89/22.82 ((
% 131.89/22.82 (image1Ex1) =>
% 131.89/22.82 ((
% 131.89/22.82 (image1Equiv) =>
% 131.89/22.82 ((
% 131.89/22.82 (image1E) =>
% 131.89/22.82 ((
% 131.89/22.82 (image1I) =>
% 131.89/22.82 ((
% 131.89/22.82 (injFuncInInjFuncSet) =>
% 131.89/22.82 ((
% 131.89/22.82 (injFuncSetFuncIn) =>
% 131.89/22.82 ((
% 131.89/22.82 (injFuncSetFuncInj) =>
% 131.89/22.82 ((
% 131.89/22.82 (surjFuncSetFuncIn) =>
% 131.89/22.82 ((
% 131.89/22.82 (surjFuncSetFuncSurj) =>
% 131.89/22.82 ((
% 131.89/22.82 (leftInvIsSurj) =>
% 131.89/22.82 ((
% 131.89/22.82 (surjCantorThm) =>
% 131.89/22.82 ((
% 131.89/22.82 (foundation2) =>
% 131.89/22.82 ((
% 131.89/22.82 (notinself) =>
% 131.89/22.82 ((
% 131.89/22.82 (notinself2) =>
% 131.89/22.82 ((
% 131.89/22.82 (omegaSp) =>
% 131.89/22.82 ((
% 131.89/22.82 (omegaSclos) =>
% 131.89/22.82 ((
% 131.89/22.82 (peano0notS) =>
% 131.89/22.82 ((
% 131.89/22.82 (peanoSinj) =>
% 131.89/22.82 ((
% 131.89/22.82 (transitivesetOp1) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintTransitive) =>
% 131.89/22.82 ((
% 131.89/22.82 (transitivesetOp2) =>
% 131.89/22.82 ((
% 131.89/22.82 (setunionTransitive) =>
% 131.89/22.82 ((
% 131.89/22.82 (ordinalMinLem1) =>
% 131.89/22.82 ((
% 131.89/22.82 (ordinalTransSet) =>
% 131.89/22.82 ((
% 131.89/22.82 (ordinalTransSet1) =>
% 131.89/22.82 ((
% 131.89/22.82 (setunionOrdinalLem1) =>
% 131.89/22.82 (ordinal @
% 131.89/22.82 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 131.89/22.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl364])).
% 131.89/22.82 thf(zip_derived_cl382, plain,
% 131.89/22.82 (~ (((exuE2) =>
% 131.89/22.82 (((nonemptyImpWitness) =>
% 131.89/22.82 (((uniqinunit) =>
% 131.89/22.82 (((notinsingleton) =>
% 131.89/22.82 (((eqinunit) =>
% 131.89/22.82 (((singletonsswitch) =>
% 131.89/22.82 (((upairsetE) =>
% 131.89/22.82 (((upairsetIL) =>
% 131.89/22.82 (((upairsetIR) =>
% 131.89/22.82 (((emptyE1) =>
% 131.89/22.82 (((vacuousDall) =>
% 131.89/22.82 (((quantDeMorgan1) =>
% 131.89/22.82 (((quantDeMorgan2) =>
% 131.89/22.82 (((quantDeMorgan3) =>
% 131.89/22.82 (((quantDeMorgan4) =>
% 131.89/22.82 (((prop2setI) =>
% 131.89/22.82 (((prop2set2propI) =>
% 131.89/22.82 (((notdexE) =>
% 131.89/22.82 (((notdallE) =>
% 131.89/22.82 (((exuI1) =>
% 131.89/22.82 (((exuI3) =>
% 131.89/22.82 (((exuI2) =>
% 131.89/22.82 (((inCongP) =>
% 131.89/22.82 (((in__Cong) =>
% 131.89/22.82 (((exuE3u) =>
% 131.89/22.82 (((exu__Cong) =>
% 131.89/22.82 (((setadjoin__Cong) =>
% 131.89/22.82 (((powerset__Cong) =>
% 131.89/22.82 (((setunion__Cong) =>
% 131.89/22.82 (((exuEu) =>
% 131.89/22.82 ((
% 131.89/22.82 (descr__Cong) =>
% 131.89/22.82 ((
% 131.89/22.82 (dsetconstr__Cong) =>
% 131.89/22.82 ((
% 131.89/22.82 (subsetI1) =>
% 131.89/22.82 ((
% 131.89/22.82 (eqimpsubset2) =>
% 131.89/22.82 ((
% 131.89/22.82 (eqimpsubset1) =>
% 131.89/22.82 ((
% 131.89/22.82 (subsetI2) =>
% 131.89/22.82 ((
% 131.89/22.82 (emptysetsubset) =>
% 131.89/22.82 ((
% 131.89/22.82 (subsetE) =>
% 131.89/22.82 ((
% 131.89/22.82 (subsetE2) =>
% 131.89/22.82 ((
% 131.89/22.82 (notsubsetI) =>
% 131.89/22.82 ((
% 131.89/22.82 (notequalI1) =>
% 131.89/22.82 ((
% 131.89/22.82 (notequalI2) =>
% 131.89/22.82 ((
% 131.89/22.82 (subsetRefl) =>
% 131.89/22.82 ((
% 131.89/22.82 (subsetTrans) =>
% 131.89/22.82 ((
% 131.89/22.82 (setadjoinSub) =>
% 131.89/22.82 ((
% 131.89/22.82 (setadjoinSub2) =>
% 131.89/22.82 ((
% 131.89/22.82 (subset2powerset) =>
% 131.89/22.82 ((
% 131.89/22.82 (setextsub) =>
% 131.89/22.82 ((
% 131.89/22.82 (subsetemptysetimpeq) =>
% 131.89/22.82 ((
% 131.89/22.82 (powersetI1) =>
% 131.89/22.82 ((
% 131.89/22.82 (powersetE1) =>
% 131.89/22.82 ((
% 131.89/22.82 (inPowerset) =>
% 131.89/22.82 ((
% 131.89/22.82 (powersetsubset) =>
% 131.89/22.82 ((
% 131.89/22.82 (sepInPowerset) =>
% 131.89/22.82 ((
% 131.89/22.82 (sepSubset) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionIL) =>
% 131.89/22.82 ((
% 131.89/22.82 (upairset2IR) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionIR) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionEcases) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionE) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionLsub) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionRsub) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectI) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectSubset5) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectEL) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectLsub) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectSubset2) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectSubset3) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectER) =>
% 131.89/22.82 ((
% 131.89/22.82 (disjointsetsI1) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectRsub) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectSubset4) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectSubset1) =>
% 131.89/22.82 ((
% 131.89/22.82 (bs114d) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusI) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusEL) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusER) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusSubset2) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusERneg) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusELneg) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusILneg) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusIRneg) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusLsub) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusSubset1) =>
% 131.89/22.82 ((
% 131.89/22.82 (symdiffE) =>
% 131.89/22.82 ((
% 131.89/22.82 (symdiffI1) =>
% 131.89/22.82 ((
% 131.89/22.82 (symdiffI2) =>
% 131.89/22.82 ((
% 131.89/22.82 (symdiffIneg1) =>
% 131.89/22.82 ((
% 131.89/22.82 (symdiffIneg2) =>
% 131.89/22.82 ((
% 131.89/22.82 (secondinupair) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairIL) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairIR) =>
% 131.89/22.82 ((
% 131.89/22.82 (kpairiskpair) =>
% 131.89/22.82 ((
% 131.89/22.82 (kpairp) =>
% 131.89/22.82 ((
% 131.89/22.82 (singletonsubset) =>
% 131.89/22.82 ((
% 131.89/22.82 (singletoninpowerset) =>
% 131.89/22.82 ((
% 131.89/22.82 (singletoninpowunion) =>
% 131.89/22.82 ((
% 131.89/22.82 (upairset2E) =>
% 131.89/22.82 ((
% 131.89/22.82 (upairsubunion) =>
% 131.89/22.82 ((
% 131.89/22.82 (upairinpowunion) =>
% 131.89/22.82 ((
% 131.89/22.82 (ubforcartprodlem1) =>
% 131.89/22.82 ((
% 131.89/22.82 (ubforcartprodlem2) =>
% 131.89/22.82 ((
% 131.89/22.82 (ubforcartprodlem3) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodpairin) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodmempair1) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodmempair) =>
% 131.89/22.82 ((
% 131.89/22.82 (setunionE2) =>
% 131.89/22.82 ((
% 131.89/22.82 (setunionsingleton1) =>
% 131.89/22.82 ((
% 131.89/22.82 (setunionsingleton2) =>
% 131.89/22.82 ((
% 131.89/22.82 (setunionsingleton) =>
% 131.89/22.82 ((
% 131.89/22.82 (singletonprop) =>
% 131.89/22.82 ((
% 131.89/22.82 (ex1E1) =>
% 131.89/22.82 ((
% 131.89/22.82 (ex1I) =>
% 131.89/22.82 ((
% 131.89/22.82 (ex1I2) =>
% 131.89/22.82 ((
% 131.89/22.82 (singletonsuniq) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairinjL1) =>
% 131.89/22.82 ((
% 131.89/22.82 (kfstsingleton) =>
% 131.89/22.82 ((
% 131.89/22.82 (theprop) =>
% 131.89/22.82 ((
% 131.89/22.82 (kfstpairEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodfstin) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairinjL2) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairinjL) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairinjR11) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairinjR12) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairinjR1) =>
% 131.89/22.82 ((
% 131.89/22.82 (upairequniteq) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairinjR2) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairinjR) =>
% 131.89/22.82 ((
% 131.89/22.82 (ksndsingleton) =>
% 131.89/22.82 ((
% 131.89/22.82 (ksndpairEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (kpairsurjEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodsndin) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodpairmemEL) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodpairmemER) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodmempaircEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodfstpairEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodsndpairEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodpairsurjEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (dpsetconstrI) =>
% 131.89/22.82 ((
% 131.89/22.82 (dpsetconstrSub) =>
% 131.89/22.82 ((
% 131.89/22.82 (setOfPairsIsBReln) =>
% 131.89/22.82 ((
% 131.89/22.82 (dpsetconstrERa) =>
% 131.89/22.82 ((
% 131.89/22.82 (dpsetconstrEL1) =>
% 131.89/22.82 ((
% 131.89/22.82 (dpsetconstrEL2) =>
% 131.89/22.82 ((
% 131.89/22.82 (dpsetconstrER) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcImageSingleton) =>
% 131.89/22.82 ((
% 131.89/22.82 (apProp) =>
% 131.89/22.82 ((
% 131.89/22.82 (app) =>
% 131.89/22.82 ((
% 131.89/22.82 (infuncsetfunc) =>
% 131.89/22.82 ((
% 131.89/22.82 (ap2p) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcinfuncset) =>
% 131.89/22.82 ((
% 131.89/22.82 (lamProp) =>
% 131.89/22.82 ((
% 131.89/22.82 (lamp) =>
% 131.89/22.82 ((
% 131.89/22.82 (lam2p) =>
% 131.89/22.82 ((
% 131.89/22.82 (brelnall1) =>
% 131.89/22.82 ((
% 131.89/22.82 (brelnall2) =>
% 131.89/22.82 ((
% 131.89/22.82 (ex1E2) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcGraphProp1) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcGraphProp3) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcGraphProp2) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcextLem) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcGraphProp4) =>
% 131.89/22.82 ((
% 131.89/22.82 (subbreln) =>
% 131.89/22.82 ((
% 131.89/22.82 (eqbreln) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcext) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcext2) =>
% 131.89/22.82 ((
% 131.89/22.82 (ap2apEq1) =>
% 131.89/22.82 ((
% 131.89/22.82 (ap2apEq2) =>
% 131.89/22.82 ((
% 131.89/22.82 (beta1) =>
% 131.89/22.82 ((
% 131.89/22.82 (eta1) =>
% 131.89/22.82 ((
% 131.89/22.82 (lam2lamEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (beta2) =>
% 131.89/22.82 ((
% 131.89/22.82 (eta2) =>
% 131.89/22.82 ((
% 131.89/22.82 (iffalseProp1) =>
% 131.89/22.82 ((
% 131.89/22.82 (iffalseProp2) =>
% 131.89/22.82 ((
% 131.89/22.82 (iftrueProp1) =>
% 131.89/22.82 ((
% 131.89/22.82 (iftrueProp2) =>
% 131.89/22.82 ((
% 131.89/22.82 (ifSingleton) =>
% 131.89/22.82 ((
% 131.89/22.82 (ifp) =>
% 131.89/22.82 ((
% 131.89/22.82 (theeq) =>
% 131.89/22.82 ((
% 131.89/22.82 (iftrue) =>
% 131.89/22.82 ((
% 131.89/22.82 (iffalse) =>
% 131.89/22.82 ((
% 131.89/22.82 (iftrueorfalse) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectT_lem) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionT_lem) =>
% 131.89/22.82 ((
% 131.89/22.82 (powersetT_lem) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusT_lem) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementT_lem) =>
% 131.89/22.82 ((
% 131.89/22.82 (setextT) =>
% 131.89/22.82 ((
% 131.89/22.82 (subsetTI) =>
% 131.89/22.82 ((
% 131.89/22.82 (powersetTI1) =>
% 131.89/22.82 ((
% 131.89/22.82 (powersetTE1) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementTI1) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementTE1) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectTELcontra) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectTERcontra) =>
% 131.89/22.82 ((
% 131.89/22.82 (contrasubsetT) =>
% 131.89/22.82 ((
% 131.89/22.82 (contrasubsetT1) =>
% 131.89/22.82 ((
% 131.89/22.82 (contrasubsetT2) =>
% 131.89/22.82 ((
% 131.89/22.82 (contrasubsetT3) =>
% 131.89/22.82 ((
% 131.89/22.82 (doubleComplementI1) =>
% 131.89/22.82 ((
% 131.89/22.82 (doubleComplementE1) =>
% 131.89/22.82 ((
% 131.89/22.82 (doubleComplementSub1) =>
% 131.89/22.82 ((
% 131.89/22.82 (doubleComplementSub2) =>
% 131.89/22.82 ((
% 131.89/22.82 (doubleComplementEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementTnotintersectT) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementImpComplementIntersect) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementSubsetComplementIntersect) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementInPowersetComplementIntersect) =>
% 131.89/22.82 ((
% 131.89/22.82 (contraSubsetComplement) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementTcontraSubset) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionTILcontra) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionTIRcontra) =>
% 131.89/22.82 ((
% 131.89/22.82 (inIntersectImpInUnion) =>
% 131.89/22.82 ((
% 131.89/22.82 (inIntersectImpInUnion2) =>
% 131.89/22.82 ((
% 131.89/22.82 (inIntersectImpInIntersectUnions) =>
% 131.89/22.82 ((
% 131.89/22.82 (intersectInPowersetIntersectUnions) =>
% 131.89/22.82 ((
% 131.89/22.82 (inComplementUnionImpNotIn1) =>
% 131.89/22.82 ((
% 131.89/22.82 (inComplementUnionImpInComplement1) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionTE) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionTEcontra) =>
% 131.89/22.82 ((
% 131.89/22.82 (demorgan2a1) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementUnionInPowersetComplement) =>
% 131.89/22.82 ((
% 131.89/22.82 (demorgan2a2) =>
% 131.89/22.82 ((
% 131.89/22.82 (demorgan1a) =>
% 131.89/22.82 ((
% 131.89/22.82 (demorgan1b) =>
% 131.89/22.82 ((
% 131.89/22.82 (demorgan1) =>
% 131.89/22.82 ((
% 131.89/22.82 (demorgan2a) =>
% 131.89/22.82 ((
% 131.89/22.82 (demorgan2b2) =>
% 131.89/22.82 ((
% 131.89/22.82 (demorgan2b) =>
% 131.89/22.82 ((
% 131.89/22.82 (demorgan2) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz13rule0) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz13rule1) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz13rule2) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz13rule3) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz13rule4) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz1_1) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz1_2) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz1_3) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz1_4) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz1_5) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1all2) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1SetBreln1) =>
% 131.89/22.82 ((
% 131.89/22.82 (choice2fnsingleton) =>
% 131.89/22.82 ((
% 131.89/22.82 (setOfPairsIsBReln1) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1all1) =>
% 131.89/22.82 ((
% 131.89/22.82 (subbreln1) =>
% 131.89/22.82 ((
% 131.89/22.82 (eqbreln1) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1invprop) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1invI) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1invE) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1compprop) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1compI) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1compE) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1compEex) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1unionprop) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1unionIL) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1unionIR) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1unionI) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1unionE) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1unionEcases) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1unionCommutes) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz2Ex) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz2W) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz2A) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz2B) =>
% 131.89/22.82 ((
% 131.89/22.82 (image1Ex) =>
% 131.89/22.82 ((
% 131.89/22.82 (image1Ex1) =>
% 131.89/22.82 ((
% 131.89/22.82 (image1Equiv) =>
% 131.89/22.82 ((
% 131.89/22.82 (image1E) =>
% 131.89/22.82 ((
% 131.89/22.82 (image1I) =>
% 131.89/22.82 ((
% 131.89/22.82 (injFuncInInjFuncSet) =>
% 131.89/22.82 ((
% 131.89/22.82 (injFuncSetFuncIn) =>
% 131.89/22.82 ((
% 131.89/22.82 (injFuncSetFuncInj) =>
% 131.89/22.82 ((
% 131.89/22.82 (surjFuncSetFuncIn) =>
% 131.89/22.82 ((
% 131.89/22.82 (surjFuncSetFuncSurj) =>
% 131.89/22.82 ((
% 131.89/22.82 (leftInvIsSurj) =>
% 131.89/22.82 ((
% 131.89/22.82 (surjCantorThm) =>
% 131.89/22.82 ((
% 131.89/22.82 (foundation2) =>
% 131.89/22.82 ((
% 131.89/22.82 (notinself) =>
% 131.89/22.82 ((
% 131.89/22.82 (notinself2) =>
% 131.89/22.82 ((
% 131.89/22.82 (omegaSp) =>
% 131.89/22.82 ((
% 131.89/22.82 (omegaSclos) =>
% 131.89/22.82 ((
% 131.89/22.82 (peano0notS) =>
% 131.89/22.82 ((
% 131.89/22.82 (peanoSinj) =>
% 131.89/22.82 ((
% 131.89/22.82 (transitivesetOp1) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintTransitive) =>
% 131.89/22.82 ((
% 131.89/22.82 (transitivesetOp2) =>
% 131.89/22.82 ((
% 131.89/22.82 (setunionTransitive) =>
% 131.89/22.82 ((
% 131.89/22.82 (ordinalMinLem1) =>
% 131.89/22.82 ((
% 131.89/22.82 (ordinalTransSet) =>
% 131.89/22.82 ((
% 131.89/22.82 (ordinalTransSet1) =>
% 131.89/22.82 ((
% 131.89/22.82 (setunionOrdinalLem1) =>
% 131.89/22.82 (ordinal @
% 131.89/22.82 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 131.89/22.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl372])).
% 131.89/22.82 thf(zip_derived_cl390, plain,
% 131.89/22.82 (~ (((nonemptyImpWitness) =>
% 131.89/22.82 (((uniqinunit) =>
% 131.89/22.82 (((notinsingleton) =>
% 131.89/22.82 (((eqinunit) =>
% 131.89/22.82 (((singletonsswitch) =>
% 131.89/22.82 (((upairsetE) =>
% 131.89/22.82 (((upairsetIL) =>
% 131.89/22.82 (((upairsetIR) =>
% 131.89/22.82 (((emptyE1) =>
% 131.89/22.82 (((vacuousDall) =>
% 131.89/22.82 (((quantDeMorgan1) =>
% 131.89/22.82 (((quantDeMorgan2) =>
% 131.89/22.82 (((quantDeMorgan3) =>
% 131.89/22.82 (((quantDeMorgan4) =>
% 131.89/22.82 (((prop2setI) =>
% 131.89/22.82 (((prop2set2propI) =>
% 131.89/22.82 (((notdexE) =>
% 131.89/22.82 (((notdallE) =>
% 131.89/22.82 (((exuI1) =>
% 131.89/22.82 (((exuI3) =>
% 131.89/22.82 (((exuI2) =>
% 131.89/22.82 (((inCongP) =>
% 131.89/22.82 (((in__Cong) =>
% 131.89/22.82 (((exuE3u) =>
% 131.89/22.82 (((exu__Cong) =>
% 131.89/22.82 (((setadjoin__Cong) =>
% 131.89/22.82 (((powerset__Cong) =>
% 131.89/22.82 (((setunion__Cong) =>
% 131.89/22.82 (((exuEu) =>
% 131.89/22.82 (((descr__Cong) =>
% 131.89/22.82 ((
% 131.89/22.82 (dsetconstr__Cong) =>
% 131.89/22.82 ((
% 131.89/22.82 (subsetI1) =>
% 131.89/22.82 ((
% 131.89/22.82 (eqimpsubset2) =>
% 131.89/22.82 ((
% 131.89/22.82 (eqimpsubset1) =>
% 131.89/22.82 ((
% 131.89/22.82 (subsetI2) =>
% 131.89/22.82 ((
% 131.89/22.82 (emptysetsubset) =>
% 131.89/22.82 ((
% 131.89/22.82 (subsetE) =>
% 131.89/22.82 ((
% 131.89/22.82 (subsetE2) =>
% 131.89/22.82 ((
% 131.89/22.82 (notsubsetI) =>
% 131.89/22.82 ((
% 131.89/22.82 (notequalI1) =>
% 131.89/22.82 ((
% 131.89/22.82 (notequalI2) =>
% 131.89/22.82 ((
% 131.89/22.82 (subsetRefl) =>
% 131.89/22.82 ((
% 131.89/22.82 (subsetTrans) =>
% 131.89/22.82 ((
% 131.89/22.82 (setadjoinSub) =>
% 131.89/22.82 ((
% 131.89/22.82 (setadjoinSub2) =>
% 131.89/22.82 ((
% 131.89/22.82 (subset2powerset) =>
% 131.89/22.82 ((
% 131.89/22.82 (setextsub) =>
% 131.89/22.82 ((
% 131.89/22.82 (subsetemptysetimpeq) =>
% 131.89/22.82 ((
% 131.89/22.82 (powersetI1) =>
% 131.89/22.82 ((
% 131.89/22.82 (powersetE1) =>
% 131.89/22.82 ((
% 131.89/22.82 (inPowerset) =>
% 131.89/22.82 ((
% 131.89/22.82 (powersetsubset) =>
% 131.89/22.82 ((
% 131.89/22.82 (sepInPowerset) =>
% 131.89/22.82 ((
% 131.89/22.82 (sepSubset) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionIL) =>
% 131.89/22.82 ((
% 131.89/22.82 (upairset2IR) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionIR) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionEcases) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionE) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionLsub) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionRsub) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectI) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectSubset5) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectEL) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectLsub) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectSubset2) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectSubset3) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectER) =>
% 131.89/22.82 ((
% 131.89/22.82 (disjointsetsI1) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectRsub) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectSubset4) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectSubset1) =>
% 131.89/22.82 ((
% 131.89/22.82 (bs114d) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusI) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusEL) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusER) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusSubset2) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusERneg) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusELneg) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusILneg) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusIRneg) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusLsub) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusSubset1) =>
% 131.89/22.82 ((
% 131.89/22.82 (symdiffE) =>
% 131.89/22.82 ((
% 131.89/22.82 (symdiffI1) =>
% 131.89/22.82 ((
% 131.89/22.82 (symdiffI2) =>
% 131.89/22.82 ((
% 131.89/22.82 (symdiffIneg1) =>
% 131.89/22.82 ((
% 131.89/22.82 (symdiffIneg2) =>
% 131.89/22.82 ((
% 131.89/22.82 (secondinupair) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairIL) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairIR) =>
% 131.89/22.82 ((
% 131.89/22.82 (kpairiskpair) =>
% 131.89/22.82 ((
% 131.89/22.82 (kpairp) =>
% 131.89/22.82 ((
% 131.89/22.82 (singletonsubset) =>
% 131.89/22.82 ((
% 131.89/22.82 (singletoninpowerset) =>
% 131.89/22.82 ((
% 131.89/22.82 (singletoninpowunion) =>
% 131.89/22.82 ((
% 131.89/22.82 (upairset2E) =>
% 131.89/22.82 ((
% 131.89/22.82 (upairsubunion) =>
% 131.89/22.82 ((
% 131.89/22.82 (upairinpowunion) =>
% 131.89/22.82 ((
% 131.89/22.82 (ubforcartprodlem1) =>
% 131.89/22.82 ((
% 131.89/22.82 (ubforcartprodlem2) =>
% 131.89/22.82 ((
% 131.89/22.82 (ubforcartprodlem3) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodpairin) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodmempair1) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodmempair) =>
% 131.89/22.82 ((
% 131.89/22.82 (setunionE2) =>
% 131.89/22.82 ((
% 131.89/22.82 (setunionsingleton1) =>
% 131.89/22.82 ((
% 131.89/22.82 (setunionsingleton2) =>
% 131.89/22.82 ((
% 131.89/22.82 (setunionsingleton) =>
% 131.89/22.82 ((
% 131.89/22.82 (singletonprop) =>
% 131.89/22.82 ((
% 131.89/22.82 (ex1E1) =>
% 131.89/22.82 ((
% 131.89/22.82 (ex1I) =>
% 131.89/22.82 ((
% 131.89/22.82 (ex1I2) =>
% 131.89/22.82 ((
% 131.89/22.82 (singletonsuniq) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairinjL1) =>
% 131.89/22.82 ((
% 131.89/22.82 (kfstsingleton) =>
% 131.89/22.82 ((
% 131.89/22.82 (theprop) =>
% 131.89/22.82 ((
% 131.89/22.82 (kfstpairEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodfstin) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairinjL2) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairinjL) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairinjR11) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairinjR12) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairinjR1) =>
% 131.89/22.82 ((
% 131.89/22.82 (upairequniteq) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairinjR2) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairinjR) =>
% 131.89/22.82 ((
% 131.89/22.82 (ksndsingleton) =>
% 131.89/22.82 ((
% 131.89/22.82 (ksndpairEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (kpairsurjEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodsndin) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodpairmemEL) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodpairmemER) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodmempaircEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodfstpairEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodsndpairEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodpairsurjEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (dpsetconstrI) =>
% 131.89/22.82 ((
% 131.89/22.82 (dpsetconstrSub) =>
% 131.89/22.82 ((
% 131.89/22.82 (setOfPairsIsBReln) =>
% 131.89/22.82 ((
% 131.89/22.82 (dpsetconstrERa) =>
% 131.89/22.82 ((
% 131.89/22.82 (dpsetconstrEL1) =>
% 131.89/22.82 ((
% 131.89/22.82 (dpsetconstrEL2) =>
% 131.89/22.82 ((
% 131.89/22.82 (dpsetconstrER) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcImageSingleton) =>
% 131.89/22.82 ((
% 131.89/22.82 (apProp) =>
% 131.89/22.82 ((
% 131.89/22.82 (app) =>
% 131.89/22.82 ((
% 131.89/22.82 (infuncsetfunc) =>
% 131.89/22.82 ((
% 131.89/22.82 (ap2p) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcinfuncset) =>
% 131.89/22.82 ((
% 131.89/22.82 (lamProp) =>
% 131.89/22.82 ((
% 131.89/22.82 (lamp) =>
% 131.89/22.82 ((
% 131.89/22.82 (lam2p) =>
% 131.89/22.82 ((
% 131.89/22.82 (brelnall1) =>
% 131.89/22.82 ((
% 131.89/22.82 (brelnall2) =>
% 131.89/22.82 ((
% 131.89/22.82 (ex1E2) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcGraphProp1) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcGraphProp3) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcGraphProp2) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcextLem) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcGraphProp4) =>
% 131.89/22.82 ((
% 131.89/22.82 (subbreln) =>
% 131.89/22.82 ((
% 131.89/22.82 (eqbreln) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcext) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcext2) =>
% 131.89/22.82 ((
% 131.89/22.82 (ap2apEq1) =>
% 131.89/22.82 ((
% 131.89/22.82 (ap2apEq2) =>
% 131.89/22.82 ((
% 131.89/22.82 (beta1) =>
% 131.89/22.82 ((
% 131.89/22.82 (eta1) =>
% 131.89/22.82 ((
% 131.89/22.82 (lam2lamEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (beta2) =>
% 131.89/22.82 ((
% 131.89/22.82 (eta2) =>
% 131.89/22.82 ((
% 131.89/22.82 (iffalseProp1) =>
% 131.89/22.82 ((
% 131.89/22.82 (iffalseProp2) =>
% 131.89/22.82 ((
% 131.89/22.82 (iftrueProp1) =>
% 131.89/22.82 ((
% 131.89/22.82 (iftrueProp2) =>
% 131.89/22.82 ((
% 131.89/22.82 (ifSingleton) =>
% 131.89/22.82 ((
% 131.89/22.82 (ifp) =>
% 131.89/22.82 ((
% 131.89/22.82 (theeq) =>
% 131.89/22.82 ((
% 131.89/22.82 (iftrue) =>
% 131.89/22.82 ((
% 131.89/22.82 (iffalse) =>
% 131.89/22.82 ((
% 131.89/22.82 (iftrueorfalse) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectT_lem) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionT_lem) =>
% 131.89/22.82 ((
% 131.89/22.82 (powersetT_lem) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusT_lem) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementT_lem) =>
% 131.89/22.82 ((
% 131.89/22.82 (setextT) =>
% 131.89/22.82 ((
% 131.89/22.82 (subsetTI) =>
% 131.89/22.82 ((
% 131.89/22.82 (powersetTI1) =>
% 131.89/22.82 ((
% 131.89/22.82 (powersetTE1) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementTI1) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementTE1) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectTELcontra) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectTERcontra) =>
% 131.89/22.82 ((
% 131.89/22.82 (contrasubsetT) =>
% 131.89/22.82 ((
% 131.89/22.82 (contrasubsetT1) =>
% 131.89/22.82 ((
% 131.89/22.82 (contrasubsetT2) =>
% 131.89/22.82 ((
% 131.89/22.82 (contrasubsetT3) =>
% 131.89/22.82 ((
% 131.89/22.82 (doubleComplementI1) =>
% 131.89/22.82 ((
% 131.89/22.82 (doubleComplementE1) =>
% 131.89/22.82 ((
% 131.89/22.82 (doubleComplementSub1) =>
% 131.89/22.82 ((
% 131.89/22.82 (doubleComplementSub2) =>
% 131.89/22.82 ((
% 131.89/22.82 (doubleComplementEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementTnotintersectT) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementImpComplementIntersect) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementSubsetComplementIntersect) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementInPowersetComplementIntersect) =>
% 131.89/22.82 ((
% 131.89/22.82 (contraSubsetComplement) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementTcontraSubset) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionTILcontra) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionTIRcontra) =>
% 131.89/22.82 ((
% 131.89/22.82 (inIntersectImpInUnion) =>
% 131.89/22.82 ((
% 131.89/22.82 (inIntersectImpInUnion2) =>
% 131.89/22.82 ((
% 131.89/22.82 (inIntersectImpInIntersectUnions) =>
% 131.89/22.82 ((
% 131.89/22.82 (intersectInPowersetIntersectUnions) =>
% 131.89/22.82 ((
% 131.89/22.82 (inComplementUnionImpNotIn1) =>
% 131.89/22.82 ((
% 131.89/22.82 (inComplementUnionImpInComplement1) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionTE) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionTEcontra) =>
% 131.89/22.82 ((
% 131.89/22.82 (demorgan2a1) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementUnionInPowersetComplement) =>
% 131.89/22.82 ((
% 131.89/22.82 (demorgan2a2) =>
% 131.89/22.82 ((
% 131.89/22.82 (demorgan1a) =>
% 131.89/22.82 ((
% 131.89/22.82 (demorgan1b) =>
% 131.89/22.82 ((
% 131.89/22.82 (demorgan1) =>
% 131.89/22.82 ((
% 131.89/22.82 (demorgan2a) =>
% 131.89/22.82 ((
% 131.89/22.82 (demorgan2b2) =>
% 131.89/22.82 ((
% 131.89/22.82 (demorgan2b) =>
% 131.89/22.82 ((
% 131.89/22.82 (demorgan2) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz13rule0) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz13rule1) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz13rule2) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz13rule3) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz13rule4) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz1_1) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz1_2) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz1_3) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz1_4) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz1_5) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1all2) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1SetBreln1) =>
% 131.89/22.82 ((
% 131.89/22.82 (choice2fnsingleton) =>
% 131.89/22.82 ((
% 131.89/22.82 (setOfPairsIsBReln1) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1all1) =>
% 131.89/22.82 ((
% 131.89/22.82 (subbreln1) =>
% 131.89/22.82 ((
% 131.89/22.82 (eqbreln1) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1invprop) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1invI) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1invE) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1compprop) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1compI) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1compE) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1compEex) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1unionprop) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1unionIL) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1unionIR) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1unionI) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1unionE) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1unionEcases) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1unionCommutes) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz2Ex) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz2W) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz2A) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz2B) =>
% 131.89/22.82 ((
% 131.89/22.82 (image1Ex) =>
% 131.89/22.82 ((
% 131.89/22.82 (image1Ex1) =>
% 131.89/22.82 ((
% 131.89/22.82 (image1Equiv) =>
% 131.89/22.82 ((
% 131.89/22.82 (image1E) =>
% 131.89/22.82 ((
% 131.89/22.82 (image1I) =>
% 131.89/22.82 ((
% 131.89/22.82 (injFuncInInjFuncSet) =>
% 131.89/22.82 ((
% 131.89/22.82 (injFuncSetFuncIn) =>
% 131.89/22.82 ((
% 131.89/22.82 (injFuncSetFuncInj) =>
% 131.89/22.82 ((
% 131.89/22.82 (surjFuncSetFuncIn) =>
% 131.89/22.82 ((
% 131.89/22.82 (surjFuncSetFuncSurj) =>
% 131.89/22.82 ((
% 131.89/22.82 (leftInvIsSurj) =>
% 131.89/22.82 ((
% 131.89/22.82 (surjCantorThm) =>
% 131.89/22.82 ((
% 131.89/22.82 (foundation2) =>
% 131.89/22.82 ((
% 131.89/22.82 (notinself) =>
% 131.89/22.82 ((
% 131.89/22.82 (notinself2) =>
% 131.89/22.82 ((
% 131.89/22.82 (omegaSp) =>
% 131.89/22.82 ((
% 131.89/22.82 (omegaSclos) =>
% 131.89/22.82 ((
% 131.89/22.82 (peano0notS) =>
% 131.89/22.82 ((
% 131.89/22.82 (peanoSinj) =>
% 131.89/22.82 ((
% 131.89/22.82 (transitivesetOp1) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintTransitive) =>
% 131.89/22.82 ((
% 131.89/22.82 (transitivesetOp2) =>
% 131.89/22.82 ((
% 131.89/22.82 (setunionTransitive) =>
% 131.89/22.82 ((
% 131.89/22.82 (ordinalMinLem1) =>
% 131.89/22.82 ((
% 131.89/22.82 (ordinalTransSet) =>
% 131.89/22.82 ((
% 131.89/22.82 (ordinalTransSet1) =>
% 131.89/22.82 ((
% 131.89/22.82 (setunionOrdinalLem1) =>
% 131.89/22.82 (ordinal @
% 131.89/22.82 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 131.89/22.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl382])).
% 131.89/22.82 thf(zip_derived_cl397, plain,
% 131.89/22.82 (~ (((uniqinunit) =>
% 131.89/22.82 (((notinsingleton) =>
% 131.89/22.82 (((eqinunit) =>
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% 131.89/22.82 (((upairsetIL) =>
% 131.89/22.82 (((upairsetIR) =>
% 131.89/22.82 (((emptyE1) =>
% 131.89/22.82 (((vacuousDall) =>
% 131.89/22.82 (((quantDeMorgan1) =>
% 131.89/22.82 (((quantDeMorgan2) =>
% 131.89/22.82 (((quantDeMorgan3) =>
% 131.89/22.82 (((quantDeMorgan4) =>
% 131.89/22.82 (((prop2setI) =>
% 131.89/22.82 (((prop2set2propI) =>
% 131.89/22.82 (((notdexE) =>
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% 131.89/22.82 (((exuI3) =>
% 131.89/22.82 (((exuI2) =>
% 131.89/22.82 (((inCongP) =>
% 131.89/22.82 (((in__Cong) =>
% 131.89/22.82 (((exuE3u) =>
% 131.89/22.82 (((exu__Cong) =>
% 131.89/22.82 (((setadjoin__Cong) =>
% 131.89/22.82 (((powerset__Cong) =>
% 131.89/22.82 (((setunion__Cong) =>
% 131.89/22.82 (((exuEu) =>
% 131.89/22.82 (((descr__Cong) =>
% 131.89/22.82 (((dsetconstr__Cong) =>
% 131.89/22.82 ((
% 131.89/22.82 (subsetI1) =>
% 131.89/22.82 ((
% 131.89/22.82 (eqimpsubset2) =>
% 131.89/22.82 ((
% 131.89/22.82 (eqimpsubset1) =>
% 131.89/22.82 ((
% 131.89/22.82 (subsetI2) =>
% 131.89/22.82 ((
% 131.89/22.82 (emptysetsubset) =>
% 131.89/22.82 ((
% 131.89/22.82 (subsetE) =>
% 131.89/22.82 ((
% 131.89/22.82 (subsetE2) =>
% 131.89/22.82 ((
% 131.89/22.82 (notsubsetI) =>
% 131.89/22.82 ((
% 131.89/22.82 (notequalI1) =>
% 131.89/22.82 ((
% 131.89/22.82 (notequalI2) =>
% 131.89/22.82 ((
% 131.89/22.82 (subsetRefl) =>
% 131.89/22.82 ((
% 131.89/22.82 (subsetTrans) =>
% 131.89/22.82 ((
% 131.89/22.82 (setadjoinSub) =>
% 131.89/22.82 ((
% 131.89/22.82 (setadjoinSub2) =>
% 131.89/22.82 ((
% 131.89/22.82 (subset2powerset) =>
% 131.89/22.82 ((
% 131.89/22.82 (setextsub) =>
% 131.89/22.82 ((
% 131.89/22.82 (subsetemptysetimpeq) =>
% 131.89/22.82 ((
% 131.89/22.82 (powersetI1) =>
% 131.89/22.82 ((
% 131.89/22.82 (powersetE1) =>
% 131.89/22.82 ((
% 131.89/22.82 (inPowerset) =>
% 131.89/22.82 ((
% 131.89/22.82 (powersetsubset) =>
% 131.89/22.82 ((
% 131.89/22.82 (sepInPowerset) =>
% 131.89/22.82 ((
% 131.89/22.82 (sepSubset) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionIL) =>
% 131.89/22.82 ((
% 131.89/22.82 (upairset2IR) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionIR) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionEcases) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionE) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionLsub) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionRsub) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectI) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectSubset5) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectEL) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectLsub) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectSubset2) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectSubset3) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectER) =>
% 131.89/22.82 ((
% 131.89/22.82 (disjointsetsI1) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectRsub) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectSubset4) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectSubset1) =>
% 131.89/22.82 ((
% 131.89/22.82 (bs114d) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusI) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusEL) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusER) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusSubset2) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusERneg) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusELneg) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusILneg) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusIRneg) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusLsub) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusSubset1) =>
% 131.89/22.82 ((
% 131.89/22.82 (symdiffE) =>
% 131.89/22.82 ((
% 131.89/22.82 (symdiffI1) =>
% 131.89/22.82 ((
% 131.89/22.82 (symdiffI2) =>
% 131.89/22.82 ((
% 131.89/22.82 (symdiffIneg1) =>
% 131.89/22.82 ((
% 131.89/22.82 (symdiffIneg2) =>
% 131.89/22.82 ((
% 131.89/22.82 (secondinupair) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairIL) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairIR) =>
% 131.89/22.82 ((
% 131.89/22.82 (kpairiskpair) =>
% 131.89/22.82 ((
% 131.89/22.82 (kpairp) =>
% 131.89/22.82 ((
% 131.89/22.82 (singletonsubset) =>
% 131.89/22.82 ((
% 131.89/22.82 (singletoninpowerset) =>
% 131.89/22.82 ((
% 131.89/22.82 (singletoninpowunion) =>
% 131.89/22.82 ((
% 131.89/22.82 (upairset2E) =>
% 131.89/22.82 ((
% 131.89/22.82 (upairsubunion) =>
% 131.89/22.82 ((
% 131.89/22.82 (upairinpowunion) =>
% 131.89/22.82 ((
% 131.89/22.82 (ubforcartprodlem1) =>
% 131.89/22.82 ((
% 131.89/22.82 (ubforcartprodlem2) =>
% 131.89/22.82 ((
% 131.89/22.82 (ubforcartprodlem3) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodpairin) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodmempair1) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodmempair) =>
% 131.89/22.82 ((
% 131.89/22.82 (setunionE2) =>
% 131.89/22.82 ((
% 131.89/22.82 (setunionsingleton1) =>
% 131.89/22.82 ((
% 131.89/22.82 (setunionsingleton2) =>
% 131.89/22.82 ((
% 131.89/22.82 (setunionsingleton) =>
% 131.89/22.82 ((
% 131.89/22.82 (singletonprop) =>
% 131.89/22.82 ((
% 131.89/22.82 (ex1E1) =>
% 131.89/22.82 ((
% 131.89/22.82 (ex1I) =>
% 131.89/22.82 ((
% 131.89/22.82 (ex1I2) =>
% 131.89/22.82 ((
% 131.89/22.82 (singletonsuniq) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairinjL1) =>
% 131.89/22.82 ((
% 131.89/22.82 (kfstsingleton) =>
% 131.89/22.82 ((
% 131.89/22.82 (theprop) =>
% 131.89/22.82 ((
% 131.89/22.82 (kfstpairEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodfstin) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairinjL2) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairinjL) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairinjR11) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairinjR12) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairinjR1) =>
% 131.89/22.82 ((
% 131.89/22.82 (upairequniteq) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairinjR2) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairinjR) =>
% 131.89/22.82 ((
% 131.89/22.82 (ksndsingleton) =>
% 131.89/22.82 ((
% 131.89/22.82 (ksndpairEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (kpairsurjEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodsndin) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodpairmemEL) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodpairmemER) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodmempaircEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodfstpairEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodsndpairEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodpairsurjEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (dpsetconstrI) =>
% 131.89/22.82 ((
% 131.89/22.82 (dpsetconstrSub) =>
% 131.89/22.82 ((
% 131.89/22.82 (setOfPairsIsBReln) =>
% 131.89/22.82 ((
% 131.89/22.82 (dpsetconstrERa) =>
% 131.89/22.82 ((
% 131.89/22.82 (dpsetconstrEL1) =>
% 131.89/22.82 ((
% 131.89/22.82 (dpsetconstrEL2) =>
% 131.89/22.82 ((
% 131.89/22.82 (dpsetconstrER) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcImageSingleton) =>
% 131.89/22.82 ((
% 131.89/22.82 (apProp) =>
% 131.89/22.82 ((
% 131.89/22.82 (app) =>
% 131.89/22.82 ((
% 131.89/22.82 (infuncsetfunc) =>
% 131.89/22.82 ((
% 131.89/22.82 (ap2p) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcinfuncset) =>
% 131.89/22.82 ((
% 131.89/22.82 (lamProp) =>
% 131.89/22.82 ((
% 131.89/22.82 (lamp) =>
% 131.89/22.82 ((
% 131.89/22.82 (lam2p) =>
% 131.89/22.82 ((
% 131.89/22.82 (brelnall1) =>
% 131.89/22.82 ((
% 131.89/22.82 (brelnall2) =>
% 131.89/22.82 ((
% 131.89/22.82 (ex1E2) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcGraphProp1) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcGraphProp3) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcGraphProp2) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcextLem) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcGraphProp4) =>
% 131.89/22.82 ((
% 131.89/22.82 (subbreln) =>
% 131.89/22.82 ((
% 131.89/22.82 (eqbreln) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcext) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcext2) =>
% 131.89/22.82 ((
% 131.89/22.82 (ap2apEq1) =>
% 131.89/22.82 ((
% 131.89/22.82 (ap2apEq2) =>
% 131.89/22.82 ((
% 131.89/22.82 (beta1) =>
% 131.89/22.82 ((
% 131.89/22.82 (eta1) =>
% 131.89/22.82 ((
% 131.89/22.82 (lam2lamEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (beta2) =>
% 131.89/22.82 ((
% 131.89/22.82 (eta2) =>
% 131.89/22.82 ((
% 131.89/22.82 (iffalseProp1) =>
% 131.89/22.82 ((
% 131.89/22.82 (iffalseProp2) =>
% 131.89/22.82 ((
% 131.89/22.82 (iftrueProp1) =>
% 131.89/22.82 ((
% 131.89/22.82 (iftrueProp2) =>
% 131.89/22.82 ((
% 131.89/22.82 (ifSingleton) =>
% 131.89/22.82 ((
% 131.89/22.82 (ifp) =>
% 131.89/22.82 ((
% 131.89/22.82 (theeq) =>
% 131.89/22.82 ((
% 131.89/22.82 (iftrue) =>
% 131.89/22.82 ((
% 131.89/22.82 (iffalse) =>
% 131.89/22.82 ((
% 131.89/22.82 (iftrueorfalse) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectT_lem) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionT_lem) =>
% 131.89/22.82 ((
% 131.89/22.82 (powersetT_lem) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusT_lem) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementT_lem) =>
% 131.89/22.82 ((
% 131.89/22.82 (setextT) =>
% 131.89/22.82 ((
% 131.89/22.82 (subsetTI) =>
% 131.89/22.82 ((
% 131.89/22.82 (powersetTI1) =>
% 131.89/22.82 ((
% 131.89/22.82 (powersetTE1) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementTI1) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementTE1) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectTELcontra) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectTERcontra) =>
% 131.89/22.82 ((
% 131.89/22.82 (contrasubsetT) =>
% 131.89/22.82 ((
% 131.89/22.82 (contrasubsetT1) =>
% 131.89/22.82 ((
% 131.89/22.82 (contrasubsetT2) =>
% 131.89/22.82 ((
% 131.89/22.82 (contrasubsetT3) =>
% 131.89/22.82 ((
% 131.89/22.82 (doubleComplementI1) =>
% 131.89/22.82 ((
% 131.89/22.82 (doubleComplementE1) =>
% 131.89/22.82 ((
% 131.89/22.82 (doubleComplementSub1) =>
% 131.89/22.82 ((
% 131.89/22.82 (doubleComplementSub2) =>
% 131.89/22.82 ((
% 131.89/22.82 (doubleComplementEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementTnotintersectT) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementImpComplementIntersect) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementSubsetComplementIntersect) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementInPowersetComplementIntersect) =>
% 131.89/22.82 ((
% 131.89/22.82 (contraSubsetComplement) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementTcontraSubset) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionTILcontra) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionTIRcontra) =>
% 131.89/22.82 ((
% 131.89/22.82 (inIntersectImpInUnion) =>
% 131.89/22.82 ((
% 131.89/22.82 (inIntersectImpInUnion2) =>
% 131.89/22.82 ((
% 131.89/22.82 (inIntersectImpInIntersectUnions) =>
% 131.89/22.82 ((
% 131.89/22.82 (intersectInPowersetIntersectUnions) =>
% 131.89/22.82 ((
% 131.89/22.82 (inComplementUnionImpNotIn1) =>
% 131.89/22.82 ((
% 131.89/22.82 (inComplementUnionImpInComplement1) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionTE) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionTEcontra) =>
% 131.89/22.82 ((
% 131.89/22.82 (demorgan2a1) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementUnionInPowersetComplement) =>
% 131.89/22.82 ((
% 131.89/22.82 (demorgan2a2) =>
% 131.89/22.82 ((
% 131.89/22.82 (demorgan1a) =>
% 131.89/22.82 ((
% 131.89/22.82 (demorgan1b) =>
% 131.89/22.82 ((
% 131.89/22.82 (demorgan1) =>
% 131.89/22.82 ((
% 131.89/22.82 (demorgan2a) =>
% 131.89/22.82 ((
% 131.89/22.82 (demorgan2b2) =>
% 131.89/22.82 ((
% 131.89/22.82 (demorgan2b) =>
% 131.89/22.82 ((
% 131.89/22.82 (demorgan2) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz13rule0) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz13rule1) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz13rule2) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz13rule3) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz13rule4) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz1_1) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz1_2) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz1_3) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz1_4) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz1_5) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1all2) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1SetBreln1) =>
% 131.89/22.82 ((
% 131.89/22.82 (choice2fnsingleton) =>
% 131.89/22.82 ((
% 131.89/22.82 (setOfPairsIsBReln1) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1all1) =>
% 131.89/22.82 ((
% 131.89/22.82 (subbreln1) =>
% 131.89/22.82 ((
% 131.89/22.82 (eqbreln1) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1invprop) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1invI) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1invE) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1compprop) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1compI) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1compE) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1compEex) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1unionprop) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1unionIL) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1unionIR) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1unionI) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1unionE) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1unionEcases) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1unionCommutes) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz2Ex) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz2W) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz2A) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz2B) =>
% 131.89/22.82 ((
% 131.89/22.82 (image1Ex) =>
% 131.89/22.82 ((
% 131.89/22.82 (image1Ex1) =>
% 131.89/22.82 ((
% 131.89/22.82 (image1Equiv) =>
% 131.89/22.82 ((
% 131.89/22.82 (image1E) =>
% 131.89/22.82 ((
% 131.89/22.82 (image1I) =>
% 131.89/22.82 ((
% 131.89/22.82 (injFuncInInjFuncSet) =>
% 131.89/22.82 ((
% 131.89/22.82 (injFuncSetFuncIn) =>
% 131.89/22.82 ((
% 131.89/22.82 (injFuncSetFuncInj) =>
% 131.89/22.82 ((
% 131.89/22.82 (surjFuncSetFuncIn) =>
% 131.89/22.82 ((
% 131.89/22.82 (surjFuncSetFuncSurj) =>
% 131.89/22.82 ((
% 131.89/22.82 (leftInvIsSurj) =>
% 131.89/22.82 ((
% 131.89/22.82 (surjCantorThm) =>
% 131.89/22.82 ((
% 131.89/22.82 (foundation2) =>
% 131.89/22.82 ((
% 131.89/22.82 (notinself) =>
% 131.89/22.82 ((
% 131.89/22.82 (notinself2) =>
% 131.89/22.82 ((
% 131.89/22.82 (omegaSp) =>
% 131.89/22.82 ((
% 131.89/22.82 (omegaSclos) =>
% 131.89/22.82 ((
% 131.89/22.82 (peano0notS) =>
% 131.89/22.82 ((
% 131.89/22.82 (peanoSinj) =>
% 131.89/22.82 ((
% 131.89/22.82 (transitivesetOp1) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintTransitive) =>
% 131.89/22.82 ((
% 131.89/22.82 (transitivesetOp2) =>
% 131.89/22.82 ((
% 131.89/22.82 (setunionTransitive) =>
% 131.89/22.82 ((
% 131.89/22.82 (ordinalMinLem1) =>
% 131.89/22.82 ((
% 131.89/22.82 (ordinalTransSet) =>
% 131.89/22.82 ((
% 131.89/22.82 (ordinalTransSet1) =>
% 131.89/22.82 ((
% 131.89/22.82 (setunionOrdinalLem1) =>
% 131.89/22.82 (ordinal @
% 131.89/22.82 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 131.89/22.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl390])).
% 131.89/22.82 thf(zip_derived_cl406, plain,
% 131.89/22.82 (~ (((notinsingleton) =>
% 131.89/22.82 (((eqinunit) =>
% 131.89/22.82 (((singletonsswitch) =>
% 131.89/22.82 (((upairsetE) =>
% 131.89/22.82 (((upairsetIL) =>
% 131.89/22.82 (((upairsetIR) =>
% 131.89/22.82 (((emptyE1) =>
% 131.89/22.82 (((vacuousDall) =>
% 131.89/22.82 (((quantDeMorgan1) =>
% 131.89/22.82 (((quantDeMorgan2) =>
% 131.89/22.82 (((quantDeMorgan3) =>
% 131.89/22.82 (((quantDeMorgan4) =>
% 131.89/22.82 (((prop2setI) =>
% 131.89/22.82 (((prop2set2propI) =>
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% 131.89/22.82 (((notdallE) =>
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% 131.89/22.82 (((exuI3) =>
% 131.89/22.82 (((exuI2) =>
% 131.89/22.82 (((inCongP) =>
% 131.89/22.82 (((in__Cong) =>
% 131.89/22.82 (((exuE3u) =>
% 131.89/22.82 (((exu__Cong) =>
% 131.89/22.82 (((setadjoin__Cong) =>
% 131.89/22.82 (((powerset__Cong) =>
% 131.89/22.82 (((setunion__Cong) =>
% 131.89/22.82 (((exuEu) =>
% 131.89/22.82 (((descr__Cong) =>
% 131.89/22.82 (((dsetconstr__Cong) =>
% 131.89/22.82 (((subsetI1) =>
% 131.89/22.82 ((
% 131.89/22.82 (eqimpsubset2) =>
% 131.89/22.82 ((
% 131.89/22.82 (eqimpsubset1) =>
% 131.89/22.82 ((
% 131.89/22.82 (subsetI2) =>
% 131.89/22.82 ((
% 131.89/22.82 (emptysetsubset) =>
% 131.89/22.82 ((
% 131.89/22.82 (subsetE) =>
% 131.89/22.82 ((
% 131.89/22.82 (subsetE2) =>
% 131.89/22.82 ((
% 131.89/22.82 (notsubsetI) =>
% 131.89/22.82 ((
% 131.89/22.82 (notequalI1) =>
% 131.89/22.82 ((
% 131.89/22.82 (notequalI2) =>
% 131.89/22.82 ((
% 131.89/22.82 (subsetRefl) =>
% 131.89/22.82 ((
% 131.89/22.82 (subsetTrans) =>
% 131.89/22.82 ((
% 131.89/22.82 (setadjoinSub) =>
% 131.89/22.82 ((
% 131.89/22.82 (setadjoinSub2) =>
% 131.89/22.82 ((
% 131.89/22.82 (subset2powerset) =>
% 131.89/22.82 ((
% 131.89/22.82 (setextsub) =>
% 131.89/22.82 ((
% 131.89/22.82 (subsetemptysetimpeq) =>
% 131.89/22.82 ((
% 131.89/22.82 (powersetI1) =>
% 131.89/22.82 ((
% 131.89/22.82 (powersetE1) =>
% 131.89/22.82 ((
% 131.89/22.82 (inPowerset) =>
% 131.89/22.82 ((
% 131.89/22.82 (powersetsubset) =>
% 131.89/22.82 ((
% 131.89/22.82 (sepInPowerset) =>
% 131.89/22.82 ((
% 131.89/22.82 (sepSubset) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionIL) =>
% 131.89/22.82 ((
% 131.89/22.82 (upairset2IR) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionIR) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionEcases) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionE) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionLsub) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionRsub) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectI) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectSubset5) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectEL) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectLsub) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectSubset2) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectSubset3) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectER) =>
% 131.89/22.82 ((
% 131.89/22.82 (disjointsetsI1) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectRsub) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectSubset4) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectSubset1) =>
% 131.89/22.82 ((
% 131.89/22.82 (bs114d) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusI) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusEL) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusER) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusSubset2) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusERneg) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusELneg) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusILneg) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusIRneg) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusLsub) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusSubset1) =>
% 131.89/22.82 ((
% 131.89/22.82 (symdiffE) =>
% 131.89/22.82 ((
% 131.89/22.82 (symdiffI1) =>
% 131.89/22.82 ((
% 131.89/22.82 (symdiffI2) =>
% 131.89/22.82 ((
% 131.89/22.82 (symdiffIneg1) =>
% 131.89/22.82 ((
% 131.89/22.82 (symdiffIneg2) =>
% 131.89/22.82 ((
% 131.89/22.82 (secondinupair) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairIL) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairIR) =>
% 131.89/22.82 ((
% 131.89/22.82 (kpairiskpair) =>
% 131.89/22.82 ((
% 131.89/22.82 (kpairp) =>
% 131.89/22.82 ((
% 131.89/22.82 (singletonsubset) =>
% 131.89/22.82 ((
% 131.89/22.82 (singletoninpowerset) =>
% 131.89/22.82 ((
% 131.89/22.82 (singletoninpowunion) =>
% 131.89/22.82 ((
% 131.89/22.82 (upairset2E) =>
% 131.89/22.82 ((
% 131.89/22.82 (upairsubunion) =>
% 131.89/22.82 ((
% 131.89/22.82 (upairinpowunion) =>
% 131.89/22.82 ((
% 131.89/22.82 (ubforcartprodlem1) =>
% 131.89/22.82 ((
% 131.89/22.82 (ubforcartprodlem2) =>
% 131.89/22.82 ((
% 131.89/22.82 (ubforcartprodlem3) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodpairin) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodmempair1) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodmempair) =>
% 131.89/22.82 ((
% 131.89/22.82 (setunionE2) =>
% 131.89/22.82 ((
% 131.89/22.82 (setunionsingleton1) =>
% 131.89/22.82 ((
% 131.89/22.82 (setunionsingleton2) =>
% 131.89/22.82 ((
% 131.89/22.82 (setunionsingleton) =>
% 131.89/22.82 ((
% 131.89/22.82 (singletonprop) =>
% 131.89/22.82 ((
% 131.89/22.82 (ex1E1) =>
% 131.89/22.82 ((
% 131.89/22.82 (ex1I) =>
% 131.89/22.82 ((
% 131.89/22.82 (ex1I2) =>
% 131.89/22.82 ((
% 131.89/22.82 (singletonsuniq) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairinjL1) =>
% 131.89/22.82 ((
% 131.89/22.82 (kfstsingleton) =>
% 131.89/22.82 ((
% 131.89/22.82 (theprop) =>
% 131.89/22.82 ((
% 131.89/22.82 (kfstpairEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodfstin) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairinjL2) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairinjL) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairinjR11) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairinjR12) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairinjR1) =>
% 131.89/22.82 ((
% 131.89/22.82 (upairequniteq) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairinjR2) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairinjR) =>
% 131.89/22.82 ((
% 131.89/22.82 (ksndsingleton) =>
% 131.89/22.82 ((
% 131.89/22.82 (ksndpairEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (kpairsurjEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodsndin) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodpairmemEL) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodpairmemER) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodmempaircEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodfstpairEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodsndpairEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodpairsurjEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (dpsetconstrI) =>
% 131.89/22.82 ((
% 131.89/22.82 (dpsetconstrSub) =>
% 131.89/22.82 ((
% 131.89/22.82 (setOfPairsIsBReln) =>
% 131.89/22.82 ((
% 131.89/22.82 (dpsetconstrERa) =>
% 131.89/22.82 ((
% 131.89/22.82 (dpsetconstrEL1) =>
% 131.89/22.82 ((
% 131.89/22.82 (dpsetconstrEL2) =>
% 131.89/22.82 ((
% 131.89/22.82 (dpsetconstrER) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcImageSingleton) =>
% 131.89/22.82 ((
% 131.89/22.82 (apProp) =>
% 131.89/22.82 ((
% 131.89/22.82 (app) =>
% 131.89/22.82 ((
% 131.89/22.82 (infuncsetfunc) =>
% 131.89/22.82 ((
% 131.89/22.82 (ap2p) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcinfuncset) =>
% 131.89/22.82 ((
% 131.89/22.82 (lamProp) =>
% 131.89/22.82 ((
% 131.89/22.82 (lamp) =>
% 131.89/22.82 ((
% 131.89/22.82 (lam2p) =>
% 131.89/22.82 ((
% 131.89/22.82 (brelnall1) =>
% 131.89/22.82 ((
% 131.89/22.82 (brelnall2) =>
% 131.89/22.82 ((
% 131.89/22.82 (ex1E2) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcGraphProp1) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcGraphProp3) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcGraphProp2) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcextLem) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcGraphProp4) =>
% 131.89/22.82 ((
% 131.89/22.82 (subbreln) =>
% 131.89/22.82 ((
% 131.89/22.82 (eqbreln) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcext) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcext2) =>
% 131.89/22.82 ((
% 131.89/22.82 (ap2apEq1) =>
% 131.89/22.82 ((
% 131.89/22.82 (ap2apEq2) =>
% 131.89/22.82 ((
% 131.89/22.82 (beta1) =>
% 131.89/22.82 ((
% 131.89/22.82 (eta1) =>
% 131.89/22.82 ((
% 131.89/22.82 (lam2lamEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (beta2) =>
% 131.89/22.82 ((
% 131.89/22.82 (eta2) =>
% 131.89/22.82 ((
% 131.89/22.82 (iffalseProp1) =>
% 131.89/22.82 ((
% 131.89/22.82 (iffalseProp2) =>
% 131.89/22.82 ((
% 131.89/22.82 (iftrueProp1) =>
% 131.89/22.82 ((
% 131.89/22.82 (iftrueProp2) =>
% 131.89/22.82 ((
% 131.89/22.82 (ifSingleton) =>
% 131.89/22.82 ((
% 131.89/22.82 (ifp) =>
% 131.89/22.82 ((
% 131.89/22.82 (theeq) =>
% 131.89/22.82 ((
% 131.89/22.82 (iftrue) =>
% 131.89/22.82 ((
% 131.89/22.82 (iffalse) =>
% 131.89/22.82 ((
% 131.89/22.82 (iftrueorfalse) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectT_lem) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionT_lem) =>
% 131.89/22.82 ((
% 131.89/22.82 (powersetT_lem) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusT_lem) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementT_lem) =>
% 131.89/22.82 ((
% 131.89/22.82 (setextT) =>
% 131.89/22.82 ((
% 131.89/22.82 (subsetTI) =>
% 131.89/22.82 ((
% 131.89/22.82 (powersetTI1) =>
% 131.89/22.82 ((
% 131.89/22.82 (powersetTE1) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementTI1) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementTE1) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectTELcontra) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectTERcontra) =>
% 131.89/22.82 ((
% 131.89/22.82 (contrasubsetT) =>
% 131.89/22.82 ((
% 131.89/22.82 (contrasubsetT1) =>
% 131.89/22.82 ((
% 131.89/22.82 (contrasubsetT2) =>
% 131.89/22.82 ((
% 131.89/22.82 (contrasubsetT3) =>
% 131.89/22.82 ((
% 131.89/22.82 (doubleComplementI1) =>
% 131.89/22.82 ((
% 131.89/22.82 (doubleComplementE1) =>
% 131.89/22.82 ((
% 131.89/22.82 (doubleComplementSub1) =>
% 131.89/22.82 ((
% 131.89/22.82 (doubleComplementSub2) =>
% 131.89/22.82 ((
% 131.89/22.82 (doubleComplementEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementTnotintersectT) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementImpComplementIntersect) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementSubsetComplementIntersect) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementInPowersetComplementIntersect) =>
% 131.89/22.82 ((
% 131.89/22.82 (contraSubsetComplement) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementTcontraSubset) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionTILcontra) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionTIRcontra) =>
% 131.89/22.82 ((
% 131.89/22.82 (inIntersectImpInUnion) =>
% 131.89/22.82 ((
% 131.89/22.82 (inIntersectImpInUnion2) =>
% 131.89/22.82 ((
% 131.89/22.82 (inIntersectImpInIntersectUnions) =>
% 131.89/22.82 ((
% 131.89/22.82 (intersectInPowersetIntersectUnions) =>
% 131.89/22.82 ((
% 131.89/22.82 (inComplementUnionImpNotIn1) =>
% 131.89/22.82 ((
% 131.89/22.82 (inComplementUnionImpInComplement1) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionTE) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionTEcontra) =>
% 131.89/22.82 ((
% 131.89/22.82 (demorgan2a1) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementUnionInPowersetComplement) =>
% 131.89/22.82 ((
% 131.89/22.82 (demorgan2a2) =>
% 131.89/22.82 ((
% 131.89/22.82 (demorgan1a) =>
% 131.89/22.82 ((
% 131.89/22.82 (demorgan1b) =>
% 131.89/22.82 ((
% 131.89/22.82 (demorgan1) =>
% 131.89/22.82 ((
% 131.89/22.82 (demorgan2a) =>
% 131.89/22.82 ((
% 131.89/22.82 (demorgan2b2) =>
% 131.89/22.82 ((
% 131.89/22.82 (demorgan2b) =>
% 131.89/22.82 ((
% 131.89/22.82 (demorgan2) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz13rule0) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz13rule1) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz13rule2) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz13rule3) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz13rule4) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz1_1) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz1_2) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz1_3) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz1_4) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz1_5) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1all2) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1SetBreln1) =>
% 131.89/22.82 ((
% 131.89/22.82 (choice2fnsingleton) =>
% 131.89/22.82 ((
% 131.89/22.82 (setOfPairsIsBReln1) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1all1) =>
% 131.89/22.82 ((
% 131.89/22.82 (subbreln1) =>
% 131.89/22.82 ((
% 131.89/22.82 (eqbreln1) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1invprop) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1invI) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1invE) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1compprop) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1compI) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1compE) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1compEex) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1unionprop) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1unionIL) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1unionIR) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1unionI) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1unionE) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1unionEcases) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1unionCommutes) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz2Ex) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz2W) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz2A) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz2B) =>
% 131.89/22.82 ((
% 131.89/22.82 (image1Ex) =>
% 131.89/22.82 ((
% 131.89/22.82 (image1Ex1) =>
% 131.89/22.82 ((
% 131.89/22.82 (image1Equiv) =>
% 131.89/22.82 ((
% 131.89/22.82 (image1E) =>
% 131.89/22.82 ((
% 131.89/22.82 (image1I) =>
% 131.89/22.82 ((
% 131.89/22.82 (injFuncInInjFuncSet) =>
% 131.89/22.82 ((
% 131.89/22.82 (injFuncSetFuncIn) =>
% 131.89/22.82 ((
% 131.89/22.82 (injFuncSetFuncInj) =>
% 131.89/22.82 ((
% 131.89/22.82 (surjFuncSetFuncIn) =>
% 131.89/22.82 ((
% 131.89/22.82 (surjFuncSetFuncSurj) =>
% 131.89/22.82 ((
% 131.89/22.82 (leftInvIsSurj) =>
% 131.89/22.82 ((
% 131.89/22.82 (surjCantorThm) =>
% 131.89/22.82 ((
% 131.89/22.82 (foundation2) =>
% 131.89/22.82 ((
% 131.89/22.82 (notinself) =>
% 131.89/22.82 ((
% 131.89/22.82 (notinself2) =>
% 131.89/22.82 ((
% 131.89/22.82 (omegaSp) =>
% 131.89/22.82 ((
% 131.89/22.82 (omegaSclos) =>
% 131.89/22.82 ((
% 131.89/22.82 (peano0notS) =>
% 131.89/22.82 ((
% 131.89/22.82 (peanoSinj) =>
% 131.89/22.82 ((
% 131.89/22.82 (transitivesetOp1) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintTransitive) =>
% 131.89/22.82 ((
% 131.89/22.82 (transitivesetOp2) =>
% 131.89/22.82 ((
% 131.89/22.82 (setunionTransitive) =>
% 131.89/22.82 ((
% 131.89/22.82 (ordinalMinLem1) =>
% 131.89/22.82 ((
% 131.89/22.82 (ordinalTransSet) =>
% 131.89/22.82 ((
% 131.89/22.82 (ordinalTransSet1) =>
% 131.89/22.82 ((
% 131.89/22.82 (setunionOrdinalLem1) =>
% 131.89/22.82 (ordinal @
% 131.89/22.82 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 131.89/22.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl397])).
% 131.89/22.82 thf(zip_derived_cl413, plain,
% 131.89/22.82 (~ (((eqinunit) =>
% 131.89/22.82 (((singletonsswitch) =>
% 131.89/22.82 (((upairsetE) =>
% 131.89/22.82 (((upairsetIL) =>
% 131.89/22.82 (((upairsetIR) =>
% 131.89/22.82 (((emptyE1) =>
% 131.89/22.82 (((vacuousDall) =>
% 131.89/22.82 (((quantDeMorgan1) =>
% 131.89/22.82 (((quantDeMorgan2) =>
% 131.89/22.82 (((quantDeMorgan3) =>
% 131.89/22.82 (((quantDeMorgan4) =>
% 131.89/22.82 (((prop2setI) =>
% 131.89/22.82 (((prop2set2propI) =>
% 131.89/22.82 (((notdexE) =>
% 131.89/22.82 (((notdallE) =>
% 131.89/22.82 (((exuI1) =>
% 131.89/22.82 (((exuI3) =>
% 131.89/22.82 (((exuI2) =>
% 131.89/22.82 (((inCongP) =>
% 131.89/22.82 (((in__Cong) =>
% 131.89/22.82 (((exuE3u) =>
% 131.89/22.82 (((exu__Cong) =>
% 131.89/22.82 (((setadjoin__Cong) =>
% 131.89/22.82 (((powerset__Cong) =>
% 131.89/22.82 (((setunion__Cong) =>
% 131.89/22.82 (((exuEu) =>
% 131.89/22.82 (((descr__Cong) =>
% 131.89/22.82 (((dsetconstr__Cong) =>
% 131.89/22.82 (((subsetI1) =>
% 131.89/22.82 (((eqimpsubset2) =>
% 131.89/22.82 ((
% 131.89/22.82 (eqimpsubset1) =>
% 131.89/22.82 ((
% 131.89/22.82 (subsetI2) =>
% 131.89/22.82 ((
% 131.89/22.82 (emptysetsubset) =>
% 131.89/22.82 ((
% 131.89/22.82 (subsetE) =>
% 131.89/22.82 ((
% 131.89/22.82 (subsetE2) =>
% 131.89/22.82 ((
% 131.89/22.82 (notsubsetI) =>
% 131.89/22.82 ((
% 131.89/22.82 (notequalI1) =>
% 131.89/22.82 ((
% 131.89/22.82 (notequalI2) =>
% 131.89/22.82 ((
% 131.89/22.82 (subsetRefl) =>
% 131.89/22.82 ((
% 131.89/22.82 (subsetTrans) =>
% 131.89/22.82 ((
% 131.89/22.82 (setadjoinSub) =>
% 131.89/22.82 ((
% 131.89/22.82 (setadjoinSub2) =>
% 131.89/22.82 ((
% 131.89/22.82 (subset2powerset) =>
% 131.89/22.82 ((
% 131.89/22.82 (setextsub) =>
% 131.89/22.82 ((
% 131.89/22.82 (subsetemptysetimpeq) =>
% 131.89/22.82 ((
% 131.89/22.82 (powersetI1) =>
% 131.89/22.82 ((
% 131.89/22.82 (powersetE1) =>
% 131.89/22.82 ((
% 131.89/22.82 (inPowerset) =>
% 131.89/22.82 ((
% 131.89/22.82 (powersetsubset) =>
% 131.89/22.82 ((
% 131.89/22.82 (sepInPowerset) =>
% 131.89/22.82 ((
% 131.89/22.82 (sepSubset) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionIL) =>
% 131.89/22.82 ((
% 131.89/22.82 (upairset2IR) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionIR) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionEcases) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionE) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionLsub) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionRsub) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectI) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectSubset5) =>
% 131.89/22.82 ((
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% 131.89/22.82 ((
% 131.89/22.82 (binintersectLsub) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectSubset2) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectSubset3) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectER) =>
% 131.89/22.82 ((
% 131.89/22.82 (disjointsetsI1) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectRsub) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectSubset4) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectSubset1) =>
% 131.89/22.82 ((
% 131.89/22.82 (bs114d) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusI) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusEL) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusER) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusSubset2) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusERneg) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusELneg) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusILneg) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusIRneg) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusLsub) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusSubset1) =>
% 131.89/22.82 ((
% 131.89/22.82 (symdiffE) =>
% 131.89/22.82 ((
% 131.89/22.82 (symdiffI1) =>
% 131.89/22.82 ((
% 131.89/22.82 (symdiffI2) =>
% 131.89/22.82 ((
% 131.89/22.82 (symdiffIneg1) =>
% 131.89/22.82 ((
% 131.89/22.82 (symdiffIneg2) =>
% 131.89/22.82 ((
% 131.89/22.82 (secondinupair) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairIL) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairIR) =>
% 131.89/22.82 ((
% 131.89/22.82 (kpairiskpair) =>
% 131.89/22.82 ((
% 131.89/22.82 (kpairp) =>
% 131.89/22.82 ((
% 131.89/22.82 (singletonsubset) =>
% 131.89/22.82 ((
% 131.89/22.82 (singletoninpowerset) =>
% 131.89/22.82 ((
% 131.89/22.82 (singletoninpowunion) =>
% 131.89/22.82 ((
% 131.89/22.82 (upairset2E) =>
% 131.89/22.82 ((
% 131.89/22.82 (upairsubunion) =>
% 131.89/22.82 ((
% 131.89/22.82 (upairinpowunion) =>
% 131.89/22.82 ((
% 131.89/22.82 (ubforcartprodlem1) =>
% 131.89/22.82 ((
% 131.89/22.82 (ubforcartprodlem2) =>
% 131.89/22.82 ((
% 131.89/22.82 (ubforcartprodlem3) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodpairin) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodmempair1) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodmempair) =>
% 131.89/22.82 ((
% 131.89/22.82 (setunionE2) =>
% 131.89/22.82 ((
% 131.89/22.82 (setunionsingleton1) =>
% 131.89/22.82 ((
% 131.89/22.82 (setunionsingleton2) =>
% 131.89/22.82 ((
% 131.89/22.82 (setunionsingleton) =>
% 131.89/22.82 ((
% 131.89/22.82 (singletonprop) =>
% 131.89/22.82 ((
% 131.89/22.82 (ex1E1) =>
% 131.89/22.82 ((
% 131.89/22.82 (ex1I) =>
% 131.89/22.82 ((
% 131.89/22.82 (ex1I2) =>
% 131.89/22.82 ((
% 131.89/22.82 (singletonsuniq) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairinjL1) =>
% 131.89/22.82 ((
% 131.89/22.82 (kfstsingleton) =>
% 131.89/22.82 ((
% 131.89/22.82 (theprop) =>
% 131.89/22.82 ((
% 131.89/22.82 (kfstpairEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodfstin) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairinjL2) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairinjL) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairinjR11) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairinjR12) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairinjR1) =>
% 131.89/22.82 ((
% 131.89/22.82 (upairequniteq) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairinjR2) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairinjR) =>
% 131.89/22.82 ((
% 131.89/22.82 (ksndsingleton) =>
% 131.89/22.82 ((
% 131.89/22.82 (ksndpairEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (kpairsurjEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodsndin) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodpairmemEL) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodpairmemER) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodmempaircEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodfstpairEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodsndpairEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodpairsurjEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (dpsetconstrI) =>
% 131.89/22.82 ((
% 131.89/22.82 (dpsetconstrSub) =>
% 131.89/22.82 ((
% 131.89/22.82 (setOfPairsIsBReln) =>
% 131.89/22.82 ((
% 131.89/22.82 (dpsetconstrERa) =>
% 131.89/22.82 ((
% 131.89/22.82 (dpsetconstrEL1) =>
% 131.89/22.82 ((
% 131.89/22.82 (dpsetconstrEL2) =>
% 131.89/22.82 ((
% 131.89/22.82 (dpsetconstrER) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcImageSingleton) =>
% 131.89/22.82 ((
% 131.89/22.82 (apProp) =>
% 131.89/22.82 ((
% 131.89/22.82 (app) =>
% 131.89/22.82 ((
% 131.89/22.82 (infuncsetfunc) =>
% 131.89/22.82 ((
% 131.89/22.82 (ap2p) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcinfuncset) =>
% 131.89/22.82 ((
% 131.89/22.82 (lamProp) =>
% 131.89/22.82 ((
% 131.89/22.82 (lamp) =>
% 131.89/22.82 ((
% 131.89/22.82 (lam2p) =>
% 131.89/22.82 ((
% 131.89/22.82 (brelnall1) =>
% 131.89/22.82 ((
% 131.89/22.82 (brelnall2) =>
% 131.89/22.82 ((
% 131.89/22.82 (ex1E2) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcGraphProp1) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcGraphProp3) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcGraphProp2) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcextLem) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcGraphProp4) =>
% 131.89/22.82 ((
% 131.89/22.82 (subbreln) =>
% 131.89/22.82 ((
% 131.89/22.82 (eqbreln) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcext) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcext2) =>
% 131.89/22.82 ((
% 131.89/22.82 (ap2apEq1) =>
% 131.89/22.82 ((
% 131.89/22.82 (ap2apEq2) =>
% 131.89/22.82 ((
% 131.89/22.82 (beta1) =>
% 131.89/22.82 ((
% 131.89/22.82 (eta1) =>
% 131.89/22.82 ((
% 131.89/22.82 (lam2lamEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (beta2) =>
% 131.89/22.82 ((
% 131.89/22.82 (eta2) =>
% 131.89/22.82 ((
% 131.89/22.82 (iffalseProp1) =>
% 131.89/22.82 ((
% 131.89/22.82 (iffalseProp2) =>
% 131.89/22.82 ((
% 131.89/22.82 (iftrueProp1) =>
% 131.89/22.82 ((
% 131.89/22.82 (iftrueProp2) =>
% 131.89/22.82 ((
% 131.89/22.82 (ifSingleton) =>
% 131.89/22.82 ((
% 131.89/22.82 (ifp) =>
% 131.89/22.82 ((
% 131.89/22.82 (theeq) =>
% 131.89/22.82 ((
% 131.89/22.82 (iftrue) =>
% 131.89/22.82 ((
% 131.89/22.82 (iffalse) =>
% 131.89/22.82 ((
% 131.89/22.82 (iftrueorfalse) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectT_lem) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionT_lem) =>
% 131.89/22.82 ((
% 131.89/22.82 (powersetT_lem) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusT_lem) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementT_lem) =>
% 131.89/22.82 ((
% 131.89/22.82 (setextT) =>
% 131.89/22.82 ((
% 131.89/22.82 (subsetTI) =>
% 131.89/22.82 ((
% 131.89/22.82 (powersetTI1) =>
% 131.89/22.82 ((
% 131.89/22.82 (powersetTE1) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementTI1) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementTE1) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectTELcontra) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectTERcontra) =>
% 131.89/22.82 ((
% 131.89/22.82 (contrasubsetT) =>
% 131.89/22.82 ((
% 131.89/22.82 (contrasubsetT1) =>
% 131.89/22.82 ((
% 131.89/22.82 (contrasubsetT2) =>
% 131.89/22.82 ((
% 131.89/22.82 (contrasubsetT3) =>
% 131.89/22.82 ((
% 131.89/22.82 (doubleComplementI1) =>
% 131.89/22.82 ((
% 131.89/22.82 (doubleComplementE1) =>
% 131.89/22.82 ((
% 131.89/22.82 (doubleComplementSub1) =>
% 131.89/22.82 ((
% 131.89/22.82 (doubleComplementSub2) =>
% 131.89/22.82 ((
% 131.89/22.82 (doubleComplementEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementTnotintersectT) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementImpComplementIntersect) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementSubsetComplementIntersect) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementInPowersetComplementIntersect) =>
% 131.89/22.82 ((
% 131.89/22.82 (contraSubsetComplement) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementTcontraSubset) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionTILcontra) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionTIRcontra) =>
% 131.89/22.82 ((
% 131.89/22.82 (inIntersectImpInUnion) =>
% 131.89/22.82 ((
% 131.89/22.82 (inIntersectImpInUnion2) =>
% 131.89/22.82 ((
% 131.89/22.82 (inIntersectImpInIntersectUnions) =>
% 131.89/22.82 ((
% 131.89/22.82 (intersectInPowersetIntersectUnions) =>
% 131.89/22.82 ((
% 131.89/22.82 (inComplementUnionImpNotIn1) =>
% 131.89/22.82 ((
% 131.89/22.82 (inComplementUnionImpInComplement1) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionTE) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionTEcontra) =>
% 131.89/22.82 ((
% 131.89/22.82 (demorgan2a1) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementUnionInPowersetComplement) =>
% 131.89/22.82 ((
% 131.89/22.82 (demorgan2a2) =>
% 131.89/22.82 ((
% 131.89/22.82 (demorgan1a) =>
% 131.89/22.82 ((
% 131.89/22.82 (demorgan1b) =>
% 131.89/22.82 ((
% 131.89/22.82 (demorgan1) =>
% 131.89/22.82 ((
% 131.89/22.82 (demorgan2a) =>
% 131.89/22.82 ((
% 131.89/22.82 (demorgan2b2) =>
% 131.89/22.82 ((
% 131.89/22.82 (demorgan2b) =>
% 131.89/22.82 ((
% 131.89/22.82 (demorgan2) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz13rule0) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz13rule1) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz13rule2) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz13rule3) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz13rule4) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz1_1) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz1_2) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz1_3) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz1_4) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz1_5) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1all2) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1SetBreln1) =>
% 131.89/22.82 ((
% 131.89/22.82 (choice2fnsingleton) =>
% 131.89/22.82 ((
% 131.89/22.82 (setOfPairsIsBReln1) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1all1) =>
% 131.89/22.82 ((
% 131.89/22.82 (subbreln1) =>
% 131.89/22.82 ((
% 131.89/22.82 (eqbreln1) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1invprop) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1invI) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1invE) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1compprop) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1compI) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1compE) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1compEex) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1unionprop) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1unionIL) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1unionIR) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1unionI) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1unionE) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1unionEcases) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1unionCommutes) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz2Ex) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz2W) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz2A) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz2B) =>
% 131.89/22.82 ((
% 131.89/22.82 (image1Ex) =>
% 131.89/22.82 ((
% 131.89/22.82 (image1Ex1) =>
% 131.89/22.82 ((
% 131.89/22.82 (image1Equiv) =>
% 131.89/22.82 ((
% 131.89/22.82 (image1E) =>
% 131.89/22.82 ((
% 131.89/22.82 (image1I) =>
% 131.89/22.82 ((
% 131.89/22.82 (injFuncInInjFuncSet) =>
% 131.89/22.82 ((
% 131.89/22.82 (injFuncSetFuncIn) =>
% 131.89/22.82 ((
% 131.89/22.82 (injFuncSetFuncInj) =>
% 131.89/22.82 ((
% 131.89/22.82 (surjFuncSetFuncIn) =>
% 131.89/22.82 ((
% 131.89/22.82 (surjFuncSetFuncSurj) =>
% 131.89/22.82 ((
% 131.89/22.82 (leftInvIsSurj) =>
% 131.89/22.82 ((
% 131.89/22.82 (surjCantorThm) =>
% 131.89/22.82 ((
% 131.89/22.82 (foundation2) =>
% 131.89/22.82 ((
% 131.89/22.82 (notinself) =>
% 131.89/22.82 ((
% 131.89/22.82 (notinself2) =>
% 131.89/22.82 ((
% 131.89/22.82 (omegaSp) =>
% 131.89/22.82 ((
% 131.89/22.82 (omegaSclos) =>
% 131.89/22.82 ((
% 131.89/22.82 (peano0notS) =>
% 131.89/22.82 ((
% 131.89/22.82 (peanoSinj) =>
% 131.89/22.82 ((
% 131.89/22.82 (transitivesetOp1) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintTransitive) =>
% 131.89/22.82 ((
% 131.89/22.82 (transitivesetOp2) =>
% 131.89/22.82 ((
% 131.89/22.82 (setunionTransitive) =>
% 131.89/22.82 ((
% 131.89/22.82 (ordinalMinLem1) =>
% 131.89/22.82 ((
% 131.89/22.82 (ordinalTransSet) =>
% 131.89/22.82 ((
% 131.89/22.82 (ordinalTransSet1) =>
% 131.89/22.82 ((
% 131.89/22.82 (setunionOrdinalLem1) =>
% 131.89/22.82 (ordinal @
% 131.89/22.82 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 131.89/22.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl406])).
% 131.89/22.82 thf(zip_derived_cl420, plain,
% 131.89/22.82 (~ (((singletonsswitch) =>
% 131.89/22.82 (((upairsetE) =>
% 131.89/22.82 (((upairsetIL) =>
% 131.89/22.82 (((upairsetIR) =>
% 131.89/22.82 (((emptyE1) =>
% 131.89/22.82 (((vacuousDall) =>
% 131.89/22.82 (((quantDeMorgan1) =>
% 131.89/22.82 (((quantDeMorgan2) =>
% 131.89/22.82 (((quantDeMorgan3) =>
% 131.89/22.82 (((quantDeMorgan4) =>
% 131.89/22.82 (((prop2setI) =>
% 131.89/22.82 (((prop2set2propI) =>
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% 131.89/22.82 (((notdallE) =>
% 131.89/22.82 (((exuI1) =>
% 131.89/22.82 (((exuI3) =>
% 131.89/22.82 (((exuI2) =>
% 131.89/22.82 (((inCongP) =>
% 131.89/22.82 (((in__Cong) =>
% 131.89/22.82 (((exuE3u) =>
% 131.89/22.82 (((exu__Cong) =>
% 131.89/22.82 (((setadjoin__Cong) =>
% 131.89/22.82 (((powerset__Cong) =>
% 131.89/22.82 (((setunion__Cong) =>
% 131.89/22.82 (((exuEu) =>
% 131.89/22.82 (((descr__Cong) =>
% 131.89/22.82 (((dsetconstr__Cong) =>
% 131.89/22.82 (((subsetI1) =>
% 131.89/22.82 (((eqimpsubset2) =>
% 131.89/22.82 (((eqimpsubset1) =>
% 131.89/22.82 ((
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% 131.89/22.82 ((
% 131.89/22.82 (emptysetsubset) =>
% 131.89/22.82 ((
% 131.89/22.82 (subsetE) =>
% 131.89/22.82 ((
% 131.89/22.82 (subsetE2) =>
% 131.89/22.82 ((
% 131.89/22.82 (notsubsetI) =>
% 131.89/22.82 ((
% 131.89/22.82 (notequalI1) =>
% 131.89/22.82 ((
% 131.89/22.82 (notequalI2) =>
% 131.89/22.82 ((
% 131.89/22.82 (subsetRefl) =>
% 131.89/22.82 ((
% 131.89/22.82 (subsetTrans) =>
% 131.89/22.82 ((
% 131.89/22.82 (setadjoinSub) =>
% 131.89/22.82 ((
% 131.89/22.82 (setadjoinSub2) =>
% 131.89/22.82 ((
% 131.89/22.82 (subset2powerset) =>
% 131.89/22.82 ((
% 131.89/22.82 (setextsub) =>
% 131.89/22.82 ((
% 131.89/22.82 (subsetemptysetimpeq) =>
% 131.89/22.82 ((
% 131.89/22.82 (powersetI1) =>
% 131.89/22.82 ((
% 131.89/22.82 (powersetE1) =>
% 131.89/22.82 ((
% 131.89/22.82 (inPowerset) =>
% 131.89/22.82 ((
% 131.89/22.82 (powersetsubset) =>
% 131.89/22.82 ((
% 131.89/22.82 (sepInPowerset) =>
% 131.89/22.82 ((
% 131.89/22.82 (sepSubset) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionIL) =>
% 131.89/22.82 ((
% 131.89/22.82 (upairset2IR) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionIR) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionEcases) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionE) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionLsub) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionRsub) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectI) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectSubset5) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectEL) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectLsub) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectSubset2) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectSubset3) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectER) =>
% 131.89/22.82 ((
% 131.89/22.82 (disjointsetsI1) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectRsub) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectSubset4) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectSubset1) =>
% 131.89/22.82 ((
% 131.89/22.82 (bs114d) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusI) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusEL) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusER) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusSubset2) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusERneg) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusELneg) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusILneg) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusIRneg) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusLsub) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusSubset1) =>
% 131.89/22.82 ((
% 131.89/22.82 (symdiffE) =>
% 131.89/22.82 ((
% 131.89/22.82 (symdiffI1) =>
% 131.89/22.82 ((
% 131.89/22.82 (symdiffI2) =>
% 131.89/22.82 ((
% 131.89/22.82 (symdiffIneg1) =>
% 131.89/22.82 ((
% 131.89/22.82 (symdiffIneg2) =>
% 131.89/22.82 ((
% 131.89/22.82 (secondinupair) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairIL) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairIR) =>
% 131.89/22.82 ((
% 131.89/22.82 (kpairiskpair) =>
% 131.89/22.82 ((
% 131.89/22.82 (kpairp) =>
% 131.89/22.82 ((
% 131.89/22.82 (singletonsubset) =>
% 131.89/22.82 ((
% 131.89/22.82 (singletoninpowerset) =>
% 131.89/22.82 ((
% 131.89/22.82 (singletoninpowunion) =>
% 131.89/22.82 ((
% 131.89/22.82 (upairset2E) =>
% 131.89/22.82 ((
% 131.89/22.82 (upairsubunion) =>
% 131.89/22.82 ((
% 131.89/22.82 (upairinpowunion) =>
% 131.89/22.82 ((
% 131.89/22.82 (ubforcartprodlem1) =>
% 131.89/22.82 ((
% 131.89/22.82 (ubforcartprodlem2) =>
% 131.89/22.82 ((
% 131.89/22.82 (ubforcartprodlem3) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodpairin) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodmempair1) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodmempair) =>
% 131.89/22.82 ((
% 131.89/22.82 (setunionE2) =>
% 131.89/22.82 ((
% 131.89/22.82 (setunionsingleton1) =>
% 131.89/22.82 ((
% 131.89/22.82 (setunionsingleton2) =>
% 131.89/22.82 ((
% 131.89/22.82 (setunionsingleton) =>
% 131.89/22.82 ((
% 131.89/22.82 (singletonprop) =>
% 131.89/22.82 ((
% 131.89/22.82 (ex1E1) =>
% 131.89/22.82 ((
% 131.89/22.82 (ex1I) =>
% 131.89/22.82 ((
% 131.89/22.82 (ex1I2) =>
% 131.89/22.82 ((
% 131.89/22.82 (singletonsuniq) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairinjL1) =>
% 131.89/22.82 ((
% 131.89/22.82 (kfstsingleton) =>
% 131.89/22.82 ((
% 131.89/22.82 (theprop) =>
% 131.89/22.82 ((
% 131.89/22.82 (kfstpairEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodfstin) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairinjL2) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairinjL) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairinjR11) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairinjR12) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairinjR1) =>
% 131.89/22.82 ((
% 131.89/22.82 (upairequniteq) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairinjR2) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairinjR) =>
% 131.89/22.82 ((
% 131.89/22.82 (ksndsingleton) =>
% 131.89/22.82 ((
% 131.89/22.82 (ksndpairEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (kpairsurjEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodsndin) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodpairmemEL) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodpairmemER) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodmempaircEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodfstpairEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodsndpairEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodpairsurjEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (dpsetconstrI) =>
% 131.89/22.82 ((
% 131.89/22.82 (dpsetconstrSub) =>
% 131.89/22.82 ((
% 131.89/22.82 (setOfPairsIsBReln) =>
% 131.89/22.82 ((
% 131.89/22.82 (dpsetconstrERa) =>
% 131.89/22.82 ((
% 131.89/22.82 (dpsetconstrEL1) =>
% 131.89/22.82 ((
% 131.89/22.82 (dpsetconstrEL2) =>
% 131.89/22.82 ((
% 131.89/22.82 (dpsetconstrER) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcImageSingleton) =>
% 131.89/22.82 ((
% 131.89/22.82 (apProp) =>
% 131.89/22.82 ((
% 131.89/22.82 (app) =>
% 131.89/22.82 ((
% 131.89/22.82 (infuncsetfunc) =>
% 131.89/22.82 ((
% 131.89/22.82 (ap2p) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcinfuncset) =>
% 131.89/22.82 ((
% 131.89/22.82 (lamProp) =>
% 131.89/22.82 ((
% 131.89/22.82 (lamp) =>
% 131.89/22.82 ((
% 131.89/22.82 (lam2p) =>
% 131.89/22.82 ((
% 131.89/22.82 (brelnall1) =>
% 131.89/22.82 ((
% 131.89/22.82 (brelnall2) =>
% 131.89/22.82 ((
% 131.89/22.82 (ex1E2) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcGraphProp1) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcGraphProp3) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcGraphProp2) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcextLem) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcGraphProp4) =>
% 131.89/22.82 ((
% 131.89/22.82 (subbreln) =>
% 131.89/22.82 ((
% 131.89/22.82 (eqbreln) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcext) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcext2) =>
% 131.89/22.82 ((
% 131.89/22.82 (ap2apEq1) =>
% 131.89/22.82 ((
% 131.89/22.82 (ap2apEq2) =>
% 131.89/22.82 ((
% 131.89/22.82 (beta1) =>
% 131.89/22.82 ((
% 131.89/22.82 (eta1) =>
% 131.89/22.82 ((
% 131.89/22.82 (lam2lamEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (beta2) =>
% 131.89/22.82 ((
% 131.89/22.82 (eta2) =>
% 131.89/22.82 ((
% 131.89/22.82 (iffalseProp1) =>
% 131.89/22.82 ((
% 131.89/22.82 (iffalseProp2) =>
% 131.89/22.82 ((
% 131.89/22.82 (iftrueProp1) =>
% 131.89/22.82 ((
% 131.89/22.82 (iftrueProp2) =>
% 131.89/22.82 ((
% 131.89/22.82 (ifSingleton) =>
% 131.89/22.82 ((
% 131.89/22.82 (ifp) =>
% 131.89/22.82 ((
% 131.89/22.82 (theeq) =>
% 131.89/22.82 ((
% 131.89/22.82 (iftrue) =>
% 131.89/22.82 ((
% 131.89/22.82 (iffalse) =>
% 131.89/22.82 ((
% 131.89/22.82 (iftrueorfalse) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectT_lem) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionT_lem) =>
% 131.89/22.82 ((
% 131.89/22.82 (powersetT_lem) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusT_lem) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementT_lem) =>
% 131.89/22.82 ((
% 131.89/22.82 (setextT) =>
% 131.89/22.82 ((
% 131.89/22.82 (subsetTI) =>
% 131.89/22.82 ((
% 131.89/22.82 (powersetTI1) =>
% 131.89/22.82 ((
% 131.89/22.82 (powersetTE1) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementTI1) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementTE1) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectTELcontra) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectTERcontra) =>
% 131.89/22.82 ((
% 131.89/22.82 (contrasubsetT) =>
% 131.89/22.82 ((
% 131.89/22.82 (contrasubsetT1) =>
% 131.89/22.82 ((
% 131.89/22.82 (contrasubsetT2) =>
% 131.89/22.82 ((
% 131.89/22.82 (contrasubsetT3) =>
% 131.89/22.82 ((
% 131.89/22.82 (doubleComplementI1) =>
% 131.89/22.82 ((
% 131.89/22.82 (doubleComplementE1) =>
% 131.89/22.82 ((
% 131.89/22.82 (doubleComplementSub1) =>
% 131.89/22.82 ((
% 131.89/22.82 (doubleComplementSub2) =>
% 131.89/22.82 ((
% 131.89/22.82 (doubleComplementEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementTnotintersectT) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementImpComplementIntersect) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementSubsetComplementIntersect) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementInPowersetComplementIntersect) =>
% 131.89/22.82 ((
% 131.89/22.82 (contraSubsetComplement) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementTcontraSubset) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionTILcontra) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionTIRcontra) =>
% 131.89/22.82 ((
% 131.89/22.82 (inIntersectImpInUnion) =>
% 131.89/22.82 ((
% 131.89/22.82 (inIntersectImpInUnion2) =>
% 131.89/22.82 ((
% 131.89/22.82 (inIntersectImpInIntersectUnions) =>
% 131.89/22.82 ((
% 131.89/22.82 (intersectInPowersetIntersectUnions) =>
% 131.89/22.82 ((
% 131.89/22.82 (inComplementUnionImpNotIn1) =>
% 131.89/22.82 ((
% 131.89/22.82 (inComplementUnionImpInComplement1) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionTE) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionTEcontra) =>
% 131.89/22.82 ((
% 131.89/22.82 (demorgan2a1) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementUnionInPowersetComplement) =>
% 131.89/22.82 ((
% 131.89/22.82 (demorgan2a2) =>
% 131.89/22.82 ((
% 131.89/22.82 (demorgan1a) =>
% 131.89/22.82 ((
% 131.89/22.82 (demorgan1b) =>
% 131.89/22.82 ((
% 131.89/22.82 (demorgan1) =>
% 131.89/22.82 ((
% 131.89/22.82 (demorgan2a) =>
% 131.89/22.82 ((
% 131.89/22.82 (demorgan2b2) =>
% 131.89/22.82 ((
% 131.89/22.82 (demorgan2b) =>
% 131.89/22.82 ((
% 131.89/22.82 (demorgan2) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz13rule0) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz13rule1) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz13rule2) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz13rule3) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz13rule4) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz1_1) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz1_2) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz1_3) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz1_4) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz1_5) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1all2) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1SetBreln1) =>
% 131.89/22.82 ((
% 131.89/22.82 (choice2fnsingleton) =>
% 131.89/22.82 ((
% 131.89/22.82 (setOfPairsIsBReln1) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1all1) =>
% 131.89/22.82 ((
% 131.89/22.82 (subbreln1) =>
% 131.89/22.82 ((
% 131.89/22.82 (eqbreln1) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1invprop) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1invI) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1invE) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1compprop) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1compI) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1compE) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1compEex) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1unionprop) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1unionIL) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1unionIR) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1unionI) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1unionE) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1unionEcases) =>
% 131.89/22.82 ((
% 131.89/22.82 (breln1unionCommutes) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz2Ex) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz2W) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz2A) =>
% 131.89/22.82 ((
% 131.89/22.82 (woz2B) =>
% 131.89/22.82 ((
% 131.89/22.82 (image1Ex) =>
% 131.89/22.82 ((
% 131.89/22.82 (image1Ex1) =>
% 131.89/22.82 ((
% 131.89/22.82 (image1Equiv) =>
% 131.89/22.82 ((
% 131.89/22.82 (image1E) =>
% 131.89/22.82 ((
% 131.89/22.82 (image1I) =>
% 131.89/22.82 ((
% 131.89/22.82 (injFuncInInjFuncSet) =>
% 131.89/22.82 ((
% 131.89/22.82 (injFuncSetFuncIn) =>
% 131.89/22.82 ((
% 131.89/22.82 (injFuncSetFuncInj) =>
% 131.89/22.82 ((
% 131.89/22.82 (surjFuncSetFuncIn) =>
% 131.89/22.82 ((
% 131.89/22.82 (surjFuncSetFuncSurj) =>
% 131.89/22.82 ((
% 131.89/22.82 (leftInvIsSurj) =>
% 131.89/22.82 ((
% 131.89/22.82 (surjCantorThm) =>
% 131.89/22.82 ((
% 131.89/22.82 (foundation2) =>
% 131.89/22.82 ((
% 131.89/22.82 (notinself) =>
% 131.89/22.82 ((
% 131.89/22.82 (notinself2) =>
% 131.89/22.82 ((
% 131.89/22.82 (omegaSp) =>
% 131.89/22.82 ((
% 131.89/22.82 (omegaSclos) =>
% 131.89/22.82 ((
% 131.89/22.82 (peano0notS) =>
% 131.89/22.82 ((
% 131.89/22.82 (peanoSinj) =>
% 131.89/22.82 ((
% 131.89/22.82 (transitivesetOp1) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintTransitive) =>
% 131.89/22.82 ((
% 131.89/22.82 (transitivesetOp2) =>
% 131.89/22.82 ((
% 131.89/22.82 (setunionTransitive) =>
% 131.89/22.82 ((
% 131.89/22.82 (ordinalMinLem1) =>
% 131.89/22.82 ((
% 131.89/22.82 (ordinalTransSet) =>
% 131.89/22.82 ((
% 131.89/22.82 (ordinalTransSet1) =>
% 131.89/22.82 ((
% 131.89/22.82 (setunionOrdinalLem1) =>
% 131.89/22.82 (ordinal @
% 131.89/22.82 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 131.89/22.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl413])).
% 131.89/22.82 thf(zip_derived_cl428, plain,
% 131.89/22.82 (~ (((upairsetE) =>
% 131.89/22.82 (((upairsetIL) =>
% 131.89/22.82 (((upairsetIR) =>
% 131.89/22.82 (((emptyE1) =>
% 131.89/22.82 (((vacuousDall) =>
% 131.89/22.82 (((quantDeMorgan1) =>
% 131.89/22.82 (((quantDeMorgan2) =>
% 131.89/22.82 (((quantDeMorgan3) =>
% 131.89/22.82 (((quantDeMorgan4) =>
% 131.89/22.82 (((prop2setI) =>
% 131.89/22.82 (((prop2set2propI) =>
% 131.89/22.82 (((notdexE) =>
% 131.89/22.82 (((notdallE) =>
% 131.89/22.82 (((exuI1) =>
% 131.89/22.82 (((exuI3) =>
% 131.89/22.82 (((exuI2) =>
% 131.89/22.82 (((inCongP) =>
% 131.89/22.82 (((in__Cong) =>
% 131.89/22.82 (((exuE3u) =>
% 131.89/22.82 (((exu__Cong) =>
% 131.89/22.82 (((setadjoin__Cong) =>
% 131.89/22.82 (((powerset__Cong) =>
% 131.89/22.82 (((setunion__Cong) =>
% 131.89/22.82 (((exuEu) =>
% 131.89/22.82 (((descr__Cong) =>
% 131.89/22.82 (((dsetconstr__Cong) =>
% 131.89/22.82 (((subsetI1) =>
% 131.89/22.82 (((eqimpsubset2) =>
% 131.89/22.82 (((eqimpsubset1) =>
% 131.89/22.82 (((subsetI2) =>
% 131.89/22.82 ((
% 131.89/22.82 (emptysetsubset) =>
% 131.89/22.82 ((
% 131.89/22.82 (subsetE) =>
% 131.89/22.82 ((
% 131.89/22.82 (subsetE2) =>
% 131.89/22.82 ((
% 131.89/22.82 (notsubsetI) =>
% 131.89/22.82 ((
% 131.89/22.82 (notequalI1) =>
% 131.89/22.82 ((
% 131.89/22.82 (notequalI2) =>
% 131.89/22.82 ((
% 131.89/22.82 (subsetRefl) =>
% 131.89/22.82 ((
% 131.89/22.82 (subsetTrans) =>
% 131.89/22.82 ((
% 131.89/22.82 (setadjoinSub) =>
% 131.89/22.82 ((
% 131.89/22.82 (setadjoinSub2) =>
% 131.89/22.82 ((
% 131.89/22.82 (subset2powerset) =>
% 131.89/22.82 ((
% 131.89/22.82 (setextsub) =>
% 131.89/22.82 ((
% 131.89/22.82 (subsetemptysetimpeq) =>
% 131.89/22.82 ((
% 131.89/22.82 (powersetI1) =>
% 131.89/22.82 ((
% 131.89/22.82 (powersetE1) =>
% 131.89/22.82 ((
% 131.89/22.82 (inPowerset) =>
% 131.89/22.82 ((
% 131.89/22.82 (powersetsubset) =>
% 131.89/22.82 ((
% 131.89/22.82 (sepInPowerset) =>
% 131.89/22.82 ((
% 131.89/22.82 (sepSubset) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionIL) =>
% 131.89/22.82 ((
% 131.89/22.82 (upairset2IR) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionIR) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionEcases) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionE) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionLsub) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionRsub) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectI) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectSubset5) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectEL) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectLsub) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectSubset2) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectSubset3) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectER) =>
% 131.89/22.82 ((
% 131.89/22.82 (disjointsetsI1) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectRsub) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectSubset4) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectSubset1) =>
% 131.89/22.82 ((
% 131.89/22.82 (bs114d) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusI) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusEL) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusER) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusSubset2) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusERneg) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusELneg) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusILneg) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusIRneg) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusLsub) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusSubset1) =>
% 131.89/22.82 ((
% 131.89/22.82 (symdiffE) =>
% 131.89/22.82 ((
% 131.89/22.82 (symdiffI1) =>
% 131.89/22.82 ((
% 131.89/22.82 (symdiffI2) =>
% 131.89/22.82 ((
% 131.89/22.82 (symdiffIneg1) =>
% 131.89/22.82 ((
% 131.89/22.82 (symdiffIneg2) =>
% 131.89/22.82 ((
% 131.89/22.82 (secondinupair) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairIL) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairIR) =>
% 131.89/22.82 ((
% 131.89/22.82 (kpairiskpair) =>
% 131.89/22.82 ((
% 131.89/22.82 (kpairp) =>
% 131.89/22.82 ((
% 131.89/22.82 (singletonsubset) =>
% 131.89/22.82 ((
% 131.89/22.82 (singletoninpowerset) =>
% 131.89/22.82 ((
% 131.89/22.82 (singletoninpowunion) =>
% 131.89/22.82 ((
% 131.89/22.82 (upairset2E) =>
% 131.89/22.82 ((
% 131.89/22.82 (upairsubunion) =>
% 131.89/22.82 ((
% 131.89/22.82 (upairinpowunion) =>
% 131.89/22.82 ((
% 131.89/22.82 (ubforcartprodlem1) =>
% 131.89/22.82 ((
% 131.89/22.82 (ubforcartprodlem2) =>
% 131.89/22.82 ((
% 131.89/22.82 (ubforcartprodlem3) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodpairin) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodmempair1) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodmempair) =>
% 131.89/22.82 ((
% 131.89/22.82 (setunionE2) =>
% 131.89/22.82 ((
% 131.89/22.82 (setunionsingleton1) =>
% 131.89/22.82 ((
% 131.89/22.82 (setunionsingleton2) =>
% 131.89/22.82 ((
% 131.89/22.82 (setunionsingleton) =>
% 131.89/22.82 ((
% 131.89/22.82 (singletonprop) =>
% 131.89/22.82 ((
% 131.89/22.82 (ex1E1) =>
% 131.89/22.82 ((
% 131.89/22.82 (ex1I) =>
% 131.89/22.82 ((
% 131.89/22.82 (ex1I2) =>
% 131.89/22.82 ((
% 131.89/22.82 (singletonsuniq) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairinjL1) =>
% 131.89/22.82 ((
% 131.89/22.82 (kfstsingleton) =>
% 131.89/22.82 ((
% 131.89/22.82 (theprop) =>
% 131.89/22.82 ((
% 131.89/22.82 (kfstpairEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodfstin) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairinjL2) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairinjL) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairinjR11) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairinjR12) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairinjR1) =>
% 131.89/22.82 ((
% 131.89/22.82 (upairequniteq) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairinjR2) =>
% 131.89/22.82 ((
% 131.89/22.82 (setukpairinjR) =>
% 131.89/22.82 ((
% 131.89/22.82 (ksndsingleton) =>
% 131.89/22.82 ((
% 131.89/22.82 (ksndpairEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (kpairsurjEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodsndin) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodpairmemEL) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodpairmemER) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodmempaircEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodfstpairEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodsndpairEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (cartprodpairsurjEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (dpsetconstrI) =>
% 131.89/22.82 ((
% 131.89/22.82 (dpsetconstrSub) =>
% 131.89/22.82 ((
% 131.89/22.82 (setOfPairsIsBReln) =>
% 131.89/22.82 ((
% 131.89/22.82 (dpsetconstrERa) =>
% 131.89/22.82 ((
% 131.89/22.82 (dpsetconstrEL1) =>
% 131.89/22.82 ((
% 131.89/22.82 (dpsetconstrEL2) =>
% 131.89/22.82 ((
% 131.89/22.82 (dpsetconstrER) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcImageSingleton) =>
% 131.89/22.82 ((
% 131.89/22.82 (apProp) =>
% 131.89/22.82 ((
% 131.89/22.82 (app) =>
% 131.89/22.82 ((
% 131.89/22.82 (infuncsetfunc) =>
% 131.89/22.82 ((
% 131.89/22.82 (ap2p) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcinfuncset) =>
% 131.89/22.82 ((
% 131.89/22.82 (lamProp) =>
% 131.89/22.82 ((
% 131.89/22.82 (lamp) =>
% 131.89/22.82 ((
% 131.89/22.82 (lam2p) =>
% 131.89/22.82 ((
% 131.89/22.82 (brelnall1) =>
% 131.89/22.82 ((
% 131.89/22.82 (brelnall2) =>
% 131.89/22.82 ((
% 131.89/22.82 (ex1E2) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcGraphProp1) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcGraphProp3) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcGraphProp2) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcextLem) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcGraphProp4) =>
% 131.89/22.82 ((
% 131.89/22.82 (subbreln) =>
% 131.89/22.82 ((
% 131.89/22.82 (eqbreln) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcext) =>
% 131.89/22.82 ((
% 131.89/22.82 (funcext2) =>
% 131.89/22.82 ((
% 131.89/22.82 (ap2apEq1) =>
% 131.89/22.82 ((
% 131.89/22.82 (ap2apEq2) =>
% 131.89/22.82 ((
% 131.89/22.82 (beta1) =>
% 131.89/22.82 ((
% 131.89/22.82 (eta1) =>
% 131.89/22.82 ((
% 131.89/22.82 (lam2lamEq) =>
% 131.89/22.82 ((
% 131.89/22.82 (beta2) =>
% 131.89/22.82 ((
% 131.89/22.82 (eta2) =>
% 131.89/22.82 ((
% 131.89/22.82 (iffalseProp1) =>
% 131.89/22.82 ((
% 131.89/22.82 (iffalseProp2) =>
% 131.89/22.82 ((
% 131.89/22.82 (iftrueProp1) =>
% 131.89/22.82 ((
% 131.89/22.82 (iftrueProp2) =>
% 131.89/22.82 ((
% 131.89/22.82 (ifSingleton) =>
% 131.89/22.82 ((
% 131.89/22.82 (ifp) =>
% 131.89/22.82 ((
% 131.89/22.82 (theeq) =>
% 131.89/22.82 ((
% 131.89/22.82 (iftrue) =>
% 131.89/22.82 ((
% 131.89/22.82 (iffalse) =>
% 131.89/22.82 ((
% 131.89/22.82 (iftrueorfalse) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectT_lem) =>
% 131.89/22.82 ((
% 131.89/22.82 (binunionT_lem) =>
% 131.89/22.82 ((
% 131.89/22.82 (powersetT_lem) =>
% 131.89/22.82 ((
% 131.89/22.82 (setminusT_lem) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementT_lem) =>
% 131.89/22.82 ((
% 131.89/22.82 (setextT) =>
% 131.89/22.82 ((
% 131.89/22.82 (subsetTI) =>
% 131.89/22.82 ((
% 131.89/22.82 (powersetTI1) =>
% 131.89/22.82 ((
% 131.89/22.82 (powersetTE1) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementTI1) =>
% 131.89/22.82 ((
% 131.89/22.82 (complementTE1) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectTELcontra) =>
% 131.89/22.82 ((
% 131.89/22.82 (binintersectTERcontra) =>
% 131.89/22.83 ((
% 131.89/22.83 (contrasubsetT) =>
% 131.89/22.83 ((
% 131.89/22.83 (contrasubsetT1) =>
% 131.89/22.83 ((
% 131.89/22.83 (contrasubsetT2) =>
% 131.89/22.83 ((
% 131.89/22.83 (contrasubsetT3) =>
% 131.89/22.83 ((
% 131.89/22.83 (doubleComplementI1) =>
% 131.89/22.83 ((
% 131.89/22.83 (doubleComplementE1) =>
% 131.89/22.83 ((
% 131.89/22.83 (doubleComplementSub1) =>
% 131.89/22.83 ((
% 131.89/22.83 (doubleComplementSub2) =>
% 131.89/22.83 ((
% 131.89/22.83 (doubleComplementEq) =>
% 131.89/22.83 ((
% 131.89/22.83 (complementTnotintersectT) =>
% 131.89/22.83 ((
% 131.89/22.83 (complementImpComplementIntersect) =>
% 131.89/22.83 ((
% 131.89/22.83 (complementSubsetComplementIntersect) =>
% 131.89/22.83 ((
% 131.89/22.83 (complementInPowersetComplementIntersect) =>
% 131.89/22.83 ((
% 131.89/22.83 (contraSubsetComplement) =>
% 131.89/22.83 ((
% 131.89/22.83 (complementTcontraSubset) =>
% 131.89/22.83 ((
% 131.89/22.83 (binunionTILcontra) =>
% 131.89/22.83 ((
% 131.89/22.83 (binunionTIRcontra) =>
% 131.89/22.83 ((
% 131.89/22.83 (inIntersectImpInUnion) =>
% 131.89/22.83 ((
% 131.89/22.83 (inIntersectImpInUnion2) =>
% 131.89/22.83 ((
% 131.89/22.83 (inIntersectImpInIntersectUnions) =>
% 131.89/22.83 ((
% 131.89/22.83 (intersectInPowersetIntersectUnions) =>
% 131.89/22.83 ((
% 131.89/22.83 (inComplementUnionImpNotIn1) =>
% 131.89/22.83 ((
% 131.89/22.83 (inComplementUnionImpInComplement1) =>
% 131.89/22.83 ((
% 131.89/22.83 (binunionTE) =>
% 131.89/22.83 ((
% 131.89/22.83 (binunionTEcontra) =>
% 131.89/22.83 ((
% 131.89/22.83 (demorgan2a1) =>
% 131.89/22.83 ((
% 131.89/22.83 (complementUnionInPowersetComplement) =>
% 131.89/22.83 ((
% 131.89/22.83 (demorgan2a2) =>
% 131.89/22.83 ((
% 131.89/22.83 (demorgan1a) =>
% 131.89/22.83 ((
% 131.89/22.83 (demorgan1b) =>
% 131.89/22.83 ((
% 131.89/22.83 (demorgan1) =>
% 131.89/22.83 ((
% 131.89/22.83 (demorgan2a) =>
% 131.89/22.83 ((
% 131.89/22.83 (demorgan2b2) =>
% 131.89/22.83 ((
% 131.89/22.83 (demorgan2b) =>
% 131.89/22.83 ((
% 131.89/22.83 (demorgan2) =>
% 131.89/22.83 ((
% 131.89/22.83 (woz13rule0) =>
% 131.89/22.83 ((
% 131.89/22.83 (woz13rule1) =>
% 131.89/22.83 ((
% 131.89/22.83 (woz13rule2) =>
% 131.89/22.83 ((
% 131.89/22.83 (woz13rule3) =>
% 131.89/22.83 ((
% 131.89/22.83 (woz13rule4) =>
% 131.89/22.83 ((
% 131.89/22.83 (woz1_1) =>
% 131.89/22.83 ((
% 131.89/22.83 (woz1_2) =>
% 131.89/22.83 ((
% 131.89/22.83 (woz1_3) =>
% 131.89/22.83 ((
% 131.89/22.83 (woz1_4) =>
% 131.89/22.83 ((
% 131.89/22.83 (woz1_5) =>
% 131.89/22.83 ((
% 131.89/22.83 (breln1all2) =>
% 131.89/22.83 ((
% 131.89/22.83 (breln1SetBreln1) =>
% 131.89/22.83 ((
% 131.89/22.83 (choice2fnsingleton) =>
% 131.89/22.83 ((
% 131.89/22.83 (setOfPairsIsBReln1) =>
% 131.89/22.83 ((
% 131.89/22.83 (breln1all1) =>
% 131.89/22.83 ((
% 131.89/22.83 (subbreln1) =>
% 131.89/22.83 ((
% 131.89/22.83 (eqbreln1) =>
% 131.89/22.83 ((
% 131.89/22.83 (breln1invprop) =>
% 131.89/22.83 ((
% 131.89/22.83 (breln1invI) =>
% 131.89/22.83 ((
% 131.89/22.83 (breln1invE) =>
% 131.89/22.83 ((
% 131.89/22.83 (breln1compprop) =>
% 131.89/22.83 ((
% 131.89/22.83 (breln1compI) =>
% 131.89/22.83 ((
% 131.89/22.83 (breln1compE) =>
% 131.89/22.83 ((
% 131.89/22.83 (breln1compEex) =>
% 131.89/22.83 ((
% 131.89/22.83 (breln1unionprop) =>
% 131.89/22.83 ((
% 131.89/22.83 (breln1unionIL) =>
% 131.89/22.83 ((
% 131.89/22.83 (breln1unionIR) =>
% 131.89/22.83 ((
% 131.89/22.83 (breln1unionI) =>
% 131.89/22.83 ((
% 131.89/22.83 (breln1unionE) =>
% 131.89/22.83 ((
% 131.89/22.83 (breln1unionEcases) =>
% 131.89/22.83 ((
% 131.89/22.83 (breln1unionCommutes) =>
% 131.89/22.83 ((
% 131.89/22.83 (woz2Ex) =>
% 131.89/22.83 ((
% 131.89/22.83 (woz2W) =>
% 131.89/22.83 ((
% 131.89/22.83 (woz2A) =>
% 131.89/22.83 ((
% 131.89/22.83 (woz2B) =>
% 131.89/22.83 ((
% 131.89/22.83 (image1Ex) =>
% 131.89/22.83 ((
% 131.89/22.83 (image1Ex1) =>
% 131.89/22.83 ((
% 131.89/22.83 (image1Equiv) =>
% 131.89/22.83 ((
% 131.89/22.83 (image1E) =>
% 131.89/22.83 ((
% 131.89/22.83 (image1I) =>
% 131.89/22.83 ((
% 131.89/22.83 (injFuncInInjFuncSet) =>
% 131.89/22.83 ((
% 131.89/22.83 (injFuncSetFuncIn) =>
% 131.89/22.83 ((
% 131.89/22.83 (injFuncSetFuncInj) =>
% 131.89/22.83 ((
% 131.89/22.83 (surjFuncSetFuncIn) =>
% 131.89/22.83 ((
% 131.89/22.83 (surjFuncSetFuncSurj) =>
% 131.89/22.83 ((
% 131.89/22.83 (leftInvIsSurj) =>
% 131.89/22.83 ((
% 131.89/22.83 (surjCantorThm) =>
% 131.89/22.83 ((
% 131.89/22.83 (foundation2) =>
% 131.89/22.83 ((
% 131.89/22.83 (notinself) =>
% 131.89/22.83 ((
% 131.89/22.83 (notinself2) =>
% 131.89/22.83 ((
% 131.89/22.83 (omegaSp) =>
% 131.89/22.83 ((
% 131.89/22.83 (omegaSclos) =>
% 131.89/22.83 ((
% 131.89/22.83 (peano0notS) =>
% 131.89/22.83 ((
% 131.89/22.83 (peanoSinj) =>
% 131.89/22.83 ((
% 131.89/22.83 (transitivesetOp1) =>
% 131.89/22.83 ((
% 131.89/22.83 (binintTransitive) =>
% 131.89/22.83 ((
% 131.89/22.83 (transitivesetOp2) =>
% 131.89/22.83 ((
% 131.89/22.83 (setunionTransitive) =>
% 131.89/22.83 ((
% 131.89/22.83 (ordinalMinLem1) =>
% 131.89/22.83 ((
% 131.89/22.83 (ordinalTransSet) =>
% 131.89/22.83 ((
% 131.89/22.83 (ordinalTransSet1) =>
% 131.89/22.83 ((
% 131.89/22.83 (setunionOrdinalLem1) =>
% 131.89/22.83 (ordinal @
% 131.89/22.83 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 131.89/22.83 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl420])).
% 131.89/22.83 thf(zip_derived_cl439, plain,
% 131.89/22.83 (~ (((upairsetIL) =>
% 131.89/22.83 (((upairsetIR) =>
% 131.89/22.83 (((emptyE1) =>
% 131.89/22.83 (((vacuousDall) =>
% 131.89/22.83 (((quantDeMorgan1) =>
% 131.89/22.83 (((quantDeMorgan2) =>
% 131.89/22.83 (((quantDeMorgan3) =>
% 131.89/22.83 (((quantDeMorgan4) =>
% 131.89/22.83 (((prop2setI) =>
% 131.89/22.83 (((prop2set2propI) =>
% 131.89/22.83 (((notdexE) =>
% 131.89/22.83 (((notdallE) =>
% 131.89/22.83 (((exuI1) =>
% 131.89/22.83 (((exuI3) =>
% 131.89/22.83 (((exuI2) =>
% 131.89/22.83 (((inCongP) =>
% 131.89/22.83 (((in__Cong) =>
% 131.89/22.83 (((exuE3u) =>
% 131.89/22.83 (((exu__Cong) =>
% 131.89/22.83 (((setadjoin__Cong) =>
% 131.89/22.83 (((powerset__Cong) =>
% 131.89/22.83 (((setunion__Cong) =>
% 131.89/22.83 (((exuEu) =>
% 131.89/22.83 (((descr__Cong) =>
% 131.89/22.83 (((dsetconstr__Cong) =>
% 131.89/22.83 (((subsetI1) =>
% 131.89/22.83 (((eqimpsubset2) =>
% 131.89/22.83 (((eqimpsubset1) =>
% 131.89/22.83 (((subsetI2) =>
% 131.89/22.83 (((emptysetsubset) =>
% 131.89/22.83 ((
% 131.89/22.83 (subsetE) =>
% 131.89/22.83 ((
% 131.89/22.83 (subsetE2) =>
% 131.89/22.83 ((
% 131.89/22.83 (notsubsetI) =>
% 131.89/22.83 ((
% 131.89/22.83 (notequalI1) =>
% 131.89/22.83 ((
% 131.89/22.83 (notequalI2) =>
% 131.89/22.83 ((
% 131.89/22.83 (subsetRefl) =>
% 131.89/22.83 ((
% 131.89/22.83 (subsetTrans) =>
% 131.89/22.83 ((
% 131.89/22.83 (setadjoinSub) =>
% 131.89/22.83 ((
% 131.89/22.83 (setadjoinSub2) =>
% 131.89/22.83 ((
% 131.89/22.83 (subset2powerset) =>
% 131.89/22.83 ((
% 131.89/22.83 (setextsub) =>
% 131.89/22.83 ((
% 131.89/22.83 (subsetemptysetimpeq) =>
% 131.89/22.83 ((
% 131.89/22.83 (powersetI1) =>
% 131.89/22.83 ((
% 131.89/22.83 (powersetE1) =>
% 131.89/22.83 ((
% 131.89/22.83 (inPowerset) =>
% 131.89/22.83 ((
% 131.89/22.83 (powersetsubset) =>
% 131.89/22.83 ((
% 131.89/22.83 (sepInPowerset) =>
% 131.89/22.83 ((
% 131.89/22.83 (sepSubset) =>
% 131.89/22.83 ((
% 131.89/22.83 (binunionIL) =>
% 131.89/22.83 ((
% 131.89/22.83 (upairset2IR) =>
% 131.89/22.83 ((
% 131.89/22.83 (binunionIR) =>
% 131.89/22.83 ((
% 131.89/22.83 (binunionEcases) =>
% 131.89/22.83 ((
% 131.89/22.83 (binunionE) =>
% 131.89/22.83 ((
% 131.89/22.83 (binunionLsub) =>
% 131.89/22.83 ((
% 131.89/22.83 (binunionRsub) =>
% 131.89/22.83 ((
% 131.89/22.83 (binintersectI) =>
% 131.89/22.83 ((
% 131.89/22.83 (binintersectSubset5) =>
% 131.89/22.83 ((
% 131.89/22.83 (binintersectEL) =>
% 131.89/22.83 ((
% 131.89/22.83 (binintersectLsub) =>
% 131.89/22.83 ((
% 131.89/22.83 (binintersectSubset2) =>
% 131.89/22.83 ((
% 131.89/22.83 (binintersectSubset3) =>
% 131.89/22.83 ((
% 131.89/22.83 (binintersectER) =>
% 131.89/22.83 ((
% 131.89/22.83 (disjointsetsI1) =>
% 131.89/22.83 ((
% 131.89/22.83 (binintersectRsub) =>
% 131.89/22.83 ((
% 131.89/22.83 (binintersectSubset4) =>
% 131.89/22.83 ((
% 131.89/22.83 (binintersectSubset1) =>
% 131.89/22.83 ((
% 131.89/22.83 (bs114d) =>
% 131.89/22.83 ((
% 131.89/22.83 (setminusI) =>
% 131.89/22.83 ((
% 131.89/22.83 (setminusEL) =>
% 131.89/22.83 ((
% 131.89/22.83 (setminusER) =>
% 131.89/22.83 ((
% 131.89/22.83 (setminusSubset2) =>
% 131.89/22.83 ((
% 131.89/22.83 (setminusERneg) =>
% 131.89/22.83 ((
% 131.89/22.83 (setminusELneg) =>
% 131.89/22.83 ((
% 131.89/22.83 (setminusILneg) =>
% 131.89/22.83 ((
% 131.89/22.83 (setminusIRneg) =>
% 131.89/22.83 ((
% 131.89/22.83 (setminusLsub) =>
% 131.89/22.83 ((
% 131.89/22.83 (setminusSubset1) =>
% 131.89/22.83 ((
% 131.89/22.83 (symdiffE) =>
% 131.89/22.83 ((
% 131.89/22.83 (symdiffI1) =>
% 131.89/22.83 ((
% 131.89/22.83 (symdiffI2) =>
% 131.89/22.83 ((
% 131.89/22.83 (symdiffIneg1) =>
% 131.89/22.83 ((
% 131.89/22.83 (symdiffIneg2) =>
% 131.89/22.83 ((
% 131.89/22.83 (secondinupair) =>
% 131.89/22.83 ((
% 131.89/22.83 (setukpairIL) =>
% 131.89/22.83 ((
% 131.89/22.83 (setukpairIR) =>
% 131.89/22.83 ((
% 131.89/22.83 (kpairiskpair) =>
% 131.89/22.83 ((
% 131.89/22.83 (kpairp) =>
% 131.89/22.83 ((
% 131.89/22.83 (singletonsubset) =>
% 131.89/22.83 ((
% 131.89/22.83 (singletoninpowerset) =>
% 131.89/22.83 ((
% 131.89/22.83 (singletoninpowunion) =>
% 131.89/22.83 ((
% 131.89/22.83 (upairset2E) =>
% 131.89/22.83 ((
% 131.89/22.83 (upairsubunion) =>
% 131.89/22.83 ((
% 131.89/22.83 (upairinpowunion) =>
% 131.89/22.83 ((
% 131.89/22.83 (ubforcartprodlem1) =>
% 131.89/22.83 ((
% 131.89/22.83 (ubforcartprodlem2) =>
% 131.89/22.83 ((
% 131.89/22.83 (ubforcartprodlem3) =>
% 131.89/22.83 ((
% 131.89/22.83 (cartprodpairin) =>
% 131.89/22.83 ((
% 131.89/22.83 (cartprodmempair1) =>
% 131.89/22.83 ((
% 131.89/22.83 (cartprodmempair) =>
% 131.89/22.83 ((
% 131.89/22.83 (setunionE2) =>
% 131.89/22.83 ((
% 131.89/22.83 (setunionsingleton1) =>
% 131.89/22.83 ((
% 131.89/22.83 (setunionsingleton2) =>
% 131.89/22.83 ((
% 131.89/22.83 (setunionsingleton) =>
% 131.89/22.83 ((
% 131.89/22.83 (singletonprop) =>
% 131.89/22.83 ((
% 131.89/22.83 (ex1E1) =>
% 131.89/22.83 ((
% 131.89/22.83 (ex1I) =>
% 131.89/22.83 ((
% 131.89/22.83 (ex1I2) =>
% 131.89/22.83 ((
% 131.89/22.83 (singletonsuniq) =>
% 131.89/22.83 ((
% 131.89/22.83 (setukpairinjL1) =>
% 131.89/22.83 ((
% 131.89/22.83 (kfstsingleton) =>
% 131.89/22.83 ((
% 131.89/22.83 (theprop) =>
% 131.89/22.83 ((
% 131.89/22.83 (kfstpairEq) =>
% 131.89/22.83 ((
% 131.89/22.83 (cartprodfstin) =>
% 131.89/22.83 ((
% 131.89/22.83 (setukpairinjL2) =>
% 131.89/22.83 ((
% 131.89/22.83 (setukpairinjL) =>
% 131.89/22.83 ((
% 131.89/22.83 (setukpairinjR11) =>
% 131.89/22.83 ((
% 131.89/22.83 (setukpairinjR12) =>
% 131.89/22.83 ((
% 131.89/22.83 (setukpairinjR1) =>
% 131.89/22.83 ((
% 131.89/22.83 (upairequniteq) =>
% 131.89/22.83 ((
% 131.89/22.83 (setukpairinjR2) =>
% 131.89/22.83 ((
% 131.89/22.83 (setukpairinjR) =>
% 131.89/22.83 ((
% 131.89/22.83 (ksndsingleton) =>
% 131.89/22.83 ((
% 131.89/22.83 (ksndpairEq) =>
% 131.89/22.83 ((
% 131.89/22.83 (kpairsurjEq) =>
% 131.89/22.83 ((
% 131.89/22.83 (cartprodsndin) =>
% 131.89/22.83 ((
% 131.89/22.83 (cartprodpairmemEL) =>
% 131.89/22.83 ((
% 131.89/22.83 (cartprodpairmemER) =>
% 131.89/22.83 ((
% 131.89/22.83 (cartprodmempaircEq) =>
% 131.89/22.83 ((
% 131.89/22.83 (cartprodfstpairEq) =>
% 131.89/22.83 ((
% 131.89/22.83 (cartprodsndpairEq) =>
% 131.89/22.83 ((
% 131.89/22.83 (cartprodpairsurjEq) =>
% 131.89/22.83 ((
% 131.89/22.83 (dpsetconstrI) =>
% 131.89/22.83 ((
% 131.89/22.83 (dpsetconstrSub) =>
% 131.89/22.83 ((
% 131.89/22.83 (setOfPairsIsBReln) =>
% 131.89/22.83 ((
% 131.89/22.83 (dpsetconstrERa) =>
% 131.89/22.83 ((
% 131.89/22.83 (dpsetconstrEL1) =>
% 131.89/22.83 ((
% 131.89/22.83 (dpsetconstrEL2) =>
% 131.89/22.83 ((
% 131.89/22.83 (dpsetconstrER) =>
% 131.89/22.83 ((
% 131.89/22.83 (funcImageSingleton) =>
% 131.89/22.83 ((
% 131.89/22.83 (apProp) =>
% 131.89/22.83 ((
% 131.89/22.83 (app) =>
% 131.89/22.83 ((
% 131.89/22.83 (infuncsetfunc) =>
% 131.89/22.83 ((
% 131.89/22.83 (ap2p) =>
% 131.89/22.83 ((
% 131.89/22.83 (funcinfuncset) =>
% 131.89/22.83 ((
% 131.89/22.83 (lamProp) =>
% 131.89/22.83 ((
% 131.89/22.83 (lamp) =>
% 131.89/22.83 ((
% 131.89/22.83 (lam2p) =>
% 131.89/22.83 ((
% 131.89/22.83 (brelnall1) =>
% 131.89/22.83 ((
% 131.89/22.83 (brelnall2) =>
% 131.89/22.83 ((
% 131.89/22.83 (ex1E2) =>
% 131.89/22.83 ((
% 131.89/22.83 (funcGraphProp1) =>
% 131.89/22.83 ((
% 131.89/22.83 (funcGraphProp3) =>
% 131.89/22.83 ((
% 131.89/22.83 (funcGraphProp2) =>
% 131.89/22.83 ((
% 131.89/22.83 (funcextLem) =>
% 131.89/22.83 ((
% 131.89/22.83 (funcGraphProp4) =>
% 131.89/22.83 ((
% 131.89/22.83 (subbreln) =>
% 131.89/22.83 ((
% 131.89/22.83 (eqbreln) =>
% 131.89/22.83 ((
% 131.89/22.83 (funcext) =>
% 131.89/22.83 ((
% 131.89/22.83 (funcext2) =>
% 131.89/22.83 ((
% 131.89/22.83 (ap2apEq1) =>
% 131.89/22.83 ((
% 131.89/22.83 (ap2apEq2) =>
% 131.89/22.83 ((
% 131.89/22.83 (beta1) =>
% 131.89/22.83 ((
% 131.89/22.83 (eta1) =>
% 131.89/22.83 ((
% 131.89/22.83 (lam2lamEq) =>
% 131.89/22.83 ((
% 131.89/22.83 (beta2) =>
% 131.89/22.83 ((
% 131.89/22.83 (eta2) =>
% 131.89/22.83 ((
% 131.89/22.83 (iffalseProp1) =>
% 131.89/22.83 ((
% 131.89/22.83 (iffalseProp2) =>
% 131.89/22.83 ((
% 131.89/22.83 (iftrueProp1) =>
% 131.89/22.83 ((
% 131.89/22.83 (iftrueProp2) =>
% 131.89/22.83 ((
% 131.89/22.83 (ifSingleton) =>
% 131.89/22.83 ((
% 131.89/22.83 (ifp) =>
% 131.89/22.83 ((
% 131.89/22.83 (theeq) =>
% 131.89/22.83 ((
% 131.89/22.83 (iftrue) =>
% 131.89/22.83 ((
% 131.89/22.83 (iffalse) =>
% 131.89/22.83 ((
% 131.89/22.83 (iftrueorfalse) =>
% 131.89/22.83 ((
% 131.89/22.83 (binintersectT_lem) =>
% 131.89/22.83 ((
% 131.89/22.83 (binunionT_lem) =>
% 131.89/22.83 ((
% 131.89/22.83 (powersetT_lem) =>
% 131.89/22.83 ((
% 131.89/22.83 (setminusT_lem) =>
% 131.89/22.83 ((
% 131.89/22.83 (complementT_lem) =>
% 131.89/22.83 ((
% 131.89/22.83 (setextT) =>
% 131.89/22.83 ((
% 131.89/22.83 (subsetTI) =>
% 131.89/22.83 ((
% 131.89/22.83 (powersetTI1) =>
% 131.89/22.83 ((
% 131.89/22.83 (powersetTE1) =>
% 131.89/22.83 ((
% 131.89/22.83 (complementTI1) =>
% 131.89/22.83 ((
% 131.89/22.83 (complementTE1) =>
% 131.89/22.83 ((
% 131.89/22.83 (binintersectTELcontra) =>
% 131.89/22.83 ((
% 131.89/22.83 (binintersectTERcontra) =>
% 131.89/22.83 ((
% 131.89/22.83 (contrasubsetT) =>
% 131.89/22.83 ((
% 131.89/22.83 (contrasubsetT1) =>
% 131.89/22.83 ((
% 131.89/22.83 (contrasubsetT2) =>
% 131.89/22.83 ((
% 131.89/22.83 (contrasubsetT3) =>
% 131.89/22.83 ((
% 131.89/22.83 (doubleComplementI1) =>
% 131.89/22.83 ((
% 131.89/22.83 (doubleComplementE1) =>
% 131.89/22.83 ((
% 131.89/22.83 (doubleComplementSub1) =>
% 131.89/22.83 ((
% 131.89/22.83 (doubleComplementSub2) =>
% 131.89/22.83 ((
% 131.89/22.83 (doubleComplementEq) =>
% 131.89/22.83 ((
% 131.89/22.83 (complementTnotintersectT) =>
% 131.89/22.83 ((
% 131.89/22.83 (complementImpComplementIntersect) =>
% 131.89/22.83 ((
% 131.89/22.83 (complementSubsetComplementIntersect) =>
% 131.89/22.83 ((
% 131.89/22.83 (complementInPowersetComplementIntersect) =>
% 131.89/22.83 ((
% 131.89/22.83 (contraSubsetComplement) =>
% 131.89/22.83 ((
% 131.89/22.83 (complementTcontraSubset) =>
% 131.89/22.83 ((
% 131.89/22.83 (binunionTILcontra) =>
% 131.89/22.83 ((
% 131.89/22.83 (binunionTIRcontra) =>
% 131.89/22.83 ((
% 131.89/22.83 (inIntersectImpInUnion) =>
% 131.89/22.83 ((
% 131.89/22.83 (inIntersectImpInUnion2) =>
% 131.89/22.83 ((
% 131.89/22.83 (inIntersectImpInIntersectUnions) =>
% 131.89/22.83 ((
% 131.89/22.83 (intersectInPowersetIntersectUnions) =>
% 131.89/22.83 ((
% 131.89/22.83 (inComplementUnionImpNotIn1) =>
% 131.89/22.83 ((
% 131.89/22.83 (inComplementUnionImpInComplement1) =>
% 131.89/22.83 ((
% 131.89/22.83 (binunionTE) =>
% 131.89/22.83 ((
% 131.89/22.83 (binunionTEcontra) =>
% 131.89/22.83 ((
% 131.89/22.83 (demorgan2a1) =>
% 131.89/22.83 ((
% 131.89/22.83 (complementUnionInPowersetComplement) =>
% 131.89/22.83 ((
% 131.89/22.83 (demorgan2a2) =>
% 131.89/22.83 ((
% 131.89/22.83 (demorgan1a) =>
% 131.89/22.83 ((
% 131.89/22.83 (demorgan1b) =>
% 131.89/22.83 ((
% 131.89/22.83 (demorgan1) =>
% 131.89/22.83 ((
% 131.89/22.83 (demorgan2a) =>
% 131.89/22.83 ((
% 131.89/22.83 (demorgan2b2) =>
% 131.89/22.83 ((
% 131.89/22.83 (demorgan2b) =>
% 131.89/22.83 ((
% 131.89/22.83 (demorgan2) =>
% 131.89/22.83 ((
% 131.89/22.83 (woz13rule0) =>
% 131.89/22.83 ((
% 131.89/22.83 (woz13rule1) =>
% 131.89/22.83 ((
% 131.89/22.83 (woz13rule2) =>
% 131.89/22.83 ((
% 131.89/22.83 (woz13rule3) =>
% 131.89/22.83 ((
% 131.89/22.83 (woz13rule4) =>
% 131.89/22.83 ((
% 131.89/22.83 (woz1_1) =>
% 131.89/22.83 ((
% 131.89/22.83 (woz1_2) =>
% 131.89/22.83 ((
% 131.89/22.83 (woz1_3) =>
% 131.89/22.83 ((
% 131.89/22.83 (woz1_4) =>
% 131.89/22.83 ((
% 131.89/22.83 (woz1_5) =>
% 131.89/22.83 ((
% 131.89/22.83 (breln1all2) =>
% 131.89/22.83 ((
% 131.89/22.83 (breln1SetBreln1) =>
% 131.89/22.83 ((
% 131.89/22.83 (choice2fnsingleton) =>
% 131.89/22.83 ((
% 131.89/22.83 (setOfPairsIsBReln1) =>
% 131.89/22.83 ((
% 131.89/22.83 (breln1all1) =>
% 131.89/22.83 ((
% 131.89/22.83 (subbreln1) =>
% 131.89/22.83 ((
% 131.89/22.83 (eqbreln1) =>
% 131.89/22.83 ((
% 131.89/22.83 (breln1invprop) =>
% 131.89/22.83 ((
% 131.89/22.83 (breln1invI) =>
% 131.89/22.83 ((
% 131.89/22.83 (breln1invE) =>
% 131.89/22.83 ((
% 131.89/22.83 (breln1compprop) =>
% 131.89/22.83 ((
% 131.89/22.83 (breln1compI) =>
% 131.89/22.83 ((
% 131.89/22.83 (breln1compE) =>
% 131.89/22.83 ((
% 131.89/22.83 (breln1compEex) =>
% 131.89/22.83 ((
% 131.89/22.83 (breln1unionprop) =>
% 131.89/22.83 ((
% 131.89/22.83 (breln1unionIL) =>
% 131.89/22.83 ((
% 131.89/22.83 (breln1unionIR) =>
% 131.89/22.83 ((
% 131.89/22.83 (breln1unionI) =>
% 131.89/22.83 ((
% 131.89/22.83 (breln1unionE) =>
% 131.89/22.83 ((
% 131.89/22.83 (breln1unionEcases) =>
% 131.89/22.83 ((
% 131.89/22.83 (breln1unionCommutes) =>
% 131.89/22.83 ((
% 131.89/22.83 (woz2Ex) =>
% 131.89/22.83 ((
% 131.89/22.83 (woz2W) =>
% 131.89/22.83 ((
% 131.89/22.83 (woz2A) =>
% 131.89/22.83 ((
% 131.89/22.83 (woz2B) =>
% 131.89/22.83 ((
% 131.89/22.83 (image1Ex) =>
% 131.89/22.83 ((
% 131.89/22.83 (image1Ex1) =>
% 131.89/22.83 ((
% 131.89/22.83 (image1Equiv) =>
% 131.89/22.83 ((
% 131.89/22.83 (image1E) =>
% 131.89/22.83 ((
% 131.89/22.83 (image1I) =>
% 131.89/22.83 ((
% 131.89/22.83 (injFuncInInjFuncSet) =>
% 131.89/22.83 ((
% 131.89/22.83 (injFuncSetFuncIn) =>
% 131.89/22.83 ((
% 131.89/22.83 (injFuncSetFuncInj) =>
% 131.89/22.83 ((
% 131.89/22.83 (surjFuncSetFuncIn) =>
% 131.89/22.83 ((
% 131.89/22.83 (surjFuncSetFuncSurj) =>
% 131.89/22.83 ((
% 131.89/22.83 (leftInvIsSurj) =>
% 131.89/22.83 ((
% 131.89/22.83 (surjCantorThm) =>
% 131.89/22.83 ((
% 131.89/22.83 (foundation2) =>
% 131.89/22.83 ((
% 131.89/22.83 (notinself) =>
% 131.89/22.83 ((
% 131.89/22.83 (notinself2) =>
% 131.89/22.83 ((
% 131.89/22.83 (omegaSp) =>
% 131.89/22.83 ((
% 131.89/22.83 (omegaSclos) =>
% 131.89/22.83 ((
% 131.89/22.83 (peano0notS) =>
% 131.89/22.83 ((
% 131.89/22.83 (peanoSinj) =>
% 131.89/22.83 ((
% 131.89/22.83 (transitivesetOp1) =>
% 131.89/22.83 ((
% 131.89/22.83 (binintTransitive) =>
% 131.89/22.83 ((
% 131.89/22.83 (transitivesetOp2) =>
% 131.89/22.83 ((
% 131.89/22.83 (setunionTransitive) =>
% 131.89/22.83 ((
% 131.89/22.83 (ordinalMinLem1) =>
% 131.89/22.83 ((
% 131.89/22.83 (ordinalTransSet) =>
% 131.89/22.83 ((
% 131.89/22.83 (ordinalTransSet1) =>
% 131.89/22.83 ((
% 131.89/22.83 (setunionOrdinalLem1) =>
% 131.89/22.83 (ordinal @
% 131.89/22.83 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 131.89/22.83 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl428])).
% 131.89/22.83 thf(zip_derived_cl449, plain,
% 131.89/22.83 (~ (((upairsetIR) =>
% 131.89/22.83 (((emptyE1) =>
% 131.89/22.83 (((vacuousDall) =>
% 131.89/22.83 (((quantDeMorgan1) =>
% 131.89/22.83 (((quantDeMorgan2) =>
% 131.89/22.83 (((quantDeMorgan3) =>
% 131.89/22.83 (((quantDeMorgan4) =>
% 131.89/22.83 (((prop2setI) =>
% 131.89/22.83 (((prop2set2propI) =>
% 131.89/22.83 (((notdexE) =>
% 131.89/22.83 (((notdallE) =>
% 131.89/22.83 (((exuI1) =>
% 131.89/22.83 (((exuI3) =>
% 131.89/22.83 (((exuI2) =>
% 131.89/22.83 (((inCongP) =>
% 131.89/22.83 (((in__Cong) =>
% 131.89/22.83 (((exuE3u) =>
% 131.89/22.83 (((exu__Cong) =>
% 131.89/22.83 (((setadjoin__Cong) =>
% 131.89/22.83 (((powerset__Cong) =>
% 131.89/22.83 (((setunion__Cong) =>
% 131.89/22.83 (((exuEu) =>
% 131.89/22.83 (((descr__Cong) =>
% 131.89/22.83 (((dsetconstr__Cong) =>
% 131.89/22.83 (((subsetI1) =>
% 131.89/22.83 (((eqimpsubset2) =>
% 131.89/22.83 (((eqimpsubset1) =>
% 131.89/22.83 (((subsetI2) =>
% 131.89/22.83 (((emptysetsubset) =>
% 131.89/22.83 (((subsetE) =>
% 131.89/22.83 ((
% 131.89/22.83 (subsetE2) =>
% 131.89/22.83 ((
% 131.89/22.83 (notsubsetI) =>
% 131.89/22.83 ((
% 131.89/22.83 (notequalI1) =>
% 131.89/22.83 ((
% 131.89/22.83 (notequalI2) =>
% 131.89/22.83 ((
% 131.89/22.83 (subsetRefl) =>
% 131.89/22.83 ((
% 131.89/22.83 (subsetTrans) =>
% 131.89/22.83 ((
% 131.89/22.83 (setadjoinSub) =>
% 131.89/22.83 ((
% 131.89/22.83 (setadjoinSub2) =>
% 131.89/22.83 ((
% 131.89/22.83 (subset2powerset) =>
% 131.89/22.83 ((
% 131.89/22.83 (setextsub) =>
% 131.89/22.83 ((
% 131.89/22.83 (subsetemptysetimpeq) =>
% 131.89/22.83 ((
% 131.89/22.83 (powersetI1) =>
% 131.89/22.83 ((
% 131.89/22.83 (powersetE1) =>
% 131.89/22.83 ((
% 131.89/22.83 (inPowerset) =>
% 131.89/22.83 ((
% 131.89/22.83 (powersetsubset) =>
% 131.89/22.83 ((
% 131.89/22.83 (sepInPowerset) =>
% 131.89/22.83 ((
% 131.89/22.83 (sepSubset) =>
% 131.89/22.83 ((
% 131.89/22.83 (binunionIL) =>
% 131.89/22.83 ((
% 131.89/22.83 (upairset2IR) =>
% 131.89/22.83 ((
% 131.89/22.83 (binunionIR) =>
% 131.89/22.83 ((
% 131.89/22.83 (binunionEcases) =>
% 131.89/22.83 ((
% 131.89/22.83 (binunionE) =>
% 131.89/22.83 ((
% 131.89/22.83 (binunionLsub) =>
% 131.89/22.83 ((
% 131.89/22.83 (binunionRsub) =>
% 131.89/22.83 ((
% 131.89/22.83 (binintersectI) =>
% 131.89/22.83 ((
% 131.89/22.83 (binintersectSubset5) =>
% 131.89/22.83 ((
% 131.89/22.83 (binintersectEL) =>
% 131.89/22.83 ((
% 131.89/22.83 (binintersectLsub) =>
% 131.89/22.83 ((
% 131.89/22.83 (binintersectSubset2) =>
% 131.89/22.83 ((
% 131.89/22.83 (binintersectSubset3) =>
% 131.89/22.83 ((
% 131.89/22.83 (binintersectER) =>
% 131.89/22.83 ((
% 131.89/22.83 (disjointsetsI1) =>
% 131.89/22.83 ((
% 131.89/22.83 (binintersectRsub) =>
% 131.89/22.83 ((
% 131.89/22.83 (binintersectSubset4) =>
% 131.89/22.83 ((
% 131.89/22.83 (binintersectSubset1) =>
% 131.89/22.83 ((
% 131.89/22.83 (bs114d) =>
% 131.89/22.83 ((
% 131.89/22.83 (setminusI) =>
% 131.89/22.83 ((
% 131.89/22.83 (setminusEL) =>
% 131.89/22.83 ((
% 131.89/22.83 (setminusER) =>
% 131.89/22.83 ((
% 131.89/22.83 (setminusSubset2) =>
% 131.89/22.83 ((
% 131.89/22.83 (setminusERneg) =>
% 131.89/22.83 ((
% 131.89/22.83 (setminusELneg) =>
% 131.89/22.83 ((
% 131.89/22.83 (setminusILneg) =>
% 131.89/22.83 ((
% 131.89/22.83 (setminusIRneg) =>
% 131.89/22.83 ((
% 131.89/22.83 (setminusLsub) =>
% 131.89/22.83 ((
% 131.89/22.83 (setminusSubset1) =>
% 131.89/22.83 ((
% 131.89/22.83 (symdiffE) =>
% 131.89/22.83 ((
% 131.89/22.83 (symdiffI1) =>
% 131.89/22.83 ((
% 131.89/22.83 (symdiffI2) =>
% 131.89/22.83 ((
% 131.89/22.83 (symdiffIneg1) =>
% 131.89/22.83 ((
% 131.89/22.83 (symdiffIneg2) =>
% 131.89/22.83 ((
% 131.89/22.83 (secondinupair) =>
% 131.89/22.83 ((
% 131.89/22.83 (setukpairIL) =>
% 131.89/22.83 ((
% 131.89/22.83 (setukpairIR) =>
% 131.89/22.83 ((
% 131.89/22.83 (kpairiskpair) =>
% 131.89/22.83 ((
% 131.89/22.83 (kpairp) =>
% 131.89/22.83 ((
% 131.89/22.83 (singletonsubset) =>
% 131.89/22.83 ((
% 131.89/22.83 (singletoninpowerset) =>
% 131.89/22.83 ((
% 131.89/22.83 (singletoninpowunion) =>
% 131.89/22.83 ((
% 131.89/22.83 (upairset2E) =>
% 131.89/22.83 ((
% 131.89/22.83 (upairsubunion) =>
% 131.89/22.83 ((
% 131.89/22.83 (upairinpowunion) =>
% 131.89/22.83 ((
% 131.89/22.83 (ubforcartprodlem1) =>
% 131.89/22.83 ((
% 131.89/22.83 (ubforcartprodlem2) =>
% 131.89/22.83 ((
% 131.89/22.83 (ubforcartprodlem3) =>
% 131.89/22.83 ((
% 131.89/22.83 (cartprodpairin) =>
% 131.89/22.83 ((
% 131.89/22.83 (cartprodmempair1) =>
% 131.89/22.83 ((
% 131.89/22.83 (cartprodmempair) =>
% 131.89/22.83 ((
% 131.89/22.83 (setunionE2) =>
% 131.89/22.83 ((
% 131.89/22.83 (setunionsingleton1) =>
% 131.89/22.83 ((
% 131.89/22.83 (setunionsingleton2) =>
% 131.89/22.83 ((
% 131.89/22.83 (setunionsingleton) =>
% 131.89/22.83 ((
% 131.89/22.83 (singletonprop) =>
% 131.89/22.83 ((
% 131.89/22.83 (ex1E1) =>
% 131.89/22.83 ((
% 131.89/22.83 (ex1I) =>
% 131.89/22.83 ((
% 131.89/22.83 (ex1I2) =>
% 131.89/22.83 ((
% 131.89/22.83 (singletonsuniq) =>
% 131.89/22.83 ((
% 131.89/22.83 (setukpairinjL1) =>
% 131.89/22.83 ((
% 131.89/22.83 (kfstsingleton) =>
% 131.89/22.83 ((
% 131.89/22.83 (theprop) =>
% 131.89/22.83 ((
% 131.89/22.83 (kfstpairEq) =>
% 131.89/22.83 ((
% 131.89/22.83 (cartprodfstin) =>
% 131.89/22.83 ((
% 131.89/22.83 (setukpairinjL2) =>
% 131.89/22.83 ((
% 131.89/22.83 (setukpairinjL) =>
% 131.89/22.83 ((
% 131.89/22.83 (setukpairinjR11) =>
% 131.89/22.83 ((
% 131.89/22.83 (setukpairinjR12) =>
% 131.89/22.83 ((
% 131.89/22.83 (setukpairinjR1) =>
% 131.89/22.83 ((
% 131.89/22.83 (upairequniteq) =>
% 131.89/22.83 ((
% 131.89/22.83 (setukpairinjR2) =>
% 131.89/22.83 ((
% 131.89/22.83 (setukpairinjR) =>
% 131.89/22.83 ((
% 131.89/22.83 (ksndsingleton) =>
% 131.89/22.83 ((
% 131.89/22.83 (ksndpairEq) =>
% 131.89/22.83 ((
% 131.89/22.83 (kpairsurjEq) =>
% 131.89/22.83 ((
% 131.89/22.83 (cartprodsndin) =>
% 131.89/22.83 ((
% 131.89/22.83 (cartprodpairmemEL) =>
% 131.89/22.83 ((
% 131.89/22.83 (cartprodpairmemER) =>
% 131.89/22.83 ((
% 131.89/22.83 (cartprodmempaircEq) =>
% 131.89/22.83 ((
% 131.89/22.83 (cartprodfstpairEq) =>
% 131.89/22.83 ((
% 131.89/22.83 (cartprodsndpairEq) =>
% 131.89/22.83 ((
% 131.89/22.83 (cartprodpairsurjEq) =>
% 131.89/22.83 ((
% 131.89/22.83 (dpsetconstrI) =>
% 131.89/22.83 ((
% 131.89/22.83 (dpsetconstrSub) =>
% 131.89/22.83 ((
% 131.89/22.83 (setOfPairsIsBReln) =>
% 131.89/22.83 ((
% 131.89/22.83 (dpsetconstrERa) =>
% 131.89/22.83 ((
% 131.89/22.83 (dpsetconstrEL1) =>
% 131.89/22.83 ((
% 131.89/22.83 (dpsetconstrEL2) =>
% 131.89/22.83 ((
% 131.89/22.83 (dpsetconstrER) =>
% 131.89/22.83 ((
% 131.89/22.83 (funcImageSingleton) =>
% 131.89/22.83 ((
% 131.89/22.83 (apProp) =>
% 131.89/22.83 ((
% 131.89/22.83 (app) =>
% 131.89/22.83 ((
% 131.89/22.83 (infuncsetfunc) =>
% 131.89/22.83 ((
% 131.89/22.83 (ap2p) =>
% 131.89/22.83 ((
% 131.89/22.83 (funcinfuncset) =>
% 131.89/22.83 ((
% 131.89/22.83 (lamProp) =>
% 131.89/22.83 ((
% 131.89/22.83 (lamp) =>
% 131.89/22.83 ((
% 131.89/22.83 (lam2p) =>
% 131.89/22.83 ((
% 131.89/22.83 (brelnall1) =>
% 131.89/22.83 ((
% 131.89/22.83 (brelnall2) =>
% 131.89/22.83 ((
% 131.89/22.83 (ex1E2) =>
% 131.89/22.83 ((
% 131.89/22.83 (funcGraphProp1) =>
% 131.89/22.83 ((
% 131.89/22.83 (funcGraphProp3) =>
% 131.89/22.83 ((
% 131.89/22.83 (funcGraphProp2) =>
% 131.89/22.83 ((
% 131.89/22.83 (funcextLem) =>
% 131.89/22.83 ((
% 131.89/22.83 (funcGraphProp4) =>
% 131.89/22.83 ((
% 131.89/22.83 (subbreln) =>
% 131.89/22.83 ((
% 131.89/22.83 (eqbreln) =>
% 131.89/22.83 ((
% 131.89/22.83 (funcext) =>
% 131.89/22.83 ((
% 131.89/22.83 (funcext2) =>
% 131.89/22.83 ((
% 131.89/22.83 (ap2apEq1) =>
% 131.89/22.83 ((
% 131.89/22.83 (ap2apEq2) =>
% 131.89/22.83 ((
% 131.89/22.83 (beta1) =>
% 131.89/22.83 ((
% 131.89/22.83 (eta1) =>
% 131.89/22.83 ((
% 131.89/22.83 (lam2lamEq) =>
% 131.89/22.83 ((
% 131.89/22.83 (beta2) =>
% 131.89/22.83 ((
% 131.89/22.83 (eta2) =>
% 131.89/22.83 ((
% 131.89/22.83 (iffalseProp1) =>
% 131.89/22.83 ((
% 131.89/22.83 (iffalseProp2) =>
% 131.89/22.83 ((
% 131.89/22.83 (iftrueProp1) =>
% 131.89/22.83 ((
% 131.89/22.83 (iftrueProp2) =>
% 131.89/22.83 ((
% 131.89/22.83 (ifSingleton) =>
% 131.89/22.83 ((
% 131.89/22.83 (ifp) =>
% 131.89/22.83 ((
% 131.89/22.83 (theeq) =>
% 131.89/22.83 ((
% 131.89/22.83 (iftrue) =>
% 131.89/22.83 ((
% 131.89/22.83 (iffalse) =>
% 131.89/22.83 ((
% 131.89/22.83 (iftrueorfalse) =>
% 131.89/22.83 ((
% 131.89/22.83 (binintersectT_lem) =>
% 131.89/22.83 ((
% 131.89/22.83 (binunionT_lem) =>
% 131.89/22.83 ((
% 131.89/22.83 (powersetT_lem) =>
% 131.89/22.83 ((
% 131.89/22.83 (setminusT_lem) =>
% 131.89/22.83 ((
% 131.89/22.83 (complementT_lem) =>
% 131.89/22.83 ((
% 131.89/22.83 (setextT) =>
% 131.89/22.83 ((
% 131.89/22.83 (subsetTI) =>
% 131.89/22.83 ((
% 131.89/22.83 (powersetTI1) =>
% 131.89/22.83 ((
% 131.89/22.83 (powersetTE1) =>
% 131.89/22.83 ((
% 131.89/22.83 (complementTI1) =>
% 131.89/22.83 ((
% 131.89/22.83 (complementTE1) =>
% 131.89/22.83 ((
% 131.89/22.83 (binintersectTELcontra) =>
% 131.89/22.83 ((
% 131.89/22.83 (binintersectTERcontra) =>
% 131.89/22.83 ((
% 131.89/22.83 (contrasubsetT) =>
% 131.89/22.83 ((
% 131.89/22.83 (contrasubsetT1) =>
% 131.89/22.83 ((
% 131.89/22.83 (contrasubsetT2) =>
% 131.89/22.83 ((
% 131.89/22.83 (contrasubsetT3) =>
% 131.89/22.83 ((
% 131.89/22.83 (doubleComplementI1) =>
% 131.89/22.83 ((
% 131.89/22.83 (doubleComplementE1) =>
% 131.89/22.83 ((
% 131.89/22.83 (doubleComplementSub1) =>
% 131.89/22.83 ((
% 131.89/22.83 (doubleComplementSub2) =>
% 131.89/22.83 ((
% 131.89/22.83 (doubleComplementEq) =>
% 131.89/22.83 ((
% 131.89/22.83 (complementTnotintersectT) =>
% 131.89/22.83 ((
% 131.89/22.83 (complementImpComplementIntersect) =>
% 131.89/22.83 ((
% 131.89/22.83 (complementSubsetComplementIntersect) =>
% 131.89/22.83 ((
% 131.89/22.83 (complementInPowersetComplementIntersect) =>
% 131.89/22.83 ((
% 131.89/22.83 (contraSubsetComplement) =>
% 131.89/22.83 ((
% 131.89/22.83 (complementTcontraSubset) =>
% 131.89/22.83 ((
% 131.89/22.83 (binunionTILcontra) =>
% 131.89/22.83 ((
% 131.89/22.83 (binunionTIRcontra) =>
% 131.89/22.83 ((
% 131.89/22.83 (inIntersectImpInUnion) =>
% 131.89/22.83 ((
% 131.89/22.83 (inIntersectImpInUnion2) =>
% 131.89/22.83 ((
% 131.89/22.83 (inIntersectImpInIntersectUnions) =>
% 131.89/22.83 ((
% 131.89/22.83 (intersectInPowersetIntersectUnions) =>
% 131.89/22.83 ((
% 131.89/22.83 (inComplementUnionImpNotIn1) =>
% 131.89/22.83 ((
% 131.89/22.83 (inComplementUnionImpInComplement1) =>
% 131.89/22.83 ((
% 131.89/22.83 (binunionTE) =>
% 131.89/22.83 ((
% 131.89/22.83 (binunionTEcontra) =>
% 131.89/22.83 ((
% 131.89/22.83 (demorgan2a1) =>
% 131.89/22.83 ((
% 131.89/22.83 (complementUnionInPowersetComplement) =>
% 131.89/22.83 ((
% 131.89/22.83 (demorgan2a2) =>
% 131.89/22.83 ((
% 131.89/22.83 (demorgan1a) =>
% 131.89/22.83 ((
% 131.89/22.83 (demorgan1b) =>
% 131.89/22.83 ((
% 131.89/22.83 (demorgan1) =>
% 131.89/22.83 ((
% 131.89/22.83 (demorgan2a) =>
% 131.89/22.83 ((
% 131.89/22.83 (demorgan2b2) =>
% 131.89/22.83 ((
% 131.89/22.83 (demorgan2b) =>
% 131.89/22.83 ((
% 131.89/22.83 (demorgan2) =>
% 131.89/22.83 ((
% 131.89/22.83 (woz13rule0) =>
% 131.89/22.83 ((
% 131.89/22.83 (woz13rule1) =>
% 131.89/22.83 ((
% 131.89/22.83 (woz13rule2) =>
% 131.89/22.83 ((
% 131.89/22.83 (woz13rule3) =>
% 131.89/22.83 ((
% 131.89/22.83 (woz13rule4) =>
% 131.89/22.83 ((
% 131.89/22.83 (woz1_1) =>
% 131.89/22.83 ((
% 131.89/22.83 (woz1_2) =>
% 131.89/22.83 ((
% 131.89/22.83 (woz1_3) =>
% 131.89/22.83 ((
% 131.89/22.83 (woz1_4) =>
% 131.89/22.83 ((
% 131.89/22.83 (woz1_5) =>
% 131.89/22.83 ((
% 131.89/22.83 (breln1all2) =>
% 131.89/22.83 ((
% 131.89/22.83 (breln1SetBreln1) =>
% 131.89/22.83 ((
% 131.89/22.83 (choice2fnsingleton) =>
% 131.89/22.83 ((
% 131.89/22.83 (setOfPairsIsBReln1) =>
% 131.89/22.83 ((
% 131.89/22.83 (breln1all1) =>
% 131.89/22.83 ((
% 131.89/22.83 (subbreln1) =>
% 131.89/22.83 ((
% 131.89/22.83 (eqbreln1) =>
% 131.89/22.83 ((
% 131.89/22.83 (breln1invprop) =>
% 131.89/22.83 ((
% 131.89/22.83 (breln1invI) =>
% 131.89/22.83 ((
% 131.89/22.83 (breln1invE) =>
% 131.89/22.83 ((
% 131.89/22.83 (breln1compprop) =>
% 131.89/22.83 ((
% 131.89/22.83 (breln1compI) =>
% 131.89/22.83 ((
% 131.89/22.83 (breln1compE) =>
% 131.89/22.83 ((
% 131.89/22.83 (breln1compEex) =>
% 131.89/22.83 ((
% 131.89/22.83 (breln1unionprop) =>
% 131.89/22.83 ((
% 131.89/22.83 (breln1unionIL) =>
% 131.89/22.83 ((
% 131.89/22.83 (breln1unionIR) =>
% 131.89/22.83 ((
% 131.89/22.83 (breln1unionI) =>
% 131.89/22.83 ((
% 131.89/22.83 (breln1unionE) =>
% 131.89/22.83 ((
% 131.89/22.83 (breln1unionEcases) =>
% 131.89/22.83 ((
% 131.89/22.83 (breln1unionCommutes) =>
% 131.89/22.83 ((
% 131.89/22.83 (woz2Ex) =>
% 131.89/22.83 ((
% 131.89/22.83 (woz2W) =>
% 131.89/22.83 ((
% 131.89/22.83 (woz2A) =>
% 131.89/22.83 ((
% 131.89/22.83 (woz2B) =>
% 131.89/22.83 ((
% 131.89/22.83 (image1Ex) =>
% 131.89/22.83 ((
% 131.89/22.83 (image1Ex1) =>
% 131.89/22.83 ((
% 131.89/22.83 (image1Equiv) =>
% 131.89/22.83 ((
% 131.89/22.83 (image1E) =>
% 131.89/22.83 ((
% 131.89/22.83 (image1I) =>
% 131.89/22.83 ((
% 131.89/22.83 (injFuncInInjFuncSet) =>
% 131.89/22.83 ((
% 131.89/22.83 (injFuncSetFuncIn) =>
% 131.89/22.83 ((
% 131.89/22.83 (injFuncSetFuncInj) =>
% 131.89/22.83 ((
% 131.89/22.83 (surjFuncSetFuncIn) =>
% 131.89/22.83 ((
% 131.89/22.83 (surjFuncSetFuncSurj) =>
% 131.89/22.83 ((
% 131.89/22.83 (leftInvIsSurj) =>
% 131.89/22.83 ((
% 131.89/22.83 (surjCantorThm) =>
% 131.89/22.83 ((
% 131.89/22.83 (foundation2) =>
% 131.89/22.83 ((
% 131.89/22.83 (notinself) =>
% 131.89/22.83 ((
% 131.89/22.83 (notinself2) =>
% 131.89/22.83 ((
% 131.89/22.83 (omegaSp) =>
% 131.89/22.83 ((
% 131.89/22.83 (omegaSclos) =>
% 131.89/22.83 ((
% 131.89/22.83 (peano0notS) =>
% 131.89/22.83 ((
% 131.89/22.83 (peanoSinj) =>
% 131.89/22.83 ((
% 131.89/22.83 (transitivesetOp1) =>
% 131.89/22.83 ((
% 131.89/22.83 (binintTransitive) =>
% 131.89/22.83 ((
% 131.89/22.83 (transitivesetOp2) =>
% 131.89/22.83 ((
% 131.89/22.83 (setunionTransitive) =>
% 131.89/22.83 ((
% 131.89/22.83 (ordinalMinLem1) =>
% 131.89/22.83 ((
% 131.89/22.83 (ordinalTransSet) =>
% 131.89/22.83 ((
% 131.89/22.83 (ordinalTransSet1) =>
% 131.89/22.83 ((
% 131.89/22.83 (setunionOrdinalLem1) =>
% 131.89/22.83 (ordinal @
% 131.89/22.83 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 131.89/22.83 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl439])).
% 131.89/22.83 thf(zip_derived_cl457, plain,
% 131.89/22.83 (~ (((emptyE1) =>
% 131.89/22.83 (((vacuousDall) =>
% 131.89/22.83 (((quantDeMorgan1) =>
% 131.89/22.83 (((quantDeMorgan2) =>
% 131.89/22.83 (((quantDeMorgan3) =>
% 131.89/22.83 (((quantDeMorgan4) =>
% 131.89/22.83 (((prop2setI) =>
% 131.89/22.83 (((prop2set2propI) =>
% 131.89/22.83 (((notdexE) =>
% 131.89/22.83 (((notdallE) =>
% 131.89/22.83 (((exuI1) =>
% 131.89/22.83 (((exuI3) =>
% 131.89/22.83 (((exuI2) =>
% 131.89/22.83 (((inCongP) =>
% 131.89/22.83 (((in__Cong) =>
% 131.89/22.83 (((exuE3u) =>
% 131.89/22.83 (((exu__Cong) =>
% 131.89/22.83 (((setadjoin__Cong) =>
% 131.89/22.83 (((powerset__Cong) =>
% 131.89/22.83 (((setunion__Cong) =>
% 131.89/22.83 (((exuEu) =>
% 131.89/22.83 (((descr__Cong) =>
% 131.89/22.83 (((dsetconstr__Cong) =>
% 131.89/22.83 (((subsetI1) =>
% 131.89/22.83 (((eqimpsubset2) =>
% 131.89/22.83 (((eqimpsubset1) =>
% 131.89/22.83 (((subsetI2) =>
% 131.89/22.83 (((emptysetsubset) =>
% 131.89/22.83 (((subsetE) =>
% 131.89/22.83 (((subsetE2) =>
% 131.89/22.83 ((
% 131.89/22.83 (notsubsetI) =>
% 131.89/22.83 ((
% 131.89/22.83 (notequalI1) =>
% 131.89/22.83 ((
% 131.89/22.83 (notequalI2) =>
% 131.89/22.83 ((
% 131.89/22.83 (subsetRefl) =>
% 131.89/22.83 ((
% 131.89/22.83 (subsetTrans) =>
% 131.89/22.83 ((
% 131.89/22.83 (setadjoinSub) =>
% 131.89/22.83 ((
% 131.89/22.83 (setadjoinSub2) =>
% 131.89/22.83 ((
% 131.89/22.83 (subset2powerset) =>
% 131.89/22.83 ((
% 131.89/22.83 (setextsub) =>
% 131.89/22.83 ((
% 131.89/22.83 (subsetemptysetimpeq) =>
% 131.89/22.83 ((
% 131.89/22.83 (powersetI1) =>
% 131.89/22.83 ((
% 131.89/22.83 (powersetE1) =>
% 131.89/22.83 ((
% 131.89/22.83 (inPowerset) =>
% 131.89/22.83 ((
% 131.89/22.83 (powersetsubset) =>
% 131.89/22.84 ((
% 131.89/22.84 (sepInPowerset) =>
% 131.89/22.84 ((
% 131.89/22.84 (sepSubset) =>
% 131.89/22.84 ((
% 131.89/22.84 (binunionIL) =>
% 131.89/22.84 ((
% 131.89/22.84 (upairset2IR) =>
% 131.89/22.84 ((
% 131.89/22.84 (binunionIR) =>
% 131.89/22.84 ((
% 131.89/22.84 (binunionEcases) =>
% 131.89/22.84 ((
% 131.89/22.84 (binunionE) =>
% 131.89/22.84 ((
% 131.89/22.84 (binunionLsub) =>
% 131.89/22.84 ((
% 131.89/22.84 (binunionRsub) =>
% 131.89/22.84 ((
% 131.89/22.84 (binintersectI) =>
% 131.89/22.84 ((
% 131.89/22.84 (binintersectSubset5) =>
% 131.89/22.84 ((
% 131.89/22.84 (binintersectEL) =>
% 131.89/22.84 ((
% 131.89/22.84 (binintersectLsub) =>
% 131.89/22.84 ((
% 131.89/22.84 (binintersectSubset2) =>
% 131.89/22.84 ((
% 131.89/22.84 (binintersectSubset3) =>
% 131.89/22.84 ((
% 131.89/22.84 (binintersectER) =>
% 131.89/22.84 ((
% 131.89/22.84 (disjointsetsI1) =>
% 131.89/22.84 ((
% 131.89/22.84 (binintersectRsub) =>
% 131.89/22.84 ((
% 131.89/22.84 (binintersectSubset4) =>
% 131.89/22.84 ((
% 131.89/22.84 (binintersectSubset1) =>
% 131.89/22.84 ((
% 131.89/22.84 (bs114d) =>
% 131.89/22.84 ((
% 131.89/22.84 (setminusI) =>
% 131.89/22.84 ((
% 131.89/22.84 (setminusEL) =>
% 131.89/22.84 ((
% 131.89/22.84 (setminusER) =>
% 131.89/22.84 ((
% 131.89/22.84 (setminusSubset2) =>
% 131.89/22.84 ((
% 131.89/22.84 (setminusERneg) =>
% 131.89/22.84 ((
% 131.89/22.84 (setminusELneg) =>
% 131.89/22.84 ((
% 131.89/22.84 (setminusILneg) =>
% 131.89/22.84 ((
% 131.89/22.84 (setminusIRneg) =>
% 131.89/22.84 ((
% 131.89/22.84 (setminusLsub) =>
% 131.89/22.84 ((
% 131.89/22.84 (setminusSubset1) =>
% 131.89/22.84 ((
% 131.89/22.84 (symdiffE) =>
% 131.89/22.84 ((
% 131.89/22.84 (symdiffI1) =>
% 131.89/22.84 ((
% 131.89/22.84 (symdiffI2) =>
% 131.89/22.84 ((
% 131.89/22.84 (symdiffIneg1) =>
% 131.89/22.84 ((
% 131.89/22.84 (symdiffIneg2) =>
% 131.89/22.84 ((
% 131.89/22.84 (secondinupair) =>
% 131.89/22.84 ((
% 131.89/22.84 (setukpairIL) =>
% 131.89/22.84 ((
% 131.89/22.84 (setukpairIR) =>
% 131.89/22.84 ((
% 131.89/22.84 (kpairiskpair) =>
% 131.89/22.84 ((
% 131.89/22.84 (kpairp) =>
% 131.89/22.84 ((
% 131.89/22.84 (singletonsubset) =>
% 131.89/22.84 ((
% 131.89/22.84 (singletoninpowerset) =>
% 131.89/22.84 ((
% 131.89/22.84 (singletoninpowunion) =>
% 131.89/22.84 ((
% 131.89/22.84 (upairset2E) =>
% 131.89/22.84 ((
% 131.89/22.84 (upairsubunion) =>
% 131.89/22.84 ((
% 131.89/22.84 (upairinpowunion) =>
% 131.89/22.84 ((
% 131.89/22.84 (ubforcartprodlem1) =>
% 131.89/22.84 ((
% 131.89/22.84 (ubforcartprodlem2) =>
% 131.89/22.84 ((
% 131.89/22.84 (ubforcartprodlem3) =>
% 131.89/22.84 ((
% 131.89/22.84 (cartprodpairin) =>
% 131.89/22.84 ((
% 131.89/22.84 (cartprodmempair1) =>
% 131.89/22.84 ((
% 131.89/22.84 (cartprodmempair) =>
% 131.89/22.84 ((
% 131.89/22.84 (setunionE2) =>
% 131.89/22.84 ((
% 131.89/22.84 (setunionsingleton1) =>
% 131.89/22.84 ((
% 131.89/22.84 (setunionsingleton2) =>
% 131.89/22.84 ((
% 131.89/22.84 (setunionsingleton) =>
% 131.89/22.84 ((
% 131.89/22.84 (singletonprop) =>
% 131.89/22.84 ((
% 131.89/22.84 (ex1E1) =>
% 131.89/22.84 ((
% 131.89/22.84 (ex1I) =>
% 131.89/22.84 ((
% 131.89/22.84 (ex1I2) =>
% 131.89/22.84 ((
% 131.89/22.84 (singletonsuniq) =>
% 131.89/22.84 ((
% 131.89/22.84 (setukpairinjL1) =>
% 131.89/22.84 ((
% 131.89/22.84 (kfstsingleton) =>
% 131.89/22.84 ((
% 131.89/22.84 (theprop) =>
% 131.89/22.84 ((
% 131.89/22.84 (kfstpairEq) =>
% 131.89/22.84 ((
% 131.89/22.84 (cartprodfstin) =>
% 131.89/22.84 ((
% 131.89/22.84 (setukpairinjL2) =>
% 131.89/22.84 ((
% 131.89/22.84 (setukpairinjL) =>
% 131.89/22.84 ((
% 131.89/22.84 (setukpairinjR11) =>
% 131.89/22.84 ((
% 131.89/22.84 (setukpairinjR12) =>
% 131.89/22.84 ((
% 131.89/22.84 (setukpairinjR1) =>
% 131.89/22.84 ((
% 131.89/22.84 (upairequniteq) =>
% 131.89/22.84 ((
% 131.89/22.84 (setukpairinjR2) =>
% 131.89/22.84 ((
% 131.89/22.84 (setukpairinjR) =>
% 131.89/22.84 ((
% 131.89/22.84 (ksndsingleton) =>
% 131.89/22.84 ((
% 131.89/22.84 (ksndpairEq) =>
% 131.89/22.84 ((
% 131.89/22.84 (kpairsurjEq) =>
% 131.89/22.84 ((
% 131.89/22.84 (cartprodsndin) =>
% 131.89/22.84 ((
% 131.89/22.84 (cartprodpairmemEL) =>
% 131.89/22.84 ((
% 131.89/22.84 (cartprodpairmemER) =>
% 131.89/22.84 ((
% 131.89/22.84 (cartprodmempaircEq) =>
% 131.89/22.84 ((
% 131.89/22.84 (cartprodfstpairEq) =>
% 131.89/22.84 ((
% 131.89/22.84 (cartprodsndpairEq) =>
% 131.89/22.84 ((
% 131.89/22.84 (cartprodpairsurjEq) =>
% 131.89/22.84 ((
% 131.89/22.84 (dpsetconstrI) =>
% 131.89/22.84 ((
% 131.89/22.84 (dpsetconstrSub) =>
% 131.89/22.84 ((
% 131.89/22.84 (setOfPairsIsBReln) =>
% 131.89/22.84 ((
% 131.89/22.84 (dpsetconstrERa) =>
% 131.89/22.84 ((
% 131.89/22.84 (dpsetconstrEL1) =>
% 131.89/22.84 ((
% 131.89/22.84 (dpsetconstrEL2) =>
% 131.89/22.84 ((
% 131.89/22.84 (dpsetconstrER) =>
% 131.89/22.84 ((
% 131.89/22.84 (funcImageSingleton) =>
% 131.89/22.84 ((
% 131.89/22.84 (apProp) =>
% 131.89/22.84 ((
% 131.89/22.84 (app) =>
% 131.89/22.84 ((
% 131.89/22.84 (infuncsetfunc) =>
% 131.89/22.84 ((
% 131.89/22.84 (ap2p) =>
% 131.89/22.84 ((
% 131.89/22.84 (funcinfuncset) =>
% 131.89/22.84 ((
% 131.89/22.84 (lamProp) =>
% 131.89/22.84 ((
% 131.89/22.84 (lamp) =>
% 131.89/22.84 ((
% 131.89/22.84 (lam2p) =>
% 131.89/22.84 ((
% 131.89/22.84 (brelnall1) =>
% 131.89/22.84 ((
% 131.89/22.84 (brelnall2) =>
% 131.89/22.84 ((
% 131.89/22.84 (ex1E2) =>
% 131.89/22.84 ((
% 131.89/22.84 (funcGraphProp1) =>
% 131.89/22.84 ((
% 131.89/22.84 (funcGraphProp3) =>
% 131.89/22.84 ((
% 131.89/22.84 (funcGraphProp2) =>
% 131.89/22.84 ((
% 131.89/22.84 (funcextLem) =>
% 131.89/22.84 ((
% 131.89/22.84 (funcGraphProp4) =>
% 131.89/22.84 ((
% 131.89/22.84 (subbreln) =>
% 131.89/22.84 ((
% 131.89/22.84 (eqbreln) =>
% 131.89/22.84 ((
% 131.89/22.84 (funcext) =>
% 131.89/22.84 ((
% 131.89/22.84 (funcext2) =>
% 131.89/22.84 ((
% 131.89/22.84 (ap2apEq1) =>
% 131.89/22.84 ((
% 131.89/22.84 (ap2apEq2) =>
% 131.89/22.84 ((
% 131.89/22.84 (beta1) =>
% 131.89/22.84 ((
% 131.89/22.84 (eta1) =>
% 131.89/22.84 ((
% 131.89/22.84 (lam2lamEq) =>
% 131.89/22.84 ((
% 131.89/22.84 (beta2) =>
% 131.89/22.84 ((
% 131.89/22.84 (eta2) =>
% 131.89/22.84 ((
% 131.89/22.84 (iffalseProp1) =>
% 131.89/22.84 ((
% 131.89/22.84 (iffalseProp2) =>
% 131.89/22.84 ((
% 131.89/22.84 (iftrueProp1) =>
% 131.89/22.84 ((
% 131.89/22.84 (iftrueProp2) =>
% 131.89/22.84 ((
% 131.89/22.84 (ifSingleton) =>
% 131.89/22.84 ((
% 131.89/22.84 (ifp) =>
% 131.89/22.84 ((
% 131.89/22.84 (theeq) =>
% 131.89/22.84 ((
% 131.89/22.84 (iftrue) =>
% 131.89/22.84 ((
% 131.89/22.84 (iffalse) =>
% 131.89/22.84 ((
% 131.89/22.84 (iftrueorfalse) =>
% 131.89/22.84 ((
% 131.89/22.84 (binintersectT_lem) =>
% 131.89/22.84 ((
% 131.89/22.84 (binunionT_lem) =>
% 131.89/22.84 ((
% 131.89/22.84 (powersetT_lem) =>
% 131.89/22.84 ((
% 131.89/22.84 (setminusT_lem) =>
% 131.89/22.84 ((
% 131.89/22.84 (complementT_lem) =>
% 131.89/22.84 ((
% 131.89/22.84 (setextT) =>
% 131.89/22.84 ((
% 131.89/22.84 (subsetTI) =>
% 131.89/22.84 ((
% 131.89/22.84 (powersetTI1) =>
% 131.89/22.84 ((
% 131.89/22.84 (powersetTE1) =>
% 131.89/22.84 ((
% 131.89/22.84 (complementTI1) =>
% 131.89/22.84 ((
% 131.89/22.84 (complementTE1) =>
% 131.89/22.84 ((
% 131.89/22.84 (binintersectTELcontra) =>
% 131.89/22.84 ((
% 131.89/22.84 (binintersectTERcontra) =>
% 131.89/22.84 ((
% 131.89/22.84 (contrasubsetT) =>
% 131.89/22.84 ((
% 131.89/22.84 (contrasubsetT1) =>
% 131.89/22.84 ((
% 131.89/22.84 (contrasubsetT2) =>
% 131.89/22.84 ((
% 131.89/22.84 (contrasubsetT3) =>
% 131.89/22.84 ((
% 131.89/22.84 (doubleComplementI1) =>
% 131.89/22.84 ((
% 131.89/22.84 (doubleComplementE1) =>
% 131.89/22.84 ((
% 131.89/22.84 (doubleComplementSub1) =>
% 131.89/22.84 ((
% 131.89/22.84 (doubleComplementSub2) =>
% 131.89/22.84 ((
% 131.89/22.84 (doubleComplementEq) =>
% 131.89/22.84 ((
% 131.89/22.84 (complementTnotintersectT) =>
% 131.89/22.84 ((
% 131.89/22.84 (complementImpComplementIntersect) =>
% 131.89/22.84 ((
% 131.89/22.84 (complementSubsetComplementIntersect) =>
% 131.89/22.84 ((
% 131.89/22.84 (complementInPowersetComplementIntersect) =>
% 131.89/22.84 ((
% 131.89/22.84 (contraSubsetComplement) =>
% 131.89/22.84 ((
% 131.89/22.84 (complementTcontraSubset) =>
% 131.89/22.84 ((
% 131.89/22.84 (binunionTILcontra) =>
% 131.89/22.84 ((
% 131.89/22.84 (binunionTIRcontra) =>
% 131.89/22.84 ((
% 131.89/22.84 (inIntersectImpInUnion) =>
% 131.89/22.84 ((
% 131.89/22.84 (inIntersectImpInUnion2) =>
% 131.89/22.84 ((
% 131.89/22.84 (inIntersectImpInIntersectUnions) =>
% 131.89/22.84 ((
% 131.89/22.84 (intersectInPowersetIntersectUnions) =>
% 131.89/22.84 ((
% 131.89/22.84 (inComplementUnionImpNotIn1) =>
% 131.89/22.84 ((
% 131.89/22.84 (inComplementUnionImpInComplement1) =>
% 131.89/22.84 ((
% 131.89/22.84 (binunionTE) =>
% 131.89/22.84 ((
% 131.89/22.84 (binunionTEcontra) =>
% 131.89/22.84 ((
% 131.89/22.84 (demorgan2a1) =>
% 131.89/22.84 ((
% 131.89/22.84 (complementUnionInPowersetComplement) =>
% 131.89/22.84 ((
% 131.89/22.84 (demorgan2a2) =>
% 131.89/22.84 ((
% 131.89/22.84 (demorgan1a) =>
% 131.89/22.84 ((
% 131.89/22.84 (demorgan1b) =>
% 131.89/22.84 ((
% 131.89/22.84 (demorgan1) =>
% 131.89/22.84 ((
% 131.89/22.84 (demorgan2a) =>
% 131.89/22.84 ((
% 131.89/22.84 (demorgan2b2) =>
% 131.89/22.84 ((
% 131.89/22.84 (demorgan2b) =>
% 131.89/22.84 ((
% 131.89/22.84 (demorgan2) =>
% 131.89/22.84 ((
% 131.89/22.84 (woz13rule0) =>
% 131.89/22.84 ((
% 131.89/22.84 (woz13rule1) =>
% 131.89/22.84 ((
% 131.89/22.84 (woz13rule2) =>
% 131.89/22.84 ((
% 131.89/22.84 (woz13rule3) =>
% 131.89/22.84 ((
% 131.89/22.84 (woz13rule4) =>
% 131.89/22.84 ((
% 131.89/22.84 (woz1_1) =>
% 131.89/22.84 ((
% 131.89/22.84 (woz1_2) =>
% 131.89/22.84 ((
% 131.89/22.84 (woz1_3) =>
% 131.89/22.84 ((
% 131.89/22.84 (woz1_4) =>
% 131.89/22.84 ((
% 131.89/22.84 (woz1_5) =>
% 131.89/22.84 ((
% 131.89/22.84 (breln1all2) =>
% 131.89/22.84 ((
% 131.89/22.84 (breln1SetBreln1) =>
% 131.89/22.84 ((
% 131.89/22.84 (choice2fnsingleton) =>
% 131.89/22.84 ((
% 131.89/22.84 (setOfPairsIsBReln1) =>
% 131.89/22.84 ((
% 131.89/22.84 (breln1all1) =>
% 131.89/22.84 ((
% 131.89/22.84 (subbreln1) =>
% 131.89/22.84 ((
% 131.89/22.84 (eqbreln1) =>
% 131.89/22.84 ((
% 131.89/22.84 (breln1invprop) =>
% 131.89/22.84 ((
% 131.89/22.84 (breln1invI) =>
% 131.89/22.84 ((
% 131.89/22.84 (breln1invE) =>
% 131.89/22.84 ((
% 131.89/22.84 (breln1compprop) =>
% 131.89/22.84 ((
% 131.89/22.84 (breln1compI) =>
% 131.89/22.84 ((
% 131.89/22.84 (breln1compE) =>
% 131.89/22.84 ((
% 131.89/22.84 (breln1compEex) =>
% 131.89/22.84 ((
% 131.89/22.84 (breln1unionprop) =>
% 131.89/22.84 ((
% 131.89/22.84 (breln1unionIL) =>
% 131.89/22.84 ((
% 131.89/22.84 (breln1unionIR) =>
% 131.89/22.84 ((
% 131.89/22.84 (breln1unionI) =>
% 131.89/22.84 ((
% 131.89/22.84 (breln1unionE) =>
% 131.89/22.84 ((
% 131.89/22.84 (breln1unionEcases) =>
% 131.89/22.84 ((
% 131.89/22.84 (breln1unionCommutes) =>
% 131.89/22.84 ((
% 131.89/22.84 (woz2Ex) =>
% 131.89/22.84 ((
% 131.89/22.84 (woz2W) =>
% 131.89/22.84 ((
% 131.89/22.84 (woz2A) =>
% 131.89/22.84 ((
% 131.89/22.84 (woz2B) =>
% 131.89/22.84 ((
% 131.89/22.84 (image1Ex) =>
% 131.89/22.84 ((
% 131.89/22.84 (image1Ex1) =>
% 131.89/22.84 ((
% 131.89/22.84 (image1Equiv) =>
% 131.89/22.84 ((
% 131.89/22.84 (image1E) =>
% 131.89/22.84 ((
% 131.89/22.84 (image1I) =>
% 131.89/22.84 ((
% 131.89/22.84 (injFuncInInjFuncSet) =>
% 131.89/22.84 ((
% 131.89/22.84 (injFuncSetFuncIn) =>
% 131.89/22.84 ((
% 131.89/22.84 (injFuncSetFuncInj) =>
% 131.89/22.84 ((
% 131.89/22.84 (surjFuncSetFuncIn) =>
% 131.89/22.84 ((
% 131.89/22.84 (surjFuncSetFuncSurj) =>
% 131.89/22.84 ((
% 131.89/22.84 (leftInvIsSurj) =>
% 131.89/22.84 ((
% 131.89/22.84 (surjCantorThm) =>
% 131.89/22.84 ((
% 131.89/22.84 (foundation2) =>
% 131.89/22.84 ((
% 131.89/22.84 (notinself) =>
% 131.89/22.84 ((
% 131.89/22.84 (notinself2) =>
% 131.89/22.84 ((
% 131.89/22.84 (omegaSp) =>
% 131.89/22.84 ((
% 131.89/22.84 (omegaSclos) =>
% 131.89/22.84 ((
% 131.89/22.84 (peano0notS) =>
% 131.89/22.84 ((
% 131.89/22.84 (peanoSinj) =>
% 131.89/22.84 ((
% 131.89/22.84 (transitivesetOp1) =>
% 131.89/22.84 ((
% 131.89/22.84 (binintTransitive) =>
% 131.89/22.84 ((
% 131.89/22.84 (transitivesetOp2) =>
% 131.89/22.84 ((
% 131.89/22.84 (setunionTransitive) =>
% 131.89/22.84 ((
% 131.89/22.84 (ordinalMinLem1) =>
% 131.89/22.84 ((
% 131.89/22.84 (ordinalTransSet) =>
% 131.89/22.84 ((
% 131.89/22.84 (ordinalTransSet1) =>
% 131.89/22.84 ((
% 131.89/22.84 (setunionOrdinalLem1) =>
% 131.89/22.84 (ordinal @
% 131.89/22.84 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 131.89/22.84 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl449])).
% 131.89/22.84 thf(zip_derived_cl465, plain,
% 131.89/22.84 (~ (((vacuousDall) =>
% 131.89/22.84 (((quantDeMorgan1) =>
% 131.89/22.84 (((quantDeMorgan2) =>
% 131.89/22.84 (((quantDeMorgan3) =>
% 131.89/22.84 (((quantDeMorgan4) =>
% 131.89/22.84 (((prop2setI) =>
% 131.89/22.84 (((prop2set2propI) =>
% 131.89/22.84 (((notdexE) =>
% 131.89/22.84 (((notdallE) =>
% 131.89/22.84 (((exuI1) =>
% 131.89/22.84 (((exuI3) =>
% 131.89/22.84 (((exuI2) =>
% 131.89/22.84 (((inCongP) =>
% 131.89/22.84 (((in__Cong) =>
% 131.89/22.84 (((exuE3u) =>
% 131.89/22.84 (((exu__Cong) =>
% 131.89/22.84 (((setadjoin__Cong) =>
% 131.89/22.84 (((powerset__Cong) =>
% 131.89/22.84 (((setunion__Cong) =>
% 131.89/22.84 (((exuEu) =>
% 131.89/22.84 (((descr__Cong) =>
% 131.89/22.84 (((dsetconstr__Cong) =>
% 131.89/22.84 (((subsetI1) =>
% 131.89/22.84 (((eqimpsubset2) =>
% 131.89/22.84 (((eqimpsubset1) =>
% 131.89/22.84 (((subsetI2) =>
% 131.89/22.84 (((emptysetsubset) =>
% 131.89/22.84 (((subsetE) =>
% 131.89/22.84 (((subsetE2) =>
% 131.89/22.84 (((notsubsetI) =>
% 131.89/22.84 ((
% 131.89/22.84 (notequalI1) =>
% 131.89/22.84 ((
% 131.89/22.84 (notequalI2) =>
% 131.89/22.84 ((
% 131.89/22.84 (subsetRefl) =>
% 131.89/22.84 ((
% 131.89/22.84 (subsetTrans) =>
% 131.89/22.84 ((
% 131.89/22.84 (setadjoinSub) =>
% 131.89/22.84 ((
% 131.89/22.84 (setadjoinSub2) =>
% 131.89/22.84 ((
% 131.89/22.84 (subset2powerset) =>
% 131.89/22.84 ((
% 131.89/22.84 (setextsub) =>
% 131.89/22.84 ((
% 131.89/22.84 (subsetemptysetimpeq) =>
% 131.89/22.84 ((
% 131.89/22.84 (powersetI1) =>
% 131.89/22.84 ((
% 131.89/22.84 (powersetE1) =>
% 131.89/22.84 ((
% 131.89/22.84 (inPowerset) =>
% 131.89/22.84 ((
% 131.89/22.84 (powersetsubset) =>
% 131.89/22.84 ((
% 131.89/22.84 (sepInPowerset) =>
% 131.89/22.84 ((
% 131.89/22.84 (sepSubset) =>
% 131.89/22.84 ((
% 131.89/22.84 (binunionIL) =>
% 131.89/22.84 ((
% 131.89/22.84 (upairset2IR) =>
% 131.89/22.84 ((
% 131.89/22.84 (binunionIR) =>
% 131.89/22.84 ((
% 131.89/22.84 (binunionEcases) =>
% 131.89/22.84 ((
% 131.89/22.84 (binunionE) =>
% 131.89/22.84 ((
% 131.89/22.84 (binunionLsub) =>
% 131.89/22.84 ((
% 131.89/22.84 (binunionRsub) =>
% 131.89/22.84 ((
% 131.89/22.84 (binintersectI) =>
% 131.89/22.84 ((
% 131.89/22.84 (binintersectSubset5) =>
% 131.89/22.84 ((
% 131.89/22.84 (binintersectEL) =>
% 131.89/22.84 ((
% 131.89/22.84 (binintersectLsub) =>
% 131.89/22.84 ((
% 131.89/22.84 (binintersectSubset2) =>
% 131.89/22.84 ((
% 131.89/22.84 (binintersectSubset3) =>
% 131.89/22.84 ((
% 131.89/22.84 (binintersectER) =>
% 131.89/22.84 ((
% 131.89/22.84 (disjointsetsI1) =>
% 131.89/22.84 ((
% 131.89/22.84 (binintersectRsub) =>
% 131.89/22.84 ((
% 131.89/22.84 (binintersectSubset4) =>
% 131.89/22.84 ((
% 131.89/22.84 (binintersectSubset1) =>
% 131.89/22.84 ((
% 131.89/22.84 (bs114d) =>
% 131.89/22.84 ((
% 131.89/22.84 (setminusI) =>
% 131.89/22.84 ((
% 131.89/22.84 (setminusEL) =>
% 131.89/22.84 ((
% 131.89/22.84 (setminusER) =>
% 131.89/22.84 ((
% 131.89/22.84 (setminusSubset2) =>
% 131.89/22.84 ((
% 131.89/22.84 (setminusERneg) =>
% 131.89/22.84 ((
% 131.89/22.84 (setminusELneg) =>
% 131.89/22.84 ((
% 131.89/22.84 (setminusILneg) =>
% 131.89/22.84 ((
% 131.89/22.84 (setminusIRneg) =>
% 131.89/22.84 ((
% 131.89/22.84 (setminusLsub) =>
% 131.89/22.84 ((
% 131.89/22.84 (setminusSubset1) =>
% 131.89/22.84 ((
% 131.89/22.84 (symdiffE) =>
% 131.89/22.84 ((
% 131.89/22.84 (symdiffI1) =>
% 131.89/22.84 ((
% 131.89/22.84 (symdiffI2) =>
% 131.89/22.84 ((
% 131.89/22.84 (symdiffIneg1) =>
% 131.89/22.84 ((
% 131.89/22.84 (symdiffIneg2) =>
% 131.89/22.84 ((
% 131.89/22.84 (secondinupair) =>
% 131.89/22.84 ((
% 131.89/22.84 (setukpairIL) =>
% 131.89/22.84 ((
% 131.89/22.84 (setukpairIR) =>
% 131.89/22.84 ((
% 131.89/22.84 (kpairiskpair) =>
% 131.89/22.84 ((
% 131.89/22.84 (kpairp) =>
% 131.89/22.84 ((
% 131.89/22.84 (singletonsubset) =>
% 131.89/22.84 ((
% 131.89/22.84 (singletoninpowerset) =>
% 131.89/22.84 ((
% 131.89/22.84 (singletoninpowunion) =>
% 131.89/22.84 ((
% 131.89/22.84 (upairset2E) =>
% 131.89/22.84 ((
% 131.89/22.84 (upairsubunion) =>
% 131.89/22.84 ((
% 131.89/22.84 (upairinpowunion) =>
% 131.89/22.84 ((
% 131.89/22.84 (ubforcartprodlem1) =>
% 131.89/22.84 ((
% 131.89/22.84 (ubforcartprodlem2) =>
% 131.89/22.84 ((
% 131.89/22.84 (ubforcartprodlem3) =>
% 131.89/22.84 ((
% 131.89/22.84 (cartprodpairin) =>
% 131.89/22.84 ((
% 131.89/22.84 (cartprodmempair1) =>
% 131.89/22.84 ((
% 131.89/22.84 (cartprodmempair) =>
% 131.89/22.84 ((
% 131.89/22.84 (setunionE2) =>
% 131.89/22.84 ((
% 131.89/22.84 (setunionsingleton1) =>
% 131.89/22.84 ((
% 131.89/22.84 (setunionsingleton2) =>
% 131.89/22.84 ((
% 131.89/22.84 (setunionsingleton) =>
% 131.89/22.84 ((
% 131.89/22.84 (singletonprop) =>
% 131.89/22.84 ((
% 131.89/22.84 (ex1E1) =>
% 131.89/22.84 ((
% 131.89/22.84 (ex1I) =>
% 131.89/22.84 ((
% 131.89/22.84 (ex1I2) =>
% 131.89/22.84 ((
% 131.89/22.84 (singletonsuniq) =>
% 131.89/22.84 ((
% 131.89/22.84 (setukpairinjL1) =>
% 131.89/22.84 ((
% 131.89/22.84 (kfstsingleton) =>
% 131.89/22.84 ((
% 131.89/22.84 (theprop) =>
% 131.89/22.84 ((
% 131.89/22.84 (kfstpairEq) =>
% 131.89/22.84 ((
% 131.89/22.84 (cartprodfstin) =>
% 131.89/22.84 ((
% 131.89/22.84 (setukpairinjL2) =>
% 131.89/22.84 ((
% 131.89/22.84 (setukpairinjL) =>
% 131.89/22.84 ((
% 131.89/22.84 (setukpairinjR11) =>
% 131.89/22.84 ((
% 131.89/22.84 (setukpairinjR12) =>
% 131.89/22.84 ((
% 131.89/22.84 (setukpairinjR1) =>
% 131.89/22.84 ((
% 131.89/22.84 (upairequniteq) =>
% 131.89/22.84 ((
% 131.89/22.84 (setukpairinjR2) =>
% 131.89/22.84 ((
% 131.89/22.84 (setukpairinjR) =>
% 131.89/22.84 ((
% 131.89/22.84 (ksndsingleton) =>
% 131.89/22.84 ((
% 131.89/22.84 (ksndpairEq) =>
% 131.89/22.84 ((
% 131.89/22.84 (kpairsurjEq) =>
% 131.89/22.84 ((
% 131.89/22.84 (cartprodsndin) =>
% 131.89/22.84 ((
% 131.89/22.84 (cartprodpairmemEL) =>
% 131.89/22.84 ((
% 131.89/22.84 (cartprodpairmemER) =>
% 131.89/22.84 ((
% 131.89/22.84 (cartprodmempaircEq) =>
% 131.89/22.84 ((
% 131.89/22.84 (cartprodfstpairEq) =>
% 131.89/22.84 ((
% 131.89/22.84 (cartprodsndpairEq) =>
% 131.89/22.84 ((
% 131.89/22.84 (cartprodpairsurjEq) =>
% 131.89/22.84 ((
% 131.89/22.84 (dpsetconstrI) =>
% 131.89/22.84 ((
% 131.89/22.84 (dpsetconstrSub) =>
% 131.89/22.84 ((
% 131.89/22.84 (setOfPairsIsBReln) =>
% 131.89/22.84 ((
% 131.89/22.84 (dpsetconstrERa) =>
% 131.89/22.84 ((
% 131.89/22.84 (dpsetconstrEL1) =>
% 131.89/22.84 ((
% 131.89/22.84 (dpsetconstrEL2) =>
% 131.89/22.84 ((
% 131.89/22.84 (dpsetconstrER) =>
% 131.89/22.84 ((
% 131.89/22.84 (funcImageSingleton) =>
% 131.89/22.84 ((
% 131.89/22.84 (apProp) =>
% 131.89/22.84 ((
% 131.89/22.84 (app) =>
% 131.89/22.84 ((
% 131.89/22.84 (infuncsetfunc) =>
% 131.89/22.84 ((
% 131.89/22.84 (ap2p) =>
% 131.89/22.84 ((
% 131.89/22.84 (funcinfuncset) =>
% 131.89/22.84 ((
% 131.89/22.84 (lamProp) =>
% 131.89/22.84 ((
% 131.89/22.84 (lamp) =>
% 131.89/22.84 ((
% 131.89/22.84 (lam2p) =>
% 131.89/22.84 ((
% 131.89/22.84 (brelnall1) =>
% 131.89/22.84 ((
% 131.89/22.84 (brelnall2) =>
% 131.89/22.84 ((
% 131.89/22.84 (ex1E2) =>
% 131.89/22.84 ((
% 131.89/22.84 (funcGraphProp1) =>
% 131.89/22.84 ((
% 131.89/22.84 (funcGraphProp3) =>
% 131.89/22.84 ((
% 131.89/22.84 (funcGraphProp2) =>
% 131.89/22.84 ((
% 131.89/22.84 (funcextLem) =>
% 131.89/22.84 ((
% 131.89/22.84 (funcGraphProp4) =>
% 131.89/22.84 ((
% 131.89/22.84 (subbreln) =>
% 131.89/22.84 ((
% 131.89/22.84 (eqbreln) =>
% 131.89/22.84 ((
% 131.89/22.84 (funcext) =>
% 131.89/22.84 ((
% 131.89/22.84 (funcext2) =>
% 131.89/22.84 ((
% 131.89/22.84 (ap2apEq1) =>
% 131.89/22.84 ((
% 131.89/22.84 (ap2apEq2) =>
% 131.89/22.84 ((
% 131.89/22.84 (beta1) =>
% 131.89/22.84 ((
% 131.89/22.84 (eta1) =>
% 131.89/22.84 ((
% 131.89/22.84 (lam2lamEq) =>
% 131.89/22.84 ((
% 131.89/22.84 (beta2) =>
% 131.89/22.84 ((
% 131.89/22.84 (eta2) =>
% 131.89/22.84 ((
% 131.89/22.84 (iffalseProp1) =>
% 131.89/22.84 ((
% 131.89/22.84 (iffalseProp2) =>
% 131.89/22.84 ((
% 131.89/22.84 (iftrueProp1) =>
% 131.89/22.84 ((
% 131.89/22.84 (iftrueProp2) =>
% 131.89/22.84 ((
% 131.89/22.84 (ifSingleton) =>
% 131.89/22.84 ((
% 131.89/22.84 (ifp) =>
% 131.89/22.84 ((
% 131.89/22.84 (theeq) =>
% 131.89/22.84 ((
% 131.89/22.84 (iftrue) =>
% 131.89/22.84 ((
% 131.89/22.84 (iffalse) =>
% 131.89/22.84 ((
% 131.89/22.84 (iftrueorfalse) =>
% 131.89/22.84 ((
% 131.89/22.84 (binintersectT_lem) =>
% 131.89/22.84 ((
% 131.89/22.84 (binunionT_lem) =>
% 131.89/22.84 ((
% 131.89/22.84 (powersetT_lem) =>
% 131.89/22.84 ((
% 131.89/22.84 (setminusT_lem) =>
% 131.89/22.84 ((
% 131.89/22.84 (complementT_lem) =>
% 131.89/22.84 ((
% 131.89/22.84 (setextT) =>
% 131.89/22.84 ((
% 131.89/22.84 (subsetTI) =>
% 131.89/22.84 ((
% 131.89/22.84 (powersetTI1) =>
% 131.89/22.84 ((
% 131.89/22.84 (powersetTE1) =>
% 131.89/22.84 ((
% 131.89/22.84 (complementTI1) =>
% 131.89/22.84 ((
% 131.89/22.84 (complementTE1) =>
% 131.89/22.84 ((
% 131.89/22.84 (binintersectTELcontra) =>
% 131.89/22.84 ((
% 131.89/22.84 (binintersectTERcontra) =>
% 131.89/22.84 ((
% 131.89/22.84 (contrasubsetT) =>
% 131.89/22.84 ((
% 131.89/22.84 (contrasubsetT1) =>
% 131.89/22.84 ((
% 131.89/22.84 (contrasubsetT2) =>
% 131.89/22.84 ((
% 131.89/22.84 (contrasubsetT3) =>
% 131.89/22.84 ((
% 131.89/22.84 (doubleComplementI1) =>
% 131.89/22.84 ((
% 131.89/22.84 (doubleComplementE1) =>
% 131.89/22.84 ((
% 131.89/22.84 (doubleComplementSub1) =>
% 131.89/22.84 ((
% 131.89/22.84 (doubleComplementSub2) =>
% 131.89/22.84 ((
% 131.89/22.84 (doubleComplementEq) =>
% 131.89/22.84 ((
% 131.89/22.84 (complementTnotintersectT) =>
% 131.89/22.84 ((
% 131.89/22.84 (complementImpComplementIntersect) =>
% 131.89/22.84 ((
% 131.89/22.84 (complementSubsetComplementIntersect) =>
% 131.89/22.84 ((
% 131.89/22.84 (complementInPowersetComplementIntersect) =>
% 131.89/22.84 ((
% 131.89/22.84 (contraSubsetComplement) =>
% 131.89/22.84 ((
% 131.89/22.84 (complementTcontraSubset) =>
% 131.89/22.84 ((
% 131.89/22.84 (binunionTILcontra) =>
% 131.89/22.84 ((
% 131.89/22.84 (binunionTIRcontra) =>
% 131.89/22.84 ((
% 131.89/22.84 (inIntersectImpInUnion) =>
% 131.89/22.84 ((
% 131.89/22.84 (inIntersectImpInUnion2) =>
% 131.89/22.84 ((
% 131.89/22.84 (inIntersectImpInIntersectUnions) =>
% 131.89/22.84 ((
% 131.89/22.84 (intersectInPowersetIntersectUnions) =>
% 131.89/22.84 ((
% 131.89/22.84 (inComplementUnionImpNotIn1) =>
% 131.89/22.84 ((
% 131.89/22.84 (inComplementUnionImpInComplement1) =>
% 131.89/22.84 ((
% 131.89/22.84 (binunionTE) =>
% 131.89/22.84 ((
% 131.89/22.84 (binunionTEcontra) =>
% 131.89/22.84 ((
% 131.89/22.84 (demorgan2a1) =>
% 131.89/22.84 ((
% 131.89/22.84 (complementUnionInPowersetComplement) =>
% 131.89/22.84 ((
% 131.89/22.84 (demorgan2a2) =>
% 131.89/22.84 ((
% 131.89/22.84 (demorgan1a) =>
% 131.89/22.84 ((
% 131.89/22.84 (demorgan1b) =>
% 131.89/22.84 ((
% 131.89/22.84 (demorgan1) =>
% 131.89/22.84 ((
% 131.89/22.84 (demorgan2a) =>
% 131.89/22.84 ((
% 131.89/22.84 (demorgan2b2) =>
% 131.89/22.84 ((
% 131.89/22.84 (demorgan2b) =>
% 131.89/22.84 ((
% 131.89/22.84 (demorgan2) =>
% 131.89/22.84 ((
% 131.89/22.84 (woz13rule0) =>
% 131.89/22.84 ((
% 131.89/22.84 (woz13rule1) =>
% 131.89/22.84 ((
% 131.89/22.84 (woz13rule2) =>
% 131.89/22.84 ((
% 131.89/22.84 (woz13rule3) =>
% 131.89/22.84 ((
% 131.89/22.84 (woz13rule4) =>
% 131.89/22.84 ((
% 131.89/22.84 (woz1_1) =>
% 131.89/22.84 ((
% 131.89/22.84 (woz1_2) =>
% 131.89/22.84 ((
% 131.89/22.84 (woz1_3) =>
% 131.89/22.84 ((
% 131.89/22.84 (woz1_4) =>
% 131.89/22.84 ((
% 131.89/22.84 (woz1_5) =>
% 131.89/22.84 ((
% 131.89/22.84 (breln1all2) =>
% 131.89/22.84 ((
% 131.89/22.84 (breln1SetBreln1) =>
% 131.89/22.84 ((
% 131.89/22.84 (choice2fnsingleton) =>
% 131.89/22.84 ((
% 131.89/22.84 (setOfPairsIsBReln1) =>
% 131.89/22.84 ((
% 131.89/22.84 (breln1all1) =>
% 131.89/22.84 ((
% 131.89/22.84 (subbreln1) =>
% 131.89/22.84 ((
% 131.89/22.84 (eqbreln1) =>
% 131.89/22.84 ((
% 131.89/22.84 (breln1invprop) =>
% 131.89/22.84 ((
% 131.89/22.84 (breln1invI) =>
% 131.89/22.84 ((
% 131.89/22.84 (breln1invE) =>
% 131.89/22.84 ((
% 131.89/22.84 (breln1compprop) =>
% 131.89/22.84 ((
% 131.89/22.84 (breln1compI) =>
% 131.89/22.84 ((
% 131.89/22.84 (breln1compE) =>
% 131.89/22.84 ((
% 131.89/22.84 (breln1compEex) =>
% 131.89/22.84 ((
% 131.89/22.84 (breln1unionprop) =>
% 131.89/22.84 ((
% 131.89/22.84 (breln1unionIL) =>
% 131.89/22.84 ((
% 131.89/22.84 (breln1unionIR) =>
% 131.89/22.84 ((
% 131.89/22.84 (breln1unionI) =>
% 131.89/22.84 ((
% 131.89/22.84 (breln1unionE) =>
% 131.89/22.84 ((
% 131.89/22.84 (breln1unionEcases) =>
% 131.89/22.84 ((
% 131.89/22.84 (breln1unionCommutes) =>
% 131.89/22.84 ((
% 131.89/22.84 (woz2Ex) =>
% 131.89/22.84 ((
% 131.89/22.84 (woz2W) =>
% 131.89/22.84 ((
% 131.89/22.84 (woz2A) =>
% 131.89/22.84 ((
% 131.89/22.84 (woz2B) =>
% 131.89/22.84 ((
% 131.89/22.84 (image1Ex) =>
% 131.89/22.84 ((
% 131.89/22.84 (image1Ex1) =>
% 131.89/22.84 ((
% 131.89/22.84 (image1Equiv) =>
% 131.89/22.84 ((
% 131.89/22.84 (image1E) =>
% 131.89/22.84 ((
% 131.89/22.84 (image1I) =>
% 131.89/22.84 ((
% 131.89/22.84 (injFuncInInjFuncSet) =>
% 131.89/22.84 ((
% 131.89/22.84 (injFuncSetFuncIn) =>
% 131.89/22.84 ((
% 131.89/22.84 (injFuncSetFuncInj) =>
% 131.89/22.84 ((
% 131.89/22.84 (surjFuncSetFuncIn) =>
% 131.89/22.84 ((
% 131.89/22.84 (surjFuncSetFuncSurj) =>
% 131.89/22.84 ((
% 131.89/22.84 (leftInvIsSurj) =>
% 131.89/22.84 ((
% 131.89/22.84 (surjCantorThm) =>
% 131.89/22.84 ((
% 131.89/22.84 (foundation2) =>
% 131.89/22.84 ((
% 131.89/22.84 (notinself) =>
% 131.89/22.84 ((
% 131.89/22.84 (notinself2) =>
% 131.89/22.84 ((
% 131.89/22.84 (omegaSp) =>
% 131.89/22.84 ((
% 131.89/22.84 (omegaSclos) =>
% 131.89/22.84 ((
% 131.89/22.84 (peano0notS) =>
% 131.89/22.84 ((
% 131.89/22.84 (peanoSinj) =>
% 131.89/22.84 ((
% 131.89/22.84 (transitivesetOp1) =>
% 131.89/22.84 ((
% 131.89/22.84 (binintTransitive) =>
% 131.89/22.84 ((
% 131.89/22.84 (transitivesetOp2) =>
% 131.89/22.84 ((
% 131.89/22.84 (setunionTransitive) =>
% 131.89/22.84 ((
% 131.89/22.84 (ordinalMinLem1) =>
% 131.89/22.84 ((
% 131.89/22.84 (ordinalTransSet) =>
% 131.89/22.84 ((
% 131.89/22.84 (ordinalTransSet1) =>
% 131.89/22.84 ((
% 131.89/22.84 (setunionOrdinalLem1) =>
% 131.89/22.84 (ordinal @
% 131.89/22.84 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 131.89/22.84 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl457])).
% 131.89/22.84 thf(zip_derived_cl471, plain,
% 131.89/22.84 (~ (((quantDeMorgan1) =>
% 131.89/22.84 (((quantDeMorgan2) =>
% 131.89/22.84 (((quantDeMorgan3) =>
% 131.89/22.84 (((quantDeMorgan4) =>
% 131.89/22.84 (((prop2setI) =>
% 131.89/22.84 (((prop2set2propI) =>
% 131.89/22.84 (((notdexE) =>
% 131.89/22.84 (((notdallE) =>
% 131.89/22.84 (((exuI1) =>
% 131.89/22.84 (((exuI3) =>
% 131.89/22.84 (((exuI2) =>
% 131.89/22.84 (((inCongP) =>
% 131.89/22.84 (((in__Cong) =>
% 131.89/22.84 (((exuE3u) =>
% 131.89/22.84 (((exu__Cong) =>
% 131.89/22.84 (((setadjoin__Cong) =>
% 131.89/22.84 (((powerset__Cong) =>
% 131.89/22.84 (((setunion__Cong) =>
% 131.89/22.84 (((exuEu) =>
% 131.89/22.84 (((descr__Cong) =>
% 131.89/22.84 (((dsetconstr__Cong) =>
% 131.89/22.84 (((subsetI1) =>
% 131.89/22.84 (((eqimpsubset2) =>
% 131.89/22.84 (((eqimpsubset1) =>
% 131.89/22.84 (((subsetI2) =>
% 131.89/22.84 (((emptysetsubset) =>
% 131.89/22.84 (((subsetE) =>
% 131.89/22.84 (((subsetE2) =>
% 131.89/22.84 (((notsubsetI) =>
% 131.89/22.84 (((notequalI1) =>
% 131.89/22.84 ((
% 131.89/22.84 (notequalI2) =>
% 131.89/22.84 ((
% 131.89/22.84 (subsetRefl) =>
% 131.89/22.84 ((
% 131.89/22.84 (subsetTrans) =>
% 131.89/22.84 ((
% 131.89/22.84 (setadjoinSub) =>
% 131.89/22.84 ((
% 131.89/22.84 (setadjoinSub2) =>
% 131.89/22.84 ((
% 131.89/22.84 (subset2powerset) =>
% 131.89/22.84 ((
% 131.89/22.84 (setextsub) =>
% 131.89/22.84 ((
% 131.89/22.84 (subsetemptysetimpeq) =>
% 131.89/22.84 ((
% 131.89/22.84 (powersetI1) =>
% 131.89/22.84 ((
% 131.89/22.84 (powersetE1) =>
% 131.89/22.84 ((
% 131.89/22.84 (inPowerset) =>
% 131.89/22.84 ((
% 131.89/22.84 (powersetsubset) =>
% 131.89/22.84 ((
% 131.89/22.84 (sepInPowerset) =>
% 131.89/22.84 ((
% 131.89/22.84 (sepSubset) =>
% 131.89/22.84 ((
% 131.89/22.84 (binunionIL) =>
% 131.89/22.84 ((
% 131.89/22.84 (upairset2IR) =>
% 131.89/22.84 ((
% 131.89/22.84 (binunionIR) =>
% 131.89/22.84 ((
% 131.89/22.84 (binunionEcases) =>
% 131.89/22.84 ((
% 131.89/22.84 (binunionE) =>
% 131.89/22.84 ((
% 131.89/22.84 (binunionLsub) =>
% 131.89/22.84 ((
% 131.89/22.84 (binunionRsub) =>
% 131.89/22.84 ((
% 131.89/22.84 (binintersectI) =>
% 131.89/22.84 ((
% 131.89/22.84 (binintersectSubset5) =>
% 131.89/22.84 ((
% 131.89/22.84 (binintersectEL) =>
% 131.89/22.84 ((
% 131.89/22.84 (binintersectLsub) =>
% 131.89/22.84 ((
% 131.89/22.84 (binintersectSubset2) =>
% 131.89/22.84 ((
% 131.89/22.84 (binintersectSubset3) =>
% 131.89/22.84 ((
% 131.89/22.84 (binintersectER) =>
% 131.89/22.84 ((
% 131.89/22.84 (disjointsetsI1) =>
% 131.89/22.84 ((
% 131.89/22.84 (binintersectRsub) =>
% 131.89/22.84 ((
% 131.89/22.84 (binintersectSubset4) =>
% 131.89/22.84 ((
% 131.89/22.84 (binintersectSubset1) =>
% 131.89/22.84 ((
% 131.89/22.84 (bs114d) =>
% 131.89/22.84 ((
% 131.89/22.84 (setminusI) =>
% 131.89/22.84 ((
% 131.89/22.84 (setminusEL) =>
% 131.89/22.84 ((
% 131.89/22.84 (setminusER) =>
% 131.89/22.84 ((
% 131.89/22.84 (setminusSubset2) =>
% 131.89/22.84 ((
% 131.89/22.84 (setminusERneg) =>
% 131.89/22.84 ((
% 131.89/22.84 (setminusELneg) =>
% 131.89/22.84 ((
% 131.89/22.84 (setminusILneg) =>
% 131.89/22.84 ((
% 131.89/22.84 (setminusIRneg) =>
% 131.89/22.84 ((
% 131.89/22.84 (setminusLsub) =>
% 131.89/22.84 ((
% 131.89/22.84 (setminusSubset1) =>
% 131.89/22.84 ((
% 131.89/22.84 (symdiffE) =>
% 131.89/22.84 ((
% 131.89/22.84 (symdiffI1) =>
% 131.89/22.84 ((
% 131.89/22.84 (symdiffI2) =>
% 131.89/22.84 ((
% 131.89/22.84 (symdiffIneg1) =>
% 131.89/22.84 ((
% 131.89/22.84 (symdiffIneg2) =>
% 131.89/22.84 ((
% 131.89/22.84 (secondinupair) =>
% 131.89/22.84 ((
% 131.89/22.84 (setukpairIL) =>
% 131.89/22.84 ((
% 131.89/22.84 (setukpairIR) =>
% 131.89/22.84 ((
% 131.89/22.84 (kpairiskpair) =>
% 131.89/22.84 ((
% 131.89/22.84 (kpairp) =>
% 131.89/22.84 ((
% 131.89/22.84 (singletonsubset) =>
% 131.89/22.84 ((
% 131.89/22.84 (singletoninpowerset) =>
% 131.89/22.84 ((
% 131.89/22.84 (singletoninpowunion) =>
% 131.89/22.84 ((
% 131.89/22.84 (upairset2E) =>
% 131.89/22.84 ((
% 131.89/22.84 (upairsubunion) =>
% 131.89/22.84 ((
% 131.89/22.84 (upairinpowunion) =>
% 131.89/22.84 ((
% 131.89/22.84 (ubforcartprodlem1) =>
% 131.89/22.84 ((
% 131.89/22.84 (ubforcartprodlem2) =>
% 131.89/22.84 ((
% 131.89/22.84 (ubforcartprodlem3) =>
% 131.89/22.84 ((
% 131.89/22.84 (cartprodpairin) =>
% 131.89/22.84 ((
% 131.89/22.84 (cartprodmempair1) =>
% 131.89/22.84 ((
% 131.89/22.84 (cartprodmempair) =>
% 131.89/22.84 ((
% 131.89/22.84 (setunionE2) =>
% 131.89/22.84 ((
% 131.89/22.84 (setunionsingleton1) =>
% 131.89/22.84 ((
% 131.89/22.84 (setunionsingleton2) =>
% 131.89/22.84 ((
% 131.89/22.84 (setunionsingleton) =>
% 131.89/22.84 ((
% 131.89/22.84 (singletonprop) =>
% 131.89/22.84 ((
% 131.89/22.84 (ex1E1) =>
% 131.89/22.84 ((
% 131.89/22.84 (ex1I) =>
% 131.89/22.84 ((
% 131.89/22.84 (ex1I2) =>
% 131.89/22.84 ((
% 131.89/22.84 (singletonsuniq) =>
% 131.89/22.84 ((
% 131.89/22.84 (setukpairinjL1) =>
% 131.89/22.84 ((
% 131.89/22.84 (kfstsingleton) =>
% 131.89/22.84 ((
% 131.89/22.84 (theprop) =>
% 131.89/22.84 ((
% 131.89/22.84 (kfstpairEq) =>
% 131.89/22.84 ((
% 131.89/22.84 (cartprodfstin) =>
% 131.89/22.84 ((
% 131.89/22.84 (setukpairinjL2) =>
% 131.89/22.84 ((
% 131.89/22.84 (setukpairinjL) =>
% 131.89/22.84 ((
% 131.89/22.84 (setukpairinjR11) =>
% 131.89/22.84 ((
% 131.89/22.84 (setukpairinjR12) =>
% 131.89/22.84 ((
% 131.89/22.84 (setukpairinjR1) =>
% 131.89/22.84 ((
% 131.89/22.84 (upairequniteq) =>
% 131.89/22.84 ((
% 131.89/22.84 (setukpairinjR2) =>
% 131.89/22.84 ((
% 131.89/22.84 (setukpairinjR) =>
% 131.89/22.84 ((
% 131.89/22.84 (ksndsingleton) =>
% 131.89/22.84 ((
% 131.89/22.84 (ksndpairEq) =>
% 131.89/22.84 ((
% 131.89/22.84 (kpairsurjEq) =>
% 131.89/22.84 ((
% 131.89/22.84 (cartprodsndin) =>
% 131.89/22.84 ((
% 131.89/22.84 (cartprodpairmemEL) =>
% 131.89/22.84 ((
% 131.89/22.84 (cartprodpairmemER) =>
% 131.89/22.84 ((
% 131.89/22.84 (cartprodmempaircEq) =>
% 131.89/22.84 ((
% 131.89/22.84 (cartprodfstpairEq) =>
% 131.89/22.84 ((
% 131.89/22.84 (cartprodsndpairEq) =>
% 131.89/22.84 ((
% 131.89/22.84 (cartprodpairsurjEq) =>
% 131.89/22.84 ((
% 131.89/22.84 (dpsetconstrI) =>
% 131.89/22.84 ((
% 131.89/22.84 (dpsetconstrSub) =>
% 131.89/22.84 ((
% 131.89/22.84 (setOfPairsIsBReln) =>
% 131.89/22.84 ((
% 131.89/22.84 (dpsetconstrERa) =>
% 131.89/22.84 ((
% 131.89/22.84 (dpsetconstrEL1) =>
% 131.89/22.84 ((
% 131.89/22.84 (dpsetconstrEL2) =>
% 131.89/22.84 ((
% 131.89/22.84 (dpsetconstrER) =>
% 131.89/22.84 ((
% 131.89/22.84 (funcImageSingleton) =>
% 131.89/22.84 ((
% 131.89/22.84 (apProp) =>
% 131.89/22.84 ((
% 131.89/22.84 (app) =>
% 131.89/22.84 ((
% 131.89/22.84 (infuncsetfunc) =>
% 131.89/22.84 ((
% 131.89/22.84 (ap2p) =>
% 131.89/22.84 ((
% 131.89/22.84 (funcinfuncset) =>
% 131.89/22.84 ((
% 131.89/22.84 (lamProp) =>
% 131.89/22.84 ((
% 131.89/22.84 (lamp) =>
% 131.89/22.84 ((
% 131.89/22.84 (lam2p) =>
% 131.89/22.84 ((
% 131.89/22.84 (brelnall1) =>
% 131.89/22.84 ((
% 131.89/22.84 (brelnall2) =>
% 131.89/22.84 ((
% 131.89/22.84 (ex1E2) =>
% 131.89/22.84 ((
% 131.89/22.84 (funcGraphProp1) =>
% 131.89/22.84 ((
% 131.89/22.84 (funcGraphProp3) =>
% 131.89/22.84 ((
% 131.89/22.84 (funcGraphProp2) =>
% 131.89/22.84 ((
% 131.89/22.84 (funcextLem) =>
% 131.89/22.84 ((
% 131.89/22.84 (funcGraphProp4) =>
% 131.89/22.84 ((
% 131.89/22.84 (subbreln) =>
% 131.89/22.84 ((
% 131.89/22.84 (eqbreln) =>
% 131.89/22.84 ((
% 131.89/22.84 (funcext) =>
% 131.89/22.84 ((
% 131.89/22.84 (funcext2) =>
% 131.89/22.84 ((
% 131.89/22.84 (ap2apEq1) =>
% 131.89/22.84 ((
% 131.89/22.84 (ap2apEq2) =>
% 131.89/22.84 ((
% 131.89/22.84 (beta1) =>
% 131.89/22.84 ((
% 131.89/22.84 (eta1) =>
% 131.89/22.84 ((
% 131.89/22.84 (lam2lamEq) =>
% 131.89/22.84 ((
% 131.89/22.84 (beta2) =>
% 131.89/22.84 ((
% 131.89/22.84 (eta2) =>
% 131.89/22.84 ((
% 131.89/22.84 (iffalseProp1) =>
% 131.89/22.84 ((
% 131.89/22.84 (iffalseProp2) =>
% 131.89/22.84 ((
% 131.89/22.84 (iftrueProp1) =>
% 131.89/22.84 ((
% 131.89/22.84 (iftrueProp2) =>
% 131.89/22.84 ((
% 131.89/22.84 (ifSingleton) =>
% 131.89/22.84 ((
% 131.89/22.84 (ifp) =>
% 131.89/22.84 ((
% 131.89/22.84 (theeq) =>
% 131.89/22.84 ((
% 131.89/22.84 (iftrue) =>
% 131.89/22.84 ((
% 131.89/22.84 (iffalse) =>
% 131.89/22.84 ((
% 131.89/22.84 (iftrueorfalse) =>
% 131.89/22.84 ((
% 131.89/22.84 (binintersectT_lem) =>
% 131.89/22.84 ((
% 131.89/22.84 (binunionT_lem) =>
% 131.89/22.84 ((
% 131.89/22.84 (powersetT_lem) =>
% 131.89/22.84 ((
% 131.89/22.84 (setminusT_lem) =>
% 131.89/22.84 ((
% 131.89/22.84 (complementT_lem) =>
% 131.89/22.84 ((
% 131.89/22.84 (setextT) =>
% 131.89/22.84 ((
% 131.89/22.84 (subsetTI) =>
% 131.89/22.84 ((
% 131.89/22.84 (powersetTI1) =>
% 131.89/22.84 ((
% 131.89/22.84 (powersetTE1) =>
% 131.89/22.84 ((
% 131.89/22.84 (complementTI1) =>
% 131.89/22.84 ((
% 131.89/22.84 (complementTE1) =>
% 131.89/22.84 ((
% 131.89/22.84 (binintersectTELcontra) =>
% 131.89/22.84 ((
% 131.89/22.84 (binintersectTERcontra) =>
% 131.89/22.84 ((
% 131.89/22.84 (contrasubsetT) =>
% 131.89/22.84 ((
% 131.89/22.84 (contrasubsetT1) =>
% 131.89/22.84 ((
% 131.89/22.84 (contrasubsetT2) =>
% 131.89/22.84 ((
% 131.89/22.84 (contrasubsetT3) =>
% 131.89/22.84 ((
% 131.89/22.84 (doubleComplementI1) =>
% 131.89/22.84 ((
% 131.89/22.84 (doubleComplementE1) =>
% 131.89/22.84 ((
% 131.89/22.84 (doubleComplementSub1) =>
% 131.89/22.84 ((
% 131.89/22.84 (doubleComplementSub2) =>
% 131.89/22.84 ((
% 131.89/22.84 (doubleComplementEq) =>
% 131.89/22.84 ((
% 131.89/22.84 (complementTnotintersectT) =>
% 131.89/22.84 ((
% 131.89/22.84 (complementImpComplementIntersect) =>
% 131.89/22.84 ((
% 131.89/22.84 (complementSubsetComplementIntersect) =>
% 131.89/22.84 ((
% 131.89/22.84 (complementInPowersetComplementIntersect) =>
% 131.89/22.84 ((
% 131.89/22.84 (contraSubsetComplement) =>
% 131.89/22.84 ((
% 131.89/22.84 (complementTcontraSubset) =>
% 131.89/22.84 ((
% 131.89/22.84 (binunionTILcontra) =>
% 131.89/22.84 ((
% 131.89/22.84 (binunionTIRcontra) =>
% 131.89/22.84 ((
% 131.89/22.84 (inIntersectImpInUnion) =>
% 131.89/22.84 ((
% 131.89/22.84 (inIntersectImpInUnion2) =>
% 131.89/22.84 ((
% 131.89/22.84 (inIntersectImpInIntersectUnions) =>
% 131.89/22.84 ((
% 131.89/22.84 (intersectInPowersetIntersectUnions) =>
% 131.89/22.84 ((
% 131.89/22.84 (inComplementUnionImpNotIn1) =>
% 131.89/22.84 ((
% 131.89/22.84 (inComplementUnionImpInComplement1) =>
% 131.89/22.84 ((
% 131.89/22.84 (binunionTE) =>
% 131.89/22.84 ((
% 131.89/22.84 (binunionTEcontra) =>
% 131.89/22.84 ((
% 131.89/22.84 (demorgan2a1) =>
% 131.89/22.84 ((
% 131.89/22.84 (complementUnionInPowersetComplement) =>
% 131.89/22.84 ((
% 131.89/22.84 (demorgan2a2) =>
% 131.89/22.84 ((
% 131.89/22.84 (demorgan1a) =>
% 131.89/22.84 ((
% 131.89/22.84 (demorgan1b) =>
% 131.89/22.84 ((
% 131.89/22.84 (demorgan1) =>
% 131.89/22.84 ((
% 131.89/22.84 (demorgan2a) =>
% 131.89/22.84 ((
% 131.89/22.84 (demorgan2b2) =>
% 131.89/22.84 ((
% 131.89/22.84 (demorgan2b) =>
% 131.89/22.84 ((
% 131.89/22.84 (demorgan2) =>
% 131.89/22.84 ((
% 131.89/22.84 (woz13rule0) =>
% 131.89/22.84 ((
% 131.89/22.84 (woz13rule1) =>
% 131.89/22.84 ((
% 131.89/22.84 (woz13rule2) =>
% 131.89/22.84 ((
% 131.89/22.84 (woz13rule3) =>
% 131.89/22.84 ((
% 131.89/22.84 (woz13rule4) =>
% 131.89/22.84 ((
% 131.89/22.84 (woz1_1) =>
% 131.89/22.84 ((
% 131.89/22.84 (woz1_2) =>
% 131.89/22.84 ((
% 131.89/22.84 (woz1_3) =>
% 131.89/22.84 ((
% 131.89/22.84 (woz1_4) =>
% 131.89/22.84 ((
% 131.89/22.84 (woz1_5) =>
% 131.89/22.84 ((
% 131.89/22.84 (breln1all2) =>
% 131.89/22.84 ((
% 131.89/22.84 (breln1SetBreln1) =>
% 131.89/22.84 ((
% 131.89/22.84 (choice2fnsingleton) =>
% 131.89/22.84 ((
% 131.89/22.84 (setOfPairsIsBReln1) =>
% 131.89/22.84 ((
% 131.89/22.84 (breln1all1) =>
% 131.89/22.84 ((
% 131.89/22.84 (subbreln1) =>
% 131.89/22.84 ((
% 131.89/22.84 (eqbreln1) =>
% 131.89/22.84 ((
% 131.89/22.84 (breln1invprop) =>
% 131.89/22.84 ((
% 131.89/22.84 (breln1invI) =>
% 131.89/22.84 ((
% 131.89/22.84 (breln1invE) =>
% 131.89/22.84 ((
% 131.89/22.84 (breln1compprop) =>
% 131.89/22.84 ((
% 131.89/22.84 (breln1compI) =>
% 131.89/22.84 ((
% 131.89/22.84 (breln1compE) =>
% 131.89/22.84 ((
% 131.89/22.84 (breln1compEex) =>
% 131.89/22.84 ((
% 131.89/22.84 (breln1unionprop) =>
% 131.89/22.84 ((
% 131.89/22.84 (breln1unionIL) =>
% 131.89/22.84 ((
% 131.89/22.84 (breln1unionIR) =>
% 131.89/22.84 ((
% 131.89/22.84 (breln1unionI) =>
% 131.89/22.84 ((
% 131.89/22.84 (breln1unionE) =>
% 131.89/22.84 ((
% 131.89/22.84 (breln1unionEcases) =>
% 131.89/22.84 ((
% 131.89/22.84 (breln1unionCommutes) =>
% 131.89/22.84 ((
% 131.89/22.84 (woz2Ex) =>
% 131.89/22.84 ((
% 131.89/22.84 (woz2W) =>
% 131.89/22.84 ((
% 131.89/22.84 (woz2A) =>
% 131.89/22.84 ((
% 131.89/22.84 (woz2B) =>
% 131.89/22.84 ((
% 131.89/22.84 (image1Ex) =>
% 131.89/22.84 ((
% 131.89/22.84 (image1Ex1) =>
% 131.89/22.84 ((
% 131.89/22.84 (image1Equiv) =>
% 131.89/22.84 ((
% 131.89/22.84 (image1E) =>
% 131.89/22.84 ((
% 131.89/22.84 (image1I) =>
% 131.89/22.84 ((
% 131.89/22.84 (injFuncInInjFuncSet) =>
% 131.89/22.84 ((
% 131.89/22.84 (injFuncSetFuncIn) =>
% 131.89/22.84 ((
% 131.89/22.84 (injFuncSetFuncInj) =>
% 131.89/22.84 ((
% 131.89/22.84 (surjFuncSetFuncIn) =>
% 131.89/22.84 ((
% 131.89/22.84 (surjFuncSetFuncSurj) =>
% 131.89/22.84 ((
% 131.89/22.84 (leftInvIsSurj) =>
% 131.89/22.84 ((
% 131.89/22.84 (surjCantorThm) =>
% 131.89/22.84 ((
% 131.89/22.84 (foundation2) =>
% 131.89/22.84 ((
% 131.89/22.84 (notinself) =>
% 131.89/22.84 ((
% 131.89/22.84 (notinself2) =>
% 131.89/22.84 ((
% 131.89/22.84 (omegaSp) =>
% 131.89/22.84 ((
% 131.89/22.84 (omegaSclos) =>
% 131.89/22.84 ((
% 131.89/22.84 (peano0notS) =>
% 131.89/22.84 ((
% 131.89/22.84 (peanoSinj) =>
% 131.89/22.84 ((
% 131.89/22.84 (transitivesetOp1) =>
% 131.89/22.84 ((
% 131.89/22.84 (binintTransitive) =>
% 131.89/22.84 ((
% 131.89/22.84 (transitivesetOp2) =>
% 131.89/22.84 ((
% 131.89/22.84 (setunionTransitive) =>
% 131.89/22.84 ((
% 131.89/22.84 (ordinalMinLem1) =>
% 131.89/22.84 ((
% 131.89/22.84 (ordinalTransSet) =>
% 131.89/22.84 ((
% 131.89/22.84 (ordinalTransSet1) =>
% 131.89/22.84 ((
% 131.89/22.84 (setunionOrdinalLem1) =>
% 131.89/22.84 (ordinal @
% 131.89/22.84 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 131.89/22.84 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl465])).
% 131.89/22.84 thf(zip_derived_cl478, plain,
% 131.89/22.84 (~ (((quantDeMorgan2) =>
% 131.89/22.84 (((quantDeMorgan3) =>
% 131.89/22.84 (((quantDeMorgan4) =>
% 131.89/22.84 (((prop2setI) =>
% 131.89/22.84 (((prop2set2propI) =>
% 131.89/22.84 (((notdexE) =>
% 131.89/22.84 (((notdallE) =>
% 131.89/22.84 (((exuI1) =>
% 131.89/22.84 (((exuI3) =>
% 131.89/22.84 (((exuI2) =>
% 131.89/22.84 (((inCongP) =>
% 131.89/22.84 (((in__Cong) =>
% 131.89/22.84 (((exuE3u) =>
% 131.89/22.84 (((exu__Cong) =>
% 131.89/22.84 (((setadjoin__Cong) =>
% 131.89/22.84 (((powerset__Cong) =>
% 131.89/22.84 (((setunion__Cong) =>
% 131.89/22.84 (((exuEu) =>
% 131.89/22.84 (((descr__Cong) =>
% 131.89/22.84 (((dsetconstr__Cong) =>
% 131.89/22.84 (((subsetI1) =>
% 131.89/22.84 (((eqimpsubset2) =>
% 131.89/22.84 (((eqimpsubset1) =>
% 131.89/22.84 (((subsetI2) =>
% 131.89/22.84 (((emptysetsubset) =>
% 131.89/22.84 (((subsetE) =>
% 131.89/22.84 (((subsetE2) =>
% 131.89/22.84 (((notsubsetI) =>
% 131.89/22.84 (((notequalI1) =>
% 131.89/22.84 (((notequalI2) =>
% 131.89/22.84 ((
% 131.89/22.84 (subsetRefl) =>
% 131.89/22.84 ((
% 131.89/22.84 (subsetTrans) =>
% 131.89/22.84 ((
% 131.89/22.84 (setadjoinSub) =>
% 131.89/22.84 ((
% 131.89/22.84 (setadjoinSub2) =>
% 131.89/22.84 ((
% 131.89/22.84 (subset2powerset) =>
% 131.89/22.84 ((
% 131.89/22.84 (setextsub) =>
% 131.89/22.84 ((
% 131.89/22.84 (subsetemptysetimpeq) =>
% 131.89/22.84 ((
% 131.89/22.84 (powersetI1) =>
% 131.89/22.84 ((
% 131.89/22.84 (powersetE1) =>
% 131.89/22.84 ((
% 131.89/22.84 (inPowerset) =>
% 131.89/22.84 ((
% 131.89/22.84 (powersetsubset) =>
% 131.89/22.84 ((
% 131.89/22.84 (sepInPowerset) =>
% 131.89/22.84 ((
% 131.89/22.84 (sepSubset) =>
% 131.89/22.84 ((
% 131.89/22.84 (binunionIL) =>
% 131.89/22.84 ((
% 131.89/22.84 (upairset2IR) =>
% 131.89/22.84 ((
% 131.89/22.84 (binunionIR) =>
% 131.89/22.84 ((
% 131.89/22.84 (binunionEcases) =>
% 131.89/22.84 ((
% 131.89/22.84 (binunionE) =>
% 131.89/22.84 ((
% 131.89/22.84 (binunionLsub) =>
% 131.89/22.84 ((
% 131.89/22.84 (binunionRsub) =>
% 131.89/22.84 ((
% 131.89/22.84 (binintersectI) =>
% 131.89/22.84 ((
% 131.89/22.84 (binintersectSubset5) =>
% 131.89/22.84 ((
% 131.89/22.84 (binintersectEL) =>
% 131.89/22.84 ((
% 131.89/22.84 (binintersectLsub) =>
% 131.89/22.84 ((
% 131.89/22.84 (binintersectSubset2) =>
% 131.89/22.84 ((
% 131.89/22.84 (binintersectSubset3) =>
% 131.89/22.84 ((
% 131.89/22.84 (binintersectER) =>
% 131.89/22.84 ((
% 131.89/22.84 (disjointsetsI1) =>
% 131.89/22.84 ((
% 131.89/22.84 (binintersectRsub) =>
% 131.89/22.84 ((
% 131.89/22.84 (binintersectSubset4) =>
% 131.89/22.84 ((
% 131.89/22.84 (binintersectSubset1) =>
% 131.89/22.84 ((
% 131.89/22.84 (bs114d) =>
% 131.89/22.84 ((
% 131.89/22.84 (setminusI) =>
% 131.89/22.84 ((
% 131.89/22.84 (setminusEL) =>
% 131.89/22.84 ((
% 131.89/22.84 (setminusER) =>
% 131.89/22.84 ((
% 131.89/22.84 (setminusSubset2) =>
% 131.89/22.84 ((
% 131.89/22.84 (setminusERneg) =>
% 131.89/22.84 ((
% 131.89/22.84 (setminusELneg) =>
% 131.89/22.84 ((
% 131.89/22.84 (setminusILneg) =>
% 131.89/22.84 ((
% 131.89/22.84 (setminusIRneg) =>
% 131.89/22.84 ((
% 131.89/22.84 (setminusLsub) =>
% 131.89/22.84 ((
% 131.89/22.84 (setminusSubset1) =>
% 131.89/22.84 ((
% 131.89/22.84 (symdiffE) =>
% 131.89/22.84 ((
% 131.89/22.84 (symdiffI1) =>
% 131.89/22.84 ((
% 131.89/22.84 (symdiffI2) =>
% 131.89/22.84 ((
% 131.89/22.84 (symdiffIneg1) =>
% 131.89/22.84 ((
% 131.89/22.84 (symdiffIneg2) =>
% 131.89/22.84 ((
% 131.89/22.84 (secondinupair) =>
% 131.89/22.84 ((
% 131.89/22.84 (setukpairIL) =>
% 131.89/22.84 ((
% 131.89/22.84 (setukpairIR) =>
% 131.89/22.84 ((
% 131.89/22.84 (kpairiskpair) =>
% 131.89/22.84 ((
% 131.89/22.84 (kpairp) =>
% 131.89/22.84 ((
% 131.89/22.84 (singletonsubset) =>
% 131.89/22.84 ((
% 131.89/22.84 (singletoninpowerset) =>
% 131.89/22.84 ((
% 131.89/22.84 (singletoninpowunion) =>
% 131.89/22.84 ((
% 131.89/22.84 (upairset2E) =>
% 131.89/22.84 ((
% 131.89/22.84 (upairsubunion) =>
% 131.89/22.84 ((
% 131.89/22.84 (upairinpowunion) =>
% 131.89/22.84 ((
% 131.89/22.84 (ubforcartprodlem1) =>
% 131.89/22.84 ((
% 131.89/22.84 (ubforcartprodlem2) =>
% 131.89/22.84 ((
% 131.89/22.84 (ubforcartprodlem3) =>
% 131.89/22.84 ((
% 131.89/22.84 (cartprodpairin) =>
% 131.89/22.84 ((
% 131.89/22.84 (cartprodmempair1) =>
% 131.89/22.84 ((
% 131.89/22.84 (cartprodmempair) =>
% 131.89/22.84 ((
% 131.89/22.84 (setunionE2) =>
% 131.89/22.84 ((
% 131.89/22.84 (setunionsingleton1) =>
% 131.89/22.84 ((
% 131.89/22.84 (setunionsingleton2) =>
% 131.89/22.84 ((
% 131.89/22.84 (setunionsingleton) =>
% 131.89/22.84 ((
% 131.89/22.84 (singletonprop) =>
% 131.89/22.84 ((
% 131.89/22.84 (ex1E1) =>
% 131.89/22.84 ((
% 131.89/22.84 (ex1I) =>
% 131.89/22.84 ((
% 131.89/22.84 (ex1I2) =>
% 131.89/22.84 ((
% 131.89/22.84 (singletonsuniq) =>
% 131.89/22.84 ((
% 131.89/22.84 (setukpairinjL1) =>
% 131.89/22.84 ((
% 131.89/22.84 (kfstsingleton) =>
% 131.89/22.84 ((
% 131.89/22.84 (theprop) =>
% 131.89/22.84 ((
% 131.89/22.84 (kfstpairEq) =>
% 131.89/22.84 ((
% 131.89/22.84 (cartprodfstin) =>
% 131.89/22.84 ((
% 131.89/22.84 (setukpairinjL2) =>
% 131.89/22.84 ((
% 131.89/22.84 (setukpairinjL) =>
% 131.89/22.84 ((
% 131.89/22.84 (setukpairinjR11) =>
% 131.89/22.84 ((
% 131.89/22.84 (setukpairinjR12) =>
% 131.89/22.84 ((
% 131.89/22.84 (setukpairinjR1) =>
% 131.89/22.84 ((
% 131.89/22.84 (upairequniteq) =>
% 131.89/22.84 ((
% 131.89/22.84 (setukpairinjR2) =>
% 131.89/22.84 ((
% 131.89/22.84 (setukpairinjR) =>
% 131.89/22.84 ((
% 131.89/22.84 (ksndsingleton) =>
% 131.89/22.84 ((
% 131.89/22.84 (ksndpairEq) =>
% 131.89/22.84 ((
% 131.89/22.84 (kpairsurjEq) =>
% 131.89/22.84 ((
% 131.89/22.84 (cartprodsndin) =>
% 131.89/22.84 ((
% 131.89/22.84 (cartprodpairmemEL) =>
% 131.89/22.84 ((
% 131.89/22.84 (cartprodpairmemER) =>
% 131.89/22.84 ((
% 131.89/22.84 (cartprodmempaircEq) =>
% 131.89/22.84 ((
% 131.89/22.84 (cartprodfstpairEq) =>
% 131.89/22.84 ((
% 131.89/22.84 (cartprodsndpairEq) =>
% 131.89/22.84 ((
% 131.89/22.84 (cartprodpairsurjEq) =>
% 131.89/22.84 ((
% 131.89/22.84 (dpsetconstrI) =>
% 131.89/22.84 ((
% 131.89/22.84 (dpsetconstrSub) =>
% 131.89/22.84 ((
% 131.89/22.84 (setOfPairsIsBReln) =>
% 131.89/22.84 ((
% 131.89/22.84 (dpsetconstrERa) =>
% 131.89/22.84 ((
% 131.89/22.84 (dpsetconstrEL1) =>
% 131.89/22.84 ((
% 131.89/22.84 (dpsetconstrEL2) =>
% 131.89/22.84 ((
% 131.89/22.84 (dpsetconstrER) =>
% 131.89/22.84 ((
% 131.89/22.84 (funcImageSingleton) =>
% 131.89/22.84 ((
% 131.89/22.84 (apProp) =>
% 131.89/22.84 ((
% 131.89/22.84 (app) =>
% 131.89/22.84 ((
% 131.89/22.84 (infuncsetfunc) =>
% 131.89/22.84 ((
% 131.89/22.84 (ap2p) =>
% 131.89/22.84 ((
% 131.89/22.84 (funcinfuncset) =>
% 131.89/22.84 ((
% 131.89/22.84 (lamProp) =>
% 131.89/22.84 ((
% 131.89/22.84 (lamp) =>
% 131.89/22.84 ((
% 131.89/22.84 (lam2p) =>
% 131.89/22.84 ((
% 131.89/22.84 (brelnall1) =>
% 131.89/22.84 ((
% 131.89/22.84 (brelnall2) =>
% 131.89/22.84 ((
% 131.89/22.84 (ex1E2) =>
% 131.89/22.84 ((
% 131.89/22.84 (funcGraphProp1) =>
% 131.89/22.84 ((
% 131.89/22.84 (funcGraphProp3) =>
% 131.89/22.84 ((
% 131.89/22.84 (funcGraphProp2) =>
% 131.89/22.84 ((
% 131.89/22.84 (funcextLem) =>
% 131.89/22.84 ((
% 131.89/22.84 (funcGraphProp4) =>
% 131.89/22.84 ((
% 131.89/22.84 (subbreln) =>
% 131.89/22.84 ((
% 131.89/22.84 (eqbreln) =>
% 131.89/22.84 ((
% 131.89/22.84 (funcext) =>
% 131.89/22.84 ((
% 131.89/22.84 (funcext2) =>
% 131.89/22.84 ((
% 131.89/22.84 (ap2apEq1) =>
% 131.89/22.84 ((
% 131.89/22.84 (ap2apEq2) =>
% 131.89/22.84 ((
% 131.89/22.84 (beta1) =>
% 131.89/22.84 ((
% 131.89/22.84 (eta1) =>
% 131.89/22.84 ((
% 131.89/22.84 (lam2lamEq) =>
% 131.89/22.84 ((
% 131.89/22.84 (beta2) =>
% 131.89/22.84 ((
% 131.89/22.84 (eta2) =>
% 131.89/22.84 ((
% 131.89/22.84 (iffalseProp1) =>
% 131.89/22.84 ((
% 131.89/22.84 (iffalseProp2) =>
% 131.89/22.84 ((
% 131.89/22.84 (iftrueProp1) =>
% 131.89/22.84 ((
% 131.89/22.84 (iftrueProp2) =>
% 131.89/22.84 ((
% 131.89/22.84 (ifSingleton) =>
% 131.89/22.84 ((
% 131.89/22.84 (ifp) =>
% 131.89/22.84 ((
% 131.89/22.84 (theeq) =>
% 131.89/22.84 ((
% 131.89/22.84 (iftrue) =>
% 131.89/22.84 ((
% 131.89/22.84 (iffalse) =>
% 131.89/22.84 ((
% 131.89/22.84 (iftrueorfalse) =>
% 131.89/22.84 ((
% 131.89/22.84 (binintersectT_lem) =>
% 131.89/22.84 ((
% 131.89/22.84 (binunionT_lem) =>
% 131.89/22.84 ((
% 131.89/22.84 (powersetT_lem) =>
% 131.89/22.84 ((
% 131.89/22.84 (setminusT_lem) =>
% 131.89/22.84 ((
% 131.89/22.84 (complementT_lem) =>
% 131.89/22.84 ((
% 131.89/22.84 (setextT) =>
% 131.89/22.84 ((
% 131.89/22.84 (subsetTI) =>
% 131.89/22.84 ((
% 131.89/22.84 (powersetTI1) =>
% 131.89/22.84 ((
% 131.89/22.84 (powersetTE1) =>
% 131.89/22.84 ((
% 131.89/22.84 (complementTI1) =>
% 131.89/22.84 ((
% 131.89/22.84 (complementTE1) =>
% 131.89/22.84 ((
% 131.89/22.84 (binintersectTELcontra) =>
% 131.89/22.84 ((
% 131.89/22.84 (binintersectTERcontra) =>
% 131.89/22.84 ((
% 131.89/22.84 (contrasubsetT) =>
% 131.89/22.84 ((
% 131.89/22.84 (contrasubsetT1) =>
% 131.89/22.84 ((
% 131.89/22.84 (contrasubsetT2) =>
% 131.89/22.84 ((
% 131.89/22.84 (contrasubsetT3) =>
% 131.89/22.84 ((
% 131.89/22.84 (doubleComplementI1) =>
% 131.89/22.84 ((
% 131.89/22.84 (doubleComplementE1) =>
% 131.89/22.84 ((
% 131.89/22.84 (doubleComplementSub1) =>
% 131.89/22.84 ((
% 131.89/22.84 (doubleComplementSub2) =>
% 131.89/22.84 ((
% 131.89/22.84 (doubleComplementEq) =>
% 131.89/22.84 ((
% 131.89/22.84 (complementTnotintersectT) =>
% 131.89/22.84 ((
% 131.89/22.84 (complementImpComplementIntersect) =>
% 131.89/22.84 ((
% 131.89/22.84 (complementSubsetComplementIntersect) =>
% 131.89/22.84 ((
% 131.89/22.84 (complementInPowersetComplementIntersect) =>
% 131.89/22.84 ((
% 131.89/22.84 (contraSubsetComplement) =>
% 131.89/22.84 ((
% 131.89/22.84 (complementTcontraSubset) =>
% 131.89/22.84 ((
% 131.89/22.84 (binunionTILcontra) =>
% 131.89/22.84 ((
% 131.89/22.84 (binunionTIRcontra) =>
% 131.89/22.84 ((
% 131.89/22.84 (inIntersectImpInUnion) =>
% 131.89/22.84 ((
% 131.89/22.84 (inIntersectImpInUnion2) =>
% 131.89/22.84 ((
% 131.89/22.84 (inIntersectImpInIntersectUnions) =>
% 131.89/22.84 ((
% 131.89/22.84 (intersectInPowersetIntersectUnions) =>
% 131.89/22.84 ((
% 131.89/22.84 (inComplementUnionImpNotIn1) =>
% 131.89/22.84 ((
% 131.89/22.84 (inComplementUnionImpInComplement1) =>
% 131.89/22.84 ((
% 131.89/22.84 (binunionTE) =>
% 131.89/22.84 ((
% 131.89/22.84 (binunionTEcontra) =>
% 131.89/22.84 ((
% 131.89/22.84 (demorgan2a1) =>
% 131.89/22.84 ((
% 131.89/22.84 (complementUnionInPowersetComplement) =>
% 131.89/22.84 ((
% 131.89/22.84 (demorgan2a2) =>
% 131.89/22.84 ((
% 131.89/22.84 (demorgan1a) =>
% 131.89/22.84 ((
% 131.89/22.84 (demorgan1b) =>
% 131.89/22.84 ((
% 131.89/22.84 (demorgan1) =>
% 131.89/22.84 ((
% 131.89/22.84 (demorgan2a) =>
% 131.89/22.84 ((
% 131.89/22.84 (demorgan2b2) =>
% 131.89/22.84 ((
% 131.89/22.84 (demorgan2b) =>
% 131.89/22.84 ((
% 131.89/22.84 (demorgan2) =>
% 131.89/22.84 ((
% 131.89/22.84 (woz13rule0) =>
% 131.89/22.84 ((
% 131.89/22.84 (woz13rule1) =>
% 131.89/22.84 ((
% 131.89/22.84 (woz13rule2) =>
% 131.89/22.84 ((
% 131.89/22.84 (woz13rule3) =>
% 131.89/22.84 ((
% 131.89/22.84 (woz13rule4) =>
% 131.89/22.84 ((
% 131.89/22.84 (woz1_1) =>
% 131.89/22.84 ((
% 131.89/22.84 (woz1_2) =>
% 131.89/22.84 ((
% 131.89/22.84 (woz1_3) =>
% 131.89/22.84 ((
% 131.89/22.84 (woz1_4) =>
% 131.89/22.84 ((
% 131.89/22.84 (woz1_5) =>
% 131.89/22.84 ((
% 131.89/22.84 (breln1all2) =>
% 131.89/22.84 ((
% 131.89/22.84 (breln1SetBreln1) =>
% 131.89/22.84 ((
% 131.89/22.84 (choice2fnsingleton) =>
% 131.89/22.84 ((
% 131.89/22.84 (setOfPairsIsBReln1) =>
% 131.89/22.84 ((
% 131.89/22.84 (breln1all1) =>
% 131.89/22.84 ((
% 131.89/22.84 (subbreln1) =>
% 131.89/22.84 ((
% 131.89/22.84 (eqbreln1) =>
% 131.89/22.84 ((
% 131.89/22.84 (breln1invprop) =>
% 131.89/22.84 ((
% 131.89/22.84 (breln1invI) =>
% 131.89/22.84 ((
% 131.89/22.84 (breln1invE) =>
% 131.89/22.84 ((
% 131.89/22.84 (breln1compprop) =>
% 131.89/22.84 ((
% 131.89/22.84 (breln1compI) =>
% 131.89/22.84 ((
% 131.89/22.84 (breln1compE) =>
% 131.89/22.84 ((
% 131.89/22.84 (breln1compEex) =>
% 131.89/22.84 ((
% 131.89/22.84 (breln1unionprop) =>
% 131.89/22.84 ((
% 131.89/22.84 (breln1unionIL) =>
% 131.89/22.84 ((
% 131.89/22.84 (breln1unionIR) =>
% 131.89/22.84 ((
% 131.89/22.84 (breln1unionI) =>
% 131.89/22.84 ((
% 131.89/22.84 (breln1unionE) =>
% 131.89/22.84 ((
% 131.89/22.84 (breln1unionEcases) =>
% 131.89/22.84 ((
% 131.89/22.84 (breln1unionCommutes) =>
% 131.89/22.84 ((
% 131.89/22.84 (woz2Ex) =>
% 131.89/22.84 ((
% 131.89/22.84 (woz2W) =>
% 131.89/22.84 ((
% 131.89/22.84 (woz2A) =>
% 131.89/22.84 ((
% 131.89/22.84 (woz2B) =>
% 131.89/22.84 ((
% 131.89/22.84 (image1Ex) =>
% 131.89/22.84 ((
% 131.89/22.84 (image1Ex1) =>
% 131.89/22.84 ((
% 131.89/22.84 (image1Equiv) =>
% 131.89/22.84 ((
% 131.89/22.84 (image1E) =>
% 131.89/22.84 ((
% 131.89/22.84 (image1I) =>
% 131.89/22.84 ((
% 131.89/22.84 (injFuncInInjFuncSet) =>
% 131.89/22.84 ((
% 131.89/22.84 (injFuncSetFuncIn) =>
% 131.89/22.84 ((
% 131.89/22.84 (injFuncSetFuncInj) =>
% 131.89/22.84 ((
% 131.89/22.84 (surjFuncSetFuncIn) =>
% 131.89/22.84 ((
% 131.89/22.84 (surjFuncSetFuncSurj) =>
% 131.89/22.84 ((
% 131.89/22.84 (leftInvIsSurj) =>
% 131.89/22.84 ((
% 131.89/22.84 (surjCantorThm) =>
% 131.89/22.84 ((
% 131.89/22.84 (foundation2) =>
% 131.89/22.84 ((
% 131.89/22.84 (notinself) =>
% 131.89/22.84 ((
% 131.89/22.84 (notinself2) =>
% 131.89/22.84 ((
% 131.89/22.84 (omegaSp) =>
% 131.89/22.84 ((
% 131.89/22.84 (omegaSclos) =>
% 131.89/22.84 ((
% 131.89/22.84 (peano0notS) =>
% 131.89/22.84 ((
% 131.89/22.84 (peanoSinj) =>
% 131.89/22.84 ((
% 131.89/22.84 (transitivesetOp1) =>
% 131.89/22.84 ((
% 131.89/22.84 (binintTransitive) =>
% 131.89/22.84 ((
% 131.89/22.84 (transitivesetOp2) =>
% 131.89/22.84 ((
% 131.89/22.84 (setunionTransitive) =>
% 131.89/22.84 ((
% 131.89/22.84 (ordinalMinLem1) =>
% 131.89/22.84 ((
% 131.89/22.84 (ordinalTransSet) =>
% 131.89/22.84 ((
% 131.89/22.84 (ordinalTransSet1) =>
% 131.89/22.84 ((
% 131.89/22.84 (setunionOrdinalLem1) =>
% 131.89/22.84 (ordinal @
% 131.89/22.84 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 131.89/22.84 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl471])).
% 131.89/22.84 thf(zip_derived_cl484, plain,
% 131.89/22.84 (~ (((quantDeMorgan3) =>
% 131.89/22.84 (((quantDeMorgan4) =>
% 131.89/22.84 (((prop2setI) =>
% 131.89/22.84 (((prop2set2propI) =>
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% 131.89/22.84 (((notdallE) =>
% 131.89/22.84 (((exuI1) =>
% 131.89/22.84 (((exuI3) =>
% 131.89/22.84 (((exuI2) =>
% 131.89/22.84 (((inCongP) =>
% 131.89/22.84 (((in__Cong) =>
% 131.89/22.84 (((exuE3u) =>
% 131.89/22.84 (((exu__Cong) =>
% 131.89/22.84 (((setadjoin__Cong) =>
% 131.89/22.84 (((powerset__Cong) =>
% 131.89/22.84 (((setunion__Cong) =>
% 131.89/22.84 (((exuEu) =>
% 131.89/22.84 (((descr__Cong) =>
% 131.89/22.84 (((dsetconstr__Cong) =>
% 131.89/22.84 (((subsetI1) =>
% 131.89/22.84 (((eqimpsubset2) =>
% 131.89/22.84 (((eqimpsubset1) =>
% 131.89/22.84 (((subsetI2) =>
% 131.89/22.84 (((emptysetsubset) =>
% 131.89/22.84 (((subsetE) =>
% 131.89/22.84 (((subsetE2) =>
% 131.89/22.84 (((notsubsetI) =>
% 131.89/22.84 (((notequalI1) =>
% 131.89/22.84 (((notequalI2) =>
% 131.89/22.84 (((subsetRefl) =>
% 131.89/22.84 ((
% 131.89/22.84 (subsetTrans) =>
% 131.89/22.84 ((
% 131.89/22.84 (setadjoinSub) =>
% 131.89/22.84 ((
% 131.89/22.84 (setadjoinSub2) =>
% 131.89/22.84 ((
% 131.89/22.84 (subset2powerset) =>
% 131.89/22.84 ((
% 131.89/22.84 (setextsub) =>
% 131.89/22.84 ((
% 131.89/22.84 (subsetemptysetimpeq) =>
% 131.89/22.84 ((
% 131.89/22.84 (powersetI1) =>
% 131.89/22.84 ((
% 131.89/22.84 (powersetE1) =>
% 131.89/22.84 ((
% 131.89/22.84 (inPowerset) =>
% 131.89/22.84 ((
% 131.89/22.84 (powersetsubset) =>
% 131.89/22.84 ((
% 131.89/22.84 (sepInPowerset) =>
% 131.89/22.84 ((
% 131.89/22.84 (sepSubset) =>
% 131.89/22.84 ((
% 131.89/22.84 (binunionIL) =>
% 131.89/22.84 ((
% 131.89/22.84 (upairset2IR) =>
% 131.89/22.84 ((
% 131.89/22.84 (binunionIR) =>
% 131.89/22.84 ((
% 131.89/22.84 (binunionEcases) =>
% 131.89/22.84 ((
% 131.89/22.84 (binunionE) =>
% 131.89/22.84 ((
% 131.89/22.84 (binunionLsub) =>
% 131.89/22.84 ((
% 131.89/22.84 (binunionRsub) =>
% 131.89/22.84 ((
% 131.89/22.84 (binintersectI) =>
% 131.89/22.84 ((
% 131.89/22.84 (binintersectSubset5) =>
% 131.89/22.84 ((
% 131.89/22.84 (binintersectEL) =>
% 131.89/22.84 ((
% 131.89/22.84 (binintersectLsub) =>
% 131.89/22.84 ((
% 131.89/22.84 (binintersectSubset2) =>
% 131.89/22.84 ((
% 131.89/22.84 (binintersectSubset3) =>
% 131.89/22.84 ((
% 131.89/22.84 (binintersectER) =>
% 131.89/22.84 ((
% 131.89/22.84 (disjointsetsI1) =>
% 131.89/22.84 ((
% 131.89/22.84 (binintersectRsub) =>
% 131.89/22.84 ((
% 131.89/22.84 (binintersectSubset4) =>
% 131.89/22.84 ((
% 131.89/22.84 (binintersectSubset1) =>
% 131.89/22.84 ((
% 131.89/22.84 (bs114d) =>
% 131.89/22.84 ((
% 131.89/22.84 (setminusI) =>
% 131.89/22.84 ((
% 131.89/22.84 (setminusEL) =>
% 131.89/22.84 ((
% 131.89/22.84 (setminusER) =>
% 131.89/22.84 ((
% 131.89/22.84 (setminusSubset2) =>
% 131.89/22.84 ((
% 131.89/22.84 (setminusERneg) =>
% 131.89/22.84 ((
% 131.89/22.84 (setminusELneg) =>
% 131.89/22.84 ((
% 131.89/22.84 (setminusILneg) =>
% 131.89/22.84 ((
% 131.89/22.84 (setminusIRneg) =>
% 131.89/22.84 ((
% 131.89/22.84 (setminusLsub) =>
% 131.89/22.84 ((
% 131.89/22.84 (setminusSubset1) =>
% 131.89/22.84 ((
% 131.89/22.84 (symdiffE) =>
% 131.89/22.84 ((
% 131.89/22.84 (symdiffI1) =>
% 131.89/22.84 ((
% 131.89/22.84 (symdiffI2) =>
% 131.89/22.84 ((
% 131.89/22.84 (symdiffIneg1) =>
% 131.89/22.84 ((
% 131.89/22.84 (symdiffIneg2) =>
% 131.89/22.84 ((
% 131.89/22.84 (secondinupair) =>
% 131.89/22.84 ((
% 131.89/22.84 (setukpairIL) =>
% 131.89/22.84 ((
% 131.89/22.84 (setukpairIR) =>
% 131.89/22.84 ((
% 131.89/22.84 (kpairiskpair) =>
% 131.89/22.84 ((
% 131.89/22.84 (kpairp) =>
% 131.89/22.84 ((
% 131.89/22.84 (singletonsubset) =>
% 131.89/22.84 ((
% 131.89/22.84 (singletoninpowerset) =>
% 131.89/22.84 ((
% 131.89/22.84 (singletoninpowunion) =>
% 131.89/22.84 ((
% 131.89/22.84 (upairset2E) =>
% 131.89/22.84 ((
% 131.89/22.84 (upairsubunion) =>
% 131.89/22.84 ((
% 131.89/22.84 (upairinpowunion) =>
% 131.89/22.84 ((
% 131.89/22.84 (ubforcartprodlem1) =>
% 131.89/22.84 ((
% 131.89/22.84 (ubforcartprodlem2) =>
% 131.89/22.84 ((
% 131.89/22.84 (ubforcartprodlem3) =>
% 131.89/22.84 ((
% 131.89/22.84 (cartprodpairin) =>
% 131.89/22.84 ((
% 131.89/22.84 (cartprodmempair1) =>
% 131.89/22.84 ((
% 131.89/22.84 (cartprodmempair) =>
% 131.89/22.84 ((
% 131.89/22.84 (setunionE2) =>
% 131.89/22.84 ((
% 131.89/22.84 (setunionsingleton1) =>
% 131.89/22.84 ((
% 131.89/22.84 (setunionsingleton2) =>
% 131.89/22.84 ((
% 131.89/22.84 (setunionsingleton) =>
% 131.89/22.84 ((
% 131.89/22.84 (singletonprop) =>
% 131.89/22.84 ((
% 131.89/22.84 (ex1E1) =>
% 131.89/22.84 ((
% 131.89/22.84 (ex1I) =>
% 131.89/22.84 ((
% 131.89/22.84 (ex1I2) =>
% 131.89/22.84 ((
% 131.89/22.84 (singletonsuniq) =>
% 131.89/22.84 ((
% 131.89/22.84 (setukpairinjL1) =>
% 131.89/22.84 ((
% 131.89/22.84 (kfstsingleton) =>
% 131.89/22.84 ((
% 131.89/22.84 (theprop) =>
% 131.89/22.84 ((
% 131.89/22.84 (kfstpairEq) =>
% 131.89/22.84 ((
% 131.89/22.84 (cartprodfstin) =>
% 131.89/22.84 ((
% 131.89/22.84 (setukpairinjL2) =>
% 131.89/22.84 ((
% 131.89/22.84 (setukpairinjL) =>
% 131.89/22.84 ((
% 131.89/22.84 (setukpairinjR11) =>
% 131.89/22.84 ((
% 131.89/22.84 (setukpairinjR12) =>
% 131.89/22.84 ((
% 131.89/22.84 (setukpairinjR1) =>
% 131.89/22.84 ((
% 131.89/22.84 (upairequniteq) =>
% 131.89/22.84 ((
% 131.89/22.84 (setukpairinjR2) =>
% 131.89/22.84 ((
% 131.89/22.84 (setukpairinjR) =>
% 131.89/22.84 ((
% 131.89/22.84 (ksndsingleton) =>
% 131.89/22.84 ((
% 131.89/22.84 (ksndpairEq) =>
% 131.89/22.84 ((
% 131.89/22.84 (kpairsurjEq) =>
% 131.89/22.84 ((
% 131.89/22.84 (cartprodsndin) =>
% 131.89/22.84 ((
% 131.89/22.84 (cartprodpairmemEL) =>
% 131.89/22.84 ((
% 131.89/22.84 (cartprodpairmemER) =>
% 131.89/22.84 ((
% 131.89/22.84 (cartprodmempaircEq) =>
% 131.89/22.84 ((
% 131.89/22.84 (cartprodfstpairEq) =>
% 131.89/22.84 ((
% 131.89/22.84 (cartprodsndpairEq) =>
% 131.89/22.84 ((
% 131.89/22.84 (cartprodpairsurjEq) =>
% 131.89/22.84 ((
% 131.89/22.84 (dpsetconstrI) =>
% 131.89/22.84 ((
% 131.89/22.84 (dpsetconstrSub) =>
% 131.89/22.84 ((
% 131.89/22.84 (setOfPairsIsBReln) =>
% 131.89/22.84 ((
% 131.89/22.84 (dpsetconstrERa) =>
% 131.89/22.84 ((
% 131.89/22.84 (dpsetconstrEL1) =>
% 131.89/22.84 ((
% 131.89/22.84 (dpsetconstrEL2) =>
% 131.89/22.84 ((
% 131.89/22.84 (dpsetconstrER) =>
% 131.89/22.84 ((
% 131.89/22.84 (funcImageSingleton) =>
% 131.89/22.84 ((
% 131.89/22.84 (apProp) =>
% 131.89/22.84 ((
% 131.89/22.84 (app) =>
% 131.89/22.84 ((
% 131.89/22.84 (infuncsetfunc) =>
% 131.89/22.84 ((
% 131.89/22.84 (ap2p) =>
% 131.89/22.84 ((
% 131.89/22.84 (funcinfuncset) =>
% 131.89/22.84 ((
% 131.89/22.84 (lamProp) =>
% 131.89/22.84 ((
% 131.89/22.84 (lamp) =>
% 131.89/22.84 ((
% 131.89/22.84 (lam2p) =>
% 131.89/22.84 ((
% 131.89/22.84 (brelnall1) =>
% 131.89/22.84 ((
% 131.89/22.84 (brelnall2) =>
% 131.89/22.84 ((
% 131.89/22.84 (ex1E2) =>
% 131.89/22.84 ((
% 131.89/22.84 (funcGraphProp1) =>
% 131.89/22.84 ((
% 131.89/22.84 (funcGraphProp3) =>
% 131.89/22.84 ((
% 131.89/22.84 (funcGraphProp2) =>
% 131.89/22.84 ((
% 131.89/22.84 (funcextLem) =>
% 131.89/22.84 ((
% 131.89/22.84 (funcGraphProp4) =>
% 131.89/22.84 ((
% 131.89/22.84 (subbreln) =>
% 131.89/22.84 ((
% 131.89/22.84 (eqbreln) =>
% 131.89/22.84 ((
% 131.89/22.84 (funcext) =>
% 131.89/22.84 ((
% 131.89/22.84 (funcext2) =>
% 131.89/22.84 ((
% 131.89/22.84 (ap2apEq1) =>
% 131.89/22.84 ((
% 131.89/22.84 (ap2apEq2) =>
% 131.89/22.84 ((
% 131.89/22.84 (beta1) =>
% 131.89/22.84 ((
% 131.89/22.84 (eta1) =>
% 131.89/22.84 ((
% 131.89/22.84 (lam2lamEq) =>
% 131.89/22.84 ((
% 131.89/22.84 (beta2) =>
% 131.89/22.84 ((
% 131.89/22.84 (eta2) =>
% 131.89/22.84 ((
% 131.89/22.84 (iffalseProp1) =>
% 131.89/22.84 ((
% 131.89/22.84 (iffalseProp2) =>
% 131.89/22.84 ((
% 131.89/22.84 (iftrueProp1) =>
% 131.89/22.84 ((
% 131.89/22.84 (iftrueProp2) =>
% 131.89/22.84 ((
% 131.89/22.84 (ifSingleton) =>
% 131.89/22.84 ((
% 131.89/22.84 (ifp) =>
% 131.89/22.84 ((
% 131.89/22.84 (theeq) =>
% 131.89/22.84 ((
% 131.89/22.84 (iftrue) =>
% 131.89/22.84 ((
% 131.89/22.84 (iffalse) =>
% 131.89/22.84 ((
% 131.89/22.84 (iftrueorfalse) =>
% 131.89/22.84 ((
% 131.89/22.84 (binintersectT_lem) =>
% 131.89/22.84 ((
% 131.89/22.84 (binunionT_lem) =>
% 131.89/22.84 ((
% 131.89/22.84 (powersetT_lem) =>
% 131.89/22.84 ((
% 131.89/22.84 (setminusT_lem) =>
% 131.89/22.84 ((
% 131.89/22.84 (complementT_lem) =>
% 131.89/22.84 ((
% 131.89/22.84 (setextT) =>
% 131.89/22.84 ((
% 131.89/22.84 (subsetTI) =>
% 131.89/22.84 ((
% 131.89/22.84 (powersetTI1) =>
% 131.89/22.84 ((
% 131.89/22.84 (powersetTE1) =>
% 131.89/22.84 ((
% 131.89/22.84 (complementTI1) =>
% 131.89/22.84 ((
% 131.89/22.84 (complementTE1) =>
% 131.89/22.84 ((
% 131.89/22.84 (binintersectTELcontra) =>
% 131.89/22.84 ((
% 131.89/22.84 (binintersectTERcontra) =>
% 131.89/22.84 ((
% 131.89/22.84 (contrasubsetT) =>
% 131.89/22.84 ((
% 131.89/22.84 (contrasubsetT1) =>
% 131.89/22.84 ((
% 131.89/22.84 (contrasubsetT2) =>
% 131.89/22.84 ((
% 131.89/22.84 (contrasubsetT3) =>
% 131.89/22.84 ((
% 131.89/22.84 (doubleComplementI1) =>
% 131.89/22.84 ((
% 131.89/22.84 (doubleComplementE1) =>
% 131.89/22.84 ((
% 131.89/22.84 (doubleComplementSub1) =>
% 131.89/22.84 ((
% 131.89/22.84 (doubleComplementSub2) =>
% 131.89/22.84 ((
% 131.89/22.84 (doubleComplementEq) =>
% 131.89/22.84 ((
% 131.89/22.84 (complementTnotintersectT) =>
% 131.89/22.84 ((
% 131.89/22.84 (complementImpComplementIntersect) =>
% 131.89/22.84 ((
% 131.89/22.84 (complementSubsetComplementIntersect) =>
% 131.89/22.84 ((
% 131.89/22.84 (complementInPowersetComplementIntersect) =>
% 131.89/22.84 ((
% 131.89/22.84 (contraSubsetComplement) =>
% 131.89/22.84 ((
% 131.89/22.84 (complementTcontraSubset) =>
% 131.89/22.84 ((
% 131.89/22.84 (binunionTILcontra) =>
% 131.89/22.84 ((
% 131.89/22.84 (binunionTIRcontra) =>
% 131.89/22.84 ((
% 131.89/22.84 (inIntersectImpInUnion) =>
% 131.89/22.84 ((
% 131.89/22.84 (inIntersectImpInUnion2) =>
% 131.89/22.84 ((
% 131.89/22.84 (inIntersectImpInIntersectUnions) =>
% 131.89/22.84 ((
% 131.89/22.84 (intersectInPowersetIntersectUnions) =>
% 131.89/22.84 ((
% 131.89/22.84 (inComplementUnionImpNotIn1) =>
% 131.89/22.84 ((
% 131.89/22.84 (inComplementUnionImpInComplement1) =>
% 131.89/22.84 ((
% 131.89/22.84 (binunionTE) =>
% 131.89/22.84 ((
% 131.89/22.84 (binunionTEcontra) =>
% 131.89/22.84 ((
% 131.89/22.84 (demorgan2a1) =>
% 131.89/22.84 ((
% 131.89/22.84 (complementUnionInPowersetComplement) =>
% 131.89/22.84 ((
% 131.89/22.84 (demorgan2a2) =>
% 131.89/22.84 ((
% 131.89/22.84 (demorgan1a) =>
% 131.89/22.84 ((
% 131.89/22.84 (demorgan1b) =>
% 131.89/22.84 ((
% 131.89/22.84 (demorgan1) =>
% 131.89/22.84 ((
% 131.89/22.84 (demorgan2a) =>
% 131.89/22.84 ((
% 131.89/22.84 (demorgan2b2) =>
% 131.89/22.84 ((
% 131.89/22.84 (demorgan2b) =>
% 131.89/22.84 ((
% 131.89/22.84 (demorgan2) =>
% 131.89/22.84 ((
% 131.89/22.84 (woz13rule0) =>
% 131.89/22.84 ((
% 131.89/22.84 (woz13rule1) =>
% 131.89/22.84 ((
% 131.89/22.84 (woz13rule2) =>
% 131.89/22.84 ((
% 131.89/22.84 (woz13rule3) =>
% 131.89/22.84 ((
% 131.89/22.84 (woz13rule4) =>
% 131.89/22.84 ((
% 131.89/22.84 (woz1_1) =>
% 131.89/22.84 ((
% 131.89/22.84 (woz1_2) =>
% 131.89/22.84 ((
% 131.89/22.84 (woz1_3) =>
% 131.89/22.84 ((
% 131.89/22.84 (woz1_4) =>
% 131.89/22.84 ((
% 131.89/22.84 (woz1_5) =>
% 131.89/22.84 ((
% 131.89/22.84 (breln1all2) =>
% 131.89/22.84 ((
% 131.89/22.84 (breln1SetBreln1) =>
% 131.89/22.84 ((
% 131.89/22.84 (choice2fnsingleton) =>
% 131.89/22.84 ((
% 131.89/22.84 (setOfPairsIsBReln1) =>
% 131.89/22.84 ((
% 131.89/22.84 (breln1all1) =>
% 131.89/22.84 ((
% 131.89/22.84 (subbreln1) =>
% 131.89/22.84 ((
% 131.89/22.84 (eqbreln1) =>
% 131.89/22.84 ((
% 131.89/22.84 (breln1invprop) =>
% 131.89/22.84 ((
% 131.89/22.84 (breln1invI) =>
% 131.89/22.84 ((
% 131.89/22.84 (breln1invE) =>
% 131.89/22.84 ((
% 131.89/22.84 (breln1compprop) =>
% 131.89/22.84 ((
% 131.89/22.84 (breln1compI) =>
% 131.89/22.84 ((
% 131.89/22.84 (breln1compE) =>
% 131.89/22.84 ((
% 131.89/22.84 (breln1compEex) =>
% 131.89/22.84 ((
% 131.89/22.84 (breln1unionprop) =>
% 131.89/22.84 ((
% 131.89/22.84 (breln1unionIL) =>
% 131.89/22.84 ((
% 131.89/22.85 (breln1unionIR) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1unionI) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1unionE) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1unionEcases) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1unionCommutes) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz2Ex) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz2W) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz2A) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz2B) =>
% 131.89/22.85 ((
% 131.89/22.85 (image1Ex) =>
% 131.89/22.85 ((
% 131.89/22.85 (image1Ex1) =>
% 131.89/22.85 ((
% 131.89/22.85 (image1Equiv) =>
% 131.89/22.85 ((
% 131.89/22.85 (image1E) =>
% 131.89/22.85 ((
% 131.89/22.85 (image1I) =>
% 131.89/22.85 ((
% 131.89/22.85 (injFuncInInjFuncSet) =>
% 131.89/22.85 ((
% 131.89/22.85 (injFuncSetFuncIn) =>
% 131.89/22.85 ((
% 131.89/22.85 (injFuncSetFuncInj) =>
% 131.89/22.85 ((
% 131.89/22.85 (surjFuncSetFuncIn) =>
% 131.89/22.85 ((
% 131.89/22.85 (surjFuncSetFuncSurj) =>
% 131.89/22.85 ((
% 131.89/22.85 (leftInvIsSurj) =>
% 131.89/22.85 ((
% 131.89/22.85 (surjCantorThm) =>
% 131.89/22.85 ((
% 131.89/22.85 (foundation2) =>
% 131.89/22.85 ((
% 131.89/22.85 (notinself) =>
% 131.89/22.85 ((
% 131.89/22.85 (notinself2) =>
% 131.89/22.85 ((
% 131.89/22.85 (omegaSp) =>
% 131.89/22.85 ((
% 131.89/22.85 (omegaSclos) =>
% 131.89/22.85 ((
% 131.89/22.85 (peano0notS) =>
% 131.89/22.85 ((
% 131.89/22.85 (peanoSinj) =>
% 131.89/22.85 ((
% 131.89/22.85 (transitivesetOp1) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintTransitive) =>
% 131.89/22.85 ((
% 131.89/22.85 (transitivesetOp2) =>
% 131.89/22.85 ((
% 131.89/22.85 (setunionTransitive) =>
% 131.89/22.85 ((
% 131.89/22.85 (ordinalMinLem1) =>
% 131.89/22.85 ((
% 131.89/22.85 (ordinalTransSet) =>
% 131.89/22.85 ((
% 131.89/22.85 (ordinalTransSet1) =>
% 131.89/22.85 ((
% 131.89/22.85 (setunionOrdinalLem1) =>
% 131.89/22.85 (ordinal @
% 131.89/22.85 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 131.89/22.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl478])).
% 131.89/22.85 thf(zip_derived_cl491, plain,
% 131.89/22.85 (~ (((quantDeMorgan4) =>
% 131.89/22.85 (((prop2setI) =>
% 131.89/22.85 (((prop2set2propI) =>
% 131.89/22.85 (((notdexE) =>
% 131.89/22.85 (((notdallE) =>
% 131.89/22.85 (((exuI1) =>
% 131.89/22.85 (((exuI3) =>
% 131.89/22.85 (((exuI2) =>
% 131.89/22.85 (((inCongP) =>
% 131.89/22.85 (((in__Cong) =>
% 131.89/22.85 (((exuE3u) =>
% 131.89/22.85 (((exu__Cong) =>
% 131.89/22.85 (((setadjoin__Cong) =>
% 131.89/22.85 (((powerset__Cong) =>
% 131.89/22.85 (((setunion__Cong) =>
% 131.89/22.85 (((exuEu) =>
% 131.89/22.85 (((descr__Cong) =>
% 131.89/22.85 (((dsetconstr__Cong) =>
% 131.89/22.85 (((subsetI1) =>
% 131.89/22.85 (((eqimpsubset2) =>
% 131.89/22.85 (((eqimpsubset1) =>
% 131.89/22.85 (((subsetI2) =>
% 131.89/22.85 (((emptysetsubset) =>
% 131.89/22.85 (((subsetE) =>
% 131.89/22.85 (((subsetE2) =>
% 131.89/22.85 (((notsubsetI) =>
% 131.89/22.85 (((notequalI1) =>
% 131.89/22.85 (((notequalI2) =>
% 131.89/22.85 (((subsetRefl) =>
% 131.89/22.85 (((subsetTrans) =>
% 131.89/22.85 ((
% 131.89/22.85 (setadjoinSub) =>
% 131.89/22.85 ((
% 131.89/22.85 (setadjoinSub2) =>
% 131.89/22.85 ((
% 131.89/22.85 (subset2powerset) =>
% 131.89/22.85 ((
% 131.89/22.85 (setextsub) =>
% 131.89/22.85 ((
% 131.89/22.85 (subsetemptysetimpeq) =>
% 131.89/22.85 ((
% 131.89/22.85 (powersetI1) =>
% 131.89/22.85 ((
% 131.89/22.85 (powersetE1) =>
% 131.89/22.85 ((
% 131.89/22.85 (inPowerset) =>
% 131.89/22.85 ((
% 131.89/22.85 (powersetsubset) =>
% 131.89/22.85 ((
% 131.89/22.85 (sepInPowerset) =>
% 131.89/22.85 ((
% 131.89/22.85 (sepSubset) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionIL) =>
% 131.89/22.85 ((
% 131.89/22.85 (upairset2IR) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionIR) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionEcases) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionE) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionLsub) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionRsub) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectI) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectSubset5) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectEL) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectLsub) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectSubset2) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectSubset3) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectER) =>
% 131.89/22.85 ((
% 131.89/22.85 (disjointsetsI1) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectRsub) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectSubset4) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectSubset1) =>
% 131.89/22.85 ((
% 131.89/22.85 (bs114d) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusI) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusEL) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusER) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusSubset2) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusERneg) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusELneg) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusILneg) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusIRneg) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusLsub) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusSubset1) =>
% 131.89/22.85 ((
% 131.89/22.85 (symdiffE) =>
% 131.89/22.85 ((
% 131.89/22.85 (symdiffI1) =>
% 131.89/22.85 ((
% 131.89/22.85 (symdiffI2) =>
% 131.89/22.85 ((
% 131.89/22.85 (symdiffIneg1) =>
% 131.89/22.85 ((
% 131.89/22.85 (symdiffIneg2) =>
% 131.89/22.85 ((
% 131.89/22.85 (secondinupair) =>
% 131.89/22.85 ((
% 131.89/22.85 (setukpairIL) =>
% 131.89/22.85 ((
% 131.89/22.85 (setukpairIR) =>
% 131.89/22.85 ((
% 131.89/22.85 (kpairiskpair) =>
% 131.89/22.85 ((
% 131.89/22.85 (kpairp) =>
% 131.89/22.85 ((
% 131.89/22.85 (singletonsubset) =>
% 131.89/22.85 ((
% 131.89/22.85 (singletoninpowerset) =>
% 131.89/22.85 ((
% 131.89/22.85 (singletoninpowunion) =>
% 131.89/22.85 ((
% 131.89/22.85 (upairset2E) =>
% 131.89/22.85 ((
% 131.89/22.85 (upairsubunion) =>
% 131.89/22.85 ((
% 131.89/22.85 (upairinpowunion) =>
% 131.89/22.85 ((
% 131.89/22.85 (ubforcartprodlem1) =>
% 131.89/22.85 ((
% 131.89/22.85 (ubforcartprodlem2) =>
% 131.89/22.85 ((
% 131.89/22.85 (ubforcartprodlem3) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodpairin) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodmempair1) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodmempair) =>
% 131.89/22.85 ((
% 131.89/22.85 (setunionE2) =>
% 131.89/22.85 ((
% 131.89/22.85 (setunionsingleton1) =>
% 131.89/22.85 ((
% 131.89/22.85 (setunionsingleton2) =>
% 131.89/22.85 ((
% 131.89/22.85 (setunionsingleton) =>
% 131.89/22.85 ((
% 131.89/22.85 (singletonprop) =>
% 131.89/22.85 ((
% 131.89/22.85 (ex1E1) =>
% 131.89/22.85 ((
% 131.89/22.85 (ex1I) =>
% 131.89/22.85 ((
% 131.89/22.85 (ex1I2) =>
% 131.89/22.85 ((
% 131.89/22.85 (singletonsuniq) =>
% 131.89/22.85 ((
% 131.89/22.85 (setukpairinjL1) =>
% 131.89/22.85 ((
% 131.89/22.85 (kfstsingleton) =>
% 131.89/22.85 ((
% 131.89/22.85 (theprop) =>
% 131.89/22.85 ((
% 131.89/22.85 (kfstpairEq) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodfstin) =>
% 131.89/22.85 ((
% 131.89/22.85 (setukpairinjL2) =>
% 131.89/22.85 ((
% 131.89/22.85 (setukpairinjL) =>
% 131.89/22.85 ((
% 131.89/22.85 (setukpairinjR11) =>
% 131.89/22.85 ((
% 131.89/22.85 (setukpairinjR12) =>
% 131.89/22.85 ((
% 131.89/22.85 (setukpairinjR1) =>
% 131.89/22.85 ((
% 131.89/22.85 (upairequniteq) =>
% 131.89/22.85 ((
% 131.89/22.85 (setukpairinjR2) =>
% 131.89/22.85 ((
% 131.89/22.85 (setukpairinjR) =>
% 131.89/22.85 ((
% 131.89/22.85 (ksndsingleton) =>
% 131.89/22.85 ((
% 131.89/22.85 (ksndpairEq) =>
% 131.89/22.85 ((
% 131.89/22.85 (kpairsurjEq) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodsndin) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodpairmemEL) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodpairmemER) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodmempaircEq) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodfstpairEq) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodsndpairEq) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodpairsurjEq) =>
% 131.89/22.85 ((
% 131.89/22.85 (dpsetconstrI) =>
% 131.89/22.85 ((
% 131.89/22.85 (dpsetconstrSub) =>
% 131.89/22.85 ((
% 131.89/22.85 (setOfPairsIsBReln) =>
% 131.89/22.85 ((
% 131.89/22.85 (dpsetconstrERa) =>
% 131.89/22.85 ((
% 131.89/22.85 (dpsetconstrEL1) =>
% 131.89/22.85 ((
% 131.89/22.85 (dpsetconstrEL2) =>
% 131.89/22.85 ((
% 131.89/22.85 (dpsetconstrER) =>
% 131.89/22.85 ((
% 131.89/22.85 (funcImageSingleton) =>
% 131.89/22.85 ((
% 131.89/22.85 (apProp) =>
% 131.89/22.85 ((
% 131.89/22.85 (app) =>
% 131.89/22.85 ((
% 131.89/22.85 (infuncsetfunc) =>
% 131.89/22.85 ((
% 131.89/22.85 (ap2p) =>
% 131.89/22.85 ((
% 131.89/22.85 (funcinfuncset) =>
% 131.89/22.85 ((
% 131.89/22.85 (lamProp) =>
% 131.89/22.85 ((
% 131.89/22.85 (lamp) =>
% 131.89/22.85 ((
% 131.89/22.85 (lam2p) =>
% 131.89/22.85 ((
% 131.89/22.85 (brelnall1) =>
% 131.89/22.85 ((
% 131.89/22.85 (brelnall2) =>
% 131.89/22.85 ((
% 131.89/22.85 (ex1E2) =>
% 131.89/22.85 ((
% 131.89/22.85 (funcGraphProp1) =>
% 131.89/22.85 ((
% 131.89/22.85 (funcGraphProp3) =>
% 131.89/22.85 ((
% 131.89/22.85 (funcGraphProp2) =>
% 131.89/22.85 ((
% 131.89/22.85 (funcextLem) =>
% 131.89/22.85 ((
% 131.89/22.85 (funcGraphProp4) =>
% 131.89/22.85 ((
% 131.89/22.85 (subbreln) =>
% 131.89/22.85 ((
% 131.89/22.85 (eqbreln) =>
% 131.89/22.85 ((
% 131.89/22.85 (funcext) =>
% 131.89/22.85 ((
% 131.89/22.85 (funcext2) =>
% 131.89/22.85 ((
% 131.89/22.85 (ap2apEq1) =>
% 131.89/22.85 ((
% 131.89/22.85 (ap2apEq2) =>
% 131.89/22.85 ((
% 131.89/22.85 (beta1) =>
% 131.89/22.85 ((
% 131.89/22.85 (eta1) =>
% 131.89/22.85 ((
% 131.89/22.85 (lam2lamEq) =>
% 131.89/22.85 ((
% 131.89/22.85 (beta2) =>
% 131.89/22.85 ((
% 131.89/22.85 (eta2) =>
% 131.89/22.85 ((
% 131.89/22.85 (iffalseProp1) =>
% 131.89/22.85 ((
% 131.89/22.85 (iffalseProp2) =>
% 131.89/22.85 ((
% 131.89/22.85 (iftrueProp1) =>
% 131.89/22.85 ((
% 131.89/22.85 (iftrueProp2) =>
% 131.89/22.85 ((
% 131.89/22.85 (ifSingleton) =>
% 131.89/22.85 ((
% 131.89/22.85 (ifp) =>
% 131.89/22.85 ((
% 131.89/22.85 (theeq) =>
% 131.89/22.85 ((
% 131.89/22.85 (iftrue) =>
% 131.89/22.85 ((
% 131.89/22.85 (iffalse) =>
% 131.89/22.85 ((
% 131.89/22.85 (iftrueorfalse) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectT_lem) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionT_lem) =>
% 131.89/22.85 ((
% 131.89/22.85 (powersetT_lem) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusT_lem) =>
% 131.89/22.85 ((
% 131.89/22.85 (complementT_lem) =>
% 131.89/22.85 ((
% 131.89/22.85 (setextT) =>
% 131.89/22.85 ((
% 131.89/22.85 (subsetTI) =>
% 131.89/22.85 ((
% 131.89/22.85 (powersetTI1) =>
% 131.89/22.85 ((
% 131.89/22.85 (powersetTE1) =>
% 131.89/22.85 ((
% 131.89/22.85 (complementTI1) =>
% 131.89/22.85 ((
% 131.89/22.85 (complementTE1) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectTELcontra) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectTERcontra) =>
% 131.89/22.85 ((
% 131.89/22.85 (contrasubsetT) =>
% 131.89/22.85 ((
% 131.89/22.85 (contrasubsetT1) =>
% 131.89/22.85 ((
% 131.89/22.85 (contrasubsetT2) =>
% 131.89/22.85 ((
% 131.89/22.85 (contrasubsetT3) =>
% 131.89/22.85 ((
% 131.89/22.85 (doubleComplementI1) =>
% 131.89/22.85 ((
% 131.89/22.85 (doubleComplementE1) =>
% 131.89/22.85 ((
% 131.89/22.85 (doubleComplementSub1) =>
% 131.89/22.85 ((
% 131.89/22.85 (doubleComplementSub2) =>
% 131.89/22.85 ((
% 131.89/22.85 (doubleComplementEq) =>
% 131.89/22.85 ((
% 131.89/22.85 (complementTnotintersectT) =>
% 131.89/22.85 ((
% 131.89/22.85 (complementImpComplementIntersect) =>
% 131.89/22.85 ((
% 131.89/22.85 (complementSubsetComplementIntersect) =>
% 131.89/22.85 ((
% 131.89/22.85 (complementInPowersetComplementIntersect) =>
% 131.89/22.85 ((
% 131.89/22.85 (contraSubsetComplement) =>
% 131.89/22.85 ((
% 131.89/22.85 (complementTcontraSubset) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionTILcontra) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionTIRcontra) =>
% 131.89/22.85 ((
% 131.89/22.85 (inIntersectImpInUnion) =>
% 131.89/22.85 ((
% 131.89/22.85 (inIntersectImpInUnion2) =>
% 131.89/22.85 ((
% 131.89/22.85 (inIntersectImpInIntersectUnions) =>
% 131.89/22.85 ((
% 131.89/22.85 (intersectInPowersetIntersectUnions) =>
% 131.89/22.85 ((
% 131.89/22.85 (inComplementUnionImpNotIn1) =>
% 131.89/22.85 ((
% 131.89/22.85 (inComplementUnionImpInComplement1) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionTE) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionTEcontra) =>
% 131.89/22.85 ((
% 131.89/22.85 (demorgan2a1) =>
% 131.89/22.85 ((
% 131.89/22.85 (complementUnionInPowersetComplement) =>
% 131.89/22.85 ((
% 131.89/22.85 (demorgan2a2) =>
% 131.89/22.85 ((
% 131.89/22.85 (demorgan1a) =>
% 131.89/22.85 ((
% 131.89/22.85 (demorgan1b) =>
% 131.89/22.85 ((
% 131.89/22.85 (demorgan1) =>
% 131.89/22.85 ((
% 131.89/22.85 (demorgan2a) =>
% 131.89/22.85 ((
% 131.89/22.85 (demorgan2b2) =>
% 131.89/22.85 ((
% 131.89/22.85 (demorgan2b) =>
% 131.89/22.85 ((
% 131.89/22.85 (demorgan2) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz13rule0) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz13rule1) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz13rule2) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz13rule3) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz13rule4) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz1_1) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz1_2) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz1_3) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz1_4) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz1_5) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1all2) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1SetBreln1) =>
% 131.89/22.85 ((
% 131.89/22.85 (choice2fnsingleton) =>
% 131.89/22.85 ((
% 131.89/22.85 (setOfPairsIsBReln1) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1all1) =>
% 131.89/22.85 ((
% 131.89/22.85 (subbreln1) =>
% 131.89/22.85 ((
% 131.89/22.85 (eqbreln1) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1invprop) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1invI) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1invE) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1compprop) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1compI) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1compE) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1compEex) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1unionprop) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1unionIL) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1unionIR) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1unionI) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1unionE) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1unionEcases) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1unionCommutes) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz2Ex) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz2W) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz2A) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz2B) =>
% 131.89/22.85 ((
% 131.89/22.85 (image1Ex) =>
% 131.89/22.85 ((
% 131.89/22.85 (image1Ex1) =>
% 131.89/22.85 ((
% 131.89/22.85 (image1Equiv) =>
% 131.89/22.85 ((
% 131.89/22.85 (image1E) =>
% 131.89/22.85 ((
% 131.89/22.85 (image1I) =>
% 131.89/22.85 ((
% 131.89/22.85 (injFuncInInjFuncSet) =>
% 131.89/22.85 ((
% 131.89/22.85 (injFuncSetFuncIn) =>
% 131.89/22.85 ((
% 131.89/22.85 (injFuncSetFuncInj) =>
% 131.89/22.85 ((
% 131.89/22.85 (surjFuncSetFuncIn) =>
% 131.89/22.85 ((
% 131.89/22.85 (surjFuncSetFuncSurj) =>
% 131.89/22.85 ((
% 131.89/22.85 (leftInvIsSurj) =>
% 131.89/22.85 ((
% 131.89/22.85 (surjCantorThm) =>
% 131.89/22.85 ((
% 131.89/22.85 (foundation2) =>
% 131.89/22.85 ((
% 131.89/22.85 (notinself) =>
% 131.89/22.85 ((
% 131.89/22.85 (notinself2) =>
% 131.89/22.85 ((
% 131.89/22.85 (omegaSp) =>
% 131.89/22.85 ((
% 131.89/22.85 (omegaSclos) =>
% 131.89/22.85 ((
% 131.89/22.85 (peano0notS) =>
% 131.89/22.85 ((
% 131.89/22.85 (peanoSinj) =>
% 131.89/22.85 ((
% 131.89/22.85 (transitivesetOp1) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintTransitive) =>
% 131.89/22.85 ((
% 131.89/22.85 (transitivesetOp2) =>
% 131.89/22.85 ((
% 131.89/22.85 (setunionTransitive) =>
% 131.89/22.85 ((
% 131.89/22.85 (ordinalMinLem1) =>
% 131.89/22.85 ((
% 131.89/22.85 (ordinalTransSet) =>
% 131.89/22.85 ((
% 131.89/22.85 (ordinalTransSet1) =>
% 131.89/22.85 ((
% 131.89/22.85 (setunionOrdinalLem1) =>
% 131.89/22.85 (ordinal @
% 131.89/22.85 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 131.89/22.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl484])).
% 131.89/22.85 thf(zip_derived_cl501, plain,
% 131.89/22.85 (~ (((prop2setI) =>
% 131.89/22.85 (((prop2set2propI) =>
% 131.89/22.85 (((notdexE) =>
% 131.89/22.85 (((notdallE) =>
% 131.89/22.85 (((exuI1) =>
% 131.89/22.85 (((exuI3) =>
% 131.89/22.85 (((exuI2) =>
% 131.89/22.85 (((inCongP) =>
% 131.89/22.85 (((in__Cong) =>
% 131.89/22.85 (((exuE3u) =>
% 131.89/22.85 (((exu__Cong) =>
% 131.89/22.85 (((setadjoin__Cong) =>
% 131.89/22.85 (((powerset__Cong) =>
% 131.89/22.85 (((setunion__Cong) =>
% 131.89/22.85 (((exuEu) =>
% 131.89/22.85 (((descr__Cong) =>
% 131.89/22.85 (((dsetconstr__Cong) =>
% 131.89/22.85 (((subsetI1) =>
% 131.89/22.85 (((eqimpsubset2) =>
% 131.89/22.85 (((eqimpsubset1) =>
% 131.89/22.85 (((subsetI2) =>
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% 131.89/22.85 (((subsetE) =>
% 131.89/22.85 (((subsetE2) =>
% 131.89/22.85 (((notsubsetI) =>
% 131.89/22.85 (((notequalI1) =>
% 131.89/22.85 (((notequalI2) =>
% 131.89/22.85 (((subsetRefl) =>
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% 131.89/22.85 (setadjoinSub2) =>
% 131.89/22.85 ((
% 131.89/22.85 (subset2powerset) =>
% 131.89/22.85 ((
% 131.89/22.85 (setextsub) =>
% 131.89/22.85 ((
% 131.89/22.85 (subsetemptysetimpeq) =>
% 131.89/22.85 ((
% 131.89/22.85 (powersetI1) =>
% 131.89/22.85 ((
% 131.89/22.85 (powersetE1) =>
% 131.89/22.85 ((
% 131.89/22.85 (inPowerset) =>
% 131.89/22.85 ((
% 131.89/22.85 (powersetsubset) =>
% 131.89/22.85 ((
% 131.89/22.85 (sepInPowerset) =>
% 131.89/22.85 ((
% 131.89/22.85 (sepSubset) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionIL) =>
% 131.89/22.85 ((
% 131.89/22.85 (upairset2IR) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionIR) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionEcases) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionE) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionLsub) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionRsub) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectI) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectSubset5) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectEL) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectLsub) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectSubset2) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectSubset3) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectER) =>
% 131.89/22.85 ((
% 131.89/22.85 (disjointsetsI1) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectRsub) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectSubset4) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectSubset1) =>
% 131.89/22.85 ((
% 131.89/22.85 (bs114d) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusI) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusEL) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusER) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusSubset2) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusERneg) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusELneg) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusILneg) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusIRneg) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusLsub) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusSubset1) =>
% 131.89/22.85 ((
% 131.89/22.85 (symdiffE) =>
% 131.89/22.85 ((
% 131.89/22.85 (symdiffI1) =>
% 131.89/22.85 ((
% 131.89/22.85 (symdiffI2) =>
% 131.89/22.85 ((
% 131.89/22.85 (symdiffIneg1) =>
% 131.89/22.85 ((
% 131.89/22.85 (symdiffIneg2) =>
% 131.89/22.85 ((
% 131.89/22.85 (secondinupair) =>
% 131.89/22.85 ((
% 131.89/22.85 (setukpairIL) =>
% 131.89/22.85 ((
% 131.89/22.85 (setukpairIR) =>
% 131.89/22.85 ((
% 131.89/22.85 (kpairiskpair) =>
% 131.89/22.85 ((
% 131.89/22.85 (kpairp) =>
% 131.89/22.85 ((
% 131.89/22.85 (singletonsubset) =>
% 131.89/22.85 ((
% 131.89/22.85 (singletoninpowerset) =>
% 131.89/22.85 ((
% 131.89/22.85 (singletoninpowunion) =>
% 131.89/22.85 ((
% 131.89/22.85 (upairset2E) =>
% 131.89/22.85 ((
% 131.89/22.85 (upairsubunion) =>
% 131.89/22.85 ((
% 131.89/22.85 (upairinpowunion) =>
% 131.89/22.85 ((
% 131.89/22.85 (ubforcartprodlem1) =>
% 131.89/22.85 ((
% 131.89/22.85 (ubforcartprodlem2) =>
% 131.89/22.85 ((
% 131.89/22.85 (ubforcartprodlem3) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodpairin) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodmempair1) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodmempair) =>
% 131.89/22.85 ((
% 131.89/22.85 (setunionE2) =>
% 131.89/22.85 ((
% 131.89/22.85 (setunionsingleton1) =>
% 131.89/22.85 ((
% 131.89/22.85 (setunionsingleton2) =>
% 131.89/22.85 ((
% 131.89/22.85 (setunionsingleton) =>
% 131.89/22.85 ((
% 131.89/22.85 (singletonprop) =>
% 131.89/22.85 ((
% 131.89/22.85 (ex1E1) =>
% 131.89/22.85 ((
% 131.89/22.85 (ex1I) =>
% 131.89/22.85 ((
% 131.89/22.85 (ex1I2) =>
% 131.89/22.85 ((
% 131.89/22.85 (singletonsuniq) =>
% 131.89/22.85 ((
% 131.89/22.85 (setukpairinjL1) =>
% 131.89/22.85 ((
% 131.89/22.85 (kfstsingleton) =>
% 131.89/22.85 ((
% 131.89/22.85 (theprop) =>
% 131.89/22.85 ((
% 131.89/22.85 (kfstpairEq) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodfstin) =>
% 131.89/22.85 ((
% 131.89/22.85 (setukpairinjL2) =>
% 131.89/22.85 ((
% 131.89/22.85 (setukpairinjL) =>
% 131.89/22.85 ((
% 131.89/22.85 (setukpairinjR11) =>
% 131.89/22.85 ((
% 131.89/22.85 (setukpairinjR12) =>
% 131.89/22.85 ((
% 131.89/22.85 (setukpairinjR1) =>
% 131.89/22.85 ((
% 131.89/22.85 (upairequniteq) =>
% 131.89/22.85 ((
% 131.89/22.85 (setukpairinjR2) =>
% 131.89/22.85 ((
% 131.89/22.85 (setukpairinjR) =>
% 131.89/22.85 ((
% 131.89/22.85 (ksndsingleton) =>
% 131.89/22.85 ((
% 131.89/22.85 (ksndpairEq) =>
% 131.89/22.85 ((
% 131.89/22.85 (kpairsurjEq) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodsndin) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodpairmemEL) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodpairmemER) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodmempaircEq) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodfstpairEq) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodsndpairEq) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodpairsurjEq) =>
% 131.89/22.85 ((
% 131.89/22.85 (dpsetconstrI) =>
% 131.89/22.85 ((
% 131.89/22.85 (dpsetconstrSub) =>
% 131.89/22.85 ((
% 131.89/22.85 (setOfPairsIsBReln) =>
% 131.89/22.85 ((
% 131.89/22.85 (dpsetconstrERa) =>
% 131.89/22.85 ((
% 131.89/22.85 (dpsetconstrEL1) =>
% 131.89/22.85 ((
% 131.89/22.85 (dpsetconstrEL2) =>
% 131.89/22.85 ((
% 131.89/22.85 (dpsetconstrER) =>
% 131.89/22.85 ((
% 131.89/22.85 (funcImageSingleton) =>
% 131.89/22.85 ((
% 131.89/22.85 (apProp) =>
% 131.89/22.85 ((
% 131.89/22.85 (app) =>
% 131.89/22.85 ((
% 131.89/22.85 (infuncsetfunc) =>
% 131.89/22.85 ((
% 131.89/22.85 (ap2p) =>
% 131.89/22.85 ((
% 131.89/22.85 (funcinfuncset) =>
% 131.89/22.85 ((
% 131.89/22.85 (lamProp) =>
% 131.89/22.85 ((
% 131.89/22.85 (lamp) =>
% 131.89/22.85 ((
% 131.89/22.85 (lam2p) =>
% 131.89/22.85 ((
% 131.89/22.85 (brelnall1) =>
% 131.89/22.85 ((
% 131.89/22.85 (brelnall2) =>
% 131.89/22.85 ((
% 131.89/22.85 (ex1E2) =>
% 131.89/22.85 ((
% 131.89/22.85 (funcGraphProp1) =>
% 131.89/22.85 ((
% 131.89/22.85 (funcGraphProp3) =>
% 131.89/22.85 ((
% 131.89/22.85 (funcGraphProp2) =>
% 131.89/22.85 ((
% 131.89/22.85 (funcextLem) =>
% 131.89/22.85 ((
% 131.89/22.85 (funcGraphProp4) =>
% 131.89/22.85 ((
% 131.89/22.85 (subbreln) =>
% 131.89/22.85 ((
% 131.89/22.85 (eqbreln) =>
% 131.89/22.85 ((
% 131.89/22.85 (funcext) =>
% 131.89/22.85 ((
% 131.89/22.85 (funcext2) =>
% 131.89/22.85 ((
% 131.89/22.85 (ap2apEq1) =>
% 131.89/22.85 ((
% 131.89/22.85 (ap2apEq2) =>
% 131.89/22.85 ((
% 131.89/22.85 (beta1) =>
% 131.89/22.85 ((
% 131.89/22.85 (eta1) =>
% 131.89/22.85 ((
% 131.89/22.85 (lam2lamEq) =>
% 131.89/22.85 ((
% 131.89/22.85 (beta2) =>
% 131.89/22.85 ((
% 131.89/22.85 (eta2) =>
% 131.89/22.85 ((
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% 131.89/22.85 ((
% 131.89/22.85 (iffalseProp2) =>
% 131.89/22.85 ((
% 131.89/22.85 (iftrueProp1) =>
% 131.89/22.85 ((
% 131.89/22.85 (iftrueProp2) =>
% 131.89/22.85 ((
% 131.89/22.85 (ifSingleton) =>
% 131.89/22.85 ((
% 131.89/22.85 (ifp) =>
% 131.89/22.85 ((
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% 131.89/22.85 ((
% 131.89/22.85 (iftrue) =>
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% 131.89/22.85 (binunionT_lem) =>
% 131.89/22.85 ((
% 131.89/22.85 (powersetT_lem) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusT_lem) =>
% 131.89/22.85 ((
% 131.89/22.85 (complementT_lem) =>
% 131.89/22.85 ((
% 131.89/22.85 (setextT) =>
% 131.89/22.85 ((
% 131.89/22.85 (subsetTI) =>
% 131.89/22.85 ((
% 131.89/22.85 (powersetTI1) =>
% 131.89/22.85 ((
% 131.89/22.85 (powersetTE1) =>
% 131.89/22.85 ((
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% 131.89/22.85 ((
% 131.89/22.85 (complementTE1) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectTELcontra) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectTERcontra) =>
% 131.89/22.85 ((
% 131.89/22.85 (contrasubsetT) =>
% 131.89/22.85 ((
% 131.89/22.85 (contrasubsetT1) =>
% 131.89/22.85 ((
% 131.89/22.85 (contrasubsetT2) =>
% 131.89/22.85 ((
% 131.89/22.85 (contrasubsetT3) =>
% 131.89/22.85 ((
% 131.89/22.85 (doubleComplementI1) =>
% 131.89/22.85 ((
% 131.89/22.85 (doubleComplementE1) =>
% 131.89/22.85 ((
% 131.89/22.85 (doubleComplementSub1) =>
% 131.89/22.85 ((
% 131.89/22.85 (doubleComplementSub2) =>
% 131.89/22.85 ((
% 131.89/22.85 (doubleComplementEq) =>
% 131.89/22.85 ((
% 131.89/22.85 (complementTnotintersectT) =>
% 131.89/22.85 ((
% 131.89/22.85 (complementImpComplementIntersect) =>
% 131.89/22.85 ((
% 131.89/22.85 (complementSubsetComplementIntersect) =>
% 131.89/22.85 ((
% 131.89/22.85 (complementInPowersetComplementIntersect) =>
% 131.89/22.85 ((
% 131.89/22.85 (contraSubsetComplement) =>
% 131.89/22.85 ((
% 131.89/22.85 (complementTcontraSubset) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionTILcontra) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionTIRcontra) =>
% 131.89/22.85 ((
% 131.89/22.85 (inIntersectImpInUnion) =>
% 131.89/22.85 ((
% 131.89/22.85 (inIntersectImpInUnion2) =>
% 131.89/22.85 ((
% 131.89/22.85 (inIntersectImpInIntersectUnions) =>
% 131.89/22.85 ((
% 131.89/22.85 (intersectInPowersetIntersectUnions) =>
% 131.89/22.85 ((
% 131.89/22.85 (inComplementUnionImpNotIn1) =>
% 131.89/22.85 ((
% 131.89/22.85 (inComplementUnionImpInComplement1) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionTE) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionTEcontra) =>
% 131.89/22.85 ((
% 131.89/22.85 (demorgan2a1) =>
% 131.89/22.85 ((
% 131.89/22.85 (complementUnionInPowersetComplement) =>
% 131.89/22.85 ((
% 131.89/22.85 (demorgan2a2) =>
% 131.89/22.85 ((
% 131.89/22.85 (demorgan1a) =>
% 131.89/22.85 ((
% 131.89/22.85 (demorgan1b) =>
% 131.89/22.85 ((
% 131.89/22.85 (demorgan1) =>
% 131.89/22.85 ((
% 131.89/22.85 (demorgan2a) =>
% 131.89/22.85 ((
% 131.89/22.85 (demorgan2b2) =>
% 131.89/22.85 ((
% 131.89/22.85 (demorgan2b) =>
% 131.89/22.85 ((
% 131.89/22.85 (demorgan2) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz13rule0) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz13rule1) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz13rule2) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz13rule3) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz13rule4) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz1_1) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz1_2) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz1_3) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz1_4) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz1_5) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1all2) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1SetBreln1) =>
% 131.89/22.85 ((
% 131.89/22.85 (choice2fnsingleton) =>
% 131.89/22.85 ((
% 131.89/22.85 (setOfPairsIsBReln1) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1all1) =>
% 131.89/22.85 ((
% 131.89/22.85 (subbreln1) =>
% 131.89/22.85 ((
% 131.89/22.85 (eqbreln1) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1invprop) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1invI) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1invE) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1compprop) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1compI) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1compE) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1compEex) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1unionprop) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1unionIL) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1unionIR) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1unionI) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1unionE) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1unionEcases) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1unionCommutes) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz2Ex) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz2W) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz2A) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz2B) =>
% 131.89/22.85 ((
% 131.89/22.85 (image1Ex) =>
% 131.89/22.85 ((
% 131.89/22.85 (image1Ex1) =>
% 131.89/22.85 ((
% 131.89/22.85 (image1Equiv) =>
% 131.89/22.85 ((
% 131.89/22.85 (image1E) =>
% 131.89/22.85 ((
% 131.89/22.85 (image1I) =>
% 131.89/22.85 ((
% 131.89/22.85 (injFuncInInjFuncSet) =>
% 131.89/22.85 ((
% 131.89/22.85 (injFuncSetFuncIn) =>
% 131.89/22.85 ((
% 131.89/22.85 (injFuncSetFuncInj) =>
% 131.89/22.85 ((
% 131.89/22.85 (surjFuncSetFuncIn) =>
% 131.89/22.85 ((
% 131.89/22.85 (surjFuncSetFuncSurj) =>
% 131.89/22.85 ((
% 131.89/22.85 (leftInvIsSurj) =>
% 131.89/22.85 ((
% 131.89/22.85 (surjCantorThm) =>
% 131.89/22.85 ((
% 131.89/22.85 (foundation2) =>
% 131.89/22.85 ((
% 131.89/22.85 (notinself) =>
% 131.89/22.85 ((
% 131.89/22.85 (notinself2) =>
% 131.89/22.85 ((
% 131.89/22.85 (omegaSp) =>
% 131.89/22.85 ((
% 131.89/22.85 (omegaSclos) =>
% 131.89/22.85 ((
% 131.89/22.85 (peano0notS) =>
% 131.89/22.85 ((
% 131.89/22.85 (peanoSinj) =>
% 131.89/22.85 ((
% 131.89/22.85 (transitivesetOp1) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintTransitive) =>
% 131.89/22.85 ((
% 131.89/22.85 (transitivesetOp2) =>
% 131.89/22.85 ((
% 131.89/22.85 (setunionTransitive) =>
% 131.89/22.85 ((
% 131.89/22.85 (ordinalMinLem1) =>
% 131.89/22.85 ((
% 131.89/22.85 (ordinalTransSet) =>
% 131.89/22.85 ((
% 131.89/22.85 (ordinalTransSet1) =>
% 131.89/22.85 ((
% 131.89/22.85 (setunionOrdinalLem1) =>
% 131.89/22.85 (ordinal @
% 131.89/22.85 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 131.89/22.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl491])).
% 131.89/22.85 thf(zip_derived_cl508, plain,
% 131.89/22.85 (~ (((prop2set2propI) =>
% 131.89/22.85 (((notdexE) =>
% 131.89/22.85 (((notdallE) =>
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% 131.89/22.85 (((exuI3) =>
% 131.89/22.85 (((exuI2) =>
% 131.89/22.85 (((inCongP) =>
% 131.89/22.85 (((in__Cong) =>
% 131.89/22.85 (((exuE3u) =>
% 131.89/22.85 (((exu__Cong) =>
% 131.89/22.85 (((setadjoin__Cong) =>
% 131.89/22.85 (((powerset__Cong) =>
% 131.89/22.85 (((setunion__Cong) =>
% 131.89/22.85 (((exuEu) =>
% 131.89/22.85 (((descr__Cong) =>
% 131.89/22.85 (((dsetconstr__Cong) =>
% 131.89/22.85 (((subsetI1) =>
% 131.89/22.85 (((eqimpsubset2) =>
% 131.89/22.85 (((eqimpsubset1) =>
% 131.89/22.85 (((subsetI2) =>
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% 131.89/22.85 (((subsetE2) =>
% 131.89/22.85 (((notsubsetI) =>
% 131.89/22.85 (((notequalI1) =>
% 131.89/22.85 (((notequalI2) =>
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% 131.89/22.85 (((subsetTrans) =>
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% 131.89/22.85 ((
% 131.89/22.85 (powersetE1) =>
% 131.89/22.85 ((
% 131.89/22.85 (inPowerset) =>
% 131.89/22.85 ((
% 131.89/22.85 (powersetsubset) =>
% 131.89/22.85 ((
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% 131.89/22.85 ((
% 131.89/22.85 (sepSubset) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionIL) =>
% 131.89/22.85 ((
% 131.89/22.85 (upairset2IR) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionIR) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionEcases) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionE) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionLsub) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionRsub) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectI) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectSubset5) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectEL) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectLsub) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectSubset2) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectSubset3) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectER) =>
% 131.89/22.85 ((
% 131.89/22.85 (disjointsetsI1) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectRsub) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectSubset4) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectSubset1) =>
% 131.89/22.85 ((
% 131.89/22.85 (bs114d) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusI) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusEL) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusER) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusSubset2) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusERneg) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusELneg) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusILneg) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusIRneg) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusLsub) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusSubset1) =>
% 131.89/22.85 ((
% 131.89/22.85 (symdiffE) =>
% 131.89/22.85 ((
% 131.89/22.85 (symdiffI1) =>
% 131.89/22.85 ((
% 131.89/22.85 (symdiffI2) =>
% 131.89/22.85 ((
% 131.89/22.85 (symdiffIneg1) =>
% 131.89/22.85 ((
% 131.89/22.85 (symdiffIneg2) =>
% 131.89/22.85 ((
% 131.89/22.85 (secondinupair) =>
% 131.89/22.85 ((
% 131.89/22.85 (setukpairIL) =>
% 131.89/22.85 ((
% 131.89/22.85 (setukpairIR) =>
% 131.89/22.85 ((
% 131.89/22.85 (kpairiskpair) =>
% 131.89/22.85 ((
% 131.89/22.85 (kpairp) =>
% 131.89/22.85 ((
% 131.89/22.85 (singletonsubset) =>
% 131.89/22.85 ((
% 131.89/22.85 (singletoninpowerset) =>
% 131.89/22.85 ((
% 131.89/22.85 (singletoninpowunion) =>
% 131.89/22.85 ((
% 131.89/22.85 (upairset2E) =>
% 131.89/22.85 ((
% 131.89/22.85 (upairsubunion) =>
% 131.89/22.85 ((
% 131.89/22.85 (upairinpowunion) =>
% 131.89/22.85 ((
% 131.89/22.85 (ubforcartprodlem1) =>
% 131.89/22.85 ((
% 131.89/22.85 (ubforcartprodlem2) =>
% 131.89/22.85 ((
% 131.89/22.85 (ubforcartprodlem3) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodpairin) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodmempair1) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodmempair) =>
% 131.89/22.85 ((
% 131.89/22.85 (setunionE2) =>
% 131.89/22.85 ((
% 131.89/22.85 (setunionsingleton1) =>
% 131.89/22.85 ((
% 131.89/22.85 (setunionsingleton2) =>
% 131.89/22.85 ((
% 131.89/22.85 (setunionsingleton) =>
% 131.89/22.85 ((
% 131.89/22.85 (singletonprop) =>
% 131.89/22.85 ((
% 131.89/22.85 (ex1E1) =>
% 131.89/22.85 ((
% 131.89/22.85 (ex1I) =>
% 131.89/22.85 ((
% 131.89/22.85 (ex1I2) =>
% 131.89/22.85 ((
% 131.89/22.85 (singletonsuniq) =>
% 131.89/22.85 ((
% 131.89/22.85 (setukpairinjL1) =>
% 131.89/22.85 ((
% 131.89/22.85 (kfstsingleton) =>
% 131.89/22.85 ((
% 131.89/22.85 (theprop) =>
% 131.89/22.85 ((
% 131.89/22.85 (kfstpairEq) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodfstin) =>
% 131.89/22.85 ((
% 131.89/22.85 (setukpairinjL2) =>
% 131.89/22.85 ((
% 131.89/22.85 (setukpairinjL) =>
% 131.89/22.85 ((
% 131.89/22.85 (setukpairinjR11) =>
% 131.89/22.85 ((
% 131.89/22.85 (setukpairinjR12) =>
% 131.89/22.85 ((
% 131.89/22.85 (setukpairinjR1) =>
% 131.89/22.85 ((
% 131.89/22.85 (upairequniteq) =>
% 131.89/22.85 ((
% 131.89/22.85 (setukpairinjR2) =>
% 131.89/22.85 ((
% 131.89/22.85 (setukpairinjR) =>
% 131.89/22.85 ((
% 131.89/22.85 (ksndsingleton) =>
% 131.89/22.85 ((
% 131.89/22.85 (ksndpairEq) =>
% 131.89/22.85 ((
% 131.89/22.85 (kpairsurjEq) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodsndin) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodpairmemEL) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodpairmemER) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodmempaircEq) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodfstpairEq) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodsndpairEq) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodpairsurjEq) =>
% 131.89/22.85 ((
% 131.89/22.85 (dpsetconstrI) =>
% 131.89/22.85 ((
% 131.89/22.85 (dpsetconstrSub) =>
% 131.89/22.85 ((
% 131.89/22.85 (setOfPairsIsBReln) =>
% 131.89/22.85 ((
% 131.89/22.85 (dpsetconstrERa) =>
% 131.89/22.85 ((
% 131.89/22.85 (dpsetconstrEL1) =>
% 131.89/22.85 ((
% 131.89/22.85 (dpsetconstrEL2) =>
% 131.89/22.85 ((
% 131.89/22.85 (dpsetconstrER) =>
% 131.89/22.85 ((
% 131.89/22.85 (funcImageSingleton) =>
% 131.89/22.85 ((
% 131.89/22.85 (apProp) =>
% 131.89/22.85 ((
% 131.89/22.85 (app) =>
% 131.89/22.85 ((
% 131.89/22.85 (infuncsetfunc) =>
% 131.89/22.85 ((
% 131.89/22.85 (ap2p) =>
% 131.89/22.85 ((
% 131.89/22.85 (funcinfuncset) =>
% 131.89/22.85 ((
% 131.89/22.85 (lamProp) =>
% 131.89/22.85 ((
% 131.89/22.85 (lamp) =>
% 131.89/22.85 ((
% 131.89/22.85 (lam2p) =>
% 131.89/22.85 ((
% 131.89/22.85 (brelnall1) =>
% 131.89/22.85 ((
% 131.89/22.85 (brelnall2) =>
% 131.89/22.85 ((
% 131.89/22.85 (ex1E2) =>
% 131.89/22.85 ((
% 131.89/22.85 (funcGraphProp1) =>
% 131.89/22.85 ((
% 131.89/22.85 (funcGraphProp3) =>
% 131.89/22.85 ((
% 131.89/22.85 (funcGraphProp2) =>
% 131.89/22.85 ((
% 131.89/22.85 (funcextLem) =>
% 131.89/22.85 ((
% 131.89/22.85 (funcGraphProp4) =>
% 131.89/22.85 ((
% 131.89/22.85 (subbreln) =>
% 131.89/22.85 ((
% 131.89/22.85 (eqbreln) =>
% 131.89/22.85 ((
% 131.89/22.85 (funcext) =>
% 131.89/22.85 ((
% 131.89/22.85 (funcext2) =>
% 131.89/22.85 ((
% 131.89/22.85 (ap2apEq1) =>
% 131.89/22.85 ((
% 131.89/22.85 (ap2apEq2) =>
% 131.89/22.85 ((
% 131.89/22.85 (beta1) =>
% 131.89/22.85 ((
% 131.89/22.85 (eta1) =>
% 131.89/22.85 ((
% 131.89/22.85 (lam2lamEq) =>
% 131.89/22.85 ((
% 131.89/22.85 (beta2) =>
% 131.89/22.85 ((
% 131.89/22.85 (eta2) =>
% 131.89/22.85 ((
% 131.89/22.85 (iffalseProp1) =>
% 131.89/22.85 ((
% 131.89/22.85 (iffalseProp2) =>
% 131.89/22.85 ((
% 131.89/22.85 (iftrueProp1) =>
% 131.89/22.85 ((
% 131.89/22.85 (iftrueProp2) =>
% 131.89/22.85 ((
% 131.89/22.85 (ifSingleton) =>
% 131.89/22.85 ((
% 131.89/22.85 (ifp) =>
% 131.89/22.85 ((
% 131.89/22.85 (theeq) =>
% 131.89/22.85 ((
% 131.89/22.85 (iftrue) =>
% 131.89/22.85 ((
% 131.89/22.85 (iffalse) =>
% 131.89/22.85 ((
% 131.89/22.85 (iftrueorfalse) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectT_lem) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionT_lem) =>
% 131.89/22.85 ((
% 131.89/22.85 (powersetT_lem) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusT_lem) =>
% 131.89/22.85 ((
% 131.89/22.85 (complementT_lem) =>
% 131.89/22.85 ((
% 131.89/22.85 (setextT) =>
% 131.89/22.85 ((
% 131.89/22.85 (subsetTI) =>
% 131.89/22.85 ((
% 131.89/22.85 (powersetTI1) =>
% 131.89/22.85 ((
% 131.89/22.85 (powersetTE1) =>
% 131.89/22.85 ((
% 131.89/22.85 (complementTI1) =>
% 131.89/22.85 ((
% 131.89/22.85 (complementTE1) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectTELcontra) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectTERcontra) =>
% 131.89/22.85 ((
% 131.89/22.85 (contrasubsetT) =>
% 131.89/22.85 ((
% 131.89/22.85 (contrasubsetT1) =>
% 131.89/22.85 ((
% 131.89/22.85 (contrasubsetT2) =>
% 131.89/22.85 ((
% 131.89/22.85 (contrasubsetT3) =>
% 131.89/22.85 ((
% 131.89/22.85 (doubleComplementI1) =>
% 131.89/22.85 ((
% 131.89/22.85 (doubleComplementE1) =>
% 131.89/22.85 ((
% 131.89/22.85 (doubleComplementSub1) =>
% 131.89/22.85 ((
% 131.89/22.85 (doubleComplementSub2) =>
% 131.89/22.85 ((
% 131.89/22.85 (doubleComplementEq) =>
% 131.89/22.85 ((
% 131.89/22.85 (complementTnotintersectT) =>
% 131.89/22.85 ((
% 131.89/22.85 (complementImpComplementIntersect) =>
% 131.89/22.85 ((
% 131.89/22.85 (complementSubsetComplementIntersect) =>
% 131.89/22.85 ((
% 131.89/22.85 (complementInPowersetComplementIntersect) =>
% 131.89/22.85 ((
% 131.89/22.85 (contraSubsetComplement) =>
% 131.89/22.85 ((
% 131.89/22.85 (complementTcontraSubset) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionTILcontra) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionTIRcontra) =>
% 131.89/22.85 ((
% 131.89/22.85 (inIntersectImpInUnion) =>
% 131.89/22.85 ((
% 131.89/22.85 (inIntersectImpInUnion2) =>
% 131.89/22.85 ((
% 131.89/22.85 (inIntersectImpInIntersectUnions) =>
% 131.89/22.85 ((
% 131.89/22.85 (intersectInPowersetIntersectUnions) =>
% 131.89/22.85 ((
% 131.89/22.85 (inComplementUnionImpNotIn1) =>
% 131.89/22.85 ((
% 131.89/22.85 (inComplementUnionImpInComplement1) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionTE) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionTEcontra) =>
% 131.89/22.85 ((
% 131.89/22.85 (demorgan2a1) =>
% 131.89/22.85 ((
% 131.89/22.85 (complementUnionInPowersetComplement) =>
% 131.89/22.85 ((
% 131.89/22.85 (demorgan2a2) =>
% 131.89/22.85 ((
% 131.89/22.85 (demorgan1a) =>
% 131.89/22.85 ((
% 131.89/22.85 (demorgan1b) =>
% 131.89/22.85 ((
% 131.89/22.85 (demorgan1) =>
% 131.89/22.85 ((
% 131.89/22.85 (demorgan2a) =>
% 131.89/22.85 ((
% 131.89/22.85 (demorgan2b2) =>
% 131.89/22.85 ((
% 131.89/22.85 (demorgan2b) =>
% 131.89/22.85 ((
% 131.89/22.85 (demorgan2) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz13rule0) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz13rule1) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz13rule2) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz13rule3) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz13rule4) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz1_1) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz1_2) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz1_3) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz1_4) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz1_5) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1all2) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1SetBreln1) =>
% 131.89/22.85 ((
% 131.89/22.85 (choice2fnsingleton) =>
% 131.89/22.85 ((
% 131.89/22.85 (setOfPairsIsBReln1) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1all1) =>
% 131.89/22.85 ((
% 131.89/22.85 (subbreln1) =>
% 131.89/22.85 ((
% 131.89/22.85 (eqbreln1) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1invprop) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1invI) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1invE) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1compprop) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1compI) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1compE) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1compEex) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1unionprop) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1unionIL) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1unionIR) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1unionI) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1unionE) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1unionEcases) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1unionCommutes) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz2Ex) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz2W) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz2A) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz2B) =>
% 131.89/22.85 ((
% 131.89/22.85 (image1Ex) =>
% 131.89/22.85 ((
% 131.89/22.85 (image1Ex1) =>
% 131.89/22.85 ((
% 131.89/22.85 (image1Equiv) =>
% 131.89/22.85 ((
% 131.89/22.85 (image1E) =>
% 131.89/22.85 ((
% 131.89/22.85 (image1I) =>
% 131.89/22.85 ((
% 131.89/22.85 (injFuncInInjFuncSet) =>
% 131.89/22.85 ((
% 131.89/22.85 (injFuncSetFuncIn) =>
% 131.89/22.85 ((
% 131.89/22.85 (injFuncSetFuncInj) =>
% 131.89/22.85 ((
% 131.89/22.85 (surjFuncSetFuncIn) =>
% 131.89/22.85 ((
% 131.89/22.85 (surjFuncSetFuncSurj) =>
% 131.89/22.85 ((
% 131.89/22.85 (leftInvIsSurj) =>
% 131.89/22.85 ((
% 131.89/22.85 (surjCantorThm) =>
% 131.89/22.85 ((
% 131.89/22.85 (foundation2) =>
% 131.89/22.85 ((
% 131.89/22.85 (notinself) =>
% 131.89/22.85 ((
% 131.89/22.85 (notinself2) =>
% 131.89/22.85 ((
% 131.89/22.85 (omegaSp) =>
% 131.89/22.85 ((
% 131.89/22.85 (omegaSclos) =>
% 131.89/22.85 ((
% 131.89/22.85 (peano0notS) =>
% 131.89/22.85 ((
% 131.89/22.85 (peanoSinj) =>
% 131.89/22.85 ((
% 131.89/22.85 (transitivesetOp1) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintTransitive) =>
% 131.89/22.85 ((
% 131.89/22.85 (transitivesetOp2) =>
% 131.89/22.85 ((
% 131.89/22.85 (setunionTransitive) =>
% 131.89/22.85 ((
% 131.89/22.85 (ordinalMinLem1) =>
% 131.89/22.85 ((
% 131.89/22.85 (ordinalTransSet) =>
% 131.89/22.85 ((
% 131.89/22.85 (ordinalTransSet1) =>
% 131.89/22.85 ((
% 131.89/22.85 (setunionOrdinalLem1) =>
% 131.89/22.85 (ordinal @
% 131.89/22.85 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 131.89/22.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl501])).
% 131.89/22.85 thf(zip_derived_cl515, plain,
% 131.89/22.85 (~ (((notdexE) =>
% 131.89/22.85 (((notdallE) =>
% 131.89/22.85 (((exuI1) =>
% 131.89/22.85 (((exuI3) =>
% 131.89/22.85 (((exuI2) =>
% 131.89/22.85 (((inCongP) =>
% 131.89/22.85 (((in__Cong) =>
% 131.89/22.85 (((exuE3u) =>
% 131.89/22.85 (((exu__Cong) =>
% 131.89/22.85 (((setadjoin__Cong) =>
% 131.89/22.85 (((powerset__Cong) =>
% 131.89/22.85 (((setunion__Cong) =>
% 131.89/22.85 (((exuEu) =>
% 131.89/22.85 (((descr__Cong) =>
% 131.89/22.85 (((dsetconstr__Cong) =>
% 131.89/22.85 (((subsetI1) =>
% 131.89/22.85 (((eqimpsubset2) =>
% 131.89/22.85 (((eqimpsubset1) =>
% 131.89/22.85 (((subsetI2) =>
% 131.89/22.85 (((emptysetsubset) =>
% 131.89/22.85 (((subsetE) =>
% 131.89/22.85 (((subsetE2) =>
% 131.89/22.85 (((notsubsetI) =>
% 131.89/22.85 (((notequalI1) =>
% 131.89/22.85 (((notequalI2) =>
% 131.89/22.85 (((subsetRefl) =>
% 131.89/22.85 (((subsetTrans) =>
% 131.89/22.85 (((setadjoinSub) =>
% 131.89/22.85 (((setadjoinSub2) =>
% 131.89/22.85 (((subset2powerset) =>
% 131.89/22.85 ((
% 131.89/22.85 (setextsub) =>
% 131.89/22.85 ((
% 131.89/22.85 (subsetemptysetimpeq) =>
% 131.89/22.85 ((
% 131.89/22.85 (powersetI1) =>
% 131.89/22.85 ((
% 131.89/22.85 (powersetE1) =>
% 131.89/22.85 ((
% 131.89/22.85 (inPowerset) =>
% 131.89/22.85 ((
% 131.89/22.85 (powersetsubset) =>
% 131.89/22.85 ((
% 131.89/22.85 (sepInPowerset) =>
% 131.89/22.85 ((
% 131.89/22.85 (sepSubset) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionIL) =>
% 131.89/22.85 ((
% 131.89/22.85 (upairset2IR) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionIR) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionEcases) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionE) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionLsub) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionRsub) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectI) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectSubset5) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectEL) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectLsub) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectSubset2) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectSubset3) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectER) =>
% 131.89/22.85 ((
% 131.89/22.85 (disjointsetsI1) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectRsub) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectSubset4) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectSubset1) =>
% 131.89/22.85 ((
% 131.89/22.85 (bs114d) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusI) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusEL) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusER) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusSubset2) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusERneg) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusELneg) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusILneg) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusIRneg) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusLsub) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusSubset1) =>
% 131.89/22.85 ((
% 131.89/22.85 (symdiffE) =>
% 131.89/22.85 ((
% 131.89/22.85 (symdiffI1) =>
% 131.89/22.85 ((
% 131.89/22.85 (symdiffI2) =>
% 131.89/22.85 ((
% 131.89/22.85 (symdiffIneg1) =>
% 131.89/22.85 ((
% 131.89/22.85 (symdiffIneg2) =>
% 131.89/22.85 ((
% 131.89/22.85 (secondinupair) =>
% 131.89/22.85 ((
% 131.89/22.85 (setukpairIL) =>
% 131.89/22.85 ((
% 131.89/22.85 (setukpairIR) =>
% 131.89/22.85 ((
% 131.89/22.85 (kpairiskpair) =>
% 131.89/22.85 ((
% 131.89/22.85 (kpairp) =>
% 131.89/22.85 ((
% 131.89/22.85 (singletonsubset) =>
% 131.89/22.85 ((
% 131.89/22.85 (singletoninpowerset) =>
% 131.89/22.85 ((
% 131.89/22.85 (singletoninpowunion) =>
% 131.89/22.85 ((
% 131.89/22.85 (upairset2E) =>
% 131.89/22.85 ((
% 131.89/22.85 (upairsubunion) =>
% 131.89/22.85 ((
% 131.89/22.85 (upairinpowunion) =>
% 131.89/22.85 ((
% 131.89/22.85 (ubforcartprodlem1) =>
% 131.89/22.85 ((
% 131.89/22.85 (ubforcartprodlem2) =>
% 131.89/22.85 ((
% 131.89/22.85 (ubforcartprodlem3) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodpairin) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodmempair1) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodmempair) =>
% 131.89/22.85 ((
% 131.89/22.85 (setunionE2) =>
% 131.89/22.85 ((
% 131.89/22.85 (setunionsingleton1) =>
% 131.89/22.85 ((
% 131.89/22.85 (setunionsingleton2) =>
% 131.89/22.85 ((
% 131.89/22.85 (setunionsingleton) =>
% 131.89/22.85 ((
% 131.89/22.85 (singletonprop) =>
% 131.89/22.85 ((
% 131.89/22.85 (ex1E1) =>
% 131.89/22.85 ((
% 131.89/22.85 (ex1I) =>
% 131.89/22.85 ((
% 131.89/22.85 (ex1I2) =>
% 131.89/22.85 ((
% 131.89/22.85 (singletonsuniq) =>
% 131.89/22.85 ((
% 131.89/22.85 (setukpairinjL1) =>
% 131.89/22.85 ((
% 131.89/22.85 (kfstsingleton) =>
% 131.89/22.85 ((
% 131.89/22.85 (theprop) =>
% 131.89/22.85 ((
% 131.89/22.85 (kfstpairEq) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodfstin) =>
% 131.89/22.85 ((
% 131.89/22.85 (setukpairinjL2) =>
% 131.89/22.85 ((
% 131.89/22.85 (setukpairinjL) =>
% 131.89/22.85 ((
% 131.89/22.85 (setukpairinjR11) =>
% 131.89/22.85 ((
% 131.89/22.85 (setukpairinjR12) =>
% 131.89/22.85 ((
% 131.89/22.85 (setukpairinjR1) =>
% 131.89/22.85 ((
% 131.89/22.85 (upairequniteq) =>
% 131.89/22.85 ((
% 131.89/22.85 (setukpairinjR2) =>
% 131.89/22.85 ((
% 131.89/22.85 (setukpairinjR) =>
% 131.89/22.85 ((
% 131.89/22.85 (ksndsingleton) =>
% 131.89/22.85 ((
% 131.89/22.85 (ksndpairEq) =>
% 131.89/22.85 ((
% 131.89/22.85 (kpairsurjEq) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodsndin) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodpairmemEL) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodpairmemER) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodmempaircEq) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodfstpairEq) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodsndpairEq) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodpairsurjEq) =>
% 131.89/22.85 ((
% 131.89/22.85 (dpsetconstrI) =>
% 131.89/22.85 ((
% 131.89/22.85 (dpsetconstrSub) =>
% 131.89/22.85 ((
% 131.89/22.85 (setOfPairsIsBReln) =>
% 131.89/22.85 ((
% 131.89/22.85 (dpsetconstrERa) =>
% 131.89/22.85 ((
% 131.89/22.85 (dpsetconstrEL1) =>
% 131.89/22.85 ((
% 131.89/22.85 (dpsetconstrEL2) =>
% 131.89/22.85 ((
% 131.89/22.85 (dpsetconstrER) =>
% 131.89/22.85 ((
% 131.89/22.85 (funcImageSingleton) =>
% 131.89/22.85 ((
% 131.89/22.85 (apProp) =>
% 131.89/22.85 ((
% 131.89/22.85 (app) =>
% 131.89/22.85 ((
% 131.89/22.85 (infuncsetfunc) =>
% 131.89/22.85 ((
% 131.89/22.85 (ap2p) =>
% 131.89/22.85 ((
% 131.89/22.85 (funcinfuncset) =>
% 131.89/22.85 ((
% 131.89/22.85 (lamProp) =>
% 131.89/22.85 ((
% 131.89/22.85 (lamp) =>
% 131.89/22.85 ((
% 131.89/22.85 (lam2p) =>
% 131.89/22.85 ((
% 131.89/22.85 (brelnall1) =>
% 131.89/22.85 ((
% 131.89/22.85 (brelnall2) =>
% 131.89/22.85 ((
% 131.89/22.85 (ex1E2) =>
% 131.89/22.85 ((
% 131.89/22.85 (funcGraphProp1) =>
% 131.89/22.85 ((
% 131.89/22.85 (funcGraphProp3) =>
% 131.89/22.85 ((
% 131.89/22.85 (funcGraphProp2) =>
% 131.89/22.85 ((
% 131.89/22.85 (funcextLem) =>
% 131.89/22.85 ((
% 131.89/22.85 (funcGraphProp4) =>
% 131.89/22.85 ((
% 131.89/22.85 (subbreln) =>
% 131.89/22.85 ((
% 131.89/22.85 (eqbreln) =>
% 131.89/22.85 ((
% 131.89/22.85 (funcext) =>
% 131.89/22.85 ((
% 131.89/22.85 (funcext2) =>
% 131.89/22.85 ((
% 131.89/22.85 (ap2apEq1) =>
% 131.89/22.85 ((
% 131.89/22.85 (ap2apEq2) =>
% 131.89/22.85 ((
% 131.89/22.85 (beta1) =>
% 131.89/22.85 ((
% 131.89/22.85 (eta1) =>
% 131.89/22.85 ((
% 131.89/22.85 (lam2lamEq) =>
% 131.89/22.85 ((
% 131.89/22.85 (beta2) =>
% 131.89/22.85 ((
% 131.89/22.85 (eta2) =>
% 131.89/22.85 ((
% 131.89/22.85 (iffalseProp1) =>
% 131.89/22.85 ((
% 131.89/22.85 (iffalseProp2) =>
% 131.89/22.85 ((
% 131.89/22.85 (iftrueProp1) =>
% 131.89/22.85 ((
% 131.89/22.85 (iftrueProp2) =>
% 131.89/22.85 ((
% 131.89/22.85 (ifSingleton) =>
% 131.89/22.85 ((
% 131.89/22.85 (ifp) =>
% 131.89/22.85 ((
% 131.89/22.85 (theeq) =>
% 131.89/22.85 ((
% 131.89/22.85 (iftrue) =>
% 131.89/22.85 ((
% 131.89/22.85 (iffalse) =>
% 131.89/22.85 ((
% 131.89/22.85 (iftrueorfalse) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectT_lem) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionT_lem) =>
% 131.89/22.85 ((
% 131.89/22.85 (powersetT_lem) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusT_lem) =>
% 131.89/22.85 ((
% 131.89/22.85 (complementT_lem) =>
% 131.89/22.85 ((
% 131.89/22.85 (setextT) =>
% 131.89/22.85 ((
% 131.89/22.85 (subsetTI) =>
% 131.89/22.85 ((
% 131.89/22.85 (powersetTI1) =>
% 131.89/22.85 ((
% 131.89/22.85 (powersetTE1) =>
% 131.89/22.85 ((
% 131.89/22.85 (complementTI1) =>
% 131.89/22.85 ((
% 131.89/22.85 (complementTE1) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectTELcontra) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectTERcontra) =>
% 131.89/22.85 ((
% 131.89/22.85 (contrasubsetT) =>
% 131.89/22.85 ((
% 131.89/22.85 (contrasubsetT1) =>
% 131.89/22.85 ((
% 131.89/22.85 (contrasubsetT2) =>
% 131.89/22.85 ((
% 131.89/22.85 (contrasubsetT3) =>
% 131.89/22.85 ((
% 131.89/22.85 (doubleComplementI1) =>
% 131.89/22.85 ((
% 131.89/22.85 (doubleComplementE1) =>
% 131.89/22.85 ((
% 131.89/22.85 (doubleComplementSub1) =>
% 131.89/22.85 ((
% 131.89/22.85 (doubleComplementSub2) =>
% 131.89/22.85 ((
% 131.89/22.85 (doubleComplementEq) =>
% 131.89/22.85 ((
% 131.89/22.85 (complementTnotintersectT) =>
% 131.89/22.85 ((
% 131.89/22.85 (complementImpComplementIntersect) =>
% 131.89/22.85 ((
% 131.89/22.85 (complementSubsetComplementIntersect) =>
% 131.89/22.85 ((
% 131.89/22.85 (complementInPowersetComplementIntersect) =>
% 131.89/22.85 ((
% 131.89/22.85 (contraSubsetComplement) =>
% 131.89/22.85 ((
% 131.89/22.85 (complementTcontraSubset) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionTILcontra) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionTIRcontra) =>
% 131.89/22.85 ((
% 131.89/22.85 (inIntersectImpInUnion) =>
% 131.89/22.85 ((
% 131.89/22.85 (inIntersectImpInUnion2) =>
% 131.89/22.85 ((
% 131.89/22.85 (inIntersectImpInIntersectUnions) =>
% 131.89/22.85 ((
% 131.89/22.85 (intersectInPowersetIntersectUnions) =>
% 131.89/22.85 ((
% 131.89/22.85 (inComplementUnionImpNotIn1) =>
% 131.89/22.85 ((
% 131.89/22.85 (inComplementUnionImpInComplement1) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionTE) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionTEcontra) =>
% 131.89/22.85 ((
% 131.89/22.85 (demorgan2a1) =>
% 131.89/22.85 ((
% 131.89/22.85 (complementUnionInPowersetComplement) =>
% 131.89/22.85 ((
% 131.89/22.85 (demorgan2a2) =>
% 131.89/22.85 ((
% 131.89/22.85 (demorgan1a) =>
% 131.89/22.85 ((
% 131.89/22.85 (demorgan1b) =>
% 131.89/22.85 ((
% 131.89/22.85 (demorgan1) =>
% 131.89/22.85 ((
% 131.89/22.85 (demorgan2a) =>
% 131.89/22.85 ((
% 131.89/22.85 (demorgan2b2) =>
% 131.89/22.85 ((
% 131.89/22.85 (demorgan2b) =>
% 131.89/22.85 ((
% 131.89/22.85 (demorgan2) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz13rule0) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz13rule1) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz13rule2) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz13rule3) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz13rule4) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz1_1) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz1_2) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz1_3) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz1_4) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz1_5) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1all2) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1SetBreln1) =>
% 131.89/22.85 ((
% 131.89/22.85 (choice2fnsingleton) =>
% 131.89/22.85 ((
% 131.89/22.85 (setOfPairsIsBReln1) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1all1) =>
% 131.89/22.85 ((
% 131.89/22.85 (subbreln1) =>
% 131.89/22.85 ((
% 131.89/22.85 (eqbreln1) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1invprop) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1invI) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1invE) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1compprop) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1compI) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1compE) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1compEex) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1unionprop) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1unionIL) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1unionIR) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1unionI) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1unionE) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1unionEcases) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1unionCommutes) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz2Ex) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz2W) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz2A) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz2B) =>
% 131.89/22.85 ((
% 131.89/22.85 (image1Ex) =>
% 131.89/22.85 ((
% 131.89/22.85 (image1Ex1) =>
% 131.89/22.85 ((
% 131.89/22.85 (image1Equiv) =>
% 131.89/22.85 ((
% 131.89/22.85 (image1E) =>
% 131.89/22.85 ((
% 131.89/22.85 (image1I) =>
% 131.89/22.85 ((
% 131.89/22.85 (injFuncInInjFuncSet) =>
% 131.89/22.85 ((
% 131.89/22.85 (injFuncSetFuncIn) =>
% 131.89/22.85 ((
% 131.89/22.85 (injFuncSetFuncInj) =>
% 131.89/22.85 ((
% 131.89/22.85 (surjFuncSetFuncIn) =>
% 131.89/22.85 ((
% 131.89/22.85 (surjFuncSetFuncSurj) =>
% 131.89/22.85 ((
% 131.89/22.85 (leftInvIsSurj) =>
% 131.89/22.85 ((
% 131.89/22.85 (surjCantorThm) =>
% 131.89/22.85 ((
% 131.89/22.85 (foundation2) =>
% 131.89/22.85 ((
% 131.89/22.85 (notinself) =>
% 131.89/22.85 ((
% 131.89/22.85 (notinself2) =>
% 131.89/22.85 ((
% 131.89/22.85 (omegaSp) =>
% 131.89/22.85 ((
% 131.89/22.85 (omegaSclos) =>
% 131.89/22.85 ((
% 131.89/22.85 (peano0notS) =>
% 131.89/22.85 ((
% 131.89/22.85 (peanoSinj) =>
% 131.89/22.85 ((
% 131.89/22.85 (transitivesetOp1) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintTransitive) =>
% 131.89/22.85 ((
% 131.89/22.85 (transitivesetOp2) =>
% 131.89/22.85 ((
% 131.89/22.85 (setunionTransitive) =>
% 131.89/22.85 ((
% 131.89/22.85 (ordinalMinLem1) =>
% 131.89/22.85 ((
% 131.89/22.85 (ordinalTransSet) =>
% 131.89/22.85 ((
% 131.89/22.85 (ordinalTransSet1) =>
% 131.89/22.85 ((
% 131.89/22.85 (setunionOrdinalLem1) =>
% 131.89/22.85 (ordinal @
% 131.89/22.85 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 131.89/22.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl508])).
% 131.89/22.85 thf(zip_derived_cl523, plain,
% 131.89/22.85 (~ (((notdallE) =>
% 131.89/22.85 (((exuI1) =>
% 131.89/22.85 (((exuI3) =>
% 131.89/22.85 (((exuI2) =>
% 131.89/22.85 (((inCongP) =>
% 131.89/22.85 (((in__Cong) =>
% 131.89/22.85 (((exuE3u) =>
% 131.89/22.85 (((exu__Cong) =>
% 131.89/22.85 (((setadjoin__Cong) =>
% 131.89/22.85 (((powerset__Cong) =>
% 131.89/22.85 (((setunion__Cong) =>
% 131.89/22.85 (((exuEu) =>
% 131.89/22.85 (((descr__Cong) =>
% 131.89/22.85 (((dsetconstr__Cong) =>
% 131.89/22.85 (((subsetI1) =>
% 131.89/22.85 (((eqimpsubset2) =>
% 131.89/22.85 (((eqimpsubset1) =>
% 131.89/22.85 (((subsetI2) =>
% 131.89/22.85 (((emptysetsubset) =>
% 131.89/22.85 (((subsetE) =>
% 131.89/22.85 (((subsetE2) =>
% 131.89/22.85 (((notsubsetI) =>
% 131.89/22.85 (((notequalI1) =>
% 131.89/22.85 (((notequalI2) =>
% 131.89/22.85 (((subsetRefl) =>
% 131.89/22.85 (((subsetTrans) =>
% 131.89/22.85 (((setadjoinSub) =>
% 131.89/22.85 (((setadjoinSub2) =>
% 131.89/22.85 (((subset2powerset) =>
% 131.89/22.85 (((setextsub) =>
% 131.89/22.85 ((
% 131.89/22.85 (subsetemptysetimpeq) =>
% 131.89/22.85 ((
% 131.89/22.85 (powersetI1) =>
% 131.89/22.85 ((
% 131.89/22.85 (powersetE1) =>
% 131.89/22.85 ((
% 131.89/22.85 (inPowerset) =>
% 131.89/22.85 ((
% 131.89/22.85 (powersetsubset) =>
% 131.89/22.85 ((
% 131.89/22.85 (sepInPowerset) =>
% 131.89/22.85 ((
% 131.89/22.85 (sepSubset) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionIL) =>
% 131.89/22.85 ((
% 131.89/22.85 (upairset2IR) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionIR) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionEcases) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionE) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionLsub) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionRsub) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectI) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectSubset5) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectEL) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectLsub) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectSubset2) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectSubset3) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectER) =>
% 131.89/22.85 ((
% 131.89/22.85 (disjointsetsI1) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectRsub) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectSubset4) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectSubset1) =>
% 131.89/22.85 ((
% 131.89/22.85 (bs114d) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusI) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusEL) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusER) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusSubset2) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusERneg) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusELneg) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusILneg) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusIRneg) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusLsub) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusSubset1) =>
% 131.89/22.85 ((
% 131.89/22.85 (symdiffE) =>
% 131.89/22.85 ((
% 131.89/22.85 (symdiffI1) =>
% 131.89/22.85 ((
% 131.89/22.85 (symdiffI2) =>
% 131.89/22.85 ((
% 131.89/22.85 (symdiffIneg1) =>
% 131.89/22.85 ((
% 131.89/22.85 (symdiffIneg2) =>
% 131.89/22.85 ((
% 131.89/22.85 (secondinupair) =>
% 131.89/22.85 ((
% 131.89/22.85 (setukpairIL) =>
% 131.89/22.85 ((
% 131.89/22.85 (setukpairIR) =>
% 131.89/22.85 ((
% 131.89/22.85 (kpairiskpair) =>
% 131.89/22.85 ((
% 131.89/22.85 (kpairp) =>
% 131.89/22.85 ((
% 131.89/22.85 (singletonsubset) =>
% 131.89/22.85 ((
% 131.89/22.85 (singletoninpowerset) =>
% 131.89/22.85 ((
% 131.89/22.85 (singletoninpowunion) =>
% 131.89/22.85 ((
% 131.89/22.85 (upairset2E) =>
% 131.89/22.85 ((
% 131.89/22.85 (upairsubunion) =>
% 131.89/22.85 ((
% 131.89/22.85 (upairinpowunion) =>
% 131.89/22.85 ((
% 131.89/22.85 (ubforcartprodlem1) =>
% 131.89/22.85 ((
% 131.89/22.85 (ubforcartprodlem2) =>
% 131.89/22.85 ((
% 131.89/22.85 (ubforcartprodlem3) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodpairin) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodmempair1) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodmempair) =>
% 131.89/22.85 ((
% 131.89/22.85 (setunionE2) =>
% 131.89/22.85 ((
% 131.89/22.85 (setunionsingleton1) =>
% 131.89/22.85 ((
% 131.89/22.85 (setunionsingleton2) =>
% 131.89/22.85 ((
% 131.89/22.85 (setunionsingleton) =>
% 131.89/22.85 ((
% 131.89/22.85 (singletonprop) =>
% 131.89/22.85 ((
% 131.89/22.85 (ex1E1) =>
% 131.89/22.85 ((
% 131.89/22.85 (ex1I) =>
% 131.89/22.85 ((
% 131.89/22.85 (ex1I2) =>
% 131.89/22.85 ((
% 131.89/22.85 (singletonsuniq) =>
% 131.89/22.85 ((
% 131.89/22.85 (setukpairinjL1) =>
% 131.89/22.85 ((
% 131.89/22.85 (kfstsingleton) =>
% 131.89/22.85 ((
% 131.89/22.85 (theprop) =>
% 131.89/22.85 ((
% 131.89/22.85 (kfstpairEq) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodfstin) =>
% 131.89/22.85 ((
% 131.89/22.85 (setukpairinjL2) =>
% 131.89/22.85 ((
% 131.89/22.85 (setukpairinjL) =>
% 131.89/22.85 ((
% 131.89/22.85 (setukpairinjR11) =>
% 131.89/22.85 ((
% 131.89/22.85 (setukpairinjR12) =>
% 131.89/22.85 ((
% 131.89/22.85 (setukpairinjR1) =>
% 131.89/22.85 ((
% 131.89/22.85 (upairequniteq) =>
% 131.89/22.85 ((
% 131.89/22.85 (setukpairinjR2) =>
% 131.89/22.85 ((
% 131.89/22.85 (setukpairinjR) =>
% 131.89/22.85 ((
% 131.89/22.85 (ksndsingleton) =>
% 131.89/22.85 ((
% 131.89/22.85 (ksndpairEq) =>
% 131.89/22.85 ((
% 131.89/22.85 (kpairsurjEq) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodsndin) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodpairmemEL) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodpairmemER) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodmempaircEq) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodfstpairEq) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodsndpairEq) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodpairsurjEq) =>
% 131.89/22.85 ((
% 131.89/22.85 (dpsetconstrI) =>
% 131.89/22.85 ((
% 131.89/22.85 (dpsetconstrSub) =>
% 131.89/22.85 ((
% 131.89/22.85 (setOfPairsIsBReln) =>
% 131.89/22.85 ((
% 131.89/22.85 (dpsetconstrERa) =>
% 131.89/22.85 ((
% 131.89/22.85 (dpsetconstrEL1) =>
% 131.89/22.85 ((
% 131.89/22.85 (dpsetconstrEL2) =>
% 131.89/22.85 ((
% 131.89/22.85 (dpsetconstrER) =>
% 131.89/22.85 ((
% 131.89/22.85 (funcImageSingleton) =>
% 131.89/22.85 ((
% 131.89/22.85 (apProp) =>
% 131.89/22.85 ((
% 131.89/22.85 (app) =>
% 131.89/22.85 ((
% 131.89/22.85 (infuncsetfunc) =>
% 131.89/22.85 ((
% 131.89/22.85 (ap2p) =>
% 131.89/22.85 ((
% 131.89/22.85 (funcinfuncset) =>
% 131.89/22.85 ((
% 131.89/22.85 (lamProp) =>
% 131.89/22.85 ((
% 131.89/22.85 (lamp) =>
% 131.89/22.85 ((
% 131.89/22.85 (lam2p) =>
% 131.89/22.85 ((
% 131.89/22.85 (brelnall1) =>
% 131.89/22.85 ((
% 131.89/22.85 (brelnall2) =>
% 131.89/22.85 ((
% 131.89/22.85 (ex1E2) =>
% 131.89/22.85 ((
% 131.89/22.85 (funcGraphProp1) =>
% 131.89/22.85 ((
% 131.89/22.85 (funcGraphProp3) =>
% 131.89/22.85 ((
% 131.89/22.85 (funcGraphProp2) =>
% 131.89/22.85 ((
% 131.89/22.85 (funcextLem) =>
% 131.89/22.85 ((
% 131.89/22.85 (funcGraphProp4) =>
% 131.89/22.85 ((
% 131.89/22.85 (subbreln) =>
% 131.89/22.85 ((
% 131.89/22.85 (eqbreln) =>
% 131.89/22.85 ((
% 131.89/22.85 (funcext) =>
% 131.89/22.85 ((
% 131.89/22.85 (funcext2) =>
% 131.89/22.85 ((
% 131.89/22.85 (ap2apEq1) =>
% 131.89/22.85 ((
% 131.89/22.85 (ap2apEq2) =>
% 131.89/22.85 ((
% 131.89/22.85 (beta1) =>
% 131.89/22.85 ((
% 131.89/22.85 (eta1) =>
% 131.89/22.85 ((
% 131.89/22.85 (lam2lamEq) =>
% 131.89/22.85 ((
% 131.89/22.85 (beta2) =>
% 131.89/22.85 ((
% 131.89/22.85 (eta2) =>
% 131.89/22.85 ((
% 131.89/22.85 (iffalseProp1) =>
% 131.89/22.85 ((
% 131.89/22.85 (iffalseProp2) =>
% 131.89/22.85 ((
% 131.89/22.85 (iftrueProp1) =>
% 131.89/22.85 ((
% 131.89/22.85 (iftrueProp2) =>
% 131.89/22.85 ((
% 131.89/22.85 (ifSingleton) =>
% 131.89/22.85 ((
% 131.89/22.85 (ifp) =>
% 131.89/22.85 ((
% 131.89/22.85 (theeq) =>
% 131.89/22.85 ((
% 131.89/22.85 (iftrue) =>
% 131.89/22.85 ((
% 131.89/22.85 (iffalse) =>
% 131.89/22.85 ((
% 131.89/22.85 (iftrueorfalse) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectT_lem) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionT_lem) =>
% 131.89/22.85 ((
% 131.89/22.85 (powersetT_lem) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusT_lem) =>
% 131.89/22.85 ((
% 131.89/22.85 (complementT_lem) =>
% 131.89/22.85 ((
% 131.89/22.85 (setextT) =>
% 131.89/22.85 ((
% 131.89/22.85 (subsetTI) =>
% 131.89/22.85 ((
% 131.89/22.85 (powersetTI1) =>
% 131.89/22.85 ((
% 131.89/22.85 (powersetTE1) =>
% 131.89/22.85 ((
% 131.89/22.85 (complementTI1) =>
% 131.89/22.85 ((
% 131.89/22.85 (complementTE1) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectTELcontra) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectTERcontra) =>
% 131.89/22.85 ((
% 131.89/22.85 (contrasubsetT) =>
% 131.89/22.85 ((
% 131.89/22.85 (contrasubsetT1) =>
% 131.89/22.85 ((
% 131.89/22.85 (contrasubsetT2) =>
% 131.89/22.85 ((
% 131.89/22.85 (contrasubsetT3) =>
% 131.89/22.85 ((
% 131.89/22.85 (doubleComplementI1) =>
% 131.89/22.85 ((
% 131.89/22.85 (doubleComplementE1) =>
% 131.89/22.85 ((
% 131.89/22.85 (doubleComplementSub1) =>
% 131.89/22.85 ((
% 131.89/22.85 (doubleComplementSub2) =>
% 131.89/22.85 ((
% 131.89/22.85 (doubleComplementEq) =>
% 131.89/22.85 ((
% 131.89/22.85 (complementTnotintersectT) =>
% 131.89/22.85 ((
% 131.89/22.85 (complementImpComplementIntersect) =>
% 131.89/22.85 ((
% 131.89/22.85 (complementSubsetComplementIntersect) =>
% 131.89/22.85 ((
% 131.89/22.85 (complementInPowersetComplementIntersect) =>
% 131.89/22.85 ((
% 131.89/22.85 (contraSubsetComplement) =>
% 131.89/22.85 ((
% 131.89/22.85 (complementTcontraSubset) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionTILcontra) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionTIRcontra) =>
% 131.89/22.85 ((
% 131.89/22.85 (inIntersectImpInUnion) =>
% 131.89/22.85 ((
% 131.89/22.85 (inIntersectImpInUnion2) =>
% 131.89/22.85 ((
% 131.89/22.85 (inIntersectImpInIntersectUnions) =>
% 131.89/22.85 ((
% 131.89/22.85 (intersectInPowersetIntersectUnions) =>
% 131.89/22.85 ((
% 131.89/22.85 (inComplementUnionImpNotIn1) =>
% 131.89/22.85 ((
% 131.89/22.85 (inComplementUnionImpInComplement1) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionTE) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionTEcontra) =>
% 131.89/22.85 ((
% 131.89/22.85 (demorgan2a1) =>
% 131.89/22.85 ((
% 131.89/22.85 (complementUnionInPowersetComplement) =>
% 131.89/22.85 ((
% 131.89/22.85 (demorgan2a2) =>
% 131.89/22.85 ((
% 131.89/22.85 (demorgan1a) =>
% 131.89/22.85 ((
% 131.89/22.85 (demorgan1b) =>
% 131.89/22.85 ((
% 131.89/22.85 (demorgan1) =>
% 131.89/22.85 ((
% 131.89/22.85 (demorgan2a) =>
% 131.89/22.85 ((
% 131.89/22.85 (demorgan2b2) =>
% 131.89/22.85 ((
% 131.89/22.85 (demorgan2b) =>
% 131.89/22.85 ((
% 131.89/22.85 (demorgan2) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz13rule0) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz13rule1) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz13rule2) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz13rule3) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz13rule4) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz1_1) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz1_2) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz1_3) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz1_4) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz1_5) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1all2) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1SetBreln1) =>
% 131.89/22.85 ((
% 131.89/22.85 (choice2fnsingleton) =>
% 131.89/22.85 ((
% 131.89/22.85 (setOfPairsIsBReln1) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1all1) =>
% 131.89/22.85 ((
% 131.89/22.85 (subbreln1) =>
% 131.89/22.85 ((
% 131.89/22.85 (eqbreln1) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1invprop) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1invI) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1invE) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1compprop) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1compI) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1compE) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1compEex) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1unionprop) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1unionIL) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1unionIR) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1unionI) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1unionE) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1unionEcases) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1unionCommutes) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz2Ex) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz2W) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz2A) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz2B) =>
% 131.89/22.85 ((
% 131.89/22.85 (image1Ex) =>
% 131.89/22.85 ((
% 131.89/22.85 (image1Ex1) =>
% 131.89/22.85 ((
% 131.89/22.85 (image1Equiv) =>
% 131.89/22.85 ((
% 131.89/22.85 (image1E) =>
% 131.89/22.85 ((
% 131.89/22.85 (image1I) =>
% 131.89/22.85 ((
% 131.89/22.85 (injFuncInInjFuncSet) =>
% 131.89/22.85 ((
% 131.89/22.85 (injFuncSetFuncIn) =>
% 131.89/22.85 ((
% 131.89/22.85 (injFuncSetFuncInj) =>
% 131.89/22.85 ((
% 131.89/22.85 (surjFuncSetFuncIn) =>
% 131.89/22.85 ((
% 131.89/22.85 (surjFuncSetFuncSurj) =>
% 131.89/22.85 ((
% 131.89/22.85 (leftInvIsSurj) =>
% 131.89/22.85 ((
% 131.89/22.85 (surjCantorThm) =>
% 131.89/22.85 ((
% 131.89/22.85 (foundation2) =>
% 131.89/22.85 ((
% 131.89/22.85 (notinself) =>
% 131.89/22.85 ((
% 131.89/22.85 (notinself2) =>
% 131.89/22.85 ((
% 131.89/22.85 (omegaSp) =>
% 131.89/22.85 ((
% 131.89/22.85 (omegaSclos) =>
% 131.89/22.85 ((
% 131.89/22.85 (peano0notS) =>
% 131.89/22.85 ((
% 131.89/22.85 (peanoSinj) =>
% 131.89/22.85 ((
% 131.89/22.85 (transitivesetOp1) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintTransitive) =>
% 131.89/22.85 ((
% 131.89/22.85 (transitivesetOp2) =>
% 131.89/22.85 ((
% 131.89/22.85 (setunionTransitive) =>
% 131.89/22.85 ((
% 131.89/22.85 (ordinalMinLem1) =>
% 131.89/22.85 ((
% 131.89/22.85 (ordinalTransSet) =>
% 131.89/22.85 ((
% 131.89/22.85 (ordinalTransSet1) =>
% 131.89/22.85 ((
% 131.89/22.85 (setunionOrdinalLem1) =>
% 131.89/22.85 (ordinal @
% 131.89/22.85 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 131.89/22.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl515])).
% 131.89/22.85 thf(zip_derived_cl535, plain,
% 131.89/22.85 (~ (((exuI1) =>
% 131.89/22.85 (((exuI3) =>
% 131.89/22.85 (((exuI2) =>
% 131.89/22.85 (((inCongP) =>
% 131.89/22.85 (((in__Cong) =>
% 131.89/22.85 (((exuE3u) =>
% 131.89/22.85 (((exu__Cong) =>
% 131.89/22.85 (((setadjoin__Cong) =>
% 131.89/22.85 (((powerset__Cong) =>
% 131.89/22.85 (((setunion__Cong) =>
% 131.89/22.85 (((exuEu) =>
% 131.89/22.85 (((descr__Cong) =>
% 131.89/22.85 (((dsetconstr__Cong) =>
% 131.89/22.85 (((subsetI1) =>
% 131.89/22.85 (((eqimpsubset2) =>
% 131.89/22.85 (((eqimpsubset1) =>
% 131.89/22.85 (((subsetI2) =>
% 131.89/22.85 (((emptysetsubset) =>
% 131.89/22.85 (((subsetE) =>
% 131.89/22.85 (((subsetE2) =>
% 131.89/22.85 (((notsubsetI) =>
% 131.89/22.85 (((notequalI1) =>
% 131.89/22.85 (((notequalI2) =>
% 131.89/22.85 (((subsetRefl) =>
% 131.89/22.85 (((subsetTrans) =>
% 131.89/22.85 (((setadjoinSub) =>
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% 131.89/22.85 (((setextsub) =>
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% 131.89/22.85 (powersetI1) =>
% 131.89/22.85 ((
% 131.89/22.85 (powersetE1) =>
% 131.89/22.85 ((
% 131.89/22.85 (inPowerset) =>
% 131.89/22.85 ((
% 131.89/22.85 (powersetsubset) =>
% 131.89/22.85 ((
% 131.89/22.85 (sepInPowerset) =>
% 131.89/22.85 ((
% 131.89/22.85 (sepSubset) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionIL) =>
% 131.89/22.85 ((
% 131.89/22.85 (upairset2IR) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionIR) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionEcases) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionE) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionLsub) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionRsub) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectI) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectSubset5) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectEL) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectLsub) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectSubset2) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectSubset3) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectER) =>
% 131.89/22.85 ((
% 131.89/22.85 (disjointsetsI1) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectRsub) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectSubset4) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectSubset1) =>
% 131.89/22.85 ((
% 131.89/22.85 (bs114d) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusI) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusEL) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusER) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusSubset2) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusERneg) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusELneg) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusILneg) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusIRneg) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusLsub) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusSubset1) =>
% 131.89/22.85 ((
% 131.89/22.85 (symdiffE) =>
% 131.89/22.85 ((
% 131.89/22.85 (symdiffI1) =>
% 131.89/22.85 ((
% 131.89/22.85 (symdiffI2) =>
% 131.89/22.85 ((
% 131.89/22.85 (symdiffIneg1) =>
% 131.89/22.85 ((
% 131.89/22.85 (symdiffIneg2) =>
% 131.89/22.85 ((
% 131.89/22.85 (secondinupair) =>
% 131.89/22.85 ((
% 131.89/22.85 (setukpairIL) =>
% 131.89/22.85 ((
% 131.89/22.85 (setukpairIR) =>
% 131.89/22.85 ((
% 131.89/22.85 (kpairiskpair) =>
% 131.89/22.85 ((
% 131.89/22.85 (kpairp) =>
% 131.89/22.85 ((
% 131.89/22.85 (singletonsubset) =>
% 131.89/22.85 ((
% 131.89/22.85 (singletoninpowerset) =>
% 131.89/22.85 ((
% 131.89/22.85 (singletoninpowunion) =>
% 131.89/22.85 ((
% 131.89/22.85 (upairset2E) =>
% 131.89/22.85 ((
% 131.89/22.85 (upairsubunion) =>
% 131.89/22.85 ((
% 131.89/22.85 (upairinpowunion) =>
% 131.89/22.85 ((
% 131.89/22.85 (ubforcartprodlem1) =>
% 131.89/22.85 ((
% 131.89/22.85 (ubforcartprodlem2) =>
% 131.89/22.85 ((
% 131.89/22.85 (ubforcartprodlem3) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodpairin) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodmempair1) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodmempair) =>
% 131.89/22.85 ((
% 131.89/22.85 (setunionE2) =>
% 131.89/22.85 ((
% 131.89/22.85 (setunionsingleton1) =>
% 131.89/22.85 ((
% 131.89/22.85 (setunionsingleton2) =>
% 131.89/22.85 ((
% 131.89/22.85 (setunionsingleton) =>
% 131.89/22.85 ((
% 131.89/22.85 (singletonprop) =>
% 131.89/22.85 ((
% 131.89/22.85 (ex1E1) =>
% 131.89/22.85 ((
% 131.89/22.85 (ex1I) =>
% 131.89/22.85 ((
% 131.89/22.85 (ex1I2) =>
% 131.89/22.85 ((
% 131.89/22.85 (singletonsuniq) =>
% 131.89/22.85 ((
% 131.89/22.85 (setukpairinjL1) =>
% 131.89/22.85 ((
% 131.89/22.85 (kfstsingleton) =>
% 131.89/22.85 ((
% 131.89/22.85 (theprop) =>
% 131.89/22.85 ((
% 131.89/22.85 (kfstpairEq) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodfstin) =>
% 131.89/22.85 ((
% 131.89/22.85 (setukpairinjL2) =>
% 131.89/22.85 ((
% 131.89/22.85 (setukpairinjL) =>
% 131.89/22.85 ((
% 131.89/22.85 (setukpairinjR11) =>
% 131.89/22.85 ((
% 131.89/22.85 (setukpairinjR12) =>
% 131.89/22.85 ((
% 131.89/22.85 (setukpairinjR1) =>
% 131.89/22.85 ((
% 131.89/22.85 (upairequniteq) =>
% 131.89/22.85 ((
% 131.89/22.85 (setukpairinjR2) =>
% 131.89/22.85 ((
% 131.89/22.85 (setukpairinjR) =>
% 131.89/22.85 ((
% 131.89/22.85 (ksndsingleton) =>
% 131.89/22.85 ((
% 131.89/22.85 (ksndpairEq) =>
% 131.89/22.85 ((
% 131.89/22.85 (kpairsurjEq) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodsndin) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodpairmemEL) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodpairmemER) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodmempaircEq) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodfstpairEq) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodsndpairEq) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodpairsurjEq) =>
% 131.89/22.85 ((
% 131.89/22.85 (dpsetconstrI) =>
% 131.89/22.85 ((
% 131.89/22.85 (dpsetconstrSub) =>
% 131.89/22.85 ((
% 131.89/22.85 (setOfPairsIsBReln) =>
% 131.89/22.85 ((
% 131.89/22.85 (dpsetconstrERa) =>
% 131.89/22.85 ((
% 131.89/22.85 (dpsetconstrEL1) =>
% 131.89/22.85 ((
% 131.89/22.85 (dpsetconstrEL2) =>
% 131.89/22.85 ((
% 131.89/22.85 (dpsetconstrER) =>
% 131.89/22.85 ((
% 131.89/22.85 (funcImageSingleton) =>
% 131.89/22.85 ((
% 131.89/22.85 (apProp) =>
% 131.89/22.85 ((
% 131.89/22.85 (app) =>
% 131.89/22.85 ((
% 131.89/22.85 (infuncsetfunc) =>
% 131.89/22.85 ((
% 131.89/22.85 (ap2p) =>
% 131.89/22.85 ((
% 131.89/22.85 (funcinfuncset) =>
% 131.89/22.85 ((
% 131.89/22.85 (lamProp) =>
% 131.89/22.85 ((
% 131.89/22.85 (lamp) =>
% 131.89/22.85 ((
% 131.89/22.85 (lam2p) =>
% 131.89/22.85 ((
% 131.89/22.85 (brelnall1) =>
% 131.89/22.85 ((
% 131.89/22.85 (brelnall2) =>
% 131.89/22.85 ((
% 131.89/22.85 (ex1E2) =>
% 131.89/22.85 ((
% 131.89/22.85 (funcGraphProp1) =>
% 131.89/22.85 ((
% 131.89/22.85 (funcGraphProp3) =>
% 131.89/22.85 ((
% 131.89/22.85 (funcGraphProp2) =>
% 131.89/22.85 ((
% 131.89/22.85 (funcextLem) =>
% 131.89/22.85 ((
% 131.89/22.85 (funcGraphProp4) =>
% 131.89/22.85 ((
% 131.89/22.85 (subbreln) =>
% 131.89/22.85 ((
% 131.89/22.85 (eqbreln) =>
% 131.89/22.85 ((
% 131.89/22.85 (funcext) =>
% 131.89/22.85 ((
% 131.89/22.85 (funcext2) =>
% 131.89/22.85 ((
% 131.89/22.85 (ap2apEq1) =>
% 131.89/22.85 ((
% 131.89/22.85 (ap2apEq2) =>
% 131.89/22.85 ((
% 131.89/22.85 (beta1) =>
% 131.89/22.85 ((
% 131.89/22.85 (eta1) =>
% 131.89/22.85 ((
% 131.89/22.85 (lam2lamEq) =>
% 131.89/22.85 ((
% 131.89/22.85 (beta2) =>
% 131.89/22.85 ((
% 131.89/22.85 (eta2) =>
% 131.89/22.85 ((
% 131.89/22.85 (iffalseProp1) =>
% 131.89/22.85 ((
% 131.89/22.85 (iffalseProp2) =>
% 131.89/22.85 ((
% 131.89/22.85 (iftrueProp1) =>
% 131.89/22.85 ((
% 131.89/22.85 (iftrueProp2) =>
% 131.89/22.85 ((
% 131.89/22.85 (ifSingleton) =>
% 131.89/22.85 ((
% 131.89/22.85 (ifp) =>
% 131.89/22.85 ((
% 131.89/22.85 (theeq) =>
% 131.89/22.85 ((
% 131.89/22.85 (iftrue) =>
% 131.89/22.85 ((
% 131.89/22.85 (iffalse) =>
% 131.89/22.85 ((
% 131.89/22.85 (iftrueorfalse) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectT_lem) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionT_lem) =>
% 131.89/22.85 ((
% 131.89/22.85 (powersetT_lem) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusT_lem) =>
% 131.89/22.85 ((
% 131.89/22.85 (complementT_lem) =>
% 131.89/22.85 ((
% 131.89/22.85 (setextT) =>
% 131.89/22.85 ((
% 131.89/22.85 (subsetTI) =>
% 131.89/22.85 ((
% 131.89/22.85 (powersetTI1) =>
% 131.89/22.85 ((
% 131.89/22.85 (powersetTE1) =>
% 131.89/22.85 ((
% 131.89/22.85 (complementTI1) =>
% 131.89/22.85 ((
% 131.89/22.85 (complementTE1) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectTELcontra) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectTERcontra) =>
% 131.89/22.85 ((
% 131.89/22.85 (contrasubsetT) =>
% 131.89/22.85 ((
% 131.89/22.85 (contrasubsetT1) =>
% 131.89/22.85 ((
% 131.89/22.85 (contrasubsetT2) =>
% 131.89/22.85 ((
% 131.89/22.85 (contrasubsetT3) =>
% 131.89/22.85 ((
% 131.89/22.85 (doubleComplementI1) =>
% 131.89/22.85 ((
% 131.89/22.85 (doubleComplementE1) =>
% 131.89/22.85 ((
% 131.89/22.85 (doubleComplementSub1) =>
% 131.89/22.85 ((
% 131.89/22.85 (doubleComplementSub2) =>
% 131.89/22.85 ((
% 131.89/22.85 (doubleComplementEq) =>
% 131.89/22.85 ((
% 131.89/22.85 (complementTnotintersectT) =>
% 131.89/22.85 ((
% 131.89/22.85 (complementImpComplementIntersect) =>
% 131.89/22.85 ((
% 131.89/22.85 (complementSubsetComplementIntersect) =>
% 131.89/22.85 ((
% 131.89/22.85 (complementInPowersetComplementIntersect) =>
% 131.89/22.85 ((
% 131.89/22.85 (contraSubsetComplement) =>
% 131.89/22.85 ((
% 131.89/22.85 (complementTcontraSubset) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionTILcontra) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionTIRcontra) =>
% 131.89/22.85 ((
% 131.89/22.85 (inIntersectImpInUnion) =>
% 131.89/22.85 ((
% 131.89/22.85 (inIntersectImpInUnion2) =>
% 131.89/22.85 ((
% 131.89/22.85 (inIntersectImpInIntersectUnions) =>
% 131.89/22.85 ((
% 131.89/22.85 (intersectInPowersetIntersectUnions) =>
% 131.89/22.85 ((
% 131.89/22.85 (inComplementUnionImpNotIn1) =>
% 131.89/22.85 ((
% 131.89/22.85 (inComplementUnionImpInComplement1) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionTE) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionTEcontra) =>
% 131.89/22.85 ((
% 131.89/22.85 (demorgan2a1) =>
% 131.89/22.85 ((
% 131.89/22.85 (complementUnionInPowersetComplement) =>
% 131.89/22.85 ((
% 131.89/22.85 (demorgan2a2) =>
% 131.89/22.85 ((
% 131.89/22.85 (demorgan1a) =>
% 131.89/22.85 ((
% 131.89/22.85 (demorgan1b) =>
% 131.89/22.85 ((
% 131.89/22.85 (demorgan1) =>
% 131.89/22.85 ((
% 131.89/22.85 (demorgan2a) =>
% 131.89/22.85 ((
% 131.89/22.85 (demorgan2b2) =>
% 131.89/22.85 ((
% 131.89/22.85 (demorgan2b) =>
% 131.89/22.85 ((
% 131.89/22.85 (demorgan2) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz13rule0) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz13rule1) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz13rule2) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz13rule3) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz13rule4) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz1_1) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz1_2) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz1_3) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz1_4) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz1_5) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1all2) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1SetBreln1) =>
% 131.89/22.85 ((
% 131.89/22.85 (choice2fnsingleton) =>
% 131.89/22.85 ((
% 131.89/22.85 (setOfPairsIsBReln1) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1all1) =>
% 131.89/22.85 ((
% 131.89/22.85 (subbreln1) =>
% 131.89/22.85 ((
% 131.89/22.85 (eqbreln1) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1invprop) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1invI) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1invE) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1compprop) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1compI) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1compE) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1compEex) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1unionprop) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1unionIL) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1unionIR) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1unionI) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1unionE) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1unionEcases) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1unionCommutes) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz2Ex) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz2W) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz2A) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz2B) =>
% 131.89/22.85 ((
% 131.89/22.85 (image1Ex) =>
% 131.89/22.85 ((
% 131.89/22.85 (image1Ex1) =>
% 131.89/22.85 ((
% 131.89/22.85 (image1Equiv) =>
% 131.89/22.85 ((
% 131.89/22.85 (image1E) =>
% 131.89/22.85 ((
% 131.89/22.85 (image1I) =>
% 131.89/22.85 ((
% 131.89/22.85 (injFuncInInjFuncSet) =>
% 131.89/22.85 ((
% 131.89/22.85 (injFuncSetFuncIn) =>
% 131.89/22.85 ((
% 131.89/22.85 (injFuncSetFuncInj) =>
% 131.89/22.85 ((
% 131.89/22.85 (surjFuncSetFuncIn) =>
% 131.89/22.85 ((
% 131.89/22.85 (surjFuncSetFuncSurj) =>
% 131.89/22.85 ((
% 131.89/22.85 (leftInvIsSurj) =>
% 131.89/22.85 ((
% 131.89/22.85 (surjCantorThm) =>
% 131.89/22.85 ((
% 131.89/22.85 (foundation2) =>
% 131.89/22.85 ((
% 131.89/22.85 (notinself) =>
% 131.89/22.85 ((
% 131.89/22.85 (notinself2) =>
% 131.89/22.85 ((
% 131.89/22.85 (omegaSp) =>
% 131.89/22.85 ((
% 131.89/22.85 (omegaSclos) =>
% 131.89/22.85 ((
% 131.89/22.85 (peano0notS) =>
% 131.89/22.85 ((
% 131.89/22.85 (peanoSinj) =>
% 131.89/22.85 ((
% 131.89/22.85 (transitivesetOp1) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintTransitive) =>
% 131.89/22.85 ((
% 131.89/22.85 (transitivesetOp2) =>
% 131.89/22.85 ((
% 131.89/22.85 (setunionTransitive) =>
% 131.89/22.85 ((
% 131.89/22.85 (ordinalMinLem1) =>
% 131.89/22.85 ((
% 131.89/22.85 (ordinalTransSet) =>
% 131.89/22.85 ((
% 131.89/22.85 (ordinalTransSet1) =>
% 131.89/22.85 ((
% 131.89/22.85 (setunionOrdinalLem1) =>
% 131.89/22.85 (ordinal @
% 131.89/22.85 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 131.89/22.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl523])).
% 131.89/22.85 thf(zip_derived_cl550, plain,
% 131.89/22.85 (~ (((exuI3) =>
% 131.89/22.85 (((exuI2) =>
% 131.89/22.85 (((inCongP) =>
% 131.89/22.85 (((in__Cong) =>
% 131.89/22.85 (((exuE3u) =>
% 131.89/22.85 (((exu__Cong) =>
% 131.89/22.85 (((setadjoin__Cong) =>
% 131.89/22.85 (((powerset__Cong) =>
% 131.89/22.85 (((setunion__Cong) =>
% 131.89/22.85 (((exuEu) =>
% 131.89/22.85 (((descr__Cong) =>
% 131.89/22.85 (((dsetconstr__Cong) =>
% 131.89/22.85 (((subsetI1) =>
% 131.89/22.85 (((eqimpsubset2) =>
% 131.89/22.85 (((eqimpsubset1) =>
% 131.89/22.85 (((subsetI2) =>
% 131.89/22.85 (((emptysetsubset) =>
% 131.89/22.85 (((subsetE) =>
% 131.89/22.85 (((subsetE2) =>
% 131.89/22.85 (((notsubsetI) =>
% 131.89/22.85 (((notequalI1) =>
% 131.89/22.85 (((notequalI2) =>
% 131.89/22.85 (((subsetRefl) =>
% 131.89/22.85 (((subsetTrans) =>
% 131.89/22.85 (((setadjoinSub) =>
% 131.89/22.85 (((setadjoinSub2) =>
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% 131.89/22.85 (((setextsub) =>
% 131.89/22.85 (((subsetemptysetimpeq) =>
% 131.89/22.85 (((powersetI1) =>
% 131.89/22.85 ((
% 131.89/22.85 (powersetE1) =>
% 131.89/22.85 ((
% 131.89/22.85 (inPowerset) =>
% 131.89/22.85 ((
% 131.89/22.85 (powersetsubset) =>
% 131.89/22.85 ((
% 131.89/22.85 (sepInPowerset) =>
% 131.89/22.85 ((
% 131.89/22.85 (sepSubset) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionIL) =>
% 131.89/22.85 ((
% 131.89/22.85 (upairset2IR) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionIR) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionEcases) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionE) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionLsub) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionRsub) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectI) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectSubset5) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectEL) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectLsub) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectSubset2) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectSubset3) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectER) =>
% 131.89/22.85 ((
% 131.89/22.85 (disjointsetsI1) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectRsub) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectSubset4) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectSubset1) =>
% 131.89/22.85 ((
% 131.89/22.85 (bs114d) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusI) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusEL) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusER) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusSubset2) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusERneg) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusELneg) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusILneg) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusIRneg) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusLsub) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusSubset1) =>
% 131.89/22.85 ((
% 131.89/22.85 (symdiffE) =>
% 131.89/22.85 ((
% 131.89/22.85 (symdiffI1) =>
% 131.89/22.85 ((
% 131.89/22.85 (symdiffI2) =>
% 131.89/22.85 ((
% 131.89/22.85 (symdiffIneg1) =>
% 131.89/22.85 ((
% 131.89/22.85 (symdiffIneg2) =>
% 131.89/22.85 ((
% 131.89/22.85 (secondinupair) =>
% 131.89/22.85 ((
% 131.89/22.85 (setukpairIL) =>
% 131.89/22.85 ((
% 131.89/22.85 (setukpairIR) =>
% 131.89/22.85 ((
% 131.89/22.85 (kpairiskpair) =>
% 131.89/22.85 ((
% 131.89/22.85 (kpairp) =>
% 131.89/22.85 ((
% 131.89/22.85 (singletonsubset) =>
% 131.89/22.85 ((
% 131.89/22.85 (singletoninpowerset) =>
% 131.89/22.85 ((
% 131.89/22.85 (singletoninpowunion) =>
% 131.89/22.85 ((
% 131.89/22.85 (upairset2E) =>
% 131.89/22.85 ((
% 131.89/22.85 (upairsubunion) =>
% 131.89/22.85 ((
% 131.89/22.85 (upairinpowunion) =>
% 131.89/22.85 ((
% 131.89/22.85 (ubforcartprodlem1) =>
% 131.89/22.85 ((
% 131.89/22.85 (ubforcartprodlem2) =>
% 131.89/22.85 ((
% 131.89/22.85 (ubforcartprodlem3) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodpairin) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodmempair1) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodmempair) =>
% 131.89/22.85 ((
% 131.89/22.85 (setunionE2) =>
% 131.89/22.85 ((
% 131.89/22.85 (setunionsingleton1) =>
% 131.89/22.85 ((
% 131.89/22.85 (setunionsingleton2) =>
% 131.89/22.85 ((
% 131.89/22.85 (setunionsingleton) =>
% 131.89/22.85 ((
% 131.89/22.85 (singletonprop) =>
% 131.89/22.85 ((
% 131.89/22.85 (ex1E1) =>
% 131.89/22.85 ((
% 131.89/22.85 (ex1I) =>
% 131.89/22.85 ((
% 131.89/22.85 (ex1I2) =>
% 131.89/22.85 ((
% 131.89/22.85 (singletonsuniq) =>
% 131.89/22.85 ((
% 131.89/22.85 (setukpairinjL1) =>
% 131.89/22.85 ((
% 131.89/22.85 (kfstsingleton) =>
% 131.89/22.85 ((
% 131.89/22.85 (theprop) =>
% 131.89/22.85 ((
% 131.89/22.85 (kfstpairEq) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodfstin) =>
% 131.89/22.85 ((
% 131.89/22.85 (setukpairinjL2) =>
% 131.89/22.85 ((
% 131.89/22.85 (setukpairinjL) =>
% 131.89/22.85 ((
% 131.89/22.85 (setukpairinjR11) =>
% 131.89/22.85 ((
% 131.89/22.85 (setukpairinjR12) =>
% 131.89/22.85 ((
% 131.89/22.85 (setukpairinjR1) =>
% 131.89/22.85 ((
% 131.89/22.85 (upairequniteq) =>
% 131.89/22.85 ((
% 131.89/22.85 (setukpairinjR2) =>
% 131.89/22.85 ((
% 131.89/22.85 (setukpairinjR) =>
% 131.89/22.85 ((
% 131.89/22.85 (ksndsingleton) =>
% 131.89/22.85 ((
% 131.89/22.85 (ksndpairEq) =>
% 131.89/22.85 ((
% 131.89/22.85 (kpairsurjEq) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodsndin) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodpairmemEL) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodpairmemER) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodmempaircEq) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodfstpairEq) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodsndpairEq) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodpairsurjEq) =>
% 131.89/22.85 ((
% 131.89/22.85 (dpsetconstrI) =>
% 131.89/22.85 ((
% 131.89/22.85 (dpsetconstrSub) =>
% 131.89/22.85 ((
% 131.89/22.85 (setOfPairsIsBReln) =>
% 131.89/22.85 ((
% 131.89/22.85 (dpsetconstrERa) =>
% 131.89/22.85 ((
% 131.89/22.85 (dpsetconstrEL1) =>
% 131.89/22.85 ((
% 131.89/22.85 (dpsetconstrEL2) =>
% 131.89/22.85 ((
% 131.89/22.85 (dpsetconstrER) =>
% 131.89/22.85 ((
% 131.89/22.85 (funcImageSingleton) =>
% 131.89/22.85 ((
% 131.89/22.85 (apProp) =>
% 131.89/22.85 ((
% 131.89/22.85 (app) =>
% 131.89/22.85 ((
% 131.89/22.85 (infuncsetfunc) =>
% 131.89/22.85 ((
% 131.89/22.85 (ap2p) =>
% 131.89/22.85 ((
% 131.89/22.85 (funcinfuncset) =>
% 131.89/22.85 ((
% 131.89/22.85 (lamProp) =>
% 131.89/22.85 ((
% 131.89/22.85 (lamp) =>
% 131.89/22.85 ((
% 131.89/22.85 (lam2p) =>
% 131.89/22.85 ((
% 131.89/22.85 (brelnall1) =>
% 131.89/22.85 ((
% 131.89/22.85 (brelnall2) =>
% 131.89/22.85 ((
% 131.89/22.85 (ex1E2) =>
% 131.89/22.85 ((
% 131.89/22.85 (funcGraphProp1) =>
% 131.89/22.85 ((
% 131.89/22.85 (funcGraphProp3) =>
% 131.89/22.85 ((
% 131.89/22.85 (funcGraphProp2) =>
% 131.89/22.85 ((
% 131.89/22.85 (funcextLem) =>
% 131.89/22.85 ((
% 131.89/22.85 (funcGraphProp4) =>
% 131.89/22.85 ((
% 131.89/22.85 (subbreln) =>
% 131.89/22.85 ((
% 131.89/22.85 (eqbreln) =>
% 131.89/22.85 ((
% 131.89/22.85 (funcext) =>
% 131.89/22.85 ((
% 131.89/22.85 (funcext2) =>
% 131.89/22.85 ((
% 131.89/22.85 (ap2apEq1) =>
% 131.89/22.85 ((
% 131.89/22.85 (ap2apEq2) =>
% 131.89/22.85 ((
% 131.89/22.85 (beta1) =>
% 131.89/22.85 ((
% 131.89/22.85 (eta1) =>
% 131.89/22.85 ((
% 131.89/22.85 (lam2lamEq) =>
% 131.89/22.85 ((
% 131.89/22.85 (beta2) =>
% 131.89/22.85 ((
% 131.89/22.85 (eta2) =>
% 131.89/22.85 ((
% 131.89/22.85 (iffalseProp1) =>
% 131.89/22.85 ((
% 131.89/22.85 (iffalseProp2) =>
% 131.89/22.85 ((
% 131.89/22.85 (iftrueProp1) =>
% 131.89/22.85 ((
% 131.89/22.85 (iftrueProp2) =>
% 131.89/22.85 ((
% 131.89/22.85 (ifSingleton) =>
% 131.89/22.85 ((
% 131.89/22.85 (ifp) =>
% 131.89/22.85 ((
% 131.89/22.85 (theeq) =>
% 131.89/22.85 ((
% 131.89/22.85 (iftrue) =>
% 131.89/22.85 ((
% 131.89/22.85 (iffalse) =>
% 131.89/22.85 ((
% 131.89/22.85 (iftrueorfalse) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectT_lem) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionT_lem) =>
% 131.89/22.85 ((
% 131.89/22.85 (powersetT_lem) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusT_lem) =>
% 131.89/22.85 ((
% 131.89/22.85 (complementT_lem) =>
% 131.89/22.85 ((
% 131.89/22.85 (setextT) =>
% 131.89/22.85 ((
% 131.89/22.85 (subsetTI) =>
% 131.89/22.85 ((
% 131.89/22.85 (powersetTI1) =>
% 131.89/22.85 ((
% 131.89/22.85 (powersetTE1) =>
% 131.89/22.85 ((
% 131.89/22.85 (complementTI1) =>
% 131.89/22.85 ((
% 131.89/22.85 (complementTE1) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectTELcontra) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectTERcontra) =>
% 131.89/22.85 ((
% 131.89/22.85 (contrasubsetT) =>
% 131.89/22.85 ((
% 131.89/22.85 (contrasubsetT1) =>
% 131.89/22.85 ((
% 131.89/22.85 (contrasubsetT2) =>
% 131.89/22.85 ((
% 131.89/22.85 (contrasubsetT3) =>
% 131.89/22.85 ((
% 131.89/22.85 (doubleComplementI1) =>
% 131.89/22.85 ((
% 131.89/22.85 (doubleComplementE1) =>
% 131.89/22.85 ((
% 131.89/22.85 (doubleComplementSub1) =>
% 131.89/22.85 ((
% 131.89/22.85 (doubleComplementSub2) =>
% 131.89/22.85 ((
% 131.89/22.85 (doubleComplementEq) =>
% 131.89/22.85 ((
% 131.89/22.85 (complementTnotintersectT) =>
% 131.89/22.85 ((
% 131.89/22.85 (complementImpComplementIntersect) =>
% 131.89/22.85 ((
% 131.89/22.85 (complementSubsetComplementIntersect) =>
% 131.89/22.85 ((
% 131.89/22.85 (complementInPowersetComplementIntersect) =>
% 131.89/22.85 ((
% 131.89/22.85 (contraSubsetComplement) =>
% 131.89/22.85 ((
% 131.89/22.85 (complementTcontraSubset) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionTILcontra) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionTIRcontra) =>
% 131.89/22.85 ((
% 131.89/22.85 (inIntersectImpInUnion) =>
% 131.89/22.85 ((
% 131.89/22.85 (inIntersectImpInUnion2) =>
% 131.89/22.85 ((
% 131.89/22.85 (inIntersectImpInIntersectUnions) =>
% 131.89/22.85 ((
% 131.89/22.85 (intersectInPowersetIntersectUnions) =>
% 131.89/22.85 ((
% 131.89/22.85 (inComplementUnionImpNotIn1) =>
% 131.89/22.85 ((
% 131.89/22.85 (inComplementUnionImpInComplement1) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionTE) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionTEcontra) =>
% 131.89/22.85 ((
% 131.89/22.85 (demorgan2a1) =>
% 131.89/22.85 ((
% 131.89/22.85 (complementUnionInPowersetComplement) =>
% 131.89/22.85 ((
% 131.89/22.85 (demorgan2a2) =>
% 131.89/22.85 ((
% 131.89/22.85 (demorgan1a) =>
% 131.89/22.85 ((
% 131.89/22.85 (demorgan1b) =>
% 131.89/22.85 ((
% 131.89/22.85 (demorgan1) =>
% 131.89/22.85 ((
% 131.89/22.85 (demorgan2a) =>
% 131.89/22.85 ((
% 131.89/22.85 (demorgan2b2) =>
% 131.89/22.85 ((
% 131.89/22.85 (demorgan2b) =>
% 131.89/22.85 ((
% 131.89/22.85 (demorgan2) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz13rule0) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz13rule1) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz13rule2) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz13rule3) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz13rule4) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz1_1) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz1_2) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz1_3) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz1_4) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz1_5) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1all2) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1SetBreln1) =>
% 131.89/22.85 ((
% 131.89/22.85 (choice2fnsingleton) =>
% 131.89/22.85 ((
% 131.89/22.85 (setOfPairsIsBReln1) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1all1) =>
% 131.89/22.85 ((
% 131.89/22.85 (subbreln1) =>
% 131.89/22.85 ((
% 131.89/22.85 (eqbreln1) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1invprop) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1invI) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1invE) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1compprop) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1compI) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1compE) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1compEex) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1unionprop) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1unionIL) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1unionIR) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1unionI) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1unionE) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1unionEcases) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1unionCommutes) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz2Ex) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz2W) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz2A) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz2B) =>
% 131.89/22.85 ((
% 131.89/22.85 (image1Ex) =>
% 131.89/22.85 ((
% 131.89/22.85 (image1Ex1) =>
% 131.89/22.85 ((
% 131.89/22.85 (image1Equiv) =>
% 131.89/22.85 ((
% 131.89/22.85 (image1E) =>
% 131.89/22.85 ((
% 131.89/22.85 (image1I) =>
% 131.89/22.85 ((
% 131.89/22.85 (injFuncInInjFuncSet) =>
% 131.89/22.85 ((
% 131.89/22.85 (injFuncSetFuncIn) =>
% 131.89/22.85 ((
% 131.89/22.85 (injFuncSetFuncInj) =>
% 131.89/22.85 ((
% 131.89/22.85 (surjFuncSetFuncIn) =>
% 131.89/22.85 ((
% 131.89/22.85 (surjFuncSetFuncSurj) =>
% 131.89/22.85 ((
% 131.89/22.85 (leftInvIsSurj) =>
% 131.89/22.85 ((
% 131.89/22.85 (surjCantorThm) =>
% 131.89/22.85 ((
% 131.89/22.85 (foundation2) =>
% 131.89/22.85 ((
% 131.89/22.85 (notinself) =>
% 131.89/22.85 ((
% 131.89/22.85 (notinself2) =>
% 131.89/22.85 ((
% 131.89/22.85 (omegaSp) =>
% 131.89/22.85 ((
% 131.89/22.85 (omegaSclos) =>
% 131.89/22.85 ((
% 131.89/22.85 (peano0notS) =>
% 131.89/22.85 ((
% 131.89/22.85 (peanoSinj) =>
% 131.89/22.85 ((
% 131.89/22.85 (transitivesetOp1) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintTransitive) =>
% 131.89/22.85 ((
% 131.89/22.85 (transitivesetOp2) =>
% 131.89/22.85 ((
% 131.89/22.85 (setunionTransitive) =>
% 131.89/22.85 ((
% 131.89/22.85 (ordinalMinLem1) =>
% 131.89/22.85 ((
% 131.89/22.85 (ordinalTransSet) =>
% 131.89/22.85 ((
% 131.89/22.85 (ordinalTransSet1) =>
% 131.89/22.85 ((
% 131.89/22.85 (setunionOrdinalLem1) =>
% 131.89/22.85 (ordinal @
% 131.89/22.85 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 131.89/22.85 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl535])).
% 131.89/22.85 thf(zip_derived_cl560, plain,
% 131.89/22.85 (~ (((exuI2) =>
% 131.89/22.85 (((inCongP) =>
% 131.89/22.85 (((in__Cong) =>
% 131.89/22.85 (((exuE3u) =>
% 131.89/22.85 (((exu__Cong) =>
% 131.89/22.85 (((setadjoin__Cong) =>
% 131.89/22.85 (((powerset__Cong) =>
% 131.89/22.85 (((setunion__Cong) =>
% 131.89/22.85 (((exuEu) =>
% 131.89/22.85 (((descr__Cong) =>
% 131.89/22.85 (((dsetconstr__Cong) =>
% 131.89/22.85 (((subsetI1) =>
% 131.89/22.85 (((eqimpsubset2) =>
% 131.89/22.85 (((eqimpsubset1) =>
% 131.89/22.85 (((subsetI2) =>
% 131.89/22.85 (((emptysetsubset) =>
% 131.89/22.85 (((subsetE) =>
% 131.89/22.85 (((subsetE2) =>
% 131.89/22.85 (((notsubsetI) =>
% 131.89/22.85 (((notequalI1) =>
% 131.89/22.85 (((notequalI2) =>
% 131.89/22.85 (((subsetRefl) =>
% 131.89/22.85 (((subsetTrans) =>
% 131.89/22.85 (((setadjoinSub) =>
% 131.89/22.85 (((setadjoinSub2) =>
% 131.89/22.85 (((subset2powerset) =>
% 131.89/22.85 (((setextsub) =>
% 131.89/22.85 (((subsetemptysetimpeq) =>
% 131.89/22.85 (((powersetI1) =>
% 131.89/22.85 (((powersetE1) =>
% 131.89/22.85 ((
% 131.89/22.85 (inPowerset) =>
% 131.89/22.85 ((
% 131.89/22.85 (powersetsubset) =>
% 131.89/22.85 ((
% 131.89/22.85 (sepInPowerset) =>
% 131.89/22.85 ((
% 131.89/22.85 (sepSubset) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionIL) =>
% 131.89/22.85 ((
% 131.89/22.85 (upairset2IR) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionIR) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionEcases) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionE) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionLsub) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionRsub) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectI) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectSubset5) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectEL) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectLsub) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectSubset2) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectSubset3) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectER) =>
% 131.89/22.85 ((
% 131.89/22.85 (disjointsetsI1) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectRsub) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectSubset4) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectSubset1) =>
% 131.89/22.85 ((
% 131.89/22.85 (bs114d) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusI) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusEL) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusER) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusSubset2) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusERneg) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusELneg) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusILneg) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusIRneg) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusLsub) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusSubset1) =>
% 131.89/22.85 ((
% 131.89/22.85 (symdiffE) =>
% 131.89/22.85 ((
% 131.89/22.85 (symdiffI1) =>
% 131.89/22.85 ((
% 131.89/22.85 (symdiffI2) =>
% 131.89/22.85 ((
% 131.89/22.85 (symdiffIneg1) =>
% 131.89/22.85 ((
% 131.89/22.85 (symdiffIneg2) =>
% 131.89/22.85 ((
% 131.89/22.85 (secondinupair) =>
% 131.89/22.85 ((
% 131.89/22.85 (setukpairIL) =>
% 131.89/22.85 ((
% 131.89/22.85 (setukpairIR) =>
% 131.89/22.85 ((
% 131.89/22.85 (kpairiskpair) =>
% 131.89/22.85 ((
% 131.89/22.85 (kpairp) =>
% 131.89/22.85 ((
% 131.89/22.85 (singletonsubset) =>
% 131.89/22.85 ((
% 131.89/22.85 (singletoninpowerset) =>
% 131.89/22.85 ((
% 131.89/22.85 (singletoninpowunion) =>
% 131.89/22.85 ((
% 131.89/22.85 (upairset2E) =>
% 131.89/22.85 ((
% 131.89/22.85 (upairsubunion) =>
% 131.89/22.85 ((
% 131.89/22.85 (upairinpowunion) =>
% 131.89/22.85 ((
% 131.89/22.85 (ubforcartprodlem1) =>
% 131.89/22.85 ((
% 131.89/22.85 (ubforcartprodlem2) =>
% 131.89/22.85 ((
% 131.89/22.85 (ubforcartprodlem3) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodpairin) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodmempair1) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodmempair) =>
% 131.89/22.85 ((
% 131.89/22.85 (setunionE2) =>
% 131.89/22.85 ((
% 131.89/22.85 (setunionsingleton1) =>
% 131.89/22.85 ((
% 131.89/22.85 (setunionsingleton2) =>
% 131.89/22.85 ((
% 131.89/22.85 (setunionsingleton) =>
% 131.89/22.85 ((
% 131.89/22.85 (singletonprop) =>
% 131.89/22.85 ((
% 131.89/22.85 (ex1E1) =>
% 131.89/22.85 ((
% 131.89/22.85 (ex1I) =>
% 131.89/22.85 ((
% 131.89/22.85 (ex1I2) =>
% 131.89/22.85 ((
% 131.89/22.85 (singletonsuniq) =>
% 131.89/22.85 ((
% 131.89/22.85 (setukpairinjL1) =>
% 131.89/22.85 ((
% 131.89/22.85 (kfstsingleton) =>
% 131.89/22.85 ((
% 131.89/22.85 (theprop) =>
% 131.89/22.85 ((
% 131.89/22.85 (kfstpairEq) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodfstin) =>
% 131.89/22.85 ((
% 131.89/22.85 (setukpairinjL2) =>
% 131.89/22.85 ((
% 131.89/22.85 (setukpairinjL) =>
% 131.89/22.85 ((
% 131.89/22.85 (setukpairinjR11) =>
% 131.89/22.85 ((
% 131.89/22.85 (setukpairinjR12) =>
% 131.89/22.85 ((
% 131.89/22.85 (setukpairinjR1) =>
% 131.89/22.85 ((
% 131.89/22.85 (upairequniteq) =>
% 131.89/22.85 ((
% 131.89/22.85 (setukpairinjR2) =>
% 131.89/22.85 ((
% 131.89/22.85 (setukpairinjR) =>
% 131.89/22.85 ((
% 131.89/22.85 (ksndsingleton) =>
% 131.89/22.85 ((
% 131.89/22.85 (ksndpairEq) =>
% 131.89/22.85 ((
% 131.89/22.85 (kpairsurjEq) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodsndin) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodpairmemEL) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodpairmemER) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodmempaircEq) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodfstpairEq) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodsndpairEq) =>
% 131.89/22.85 ((
% 131.89/22.85 (cartprodpairsurjEq) =>
% 131.89/22.85 ((
% 131.89/22.85 (dpsetconstrI) =>
% 131.89/22.85 ((
% 131.89/22.85 (dpsetconstrSub) =>
% 131.89/22.85 ((
% 131.89/22.85 (setOfPairsIsBReln) =>
% 131.89/22.85 ((
% 131.89/22.85 (dpsetconstrERa) =>
% 131.89/22.85 ((
% 131.89/22.85 (dpsetconstrEL1) =>
% 131.89/22.85 ((
% 131.89/22.85 (dpsetconstrEL2) =>
% 131.89/22.85 ((
% 131.89/22.85 (dpsetconstrER) =>
% 131.89/22.85 ((
% 131.89/22.85 (funcImageSingleton) =>
% 131.89/22.85 ((
% 131.89/22.85 (apProp) =>
% 131.89/22.85 ((
% 131.89/22.85 (app) =>
% 131.89/22.85 ((
% 131.89/22.85 (infuncsetfunc) =>
% 131.89/22.85 ((
% 131.89/22.85 (ap2p) =>
% 131.89/22.85 ((
% 131.89/22.85 (funcinfuncset) =>
% 131.89/22.85 ((
% 131.89/22.85 (lamProp) =>
% 131.89/22.85 ((
% 131.89/22.85 (lamp) =>
% 131.89/22.85 ((
% 131.89/22.85 (lam2p) =>
% 131.89/22.85 ((
% 131.89/22.85 (brelnall1) =>
% 131.89/22.85 ((
% 131.89/22.85 (brelnall2) =>
% 131.89/22.85 ((
% 131.89/22.85 (ex1E2) =>
% 131.89/22.85 ((
% 131.89/22.85 (funcGraphProp1) =>
% 131.89/22.85 ((
% 131.89/22.85 (funcGraphProp3) =>
% 131.89/22.85 ((
% 131.89/22.85 (funcGraphProp2) =>
% 131.89/22.85 ((
% 131.89/22.85 (funcextLem) =>
% 131.89/22.85 ((
% 131.89/22.85 (funcGraphProp4) =>
% 131.89/22.85 ((
% 131.89/22.85 (subbreln) =>
% 131.89/22.85 ((
% 131.89/22.85 (eqbreln) =>
% 131.89/22.85 ((
% 131.89/22.85 (funcext) =>
% 131.89/22.85 ((
% 131.89/22.85 (funcext2) =>
% 131.89/22.85 ((
% 131.89/22.85 (ap2apEq1) =>
% 131.89/22.85 ((
% 131.89/22.85 (ap2apEq2) =>
% 131.89/22.85 ((
% 131.89/22.85 (beta1) =>
% 131.89/22.85 ((
% 131.89/22.85 (eta1) =>
% 131.89/22.85 ((
% 131.89/22.85 (lam2lamEq) =>
% 131.89/22.85 ((
% 131.89/22.85 (beta2) =>
% 131.89/22.85 ((
% 131.89/22.85 (eta2) =>
% 131.89/22.85 ((
% 131.89/22.85 (iffalseProp1) =>
% 131.89/22.85 ((
% 131.89/22.85 (iffalseProp2) =>
% 131.89/22.85 ((
% 131.89/22.85 (iftrueProp1) =>
% 131.89/22.85 ((
% 131.89/22.85 (iftrueProp2) =>
% 131.89/22.85 ((
% 131.89/22.85 (ifSingleton) =>
% 131.89/22.85 ((
% 131.89/22.85 (ifp) =>
% 131.89/22.85 ((
% 131.89/22.85 (theeq) =>
% 131.89/22.85 ((
% 131.89/22.85 (iftrue) =>
% 131.89/22.85 ((
% 131.89/22.85 (iffalse) =>
% 131.89/22.85 ((
% 131.89/22.85 (iftrueorfalse) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectT_lem) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionT_lem) =>
% 131.89/22.85 ((
% 131.89/22.85 (powersetT_lem) =>
% 131.89/22.85 ((
% 131.89/22.85 (setminusT_lem) =>
% 131.89/22.85 ((
% 131.89/22.85 (complementT_lem) =>
% 131.89/22.85 ((
% 131.89/22.85 (setextT) =>
% 131.89/22.85 ((
% 131.89/22.85 (subsetTI) =>
% 131.89/22.85 ((
% 131.89/22.85 (powersetTI1) =>
% 131.89/22.85 ((
% 131.89/22.85 (powersetTE1) =>
% 131.89/22.85 ((
% 131.89/22.85 (complementTI1) =>
% 131.89/22.85 ((
% 131.89/22.85 (complementTE1) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectTELcontra) =>
% 131.89/22.85 ((
% 131.89/22.85 (binintersectTERcontra) =>
% 131.89/22.85 ((
% 131.89/22.85 (contrasubsetT) =>
% 131.89/22.85 ((
% 131.89/22.85 (contrasubsetT1) =>
% 131.89/22.85 ((
% 131.89/22.85 (contrasubsetT2) =>
% 131.89/22.85 ((
% 131.89/22.85 (contrasubsetT3) =>
% 131.89/22.85 ((
% 131.89/22.85 (doubleComplementI1) =>
% 131.89/22.85 ((
% 131.89/22.85 (doubleComplementE1) =>
% 131.89/22.85 ((
% 131.89/22.85 (doubleComplementSub1) =>
% 131.89/22.85 ((
% 131.89/22.85 (doubleComplementSub2) =>
% 131.89/22.85 ((
% 131.89/22.85 (doubleComplementEq) =>
% 131.89/22.85 ((
% 131.89/22.85 (complementTnotintersectT) =>
% 131.89/22.85 ((
% 131.89/22.85 (complementImpComplementIntersect) =>
% 131.89/22.85 ((
% 131.89/22.85 (complementSubsetComplementIntersect) =>
% 131.89/22.85 ((
% 131.89/22.85 (complementInPowersetComplementIntersect) =>
% 131.89/22.85 ((
% 131.89/22.85 (contraSubsetComplement) =>
% 131.89/22.85 ((
% 131.89/22.85 (complementTcontraSubset) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionTILcontra) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionTIRcontra) =>
% 131.89/22.85 ((
% 131.89/22.85 (inIntersectImpInUnion) =>
% 131.89/22.85 ((
% 131.89/22.85 (inIntersectImpInUnion2) =>
% 131.89/22.85 ((
% 131.89/22.85 (inIntersectImpInIntersectUnions) =>
% 131.89/22.85 ((
% 131.89/22.85 (intersectInPowersetIntersectUnions) =>
% 131.89/22.85 ((
% 131.89/22.85 (inComplementUnionImpNotIn1) =>
% 131.89/22.85 ((
% 131.89/22.85 (inComplementUnionImpInComplement1) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionTE) =>
% 131.89/22.85 ((
% 131.89/22.85 (binunionTEcontra) =>
% 131.89/22.85 ((
% 131.89/22.85 (demorgan2a1) =>
% 131.89/22.85 ((
% 131.89/22.85 (complementUnionInPowersetComplement) =>
% 131.89/22.85 ((
% 131.89/22.85 (demorgan2a2) =>
% 131.89/22.85 ((
% 131.89/22.85 (demorgan1a) =>
% 131.89/22.85 ((
% 131.89/22.85 (demorgan1b) =>
% 131.89/22.85 ((
% 131.89/22.85 (demorgan1) =>
% 131.89/22.85 ((
% 131.89/22.85 (demorgan2a) =>
% 131.89/22.85 ((
% 131.89/22.85 (demorgan2b2) =>
% 131.89/22.85 ((
% 131.89/22.85 (demorgan2b) =>
% 131.89/22.85 ((
% 131.89/22.85 (demorgan2) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz13rule0) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz13rule1) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz13rule2) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz13rule3) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz13rule4) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz1_1) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz1_2) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz1_3) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz1_4) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz1_5) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1all2) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1SetBreln1) =>
% 131.89/22.85 ((
% 131.89/22.85 (choice2fnsingleton) =>
% 131.89/22.85 ((
% 131.89/22.85 (setOfPairsIsBReln1) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1all1) =>
% 131.89/22.85 ((
% 131.89/22.85 (subbreln1) =>
% 131.89/22.85 ((
% 131.89/22.85 (eqbreln1) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1invprop) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1invI) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1invE) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1compprop) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1compI) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1compE) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1compEex) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1unionprop) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1unionIL) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1unionIR) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1unionI) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1unionE) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1unionEcases) =>
% 131.89/22.85 ((
% 131.89/22.85 (breln1unionCommutes) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz2Ex) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz2W) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz2A) =>
% 131.89/22.85 ((
% 131.89/22.85 (woz2B) =>
% 131.89/22.85 ((
% 131.89/22.85 (image1Ex) =>
% 131.89/22.85 ((
% 131.89/22.85 (image1Ex1) =>
% 131.89/22.85 ((
% 131.89/22.85 (image1Equiv) =>
% 131.89/22.85 ((
% 131.89/22.85 (image1E) =>
% 131.89/22.85 ((
% 131.89/22.85 (image1I) =>
% 131.89/22.85 ((
% 131.89/22.85 (injFuncInInjFuncSet) =>
% 131.89/22.85 ((
% 131.89/22.85 (injFuncSetFuncIn) =>
% 131.89/22.85 ((
% 131.89/22.85 (injFuncSetFuncInj) =>
% 131.89/22.85 ((
% 131.89/22.85 (surjFuncSetFuncIn) =>
% 131.89/22.85 ((
% 131.89/22.85 (surjFuncSetFuncSurj) =>
% 131.89/22.85 ((
% 131.89/22.85 (leftInvIsSurj) =>
% 131.89/22.85 ((
% 131.89/22.85 (surjCantorThm) =>
% 131.89/22.85 ((
% 131.89/22.85 (foundation2) =>
% 131.89/22.85 ((
% 131.89/22.85 (notinself) =>
% 131.89/22.85 ((
% 131.89/22.85 (notinself2) =>
% 131.89/22.85 ((
% 131.89/22.85 (omegaSp) =>
% 131.89/22.85 ((
% 131.89/22.85 (omegaSclos) =>
% 132.32/22.87 ((
% 132.32/22.87 (peano0notS) =>
% 132.32/22.87 ((
% 132.32/22.87 (peanoSinj) =>
% 132.32/22.87 ((
% 132.32/22.87 (transitivesetOp1) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintTransitive) =>
% 132.32/22.87 ((
% 132.32/22.87 (transitivesetOp2) =>
% 132.32/22.87 ((
% 132.32/22.87 (setunionTransitive) =>
% 132.32/22.87 ((
% 132.32/22.87 (ordinalMinLem1) =>
% 132.32/22.87 ((
% 132.32/22.87 (ordinalTransSet) =>
% 132.32/22.87 ((
% 132.32/22.87 (ordinalTransSet1) =>
% 132.32/22.87 ((
% 132.32/22.87 (setunionOrdinalLem1) =>
% 132.32/22.87 (ordinal @
% 132.32/22.87 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.32/22.87 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl550])).
% 132.32/22.87 thf(zip_derived_cl568, plain,
% 132.32/22.87 (~ (((inCongP) =>
% 132.32/22.87 (((in__Cong) =>
% 132.32/22.87 (((exuE3u) =>
% 132.32/22.87 (((exu__Cong) =>
% 132.32/22.87 (((setadjoin__Cong) =>
% 132.32/22.87 (((powerset__Cong) =>
% 132.32/22.87 (((setunion__Cong) =>
% 132.32/22.87 (((exuEu) =>
% 132.32/22.87 (((descr__Cong) =>
% 132.32/22.87 (((dsetconstr__Cong) =>
% 132.32/22.87 (((subsetI1) =>
% 132.32/22.87 (((eqimpsubset2) =>
% 132.32/22.87 (((eqimpsubset1) =>
% 132.32/22.87 (((subsetI2) =>
% 132.32/22.87 (((emptysetsubset) =>
% 132.32/22.87 (((subsetE) =>
% 132.32/22.87 (((subsetE2) =>
% 132.32/22.87 (((notsubsetI) =>
% 132.32/22.87 (((notequalI1) =>
% 132.32/22.87 (((notequalI2) =>
% 132.32/22.87 (((subsetRefl) =>
% 132.32/22.87 (((subsetTrans) =>
% 132.32/22.87 (((setadjoinSub) =>
% 132.32/22.87 (((setadjoinSub2) =>
% 132.32/22.87 (((subset2powerset) =>
% 132.32/22.87 (((setextsub) =>
% 132.32/22.87 (((subsetemptysetimpeq) =>
% 132.32/22.87 (((powersetI1) =>
% 132.32/22.87 (((powersetE1) =>
% 132.32/22.87 (((inPowerset) =>
% 132.32/22.87 ((
% 132.32/22.87 (powersetsubset) =>
% 132.32/22.87 ((
% 132.32/22.87 (sepInPowerset) =>
% 132.32/22.87 ((
% 132.32/22.87 (sepSubset) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionIL) =>
% 132.32/22.87 ((
% 132.32/22.87 (upairset2IR) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionIR) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionEcases) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionE) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionLsub) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionRsub) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectI) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectSubset5) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectEL) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectLsub) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectSubset2) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectSubset3) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectER) =>
% 132.32/22.87 ((
% 132.32/22.87 (disjointsetsI1) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectRsub) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectSubset4) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectSubset1) =>
% 132.32/22.87 ((
% 132.32/22.87 (bs114d) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusI) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusEL) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusER) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusSubset2) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusERneg) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusELneg) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusILneg) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusIRneg) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusLsub) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusSubset1) =>
% 132.32/22.87 ((
% 132.32/22.87 (symdiffE) =>
% 132.32/22.87 ((
% 132.32/22.87 (symdiffI1) =>
% 132.32/22.87 ((
% 132.32/22.87 (symdiffI2) =>
% 132.32/22.87 ((
% 132.32/22.87 (symdiffIneg1) =>
% 132.32/22.87 ((
% 132.32/22.87 (symdiffIneg2) =>
% 132.32/22.87 ((
% 132.32/22.87 (secondinupair) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairIL) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairIR) =>
% 132.32/22.87 ((
% 132.32/22.87 (kpairiskpair) =>
% 132.32/22.87 ((
% 132.32/22.87 (kpairp) =>
% 132.32/22.87 ((
% 132.32/22.87 (singletonsubset) =>
% 132.32/22.87 ((
% 132.32/22.87 (singletoninpowerset) =>
% 132.32/22.87 ((
% 132.32/22.87 (singletoninpowunion) =>
% 132.32/22.87 ((
% 132.32/22.87 (upairset2E) =>
% 132.32/22.87 ((
% 132.32/22.87 (upairsubunion) =>
% 132.32/22.87 ((
% 132.32/22.87 (upairinpowunion) =>
% 132.32/22.87 ((
% 132.32/22.87 (ubforcartprodlem1) =>
% 132.32/22.87 ((
% 132.32/22.87 (ubforcartprodlem2) =>
% 132.32/22.87 ((
% 132.32/22.87 (ubforcartprodlem3) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodpairin) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodmempair1) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodmempair) =>
% 132.32/22.87 ((
% 132.32/22.87 (setunionE2) =>
% 132.32/22.87 ((
% 132.32/22.87 (setunionsingleton1) =>
% 132.32/22.87 ((
% 132.32/22.87 (setunionsingleton2) =>
% 132.32/22.87 ((
% 132.32/22.87 (setunionsingleton) =>
% 132.32/22.87 ((
% 132.32/22.87 (singletonprop) =>
% 132.32/22.87 ((
% 132.32/22.87 (ex1E1) =>
% 132.32/22.87 ((
% 132.32/22.87 (ex1I) =>
% 132.32/22.87 ((
% 132.32/22.87 (ex1I2) =>
% 132.32/22.87 ((
% 132.32/22.87 (singletonsuniq) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairinjL1) =>
% 132.32/22.87 ((
% 132.32/22.87 (kfstsingleton) =>
% 132.32/22.87 ((
% 132.32/22.87 (theprop) =>
% 132.32/22.87 ((
% 132.32/22.87 (kfstpairEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodfstin) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairinjL2) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairinjL) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairinjR11) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairinjR12) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairinjR1) =>
% 132.32/22.87 ((
% 132.32/22.87 (upairequniteq) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairinjR2) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairinjR) =>
% 132.32/22.87 ((
% 132.32/22.87 (ksndsingleton) =>
% 132.32/22.87 ((
% 132.32/22.87 (ksndpairEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (kpairsurjEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodsndin) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodpairmemEL) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodpairmemER) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodmempaircEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodfstpairEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodsndpairEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodpairsurjEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (dpsetconstrI) =>
% 132.32/22.87 ((
% 132.32/22.87 (dpsetconstrSub) =>
% 132.32/22.87 ((
% 132.32/22.87 (setOfPairsIsBReln) =>
% 132.32/22.87 ((
% 132.32/22.87 (dpsetconstrERa) =>
% 132.32/22.87 ((
% 132.32/22.87 (dpsetconstrEL1) =>
% 132.32/22.87 ((
% 132.32/22.87 (dpsetconstrEL2) =>
% 132.32/22.87 ((
% 132.32/22.87 (dpsetconstrER) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcImageSingleton) =>
% 132.32/22.87 ((
% 132.32/22.87 (apProp) =>
% 132.32/22.87 ((
% 132.32/22.87 (app) =>
% 132.32/22.87 ((
% 132.32/22.87 (infuncsetfunc) =>
% 132.32/22.87 ((
% 132.32/22.87 (ap2p) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcinfuncset) =>
% 132.32/22.87 ((
% 132.32/22.87 (lamProp) =>
% 132.32/22.87 ((
% 132.32/22.87 (lamp) =>
% 132.32/22.87 ((
% 132.32/22.87 (lam2p) =>
% 132.32/22.87 ((
% 132.32/22.87 (brelnall1) =>
% 132.32/22.87 ((
% 132.32/22.87 (brelnall2) =>
% 132.32/22.87 ((
% 132.32/22.87 (ex1E2) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcGraphProp1) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcGraphProp3) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcGraphProp2) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcextLem) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcGraphProp4) =>
% 132.32/22.87 ((
% 132.32/22.87 (subbreln) =>
% 132.32/22.87 ((
% 132.32/22.87 (eqbreln) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcext) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcext2) =>
% 132.32/22.87 ((
% 132.32/22.87 (ap2apEq1) =>
% 132.32/22.87 ((
% 132.32/22.87 (ap2apEq2) =>
% 132.32/22.87 ((
% 132.32/22.87 (beta1) =>
% 132.32/22.87 ((
% 132.32/22.87 (eta1) =>
% 132.32/22.87 ((
% 132.32/22.87 (lam2lamEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (beta2) =>
% 132.32/22.87 ((
% 132.32/22.87 (eta2) =>
% 132.32/22.87 ((
% 132.32/22.87 (iffalseProp1) =>
% 132.32/22.87 ((
% 132.32/22.87 (iffalseProp2) =>
% 132.32/22.87 ((
% 132.32/22.87 (iftrueProp1) =>
% 132.32/22.87 ((
% 132.32/22.87 (iftrueProp2) =>
% 132.32/22.87 ((
% 132.32/22.87 (ifSingleton) =>
% 132.32/22.87 ((
% 132.32/22.87 (ifp) =>
% 132.32/22.87 ((
% 132.32/22.87 (theeq) =>
% 132.32/22.87 ((
% 132.32/22.87 (iftrue) =>
% 132.32/22.87 ((
% 132.32/22.87 (iffalse) =>
% 132.32/22.87 ((
% 132.32/22.87 (iftrueorfalse) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectT_lem) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionT_lem) =>
% 132.32/22.87 ((
% 132.32/22.87 (powersetT_lem) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusT_lem) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementT_lem) =>
% 132.32/22.87 ((
% 132.32/22.87 (setextT) =>
% 132.32/22.87 ((
% 132.32/22.87 (subsetTI) =>
% 132.32/22.87 ((
% 132.32/22.87 (powersetTI1) =>
% 132.32/22.87 ((
% 132.32/22.87 (powersetTE1) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementTI1) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementTE1) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectTELcontra) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectTERcontra) =>
% 132.32/22.87 ((
% 132.32/22.87 (contrasubsetT) =>
% 132.32/22.87 ((
% 132.32/22.87 (contrasubsetT1) =>
% 132.32/22.87 ((
% 132.32/22.87 (contrasubsetT2) =>
% 132.32/22.87 ((
% 132.32/22.87 (contrasubsetT3) =>
% 132.32/22.87 ((
% 132.32/22.87 (doubleComplementI1) =>
% 132.32/22.87 ((
% 132.32/22.87 (doubleComplementE1) =>
% 132.32/22.87 ((
% 132.32/22.87 (doubleComplementSub1) =>
% 132.32/22.87 ((
% 132.32/22.87 (doubleComplementSub2) =>
% 132.32/22.87 ((
% 132.32/22.87 (doubleComplementEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementTnotintersectT) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementImpComplementIntersect) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementSubsetComplementIntersect) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementInPowersetComplementIntersect) =>
% 132.32/22.87 ((
% 132.32/22.87 (contraSubsetComplement) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementTcontraSubset) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionTILcontra) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionTIRcontra) =>
% 132.32/22.87 ((
% 132.32/22.87 (inIntersectImpInUnion) =>
% 132.32/22.87 ((
% 132.32/22.87 (inIntersectImpInUnion2) =>
% 132.32/22.87 ((
% 132.32/22.87 (inIntersectImpInIntersectUnions) =>
% 132.32/22.87 ((
% 132.32/22.87 (intersectInPowersetIntersectUnions) =>
% 132.32/22.87 ((
% 132.32/22.87 (inComplementUnionImpNotIn1) =>
% 132.32/22.87 ((
% 132.32/22.87 (inComplementUnionImpInComplement1) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionTE) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionTEcontra) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan2a1) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementUnionInPowersetComplement) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan2a2) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan1a) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan1b) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan1) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan2a) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan2b2) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan2b) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan2) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz13rule0) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz13rule1) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz13rule2) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz13rule3) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz13rule4) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz1_1) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz1_2) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz1_3) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz1_4) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz1_5) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1all2) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1SetBreln1) =>
% 132.32/22.87 ((
% 132.32/22.87 (choice2fnsingleton) =>
% 132.32/22.87 ((
% 132.32/22.87 (setOfPairsIsBReln1) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1all1) =>
% 132.32/22.87 ((
% 132.32/22.87 (subbreln1) =>
% 132.32/22.87 ((
% 132.32/22.87 (eqbreln1) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1invprop) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1invI) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1invE) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1compprop) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1compI) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1compE) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1compEex) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1unionprop) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1unionIL) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1unionIR) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1unionI) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1unionE) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1unionEcases) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1unionCommutes) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz2Ex) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz2W) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz2A) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz2B) =>
% 132.32/22.87 ((
% 132.32/22.87 (image1Ex) =>
% 132.32/22.87 ((
% 132.32/22.87 (image1Ex1) =>
% 132.32/22.87 ((
% 132.32/22.87 (image1Equiv) =>
% 132.32/22.87 ((
% 132.32/22.87 (image1E) =>
% 132.32/22.87 ((
% 132.32/22.87 (image1I) =>
% 132.32/22.87 ((
% 132.32/22.87 (injFuncInInjFuncSet) =>
% 132.32/22.87 ((
% 132.32/22.87 (injFuncSetFuncIn) =>
% 132.32/22.87 ((
% 132.32/22.87 (injFuncSetFuncInj) =>
% 132.32/22.87 ((
% 132.32/22.87 (surjFuncSetFuncIn) =>
% 132.32/22.87 ((
% 132.32/22.87 (surjFuncSetFuncSurj) =>
% 132.32/22.87 ((
% 132.32/22.87 (leftInvIsSurj) =>
% 132.32/22.87 ((
% 132.32/22.87 (surjCantorThm) =>
% 132.32/22.87 ((
% 132.32/22.87 (foundation2) =>
% 132.32/22.87 ((
% 132.32/22.87 (notinself) =>
% 132.32/22.87 ((
% 132.32/22.87 (notinself2) =>
% 132.32/22.87 ((
% 132.32/22.87 (omegaSp) =>
% 132.32/22.87 ((
% 132.32/22.87 (omegaSclos) =>
% 132.32/22.87 ((
% 132.32/22.87 (peano0notS) =>
% 132.32/22.87 ((
% 132.32/22.87 (peanoSinj) =>
% 132.32/22.87 ((
% 132.32/22.87 (transitivesetOp1) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintTransitive) =>
% 132.32/22.87 ((
% 132.32/22.87 (transitivesetOp2) =>
% 132.32/22.87 ((
% 132.32/22.87 (setunionTransitive) =>
% 132.32/22.87 ((
% 132.32/22.87 (ordinalMinLem1) =>
% 132.32/22.87 ((
% 132.32/22.87 (ordinalTransSet) =>
% 132.32/22.87 ((
% 132.32/22.87 (ordinalTransSet1) =>
% 132.32/22.87 ((
% 132.32/22.87 (setunionOrdinalLem1) =>
% 132.32/22.87 (ordinal @
% 132.32/22.87 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.32/22.87 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl560])).
% 132.32/22.87 thf(zip_derived_cl578, plain,
% 132.32/22.87 (~ (((in__Cong) =>
% 132.32/22.87 (((exuE3u) =>
% 132.32/22.87 (((exu__Cong) =>
% 132.32/22.87 (((setadjoin__Cong) =>
% 132.32/22.87 (((powerset__Cong) =>
% 132.32/22.87 (((setunion__Cong) =>
% 132.32/22.87 (((exuEu) =>
% 132.32/22.87 (((descr__Cong) =>
% 132.32/22.87 (((dsetconstr__Cong) =>
% 132.32/22.87 (((subsetI1) =>
% 132.32/22.87 (((eqimpsubset2) =>
% 132.32/22.87 (((eqimpsubset1) =>
% 132.32/22.87 (((subsetI2) =>
% 132.32/22.87 (((emptysetsubset) =>
% 132.32/22.87 (((subsetE) =>
% 132.32/22.87 (((subsetE2) =>
% 132.32/22.87 (((notsubsetI) =>
% 132.32/22.87 (((notequalI1) =>
% 132.32/22.87 (((notequalI2) =>
% 132.32/22.87 (((subsetRefl) =>
% 132.32/22.87 (((subsetTrans) =>
% 132.32/22.87 (((setadjoinSub) =>
% 132.32/22.87 (((setadjoinSub2) =>
% 132.32/22.87 (((subset2powerset) =>
% 132.32/22.87 (((setextsub) =>
% 132.32/22.87 (((subsetemptysetimpeq) =>
% 132.32/22.87 (((powersetI1) =>
% 132.32/22.87 (((powersetE1) =>
% 132.32/22.87 (((inPowerset) =>
% 132.32/22.87 (((powersetsubset) =>
% 132.32/22.87 ((
% 132.32/22.87 (sepInPowerset) =>
% 132.32/22.87 ((
% 132.32/22.87 (sepSubset) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionIL) =>
% 132.32/22.87 ((
% 132.32/22.87 (upairset2IR) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionIR) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionEcases) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionE) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionLsub) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionRsub) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectI) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectSubset5) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectEL) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectLsub) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectSubset2) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectSubset3) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectER) =>
% 132.32/22.87 ((
% 132.32/22.87 (disjointsetsI1) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectRsub) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectSubset4) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectSubset1) =>
% 132.32/22.87 ((
% 132.32/22.87 (bs114d) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusI) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusEL) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusER) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusSubset2) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusERneg) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusELneg) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusILneg) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusIRneg) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusLsub) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusSubset1) =>
% 132.32/22.87 ((
% 132.32/22.87 (symdiffE) =>
% 132.32/22.87 ((
% 132.32/22.87 (symdiffI1) =>
% 132.32/22.87 ((
% 132.32/22.87 (symdiffI2) =>
% 132.32/22.87 ((
% 132.32/22.87 (symdiffIneg1) =>
% 132.32/22.87 ((
% 132.32/22.87 (symdiffIneg2) =>
% 132.32/22.87 ((
% 132.32/22.87 (secondinupair) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairIL) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairIR) =>
% 132.32/22.87 ((
% 132.32/22.87 (kpairiskpair) =>
% 132.32/22.87 ((
% 132.32/22.87 (kpairp) =>
% 132.32/22.87 ((
% 132.32/22.87 (singletonsubset) =>
% 132.32/22.87 ((
% 132.32/22.87 (singletoninpowerset) =>
% 132.32/22.87 ((
% 132.32/22.87 (singletoninpowunion) =>
% 132.32/22.87 ((
% 132.32/22.87 (upairset2E) =>
% 132.32/22.87 ((
% 132.32/22.87 (upairsubunion) =>
% 132.32/22.87 ((
% 132.32/22.87 (upairinpowunion) =>
% 132.32/22.87 ((
% 132.32/22.87 (ubforcartprodlem1) =>
% 132.32/22.87 ((
% 132.32/22.87 (ubforcartprodlem2) =>
% 132.32/22.87 ((
% 132.32/22.87 (ubforcartprodlem3) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodpairin) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodmempair1) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodmempair) =>
% 132.32/22.87 ((
% 132.32/22.87 (setunionE2) =>
% 132.32/22.87 ((
% 132.32/22.87 (setunionsingleton1) =>
% 132.32/22.87 ((
% 132.32/22.87 (setunionsingleton2) =>
% 132.32/22.87 ((
% 132.32/22.87 (setunionsingleton) =>
% 132.32/22.87 ((
% 132.32/22.87 (singletonprop) =>
% 132.32/22.87 ((
% 132.32/22.87 (ex1E1) =>
% 132.32/22.87 ((
% 132.32/22.87 (ex1I) =>
% 132.32/22.87 ((
% 132.32/22.87 (ex1I2) =>
% 132.32/22.87 ((
% 132.32/22.87 (singletonsuniq) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairinjL1) =>
% 132.32/22.87 ((
% 132.32/22.87 (kfstsingleton) =>
% 132.32/22.87 ((
% 132.32/22.87 (theprop) =>
% 132.32/22.87 ((
% 132.32/22.87 (kfstpairEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodfstin) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairinjL2) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairinjL) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairinjR11) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairinjR12) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairinjR1) =>
% 132.32/22.87 ((
% 132.32/22.87 (upairequniteq) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairinjR2) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairinjR) =>
% 132.32/22.87 ((
% 132.32/22.87 (ksndsingleton) =>
% 132.32/22.87 ((
% 132.32/22.87 (ksndpairEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (kpairsurjEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodsndin) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodpairmemEL) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodpairmemER) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodmempaircEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodfstpairEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodsndpairEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodpairsurjEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (dpsetconstrI) =>
% 132.32/22.87 ((
% 132.32/22.87 (dpsetconstrSub) =>
% 132.32/22.87 ((
% 132.32/22.87 (setOfPairsIsBReln) =>
% 132.32/22.87 ((
% 132.32/22.87 (dpsetconstrERa) =>
% 132.32/22.87 ((
% 132.32/22.87 (dpsetconstrEL1) =>
% 132.32/22.87 ((
% 132.32/22.87 (dpsetconstrEL2) =>
% 132.32/22.87 ((
% 132.32/22.87 (dpsetconstrER) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcImageSingleton) =>
% 132.32/22.87 ((
% 132.32/22.87 (apProp) =>
% 132.32/22.87 ((
% 132.32/22.87 (app) =>
% 132.32/22.87 ((
% 132.32/22.87 (infuncsetfunc) =>
% 132.32/22.87 ((
% 132.32/22.87 (ap2p) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcinfuncset) =>
% 132.32/22.87 ((
% 132.32/22.87 (lamProp) =>
% 132.32/22.87 ((
% 132.32/22.87 (lamp) =>
% 132.32/22.87 ((
% 132.32/22.87 (lam2p) =>
% 132.32/22.87 ((
% 132.32/22.87 (brelnall1) =>
% 132.32/22.87 ((
% 132.32/22.87 (brelnall2) =>
% 132.32/22.87 ((
% 132.32/22.87 (ex1E2) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcGraphProp1) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcGraphProp3) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcGraphProp2) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcextLem) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcGraphProp4) =>
% 132.32/22.87 ((
% 132.32/22.87 (subbreln) =>
% 132.32/22.87 ((
% 132.32/22.87 (eqbreln) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcext) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcext2) =>
% 132.32/22.87 ((
% 132.32/22.87 (ap2apEq1) =>
% 132.32/22.87 ((
% 132.32/22.87 (ap2apEq2) =>
% 132.32/22.87 ((
% 132.32/22.87 (beta1) =>
% 132.32/22.87 ((
% 132.32/22.87 (eta1) =>
% 132.32/22.87 ((
% 132.32/22.87 (lam2lamEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (beta2) =>
% 132.32/22.87 ((
% 132.32/22.87 (eta2) =>
% 132.32/22.87 ((
% 132.32/22.87 (iffalseProp1) =>
% 132.32/22.87 ((
% 132.32/22.87 (iffalseProp2) =>
% 132.32/22.87 ((
% 132.32/22.87 (iftrueProp1) =>
% 132.32/22.87 ((
% 132.32/22.87 (iftrueProp2) =>
% 132.32/22.87 ((
% 132.32/22.87 (ifSingleton) =>
% 132.32/22.87 ((
% 132.32/22.87 (ifp) =>
% 132.32/22.87 ((
% 132.32/22.87 (theeq) =>
% 132.32/22.87 ((
% 132.32/22.87 (iftrue) =>
% 132.32/22.87 ((
% 132.32/22.87 (iffalse) =>
% 132.32/22.87 ((
% 132.32/22.87 (iftrueorfalse) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectT_lem) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionT_lem) =>
% 132.32/22.87 ((
% 132.32/22.87 (powersetT_lem) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusT_lem) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementT_lem) =>
% 132.32/22.87 ((
% 132.32/22.87 (setextT) =>
% 132.32/22.87 ((
% 132.32/22.87 (subsetTI) =>
% 132.32/22.87 ((
% 132.32/22.87 (powersetTI1) =>
% 132.32/22.87 ((
% 132.32/22.87 (powersetTE1) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementTI1) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementTE1) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectTELcontra) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectTERcontra) =>
% 132.32/22.87 ((
% 132.32/22.87 (contrasubsetT) =>
% 132.32/22.87 ((
% 132.32/22.87 (contrasubsetT1) =>
% 132.32/22.87 ((
% 132.32/22.87 (contrasubsetT2) =>
% 132.32/22.87 ((
% 132.32/22.87 (contrasubsetT3) =>
% 132.32/22.87 ((
% 132.32/22.87 (doubleComplementI1) =>
% 132.32/22.87 ((
% 132.32/22.87 (doubleComplementE1) =>
% 132.32/22.87 ((
% 132.32/22.87 (doubleComplementSub1) =>
% 132.32/22.87 ((
% 132.32/22.87 (doubleComplementSub2) =>
% 132.32/22.87 ((
% 132.32/22.87 (doubleComplementEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementTnotintersectT) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementImpComplementIntersect) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementSubsetComplementIntersect) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementInPowersetComplementIntersect) =>
% 132.32/22.87 ((
% 132.32/22.87 (contraSubsetComplement) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementTcontraSubset) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionTILcontra) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionTIRcontra) =>
% 132.32/22.87 ((
% 132.32/22.87 (inIntersectImpInUnion) =>
% 132.32/22.87 ((
% 132.32/22.87 (inIntersectImpInUnion2) =>
% 132.32/22.87 ((
% 132.32/22.87 (inIntersectImpInIntersectUnions) =>
% 132.32/22.87 ((
% 132.32/22.87 (intersectInPowersetIntersectUnions) =>
% 132.32/22.87 ((
% 132.32/22.87 (inComplementUnionImpNotIn1) =>
% 132.32/22.87 ((
% 132.32/22.87 (inComplementUnionImpInComplement1) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionTE) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionTEcontra) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan2a1) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementUnionInPowersetComplement) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan2a2) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan1a) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan1b) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan1) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan2a) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan2b2) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan2b) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan2) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz13rule0) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz13rule1) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz13rule2) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz13rule3) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz13rule4) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz1_1) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz1_2) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz1_3) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz1_4) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz1_5) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1all2) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1SetBreln1) =>
% 132.32/22.87 ((
% 132.32/22.87 (choice2fnsingleton) =>
% 132.32/22.87 ((
% 132.32/22.87 (setOfPairsIsBReln1) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1all1) =>
% 132.32/22.87 ((
% 132.32/22.87 (subbreln1) =>
% 132.32/22.87 ((
% 132.32/22.87 (eqbreln1) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1invprop) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1invI) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1invE) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1compprop) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1compI) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1compE) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1compEex) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1unionprop) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1unionIL) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1unionIR) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1unionI) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1unionE) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1unionEcases) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1unionCommutes) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz2Ex) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz2W) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz2A) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz2B) =>
% 132.32/22.87 ((
% 132.32/22.87 (image1Ex) =>
% 132.32/22.87 ((
% 132.32/22.87 (image1Ex1) =>
% 132.32/22.87 ((
% 132.32/22.87 (image1Equiv) =>
% 132.32/22.87 ((
% 132.32/22.87 (image1E) =>
% 132.32/22.87 ((
% 132.32/22.87 (image1I) =>
% 132.32/22.87 ((
% 132.32/22.87 (injFuncInInjFuncSet) =>
% 132.32/22.87 ((
% 132.32/22.87 (injFuncSetFuncIn) =>
% 132.32/22.87 ((
% 132.32/22.87 (injFuncSetFuncInj) =>
% 132.32/22.87 ((
% 132.32/22.87 (surjFuncSetFuncIn) =>
% 132.32/22.87 ((
% 132.32/22.87 (surjFuncSetFuncSurj) =>
% 132.32/22.87 ((
% 132.32/22.87 (leftInvIsSurj) =>
% 132.32/22.87 ((
% 132.32/22.87 (surjCantorThm) =>
% 132.32/22.87 ((
% 132.32/22.87 (foundation2) =>
% 132.32/22.87 ((
% 132.32/22.87 (notinself) =>
% 132.32/22.87 ((
% 132.32/22.87 (notinself2) =>
% 132.32/22.87 ((
% 132.32/22.87 (omegaSp) =>
% 132.32/22.87 ((
% 132.32/22.87 (omegaSclos) =>
% 132.32/22.87 ((
% 132.32/22.87 (peano0notS) =>
% 132.32/22.87 ((
% 132.32/22.87 (peanoSinj) =>
% 132.32/22.87 ((
% 132.32/22.87 (transitivesetOp1) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintTransitive) =>
% 132.32/22.87 ((
% 132.32/22.87 (transitivesetOp2) =>
% 132.32/22.87 ((
% 132.32/22.87 (setunionTransitive) =>
% 132.32/22.87 ((
% 132.32/22.87 (ordinalMinLem1) =>
% 132.32/22.87 ((
% 132.32/22.87 (ordinalTransSet) =>
% 132.32/22.87 ((
% 132.32/22.87 (ordinalTransSet1) =>
% 132.32/22.87 ((
% 132.32/22.87 (setunionOrdinalLem1) =>
% 132.32/22.87 (ordinal @
% 132.32/22.87 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.32/22.87 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl568])).
% 132.32/22.87 thf(zip_derived_cl588, plain,
% 132.32/22.87 (~ (((exuE3u) =>
% 132.32/22.87 (((exu__Cong) =>
% 132.32/22.87 (((setadjoin__Cong) =>
% 132.32/22.87 (((powerset__Cong) =>
% 132.32/22.87 (((setunion__Cong) =>
% 132.32/22.87 (((exuEu) =>
% 132.32/22.87 (((descr__Cong) =>
% 132.32/22.87 (((dsetconstr__Cong) =>
% 132.32/22.87 (((subsetI1) =>
% 132.32/22.87 (((eqimpsubset2) =>
% 132.32/22.87 (((eqimpsubset1) =>
% 132.32/22.87 (((subsetI2) =>
% 132.32/22.87 (((emptysetsubset) =>
% 132.32/22.87 (((subsetE) =>
% 132.32/22.87 (((subsetE2) =>
% 132.32/22.87 (((notsubsetI) =>
% 132.32/22.87 (((notequalI1) =>
% 132.32/22.87 (((notequalI2) =>
% 132.32/22.87 (((subsetRefl) =>
% 132.32/22.87 (((subsetTrans) =>
% 132.32/22.87 (((setadjoinSub) =>
% 132.32/22.87 (((setadjoinSub2) =>
% 132.32/22.87 (((subset2powerset) =>
% 132.32/22.87 (((setextsub) =>
% 132.32/22.87 (((subsetemptysetimpeq) =>
% 132.32/22.87 (((powersetI1) =>
% 132.32/22.87 (((powersetE1) =>
% 132.32/22.87 (((inPowerset) =>
% 132.32/22.87 (((powersetsubset) =>
% 132.32/22.87 (((sepInPowerset) =>
% 132.32/22.87 ((
% 132.32/22.87 (sepSubset) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionIL) =>
% 132.32/22.87 ((
% 132.32/22.87 (upairset2IR) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionIR) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionEcases) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionE) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionLsub) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionRsub) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectI) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectSubset5) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectEL) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectLsub) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectSubset2) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectSubset3) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectER) =>
% 132.32/22.87 ((
% 132.32/22.87 (disjointsetsI1) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectRsub) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectSubset4) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectSubset1) =>
% 132.32/22.87 ((
% 132.32/22.87 (bs114d) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusI) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusEL) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusER) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusSubset2) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusERneg) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusELneg) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusILneg) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusIRneg) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusLsub) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusSubset1) =>
% 132.32/22.87 ((
% 132.32/22.87 (symdiffE) =>
% 132.32/22.87 ((
% 132.32/22.87 (symdiffI1) =>
% 132.32/22.87 ((
% 132.32/22.87 (symdiffI2) =>
% 132.32/22.87 ((
% 132.32/22.87 (symdiffIneg1) =>
% 132.32/22.87 ((
% 132.32/22.87 (symdiffIneg2) =>
% 132.32/22.87 ((
% 132.32/22.87 (secondinupair) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairIL) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairIR) =>
% 132.32/22.87 ((
% 132.32/22.87 (kpairiskpair) =>
% 132.32/22.87 ((
% 132.32/22.87 (kpairp) =>
% 132.32/22.87 ((
% 132.32/22.87 (singletonsubset) =>
% 132.32/22.87 ((
% 132.32/22.87 (singletoninpowerset) =>
% 132.32/22.87 ((
% 132.32/22.87 (singletoninpowunion) =>
% 132.32/22.87 ((
% 132.32/22.87 (upairset2E) =>
% 132.32/22.87 ((
% 132.32/22.87 (upairsubunion) =>
% 132.32/22.87 ((
% 132.32/22.87 (upairinpowunion) =>
% 132.32/22.87 ((
% 132.32/22.87 (ubforcartprodlem1) =>
% 132.32/22.87 ((
% 132.32/22.87 (ubforcartprodlem2) =>
% 132.32/22.87 ((
% 132.32/22.87 (ubforcartprodlem3) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodpairin) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodmempair1) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodmempair) =>
% 132.32/22.87 ((
% 132.32/22.87 (setunionE2) =>
% 132.32/22.87 ((
% 132.32/22.87 (setunionsingleton1) =>
% 132.32/22.87 ((
% 132.32/22.87 (setunionsingleton2) =>
% 132.32/22.87 ((
% 132.32/22.87 (setunionsingleton) =>
% 132.32/22.87 ((
% 132.32/22.87 (singletonprop) =>
% 132.32/22.87 ((
% 132.32/22.87 (ex1E1) =>
% 132.32/22.87 ((
% 132.32/22.87 (ex1I) =>
% 132.32/22.87 ((
% 132.32/22.87 (ex1I2) =>
% 132.32/22.87 ((
% 132.32/22.87 (singletonsuniq) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairinjL1) =>
% 132.32/22.87 ((
% 132.32/22.87 (kfstsingleton) =>
% 132.32/22.87 ((
% 132.32/22.87 (theprop) =>
% 132.32/22.87 ((
% 132.32/22.87 (kfstpairEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodfstin) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairinjL2) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairinjL) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairinjR11) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairinjR12) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairinjR1) =>
% 132.32/22.87 ((
% 132.32/22.87 (upairequniteq) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairinjR2) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairinjR) =>
% 132.32/22.87 ((
% 132.32/22.87 (ksndsingleton) =>
% 132.32/22.87 ((
% 132.32/22.87 (ksndpairEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (kpairsurjEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodsndin) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodpairmemEL) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodpairmemER) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodmempaircEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodfstpairEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodsndpairEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodpairsurjEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (dpsetconstrI) =>
% 132.32/22.87 ((
% 132.32/22.87 (dpsetconstrSub) =>
% 132.32/22.87 ((
% 132.32/22.87 (setOfPairsIsBReln) =>
% 132.32/22.87 ((
% 132.32/22.87 (dpsetconstrERa) =>
% 132.32/22.87 ((
% 132.32/22.87 (dpsetconstrEL1) =>
% 132.32/22.87 ((
% 132.32/22.87 (dpsetconstrEL2) =>
% 132.32/22.87 ((
% 132.32/22.87 (dpsetconstrER) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcImageSingleton) =>
% 132.32/22.87 ((
% 132.32/22.87 (apProp) =>
% 132.32/22.87 ((
% 132.32/22.87 (app) =>
% 132.32/22.87 ((
% 132.32/22.87 (infuncsetfunc) =>
% 132.32/22.87 ((
% 132.32/22.87 (ap2p) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcinfuncset) =>
% 132.32/22.87 ((
% 132.32/22.87 (lamProp) =>
% 132.32/22.87 ((
% 132.32/22.87 (lamp) =>
% 132.32/22.87 ((
% 132.32/22.87 (lam2p) =>
% 132.32/22.87 ((
% 132.32/22.87 (brelnall1) =>
% 132.32/22.87 ((
% 132.32/22.87 (brelnall2) =>
% 132.32/22.87 ((
% 132.32/22.87 (ex1E2) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcGraphProp1) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcGraphProp3) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcGraphProp2) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcextLem) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcGraphProp4) =>
% 132.32/22.87 ((
% 132.32/22.87 (subbreln) =>
% 132.32/22.87 ((
% 132.32/22.87 (eqbreln) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcext) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcext2) =>
% 132.32/22.87 ((
% 132.32/22.87 (ap2apEq1) =>
% 132.32/22.87 ((
% 132.32/22.87 (ap2apEq2) =>
% 132.32/22.87 ((
% 132.32/22.87 (beta1) =>
% 132.32/22.87 ((
% 132.32/22.87 (eta1) =>
% 132.32/22.87 ((
% 132.32/22.87 (lam2lamEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (beta2) =>
% 132.32/22.87 ((
% 132.32/22.87 (eta2) =>
% 132.32/22.87 ((
% 132.32/22.87 (iffalseProp1) =>
% 132.32/22.87 ((
% 132.32/22.87 (iffalseProp2) =>
% 132.32/22.87 ((
% 132.32/22.87 (iftrueProp1) =>
% 132.32/22.87 ((
% 132.32/22.87 (iftrueProp2) =>
% 132.32/22.87 ((
% 132.32/22.87 (ifSingleton) =>
% 132.32/22.87 ((
% 132.32/22.87 (ifp) =>
% 132.32/22.87 ((
% 132.32/22.87 (theeq) =>
% 132.32/22.87 ((
% 132.32/22.87 (iftrue) =>
% 132.32/22.87 ((
% 132.32/22.87 (iffalse) =>
% 132.32/22.87 ((
% 132.32/22.87 (iftrueorfalse) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectT_lem) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionT_lem) =>
% 132.32/22.87 ((
% 132.32/22.87 (powersetT_lem) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusT_lem) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementT_lem) =>
% 132.32/22.87 ((
% 132.32/22.87 (setextT) =>
% 132.32/22.87 ((
% 132.32/22.87 (subsetTI) =>
% 132.32/22.87 ((
% 132.32/22.87 (powersetTI1) =>
% 132.32/22.87 ((
% 132.32/22.87 (powersetTE1) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementTI1) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementTE1) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectTELcontra) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectTERcontra) =>
% 132.32/22.87 ((
% 132.32/22.87 (contrasubsetT) =>
% 132.32/22.87 ((
% 132.32/22.87 (contrasubsetT1) =>
% 132.32/22.87 ((
% 132.32/22.87 (contrasubsetT2) =>
% 132.32/22.87 ((
% 132.32/22.87 (contrasubsetT3) =>
% 132.32/22.87 ((
% 132.32/22.87 (doubleComplementI1) =>
% 132.32/22.87 ((
% 132.32/22.87 (doubleComplementE1) =>
% 132.32/22.87 ((
% 132.32/22.87 (doubleComplementSub1) =>
% 132.32/22.87 ((
% 132.32/22.87 (doubleComplementSub2) =>
% 132.32/22.87 ((
% 132.32/22.87 (doubleComplementEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementTnotintersectT) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementImpComplementIntersect) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementSubsetComplementIntersect) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementInPowersetComplementIntersect) =>
% 132.32/22.87 ((
% 132.32/22.87 (contraSubsetComplement) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementTcontraSubset) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionTILcontra) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionTIRcontra) =>
% 132.32/22.87 ((
% 132.32/22.87 (inIntersectImpInUnion) =>
% 132.32/22.87 ((
% 132.32/22.87 (inIntersectImpInUnion2) =>
% 132.32/22.87 ((
% 132.32/22.87 (inIntersectImpInIntersectUnions) =>
% 132.32/22.87 ((
% 132.32/22.87 (intersectInPowersetIntersectUnions) =>
% 132.32/22.87 ((
% 132.32/22.87 (inComplementUnionImpNotIn1) =>
% 132.32/22.87 ((
% 132.32/22.87 (inComplementUnionImpInComplement1) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionTE) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionTEcontra) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan2a1) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementUnionInPowersetComplement) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan2a2) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan1a) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan1b) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan1) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan2a) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan2b2) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan2b) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan2) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz13rule0) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz13rule1) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz13rule2) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz13rule3) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz13rule4) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz1_1) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz1_2) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz1_3) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz1_4) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz1_5) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1all2) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1SetBreln1) =>
% 132.32/22.87 ((
% 132.32/22.87 (choice2fnsingleton) =>
% 132.32/22.87 ((
% 132.32/22.87 (setOfPairsIsBReln1) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1all1) =>
% 132.32/22.87 ((
% 132.32/22.87 (subbreln1) =>
% 132.32/22.87 ((
% 132.32/22.87 (eqbreln1) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1invprop) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1invI) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1invE) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1compprop) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1compI) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1compE) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1compEex) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1unionprop) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1unionIL) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1unionIR) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1unionI) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1unionE) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1unionEcases) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1unionCommutes) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz2Ex) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz2W) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz2A) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz2B) =>
% 132.32/22.87 ((
% 132.32/22.87 (image1Ex) =>
% 132.32/22.87 ((
% 132.32/22.87 (image1Ex1) =>
% 132.32/22.87 ((
% 132.32/22.87 (image1Equiv) =>
% 132.32/22.87 ((
% 132.32/22.87 (image1E) =>
% 132.32/22.87 ((
% 132.32/22.87 (image1I) =>
% 132.32/22.87 ((
% 132.32/22.87 (injFuncInInjFuncSet) =>
% 132.32/22.87 ((
% 132.32/22.87 (injFuncSetFuncIn) =>
% 132.32/22.87 ((
% 132.32/22.87 (injFuncSetFuncInj) =>
% 132.32/22.87 ((
% 132.32/22.87 (surjFuncSetFuncIn) =>
% 132.32/22.87 ((
% 132.32/22.87 (surjFuncSetFuncSurj) =>
% 132.32/22.87 ((
% 132.32/22.87 (leftInvIsSurj) =>
% 132.32/22.87 ((
% 132.32/22.87 (surjCantorThm) =>
% 132.32/22.87 ((
% 132.32/22.87 (foundation2) =>
% 132.32/22.87 ((
% 132.32/22.87 (notinself) =>
% 132.32/22.87 ((
% 132.32/22.87 (notinself2) =>
% 132.32/22.87 ((
% 132.32/22.87 (omegaSp) =>
% 132.32/22.87 ((
% 132.32/22.87 (omegaSclos) =>
% 132.32/22.87 ((
% 132.32/22.87 (peano0notS) =>
% 132.32/22.87 ((
% 132.32/22.87 (peanoSinj) =>
% 132.32/22.87 ((
% 132.32/22.87 (transitivesetOp1) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintTransitive) =>
% 132.32/22.87 ((
% 132.32/22.87 (transitivesetOp2) =>
% 132.32/22.87 ((
% 132.32/22.87 (setunionTransitive) =>
% 132.32/22.87 ((
% 132.32/22.87 (ordinalMinLem1) =>
% 132.32/22.87 ((
% 132.32/22.87 (ordinalTransSet) =>
% 132.32/22.87 ((
% 132.32/22.87 (ordinalTransSet1) =>
% 132.32/22.87 ((
% 132.32/22.87 (setunionOrdinalLem1) =>
% 132.32/22.87 (ordinal @
% 132.32/22.87 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.32/22.87 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl578])).
% 132.32/22.87 thf(zip_derived_cl598, plain,
% 132.32/22.87 (~ (((exu__Cong) =>
% 132.32/22.87 (((setadjoin__Cong) =>
% 132.32/22.87 (((powerset__Cong) =>
% 132.32/22.87 (((setunion__Cong) =>
% 132.32/22.87 (((exuEu) =>
% 132.32/22.87 (((descr__Cong) =>
% 132.32/22.87 (((dsetconstr__Cong) =>
% 132.32/22.87 (((subsetI1) =>
% 132.32/22.87 (((eqimpsubset2) =>
% 132.32/22.87 (((eqimpsubset1) =>
% 132.32/22.87 (((subsetI2) =>
% 132.32/22.87 (((emptysetsubset) =>
% 132.32/22.87 (((subsetE) =>
% 132.32/22.87 (((subsetE2) =>
% 132.32/22.87 (((notsubsetI) =>
% 132.32/22.87 (((notequalI1) =>
% 132.32/22.87 (((notequalI2) =>
% 132.32/22.87 (((subsetRefl) =>
% 132.32/22.87 (((subsetTrans) =>
% 132.32/22.87 (((setadjoinSub) =>
% 132.32/22.87 (((setadjoinSub2) =>
% 132.32/22.87 (((subset2powerset) =>
% 132.32/22.87 (((setextsub) =>
% 132.32/22.87 (((subsetemptysetimpeq) =>
% 132.32/22.87 (((powersetI1) =>
% 132.32/22.87 (((powersetE1) =>
% 132.32/22.87 (((inPowerset) =>
% 132.32/22.87 (((powersetsubset) =>
% 132.32/22.87 (((sepInPowerset) =>
% 132.32/22.87 (((sepSubset) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionIL) =>
% 132.32/22.87 ((
% 132.32/22.87 (upairset2IR) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionIR) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionEcases) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionE) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionLsub) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionRsub) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectI) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectSubset5) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectEL) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectLsub) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectSubset2) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectSubset3) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectER) =>
% 132.32/22.87 ((
% 132.32/22.87 (disjointsetsI1) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectRsub) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectSubset4) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectSubset1) =>
% 132.32/22.87 ((
% 132.32/22.87 (bs114d) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusI) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusEL) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusER) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusSubset2) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusERneg) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusELneg) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusILneg) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusIRneg) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusLsub) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusSubset1) =>
% 132.32/22.87 ((
% 132.32/22.87 (symdiffE) =>
% 132.32/22.87 ((
% 132.32/22.87 (symdiffI1) =>
% 132.32/22.87 ((
% 132.32/22.87 (symdiffI2) =>
% 132.32/22.87 ((
% 132.32/22.87 (symdiffIneg1) =>
% 132.32/22.87 ((
% 132.32/22.87 (symdiffIneg2) =>
% 132.32/22.87 ((
% 132.32/22.87 (secondinupair) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairIL) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairIR) =>
% 132.32/22.87 ((
% 132.32/22.87 (kpairiskpair) =>
% 132.32/22.87 ((
% 132.32/22.87 (kpairp) =>
% 132.32/22.87 ((
% 132.32/22.87 (singletonsubset) =>
% 132.32/22.87 ((
% 132.32/22.87 (singletoninpowerset) =>
% 132.32/22.87 ((
% 132.32/22.87 (singletoninpowunion) =>
% 132.32/22.87 ((
% 132.32/22.87 (upairset2E) =>
% 132.32/22.87 ((
% 132.32/22.87 (upairsubunion) =>
% 132.32/22.87 ((
% 132.32/22.87 (upairinpowunion) =>
% 132.32/22.87 ((
% 132.32/22.87 (ubforcartprodlem1) =>
% 132.32/22.87 ((
% 132.32/22.87 (ubforcartprodlem2) =>
% 132.32/22.87 ((
% 132.32/22.87 (ubforcartprodlem3) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodpairin) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodmempair1) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodmempair) =>
% 132.32/22.87 ((
% 132.32/22.87 (setunionE2) =>
% 132.32/22.87 ((
% 132.32/22.87 (setunionsingleton1) =>
% 132.32/22.87 ((
% 132.32/22.87 (setunionsingleton2) =>
% 132.32/22.87 ((
% 132.32/22.87 (setunionsingleton) =>
% 132.32/22.87 ((
% 132.32/22.87 (singletonprop) =>
% 132.32/22.87 ((
% 132.32/22.87 (ex1E1) =>
% 132.32/22.87 ((
% 132.32/22.87 (ex1I) =>
% 132.32/22.87 ((
% 132.32/22.87 (ex1I2) =>
% 132.32/22.87 ((
% 132.32/22.87 (singletonsuniq) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairinjL1) =>
% 132.32/22.87 ((
% 132.32/22.87 (kfstsingleton) =>
% 132.32/22.87 ((
% 132.32/22.87 (theprop) =>
% 132.32/22.87 ((
% 132.32/22.87 (kfstpairEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodfstin) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairinjL2) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairinjL) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairinjR11) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairinjR12) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairinjR1) =>
% 132.32/22.87 ((
% 132.32/22.87 (upairequniteq) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairinjR2) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairinjR) =>
% 132.32/22.87 ((
% 132.32/22.87 (ksndsingleton) =>
% 132.32/22.87 ((
% 132.32/22.87 (ksndpairEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (kpairsurjEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodsndin) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodpairmemEL) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodpairmemER) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodmempaircEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodfstpairEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodsndpairEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodpairsurjEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (dpsetconstrI) =>
% 132.32/22.87 ((
% 132.32/22.87 (dpsetconstrSub) =>
% 132.32/22.87 ((
% 132.32/22.87 (setOfPairsIsBReln) =>
% 132.32/22.87 ((
% 132.32/22.87 (dpsetconstrERa) =>
% 132.32/22.87 ((
% 132.32/22.87 (dpsetconstrEL1) =>
% 132.32/22.87 ((
% 132.32/22.87 (dpsetconstrEL2) =>
% 132.32/22.87 ((
% 132.32/22.87 (dpsetconstrER) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcImageSingleton) =>
% 132.32/22.87 ((
% 132.32/22.87 (apProp) =>
% 132.32/22.87 ((
% 132.32/22.87 (app) =>
% 132.32/22.87 ((
% 132.32/22.87 (infuncsetfunc) =>
% 132.32/22.87 ((
% 132.32/22.87 (ap2p) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcinfuncset) =>
% 132.32/22.87 ((
% 132.32/22.87 (lamProp) =>
% 132.32/22.87 ((
% 132.32/22.87 (lamp) =>
% 132.32/22.87 ((
% 132.32/22.87 (lam2p) =>
% 132.32/22.87 ((
% 132.32/22.87 (brelnall1) =>
% 132.32/22.87 ((
% 132.32/22.87 (brelnall2) =>
% 132.32/22.87 ((
% 132.32/22.87 (ex1E2) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcGraphProp1) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcGraphProp3) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcGraphProp2) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcextLem) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcGraphProp4) =>
% 132.32/22.87 ((
% 132.32/22.87 (subbreln) =>
% 132.32/22.87 ((
% 132.32/22.87 (eqbreln) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcext) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcext2) =>
% 132.32/22.87 ((
% 132.32/22.87 (ap2apEq1) =>
% 132.32/22.87 ((
% 132.32/22.87 (ap2apEq2) =>
% 132.32/22.87 ((
% 132.32/22.87 (beta1) =>
% 132.32/22.87 ((
% 132.32/22.87 (eta1) =>
% 132.32/22.87 ((
% 132.32/22.87 (lam2lamEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (beta2) =>
% 132.32/22.87 ((
% 132.32/22.87 (eta2) =>
% 132.32/22.87 ((
% 132.32/22.87 (iffalseProp1) =>
% 132.32/22.87 ((
% 132.32/22.87 (iffalseProp2) =>
% 132.32/22.87 ((
% 132.32/22.87 (iftrueProp1) =>
% 132.32/22.87 ((
% 132.32/22.87 (iftrueProp2) =>
% 132.32/22.87 ((
% 132.32/22.87 (ifSingleton) =>
% 132.32/22.87 ((
% 132.32/22.87 (ifp) =>
% 132.32/22.87 ((
% 132.32/22.87 (theeq) =>
% 132.32/22.87 ((
% 132.32/22.87 (iftrue) =>
% 132.32/22.87 ((
% 132.32/22.87 (iffalse) =>
% 132.32/22.87 ((
% 132.32/22.87 (iftrueorfalse) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectT_lem) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionT_lem) =>
% 132.32/22.87 ((
% 132.32/22.87 (powersetT_lem) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusT_lem) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementT_lem) =>
% 132.32/22.87 ((
% 132.32/22.87 (setextT) =>
% 132.32/22.87 ((
% 132.32/22.87 (subsetTI) =>
% 132.32/22.87 ((
% 132.32/22.87 (powersetTI1) =>
% 132.32/22.87 ((
% 132.32/22.87 (powersetTE1) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementTI1) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementTE1) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectTELcontra) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectTERcontra) =>
% 132.32/22.87 ((
% 132.32/22.87 (contrasubsetT) =>
% 132.32/22.87 ((
% 132.32/22.87 (contrasubsetT1) =>
% 132.32/22.87 ((
% 132.32/22.87 (contrasubsetT2) =>
% 132.32/22.87 ((
% 132.32/22.87 (contrasubsetT3) =>
% 132.32/22.87 ((
% 132.32/22.87 (doubleComplementI1) =>
% 132.32/22.87 ((
% 132.32/22.87 (doubleComplementE1) =>
% 132.32/22.87 ((
% 132.32/22.87 (doubleComplementSub1) =>
% 132.32/22.87 ((
% 132.32/22.87 (doubleComplementSub2) =>
% 132.32/22.87 ((
% 132.32/22.87 (doubleComplementEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementTnotintersectT) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementImpComplementIntersect) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementSubsetComplementIntersect) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementInPowersetComplementIntersect) =>
% 132.32/22.87 ((
% 132.32/22.87 (contraSubsetComplement) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementTcontraSubset) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionTILcontra) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionTIRcontra) =>
% 132.32/22.87 ((
% 132.32/22.87 (inIntersectImpInUnion) =>
% 132.32/22.87 ((
% 132.32/22.87 (inIntersectImpInUnion2) =>
% 132.32/22.87 ((
% 132.32/22.87 (inIntersectImpInIntersectUnions) =>
% 132.32/22.87 ((
% 132.32/22.87 (intersectInPowersetIntersectUnions) =>
% 132.32/22.87 ((
% 132.32/22.87 (inComplementUnionImpNotIn1) =>
% 132.32/22.87 ((
% 132.32/22.87 (inComplementUnionImpInComplement1) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionTE) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionTEcontra) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan2a1) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementUnionInPowersetComplement) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan2a2) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan1a) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan1b) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan1) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan2a) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan2b2) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan2b) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan2) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz13rule0) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz13rule1) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz13rule2) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz13rule3) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz13rule4) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz1_1) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz1_2) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz1_3) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz1_4) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz1_5) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1all2) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1SetBreln1) =>
% 132.32/22.87 ((
% 132.32/22.87 (choice2fnsingleton) =>
% 132.32/22.87 ((
% 132.32/22.87 (setOfPairsIsBReln1) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1all1) =>
% 132.32/22.87 ((
% 132.32/22.87 (subbreln1) =>
% 132.32/22.87 ((
% 132.32/22.87 (eqbreln1) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1invprop) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1invI) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1invE) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1compprop) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1compI) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1compE) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1compEex) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1unionprop) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1unionIL) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1unionIR) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1unionI) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1unionE) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1unionEcases) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1unionCommutes) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz2Ex) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz2W) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz2A) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz2B) =>
% 132.32/22.87 ((
% 132.32/22.87 (image1Ex) =>
% 132.32/22.87 ((
% 132.32/22.87 (image1Ex1) =>
% 132.32/22.87 ((
% 132.32/22.87 (image1Equiv) =>
% 132.32/22.87 ((
% 132.32/22.87 (image1E) =>
% 132.32/22.87 ((
% 132.32/22.87 (image1I) =>
% 132.32/22.87 ((
% 132.32/22.87 (injFuncInInjFuncSet) =>
% 132.32/22.87 ((
% 132.32/22.87 (injFuncSetFuncIn) =>
% 132.32/22.87 ((
% 132.32/22.87 (injFuncSetFuncInj) =>
% 132.32/22.87 ((
% 132.32/22.87 (surjFuncSetFuncIn) =>
% 132.32/22.87 ((
% 132.32/22.87 (surjFuncSetFuncSurj) =>
% 132.32/22.87 ((
% 132.32/22.87 (leftInvIsSurj) =>
% 132.32/22.87 ((
% 132.32/22.87 (surjCantorThm) =>
% 132.32/22.87 ((
% 132.32/22.87 (foundation2) =>
% 132.32/22.87 ((
% 132.32/22.87 (notinself) =>
% 132.32/22.87 ((
% 132.32/22.87 (notinself2) =>
% 132.32/22.87 ((
% 132.32/22.87 (omegaSp) =>
% 132.32/22.87 ((
% 132.32/22.87 (omegaSclos) =>
% 132.32/22.87 ((
% 132.32/22.87 (peano0notS) =>
% 132.32/22.87 ((
% 132.32/22.87 (peanoSinj) =>
% 132.32/22.87 ((
% 132.32/22.87 (transitivesetOp1) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintTransitive) =>
% 132.32/22.87 ((
% 132.32/22.87 (transitivesetOp2) =>
% 132.32/22.87 ((
% 132.32/22.87 (setunionTransitive) =>
% 132.32/22.87 ((
% 132.32/22.87 (ordinalMinLem1) =>
% 132.32/22.87 ((
% 132.32/22.87 (ordinalTransSet) =>
% 132.32/22.87 ((
% 132.32/22.87 (ordinalTransSet1) =>
% 132.32/22.87 ((
% 132.32/22.87 (setunionOrdinalLem1) =>
% 132.32/22.87 (ordinal @
% 132.32/22.87 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.32/22.87 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl588])).
% 132.32/22.87 thf(zip_derived_cl609, plain,
% 132.32/22.87 (~ (((setadjoin__Cong) =>
% 132.32/22.87 (((powerset__Cong) =>
% 132.32/22.87 (((setunion__Cong) =>
% 132.32/22.87 (((exuEu) =>
% 132.32/22.87 (((descr__Cong) =>
% 132.32/22.87 (((dsetconstr__Cong) =>
% 132.32/22.87 (((subsetI1) =>
% 132.32/22.87 (((eqimpsubset2) =>
% 132.32/22.87 (((eqimpsubset1) =>
% 132.32/22.87 (((subsetI2) =>
% 132.32/22.87 (((emptysetsubset) =>
% 132.32/22.87 (((subsetE) =>
% 132.32/22.87 (((subsetE2) =>
% 132.32/22.87 (((notsubsetI) =>
% 132.32/22.87 (((notequalI1) =>
% 132.32/22.87 (((notequalI2) =>
% 132.32/22.87 (((subsetRefl) =>
% 132.32/22.87 (((subsetTrans) =>
% 132.32/22.87 (((setadjoinSub) =>
% 132.32/22.87 (((setadjoinSub2) =>
% 132.32/22.87 (((subset2powerset) =>
% 132.32/22.87 (((setextsub) =>
% 132.32/22.87 (((subsetemptysetimpeq) =>
% 132.32/22.87 (((powersetI1) =>
% 132.32/22.87 (((powersetE1) =>
% 132.32/22.87 (((inPowerset) =>
% 132.32/22.87 (((powersetsubset) =>
% 132.32/22.87 (((sepInPowerset) =>
% 132.32/22.87 (((sepSubset) =>
% 132.32/22.87 (((binunionIL) =>
% 132.32/22.87 ((
% 132.32/22.87 (upairset2IR) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionIR) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionEcases) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionE) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionLsub) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionRsub) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectI) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectSubset5) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectEL) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectLsub) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectSubset2) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectSubset3) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectER) =>
% 132.32/22.87 ((
% 132.32/22.87 (disjointsetsI1) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectRsub) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectSubset4) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectSubset1) =>
% 132.32/22.87 ((
% 132.32/22.87 (bs114d) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusI) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusEL) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusER) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusSubset2) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusERneg) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusELneg) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusILneg) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusIRneg) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusLsub) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusSubset1) =>
% 132.32/22.87 ((
% 132.32/22.87 (symdiffE) =>
% 132.32/22.87 ((
% 132.32/22.87 (symdiffI1) =>
% 132.32/22.87 ((
% 132.32/22.87 (symdiffI2) =>
% 132.32/22.87 ((
% 132.32/22.87 (symdiffIneg1) =>
% 132.32/22.87 ((
% 132.32/22.87 (symdiffIneg2) =>
% 132.32/22.87 ((
% 132.32/22.87 (secondinupair) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairIL) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairIR) =>
% 132.32/22.87 ((
% 132.32/22.87 (kpairiskpair) =>
% 132.32/22.87 ((
% 132.32/22.87 (kpairp) =>
% 132.32/22.87 ((
% 132.32/22.87 (singletonsubset) =>
% 132.32/22.87 ((
% 132.32/22.87 (singletoninpowerset) =>
% 132.32/22.87 ((
% 132.32/22.87 (singletoninpowunion) =>
% 132.32/22.87 ((
% 132.32/22.87 (upairset2E) =>
% 132.32/22.87 ((
% 132.32/22.87 (upairsubunion) =>
% 132.32/22.87 ((
% 132.32/22.87 (upairinpowunion) =>
% 132.32/22.87 ((
% 132.32/22.87 (ubforcartprodlem1) =>
% 132.32/22.87 ((
% 132.32/22.87 (ubforcartprodlem2) =>
% 132.32/22.87 ((
% 132.32/22.87 (ubforcartprodlem3) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodpairin) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodmempair1) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodmempair) =>
% 132.32/22.87 ((
% 132.32/22.87 (setunionE2) =>
% 132.32/22.87 ((
% 132.32/22.87 (setunionsingleton1) =>
% 132.32/22.87 ((
% 132.32/22.87 (setunionsingleton2) =>
% 132.32/22.87 ((
% 132.32/22.87 (setunionsingleton) =>
% 132.32/22.87 ((
% 132.32/22.87 (singletonprop) =>
% 132.32/22.87 ((
% 132.32/22.87 (ex1E1) =>
% 132.32/22.87 ((
% 132.32/22.87 (ex1I) =>
% 132.32/22.87 ((
% 132.32/22.87 (ex1I2) =>
% 132.32/22.87 ((
% 132.32/22.87 (singletonsuniq) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairinjL1) =>
% 132.32/22.87 ((
% 132.32/22.87 (kfstsingleton) =>
% 132.32/22.87 ((
% 132.32/22.87 (theprop) =>
% 132.32/22.87 ((
% 132.32/22.87 (kfstpairEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodfstin) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairinjL2) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairinjL) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairinjR11) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairinjR12) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairinjR1) =>
% 132.32/22.87 ((
% 132.32/22.87 (upairequniteq) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairinjR2) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairinjR) =>
% 132.32/22.87 ((
% 132.32/22.87 (ksndsingleton) =>
% 132.32/22.87 ((
% 132.32/22.87 (ksndpairEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (kpairsurjEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodsndin) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodpairmemEL) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodpairmemER) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodmempaircEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodfstpairEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodsndpairEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodpairsurjEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (dpsetconstrI) =>
% 132.32/22.87 ((
% 132.32/22.87 (dpsetconstrSub) =>
% 132.32/22.87 ((
% 132.32/22.87 (setOfPairsIsBReln) =>
% 132.32/22.87 ((
% 132.32/22.87 (dpsetconstrERa) =>
% 132.32/22.87 ((
% 132.32/22.87 (dpsetconstrEL1) =>
% 132.32/22.87 ((
% 132.32/22.87 (dpsetconstrEL2) =>
% 132.32/22.87 ((
% 132.32/22.87 (dpsetconstrER) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcImageSingleton) =>
% 132.32/22.87 ((
% 132.32/22.87 (apProp) =>
% 132.32/22.87 ((
% 132.32/22.87 (app) =>
% 132.32/22.87 ((
% 132.32/22.87 (infuncsetfunc) =>
% 132.32/22.87 ((
% 132.32/22.87 (ap2p) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcinfuncset) =>
% 132.32/22.87 ((
% 132.32/22.87 (lamProp) =>
% 132.32/22.87 ((
% 132.32/22.87 (lamp) =>
% 132.32/22.87 ((
% 132.32/22.87 (lam2p) =>
% 132.32/22.87 ((
% 132.32/22.87 (brelnall1) =>
% 132.32/22.87 ((
% 132.32/22.87 (brelnall2) =>
% 132.32/22.87 ((
% 132.32/22.87 (ex1E2) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcGraphProp1) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcGraphProp3) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcGraphProp2) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcextLem) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcGraphProp4) =>
% 132.32/22.87 ((
% 132.32/22.87 (subbreln) =>
% 132.32/22.87 ((
% 132.32/22.87 (eqbreln) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcext) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcext2) =>
% 132.32/22.87 ((
% 132.32/22.87 (ap2apEq1) =>
% 132.32/22.87 ((
% 132.32/22.87 (ap2apEq2) =>
% 132.32/22.87 ((
% 132.32/22.87 (beta1) =>
% 132.32/22.87 ((
% 132.32/22.87 (eta1) =>
% 132.32/22.87 ((
% 132.32/22.87 (lam2lamEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (beta2) =>
% 132.32/22.87 ((
% 132.32/22.87 (eta2) =>
% 132.32/22.87 ((
% 132.32/22.87 (iffalseProp1) =>
% 132.32/22.87 ((
% 132.32/22.87 (iffalseProp2) =>
% 132.32/22.87 ((
% 132.32/22.87 (iftrueProp1) =>
% 132.32/22.87 ((
% 132.32/22.87 (iftrueProp2) =>
% 132.32/22.87 ((
% 132.32/22.87 (ifSingleton) =>
% 132.32/22.87 ((
% 132.32/22.87 (ifp) =>
% 132.32/22.87 ((
% 132.32/22.87 (theeq) =>
% 132.32/22.87 ((
% 132.32/22.87 (iftrue) =>
% 132.32/22.87 ((
% 132.32/22.87 (iffalse) =>
% 132.32/22.87 ((
% 132.32/22.87 (iftrueorfalse) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectT_lem) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionT_lem) =>
% 132.32/22.87 ((
% 132.32/22.87 (powersetT_lem) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusT_lem) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementT_lem) =>
% 132.32/22.87 ((
% 132.32/22.87 (setextT) =>
% 132.32/22.87 ((
% 132.32/22.87 (subsetTI) =>
% 132.32/22.87 ((
% 132.32/22.87 (powersetTI1) =>
% 132.32/22.87 ((
% 132.32/22.87 (powersetTE1) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementTI1) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementTE1) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectTELcontra) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectTERcontra) =>
% 132.32/22.87 ((
% 132.32/22.87 (contrasubsetT) =>
% 132.32/22.87 ((
% 132.32/22.87 (contrasubsetT1) =>
% 132.32/22.87 ((
% 132.32/22.87 (contrasubsetT2) =>
% 132.32/22.87 ((
% 132.32/22.87 (contrasubsetT3) =>
% 132.32/22.87 ((
% 132.32/22.87 (doubleComplementI1) =>
% 132.32/22.87 ((
% 132.32/22.87 (doubleComplementE1) =>
% 132.32/22.87 ((
% 132.32/22.87 (doubleComplementSub1) =>
% 132.32/22.87 ((
% 132.32/22.87 (doubleComplementSub2) =>
% 132.32/22.87 ((
% 132.32/22.87 (doubleComplementEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementTnotintersectT) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementImpComplementIntersect) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementSubsetComplementIntersect) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementInPowersetComplementIntersect) =>
% 132.32/22.87 ((
% 132.32/22.87 (contraSubsetComplement) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementTcontraSubset) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionTILcontra) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionTIRcontra) =>
% 132.32/22.87 ((
% 132.32/22.87 (inIntersectImpInUnion) =>
% 132.32/22.87 ((
% 132.32/22.87 (inIntersectImpInUnion2) =>
% 132.32/22.87 ((
% 132.32/22.87 (inIntersectImpInIntersectUnions) =>
% 132.32/22.87 ((
% 132.32/22.87 (intersectInPowersetIntersectUnions) =>
% 132.32/22.87 ((
% 132.32/22.87 (inComplementUnionImpNotIn1) =>
% 132.32/22.87 ((
% 132.32/22.87 (inComplementUnionImpInComplement1) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionTE) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionTEcontra) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan2a1) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementUnionInPowersetComplement) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan2a2) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan1a) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan1b) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan1) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan2a) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan2b2) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan2b) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan2) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz13rule0) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz13rule1) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz13rule2) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz13rule3) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz13rule4) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz1_1) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz1_2) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz1_3) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz1_4) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz1_5) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1all2) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1SetBreln1) =>
% 132.32/22.87 ((
% 132.32/22.87 (choice2fnsingleton) =>
% 132.32/22.87 ((
% 132.32/22.87 (setOfPairsIsBReln1) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1all1) =>
% 132.32/22.87 ((
% 132.32/22.87 (subbreln1) =>
% 132.32/22.87 ((
% 132.32/22.87 (eqbreln1) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1invprop) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1invI) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1invE) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1compprop) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1compI) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1compE) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1compEex) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1unionprop) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1unionIL) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1unionIR) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1unionI) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1unionE) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1unionEcases) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1unionCommutes) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz2Ex) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz2W) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz2A) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz2B) =>
% 132.32/22.87 ((
% 132.32/22.87 (image1Ex) =>
% 132.32/22.87 ((
% 132.32/22.87 (image1Ex1) =>
% 132.32/22.87 ((
% 132.32/22.87 (image1Equiv) =>
% 132.32/22.87 ((
% 132.32/22.87 (image1E) =>
% 132.32/22.87 ((
% 132.32/22.87 (image1I) =>
% 132.32/22.87 ((
% 132.32/22.87 (injFuncInInjFuncSet) =>
% 132.32/22.87 ((
% 132.32/22.87 (injFuncSetFuncIn) =>
% 132.32/22.87 ((
% 132.32/22.87 (injFuncSetFuncInj) =>
% 132.32/22.87 ((
% 132.32/22.87 (surjFuncSetFuncIn) =>
% 132.32/22.87 ((
% 132.32/22.87 (surjFuncSetFuncSurj) =>
% 132.32/22.87 ((
% 132.32/22.87 (leftInvIsSurj) =>
% 132.32/22.87 ((
% 132.32/22.87 (surjCantorThm) =>
% 132.32/22.87 ((
% 132.32/22.87 (foundation2) =>
% 132.32/22.87 ((
% 132.32/22.87 (notinself) =>
% 132.32/22.87 ((
% 132.32/22.87 (notinself2) =>
% 132.32/22.87 ((
% 132.32/22.87 (omegaSp) =>
% 132.32/22.87 ((
% 132.32/22.87 (omegaSclos) =>
% 132.32/22.87 ((
% 132.32/22.87 (peano0notS) =>
% 132.32/22.87 ((
% 132.32/22.87 (peanoSinj) =>
% 132.32/22.87 ((
% 132.32/22.87 (transitivesetOp1) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintTransitive) =>
% 132.32/22.87 ((
% 132.32/22.87 (transitivesetOp2) =>
% 132.32/22.87 ((
% 132.32/22.87 (setunionTransitive) =>
% 132.32/22.87 ((
% 132.32/22.87 (ordinalMinLem1) =>
% 132.32/22.87 ((
% 132.32/22.87 (ordinalTransSet) =>
% 132.32/22.87 ((
% 132.32/22.87 (ordinalTransSet1) =>
% 132.32/22.87 ((
% 132.32/22.87 (setunionOrdinalLem1) =>
% 132.32/22.87 (ordinal @
% 132.32/22.87 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.32/22.87 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl598])).
% 132.32/22.87 thf(zip_derived_cl623, plain,
% 132.32/22.87 (~ (((powerset__Cong) =>
% 132.32/22.87 (((setunion__Cong) =>
% 132.32/22.87 (((exuEu) =>
% 132.32/22.87 (((descr__Cong) =>
% 132.32/22.87 (((dsetconstr__Cong) =>
% 132.32/22.87 (((subsetI1) =>
% 132.32/22.87 (((eqimpsubset2) =>
% 132.32/22.87 (((eqimpsubset1) =>
% 132.32/22.87 (((subsetI2) =>
% 132.32/22.87 (((emptysetsubset) =>
% 132.32/22.87 (((subsetE) =>
% 132.32/22.87 (((subsetE2) =>
% 132.32/22.87 (((notsubsetI) =>
% 132.32/22.87 (((notequalI1) =>
% 132.32/22.87 (((notequalI2) =>
% 132.32/22.87 (((subsetRefl) =>
% 132.32/22.87 (((subsetTrans) =>
% 132.32/22.87 (((setadjoinSub) =>
% 132.32/22.87 (((setadjoinSub2) =>
% 132.32/22.87 (((subset2powerset) =>
% 132.32/22.87 (((setextsub) =>
% 132.32/22.87 (((subsetemptysetimpeq) =>
% 132.32/22.87 (((powersetI1) =>
% 132.32/22.87 (((powersetE1) =>
% 132.32/22.87 (((inPowerset) =>
% 132.32/22.87 (((powersetsubset) =>
% 132.32/22.87 (((sepInPowerset) =>
% 132.32/22.87 (((sepSubset) =>
% 132.32/22.87 (((binunionIL) =>
% 132.32/22.87 (((upairset2IR) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionIR) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionEcases) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionE) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionLsub) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionRsub) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectI) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectSubset5) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectEL) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectLsub) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectSubset2) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectSubset3) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectER) =>
% 132.32/22.87 ((
% 132.32/22.87 (disjointsetsI1) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectRsub) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectSubset4) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectSubset1) =>
% 132.32/22.87 ((
% 132.32/22.87 (bs114d) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusI) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusEL) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusER) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusSubset2) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusERneg) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusELneg) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusILneg) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusIRneg) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusLsub) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusSubset1) =>
% 132.32/22.87 ((
% 132.32/22.87 (symdiffE) =>
% 132.32/22.87 ((
% 132.32/22.87 (symdiffI1) =>
% 132.32/22.87 ((
% 132.32/22.87 (symdiffI2) =>
% 132.32/22.87 ((
% 132.32/22.87 (symdiffIneg1) =>
% 132.32/22.87 ((
% 132.32/22.87 (symdiffIneg2) =>
% 132.32/22.87 ((
% 132.32/22.87 (secondinupair) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairIL) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairIR) =>
% 132.32/22.87 ((
% 132.32/22.87 (kpairiskpair) =>
% 132.32/22.87 ((
% 132.32/22.87 (kpairp) =>
% 132.32/22.87 ((
% 132.32/22.87 (singletonsubset) =>
% 132.32/22.87 ((
% 132.32/22.87 (singletoninpowerset) =>
% 132.32/22.87 ((
% 132.32/22.87 (singletoninpowunion) =>
% 132.32/22.87 ((
% 132.32/22.87 (upairset2E) =>
% 132.32/22.87 ((
% 132.32/22.87 (upairsubunion) =>
% 132.32/22.87 ((
% 132.32/22.87 (upairinpowunion) =>
% 132.32/22.87 ((
% 132.32/22.87 (ubforcartprodlem1) =>
% 132.32/22.87 ((
% 132.32/22.87 (ubforcartprodlem2) =>
% 132.32/22.87 ((
% 132.32/22.87 (ubforcartprodlem3) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodpairin) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodmempair1) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodmempair) =>
% 132.32/22.87 ((
% 132.32/22.87 (setunionE2) =>
% 132.32/22.87 ((
% 132.32/22.87 (setunionsingleton1) =>
% 132.32/22.87 ((
% 132.32/22.87 (setunionsingleton2) =>
% 132.32/22.87 ((
% 132.32/22.87 (setunionsingleton) =>
% 132.32/22.87 ((
% 132.32/22.87 (singletonprop) =>
% 132.32/22.87 ((
% 132.32/22.87 (ex1E1) =>
% 132.32/22.87 ((
% 132.32/22.87 (ex1I) =>
% 132.32/22.87 ((
% 132.32/22.87 (ex1I2) =>
% 132.32/22.87 ((
% 132.32/22.87 (singletonsuniq) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairinjL1) =>
% 132.32/22.87 ((
% 132.32/22.87 (kfstsingleton) =>
% 132.32/22.87 ((
% 132.32/22.87 (theprop) =>
% 132.32/22.87 ((
% 132.32/22.87 (kfstpairEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodfstin) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairinjL2) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairinjL) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairinjR11) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairinjR12) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairinjR1) =>
% 132.32/22.87 ((
% 132.32/22.87 (upairequniteq) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairinjR2) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairinjR) =>
% 132.32/22.87 ((
% 132.32/22.87 (ksndsingleton) =>
% 132.32/22.87 ((
% 132.32/22.87 (ksndpairEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (kpairsurjEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodsndin) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodpairmemEL) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodpairmemER) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodmempaircEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodfstpairEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodsndpairEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodpairsurjEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (dpsetconstrI) =>
% 132.32/22.87 ((
% 132.32/22.87 (dpsetconstrSub) =>
% 132.32/22.87 ((
% 132.32/22.87 (setOfPairsIsBReln) =>
% 132.32/22.87 ((
% 132.32/22.87 (dpsetconstrERa) =>
% 132.32/22.87 ((
% 132.32/22.87 (dpsetconstrEL1) =>
% 132.32/22.87 ((
% 132.32/22.87 (dpsetconstrEL2) =>
% 132.32/22.87 ((
% 132.32/22.87 (dpsetconstrER) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcImageSingleton) =>
% 132.32/22.87 ((
% 132.32/22.87 (apProp) =>
% 132.32/22.87 ((
% 132.32/22.87 (app) =>
% 132.32/22.87 ((
% 132.32/22.87 (infuncsetfunc) =>
% 132.32/22.87 ((
% 132.32/22.87 (ap2p) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcinfuncset) =>
% 132.32/22.87 ((
% 132.32/22.87 (lamProp) =>
% 132.32/22.87 ((
% 132.32/22.87 (lamp) =>
% 132.32/22.87 ((
% 132.32/22.87 (lam2p) =>
% 132.32/22.87 ((
% 132.32/22.87 (brelnall1) =>
% 132.32/22.87 ((
% 132.32/22.87 (brelnall2) =>
% 132.32/22.87 ((
% 132.32/22.87 (ex1E2) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcGraphProp1) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcGraphProp3) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcGraphProp2) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcextLem) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcGraphProp4) =>
% 132.32/22.87 ((
% 132.32/22.87 (subbreln) =>
% 132.32/22.87 ((
% 132.32/22.87 (eqbreln) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcext) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcext2) =>
% 132.32/22.87 ((
% 132.32/22.87 (ap2apEq1) =>
% 132.32/22.87 ((
% 132.32/22.87 (ap2apEq2) =>
% 132.32/22.87 ((
% 132.32/22.87 (beta1) =>
% 132.32/22.87 ((
% 132.32/22.87 (eta1) =>
% 132.32/22.87 ((
% 132.32/22.87 (lam2lamEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (beta2) =>
% 132.32/22.87 ((
% 132.32/22.87 (eta2) =>
% 132.32/22.87 ((
% 132.32/22.87 (iffalseProp1) =>
% 132.32/22.87 ((
% 132.32/22.87 (iffalseProp2) =>
% 132.32/22.87 ((
% 132.32/22.87 (iftrueProp1) =>
% 132.32/22.87 ((
% 132.32/22.87 (iftrueProp2) =>
% 132.32/22.87 ((
% 132.32/22.87 (ifSingleton) =>
% 132.32/22.87 ((
% 132.32/22.87 (ifp) =>
% 132.32/22.87 ((
% 132.32/22.87 (theeq) =>
% 132.32/22.87 ((
% 132.32/22.87 (iftrue) =>
% 132.32/22.87 ((
% 132.32/22.87 (iffalse) =>
% 132.32/22.87 ((
% 132.32/22.87 (iftrueorfalse) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectT_lem) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionT_lem) =>
% 132.32/22.87 ((
% 132.32/22.87 (powersetT_lem) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusT_lem) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementT_lem) =>
% 132.32/22.87 ((
% 132.32/22.87 (setextT) =>
% 132.32/22.87 ((
% 132.32/22.87 (subsetTI) =>
% 132.32/22.87 ((
% 132.32/22.87 (powersetTI1) =>
% 132.32/22.87 ((
% 132.32/22.87 (powersetTE1) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementTI1) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementTE1) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectTELcontra) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectTERcontra) =>
% 132.32/22.87 ((
% 132.32/22.87 (contrasubsetT) =>
% 132.32/22.87 ((
% 132.32/22.87 (contrasubsetT1) =>
% 132.32/22.87 ((
% 132.32/22.87 (contrasubsetT2) =>
% 132.32/22.87 ((
% 132.32/22.87 (contrasubsetT3) =>
% 132.32/22.87 ((
% 132.32/22.87 (doubleComplementI1) =>
% 132.32/22.87 ((
% 132.32/22.87 (doubleComplementE1) =>
% 132.32/22.87 ((
% 132.32/22.87 (doubleComplementSub1) =>
% 132.32/22.87 ((
% 132.32/22.87 (doubleComplementSub2) =>
% 132.32/22.87 ((
% 132.32/22.87 (doubleComplementEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementTnotintersectT) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementImpComplementIntersect) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementSubsetComplementIntersect) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementInPowersetComplementIntersect) =>
% 132.32/22.87 ((
% 132.32/22.87 (contraSubsetComplement) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementTcontraSubset) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionTILcontra) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionTIRcontra) =>
% 132.32/22.87 ((
% 132.32/22.87 (inIntersectImpInUnion) =>
% 132.32/22.87 ((
% 132.32/22.87 (inIntersectImpInUnion2) =>
% 132.32/22.87 ((
% 132.32/22.87 (inIntersectImpInIntersectUnions) =>
% 132.32/22.87 ((
% 132.32/22.87 (intersectInPowersetIntersectUnions) =>
% 132.32/22.87 ((
% 132.32/22.87 (inComplementUnionImpNotIn1) =>
% 132.32/22.87 ((
% 132.32/22.87 (inComplementUnionImpInComplement1) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionTE) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionTEcontra) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan2a1) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementUnionInPowersetComplement) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan2a2) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan1a) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan1b) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan1) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan2a) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan2b2) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan2b) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan2) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz13rule0) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz13rule1) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz13rule2) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz13rule3) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz13rule4) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz1_1) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz1_2) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz1_3) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz1_4) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz1_5) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1all2) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1SetBreln1) =>
% 132.32/22.87 ((
% 132.32/22.87 (choice2fnsingleton) =>
% 132.32/22.87 ((
% 132.32/22.87 (setOfPairsIsBReln1) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1all1) =>
% 132.32/22.87 ((
% 132.32/22.87 (subbreln1) =>
% 132.32/22.87 ((
% 132.32/22.87 (eqbreln1) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1invprop) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1invI) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1invE) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1compprop) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1compI) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1compE) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1compEex) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1unionprop) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1unionIL) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1unionIR) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1unionI) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1unionE) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1unionEcases) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1unionCommutes) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz2Ex) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz2W) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz2A) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz2B) =>
% 132.32/22.87 ((
% 132.32/22.87 (image1Ex) =>
% 132.32/22.87 ((
% 132.32/22.87 (image1Ex1) =>
% 132.32/22.87 ((
% 132.32/22.87 (image1Equiv) =>
% 132.32/22.87 ((
% 132.32/22.87 (image1E) =>
% 132.32/22.87 ((
% 132.32/22.87 (image1I) =>
% 132.32/22.87 ((
% 132.32/22.87 (injFuncInInjFuncSet) =>
% 132.32/22.87 ((
% 132.32/22.87 (injFuncSetFuncIn) =>
% 132.32/22.87 ((
% 132.32/22.87 (injFuncSetFuncInj) =>
% 132.32/22.87 ((
% 132.32/22.87 (surjFuncSetFuncIn) =>
% 132.32/22.87 ((
% 132.32/22.87 (surjFuncSetFuncSurj) =>
% 132.32/22.87 ((
% 132.32/22.87 (leftInvIsSurj) =>
% 132.32/22.87 ((
% 132.32/22.87 (surjCantorThm) =>
% 132.32/22.87 ((
% 132.32/22.87 (foundation2) =>
% 132.32/22.87 ((
% 132.32/22.87 (notinself) =>
% 132.32/22.87 ((
% 132.32/22.87 (notinself2) =>
% 132.32/22.87 ((
% 132.32/22.87 (omegaSp) =>
% 132.32/22.87 ((
% 132.32/22.87 (omegaSclos) =>
% 132.32/22.87 ((
% 132.32/22.87 (peano0notS) =>
% 132.32/22.87 ((
% 132.32/22.87 (peanoSinj) =>
% 132.32/22.87 ((
% 132.32/22.87 (transitivesetOp1) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintTransitive) =>
% 132.32/22.87 ((
% 132.32/22.87 (transitivesetOp2) =>
% 132.32/22.87 ((
% 132.32/22.87 (setunionTransitive) =>
% 132.32/22.87 ((
% 132.32/22.87 (ordinalMinLem1) =>
% 132.32/22.87 ((
% 132.32/22.87 (ordinalTransSet) =>
% 132.32/22.87 ((
% 132.32/22.87 (ordinalTransSet1) =>
% 132.32/22.87 ((
% 132.32/22.87 (setunionOrdinalLem1) =>
% 132.32/22.87 (ordinal @
% 132.32/22.87 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.32/22.87 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl609])).
% 132.32/22.87 thf(zip_derived_cl637, plain,
% 132.32/22.87 (~ (((setunion__Cong) =>
% 132.32/22.87 (((exuEu) =>
% 132.32/22.87 (((descr__Cong) =>
% 132.32/22.87 (((dsetconstr__Cong) =>
% 132.32/22.87 (((subsetI1) =>
% 132.32/22.87 (((eqimpsubset2) =>
% 132.32/22.87 (((eqimpsubset1) =>
% 132.32/22.87 (((subsetI2) =>
% 132.32/22.87 (((emptysetsubset) =>
% 132.32/22.87 (((subsetE) =>
% 132.32/22.87 (((subsetE2) =>
% 132.32/22.87 (((notsubsetI) =>
% 132.32/22.87 (((notequalI1) =>
% 132.32/22.87 (((notequalI2) =>
% 132.32/22.87 (((subsetRefl) =>
% 132.32/22.87 (((subsetTrans) =>
% 132.32/22.87 (((setadjoinSub) =>
% 132.32/22.87 (((setadjoinSub2) =>
% 132.32/22.87 (((subset2powerset) =>
% 132.32/22.87 (((setextsub) =>
% 132.32/22.87 (((subsetemptysetimpeq) =>
% 132.32/22.87 (((powersetI1) =>
% 132.32/22.87 (((powersetE1) =>
% 132.32/22.87 (((inPowerset) =>
% 132.32/22.87 (((powersetsubset) =>
% 132.32/22.87 (((sepInPowerset) =>
% 132.32/22.87 (((sepSubset) =>
% 132.32/22.87 (((binunionIL) =>
% 132.32/22.87 (((upairset2IR) =>
% 132.32/22.87 (((binunionIR) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionEcases) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionE) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionLsub) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionRsub) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectI) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectSubset5) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectEL) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectLsub) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectSubset2) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectSubset3) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectER) =>
% 132.32/22.87 ((
% 132.32/22.87 (disjointsetsI1) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectRsub) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectSubset4) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectSubset1) =>
% 132.32/22.87 ((
% 132.32/22.87 (bs114d) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusI) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusEL) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusER) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusSubset2) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusERneg) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusELneg) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusILneg) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusIRneg) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusLsub) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusSubset1) =>
% 132.32/22.87 ((
% 132.32/22.87 (symdiffE) =>
% 132.32/22.87 ((
% 132.32/22.87 (symdiffI1) =>
% 132.32/22.87 ((
% 132.32/22.87 (symdiffI2) =>
% 132.32/22.87 ((
% 132.32/22.87 (symdiffIneg1) =>
% 132.32/22.87 ((
% 132.32/22.87 (symdiffIneg2) =>
% 132.32/22.87 ((
% 132.32/22.87 (secondinupair) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairIL) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairIR) =>
% 132.32/22.87 ((
% 132.32/22.87 (kpairiskpair) =>
% 132.32/22.87 ((
% 132.32/22.87 (kpairp) =>
% 132.32/22.87 ((
% 132.32/22.87 (singletonsubset) =>
% 132.32/22.87 ((
% 132.32/22.87 (singletoninpowerset) =>
% 132.32/22.87 ((
% 132.32/22.87 (singletoninpowunion) =>
% 132.32/22.87 ((
% 132.32/22.87 (upairset2E) =>
% 132.32/22.87 ((
% 132.32/22.87 (upairsubunion) =>
% 132.32/22.87 ((
% 132.32/22.87 (upairinpowunion) =>
% 132.32/22.87 ((
% 132.32/22.87 (ubforcartprodlem1) =>
% 132.32/22.87 ((
% 132.32/22.87 (ubforcartprodlem2) =>
% 132.32/22.87 ((
% 132.32/22.87 (ubforcartprodlem3) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodpairin) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodmempair1) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodmempair) =>
% 132.32/22.87 ((
% 132.32/22.87 (setunionE2) =>
% 132.32/22.87 ((
% 132.32/22.87 (setunionsingleton1) =>
% 132.32/22.87 ((
% 132.32/22.87 (setunionsingleton2) =>
% 132.32/22.87 ((
% 132.32/22.87 (setunionsingleton) =>
% 132.32/22.87 ((
% 132.32/22.87 (singletonprop) =>
% 132.32/22.87 ((
% 132.32/22.87 (ex1E1) =>
% 132.32/22.87 ((
% 132.32/22.87 (ex1I) =>
% 132.32/22.87 ((
% 132.32/22.87 (ex1I2) =>
% 132.32/22.87 ((
% 132.32/22.87 (singletonsuniq) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairinjL1) =>
% 132.32/22.87 ((
% 132.32/22.87 (kfstsingleton) =>
% 132.32/22.87 ((
% 132.32/22.87 (theprop) =>
% 132.32/22.87 ((
% 132.32/22.87 (kfstpairEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodfstin) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairinjL2) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairinjL) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairinjR11) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairinjR12) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairinjR1) =>
% 132.32/22.87 ((
% 132.32/22.87 (upairequniteq) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairinjR2) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairinjR) =>
% 132.32/22.87 ((
% 132.32/22.87 (ksndsingleton) =>
% 132.32/22.87 ((
% 132.32/22.87 (ksndpairEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (kpairsurjEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodsndin) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodpairmemEL) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodpairmemER) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodmempaircEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodfstpairEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodsndpairEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodpairsurjEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (dpsetconstrI) =>
% 132.32/22.87 ((
% 132.32/22.87 (dpsetconstrSub) =>
% 132.32/22.87 ((
% 132.32/22.87 (setOfPairsIsBReln) =>
% 132.32/22.87 ((
% 132.32/22.87 (dpsetconstrERa) =>
% 132.32/22.87 ((
% 132.32/22.87 (dpsetconstrEL1) =>
% 132.32/22.87 ((
% 132.32/22.87 (dpsetconstrEL2) =>
% 132.32/22.87 ((
% 132.32/22.87 (dpsetconstrER) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcImageSingleton) =>
% 132.32/22.87 ((
% 132.32/22.87 (apProp) =>
% 132.32/22.87 ((
% 132.32/22.87 (app) =>
% 132.32/22.87 ((
% 132.32/22.87 (infuncsetfunc) =>
% 132.32/22.87 ((
% 132.32/22.87 (ap2p) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcinfuncset) =>
% 132.32/22.87 ((
% 132.32/22.87 (lamProp) =>
% 132.32/22.87 ((
% 132.32/22.87 (lamp) =>
% 132.32/22.87 ((
% 132.32/22.87 (lam2p) =>
% 132.32/22.87 ((
% 132.32/22.87 (brelnall1) =>
% 132.32/22.87 ((
% 132.32/22.87 (brelnall2) =>
% 132.32/22.87 ((
% 132.32/22.87 (ex1E2) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcGraphProp1) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcGraphProp3) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcGraphProp2) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcextLem) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcGraphProp4) =>
% 132.32/22.87 ((
% 132.32/22.87 (subbreln) =>
% 132.32/22.87 ((
% 132.32/22.87 (eqbreln) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcext) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcext2) =>
% 132.32/22.87 ((
% 132.32/22.87 (ap2apEq1) =>
% 132.32/22.87 ((
% 132.32/22.87 (ap2apEq2) =>
% 132.32/22.87 ((
% 132.32/22.87 (beta1) =>
% 132.32/22.87 ((
% 132.32/22.87 (eta1) =>
% 132.32/22.87 ((
% 132.32/22.87 (lam2lamEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (beta2) =>
% 132.32/22.87 ((
% 132.32/22.87 (eta2) =>
% 132.32/22.87 ((
% 132.32/22.87 (iffalseProp1) =>
% 132.32/22.87 ((
% 132.32/22.87 (iffalseProp2) =>
% 132.32/22.87 ((
% 132.32/22.87 (iftrueProp1) =>
% 132.32/22.87 ((
% 132.32/22.87 (iftrueProp2) =>
% 132.32/22.87 ((
% 132.32/22.87 (ifSingleton) =>
% 132.32/22.87 ((
% 132.32/22.87 (ifp) =>
% 132.32/22.87 ((
% 132.32/22.87 (theeq) =>
% 132.32/22.87 ((
% 132.32/22.87 (iftrue) =>
% 132.32/22.87 ((
% 132.32/22.87 (iffalse) =>
% 132.32/22.87 ((
% 132.32/22.87 (iftrueorfalse) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectT_lem) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionT_lem) =>
% 132.32/22.87 ((
% 132.32/22.87 (powersetT_lem) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusT_lem) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementT_lem) =>
% 132.32/22.87 ((
% 132.32/22.87 (setextT) =>
% 132.32/22.87 ((
% 132.32/22.87 (subsetTI) =>
% 132.32/22.87 ((
% 132.32/22.87 (powersetTI1) =>
% 132.32/22.87 ((
% 132.32/22.87 (powersetTE1) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementTI1) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementTE1) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectTELcontra) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectTERcontra) =>
% 132.32/22.87 ((
% 132.32/22.87 (contrasubsetT) =>
% 132.32/22.87 ((
% 132.32/22.87 (contrasubsetT1) =>
% 132.32/22.87 ((
% 132.32/22.87 (contrasubsetT2) =>
% 132.32/22.87 ((
% 132.32/22.87 (contrasubsetT3) =>
% 132.32/22.87 ((
% 132.32/22.87 (doubleComplementI1) =>
% 132.32/22.87 ((
% 132.32/22.87 (doubleComplementE1) =>
% 132.32/22.87 ((
% 132.32/22.87 (doubleComplementSub1) =>
% 132.32/22.87 ((
% 132.32/22.87 (doubleComplementSub2) =>
% 132.32/22.87 ((
% 132.32/22.87 (doubleComplementEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementTnotintersectT) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementImpComplementIntersect) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementSubsetComplementIntersect) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementInPowersetComplementIntersect) =>
% 132.32/22.87 ((
% 132.32/22.87 (contraSubsetComplement) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementTcontraSubset) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionTILcontra) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionTIRcontra) =>
% 132.32/22.87 ((
% 132.32/22.87 (inIntersectImpInUnion) =>
% 132.32/22.87 ((
% 132.32/22.87 (inIntersectImpInUnion2) =>
% 132.32/22.87 ((
% 132.32/22.87 (inIntersectImpInIntersectUnions) =>
% 132.32/22.87 ((
% 132.32/22.87 (intersectInPowersetIntersectUnions) =>
% 132.32/22.87 ((
% 132.32/22.87 (inComplementUnionImpNotIn1) =>
% 132.32/22.87 ((
% 132.32/22.87 (inComplementUnionImpInComplement1) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionTE) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionTEcontra) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan2a1) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementUnionInPowersetComplement) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan2a2) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan1a) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan1b) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan1) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan2a) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan2b2) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan2b) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan2) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz13rule0) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz13rule1) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz13rule2) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz13rule3) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz13rule4) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz1_1) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz1_2) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz1_3) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz1_4) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz1_5) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1all2) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1SetBreln1) =>
% 132.32/22.87 ((
% 132.32/22.87 (choice2fnsingleton) =>
% 132.32/22.87 ((
% 132.32/22.87 (setOfPairsIsBReln1) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1all1) =>
% 132.32/22.87 ((
% 132.32/22.87 (subbreln1) =>
% 132.32/22.87 ((
% 132.32/22.87 (eqbreln1) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1invprop) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1invI) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1invE) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1compprop) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1compI) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1compE) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1compEex) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1unionprop) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1unionIL) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1unionIR) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1unionI) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1unionE) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1unionEcases) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1unionCommutes) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz2Ex) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz2W) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz2A) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz2B) =>
% 132.32/22.87 ((
% 132.32/22.87 (image1Ex) =>
% 132.32/22.87 ((
% 132.32/22.87 (image1Ex1) =>
% 132.32/22.87 ((
% 132.32/22.87 (image1Equiv) =>
% 132.32/22.87 ((
% 132.32/22.87 (image1E) =>
% 132.32/22.87 ((
% 132.32/22.87 (image1I) =>
% 132.32/22.87 ((
% 132.32/22.87 (injFuncInInjFuncSet) =>
% 132.32/22.87 ((
% 132.32/22.87 (injFuncSetFuncIn) =>
% 132.32/22.87 ((
% 132.32/22.87 (injFuncSetFuncInj) =>
% 132.32/22.87 ((
% 132.32/22.87 (surjFuncSetFuncIn) =>
% 132.32/22.87 ((
% 132.32/22.87 (surjFuncSetFuncSurj) =>
% 132.32/22.87 ((
% 132.32/22.87 (leftInvIsSurj) =>
% 132.32/22.87 ((
% 132.32/22.87 (surjCantorThm) =>
% 132.32/22.87 ((
% 132.32/22.87 (foundation2) =>
% 132.32/22.87 ((
% 132.32/22.87 (notinself) =>
% 132.32/22.87 ((
% 132.32/22.87 (notinself2) =>
% 132.32/22.87 ((
% 132.32/22.87 (omegaSp) =>
% 132.32/22.87 ((
% 132.32/22.87 (omegaSclos) =>
% 132.32/22.87 ((
% 132.32/22.87 (peano0notS) =>
% 132.32/22.87 ((
% 132.32/22.87 (peanoSinj) =>
% 132.32/22.87 ((
% 132.32/22.87 (transitivesetOp1) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintTransitive) =>
% 132.32/22.87 ((
% 132.32/22.87 (transitivesetOp2) =>
% 132.32/22.87 ((
% 132.32/22.87 (setunionTransitive) =>
% 132.32/22.87 ((
% 132.32/22.87 (ordinalMinLem1) =>
% 132.32/22.87 ((
% 132.32/22.87 (ordinalTransSet) =>
% 132.32/22.87 ((
% 132.32/22.87 (ordinalTransSet1) =>
% 132.32/22.87 ((
% 132.32/22.87 (setunionOrdinalLem1) =>
% 132.32/22.87 (ordinal @
% 132.32/22.87 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.32/22.87 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl623])).
% 132.32/22.87 thf(zip_derived_cl652, plain,
% 132.32/22.87 (~ (((exuEu) =>
% 132.32/22.87 (((descr__Cong) =>
% 132.32/22.87 (((dsetconstr__Cong) =>
% 132.32/22.87 (((subsetI1) =>
% 132.32/22.87 (((eqimpsubset2) =>
% 132.32/22.87 (((eqimpsubset1) =>
% 132.32/22.87 (((subsetI2) =>
% 132.32/22.87 (((emptysetsubset) =>
% 132.32/22.87 (((subsetE) =>
% 132.32/22.87 (((subsetE2) =>
% 132.32/22.87 (((notsubsetI) =>
% 132.32/22.87 (((notequalI1) =>
% 132.32/22.87 (((notequalI2) =>
% 132.32/22.87 (((subsetRefl) =>
% 132.32/22.87 (((subsetTrans) =>
% 132.32/22.87 (((setadjoinSub) =>
% 132.32/22.87 (((setadjoinSub2) =>
% 132.32/22.87 (((subset2powerset) =>
% 132.32/22.87 (((setextsub) =>
% 132.32/22.87 (((subsetemptysetimpeq) =>
% 132.32/22.87 (((powersetI1) =>
% 132.32/22.87 (((powersetE1) =>
% 132.32/22.87 (((inPowerset) =>
% 132.32/22.87 (((powersetsubset) =>
% 132.32/22.87 (((sepInPowerset) =>
% 132.32/22.87 (((sepSubset) =>
% 132.32/22.87 (((binunionIL) =>
% 132.32/22.87 (((upairset2IR) =>
% 132.32/22.87 (((binunionIR) =>
% 132.32/22.87 (((binunionEcases) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionE) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionLsub) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionRsub) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectI) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectSubset5) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectEL) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectLsub) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectSubset2) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectSubset3) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectER) =>
% 132.32/22.87 ((
% 132.32/22.87 (disjointsetsI1) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectRsub) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectSubset4) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectSubset1) =>
% 132.32/22.87 ((
% 132.32/22.87 (bs114d) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusI) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusEL) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusER) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusSubset2) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusERneg) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusELneg) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusILneg) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusIRneg) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusLsub) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusSubset1) =>
% 132.32/22.87 ((
% 132.32/22.87 (symdiffE) =>
% 132.32/22.87 ((
% 132.32/22.87 (symdiffI1) =>
% 132.32/22.87 ((
% 132.32/22.87 (symdiffI2) =>
% 132.32/22.87 ((
% 132.32/22.87 (symdiffIneg1) =>
% 132.32/22.87 ((
% 132.32/22.87 (symdiffIneg2) =>
% 132.32/22.87 ((
% 132.32/22.87 (secondinupair) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairIL) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairIR) =>
% 132.32/22.87 ((
% 132.32/22.87 (kpairiskpair) =>
% 132.32/22.87 ((
% 132.32/22.87 (kpairp) =>
% 132.32/22.87 ((
% 132.32/22.87 (singletonsubset) =>
% 132.32/22.87 ((
% 132.32/22.87 (singletoninpowerset) =>
% 132.32/22.87 ((
% 132.32/22.87 (singletoninpowunion) =>
% 132.32/22.87 ((
% 132.32/22.87 (upairset2E) =>
% 132.32/22.87 ((
% 132.32/22.87 (upairsubunion) =>
% 132.32/22.87 ((
% 132.32/22.87 (upairinpowunion) =>
% 132.32/22.87 ((
% 132.32/22.87 (ubforcartprodlem1) =>
% 132.32/22.87 ((
% 132.32/22.87 (ubforcartprodlem2) =>
% 132.32/22.87 ((
% 132.32/22.87 (ubforcartprodlem3) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodpairin) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodmempair1) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodmempair) =>
% 132.32/22.87 ((
% 132.32/22.87 (setunionE2) =>
% 132.32/22.87 ((
% 132.32/22.87 (setunionsingleton1) =>
% 132.32/22.87 ((
% 132.32/22.87 (setunionsingleton2) =>
% 132.32/22.87 ((
% 132.32/22.87 (setunionsingleton) =>
% 132.32/22.87 ((
% 132.32/22.87 (singletonprop) =>
% 132.32/22.87 ((
% 132.32/22.87 (ex1E1) =>
% 132.32/22.87 ((
% 132.32/22.87 (ex1I) =>
% 132.32/22.87 ((
% 132.32/22.87 (ex1I2) =>
% 132.32/22.87 ((
% 132.32/22.87 (singletonsuniq) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairinjL1) =>
% 132.32/22.87 ((
% 132.32/22.87 (kfstsingleton) =>
% 132.32/22.87 ((
% 132.32/22.87 (theprop) =>
% 132.32/22.87 ((
% 132.32/22.87 (kfstpairEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodfstin) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairinjL2) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairinjL) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairinjR11) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairinjR12) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairinjR1) =>
% 132.32/22.87 ((
% 132.32/22.87 (upairequniteq) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairinjR2) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairinjR) =>
% 132.32/22.87 ((
% 132.32/22.87 (ksndsingleton) =>
% 132.32/22.87 ((
% 132.32/22.87 (ksndpairEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (kpairsurjEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodsndin) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodpairmemEL) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodpairmemER) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodmempaircEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodfstpairEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodsndpairEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodpairsurjEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (dpsetconstrI) =>
% 132.32/22.87 ((
% 132.32/22.87 (dpsetconstrSub) =>
% 132.32/22.87 ((
% 132.32/22.87 (setOfPairsIsBReln) =>
% 132.32/22.87 ((
% 132.32/22.87 (dpsetconstrERa) =>
% 132.32/22.87 ((
% 132.32/22.87 (dpsetconstrEL1) =>
% 132.32/22.87 ((
% 132.32/22.87 (dpsetconstrEL2) =>
% 132.32/22.87 ((
% 132.32/22.87 (dpsetconstrER) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcImageSingleton) =>
% 132.32/22.87 ((
% 132.32/22.87 (apProp) =>
% 132.32/22.87 ((
% 132.32/22.87 (app) =>
% 132.32/22.87 ((
% 132.32/22.87 (infuncsetfunc) =>
% 132.32/22.87 ((
% 132.32/22.87 (ap2p) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcinfuncset) =>
% 132.32/22.87 ((
% 132.32/22.87 (lamProp) =>
% 132.32/22.87 ((
% 132.32/22.87 (lamp) =>
% 132.32/22.87 ((
% 132.32/22.87 (lam2p) =>
% 132.32/22.87 ((
% 132.32/22.87 (brelnall1) =>
% 132.32/22.87 ((
% 132.32/22.87 (brelnall2) =>
% 132.32/22.87 ((
% 132.32/22.87 (ex1E2) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcGraphProp1) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcGraphProp3) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcGraphProp2) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcextLem) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcGraphProp4) =>
% 132.32/22.87 ((
% 132.32/22.87 (subbreln) =>
% 132.32/22.87 ((
% 132.32/22.87 (eqbreln) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcext) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcext2) =>
% 132.32/22.87 ((
% 132.32/22.87 (ap2apEq1) =>
% 132.32/22.87 ((
% 132.32/22.87 (ap2apEq2) =>
% 132.32/22.87 ((
% 132.32/22.87 (beta1) =>
% 132.32/22.87 ((
% 132.32/22.87 (eta1) =>
% 132.32/22.87 ((
% 132.32/22.87 (lam2lamEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (beta2) =>
% 132.32/22.87 ((
% 132.32/22.87 (eta2) =>
% 132.32/22.87 ((
% 132.32/22.87 (iffalseProp1) =>
% 132.32/22.87 ((
% 132.32/22.87 (iffalseProp2) =>
% 132.32/22.87 ((
% 132.32/22.87 (iftrueProp1) =>
% 132.32/22.87 ((
% 132.32/22.87 (iftrueProp2) =>
% 132.32/22.87 ((
% 132.32/22.87 (ifSingleton) =>
% 132.32/22.87 ((
% 132.32/22.87 (ifp) =>
% 132.32/22.87 ((
% 132.32/22.87 (theeq) =>
% 132.32/22.87 ((
% 132.32/22.87 (iftrue) =>
% 132.32/22.87 ((
% 132.32/22.87 (iffalse) =>
% 132.32/22.87 ((
% 132.32/22.87 (iftrueorfalse) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectT_lem) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionT_lem) =>
% 132.32/22.87 ((
% 132.32/22.87 (powersetT_lem) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusT_lem) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementT_lem) =>
% 132.32/22.87 ((
% 132.32/22.87 (setextT) =>
% 132.32/22.87 ((
% 132.32/22.87 (subsetTI) =>
% 132.32/22.87 ((
% 132.32/22.87 (powersetTI1) =>
% 132.32/22.87 ((
% 132.32/22.87 (powersetTE1) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementTI1) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementTE1) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectTELcontra) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectTERcontra) =>
% 132.32/22.87 ((
% 132.32/22.87 (contrasubsetT) =>
% 132.32/22.87 ((
% 132.32/22.87 (contrasubsetT1) =>
% 132.32/22.87 ((
% 132.32/22.87 (contrasubsetT2) =>
% 132.32/22.87 ((
% 132.32/22.87 (contrasubsetT3) =>
% 132.32/22.87 ((
% 132.32/22.87 (doubleComplementI1) =>
% 132.32/22.87 ((
% 132.32/22.87 (doubleComplementE1) =>
% 132.32/22.87 ((
% 132.32/22.87 (doubleComplementSub1) =>
% 132.32/22.87 ((
% 132.32/22.87 (doubleComplementSub2) =>
% 132.32/22.87 ((
% 132.32/22.87 (doubleComplementEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementTnotintersectT) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementImpComplementIntersect) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementSubsetComplementIntersect) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementInPowersetComplementIntersect) =>
% 132.32/22.87 ((
% 132.32/22.87 (contraSubsetComplement) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementTcontraSubset) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionTILcontra) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionTIRcontra) =>
% 132.32/22.87 ((
% 132.32/22.87 (inIntersectImpInUnion) =>
% 132.32/22.87 ((
% 132.32/22.87 (inIntersectImpInUnion2) =>
% 132.32/22.87 ((
% 132.32/22.87 (inIntersectImpInIntersectUnions) =>
% 132.32/22.87 ((
% 132.32/22.87 (intersectInPowersetIntersectUnions) =>
% 132.32/22.87 ((
% 132.32/22.87 (inComplementUnionImpNotIn1) =>
% 132.32/22.87 ((
% 132.32/22.87 (inComplementUnionImpInComplement1) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionTE) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionTEcontra) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan2a1) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementUnionInPowersetComplement) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan2a2) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan1a) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan1b) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan1) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan2a) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan2b2) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan2b) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan2) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz13rule0) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz13rule1) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz13rule2) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz13rule3) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz13rule4) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz1_1) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz1_2) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz1_3) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz1_4) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz1_5) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1all2) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1SetBreln1) =>
% 132.32/22.87 ((
% 132.32/22.87 (choice2fnsingleton) =>
% 132.32/22.87 ((
% 132.32/22.87 (setOfPairsIsBReln1) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1all1) =>
% 132.32/22.87 ((
% 132.32/22.87 (subbreln1) =>
% 132.32/22.87 ((
% 132.32/22.87 (eqbreln1) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1invprop) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1invI) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1invE) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1compprop) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1compI) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1compE) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1compEex) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1unionprop) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1unionIL) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1unionIR) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1unionI) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1unionE) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1unionEcases) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1unionCommutes) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz2Ex) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz2W) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz2A) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz2B) =>
% 132.32/22.87 ((
% 132.32/22.87 (image1Ex) =>
% 132.32/22.87 ((
% 132.32/22.87 (image1Ex1) =>
% 132.32/22.87 ((
% 132.32/22.87 (image1Equiv) =>
% 132.32/22.87 ((
% 132.32/22.87 (image1E) =>
% 132.32/22.87 ((
% 132.32/22.87 (image1I) =>
% 132.32/22.87 ((
% 132.32/22.87 (injFuncInInjFuncSet) =>
% 132.32/22.87 ((
% 132.32/22.87 (injFuncSetFuncIn) =>
% 132.32/22.87 ((
% 132.32/22.87 (injFuncSetFuncInj) =>
% 132.32/22.87 ((
% 132.32/22.87 (surjFuncSetFuncIn) =>
% 132.32/22.87 ((
% 132.32/22.87 (surjFuncSetFuncSurj) =>
% 132.32/22.87 ((
% 132.32/22.87 (leftInvIsSurj) =>
% 132.32/22.87 ((
% 132.32/22.87 (surjCantorThm) =>
% 132.32/22.87 ((
% 132.32/22.87 (foundation2) =>
% 132.32/22.87 ((
% 132.32/22.87 (notinself) =>
% 132.32/22.87 ((
% 132.32/22.87 (notinself2) =>
% 132.32/22.87 ((
% 132.32/22.87 (omegaSp) =>
% 132.32/22.87 ((
% 132.32/22.87 (omegaSclos) =>
% 132.32/22.87 ((
% 132.32/22.87 (peano0notS) =>
% 132.32/22.87 ((
% 132.32/22.87 (peanoSinj) =>
% 132.32/22.87 ((
% 132.32/22.87 (transitivesetOp1) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintTransitive) =>
% 132.32/22.87 ((
% 132.32/22.87 (transitivesetOp2) =>
% 132.32/22.87 ((
% 132.32/22.87 (setunionTransitive) =>
% 132.32/22.87 ((
% 132.32/22.87 (ordinalMinLem1) =>
% 132.32/22.87 ((
% 132.32/22.87 (ordinalTransSet) =>
% 132.32/22.87 ((
% 132.32/22.87 (ordinalTransSet1) =>
% 132.32/22.87 ((
% 132.32/22.87 (setunionOrdinalLem1) =>
% 132.32/22.87 (ordinal @
% 132.32/22.87 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.32/22.87 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl637])).
% 132.32/22.87 thf(zip_derived_cl664, plain,
% 132.32/22.87 (~ (((descr__Cong) =>
% 132.32/22.87 (((dsetconstr__Cong) =>
% 132.32/22.87 (((subsetI1) =>
% 132.32/22.87 (((eqimpsubset2) =>
% 132.32/22.87 (((eqimpsubset1) =>
% 132.32/22.87 (((subsetI2) =>
% 132.32/22.87 (((emptysetsubset) =>
% 132.32/22.87 (((subsetE) =>
% 132.32/22.87 (((subsetE2) =>
% 132.32/22.87 (((notsubsetI) =>
% 132.32/22.87 (((notequalI1) =>
% 132.32/22.87 (((notequalI2) =>
% 132.32/22.87 (((subsetRefl) =>
% 132.32/22.87 (((subsetTrans) =>
% 132.32/22.87 (((setadjoinSub) =>
% 132.32/22.87 (((setadjoinSub2) =>
% 132.32/22.87 (((subset2powerset) =>
% 132.32/22.87 (((setextsub) =>
% 132.32/22.87 (((subsetemptysetimpeq) =>
% 132.32/22.87 (((powersetI1) =>
% 132.32/22.87 (((powersetE1) =>
% 132.32/22.87 (((inPowerset) =>
% 132.32/22.87 (((powersetsubset) =>
% 132.32/22.87 (((sepInPowerset) =>
% 132.32/22.87 (((sepSubset) =>
% 132.32/22.87 (((binunionIL) =>
% 132.32/22.87 (((upairset2IR) =>
% 132.32/22.87 (((binunionIR) =>
% 132.32/22.87 (((binunionEcases) =>
% 132.32/22.87 (((binunionE) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionLsub) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionRsub) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectI) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectSubset5) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectEL) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectLsub) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectSubset2) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectSubset3) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectER) =>
% 132.32/22.87 ((
% 132.32/22.87 (disjointsetsI1) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectRsub) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectSubset4) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectSubset1) =>
% 132.32/22.87 ((
% 132.32/22.87 (bs114d) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusI) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusEL) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusER) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusSubset2) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusERneg) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusELneg) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusILneg) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusIRneg) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusLsub) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusSubset1) =>
% 132.32/22.87 ((
% 132.32/22.87 (symdiffE) =>
% 132.32/22.87 ((
% 132.32/22.87 (symdiffI1) =>
% 132.32/22.87 ((
% 132.32/22.87 (symdiffI2) =>
% 132.32/22.87 ((
% 132.32/22.87 (symdiffIneg1) =>
% 132.32/22.87 ((
% 132.32/22.87 (symdiffIneg2) =>
% 132.32/22.87 ((
% 132.32/22.87 (secondinupair) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairIL) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairIR) =>
% 132.32/22.87 ((
% 132.32/22.87 (kpairiskpair) =>
% 132.32/22.87 ((
% 132.32/22.87 (kpairp) =>
% 132.32/22.87 ((
% 132.32/22.87 (singletonsubset) =>
% 132.32/22.87 ((
% 132.32/22.87 (singletoninpowerset) =>
% 132.32/22.87 ((
% 132.32/22.87 (singletoninpowunion) =>
% 132.32/22.87 ((
% 132.32/22.87 (upairset2E) =>
% 132.32/22.87 ((
% 132.32/22.87 (upairsubunion) =>
% 132.32/22.87 ((
% 132.32/22.87 (upairinpowunion) =>
% 132.32/22.87 ((
% 132.32/22.87 (ubforcartprodlem1) =>
% 132.32/22.87 ((
% 132.32/22.87 (ubforcartprodlem2) =>
% 132.32/22.87 ((
% 132.32/22.87 (ubforcartprodlem3) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodpairin) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodmempair1) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodmempair) =>
% 132.32/22.87 ((
% 132.32/22.87 (setunionE2) =>
% 132.32/22.87 ((
% 132.32/22.87 (setunionsingleton1) =>
% 132.32/22.87 ((
% 132.32/22.87 (setunionsingleton2) =>
% 132.32/22.87 ((
% 132.32/22.87 (setunionsingleton) =>
% 132.32/22.87 ((
% 132.32/22.87 (singletonprop) =>
% 132.32/22.87 ((
% 132.32/22.87 (ex1E1) =>
% 132.32/22.87 ((
% 132.32/22.87 (ex1I) =>
% 132.32/22.87 ((
% 132.32/22.87 (ex1I2) =>
% 132.32/22.87 ((
% 132.32/22.87 (singletonsuniq) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairinjL1) =>
% 132.32/22.87 ((
% 132.32/22.87 (kfstsingleton) =>
% 132.32/22.87 ((
% 132.32/22.87 (theprop) =>
% 132.32/22.87 ((
% 132.32/22.87 (kfstpairEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodfstin) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairinjL2) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairinjL) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairinjR11) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairinjR12) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairinjR1) =>
% 132.32/22.87 ((
% 132.32/22.87 (upairequniteq) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairinjR2) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairinjR) =>
% 132.32/22.87 ((
% 132.32/22.87 (ksndsingleton) =>
% 132.32/22.87 ((
% 132.32/22.87 (ksndpairEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (kpairsurjEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodsndin) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodpairmemEL) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodpairmemER) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodmempaircEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodfstpairEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodsndpairEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodpairsurjEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (dpsetconstrI) =>
% 132.32/22.87 ((
% 132.32/22.87 (dpsetconstrSub) =>
% 132.32/22.87 ((
% 132.32/22.87 (setOfPairsIsBReln) =>
% 132.32/22.87 ((
% 132.32/22.87 (dpsetconstrERa) =>
% 132.32/22.87 ((
% 132.32/22.87 (dpsetconstrEL1) =>
% 132.32/22.87 ((
% 132.32/22.87 (dpsetconstrEL2) =>
% 132.32/22.87 ((
% 132.32/22.87 (dpsetconstrER) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcImageSingleton) =>
% 132.32/22.87 ((
% 132.32/22.87 (apProp) =>
% 132.32/22.87 ((
% 132.32/22.87 (app) =>
% 132.32/22.87 ((
% 132.32/22.87 (infuncsetfunc) =>
% 132.32/22.87 ((
% 132.32/22.87 (ap2p) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcinfuncset) =>
% 132.32/22.87 ((
% 132.32/22.87 (lamProp) =>
% 132.32/22.87 ((
% 132.32/22.87 (lamp) =>
% 132.32/22.87 ((
% 132.32/22.87 (lam2p) =>
% 132.32/22.87 ((
% 132.32/22.87 (brelnall1) =>
% 132.32/22.87 ((
% 132.32/22.87 (brelnall2) =>
% 132.32/22.87 ((
% 132.32/22.87 (ex1E2) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcGraphProp1) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcGraphProp3) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcGraphProp2) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcextLem) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcGraphProp4) =>
% 132.32/22.87 ((
% 132.32/22.87 (subbreln) =>
% 132.32/22.87 ((
% 132.32/22.87 (eqbreln) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcext) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcext2) =>
% 132.32/22.87 ((
% 132.32/22.87 (ap2apEq1) =>
% 132.32/22.87 ((
% 132.32/22.87 (ap2apEq2) =>
% 132.32/22.87 ((
% 132.32/22.87 (beta1) =>
% 132.32/22.87 ((
% 132.32/22.87 (eta1) =>
% 132.32/22.87 ((
% 132.32/22.87 (lam2lamEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (beta2) =>
% 132.32/22.87 ((
% 132.32/22.87 (eta2) =>
% 132.32/22.87 ((
% 132.32/22.87 (iffalseProp1) =>
% 132.32/22.87 ((
% 132.32/22.87 (iffalseProp2) =>
% 132.32/22.87 ((
% 132.32/22.87 (iftrueProp1) =>
% 132.32/22.87 ((
% 132.32/22.87 (iftrueProp2) =>
% 132.32/22.87 ((
% 132.32/22.87 (ifSingleton) =>
% 132.32/22.87 ((
% 132.32/22.87 (ifp) =>
% 132.32/22.87 ((
% 132.32/22.87 (theeq) =>
% 132.32/22.87 ((
% 132.32/22.87 (iftrue) =>
% 132.32/22.87 ((
% 132.32/22.87 (iffalse) =>
% 132.32/22.87 ((
% 132.32/22.87 (iftrueorfalse) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectT_lem) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionT_lem) =>
% 132.32/22.87 ((
% 132.32/22.87 (powersetT_lem) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusT_lem) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementT_lem) =>
% 132.32/22.87 ((
% 132.32/22.87 (setextT) =>
% 132.32/22.87 ((
% 132.32/22.87 (subsetTI) =>
% 132.32/22.87 ((
% 132.32/22.87 (powersetTI1) =>
% 132.32/22.87 ((
% 132.32/22.87 (powersetTE1) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementTI1) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementTE1) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectTELcontra) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectTERcontra) =>
% 132.32/22.87 ((
% 132.32/22.87 (contrasubsetT) =>
% 132.32/22.87 ((
% 132.32/22.87 (contrasubsetT1) =>
% 132.32/22.87 ((
% 132.32/22.87 (contrasubsetT2) =>
% 132.32/22.87 ((
% 132.32/22.87 (contrasubsetT3) =>
% 132.32/22.87 ((
% 132.32/22.87 (doubleComplementI1) =>
% 132.32/22.87 ((
% 132.32/22.87 (doubleComplementE1) =>
% 132.32/22.87 ((
% 132.32/22.87 (doubleComplementSub1) =>
% 132.32/22.87 ((
% 132.32/22.87 (doubleComplementSub2) =>
% 132.32/22.87 ((
% 132.32/22.87 (doubleComplementEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementTnotintersectT) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementImpComplementIntersect) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementSubsetComplementIntersect) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementInPowersetComplementIntersect) =>
% 132.32/22.87 ((
% 132.32/22.87 (contraSubsetComplement) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementTcontraSubset) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionTILcontra) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionTIRcontra) =>
% 132.32/22.87 ((
% 132.32/22.87 (inIntersectImpInUnion) =>
% 132.32/22.87 ((
% 132.32/22.87 (inIntersectImpInUnion2) =>
% 132.32/22.87 ((
% 132.32/22.87 (inIntersectImpInIntersectUnions) =>
% 132.32/22.87 ((
% 132.32/22.87 (intersectInPowersetIntersectUnions) =>
% 132.32/22.87 ((
% 132.32/22.87 (inComplementUnionImpNotIn1) =>
% 132.32/22.87 ((
% 132.32/22.87 (inComplementUnionImpInComplement1) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionTE) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionTEcontra) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan2a1) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementUnionInPowersetComplement) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan2a2) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan1a) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan1b) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan1) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan2a) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan2b2) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan2b) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan2) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz13rule0) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz13rule1) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz13rule2) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz13rule3) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz13rule4) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz1_1) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz1_2) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz1_3) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz1_4) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz1_5) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1all2) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1SetBreln1) =>
% 132.32/22.87 ((
% 132.32/22.87 (choice2fnsingleton) =>
% 132.32/22.87 ((
% 132.32/22.87 (setOfPairsIsBReln1) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1all1) =>
% 132.32/22.87 ((
% 132.32/22.87 (subbreln1) =>
% 132.32/22.87 ((
% 132.32/22.87 (eqbreln1) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1invprop) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1invI) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1invE) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1compprop) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1compI) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1compE) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1compEex) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1unionprop) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1unionIL) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1unionIR) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1unionI) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1unionE) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1unionEcases) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1unionCommutes) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz2Ex) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz2W) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz2A) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz2B) =>
% 132.32/22.87 ((
% 132.32/22.87 (image1Ex) =>
% 132.32/22.87 ((
% 132.32/22.87 (image1Ex1) =>
% 132.32/22.87 ((
% 132.32/22.87 (image1Equiv) =>
% 132.32/22.87 ((
% 132.32/22.87 (image1E) =>
% 132.32/22.87 ((
% 132.32/22.87 (image1I) =>
% 132.32/22.87 ((
% 132.32/22.87 (injFuncInInjFuncSet) =>
% 132.32/22.87 ((
% 132.32/22.87 (injFuncSetFuncIn) =>
% 132.32/22.87 ((
% 132.32/22.87 (injFuncSetFuncInj) =>
% 132.32/22.87 ((
% 132.32/22.87 (surjFuncSetFuncIn) =>
% 132.32/22.87 ((
% 132.32/22.87 (surjFuncSetFuncSurj) =>
% 132.32/22.87 ((
% 132.32/22.87 (leftInvIsSurj) =>
% 132.32/22.87 ((
% 132.32/22.87 (surjCantorThm) =>
% 132.32/22.87 ((
% 132.32/22.87 (foundation2) =>
% 132.32/22.87 ((
% 132.32/22.87 (notinself) =>
% 132.32/22.87 ((
% 132.32/22.87 (notinself2) =>
% 132.32/22.87 ((
% 132.32/22.87 (omegaSp) =>
% 132.32/22.87 ((
% 132.32/22.87 (omegaSclos) =>
% 132.32/22.87 ((
% 132.32/22.87 (peano0notS) =>
% 132.32/22.87 ((
% 132.32/22.87 (peanoSinj) =>
% 132.32/22.87 ((
% 132.32/22.87 (transitivesetOp1) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintTransitive) =>
% 132.32/22.87 ((
% 132.32/22.87 (transitivesetOp2) =>
% 132.32/22.87 ((
% 132.32/22.87 (setunionTransitive) =>
% 132.32/22.87 ((
% 132.32/22.87 (ordinalMinLem1) =>
% 132.32/22.87 ((
% 132.32/22.87 (ordinalTransSet) =>
% 132.32/22.87 ((
% 132.32/22.87 (ordinalTransSet1) =>
% 132.32/22.87 ((
% 132.32/22.87 (setunionOrdinalLem1) =>
% 132.32/22.87 (ordinal @
% 132.32/22.87 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.32/22.87 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl652])).
% 132.32/22.87 thf(zip_derived_cl681, plain,
% 132.32/22.87 (~ (((dsetconstr__Cong) =>
% 132.32/22.87 (((subsetI1) =>
% 132.32/22.87 (((eqimpsubset2) =>
% 132.32/22.87 (((eqimpsubset1) =>
% 132.32/22.87 (((subsetI2) =>
% 132.32/22.87 (((emptysetsubset) =>
% 132.32/22.87 (((subsetE) =>
% 132.32/22.87 (((subsetE2) =>
% 132.32/22.87 (((notsubsetI) =>
% 132.32/22.87 (((notequalI1) =>
% 132.32/22.87 (((notequalI2) =>
% 132.32/22.87 (((subsetRefl) =>
% 132.32/22.87 (((subsetTrans) =>
% 132.32/22.87 (((setadjoinSub) =>
% 132.32/22.87 (((setadjoinSub2) =>
% 132.32/22.87 (((subset2powerset) =>
% 132.32/22.87 (((setextsub) =>
% 132.32/22.87 (((subsetemptysetimpeq) =>
% 132.32/22.87 (((powersetI1) =>
% 132.32/22.87 (((powersetE1) =>
% 132.32/22.87 (((inPowerset) =>
% 132.32/22.87 (((powersetsubset) =>
% 132.32/22.87 (((sepInPowerset) =>
% 132.32/22.87 (((sepSubset) =>
% 132.32/22.87 (((binunionIL) =>
% 132.32/22.87 (((upairset2IR) =>
% 132.32/22.87 (((binunionIR) =>
% 132.32/22.87 (((binunionEcases) =>
% 132.32/22.87 (((binunionE) =>
% 132.32/22.87 (((binunionLsub) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionRsub) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectI) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectSubset5) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectEL) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectLsub) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectSubset2) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectSubset3) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectER) =>
% 132.32/22.87 ((
% 132.32/22.87 (disjointsetsI1) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectRsub) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectSubset4) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectSubset1) =>
% 132.32/22.87 ((
% 132.32/22.87 (bs114d) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusI) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusEL) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusER) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusSubset2) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusERneg) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusELneg) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusILneg) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusIRneg) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusLsub) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusSubset1) =>
% 132.32/22.87 ((
% 132.32/22.87 (symdiffE) =>
% 132.32/22.87 ((
% 132.32/22.87 (symdiffI1) =>
% 132.32/22.87 ((
% 132.32/22.87 (symdiffI2) =>
% 132.32/22.87 ((
% 132.32/22.87 (symdiffIneg1) =>
% 132.32/22.87 ((
% 132.32/22.87 (symdiffIneg2) =>
% 132.32/22.87 ((
% 132.32/22.87 (secondinupair) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairIL) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairIR) =>
% 132.32/22.87 ((
% 132.32/22.87 (kpairiskpair) =>
% 132.32/22.87 ((
% 132.32/22.87 (kpairp) =>
% 132.32/22.87 ((
% 132.32/22.87 (singletonsubset) =>
% 132.32/22.87 ((
% 132.32/22.87 (singletoninpowerset) =>
% 132.32/22.87 ((
% 132.32/22.87 (singletoninpowunion) =>
% 132.32/22.87 ((
% 132.32/22.87 (upairset2E) =>
% 132.32/22.87 ((
% 132.32/22.87 (upairsubunion) =>
% 132.32/22.87 ((
% 132.32/22.87 (upairinpowunion) =>
% 132.32/22.87 ((
% 132.32/22.87 (ubforcartprodlem1) =>
% 132.32/22.87 ((
% 132.32/22.87 (ubforcartprodlem2) =>
% 132.32/22.87 ((
% 132.32/22.87 (ubforcartprodlem3) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodpairin) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodmempair1) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodmempair) =>
% 132.32/22.87 ((
% 132.32/22.87 (setunionE2) =>
% 132.32/22.87 ((
% 132.32/22.87 (setunionsingleton1) =>
% 132.32/22.87 ((
% 132.32/22.87 (setunionsingleton2) =>
% 132.32/22.87 ((
% 132.32/22.87 (setunionsingleton) =>
% 132.32/22.87 ((
% 132.32/22.87 (singletonprop) =>
% 132.32/22.87 ((
% 132.32/22.87 (ex1E1) =>
% 132.32/22.87 ((
% 132.32/22.87 (ex1I) =>
% 132.32/22.87 ((
% 132.32/22.87 (ex1I2) =>
% 132.32/22.87 ((
% 132.32/22.87 (singletonsuniq) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairinjL1) =>
% 132.32/22.87 ((
% 132.32/22.87 (kfstsingleton) =>
% 132.32/22.87 ((
% 132.32/22.87 (theprop) =>
% 132.32/22.87 ((
% 132.32/22.87 (kfstpairEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodfstin) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairinjL2) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairinjL) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairinjR11) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairinjR12) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairinjR1) =>
% 132.32/22.87 ((
% 132.32/22.87 (upairequniteq) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairinjR2) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairinjR) =>
% 132.32/22.87 ((
% 132.32/22.87 (ksndsingleton) =>
% 132.32/22.87 ((
% 132.32/22.87 (ksndpairEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (kpairsurjEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodsndin) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodpairmemEL) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodpairmemER) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodmempaircEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodfstpairEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodsndpairEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodpairsurjEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (dpsetconstrI) =>
% 132.32/22.87 ((
% 132.32/22.87 (dpsetconstrSub) =>
% 132.32/22.87 ((
% 132.32/22.87 (setOfPairsIsBReln) =>
% 132.32/22.87 ((
% 132.32/22.87 (dpsetconstrERa) =>
% 132.32/22.87 ((
% 132.32/22.87 (dpsetconstrEL1) =>
% 132.32/22.87 ((
% 132.32/22.87 (dpsetconstrEL2) =>
% 132.32/22.87 ((
% 132.32/22.87 (dpsetconstrER) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcImageSingleton) =>
% 132.32/22.87 ((
% 132.32/22.87 (apProp) =>
% 132.32/22.87 ((
% 132.32/22.87 (app) =>
% 132.32/22.87 ((
% 132.32/22.87 (infuncsetfunc) =>
% 132.32/22.87 ((
% 132.32/22.87 (ap2p) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcinfuncset) =>
% 132.32/22.87 ((
% 132.32/22.87 (lamProp) =>
% 132.32/22.87 ((
% 132.32/22.87 (lamp) =>
% 132.32/22.87 ((
% 132.32/22.87 (lam2p) =>
% 132.32/22.87 ((
% 132.32/22.87 (brelnall1) =>
% 132.32/22.87 ((
% 132.32/22.87 (brelnall2) =>
% 132.32/22.87 ((
% 132.32/22.87 (ex1E2) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcGraphProp1) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcGraphProp3) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcGraphProp2) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcextLem) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcGraphProp4) =>
% 132.32/22.87 ((
% 132.32/22.87 (subbreln) =>
% 132.32/22.87 ((
% 132.32/22.87 (eqbreln) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcext) =>
% 132.32/22.87 ((
% 132.32/22.87 (funcext2) =>
% 132.32/22.87 ((
% 132.32/22.87 (ap2apEq1) =>
% 132.32/22.87 ((
% 132.32/22.87 (ap2apEq2) =>
% 132.32/22.87 ((
% 132.32/22.87 (beta1) =>
% 132.32/22.87 ((
% 132.32/22.87 (eta1) =>
% 132.32/22.87 ((
% 132.32/22.87 (lam2lamEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (beta2) =>
% 132.32/22.87 ((
% 132.32/22.87 (eta2) =>
% 132.32/22.87 ((
% 132.32/22.87 (iffalseProp1) =>
% 132.32/22.87 ((
% 132.32/22.87 (iffalseProp2) =>
% 132.32/22.87 ((
% 132.32/22.87 (iftrueProp1) =>
% 132.32/22.87 ((
% 132.32/22.87 (iftrueProp2) =>
% 132.32/22.87 ((
% 132.32/22.87 (ifSingleton) =>
% 132.32/22.87 ((
% 132.32/22.87 (ifp) =>
% 132.32/22.87 ((
% 132.32/22.87 (theeq) =>
% 132.32/22.87 ((
% 132.32/22.87 (iftrue) =>
% 132.32/22.87 ((
% 132.32/22.87 (iffalse) =>
% 132.32/22.87 ((
% 132.32/22.87 (iftrueorfalse) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectT_lem) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionT_lem) =>
% 132.32/22.87 ((
% 132.32/22.87 (powersetT_lem) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusT_lem) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementT_lem) =>
% 132.32/22.87 ((
% 132.32/22.87 (setextT) =>
% 132.32/22.87 ((
% 132.32/22.87 (subsetTI) =>
% 132.32/22.87 ((
% 132.32/22.87 (powersetTI1) =>
% 132.32/22.87 ((
% 132.32/22.87 (powersetTE1) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementTI1) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementTE1) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectTELcontra) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectTERcontra) =>
% 132.32/22.87 ((
% 132.32/22.87 (contrasubsetT) =>
% 132.32/22.87 ((
% 132.32/22.87 (contrasubsetT1) =>
% 132.32/22.87 ((
% 132.32/22.87 (contrasubsetT2) =>
% 132.32/22.87 ((
% 132.32/22.87 (contrasubsetT3) =>
% 132.32/22.87 ((
% 132.32/22.87 (doubleComplementI1) =>
% 132.32/22.87 ((
% 132.32/22.87 (doubleComplementE1) =>
% 132.32/22.87 ((
% 132.32/22.87 (doubleComplementSub1) =>
% 132.32/22.87 ((
% 132.32/22.87 (doubleComplementSub2) =>
% 132.32/22.87 ((
% 132.32/22.87 (doubleComplementEq) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementTnotintersectT) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementImpComplementIntersect) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementSubsetComplementIntersect) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementInPowersetComplementIntersect) =>
% 132.32/22.87 ((
% 132.32/22.87 (contraSubsetComplement) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementTcontraSubset) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionTILcontra) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionTIRcontra) =>
% 132.32/22.87 ((
% 132.32/22.87 (inIntersectImpInUnion) =>
% 132.32/22.87 ((
% 132.32/22.87 (inIntersectImpInUnion2) =>
% 132.32/22.87 ((
% 132.32/22.87 (inIntersectImpInIntersectUnions) =>
% 132.32/22.87 ((
% 132.32/22.87 (intersectInPowersetIntersectUnions) =>
% 132.32/22.87 ((
% 132.32/22.87 (inComplementUnionImpNotIn1) =>
% 132.32/22.87 ((
% 132.32/22.87 (inComplementUnionImpInComplement1) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionTE) =>
% 132.32/22.87 ((
% 132.32/22.87 (binunionTEcontra) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan2a1) =>
% 132.32/22.87 ((
% 132.32/22.87 (complementUnionInPowersetComplement) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan2a2) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan1a) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan1b) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan1) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan2a) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan2b2) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan2b) =>
% 132.32/22.87 ((
% 132.32/22.87 (demorgan2) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz13rule0) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz13rule1) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz13rule2) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz13rule3) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz13rule4) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz1_1) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz1_2) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz1_3) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz1_4) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz1_5) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1all2) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1SetBreln1) =>
% 132.32/22.87 ((
% 132.32/22.87 (choice2fnsingleton) =>
% 132.32/22.87 ((
% 132.32/22.87 (setOfPairsIsBReln1) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1all1) =>
% 132.32/22.87 ((
% 132.32/22.87 (subbreln1) =>
% 132.32/22.87 ((
% 132.32/22.87 (eqbreln1) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1invprop) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1invI) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1invE) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1compprop) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1compI) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1compE) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1compEex) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1unionprop) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1unionIL) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1unionIR) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1unionI) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1unionE) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1unionEcases) =>
% 132.32/22.87 ((
% 132.32/22.87 (breln1unionCommutes) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz2Ex) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz2W) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz2A) =>
% 132.32/22.87 ((
% 132.32/22.87 (woz2B) =>
% 132.32/22.87 ((
% 132.32/22.87 (image1Ex) =>
% 132.32/22.87 ((
% 132.32/22.87 (image1Ex1) =>
% 132.32/22.87 ((
% 132.32/22.87 (image1Equiv) =>
% 132.32/22.87 ((
% 132.32/22.87 (image1E) =>
% 132.32/22.87 ((
% 132.32/22.87 (image1I) =>
% 132.32/22.87 ((
% 132.32/22.87 (injFuncInInjFuncSet) =>
% 132.32/22.87 ((
% 132.32/22.87 (injFuncSetFuncIn) =>
% 132.32/22.87 ((
% 132.32/22.87 (injFuncSetFuncInj) =>
% 132.32/22.87 ((
% 132.32/22.87 (surjFuncSetFuncIn) =>
% 132.32/22.87 ((
% 132.32/22.87 (surjFuncSetFuncSurj) =>
% 132.32/22.87 ((
% 132.32/22.87 (leftInvIsSurj) =>
% 132.32/22.87 ((
% 132.32/22.87 (surjCantorThm) =>
% 132.32/22.87 ((
% 132.32/22.87 (foundation2) =>
% 132.32/22.87 ((
% 132.32/22.87 (notinself) =>
% 132.32/22.87 ((
% 132.32/22.87 (notinself2) =>
% 132.32/22.87 ((
% 132.32/22.87 (omegaSp) =>
% 132.32/22.87 ((
% 132.32/22.87 (omegaSclos) =>
% 132.32/22.87 ((
% 132.32/22.87 (peano0notS) =>
% 132.32/22.87 ((
% 132.32/22.87 (peanoSinj) =>
% 132.32/22.87 ((
% 132.32/22.87 (transitivesetOp1) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintTransitive) =>
% 132.32/22.87 ((
% 132.32/22.87 (transitivesetOp2) =>
% 132.32/22.87 ((
% 132.32/22.87 (setunionTransitive) =>
% 132.32/22.87 ((
% 132.32/22.87 (ordinalMinLem1) =>
% 132.32/22.87 ((
% 132.32/22.87 (ordinalTransSet) =>
% 132.32/22.87 ((
% 132.32/22.87 (ordinalTransSet1) =>
% 132.32/22.87 ((
% 132.32/22.87 (setunionOrdinalLem1) =>
% 132.32/22.87 (ordinal @
% 132.32/22.87 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.32/22.87 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl664])).
% 132.32/22.87 thf(zip_derived_cl698, plain,
% 132.32/22.87 (~ (((subsetI1) =>
% 132.32/22.87 (((eqimpsubset2) =>
% 132.32/22.87 (((eqimpsubset1) =>
% 132.32/22.87 (((subsetI2) =>
% 132.32/22.87 (((emptysetsubset) =>
% 132.32/22.87 (((subsetE) =>
% 132.32/22.87 (((subsetE2) =>
% 132.32/22.87 (((notsubsetI) =>
% 132.32/22.87 (((notequalI1) =>
% 132.32/22.87 (((notequalI2) =>
% 132.32/22.87 (((subsetRefl) =>
% 132.32/22.87 (((subsetTrans) =>
% 132.32/22.87 (((setadjoinSub) =>
% 132.32/22.87 (((setadjoinSub2) =>
% 132.32/22.87 (((subset2powerset) =>
% 132.32/22.87 (((setextsub) =>
% 132.32/22.87 (((subsetemptysetimpeq) =>
% 132.32/22.87 (((powersetI1) =>
% 132.32/22.87 (((powersetE1) =>
% 132.32/22.87 (((inPowerset) =>
% 132.32/22.87 (((powersetsubset) =>
% 132.32/22.87 (((sepInPowerset) =>
% 132.32/22.87 (((sepSubset) =>
% 132.32/22.87 (((binunionIL) =>
% 132.32/22.87 (((upairset2IR) =>
% 132.32/22.87 (((binunionIR) =>
% 132.32/22.87 (((binunionEcases) =>
% 132.32/22.87 (((binunionE) =>
% 132.32/22.87 (((binunionLsub) =>
% 132.32/22.87 (((binunionRsub) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectI) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectSubset5) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectEL) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectLsub) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectSubset2) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectSubset3) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectER) =>
% 132.32/22.87 ((
% 132.32/22.87 (disjointsetsI1) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectRsub) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectSubset4) =>
% 132.32/22.87 ((
% 132.32/22.87 (binintersectSubset1) =>
% 132.32/22.87 ((
% 132.32/22.87 (bs114d) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusI) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusEL) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusER) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusSubset2) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusERneg) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusELneg) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusILneg) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusIRneg) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusLsub) =>
% 132.32/22.87 ((
% 132.32/22.87 (setminusSubset1) =>
% 132.32/22.87 ((
% 132.32/22.87 (symdiffE) =>
% 132.32/22.87 ((
% 132.32/22.87 (symdiffI1) =>
% 132.32/22.87 ((
% 132.32/22.87 (symdiffI2) =>
% 132.32/22.87 ((
% 132.32/22.87 (symdiffIneg1) =>
% 132.32/22.87 ((
% 132.32/22.87 (symdiffIneg2) =>
% 132.32/22.87 ((
% 132.32/22.87 (secondinupair) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairIL) =>
% 132.32/22.87 ((
% 132.32/22.87 (setukpairIR) =>
% 132.32/22.87 ((
% 132.32/22.87 (kpairiskpair) =>
% 132.32/22.87 ((
% 132.32/22.87 (kpairp) =>
% 132.32/22.87 ((
% 132.32/22.87 (singletonsubset) =>
% 132.32/22.87 ((
% 132.32/22.87 (singletoninpowerset) =>
% 132.32/22.87 ((
% 132.32/22.87 (singletoninpowunion) =>
% 132.32/22.87 ((
% 132.32/22.87 (upairset2E) =>
% 132.32/22.87 ((
% 132.32/22.87 (upairsubunion) =>
% 132.32/22.87 ((
% 132.32/22.87 (upairinpowunion) =>
% 132.32/22.87 ((
% 132.32/22.87 (ubforcartprodlem1) =>
% 132.32/22.87 ((
% 132.32/22.87 (ubforcartprodlem2) =>
% 132.32/22.87 ((
% 132.32/22.87 (ubforcartprodlem3) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodpairin) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodmempair1) =>
% 132.32/22.87 ((
% 132.32/22.87 (cartprodmempair) =>
% 132.32/22.88 ((
% 132.32/22.88 (setunionE2) =>
% 132.32/22.88 ((
% 132.32/22.88 (setunionsingleton1) =>
% 132.32/22.88 ((
% 132.32/22.88 (setunionsingleton2) =>
% 132.32/22.88 ((
% 132.32/22.88 (setunionsingleton) =>
% 132.32/22.88 ((
% 132.32/22.88 (singletonprop) =>
% 132.32/22.88 ((
% 132.32/22.88 (ex1E1) =>
% 132.32/22.88 ((
% 132.32/22.88 (ex1I) =>
% 132.32/22.88 ((
% 132.32/22.88 (ex1I2) =>
% 132.32/22.88 ((
% 132.32/22.88 (singletonsuniq) =>
% 132.32/22.88 ((
% 132.32/22.88 (setukpairinjL1) =>
% 132.32/22.88 ((
% 132.32/22.88 (kfstsingleton) =>
% 132.32/22.88 ((
% 132.32/22.88 (theprop) =>
% 132.32/22.88 ((
% 132.32/22.88 (kfstpairEq) =>
% 132.32/22.88 ((
% 132.32/22.88 (cartprodfstin) =>
% 132.32/22.88 ((
% 132.32/22.88 (setukpairinjL2) =>
% 132.32/22.88 ((
% 132.32/22.88 (setukpairinjL) =>
% 132.32/22.88 ((
% 132.32/22.88 (setukpairinjR11) =>
% 132.32/22.88 ((
% 132.32/22.88 (setukpairinjR12) =>
% 132.32/22.88 ((
% 132.32/22.88 (setukpairinjR1) =>
% 132.32/22.88 ((
% 132.32/22.88 (upairequniteq) =>
% 132.32/22.88 ((
% 132.32/22.88 (setukpairinjR2) =>
% 132.32/22.88 ((
% 132.32/22.88 (setukpairinjR) =>
% 132.32/22.88 ((
% 132.32/22.88 (ksndsingleton) =>
% 132.32/22.88 ((
% 132.32/22.88 (ksndpairEq) =>
% 132.32/22.88 ((
% 132.32/22.88 (kpairsurjEq) =>
% 132.32/22.88 ((
% 132.32/22.88 (cartprodsndin) =>
% 132.32/22.88 ((
% 132.32/22.88 (cartprodpairmemEL) =>
% 132.32/22.88 ((
% 132.32/22.88 (cartprodpairmemER) =>
% 132.32/22.88 ((
% 132.32/22.88 (cartprodmempaircEq) =>
% 132.32/22.88 ((
% 132.32/22.88 (cartprodfstpairEq) =>
% 132.32/22.88 ((
% 132.32/22.88 (cartprodsndpairEq) =>
% 132.32/22.88 ((
% 132.32/22.88 (cartprodpairsurjEq) =>
% 132.32/22.88 ((
% 132.32/22.88 (dpsetconstrI) =>
% 132.32/22.88 ((
% 132.32/22.88 (dpsetconstrSub) =>
% 132.32/22.88 ((
% 132.32/22.88 (setOfPairsIsBReln) =>
% 132.32/22.88 ((
% 132.32/22.88 (dpsetconstrERa) =>
% 132.32/22.88 ((
% 132.32/22.88 (dpsetconstrEL1) =>
% 132.32/22.88 ((
% 132.32/22.88 (dpsetconstrEL2) =>
% 132.32/22.88 ((
% 132.32/22.88 (dpsetconstrER) =>
% 132.32/22.88 ((
% 132.32/22.88 (funcImageSingleton) =>
% 132.32/22.88 ((
% 132.32/22.88 (apProp) =>
% 132.32/22.88 ((
% 132.32/22.88 (app) =>
% 132.32/22.88 ((
% 132.32/22.88 (infuncsetfunc) =>
% 132.32/22.88 ((
% 132.32/22.88 (ap2p) =>
% 132.32/22.88 ((
% 132.32/22.88 (funcinfuncset) =>
% 132.32/22.88 ((
% 132.32/22.88 (lamProp) =>
% 132.32/22.88 ((
% 132.32/22.88 (lamp) =>
% 132.32/22.88 ((
% 132.32/22.88 (lam2p) =>
% 132.32/22.88 ((
% 132.32/22.88 (brelnall1) =>
% 132.32/22.88 ((
% 132.32/22.88 (brelnall2) =>
% 132.32/22.88 ((
% 132.32/22.88 (ex1E2) =>
% 132.32/22.88 ((
% 132.32/22.88 (funcGraphProp1) =>
% 132.32/22.88 ((
% 132.32/22.88 (funcGraphProp3) =>
% 132.32/22.88 ((
% 132.32/22.88 (funcGraphProp2) =>
% 132.32/22.88 ((
% 132.32/22.88 (funcextLem) =>
% 132.32/22.88 ((
% 132.32/22.88 (funcGraphProp4) =>
% 132.32/22.88 ((
% 132.32/22.88 (subbreln) =>
% 132.32/22.88 ((
% 132.32/22.88 (eqbreln) =>
% 132.32/22.88 ((
% 132.32/22.88 (funcext) =>
% 132.32/22.88 ((
% 132.32/22.88 (funcext2) =>
% 132.32/22.88 ((
% 132.32/22.88 (ap2apEq1) =>
% 132.32/22.88 ((
% 132.32/22.88 (ap2apEq2) =>
% 132.32/22.88 ((
% 132.32/22.88 (beta1) =>
% 132.32/22.88 ((
% 132.32/22.88 (eta1) =>
% 132.32/22.88 ((
% 132.32/22.88 (lam2lamEq) =>
% 132.32/22.88 ((
% 132.32/22.88 (beta2) =>
% 132.32/22.88 ((
% 132.32/22.88 (eta2) =>
% 132.32/22.88 ((
% 132.32/22.88 (iffalseProp1) =>
% 132.32/22.88 ((
% 132.32/22.88 (iffalseProp2) =>
% 132.32/22.88 ((
% 132.32/22.88 (iftrueProp1) =>
% 132.32/22.88 ((
% 132.32/22.88 (iftrueProp2) =>
% 132.32/22.88 ((
% 132.32/22.88 (ifSingleton) =>
% 132.32/22.88 ((
% 132.32/22.88 (ifp) =>
% 132.32/22.88 ((
% 132.32/22.88 (theeq) =>
% 132.32/22.88 ((
% 132.32/22.88 (iftrue) =>
% 132.32/22.88 ((
% 132.32/22.88 (iffalse) =>
% 132.32/22.88 ((
% 132.32/22.88 (iftrueorfalse) =>
% 132.32/22.88 ((
% 132.32/22.88 (binintersectT_lem) =>
% 132.32/22.88 ((
% 132.32/22.88 (binunionT_lem) =>
% 132.32/22.88 ((
% 132.32/22.88 (powersetT_lem) =>
% 132.32/22.88 ((
% 132.32/22.88 (setminusT_lem) =>
% 132.32/22.88 ((
% 132.32/22.88 (complementT_lem) =>
% 132.32/22.88 ((
% 132.32/22.88 (setextT) =>
% 132.32/22.88 ((
% 132.32/22.88 (subsetTI) =>
% 132.32/22.88 ((
% 132.32/22.88 (powersetTI1) =>
% 132.32/22.88 ((
% 132.32/22.88 (powersetTE1) =>
% 132.32/22.88 ((
% 132.32/22.88 (complementTI1) =>
% 132.32/22.88 ((
% 132.32/22.88 (complementTE1) =>
% 132.32/22.88 ((
% 132.32/22.88 (binintersectTELcontra) =>
% 132.32/22.88 ((
% 132.32/22.88 (binintersectTERcontra) =>
% 132.32/22.88 ((
% 132.32/22.88 (contrasubsetT) =>
% 132.32/22.88 ((
% 132.32/22.88 (contrasubsetT1) =>
% 132.32/22.88 ((
% 132.32/22.88 (contrasubsetT2) =>
% 132.32/22.88 ((
% 132.32/22.88 (contrasubsetT3) =>
% 132.32/22.88 ((
% 132.32/22.88 (doubleComplementI1) =>
% 132.32/22.88 ((
% 132.32/22.88 (doubleComplementE1) =>
% 132.32/22.88 ((
% 132.32/22.88 (doubleComplementSub1) =>
% 132.32/22.88 ((
% 132.32/22.88 (doubleComplementSub2) =>
% 132.32/22.88 ((
% 132.32/22.88 (doubleComplementEq) =>
% 132.32/22.88 ((
% 132.32/22.88 (complementTnotintersectT) =>
% 132.32/22.88 ((
% 132.32/22.88 (complementImpComplementIntersect) =>
% 132.32/22.88 ((
% 132.32/22.88 (complementSubsetComplementIntersect) =>
% 132.32/22.88 ((
% 132.32/22.88 (complementInPowersetComplementIntersect) =>
% 132.32/22.88 ((
% 132.32/22.88 (contraSubsetComplement) =>
% 132.32/22.88 ((
% 132.32/22.88 (complementTcontraSubset) =>
% 132.32/22.88 ((
% 132.32/22.88 (binunionTILcontra) =>
% 132.32/22.88 ((
% 132.32/22.88 (binunionTIRcontra) =>
% 132.32/22.88 ((
% 132.32/22.88 (inIntersectImpInUnion) =>
% 132.32/22.88 ((
% 132.32/22.88 (inIntersectImpInUnion2) =>
% 132.32/22.88 ((
% 132.32/22.88 (inIntersectImpInIntersectUnions) =>
% 132.32/22.88 ((
% 132.32/22.88 (intersectInPowersetIntersectUnions) =>
% 132.32/22.88 ((
% 132.32/22.88 (inComplementUnionImpNotIn1) =>
% 132.32/22.88 ((
% 132.32/22.88 (inComplementUnionImpInComplement1) =>
% 132.32/22.88 ((
% 132.32/22.88 (binunionTE) =>
% 132.32/22.88 ((
% 132.32/22.88 (binunionTEcontra) =>
% 132.32/22.88 ((
% 132.32/22.88 (demorgan2a1) =>
% 132.32/22.88 ((
% 132.32/22.88 (complementUnionInPowersetComplement) =>
% 132.32/22.88 ((
% 132.32/22.88 (demorgan2a2) =>
% 132.32/22.88 ((
% 132.32/22.88 (demorgan1a) =>
% 132.32/22.88 ((
% 132.32/22.88 (demorgan1b) =>
% 132.32/22.88 ((
% 132.32/22.88 (demorgan1) =>
% 132.32/22.88 ((
% 132.32/22.88 (demorgan2a) =>
% 132.32/22.88 ((
% 132.32/22.88 (demorgan2b2) =>
% 132.32/22.88 ((
% 132.32/22.88 (demorgan2b) =>
% 132.32/22.88 ((
% 132.32/22.88 (demorgan2) =>
% 132.32/22.88 ((
% 132.32/22.88 (woz13rule0) =>
% 132.32/22.88 ((
% 132.32/22.88 (woz13rule1) =>
% 132.32/22.88 ((
% 132.32/22.88 (woz13rule2) =>
% 132.32/22.88 ((
% 132.32/22.88 (woz13rule3) =>
% 132.32/22.88 ((
% 132.32/22.88 (woz13rule4) =>
% 132.32/22.88 ((
% 132.32/22.88 (woz1_1) =>
% 132.32/22.88 ((
% 132.32/22.88 (woz1_2) =>
% 132.32/22.88 ((
% 132.32/22.88 (woz1_3) =>
% 132.32/22.88 ((
% 132.32/22.88 (woz1_4) =>
% 132.32/22.88 ((
% 132.32/22.88 (woz1_5) =>
% 132.32/22.88 ((
% 132.32/22.88 (breln1all2) =>
% 132.32/22.88 ((
% 132.32/22.88 (breln1SetBreln1) =>
% 132.32/22.88 ((
% 132.32/22.88 (choice2fnsingleton) =>
% 132.32/22.88 ((
% 132.32/22.88 (setOfPairsIsBReln1) =>
% 132.32/22.88 ((
% 132.32/22.88 (breln1all1) =>
% 132.32/22.88 ((
% 132.32/22.88 (subbreln1) =>
% 132.32/22.88 ((
% 132.32/22.88 (eqbreln1) =>
% 132.32/22.88 ((
% 132.32/22.88 (breln1invprop) =>
% 132.32/22.88 ((
% 132.32/22.88 (breln1invI) =>
% 132.32/22.88 ((
% 132.32/22.88 (breln1invE) =>
% 132.32/22.88 ((
% 132.32/22.88 (breln1compprop) =>
% 132.32/22.88 ((
% 132.32/22.88 (breln1compI) =>
% 132.32/22.88 ((
% 132.32/22.88 (breln1compE) =>
% 132.32/22.88 ((
% 132.32/22.88 (breln1compEex) =>
% 132.32/22.88 ((
% 132.32/22.88 (breln1unionprop) =>
% 132.32/22.88 ((
% 132.32/22.88 (breln1unionIL) =>
% 132.32/22.88 ((
% 132.32/22.88 (breln1unionIR) =>
% 132.32/22.88 ((
% 132.32/22.88 (breln1unionI) =>
% 132.32/22.88 ((
% 132.32/22.88 (breln1unionE) =>
% 132.32/22.88 ((
% 132.32/22.88 (breln1unionEcases) =>
% 132.32/22.88 ((
% 132.32/22.88 (breln1unionCommutes) =>
% 132.32/22.88 ((
% 132.32/22.88 (woz2Ex) =>
% 132.32/22.88 ((
% 132.32/22.88 (woz2W) =>
% 132.32/22.88 ((
% 132.32/22.88 (woz2A) =>
% 132.32/22.88 ((
% 132.32/22.88 (woz2B) =>
% 132.32/22.88 ((
% 132.32/22.88 (image1Ex) =>
% 132.32/22.88 ((
% 132.32/22.88 (image1Ex1) =>
% 132.32/22.88 ((
% 132.32/22.88 (image1Equiv) =>
% 132.32/22.88 ((
% 132.32/22.88 (image1E) =>
% 132.32/22.88 ((
% 132.32/22.88 (image1I) =>
% 132.32/22.88 ((
% 132.32/22.88 (injFuncInInjFuncSet) =>
% 132.32/22.88 ((
% 132.32/22.88 (injFuncSetFuncIn) =>
% 132.32/22.88 ((
% 132.32/22.88 (injFuncSetFuncInj) =>
% 132.32/22.88 ((
% 132.32/22.88 (surjFuncSetFuncIn) =>
% 132.32/22.88 ((
% 132.32/22.88 (surjFuncSetFuncSurj) =>
% 132.32/22.88 ((
% 132.32/22.88 (leftInvIsSurj) =>
% 132.32/22.88 ((
% 132.32/22.88 (surjCantorThm) =>
% 132.32/22.88 ((
% 132.32/22.88 (foundation2) =>
% 132.32/22.88 ((
% 132.32/22.88 (notinself) =>
% 132.32/22.88 ((
% 132.32/22.88 (notinself2) =>
% 132.32/22.88 ((
% 132.32/22.88 (omegaSp) =>
% 132.32/22.88 ((
% 132.32/22.88 (omegaSclos) =>
% 132.32/22.88 ((
% 132.32/22.88 (peano0notS) =>
% 132.32/22.88 ((
% 132.32/22.88 (peanoSinj) =>
% 132.32/22.88 ((
% 132.32/22.88 (transitivesetOp1) =>
% 132.32/22.88 ((
% 132.32/22.88 (binintTransitive) =>
% 132.32/22.88 ((
% 132.32/22.88 (transitivesetOp2) =>
% 132.32/22.88 ((
% 132.32/22.88 (setunionTransitive) =>
% 132.32/22.88 ((
% 132.32/22.88 (ordinalMinLem1) =>
% 132.32/22.88 ((
% 132.32/22.88 (ordinalTransSet) =>
% 132.32/22.88 ((
% 132.32/22.88 (ordinalTransSet1) =>
% 132.32/22.88 ((
% 132.32/22.88 (setunionOrdinalLem1) =>
% 132.32/22.88 (ordinal @
% 132.32/22.88 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.32/22.88 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl681])).
% 132.32/22.88 thf(zip_derived_cl712, plain,
% 132.32/22.88 (~ (((eqimpsubset2) =>
% 132.32/22.88 (((eqimpsubset1) =>
% 132.32/22.88 (((subsetI2) =>
% 132.32/22.88 (((emptysetsubset) =>
% 132.32/22.88 (((subsetE) =>
% 132.32/22.88 (((subsetE2) =>
% 132.32/22.88 (((notsubsetI) =>
% 132.32/22.88 (((notequalI1) =>
% 132.32/22.88 (((notequalI2) =>
% 132.32/22.88 (((subsetRefl) =>
% 132.32/22.88 (((subsetTrans) =>
% 132.32/22.88 (((setadjoinSub) =>
% 132.32/22.88 (((setadjoinSub2) =>
% 132.32/22.88 (((subset2powerset) =>
% 132.32/22.88 (((setextsub) =>
% 132.32/22.88 (((subsetemptysetimpeq) =>
% 132.32/22.88 (((powersetI1) =>
% 132.32/22.88 (((powersetE1) =>
% 132.32/22.88 (((inPowerset) =>
% 132.32/22.88 (((powersetsubset) =>
% 132.32/22.88 (((sepInPowerset) =>
% 132.32/22.88 (((sepSubset) =>
% 132.32/22.88 (((binunionIL) =>
% 132.32/22.88 (((upairset2IR) =>
% 132.32/22.88 (((binunionIR) =>
% 132.32/22.88 (((binunionEcases) =>
% 132.32/22.88 (((binunionE) =>
% 132.32/22.88 (((binunionLsub) =>
% 132.32/22.88 (((binunionRsub) =>
% 132.32/22.88 (((binintersectI) =>
% 132.32/22.88 ((
% 132.32/22.88 (binintersectSubset5) =>
% 132.32/22.88 ((
% 132.32/22.88 (binintersectEL) =>
% 132.32/22.88 ((
% 132.32/22.88 (binintersectLsub) =>
% 132.32/22.88 ((
% 132.32/22.88 (binintersectSubset2) =>
% 132.32/22.88 ((
% 132.32/22.88 (binintersectSubset3) =>
% 132.32/22.88 ((
% 132.32/22.88 (binintersectER) =>
% 132.32/22.88 ((
% 132.32/22.88 (disjointsetsI1) =>
% 132.32/22.88 ((
% 132.32/22.88 (binintersectRsub) =>
% 132.32/22.88 ((
% 132.32/22.88 (binintersectSubset4) =>
% 132.32/22.88 ((
% 132.32/22.88 (binintersectSubset1) =>
% 132.32/22.88 ((
% 132.32/22.88 (bs114d) =>
% 132.32/22.88 ((
% 132.32/22.88 (setminusI) =>
% 132.32/22.88 ((
% 132.32/22.88 (setminusEL) =>
% 132.32/22.88 ((
% 132.32/22.88 (setminusER) =>
% 132.32/22.88 ((
% 132.32/22.88 (setminusSubset2) =>
% 132.32/22.88 ((
% 132.32/22.88 (setminusERneg) =>
% 132.32/22.88 ((
% 132.32/22.88 (setminusELneg) =>
% 132.32/22.88 ((
% 132.32/22.88 (setminusILneg) =>
% 132.32/22.88 ((
% 132.32/22.88 (setminusIRneg) =>
% 132.32/22.88 ((
% 132.32/22.88 (setminusLsub) =>
% 132.32/22.88 ((
% 132.32/22.88 (setminusSubset1) =>
% 132.32/22.88 ((
% 132.32/22.88 (symdiffE) =>
% 132.32/22.88 ((
% 132.32/22.88 (symdiffI1) =>
% 132.32/22.88 ((
% 132.32/22.88 (symdiffI2) =>
% 132.32/22.88 ((
% 132.32/22.88 (symdiffIneg1) =>
% 132.32/22.88 ((
% 132.32/22.88 (symdiffIneg2) =>
% 132.32/22.88 ((
% 132.32/22.88 (secondinupair) =>
% 132.32/22.88 ((
% 132.32/22.88 (setukpairIL) =>
% 132.32/22.88 ((
% 132.32/22.88 (setukpairIR) =>
% 132.32/22.88 ((
% 132.32/22.88 (kpairiskpair) =>
% 132.32/22.88 ((
% 132.32/22.88 (kpairp) =>
% 132.32/22.88 ((
% 132.32/22.88 (singletonsubset) =>
% 132.32/22.88 ((
% 132.32/22.88 (singletoninpowerset) =>
% 132.32/22.88 ((
% 132.32/22.88 (singletoninpowunion) =>
% 132.32/22.88 ((
% 132.32/22.88 (upairset2E) =>
% 132.32/22.88 ((
% 132.32/22.88 (upairsubunion) =>
% 132.32/22.88 ((
% 132.32/22.88 (upairinpowunion) =>
% 132.32/22.88 ((
% 132.32/22.88 (ubforcartprodlem1) =>
% 132.32/22.88 ((
% 132.32/22.88 (ubforcartprodlem2) =>
% 132.32/22.88 ((
% 132.32/22.88 (ubforcartprodlem3) =>
% 132.32/22.88 ((
% 132.32/22.88 (cartprodpairin) =>
% 132.32/22.88 ((
% 132.32/22.88 (cartprodmempair1) =>
% 132.32/22.88 ((
% 132.32/22.88 (cartprodmempair) =>
% 132.32/22.88 ((
% 132.32/22.88 (setunionE2) =>
% 132.32/22.88 ((
% 132.32/22.88 (setunionsingleton1) =>
% 132.32/22.88 ((
% 132.32/22.88 (setunionsingleton2) =>
% 132.32/22.88 ((
% 132.32/22.88 (setunionsingleton) =>
% 132.32/22.88 ((
% 132.32/22.88 (singletonprop) =>
% 132.32/22.88 ((
% 132.32/22.88 (ex1E1) =>
% 132.32/22.88 ((
% 132.32/22.88 (ex1I) =>
% 132.32/22.88 ((
% 132.32/22.88 (ex1I2) =>
% 132.32/22.88 ((
% 132.32/22.88 (singletonsuniq) =>
% 132.32/22.88 ((
% 132.32/22.88 (setukpairinjL1) =>
% 132.32/22.88 ((
% 132.32/22.88 (kfstsingleton) =>
% 132.32/22.88 ((
% 132.32/22.88 (theprop) =>
% 132.32/22.88 ((
% 132.32/22.88 (kfstpairEq) =>
% 132.32/22.88 ((
% 132.32/22.88 (cartprodfstin) =>
% 132.32/22.88 ((
% 132.32/22.88 (setukpairinjL2) =>
% 132.32/22.88 ((
% 132.32/22.88 (setukpairinjL) =>
% 132.32/22.88 ((
% 132.32/22.88 (setukpairinjR11) =>
% 132.32/22.88 ((
% 132.32/22.88 (setukpairinjR12) =>
% 132.32/22.88 ((
% 132.32/22.88 (setukpairinjR1) =>
% 132.32/22.88 ((
% 132.32/22.88 (upairequniteq) =>
% 132.32/22.88 ((
% 132.32/22.88 (setukpairinjR2) =>
% 132.32/22.88 ((
% 132.32/22.88 (setukpairinjR) =>
% 132.32/22.88 ((
% 132.32/22.88 (ksndsingleton) =>
% 132.32/22.88 ((
% 132.32/22.88 (ksndpairEq) =>
% 132.32/22.88 ((
% 132.32/22.88 (kpairsurjEq) =>
% 132.32/22.88 ((
% 132.32/22.88 (cartprodsndin) =>
% 132.32/22.88 ((
% 132.32/22.88 (cartprodpairmemEL) =>
% 132.32/22.88 ((
% 132.32/22.88 (cartprodpairmemER) =>
% 132.32/22.88 ((
% 132.32/22.88 (cartprodmempaircEq) =>
% 132.32/22.88 ((
% 132.32/22.88 (cartprodfstpairEq) =>
% 132.32/22.88 ((
% 132.32/22.88 (cartprodsndpairEq) =>
% 132.32/22.88 ((
% 132.32/22.88 (cartprodpairsurjEq) =>
% 132.32/22.88 ((
% 132.32/22.88 (dpsetconstrI) =>
% 132.32/22.88 ((
% 132.32/22.88 (dpsetconstrSub) =>
% 132.32/22.88 ((
% 132.32/22.88 (setOfPairsIsBReln) =>
% 132.32/22.88 ((
% 132.32/22.88 (dpsetconstrERa) =>
% 132.32/22.88 ((
% 132.32/22.88 (dpsetconstrEL1) =>
% 132.32/22.88 ((
% 132.32/22.88 (dpsetconstrEL2) =>
% 132.32/22.88 ((
% 132.32/22.88 (dpsetconstrER) =>
% 132.32/22.88 ((
% 132.32/22.88 (funcImageSingleton) =>
% 132.32/22.88 ((
% 132.32/22.88 (apProp) =>
% 132.32/22.88 ((
% 132.32/22.88 (app) =>
% 132.32/22.88 ((
% 132.32/22.88 (infuncsetfunc) =>
% 132.32/22.88 ((
% 132.32/22.88 (ap2p) =>
% 132.32/22.88 ((
% 132.32/22.88 (funcinfuncset) =>
% 132.32/22.88 ((
% 132.32/22.88 (lamProp) =>
% 132.32/22.88 ((
% 132.32/22.88 (lamp) =>
% 132.32/22.88 ((
% 132.32/22.88 (lam2p) =>
% 132.32/22.88 ((
% 132.32/22.88 (brelnall1) =>
% 132.32/22.88 ((
% 132.32/22.88 (brelnall2) =>
% 132.32/22.88 ((
% 132.32/22.88 (ex1E2) =>
% 132.32/22.88 ((
% 132.32/22.88 (funcGraphProp1) =>
% 132.32/22.88 ((
% 132.32/22.88 (funcGraphProp3) =>
% 132.32/22.88 ((
% 132.32/22.88 (funcGraphProp2) =>
% 132.32/22.88 ((
% 132.32/22.88 (funcextLem) =>
% 132.32/22.88 ((
% 132.32/22.88 (funcGraphProp4) =>
% 132.32/22.88 ((
% 132.32/22.88 (subbreln) =>
% 132.32/22.88 ((
% 132.32/22.88 (eqbreln) =>
% 132.32/22.88 ((
% 132.32/22.88 (funcext) =>
% 132.32/22.88 ((
% 132.32/22.88 (funcext2) =>
% 132.32/22.88 ((
% 132.32/22.88 (ap2apEq1) =>
% 132.32/22.88 ((
% 132.32/22.88 (ap2apEq2) =>
% 132.32/22.88 ((
% 132.32/22.88 (beta1) =>
% 132.32/22.88 ((
% 132.32/22.88 (eta1) =>
% 132.32/22.88 ((
% 132.32/22.88 (lam2lamEq) =>
% 132.32/22.88 ((
% 132.32/22.88 (beta2) =>
% 132.32/22.88 ((
% 132.32/22.88 (eta2) =>
% 132.32/22.88 ((
% 132.32/22.88 (iffalseProp1) =>
% 132.32/22.88 ((
% 132.32/22.88 (iffalseProp2) =>
% 132.32/22.88 ((
% 132.32/22.88 (iftrueProp1) =>
% 132.32/22.88 ((
% 132.32/22.88 (iftrueProp2) =>
% 132.32/22.88 ((
% 132.32/22.88 (ifSingleton) =>
% 132.32/22.88 ((
% 132.32/22.88 (ifp) =>
% 132.32/22.88 ((
% 132.32/22.88 (theeq) =>
% 132.32/22.88 ((
% 132.32/22.88 (iftrue) =>
% 132.32/22.88 ((
% 132.32/22.88 (iffalse) =>
% 132.32/22.88 ((
% 132.32/22.88 (iftrueorfalse) =>
% 132.32/22.88 ((
% 132.32/22.88 (binintersectT_lem) =>
% 132.32/22.88 ((
% 132.32/22.88 (binunionT_lem) =>
% 132.32/22.88 ((
% 132.32/22.88 (powersetT_lem) =>
% 132.32/22.88 ((
% 132.32/22.88 (setminusT_lem) =>
% 132.32/22.88 ((
% 132.32/22.88 (complementT_lem) =>
% 132.32/22.88 ((
% 132.32/22.88 (setextT) =>
% 132.32/22.88 ((
% 132.32/22.88 (subsetTI) =>
% 132.32/22.88 ((
% 132.32/22.88 (powersetTI1) =>
% 132.32/22.88 ((
% 132.32/22.88 (powersetTE1) =>
% 132.32/22.88 ((
% 132.32/22.88 (complementTI1) =>
% 132.32/22.88 ((
% 132.32/22.88 (complementTE1) =>
% 132.32/22.88 ((
% 132.32/22.88 (binintersectTELcontra) =>
% 132.32/22.88 ((
% 132.32/22.88 (binintersectTERcontra) =>
% 132.32/22.88 ((
% 132.32/22.88 (contrasubsetT) =>
% 132.32/22.88 ((
% 132.32/22.88 (contrasubsetT1) =>
% 132.32/22.88 ((
% 132.32/22.88 (contrasubsetT2) =>
% 132.32/22.88 ((
% 132.32/22.88 (contrasubsetT3) =>
% 132.32/22.88 ((
% 132.32/22.88 (doubleComplementI1) =>
% 132.32/22.88 ((
% 132.32/22.88 (doubleComplementE1) =>
% 132.32/22.88 ((
% 132.32/22.88 (doubleComplementSub1) =>
% 132.32/22.88 ((
% 132.32/22.88 (doubleComplementSub2) =>
% 132.32/22.88 ((
% 132.32/22.88 (doubleComplementEq) =>
% 132.32/22.88 ((
% 132.32/22.88 (complementTnotintersectT) =>
% 132.32/22.88 ((
% 132.32/22.88 (complementImpComplementIntersect) =>
% 132.32/22.88 ((
% 132.32/22.88 (complementSubsetComplementIntersect) =>
% 132.32/22.88 ((
% 132.32/22.88 (complementInPowersetComplementIntersect) =>
% 132.32/22.88 ((
% 132.32/22.88 (contraSubsetComplement) =>
% 132.32/22.88 ((
% 132.32/22.88 (complementTcontraSubset) =>
% 132.32/22.88 ((
% 132.32/22.88 (binunionTILcontra) =>
% 132.32/22.88 ((
% 132.32/22.88 (binunionTIRcontra) =>
% 132.32/22.88 ((
% 132.32/22.88 (inIntersectImpInUnion) =>
% 132.32/22.88 ((
% 132.32/22.88 (inIntersectImpInUnion2) =>
% 132.32/22.88 ((
% 132.32/22.88 (inIntersectImpInIntersectUnions) =>
% 132.32/22.88 ((
% 132.32/22.88 (intersectInPowersetIntersectUnions) =>
% 132.32/22.88 ((
% 132.32/22.88 (inComplementUnionImpNotIn1) =>
% 132.32/22.88 ((
% 132.32/22.88 (inComplementUnionImpInComplement1) =>
% 132.32/22.88 ((
% 132.32/22.88 (binunionTE) =>
% 132.32/22.88 ((
% 132.32/22.88 (binunionTEcontra) =>
% 132.32/22.88 ((
% 132.32/22.88 (demorgan2a1) =>
% 132.32/22.88 ((
% 132.32/22.88 (complementUnionInPowersetComplement) =>
% 132.32/22.88 ((
% 132.32/22.88 (demorgan2a2) =>
% 132.32/22.88 ((
% 132.32/22.88 (demorgan1a) =>
% 132.32/22.88 ((
% 132.32/22.88 (demorgan1b) =>
% 132.32/22.88 ((
% 132.32/22.88 (demorgan1) =>
% 132.32/22.88 ((
% 132.32/22.88 (demorgan2a) =>
% 132.32/22.88 ((
% 132.32/22.88 (demorgan2b2) =>
% 132.32/22.88 ((
% 132.32/22.88 (demorgan2b) =>
% 132.32/22.88 ((
% 132.32/22.88 (demorgan2) =>
% 132.32/22.88 ((
% 132.32/22.88 (woz13rule0) =>
% 132.32/22.88 ((
% 132.32/22.88 (woz13rule1) =>
% 132.32/22.88 ((
% 132.32/22.88 (woz13rule2) =>
% 132.32/22.88 ((
% 132.32/22.88 (woz13rule3) =>
% 132.32/22.88 ((
% 132.32/22.88 (woz13rule4) =>
% 132.32/22.88 ((
% 132.32/22.88 (woz1_1) =>
% 132.32/22.88 ((
% 132.32/22.88 (woz1_2) =>
% 132.32/22.88 ((
% 132.32/22.88 (woz1_3) =>
% 132.32/22.88 ((
% 132.32/22.88 (woz1_4) =>
% 132.32/22.88 ((
% 132.32/22.88 (woz1_5) =>
% 132.32/22.88 ((
% 132.32/22.88 (breln1all2) =>
% 132.32/22.88 ((
% 132.32/22.88 (breln1SetBreln1) =>
% 132.32/22.88 ((
% 132.32/22.88 (choice2fnsingleton) =>
% 132.32/22.88 ((
% 132.32/22.88 (setOfPairsIsBReln1) =>
% 132.32/22.88 ((
% 132.32/22.88 (breln1all1) =>
% 132.32/22.88 ((
% 132.32/22.88 (subbreln1) =>
% 132.32/22.88 ((
% 132.32/22.88 (eqbreln1) =>
% 132.32/22.88 ((
% 132.32/22.88 (breln1invprop) =>
% 132.32/22.88 ((
% 132.32/22.88 (breln1invI) =>
% 132.32/22.88 ((
% 132.32/22.88 (breln1invE) =>
% 132.32/22.88 ((
% 132.32/22.88 (breln1compprop) =>
% 132.32/22.88 ((
% 132.32/22.88 (breln1compI) =>
% 132.32/22.88 ((
% 132.32/22.88 (breln1compE) =>
% 132.32/22.88 ((
% 132.32/22.88 (breln1compEex) =>
% 132.32/22.88 ((
% 132.32/22.88 (breln1unionprop) =>
% 132.32/22.88 ((
% 132.32/22.88 (breln1unionIL) =>
% 132.32/22.88 ((
% 132.32/22.88 (breln1unionIR) =>
% 132.32/22.88 ((
% 132.32/22.88 (breln1unionI) =>
% 132.32/22.88 ((
% 132.32/22.88 (breln1unionE) =>
% 132.32/22.88 ((
% 132.32/22.88 (breln1unionEcases) =>
% 132.32/22.88 ((
% 132.32/22.88 (breln1unionCommutes) =>
% 132.32/22.88 ((
% 132.32/22.88 (woz2Ex) =>
% 132.32/22.88 ((
% 132.32/22.88 (woz2W) =>
% 132.32/22.88 ((
% 132.32/22.88 (woz2A) =>
% 132.32/22.88 ((
% 132.32/22.88 (woz2B) =>
% 132.32/22.88 ((
% 132.32/22.88 (image1Ex) =>
% 132.32/22.88 ((
% 132.32/22.88 (image1Ex1) =>
% 132.32/22.88 ((
% 132.32/22.88 (image1Equiv) =>
% 132.32/22.88 ((
% 132.32/22.88 (image1E) =>
% 132.32/22.88 ((
% 132.32/22.88 (image1I) =>
% 132.32/22.88 ((
% 132.32/22.88 (injFuncInInjFuncSet) =>
% 132.32/22.88 ((
% 132.32/22.88 (injFuncSetFuncIn) =>
% 132.32/22.88 ((
% 132.32/22.88 (injFuncSetFuncInj) =>
% 132.32/22.88 ((
% 132.32/22.88 (surjFuncSetFuncIn) =>
% 132.32/22.88 ((
% 132.32/22.88 (surjFuncSetFuncSurj) =>
% 132.32/22.88 ((
% 132.32/22.88 (leftInvIsSurj) =>
% 132.32/22.88 ((
% 132.32/22.88 (surjCantorThm) =>
% 132.32/22.88 ((
% 132.32/22.88 (foundation2) =>
% 132.32/22.88 ((
% 132.32/22.88 (notinself) =>
% 132.32/22.88 ((
% 132.32/22.88 (notinself2) =>
% 132.32/22.88 ((
% 132.32/22.88 (omegaSp) =>
% 132.32/22.88 ((
% 132.32/22.88 (omegaSclos) =>
% 132.32/22.88 ((
% 132.32/22.88 (peano0notS) =>
% 132.32/22.88 ((
% 132.32/22.88 (peanoSinj) =>
% 132.32/22.88 ((
% 132.32/22.88 (transitivesetOp1) =>
% 132.32/22.88 ((
% 132.32/22.88 (binintTransitive) =>
% 132.32/22.88 ((
% 132.32/22.88 (transitivesetOp2) =>
% 132.32/22.88 ((
% 132.32/22.88 (setunionTransitive) =>
% 132.32/22.88 ((
% 132.32/22.88 (ordinalMinLem1) =>
% 132.32/22.88 ((
% 132.32/22.88 (ordinalTransSet) =>
% 132.32/22.88 ((
% 132.32/22.88 (ordinalTransSet1) =>
% 132.32/22.88 ((
% 132.32/22.88 (setunionOrdinalLem1) =>
% 132.32/22.88 (ordinal @
% 132.32/22.88 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.32/22.88 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl698])).
% 132.32/22.88 thf(zip_derived_cl725, plain,
% 132.32/22.88 (~ (((eqimpsubset1) =>
% 132.32/22.88 (((subsetI2) =>
% 132.32/22.88 (((emptysetsubset) =>
% 132.32/22.88 (((subsetE) =>
% 132.32/22.88 (((subsetE2) =>
% 132.32/22.88 (((notsubsetI) =>
% 132.32/22.88 (((notequalI1) =>
% 132.32/22.88 (((notequalI2) =>
% 132.32/22.88 (((subsetRefl) =>
% 132.32/22.88 (((subsetTrans) =>
% 132.32/22.88 (((setadjoinSub) =>
% 132.32/22.88 (((setadjoinSub2) =>
% 132.32/22.88 (((subset2powerset) =>
% 132.32/22.88 (((setextsub) =>
% 132.32/22.88 (((subsetemptysetimpeq) =>
% 132.32/22.88 (((powersetI1) =>
% 132.32/22.88 (((powersetE1) =>
% 132.32/22.88 (((inPowerset) =>
% 132.32/22.88 (((powersetsubset) =>
% 132.32/22.88 (((sepInPowerset) =>
% 132.32/22.88 (((sepSubset) =>
% 132.32/22.88 (((binunionIL) =>
% 132.32/22.88 (((upairset2IR) =>
% 132.32/22.88 (((binunionIR) =>
% 132.32/22.88 (((binunionEcases) =>
% 132.32/22.88 (((binunionE) =>
% 132.32/22.88 (((binunionLsub) =>
% 132.32/22.88 (((binunionRsub) =>
% 132.32/22.88 (((binintersectI) =>
% 132.32/22.88 (((binintersectSubset5) =>
% 132.32/22.88 ((
% 132.32/22.88 (binintersectEL) =>
% 132.32/22.88 ((
% 132.32/22.88 (binintersectLsub) =>
% 132.32/22.88 ((
% 132.32/22.88 (binintersectSubset2) =>
% 132.32/22.88 ((
% 132.32/22.88 (binintersectSubset3) =>
% 132.32/22.88 ((
% 132.32/22.88 (binintersectER) =>
% 132.32/22.88 ((
% 132.32/22.88 (disjointsetsI1) =>
% 132.32/22.88 ((
% 132.32/22.88 (binintersectRsub) =>
% 132.32/22.88 ((
% 132.32/22.88 (binintersectSubset4) =>
% 132.32/22.88 ((
% 132.32/22.88 (binintersectSubset1) =>
% 132.32/22.88 ((
% 132.32/22.88 (bs114d) =>
% 132.32/22.88 ((
% 132.32/22.88 (setminusI) =>
% 132.32/22.88 ((
% 132.32/22.88 (setminusEL) =>
% 132.32/22.88 ((
% 132.32/22.88 (setminusER) =>
% 132.32/22.88 ((
% 132.32/22.88 (setminusSubset2) =>
% 132.32/22.88 ((
% 132.32/22.88 (setminusERneg) =>
% 132.32/22.88 ((
% 132.32/22.88 (setminusELneg) =>
% 132.32/22.88 ((
% 132.32/22.88 (setminusILneg) =>
% 132.32/22.88 ((
% 132.32/22.88 (setminusIRneg) =>
% 132.32/22.88 ((
% 132.32/22.88 (setminusLsub) =>
% 132.32/22.88 ((
% 132.32/22.88 (setminusSubset1) =>
% 132.32/22.88 ((
% 132.32/22.88 (symdiffE) =>
% 132.32/22.88 ((
% 132.32/22.88 (symdiffI1) =>
% 132.32/22.88 ((
% 132.32/22.88 (symdiffI2) =>
% 132.32/22.88 ((
% 132.32/22.88 (symdiffIneg1) =>
% 132.32/22.88 ((
% 132.32/22.88 (symdiffIneg2) =>
% 132.32/22.88 ((
% 132.32/22.88 (secondinupair) =>
% 132.32/22.88 ((
% 132.32/22.88 (setukpairIL) =>
% 132.32/22.88 ((
% 132.32/22.88 (setukpairIR) =>
% 132.32/22.88 ((
% 132.32/22.88 (kpairiskpair) =>
% 132.32/22.88 ((
% 132.32/22.88 (kpairp) =>
% 132.32/22.88 ((
% 132.32/22.88 (singletonsubset) =>
% 132.32/22.88 ((
% 132.32/22.88 (singletoninpowerset) =>
% 132.32/22.88 ((
% 132.32/22.88 (singletoninpowunion) =>
% 132.32/22.88 ((
% 132.32/22.88 (upairset2E) =>
% 132.32/22.88 ((
% 132.32/22.88 (upairsubunion) =>
% 132.32/22.88 ((
% 132.32/22.88 (upairinpowunion) =>
% 132.32/22.88 ((
% 132.32/22.88 (ubforcartprodlem1) =>
% 132.32/22.88 ((
% 132.32/22.88 (ubforcartprodlem2) =>
% 132.32/22.88 ((
% 132.32/22.88 (ubforcartprodlem3) =>
% 132.32/22.88 ((
% 132.32/22.88 (cartprodpairin) =>
% 132.32/22.88 ((
% 132.32/22.88 (cartprodmempair1) =>
% 132.32/22.88 ((
% 132.32/22.88 (cartprodmempair) =>
% 132.32/22.88 ((
% 132.32/22.88 (setunionE2) =>
% 132.32/22.88 ((
% 132.32/22.88 (setunionsingleton1) =>
% 132.32/22.88 ((
% 132.32/22.88 (setunionsingleton2) =>
% 132.32/22.88 ((
% 132.32/22.88 (setunionsingleton) =>
% 132.32/22.88 ((
% 132.32/22.88 (singletonprop) =>
% 132.32/22.88 ((
% 132.32/22.88 (ex1E1) =>
% 132.32/22.88 ((
% 132.32/22.88 (ex1I) =>
% 132.32/22.88 ((
% 132.32/22.88 (ex1I2) =>
% 132.32/22.88 ((
% 132.32/22.88 (singletonsuniq) =>
% 132.32/22.88 ((
% 132.32/22.88 (setukpairinjL1) =>
% 132.32/22.88 ((
% 132.32/22.88 (kfstsingleton) =>
% 132.32/22.88 ((
% 132.32/22.88 (theprop) =>
% 132.32/22.88 ((
% 132.32/22.88 (kfstpairEq) =>
% 132.32/22.88 ((
% 132.32/22.88 (cartprodfstin) =>
% 132.32/22.88 ((
% 132.32/22.88 (setukpairinjL2) =>
% 132.32/22.88 ((
% 132.32/22.88 (setukpairinjL) =>
% 132.32/22.88 ((
% 132.32/22.88 (setukpairinjR11) =>
% 132.32/22.88 ((
% 132.32/22.88 (setukpairinjR12) =>
% 132.32/22.88 ((
% 132.32/22.88 (setukpairinjR1) =>
% 132.32/22.88 ((
% 132.32/22.88 (upairequniteq) =>
% 132.32/22.88 ((
% 132.32/22.88 (setukpairinjR2) =>
% 132.32/22.88 ((
% 132.32/22.88 (setukpairinjR) =>
% 132.32/22.88 ((
% 132.32/22.88 (ksndsingleton) =>
% 132.32/22.88 ((
% 132.32/22.88 (ksndpairEq) =>
% 132.32/22.88 ((
% 132.32/22.88 (kpairsurjEq) =>
% 132.32/22.88 ((
% 132.32/22.88 (cartprodsndin) =>
% 132.32/22.88 ((
% 132.32/22.88 (cartprodpairmemEL) =>
% 132.32/22.88 ((
% 132.32/22.88 (cartprodpairmemER) =>
% 132.32/22.88 ((
% 132.32/22.88 (cartprodmempaircEq) =>
% 132.32/22.88 ((
% 132.32/22.88 (cartprodfstpairEq) =>
% 132.32/22.88 ((
% 132.32/22.88 (cartprodsndpairEq) =>
% 132.32/22.88 ((
% 132.32/22.88 (cartprodpairsurjEq) =>
% 132.32/22.88 ((
% 132.32/22.88 (dpsetconstrI) =>
% 132.32/22.88 ((
% 132.32/22.88 (dpsetconstrSub) =>
% 132.32/22.88 ((
% 132.32/22.88 (setOfPairsIsBReln) =>
% 132.32/22.88 ((
% 132.32/22.88 (dpsetconstrERa) =>
% 132.32/22.88 ((
% 132.32/22.88 (dpsetconstrEL1) =>
% 132.32/22.88 ((
% 132.32/22.88 (dpsetconstrEL2) =>
% 132.32/22.88 ((
% 132.32/22.88 (dpsetconstrER) =>
% 132.32/22.88 ((
% 132.32/22.88 (funcImageSingleton) =>
% 132.32/22.88 ((
% 132.32/22.88 (apProp) =>
% 132.32/22.88 ((
% 132.32/22.88 (app) =>
% 132.32/22.88 ((
% 132.32/22.88 (infuncsetfunc) =>
% 132.32/22.88 ((
% 132.32/22.88 (ap2p) =>
% 132.32/22.88 ((
% 132.32/22.88 (funcinfuncset) =>
% 132.32/22.88 ((
% 132.32/22.88 (lamProp) =>
% 132.32/22.88 ((
% 132.32/22.88 (lamp) =>
% 132.32/22.88 ((
% 132.32/22.88 (lam2p) =>
% 132.32/22.88 ((
% 132.32/22.88 (brelnall1) =>
% 132.32/22.88 ((
% 132.32/22.88 (brelnall2) =>
% 132.32/22.88 ((
% 132.32/22.88 (ex1E2) =>
% 132.32/22.88 ((
% 132.32/22.88 (funcGraphProp1) =>
% 132.32/22.88 ((
% 132.32/22.88 (funcGraphProp3) =>
% 132.32/22.88 ((
% 132.32/22.88 (funcGraphProp2) =>
% 132.32/22.88 ((
% 132.32/22.88 (funcextLem) =>
% 132.32/22.88 ((
% 132.32/22.88 (funcGraphProp4) =>
% 132.32/22.88 ((
% 132.32/22.88 (subbreln) =>
% 132.32/22.88 ((
% 132.32/22.88 (eqbreln) =>
% 132.32/22.88 ((
% 132.32/22.88 (funcext) =>
% 132.32/22.88 ((
% 132.32/22.88 (funcext2) =>
% 132.32/22.88 ((
% 132.32/22.88 (ap2apEq1) =>
% 132.32/22.88 ((
% 132.32/22.88 (ap2apEq2) =>
% 132.32/22.88 ((
% 132.32/22.88 (beta1) =>
% 132.32/22.88 ((
% 132.32/22.88 (eta1) =>
% 132.32/22.88 ((
% 132.32/22.88 (lam2lamEq) =>
% 132.32/22.88 ((
% 132.32/22.88 (beta2) =>
% 132.32/22.88 ((
% 132.32/22.88 (eta2) =>
% 132.32/22.88 ((
% 132.32/22.88 (iffalseProp1) =>
% 132.32/22.88 ((
% 132.32/22.88 (iffalseProp2) =>
% 132.32/22.88 ((
% 132.32/22.88 (iftrueProp1) =>
% 132.32/22.88 ((
% 132.32/22.88 (iftrueProp2) =>
% 132.32/22.88 ((
% 132.32/22.88 (ifSingleton) =>
% 132.32/22.88 ((
% 132.32/22.88 (ifp) =>
% 132.32/22.88 ((
% 132.32/22.88 (theeq) =>
% 132.32/22.88 ((
% 132.32/22.88 (iftrue) =>
% 132.32/22.88 ((
% 132.32/22.88 (iffalse) =>
% 132.32/22.88 ((
% 132.32/22.88 (iftrueorfalse) =>
% 132.32/22.88 ((
% 132.32/22.88 (binintersectT_lem) =>
% 132.32/22.88 ((
% 132.32/22.88 (binunionT_lem) =>
% 132.32/22.88 ((
% 132.32/22.88 (powersetT_lem) =>
% 132.32/22.88 ((
% 132.32/22.88 (setminusT_lem) =>
% 132.32/22.88 ((
% 132.32/22.88 (complementT_lem) =>
% 132.32/22.88 ((
% 132.32/22.88 (setextT) =>
% 132.32/22.88 ((
% 132.32/22.88 (subsetTI) =>
% 132.32/22.88 ((
% 132.32/22.88 (powersetTI1) =>
% 132.32/22.88 ((
% 132.32/22.88 (powersetTE1) =>
% 132.32/22.88 ((
% 132.32/22.88 (complementTI1) =>
% 132.32/22.88 ((
% 132.32/22.88 (complementTE1) =>
% 132.32/22.88 ((
% 132.32/22.88 (binintersectTELcontra) =>
% 132.32/22.88 ((
% 132.32/22.88 (binintersectTERcontra) =>
% 132.32/22.88 ((
% 132.32/22.88 (contrasubsetT) =>
% 132.32/22.88 ((
% 132.32/22.88 (contrasubsetT1) =>
% 132.32/22.88 ((
% 132.32/22.88 (contrasubsetT2) =>
% 132.32/22.88 ((
% 132.32/22.88 (contrasubsetT3) =>
% 132.32/22.88 ((
% 132.32/22.88 (doubleComplementI1) =>
% 132.32/22.88 ((
% 132.32/22.88 (doubleComplementE1) =>
% 132.32/22.88 ((
% 132.32/22.88 (doubleComplementSub1) =>
% 132.32/22.88 ((
% 132.32/22.88 (doubleComplementSub2) =>
% 132.32/22.88 ((
% 132.32/22.88 (doubleComplementEq) =>
% 132.32/22.88 ((
% 132.32/22.88 (complementTnotintersectT) =>
% 132.32/22.88 ((
% 132.32/22.88 (complementImpComplementIntersect) =>
% 132.32/22.88 ((
% 132.32/22.88 (complementSubsetComplementIntersect) =>
% 132.32/22.88 ((
% 132.32/22.88 (complementInPowersetComplementIntersect) =>
% 132.32/22.88 ((
% 132.32/22.88 (contraSubsetComplement) =>
% 132.32/22.88 ((
% 132.32/22.88 (complementTcontraSubset) =>
% 132.32/22.88 ((
% 132.32/22.88 (binunionTILcontra) =>
% 132.32/22.88 ((
% 132.32/22.88 (binunionTIRcontra) =>
% 132.32/22.88 ((
% 132.32/22.88 (inIntersectImpInUnion) =>
% 132.32/22.88 ((
% 132.32/22.88 (inIntersectImpInUnion2) =>
% 132.32/22.88 ((
% 132.32/22.88 (inIntersectImpInIntersectUnions) =>
% 132.32/22.88 ((
% 132.32/22.88 (intersectInPowersetIntersectUnions) =>
% 132.32/22.88 ((
% 132.32/22.88 (inComplementUnionImpNotIn1) =>
% 132.32/22.88 ((
% 132.32/22.88 (inComplementUnionImpInComplement1) =>
% 132.32/22.88 ((
% 132.32/22.88 (binunionTE) =>
% 132.32/22.88 ((
% 132.32/22.88 (binunionTEcontra) =>
% 132.32/22.88 ((
% 132.32/22.88 (demorgan2a1) =>
% 132.32/22.88 ((
% 132.32/22.88 (complementUnionInPowersetComplement) =>
% 132.32/22.88 ((
% 132.32/22.88 (demorgan2a2) =>
% 132.32/22.88 ((
% 132.32/22.88 (demorgan1a) =>
% 132.32/22.88 ((
% 132.32/22.88 (demorgan1b) =>
% 132.32/22.88 ((
% 132.32/22.88 (demorgan1) =>
% 132.32/22.88 ((
% 132.32/22.88 (demorgan2a) =>
% 132.32/22.88 ((
% 132.32/22.88 (demorgan2b2) =>
% 132.32/22.88 ((
% 132.32/22.88 (demorgan2b) =>
% 132.32/22.88 ((
% 132.32/22.88 (demorgan2) =>
% 132.32/22.88 ((
% 132.32/22.88 (woz13rule0) =>
% 132.32/22.88 ((
% 132.32/22.88 (woz13rule1) =>
% 132.32/22.88 ((
% 132.32/22.88 (woz13rule2) =>
% 132.32/22.88 ((
% 132.32/22.88 (woz13rule3) =>
% 132.32/22.88 ((
% 132.32/22.88 (woz13rule4) =>
% 132.32/22.88 ((
% 132.32/22.88 (woz1_1) =>
% 132.32/22.88 ((
% 132.32/22.88 (woz1_2) =>
% 132.32/22.88 ((
% 132.32/22.88 (woz1_3) =>
% 132.32/22.88 ((
% 132.32/22.88 (woz1_4) =>
% 132.32/22.88 ((
% 132.32/22.88 (woz1_5) =>
% 132.32/22.88 ((
% 132.32/22.88 (breln1all2) =>
% 132.32/22.88 ((
% 132.32/22.88 (breln1SetBreln1) =>
% 132.32/22.88 ((
% 132.32/22.88 (choice2fnsingleton) =>
% 132.32/22.88 ((
% 132.32/22.88 (setOfPairsIsBReln1) =>
% 132.32/22.88 ((
% 132.32/22.88 (breln1all1) =>
% 132.32/22.88 ((
% 132.32/22.88 (subbreln1) =>
% 132.32/22.88 ((
% 132.32/22.88 (eqbreln1) =>
% 132.32/22.88 ((
% 132.32/22.88 (breln1invprop) =>
% 132.32/22.88 ((
% 132.32/22.88 (breln1invI) =>
% 132.32/22.88 ((
% 132.32/22.88 (breln1invE) =>
% 132.32/22.88 ((
% 132.32/22.88 (breln1compprop) =>
% 132.32/22.88 ((
% 132.32/22.88 (breln1compI) =>
% 132.32/22.88 ((
% 132.32/22.88 (breln1compE) =>
% 132.32/22.88 ((
% 132.32/22.88 (breln1compEex) =>
% 132.32/22.88 ((
% 132.32/22.88 (breln1unionprop) =>
% 132.32/22.88 ((
% 132.32/22.88 (breln1unionIL) =>
% 132.32/22.88 ((
% 132.32/22.88 (breln1unionIR) =>
% 132.32/22.88 ((
% 132.32/22.88 (breln1unionI) =>
% 132.32/22.88 ((
% 132.32/22.88 (breln1unionE) =>
% 132.32/22.88 ((
% 132.32/22.88 (breln1unionEcases) =>
% 132.32/22.88 ((
% 132.32/22.88 (breln1unionCommutes) =>
% 132.32/22.88 ((
% 132.32/22.88 (woz2Ex) =>
% 132.32/22.88 ((
% 132.32/22.88 (woz2W) =>
% 132.32/22.88 ((
% 132.32/22.88 (woz2A) =>
% 132.32/22.88 ((
% 132.32/22.88 (woz2B) =>
% 132.32/22.88 ((
% 132.32/22.88 (image1Ex) =>
% 132.32/22.88 ((
% 132.32/22.88 (image1Ex1) =>
% 132.32/22.88 ((
% 132.32/22.88 (image1Equiv) =>
% 132.32/22.88 ((
% 132.32/22.88 (image1E) =>
% 132.32/22.88 ((
% 132.32/22.88 (image1I) =>
% 132.32/22.88 ((
% 132.32/22.88 (injFuncInInjFuncSet) =>
% 132.32/22.88 ((
% 132.32/22.88 (injFuncSetFuncIn) =>
% 132.32/22.88 ((
% 132.32/22.88 (injFuncSetFuncInj) =>
% 132.32/22.88 ((
% 132.32/22.88 (surjFuncSetFuncIn) =>
% 132.32/22.88 ((
% 132.32/22.88 (surjFuncSetFuncSurj) =>
% 132.32/22.88 ((
% 132.32/22.88 (leftInvIsSurj) =>
% 132.32/22.88 ((
% 132.32/22.88 (surjCantorThm) =>
% 132.32/22.88 ((
% 132.32/22.89 (foundation2) =>
% 132.32/22.89 ((
% 132.32/22.89 (notinself) =>
% 132.32/22.89 ((
% 132.32/22.89 (notinself2) =>
% 132.32/22.89 ((
% 132.32/22.89 (omegaSp) =>
% 132.32/22.89 ((
% 132.32/22.89 (omegaSclos) =>
% 132.32/22.89 ((
% 132.32/22.89 (peano0notS) =>
% 132.32/22.89 ((
% 132.32/22.89 (peanoSinj) =>
% 132.32/22.89 ((
% 132.32/22.89 (transitivesetOp1) =>
% 132.32/22.89 ((
% 132.32/22.89 (binintTransitive) =>
% 132.32/22.89 ((
% 132.32/22.89 (transitivesetOp2) =>
% 132.32/22.89 ((
% 132.32/22.89 (setunionTransitive) =>
% 132.32/22.89 ((
% 132.32/22.89 (ordinalMinLem1) =>
% 132.32/22.89 ((
% 132.32/22.89 (ordinalTransSet) =>
% 132.32/22.89 ((
% 132.32/22.89 (ordinalTransSet1) =>
% 132.32/22.89 ((
% 132.32/22.89 (setunionOrdinalLem1) =>
% 132.32/22.89 (ordinal @
% 132.32/22.89 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.32/22.89 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl712])).
% 132.32/22.89 thf(zip_derived_cl735, plain,
% 132.32/22.89 (~ (((subsetI2) =>
% 132.32/22.89 (((emptysetsubset) =>
% 132.32/22.89 (((subsetE) =>
% 132.32/22.89 (((subsetE2) =>
% 132.32/22.89 (((notsubsetI) =>
% 132.32/22.89 (((notequalI1) =>
% 132.32/22.89 (((notequalI2) =>
% 132.32/22.89 (((subsetRefl) =>
% 132.32/22.89 (((subsetTrans) =>
% 132.32/22.89 (((setadjoinSub) =>
% 132.32/22.89 (((setadjoinSub2) =>
% 132.32/22.89 (((subset2powerset) =>
% 132.32/22.89 (((setextsub) =>
% 132.32/22.89 (((subsetemptysetimpeq) =>
% 132.32/22.89 (((powersetI1) =>
% 132.32/22.89 (((powersetE1) =>
% 132.32/22.89 (((inPowerset) =>
% 132.32/22.89 (((powersetsubset) =>
% 132.32/22.89 (((sepInPowerset) =>
% 132.32/22.89 (((sepSubset) =>
% 132.32/22.89 (((binunionIL) =>
% 132.32/22.89 (((upairset2IR) =>
% 132.32/22.89 (((binunionIR) =>
% 132.32/22.89 (((binunionEcases) =>
% 132.32/22.89 (((binunionE) =>
% 132.32/22.89 (((binunionLsub) =>
% 132.32/22.89 (((binunionRsub) =>
% 132.32/22.89 (((binintersectI) =>
% 132.32/22.89 (((binintersectSubset5) =>
% 132.32/22.89 (((binintersectEL) =>
% 132.32/22.89 ((
% 132.32/22.89 (binintersectLsub) =>
% 132.32/22.89 ((
% 132.32/22.89 (binintersectSubset2) =>
% 132.32/22.89 ((
% 132.32/22.89 (binintersectSubset3) =>
% 132.32/22.89 ((
% 132.32/22.89 (binintersectER) =>
% 132.32/22.89 ((
% 132.32/22.89 (disjointsetsI1) =>
% 132.32/22.89 ((
% 132.32/22.89 (binintersectRsub) =>
% 132.32/22.89 ((
% 132.32/22.89 (binintersectSubset4) =>
% 132.32/22.89 ((
% 132.32/22.89 (binintersectSubset1) =>
% 132.32/22.89 ((
% 132.32/22.89 (bs114d) =>
% 132.32/22.89 ((
% 132.32/22.89 (setminusI) =>
% 132.32/22.89 ((
% 132.32/22.89 (setminusEL) =>
% 132.32/22.89 ((
% 132.32/22.89 (setminusER) =>
% 132.32/22.89 ((
% 132.32/22.89 (setminusSubset2) =>
% 132.32/22.89 ((
% 132.32/22.89 (setminusERneg) =>
% 132.32/22.89 ((
% 132.32/22.89 (setminusELneg) =>
% 132.32/22.89 ((
% 132.32/22.89 (setminusILneg) =>
% 132.32/22.89 ((
% 132.32/22.89 (setminusIRneg) =>
% 132.32/22.89 ((
% 132.32/22.89 (setminusLsub) =>
% 132.32/22.89 ((
% 132.32/22.89 (setminusSubset1) =>
% 132.32/22.89 ((
% 132.32/22.89 (symdiffE) =>
% 132.32/22.89 ((
% 132.32/22.89 (symdiffI1) =>
% 132.32/22.89 ((
% 132.32/22.89 (symdiffI2) =>
% 132.32/22.89 ((
% 132.32/22.89 (symdiffIneg1) =>
% 132.32/22.89 ((
% 132.32/22.89 (symdiffIneg2) =>
% 132.32/22.89 ((
% 132.32/22.89 (secondinupair) =>
% 132.32/22.89 ((
% 132.32/22.89 (setukpairIL) =>
% 132.32/22.89 ((
% 132.32/22.89 (setukpairIR) =>
% 132.32/22.89 ((
% 132.32/22.89 (kpairiskpair) =>
% 132.32/22.89 ((
% 132.32/22.89 (kpairp) =>
% 132.32/22.89 ((
% 132.32/22.89 (singletonsubset) =>
% 132.32/22.89 ((
% 132.32/22.89 (singletoninpowerset) =>
% 132.32/22.89 ((
% 132.32/22.89 (singletoninpowunion) =>
% 132.32/22.89 ((
% 132.32/22.89 (upairset2E) =>
% 132.32/22.89 ((
% 132.32/22.89 (upairsubunion) =>
% 132.32/22.89 ((
% 132.32/22.89 (upairinpowunion) =>
% 132.32/22.89 ((
% 132.32/22.89 (ubforcartprodlem1) =>
% 132.32/22.89 ((
% 132.32/22.89 (ubforcartprodlem2) =>
% 132.32/22.89 ((
% 132.32/22.89 (ubforcartprodlem3) =>
% 132.32/22.89 ((
% 132.32/22.89 (cartprodpairin) =>
% 132.32/22.89 ((
% 132.32/22.89 (cartprodmempair1) =>
% 132.32/22.89 ((
% 132.32/22.89 (cartprodmempair) =>
% 132.32/22.89 ((
% 132.32/22.89 (setunionE2) =>
% 132.32/22.89 ((
% 132.32/22.89 (setunionsingleton1) =>
% 132.32/22.89 ((
% 132.32/22.89 (setunionsingleton2) =>
% 132.32/22.89 ((
% 132.32/22.89 (setunionsingleton) =>
% 132.32/22.89 ((
% 132.32/22.89 (singletonprop) =>
% 132.32/22.89 ((
% 132.32/22.89 (ex1E1) =>
% 132.32/22.89 ((
% 132.32/22.89 (ex1I) =>
% 132.32/22.89 ((
% 132.32/22.89 (ex1I2) =>
% 132.32/22.89 ((
% 132.32/22.89 (singletonsuniq) =>
% 132.32/22.89 ((
% 132.32/22.89 (setukpairinjL1) =>
% 132.32/22.89 ((
% 132.32/22.89 (kfstsingleton) =>
% 132.32/22.89 ((
% 132.32/22.89 (theprop) =>
% 132.32/22.89 ((
% 132.32/22.89 (kfstpairEq) =>
% 132.32/22.89 ((
% 132.32/22.89 (cartprodfstin) =>
% 132.32/22.89 ((
% 132.32/22.89 (setukpairinjL2) =>
% 132.32/22.89 ((
% 132.32/22.89 (setukpairinjL) =>
% 132.32/22.89 ((
% 132.32/22.89 (setukpairinjR11) =>
% 132.32/22.89 ((
% 132.32/22.89 (setukpairinjR12) =>
% 132.32/22.89 ((
% 132.32/22.89 (setukpairinjR1) =>
% 132.32/22.89 ((
% 132.32/22.89 (upairequniteq) =>
% 132.32/22.89 ((
% 132.32/22.89 (setukpairinjR2) =>
% 132.32/22.89 ((
% 132.32/22.89 (setukpairinjR) =>
% 132.32/22.89 ((
% 132.32/22.89 (ksndsingleton) =>
% 132.32/22.89 ((
% 132.32/22.89 (ksndpairEq) =>
% 132.32/22.89 ((
% 132.32/22.89 (kpairsurjEq) =>
% 132.32/22.89 ((
% 132.32/22.89 (cartprodsndin) =>
% 132.32/22.89 ((
% 132.32/22.89 (cartprodpairmemEL) =>
% 132.32/22.89 ((
% 132.32/22.89 (cartprodpairmemER) =>
% 132.32/22.89 ((
% 132.32/22.89 (cartprodmempaircEq) =>
% 132.32/22.89 ((
% 132.32/22.89 (cartprodfstpairEq) =>
% 132.32/22.89 ((
% 132.32/22.89 (cartprodsndpairEq) =>
% 132.32/22.89 ((
% 132.32/22.89 (cartprodpairsurjEq) =>
% 132.32/22.89 ((
% 132.32/22.89 (dpsetconstrI) =>
% 132.32/22.89 ((
% 132.32/22.89 (dpsetconstrSub) =>
% 132.32/22.89 ((
% 132.32/22.89 (setOfPairsIsBReln) =>
% 132.32/22.89 ((
% 132.32/22.89 (dpsetconstrERa) =>
% 132.32/22.89 ((
% 132.32/22.89 (dpsetconstrEL1) =>
% 132.32/22.89 ((
% 132.32/22.89 (dpsetconstrEL2) =>
% 132.32/22.89 ((
% 132.32/22.89 (dpsetconstrER) =>
% 132.32/22.89 ((
% 132.32/22.89 (funcImageSingleton) =>
% 132.32/22.89 ((
% 132.32/22.89 (apProp) =>
% 132.32/22.89 ((
% 132.32/22.89 (app) =>
% 132.32/22.89 ((
% 132.32/22.89 (infuncsetfunc) =>
% 132.32/22.89 ((
% 132.32/22.89 (ap2p) =>
% 132.32/22.89 ((
% 132.32/22.89 (funcinfuncset) =>
% 132.32/22.89 ((
% 132.32/22.89 (lamProp) =>
% 132.32/22.89 ((
% 132.32/22.89 (lamp) =>
% 132.32/22.89 ((
% 132.32/22.89 (lam2p) =>
% 132.32/22.89 ((
% 132.32/22.89 (brelnall1) =>
% 132.32/22.89 ((
% 132.32/22.89 (brelnall2) =>
% 132.32/22.89 ((
% 132.32/22.89 (ex1E2) =>
% 132.32/22.89 ((
% 132.32/22.89 (funcGraphProp1) =>
% 132.32/22.89 ((
% 132.32/22.89 (funcGraphProp3) =>
% 132.32/22.89 ((
% 132.32/22.89 (funcGraphProp2) =>
% 132.32/22.89 ((
% 132.32/22.89 (funcextLem) =>
% 132.32/22.89 ((
% 132.32/22.89 (funcGraphProp4) =>
% 132.32/22.89 ((
% 132.32/22.89 (subbreln) =>
% 132.32/22.89 ((
% 132.32/22.89 (eqbreln) =>
% 132.32/22.89 ((
% 132.32/22.89 (funcext) =>
% 132.32/22.89 ((
% 132.32/22.89 (funcext2) =>
% 132.32/22.89 ((
% 132.32/22.89 (ap2apEq1) =>
% 132.32/22.89 ((
% 132.32/22.89 (ap2apEq2) =>
% 132.32/22.89 ((
% 132.32/22.89 (beta1) =>
% 132.32/22.89 ((
% 132.32/22.89 (eta1) =>
% 132.32/22.89 ((
% 132.32/22.89 (lam2lamEq) =>
% 132.32/22.89 ((
% 132.32/22.89 (beta2) =>
% 132.32/22.89 ((
% 132.32/22.89 (eta2) =>
% 132.32/22.89 ((
% 132.32/22.89 (iffalseProp1) =>
% 132.32/22.89 ((
% 132.32/22.89 (iffalseProp2) =>
% 132.32/22.89 ((
% 132.32/22.89 (iftrueProp1) =>
% 132.32/22.89 ((
% 132.32/22.89 (iftrueProp2) =>
% 132.32/22.89 ((
% 132.32/22.89 (ifSingleton) =>
% 132.32/22.89 ((
% 132.32/22.89 (ifp) =>
% 132.32/22.89 ((
% 132.32/22.89 (theeq) =>
% 132.32/22.89 ((
% 132.32/22.89 (iftrue) =>
% 132.32/22.89 ((
% 132.32/22.89 (iffalse) =>
% 132.32/22.89 ((
% 132.32/22.89 (iftrueorfalse) =>
% 132.32/22.89 ((
% 132.32/22.89 (binintersectT_lem) =>
% 132.32/22.89 ((
% 132.32/22.89 (binunionT_lem) =>
% 132.32/22.89 ((
% 132.32/22.89 (powersetT_lem) =>
% 132.32/22.89 ((
% 132.32/22.89 (setminusT_lem) =>
% 132.32/22.89 ((
% 132.32/22.89 (complementT_lem) =>
% 132.32/22.89 ((
% 132.32/22.89 (setextT) =>
% 132.32/22.89 ((
% 132.32/22.89 (subsetTI) =>
% 132.32/22.89 ((
% 132.32/22.89 (powersetTI1) =>
% 132.32/22.89 ((
% 132.32/22.89 (powersetTE1) =>
% 132.32/22.89 ((
% 132.32/22.89 (complementTI1) =>
% 132.32/22.89 ((
% 132.32/22.89 (complementTE1) =>
% 132.32/22.89 ((
% 132.32/22.89 (binintersectTELcontra) =>
% 132.32/22.89 ((
% 132.32/22.89 (binintersectTERcontra) =>
% 132.32/22.89 ((
% 132.32/22.89 (contrasubsetT) =>
% 132.32/22.89 ((
% 132.32/22.89 (contrasubsetT1) =>
% 132.32/22.89 ((
% 132.32/22.89 (contrasubsetT2) =>
% 132.32/22.89 ((
% 132.32/22.89 (contrasubsetT3) =>
% 132.32/22.89 ((
% 132.32/22.89 (doubleComplementI1) =>
% 132.32/22.89 ((
% 132.32/22.89 (doubleComplementE1) =>
% 132.32/22.89 ((
% 132.32/22.89 (doubleComplementSub1) =>
% 132.32/22.89 ((
% 132.32/22.89 (doubleComplementSub2) =>
% 132.32/22.89 ((
% 132.32/22.89 (doubleComplementEq) =>
% 132.32/22.89 ((
% 132.32/22.89 (complementTnotintersectT) =>
% 132.32/22.89 ((
% 132.32/22.89 (complementImpComplementIntersect) =>
% 132.32/22.89 ((
% 132.32/22.89 (complementSubsetComplementIntersect) =>
% 132.32/22.89 ((
% 132.32/22.89 (complementInPowersetComplementIntersect) =>
% 132.32/22.89 ((
% 132.32/22.89 (contraSubsetComplement) =>
% 132.32/22.89 ((
% 132.32/22.89 (complementTcontraSubset) =>
% 132.32/22.89 ((
% 132.32/22.89 (binunionTILcontra) =>
% 132.32/22.89 ((
% 132.32/22.89 (binunionTIRcontra) =>
% 132.32/22.89 ((
% 132.32/22.89 (inIntersectImpInUnion) =>
% 132.32/22.89 ((
% 132.32/22.89 (inIntersectImpInUnion2) =>
% 132.32/22.89 ((
% 132.32/22.89 (inIntersectImpInIntersectUnions) =>
% 132.32/22.89 ((
% 132.32/22.89 (intersectInPowersetIntersectUnions) =>
% 132.32/22.89 ((
% 132.32/22.89 (inComplementUnionImpNotIn1) =>
% 132.32/22.89 ((
% 132.32/22.89 (inComplementUnionImpInComplement1) =>
% 132.32/22.89 ((
% 132.32/22.89 (binunionTE) =>
% 132.32/22.89 ((
% 132.32/22.89 (binunionTEcontra) =>
% 132.32/22.89 ((
% 132.32/22.89 (demorgan2a1) =>
% 132.32/22.89 ((
% 132.32/22.89 (complementUnionInPowersetComplement) =>
% 132.32/22.89 ((
% 132.32/22.89 (demorgan2a2) =>
% 132.32/22.89 ((
% 132.32/22.89 (demorgan1a) =>
% 132.32/22.89 ((
% 132.32/22.89 (demorgan1b) =>
% 132.32/22.89 ((
% 132.32/22.89 (demorgan1) =>
% 132.32/22.89 ((
% 132.32/22.89 (demorgan2a) =>
% 132.32/22.89 ((
% 132.32/22.89 (demorgan2b2) =>
% 132.32/22.89 ((
% 132.32/22.89 (demorgan2b) =>
% 132.32/22.89 ((
% 132.32/22.89 (demorgan2) =>
% 132.32/22.89 ((
% 132.32/22.89 (woz13rule0) =>
% 132.32/22.89 ((
% 132.32/22.89 (woz13rule1) =>
% 132.32/22.89 ((
% 132.32/22.89 (woz13rule2) =>
% 132.32/22.89 ((
% 132.32/22.89 (woz13rule3) =>
% 132.32/22.89 ((
% 132.32/22.89 (woz13rule4) =>
% 132.32/22.89 ((
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% 132.32/22.89 ((
% 132.32/22.89 (woz1_2) =>
% 132.32/22.89 ((
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% 132.32/22.89 ((
% 132.32/22.89 (woz1_4) =>
% 132.32/22.89 ((
% 132.32/22.89 (woz1_5) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1all2) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1SetBreln1) =>
% 132.32/22.89 ((
% 132.32/22.89 (choice2fnsingleton) =>
% 132.32/22.89 ((
% 132.32/22.89 (setOfPairsIsBReln1) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1all1) =>
% 132.32/22.89 ((
% 132.32/22.89 (subbreln1) =>
% 132.32/22.89 ((
% 132.32/22.89 (eqbreln1) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1invprop) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1invI) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1invE) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1compprop) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1compI) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1compE) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1compEex) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1unionprop) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1unionIL) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1unionIR) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1unionI) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1unionE) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1unionEcases) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1unionCommutes) =>
% 132.32/22.89 ((
% 132.32/22.89 (woz2Ex) =>
% 132.32/22.89 ((
% 132.32/22.89 (woz2W) =>
% 132.32/22.89 ((
% 132.32/22.89 (woz2A) =>
% 132.32/22.89 ((
% 132.32/22.89 (woz2B) =>
% 132.32/22.89 ((
% 132.32/22.89 (image1Ex) =>
% 132.32/22.89 ((
% 132.32/22.89 (image1Ex1) =>
% 132.32/22.89 ((
% 132.32/22.89 (image1Equiv) =>
% 132.32/22.89 ((
% 132.32/22.89 (image1E) =>
% 132.32/22.89 ((
% 132.32/22.89 (image1I) =>
% 132.32/22.89 ((
% 132.32/22.89 (injFuncInInjFuncSet) =>
% 132.32/22.89 ((
% 132.32/22.89 (injFuncSetFuncIn) =>
% 132.32/22.89 ((
% 132.32/22.89 (injFuncSetFuncInj) =>
% 132.32/22.89 ((
% 132.32/22.89 (surjFuncSetFuncIn) =>
% 132.32/22.89 ((
% 132.32/22.89 (surjFuncSetFuncSurj) =>
% 132.32/22.89 ((
% 132.32/22.89 (leftInvIsSurj) =>
% 132.32/22.89 ((
% 132.32/22.89 (surjCantorThm) =>
% 132.32/22.89 ((
% 132.32/22.89 (foundation2) =>
% 132.32/22.89 ((
% 132.32/22.89 (notinself) =>
% 132.32/22.89 ((
% 132.32/22.89 (notinself2) =>
% 132.32/22.89 ((
% 132.32/22.89 (omegaSp) =>
% 132.32/22.89 ((
% 132.32/22.89 (omegaSclos) =>
% 132.32/22.89 ((
% 132.32/22.89 (peano0notS) =>
% 132.32/22.89 ((
% 132.32/22.89 (peanoSinj) =>
% 132.32/22.89 ((
% 132.32/22.89 (transitivesetOp1) =>
% 132.32/22.89 ((
% 132.32/22.89 (binintTransitive) =>
% 132.32/22.89 ((
% 132.32/22.89 (transitivesetOp2) =>
% 132.32/22.89 ((
% 132.32/22.89 (setunionTransitive) =>
% 132.32/22.89 ((
% 132.32/22.89 (ordinalMinLem1) =>
% 132.32/22.89 ((
% 132.32/22.89 (ordinalTransSet) =>
% 132.32/22.89 ((
% 132.32/22.89 (ordinalTransSet1) =>
% 132.32/22.89 ((
% 132.32/22.89 (setunionOrdinalLem1) =>
% 132.32/22.89 (ordinal @
% 132.32/22.89 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.32/22.89 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl725])).
% 132.32/22.89 thf(zip_derived_cl746, plain,
% 132.32/22.89 (~ (((emptysetsubset) =>
% 132.32/22.89 (((subsetE) =>
% 132.32/22.89 (((subsetE2) =>
% 132.32/22.89 (((notsubsetI) =>
% 132.32/22.89 (((notequalI1) =>
% 132.32/22.89 (((notequalI2) =>
% 132.32/22.89 (((subsetRefl) =>
% 132.32/22.89 (((subsetTrans) =>
% 132.32/22.89 (((setadjoinSub) =>
% 132.32/22.89 (((setadjoinSub2) =>
% 132.32/22.89 (((subset2powerset) =>
% 132.32/22.89 (((setextsub) =>
% 132.32/22.89 (((subsetemptysetimpeq) =>
% 132.32/22.89 (((powersetI1) =>
% 132.32/22.89 (((powersetE1) =>
% 132.32/22.89 (((inPowerset) =>
% 132.32/22.89 (((powersetsubset) =>
% 132.32/22.89 (((sepInPowerset) =>
% 132.32/22.89 (((sepSubset) =>
% 132.32/22.89 (((binunionIL) =>
% 132.32/22.89 (((upairset2IR) =>
% 132.32/22.89 (((binunionIR) =>
% 132.32/22.89 (((binunionEcases) =>
% 132.32/22.89 (((binunionE) =>
% 132.32/22.89 (((binunionLsub) =>
% 132.32/22.89 (((binunionRsub) =>
% 132.32/22.89 (((binintersectI) =>
% 132.32/22.89 (((binintersectSubset5) =>
% 132.32/22.89 (((binintersectEL) =>
% 132.32/22.89 (((binintersectLsub) =>
% 132.32/22.89 ((
% 132.32/22.89 (binintersectSubset2) =>
% 132.32/22.89 ((
% 132.32/22.89 (binintersectSubset3) =>
% 132.32/22.89 ((
% 132.32/22.89 (binintersectER) =>
% 132.32/22.89 ((
% 132.32/22.89 (disjointsetsI1) =>
% 132.32/22.89 ((
% 132.32/22.89 (binintersectRsub) =>
% 132.32/22.89 ((
% 132.32/22.89 (binintersectSubset4) =>
% 132.32/22.89 ((
% 132.32/22.89 (binintersectSubset1) =>
% 132.32/22.89 ((
% 132.32/22.89 (bs114d) =>
% 132.32/22.89 ((
% 132.32/22.89 (setminusI) =>
% 132.32/22.89 ((
% 132.32/22.89 (setminusEL) =>
% 132.32/22.89 ((
% 132.32/22.89 (setminusER) =>
% 132.32/22.89 ((
% 132.32/22.89 (setminusSubset2) =>
% 132.32/22.89 ((
% 132.32/22.89 (setminusERneg) =>
% 132.32/22.89 ((
% 132.32/22.89 (setminusELneg) =>
% 132.32/22.89 ((
% 132.32/22.89 (setminusILneg) =>
% 132.32/22.89 ((
% 132.32/22.89 (setminusIRneg) =>
% 132.32/22.89 ((
% 132.32/22.89 (setminusLsub) =>
% 132.32/22.89 ((
% 132.32/22.89 (setminusSubset1) =>
% 132.32/22.89 ((
% 132.32/22.89 (symdiffE) =>
% 132.32/22.89 ((
% 132.32/22.89 (symdiffI1) =>
% 132.32/22.89 ((
% 132.32/22.89 (symdiffI2) =>
% 132.32/22.89 ((
% 132.32/22.89 (symdiffIneg1) =>
% 132.32/22.89 ((
% 132.32/22.89 (symdiffIneg2) =>
% 132.32/22.89 ((
% 132.32/22.89 (secondinupair) =>
% 132.32/22.89 ((
% 132.32/22.89 (setukpairIL) =>
% 132.32/22.89 ((
% 132.32/22.89 (setukpairIR) =>
% 132.32/22.89 ((
% 132.32/22.89 (kpairiskpair) =>
% 132.32/22.89 ((
% 132.32/22.89 (kpairp) =>
% 132.32/22.89 ((
% 132.32/22.89 (singletonsubset) =>
% 132.32/22.89 ((
% 132.32/22.89 (singletoninpowerset) =>
% 132.32/22.89 ((
% 132.32/22.89 (singletoninpowunion) =>
% 132.32/22.89 ((
% 132.32/22.89 (upairset2E) =>
% 132.32/22.89 ((
% 132.32/22.89 (upairsubunion) =>
% 132.32/22.89 ((
% 132.32/22.89 (upairinpowunion) =>
% 132.32/22.89 ((
% 132.32/22.89 (ubforcartprodlem1) =>
% 132.32/22.89 ((
% 132.32/22.89 (ubforcartprodlem2) =>
% 132.32/22.89 ((
% 132.32/22.89 (ubforcartprodlem3) =>
% 132.32/22.89 ((
% 132.32/22.89 (cartprodpairin) =>
% 132.32/22.89 ((
% 132.32/22.89 (cartprodmempair1) =>
% 132.32/22.89 ((
% 132.32/22.89 (cartprodmempair) =>
% 132.32/22.89 ((
% 132.32/22.89 (setunionE2) =>
% 132.32/22.89 ((
% 132.32/22.89 (setunionsingleton1) =>
% 132.32/22.89 ((
% 132.32/22.89 (setunionsingleton2) =>
% 132.32/22.89 ((
% 132.32/22.89 (setunionsingleton) =>
% 132.32/22.89 ((
% 132.32/22.89 (singletonprop) =>
% 132.32/22.89 ((
% 132.32/22.89 (ex1E1) =>
% 132.32/22.89 ((
% 132.32/22.89 (ex1I) =>
% 132.32/22.89 ((
% 132.32/22.89 (ex1I2) =>
% 132.32/22.89 ((
% 132.32/22.89 (singletonsuniq) =>
% 132.32/22.89 ((
% 132.32/22.89 (setukpairinjL1) =>
% 132.32/22.89 ((
% 132.32/22.89 (kfstsingleton) =>
% 132.32/22.89 ((
% 132.32/22.89 (theprop) =>
% 132.32/22.89 ((
% 132.32/22.89 (kfstpairEq) =>
% 132.32/22.89 ((
% 132.32/22.89 (cartprodfstin) =>
% 132.32/22.89 ((
% 132.32/22.89 (setukpairinjL2) =>
% 132.32/22.89 ((
% 132.32/22.89 (setukpairinjL) =>
% 132.32/22.89 ((
% 132.32/22.89 (setukpairinjR11) =>
% 132.32/22.89 ((
% 132.32/22.89 (setukpairinjR12) =>
% 132.32/22.89 ((
% 132.32/22.89 (setukpairinjR1) =>
% 132.32/22.89 ((
% 132.32/22.89 (upairequniteq) =>
% 132.32/22.89 ((
% 132.32/22.89 (setukpairinjR2) =>
% 132.32/22.89 ((
% 132.32/22.89 (setukpairinjR) =>
% 132.32/22.89 ((
% 132.32/22.89 (ksndsingleton) =>
% 132.32/22.89 ((
% 132.32/22.89 (ksndpairEq) =>
% 132.32/22.89 ((
% 132.32/22.89 (kpairsurjEq) =>
% 132.32/22.89 ((
% 132.32/22.89 (cartprodsndin) =>
% 132.32/22.89 ((
% 132.32/22.89 (cartprodpairmemEL) =>
% 132.32/22.89 ((
% 132.32/22.89 (cartprodpairmemER) =>
% 132.32/22.89 ((
% 132.32/22.89 (cartprodmempaircEq) =>
% 132.32/22.89 ((
% 132.32/22.89 (cartprodfstpairEq) =>
% 132.32/22.89 ((
% 132.32/22.89 (cartprodsndpairEq) =>
% 132.32/22.89 ((
% 132.32/22.89 (cartprodpairsurjEq) =>
% 132.32/22.89 ((
% 132.32/22.89 (dpsetconstrI) =>
% 132.32/22.89 ((
% 132.32/22.89 (dpsetconstrSub) =>
% 132.32/22.89 ((
% 132.32/22.89 (setOfPairsIsBReln) =>
% 132.32/22.89 ((
% 132.32/22.89 (dpsetconstrERa) =>
% 132.32/22.89 ((
% 132.32/22.89 (dpsetconstrEL1) =>
% 132.32/22.89 ((
% 132.32/22.89 (dpsetconstrEL2) =>
% 132.32/22.89 ((
% 132.32/22.89 (dpsetconstrER) =>
% 132.32/22.89 ((
% 132.32/22.89 (funcImageSingleton) =>
% 132.32/22.89 ((
% 132.32/22.89 (apProp) =>
% 132.32/22.89 ((
% 132.32/22.89 (app) =>
% 132.32/22.89 ((
% 132.32/22.89 (infuncsetfunc) =>
% 132.32/22.89 ((
% 132.32/22.89 (ap2p) =>
% 132.32/22.89 ((
% 132.32/22.89 (funcinfuncset) =>
% 132.32/22.89 ((
% 132.32/22.89 (lamProp) =>
% 132.32/22.89 ((
% 132.32/22.89 (lamp) =>
% 132.32/22.89 ((
% 132.32/22.89 (lam2p) =>
% 132.32/22.89 ((
% 132.32/22.89 (brelnall1) =>
% 132.32/22.89 ((
% 132.32/22.89 (brelnall2) =>
% 132.32/22.89 ((
% 132.32/22.89 (ex1E2) =>
% 132.32/22.89 ((
% 132.32/22.89 (funcGraphProp1) =>
% 132.32/22.89 ((
% 132.32/22.89 (funcGraphProp3) =>
% 132.32/22.89 ((
% 132.32/22.89 (funcGraphProp2) =>
% 132.32/22.89 ((
% 132.32/22.89 (funcextLem) =>
% 132.32/22.89 ((
% 132.32/22.89 (funcGraphProp4) =>
% 132.32/22.89 ((
% 132.32/22.89 (subbreln) =>
% 132.32/22.89 ((
% 132.32/22.89 (eqbreln) =>
% 132.32/22.89 ((
% 132.32/22.89 (funcext) =>
% 132.32/22.89 ((
% 132.32/22.89 (funcext2) =>
% 132.32/22.89 ((
% 132.32/22.89 (ap2apEq1) =>
% 132.32/22.89 ((
% 132.32/22.89 (ap2apEq2) =>
% 132.32/22.89 ((
% 132.32/22.89 (beta1) =>
% 132.32/22.89 ((
% 132.32/22.89 (eta1) =>
% 132.32/22.89 ((
% 132.32/22.89 (lam2lamEq) =>
% 132.32/22.89 ((
% 132.32/22.89 (beta2) =>
% 132.32/22.89 ((
% 132.32/22.89 (eta2) =>
% 132.32/22.89 ((
% 132.32/22.89 (iffalseProp1) =>
% 132.32/22.89 ((
% 132.32/22.89 (iffalseProp2) =>
% 132.32/22.89 ((
% 132.32/22.89 (iftrueProp1) =>
% 132.32/22.89 ((
% 132.32/22.89 (iftrueProp2) =>
% 132.32/22.89 ((
% 132.32/22.89 (ifSingleton) =>
% 132.32/22.89 ((
% 132.32/22.89 (ifp) =>
% 132.32/22.89 ((
% 132.32/22.89 (theeq) =>
% 132.32/22.89 ((
% 132.32/22.89 (iftrue) =>
% 132.32/22.89 ((
% 132.32/22.89 (iffalse) =>
% 132.32/22.89 ((
% 132.32/22.89 (iftrueorfalse) =>
% 132.32/22.89 ((
% 132.32/22.89 (binintersectT_lem) =>
% 132.32/22.89 ((
% 132.32/22.89 (binunionT_lem) =>
% 132.32/22.89 ((
% 132.32/22.89 (powersetT_lem) =>
% 132.32/22.89 ((
% 132.32/22.89 (setminusT_lem) =>
% 132.32/22.89 ((
% 132.32/22.89 (complementT_lem) =>
% 132.32/22.89 ((
% 132.32/22.89 (setextT) =>
% 132.32/22.89 ((
% 132.32/22.89 (subsetTI) =>
% 132.32/22.89 ((
% 132.32/22.89 (powersetTI1) =>
% 132.32/22.89 ((
% 132.32/22.89 (powersetTE1) =>
% 132.32/22.89 ((
% 132.32/22.89 (complementTI1) =>
% 132.32/22.89 ((
% 132.32/22.89 (complementTE1) =>
% 132.32/22.89 ((
% 132.32/22.89 (binintersectTELcontra) =>
% 132.32/22.89 ((
% 132.32/22.89 (binintersectTERcontra) =>
% 132.32/22.89 ((
% 132.32/22.89 (contrasubsetT) =>
% 132.32/22.89 ((
% 132.32/22.89 (contrasubsetT1) =>
% 132.32/22.89 ((
% 132.32/22.89 (contrasubsetT2) =>
% 132.32/22.89 ((
% 132.32/22.89 (contrasubsetT3) =>
% 132.32/22.89 ((
% 132.32/22.89 (doubleComplementI1) =>
% 132.32/22.89 ((
% 132.32/22.89 (doubleComplementE1) =>
% 132.32/22.89 ((
% 132.32/22.89 (doubleComplementSub1) =>
% 132.32/22.89 ((
% 132.32/22.89 (doubleComplementSub2) =>
% 132.32/22.89 ((
% 132.32/22.89 (doubleComplementEq) =>
% 132.32/22.89 ((
% 132.32/22.89 (complementTnotintersectT) =>
% 132.32/22.89 ((
% 132.32/22.89 (complementImpComplementIntersect) =>
% 132.32/22.89 ((
% 132.32/22.89 (complementSubsetComplementIntersect) =>
% 132.32/22.89 ((
% 132.32/22.89 (complementInPowersetComplementIntersect) =>
% 132.32/22.89 ((
% 132.32/22.89 (contraSubsetComplement) =>
% 132.32/22.89 ((
% 132.32/22.89 (complementTcontraSubset) =>
% 132.32/22.89 ((
% 132.32/22.89 (binunionTILcontra) =>
% 132.32/22.89 ((
% 132.32/22.89 (binunionTIRcontra) =>
% 132.32/22.89 ((
% 132.32/22.89 (inIntersectImpInUnion) =>
% 132.32/22.89 ((
% 132.32/22.89 (inIntersectImpInUnion2) =>
% 132.32/22.89 ((
% 132.32/22.89 (inIntersectImpInIntersectUnions) =>
% 132.32/22.89 ((
% 132.32/22.89 (intersectInPowersetIntersectUnions) =>
% 132.32/22.89 ((
% 132.32/22.89 (inComplementUnionImpNotIn1) =>
% 132.32/22.89 ((
% 132.32/22.89 (inComplementUnionImpInComplement1) =>
% 132.32/22.89 ((
% 132.32/22.89 (binunionTE) =>
% 132.32/22.89 ((
% 132.32/22.89 (binunionTEcontra) =>
% 132.32/22.89 ((
% 132.32/22.89 (demorgan2a1) =>
% 132.32/22.89 ((
% 132.32/22.89 (complementUnionInPowersetComplement) =>
% 132.32/22.89 ((
% 132.32/22.89 (demorgan2a2) =>
% 132.32/22.89 ((
% 132.32/22.89 (demorgan1a) =>
% 132.32/22.89 ((
% 132.32/22.89 (demorgan1b) =>
% 132.32/22.89 ((
% 132.32/22.89 (demorgan1) =>
% 132.32/22.89 ((
% 132.32/22.89 (demorgan2a) =>
% 132.32/22.89 ((
% 132.32/22.89 (demorgan2b2) =>
% 132.32/22.89 ((
% 132.32/22.89 (demorgan2b) =>
% 132.32/22.89 ((
% 132.32/22.89 (demorgan2) =>
% 132.32/22.89 ((
% 132.32/22.89 (woz13rule0) =>
% 132.32/22.89 ((
% 132.32/22.89 (woz13rule1) =>
% 132.32/22.89 ((
% 132.32/22.89 (woz13rule2) =>
% 132.32/22.89 ((
% 132.32/22.89 (woz13rule3) =>
% 132.32/22.89 ((
% 132.32/22.89 (woz13rule4) =>
% 132.32/22.89 ((
% 132.32/22.89 (woz1_1) =>
% 132.32/22.89 ((
% 132.32/22.89 (woz1_2) =>
% 132.32/22.89 ((
% 132.32/22.89 (woz1_3) =>
% 132.32/22.89 ((
% 132.32/22.89 (woz1_4) =>
% 132.32/22.89 ((
% 132.32/22.89 (woz1_5) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1all2) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1SetBreln1) =>
% 132.32/22.89 ((
% 132.32/22.89 (choice2fnsingleton) =>
% 132.32/22.89 ((
% 132.32/22.89 (setOfPairsIsBReln1) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1all1) =>
% 132.32/22.89 ((
% 132.32/22.89 (subbreln1) =>
% 132.32/22.89 ((
% 132.32/22.89 (eqbreln1) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1invprop) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1invI) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1invE) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1compprop) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1compI) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1compE) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1compEex) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1unionprop) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1unionIL) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1unionIR) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1unionI) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1unionE) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1unionEcases) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1unionCommutes) =>
% 132.32/22.89 ((
% 132.32/22.89 (woz2Ex) =>
% 132.32/22.89 ((
% 132.32/22.89 (woz2W) =>
% 132.32/22.89 ((
% 132.32/22.89 (woz2A) =>
% 132.32/22.89 ((
% 132.32/22.89 (woz2B) =>
% 132.32/22.89 ((
% 132.32/22.89 (image1Ex) =>
% 132.32/22.89 ((
% 132.32/22.89 (image1Ex1) =>
% 132.32/22.89 ((
% 132.32/22.89 (image1Equiv) =>
% 132.32/22.89 ((
% 132.32/22.89 (image1E) =>
% 132.32/22.89 ((
% 132.32/22.89 (image1I) =>
% 132.32/22.89 ((
% 132.32/22.89 (injFuncInInjFuncSet) =>
% 132.32/22.89 ((
% 132.32/22.89 (injFuncSetFuncIn) =>
% 132.32/22.89 ((
% 132.32/22.89 (injFuncSetFuncInj) =>
% 132.32/22.89 ((
% 132.32/22.89 (surjFuncSetFuncIn) =>
% 132.32/22.89 ((
% 132.32/22.89 (surjFuncSetFuncSurj) =>
% 132.32/22.89 ((
% 132.32/22.89 (leftInvIsSurj) =>
% 132.32/22.89 ((
% 132.32/22.89 (surjCantorThm) =>
% 132.32/22.89 ((
% 132.32/22.89 (foundation2) =>
% 132.32/22.89 ((
% 132.32/22.89 (notinself) =>
% 132.32/22.89 ((
% 132.32/22.89 (notinself2) =>
% 132.32/22.89 ((
% 132.32/22.89 (omegaSp) =>
% 132.32/22.89 ((
% 132.32/22.89 (omegaSclos) =>
% 132.32/22.89 ((
% 132.32/22.89 (peano0notS) =>
% 132.32/22.89 ((
% 132.32/22.89 (peanoSinj) =>
% 132.32/22.89 ((
% 132.32/22.89 (transitivesetOp1) =>
% 132.32/22.89 ((
% 132.32/22.89 (binintTransitive) =>
% 132.32/22.89 ((
% 132.32/22.89 (transitivesetOp2) =>
% 132.32/22.89 ((
% 132.32/22.89 (setunionTransitive) =>
% 132.32/22.89 ((
% 132.32/22.89 (ordinalMinLem1) =>
% 132.32/22.89 ((
% 132.32/22.89 (ordinalTransSet) =>
% 132.32/22.89 ((
% 132.32/22.89 (ordinalTransSet1) =>
% 132.32/22.89 ((
% 132.32/22.89 (setunionOrdinalLem1) =>
% 132.32/22.89 (ordinal @
% 132.32/22.89 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.32/22.89 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl735])).
% 132.32/22.89 thf(zip_derived_cl758, plain,
% 132.32/22.89 (~ (((subsetE) =>
% 132.32/22.89 (((subsetE2) =>
% 132.32/22.89 (((notsubsetI) =>
% 132.32/22.89 (((notequalI1) =>
% 132.32/22.89 (((notequalI2) =>
% 132.32/22.89 (((subsetRefl) =>
% 132.32/22.89 (((subsetTrans) =>
% 132.32/22.89 (((setadjoinSub) =>
% 132.32/22.89 (((setadjoinSub2) =>
% 132.32/22.89 (((subset2powerset) =>
% 132.32/22.89 (((setextsub) =>
% 132.32/22.89 (((subsetemptysetimpeq) =>
% 132.32/22.89 (((powersetI1) =>
% 132.32/22.89 (((powersetE1) =>
% 132.32/22.89 (((inPowerset) =>
% 132.32/22.89 (((powersetsubset) =>
% 132.32/22.89 (((sepInPowerset) =>
% 132.32/22.89 (((sepSubset) =>
% 132.32/22.89 (((binunionIL) =>
% 132.32/22.89 (((upairset2IR) =>
% 132.32/22.89 (((binunionIR) =>
% 132.32/22.89 (((binunionEcases) =>
% 132.32/22.89 (((binunionE) =>
% 132.32/22.89 (((binunionLsub) =>
% 132.32/22.89 (((binunionRsub) =>
% 132.32/22.89 (((binintersectI) =>
% 132.32/22.89 (((binintersectSubset5) =>
% 132.32/22.89 (((binintersectEL) =>
% 132.32/22.89 (((binintersectLsub) =>
% 132.32/22.89 (((binintersectSubset2) =>
% 132.32/22.89 ((
% 132.32/22.89 (binintersectSubset3) =>
% 132.32/22.89 ((
% 132.32/22.89 (binintersectER) =>
% 132.32/22.89 ((
% 132.32/22.89 (disjointsetsI1) =>
% 132.32/22.89 ((
% 132.32/22.89 (binintersectRsub) =>
% 132.32/22.89 ((
% 132.32/22.89 (binintersectSubset4) =>
% 132.32/22.89 ((
% 132.32/22.89 (binintersectSubset1) =>
% 132.32/22.89 ((
% 132.32/22.89 (bs114d) =>
% 132.32/22.89 ((
% 132.32/22.89 (setminusI) =>
% 132.32/22.89 ((
% 132.32/22.89 (setminusEL) =>
% 132.32/22.89 ((
% 132.32/22.89 (setminusER) =>
% 132.32/22.89 ((
% 132.32/22.89 (setminusSubset2) =>
% 132.32/22.89 ((
% 132.32/22.89 (setminusERneg) =>
% 132.32/22.89 ((
% 132.32/22.89 (setminusELneg) =>
% 132.32/22.89 ((
% 132.32/22.89 (setminusILneg) =>
% 132.32/22.89 ((
% 132.32/22.89 (setminusIRneg) =>
% 132.32/22.89 ((
% 132.32/22.89 (setminusLsub) =>
% 132.32/22.89 ((
% 132.32/22.89 (setminusSubset1) =>
% 132.32/22.89 ((
% 132.32/22.89 (symdiffE) =>
% 132.32/22.89 ((
% 132.32/22.89 (symdiffI1) =>
% 132.32/22.89 ((
% 132.32/22.89 (symdiffI2) =>
% 132.32/22.89 ((
% 132.32/22.89 (symdiffIneg1) =>
% 132.32/22.89 ((
% 132.32/22.89 (symdiffIneg2) =>
% 132.32/22.89 ((
% 132.32/22.89 (secondinupair) =>
% 132.32/22.89 ((
% 132.32/22.89 (setukpairIL) =>
% 132.32/22.89 ((
% 132.32/22.89 (setukpairIR) =>
% 132.32/22.89 ((
% 132.32/22.89 (kpairiskpair) =>
% 132.32/22.89 ((
% 132.32/22.89 (kpairp) =>
% 132.32/22.89 ((
% 132.32/22.89 (singletonsubset) =>
% 132.32/22.89 ((
% 132.32/22.89 (singletoninpowerset) =>
% 132.32/22.89 ((
% 132.32/22.89 (singletoninpowunion) =>
% 132.32/22.89 ((
% 132.32/22.89 (upairset2E) =>
% 132.32/22.89 ((
% 132.32/22.89 (upairsubunion) =>
% 132.32/22.89 ((
% 132.32/22.89 (upairinpowunion) =>
% 132.32/22.89 ((
% 132.32/22.89 (ubforcartprodlem1) =>
% 132.32/22.89 ((
% 132.32/22.89 (ubforcartprodlem2) =>
% 132.32/22.89 ((
% 132.32/22.89 (ubforcartprodlem3) =>
% 132.32/22.89 ((
% 132.32/22.89 (cartprodpairin) =>
% 132.32/22.89 ((
% 132.32/22.89 (cartprodmempair1) =>
% 132.32/22.89 ((
% 132.32/22.89 (cartprodmempair) =>
% 132.32/22.89 ((
% 132.32/22.89 (setunionE2) =>
% 132.32/22.89 ((
% 132.32/22.89 (setunionsingleton1) =>
% 132.32/22.89 ((
% 132.32/22.89 (setunionsingleton2) =>
% 132.32/22.89 ((
% 132.32/22.89 (setunionsingleton) =>
% 132.32/22.89 ((
% 132.32/22.89 (singletonprop) =>
% 132.32/22.89 ((
% 132.32/22.89 (ex1E1) =>
% 132.32/22.89 ((
% 132.32/22.89 (ex1I) =>
% 132.32/22.89 ((
% 132.32/22.89 (ex1I2) =>
% 132.32/22.89 ((
% 132.32/22.89 (singletonsuniq) =>
% 132.32/22.89 ((
% 132.32/22.89 (setukpairinjL1) =>
% 132.32/22.89 ((
% 132.32/22.89 (kfstsingleton) =>
% 132.32/22.89 ((
% 132.32/22.89 (theprop) =>
% 132.32/22.89 ((
% 132.32/22.89 (kfstpairEq) =>
% 132.32/22.89 ((
% 132.32/22.89 (cartprodfstin) =>
% 132.32/22.89 ((
% 132.32/22.89 (setukpairinjL2) =>
% 132.32/22.89 ((
% 132.32/22.89 (setukpairinjL) =>
% 132.32/22.89 ((
% 132.32/22.89 (setukpairinjR11) =>
% 132.32/22.89 ((
% 132.32/22.89 (setukpairinjR12) =>
% 132.32/22.89 ((
% 132.32/22.89 (setukpairinjR1) =>
% 132.32/22.89 ((
% 132.32/22.89 (upairequniteq) =>
% 132.32/22.89 ((
% 132.32/22.89 (setukpairinjR2) =>
% 132.32/22.89 ((
% 132.32/22.89 (setukpairinjR) =>
% 132.32/22.89 ((
% 132.32/22.89 (ksndsingleton) =>
% 132.32/22.89 ((
% 132.32/22.89 (ksndpairEq) =>
% 132.32/22.89 ((
% 132.32/22.89 (kpairsurjEq) =>
% 132.32/22.89 ((
% 132.32/22.89 (cartprodsndin) =>
% 132.32/22.89 ((
% 132.32/22.89 (cartprodpairmemEL) =>
% 132.32/22.89 ((
% 132.32/22.89 (cartprodpairmemER) =>
% 132.32/22.89 ((
% 132.32/22.89 (cartprodmempaircEq) =>
% 132.32/22.89 ((
% 132.32/22.89 (cartprodfstpairEq) =>
% 132.32/22.89 ((
% 132.32/22.89 (cartprodsndpairEq) =>
% 132.32/22.89 ((
% 132.32/22.89 (cartprodpairsurjEq) =>
% 132.32/22.89 ((
% 132.32/22.89 (dpsetconstrI) =>
% 132.32/22.89 ((
% 132.32/22.89 (dpsetconstrSub) =>
% 132.32/22.89 ((
% 132.32/22.89 (setOfPairsIsBReln) =>
% 132.32/22.89 ((
% 132.32/22.89 (dpsetconstrERa) =>
% 132.32/22.89 ((
% 132.32/22.89 (dpsetconstrEL1) =>
% 132.32/22.89 ((
% 132.32/22.89 (dpsetconstrEL2) =>
% 132.32/22.89 ((
% 132.32/22.89 (dpsetconstrER) =>
% 132.32/22.89 ((
% 132.32/22.89 (funcImageSingleton) =>
% 132.32/22.89 ((
% 132.32/22.89 (apProp) =>
% 132.32/22.89 ((
% 132.32/22.89 (app) =>
% 132.32/22.89 ((
% 132.32/22.89 (infuncsetfunc) =>
% 132.32/22.89 ((
% 132.32/22.89 (ap2p) =>
% 132.32/22.89 ((
% 132.32/22.89 (funcinfuncset) =>
% 132.32/22.89 ((
% 132.32/22.89 (lamProp) =>
% 132.32/22.89 ((
% 132.32/22.89 (lamp) =>
% 132.32/22.89 ((
% 132.32/22.89 (lam2p) =>
% 132.32/22.89 ((
% 132.32/22.89 (brelnall1) =>
% 132.32/22.89 ((
% 132.32/22.89 (brelnall2) =>
% 132.32/22.89 ((
% 132.32/22.89 (ex1E2) =>
% 132.32/22.89 ((
% 132.32/22.89 (funcGraphProp1) =>
% 132.32/22.89 ((
% 132.32/22.89 (funcGraphProp3) =>
% 132.32/22.89 ((
% 132.32/22.89 (funcGraphProp2) =>
% 132.32/22.89 ((
% 132.32/22.89 (funcextLem) =>
% 132.32/22.89 ((
% 132.32/22.89 (funcGraphProp4) =>
% 132.32/22.89 ((
% 132.32/22.89 (subbreln) =>
% 132.32/22.89 ((
% 132.32/22.89 (eqbreln) =>
% 132.32/22.89 ((
% 132.32/22.89 (funcext) =>
% 132.32/22.89 ((
% 132.32/22.89 (funcext2) =>
% 132.32/22.89 ((
% 132.32/22.89 (ap2apEq1) =>
% 132.32/22.89 ((
% 132.32/22.89 (ap2apEq2) =>
% 132.32/22.89 ((
% 132.32/22.89 (beta1) =>
% 132.32/22.89 ((
% 132.32/22.89 (eta1) =>
% 132.32/22.89 ((
% 132.32/22.89 (lam2lamEq) =>
% 132.32/22.89 ((
% 132.32/22.89 (beta2) =>
% 132.32/22.89 ((
% 132.32/22.89 (eta2) =>
% 132.32/22.89 ((
% 132.32/22.89 (iffalseProp1) =>
% 132.32/22.89 ((
% 132.32/22.89 (iffalseProp2) =>
% 132.32/22.89 ((
% 132.32/22.89 (iftrueProp1) =>
% 132.32/22.89 ((
% 132.32/22.89 (iftrueProp2) =>
% 132.32/22.89 ((
% 132.32/22.89 (ifSingleton) =>
% 132.32/22.89 ((
% 132.32/22.89 (ifp) =>
% 132.32/22.89 ((
% 132.32/22.89 (theeq) =>
% 132.32/22.89 ((
% 132.32/22.89 (iftrue) =>
% 132.32/22.89 ((
% 132.32/22.89 (iffalse) =>
% 132.32/22.89 ((
% 132.32/22.89 (iftrueorfalse) =>
% 132.32/22.89 ((
% 132.32/22.89 (binintersectT_lem) =>
% 132.32/22.89 ((
% 132.32/22.89 (binunionT_lem) =>
% 132.32/22.89 ((
% 132.32/22.89 (powersetT_lem) =>
% 132.32/22.89 ((
% 132.32/22.89 (setminusT_lem) =>
% 132.32/22.89 ((
% 132.32/22.89 (complementT_lem) =>
% 132.32/22.89 ((
% 132.32/22.89 (setextT) =>
% 132.32/22.89 ((
% 132.32/22.89 (subsetTI) =>
% 132.32/22.89 ((
% 132.32/22.89 (powersetTI1) =>
% 132.32/22.89 ((
% 132.32/22.89 (powersetTE1) =>
% 132.32/22.89 ((
% 132.32/22.89 (complementTI1) =>
% 132.32/22.89 ((
% 132.32/22.89 (complementTE1) =>
% 132.32/22.89 ((
% 132.32/22.89 (binintersectTELcontra) =>
% 132.32/22.89 ((
% 132.32/22.89 (binintersectTERcontra) =>
% 132.32/22.89 ((
% 132.32/22.89 (contrasubsetT) =>
% 132.32/22.89 ((
% 132.32/22.89 (contrasubsetT1) =>
% 132.32/22.89 ((
% 132.32/22.89 (contrasubsetT2) =>
% 132.32/22.89 ((
% 132.32/22.89 (contrasubsetT3) =>
% 132.32/22.89 ((
% 132.32/22.89 (doubleComplementI1) =>
% 132.32/22.89 ((
% 132.32/22.89 (doubleComplementE1) =>
% 132.32/22.89 ((
% 132.32/22.89 (doubleComplementSub1) =>
% 132.32/22.89 ((
% 132.32/22.89 (doubleComplementSub2) =>
% 132.32/22.89 ((
% 132.32/22.89 (doubleComplementEq) =>
% 132.32/22.89 ((
% 132.32/22.89 (complementTnotintersectT) =>
% 132.32/22.89 ((
% 132.32/22.89 (complementImpComplementIntersect) =>
% 132.32/22.89 ((
% 132.32/22.89 (complementSubsetComplementIntersect) =>
% 132.32/22.89 ((
% 132.32/22.89 (complementInPowersetComplementIntersect) =>
% 132.32/22.89 ((
% 132.32/22.89 (contraSubsetComplement) =>
% 132.32/22.89 ((
% 132.32/22.89 (complementTcontraSubset) =>
% 132.32/22.89 ((
% 132.32/22.89 (binunionTILcontra) =>
% 132.32/22.89 ((
% 132.32/22.89 (binunionTIRcontra) =>
% 132.32/22.89 ((
% 132.32/22.89 (inIntersectImpInUnion) =>
% 132.32/22.89 ((
% 132.32/22.89 (inIntersectImpInUnion2) =>
% 132.32/22.89 ((
% 132.32/22.89 (inIntersectImpInIntersectUnions) =>
% 132.32/22.89 ((
% 132.32/22.89 (intersectInPowersetIntersectUnions) =>
% 132.32/22.89 ((
% 132.32/22.89 (inComplementUnionImpNotIn1) =>
% 132.32/22.89 ((
% 132.32/22.89 (inComplementUnionImpInComplement1) =>
% 132.32/22.89 ((
% 132.32/22.89 (binunionTE) =>
% 132.32/22.89 ((
% 132.32/22.89 (binunionTEcontra) =>
% 132.32/22.89 ((
% 132.32/22.89 (demorgan2a1) =>
% 132.32/22.89 ((
% 132.32/22.89 (complementUnionInPowersetComplement) =>
% 132.32/22.89 ((
% 132.32/22.89 (demorgan2a2) =>
% 132.32/22.89 ((
% 132.32/22.89 (demorgan1a) =>
% 132.32/22.89 ((
% 132.32/22.89 (demorgan1b) =>
% 132.32/22.89 ((
% 132.32/22.89 (demorgan1) =>
% 132.32/22.89 ((
% 132.32/22.89 (demorgan2a) =>
% 132.32/22.89 ((
% 132.32/22.89 (demorgan2b2) =>
% 132.32/22.89 ((
% 132.32/22.89 (demorgan2b) =>
% 132.32/22.89 ((
% 132.32/22.89 (demorgan2) =>
% 132.32/22.89 ((
% 132.32/22.89 (woz13rule0) =>
% 132.32/22.89 ((
% 132.32/22.89 (woz13rule1) =>
% 132.32/22.89 ((
% 132.32/22.89 (woz13rule2) =>
% 132.32/22.89 ((
% 132.32/22.89 (woz13rule3) =>
% 132.32/22.89 ((
% 132.32/22.89 (woz13rule4) =>
% 132.32/22.89 ((
% 132.32/22.89 (woz1_1) =>
% 132.32/22.89 ((
% 132.32/22.89 (woz1_2) =>
% 132.32/22.89 ((
% 132.32/22.89 (woz1_3) =>
% 132.32/22.89 ((
% 132.32/22.89 (woz1_4) =>
% 132.32/22.89 ((
% 132.32/22.89 (woz1_5) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1all2) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1SetBreln1) =>
% 132.32/22.89 ((
% 132.32/22.89 (choice2fnsingleton) =>
% 132.32/22.89 ((
% 132.32/22.89 (setOfPairsIsBReln1) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1all1) =>
% 132.32/22.89 ((
% 132.32/22.89 (subbreln1) =>
% 132.32/22.89 ((
% 132.32/22.89 (eqbreln1) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1invprop) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1invI) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1invE) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1compprop) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1compI) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1compE) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1compEex) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1unionprop) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1unionIL) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1unionIR) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1unionI) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1unionE) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1unionEcases) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1unionCommutes) =>
% 132.32/22.89 ((
% 132.32/22.89 (woz2Ex) =>
% 132.32/22.89 ((
% 132.32/22.89 (woz2W) =>
% 132.32/22.89 ((
% 132.32/22.89 (woz2A) =>
% 132.32/22.89 ((
% 132.32/22.89 (woz2B) =>
% 132.32/22.89 ((
% 132.32/22.89 (image1Ex) =>
% 132.32/22.89 ((
% 132.32/22.89 (image1Ex1) =>
% 132.32/22.89 ((
% 132.32/22.89 (image1Equiv) =>
% 132.32/22.89 ((
% 132.32/22.89 (image1E) =>
% 132.32/22.89 ((
% 132.32/22.89 (image1I) =>
% 132.32/22.89 ((
% 132.32/22.89 (injFuncInInjFuncSet) =>
% 132.32/22.89 ((
% 132.32/22.89 (injFuncSetFuncIn) =>
% 132.32/22.89 ((
% 132.32/22.89 (injFuncSetFuncInj) =>
% 132.32/22.89 ((
% 132.32/22.89 (surjFuncSetFuncIn) =>
% 132.32/22.89 ((
% 132.32/22.89 (surjFuncSetFuncSurj) =>
% 132.32/22.89 ((
% 132.32/22.89 (leftInvIsSurj) =>
% 132.32/22.89 ((
% 132.32/22.89 (surjCantorThm) =>
% 132.32/22.89 ((
% 132.32/22.89 (foundation2) =>
% 132.32/22.89 ((
% 132.32/22.89 (notinself) =>
% 132.32/22.89 ((
% 132.32/22.89 (notinself2) =>
% 132.32/22.89 ((
% 132.32/22.89 (omegaSp) =>
% 132.32/22.89 ((
% 132.32/22.89 (omegaSclos) =>
% 132.32/22.89 ((
% 132.32/22.89 (peano0notS) =>
% 132.32/22.89 ((
% 132.32/22.89 (peanoSinj) =>
% 132.32/22.89 ((
% 132.32/22.89 (transitivesetOp1) =>
% 132.32/22.89 ((
% 132.32/22.89 (binintTransitive) =>
% 132.32/22.89 ((
% 132.32/22.89 (transitivesetOp2) =>
% 132.32/22.89 ((
% 132.32/22.89 (setunionTransitive) =>
% 132.32/22.89 ((
% 132.32/22.89 (ordinalMinLem1) =>
% 132.32/22.89 ((
% 132.32/22.89 (ordinalTransSet) =>
% 132.32/22.89 ((
% 132.32/22.89 (ordinalTransSet1) =>
% 132.32/22.89 ((
% 132.32/22.89 (setunionOrdinalLem1) =>
% 132.32/22.89 (ordinal @
% 132.32/22.89 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.32/22.89 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl746])).
% 132.32/22.89 thf(zip_derived_cl770, plain,
% 132.32/22.89 (~ (((subsetE2) =>
% 132.32/22.89 (((notsubsetI) =>
% 132.32/22.89 (((notequalI1) =>
% 132.32/22.89 (((notequalI2) =>
% 132.32/22.89 (((subsetRefl) =>
% 132.32/22.89 (((subsetTrans) =>
% 132.32/22.89 (((setadjoinSub) =>
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% 132.32/22.89 (((binunionIR) =>
% 132.32/22.89 (((binunionEcases) =>
% 132.32/22.89 (((binunionE) =>
% 132.32/22.89 (((binunionLsub) =>
% 132.32/22.89 (((binunionRsub) =>
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% 132.32/22.89 (((binintersectSubset5) =>
% 132.32/22.89 (((binintersectEL) =>
% 132.32/22.89 (((binintersectLsub) =>
% 132.32/22.89 (((binintersectSubset2) =>
% 132.32/22.89 (((binintersectSubset3) =>
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% 132.32/22.89 ((
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% 132.32/22.89 ((
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% 132.32/22.89 ((
% 132.32/22.89 (binintersectSubset4) =>
% 132.32/22.89 ((
% 132.32/22.89 (binintersectSubset1) =>
% 132.32/22.89 ((
% 132.32/22.89 (bs114d) =>
% 132.32/22.89 ((
% 132.32/22.89 (setminusI) =>
% 132.32/22.89 ((
% 132.32/22.89 (setminusEL) =>
% 132.32/22.89 ((
% 132.32/22.89 (setminusER) =>
% 132.32/22.89 ((
% 132.32/22.89 (setminusSubset2) =>
% 132.32/22.89 ((
% 132.32/22.89 (setminusERneg) =>
% 132.32/22.89 ((
% 132.32/22.89 (setminusELneg) =>
% 132.32/22.89 ((
% 132.32/22.89 (setminusILneg) =>
% 132.32/22.89 ((
% 132.32/22.89 (setminusIRneg) =>
% 132.32/22.89 ((
% 132.32/22.89 (setminusLsub) =>
% 132.32/22.89 ((
% 132.32/22.89 (setminusSubset1) =>
% 132.32/22.89 ((
% 132.32/22.89 (symdiffE) =>
% 132.32/22.89 ((
% 132.32/22.89 (symdiffI1) =>
% 132.32/22.89 ((
% 132.32/22.89 (symdiffI2) =>
% 132.32/22.89 ((
% 132.32/22.89 (symdiffIneg1) =>
% 132.32/22.89 ((
% 132.32/22.89 (symdiffIneg2) =>
% 132.32/22.89 ((
% 132.32/22.89 (secondinupair) =>
% 132.32/22.89 ((
% 132.32/22.89 (setukpairIL) =>
% 132.32/22.89 ((
% 132.32/22.89 (setukpairIR) =>
% 132.32/22.89 ((
% 132.32/22.89 (kpairiskpair) =>
% 132.32/22.89 ((
% 132.32/22.89 (kpairp) =>
% 132.32/22.89 ((
% 132.32/22.89 (singletonsubset) =>
% 132.32/22.89 ((
% 132.32/22.89 (singletoninpowerset) =>
% 132.32/22.89 ((
% 132.32/22.89 (singletoninpowunion) =>
% 132.32/22.89 ((
% 132.32/22.89 (upairset2E) =>
% 132.32/22.89 ((
% 132.32/22.89 (upairsubunion) =>
% 132.32/22.89 ((
% 132.32/22.89 (upairinpowunion) =>
% 132.32/22.89 ((
% 132.32/22.89 (ubforcartprodlem1) =>
% 132.32/22.89 ((
% 132.32/22.89 (ubforcartprodlem2) =>
% 132.32/22.89 ((
% 132.32/22.89 (ubforcartprodlem3) =>
% 132.32/22.89 ((
% 132.32/22.89 (cartprodpairin) =>
% 132.32/22.89 ((
% 132.32/22.89 (cartprodmempair1) =>
% 132.32/22.89 ((
% 132.32/22.89 (cartprodmempair) =>
% 132.32/22.89 ((
% 132.32/22.89 (setunionE2) =>
% 132.32/22.89 ((
% 132.32/22.89 (setunionsingleton1) =>
% 132.32/22.89 ((
% 132.32/22.89 (setunionsingleton2) =>
% 132.32/22.89 ((
% 132.32/22.89 (setunionsingleton) =>
% 132.32/22.89 ((
% 132.32/22.89 (singletonprop) =>
% 132.32/22.89 ((
% 132.32/22.89 (ex1E1) =>
% 132.32/22.89 ((
% 132.32/22.89 (ex1I) =>
% 132.32/22.89 ((
% 132.32/22.89 (ex1I2) =>
% 132.32/22.89 ((
% 132.32/22.89 (singletonsuniq) =>
% 132.32/22.89 ((
% 132.32/22.89 (setukpairinjL1) =>
% 132.32/22.89 ((
% 132.32/22.89 (kfstsingleton) =>
% 132.32/22.89 ((
% 132.32/22.89 (theprop) =>
% 132.32/22.89 ((
% 132.32/22.89 (kfstpairEq) =>
% 132.32/22.89 ((
% 132.32/22.89 (cartprodfstin) =>
% 132.32/22.89 ((
% 132.32/22.89 (setukpairinjL2) =>
% 132.32/22.89 ((
% 132.32/22.89 (setukpairinjL) =>
% 132.32/22.89 ((
% 132.32/22.89 (setukpairinjR11) =>
% 132.32/22.89 ((
% 132.32/22.89 (setukpairinjR12) =>
% 132.32/22.89 ((
% 132.32/22.89 (setukpairinjR1) =>
% 132.32/22.89 ((
% 132.32/22.89 (upairequniteq) =>
% 132.32/22.89 ((
% 132.32/22.89 (setukpairinjR2) =>
% 132.32/22.89 ((
% 132.32/22.89 (setukpairinjR) =>
% 132.32/22.89 ((
% 132.32/22.89 (ksndsingleton) =>
% 132.32/22.89 ((
% 132.32/22.89 (ksndpairEq) =>
% 132.32/22.89 ((
% 132.32/22.89 (kpairsurjEq) =>
% 132.32/22.89 ((
% 132.32/22.89 (cartprodsndin) =>
% 132.32/22.89 ((
% 132.32/22.89 (cartprodpairmemEL) =>
% 132.32/22.89 ((
% 132.32/22.89 (cartprodpairmemER) =>
% 132.32/22.89 ((
% 132.32/22.89 (cartprodmempaircEq) =>
% 132.32/22.89 ((
% 132.32/22.89 (cartprodfstpairEq) =>
% 132.32/22.89 ((
% 132.32/22.89 (cartprodsndpairEq) =>
% 132.32/22.89 ((
% 132.32/22.89 (cartprodpairsurjEq) =>
% 132.32/22.89 ((
% 132.32/22.89 (dpsetconstrI) =>
% 132.32/22.89 ((
% 132.32/22.89 (dpsetconstrSub) =>
% 132.32/22.89 ((
% 132.32/22.89 (setOfPairsIsBReln) =>
% 132.32/22.89 ((
% 132.32/22.89 (dpsetconstrERa) =>
% 132.32/22.89 ((
% 132.32/22.89 (dpsetconstrEL1) =>
% 132.32/22.89 ((
% 132.32/22.89 (dpsetconstrEL2) =>
% 132.32/22.89 ((
% 132.32/22.89 (dpsetconstrER) =>
% 132.32/22.89 ((
% 132.32/22.89 (funcImageSingleton) =>
% 132.32/22.89 ((
% 132.32/22.89 (apProp) =>
% 132.32/22.89 ((
% 132.32/22.89 (app) =>
% 132.32/22.89 ((
% 132.32/22.89 (infuncsetfunc) =>
% 132.32/22.89 ((
% 132.32/22.89 (ap2p) =>
% 132.32/22.89 ((
% 132.32/22.89 (funcinfuncset) =>
% 132.32/22.89 ((
% 132.32/22.89 (lamProp) =>
% 132.32/22.89 ((
% 132.32/22.89 (lamp) =>
% 132.32/22.89 ((
% 132.32/22.89 (lam2p) =>
% 132.32/22.89 ((
% 132.32/22.89 (brelnall1) =>
% 132.32/22.89 ((
% 132.32/22.89 (brelnall2) =>
% 132.32/22.89 ((
% 132.32/22.89 (ex1E2) =>
% 132.32/22.89 ((
% 132.32/22.89 (funcGraphProp1) =>
% 132.32/22.89 ((
% 132.32/22.89 (funcGraphProp3) =>
% 132.32/22.89 ((
% 132.32/22.89 (funcGraphProp2) =>
% 132.32/22.89 ((
% 132.32/22.89 (funcextLem) =>
% 132.32/22.89 ((
% 132.32/22.89 (funcGraphProp4) =>
% 132.32/22.89 ((
% 132.32/22.89 (subbreln) =>
% 132.32/22.89 ((
% 132.32/22.89 (eqbreln) =>
% 132.32/22.89 ((
% 132.32/22.89 (funcext) =>
% 132.32/22.89 ((
% 132.32/22.89 (funcext2) =>
% 132.32/22.89 ((
% 132.32/22.89 (ap2apEq1) =>
% 132.32/22.89 ((
% 132.32/22.89 (ap2apEq2) =>
% 132.32/22.89 ((
% 132.32/22.89 (beta1) =>
% 132.32/22.89 ((
% 132.32/22.89 (eta1) =>
% 132.32/22.89 ((
% 132.32/22.89 (lam2lamEq) =>
% 132.32/22.89 ((
% 132.32/22.89 (beta2) =>
% 132.32/22.89 ((
% 132.32/22.89 (eta2) =>
% 132.32/22.89 ((
% 132.32/22.89 (iffalseProp1) =>
% 132.32/22.89 ((
% 132.32/22.89 (iffalseProp2) =>
% 132.32/22.89 ((
% 132.32/22.89 (iftrueProp1) =>
% 132.32/22.89 ((
% 132.32/22.89 (iftrueProp2) =>
% 132.32/22.89 ((
% 132.32/22.89 (ifSingleton) =>
% 132.32/22.89 ((
% 132.32/22.89 (ifp) =>
% 132.32/22.89 ((
% 132.32/22.89 (theeq) =>
% 132.32/22.89 ((
% 132.32/22.89 (iftrue) =>
% 132.32/22.89 ((
% 132.32/22.89 (iffalse) =>
% 132.32/22.89 ((
% 132.32/22.89 (iftrueorfalse) =>
% 132.32/22.89 ((
% 132.32/22.89 (binintersectT_lem) =>
% 132.32/22.89 ((
% 132.32/22.89 (binunionT_lem) =>
% 132.32/22.89 ((
% 132.32/22.89 (powersetT_lem) =>
% 132.32/22.89 ((
% 132.32/22.89 (setminusT_lem) =>
% 132.32/22.89 ((
% 132.32/22.89 (complementT_lem) =>
% 132.32/22.89 ((
% 132.32/22.89 (setextT) =>
% 132.32/22.89 ((
% 132.32/22.89 (subsetTI) =>
% 132.32/22.89 ((
% 132.32/22.89 (powersetTI1) =>
% 132.32/22.89 ((
% 132.32/22.89 (powersetTE1) =>
% 132.32/22.89 ((
% 132.32/22.89 (complementTI1) =>
% 132.32/22.89 ((
% 132.32/22.89 (complementTE1) =>
% 132.32/22.89 ((
% 132.32/22.89 (binintersectTELcontra) =>
% 132.32/22.89 ((
% 132.32/22.89 (binintersectTERcontra) =>
% 132.32/22.89 ((
% 132.32/22.89 (contrasubsetT) =>
% 132.32/22.89 ((
% 132.32/22.89 (contrasubsetT1) =>
% 132.32/22.89 ((
% 132.32/22.89 (contrasubsetT2) =>
% 132.32/22.89 ((
% 132.32/22.89 (contrasubsetT3) =>
% 132.32/22.89 ((
% 132.32/22.89 (doubleComplementI1) =>
% 132.32/22.89 ((
% 132.32/22.89 (doubleComplementE1) =>
% 132.32/22.89 ((
% 132.32/22.89 (doubleComplementSub1) =>
% 132.32/22.89 ((
% 132.32/22.89 (doubleComplementSub2) =>
% 132.32/22.89 ((
% 132.32/22.89 (doubleComplementEq) =>
% 132.32/22.89 ((
% 132.32/22.89 (complementTnotintersectT) =>
% 132.32/22.89 ((
% 132.32/22.89 (complementImpComplementIntersect) =>
% 132.32/22.89 ((
% 132.32/22.89 (complementSubsetComplementIntersect) =>
% 132.32/22.89 ((
% 132.32/22.89 (complementInPowersetComplementIntersect) =>
% 132.32/22.89 ((
% 132.32/22.89 (contraSubsetComplement) =>
% 132.32/22.89 ((
% 132.32/22.89 (complementTcontraSubset) =>
% 132.32/22.89 ((
% 132.32/22.89 (binunionTILcontra) =>
% 132.32/22.89 ((
% 132.32/22.89 (binunionTIRcontra) =>
% 132.32/22.89 ((
% 132.32/22.89 (inIntersectImpInUnion) =>
% 132.32/22.89 ((
% 132.32/22.89 (inIntersectImpInUnion2) =>
% 132.32/22.89 ((
% 132.32/22.89 (inIntersectImpInIntersectUnions) =>
% 132.32/22.89 ((
% 132.32/22.89 (intersectInPowersetIntersectUnions) =>
% 132.32/22.89 ((
% 132.32/22.89 (inComplementUnionImpNotIn1) =>
% 132.32/22.89 ((
% 132.32/22.89 (inComplementUnionImpInComplement1) =>
% 132.32/22.89 ((
% 132.32/22.89 (binunionTE) =>
% 132.32/22.89 ((
% 132.32/22.89 (binunionTEcontra) =>
% 132.32/22.89 ((
% 132.32/22.89 (demorgan2a1) =>
% 132.32/22.89 ((
% 132.32/22.89 (complementUnionInPowersetComplement) =>
% 132.32/22.89 ((
% 132.32/22.89 (demorgan2a2) =>
% 132.32/22.89 ((
% 132.32/22.89 (demorgan1a) =>
% 132.32/22.89 ((
% 132.32/22.89 (demorgan1b) =>
% 132.32/22.89 ((
% 132.32/22.89 (demorgan1) =>
% 132.32/22.89 ((
% 132.32/22.89 (demorgan2a) =>
% 132.32/22.89 ((
% 132.32/22.89 (demorgan2b2) =>
% 132.32/22.89 ((
% 132.32/22.89 (demorgan2b) =>
% 132.32/22.89 ((
% 132.32/22.89 (demorgan2) =>
% 132.32/22.89 ((
% 132.32/22.89 (woz13rule0) =>
% 132.32/22.89 ((
% 132.32/22.89 (woz13rule1) =>
% 132.32/22.89 ((
% 132.32/22.89 (woz13rule2) =>
% 132.32/22.89 ((
% 132.32/22.89 (woz13rule3) =>
% 132.32/22.89 ((
% 132.32/22.89 (woz13rule4) =>
% 132.32/22.89 ((
% 132.32/22.89 (woz1_1) =>
% 132.32/22.89 ((
% 132.32/22.89 (woz1_2) =>
% 132.32/22.89 ((
% 132.32/22.89 (woz1_3) =>
% 132.32/22.89 ((
% 132.32/22.89 (woz1_4) =>
% 132.32/22.89 ((
% 132.32/22.89 (woz1_5) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1all2) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1SetBreln1) =>
% 132.32/22.89 ((
% 132.32/22.89 (choice2fnsingleton) =>
% 132.32/22.89 ((
% 132.32/22.89 (setOfPairsIsBReln1) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1all1) =>
% 132.32/22.89 ((
% 132.32/22.89 (subbreln1) =>
% 132.32/22.89 ((
% 132.32/22.89 (eqbreln1) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1invprop) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1invI) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1invE) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1compprop) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1compI) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1compE) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1compEex) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1unionprop) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1unionIL) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1unionIR) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1unionI) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1unionE) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1unionEcases) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1unionCommutes) =>
% 132.32/22.89 ((
% 132.32/22.89 (woz2Ex) =>
% 132.32/22.89 ((
% 132.32/22.89 (woz2W) =>
% 132.32/22.89 ((
% 132.32/22.89 (woz2A) =>
% 132.32/22.89 ((
% 132.32/22.89 (woz2B) =>
% 132.32/22.89 ((
% 132.32/22.89 (image1Ex) =>
% 132.32/22.89 ((
% 132.32/22.89 (image1Ex1) =>
% 132.32/22.89 ((
% 132.32/22.89 (image1Equiv) =>
% 132.32/22.89 ((
% 132.32/22.89 (image1E) =>
% 132.32/22.89 ((
% 132.32/22.89 (image1I) =>
% 132.32/22.89 ((
% 132.32/22.89 (injFuncInInjFuncSet) =>
% 132.32/22.89 ((
% 132.32/22.89 (injFuncSetFuncIn) =>
% 132.32/22.89 ((
% 132.32/22.89 (injFuncSetFuncInj) =>
% 132.32/22.89 ((
% 132.32/22.89 (surjFuncSetFuncIn) =>
% 132.32/22.89 ((
% 132.32/22.89 (surjFuncSetFuncSurj) =>
% 132.32/22.89 ((
% 132.32/22.89 (leftInvIsSurj) =>
% 132.32/22.89 ((
% 132.32/22.89 (surjCantorThm) =>
% 132.32/22.89 ((
% 132.32/22.89 (foundation2) =>
% 132.32/22.89 ((
% 132.32/22.89 (notinself) =>
% 132.32/22.89 ((
% 132.32/22.89 (notinself2) =>
% 132.32/22.89 ((
% 132.32/22.89 (omegaSp) =>
% 132.32/22.89 ((
% 132.32/22.89 (omegaSclos) =>
% 132.32/22.89 ((
% 132.32/22.89 (peano0notS) =>
% 132.32/22.89 ((
% 132.32/22.89 (peanoSinj) =>
% 132.32/22.89 ((
% 132.32/22.89 (transitivesetOp1) =>
% 132.32/22.89 ((
% 132.32/22.89 (binintTransitive) =>
% 132.32/22.89 ((
% 132.32/22.89 (transitivesetOp2) =>
% 132.32/22.89 ((
% 132.32/22.89 (setunionTransitive) =>
% 132.32/22.89 ((
% 132.32/22.89 (ordinalMinLem1) =>
% 132.32/22.89 ((
% 132.32/22.89 (ordinalTransSet) =>
% 132.32/22.89 ((
% 132.32/22.89 (ordinalTransSet1) =>
% 132.32/22.89 ((
% 132.32/22.89 (setunionOrdinalLem1) =>
% 132.32/22.89 (ordinal @
% 132.32/22.89 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.32/22.89 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl758])).
% 132.32/22.89 thf(zip_derived_cl783, plain,
% 132.32/22.89 (~ (((notsubsetI) =>
% 132.32/22.89 (((notequalI1) =>
% 132.32/22.89 (((notequalI2) =>
% 132.32/22.89 (((subsetRefl) =>
% 132.32/22.89 (((subsetTrans) =>
% 132.32/22.89 (((setadjoinSub) =>
% 132.32/22.89 (((setadjoinSub2) =>
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% 132.32/22.89 (((setextsub) =>
% 132.32/22.89 (((subsetemptysetimpeq) =>
% 132.32/22.89 (((powersetI1) =>
% 132.32/22.89 (((powersetE1) =>
% 132.32/22.89 (((inPowerset) =>
% 132.32/22.89 (((powersetsubset) =>
% 132.32/22.89 (((sepInPowerset) =>
% 132.32/22.89 (((sepSubset) =>
% 132.32/22.89 (((binunionIL) =>
% 132.32/22.89 (((upairset2IR) =>
% 132.32/22.89 (((binunionIR) =>
% 132.32/22.89 (((binunionEcases) =>
% 132.32/22.89 (((binunionE) =>
% 132.32/22.89 (((binunionLsub) =>
% 132.32/22.89 (((binunionRsub) =>
% 132.32/22.89 (((binintersectI) =>
% 132.32/22.89 (((binintersectSubset5) =>
% 132.32/22.89 (((binintersectEL) =>
% 132.32/22.89 (((binintersectLsub) =>
% 132.32/22.89 (((binintersectSubset2) =>
% 132.32/22.89 (((binintersectSubset3) =>
% 132.32/22.89 (((binintersectER) =>
% 132.32/22.89 ((
% 132.32/22.89 (disjointsetsI1) =>
% 132.32/22.89 ((
% 132.32/22.89 (binintersectRsub) =>
% 132.32/22.89 ((
% 132.32/22.89 (binintersectSubset4) =>
% 132.32/22.89 ((
% 132.32/22.89 (binintersectSubset1) =>
% 132.32/22.89 ((
% 132.32/22.89 (bs114d) =>
% 132.32/22.89 ((
% 132.32/22.89 (setminusI) =>
% 132.32/22.89 ((
% 132.32/22.89 (setminusEL) =>
% 132.32/22.89 ((
% 132.32/22.89 (setminusER) =>
% 132.32/22.89 ((
% 132.32/22.89 (setminusSubset2) =>
% 132.32/22.89 ((
% 132.32/22.89 (setminusERneg) =>
% 132.32/22.89 ((
% 132.32/22.89 (setminusELneg) =>
% 132.32/22.89 ((
% 132.32/22.89 (setminusILneg) =>
% 132.32/22.89 ((
% 132.32/22.89 (setminusIRneg) =>
% 132.32/22.89 ((
% 132.32/22.89 (setminusLsub) =>
% 132.32/22.89 ((
% 132.32/22.89 (setminusSubset1) =>
% 132.32/22.89 ((
% 132.32/22.89 (symdiffE) =>
% 132.32/22.89 ((
% 132.32/22.89 (symdiffI1) =>
% 132.32/22.89 ((
% 132.32/22.89 (symdiffI2) =>
% 132.32/22.89 ((
% 132.32/22.89 (symdiffIneg1) =>
% 132.32/22.89 ((
% 132.32/22.89 (symdiffIneg2) =>
% 132.32/22.89 ((
% 132.32/22.89 (secondinupair) =>
% 132.32/22.89 ((
% 132.32/22.89 (setukpairIL) =>
% 132.32/22.89 ((
% 132.32/22.89 (setukpairIR) =>
% 132.32/22.89 ((
% 132.32/22.89 (kpairiskpair) =>
% 132.32/22.89 ((
% 132.32/22.89 (kpairp) =>
% 132.32/22.89 ((
% 132.32/22.89 (singletonsubset) =>
% 132.32/22.89 ((
% 132.32/22.89 (singletoninpowerset) =>
% 132.32/22.89 ((
% 132.32/22.89 (singletoninpowunion) =>
% 132.32/22.89 ((
% 132.32/22.89 (upairset2E) =>
% 132.32/22.89 ((
% 132.32/22.89 (upairsubunion) =>
% 132.32/22.89 ((
% 132.32/22.89 (upairinpowunion) =>
% 132.32/22.89 ((
% 132.32/22.89 (ubforcartprodlem1) =>
% 132.32/22.89 ((
% 132.32/22.89 (ubforcartprodlem2) =>
% 132.32/22.89 ((
% 132.32/22.89 (ubforcartprodlem3) =>
% 132.32/22.89 ((
% 132.32/22.89 (cartprodpairin) =>
% 132.32/22.89 ((
% 132.32/22.89 (cartprodmempair1) =>
% 132.32/22.89 ((
% 132.32/22.89 (cartprodmempair) =>
% 132.32/22.89 ((
% 132.32/22.89 (setunionE2) =>
% 132.32/22.89 ((
% 132.32/22.89 (setunionsingleton1) =>
% 132.32/22.89 ((
% 132.32/22.89 (setunionsingleton2) =>
% 132.32/22.89 ((
% 132.32/22.89 (setunionsingleton) =>
% 132.32/22.89 ((
% 132.32/22.89 (singletonprop) =>
% 132.32/22.89 ((
% 132.32/22.89 (ex1E1) =>
% 132.32/22.89 ((
% 132.32/22.89 (ex1I) =>
% 132.32/22.89 ((
% 132.32/22.89 (ex1I2) =>
% 132.32/22.89 ((
% 132.32/22.89 (singletonsuniq) =>
% 132.32/22.89 ((
% 132.32/22.89 (setukpairinjL1) =>
% 132.32/22.89 ((
% 132.32/22.89 (kfstsingleton) =>
% 132.32/22.89 ((
% 132.32/22.89 (theprop) =>
% 132.32/22.89 ((
% 132.32/22.89 (kfstpairEq) =>
% 132.32/22.89 ((
% 132.32/22.89 (cartprodfstin) =>
% 132.32/22.89 ((
% 132.32/22.89 (setukpairinjL2) =>
% 132.32/22.89 ((
% 132.32/22.89 (setukpairinjL) =>
% 132.32/22.89 ((
% 132.32/22.89 (setukpairinjR11) =>
% 132.32/22.89 ((
% 132.32/22.89 (setukpairinjR12) =>
% 132.32/22.89 ((
% 132.32/22.89 (setukpairinjR1) =>
% 132.32/22.89 ((
% 132.32/22.89 (upairequniteq) =>
% 132.32/22.89 ((
% 132.32/22.89 (setukpairinjR2) =>
% 132.32/22.89 ((
% 132.32/22.89 (setukpairinjR) =>
% 132.32/22.89 ((
% 132.32/22.89 (ksndsingleton) =>
% 132.32/22.89 ((
% 132.32/22.89 (ksndpairEq) =>
% 132.32/22.89 ((
% 132.32/22.89 (kpairsurjEq) =>
% 132.32/22.89 ((
% 132.32/22.89 (cartprodsndin) =>
% 132.32/22.89 ((
% 132.32/22.89 (cartprodpairmemEL) =>
% 132.32/22.89 ((
% 132.32/22.89 (cartprodpairmemER) =>
% 132.32/22.89 ((
% 132.32/22.89 (cartprodmempaircEq) =>
% 132.32/22.89 ((
% 132.32/22.89 (cartprodfstpairEq) =>
% 132.32/22.89 ((
% 132.32/22.89 (cartprodsndpairEq) =>
% 132.32/22.89 ((
% 132.32/22.89 (cartprodpairsurjEq) =>
% 132.32/22.89 ((
% 132.32/22.89 (dpsetconstrI) =>
% 132.32/22.89 ((
% 132.32/22.89 (dpsetconstrSub) =>
% 132.32/22.89 ((
% 132.32/22.89 (setOfPairsIsBReln) =>
% 132.32/22.89 ((
% 132.32/22.89 (dpsetconstrERa) =>
% 132.32/22.89 ((
% 132.32/22.89 (dpsetconstrEL1) =>
% 132.32/22.89 ((
% 132.32/22.89 (dpsetconstrEL2) =>
% 132.32/22.89 ((
% 132.32/22.89 (dpsetconstrER) =>
% 132.32/22.89 ((
% 132.32/22.89 (funcImageSingleton) =>
% 132.32/22.89 ((
% 132.32/22.89 (apProp) =>
% 132.32/22.89 ((
% 132.32/22.89 (app) =>
% 132.32/22.89 ((
% 132.32/22.89 (infuncsetfunc) =>
% 132.32/22.89 ((
% 132.32/22.89 (ap2p) =>
% 132.32/22.89 ((
% 132.32/22.89 (funcinfuncset) =>
% 132.32/22.89 ((
% 132.32/22.89 (lamProp) =>
% 132.32/22.89 ((
% 132.32/22.89 (lamp) =>
% 132.32/22.89 ((
% 132.32/22.89 (lam2p) =>
% 132.32/22.89 ((
% 132.32/22.89 (brelnall1) =>
% 132.32/22.89 ((
% 132.32/22.89 (brelnall2) =>
% 132.32/22.89 ((
% 132.32/22.89 (ex1E2) =>
% 132.32/22.89 ((
% 132.32/22.89 (funcGraphProp1) =>
% 132.32/22.89 ((
% 132.32/22.89 (funcGraphProp3) =>
% 132.32/22.89 ((
% 132.32/22.89 (funcGraphProp2) =>
% 132.32/22.89 ((
% 132.32/22.89 (funcextLem) =>
% 132.32/22.89 ((
% 132.32/22.89 (funcGraphProp4) =>
% 132.32/22.89 ((
% 132.32/22.89 (subbreln) =>
% 132.32/22.89 ((
% 132.32/22.89 (eqbreln) =>
% 132.32/22.89 ((
% 132.32/22.89 (funcext) =>
% 132.32/22.89 ((
% 132.32/22.89 (funcext2) =>
% 132.32/22.89 ((
% 132.32/22.89 (ap2apEq1) =>
% 132.32/22.89 ((
% 132.32/22.89 (ap2apEq2) =>
% 132.32/22.89 ((
% 132.32/22.89 (beta1) =>
% 132.32/22.89 ((
% 132.32/22.89 (eta1) =>
% 132.32/22.89 ((
% 132.32/22.89 (lam2lamEq) =>
% 132.32/22.89 ((
% 132.32/22.89 (beta2) =>
% 132.32/22.89 ((
% 132.32/22.89 (eta2) =>
% 132.32/22.89 ((
% 132.32/22.89 (iffalseProp1) =>
% 132.32/22.89 ((
% 132.32/22.89 (iffalseProp2) =>
% 132.32/22.89 ((
% 132.32/22.89 (iftrueProp1) =>
% 132.32/22.89 ((
% 132.32/22.89 (iftrueProp2) =>
% 132.32/22.89 ((
% 132.32/22.89 (ifSingleton) =>
% 132.32/22.89 ((
% 132.32/22.89 (ifp) =>
% 132.32/22.89 ((
% 132.32/22.89 (theeq) =>
% 132.32/22.89 ((
% 132.32/22.89 (iftrue) =>
% 132.32/22.89 ((
% 132.32/22.89 (iffalse) =>
% 132.32/22.89 ((
% 132.32/22.89 (iftrueorfalse) =>
% 132.32/22.89 ((
% 132.32/22.89 (binintersectT_lem) =>
% 132.32/22.89 ((
% 132.32/22.89 (binunionT_lem) =>
% 132.32/22.89 ((
% 132.32/22.89 (powersetT_lem) =>
% 132.32/22.89 ((
% 132.32/22.89 (setminusT_lem) =>
% 132.32/22.89 ((
% 132.32/22.89 (complementT_lem) =>
% 132.32/22.89 ((
% 132.32/22.89 (setextT) =>
% 132.32/22.89 ((
% 132.32/22.89 (subsetTI) =>
% 132.32/22.89 ((
% 132.32/22.89 (powersetTI1) =>
% 132.32/22.89 ((
% 132.32/22.89 (powersetTE1) =>
% 132.32/22.89 ((
% 132.32/22.89 (complementTI1) =>
% 132.32/22.89 ((
% 132.32/22.89 (complementTE1) =>
% 132.32/22.89 ((
% 132.32/22.89 (binintersectTELcontra) =>
% 132.32/22.89 ((
% 132.32/22.89 (binintersectTERcontra) =>
% 132.32/22.89 ((
% 132.32/22.89 (contrasubsetT) =>
% 132.32/22.89 ((
% 132.32/22.89 (contrasubsetT1) =>
% 132.32/22.89 ((
% 132.32/22.89 (contrasubsetT2) =>
% 132.32/22.89 ((
% 132.32/22.89 (contrasubsetT3) =>
% 132.32/22.89 ((
% 132.32/22.89 (doubleComplementI1) =>
% 132.32/22.89 ((
% 132.32/22.89 (doubleComplementE1) =>
% 132.32/22.89 ((
% 132.32/22.89 (doubleComplementSub1) =>
% 132.32/22.89 ((
% 132.32/22.89 (doubleComplementSub2) =>
% 132.32/22.89 ((
% 132.32/22.89 (doubleComplementEq) =>
% 132.32/22.89 ((
% 132.32/22.89 (complementTnotintersectT) =>
% 132.32/22.89 ((
% 132.32/22.89 (complementImpComplementIntersect) =>
% 132.32/22.89 ((
% 132.32/22.89 (complementSubsetComplementIntersect) =>
% 132.32/22.89 ((
% 132.32/22.89 (complementInPowersetComplementIntersect) =>
% 132.32/22.89 ((
% 132.32/22.89 (contraSubsetComplement) =>
% 132.32/22.89 ((
% 132.32/22.89 (complementTcontraSubset) =>
% 132.32/22.89 ((
% 132.32/22.89 (binunionTILcontra) =>
% 132.32/22.89 ((
% 132.32/22.89 (binunionTIRcontra) =>
% 132.32/22.89 ((
% 132.32/22.89 (inIntersectImpInUnion) =>
% 132.32/22.89 ((
% 132.32/22.89 (inIntersectImpInUnion2) =>
% 132.32/22.89 ((
% 132.32/22.89 (inIntersectImpInIntersectUnions) =>
% 132.32/22.89 ((
% 132.32/22.89 (intersectInPowersetIntersectUnions) =>
% 132.32/22.89 ((
% 132.32/22.89 (inComplementUnionImpNotIn1) =>
% 132.32/22.89 ((
% 132.32/22.89 (inComplementUnionImpInComplement1) =>
% 132.32/22.89 ((
% 132.32/22.89 (binunionTE) =>
% 132.32/22.89 ((
% 132.32/22.89 (binunionTEcontra) =>
% 132.32/22.89 ((
% 132.32/22.89 (demorgan2a1) =>
% 132.32/22.89 ((
% 132.32/22.89 (complementUnionInPowersetComplement) =>
% 132.32/22.89 ((
% 132.32/22.89 (demorgan2a2) =>
% 132.32/22.89 ((
% 132.32/22.89 (demorgan1a) =>
% 132.32/22.89 ((
% 132.32/22.89 (demorgan1b) =>
% 132.32/22.89 ((
% 132.32/22.89 (demorgan1) =>
% 132.32/22.89 ((
% 132.32/22.89 (demorgan2a) =>
% 132.32/22.89 ((
% 132.32/22.89 (demorgan2b2) =>
% 132.32/22.89 ((
% 132.32/22.89 (demorgan2b) =>
% 132.32/22.89 ((
% 132.32/22.89 (demorgan2) =>
% 132.32/22.89 ((
% 132.32/22.89 (woz13rule0) =>
% 132.32/22.89 ((
% 132.32/22.89 (woz13rule1) =>
% 132.32/22.89 ((
% 132.32/22.89 (woz13rule2) =>
% 132.32/22.89 ((
% 132.32/22.89 (woz13rule3) =>
% 132.32/22.89 ((
% 132.32/22.89 (woz13rule4) =>
% 132.32/22.89 ((
% 132.32/22.89 (woz1_1) =>
% 132.32/22.89 ((
% 132.32/22.89 (woz1_2) =>
% 132.32/22.89 ((
% 132.32/22.89 (woz1_3) =>
% 132.32/22.89 ((
% 132.32/22.89 (woz1_4) =>
% 132.32/22.89 ((
% 132.32/22.89 (woz1_5) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1all2) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1SetBreln1) =>
% 132.32/22.89 ((
% 132.32/22.89 (choice2fnsingleton) =>
% 132.32/22.89 ((
% 132.32/22.89 (setOfPairsIsBReln1) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1all1) =>
% 132.32/22.89 ((
% 132.32/22.89 (subbreln1) =>
% 132.32/22.89 ((
% 132.32/22.89 (eqbreln1) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1invprop) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1invI) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1invE) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1compprop) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1compI) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1compE) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1compEex) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1unionprop) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1unionIL) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1unionIR) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1unionI) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1unionE) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1unionEcases) =>
% 132.32/22.89 ((
% 132.32/22.89 (breln1unionCommutes) =>
% 132.32/22.89 ((
% 132.32/22.89 (woz2Ex) =>
% 132.32/22.89 ((
% 132.32/22.89 (woz2W) =>
% 132.32/22.89 ((
% 132.32/22.89 (woz2A) =>
% 132.32/22.89 ((
% 132.32/22.89 (woz2B) =>
% 132.32/22.89 ((
% 132.32/22.89 (image1Ex) =>
% 132.32/22.89 ((
% 132.32/22.89 (image1Ex1) =>
% 132.32/22.89 ((
% 132.32/22.89 (image1Equiv) =>
% 132.32/22.89 ((
% 132.32/22.89 (image1E) =>
% 132.32/22.89 ((
% 132.32/22.89 (image1I) =>
% 132.32/22.89 ((
% 132.32/22.89 (injFuncInInjFuncSet) =>
% 132.32/22.89 ((
% 132.32/22.89 (injFuncSetFuncIn) =>
% 132.32/22.89 ((
% 132.32/22.89 (injFuncSetFuncInj) =>
% 132.32/22.89 ((
% 132.32/22.89 (surjFuncSetFuncIn) =>
% 132.32/22.89 ((
% 132.32/22.89 (surjFuncSetFuncSurj) =>
% 132.32/22.89 ((
% 132.32/22.89 (leftInvIsSurj) =>
% 132.32/22.89 ((
% 132.32/22.89 (surjCantorThm) =>
% 132.32/22.89 ((
% 132.32/22.89 (foundation2) =>
% 132.32/22.89 ((
% 132.32/22.89 (notinself) =>
% 132.32/22.89 ((
% 132.32/22.89 (notinself2) =>
% 132.32/22.89 ((
% 132.32/22.89 (omegaSp) =>
% 132.32/22.89 ((
% 132.32/22.89 (omegaSclos) =>
% 132.32/22.89 ((
% 132.32/22.89 (peano0notS) =>
% 132.32/22.89 ((
% 132.32/22.89 (peanoSinj) =>
% 132.32/22.89 ((
% 132.32/22.89 (transitivesetOp1) =>
% 132.32/22.89 ((
% 132.32/22.89 (binintTransitive) =>
% 132.32/22.89 ((
% 132.32/22.89 (transitivesetOp2) =>
% 132.32/22.89 ((
% 132.32/22.89 (setunionTransitive) =>
% 132.32/22.89 ((
% 132.32/22.89 (ordinalMinLem1) =>
% 132.32/22.89 ((
% 132.32/22.89 (ordinalTransSet) =>
% 132.32/22.89 ((
% 132.32/22.89 (ordinalTransSet1) =>
% 132.32/22.89 ((
% 132.32/22.89 (setunionOrdinalLem1) =>
% 132.32/22.89 (ordinal @
% 132.32/22.89 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.32/22.89 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl770])).
% 132.32/22.89 thf(zip_derived_cl795, plain,
% 132.32/22.89 (~ (((notequalI1) =>
% 132.32/22.89 (((notequalI2) =>
% 132.32/22.89 (((subsetRefl) =>
% 132.32/22.89 (((subsetTrans) =>
% 132.32/22.89 (((setadjoinSub) =>
% 132.32/22.89 (((setadjoinSub2) =>
% 132.32/22.89 (((subset2powerset) =>
% 132.32/22.89 (((setextsub) =>
% 132.32/22.89 (((subsetemptysetimpeq) =>
% 132.32/22.89 (((powersetI1) =>
% 132.32/22.89 (((powersetE1) =>
% 132.32/22.89 (((inPowerset) =>
% 132.32/22.89 (((powersetsubset) =>
% 132.32/22.89 (((sepInPowerset) =>
% 132.32/22.89 (((sepSubset) =>
% 132.32/22.89 (((binunionIL) =>
% 132.32/22.89 (((upairset2IR) =>
% 132.32/22.89 (((binunionIR) =>
% 132.32/22.89 (((binunionEcases) =>
% 132.32/22.89 (((binunionE) =>
% 132.32/22.89 (((binunionLsub) =>
% 132.32/22.89 (((binunionRsub) =>
% 132.32/22.89 (((binintersectI) =>
% 132.32/22.89 (((binintersectSubset5) =>
% 132.32/22.89 (((binintersectEL) =>
% 132.32/22.89 (((binintersectLsub) =>
% 132.32/22.89 (((binintersectSubset2) =>
% 132.32/22.89 (((binintersectSubset3) =>
% 132.32/22.89 (((binintersectER) =>
% 132.32/22.89 (((disjointsetsI1) =>
% 132.32/22.89 ((
% 132.32/22.89 (binintersectRsub) =>
% 132.32/22.89 ((
% 132.32/22.89 (binintersectSubset4) =>
% 132.32/22.89 ((
% 132.32/22.89 (binintersectSubset1) =>
% 132.32/22.89 ((
% 132.32/22.89 (bs114d) =>
% 132.32/22.89 ((
% 132.32/22.89 (setminusI) =>
% 132.32/22.89 ((
% 132.32/22.89 (setminusEL) =>
% 132.32/22.89 ((
% 132.32/22.89 (setminusER) =>
% 132.32/22.89 ((
% 132.32/22.89 (setminusSubset2) =>
% 132.32/22.89 ((
% 132.32/22.89 (setminusERneg) =>
% 132.32/22.89 ((
% 132.32/22.89 (setminusELneg) =>
% 132.32/22.89 ((
% 132.32/22.89 (setminusILneg) =>
% 132.32/22.89 ((
% 132.32/22.89 (setminusIRneg) =>
% 132.32/22.89 ((
% 132.32/22.89 (setminusLsub) =>
% 132.32/22.89 ((
% 132.32/22.89 (setminusSubset1) =>
% 132.32/22.89 ((
% 132.32/22.89 (symdiffE) =>
% 132.32/22.89 ((
% 132.32/22.89 (symdiffI1) =>
% 132.32/22.89 ((
% 132.32/22.89 (symdiffI2) =>
% 132.32/22.89 ((
% 132.32/22.89 (symdiffIneg1) =>
% 132.32/22.89 ((
% 132.32/22.89 (symdiffIneg2) =>
% 132.32/22.89 ((
% 132.32/22.89 (secondinupair) =>
% 132.32/22.89 ((
% 132.32/22.89 (setukpairIL) =>
% 132.32/22.89 ((
% 132.32/22.89 (setukpairIR) =>
% 132.32/22.89 ((
% 132.32/22.89 (kpairiskpair) =>
% 132.32/22.89 ((
% 132.32/22.89 (kpairp) =>
% 132.32/22.89 ((
% 132.32/22.89 (singletonsubset) =>
% 132.32/22.89 ((
% 132.32/22.89 (singletoninpowerset) =>
% 132.32/22.89 ((
% 132.32/22.89 (singletoninpowunion) =>
% 132.32/22.89 ((
% 132.32/22.89 (upairset2E) =>
% 132.32/22.90 ((
% 132.32/22.90 (upairsubunion) =>
% 132.32/22.90 ((
% 132.32/22.90 (upairinpowunion) =>
% 132.32/22.90 ((
% 132.32/22.90 (ubforcartprodlem1) =>
% 132.32/22.90 ((
% 132.32/22.90 (ubforcartprodlem2) =>
% 132.32/22.90 ((
% 132.32/22.90 (ubforcartprodlem3) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodpairin) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodmempair1) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodmempair) =>
% 132.32/22.90 ((
% 132.32/22.90 (setunionE2) =>
% 132.32/22.90 ((
% 132.32/22.90 (setunionsingleton1) =>
% 132.32/22.90 ((
% 132.32/22.90 (setunionsingleton2) =>
% 132.32/22.90 ((
% 132.32/22.90 (setunionsingleton) =>
% 132.32/22.90 ((
% 132.32/22.90 (singletonprop) =>
% 132.32/22.90 ((
% 132.32/22.90 (ex1E1) =>
% 132.32/22.90 ((
% 132.32/22.90 (ex1I) =>
% 132.32/22.90 ((
% 132.32/22.90 (ex1I2) =>
% 132.32/22.90 ((
% 132.32/22.90 (singletonsuniq) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairinjL1) =>
% 132.32/22.90 ((
% 132.32/22.90 (kfstsingleton) =>
% 132.32/22.90 ((
% 132.32/22.90 (theprop) =>
% 132.32/22.90 ((
% 132.32/22.90 (kfstpairEq) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodfstin) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairinjL2) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairinjL) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairinjR11) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairinjR12) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairinjR1) =>
% 132.32/22.90 ((
% 132.32/22.90 (upairequniteq) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairinjR2) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairinjR) =>
% 132.32/22.90 ((
% 132.32/22.90 (ksndsingleton) =>
% 132.32/22.90 ((
% 132.32/22.90 (ksndpairEq) =>
% 132.32/22.90 ((
% 132.32/22.90 (kpairsurjEq) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodsndin) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodpairmemEL) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodpairmemER) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodmempaircEq) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodfstpairEq) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodsndpairEq) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodpairsurjEq) =>
% 132.32/22.90 ((
% 132.32/22.90 (dpsetconstrI) =>
% 132.32/22.90 ((
% 132.32/22.90 (dpsetconstrSub) =>
% 132.32/22.90 ((
% 132.32/22.90 (setOfPairsIsBReln) =>
% 132.32/22.90 ((
% 132.32/22.90 (dpsetconstrERa) =>
% 132.32/22.90 ((
% 132.32/22.90 (dpsetconstrEL1) =>
% 132.32/22.90 ((
% 132.32/22.90 (dpsetconstrEL2) =>
% 132.32/22.90 ((
% 132.32/22.90 (dpsetconstrER) =>
% 132.32/22.90 ((
% 132.32/22.90 (funcImageSingleton) =>
% 132.32/22.90 ((
% 132.32/22.90 (apProp) =>
% 132.32/22.90 ((
% 132.32/22.90 (app) =>
% 132.32/22.90 ((
% 132.32/22.90 (infuncsetfunc) =>
% 132.32/22.90 ((
% 132.32/22.90 (ap2p) =>
% 132.32/22.90 ((
% 132.32/22.90 (funcinfuncset) =>
% 132.32/22.90 ((
% 132.32/22.90 (lamProp) =>
% 132.32/22.90 ((
% 132.32/22.90 (lamp) =>
% 132.32/22.90 ((
% 132.32/22.90 (lam2p) =>
% 132.32/22.90 ((
% 132.32/22.90 (brelnall1) =>
% 132.32/22.90 ((
% 132.32/22.90 (brelnall2) =>
% 132.32/22.90 ((
% 132.32/22.90 (ex1E2) =>
% 132.32/22.90 ((
% 132.32/22.90 (funcGraphProp1) =>
% 132.32/22.90 ((
% 132.32/22.90 (funcGraphProp3) =>
% 132.32/22.90 ((
% 132.32/22.90 (funcGraphProp2) =>
% 132.32/22.90 ((
% 132.32/22.90 (funcextLem) =>
% 132.32/22.90 ((
% 132.32/22.90 (funcGraphProp4) =>
% 132.32/22.90 ((
% 132.32/22.90 (subbreln) =>
% 132.32/22.90 ((
% 132.32/22.90 (eqbreln) =>
% 132.32/22.90 ((
% 132.32/22.90 (funcext) =>
% 132.32/22.90 ((
% 132.32/22.90 (funcext2) =>
% 132.32/22.90 ((
% 132.32/22.90 (ap2apEq1) =>
% 132.32/22.90 ((
% 132.32/22.90 (ap2apEq2) =>
% 132.32/22.90 ((
% 132.32/22.90 (beta1) =>
% 132.32/22.90 ((
% 132.32/22.90 (eta1) =>
% 132.32/22.90 ((
% 132.32/22.90 (lam2lamEq) =>
% 132.32/22.90 ((
% 132.32/22.90 (beta2) =>
% 132.32/22.90 ((
% 132.32/22.90 (eta2) =>
% 132.32/22.90 ((
% 132.32/22.90 (iffalseProp1) =>
% 132.32/22.90 ((
% 132.32/22.90 (iffalseProp2) =>
% 132.32/22.90 ((
% 132.32/22.90 (iftrueProp1) =>
% 132.32/22.90 ((
% 132.32/22.90 (iftrueProp2) =>
% 132.32/22.90 ((
% 132.32/22.90 (ifSingleton) =>
% 132.32/22.90 ((
% 132.32/22.90 (ifp) =>
% 132.32/22.90 ((
% 132.32/22.90 (theeq) =>
% 132.32/22.90 ((
% 132.32/22.90 (iftrue) =>
% 132.32/22.90 ((
% 132.32/22.90 (iffalse) =>
% 132.32/22.90 ((
% 132.32/22.90 (iftrueorfalse) =>
% 132.32/22.90 ((
% 132.32/22.90 (binintersectT_lem) =>
% 132.32/22.90 ((
% 132.32/22.90 (binunionT_lem) =>
% 132.32/22.90 ((
% 132.32/22.90 (powersetT_lem) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusT_lem) =>
% 132.32/22.90 ((
% 132.32/22.90 (complementT_lem) =>
% 132.32/22.90 ((
% 132.32/22.90 (setextT) =>
% 132.32/22.90 ((
% 132.32/22.90 (subsetTI) =>
% 132.32/22.90 ((
% 132.32/22.90 (powersetTI1) =>
% 132.32/22.90 ((
% 132.32/22.90 (powersetTE1) =>
% 132.32/22.90 ((
% 132.32/22.90 (complementTI1) =>
% 132.32/22.90 ((
% 132.32/22.90 (complementTE1) =>
% 132.32/22.90 ((
% 132.32/22.90 (binintersectTELcontra) =>
% 132.32/22.90 ((
% 132.32/22.90 (binintersectTERcontra) =>
% 132.32/22.90 ((
% 132.32/22.90 (contrasubsetT) =>
% 132.32/22.90 ((
% 132.32/22.90 (contrasubsetT1) =>
% 132.32/22.90 ((
% 132.32/22.90 (contrasubsetT2) =>
% 132.32/22.90 ((
% 132.32/22.90 (contrasubsetT3) =>
% 132.32/22.90 ((
% 132.32/22.90 (doubleComplementI1) =>
% 132.32/22.90 ((
% 132.32/22.90 (doubleComplementE1) =>
% 132.32/22.90 ((
% 132.32/22.90 (doubleComplementSub1) =>
% 132.32/22.90 ((
% 132.32/22.90 (doubleComplementSub2) =>
% 132.32/22.90 ((
% 132.32/22.90 (doubleComplementEq) =>
% 132.32/22.90 ((
% 132.32/22.90 (complementTnotintersectT) =>
% 132.32/22.90 ((
% 132.32/22.90 (complementImpComplementIntersect) =>
% 132.32/22.90 ((
% 132.32/22.90 (complementSubsetComplementIntersect) =>
% 132.32/22.90 ((
% 132.32/22.90 (complementInPowersetComplementIntersect) =>
% 132.32/22.90 ((
% 132.32/22.90 (contraSubsetComplement) =>
% 132.32/22.90 ((
% 132.32/22.90 (complementTcontraSubset) =>
% 132.32/22.90 ((
% 132.32/22.90 (binunionTILcontra) =>
% 132.32/22.90 ((
% 132.32/22.90 (binunionTIRcontra) =>
% 132.32/22.90 ((
% 132.32/22.90 (inIntersectImpInUnion) =>
% 132.32/22.90 ((
% 132.32/22.90 (inIntersectImpInUnion2) =>
% 132.32/22.90 ((
% 132.32/22.90 (inIntersectImpInIntersectUnions) =>
% 132.32/22.90 ((
% 132.32/22.90 (intersectInPowersetIntersectUnions) =>
% 132.32/22.90 ((
% 132.32/22.90 (inComplementUnionImpNotIn1) =>
% 132.32/22.90 ((
% 132.32/22.90 (inComplementUnionImpInComplement1) =>
% 132.32/22.90 ((
% 132.32/22.90 (binunionTE) =>
% 132.32/22.90 ((
% 132.32/22.90 (binunionTEcontra) =>
% 132.32/22.90 ((
% 132.32/22.90 (demorgan2a1) =>
% 132.32/22.90 ((
% 132.32/22.90 (complementUnionInPowersetComplement) =>
% 132.32/22.90 ((
% 132.32/22.90 (demorgan2a2) =>
% 132.32/22.90 ((
% 132.32/22.90 (demorgan1a) =>
% 132.32/22.90 ((
% 132.32/22.90 (demorgan1b) =>
% 132.32/22.90 ((
% 132.32/22.90 (demorgan1) =>
% 132.32/22.90 ((
% 132.32/22.90 (demorgan2a) =>
% 132.32/22.90 ((
% 132.32/22.90 (demorgan2b2) =>
% 132.32/22.90 ((
% 132.32/22.90 (demorgan2b) =>
% 132.32/22.90 ((
% 132.32/22.90 (demorgan2) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz13rule0) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz13rule1) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz13rule2) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz13rule3) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz13rule4) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz1_1) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz1_2) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz1_3) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz1_4) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz1_5) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1all2) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1SetBreln1) =>
% 132.32/22.90 ((
% 132.32/22.90 (choice2fnsingleton) =>
% 132.32/22.90 ((
% 132.32/22.90 (setOfPairsIsBReln1) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1all1) =>
% 132.32/22.90 ((
% 132.32/22.90 (subbreln1) =>
% 132.32/22.90 ((
% 132.32/22.90 (eqbreln1) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1invprop) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1invI) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1invE) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1compprop) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1compI) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1compE) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1compEex) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1unionprop) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1unionIL) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1unionIR) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1unionI) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1unionE) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1unionEcases) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1unionCommutes) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz2Ex) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz2W) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz2A) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz2B) =>
% 132.32/22.90 ((
% 132.32/22.90 (image1Ex) =>
% 132.32/22.90 ((
% 132.32/22.90 (image1Ex1) =>
% 132.32/22.90 ((
% 132.32/22.90 (image1Equiv) =>
% 132.32/22.90 ((
% 132.32/22.90 (image1E) =>
% 132.32/22.90 ((
% 132.32/22.90 (image1I) =>
% 132.32/22.90 ((
% 132.32/22.90 (injFuncInInjFuncSet) =>
% 132.32/22.90 ((
% 132.32/22.90 (injFuncSetFuncIn) =>
% 132.32/22.90 ((
% 132.32/22.90 (injFuncSetFuncInj) =>
% 132.32/22.90 ((
% 132.32/22.90 (surjFuncSetFuncIn) =>
% 132.32/22.90 ((
% 132.32/22.90 (surjFuncSetFuncSurj) =>
% 132.32/22.90 ((
% 132.32/22.90 (leftInvIsSurj) =>
% 132.32/22.90 ((
% 132.32/22.90 (surjCantorThm) =>
% 132.32/22.90 ((
% 132.32/22.90 (foundation2) =>
% 132.32/22.90 ((
% 132.32/22.90 (notinself) =>
% 132.32/22.90 ((
% 132.32/22.90 (notinself2) =>
% 132.32/22.90 ((
% 132.32/22.90 (omegaSp) =>
% 132.32/22.90 ((
% 132.32/22.90 (omegaSclos) =>
% 132.32/22.90 ((
% 132.32/22.90 (peano0notS) =>
% 132.32/22.90 ((
% 132.32/22.90 (peanoSinj) =>
% 132.32/22.90 ((
% 132.32/22.90 (transitivesetOp1) =>
% 132.32/22.90 ((
% 132.32/22.90 (binintTransitive) =>
% 132.32/22.90 ((
% 132.32/22.90 (transitivesetOp2) =>
% 132.32/22.90 ((
% 132.32/22.90 (setunionTransitive) =>
% 132.32/22.90 ((
% 132.32/22.90 (ordinalMinLem1) =>
% 132.32/22.90 ((
% 132.32/22.90 (ordinalTransSet) =>
% 132.32/22.90 ((
% 132.32/22.90 (ordinalTransSet1) =>
% 132.32/22.90 ((
% 132.32/22.90 (setunionOrdinalLem1) =>
% 132.32/22.90 (ordinal @
% 132.32/22.90 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.32/22.90 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl783])).
% 132.32/22.90 thf(zip_derived_cl805, plain,
% 132.32/22.90 (~ (((notequalI2) =>
% 132.32/22.90 (((subsetRefl) =>
% 132.32/22.90 (((subsetTrans) =>
% 132.32/22.90 (((setadjoinSub) =>
% 132.32/22.90 (((setadjoinSub2) =>
% 132.32/22.90 (((subset2powerset) =>
% 132.32/22.90 (((setextsub) =>
% 132.32/22.90 (((subsetemptysetimpeq) =>
% 132.32/22.90 (((powersetI1) =>
% 132.32/22.90 (((powersetE1) =>
% 132.32/22.90 (((inPowerset) =>
% 132.32/22.90 (((powersetsubset) =>
% 132.32/22.90 (((sepInPowerset) =>
% 132.32/22.90 (((sepSubset) =>
% 132.32/22.90 (((binunionIL) =>
% 132.32/22.90 (((upairset2IR) =>
% 132.32/22.90 (((binunionIR) =>
% 132.32/22.90 (((binunionEcases) =>
% 132.32/22.90 (((binunionE) =>
% 132.32/22.90 (((binunionLsub) =>
% 132.32/22.90 (((binunionRsub) =>
% 132.32/22.90 (((binintersectI) =>
% 132.32/22.90 (((binintersectSubset5) =>
% 132.32/22.90 (((binintersectEL) =>
% 132.32/22.90 (((binintersectLsub) =>
% 132.32/22.90 (((binintersectSubset2) =>
% 132.32/22.90 (((binintersectSubset3) =>
% 132.32/22.90 (((binintersectER) =>
% 132.32/22.90 (((disjointsetsI1) =>
% 132.32/22.90 (((binintersectRsub) =>
% 132.32/22.90 ((
% 132.32/22.90 (binintersectSubset4) =>
% 132.32/22.90 ((
% 132.32/22.90 (binintersectSubset1) =>
% 132.32/22.90 ((
% 132.32/22.90 (bs114d) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusI) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusEL) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusER) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusSubset2) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusERneg) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusELneg) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusILneg) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusIRneg) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusLsub) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusSubset1) =>
% 132.32/22.90 ((
% 132.32/22.90 (symdiffE) =>
% 132.32/22.90 ((
% 132.32/22.90 (symdiffI1) =>
% 132.32/22.90 ((
% 132.32/22.90 (symdiffI2) =>
% 132.32/22.90 ((
% 132.32/22.90 (symdiffIneg1) =>
% 132.32/22.90 ((
% 132.32/22.90 (symdiffIneg2) =>
% 132.32/22.90 ((
% 132.32/22.90 (secondinupair) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairIL) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairIR) =>
% 132.32/22.90 ((
% 132.32/22.90 (kpairiskpair) =>
% 132.32/22.90 ((
% 132.32/22.90 (kpairp) =>
% 132.32/22.90 ((
% 132.32/22.90 (singletonsubset) =>
% 132.32/22.90 ((
% 132.32/22.90 (singletoninpowerset) =>
% 132.32/22.90 ((
% 132.32/22.90 (singletoninpowunion) =>
% 132.32/22.90 ((
% 132.32/22.90 (upairset2E) =>
% 132.32/22.90 ((
% 132.32/22.90 (upairsubunion) =>
% 132.32/22.90 ((
% 132.32/22.90 (upairinpowunion) =>
% 132.32/22.90 ((
% 132.32/22.90 (ubforcartprodlem1) =>
% 132.32/22.90 ((
% 132.32/22.90 (ubforcartprodlem2) =>
% 132.32/22.90 ((
% 132.32/22.90 (ubforcartprodlem3) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodpairin) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodmempair1) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodmempair) =>
% 132.32/22.90 ((
% 132.32/22.90 (setunionE2) =>
% 132.32/22.90 ((
% 132.32/22.90 (setunionsingleton1) =>
% 132.32/22.90 ((
% 132.32/22.90 (setunionsingleton2) =>
% 132.32/22.90 ((
% 132.32/22.90 (setunionsingleton) =>
% 132.32/22.90 ((
% 132.32/22.90 (singletonprop) =>
% 132.32/22.90 ((
% 132.32/22.90 (ex1E1) =>
% 132.32/22.90 ((
% 132.32/22.90 (ex1I) =>
% 132.32/22.90 ((
% 132.32/22.90 (ex1I2) =>
% 132.32/22.90 ((
% 132.32/22.90 (singletonsuniq) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairinjL1) =>
% 132.32/22.90 ((
% 132.32/22.90 (kfstsingleton) =>
% 132.32/22.90 ((
% 132.32/22.90 (theprop) =>
% 132.32/22.90 ((
% 132.32/22.90 (kfstpairEq) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodfstin) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairinjL2) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairinjL) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairinjR11) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairinjR12) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairinjR1) =>
% 132.32/22.90 ((
% 132.32/22.90 (upairequniteq) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairinjR2) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairinjR) =>
% 132.32/22.90 ((
% 132.32/22.90 (ksndsingleton) =>
% 132.32/22.90 ((
% 132.32/22.90 (ksndpairEq) =>
% 132.32/22.90 ((
% 132.32/22.90 (kpairsurjEq) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodsndin) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodpairmemEL) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodpairmemER) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodmempaircEq) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodfstpairEq) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodsndpairEq) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodpairsurjEq) =>
% 132.32/22.90 ((
% 132.32/22.90 (dpsetconstrI) =>
% 132.32/22.90 ((
% 132.32/22.90 (dpsetconstrSub) =>
% 132.32/22.90 ((
% 132.32/22.90 (setOfPairsIsBReln) =>
% 132.32/22.90 ((
% 132.32/22.90 (dpsetconstrERa) =>
% 132.32/22.90 ((
% 132.32/22.90 (dpsetconstrEL1) =>
% 132.32/22.90 ((
% 132.32/22.90 (dpsetconstrEL2) =>
% 132.32/22.90 ((
% 132.32/22.90 (dpsetconstrER) =>
% 132.32/22.90 ((
% 132.32/22.90 (funcImageSingleton) =>
% 132.32/22.90 ((
% 132.32/22.90 (apProp) =>
% 132.32/22.90 ((
% 132.32/22.90 (app) =>
% 132.32/22.90 ((
% 132.32/22.90 (infuncsetfunc) =>
% 132.32/22.90 ((
% 132.32/22.90 (ap2p) =>
% 132.32/22.90 ((
% 132.32/22.90 (funcinfuncset) =>
% 132.32/22.90 ((
% 132.32/22.90 (lamProp) =>
% 132.32/22.90 ((
% 132.32/22.90 (lamp) =>
% 132.32/22.90 ((
% 132.32/22.90 (lam2p) =>
% 132.32/22.90 ((
% 132.32/22.90 (brelnall1) =>
% 132.32/22.90 ((
% 132.32/22.90 (brelnall2) =>
% 132.32/22.90 ((
% 132.32/22.90 (ex1E2) =>
% 132.32/22.90 ((
% 132.32/22.90 (funcGraphProp1) =>
% 132.32/22.90 ((
% 132.32/22.90 (funcGraphProp3) =>
% 132.32/22.90 ((
% 132.32/22.90 (funcGraphProp2) =>
% 132.32/22.90 ((
% 132.32/22.90 (funcextLem) =>
% 132.32/22.90 ((
% 132.32/22.90 (funcGraphProp4) =>
% 132.32/22.90 ((
% 132.32/22.90 (subbreln) =>
% 132.32/22.90 ((
% 132.32/22.90 (eqbreln) =>
% 132.32/22.90 ((
% 132.32/22.90 (funcext) =>
% 132.32/22.90 ((
% 132.32/22.90 (funcext2) =>
% 132.32/22.90 ((
% 132.32/22.90 (ap2apEq1) =>
% 132.32/22.90 ((
% 132.32/22.90 (ap2apEq2) =>
% 132.32/22.90 ((
% 132.32/22.90 (beta1) =>
% 132.32/22.90 ((
% 132.32/22.90 (eta1) =>
% 132.32/22.90 ((
% 132.32/22.90 (lam2lamEq) =>
% 132.32/22.90 ((
% 132.32/22.90 (beta2) =>
% 132.32/22.90 ((
% 132.32/22.90 (eta2) =>
% 132.32/22.90 ((
% 132.32/22.90 (iffalseProp1) =>
% 132.32/22.90 ((
% 132.32/22.90 (iffalseProp2) =>
% 132.32/22.90 ((
% 132.32/22.90 (iftrueProp1) =>
% 132.32/22.90 ((
% 132.32/22.90 (iftrueProp2) =>
% 132.32/22.90 ((
% 132.32/22.90 (ifSingleton) =>
% 132.32/22.90 ((
% 132.32/22.90 (ifp) =>
% 132.32/22.90 ((
% 132.32/22.90 (theeq) =>
% 132.32/22.90 ((
% 132.32/22.90 (iftrue) =>
% 132.32/22.90 ((
% 132.32/22.90 (iffalse) =>
% 132.32/22.90 ((
% 132.32/22.90 (iftrueorfalse) =>
% 132.32/22.90 ((
% 132.32/22.90 (binintersectT_lem) =>
% 132.32/22.90 ((
% 132.32/22.90 (binunionT_lem) =>
% 132.32/22.90 ((
% 132.32/22.90 (powersetT_lem) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusT_lem) =>
% 132.32/22.90 ((
% 132.32/22.90 (complementT_lem) =>
% 132.32/22.90 ((
% 132.32/22.90 (setextT) =>
% 132.32/22.90 ((
% 132.32/22.90 (subsetTI) =>
% 132.32/22.90 ((
% 132.32/22.90 (powersetTI1) =>
% 132.32/22.90 ((
% 132.32/22.90 (powersetTE1) =>
% 132.32/22.90 ((
% 132.32/22.90 (complementTI1) =>
% 132.32/22.90 ((
% 132.32/22.90 (complementTE1) =>
% 132.32/22.90 ((
% 132.32/22.90 (binintersectTELcontra) =>
% 132.32/22.90 ((
% 132.32/22.90 (binintersectTERcontra) =>
% 132.32/22.90 ((
% 132.32/22.90 (contrasubsetT) =>
% 132.32/22.90 ((
% 132.32/22.90 (contrasubsetT1) =>
% 132.32/22.90 ((
% 132.32/22.90 (contrasubsetT2) =>
% 132.32/22.90 ((
% 132.32/22.90 (contrasubsetT3) =>
% 132.32/22.90 ((
% 132.32/22.90 (doubleComplementI1) =>
% 132.32/22.90 ((
% 132.32/22.90 (doubleComplementE1) =>
% 132.32/22.90 ((
% 132.32/22.90 (doubleComplementSub1) =>
% 132.32/22.90 ((
% 132.32/22.90 (doubleComplementSub2) =>
% 132.32/22.90 ((
% 132.32/22.90 (doubleComplementEq) =>
% 132.32/22.90 ((
% 132.32/22.90 (complementTnotintersectT) =>
% 132.32/22.90 ((
% 132.32/22.90 (complementImpComplementIntersect) =>
% 132.32/22.90 ((
% 132.32/22.90 (complementSubsetComplementIntersect) =>
% 132.32/22.90 ((
% 132.32/22.90 (complementInPowersetComplementIntersect) =>
% 132.32/22.90 ((
% 132.32/22.90 (contraSubsetComplement) =>
% 132.32/22.90 ((
% 132.32/22.90 (complementTcontraSubset) =>
% 132.32/22.90 ((
% 132.32/22.90 (binunionTILcontra) =>
% 132.32/22.90 ((
% 132.32/22.90 (binunionTIRcontra) =>
% 132.32/22.90 ((
% 132.32/22.90 (inIntersectImpInUnion) =>
% 132.32/22.90 ((
% 132.32/22.90 (inIntersectImpInUnion2) =>
% 132.32/22.90 ((
% 132.32/22.90 (inIntersectImpInIntersectUnions) =>
% 132.32/22.90 ((
% 132.32/22.90 (intersectInPowersetIntersectUnions) =>
% 132.32/22.90 ((
% 132.32/22.90 (inComplementUnionImpNotIn1) =>
% 132.32/22.90 ((
% 132.32/22.90 (inComplementUnionImpInComplement1) =>
% 132.32/22.90 ((
% 132.32/22.90 (binunionTE) =>
% 132.32/22.90 ((
% 132.32/22.90 (binunionTEcontra) =>
% 132.32/22.90 ((
% 132.32/22.90 (demorgan2a1) =>
% 132.32/22.90 ((
% 132.32/22.90 (complementUnionInPowersetComplement) =>
% 132.32/22.90 ((
% 132.32/22.90 (demorgan2a2) =>
% 132.32/22.90 ((
% 132.32/22.90 (demorgan1a) =>
% 132.32/22.90 ((
% 132.32/22.90 (demorgan1b) =>
% 132.32/22.90 ((
% 132.32/22.90 (demorgan1) =>
% 132.32/22.90 ((
% 132.32/22.90 (demorgan2a) =>
% 132.32/22.90 ((
% 132.32/22.90 (demorgan2b2) =>
% 132.32/22.90 ((
% 132.32/22.90 (demorgan2b) =>
% 132.32/22.90 ((
% 132.32/22.90 (demorgan2) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz13rule0) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz13rule1) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz13rule2) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz13rule3) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz13rule4) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz1_1) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz1_2) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz1_3) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz1_4) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz1_5) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1all2) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1SetBreln1) =>
% 132.32/22.90 ((
% 132.32/22.90 (choice2fnsingleton) =>
% 132.32/22.90 ((
% 132.32/22.90 (setOfPairsIsBReln1) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1all1) =>
% 132.32/22.90 ((
% 132.32/22.90 (subbreln1) =>
% 132.32/22.90 ((
% 132.32/22.90 (eqbreln1) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1invprop) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1invI) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1invE) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1compprop) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1compI) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1compE) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1compEex) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1unionprop) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1unionIL) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1unionIR) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1unionI) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1unionE) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1unionEcases) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1unionCommutes) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz2Ex) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz2W) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz2A) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz2B) =>
% 132.32/22.90 ((
% 132.32/22.90 (image1Ex) =>
% 132.32/22.90 ((
% 132.32/22.90 (image1Ex1) =>
% 132.32/22.90 ((
% 132.32/22.90 (image1Equiv) =>
% 132.32/22.90 ((
% 132.32/22.90 (image1E) =>
% 132.32/22.90 ((
% 132.32/22.90 (image1I) =>
% 132.32/22.90 ((
% 132.32/22.90 (injFuncInInjFuncSet) =>
% 132.32/22.90 ((
% 132.32/22.90 (injFuncSetFuncIn) =>
% 132.32/22.90 ((
% 132.32/22.90 (injFuncSetFuncInj) =>
% 132.32/22.90 ((
% 132.32/22.90 (surjFuncSetFuncIn) =>
% 132.32/22.90 ((
% 132.32/22.90 (surjFuncSetFuncSurj) =>
% 132.32/22.90 ((
% 132.32/22.90 (leftInvIsSurj) =>
% 132.32/22.90 ((
% 132.32/22.90 (surjCantorThm) =>
% 132.32/22.90 ((
% 132.32/22.90 (foundation2) =>
% 132.32/22.90 ((
% 132.32/22.90 (notinself) =>
% 132.32/22.90 ((
% 132.32/22.90 (notinself2) =>
% 132.32/22.90 ((
% 132.32/22.90 (omegaSp) =>
% 132.32/22.90 ((
% 132.32/22.90 (omegaSclos) =>
% 132.32/22.90 ((
% 132.32/22.90 (peano0notS) =>
% 132.32/22.90 ((
% 132.32/22.90 (peanoSinj) =>
% 132.32/22.90 ((
% 132.32/22.90 (transitivesetOp1) =>
% 132.32/22.90 ((
% 132.32/22.90 (binintTransitive) =>
% 132.32/22.90 ((
% 132.32/22.90 (transitivesetOp2) =>
% 132.32/22.90 ((
% 132.32/22.90 (setunionTransitive) =>
% 132.32/22.90 ((
% 132.32/22.90 (ordinalMinLem1) =>
% 132.32/22.90 ((
% 132.32/22.90 (ordinalTransSet) =>
% 132.32/22.90 ((
% 132.32/22.90 (ordinalTransSet1) =>
% 132.32/22.90 ((
% 132.32/22.90 (setunionOrdinalLem1) =>
% 132.32/22.90 (ordinal @
% 132.32/22.90 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.32/22.90 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl795])).
% 132.32/22.90 thf(zip_derived_cl813, plain,
% 132.32/22.90 (~ (((subsetRefl) =>
% 132.32/22.90 (((subsetTrans) =>
% 132.32/22.90 (((setadjoinSub) =>
% 132.32/22.90 (((setadjoinSub2) =>
% 132.32/22.90 (((subset2powerset) =>
% 132.32/22.90 (((setextsub) =>
% 132.32/22.90 (((subsetemptysetimpeq) =>
% 132.32/22.90 (((powersetI1) =>
% 132.32/22.90 (((powersetE1) =>
% 132.32/22.90 (((inPowerset) =>
% 132.32/22.90 (((powersetsubset) =>
% 132.32/22.90 (((sepInPowerset) =>
% 132.32/22.90 (((sepSubset) =>
% 132.32/22.90 (((binunionIL) =>
% 132.32/22.90 (((upairset2IR) =>
% 132.32/22.90 (((binunionIR) =>
% 132.32/22.90 (((binunionEcases) =>
% 132.32/22.90 (((binunionE) =>
% 132.32/22.90 (((binunionLsub) =>
% 132.32/22.90 (((binunionRsub) =>
% 132.32/22.90 (((binintersectI) =>
% 132.32/22.90 (((binintersectSubset5) =>
% 132.32/22.90 (((binintersectEL) =>
% 132.32/22.90 (((binintersectLsub) =>
% 132.32/22.90 (((binintersectSubset2) =>
% 132.32/22.90 (((binintersectSubset3) =>
% 132.32/22.90 (((binintersectER) =>
% 132.32/22.90 (((disjointsetsI1) =>
% 132.32/22.90 (((binintersectRsub) =>
% 132.32/22.90 (((binintersectSubset4) =>
% 132.32/22.90 ((
% 132.32/22.90 (binintersectSubset1) =>
% 132.32/22.90 ((
% 132.32/22.90 (bs114d) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusI) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusEL) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusER) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusSubset2) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusERneg) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusELneg) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusILneg) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusIRneg) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusLsub) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusSubset1) =>
% 132.32/22.90 ((
% 132.32/22.90 (symdiffE) =>
% 132.32/22.90 ((
% 132.32/22.90 (symdiffI1) =>
% 132.32/22.90 ((
% 132.32/22.90 (symdiffI2) =>
% 132.32/22.90 ((
% 132.32/22.90 (symdiffIneg1) =>
% 132.32/22.90 ((
% 132.32/22.90 (symdiffIneg2) =>
% 132.32/22.90 ((
% 132.32/22.90 (secondinupair) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairIL) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairIR) =>
% 132.32/22.90 ((
% 132.32/22.90 (kpairiskpair) =>
% 132.32/22.90 ((
% 132.32/22.90 (kpairp) =>
% 132.32/22.90 ((
% 132.32/22.90 (singletonsubset) =>
% 132.32/22.90 ((
% 132.32/22.90 (singletoninpowerset) =>
% 132.32/22.90 ((
% 132.32/22.90 (singletoninpowunion) =>
% 132.32/22.90 ((
% 132.32/22.90 (upairset2E) =>
% 132.32/22.90 ((
% 132.32/22.90 (upairsubunion) =>
% 132.32/22.90 ((
% 132.32/22.90 (upairinpowunion) =>
% 132.32/22.90 ((
% 132.32/22.90 (ubforcartprodlem1) =>
% 132.32/22.90 ((
% 132.32/22.90 (ubforcartprodlem2) =>
% 132.32/22.90 ((
% 132.32/22.90 (ubforcartprodlem3) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodpairin) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodmempair1) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodmempair) =>
% 132.32/22.90 ((
% 132.32/22.90 (setunionE2) =>
% 132.32/22.90 ((
% 132.32/22.90 (setunionsingleton1) =>
% 132.32/22.90 ((
% 132.32/22.90 (setunionsingleton2) =>
% 132.32/22.90 ((
% 132.32/22.90 (setunionsingleton) =>
% 132.32/22.90 ((
% 132.32/22.90 (singletonprop) =>
% 132.32/22.90 ((
% 132.32/22.90 (ex1E1) =>
% 132.32/22.90 ((
% 132.32/22.90 (ex1I) =>
% 132.32/22.90 ((
% 132.32/22.90 (ex1I2) =>
% 132.32/22.90 ((
% 132.32/22.90 (singletonsuniq) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairinjL1) =>
% 132.32/22.90 ((
% 132.32/22.90 (kfstsingleton) =>
% 132.32/22.90 ((
% 132.32/22.90 (theprop) =>
% 132.32/22.90 ((
% 132.32/22.90 (kfstpairEq) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodfstin) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairinjL2) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairinjL) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairinjR11) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairinjR12) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairinjR1) =>
% 132.32/22.90 ((
% 132.32/22.90 (upairequniteq) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairinjR2) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairinjR) =>
% 132.32/22.90 ((
% 132.32/22.90 (ksndsingleton) =>
% 132.32/22.90 ((
% 132.32/22.90 (ksndpairEq) =>
% 132.32/22.90 ((
% 132.32/22.90 (kpairsurjEq) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodsndin) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodpairmemEL) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodpairmemER) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodmempaircEq) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodfstpairEq) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodsndpairEq) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodpairsurjEq) =>
% 132.32/22.90 ((
% 132.32/22.90 (dpsetconstrI) =>
% 132.32/22.90 ((
% 132.32/22.90 (dpsetconstrSub) =>
% 132.32/22.90 ((
% 132.32/22.90 (setOfPairsIsBReln) =>
% 132.32/22.90 ((
% 132.32/22.90 (dpsetconstrERa) =>
% 132.32/22.90 ((
% 132.32/22.90 (dpsetconstrEL1) =>
% 132.32/22.90 ((
% 132.32/22.90 (dpsetconstrEL2) =>
% 132.32/22.90 ((
% 132.32/22.90 (dpsetconstrER) =>
% 132.32/22.90 ((
% 132.32/22.90 (funcImageSingleton) =>
% 132.32/22.90 ((
% 132.32/22.90 (apProp) =>
% 132.32/22.90 ((
% 132.32/22.90 (app) =>
% 132.32/22.90 ((
% 132.32/22.90 (infuncsetfunc) =>
% 132.32/22.90 ((
% 132.32/22.90 (ap2p) =>
% 132.32/22.90 ((
% 132.32/22.90 (funcinfuncset) =>
% 132.32/22.90 ((
% 132.32/22.90 (lamProp) =>
% 132.32/22.90 ((
% 132.32/22.90 (lamp) =>
% 132.32/22.90 ((
% 132.32/22.90 (lam2p) =>
% 132.32/22.90 ((
% 132.32/22.90 (brelnall1) =>
% 132.32/22.90 ((
% 132.32/22.90 (brelnall2) =>
% 132.32/22.90 ((
% 132.32/22.90 (ex1E2) =>
% 132.32/22.90 ((
% 132.32/22.90 (funcGraphProp1) =>
% 132.32/22.90 ((
% 132.32/22.90 (funcGraphProp3) =>
% 132.32/22.90 ((
% 132.32/22.90 (funcGraphProp2) =>
% 132.32/22.90 ((
% 132.32/22.90 (funcextLem) =>
% 132.32/22.90 ((
% 132.32/22.90 (funcGraphProp4) =>
% 132.32/22.90 ((
% 132.32/22.90 (subbreln) =>
% 132.32/22.90 ((
% 132.32/22.90 (eqbreln) =>
% 132.32/22.90 ((
% 132.32/22.90 (funcext) =>
% 132.32/22.90 ((
% 132.32/22.90 (funcext2) =>
% 132.32/22.90 ((
% 132.32/22.90 (ap2apEq1) =>
% 132.32/22.90 ((
% 132.32/22.90 (ap2apEq2) =>
% 132.32/22.90 ((
% 132.32/22.90 (beta1) =>
% 132.32/22.90 ((
% 132.32/22.90 (eta1) =>
% 132.32/22.90 ((
% 132.32/22.90 (lam2lamEq) =>
% 132.32/22.90 ((
% 132.32/22.90 (beta2) =>
% 132.32/22.90 ((
% 132.32/22.90 (eta2) =>
% 132.32/22.90 ((
% 132.32/22.90 (iffalseProp1) =>
% 132.32/22.90 ((
% 132.32/22.90 (iffalseProp2) =>
% 132.32/22.90 ((
% 132.32/22.90 (iftrueProp1) =>
% 132.32/22.90 ((
% 132.32/22.90 (iftrueProp2) =>
% 132.32/22.90 ((
% 132.32/22.90 (ifSingleton) =>
% 132.32/22.90 ((
% 132.32/22.90 (ifp) =>
% 132.32/22.90 ((
% 132.32/22.90 (theeq) =>
% 132.32/22.90 ((
% 132.32/22.90 (iftrue) =>
% 132.32/22.90 ((
% 132.32/22.90 (iffalse) =>
% 132.32/22.90 ((
% 132.32/22.90 (iftrueorfalse) =>
% 132.32/22.90 ((
% 132.32/22.90 (binintersectT_lem) =>
% 132.32/22.90 ((
% 132.32/22.90 (binunionT_lem) =>
% 132.32/22.90 ((
% 132.32/22.90 (powersetT_lem) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusT_lem) =>
% 132.32/22.90 ((
% 132.32/22.90 (complementT_lem) =>
% 132.32/22.90 ((
% 132.32/22.90 (setextT) =>
% 132.32/22.90 ((
% 132.32/22.90 (subsetTI) =>
% 132.32/22.90 ((
% 132.32/22.90 (powersetTI1) =>
% 132.32/22.90 ((
% 132.32/22.90 (powersetTE1) =>
% 132.32/22.90 ((
% 132.32/22.90 (complementTI1) =>
% 132.32/22.90 ((
% 132.32/22.90 (complementTE1) =>
% 132.32/22.90 ((
% 132.32/22.90 (binintersectTELcontra) =>
% 132.32/22.90 ((
% 132.32/22.90 (binintersectTERcontra) =>
% 132.32/22.90 ((
% 132.32/22.90 (contrasubsetT) =>
% 132.32/22.90 ((
% 132.32/22.90 (contrasubsetT1) =>
% 132.32/22.90 ((
% 132.32/22.90 (contrasubsetT2) =>
% 132.32/22.90 ((
% 132.32/22.90 (contrasubsetT3) =>
% 132.32/22.90 ((
% 132.32/22.90 (doubleComplementI1) =>
% 132.32/22.90 ((
% 132.32/22.90 (doubleComplementE1) =>
% 132.32/22.90 ((
% 132.32/22.90 (doubleComplementSub1) =>
% 132.32/22.90 ((
% 132.32/22.90 (doubleComplementSub2) =>
% 132.32/22.90 ((
% 132.32/22.90 (doubleComplementEq) =>
% 132.32/22.90 ((
% 132.32/22.90 (complementTnotintersectT) =>
% 132.32/22.90 ((
% 132.32/22.90 (complementImpComplementIntersect) =>
% 132.32/22.90 ((
% 132.32/22.90 (complementSubsetComplementIntersect) =>
% 132.32/22.90 ((
% 132.32/22.90 (complementInPowersetComplementIntersect) =>
% 132.32/22.90 ((
% 132.32/22.90 (contraSubsetComplement) =>
% 132.32/22.90 ((
% 132.32/22.90 (complementTcontraSubset) =>
% 132.32/22.90 ((
% 132.32/22.90 (binunionTILcontra) =>
% 132.32/22.90 ((
% 132.32/22.90 (binunionTIRcontra) =>
% 132.32/22.90 ((
% 132.32/22.90 (inIntersectImpInUnion) =>
% 132.32/22.90 ((
% 132.32/22.90 (inIntersectImpInUnion2) =>
% 132.32/22.90 ((
% 132.32/22.90 (inIntersectImpInIntersectUnions) =>
% 132.32/22.90 ((
% 132.32/22.90 (intersectInPowersetIntersectUnions) =>
% 132.32/22.90 ((
% 132.32/22.90 (inComplementUnionImpNotIn1) =>
% 132.32/22.90 ((
% 132.32/22.90 (inComplementUnionImpInComplement1) =>
% 132.32/22.90 ((
% 132.32/22.90 (binunionTE) =>
% 132.32/22.90 ((
% 132.32/22.90 (binunionTEcontra) =>
% 132.32/22.90 ((
% 132.32/22.90 (demorgan2a1) =>
% 132.32/22.90 ((
% 132.32/22.90 (complementUnionInPowersetComplement) =>
% 132.32/22.90 ((
% 132.32/22.90 (demorgan2a2) =>
% 132.32/22.90 ((
% 132.32/22.90 (demorgan1a) =>
% 132.32/22.90 ((
% 132.32/22.90 (demorgan1b) =>
% 132.32/22.90 ((
% 132.32/22.90 (demorgan1) =>
% 132.32/22.90 ((
% 132.32/22.90 (demorgan2a) =>
% 132.32/22.90 ((
% 132.32/22.90 (demorgan2b2) =>
% 132.32/22.90 ((
% 132.32/22.90 (demorgan2b) =>
% 132.32/22.90 ((
% 132.32/22.90 (demorgan2) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz13rule0) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz13rule1) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz13rule2) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz13rule3) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz13rule4) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz1_1) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz1_2) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz1_3) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz1_4) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz1_5) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1all2) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1SetBreln1) =>
% 132.32/22.90 ((
% 132.32/22.90 (choice2fnsingleton) =>
% 132.32/22.90 ((
% 132.32/22.90 (setOfPairsIsBReln1) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1all1) =>
% 132.32/22.90 ((
% 132.32/22.90 (subbreln1) =>
% 132.32/22.90 ((
% 132.32/22.90 (eqbreln1) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1invprop) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1invI) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1invE) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1compprop) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1compI) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1compE) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1compEex) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1unionprop) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1unionIL) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1unionIR) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1unionI) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1unionE) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1unionEcases) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1unionCommutes) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz2Ex) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz2W) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz2A) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz2B) =>
% 132.32/22.90 ((
% 132.32/22.90 (image1Ex) =>
% 132.32/22.90 ((
% 132.32/22.90 (image1Ex1) =>
% 132.32/22.90 ((
% 132.32/22.90 (image1Equiv) =>
% 132.32/22.90 ((
% 132.32/22.90 (image1E) =>
% 132.32/22.90 ((
% 132.32/22.90 (image1I) =>
% 132.32/22.90 ((
% 132.32/22.90 (injFuncInInjFuncSet) =>
% 132.32/22.90 ((
% 132.32/22.90 (injFuncSetFuncIn) =>
% 132.32/22.90 ((
% 132.32/22.90 (injFuncSetFuncInj) =>
% 132.32/22.90 ((
% 132.32/22.90 (surjFuncSetFuncIn) =>
% 132.32/22.90 ((
% 132.32/22.90 (surjFuncSetFuncSurj) =>
% 132.32/22.90 ((
% 132.32/22.90 (leftInvIsSurj) =>
% 132.32/22.90 ((
% 132.32/22.90 (surjCantorThm) =>
% 132.32/22.90 ((
% 132.32/22.90 (foundation2) =>
% 132.32/22.90 ((
% 132.32/22.90 (notinself) =>
% 132.32/22.90 ((
% 132.32/22.90 (notinself2) =>
% 132.32/22.90 ((
% 132.32/22.90 (omegaSp) =>
% 132.32/22.90 ((
% 132.32/22.90 (omegaSclos) =>
% 132.32/22.90 ((
% 132.32/22.90 (peano0notS) =>
% 132.32/22.90 ((
% 132.32/22.90 (peanoSinj) =>
% 132.32/22.90 ((
% 132.32/22.90 (transitivesetOp1) =>
% 132.32/22.90 ((
% 132.32/22.90 (binintTransitive) =>
% 132.32/22.90 ((
% 132.32/22.90 (transitivesetOp2) =>
% 132.32/22.90 ((
% 132.32/22.90 (setunionTransitive) =>
% 132.32/22.90 ((
% 132.32/22.90 (ordinalMinLem1) =>
% 132.32/22.90 ((
% 132.32/22.90 (ordinalTransSet) =>
% 132.32/22.90 ((
% 132.32/22.90 (ordinalTransSet1) =>
% 132.32/22.90 ((
% 132.32/22.90 (setunionOrdinalLem1) =>
% 132.32/22.90 (ordinal @
% 132.32/22.90 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.32/22.90 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl805])).
% 132.32/22.90 thf(zip_derived_cl823, plain,
% 132.32/22.90 (~ (((subsetTrans) =>
% 132.32/22.90 (((setadjoinSub) =>
% 132.32/22.90 (((setadjoinSub2) =>
% 132.32/22.90 (((subset2powerset) =>
% 132.32/22.90 (((setextsub) =>
% 132.32/22.90 (((subsetemptysetimpeq) =>
% 132.32/22.90 (((powersetI1) =>
% 132.32/22.90 (((powersetE1) =>
% 132.32/22.90 (((inPowerset) =>
% 132.32/22.90 (((powersetsubset) =>
% 132.32/22.90 (((sepInPowerset) =>
% 132.32/22.90 (((sepSubset) =>
% 132.32/22.90 (((binunionIL) =>
% 132.32/22.90 (((upairset2IR) =>
% 132.32/22.90 (((binunionIR) =>
% 132.32/22.90 (((binunionEcases) =>
% 132.32/22.90 (((binunionE) =>
% 132.32/22.90 (((binunionLsub) =>
% 132.32/22.90 (((binunionRsub) =>
% 132.32/22.90 (((binintersectI) =>
% 132.32/22.90 (((binintersectSubset5) =>
% 132.32/22.90 (((binintersectEL) =>
% 132.32/22.90 (((binintersectLsub) =>
% 132.32/22.90 (((binintersectSubset2) =>
% 132.32/22.90 (((binintersectSubset3) =>
% 132.32/22.90 (((binintersectER) =>
% 132.32/22.90 (((disjointsetsI1) =>
% 132.32/22.90 (((binintersectRsub) =>
% 132.32/22.90 (((binintersectSubset4) =>
% 132.32/22.90 (((binintersectSubset1) =>
% 132.32/22.90 ((
% 132.32/22.90 (bs114d) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusI) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusEL) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusER) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusSubset2) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusERneg) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusELneg) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusILneg) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusIRneg) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusLsub) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusSubset1) =>
% 132.32/22.90 ((
% 132.32/22.90 (symdiffE) =>
% 132.32/22.90 ((
% 132.32/22.90 (symdiffI1) =>
% 132.32/22.90 ((
% 132.32/22.90 (symdiffI2) =>
% 132.32/22.90 ((
% 132.32/22.90 (symdiffIneg1) =>
% 132.32/22.90 ((
% 132.32/22.90 (symdiffIneg2) =>
% 132.32/22.90 ((
% 132.32/22.90 (secondinupair) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairIL) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairIR) =>
% 132.32/22.90 ((
% 132.32/22.90 (kpairiskpair) =>
% 132.32/22.90 ((
% 132.32/22.90 (kpairp) =>
% 132.32/22.90 ((
% 132.32/22.90 (singletonsubset) =>
% 132.32/22.90 ((
% 132.32/22.90 (singletoninpowerset) =>
% 132.32/22.90 ((
% 132.32/22.90 (singletoninpowunion) =>
% 132.32/22.90 ((
% 132.32/22.90 (upairset2E) =>
% 132.32/22.90 ((
% 132.32/22.90 (upairsubunion) =>
% 132.32/22.90 ((
% 132.32/22.90 (upairinpowunion) =>
% 132.32/22.90 ((
% 132.32/22.90 (ubforcartprodlem1) =>
% 132.32/22.90 ((
% 132.32/22.90 (ubforcartprodlem2) =>
% 132.32/22.90 ((
% 132.32/22.90 (ubforcartprodlem3) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodpairin) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodmempair1) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodmempair) =>
% 132.32/22.90 ((
% 132.32/22.90 (setunionE2) =>
% 132.32/22.90 ((
% 132.32/22.90 (setunionsingleton1) =>
% 132.32/22.90 ((
% 132.32/22.90 (setunionsingleton2) =>
% 132.32/22.90 ((
% 132.32/22.90 (setunionsingleton) =>
% 132.32/22.90 ((
% 132.32/22.90 (singletonprop) =>
% 132.32/22.90 ((
% 132.32/22.90 (ex1E1) =>
% 132.32/22.90 ((
% 132.32/22.90 (ex1I) =>
% 132.32/22.90 ((
% 132.32/22.90 (ex1I2) =>
% 132.32/22.90 ((
% 132.32/22.90 (singletonsuniq) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairinjL1) =>
% 132.32/22.90 ((
% 132.32/22.90 (kfstsingleton) =>
% 132.32/22.90 ((
% 132.32/22.90 (theprop) =>
% 132.32/22.90 ((
% 132.32/22.90 (kfstpairEq) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodfstin) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairinjL2) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairinjL) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairinjR11) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairinjR12) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairinjR1) =>
% 132.32/22.90 ((
% 132.32/22.90 (upairequniteq) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairinjR2) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairinjR) =>
% 132.32/22.90 ((
% 132.32/22.90 (ksndsingleton) =>
% 132.32/22.90 ((
% 132.32/22.90 (ksndpairEq) =>
% 132.32/22.90 ((
% 132.32/22.90 (kpairsurjEq) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodsndin) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodpairmemEL) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodpairmemER) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodmempaircEq) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodfstpairEq) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodsndpairEq) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodpairsurjEq) =>
% 132.32/22.90 ((
% 132.32/22.90 (dpsetconstrI) =>
% 132.32/22.90 ((
% 132.32/22.90 (dpsetconstrSub) =>
% 132.32/22.90 ((
% 132.32/22.90 (setOfPairsIsBReln) =>
% 132.32/22.90 ((
% 132.32/22.90 (dpsetconstrERa) =>
% 132.32/22.90 ((
% 132.32/22.90 (dpsetconstrEL1) =>
% 132.32/22.90 ((
% 132.32/22.90 (dpsetconstrEL2) =>
% 132.32/22.90 ((
% 132.32/22.90 (dpsetconstrER) =>
% 132.32/22.90 ((
% 132.32/22.90 (funcImageSingleton) =>
% 132.32/22.90 ((
% 132.32/22.90 (apProp) =>
% 132.32/22.90 ((
% 132.32/22.90 (app) =>
% 132.32/22.90 ((
% 132.32/22.90 (infuncsetfunc) =>
% 132.32/22.90 ((
% 132.32/22.90 (ap2p) =>
% 132.32/22.90 ((
% 132.32/22.90 (funcinfuncset) =>
% 132.32/22.90 ((
% 132.32/22.90 (lamProp) =>
% 132.32/22.90 ((
% 132.32/22.90 (lamp) =>
% 132.32/22.90 ((
% 132.32/22.90 (lam2p) =>
% 132.32/22.90 ((
% 132.32/22.90 (brelnall1) =>
% 132.32/22.90 ((
% 132.32/22.90 (brelnall2) =>
% 132.32/22.90 ((
% 132.32/22.90 (ex1E2) =>
% 132.32/22.90 ((
% 132.32/22.90 (funcGraphProp1) =>
% 132.32/22.90 ((
% 132.32/22.90 (funcGraphProp3) =>
% 132.32/22.90 ((
% 132.32/22.90 (funcGraphProp2) =>
% 132.32/22.90 ((
% 132.32/22.90 (funcextLem) =>
% 132.32/22.90 ((
% 132.32/22.90 (funcGraphProp4) =>
% 132.32/22.90 ((
% 132.32/22.90 (subbreln) =>
% 132.32/22.90 ((
% 132.32/22.90 (eqbreln) =>
% 132.32/22.90 ((
% 132.32/22.90 (funcext) =>
% 132.32/22.90 ((
% 132.32/22.90 (funcext2) =>
% 132.32/22.90 ((
% 132.32/22.90 (ap2apEq1) =>
% 132.32/22.90 ((
% 132.32/22.90 (ap2apEq2) =>
% 132.32/22.90 ((
% 132.32/22.90 (beta1) =>
% 132.32/22.90 ((
% 132.32/22.90 (eta1) =>
% 132.32/22.90 ((
% 132.32/22.90 (lam2lamEq) =>
% 132.32/22.90 ((
% 132.32/22.90 (beta2) =>
% 132.32/22.90 ((
% 132.32/22.90 (eta2) =>
% 132.32/22.90 ((
% 132.32/22.90 (iffalseProp1) =>
% 132.32/22.90 ((
% 132.32/22.90 (iffalseProp2) =>
% 132.32/22.90 ((
% 132.32/22.90 (iftrueProp1) =>
% 132.32/22.90 ((
% 132.32/22.90 (iftrueProp2) =>
% 132.32/22.90 ((
% 132.32/22.90 (ifSingleton) =>
% 132.32/22.90 ((
% 132.32/22.90 (ifp) =>
% 132.32/22.90 ((
% 132.32/22.90 (theeq) =>
% 132.32/22.90 ((
% 132.32/22.90 (iftrue) =>
% 132.32/22.90 ((
% 132.32/22.90 (iffalse) =>
% 132.32/22.90 ((
% 132.32/22.90 (iftrueorfalse) =>
% 132.32/22.90 ((
% 132.32/22.90 (binintersectT_lem) =>
% 132.32/22.90 ((
% 132.32/22.90 (binunionT_lem) =>
% 132.32/22.90 ((
% 132.32/22.90 (powersetT_lem) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusT_lem) =>
% 132.32/22.90 ((
% 132.32/22.90 (complementT_lem) =>
% 132.32/22.90 ((
% 132.32/22.90 (setextT) =>
% 132.32/22.90 ((
% 132.32/22.90 (subsetTI) =>
% 132.32/22.90 ((
% 132.32/22.90 (powersetTI1) =>
% 132.32/22.90 ((
% 132.32/22.90 (powersetTE1) =>
% 132.32/22.90 ((
% 132.32/22.90 (complementTI1) =>
% 132.32/22.90 ((
% 132.32/22.90 (complementTE1) =>
% 132.32/22.90 ((
% 132.32/22.90 (binintersectTELcontra) =>
% 132.32/22.90 ((
% 132.32/22.90 (binintersectTERcontra) =>
% 132.32/22.90 ((
% 132.32/22.90 (contrasubsetT) =>
% 132.32/22.90 ((
% 132.32/22.90 (contrasubsetT1) =>
% 132.32/22.90 ((
% 132.32/22.90 (contrasubsetT2) =>
% 132.32/22.90 ((
% 132.32/22.90 (contrasubsetT3) =>
% 132.32/22.90 ((
% 132.32/22.90 (doubleComplementI1) =>
% 132.32/22.90 ((
% 132.32/22.90 (doubleComplementE1) =>
% 132.32/22.90 ((
% 132.32/22.90 (doubleComplementSub1) =>
% 132.32/22.90 ((
% 132.32/22.90 (doubleComplementSub2) =>
% 132.32/22.90 ((
% 132.32/22.90 (doubleComplementEq) =>
% 132.32/22.90 ((
% 132.32/22.90 (complementTnotintersectT) =>
% 132.32/22.90 ((
% 132.32/22.90 (complementImpComplementIntersect) =>
% 132.32/22.90 ((
% 132.32/22.90 (complementSubsetComplementIntersect) =>
% 132.32/22.90 ((
% 132.32/22.90 (complementInPowersetComplementIntersect) =>
% 132.32/22.90 ((
% 132.32/22.90 (contraSubsetComplement) =>
% 132.32/22.90 ((
% 132.32/22.90 (complementTcontraSubset) =>
% 132.32/22.90 ((
% 132.32/22.90 (binunionTILcontra) =>
% 132.32/22.90 ((
% 132.32/22.90 (binunionTIRcontra) =>
% 132.32/22.90 ((
% 132.32/22.90 (inIntersectImpInUnion) =>
% 132.32/22.90 ((
% 132.32/22.90 (inIntersectImpInUnion2) =>
% 132.32/22.90 ((
% 132.32/22.90 (inIntersectImpInIntersectUnions) =>
% 132.32/22.90 ((
% 132.32/22.90 (intersectInPowersetIntersectUnions) =>
% 132.32/22.90 ((
% 132.32/22.90 (inComplementUnionImpNotIn1) =>
% 132.32/22.90 ((
% 132.32/22.90 (inComplementUnionImpInComplement1) =>
% 132.32/22.90 ((
% 132.32/22.90 (binunionTE) =>
% 132.32/22.90 ((
% 132.32/22.90 (binunionTEcontra) =>
% 132.32/22.90 ((
% 132.32/22.90 (demorgan2a1) =>
% 132.32/22.90 ((
% 132.32/22.90 (complementUnionInPowersetComplement) =>
% 132.32/22.90 ((
% 132.32/22.90 (demorgan2a2) =>
% 132.32/22.90 ((
% 132.32/22.90 (demorgan1a) =>
% 132.32/22.90 ((
% 132.32/22.90 (demorgan1b) =>
% 132.32/22.90 ((
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% 132.32/22.90 ((
% 132.32/22.90 (demorgan2a) =>
% 132.32/22.90 ((
% 132.32/22.90 (demorgan2b2) =>
% 132.32/22.90 ((
% 132.32/22.90 (demorgan2b) =>
% 132.32/22.90 ((
% 132.32/22.90 (demorgan2) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz13rule0) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz13rule1) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz13rule2) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz13rule3) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz13rule4) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz1_1) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz1_2) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz1_3) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz1_4) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz1_5) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1all2) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1SetBreln1) =>
% 132.32/22.90 ((
% 132.32/22.90 (choice2fnsingleton) =>
% 132.32/22.90 ((
% 132.32/22.90 (setOfPairsIsBReln1) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1all1) =>
% 132.32/22.90 ((
% 132.32/22.90 (subbreln1) =>
% 132.32/22.90 ((
% 132.32/22.90 (eqbreln1) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1invprop) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1invI) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1invE) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1compprop) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1compI) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1compE) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1compEex) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1unionprop) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1unionIL) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1unionIR) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1unionI) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1unionE) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1unionEcases) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1unionCommutes) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz2Ex) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz2W) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz2A) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz2B) =>
% 132.32/22.90 ((
% 132.32/22.90 (image1Ex) =>
% 132.32/22.90 ((
% 132.32/22.90 (image1Ex1) =>
% 132.32/22.90 ((
% 132.32/22.90 (image1Equiv) =>
% 132.32/22.90 ((
% 132.32/22.90 (image1E) =>
% 132.32/22.90 ((
% 132.32/22.90 (image1I) =>
% 132.32/22.90 ((
% 132.32/22.90 (injFuncInInjFuncSet) =>
% 132.32/22.90 ((
% 132.32/22.90 (injFuncSetFuncIn) =>
% 132.32/22.90 ((
% 132.32/22.90 (injFuncSetFuncInj) =>
% 132.32/22.90 ((
% 132.32/22.90 (surjFuncSetFuncIn) =>
% 132.32/22.90 ((
% 132.32/22.90 (surjFuncSetFuncSurj) =>
% 132.32/22.90 ((
% 132.32/22.90 (leftInvIsSurj) =>
% 132.32/22.90 ((
% 132.32/22.90 (surjCantorThm) =>
% 132.32/22.90 ((
% 132.32/22.90 (foundation2) =>
% 132.32/22.90 ((
% 132.32/22.90 (notinself) =>
% 132.32/22.90 ((
% 132.32/22.90 (notinself2) =>
% 132.32/22.90 ((
% 132.32/22.90 (omegaSp) =>
% 132.32/22.90 ((
% 132.32/22.90 (omegaSclos) =>
% 132.32/22.90 ((
% 132.32/22.90 (peano0notS) =>
% 132.32/22.90 ((
% 132.32/22.90 (peanoSinj) =>
% 132.32/22.90 ((
% 132.32/22.90 (transitivesetOp1) =>
% 132.32/22.90 ((
% 132.32/22.90 (binintTransitive) =>
% 132.32/22.90 ((
% 132.32/22.90 (transitivesetOp2) =>
% 132.32/22.90 ((
% 132.32/22.90 (setunionTransitive) =>
% 132.32/22.90 ((
% 132.32/22.90 (ordinalMinLem1) =>
% 132.32/22.90 ((
% 132.32/22.90 (ordinalTransSet) =>
% 132.32/22.90 ((
% 132.32/22.90 (ordinalTransSet1) =>
% 132.32/22.90 ((
% 132.32/22.90 (setunionOrdinalLem1) =>
% 132.32/22.90 (ordinal @
% 132.32/22.90 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.32/22.90 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl813])).
% 132.32/22.90 thf(zip_derived_cl833, plain,
% 132.32/22.90 (~ (((setadjoinSub) =>
% 132.32/22.90 (((setadjoinSub2) =>
% 132.32/22.90 (((subset2powerset) =>
% 132.32/22.90 (((setextsub) =>
% 132.32/22.90 (((subsetemptysetimpeq) =>
% 132.32/22.90 (((powersetI1) =>
% 132.32/22.90 (((powersetE1) =>
% 132.32/22.90 (((inPowerset) =>
% 132.32/22.90 (((powersetsubset) =>
% 132.32/22.90 (((sepInPowerset) =>
% 132.32/22.90 (((sepSubset) =>
% 132.32/22.90 (((binunionIL) =>
% 132.32/22.90 (((upairset2IR) =>
% 132.32/22.90 (((binunionIR) =>
% 132.32/22.90 (((binunionEcases) =>
% 132.32/22.90 (((binunionE) =>
% 132.32/22.90 (((binunionLsub) =>
% 132.32/22.90 (((binunionRsub) =>
% 132.32/22.90 (((binintersectI) =>
% 132.32/22.90 (((binintersectSubset5) =>
% 132.32/22.90 (((binintersectEL) =>
% 132.32/22.90 (((binintersectLsub) =>
% 132.32/22.90 (((binintersectSubset2) =>
% 132.32/22.90 (((binintersectSubset3) =>
% 132.32/22.90 (((binintersectER) =>
% 132.32/22.90 (((disjointsetsI1) =>
% 132.32/22.90 (((binintersectRsub) =>
% 132.32/22.90 (((binintersectSubset4) =>
% 132.32/22.90 (((binintersectSubset1) =>
% 132.32/22.90 (((bs114d) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusI) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusEL) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusER) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusSubset2) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusERneg) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusELneg) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusILneg) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusIRneg) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusLsub) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusSubset1) =>
% 132.32/22.90 ((
% 132.32/22.90 (symdiffE) =>
% 132.32/22.90 ((
% 132.32/22.90 (symdiffI1) =>
% 132.32/22.90 ((
% 132.32/22.90 (symdiffI2) =>
% 132.32/22.90 ((
% 132.32/22.90 (symdiffIneg1) =>
% 132.32/22.90 ((
% 132.32/22.90 (symdiffIneg2) =>
% 132.32/22.90 ((
% 132.32/22.90 (secondinupair) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairIL) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairIR) =>
% 132.32/22.90 ((
% 132.32/22.90 (kpairiskpair) =>
% 132.32/22.90 ((
% 132.32/22.90 (kpairp) =>
% 132.32/22.90 ((
% 132.32/22.90 (singletonsubset) =>
% 132.32/22.90 ((
% 132.32/22.90 (singletoninpowerset) =>
% 132.32/22.90 ((
% 132.32/22.90 (singletoninpowunion) =>
% 132.32/22.90 ((
% 132.32/22.90 (upairset2E) =>
% 132.32/22.90 ((
% 132.32/22.90 (upairsubunion) =>
% 132.32/22.90 ((
% 132.32/22.90 (upairinpowunion) =>
% 132.32/22.90 ((
% 132.32/22.90 (ubforcartprodlem1) =>
% 132.32/22.90 ((
% 132.32/22.90 (ubforcartprodlem2) =>
% 132.32/22.90 ((
% 132.32/22.90 (ubforcartprodlem3) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodpairin) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodmempair1) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodmempair) =>
% 132.32/22.90 ((
% 132.32/22.90 (setunionE2) =>
% 132.32/22.90 ((
% 132.32/22.90 (setunionsingleton1) =>
% 132.32/22.90 ((
% 132.32/22.90 (setunionsingleton2) =>
% 132.32/22.90 ((
% 132.32/22.90 (setunionsingleton) =>
% 132.32/22.90 ((
% 132.32/22.90 (singletonprop) =>
% 132.32/22.90 ((
% 132.32/22.90 (ex1E1) =>
% 132.32/22.90 ((
% 132.32/22.90 (ex1I) =>
% 132.32/22.90 ((
% 132.32/22.90 (ex1I2) =>
% 132.32/22.90 ((
% 132.32/22.90 (singletonsuniq) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairinjL1) =>
% 132.32/22.90 ((
% 132.32/22.90 (kfstsingleton) =>
% 132.32/22.90 ((
% 132.32/22.90 (theprop) =>
% 132.32/22.90 ((
% 132.32/22.90 (kfstpairEq) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodfstin) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairinjL2) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairinjL) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairinjR11) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairinjR12) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairinjR1) =>
% 132.32/22.90 ((
% 132.32/22.90 (upairequniteq) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairinjR2) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairinjR) =>
% 132.32/22.90 ((
% 132.32/22.90 (ksndsingleton) =>
% 132.32/22.90 ((
% 132.32/22.90 (ksndpairEq) =>
% 132.32/22.90 ((
% 132.32/22.90 (kpairsurjEq) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodsndin) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodpairmemEL) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodpairmemER) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodmempaircEq) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodfstpairEq) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodsndpairEq) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodpairsurjEq) =>
% 132.32/22.90 ((
% 132.32/22.90 (dpsetconstrI) =>
% 132.32/22.90 ((
% 132.32/22.90 (dpsetconstrSub) =>
% 132.32/22.90 ((
% 132.32/22.90 (setOfPairsIsBReln) =>
% 132.32/22.90 ((
% 132.32/22.90 (dpsetconstrERa) =>
% 132.32/22.90 ((
% 132.32/22.90 (dpsetconstrEL1) =>
% 132.32/22.90 ((
% 132.32/22.90 (dpsetconstrEL2) =>
% 132.32/22.90 ((
% 132.32/22.90 (dpsetconstrER) =>
% 132.32/22.90 ((
% 132.32/22.90 (funcImageSingleton) =>
% 132.32/22.90 ((
% 132.32/22.90 (apProp) =>
% 132.32/22.90 ((
% 132.32/22.90 (app) =>
% 132.32/22.90 ((
% 132.32/22.90 (infuncsetfunc) =>
% 132.32/22.90 ((
% 132.32/22.90 (ap2p) =>
% 132.32/22.90 ((
% 132.32/22.90 (funcinfuncset) =>
% 132.32/22.90 ((
% 132.32/22.90 (lamProp) =>
% 132.32/22.90 ((
% 132.32/22.90 (lamp) =>
% 132.32/22.90 ((
% 132.32/22.90 (lam2p) =>
% 132.32/22.90 ((
% 132.32/22.90 (brelnall1) =>
% 132.32/22.90 ((
% 132.32/22.90 (brelnall2) =>
% 132.32/22.90 ((
% 132.32/22.90 (ex1E2) =>
% 132.32/22.90 ((
% 132.32/22.90 (funcGraphProp1) =>
% 132.32/22.90 ((
% 132.32/22.90 (funcGraphProp3) =>
% 132.32/22.90 ((
% 132.32/22.90 (funcGraphProp2) =>
% 132.32/22.90 ((
% 132.32/22.90 (funcextLem) =>
% 132.32/22.90 ((
% 132.32/22.90 (funcGraphProp4) =>
% 132.32/22.90 ((
% 132.32/22.90 (subbreln) =>
% 132.32/22.90 ((
% 132.32/22.90 (eqbreln) =>
% 132.32/22.90 ((
% 132.32/22.90 (funcext) =>
% 132.32/22.90 ((
% 132.32/22.90 (funcext2) =>
% 132.32/22.90 ((
% 132.32/22.90 (ap2apEq1) =>
% 132.32/22.90 ((
% 132.32/22.90 (ap2apEq2) =>
% 132.32/22.90 ((
% 132.32/22.90 (beta1) =>
% 132.32/22.90 ((
% 132.32/22.90 (eta1) =>
% 132.32/22.90 ((
% 132.32/22.90 (lam2lamEq) =>
% 132.32/22.90 ((
% 132.32/22.90 (beta2) =>
% 132.32/22.90 ((
% 132.32/22.90 (eta2) =>
% 132.32/22.90 ((
% 132.32/22.90 (iffalseProp1) =>
% 132.32/22.90 ((
% 132.32/22.90 (iffalseProp2) =>
% 132.32/22.90 ((
% 132.32/22.90 (iftrueProp1) =>
% 132.32/22.90 ((
% 132.32/22.90 (iftrueProp2) =>
% 132.32/22.90 ((
% 132.32/22.90 (ifSingleton) =>
% 132.32/22.90 ((
% 132.32/22.90 (ifp) =>
% 132.32/22.90 ((
% 132.32/22.90 (theeq) =>
% 132.32/22.90 ((
% 132.32/22.90 (iftrue) =>
% 132.32/22.90 ((
% 132.32/22.90 (iffalse) =>
% 132.32/22.90 ((
% 132.32/22.90 (iftrueorfalse) =>
% 132.32/22.90 ((
% 132.32/22.90 (binintersectT_lem) =>
% 132.32/22.90 ((
% 132.32/22.90 (binunionT_lem) =>
% 132.32/22.90 ((
% 132.32/22.90 (powersetT_lem) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusT_lem) =>
% 132.32/22.90 ((
% 132.32/22.90 (complementT_lem) =>
% 132.32/22.90 ((
% 132.32/22.90 (setextT) =>
% 132.32/22.90 ((
% 132.32/22.90 (subsetTI) =>
% 132.32/22.90 ((
% 132.32/22.90 (powersetTI1) =>
% 132.32/22.90 ((
% 132.32/22.90 (powersetTE1) =>
% 132.32/22.90 ((
% 132.32/22.90 (complementTI1) =>
% 132.32/22.90 ((
% 132.32/22.90 (complementTE1) =>
% 132.32/22.90 ((
% 132.32/22.90 (binintersectTELcontra) =>
% 132.32/22.90 ((
% 132.32/22.90 (binintersectTERcontra) =>
% 132.32/22.90 ((
% 132.32/22.90 (contrasubsetT) =>
% 132.32/22.90 ((
% 132.32/22.90 (contrasubsetT1) =>
% 132.32/22.90 ((
% 132.32/22.90 (contrasubsetT2) =>
% 132.32/22.90 ((
% 132.32/22.90 (contrasubsetT3) =>
% 132.32/22.90 ((
% 132.32/22.90 (doubleComplementI1) =>
% 132.32/22.90 ((
% 132.32/22.90 (doubleComplementE1) =>
% 132.32/22.90 ((
% 132.32/22.90 (doubleComplementSub1) =>
% 132.32/22.90 ((
% 132.32/22.90 (doubleComplementSub2) =>
% 132.32/22.90 ((
% 132.32/22.90 (doubleComplementEq) =>
% 132.32/22.90 ((
% 132.32/22.90 (complementTnotintersectT) =>
% 132.32/22.90 ((
% 132.32/22.90 (complementImpComplementIntersect) =>
% 132.32/22.90 ((
% 132.32/22.90 (complementSubsetComplementIntersect) =>
% 132.32/22.90 ((
% 132.32/22.90 (complementInPowersetComplementIntersect) =>
% 132.32/22.90 ((
% 132.32/22.90 (contraSubsetComplement) =>
% 132.32/22.90 ((
% 132.32/22.90 (complementTcontraSubset) =>
% 132.32/22.90 ((
% 132.32/22.90 (binunionTILcontra) =>
% 132.32/22.90 ((
% 132.32/22.90 (binunionTIRcontra) =>
% 132.32/22.90 ((
% 132.32/22.90 (inIntersectImpInUnion) =>
% 132.32/22.90 ((
% 132.32/22.90 (inIntersectImpInUnion2) =>
% 132.32/22.90 ((
% 132.32/22.90 (inIntersectImpInIntersectUnions) =>
% 132.32/22.90 ((
% 132.32/22.90 (intersectInPowersetIntersectUnions) =>
% 132.32/22.90 ((
% 132.32/22.90 (inComplementUnionImpNotIn1) =>
% 132.32/22.90 ((
% 132.32/22.90 (inComplementUnionImpInComplement1) =>
% 132.32/22.90 ((
% 132.32/22.90 (binunionTE) =>
% 132.32/22.90 ((
% 132.32/22.90 (binunionTEcontra) =>
% 132.32/22.90 ((
% 132.32/22.90 (demorgan2a1) =>
% 132.32/22.90 ((
% 132.32/22.90 (complementUnionInPowersetComplement) =>
% 132.32/22.90 ((
% 132.32/22.90 (demorgan2a2) =>
% 132.32/22.90 ((
% 132.32/22.90 (demorgan1a) =>
% 132.32/22.90 ((
% 132.32/22.90 (demorgan1b) =>
% 132.32/22.90 ((
% 132.32/22.90 (demorgan1) =>
% 132.32/22.90 ((
% 132.32/22.90 (demorgan2a) =>
% 132.32/22.90 ((
% 132.32/22.90 (demorgan2b2) =>
% 132.32/22.90 ((
% 132.32/22.90 (demorgan2b) =>
% 132.32/22.90 ((
% 132.32/22.90 (demorgan2) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz13rule0) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz13rule1) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz13rule2) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz13rule3) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz13rule4) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz1_1) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz1_2) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz1_3) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz1_4) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz1_5) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1all2) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1SetBreln1) =>
% 132.32/22.90 ((
% 132.32/22.90 (choice2fnsingleton) =>
% 132.32/22.90 ((
% 132.32/22.90 (setOfPairsIsBReln1) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1all1) =>
% 132.32/22.90 ((
% 132.32/22.90 (subbreln1) =>
% 132.32/22.90 ((
% 132.32/22.90 (eqbreln1) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1invprop) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1invI) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1invE) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1compprop) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1compI) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1compE) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1compEex) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1unionprop) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1unionIL) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1unionIR) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1unionI) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1unionE) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1unionEcases) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1unionCommutes) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz2Ex) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz2W) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz2A) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz2B) =>
% 132.32/22.90 ((
% 132.32/22.90 (image1Ex) =>
% 132.32/22.90 ((
% 132.32/22.90 (image1Ex1) =>
% 132.32/22.90 ((
% 132.32/22.90 (image1Equiv) =>
% 132.32/22.90 ((
% 132.32/22.90 (image1E) =>
% 132.32/22.90 ((
% 132.32/22.90 (image1I) =>
% 132.32/22.90 ((
% 132.32/22.90 (injFuncInInjFuncSet) =>
% 132.32/22.90 ((
% 132.32/22.90 (injFuncSetFuncIn) =>
% 132.32/22.90 ((
% 132.32/22.90 (injFuncSetFuncInj) =>
% 132.32/22.90 ((
% 132.32/22.90 (surjFuncSetFuncIn) =>
% 132.32/22.90 ((
% 132.32/22.90 (surjFuncSetFuncSurj) =>
% 132.32/22.90 ((
% 132.32/22.90 (leftInvIsSurj) =>
% 132.32/22.90 ((
% 132.32/22.90 (surjCantorThm) =>
% 132.32/22.90 ((
% 132.32/22.90 (foundation2) =>
% 132.32/22.90 ((
% 132.32/22.90 (notinself) =>
% 132.32/22.90 ((
% 132.32/22.90 (notinself2) =>
% 132.32/22.90 ((
% 132.32/22.90 (omegaSp) =>
% 132.32/22.90 ((
% 132.32/22.90 (omegaSclos) =>
% 132.32/22.90 ((
% 132.32/22.90 (peano0notS) =>
% 132.32/22.90 ((
% 132.32/22.90 (peanoSinj) =>
% 132.32/22.90 ((
% 132.32/22.90 (transitivesetOp1) =>
% 132.32/22.90 ((
% 132.32/22.90 (binintTransitive) =>
% 132.32/22.90 ((
% 132.32/22.90 (transitivesetOp2) =>
% 132.32/22.90 ((
% 132.32/22.90 (setunionTransitive) =>
% 132.32/22.90 ((
% 132.32/22.90 (ordinalMinLem1) =>
% 132.32/22.90 ((
% 132.32/22.90 (ordinalTransSet) =>
% 132.32/22.90 ((
% 132.32/22.90 (ordinalTransSet1) =>
% 132.32/22.90 ((
% 132.32/22.90 (setunionOrdinalLem1) =>
% 132.32/22.90 (ordinal @
% 132.32/22.90 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.32/22.90 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl823])).
% 132.32/22.90 thf(zip_derived_cl843, plain,
% 132.32/22.90 (~ (((setadjoinSub2) =>
% 132.32/22.90 (((subset2powerset) =>
% 132.32/22.90 (((setextsub) =>
% 132.32/22.90 (((subsetemptysetimpeq) =>
% 132.32/22.90 (((powersetI1) =>
% 132.32/22.90 (((powersetE1) =>
% 132.32/22.90 (((inPowerset) =>
% 132.32/22.90 (((powersetsubset) =>
% 132.32/22.90 (((sepInPowerset) =>
% 132.32/22.90 (((sepSubset) =>
% 132.32/22.90 (((binunionIL) =>
% 132.32/22.90 (((upairset2IR) =>
% 132.32/22.90 (((binunionIR) =>
% 132.32/22.90 (((binunionEcases) =>
% 132.32/22.90 (((binunionE) =>
% 132.32/22.90 (((binunionLsub) =>
% 132.32/22.90 (((binunionRsub) =>
% 132.32/22.90 (((binintersectI) =>
% 132.32/22.90 (((binintersectSubset5) =>
% 132.32/22.90 (((binintersectEL) =>
% 132.32/22.90 (((binintersectLsub) =>
% 132.32/22.90 (((binintersectSubset2) =>
% 132.32/22.90 (((binintersectSubset3) =>
% 132.32/22.90 (((binintersectER) =>
% 132.32/22.90 (((disjointsetsI1) =>
% 132.32/22.90 (((binintersectRsub) =>
% 132.32/22.90 (((binintersectSubset4) =>
% 132.32/22.90 (((binintersectSubset1) =>
% 132.32/22.90 (((bs114d) =>
% 132.32/22.90 (((setminusI) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusEL) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusER) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusSubset2) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusERneg) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusELneg) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusILneg) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusIRneg) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusLsub) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusSubset1) =>
% 132.32/22.90 ((
% 132.32/22.90 (symdiffE) =>
% 132.32/22.90 ((
% 132.32/22.90 (symdiffI1) =>
% 132.32/22.90 ((
% 132.32/22.90 (symdiffI2) =>
% 132.32/22.90 ((
% 132.32/22.90 (symdiffIneg1) =>
% 132.32/22.90 ((
% 132.32/22.90 (symdiffIneg2) =>
% 132.32/22.90 ((
% 132.32/22.90 (secondinupair) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairIL) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairIR) =>
% 132.32/22.90 ((
% 132.32/22.90 (kpairiskpair) =>
% 132.32/22.90 ((
% 132.32/22.90 (kpairp) =>
% 132.32/22.90 ((
% 132.32/22.90 (singletonsubset) =>
% 132.32/22.90 ((
% 132.32/22.90 (singletoninpowerset) =>
% 132.32/22.90 ((
% 132.32/22.90 (singletoninpowunion) =>
% 132.32/22.90 ((
% 132.32/22.90 (upairset2E) =>
% 132.32/22.90 ((
% 132.32/22.90 (upairsubunion) =>
% 132.32/22.90 ((
% 132.32/22.90 (upairinpowunion) =>
% 132.32/22.90 ((
% 132.32/22.90 (ubforcartprodlem1) =>
% 132.32/22.90 ((
% 132.32/22.90 (ubforcartprodlem2) =>
% 132.32/22.90 ((
% 132.32/22.90 (ubforcartprodlem3) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodpairin) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodmempair1) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodmempair) =>
% 132.32/22.90 ((
% 132.32/22.90 (setunionE2) =>
% 132.32/22.90 ((
% 132.32/22.90 (setunionsingleton1) =>
% 132.32/22.90 ((
% 132.32/22.90 (setunionsingleton2) =>
% 132.32/22.90 ((
% 132.32/22.90 (setunionsingleton) =>
% 132.32/22.90 ((
% 132.32/22.90 (singletonprop) =>
% 132.32/22.90 ((
% 132.32/22.90 (ex1E1) =>
% 132.32/22.90 ((
% 132.32/22.90 (ex1I) =>
% 132.32/22.90 ((
% 132.32/22.90 (ex1I2) =>
% 132.32/22.90 ((
% 132.32/22.90 (singletonsuniq) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairinjL1) =>
% 132.32/22.90 ((
% 132.32/22.90 (kfstsingleton) =>
% 132.32/22.90 ((
% 132.32/22.90 (theprop) =>
% 132.32/22.90 ((
% 132.32/22.90 (kfstpairEq) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodfstin) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairinjL2) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairinjL) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairinjR11) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairinjR12) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairinjR1) =>
% 132.32/22.90 ((
% 132.32/22.90 (upairequniteq) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairinjR2) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairinjR) =>
% 132.32/22.90 ((
% 132.32/22.90 (ksndsingleton) =>
% 132.32/22.90 ((
% 132.32/22.90 (ksndpairEq) =>
% 132.32/22.90 ((
% 132.32/22.90 (kpairsurjEq) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodsndin) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodpairmemEL) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodpairmemER) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodmempaircEq) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodfstpairEq) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodsndpairEq) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodpairsurjEq) =>
% 132.32/22.90 ((
% 132.32/22.90 (dpsetconstrI) =>
% 132.32/22.90 ((
% 132.32/22.90 (dpsetconstrSub) =>
% 132.32/22.90 ((
% 132.32/22.90 (setOfPairsIsBReln) =>
% 132.32/22.90 ((
% 132.32/22.90 (dpsetconstrERa) =>
% 132.32/22.90 ((
% 132.32/22.90 (dpsetconstrEL1) =>
% 132.32/22.90 ((
% 132.32/22.90 (dpsetconstrEL2) =>
% 132.32/22.90 ((
% 132.32/22.90 (dpsetconstrER) =>
% 132.32/22.90 ((
% 132.32/22.90 (funcImageSingleton) =>
% 132.32/22.90 ((
% 132.32/22.90 (apProp) =>
% 132.32/22.90 ((
% 132.32/22.90 (app) =>
% 132.32/22.90 ((
% 132.32/22.90 (infuncsetfunc) =>
% 132.32/22.90 ((
% 132.32/22.90 (ap2p) =>
% 132.32/22.90 ((
% 132.32/22.90 (funcinfuncset) =>
% 132.32/22.90 ((
% 132.32/22.90 (lamProp) =>
% 132.32/22.90 ((
% 132.32/22.90 (lamp) =>
% 132.32/22.90 ((
% 132.32/22.90 (lam2p) =>
% 132.32/22.90 ((
% 132.32/22.90 (brelnall1) =>
% 132.32/22.90 ((
% 132.32/22.90 (brelnall2) =>
% 132.32/22.90 ((
% 132.32/22.90 (ex1E2) =>
% 132.32/22.90 ((
% 132.32/22.90 (funcGraphProp1) =>
% 132.32/22.90 ((
% 132.32/22.90 (funcGraphProp3) =>
% 132.32/22.90 ((
% 132.32/22.90 (funcGraphProp2) =>
% 132.32/22.90 ((
% 132.32/22.90 (funcextLem) =>
% 132.32/22.90 ((
% 132.32/22.90 (funcGraphProp4) =>
% 132.32/22.90 ((
% 132.32/22.90 (subbreln) =>
% 132.32/22.90 ((
% 132.32/22.90 (eqbreln) =>
% 132.32/22.90 ((
% 132.32/22.90 (funcext) =>
% 132.32/22.90 ((
% 132.32/22.90 (funcext2) =>
% 132.32/22.90 ((
% 132.32/22.90 (ap2apEq1) =>
% 132.32/22.90 ((
% 132.32/22.90 (ap2apEq2) =>
% 132.32/22.90 ((
% 132.32/22.90 (beta1) =>
% 132.32/22.90 ((
% 132.32/22.90 (eta1) =>
% 132.32/22.90 ((
% 132.32/22.90 (lam2lamEq) =>
% 132.32/22.90 ((
% 132.32/22.90 (beta2) =>
% 132.32/22.90 ((
% 132.32/22.90 (eta2) =>
% 132.32/22.90 ((
% 132.32/22.90 (iffalseProp1) =>
% 132.32/22.90 ((
% 132.32/22.90 (iffalseProp2) =>
% 132.32/22.90 ((
% 132.32/22.90 (iftrueProp1) =>
% 132.32/22.90 ((
% 132.32/22.90 (iftrueProp2) =>
% 132.32/22.90 ((
% 132.32/22.90 (ifSingleton) =>
% 132.32/22.90 ((
% 132.32/22.90 (ifp) =>
% 132.32/22.90 ((
% 132.32/22.90 (theeq) =>
% 132.32/22.90 ((
% 132.32/22.90 (iftrue) =>
% 132.32/22.90 ((
% 132.32/22.90 (iffalse) =>
% 132.32/22.90 ((
% 132.32/22.90 (iftrueorfalse) =>
% 132.32/22.90 ((
% 132.32/22.90 (binintersectT_lem) =>
% 132.32/22.90 ((
% 132.32/22.90 (binunionT_lem) =>
% 132.32/22.90 ((
% 132.32/22.90 (powersetT_lem) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusT_lem) =>
% 132.32/22.90 ((
% 132.32/22.90 (complementT_lem) =>
% 132.32/22.90 ((
% 132.32/22.90 (setextT) =>
% 132.32/22.90 ((
% 132.32/22.90 (subsetTI) =>
% 132.32/22.90 ((
% 132.32/22.90 (powersetTI1) =>
% 132.32/22.90 ((
% 132.32/22.90 (powersetTE1) =>
% 132.32/22.90 ((
% 132.32/22.90 (complementTI1) =>
% 132.32/22.90 ((
% 132.32/22.90 (complementTE1) =>
% 132.32/22.90 ((
% 132.32/22.90 (binintersectTELcontra) =>
% 132.32/22.90 ((
% 132.32/22.90 (binintersectTERcontra) =>
% 132.32/22.90 ((
% 132.32/22.90 (contrasubsetT) =>
% 132.32/22.90 ((
% 132.32/22.90 (contrasubsetT1) =>
% 132.32/22.90 ((
% 132.32/22.90 (contrasubsetT2) =>
% 132.32/22.90 ((
% 132.32/22.90 (contrasubsetT3) =>
% 132.32/22.90 ((
% 132.32/22.90 (doubleComplementI1) =>
% 132.32/22.90 ((
% 132.32/22.90 (doubleComplementE1) =>
% 132.32/22.90 ((
% 132.32/22.90 (doubleComplementSub1) =>
% 132.32/22.90 ((
% 132.32/22.90 (doubleComplementSub2) =>
% 132.32/22.90 ((
% 132.32/22.90 (doubleComplementEq) =>
% 132.32/22.90 ((
% 132.32/22.90 (complementTnotintersectT) =>
% 132.32/22.90 ((
% 132.32/22.90 (complementImpComplementIntersect) =>
% 132.32/22.90 ((
% 132.32/22.90 (complementSubsetComplementIntersect) =>
% 132.32/22.90 ((
% 132.32/22.90 (complementInPowersetComplementIntersect) =>
% 132.32/22.90 ((
% 132.32/22.90 (contraSubsetComplement) =>
% 132.32/22.90 ((
% 132.32/22.90 (complementTcontraSubset) =>
% 132.32/22.90 ((
% 132.32/22.90 (binunionTILcontra) =>
% 132.32/22.90 ((
% 132.32/22.90 (binunionTIRcontra) =>
% 132.32/22.90 ((
% 132.32/22.90 (inIntersectImpInUnion) =>
% 132.32/22.90 ((
% 132.32/22.90 (inIntersectImpInUnion2) =>
% 132.32/22.90 ((
% 132.32/22.90 (inIntersectImpInIntersectUnions) =>
% 132.32/22.90 ((
% 132.32/22.90 (intersectInPowersetIntersectUnions) =>
% 132.32/22.90 ((
% 132.32/22.90 (inComplementUnionImpNotIn1) =>
% 132.32/22.90 ((
% 132.32/22.90 (inComplementUnionImpInComplement1) =>
% 132.32/22.90 ((
% 132.32/22.90 (binunionTE) =>
% 132.32/22.90 ((
% 132.32/22.90 (binunionTEcontra) =>
% 132.32/22.90 ((
% 132.32/22.90 (demorgan2a1) =>
% 132.32/22.90 ((
% 132.32/22.90 (complementUnionInPowersetComplement) =>
% 132.32/22.90 ((
% 132.32/22.90 (demorgan2a2) =>
% 132.32/22.90 ((
% 132.32/22.90 (demorgan1a) =>
% 132.32/22.90 ((
% 132.32/22.90 (demorgan1b) =>
% 132.32/22.90 ((
% 132.32/22.90 (demorgan1) =>
% 132.32/22.90 ((
% 132.32/22.90 (demorgan2a) =>
% 132.32/22.90 ((
% 132.32/22.90 (demorgan2b2) =>
% 132.32/22.90 ((
% 132.32/22.90 (demorgan2b) =>
% 132.32/22.90 ((
% 132.32/22.90 (demorgan2) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz13rule0) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz13rule1) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz13rule2) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz13rule3) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz13rule4) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz1_1) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz1_2) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz1_3) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz1_4) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz1_5) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1all2) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1SetBreln1) =>
% 132.32/22.90 ((
% 132.32/22.90 (choice2fnsingleton) =>
% 132.32/22.90 ((
% 132.32/22.90 (setOfPairsIsBReln1) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1all1) =>
% 132.32/22.90 ((
% 132.32/22.90 (subbreln1) =>
% 132.32/22.90 ((
% 132.32/22.90 (eqbreln1) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1invprop) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1invI) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1invE) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1compprop) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1compI) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1compE) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1compEex) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1unionprop) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1unionIL) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1unionIR) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1unionI) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1unionE) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1unionEcases) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1unionCommutes) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz2Ex) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz2W) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz2A) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz2B) =>
% 132.32/22.90 ((
% 132.32/22.90 (image1Ex) =>
% 132.32/22.90 ((
% 132.32/22.90 (image1Ex1) =>
% 132.32/22.90 ((
% 132.32/22.90 (image1Equiv) =>
% 132.32/22.90 ((
% 132.32/22.90 (image1E) =>
% 132.32/22.90 ((
% 132.32/22.90 (image1I) =>
% 132.32/22.90 ((
% 132.32/22.90 (injFuncInInjFuncSet) =>
% 132.32/22.90 ((
% 132.32/22.90 (injFuncSetFuncIn) =>
% 132.32/22.90 ((
% 132.32/22.90 (injFuncSetFuncInj) =>
% 132.32/22.90 ((
% 132.32/22.90 (surjFuncSetFuncIn) =>
% 132.32/22.90 ((
% 132.32/22.90 (surjFuncSetFuncSurj) =>
% 132.32/22.90 ((
% 132.32/22.90 (leftInvIsSurj) =>
% 132.32/22.90 ((
% 132.32/22.90 (surjCantorThm) =>
% 132.32/22.90 ((
% 132.32/22.90 (foundation2) =>
% 132.32/22.90 ((
% 132.32/22.90 (notinself) =>
% 132.32/22.90 ((
% 132.32/22.90 (notinself2) =>
% 132.32/22.90 ((
% 132.32/22.90 (omegaSp) =>
% 132.32/22.90 ((
% 132.32/22.90 (omegaSclos) =>
% 132.32/22.90 ((
% 132.32/22.90 (peano0notS) =>
% 132.32/22.90 ((
% 132.32/22.90 (peanoSinj) =>
% 132.32/22.90 ((
% 132.32/22.90 (transitivesetOp1) =>
% 132.32/22.90 ((
% 132.32/22.90 (binintTransitive) =>
% 132.32/22.90 ((
% 132.32/22.90 (transitivesetOp2) =>
% 132.32/22.90 ((
% 132.32/22.90 (setunionTransitive) =>
% 132.32/22.90 ((
% 132.32/22.90 (ordinalMinLem1) =>
% 132.32/22.90 ((
% 132.32/22.90 (ordinalTransSet) =>
% 132.32/22.90 ((
% 132.32/22.90 (ordinalTransSet1) =>
% 132.32/22.90 ((
% 132.32/22.90 (setunionOrdinalLem1) =>
% 132.32/22.90 (ordinal @
% 132.32/22.90 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.32/22.90 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl833])).
% 132.32/22.90 thf(zip_derived_cl851, plain,
% 132.32/22.90 (~ (((subset2powerset) =>
% 132.32/22.90 (((setextsub) =>
% 132.32/22.90 (((subsetemptysetimpeq) =>
% 132.32/22.90 (((powersetI1) =>
% 132.32/22.90 (((powersetE1) =>
% 132.32/22.90 (((inPowerset) =>
% 132.32/22.90 (((powersetsubset) =>
% 132.32/22.90 (((sepInPowerset) =>
% 132.32/22.90 (((sepSubset) =>
% 132.32/22.90 (((binunionIL) =>
% 132.32/22.90 (((upairset2IR) =>
% 132.32/22.90 (((binunionIR) =>
% 132.32/22.90 (((binunionEcases) =>
% 132.32/22.90 (((binunionE) =>
% 132.32/22.90 (((binunionLsub) =>
% 132.32/22.90 (((binunionRsub) =>
% 132.32/22.90 (((binintersectI) =>
% 132.32/22.90 (((binintersectSubset5) =>
% 132.32/22.90 (((binintersectEL) =>
% 132.32/22.90 (((binintersectLsub) =>
% 132.32/22.90 (((binintersectSubset2) =>
% 132.32/22.90 (((binintersectSubset3) =>
% 132.32/22.90 (((binintersectER) =>
% 132.32/22.90 (((disjointsetsI1) =>
% 132.32/22.90 (((binintersectRsub) =>
% 132.32/22.90 (((binintersectSubset4) =>
% 132.32/22.90 (((binintersectSubset1) =>
% 132.32/22.90 (((bs114d) =>
% 132.32/22.90 (((setminusI) =>
% 132.32/22.90 (((setminusEL) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusER) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusSubset2) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusERneg) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusELneg) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusILneg) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusIRneg) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusLsub) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusSubset1) =>
% 132.32/22.90 ((
% 132.32/22.90 (symdiffE) =>
% 132.32/22.90 ((
% 132.32/22.90 (symdiffI1) =>
% 132.32/22.90 ((
% 132.32/22.90 (symdiffI2) =>
% 132.32/22.90 ((
% 132.32/22.90 (symdiffIneg1) =>
% 132.32/22.90 ((
% 132.32/22.90 (symdiffIneg2) =>
% 132.32/22.90 ((
% 132.32/22.90 (secondinupair) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairIL) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairIR) =>
% 132.32/22.90 ((
% 132.32/22.90 (kpairiskpair) =>
% 132.32/22.90 ((
% 132.32/22.90 (kpairp) =>
% 132.32/22.90 ((
% 132.32/22.90 (singletonsubset) =>
% 132.32/22.90 ((
% 132.32/22.90 (singletoninpowerset) =>
% 132.32/22.90 ((
% 132.32/22.90 (singletoninpowunion) =>
% 132.32/22.90 ((
% 132.32/22.90 (upairset2E) =>
% 132.32/22.90 ((
% 132.32/22.90 (upairsubunion) =>
% 132.32/22.90 ((
% 132.32/22.90 (upairinpowunion) =>
% 132.32/22.90 ((
% 132.32/22.90 (ubforcartprodlem1) =>
% 132.32/22.90 ((
% 132.32/22.90 (ubforcartprodlem2) =>
% 132.32/22.90 ((
% 132.32/22.90 (ubforcartprodlem3) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodpairin) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodmempair1) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodmempair) =>
% 132.32/22.90 ((
% 132.32/22.90 (setunionE2) =>
% 132.32/22.90 ((
% 132.32/22.90 (setunionsingleton1) =>
% 132.32/22.90 ((
% 132.32/22.90 (setunionsingleton2) =>
% 132.32/22.90 ((
% 132.32/22.90 (setunionsingleton) =>
% 132.32/22.90 ((
% 132.32/22.90 (singletonprop) =>
% 132.32/22.90 ((
% 132.32/22.90 (ex1E1) =>
% 132.32/22.90 ((
% 132.32/22.90 (ex1I) =>
% 132.32/22.90 ((
% 132.32/22.90 (ex1I2) =>
% 132.32/22.90 ((
% 132.32/22.90 (singletonsuniq) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairinjL1) =>
% 132.32/22.90 ((
% 132.32/22.90 (kfstsingleton) =>
% 132.32/22.90 ((
% 132.32/22.90 (theprop) =>
% 132.32/22.90 ((
% 132.32/22.90 (kfstpairEq) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodfstin) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairinjL2) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairinjL) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairinjR11) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairinjR12) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairinjR1) =>
% 132.32/22.90 ((
% 132.32/22.90 (upairequniteq) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairinjR2) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairinjR) =>
% 132.32/22.90 ((
% 132.32/22.90 (ksndsingleton) =>
% 132.32/22.90 ((
% 132.32/22.90 (ksndpairEq) =>
% 132.32/22.90 ((
% 132.32/22.90 (kpairsurjEq) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodsndin) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodpairmemEL) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodpairmemER) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodmempaircEq) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodfstpairEq) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodsndpairEq) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodpairsurjEq) =>
% 132.32/22.90 ((
% 132.32/22.90 (dpsetconstrI) =>
% 132.32/22.90 ((
% 132.32/22.90 (dpsetconstrSub) =>
% 132.32/22.90 ((
% 132.32/22.90 (setOfPairsIsBReln) =>
% 132.32/22.90 ((
% 132.32/22.90 (dpsetconstrERa) =>
% 132.32/22.90 ((
% 132.32/22.90 (dpsetconstrEL1) =>
% 132.32/22.90 ((
% 132.32/22.90 (dpsetconstrEL2) =>
% 132.32/22.90 ((
% 132.32/22.90 (dpsetconstrER) =>
% 132.32/22.90 ((
% 132.32/22.90 (funcImageSingleton) =>
% 132.32/22.90 ((
% 132.32/22.90 (apProp) =>
% 132.32/22.90 ((
% 132.32/22.90 (app) =>
% 132.32/22.90 ((
% 132.32/22.90 (infuncsetfunc) =>
% 132.32/22.90 ((
% 132.32/22.90 (ap2p) =>
% 132.32/22.90 ((
% 132.32/22.90 (funcinfuncset) =>
% 132.32/22.90 ((
% 132.32/22.90 (lamProp) =>
% 132.32/22.90 ((
% 132.32/22.90 (lamp) =>
% 132.32/22.90 ((
% 132.32/22.90 (lam2p) =>
% 132.32/22.90 ((
% 132.32/22.90 (brelnall1) =>
% 132.32/22.90 ((
% 132.32/22.90 (brelnall2) =>
% 132.32/22.90 ((
% 132.32/22.90 (ex1E2) =>
% 132.32/22.90 ((
% 132.32/22.90 (funcGraphProp1) =>
% 132.32/22.90 ((
% 132.32/22.90 (funcGraphProp3) =>
% 132.32/22.90 ((
% 132.32/22.90 (funcGraphProp2) =>
% 132.32/22.90 ((
% 132.32/22.90 (funcextLem) =>
% 132.32/22.90 ((
% 132.32/22.90 (funcGraphProp4) =>
% 132.32/22.90 ((
% 132.32/22.90 (subbreln) =>
% 132.32/22.90 ((
% 132.32/22.90 (eqbreln) =>
% 132.32/22.90 ((
% 132.32/22.90 (funcext) =>
% 132.32/22.90 ((
% 132.32/22.90 (funcext2) =>
% 132.32/22.90 ((
% 132.32/22.90 (ap2apEq1) =>
% 132.32/22.90 ((
% 132.32/22.90 (ap2apEq2) =>
% 132.32/22.90 ((
% 132.32/22.90 (beta1) =>
% 132.32/22.90 ((
% 132.32/22.90 (eta1) =>
% 132.32/22.90 ((
% 132.32/22.90 (lam2lamEq) =>
% 132.32/22.90 ((
% 132.32/22.90 (beta2) =>
% 132.32/22.90 ((
% 132.32/22.90 (eta2) =>
% 132.32/22.90 ((
% 132.32/22.90 (iffalseProp1) =>
% 132.32/22.90 ((
% 132.32/22.90 (iffalseProp2) =>
% 132.32/22.90 ((
% 132.32/22.90 (iftrueProp1) =>
% 132.32/22.90 ((
% 132.32/22.90 (iftrueProp2) =>
% 132.32/22.90 ((
% 132.32/22.90 (ifSingleton) =>
% 132.32/22.90 ((
% 132.32/22.90 (ifp) =>
% 132.32/22.90 ((
% 132.32/22.90 (theeq) =>
% 132.32/22.90 ((
% 132.32/22.90 (iftrue) =>
% 132.32/22.90 ((
% 132.32/22.90 (iffalse) =>
% 132.32/22.90 ((
% 132.32/22.90 (iftrueorfalse) =>
% 132.32/22.90 ((
% 132.32/22.90 (binintersectT_lem) =>
% 132.32/22.90 ((
% 132.32/22.90 (binunionT_lem) =>
% 132.32/22.90 ((
% 132.32/22.90 (powersetT_lem) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusT_lem) =>
% 132.32/22.90 ((
% 132.32/22.90 (complementT_lem) =>
% 132.32/22.90 ((
% 132.32/22.90 (setextT) =>
% 132.32/22.90 ((
% 132.32/22.90 (subsetTI) =>
% 132.32/22.90 ((
% 132.32/22.90 (powersetTI1) =>
% 132.32/22.90 ((
% 132.32/22.90 (powersetTE1) =>
% 132.32/22.90 ((
% 132.32/22.90 (complementTI1) =>
% 132.32/22.90 ((
% 132.32/22.90 (complementTE1) =>
% 132.32/22.90 ((
% 132.32/22.90 (binintersectTELcontra) =>
% 132.32/22.90 ((
% 132.32/22.90 (binintersectTERcontra) =>
% 132.32/22.90 ((
% 132.32/22.90 (contrasubsetT) =>
% 132.32/22.90 ((
% 132.32/22.90 (contrasubsetT1) =>
% 132.32/22.90 ((
% 132.32/22.90 (contrasubsetT2) =>
% 132.32/22.90 ((
% 132.32/22.90 (contrasubsetT3) =>
% 132.32/22.90 ((
% 132.32/22.90 (doubleComplementI1) =>
% 132.32/22.90 ((
% 132.32/22.90 (doubleComplementE1) =>
% 132.32/22.90 ((
% 132.32/22.90 (doubleComplementSub1) =>
% 132.32/22.90 ((
% 132.32/22.90 (doubleComplementSub2) =>
% 132.32/22.90 ((
% 132.32/22.90 (doubleComplementEq) =>
% 132.32/22.90 ((
% 132.32/22.90 (complementTnotintersectT) =>
% 132.32/22.90 ((
% 132.32/22.90 (complementImpComplementIntersect) =>
% 132.32/22.90 ((
% 132.32/22.90 (complementSubsetComplementIntersect) =>
% 132.32/22.90 ((
% 132.32/22.90 (complementInPowersetComplementIntersect) =>
% 132.32/22.90 ((
% 132.32/22.90 (contraSubsetComplement) =>
% 132.32/22.90 ((
% 132.32/22.90 (complementTcontraSubset) =>
% 132.32/22.90 ((
% 132.32/22.90 (binunionTILcontra) =>
% 132.32/22.90 ((
% 132.32/22.90 (binunionTIRcontra) =>
% 132.32/22.90 ((
% 132.32/22.90 (inIntersectImpInUnion) =>
% 132.32/22.90 ((
% 132.32/22.90 (inIntersectImpInUnion2) =>
% 132.32/22.90 ((
% 132.32/22.90 (inIntersectImpInIntersectUnions) =>
% 132.32/22.90 ((
% 132.32/22.90 (intersectInPowersetIntersectUnions) =>
% 132.32/22.90 ((
% 132.32/22.90 (inComplementUnionImpNotIn1) =>
% 132.32/22.90 ((
% 132.32/22.90 (inComplementUnionImpInComplement1) =>
% 132.32/22.90 ((
% 132.32/22.90 (binunionTE) =>
% 132.32/22.90 ((
% 132.32/22.90 (binunionTEcontra) =>
% 132.32/22.90 ((
% 132.32/22.90 (demorgan2a1) =>
% 132.32/22.90 ((
% 132.32/22.90 (complementUnionInPowersetComplement) =>
% 132.32/22.90 ((
% 132.32/22.90 (demorgan2a2) =>
% 132.32/22.90 ((
% 132.32/22.90 (demorgan1a) =>
% 132.32/22.90 ((
% 132.32/22.90 (demorgan1b) =>
% 132.32/22.90 ((
% 132.32/22.90 (demorgan1) =>
% 132.32/22.90 ((
% 132.32/22.90 (demorgan2a) =>
% 132.32/22.90 ((
% 132.32/22.90 (demorgan2b2) =>
% 132.32/22.90 ((
% 132.32/22.90 (demorgan2b) =>
% 132.32/22.90 ((
% 132.32/22.90 (demorgan2) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz13rule0) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz13rule1) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz13rule2) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz13rule3) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz13rule4) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz1_1) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz1_2) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz1_3) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz1_4) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz1_5) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1all2) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1SetBreln1) =>
% 132.32/22.90 ((
% 132.32/22.90 (choice2fnsingleton) =>
% 132.32/22.90 ((
% 132.32/22.90 (setOfPairsIsBReln1) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1all1) =>
% 132.32/22.90 ((
% 132.32/22.90 (subbreln1) =>
% 132.32/22.90 ((
% 132.32/22.90 (eqbreln1) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1invprop) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1invI) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1invE) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1compprop) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1compI) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1compE) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1compEex) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1unionprop) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1unionIL) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1unionIR) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1unionI) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1unionE) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1unionEcases) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1unionCommutes) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz2Ex) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz2W) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz2A) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz2B) =>
% 132.32/22.90 ((
% 132.32/22.90 (image1Ex) =>
% 132.32/22.90 ((
% 132.32/22.90 (image1Ex1) =>
% 132.32/22.90 ((
% 132.32/22.90 (image1Equiv) =>
% 132.32/22.90 ((
% 132.32/22.90 (image1E) =>
% 132.32/22.90 ((
% 132.32/22.90 (image1I) =>
% 132.32/22.90 ((
% 132.32/22.90 (injFuncInInjFuncSet) =>
% 132.32/22.90 ((
% 132.32/22.90 (injFuncSetFuncIn) =>
% 132.32/22.90 ((
% 132.32/22.90 (injFuncSetFuncInj) =>
% 132.32/22.90 ((
% 132.32/22.90 (surjFuncSetFuncIn) =>
% 132.32/22.90 ((
% 132.32/22.90 (surjFuncSetFuncSurj) =>
% 132.32/22.90 ((
% 132.32/22.90 (leftInvIsSurj) =>
% 132.32/22.90 ((
% 132.32/22.90 (surjCantorThm) =>
% 132.32/22.90 ((
% 132.32/22.90 (foundation2) =>
% 132.32/22.90 ((
% 132.32/22.90 (notinself) =>
% 132.32/22.90 ((
% 132.32/22.90 (notinself2) =>
% 132.32/22.90 ((
% 132.32/22.90 (omegaSp) =>
% 132.32/22.90 ((
% 132.32/22.90 (omegaSclos) =>
% 132.32/22.90 ((
% 132.32/22.90 (peano0notS) =>
% 132.32/22.90 ((
% 132.32/22.90 (peanoSinj) =>
% 132.32/22.90 ((
% 132.32/22.90 (transitivesetOp1) =>
% 132.32/22.90 ((
% 132.32/22.90 (binintTransitive) =>
% 132.32/22.90 ((
% 132.32/22.90 (transitivesetOp2) =>
% 132.32/22.90 ((
% 132.32/22.90 (setunionTransitive) =>
% 132.32/22.90 ((
% 132.32/22.90 (ordinalMinLem1) =>
% 132.32/22.90 ((
% 132.32/22.90 (ordinalTransSet) =>
% 132.32/22.90 ((
% 132.32/22.90 (ordinalTransSet1) =>
% 132.32/22.90 ((
% 132.32/22.90 (setunionOrdinalLem1) =>
% 132.32/22.90 (ordinal @
% 132.32/22.90 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.32/22.90 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl843])).
% 132.32/22.90 thf(zip_derived_cl857, plain,
% 132.32/22.90 (~ (((setextsub) =>
% 132.32/22.90 (((subsetemptysetimpeq) =>
% 132.32/22.90 (((powersetI1) =>
% 132.32/22.90 (((powersetE1) =>
% 132.32/22.90 (((inPowerset) =>
% 132.32/22.90 (((powersetsubset) =>
% 132.32/22.90 (((sepInPowerset) =>
% 132.32/22.90 (((sepSubset) =>
% 132.32/22.90 (((binunionIL) =>
% 132.32/22.90 (((upairset2IR) =>
% 132.32/22.90 (((binunionIR) =>
% 132.32/22.90 (((binunionEcases) =>
% 132.32/22.90 (((binunionE) =>
% 132.32/22.90 (((binunionLsub) =>
% 132.32/22.90 (((binunionRsub) =>
% 132.32/22.90 (((binintersectI) =>
% 132.32/22.90 (((binintersectSubset5) =>
% 132.32/22.90 (((binintersectEL) =>
% 132.32/22.90 (((binintersectLsub) =>
% 132.32/22.90 (((binintersectSubset2) =>
% 132.32/22.90 (((binintersectSubset3) =>
% 132.32/22.90 (((binintersectER) =>
% 132.32/22.90 (((disjointsetsI1) =>
% 132.32/22.90 (((binintersectRsub) =>
% 132.32/22.90 (((binintersectSubset4) =>
% 132.32/22.90 (((binintersectSubset1) =>
% 132.32/22.90 (((bs114d) =>
% 132.32/22.90 (((setminusI) =>
% 132.32/22.90 (((setminusEL) =>
% 132.32/22.90 (((setminusER) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusSubset2) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusERneg) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusELneg) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusILneg) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusIRneg) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusLsub) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusSubset1) =>
% 132.32/22.90 ((
% 132.32/22.90 (symdiffE) =>
% 132.32/22.90 ((
% 132.32/22.90 (symdiffI1) =>
% 132.32/22.90 ((
% 132.32/22.90 (symdiffI2) =>
% 132.32/22.90 ((
% 132.32/22.90 (symdiffIneg1) =>
% 132.32/22.90 ((
% 132.32/22.90 (symdiffIneg2) =>
% 132.32/22.90 ((
% 132.32/22.90 (secondinupair) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairIL) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairIR) =>
% 132.32/22.90 ((
% 132.32/22.90 (kpairiskpair) =>
% 132.32/22.90 ((
% 132.32/22.90 (kpairp) =>
% 132.32/22.90 ((
% 132.32/22.90 (singletonsubset) =>
% 132.32/22.90 ((
% 132.32/22.90 (singletoninpowerset) =>
% 132.32/22.90 ((
% 132.32/22.90 (singletoninpowunion) =>
% 132.32/22.90 ((
% 132.32/22.90 (upairset2E) =>
% 132.32/22.90 ((
% 132.32/22.90 (upairsubunion) =>
% 132.32/22.90 ((
% 132.32/22.90 (upairinpowunion) =>
% 132.32/22.90 ((
% 132.32/22.90 (ubforcartprodlem1) =>
% 132.32/22.90 ((
% 132.32/22.90 (ubforcartprodlem2) =>
% 132.32/22.90 ((
% 132.32/22.90 (ubforcartprodlem3) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodpairin) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodmempair1) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodmempair) =>
% 132.32/22.90 ((
% 132.32/22.90 (setunionE2) =>
% 132.32/22.90 ((
% 132.32/22.90 (setunionsingleton1) =>
% 132.32/22.90 ((
% 132.32/22.90 (setunionsingleton2) =>
% 132.32/22.90 ((
% 132.32/22.90 (setunionsingleton) =>
% 132.32/22.90 ((
% 132.32/22.90 (singletonprop) =>
% 132.32/22.90 ((
% 132.32/22.90 (ex1E1) =>
% 132.32/22.90 ((
% 132.32/22.90 (ex1I) =>
% 132.32/22.90 ((
% 132.32/22.90 (ex1I2) =>
% 132.32/22.90 ((
% 132.32/22.90 (singletonsuniq) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairinjL1) =>
% 132.32/22.90 ((
% 132.32/22.90 (kfstsingleton) =>
% 132.32/22.90 ((
% 132.32/22.90 (theprop) =>
% 132.32/22.90 ((
% 132.32/22.90 (kfstpairEq) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodfstin) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairinjL2) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairinjL) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairinjR11) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairinjR12) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairinjR1) =>
% 132.32/22.90 ((
% 132.32/22.90 (upairequniteq) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairinjR2) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairinjR) =>
% 132.32/22.90 ((
% 132.32/22.90 (ksndsingleton) =>
% 132.32/22.90 ((
% 132.32/22.90 (ksndpairEq) =>
% 132.32/22.90 ((
% 132.32/22.90 (kpairsurjEq) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodsndin) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodpairmemEL) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodpairmemER) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodmempaircEq) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodfstpairEq) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodsndpairEq) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodpairsurjEq) =>
% 132.32/22.90 ((
% 132.32/22.90 (dpsetconstrI) =>
% 132.32/22.90 ((
% 132.32/22.90 (dpsetconstrSub) =>
% 132.32/22.90 ((
% 132.32/22.90 (setOfPairsIsBReln) =>
% 132.32/22.90 ((
% 132.32/22.90 (dpsetconstrERa) =>
% 132.32/22.90 ((
% 132.32/22.90 (dpsetconstrEL1) =>
% 132.32/22.90 ((
% 132.32/22.90 (dpsetconstrEL2) =>
% 132.32/22.90 ((
% 132.32/22.90 (dpsetconstrER) =>
% 132.32/22.90 ((
% 132.32/22.90 (funcImageSingleton) =>
% 132.32/22.90 ((
% 132.32/22.90 (apProp) =>
% 132.32/22.90 ((
% 132.32/22.90 (app) =>
% 132.32/22.90 ((
% 132.32/22.90 (infuncsetfunc) =>
% 132.32/22.90 ((
% 132.32/22.90 (ap2p) =>
% 132.32/22.90 ((
% 132.32/22.90 (funcinfuncset) =>
% 132.32/22.90 ((
% 132.32/22.90 (lamProp) =>
% 132.32/22.90 ((
% 132.32/22.90 (lamp) =>
% 132.32/22.90 ((
% 132.32/22.90 (lam2p) =>
% 132.32/22.90 ((
% 132.32/22.90 (brelnall1) =>
% 132.32/22.90 ((
% 132.32/22.90 (brelnall2) =>
% 132.32/22.90 ((
% 132.32/22.90 (ex1E2) =>
% 132.32/22.90 ((
% 132.32/22.90 (funcGraphProp1) =>
% 132.32/22.90 ((
% 132.32/22.90 (funcGraphProp3) =>
% 132.32/22.90 ((
% 132.32/22.90 (funcGraphProp2) =>
% 132.32/22.90 ((
% 132.32/22.90 (funcextLem) =>
% 132.32/22.90 ((
% 132.32/22.90 (funcGraphProp4) =>
% 132.32/22.90 ((
% 132.32/22.90 (subbreln) =>
% 132.32/22.90 ((
% 132.32/22.90 (eqbreln) =>
% 132.32/22.90 ((
% 132.32/22.90 (funcext) =>
% 132.32/22.90 ((
% 132.32/22.90 (funcext2) =>
% 132.32/22.90 ((
% 132.32/22.90 (ap2apEq1) =>
% 132.32/22.90 ((
% 132.32/22.90 (ap2apEq2) =>
% 132.32/22.90 ((
% 132.32/22.90 (beta1) =>
% 132.32/22.90 ((
% 132.32/22.90 (eta1) =>
% 132.32/22.90 ((
% 132.32/22.90 (lam2lamEq) =>
% 132.32/22.90 ((
% 132.32/22.90 (beta2) =>
% 132.32/22.90 ((
% 132.32/22.90 (eta2) =>
% 132.32/22.90 ((
% 132.32/22.90 (iffalseProp1) =>
% 132.32/22.90 ((
% 132.32/22.90 (iffalseProp2) =>
% 132.32/22.90 ((
% 132.32/22.90 (iftrueProp1) =>
% 132.32/22.90 ((
% 132.32/22.90 (iftrueProp2) =>
% 132.32/22.90 ((
% 132.32/22.90 (ifSingleton) =>
% 132.32/22.90 ((
% 132.32/22.90 (ifp) =>
% 132.32/22.90 ((
% 132.32/22.90 (theeq) =>
% 132.32/22.90 ((
% 132.32/22.90 (iftrue) =>
% 132.32/22.90 ((
% 132.32/22.90 (iffalse) =>
% 132.32/22.90 ((
% 132.32/22.90 (iftrueorfalse) =>
% 132.32/22.90 ((
% 132.32/22.90 (binintersectT_lem) =>
% 132.32/22.90 ((
% 132.32/22.90 (binunionT_lem) =>
% 132.32/22.90 ((
% 132.32/22.90 (powersetT_lem) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusT_lem) =>
% 132.32/22.90 ((
% 132.32/22.90 (complementT_lem) =>
% 132.32/22.90 ((
% 132.32/22.90 (setextT) =>
% 132.32/22.90 ((
% 132.32/22.90 (subsetTI) =>
% 132.32/22.90 ((
% 132.32/22.90 (powersetTI1) =>
% 132.32/22.90 ((
% 132.32/22.90 (powersetTE1) =>
% 132.32/22.90 ((
% 132.32/22.90 (complementTI1) =>
% 132.32/22.90 ((
% 132.32/22.90 (complementTE1) =>
% 132.32/22.90 ((
% 132.32/22.90 (binintersectTELcontra) =>
% 132.32/22.90 ((
% 132.32/22.90 (binintersectTERcontra) =>
% 132.32/22.90 ((
% 132.32/22.90 (contrasubsetT) =>
% 132.32/22.90 ((
% 132.32/22.90 (contrasubsetT1) =>
% 132.32/22.90 ((
% 132.32/22.90 (contrasubsetT2) =>
% 132.32/22.90 ((
% 132.32/22.90 (contrasubsetT3) =>
% 132.32/22.90 ((
% 132.32/22.90 (doubleComplementI1) =>
% 132.32/22.90 ((
% 132.32/22.90 (doubleComplementE1) =>
% 132.32/22.90 ((
% 132.32/22.90 (doubleComplementSub1) =>
% 132.32/22.90 ((
% 132.32/22.90 (doubleComplementSub2) =>
% 132.32/22.90 ((
% 132.32/22.90 (doubleComplementEq) =>
% 132.32/22.90 ((
% 132.32/22.90 (complementTnotintersectT) =>
% 132.32/22.90 ((
% 132.32/22.90 (complementImpComplementIntersect) =>
% 132.32/22.90 ((
% 132.32/22.90 (complementSubsetComplementIntersect) =>
% 132.32/22.90 ((
% 132.32/22.90 (complementInPowersetComplementIntersect) =>
% 132.32/22.90 ((
% 132.32/22.90 (contraSubsetComplement) =>
% 132.32/22.90 ((
% 132.32/22.90 (complementTcontraSubset) =>
% 132.32/22.90 ((
% 132.32/22.90 (binunionTILcontra) =>
% 132.32/22.90 ((
% 132.32/22.90 (binunionTIRcontra) =>
% 132.32/22.90 ((
% 132.32/22.90 (inIntersectImpInUnion) =>
% 132.32/22.90 ((
% 132.32/22.90 (inIntersectImpInUnion2) =>
% 132.32/22.90 ((
% 132.32/22.90 (inIntersectImpInIntersectUnions) =>
% 132.32/22.90 ((
% 132.32/22.90 (intersectInPowersetIntersectUnions) =>
% 132.32/22.90 ((
% 132.32/22.90 (inComplementUnionImpNotIn1) =>
% 132.32/22.90 ((
% 132.32/22.90 (inComplementUnionImpInComplement1) =>
% 132.32/22.90 ((
% 132.32/22.90 (binunionTE) =>
% 132.32/22.90 ((
% 132.32/22.90 (binunionTEcontra) =>
% 132.32/22.90 ((
% 132.32/22.90 (demorgan2a1) =>
% 132.32/22.90 ((
% 132.32/22.90 (complementUnionInPowersetComplement) =>
% 132.32/22.90 ((
% 132.32/22.90 (demorgan2a2) =>
% 132.32/22.90 ((
% 132.32/22.90 (demorgan1a) =>
% 132.32/22.90 ((
% 132.32/22.90 (demorgan1b) =>
% 132.32/22.90 ((
% 132.32/22.90 (demorgan1) =>
% 132.32/22.90 ((
% 132.32/22.90 (demorgan2a) =>
% 132.32/22.90 ((
% 132.32/22.90 (demorgan2b2) =>
% 132.32/22.90 ((
% 132.32/22.90 (demorgan2b) =>
% 132.32/22.90 ((
% 132.32/22.90 (demorgan2) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz13rule0) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz13rule1) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz13rule2) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz13rule3) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz13rule4) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz1_1) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz1_2) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz1_3) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz1_4) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz1_5) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1all2) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1SetBreln1) =>
% 132.32/22.90 ((
% 132.32/22.90 (choice2fnsingleton) =>
% 132.32/22.90 ((
% 132.32/22.90 (setOfPairsIsBReln1) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1all1) =>
% 132.32/22.90 ((
% 132.32/22.90 (subbreln1) =>
% 132.32/22.90 ((
% 132.32/22.90 (eqbreln1) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1invprop) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1invI) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1invE) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1compprop) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1compI) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1compE) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1compEex) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1unionprop) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1unionIL) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1unionIR) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1unionI) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1unionE) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1unionEcases) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1unionCommutes) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz2Ex) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz2W) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz2A) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz2B) =>
% 132.32/22.90 ((
% 132.32/22.90 (image1Ex) =>
% 132.32/22.90 ((
% 132.32/22.90 (image1Ex1) =>
% 132.32/22.90 ((
% 132.32/22.90 (image1Equiv) =>
% 132.32/22.90 ((
% 132.32/22.90 (image1E) =>
% 132.32/22.90 ((
% 132.32/22.90 (image1I) =>
% 132.32/22.90 ((
% 132.32/22.90 (injFuncInInjFuncSet) =>
% 132.32/22.90 ((
% 132.32/22.90 (injFuncSetFuncIn) =>
% 132.32/22.90 ((
% 132.32/22.90 (injFuncSetFuncInj) =>
% 132.32/22.90 ((
% 132.32/22.90 (surjFuncSetFuncIn) =>
% 132.32/22.90 ((
% 132.32/22.90 (surjFuncSetFuncSurj) =>
% 132.32/22.90 ((
% 132.32/22.90 (leftInvIsSurj) =>
% 132.32/22.90 ((
% 132.32/22.90 (surjCantorThm) =>
% 132.32/22.90 ((
% 132.32/22.90 (foundation2) =>
% 132.32/22.90 ((
% 132.32/22.90 (notinself) =>
% 132.32/22.90 ((
% 132.32/22.90 (notinself2) =>
% 132.32/22.90 ((
% 132.32/22.90 (omegaSp) =>
% 132.32/22.90 ((
% 132.32/22.90 (omegaSclos) =>
% 132.32/22.90 ((
% 132.32/22.90 (peano0notS) =>
% 132.32/22.90 ((
% 132.32/22.90 (peanoSinj) =>
% 132.32/22.90 ((
% 132.32/22.90 (transitivesetOp1) =>
% 132.32/22.90 ((
% 132.32/22.90 (binintTransitive) =>
% 132.32/22.90 ((
% 132.32/22.90 (transitivesetOp2) =>
% 132.32/22.90 ((
% 132.32/22.90 (setunionTransitive) =>
% 132.32/22.90 ((
% 132.32/22.90 (ordinalMinLem1) =>
% 132.32/22.90 ((
% 132.32/22.90 (ordinalTransSet) =>
% 132.32/22.90 ((
% 132.32/22.90 (ordinalTransSet1) =>
% 132.32/22.90 ((
% 132.32/22.90 (setunionOrdinalLem1) =>
% 132.32/22.90 (ordinal @
% 132.32/22.90 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.32/22.90 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl851])).
% 132.32/22.90 thf(zip_derived_cl864, plain,
% 132.32/22.90 (~ (((subsetemptysetimpeq) =>
% 132.32/22.90 (((powersetI1) =>
% 132.32/22.90 (((powersetE1) =>
% 132.32/22.90 (((inPowerset) =>
% 132.32/22.90 (((powersetsubset) =>
% 132.32/22.90 (((sepInPowerset) =>
% 132.32/22.90 (((sepSubset) =>
% 132.32/22.90 (((binunionIL) =>
% 132.32/22.90 (((upairset2IR) =>
% 132.32/22.90 (((binunionIR) =>
% 132.32/22.90 (((binunionEcases) =>
% 132.32/22.90 (((binunionE) =>
% 132.32/22.90 (((binunionLsub) =>
% 132.32/22.90 (((binunionRsub) =>
% 132.32/22.90 (((binintersectI) =>
% 132.32/22.90 (((binintersectSubset5) =>
% 132.32/22.90 (((binintersectEL) =>
% 132.32/22.90 (((binintersectLsub) =>
% 132.32/22.90 (((binintersectSubset2) =>
% 132.32/22.90 (((binintersectSubset3) =>
% 132.32/22.90 (((binintersectER) =>
% 132.32/22.90 (((disjointsetsI1) =>
% 132.32/22.90 (((binintersectRsub) =>
% 132.32/22.90 (((binintersectSubset4) =>
% 132.32/22.90 (((binintersectSubset1) =>
% 132.32/22.90 (((bs114d) =>
% 132.32/22.90 (((setminusI) =>
% 132.32/22.90 (((setminusEL) =>
% 132.32/22.90 (((setminusER) =>
% 132.32/22.90 (((setminusSubset2) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusERneg) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusELneg) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusILneg) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusIRneg) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusLsub) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusSubset1) =>
% 132.32/22.90 ((
% 132.32/22.90 (symdiffE) =>
% 132.32/22.90 ((
% 132.32/22.90 (symdiffI1) =>
% 132.32/22.90 ((
% 132.32/22.90 (symdiffI2) =>
% 132.32/22.90 ((
% 132.32/22.90 (symdiffIneg1) =>
% 132.32/22.90 ((
% 132.32/22.90 (symdiffIneg2) =>
% 132.32/22.90 ((
% 132.32/22.90 (secondinupair) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairIL) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairIR) =>
% 132.32/22.90 ((
% 132.32/22.90 (kpairiskpair) =>
% 132.32/22.90 ((
% 132.32/22.90 (kpairp) =>
% 132.32/22.90 ((
% 132.32/22.90 (singletonsubset) =>
% 132.32/22.90 ((
% 132.32/22.90 (singletoninpowerset) =>
% 132.32/22.90 ((
% 132.32/22.90 (singletoninpowunion) =>
% 132.32/22.90 ((
% 132.32/22.90 (upairset2E) =>
% 132.32/22.90 ((
% 132.32/22.90 (upairsubunion) =>
% 132.32/22.90 ((
% 132.32/22.90 (upairinpowunion) =>
% 132.32/22.90 ((
% 132.32/22.90 (ubforcartprodlem1) =>
% 132.32/22.90 ((
% 132.32/22.90 (ubforcartprodlem2) =>
% 132.32/22.90 ((
% 132.32/22.90 (ubforcartprodlem3) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodpairin) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodmempair1) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodmempair) =>
% 132.32/22.90 ((
% 132.32/22.90 (setunionE2) =>
% 132.32/22.90 ((
% 132.32/22.90 (setunionsingleton1) =>
% 132.32/22.90 ((
% 132.32/22.90 (setunionsingleton2) =>
% 132.32/22.90 ((
% 132.32/22.90 (setunionsingleton) =>
% 132.32/22.90 ((
% 132.32/22.90 (singletonprop) =>
% 132.32/22.90 ((
% 132.32/22.90 (ex1E1) =>
% 132.32/22.90 ((
% 132.32/22.90 (ex1I) =>
% 132.32/22.90 ((
% 132.32/22.90 (ex1I2) =>
% 132.32/22.90 ((
% 132.32/22.90 (singletonsuniq) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairinjL1) =>
% 132.32/22.90 ((
% 132.32/22.90 (kfstsingleton) =>
% 132.32/22.90 ((
% 132.32/22.90 (theprop) =>
% 132.32/22.90 ((
% 132.32/22.90 (kfstpairEq) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodfstin) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairinjL2) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairinjL) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairinjR11) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairinjR12) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairinjR1) =>
% 132.32/22.90 ((
% 132.32/22.90 (upairequniteq) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairinjR2) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairinjR) =>
% 132.32/22.90 ((
% 132.32/22.90 (ksndsingleton) =>
% 132.32/22.90 ((
% 132.32/22.90 (ksndpairEq) =>
% 132.32/22.90 ((
% 132.32/22.90 (kpairsurjEq) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodsndin) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodpairmemEL) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodpairmemER) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodmempaircEq) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodfstpairEq) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodsndpairEq) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodpairsurjEq) =>
% 132.32/22.90 ((
% 132.32/22.90 (dpsetconstrI) =>
% 132.32/22.90 ((
% 132.32/22.90 (dpsetconstrSub) =>
% 132.32/22.90 ((
% 132.32/22.90 (setOfPairsIsBReln) =>
% 132.32/22.90 ((
% 132.32/22.90 (dpsetconstrERa) =>
% 132.32/22.90 ((
% 132.32/22.90 (dpsetconstrEL1) =>
% 132.32/22.90 ((
% 132.32/22.90 (dpsetconstrEL2) =>
% 132.32/22.90 ((
% 132.32/22.90 (dpsetconstrER) =>
% 132.32/22.90 ((
% 132.32/22.90 (funcImageSingleton) =>
% 132.32/22.90 ((
% 132.32/22.90 (apProp) =>
% 132.32/22.90 ((
% 132.32/22.90 (app) =>
% 132.32/22.90 ((
% 132.32/22.90 (infuncsetfunc) =>
% 132.32/22.90 ((
% 132.32/22.90 (ap2p) =>
% 132.32/22.90 ((
% 132.32/22.90 (funcinfuncset) =>
% 132.32/22.90 ((
% 132.32/22.90 (lamProp) =>
% 132.32/22.90 ((
% 132.32/22.90 (lamp) =>
% 132.32/22.90 ((
% 132.32/22.90 (lam2p) =>
% 132.32/22.90 ((
% 132.32/22.90 (brelnall1) =>
% 132.32/22.90 ((
% 132.32/22.90 (brelnall2) =>
% 132.32/22.90 ((
% 132.32/22.90 (ex1E2) =>
% 132.32/22.90 ((
% 132.32/22.90 (funcGraphProp1) =>
% 132.32/22.90 ((
% 132.32/22.90 (funcGraphProp3) =>
% 132.32/22.90 ((
% 132.32/22.90 (funcGraphProp2) =>
% 132.32/22.90 ((
% 132.32/22.90 (funcextLem) =>
% 132.32/22.90 ((
% 132.32/22.90 (funcGraphProp4) =>
% 132.32/22.90 ((
% 132.32/22.90 (subbreln) =>
% 132.32/22.90 ((
% 132.32/22.90 (eqbreln) =>
% 132.32/22.90 ((
% 132.32/22.90 (funcext) =>
% 132.32/22.90 ((
% 132.32/22.90 (funcext2) =>
% 132.32/22.90 ((
% 132.32/22.90 (ap2apEq1) =>
% 132.32/22.90 ((
% 132.32/22.90 (ap2apEq2) =>
% 132.32/22.90 ((
% 132.32/22.90 (beta1) =>
% 132.32/22.90 ((
% 132.32/22.90 (eta1) =>
% 132.32/22.90 ((
% 132.32/22.90 (lam2lamEq) =>
% 132.32/22.90 ((
% 132.32/22.90 (beta2) =>
% 132.32/22.90 ((
% 132.32/22.90 (eta2) =>
% 132.32/22.90 ((
% 132.32/22.90 (iffalseProp1) =>
% 132.32/22.90 ((
% 132.32/22.90 (iffalseProp2) =>
% 132.32/22.90 ((
% 132.32/22.90 (iftrueProp1) =>
% 132.32/22.90 ((
% 132.32/22.90 (iftrueProp2) =>
% 132.32/22.90 ((
% 132.32/22.90 (ifSingleton) =>
% 132.32/22.90 ((
% 132.32/22.90 (ifp) =>
% 132.32/22.90 ((
% 132.32/22.90 (theeq) =>
% 132.32/22.90 ((
% 132.32/22.90 (iftrue) =>
% 132.32/22.90 ((
% 132.32/22.90 (iffalse) =>
% 132.32/22.90 ((
% 132.32/22.90 (iftrueorfalse) =>
% 132.32/22.90 ((
% 132.32/22.90 (binintersectT_lem) =>
% 132.32/22.90 ((
% 132.32/22.90 (binunionT_lem) =>
% 132.32/22.90 ((
% 132.32/22.90 (powersetT_lem) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusT_lem) =>
% 132.32/22.90 ((
% 132.32/22.90 (complementT_lem) =>
% 132.32/22.90 ((
% 132.32/22.90 (setextT) =>
% 132.32/22.90 ((
% 132.32/22.90 (subsetTI) =>
% 132.32/22.90 ((
% 132.32/22.90 (powersetTI1) =>
% 132.32/22.90 ((
% 132.32/22.90 (powersetTE1) =>
% 132.32/22.90 ((
% 132.32/22.90 (complementTI1) =>
% 132.32/22.90 ((
% 132.32/22.90 (complementTE1) =>
% 132.32/22.90 ((
% 132.32/22.90 (binintersectTELcontra) =>
% 132.32/22.90 ((
% 132.32/22.90 (binintersectTERcontra) =>
% 132.32/22.90 ((
% 132.32/22.90 (contrasubsetT) =>
% 132.32/22.90 ((
% 132.32/22.90 (contrasubsetT1) =>
% 132.32/22.90 ((
% 132.32/22.90 (contrasubsetT2) =>
% 132.32/22.90 ((
% 132.32/22.90 (contrasubsetT3) =>
% 132.32/22.90 ((
% 132.32/22.90 (doubleComplementI1) =>
% 132.32/22.90 ((
% 132.32/22.90 (doubleComplementE1) =>
% 132.32/22.90 ((
% 132.32/22.90 (doubleComplementSub1) =>
% 132.32/22.90 ((
% 132.32/22.90 (doubleComplementSub2) =>
% 132.32/22.90 ((
% 132.32/22.90 (doubleComplementEq) =>
% 132.32/22.90 ((
% 132.32/22.90 (complementTnotintersectT) =>
% 132.32/22.90 ((
% 132.32/22.90 (complementImpComplementIntersect) =>
% 132.32/22.90 ((
% 132.32/22.90 (complementSubsetComplementIntersect) =>
% 132.32/22.90 ((
% 132.32/22.90 (complementInPowersetComplementIntersect) =>
% 132.32/22.90 ((
% 132.32/22.90 (contraSubsetComplement) =>
% 132.32/22.90 ((
% 132.32/22.90 (complementTcontraSubset) =>
% 132.32/22.90 ((
% 132.32/22.90 (binunionTILcontra) =>
% 132.32/22.90 ((
% 132.32/22.90 (binunionTIRcontra) =>
% 132.32/22.90 ((
% 132.32/22.90 (inIntersectImpInUnion) =>
% 132.32/22.90 ((
% 132.32/22.90 (inIntersectImpInUnion2) =>
% 132.32/22.90 ((
% 132.32/22.90 (inIntersectImpInIntersectUnions) =>
% 132.32/22.90 ((
% 132.32/22.90 (intersectInPowersetIntersectUnions) =>
% 132.32/22.90 ((
% 132.32/22.90 (inComplementUnionImpNotIn1) =>
% 132.32/22.90 ((
% 132.32/22.90 (inComplementUnionImpInComplement1) =>
% 132.32/22.90 ((
% 132.32/22.90 (binunionTE) =>
% 132.32/22.90 ((
% 132.32/22.90 (binunionTEcontra) =>
% 132.32/22.90 ((
% 132.32/22.90 (demorgan2a1) =>
% 132.32/22.90 ((
% 132.32/22.90 (complementUnionInPowersetComplement) =>
% 132.32/22.90 ((
% 132.32/22.90 (demorgan2a2) =>
% 132.32/22.90 ((
% 132.32/22.90 (demorgan1a) =>
% 132.32/22.90 ((
% 132.32/22.90 (demorgan1b) =>
% 132.32/22.90 ((
% 132.32/22.90 (demorgan1) =>
% 132.32/22.90 ((
% 132.32/22.90 (demorgan2a) =>
% 132.32/22.90 ((
% 132.32/22.90 (demorgan2b2) =>
% 132.32/22.90 ((
% 132.32/22.90 (demorgan2b) =>
% 132.32/22.90 ((
% 132.32/22.90 (demorgan2) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz13rule0) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz13rule1) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz13rule2) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz13rule3) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz13rule4) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz1_1) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz1_2) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz1_3) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz1_4) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz1_5) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1all2) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1SetBreln1) =>
% 132.32/22.90 ((
% 132.32/22.90 (choice2fnsingleton) =>
% 132.32/22.90 ((
% 132.32/22.90 (setOfPairsIsBReln1) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1all1) =>
% 132.32/22.90 ((
% 132.32/22.90 (subbreln1) =>
% 132.32/22.90 ((
% 132.32/22.90 (eqbreln1) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1invprop) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1invI) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1invE) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1compprop) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1compI) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1compE) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1compEex) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1unionprop) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1unionIL) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1unionIR) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1unionI) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1unionE) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1unionEcases) =>
% 132.32/22.90 ((
% 132.32/22.90 (breln1unionCommutes) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz2Ex) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz2W) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz2A) =>
% 132.32/22.90 ((
% 132.32/22.90 (woz2B) =>
% 132.32/22.90 ((
% 132.32/22.90 (image1Ex) =>
% 132.32/22.90 ((
% 132.32/22.90 (image1Ex1) =>
% 132.32/22.90 ((
% 132.32/22.90 (image1Equiv) =>
% 132.32/22.90 ((
% 132.32/22.90 (image1E) =>
% 132.32/22.90 ((
% 132.32/22.90 (image1I) =>
% 132.32/22.90 ((
% 132.32/22.90 (injFuncInInjFuncSet) =>
% 132.32/22.90 ((
% 132.32/22.90 (injFuncSetFuncIn) =>
% 132.32/22.90 ((
% 132.32/22.90 (injFuncSetFuncInj) =>
% 132.32/22.90 ((
% 132.32/22.90 (surjFuncSetFuncIn) =>
% 132.32/22.90 ((
% 132.32/22.90 (surjFuncSetFuncSurj) =>
% 132.32/22.90 ((
% 132.32/22.90 (leftInvIsSurj) =>
% 132.32/22.90 ((
% 132.32/22.90 (surjCantorThm) =>
% 132.32/22.90 ((
% 132.32/22.90 (foundation2) =>
% 132.32/22.90 ((
% 132.32/22.90 (notinself) =>
% 132.32/22.90 ((
% 132.32/22.90 (notinself2) =>
% 132.32/22.90 ((
% 132.32/22.90 (omegaSp) =>
% 132.32/22.90 ((
% 132.32/22.90 (omegaSclos) =>
% 132.32/22.90 ((
% 132.32/22.90 (peano0notS) =>
% 132.32/22.90 ((
% 132.32/22.90 (peanoSinj) =>
% 132.32/22.90 ((
% 132.32/22.90 (transitivesetOp1) =>
% 132.32/22.90 ((
% 132.32/22.90 (binintTransitive) =>
% 132.32/22.90 ((
% 132.32/22.90 (transitivesetOp2) =>
% 132.32/22.90 ((
% 132.32/22.90 (setunionTransitive) =>
% 132.32/22.90 ((
% 132.32/22.90 (ordinalMinLem1) =>
% 132.32/22.90 ((
% 132.32/22.90 (ordinalTransSet) =>
% 132.32/22.90 ((
% 132.32/22.90 (ordinalTransSet1) =>
% 132.32/22.90 ((
% 132.32/22.90 (setunionOrdinalLem1) =>
% 132.32/22.90 (ordinal @
% 132.32/22.90 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.32/22.90 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl857])).
% 132.32/22.90 thf(zip_derived_cl872, plain,
% 132.32/22.90 (~ (((powersetI1) =>
% 132.32/22.90 (((powersetE1) =>
% 132.32/22.90 (((inPowerset) =>
% 132.32/22.90 (((powersetsubset) =>
% 132.32/22.90 (((sepInPowerset) =>
% 132.32/22.90 (((sepSubset) =>
% 132.32/22.90 (((binunionIL) =>
% 132.32/22.90 (((upairset2IR) =>
% 132.32/22.90 (((binunionIR) =>
% 132.32/22.90 (((binunionEcases) =>
% 132.32/22.90 (((binunionE) =>
% 132.32/22.90 (((binunionLsub) =>
% 132.32/22.90 (((binunionRsub) =>
% 132.32/22.90 (((binintersectI) =>
% 132.32/22.90 (((binintersectSubset5) =>
% 132.32/22.90 (((binintersectEL) =>
% 132.32/22.90 (((binintersectLsub) =>
% 132.32/22.90 (((binintersectSubset2) =>
% 132.32/22.90 (((binintersectSubset3) =>
% 132.32/22.90 (((binintersectER) =>
% 132.32/22.90 (((disjointsetsI1) =>
% 132.32/22.90 (((binintersectRsub) =>
% 132.32/22.90 (((binintersectSubset4) =>
% 132.32/22.90 (((binintersectSubset1) =>
% 132.32/22.90 (((bs114d) =>
% 132.32/22.90 (((setminusI) =>
% 132.32/22.90 (((setminusEL) =>
% 132.32/22.90 (((setminusER) =>
% 132.32/22.90 (((setminusSubset2) =>
% 132.32/22.90 (((setminusERneg) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusELneg) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusILneg) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusIRneg) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusLsub) =>
% 132.32/22.90 ((
% 132.32/22.90 (setminusSubset1) =>
% 132.32/22.90 ((
% 132.32/22.90 (symdiffE) =>
% 132.32/22.90 ((
% 132.32/22.90 (symdiffI1) =>
% 132.32/22.90 ((
% 132.32/22.90 (symdiffI2) =>
% 132.32/22.90 ((
% 132.32/22.90 (symdiffIneg1) =>
% 132.32/22.90 ((
% 132.32/22.90 (symdiffIneg2) =>
% 132.32/22.90 ((
% 132.32/22.90 (secondinupair) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairIL) =>
% 132.32/22.90 ((
% 132.32/22.90 (setukpairIR) =>
% 132.32/22.90 ((
% 132.32/22.90 (kpairiskpair) =>
% 132.32/22.90 ((
% 132.32/22.90 (kpairp) =>
% 132.32/22.90 ((
% 132.32/22.90 (singletonsubset) =>
% 132.32/22.90 ((
% 132.32/22.90 (singletoninpowerset) =>
% 132.32/22.90 ((
% 132.32/22.90 (singletoninpowunion) =>
% 132.32/22.90 ((
% 132.32/22.90 (upairset2E) =>
% 132.32/22.90 ((
% 132.32/22.90 (upairsubunion) =>
% 132.32/22.90 ((
% 132.32/22.90 (upairinpowunion) =>
% 132.32/22.90 ((
% 132.32/22.90 (ubforcartprodlem1) =>
% 132.32/22.90 ((
% 132.32/22.90 (ubforcartprodlem2) =>
% 132.32/22.90 ((
% 132.32/22.90 (ubforcartprodlem3) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodpairin) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodmempair1) =>
% 132.32/22.90 ((
% 132.32/22.90 (cartprodmempair) =>
% 132.32/22.90 ((
% 132.32/22.90 (setunionE2) =>
% 132.32/22.90 ((
% 132.32/22.90 (setunionsingleton1) =>
% 132.32/22.90 ((
% 132.32/22.90 (setunionsingleton2) =>
% 132.32/22.90 ((
% 132.32/22.90 (setunionsingleton) =>
% 132.32/22.90 ((
% 132.32/22.90 (singletonprop) =>
% 132.32/22.90 ((
% 132.32/22.90 (ex1E1) =>
% 132.32/22.90 ((
% 132.32/22.90 (ex1I) =>
% 132.32/22.90 ((
% 132.32/22.90 (ex1I2) =>
% 132.59/22.92 ((
% 132.59/22.92 (singletonsuniq) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjL1) =>
% 132.59/22.92 ((
% 132.59/22.92 (kfstsingleton) =>
% 132.59/22.92 ((
% 132.59/22.92 (theprop) =>
% 132.59/22.92 ((
% 132.59/22.92 (kfstpairEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodfstin) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjL2) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjL) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjR11) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjR12) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjR1) =>
% 132.59/22.92 ((
% 132.59/22.92 (upairequniteq) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjR2) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjR) =>
% 132.59/22.92 ((
% 132.59/22.92 (ksndsingleton) =>
% 132.59/22.92 ((
% 132.59/22.92 (ksndpairEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (kpairsurjEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodsndin) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodpairmemEL) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodpairmemER) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodmempaircEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodfstpairEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodsndpairEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodpairsurjEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (dpsetconstrI) =>
% 132.59/22.92 ((
% 132.59/22.92 (dpsetconstrSub) =>
% 132.59/22.92 ((
% 132.59/22.92 (setOfPairsIsBReln) =>
% 132.59/22.92 ((
% 132.59/22.92 (dpsetconstrERa) =>
% 132.59/22.92 ((
% 132.59/22.92 (dpsetconstrEL1) =>
% 132.59/22.92 ((
% 132.59/22.92 (dpsetconstrEL2) =>
% 132.59/22.92 ((
% 132.59/22.92 (dpsetconstrER) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcImageSingleton) =>
% 132.59/22.92 ((
% 132.59/22.92 (apProp) =>
% 132.59/22.92 ((
% 132.59/22.92 (app) =>
% 132.59/22.92 ((
% 132.59/22.92 (infuncsetfunc) =>
% 132.59/22.92 ((
% 132.59/22.92 (ap2p) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcinfuncset) =>
% 132.59/22.92 ((
% 132.59/22.92 (lamProp) =>
% 132.59/22.92 ((
% 132.59/22.92 (lamp) =>
% 132.59/22.92 ((
% 132.59/22.92 (lam2p) =>
% 132.59/22.92 ((
% 132.59/22.92 (brelnall1) =>
% 132.59/22.92 ((
% 132.59/22.92 (brelnall2) =>
% 132.59/22.92 ((
% 132.59/22.92 (ex1E2) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcGraphProp1) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcGraphProp3) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcGraphProp2) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcextLem) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcGraphProp4) =>
% 132.59/22.92 ((
% 132.59/22.92 (subbreln) =>
% 132.59/22.92 ((
% 132.59/22.92 (eqbreln) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcext) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcext2) =>
% 132.59/22.92 ((
% 132.59/22.92 (ap2apEq1) =>
% 132.59/22.92 ((
% 132.59/22.92 (ap2apEq2) =>
% 132.59/22.92 ((
% 132.59/22.92 (beta1) =>
% 132.59/22.92 ((
% 132.59/22.92 (eta1) =>
% 132.59/22.92 ((
% 132.59/22.92 (lam2lamEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (beta2) =>
% 132.59/22.92 ((
% 132.59/22.92 (eta2) =>
% 132.59/22.92 ((
% 132.59/22.92 (iffalseProp1) =>
% 132.59/22.92 ((
% 132.59/22.92 (iffalseProp2) =>
% 132.59/22.92 ((
% 132.59/22.92 (iftrueProp1) =>
% 132.59/22.92 ((
% 132.59/22.92 (iftrueProp2) =>
% 132.59/22.92 ((
% 132.59/22.92 (ifSingleton) =>
% 132.59/22.92 ((
% 132.59/22.92 (ifp) =>
% 132.59/22.92 ((
% 132.59/22.92 (theeq) =>
% 132.59/22.92 ((
% 132.59/22.92 (iftrue) =>
% 132.59/22.92 ((
% 132.59/22.92 (iffalse) =>
% 132.59/22.92 ((
% 132.59/22.92 (iftrueorfalse) =>
% 132.59/22.92 ((
% 132.59/22.92 (binintersectT_lem) =>
% 132.59/22.92 ((
% 132.59/22.92 (binunionT_lem) =>
% 132.59/22.92 ((
% 132.59/22.92 (powersetT_lem) =>
% 132.59/22.92 ((
% 132.59/22.92 (setminusT_lem) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementT_lem) =>
% 132.59/22.92 ((
% 132.59/22.92 (setextT) =>
% 132.59/22.92 ((
% 132.59/22.92 (subsetTI) =>
% 132.59/22.92 ((
% 132.59/22.92 (powersetTI1) =>
% 132.59/22.92 ((
% 132.59/22.92 (powersetTE1) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementTI1) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementTE1) =>
% 132.59/22.92 ((
% 132.59/22.92 (binintersectTELcontra) =>
% 132.59/22.92 ((
% 132.59/22.92 (binintersectTERcontra) =>
% 132.59/22.92 ((
% 132.59/22.92 (contrasubsetT) =>
% 132.59/22.92 ((
% 132.59/22.92 (contrasubsetT1) =>
% 132.59/22.92 ((
% 132.59/22.92 (contrasubsetT2) =>
% 132.59/22.92 ((
% 132.59/22.92 (contrasubsetT3) =>
% 132.59/22.92 ((
% 132.59/22.92 (doubleComplementI1) =>
% 132.59/22.92 ((
% 132.59/22.92 (doubleComplementE1) =>
% 132.59/22.92 ((
% 132.59/22.92 (doubleComplementSub1) =>
% 132.59/22.92 ((
% 132.59/22.92 (doubleComplementSub2) =>
% 132.59/22.92 ((
% 132.59/22.92 (doubleComplementEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementTnotintersectT) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementImpComplementIntersect) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementSubsetComplementIntersect) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementInPowersetComplementIntersect) =>
% 132.59/22.92 ((
% 132.59/22.92 (contraSubsetComplement) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementTcontraSubset) =>
% 132.59/22.92 ((
% 132.59/22.92 (binunionTILcontra) =>
% 132.59/22.92 ((
% 132.59/22.92 (binunionTIRcontra) =>
% 132.59/22.92 ((
% 132.59/22.92 (inIntersectImpInUnion) =>
% 132.59/22.92 ((
% 132.59/22.92 (inIntersectImpInUnion2) =>
% 132.59/22.92 ((
% 132.59/22.92 (inIntersectImpInIntersectUnions) =>
% 132.59/22.92 ((
% 132.59/22.92 (intersectInPowersetIntersectUnions) =>
% 132.59/22.92 ((
% 132.59/22.92 (inComplementUnionImpNotIn1) =>
% 132.59/22.92 ((
% 132.59/22.92 (inComplementUnionImpInComplement1) =>
% 132.59/22.92 ((
% 132.59/22.92 (binunionTE) =>
% 132.59/22.92 ((
% 132.59/22.92 (binunionTEcontra) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan2a1) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementUnionInPowersetComplement) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan2a2) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan1a) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan1b) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan1) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan2a) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan2b2) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan2b) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan2) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz13rule0) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz13rule1) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz13rule2) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz13rule3) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz13rule4) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz1_1) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz1_2) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz1_3) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz1_4) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz1_5) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1all2) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1SetBreln1) =>
% 132.59/22.92 ((
% 132.59/22.92 (choice2fnsingleton) =>
% 132.59/22.92 ((
% 132.59/22.92 (setOfPairsIsBReln1) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1all1) =>
% 132.59/22.92 ((
% 132.59/22.92 (subbreln1) =>
% 132.59/22.92 ((
% 132.59/22.92 (eqbreln1) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1invprop) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1invI) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1invE) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1compprop) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1compI) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1compE) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1compEex) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1unionprop) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1unionIL) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1unionIR) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1unionI) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1unionE) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1unionEcases) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1unionCommutes) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz2Ex) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz2W) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz2A) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz2B) =>
% 132.59/22.92 ((
% 132.59/22.92 (image1Ex) =>
% 132.59/22.92 ((
% 132.59/22.92 (image1Ex1) =>
% 132.59/22.92 ((
% 132.59/22.92 (image1Equiv) =>
% 132.59/22.92 ((
% 132.59/22.92 (image1E) =>
% 132.59/22.92 ((
% 132.59/22.92 (image1I) =>
% 132.59/22.92 ((
% 132.59/22.92 (injFuncInInjFuncSet) =>
% 132.59/22.92 ((
% 132.59/22.92 (injFuncSetFuncIn) =>
% 132.59/22.92 ((
% 132.59/22.92 (injFuncSetFuncInj) =>
% 132.59/22.92 ((
% 132.59/22.92 (surjFuncSetFuncIn) =>
% 132.59/22.92 ((
% 132.59/22.92 (surjFuncSetFuncSurj) =>
% 132.59/22.92 ((
% 132.59/22.92 (leftInvIsSurj) =>
% 132.59/22.92 ((
% 132.59/22.92 (surjCantorThm) =>
% 132.59/22.92 ((
% 132.59/22.92 (foundation2) =>
% 132.59/22.92 ((
% 132.59/22.92 (notinself) =>
% 132.59/22.92 ((
% 132.59/22.92 (notinself2) =>
% 132.59/22.92 ((
% 132.59/22.92 (omegaSp) =>
% 132.59/22.92 ((
% 132.59/22.92 (omegaSclos) =>
% 132.59/22.92 ((
% 132.59/22.92 (peano0notS) =>
% 132.59/22.92 ((
% 132.59/22.92 (peanoSinj) =>
% 132.59/22.92 ((
% 132.59/22.92 (transitivesetOp1) =>
% 132.59/22.92 ((
% 132.59/22.92 (binintTransitive) =>
% 132.59/22.92 ((
% 132.59/22.92 (transitivesetOp2) =>
% 132.59/22.92 ((
% 132.59/22.92 (setunionTransitive) =>
% 132.59/22.92 ((
% 132.59/22.92 (ordinalMinLem1) =>
% 132.59/22.92 ((
% 132.59/22.92 (ordinalTransSet) =>
% 132.59/22.92 ((
% 132.59/22.92 (ordinalTransSet1) =>
% 132.59/22.92 ((
% 132.59/22.92 (setunionOrdinalLem1) =>
% 132.59/22.92 (ordinal @
% 132.59/22.92 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.59/22.92 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl864])).
% 132.59/22.92 thf(zip_derived_cl879, plain,
% 132.59/22.92 (~ (((powersetE1) =>
% 132.59/22.92 (((inPowerset) =>
% 132.59/22.92 (((powersetsubset) =>
% 132.59/22.92 (((sepInPowerset) =>
% 132.59/22.92 (((sepSubset) =>
% 132.59/22.92 (((binunionIL) =>
% 132.59/22.92 (((upairset2IR) =>
% 132.59/22.92 (((binunionIR) =>
% 132.59/22.92 (((binunionEcases) =>
% 132.59/22.92 (((binunionE) =>
% 132.59/22.92 (((binunionLsub) =>
% 132.59/22.92 (((binunionRsub) =>
% 132.59/22.92 (((binintersectI) =>
% 132.59/22.92 (((binintersectSubset5) =>
% 132.59/22.92 (((binintersectEL) =>
% 132.59/22.92 (((binintersectLsub) =>
% 132.59/22.92 (((binintersectSubset2) =>
% 132.59/22.92 (((binintersectSubset3) =>
% 132.59/22.92 (((binintersectER) =>
% 132.59/22.92 (((disjointsetsI1) =>
% 132.59/22.92 (((binintersectRsub) =>
% 132.59/22.92 (((binintersectSubset4) =>
% 132.59/22.92 (((binintersectSubset1) =>
% 132.59/22.92 (((bs114d) =>
% 132.59/22.92 (((setminusI) =>
% 132.59/22.92 (((setminusEL) =>
% 132.59/22.92 (((setminusER) =>
% 132.59/22.92 (((setminusSubset2) =>
% 132.59/22.92 (((setminusERneg) =>
% 132.59/22.92 (((setminusELneg) =>
% 132.59/22.92 ((
% 132.59/22.92 (setminusILneg) =>
% 132.59/22.92 ((
% 132.59/22.92 (setminusIRneg) =>
% 132.59/22.92 ((
% 132.59/22.92 (setminusLsub) =>
% 132.59/22.92 ((
% 132.59/22.92 (setminusSubset1) =>
% 132.59/22.92 ((
% 132.59/22.92 (symdiffE) =>
% 132.59/22.92 ((
% 132.59/22.92 (symdiffI1) =>
% 132.59/22.92 ((
% 132.59/22.92 (symdiffI2) =>
% 132.59/22.92 ((
% 132.59/22.92 (symdiffIneg1) =>
% 132.59/22.92 ((
% 132.59/22.92 (symdiffIneg2) =>
% 132.59/22.92 ((
% 132.59/22.92 (secondinupair) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairIL) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairIR) =>
% 132.59/22.92 ((
% 132.59/22.92 (kpairiskpair) =>
% 132.59/22.92 ((
% 132.59/22.92 (kpairp) =>
% 132.59/22.92 ((
% 132.59/22.92 (singletonsubset) =>
% 132.59/22.92 ((
% 132.59/22.92 (singletoninpowerset) =>
% 132.59/22.92 ((
% 132.59/22.92 (singletoninpowunion) =>
% 132.59/22.92 ((
% 132.59/22.92 (upairset2E) =>
% 132.59/22.92 ((
% 132.59/22.92 (upairsubunion) =>
% 132.59/22.92 ((
% 132.59/22.92 (upairinpowunion) =>
% 132.59/22.92 ((
% 132.59/22.92 (ubforcartprodlem1) =>
% 132.59/22.92 ((
% 132.59/22.92 (ubforcartprodlem2) =>
% 132.59/22.92 ((
% 132.59/22.92 (ubforcartprodlem3) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodpairin) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodmempair1) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodmempair) =>
% 132.59/22.92 ((
% 132.59/22.92 (setunionE2) =>
% 132.59/22.92 ((
% 132.59/22.92 (setunionsingleton1) =>
% 132.59/22.92 ((
% 132.59/22.92 (setunionsingleton2) =>
% 132.59/22.92 ((
% 132.59/22.92 (setunionsingleton) =>
% 132.59/22.92 ((
% 132.59/22.92 (singletonprop) =>
% 132.59/22.92 ((
% 132.59/22.92 (ex1E1) =>
% 132.59/22.92 ((
% 132.59/22.92 (ex1I) =>
% 132.59/22.92 ((
% 132.59/22.92 (ex1I2) =>
% 132.59/22.92 ((
% 132.59/22.92 (singletonsuniq) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjL1) =>
% 132.59/22.92 ((
% 132.59/22.92 (kfstsingleton) =>
% 132.59/22.92 ((
% 132.59/22.92 (theprop) =>
% 132.59/22.92 ((
% 132.59/22.92 (kfstpairEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodfstin) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjL2) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjL) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjR11) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjR12) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjR1) =>
% 132.59/22.92 ((
% 132.59/22.92 (upairequniteq) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjR2) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjR) =>
% 132.59/22.92 ((
% 132.59/22.92 (ksndsingleton) =>
% 132.59/22.92 ((
% 132.59/22.92 (ksndpairEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (kpairsurjEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodsndin) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodpairmemEL) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodpairmemER) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodmempaircEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodfstpairEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodsndpairEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodpairsurjEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (dpsetconstrI) =>
% 132.59/22.92 ((
% 132.59/22.92 (dpsetconstrSub) =>
% 132.59/22.92 ((
% 132.59/22.92 (setOfPairsIsBReln) =>
% 132.59/22.92 ((
% 132.59/22.92 (dpsetconstrERa) =>
% 132.59/22.92 ((
% 132.59/22.92 (dpsetconstrEL1) =>
% 132.59/22.92 ((
% 132.59/22.92 (dpsetconstrEL2) =>
% 132.59/22.92 ((
% 132.59/22.92 (dpsetconstrER) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcImageSingleton) =>
% 132.59/22.92 ((
% 132.59/22.92 (apProp) =>
% 132.59/22.92 ((
% 132.59/22.92 (app) =>
% 132.59/22.92 ((
% 132.59/22.92 (infuncsetfunc) =>
% 132.59/22.92 ((
% 132.59/22.92 (ap2p) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcinfuncset) =>
% 132.59/22.92 ((
% 132.59/22.92 (lamProp) =>
% 132.59/22.92 ((
% 132.59/22.92 (lamp) =>
% 132.59/22.92 ((
% 132.59/22.92 (lam2p) =>
% 132.59/22.92 ((
% 132.59/22.92 (brelnall1) =>
% 132.59/22.92 ((
% 132.59/22.92 (brelnall2) =>
% 132.59/22.92 ((
% 132.59/22.92 (ex1E2) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcGraphProp1) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcGraphProp3) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcGraphProp2) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcextLem) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcGraphProp4) =>
% 132.59/22.92 ((
% 132.59/22.92 (subbreln) =>
% 132.59/22.92 ((
% 132.59/22.92 (eqbreln) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcext) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcext2) =>
% 132.59/22.92 ((
% 132.59/22.92 (ap2apEq1) =>
% 132.59/22.92 ((
% 132.59/22.92 (ap2apEq2) =>
% 132.59/22.92 ((
% 132.59/22.92 (beta1) =>
% 132.59/22.92 ((
% 132.59/22.92 (eta1) =>
% 132.59/22.92 ((
% 132.59/22.92 (lam2lamEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (beta2) =>
% 132.59/22.92 ((
% 132.59/22.92 (eta2) =>
% 132.59/22.92 ((
% 132.59/22.92 (iffalseProp1) =>
% 132.59/22.92 ((
% 132.59/22.92 (iffalseProp2) =>
% 132.59/22.92 ((
% 132.59/22.92 (iftrueProp1) =>
% 132.59/22.92 ((
% 132.59/22.92 (iftrueProp2) =>
% 132.59/22.92 ((
% 132.59/22.92 (ifSingleton) =>
% 132.59/22.92 ((
% 132.59/22.92 (ifp) =>
% 132.59/22.92 ((
% 132.59/22.92 (theeq) =>
% 132.59/22.92 ((
% 132.59/22.92 (iftrue) =>
% 132.59/22.92 ((
% 132.59/22.92 (iffalse) =>
% 132.59/22.92 ((
% 132.59/22.92 (iftrueorfalse) =>
% 132.59/22.92 ((
% 132.59/22.92 (binintersectT_lem) =>
% 132.59/22.92 ((
% 132.59/22.92 (binunionT_lem) =>
% 132.59/22.92 ((
% 132.59/22.92 (powersetT_lem) =>
% 132.59/22.92 ((
% 132.59/22.92 (setminusT_lem) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementT_lem) =>
% 132.59/22.92 ((
% 132.59/22.92 (setextT) =>
% 132.59/22.92 ((
% 132.59/22.92 (subsetTI) =>
% 132.59/22.92 ((
% 132.59/22.92 (powersetTI1) =>
% 132.59/22.92 ((
% 132.59/22.92 (powersetTE1) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementTI1) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementTE1) =>
% 132.59/22.92 ((
% 132.59/22.92 (binintersectTELcontra) =>
% 132.59/22.92 ((
% 132.59/22.92 (binintersectTERcontra) =>
% 132.59/22.92 ((
% 132.59/22.92 (contrasubsetT) =>
% 132.59/22.92 ((
% 132.59/22.92 (contrasubsetT1) =>
% 132.59/22.92 ((
% 132.59/22.92 (contrasubsetT2) =>
% 132.59/22.92 ((
% 132.59/22.92 (contrasubsetT3) =>
% 132.59/22.92 ((
% 132.59/22.92 (doubleComplementI1) =>
% 132.59/22.92 ((
% 132.59/22.92 (doubleComplementE1) =>
% 132.59/22.92 ((
% 132.59/22.92 (doubleComplementSub1) =>
% 132.59/22.92 ((
% 132.59/22.92 (doubleComplementSub2) =>
% 132.59/22.92 ((
% 132.59/22.92 (doubleComplementEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementTnotintersectT) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementImpComplementIntersect) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementSubsetComplementIntersect) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementInPowersetComplementIntersect) =>
% 132.59/22.92 ((
% 132.59/22.92 (contraSubsetComplement) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementTcontraSubset) =>
% 132.59/22.92 ((
% 132.59/22.92 (binunionTILcontra) =>
% 132.59/22.92 ((
% 132.59/22.92 (binunionTIRcontra) =>
% 132.59/22.92 ((
% 132.59/22.92 (inIntersectImpInUnion) =>
% 132.59/22.92 ((
% 132.59/22.92 (inIntersectImpInUnion2) =>
% 132.59/22.92 ((
% 132.59/22.92 (inIntersectImpInIntersectUnions) =>
% 132.59/22.92 ((
% 132.59/22.92 (intersectInPowersetIntersectUnions) =>
% 132.59/22.92 ((
% 132.59/22.92 (inComplementUnionImpNotIn1) =>
% 132.59/22.92 ((
% 132.59/22.92 (inComplementUnionImpInComplement1) =>
% 132.59/22.92 ((
% 132.59/22.92 (binunionTE) =>
% 132.59/22.92 ((
% 132.59/22.92 (binunionTEcontra) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan2a1) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementUnionInPowersetComplement) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan2a2) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan1a) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan1b) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan1) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan2a) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan2b2) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan2b) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan2) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz13rule0) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz13rule1) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz13rule2) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz13rule3) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz13rule4) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz1_1) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz1_2) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz1_3) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz1_4) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz1_5) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1all2) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1SetBreln1) =>
% 132.59/22.92 ((
% 132.59/22.92 (choice2fnsingleton) =>
% 132.59/22.92 ((
% 132.59/22.92 (setOfPairsIsBReln1) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1all1) =>
% 132.59/22.92 ((
% 132.59/22.92 (subbreln1) =>
% 132.59/22.92 ((
% 132.59/22.92 (eqbreln1) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1invprop) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1invI) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1invE) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1compprop) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1compI) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1compE) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1compEex) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1unionprop) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1unionIL) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1unionIR) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1unionI) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1unionE) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1unionEcases) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1unionCommutes) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz2Ex) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz2W) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz2A) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz2B) =>
% 132.59/22.92 ((
% 132.59/22.92 (image1Ex) =>
% 132.59/22.92 ((
% 132.59/22.92 (image1Ex1) =>
% 132.59/22.92 ((
% 132.59/22.92 (image1Equiv) =>
% 132.59/22.92 ((
% 132.59/22.92 (image1E) =>
% 132.59/22.92 ((
% 132.59/22.92 (image1I) =>
% 132.59/22.92 ((
% 132.59/22.92 (injFuncInInjFuncSet) =>
% 132.59/22.92 ((
% 132.59/22.92 (injFuncSetFuncIn) =>
% 132.59/22.92 ((
% 132.59/22.92 (injFuncSetFuncInj) =>
% 132.59/22.92 ((
% 132.59/22.92 (surjFuncSetFuncIn) =>
% 132.59/22.92 ((
% 132.59/22.92 (surjFuncSetFuncSurj) =>
% 132.59/22.92 ((
% 132.59/22.92 (leftInvIsSurj) =>
% 132.59/22.92 ((
% 132.59/22.92 (surjCantorThm) =>
% 132.59/22.92 ((
% 132.59/22.92 (foundation2) =>
% 132.59/22.92 ((
% 132.59/22.92 (notinself) =>
% 132.59/22.92 ((
% 132.59/22.92 (notinself2) =>
% 132.59/22.92 ((
% 132.59/22.92 (omegaSp) =>
% 132.59/22.92 ((
% 132.59/22.92 (omegaSclos) =>
% 132.59/22.92 ((
% 132.59/22.92 (peano0notS) =>
% 132.59/22.92 ((
% 132.59/22.92 (peanoSinj) =>
% 132.59/22.92 ((
% 132.59/22.92 (transitivesetOp1) =>
% 132.59/22.92 ((
% 132.59/22.92 (binintTransitive) =>
% 132.59/22.92 ((
% 132.59/22.92 (transitivesetOp2) =>
% 132.59/22.92 ((
% 132.59/22.92 (setunionTransitive) =>
% 132.59/22.92 ((
% 132.59/22.92 (ordinalMinLem1) =>
% 132.59/22.92 ((
% 132.59/22.92 (ordinalTransSet) =>
% 132.59/22.92 ((
% 132.59/22.92 (ordinalTransSet1) =>
% 132.59/22.92 ((
% 132.59/22.92 (setunionOrdinalLem1) =>
% 132.59/22.92 (ordinal @
% 132.59/22.92 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.59/22.92 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl872])).
% 132.59/22.92 thf(zip_derived_cl886, plain,
% 132.59/22.92 (~ (((inPowerset) =>
% 132.59/22.92 (((powersetsubset) =>
% 132.59/22.92 (((sepInPowerset) =>
% 132.59/22.92 (((sepSubset) =>
% 132.59/22.92 (((binunionIL) =>
% 132.59/22.92 (((upairset2IR) =>
% 132.59/22.92 (((binunionIR) =>
% 132.59/22.92 (((binunionEcases) =>
% 132.59/22.92 (((binunionE) =>
% 132.59/22.92 (((binunionLsub) =>
% 132.59/22.92 (((binunionRsub) =>
% 132.59/22.92 (((binintersectI) =>
% 132.59/22.92 (((binintersectSubset5) =>
% 132.59/22.92 (((binintersectEL) =>
% 132.59/22.92 (((binintersectLsub) =>
% 132.59/22.92 (((binintersectSubset2) =>
% 132.59/22.92 (((binintersectSubset3) =>
% 132.59/22.92 (((binintersectER) =>
% 132.59/22.92 (((disjointsetsI1) =>
% 132.59/22.92 (((binintersectRsub) =>
% 132.59/22.92 (((binintersectSubset4) =>
% 132.59/22.92 (((binintersectSubset1) =>
% 132.59/22.92 (((bs114d) =>
% 132.59/22.92 (((setminusI) =>
% 132.59/22.92 (((setminusEL) =>
% 132.59/22.92 (((setminusER) =>
% 132.59/22.92 (((setminusSubset2) =>
% 132.59/22.92 (((setminusERneg) =>
% 132.59/22.92 (((setminusELneg) =>
% 132.59/22.92 (((setminusILneg) =>
% 132.59/22.92 ((
% 132.59/22.92 (setminusIRneg) =>
% 132.59/22.92 ((
% 132.59/22.92 (setminusLsub) =>
% 132.59/22.92 ((
% 132.59/22.92 (setminusSubset1) =>
% 132.59/22.92 ((
% 132.59/22.92 (symdiffE) =>
% 132.59/22.92 ((
% 132.59/22.92 (symdiffI1) =>
% 132.59/22.92 ((
% 132.59/22.92 (symdiffI2) =>
% 132.59/22.92 ((
% 132.59/22.92 (symdiffIneg1) =>
% 132.59/22.92 ((
% 132.59/22.92 (symdiffIneg2) =>
% 132.59/22.92 ((
% 132.59/22.92 (secondinupair) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairIL) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairIR) =>
% 132.59/22.92 ((
% 132.59/22.92 (kpairiskpair) =>
% 132.59/22.92 ((
% 132.59/22.92 (kpairp) =>
% 132.59/22.92 ((
% 132.59/22.92 (singletonsubset) =>
% 132.59/22.92 ((
% 132.59/22.92 (singletoninpowerset) =>
% 132.59/22.92 ((
% 132.59/22.92 (singletoninpowunion) =>
% 132.59/22.92 ((
% 132.59/22.92 (upairset2E) =>
% 132.59/22.92 ((
% 132.59/22.92 (upairsubunion) =>
% 132.59/22.92 ((
% 132.59/22.92 (upairinpowunion) =>
% 132.59/22.92 ((
% 132.59/22.92 (ubforcartprodlem1) =>
% 132.59/22.92 ((
% 132.59/22.92 (ubforcartprodlem2) =>
% 132.59/22.92 ((
% 132.59/22.92 (ubforcartprodlem3) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodpairin) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodmempair1) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodmempair) =>
% 132.59/22.92 ((
% 132.59/22.92 (setunionE2) =>
% 132.59/22.92 ((
% 132.59/22.92 (setunionsingleton1) =>
% 132.59/22.92 ((
% 132.59/22.92 (setunionsingleton2) =>
% 132.59/22.92 ((
% 132.59/22.92 (setunionsingleton) =>
% 132.59/22.92 ((
% 132.59/22.92 (singletonprop) =>
% 132.59/22.92 ((
% 132.59/22.92 (ex1E1) =>
% 132.59/22.92 ((
% 132.59/22.92 (ex1I) =>
% 132.59/22.92 ((
% 132.59/22.92 (ex1I2) =>
% 132.59/22.92 ((
% 132.59/22.92 (singletonsuniq) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjL1) =>
% 132.59/22.92 ((
% 132.59/22.92 (kfstsingleton) =>
% 132.59/22.92 ((
% 132.59/22.92 (theprop) =>
% 132.59/22.92 ((
% 132.59/22.92 (kfstpairEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodfstin) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjL2) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjL) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjR11) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjR12) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjR1) =>
% 132.59/22.92 ((
% 132.59/22.92 (upairequniteq) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjR2) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjR) =>
% 132.59/22.92 ((
% 132.59/22.92 (ksndsingleton) =>
% 132.59/22.92 ((
% 132.59/22.92 (ksndpairEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (kpairsurjEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodsndin) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodpairmemEL) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodpairmemER) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodmempaircEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodfstpairEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodsndpairEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodpairsurjEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (dpsetconstrI) =>
% 132.59/22.92 ((
% 132.59/22.92 (dpsetconstrSub) =>
% 132.59/22.92 ((
% 132.59/22.92 (setOfPairsIsBReln) =>
% 132.59/22.92 ((
% 132.59/22.92 (dpsetconstrERa) =>
% 132.59/22.92 ((
% 132.59/22.92 (dpsetconstrEL1) =>
% 132.59/22.92 ((
% 132.59/22.92 (dpsetconstrEL2) =>
% 132.59/22.92 ((
% 132.59/22.92 (dpsetconstrER) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcImageSingleton) =>
% 132.59/22.92 ((
% 132.59/22.92 (apProp) =>
% 132.59/22.92 ((
% 132.59/22.92 (app) =>
% 132.59/22.92 ((
% 132.59/22.92 (infuncsetfunc) =>
% 132.59/22.92 ((
% 132.59/22.92 (ap2p) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcinfuncset) =>
% 132.59/22.92 ((
% 132.59/22.92 (lamProp) =>
% 132.59/22.92 ((
% 132.59/22.92 (lamp) =>
% 132.59/22.92 ((
% 132.59/22.92 (lam2p) =>
% 132.59/22.92 ((
% 132.59/22.92 (brelnall1) =>
% 132.59/22.92 ((
% 132.59/22.92 (brelnall2) =>
% 132.59/22.92 ((
% 132.59/22.92 (ex1E2) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcGraphProp1) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcGraphProp3) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcGraphProp2) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcextLem) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcGraphProp4) =>
% 132.59/22.92 ((
% 132.59/22.92 (subbreln) =>
% 132.59/22.92 ((
% 132.59/22.92 (eqbreln) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcext) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcext2) =>
% 132.59/22.92 ((
% 132.59/22.92 (ap2apEq1) =>
% 132.59/22.92 ((
% 132.59/22.92 (ap2apEq2) =>
% 132.59/22.92 ((
% 132.59/22.92 (beta1) =>
% 132.59/22.92 ((
% 132.59/22.92 (eta1) =>
% 132.59/22.92 ((
% 132.59/22.92 (lam2lamEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (beta2) =>
% 132.59/22.92 ((
% 132.59/22.92 (eta2) =>
% 132.59/22.92 ((
% 132.59/22.92 (iffalseProp1) =>
% 132.59/22.92 ((
% 132.59/22.92 (iffalseProp2) =>
% 132.59/22.92 ((
% 132.59/22.92 (iftrueProp1) =>
% 132.59/22.92 ((
% 132.59/22.92 (iftrueProp2) =>
% 132.59/22.92 ((
% 132.59/22.92 (ifSingleton) =>
% 132.59/22.92 ((
% 132.59/22.92 (ifp) =>
% 132.59/22.92 ((
% 132.59/22.92 (theeq) =>
% 132.59/22.92 ((
% 132.59/22.92 (iftrue) =>
% 132.59/22.92 ((
% 132.59/22.92 (iffalse) =>
% 132.59/22.92 ((
% 132.59/22.92 (iftrueorfalse) =>
% 132.59/22.92 ((
% 132.59/22.92 (binintersectT_lem) =>
% 132.59/22.92 ((
% 132.59/22.92 (binunionT_lem) =>
% 132.59/22.92 ((
% 132.59/22.92 (powersetT_lem) =>
% 132.59/22.92 ((
% 132.59/22.92 (setminusT_lem) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementT_lem) =>
% 132.59/22.92 ((
% 132.59/22.92 (setextT) =>
% 132.59/22.92 ((
% 132.59/22.92 (subsetTI) =>
% 132.59/22.92 ((
% 132.59/22.92 (powersetTI1) =>
% 132.59/22.92 ((
% 132.59/22.92 (powersetTE1) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementTI1) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementTE1) =>
% 132.59/22.92 ((
% 132.59/22.92 (binintersectTELcontra) =>
% 132.59/22.92 ((
% 132.59/22.92 (binintersectTERcontra) =>
% 132.59/22.92 ((
% 132.59/22.92 (contrasubsetT) =>
% 132.59/22.92 ((
% 132.59/22.92 (contrasubsetT1) =>
% 132.59/22.92 ((
% 132.59/22.92 (contrasubsetT2) =>
% 132.59/22.92 ((
% 132.59/22.92 (contrasubsetT3) =>
% 132.59/22.92 ((
% 132.59/22.92 (doubleComplementI1) =>
% 132.59/22.92 ((
% 132.59/22.92 (doubleComplementE1) =>
% 132.59/22.92 ((
% 132.59/22.92 (doubleComplementSub1) =>
% 132.59/22.92 ((
% 132.59/22.92 (doubleComplementSub2) =>
% 132.59/22.92 ((
% 132.59/22.92 (doubleComplementEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementTnotintersectT) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementImpComplementIntersect) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementSubsetComplementIntersect) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementInPowersetComplementIntersect) =>
% 132.59/22.92 ((
% 132.59/22.92 (contraSubsetComplement) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementTcontraSubset) =>
% 132.59/22.92 ((
% 132.59/22.92 (binunionTILcontra) =>
% 132.59/22.92 ((
% 132.59/22.92 (binunionTIRcontra) =>
% 132.59/22.92 ((
% 132.59/22.92 (inIntersectImpInUnion) =>
% 132.59/22.92 ((
% 132.59/22.92 (inIntersectImpInUnion2) =>
% 132.59/22.92 ((
% 132.59/22.92 (inIntersectImpInIntersectUnions) =>
% 132.59/22.92 ((
% 132.59/22.92 (intersectInPowersetIntersectUnions) =>
% 132.59/22.92 ((
% 132.59/22.92 (inComplementUnionImpNotIn1) =>
% 132.59/22.92 ((
% 132.59/22.92 (inComplementUnionImpInComplement1) =>
% 132.59/22.92 ((
% 132.59/22.92 (binunionTE) =>
% 132.59/22.92 ((
% 132.59/22.92 (binunionTEcontra) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan2a1) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementUnionInPowersetComplement) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan2a2) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan1a) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan1b) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan1) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan2a) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan2b2) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan2b) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan2) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz13rule0) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz13rule1) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz13rule2) =>
% 132.59/22.92 ((
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% 132.59/22.92 ((
% 132.59/22.92 (woz13rule4) =>
% 132.59/22.92 ((
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% 132.59/22.92 ((
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% 132.59/22.92 ((
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% 132.59/22.92 ((
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% 132.59/22.92 ((
% 132.59/22.92 (woz1_5) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1all2) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1SetBreln1) =>
% 132.59/22.92 ((
% 132.59/22.92 (choice2fnsingleton) =>
% 132.59/22.92 ((
% 132.59/22.92 (setOfPairsIsBReln1) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1all1) =>
% 132.59/22.92 ((
% 132.59/22.92 (subbreln1) =>
% 132.59/22.92 ((
% 132.59/22.92 (eqbreln1) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1invprop) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1invI) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1invE) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1compprop) =>
% 132.59/22.92 ((
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% 132.59/22.92 ((
% 132.59/22.92 (breln1compE) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1compEex) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1unionprop) =>
% 132.59/22.92 ((
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% 132.59/22.92 ((
% 132.59/22.92 (breln1unionIR) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1unionI) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1unionE) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1unionEcases) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1unionCommutes) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz2Ex) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz2W) =>
% 132.59/22.92 ((
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% 132.59/22.92 ((
% 132.59/22.92 (woz2B) =>
% 132.59/22.92 ((
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% 132.59/22.92 ((
% 132.59/22.92 (image1Ex1) =>
% 132.59/22.92 ((
% 132.59/22.92 (image1Equiv) =>
% 132.59/22.92 ((
% 132.59/22.92 (image1E) =>
% 132.59/22.92 ((
% 132.59/22.92 (image1I) =>
% 132.59/22.92 ((
% 132.59/22.92 (injFuncInInjFuncSet) =>
% 132.59/22.92 ((
% 132.59/22.92 (injFuncSetFuncIn) =>
% 132.59/22.92 ((
% 132.59/22.92 (injFuncSetFuncInj) =>
% 132.59/22.92 ((
% 132.59/22.92 (surjFuncSetFuncIn) =>
% 132.59/22.92 ((
% 132.59/22.92 (surjFuncSetFuncSurj) =>
% 132.59/22.92 ((
% 132.59/22.92 (leftInvIsSurj) =>
% 132.59/22.92 ((
% 132.59/22.92 (surjCantorThm) =>
% 132.59/22.92 ((
% 132.59/22.92 (foundation2) =>
% 132.59/22.92 ((
% 132.59/22.92 (notinself) =>
% 132.59/22.92 ((
% 132.59/22.92 (notinself2) =>
% 132.59/22.92 ((
% 132.59/22.92 (omegaSp) =>
% 132.59/22.92 ((
% 132.59/22.92 (omegaSclos) =>
% 132.59/22.92 ((
% 132.59/22.92 (peano0notS) =>
% 132.59/22.92 ((
% 132.59/22.92 (peanoSinj) =>
% 132.59/22.92 ((
% 132.59/22.92 (transitivesetOp1) =>
% 132.59/22.92 ((
% 132.59/22.92 (binintTransitive) =>
% 132.59/22.92 ((
% 132.59/22.92 (transitivesetOp2) =>
% 132.59/22.92 ((
% 132.59/22.92 (setunionTransitive) =>
% 132.59/22.92 ((
% 132.59/22.92 (ordinalMinLem1) =>
% 132.59/22.92 ((
% 132.59/22.92 (ordinalTransSet) =>
% 132.59/22.92 ((
% 132.59/22.92 (ordinalTransSet1) =>
% 132.59/22.92 ((
% 132.59/22.92 (setunionOrdinalLem1) =>
% 132.59/22.92 (ordinal @
% 132.59/22.92 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.59/22.92 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl879])).
% 132.59/22.92 thf(zip_derived_cl892, plain,
% 132.59/22.92 (~ (((powersetsubset) =>
% 132.59/22.92 (((sepInPowerset) =>
% 132.59/22.92 (((sepSubset) =>
% 132.59/22.92 (((binunionIL) =>
% 132.59/22.92 (((upairset2IR) =>
% 132.59/22.92 (((binunionIR) =>
% 132.59/22.92 (((binunionEcases) =>
% 132.59/22.92 (((binunionE) =>
% 132.59/22.92 (((binunionLsub) =>
% 132.59/22.92 (((binunionRsub) =>
% 132.59/22.92 (((binintersectI) =>
% 132.59/22.92 (((binintersectSubset5) =>
% 132.59/22.92 (((binintersectEL) =>
% 132.59/22.92 (((binintersectLsub) =>
% 132.59/22.92 (((binintersectSubset2) =>
% 132.59/22.92 (((binintersectSubset3) =>
% 132.59/22.92 (((binintersectER) =>
% 132.59/22.92 (((disjointsetsI1) =>
% 132.59/22.92 (((binintersectRsub) =>
% 132.59/22.92 (((binintersectSubset4) =>
% 132.59/22.92 (((binintersectSubset1) =>
% 132.59/22.92 (((bs114d) =>
% 132.59/22.92 (((setminusI) =>
% 132.59/22.92 (((setminusEL) =>
% 132.59/22.92 (((setminusER) =>
% 132.59/22.92 (((setminusSubset2) =>
% 132.59/22.92 (((setminusERneg) =>
% 132.59/22.92 (((setminusELneg) =>
% 132.59/22.92 (((setminusILneg) =>
% 132.59/22.92 (((setminusIRneg) =>
% 132.59/22.92 ((
% 132.59/22.92 (setminusLsub) =>
% 132.59/22.92 ((
% 132.59/22.92 (setminusSubset1) =>
% 132.59/22.92 ((
% 132.59/22.92 (symdiffE) =>
% 132.59/22.92 ((
% 132.59/22.92 (symdiffI1) =>
% 132.59/22.92 ((
% 132.59/22.92 (symdiffI2) =>
% 132.59/22.92 ((
% 132.59/22.92 (symdiffIneg1) =>
% 132.59/22.92 ((
% 132.59/22.92 (symdiffIneg2) =>
% 132.59/22.92 ((
% 132.59/22.92 (secondinupair) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairIL) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairIR) =>
% 132.59/22.92 ((
% 132.59/22.92 (kpairiskpair) =>
% 132.59/22.92 ((
% 132.59/22.92 (kpairp) =>
% 132.59/22.92 ((
% 132.59/22.92 (singletonsubset) =>
% 132.59/22.92 ((
% 132.59/22.92 (singletoninpowerset) =>
% 132.59/22.92 ((
% 132.59/22.92 (singletoninpowunion) =>
% 132.59/22.92 ((
% 132.59/22.92 (upairset2E) =>
% 132.59/22.92 ((
% 132.59/22.92 (upairsubunion) =>
% 132.59/22.92 ((
% 132.59/22.92 (upairinpowunion) =>
% 132.59/22.92 ((
% 132.59/22.92 (ubforcartprodlem1) =>
% 132.59/22.92 ((
% 132.59/22.92 (ubforcartprodlem2) =>
% 132.59/22.92 ((
% 132.59/22.92 (ubforcartprodlem3) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodpairin) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodmempair1) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodmempair) =>
% 132.59/22.92 ((
% 132.59/22.92 (setunionE2) =>
% 132.59/22.92 ((
% 132.59/22.92 (setunionsingleton1) =>
% 132.59/22.92 ((
% 132.59/22.92 (setunionsingleton2) =>
% 132.59/22.92 ((
% 132.59/22.92 (setunionsingleton) =>
% 132.59/22.92 ((
% 132.59/22.92 (singletonprop) =>
% 132.59/22.92 ((
% 132.59/22.92 (ex1E1) =>
% 132.59/22.92 ((
% 132.59/22.92 (ex1I) =>
% 132.59/22.92 ((
% 132.59/22.92 (ex1I2) =>
% 132.59/22.92 ((
% 132.59/22.92 (singletonsuniq) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjL1) =>
% 132.59/22.92 ((
% 132.59/22.92 (kfstsingleton) =>
% 132.59/22.92 ((
% 132.59/22.92 (theprop) =>
% 132.59/22.92 ((
% 132.59/22.92 (kfstpairEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodfstin) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjL2) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjL) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjR11) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjR12) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjR1) =>
% 132.59/22.92 ((
% 132.59/22.92 (upairequniteq) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjR2) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjR) =>
% 132.59/22.92 ((
% 132.59/22.92 (ksndsingleton) =>
% 132.59/22.92 ((
% 132.59/22.92 (ksndpairEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (kpairsurjEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodsndin) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodpairmemEL) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodpairmemER) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodmempaircEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodfstpairEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodsndpairEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodpairsurjEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (dpsetconstrI) =>
% 132.59/22.92 ((
% 132.59/22.92 (dpsetconstrSub) =>
% 132.59/22.92 ((
% 132.59/22.92 (setOfPairsIsBReln) =>
% 132.59/22.92 ((
% 132.59/22.92 (dpsetconstrERa) =>
% 132.59/22.92 ((
% 132.59/22.92 (dpsetconstrEL1) =>
% 132.59/22.92 ((
% 132.59/22.92 (dpsetconstrEL2) =>
% 132.59/22.92 ((
% 132.59/22.92 (dpsetconstrER) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcImageSingleton) =>
% 132.59/22.92 ((
% 132.59/22.92 (apProp) =>
% 132.59/22.92 ((
% 132.59/22.92 (app) =>
% 132.59/22.92 ((
% 132.59/22.92 (infuncsetfunc) =>
% 132.59/22.92 ((
% 132.59/22.92 (ap2p) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcinfuncset) =>
% 132.59/22.92 ((
% 132.59/22.92 (lamProp) =>
% 132.59/22.92 ((
% 132.59/22.92 (lamp) =>
% 132.59/22.92 ((
% 132.59/22.92 (lam2p) =>
% 132.59/22.92 ((
% 132.59/22.92 (brelnall1) =>
% 132.59/22.92 ((
% 132.59/22.92 (brelnall2) =>
% 132.59/22.92 ((
% 132.59/22.92 (ex1E2) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcGraphProp1) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcGraphProp3) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcGraphProp2) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcextLem) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcGraphProp4) =>
% 132.59/22.92 ((
% 132.59/22.92 (subbreln) =>
% 132.59/22.92 ((
% 132.59/22.92 (eqbreln) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcext) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcext2) =>
% 132.59/22.92 ((
% 132.59/22.92 (ap2apEq1) =>
% 132.59/22.92 ((
% 132.59/22.92 (ap2apEq2) =>
% 132.59/22.92 ((
% 132.59/22.92 (beta1) =>
% 132.59/22.92 ((
% 132.59/22.92 (eta1) =>
% 132.59/22.92 ((
% 132.59/22.92 (lam2lamEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (beta2) =>
% 132.59/22.92 ((
% 132.59/22.92 (eta2) =>
% 132.59/22.92 ((
% 132.59/22.92 (iffalseProp1) =>
% 132.59/22.92 ((
% 132.59/22.92 (iffalseProp2) =>
% 132.59/22.92 ((
% 132.59/22.92 (iftrueProp1) =>
% 132.59/22.92 ((
% 132.59/22.92 (iftrueProp2) =>
% 132.59/22.92 ((
% 132.59/22.92 (ifSingleton) =>
% 132.59/22.92 ((
% 132.59/22.92 (ifp) =>
% 132.59/22.92 ((
% 132.59/22.92 (theeq) =>
% 132.59/22.92 ((
% 132.59/22.92 (iftrue) =>
% 132.59/22.92 ((
% 132.59/22.92 (iffalse) =>
% 132.59/22.92 ((
% 132.59/22.92 (iftrueorfalse) =>
% 132.59/22.92 ((
% 132.59/22.92 (binintersectT_lem) =>
% 132.59/22.92 ((
% 132.59/22.92 (binunionT_lem) =>
% 132.59/22.92 ((
% 132.59/22.92 (powersetT_lem) =>
% 132.59/22.92 ((
% 132.59/22.92 (setminusT_lem) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementT_lem) =>
% 132.59/22.92 ((
% 132.59/22.92 (setextT) =>
% 132.59/22.92 ((
% 132.59/22.92 (subsetTI) =>
% 132.59/22.92 ((
% 132.59/22.92 (powersetTI1) =>
% 132.59/22.92 ((
% 132.59/22.92 (powersetTE1) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementTI1) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementTE1) =>
% 132.59/22.92 ((
% 132.59/22.92 (binintersectTELcontra) =>
% 132.59/22.92 ((
% 132.59/22.92 (binintersectTERcontra) =>
% 132.59/22.92 ((
% 132.59/22.92 (contrasubsetT) =>
% 132.59/22.92 ((
% 132.59/22.92 (contrasubsetT1) =>
% 132.59/22.92 ((
% 132.59/22.92 (contrasubsetT2) =>
% 132.59/22.92 ((
% 132.59/22.92 (contrasubsetT3) =>
% 132.59/22.92 ((
% 132.59/22.92 (doubleComplementI1) =>
% 132.59/22.92 ((
% 132.59/22.92 (doubleComplementE1) =>
% 132.59/22.92 ((
% 132.59/22.92 (doubleComplementSub1) =>
% 132.59/22.92 ((
% 132.59/22.92 (doubleComplementSub2) =>
% 132.59/22.92 ((
% 132.59/22.92 (doubleComplementEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementTnotintersectT) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementImpComplementIntersect) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementSubsetComplementIntersect) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementInPowersetComplementIntersect) =>
% 132.59/22.92 ((
% 132.59/22.92 (contraSubsetComplement) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementTcontraSubset) =>
% 132.59/22.92 ((
% 132.59/22.92 (binunionTILcontra) =>
% 132.59/22.92 ((
% 132.59/22.92 (binunionTIRcontra) =>
% 132.59/22.92 ((
% 132.59/22.92 (inIntersectImpInUnion) =>
% 132.59/22.92 ((
% 132.59/22.92 (inIntersectImpInUnion2) =>
% 132.59/22.92 ((
% 132.59/22.92 (inIntersectImpInIntersectUnions) =>
% 132.59/22.92 ((
% 132.59/22.92 (intersectInPowersetIntersectUnions) =>
% 132.59/22.92 ((
% 132.59/22.92 (inComplementUnionImpNotIn1) =>
% 132.59/22.92 ((
% 132.59/22.92 (inComplementUnionImpInComplement1) =>
% 132.59/22.92 ((
% 132.59/22.92 (binunionTE) =>
% 132.59/22.92 ((
% 132.59/22.92 (binunionTEcontra) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan2a1) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementUnionInPowersetComplement) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan2a2) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan1a) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan1b) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan1) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan2a) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan2b2) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan2b) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan2) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz13rule0) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz13rule1) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz13rule2) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz13rule3) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz13rule4) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz1_1) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz1_2) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz1_3) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz1_4) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz1_5) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1all2) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1SetBreln1) =>
% 132.59/22.92 ((
% 132.59/22.92 (choice2fnsingleton) =>
% 132.59/22.92 ((
% 132.59/22.92 (setOfPairsIsBReln1) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1all1) =>
% 132.59/22.92 ((
% 132.59/22.92 (subbreln1) =>
% 132.59/22.92 ((
% 132.59/22.92 (eqbreln1) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1invprop) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1invI) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1invE) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1compprop) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1compI) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1compE) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1compEex) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1unionprop) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1unionIL) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1unionIR) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1unionI) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1unionE) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1unionEcases) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1unionCommutes) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz2Ex) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz2W) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz2A) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz2B) =>
% 132.59/22.92 ((
% 132.59/22.92 (image1Ex) =>
% 132.59/22.92 ((
% 132.59/22.92 (image1Ex1) =>
% 132.59/22.92 ((
% 132.59/22.92 (image1Equiv) =>
% 132.59/22.92 ((
% 132.59/22.92 (image1E) =>
% 132.59/22.92 ((
% 132.59/22.92 (image1I) =>
% 132.59/22.92 ((
% 132.59/22.92 (injFuncInInjFuncSet) =>
% 132.59/22.92 ((
% 132.59/22.92 (injFuncSetFuncIn) =>
% 132.59/22.92 ((
% 132.59/22.92 (injFuncSetFuncInj) =>
% 132.59/22.92 ((
% 132.59/22.92 (surjFuncSetFuncIn) =>
% 132.59/22.92 ((
% 132.59/22.92 (surjFuncSetFuncSurj) =>
% 132.59/22.92 ((
% 132.59/22.92 (leftInvIsSurj) =>
% 132.59/22.92 ((
% 132.59/22.92 (surjCantorThm) =>
% 132.59/22.92 ((
% 132.59/22.92 (foundation2) =>
% 132.59/22.92 ((
% 132.59/22.92 (notinself) =>
% 132.59/22.92 ((
% 132.59/22.92 (notinself2) =>
% 132.59/22.92 ((
% 132.59/22.92 (omegaSp) =>
% 132.59/22.92 ((
% 132.59/22.92 (omegaSclos) =>
% 132.59/22.92 ((
% 132.59/22.92 (peano0notS) =>
% 132.59/22.92 ((
% 132.59/22.92 (peanoSinj) =>
% 132.59/22.92 ((
% 132.59/22.92 (transitivesetOp1) =>
% 132.59/22.92 ((
% 132.59/22.92 (binintTransitive) =>
% 132.59/22.92 ((
% 132.59/22.92 (transitivesetOp2) =>
% 132.59/22.92 ((
% 132.59/22.92 (setunionTransitive) =>
% 132.59/22.92 ((
% 132.59/22.92 (ordinalMinLem1) =>
% 132.59/22.92 ((
% 132.59/22.92 (ordinalTransSet) =>
% 132.59/22.92 ((
% 132.59/22.92 (ordinalTransSet1) =>
% 132.59/22.92 ((
% 132.59/22.92 (setunionOrdinalLem1) =>
% 132.59/22.92 (ordinal @
% 132.59/22.92 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.59/22.92 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl886])).
% 132.59/22.92 thf(zip_derived_cl899, plain,
% 132.59/22.92 (~ (((sepInPowerset) =>
% 132.59/22.92 (((sepSubset) =>
% 132.59/22.92 (((binunionIL) =>
% 132.59/22.92 (((upairset2IR) =>
% 132.59/22.92 (((binunionIR) =>
% 132.59/22.92 (((binunionEcases) =>
% 132.59/22.92 (((binunionE) =>
% 132.59/22.92 (((binunionLsub) =>
% 132.59/22.92 (((binunionRsub) =>
% 132.59/22.92 (((binintersectI) =>
% 132.59/22.92 (((binintersectSubset5) =>
% 132.59/22.92 (((binintersectEL) =>
% 132.59/22.92 (((binintersectLsub) =>
% 132.59/22.92 (((binintersectSubset2) =>
% 132.59/22.92 (((binintersectSubset3) =>
% 132.59/22.92 (((binintersectER) =>
% 132.59/22.92 (((disjointsetsI1) =>
% 132.59/22.92 (((binintersectRsub) =>
% 132.59/22.92 (((binintersectSubset4) =>
% 132.59/22.92 (((binintersectSubset1) =>
% 132.59/22.92 (((bs114d) =>
% 132.59/22.92 (((setminusI) =>
% 132.59/22.92 (((setminusEL) =>
% 132.59/22.92 (((setminusER) =>
% 132.59/22.92 (((setminusSubset2) =>
% 132.59/22.92 (((setminusERneg) =>
% 132.59/22.92 (((setminusELneg) =>
% 132.59/22.92 (((setminusILneg) =>
% 132.59/22.92 (((setminusIRneg) =>
% 132.59/22.92 (((setminusLsub) =>
% 132.59/22.92 ((
% 132.59/22.92 (setminusSubset1) =>
% 132.59/22.92 ((
% 132.59/22.92 (symdiffE) =>
% 132.59/22.92 ((
% 132.59/22.92 (symdiffI1) =>
% 132.59/22.92 ((
% 132.59/22.92 (symdiffI2) =>
% 132.59/22.92 ((
% 132.59/22.92 (symdiffIneg1) =>
% 132.59/22.92 ((
% 132.59/22.92 (symdiffIneg2) =>
% 132.59/22.92 ((
% 132.59/22.92 (secondinupair) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairIL) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairIR) =>
% 132.59/22.92 ((
% 132.59/22.92 (kpairiskpair) =>
% 132.59/22.92 ((
% 132.59/22.92 (kpairp) =>
% 132.59/22.92 ((
% 132.59/22.92 (singletonsubset) =>
% 132.59/22.92 ((
% 132.59/22.92 (singletoninpowerset) =>
% 132.59/22.92 ((
% 132.59/22.92 (singletoninpowunion) =>
% 132.59/22.92 ((
% 132.59/22.92 (upairset2E) =>
% 132.59/22.92 ((
% 132.59/22.92 (upairsubunion) =>
% 132.59/22.92 ((
% 132.59/22.92 (upairinpowunion) =>
% 132.59/22.92 ((
% 132.59/22.92 (ubforcartprodlem1) =>
% 132.59/22.92 ((
% 132.59/22.92 (ubforcartprodlem2) =>
% 132.59/22.92 ((
% 132.59/22.92 (ubforcartprodlem3) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodpairin) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodmempair1) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodmempair) =>
% 132.59/22.92 ((
% 132.59/22.92 (setunionE2) =>
% 132.59/22.92 ((
% 132.59/22.92 (setunionsingleton1) =>
% 132.59/22.92 ((
% 132.59/22.92 (setunionsingleton2) =>
% 132.59/22.92 ((
% 132.59/22.92 (setunionsingleton) =>
% 132.59/22.92 ((
% 132.59/22.92 (singletonprop) =>
% 132.59/22.92 ((
% 132.59/22.92 (ex1E1) =>
% 132.59/22.92 ((
% 132.59/22.92 (ex1I) =>
% 132.59/22.92 ((
% 132.59/22.92 (ex1I2) =>
% 132.59/22.92 ((
% 132.59/22.92 (singletonsuniq) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjL1) =>
% 132.59/22.92 ((
% 132.59/22.92 (kfstsingleton) =>
% 132.59/22.92 ((
% 132.59/22.92 (theprop) =>
% 132.59/22.92 ((
% 132.59/22.92 (kfstpairEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodfstin) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjL2) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjL) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjR11) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjR12) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjR1) =>
% 132.59/22.92 ((
% 132.59/22.92 (upairequniteq) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjR2) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjR) =>
% 132.59/22.92 ((
% 132.59/22.92 (ksndsingleton) =>
% 132.59/22.92 ((
% 132.59/22.92 (ksndpairEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (kpairsurjEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodsndin) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodpairmemEL) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodpairmemER) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodmempaircEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodfstpairEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodsndpairEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodpairsurjEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (dpsetconstrI) =>
% 132.59/22.92 ((
% 132.59/22.92 (dpsetconstrSub) =>
% 132.59/22.92 ((
% 132.59/22.92 (setOfPairsIsBReln) =>
% 132.59/22.92 ((
% 132.59/22.92 (dpsetconstrERa) =>
% 132.59/22.92 ((
% 132.59/22.92 (dpsetconstrEL1) =>
% 132.59/22.92 ((
% 132.59/22.92 (dpsetconstrEL2) =>
% 132.59/22.92 ((
% 132.59/22.92 (dpsetconstrER) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcImageSingleton) =>
% 132.59/22.92 ((
% 132.59/22.92 (apProp) =>
% 132.59/22.92 ((
% 132.59/22.92 (app) =>
% 132.59/22.92 ((
% 132.59/22.92 (infuncsetfunc) =>
% 132.59/22.92 ((
% 132.59/22.92 (ap2p) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcinfuncset) =>
% 132.59/22.92 ((
% 132.59/22.92 (lamProp) =>
% 132.59/22.92 ((
% 132.59/22.92 (lamp) =>
% 132.59/22.92 ((
% 132.59/22.92 (lam2p) =>
% 132.59/22.92 ((
% 132.59/22.92 (brelnall1) =>
% 132.59/22.92 ((
% 132.59/22.92 (brelnall2) =>
% 132.59/22.92 ((
% 132.59/22.92 (ex1E2) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcGraphProp1) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcGraphProp3) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcGraphProp2) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcextLem) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcGraphProp4) =>
% 132.59/22.92 ((
% 132.59/22.92 (subbreln) =>
% 132.59/22.92 ((
% 132.59/22.92 (eqbreln) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcext) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcext2) =>
% 132.59/22.92 ((
% 132.59/22.92 (ap2apEq1) =>
% 132.59/22.92 ((
% 132.59/22.92 (ap2apEq2) =>
% 132.59/22.92 ((
% 132.59/22.92 (beta1) =>
% 132.59/22.92 ((
% 132.59/22.92 (eta1) =>
% 132.59/22.92 ((
% 132.59/22.92 (lam2lamEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (beta2) =>
% 132.59/22.92 ((
% 132.59/22.92 (eta2) =>
% 132.59/22.92 ((
% 132.59/22.92 (iffalseProp1) =>
% 132.59/22.92 ((
% 132.59/22.92 (iffalseProp2) =>
% 132.59/22.92 ((
% 132.59/22.92 (iftrueProp1) =>
% 132.59/22.92 ((
% 132.59/22.92 (iftrueProp2) =>
% 132.59/22.92 ((
% 132.59/22.92 (ifSingleton) =>
% 132.59/22.92 ((
% 132.59/22.92 (ifp) =>
% 132.59/22.92 ((
% 132.59/22.92 (theeq) =>
% 132.59/22.92 ((
% 132.59/22.92 (iftrue) =>
% 132.59/22.92 ((
% 132.59/22.92 (iffalse) =>
% 132.59/22.92 ((
% 132.59/22.92 (iftrueorfalse) =>
% 132.59/22.92 ((
% 132.59/22.92 (binintersectT_lem) =>
% 132.59/22.92 ((
% 132.59/22.92 (binunionT_lem) =>
% 132.59/22.92 ((
% 132.59/22.92 (powersetT_lem) =>
% 132.59/22.92 ((
% 132.59/22.92 (setminusT_lem) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementT_lem) =>
% 132.59/22.92 ((
% 132.59/22.92 (setextT) =>
% 132.59/22.92 ((
% 132.59/22.92 (subsetTI) =>
% 132.59/22.92 ((
% 132.59/22.92 (powersetTI1) =>
% 132.59/22.92 ((
% 132.59/22.92 (powersetTE1) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementTI1) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementTE1) =>
% 132.59/22.92 ((
% 132.59/22.92 (binintersectTELcontra) =>
% 132.59/22.92 ((
% 132.59/22.92 (binintersectTERcontra) =>
% 132.59/22.92 ((
% 132.59/22.92 (contrasubsetT) =>
% 132.59/22.92 ((
% 132.59/22.92 (contrasubsetT1) =>
% 132.59/22.92 ((
% 132.59/22.92 (contrasubsetT2) =>
% 132.59/22.92 ((
% 132.59/22.92 (contrasubsetT3) =>
% 132.59/22.92 ((
% 132.59/22.92 (doubleComplementI1) =>
% 132.59/22.92 ((
% 132.59/22.92 (doubleComplementE1) =>
% 132.59/22.92 ((
% 132.59/22.92 (doubleComplementSub1) =>
% 132.59/22.92 ((
% 132.59/22.92 (doubleComplementSub2) =>
% 132.59/22.92 ((
% 132.59/22.92 (doubleComplementEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementTnotintersectT) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementImpComplementIntersect) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementSubsetComplementIntersect) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementInPowersetComplementIntersect) =>
% 132.59/22.92 ((
% 132.59/22.92 (contraSubsetComplement) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementTcontraSubset) =>
% 132.59/22.92 ((
% 132.59/22.92 (binunionTILcontra) =>
% 132.59/22.92 ((
% 132.59/22.92 (binunionTIRcontra) =>
% 132.59/22.92 ((
% 132.59/22.92 (inIntersectImpInUnion) =>
% 132.59/22.92 ((
% 132.59/22.92 (inIntersectImpInUnion2) =>
% 132.59/22.92 ((
% 132.59/22.92 (inIntersectImpInIntersectUnions) =>
% 132.59/22.92 ((
% 132.59/22.92 (intersectInPowersetIntersectUnions) =>
% 132.59/22.92 ((
% 132.59/22.92 (inComplementUnionImpNotIn1) =>
% 132.59/22.92 ((
% 132.59/22.92 (inComplementUnionImpInComplement1) =>
% 132.59/22.92 ((
% 132.59/22.92 (binunionTE) =>
% 132.59/22.92 ((
% 132.59/22.92 (binunionTEcontra) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan2a1) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementUnionInPowersetComplement) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan2a2) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan1a) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan1b) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan1) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan2a) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan2b2) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan2b) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan2) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz13rule0) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz13rule1) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz13rule2) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz13rule3) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz13rule4) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz1_1) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz1_2) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz1_3) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz1_4) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz1_5) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1all2) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1SetBreln1) =>
% 132.59/22.92 ((
% 132.59/22.92 (choice2fnsingleton) =>
% 132.59/22.92 ((
% 132.59/22.92 (setOfPairsIsBReln1) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1all1) =>
% 132.59/22.92 ((
% 132.59/22.92 (subbreln1) =>
% 132.59/22.92 ((
% 132.59/22.92 (eqbreln1) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1invprop) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1invI) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1invE) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1compprop) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1compI) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1compE) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1compEex) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1unionprop) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1unionIL) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1unionIR) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1unionI) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1unionE) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1unionEcases) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1unionCommutes) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz2Ex) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz2W) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz2A) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz2B) =>
% 132.59/22.92 ((
% 132.59/22.92 (image1Ex) =>
% 132.59/22.92 ((
% 132.59/22.92 (image1Ex1) =>
% 132.59/22.92 ((
% 132.59/22.92 (image1Equiv) =>
% 132.59/22.92 ((
% 132.59/22.92 (image1E) =>
% 132.59/22.92 ((
% 132.59/22.92 (image1I) =>
% 132.59/22.92 ((
% 132.59/22.92 (injFuncInInjFuncSet) =>
% 132.59/22.92 ((
% 132.59/22.92 (injFuncSetFuncIn) =>
% 132.59/22.92 ((
% 132.59/22.92 (injFuncSetFuncInj) =>
% 132.59/22.92 ((
% 132.59/22.92 (surjFuncSetFuncIn) =>
% 132.59/22.92 ((
% 132.59/22.92 (surjFuncSetFuncSurj) =>
% 132.59/22.92 ((
% 132.59/22.92 (leftInvIsSurj) =>
% 132.59/22.92 ((
% 132.59/22.92 (surjCantorThm) =>
% 132.59/22.92 ((
% 132.59/22.92 (foundation2) =>
% 132.59/22.92 ((
% 132.59/22.92 (notinself) =>
% 132.59/22.92 ((
% 132.59/22.92 (notinself2) =>
% 132.59/22.92 ((
% 132.59/22.92 (omegaSp) =>
% 132.59/22.92 ((
% 132.59/22.92 (omegaSclos) =>
% 132.59/22.92 ((
% 132.59/22.92 (peano0notS) =>
% 132.59/22.92 ((
% 132.59/22.92 (peanoSinj) =>
% 132.59/22.92 ((
% 132.59/22.92 (transitivesetOp1) =>
% 132.59/22.92 ((
% 132.59/22.92 (binintTransitive) =>
% 132.59/22.92 ((
% 132.59/22.92 (transitivesetOp2) =>
% 132.59/22.92 ((
% 132.59/22.92 (setunionTransitive) =>
% 132.59/22.92 ((
% 132.59/22.92 (ordinalMinLem1) =>
% 132.59/22.92 ((
% 132.59/22.92 (ordinalTransSet) =>
% 132.59/22.92 ((
% 132.59/22.92 (ordinalTransSet1) =>
% 132.59/22.92 ((
% 132.59/22.92 (setunionOrdinalLem1) =>
% 132.59/22.92 (ordinal @
% 132.59/22.92 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.59/22.92 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl892])).
% 132.59/22.92 thf(zip_derived_cl906, plain,
% 132.59/22.92 (~ (((sepSubset) =>
% 132.59/22.92 (((binunionIL) =>
% 132.59/22.92 (((upairset2IR) =>
% 132.59/22.92 (((binunionIR) =>
% 132.59/22.92 (((binunionEcases) =>
% 132.59/22.92 (((binunionE) =>
% 132.59/22.92 (((binunionLsub) =>
% 132.59/22.92 (((binunionRsub) =>
% 132.59/22.92 (((binintersectI) =>
% 132.59/22.92 (((binintersectSubset5) =>
% 132.59/22.92 (((binintersectEL) =>
% 132.59/22.92 (((binintersectLsub) =>
% 132.59/22.92 (((binintersectSubset2) =>
% 132.59/22.92 (((binintersectSubset3) =>
% 132.59/22.92 (((binintersectER) =>
% 132.59/22.92 (((disjointsetsI1) =>
% 132.59/22.92 (((binintersectRsub) =>
% 132.59/22.92 (((binintersectSubset4) =>
% 132.59/22.92 (((binintersectSubset1) =>
% 132.59/22.92 (((bs114d) =>
% 132.59/22.92 (((setminusI) =>
% 132.59/22.92 (((setminusEL) =>
% 132.59/22.92 (((setminusER) =>
% 132.59/22.92 (((setminusSubset2) =>
% 132.59/22.92 (((setminusERneg) =>
% 132.59/22.92 (((setminusELneg) =>
% 132.59/22.92 (((setminusILneg) =>
% 132.59/22.92 (((setminusIRneg) =>
% 132.59/22.92 (((setminusLsub) =>
% 132.59/22.92 (((setminusSubset1) =>
% 132.59/22.92 ((
% 132.59/22.92 (symdiffE) =>
% 132.59/22.92 ((
% 132.59/22.92 (symdiffI1) =>
% 132.59/22.92 ((
% 132.59/22.92 (symdiffI2) =>
% 132.59/22.92 ((
% 132.59/22.92 (symdiffIneg1) =>
% 132.59/22.92 ((
% 132.59/22.92 (symdiffIneg2) =>
% 132.59/22.92 ((
% 132.59/22.92 (secondinupair) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairIL) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairIR) =>
% 132.59/22.92 ((
% 132.59/22.92 (kpairiskpair) =>
% 132.59/22.92 ((
% 132.59/22.92 (kpairp) =>
% 132.59/22.92 ((
% 132.59/22.92 (singletonsubset) =>
% 132.59/22.92 ((
% 132.59/22.92 (singletoninpowerset) =>
% 132.59/22.92 ((
% 132.59/22.92 (singletoninpowunion) =>
% 132.59/22.92 ((
% 132.59/22.92 (upairset2E) =>
% 132.59/22.92 ((
% 132.59/22.92 (upairsubunion) =>
% 132.59/22.92 ((
% 132.59/22.92 (upairinpowunion) =>
% 132.59/22.92 ((
% 132.59/22.92 (ubforcartprodlem1) =>
% 132.59/22.92 ((
% 132.59/22.92 (ubforcartprodlem2) =>
% 132.59/22.92 ((
% 132.59/22.92 (ubforcartprodlem3) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodpairin) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodmempair1) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodmempair) =>
% 132.59/22.92 ((
% 132.59/22.92 (setunionE2) =>
% 132.59/22.92 ((
% 132.59/22.92 (setunionsingleton1) =>
% 132.59/22.92 ((
% 132.59/22.92 (setunionsingleton2) =>
% 132.59/22.92 ((
% 132.59/22.92 (setunionsingleton) =>
% 132.59/22.92 ((
% 132.59/22.92 (singletonprop) =>
% 132.59/22.92 ((
% 132.59/22.92 (ex1E1) =>
% 132.59/22.92 ((
% 132.59/22.92 (ex1I) =>
% 132.59/22.92 ((
% 132.59/22.92 (ex1I2) =>
% 132.59/22.92 ((
% 132.59/22.92 (singletonsuniq) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjL1) =>
% 132.59/22.92 ((
% 132.59/22.92 (kfstsingleton) =>
% 132.59/22.92 ((
% 132.59/22.92 (theprop) =>
% 132.59/22.92 ((
% 132.59/22.92 (kfstpairEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodfstin) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjL2) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjL) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjR11) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjR12) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjR1) =>
% 132.59/22.92 ((
% 132.59/22.92 (upairequniteq) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjR2) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjR) =>
% 132.59/22.92 ((
% 132.59/22.92 (ksndsingleton) =>
% 132.59/22.92 ((
% 132.59/22.92 (ksndpairEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (kpairsurjEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodsndin) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodpairmemEL) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodpairmemER) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodmempaircEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodfstpairEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodsndpairEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodpairsurjEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (dpsetconstrI) =>
% 132.59/22.92 ((
% 132.59/22.92 (dpsetconstrSub) =>
% 132.59/22.92 ((
% 132.59/22.92 (setOfPairsIsBReln) =>
% 132.59/22.92 ((
% 132.59/22.92 (dpsetconstrERa) =>
% 132.59/22.92 ((
% 132.59/22.92 (dpsetconstrEL1) =>
% 132.59/22.92 ((
% 132.59/22.92 (dpsetconstrEL2) =>
% 132.59/22.92 ((
% 132.59/22.92 (dpsetconstrER) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcImageSingleton) =>
% 132.59/22.92 ((
% 132.59/22.92 (apProp) =>
% 132.59/22.92 ((
% 132.59/22.92 (app) =>
% 132.59/22.92 ((
% 132.59/22.92 (infuncsetfunc) =>
% 132.59/22.92 ((
% 132.59/22.92 (ap2p) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcinfuncset) =>
% 132.59/22.92 ((
% 132.59/22.92 (lamProp) =>
% 132.59/22.92 ((
% 132.59/22.92 (lamp) =>
% 132.59/22.92 ((
% 132.59/22.92 (lam2p) =>
% 132.59/22.92 ((
% 132.59/22.92 (brelnall1) =>
% 132.59/22.92 ((
% 132.59/22.92 (brelnall2) =>
% 132.59/22.92 ((
% 132.59/22.92 (ex1E2) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcGraphProp1) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcGraphProp3) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcGraphProp2) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcextLem) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcGraphProp4) =>
% 132.59/22.92 ((
% 132.59/22.92 (subbreln) =>
% 132.59/22.92 ((
% 132.59/22.92 (eqbreln) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcext) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcext2) =>
% 132.59/22.92 ((
% 132.59/22.92 (ap2apEq1) =>
% 132.59/22.92 ((
% 132.59/22.92 (ap2apEq2) =>
% 132.59/22.92 ((
% 132.59/22.92 (beta1) =>
% 132.59/22.92 ((
% 132.59/22.92 (eta1) =>
% 132.59/22.92 ((
% 132.59/22.92 (lam2lamEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (beta2) =>
% 132.59/22.92 ((
% 132.59/22.92 (eta2) =>
% 132.59/22.92 ((
% 132.59/22.92 (iffalseProp1) =>
% 132.59/22.92 ((
% 132.59/22.92 (iffalseProp2) =>
% 132.59/22.92 ((
% 132.59/22.92 (iftrueProp1) =>
% 132.59/22.92 ((
% 132.59/22.92 (iftrueProp2) =>
% 132.59/22.92 ((
% 132.59/22.92 (ifSingleton) =>
% 132.59/22.92 ((
% 132.59/22.92 (ifp) =>
% 132.59/22.92 ((
% 132.59/22.92 (theeq) =>
% 132.59/22.92 ((
% 132.59/22.92 (iftrue) =>
% 132.59/22.92 ((
% 132.59/22.92 (iffalse) =>
% 132.59/22.92 ((
% 132.59/22.92 (iftrueorfalse) =>
% 132.59/22.92 ((
% 132.59/22.92 (binintersectT_lem) =>
% 132.59/22.92 ((
% 132.59/22.92 (binunionT_lem) =>
% 132.59/22.92 ((
% 132.59/22.92 (powersetT_lem) =>
% 132.59/22.92 ((
% 132.59/22.92 (setminusT_lem) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementT_lem) =>
% 132.59/22.92 ((
% 132.59/22.92 (setextT) =>
% 132.59/22.92 ((
% 132.59/22.92 (subsetTI) =>
% 132.59/22.92 ((
% 132.59/22.92 (powersetTI1) =>
% 132.59/22.92 ((
% 132.59/22.92 (powersetTE1) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementTI1) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementTE1) =>
% 132.59/22.92 ((
% 132.59/22.92 (binintersectTELcontra) =>
% 132.59/22.92 ((
% 132.59/22.92 (binintersectTERcontra) =>
% 132.59/22.92 ((
% 132.59/22.92 (contrasubsetT) =>
% 132.59/22.92 ((
% 132.59/22.92 (contrasubsetT1) =>
% 132.59/22.92 ((
% 132.59/22.92 (contrasubsetT2) =>
% 132.59/22.92 ((
% 132.59/22.92 (contrasubsetT3) =>
% 132.59/22.92 ((
% 132.59/22.92 (doubleComplementI1) =>
% 132.59/22.92 ((
% 132.59/22.92 (doubleComplementE1) =>
% 132.59/22.92 ((
% 132.59/22.92 (doubleComplementSub1) =>
% 132.59/22.92 ((
% 132.59/22.92 (doubleComplementSub2) =>
% 132.59/22.92 ((
% 132.59/22.92 (doubleComplementEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementTnotintersectT) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementImpComplementIntersect) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementSubsetComplementIntersect) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementInPowersetComplementIntersect) =>
% 132.59/22.92 ((
% 132.59/22.92 (contraSubsetComplement) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementTcontraSubset) =>
% 132.59/22.92 ((
% 132.59/22.92 (binunionTILcontra) =>
% 132.59/22.92 ((
% 132.59/22.92 (binunionTIRcontra) =>
% 132.59/22.92 ((
% 132.59/22.92 (inIntersectImpInUnion) =>
% 132.59/22.92 ((
% 132.59/22.92 (inIntersectImpInUnion2) =>
% 132.59/22.92 ((
% 132.59/22.92 (inIntersectImpInIntersectUnions) =>
% 132.59/22.92 ((
% 132.59/22.92 (intersectInPowersetIntersectUnions) =>
% 132.59/22.92 ((
% 132.59/22.92 (inComplementUnionImpNotIn1) =>
% 132.59/22.92 ((
% 132.59/22.92 (inComplementUnionImpInComplement1) =>
% 132.59/22.92 ((
% 132.59/22.92 (binunionTE) =>
% 132.59/22.92 ((
% 132.59/22.92 (binunionTEcontra) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan2a1) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementUnionInPowersetComplement) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan2a2) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan1a) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan1b) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan1) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan2a) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan2b2) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan2b) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan2) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz13rule0) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz13rule1) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz13rule2) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz13rule3) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz13rule4) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz1_1) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz1_2) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz1_3) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz1_4) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz1_5) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1all2) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1SetBreln1) =>
% 132.59/22.92 ((
% 132.59/22.92 (choice2fnsingleton) =>
% 132.59/22.92 ((
% 132.59/22.92 (setOfPairsIsBReln1) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1all1) =>
% 132.59/22.92 ((
% 132.59/22.92 (subbreln1) =>
% 132.59/22.92 ((
% 132.59/22.92 (eqbreln1) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1invprop) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1invI) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1invE) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1compprop) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1compI) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1compE) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1compEex) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1unionprop) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1unionIL) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1unionIR) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1unionI) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1unionE) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1unionEcases) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1unionCommutes) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz2Ex) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz2W) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz2A) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz2B) =>
% 132.59/22.92 ((
% 132.59/22.92 (image1Ex) =>
% 132.59/22.92 ((
% 132.59/22.92 (image1Ex1) =>
% 132.59/22.92 ((
% 132.59/22.92 (image1Equiv) =>
% 132.59/22.92 ((
% 132.59/22.92 (image1E) =>
% 132.59/22.92 ((
% 132.59/22.92 (image1I) =>
% 132.59/22.92 ((
% 132.59/22.92 (injFuncInInjFuncSet) =>
% 132.59/22.92 ((
% 132.59/22.92 (injFuncSetFuncIn) =>
% 132.59/22.92 ((
% 132.59/22.92 (injFuncSetFuncInj) =>
% 132.59/22.92 ((
% 132.59/22.92 (surjFuncSetFuncIn) =>
% 132.59/22.92 ((
% 132.59/22.92 (surjFuncSetFuncSurj) =>
% 132.59/22.92 ((
% 132.59/22.92 (leftInvIsSurj) =>
% 132.59/22.92 ((
% 132.59/22.92 (surjCantorThm) =>
% 132.59/22.92 ((
% 132.59/22.92 (foundation2) =>
% 132.59/22.92 ((
% 132.59/22.92 (notinself) =>
% 132.59/22.92 ((
% 132.59/22.92 (notinself2) =>
% 132.59/22.92 ((
% 132.59/22.92 (omegaSp) =>
% 132.59/22.92 ((
% 132.59/22.92 (omegaSclos) =>
% 132.59/22.92 ((
% 132.59/22.92 (peano0notS) =>
% 132.59/22.92 ((
% 132.59/22.92 (peanoSinj) =>
% 132.59/22.92 ((
% 132.59/22.92 (transitivesetOp1) =>
% 132.59/22.92 ((
% 132.59/22.92 (binintTransitive) =>
% 132.59/22.92 ((
% 132.59/22.92 (transitivesetOp2) =>
% 132.59/22.92 ((
% 132.59/22.92 (setunionTransitive) =>
% 132.59/22.92 ((
% 132.59/22.92 (ordinalMinLem1) =>
% 132.59/22.92 ((
% 132.59/22.92 (ordinalTransSet) =>
% 132.59/22.92 ((
% 132.59/22.92 (ordinalTransSet1) =>
% 132.59/22.92 ((
% 132.59/22.92 (setunionOrdinalLem1) =>
% 132.59/22.92 (ordinal @
% 132.59/22.92 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.59/22.92 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl899])).
% 132.59/22.92 thf(zip_derived_cl911, plain,
% 132.59/22.92 (~ (((binunionIL) =>
% 132.59/22.92 (((upairset2IR) =>
% 132.59/22.92 (((binunionIR) =>
% 132.59/22.92 (((binunionEcases) =>
% 132.59/22.92 (((binunionE) =>
% 132.59/22.92 (((binunionLsub) =>
% 132.59/22.92 (((binunionRsub) =>
% 132.59/22.92 (((binintersectI) =>
% 132.59/22.92 (((binintersectSubset5) =>
% 132.59/22.92 (((binintersectEL) =>
% 132.59/22.92 (((binintersectLsub) =>
% 132.59/22.92 (((binintersectSubset2) =>
% 132.59/22.92 (((binintersectSubset3) =>
% 132.59/22.92 (((binintersectER) =>
% 132.59/22.92 (((disjointsetsI1) =>
% 132.59/22.92 (((binintersectRsub) =>
% 132.59/22.92 (((binintersectSubset4) =>
% 132.59/22.92 (((binintersectSubset1) =>
% 132.59/22.92 (((bs114d) =>
% 132.59/22.92 (((setminusI) =>
% 132.59/22.92 (((setminusEL) =>
% 132.59/22.92 (((setminusER) =>
% 132.59/22.92 (((setminusSubset2) =>
% 132.59/22.92 (((setminusERneg) =>
% 132.59/22.92 (((setminusELneg) =>
% 132.59/22.92 (((setminusILneg) =>
% 132.59/22.92 (((setminusIRneg) =>
% 132.59/22.92 (((setminusLsub) =>
% 132.59/22.92 (((setminusSubset1) =>
% 132.59/22.92 (((symdiffE) =>
% 132.59/22.92 ((
% 132.59/22.92 (symdiffI1) =>
% 132.59/22.92 ((
% 132.59/22.92 (symdiffI2) =>
% 132.59/22.92 ((
% 132.59/22.92 (symdiffIneg1) =>
% 132.59/22.92 ((
% 132.59/22.92 (symdiffIneg2) =>
% 132.59/22.92 ((
% 132.59/22.92 (secondinupair) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairIL) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairIR) =>
% 132.59/22.92 ((
% 132.59/22.92 (kpairiskpair) =>
% 132.59/22.92 ((
% 132.59/22.92 (kpairp) =>
% 132.59/22.92 ((
% 132.59/22.92 (singletonsubset) =>
% 132.59/22.92 ((
% 132.59/22.92 (singletoninpowerset) =>
% 132.59/22.92 ((
% 132.59/22.92 (singletoninpowunion) =>
% 132.59/22.92 ((
% 132.59/22.92 (upairset2E) =>
% 132.59/22.92 ((
% 132.59/22.92 (upairsubunion) =>
% 132.59/22.92 ((
% 132.59/22.92 (upairinpowunion) =>
% 132.59/22.92 ((
% 132.59/22.92 (ubforcartprodlem1) =>
% 132.59/22.92 ((
% 132.59/22.92 (ubforcartprodlem2) =>
% 132.59/22.92 ((
% 132.59/22.92 (ubforcartprodlem3) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodpairin) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodmempair1) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodmempair) =>
% 132.59/22.92 ((
% 132.59/22.92 (setunionE2) =>
% 132.59/22.92 ((
% 132.59/22.92 (setunionsingleton1) =>
% 132.59/22.92 ((
% 132.59/22.92 (setunionsingleton2) =>
% 132.59/22.92 ((
% 132.59/22.92 (setunionsingleton) =>
% 132.59/22.92 ((
% 132.59/22.92 (singletonprop) =>
% 132.59/22.92 ((
% 132.59/22.92 (ex1E1) =>
% 132.59/22.92 ((
% 132.59/22.92 (ex1I) =>
% 132.59/22.92 ((
% 132.59/22.92 (ex1I2) =>
% 132.59/22.92 ((
% 132.59/22.92 (singletonsuniq) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjL1) =>
% 132.59/22.92 ((
% 132.59/22.92 (kfstsingleton) =>
% 132.59/22.92 ((
% 132.59/22.92 (theprop) =>
% 132.59/22.92 ((
% 132.59/22.92 (kfstpairEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodfstin) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjL2) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjL) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjR11) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjR12) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjR1) =>
% 132.59/22.92 ((
% 132.59/22.92 (upairequniteq) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjR2) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjR) =>
% 132.59/22.92 ((
% 132.59/22.92 (ksndsingleton) =>
% 132.59/22.92 ((
% 132.59/22.92 (ksndpairEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (kpairsurjEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodsndin) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodpairmemEL) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodpairmemER) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodmempaircEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodfstpairEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodsndpairEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodpairsurjEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (dpsetconstrI) =>
% 132.59/22.92 ((
% 132.59/22.92 (dpsetconstrSub) =>
% 132.59/22.92 ((
% 132.59/22.92 (setOfPairsIsBReln) =>
% 132.59/22.92 ((
% 132.59/22.92 (dpsetconstrERa) =>
% 132.59/22.92 ((
% 132.59/22.92 (dpsetconstrEL1) =>
% 132.59/22.92 ((
% 132.59/22.92 (dpsetconstrEL2) =>
% 132.59/22.92 ((
% 132.59/22.92 (dpsetconstrER) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcImageSingleton) =>
% 132.59/22.92 ((
% 132.59/22.92 (apProp) =>
% 132.59/22.92 ((
% 132.59/22.92 (app) =>
% 132.59/22.92 ((
% 132.59/22.92 (infuncsetfunc) =>
% 132.59/22.92 ((
% 132.59/22.92 (ap2p) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcinfuncset) =>
% 132.59/22.92 ((
% 132.59/22.92 (lamProp) =>
% 132.59/22.92 ((
% 132.59/22.92 (lamp) =>
% 132.59/22.92 ((
% 132.59/22.92 (lam2p) =>
% 132.59/22.92 ((
% 132.59/22.92 (brelnall1) =>
% 132.59/22.92 ((
% 132.59/22.92 (brelnall2) =>
% 132.59/22.92 ((
% 132.59/22.92 (ex1E2) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcGraphProp1) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcGraphProp3) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcGraphProp2) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcextLem) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcGraphProp4) =>
% 132.59/22.92 ((
% 132.59/22.92 (subbreln) =>
% 132.59/22.92 ((
% 132.59/22.92 (eqbreln) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcext) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcext2) =>
% 132.59/22.92 ((
% 132.59/22.92 (ap2apEq1) =>
% 132.59/22.92 ((
% 132.59/22.92 (ap2apEq2) =>
% 132.59/22.92 ((
% 132.59/22.92 (beta1) =>
% 132.59/22.92 ((
% 132.59/22.92 (eta1) =>
% 132.59/22.92 ((
% 132.59/22.92 (lam2lamEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (beta2) =>
% 132.59/22.92 ((
% 132.59/22.92 (eta2) =>
% 132.59/22.92 ((
% 132.59/22.92 (iffalseProp1) =>
% 132.59/22.92 ((
% 132.59/22.92 (iffalseProp2) =>
% 132.59/22.92 ((
% 132.59/22.92 (iftrueProp1) =>
% 132.59/22.92 ((
% 132.59/22.92 (iftrueProp2) =>
% 132.59/22.92 ((
% 132.59/22.92 (ifSingleton) =>
% 132.59/22.92 ((
% 132.59/22.92 (ifp) =>
% 132.59/22.92 ((
% 132.59/22.92 (theeq) =>
% 132.59/22.92 ((
% 132.59/22.92 (iftrue) =>
% 132.59/22.92 ((
% 132.59/22.92 (iffalse) =>
% 132.59/22.92 ((
% 132.59/22.92 (iftrueorfalse) =>
% 132.59/22.92 ((
% 132.59/22.92 (binintersectT_lem) =>
% 132.59/22.92 ((
% 132.59/22.92 (binunionT_lem) =>
% 132.59/22.92 ((
% 132.59/22.92 (powersetT_lem) =>
% 132.59/22.92 ((
% 132.59/22.92 (setminusT_lem) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementT_lem) =>
% 132.59/22.92 ((
% 132.59/22.92 (setextT) =>
% 132.59/22.92 ((
% 132.59/22.92 (subsetTI) =>
% 132.59/22.92 ((
% 132.59/22.92 (powersetTI1) =>
% 132.59/22.92 ((
% 132.59/22.92 (powersetTE1) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementTI1) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementTE1) =>
% 132.59/22.92 ((
% 132.59/22.92 (binintersectTELcontra) =>
% 132.59/22.92 ((
% 132.59/22.92 (binintersectTERcontra) =>
% 132.59/22.92 ((
% 132.59/22.92 (contrasubsetT) =>
% 132.59/22.92 ((
% 132.59/22.92 (contrasubsetT1) =>
% 132.59/22.92 ((
% 132.59/22.92 (contrasubsetT2) =>
% 132.59/22.92 ((
% 132.59/22.92 (contrasubsetT3) =>
% 132.59/22.92 ((
% 132.59/22.92 (doubleComplementI1) =>
% 132.59/22.92 ((
% 132.59/22.92 (doubleComplementE1) =>
% 132.59/22.92 ((
% 132.59/22.92 (doubleComplementSub1) =>
% 132.59/22.92 ((
% 132.59/22.92 (doubleComplementSub2) =>
% 132.59/22.92 ((
% 132.59/22.92 (doubleComplementEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementTnotintersectT) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementImpComplementIntersect) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementSubsetComplementIntersect) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementInPowersetComplementIntersect) =>
% 132.59/22.92 ((
% 132.59/22.92 (contraSubsetComplement) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementTcontraSubset) =>
% 132.59/22.92 ((
% 132.59/22.92 (binunionTILcontra) =>
% 132.59/22.92 ((
% 132.59/22.92 (binunionTIRcontra) =>
% 132.59/22.92 ((
% 132.59/22.92 (inIntersectImpInUnion) =>
% 132.59/22.92 ((
% 132.59/22.92 (inIntersectImpInUnion2) =>
% 132.59/22.92 ((
% 132.59/22.92 (inIntersectImpInIntersectUnions) =>
% 132.59/22.92 ((
% 132.59/22.92 (intersectInPowersetIntersectUnions) =>
% 132.59/22.92 ((
% 132.59/22.92 (inComplementUnionImpNotIn1) =>
% 132.59/22.92 ((
% 132.59/22.92 (inComplementUnionImpInComplement1) =>
% 132.59/22.92 ((
% 132.59/22.92 (binunionTE) =>
% 132.59/22.92 ((
% 132.59/22.92 (binunionTEcontra) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan2a1) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementUnionInPowersetComplement) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan2a2) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan1a) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan1b) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan1) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan2a) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan2b2) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan2b) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan2) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz13rule0) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz13rule1) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz13rule2) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz13rule3) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz13rule4) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz1_1) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz1_2) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz1_3) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz1_4) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz1_5) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1all2) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1SetBreln1) =>
% 132.59/22.92 ((
% 132.59/22.92 (choice2fnsingleton) =>
% 132.59/22.92 ((
% 132.59/22.92 (setOfPairsIsBReln1) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1all1) =>
% 132.59/22.92 ((
% 132.59/22.92 (subbreln1) =>
% 132.59/22.92 ((
% 132.59/22.92 (eqbreln1) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1invprop) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1invI) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1invE) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1compprop) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1compI) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1compE) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1compEex) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1unionprop) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1unionIL) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1unionIR) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1unionI) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1unionE) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1unionEcases) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1unionCommutes) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz2Ex) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz2W) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz2A) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz2B) =>
% 132.59/22.92 ((
% 132.59/22.92 (image1Ex) =>
% 132.59/22.92 ((
% 132.59/22.92 (image1Ex1) =>
% 132.59/22.92 ((
% 132.59/22.92 (image1Equiv) =>
% 132.59/22.92 ((
% 132.59/22.92 (image1E) =>
% 132.59/22.92 ((
% 132.59/22.92 (image1I) =>
% 132.59/22.92 ((
% 132.59/22.92 (injFuncInInjFuncSet) =>
% 132.59/22.92 ((
% 132.59/22.92 (injFuncSetFuncIn) =>
% 132.59/22.92 ((
% 132.59/22.92 (injFuncSetFuncInj) =>
% 132.59/22.92 ((
% 132.59/22.92 (surjFuncSetFuncIn) =>
% 132.59/22.92 ((
% 132.59/22.92 (surjFuncSetFuncSurj) =>
% 132.59/22.92 ((
% 132.59/22.92 (leftInvIsSurj) =>
% 132.59/22.92 ((
% 132.59/22.92 (surjCantorThm) =>
% 132.59/22.92 ((
% 132.59/22.92 (foundation2) =>
% 132.59/22.92 ((
% 132.59/22.92 (notinself) =>
% 132.59/22.92 ((
% 132.59/22.92 (notinself2) =>
% 132.59/22.92 ((
% 132.59/22.92 (omegaSp) =>
% 132.59/22.92 ((
% 132.59/22.92 (omegaSclos) =>
% 132.59/22.92 ((
% 132.59/22.92 (peano0notS) =>
% 132.59/22.92 ((
% 132.59/22.92 (peanoSinj) =>
% 132.59/22.92 ((
% 132.59/22.92 (transitivesetOp1) =>
% 132.59/22.92 ((
% 132.59/22.92 (binintTransitive) =>
% 132.59/22.92 ((
% 132.59/22.92 (transitivesetOp2) =>
% 132.59/22.92 ((
% 132.59/22.92 (setunionTransitive) =>
% 132.59/22.92 ((
% 132.59/22.92 (ordinalMinLem1) =>
% 132.59/22.92 ((
% 132.59/22.92 (ordinalTransSet) =>
% 132.59/22.92 ((
% 132.59/22.92 (ordinalTransSet1) =>
% 132.59/22.92 ((
% 132.59/22.92 (setunionOrdinalLem1) =>
% 132.59/22.92 (ordinal @
% 132.59/22.92 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.59/22.92 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl906])).
% 132.59/22.92 thf(zip_derived_cl917, plain,
% 132.59/22.92 (~ (((upairset2IR) =>
% 132.59/22.92 (((binunionIR) =>
% 132.59/22.92 (((binunionEcases) =>
% 132.59/22.92 (((binunionE) =>
% 132.59/22.92 (((binunionLsub) =>
% 132.59/22.92 (((binunionRsub) =>
% 132.59/22.92 (((binintersectI) =>
% 132.59/22.92 (((binintersectSubset5) =>
% 132.59/22.92 (((binintersectEL) =>
% 132.59/22.92 (((binintersectLsub) =>
% 132.59/22.92 (((binintersectSubset2) =>
% 132.59/22.92 (((binintersectSubset3) =>
% 132.59/22.92 (((binintersectER) =>
% 132.59/22.92 (((disjointsetsI1) =>
% 132.59/22.92 (((binintersectRsub) =>
% 132.59/22.92 (((binintersectSubset4) =>
% 132.59/22.92 (((binintersectSubset1) =>
% 132.59/22.92 (((bs114d) =>
% 132.59/22.92 (((setminusI) =>
% 132.59/22.92 (((setminusEL) =>
% 132.59/22.92 (((setminusER) =>
% 132.59/22.92 (((setminusSubset2) =>
% 132.59/22.92 (((setminusERneg) =>
% 132.59/22.92 (((setminusELneg) =>
% 132.59/22.92 (((setminusILneg) =>
% 132.59/22.92 (((setminusIRneg) =>
% 132.59/22.92 (((setminusLsub) =>
% 132.59/22.92 (((setminusSubset1) =>
% 132.59/22.92 (((symdiffE) =>
% 132.59/22.92 (((symdiffI1) =>
% 132.59/22.92 ((
% 132.59/22.92 (symdiffI2) =>
% 132.59/22.92 ((
% 132.59/22.92 (symdiffIneg1) =>
% 132.59/22.92 ((
% 132.59/22.92 (symdiffIneg2) =>
% 132.59/22.92 ((
% 132.59/22.92 (secondinupair) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairIL) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairIR) =>
% 132.59/22.92 ((
% 132.59/22.92 (kpairiskpair) =>
% 132.59/22.92 ((
% 132.59/22.92 (kpairp) =>
% 132.59/22.92 ((
% 132.59/22.92 (singletonsubset) =>
% 132.59/22.92 ((
% 132.59/22.92 (singletoninpowerset) =>
% 132.59/22.92 ((
% 132.59/22.92 (singletoninpowunion) =>
% 132.59/22.92 ((
% 132.59/22.92 (upairset2E) =>
% 132.59/22.92 ((
% 132.59/22.92 (upairsubunion) =>
% 132.59/22.92 ((
% 132.59/22.92 (upairinpowunion) =>
% 132.59/22.92 ((
% 132.59/22.92 (ubforcartprodlem1) =>
% 132.59/22.92 ((
% 132.59/22.92 (ubforcartprodlem2) =>
% 132.59/22.92 ((
% 132.59/22.92 (ubforcartprodlem3) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodpairin) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodmempair1) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodmempair) =>
% 132.59/22.92 ((
% 132.59/22.92 (setunionE2) =>
% 132.59/22.92 ((
% 132.59/22.92 (setunionsingleton1) =>
% 132.59/22.92 ((
% 132.59/22.92 (setunionsingleton2) =>
% 132.59/22.92 ((
% 132.59/22.92 (setunionsingleton) =>
% 132.59/22.92 ((
% 132.59/22.92 (singletonprop) =>
% 132.59/22.92 ((
% 132.59/22.92 (ex1E1) =>
% 132.59/22.92 ((
% 132.59/22.92 (ex1I) =>
% 132.59/22.92 ((
% 132.59/22.92 (ex1I2) =>
% 132.59/22.92 ((
% 132.59/22.92 (singletonsuniq) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjL1) =>
% 132.59/22.92 ((
% 132.59/22.92 (kfstsingleton) =>
% 132.59/22.92 ((
% 132.59/22.92 (theprop) =>
% 132.59/22.92 ((
% 132.59/22.92 (kfstpairEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodfstin) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjL2) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjL) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjR11) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjR12) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjR1) =>
% 132.59/22.92 ((
% 132.59/22.92 (upairequniteq) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjR2) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjR) =>
% 132.59/22.92 ((
% 132.59/22.92 (ksndsingleton) =>
% 132.59/22.92 ((
% 132.59/22.92 (ksndpairEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (kpairsurjEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodsndin) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodpairmemEL) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodpairmemER) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodmempaircEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodfstpairEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodsndpairEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodpairsurjEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (dpsetconstrI) =>
% 132.59/22.92 ((
% 132.59/22.92 (dpsetconstrSub) =>
% 132.59/22.92 ((
% 132.59/22.92 (setOfPairsIsBReln) =>
% 132.59/22.92 ((
% 132.59/22.92 (dpsetconstrERa) =>
% 132.59/22.92 ((
% 132.59/22.92 (dpsetconstrEL1) =>
% 132.59/22.92 ((
% 132.59/22.92 (dpsetconstrEL2) =>
% 132.59/22.92 ((
% 132.59/22.92 (dpsetconstrER) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcImageSingleton) =>
% 132.59/22.92 ((
% 132.59/22.92 (apProp) =>
% 132.59/22.92 ((
% 132.59/22.92 (app) =>
% 132.59/22.92 ((
% 132.59/22.92 (infuncsetfunc) =>
% 132.59/22.92 ((
% 132.59/22.92 (ap2p) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcinfuncset) =>
% 132.59/22.92 ((
% 132.59/22.92 (lamProp) =>
% 132.59/22.92 ((
% 132.59/22.92 (lamp) =>
% 132.59/22.92 ((
% 132.59/22.92 (lam2p) =>
% 132.59/22.92 ((
% 132.59/22.92 (brelnall1) =>
% 132.59/22.92 ((
% 132.59/22.92 (brelnall2) =>
% 132.59/22.92 ((
% 132.59/22.92 (ex1E2) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcGraphProp1) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcGraphProp3) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcGraphProp2) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcextLem) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcGraphProp4) =>
% 132.59/22.92 ((
% 132.59/22.92 (subbreln) =>
% 132.59/22.92 ((
% 132.59/22.92 (eqbreln) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcext) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcext2) =>
% 132.59/22.92 ((
% 132.59/22.92 (ap2apEq1) =>
% 132.59/22.92 ((
% 132.59/22.92 (ap2apEq2) =>
% 132.59/22.92 ((
% 132.59/22.92 (beta1) =>
% 132.59/22.92 ((
% 132.59/22.92 (eta1) =>
% 132.59/22.92 ((
% 132.59/22.92 (lam2lamEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (beta2) =>
% 132.59/22.92 ((
% 132.59/22.92 (eta2) =>
% 132.59/22.92 ((
% 132.59/22.92 (iffalseProp1) =>
% 132.59/22.92 ((
% 132.59/22.92 (iffalseProp2) =>
% 132.59/22.92 ((
% 132.59/22.92 (iftrueProp1) =>
% 132.59/22.92 ((
% 132.59/22.92 (iftrueProp2) =>
% 132.59/22.92 ((
% 132.59/22.92 (ifSingleton) =>
% 132.59/22.92 ((
% 132.59/22.92 (ifp) =>
% 132.59/22.92 ((
% 132.59/22.92 (theeq) =>
% 132.59/22.92 ((
% 132.59/22.92 (iftrue) =>
% 132.59/22.92 ((
% 132.59/22.92 (iffalse) =>
% 132.59/22.92 ((
% 132.59/22.92 (iftrueorfalse) =>
% 132.59/22.92 ((
% 132.59/22.92 (binintersectT_lem) =>
% 132.59/22.92 ((
% 132.59/22.92 (binunionT_lem) =>
% 132.59/22.92 ((
% 132.59/22.92 (powersetT_lem) =>
% 132.59/22.92 ((
% 132.59/22.92 (setminusT_lem) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementT_lem) =>
% 132.59/22.92 ((
% 132.59/22.92 (setextT) =>
% 132.59/22.92 ((
% 132.59/22.92 (subsetTI) =>
% 132.59/22.92 ((
% 132.59/22.92 (powersetTI1) =>
% 132.59/22.92 ((
% 132.59/22.92 (powersetTE1) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementTI1) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementTE1) =>
% 132.59/22.92 ((
% 132.59/22.92 (binintersectTELcontra) =>
% 132.59/22.92 ((
% 132.59/22.92 (binintersectTERcontra) =>
% 132.59/22.92 ((
% 132.59/22.92 (contrasubsetT) =>
% 132.59/22.92 ((
% 132.59/22.92 (contrasubsetT1) =>
% 132.59/22.92 ((
% 132.59/22.92 (contrasubsetT2) =>
% 132.59/22.92 ((
% 132.59/22.92 (contrasubsetT3) =>
% 132.59/22.92 ((
% 132.59/22.92 (doubleComplementI1) =>
% 132.59/22.92 ((
% 132.59/22.92 (doubleComplementE1) =>
% 132.59/22.92 ((
% 132.59/22.92 (doubleComplementSub1) =>
% 132.59/22.92 ((
% 132.59/22.92 (doubleComplementSub2) =>
% 132.59/22.92 ((
% 132.59/22.92 (doubleComplementEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementTnotintersectT) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementImpComplementIntersect) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementSubsetComplementIntersect) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementInPowersetComplementIntersect) =>
% 132.59/22.92 ((
% 132.59/22.92 (contraSubsetComplement) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementTcontraSubset) =>
% 132.59/22.92 ((
% 132.59/22.92 (binunionTILcontra) =>
% 132.59/22.92 ((
% 132.59/22.92 (binunionTIRcontra) =>
% 132.59/22.92 ((
% 132.59/22.92 (inIntersectImpInUnion) =>
% 132.59/22.92 ((
% 132.59/22.92 (inIntersectImpInUnion2) =>
% 132.59/22.92 ((
% 132.59/22.92 (inIntersectImpInIntersectUnions) =>
% 132.59/22.92 ((
% 132.59/22.92 (intersectInPowersetIntersectUnions) =>
% 132.59/22.92 ((
% 132.59/22.92 (inComplementUnionImpNotIn1) =>
% 132.59/22.92 ((
% 132.59/22.92 (inComplementUnionImpInComplement1) =>
% 132.59/22.92 ((
% 132.59/22.92 (binunionTE) =>
% 132.59/22.92 ((
% 132.59/22.92 (binunionTEcontra) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan2a1) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementUnionInPowersetComplement) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan2a2) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan1a) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan1b) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan1) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan2a) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan2b2) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan2b) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan2) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz13rule0) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz13rule1) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz13rule2) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz13rule3) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz13rule4) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz1_1) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz1_2) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz1_3) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz1_4) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz1_5) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1all2) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1SetBreln1) =>
% 132.59/22.92 ((
% 132.59/22.92 (choice2fnsingleton) =>
% 132.59/22.92 ((
% 132.59/22.92 (setOfPairsIsBReln1) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1all1) =>
% 132.59/22.92 ((
% 132.59/22.92 (subbreln1) =>
% 132.59/22.92 ((
% 132.59/22.92 (eqbreln1) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1invprop) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1invI) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1invE) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1compprop) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1compI) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1compE) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1compEex) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1unionprop) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1unionIL) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1unionIR) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1unionI) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1unionE) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1unionEcases) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1unionCommutes) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz2Ex) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz2W) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz2A) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz2B) =>
% 132.59/22.92 ((
% 132.59/22.92 (image1Ex) =>
% 132.59/22.92 ((
% 132.59/22.92 (image1Ex1) =>
% 132.59/22.92 ((
% 132.59/22.92 (image1Equiv) =>
% 132.59/22.92 ((
% 132.59/22.92 (image1E) =>
% 132.59/22.92 ((
% 132.59/22.92 (image1I) =>
% 132.59/22.92 ((
% 132.59/22.92 (injFuncInInjFuncSet) =>
% 132.59/22.92 ((
% 132.59/22.92 (injFuncSetFuncIn) =>
% 132.59/22.92 ((
% 132.59/22.92 (injFuncSetFuncInj) =>
% 132.59/22.92 ((
% 132.59/22.92 (surjFuncSetFuncIn) =>
% 132.59/22.92 ((
% 132.59/22.92 (surjFuncSetFuncSurj) =>
% 132.59/22.92 ((
% 132.59/22.92 (leftInvIsSurj) =>
% 132.59/22.92 ((
% 132.59/22.92 (surjCantorThm) =>
% 132.59/22.92 ((
% 132.59/22.92 (foundation2) =>
% 132.59/22.92 ((
% 132.59/22.92 (notinself) =>
% 132.59/22.92 ((
% 132.59/22.92 (notinself2) =>
% 132.59/22.92 ((
% 132.59/22.92 (omegaSp) =>
% 132.59/22.92 ((
% 132.59/22.92 (omegaSclos) =>
% 132.59/22.92 ((
% 132.59/22.92 (peano0notS) =>
% 132.59/22.92 ((
% 132.59/22.92 (peanoSinj) =>
% 132.59/22.92 ((
% 132.59/22.92 (transitivesetOp1) =>
% 132.59/22.92 ((
% 132.59/22.92 (binintTransitive) =>
% 132.59/22.92 ((
% 132.59/22.92 (transitivesetOp2) =>
% 132.59/22.92 ((
% 132.59/22.92 (setunionTransitive) =>
% 132.59/22.92 ((
% 132.59/22.92 (ordinalMinLem1) =>
% 132.59/22.92 ((
% 132.59/22.92 (ordinalTransSet) =>
% 132.59/22.92 ((
% 132.59/22.92 (ordinalTransSet1) =>
% 132.59/22.92 ((
% 132.59/22.92 (setunionOrdinalLem1) =>
% 132.59/22.92 (ordinal @
% 132.59/22.92 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.59/22.92 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl911])).
% 132.59/22.92 thf(zip_derived_cl924, plain,
% 132.59/22.92 (~ (((binunionIR) =>
% 132.59/22.92 (((binunionEcases) =>
% 132.59/22.92 (((binunionE) =>
% 132.59/22.92 (((binunionLsub) =>
% 132.59/22.92 (((binunionRsub) =>
% 132.59/22.92 (((binintersectI) =>
% 132.59/22.92 (((binintersectSubset5) =>
% 132.59/22.92 (((binintersectEL) =>
% 132.59/22.92 (((binintersectLsub) =>
% 132.59/22.92 (((binintersectSubset2) =>
% 132.59/22.92 (((binintersectSubset3) =>
% 132.59/22.92 (((binintersectER) =>
% 132.59/22.92 (((disjointsetsI1) =>
% 132.59/22.92 (((binintersectRsub) =>
% 132.59/22.92 (((binintersectSubset4) =>
% 132.59/22.92 (((binintersectSubset1) =>
% 132.59/22.92 (((bs114d) =>
% 132.59/22.92 (((setminusI) =>
% 132.59/22.92 (((setminusEL) =>
% 132.59/22.92 (((setminusER) =>
% 132.59/22.92 (((setminusSubset2) =>
% 132.59/22.92 (((setminusERneg) =>
% 132.59/22.92 (((setminusELneg) =>
% 132.59/22.92 (((setminusILneg) =>
% 132.59/22.92 (((setminusIRneg) =>
% 132.59/22.92 (((setminusLsub) =>
% 132.59/22.92 (((setminusSubset1) =>
% 132.59/22.92 (((symdiffE) =>
% 132.59/22.92 (((symdiffI1) =>
% 132.59/22.92 (((symdiffI2) =>
% 132.59/22.92 ((
% 132.59/22.92 (symdiffIneg1) =>
% 132.59/22.92 ((
% 132.59/22.92 (symdiffIneg2) =>
% 132.59/22.92 ((
% 132.59/22.92 (secondinupair) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairIL) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairIR) =>
% 132.59/22.92 ((
% 132.59/22.92 (kpairiskpair) =>
% 132.59/22.92 ((
% 132.59/22.92 (kpairp) =>
% 132.59/22.92 ((
% 132.59/22.92 (singletonsubset) =>
% 132.59/22.92 ((
% 132.59/22.92 (singletoninpowerset) =>
% 132.59/22.92 ((
% 132.59/22.92 (singletoninpowunion) =>
% 132.59/22.92 ((
% 132.59/22.92 (upairset2E) =>
% 132.59/22.92 ((
% 132.59/22.92 (upairsubunion) =>
% 132.59/22.92 ((
% 132.59/22.92 (upairinpowunion) =>
% 132.59/22.92 ((
% 132.59/22.92 (ubforcartprodlem1) =>
% 132.59/22.92 ((
% 132.59/22.92 (ubforcartprodlem2) =>
% 132.59/22.92 ((
% 132.59/22.92 (ubforcartprodlem3) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodpairin) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodmempair1) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodmempair) =>
% 132.59/22.92 ((
% 132.59/22.92 (setunionE2) =>
% 132.59/22.92 ((
% 132.59/22.92 (setunionsingleton1) =>
% 132.59/22.92 ((
% 132.59/22.92 (setunionsingleton2) =>
% 132.59/22.92 ((
% 132.59/22.92 (setunionsingleton) =>
% 132.59/22.92 ((
% 132.59/22.92 (singletonprop) =>
% 132.59/22.92 ((
% 132.59/22.92 (ex1E1) =>
% 132.59/22.92 ((
% 132.59/22.92 (ex1I) =>
% 132.59/22.92 ((
% 132.59/22.92 (ex1I2) =>
% 132.59/22.92 ((
% 132.59/22.92 (singletonsuniq) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjL1) =>
% 132.59/22.92 ((
% 132.59/22.92 (kfstsingleton) =>
% 132.59/22.92 ((
% 132.59/22.92 (theprop) =>
% 132.59/22.92 ((
% 132.59/22.92 (kfstpairEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodfstin) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjL2) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjL) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjR11) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjR12) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjR1) =>
% 132.59/22.92 ((
% 132.59/22.92 (upairequniteq) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjR2) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjR) =>
% 132.59/22.92 ((
% 132.59/22.92 (ksndsingleton) =>
% 132.59/22.92 ((
% 132.59/22.92 (ksndpairEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (kpairsurjEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodsndin) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodpairmemEL) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodpairmemER) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodmempaircEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodfstpairEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodsndpairEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodpairsurjEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (dpsetconstrI) =>
% 132.59/22.92 ((
% 132.59/22.92 (dpsetconstrSub) =>
% 132.59/22.92 ((
% 132.59/22.92 (setOfPairsIsBReln) =>
% 132.59/22.92 ((
% 132.59/22.92 (dpsetconstrERa) =>
% 132.59/22.92 ((
% 132.59/22.92 (dpsetconstrEL1) =>
% 132.59/22.92 ((
% 132.59/22.92 (dpsetconstrEL2) =>
% 132.59/22.92 ((
% 132.59/22.92 (dpsetconstrER) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcImageSingleton) =>
% 132.59/22.92 ((
% 132.59/22.92 (apProp) =>
% 132.59/22.92 ((
% 132.59/22.92 (app) =>
% 132.59/22.92 ((
% 132.59/22.92 (infuncsetfunc) =>
% 132.59/22.92 ((
% 132.59/22.92 (ap2p) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcinfuncset) =>
% 132.59/22.92 ((
% 132.59/22.92 (lamProp) =>
% 132.59/22.92 ((
% 132.59/22.92 (lamp) =>
% 132.59/22.92 ((
% 132.59/22.92 (lam2p) =>
% 132.59/22.92 ((
% 132.59/22.92 (brelnall1) =>
% 132.59/22.92 ((
% 132.59/22.92 (brelnall2) =>
% 132.59/22.92 ((
% 132.59/22.92 (ex1E2) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcGraphProp1) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcGraphProp3) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcGraphProp2) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcextLem) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcGraphProp4) =>
% 132.59/22.92 ((
% 132.59/22.92 (subbreln) =>
% 132.59/22.92 ((
% 132.59/22.92 (eqbreln) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcext) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcext2) =>
% 132.59/22.92 ((
% 132.59/22.92 (ap2apEq1) =>
% 132.59/22.92 ((
% 132.59/22.92 (ap2apEq2) =>
% 132.59/22.92 ((
% 132.59/22.92 (beta1) =>
% 132.59/22.92 ((
% 132.59/22.92 (eta1) =>
% 132.59/22.92 ((
% 132.59/22.92 (lam2lamEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (beta2) =>
% 132.59/22.92 ((
% 132.59/22.92 (eta2) =>
% 132.59/22.92 ((
% 132.59/22.92 (iffalseProp1) =>
% 132.59/22.92 ((
% 132.59/22.92 (iffalseProp2) =>
% 132.59/22.92 ((
% 132.59/22.92 (iftrueProp1) =>
% 132.59/22.92 ((
% 132.59/22.92 (iftrueProp2) =>
% 132.59/22.92 ((
% 132.59/22.92 (ifSingleton) =>
% 132.59/22.92 ((
% 132.59/22.92 (ifp) =>
% 132.59/22.92 ((
% 132.59/22.92 (theeq) =>
% 132.59/22.92 ((
% 132.59/22.92 (iftrue) =>
% 132.59/22.92 ((
% 132.59/22.92 (iffalse) =>
% 132.59/22.92 ((
% 132.59/22.92 (iftrueorfalse) =>
% 132.59/22.92 ((
% 132.59/22.92 (binintersectT_lem) =>
% 132.59/22.92 ((
% 132.59/22.92 (binunionT_lem) =>
% 132.59/22.92 ((
% 132.59/22.92 (powersetT_lem) =>
% 132.59/22.92 ((
% 132.59/22.92 (setminusT_lem) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementT_lem) =>
% 132.59/22.92 ((
% 132.59/22.92 (setextT) =>
% 132.59/22.92 ((
% 132.59/22.92 (subsetTI) =>
% 132.59/22.92 ((
% 132.59/22.92 (powersetTI1) =>
% 132.59/22.92 ((
% 132.59/22.92 (powersetTE1) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementTI1) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementTE1) =>
% 132.59/22.92 ((
% 132.59/22.92 (binintersectTELcontra) =>
% 132.59/22.92 ((
% 132.59/22.92 (binintersectTERcontra) =>
% 132.59/22.92 ((
% 132.59/22.92 (contrasubsetT) =>
% 132.59/22.92 ((
% 132.59/22.92 (contrasubsetT1) =>
% 132.59/22.92 ((
% 132.59/22.92 (contrasubsetT2) =>
% 132.59/22.92 ((
% 132.59/22.92 (contrasubsetT3) =>
% 132.59/22.92 ((
% 132.59/22.92 (doubleComplementI1) =>
% 132.59/22.92 ((
% 132.59/22.92 (doubleComplementE1) =>
% 132.59/22.92 ((
% 132.59/22.92 (doubleComplementSub1) =>
% 132.59/22.92 ((
% 132.59/22.92 (doubleComplementSub2) =>
% 132.59/22.92 ((
% 132.59/22.92 (doubleComplementEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementTnotintersectT) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementImpComplementIntersect) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementSubsetComplementIntersect) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementInPowersetComplementIntersect) =>
% 132.59/22.92 ((
% 132.59/22.92 (contraSubsetComplement) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementTcontraSubset) =>
% 132.59/22.92 ((
% 132.59/22.92 (binunionTILcontra) =>
% 132.59/22.92 ((
% 132.59/22.92 (binunionTIRcontra) =>
% 132.59/22.92 ((
% 132.59/22.92 (inIntersectImpInUnion) =>
% 132.59/22.92 ((
% 132.59/22.92 (inIntersectImpInUnion2) =>
% 132.59/22.92 ((
% 132.59/22.92 (inIntersectImpInIntersectUnions) =>
% 132.59/22.92 ((
% 132.59/22.92 (intersectInPowersetIntersectUnions) =>
% 132.59/22.92 ((
% 132.59/22.92 (inComplementUnionImpNotIn1) =>
% 132.59/22.92 ((
% 132.59/22.92 (inComplementUnionImpInComplement1) =>
% 132.59/22.92 ((
% 132.59/22.92 (binunionTE) =>
% 132.59/22.92 ((
% 132.59/22.92 (binunionTEcontra) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan2a1) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementUnionInPowersetComplement) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan2a2) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan1a) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan1b) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan1) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan2a) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan2b2) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan2b) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan2) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz13rule0) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz13rule1) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz13rule2) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz13rule3) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz13rule4) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz1_1) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz1_2) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz1_3) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz1_4) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz1_5) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1all2) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1SetBreln1) =>
% 132.59/22.92 ((
% 132.59/22.92 (choice2fnsingleton) =>
% 132.59/22.92 ((
% 132.59/22.92 (setOfPairsIsBReln1) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1all1) =>
% 132.59/22.92 ((
% 132.59/22.92 (subbreln1) =>
% 132.59/22.92 ((
% 132.59/22.92 (eqbreln1) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1invprop) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1invI) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1invE) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1compprop) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1compI) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1compE) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1compEex) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1unionprop) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1unionIL) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1unionIR) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1unionI) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1unionE) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1unionEcases) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1unionCommutes) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz2Ex) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz2W) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz2A) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz2B) =>
% 132.59/22.92 ((
% 132.59/22.92 (image1Ex) =>
% 132.59/22.92 ((
% 132.59/22.92 (image1Ex1) =>
% 132.59/22.92 ((
% 132.59/22.92 (image1Equiv) =>
% 132.59/22.92 ((
% 132.59/22.92 (image1E) =>
% 132.59/22.92 ((
% 132.59/22.92 (image1I) =>
% 132.59/22.92 ((
% 132.59/22.92 (injFuncInInjFuncSet) =>
% 132.59/22.92 ((
% 132.59/22.92 (injFuncSetFuncIn) =>
% 132.59/22.92 ((
% 132.59/22.92 (injFuncSetFuncInj) =>
% 132.59/22.92 ((
% 132.59/22.92 (surjFuncSetFuncIn) =>
% 132.59/22.92 ((
% 132.59/22.92 (surjFuncSetFuncSurj) =>
% 132.59/22.92 ((
% 132.59/22.92 (leftInvIsSurj) =>
% 132.59/22.92 ((
% 132.59/22.92 (surjCantorThm) =>
% 132.59/22.92 ((
% 132.59/22.92 (foundation2) =>
% 132.59/22.92 ((
% 132.59/22.92 (notinself) =>
% 132.59/22.92 ((
% 132.59/22.92 (notinself2) =>
% 132.59/22.92 ((
% 132.59/22.92 (omegaSp) =>
% 132.59/22.92 ((
% 132.59/22.92 (omegaSclos) =>
% 132.59/22.92 ((
% 132.59/22.92 (peano0notS) =>
% 132.59/22.92 ((
% 132.59/22.92 (peanoSinj) =>
% 132.59/22.92 ((
% 132.59/22.92 (transitivesetOp1) =>
% 132.59/22.92 ((
% 132.59/22.92 (binintTransitive) =>
% 132.59/22.92 ((
% 132.59/22.92 (transitivesetOp2) =>
% 132.59/22.92 ((
% 132.59/22.92 (setunionTransitive) =>
% 132.59/22.92 ((
% 132.59/22.92 (ordinalMinLem1) =>
% 132.59/22.92 ((
% 132.59/22.92 (ordinalTransSet) =>
% 132.59/22.92 ((
% 132.59/22.92 (ordinalTransSet1) =>
% 132.59/22.92 ((
% 132.59/22.92 (setunionOrdinalLem1) =>
% 132.59/22.92 (ordinal @
% 132.59/22.92 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.59/22.92 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl917])).
% 132.59/22.92 thf(zip_derived_cl929, plain,
% 132.59/22.92 (~ (((binunionEcases) =>
% 132.59/22.92 (((binunionE) =>
% 132.59/22.92 (((binunionLsub) =>
% 132.59/22.92 (((binunionRsub) =>
% 132.59/22.92 (((binintersectI) =>
% 132.59/22.92 (((binintersectSubset5) =>
% 132.59/22.92 (((binintersectEL) =>
% 132.59/22.92 (((binintersectLsub) =>
% 132.59/22.92 (((binintersectSubset2) =>
% 132.59/22.92 (((binintersectSubset3) =>
% 132.59/22.92 (((binintersectER) =>
% 132.59/22.92 (((disjointsetsI1) =>
% 132.59/22.92 (((binintersectRsub) =>
% 132.59/22.92 (((binintersectSubset4) =>
% 132.59/22.92 (((binintersectSubset1) =>
% 132.59/22.92 (((bs114d) =>
% 132.59/22.92 (((setminusI) =>
% 132.59/22.92 (((setminusEL) =>
% 132.59/22.92 (((setminusER) =>
% 132.59/22.92 (((setminusSubset2) =>
% 132.59/22.92 (((setminusERneg) =>
% 132.59/22.92 (((setminusELneg) =>
% 132.59/22.92 (((setminusILneg) =>
% 132.59/22.92 (((setminusIRneg) =>
% 132.59/22.92 (((setminusLsub) =>
% 132.59/22.92 (((setminusSubset1) =>
% 132.59/22.92 (((symdiffE) =>
% 132.59/22.92 (((symdiffI1) =>
% 132.59/22.92 (((symdiffI2) =>
% 132.59/22.92 (((symdiffIneg1) =>
% 132.59/22.92 ((
% 132.59/22.92 (symdiffIneg2) =>
% 132.59/22.92 ((
% 132.59/22.92 (secondinupair) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairIL) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairIR) =>
% 132.59/22.92 ((
% 132.59/22.92 (kpairiskpair) =>
% 132.59/22.92 ((
% 132.59/22.92 (kpairp) =>
% 132.59/22.92 ((
% 132.59/22.92 (singletonsubset) =>
% 132.59/22.92 ((
% 132.59/22.92 (singletoninpowerset) =>
% 132.59/22.92 ((
% 132.59/22.92 (singletoninpowunion) =>
% 132.59/22.92 ((
% 132.59/22.92 (upairset2E) =>
% 132.59/22.92 ((
% 132.59/22.92 (upairsubunion) =>
% 132.59/22.92 ((
% 132.59/22.92 (upairinpowunion) =>
% 132.59/22.92 ((
% 132.59/22.92 (ubforcartprodlem1) =>
% 132.59/22.92 ((
% 132.59/22.92 (ubforcartprodlem2) =>
% 132.59/22.92 ((
% 132.59/22.92 (ubforcartprodlem3) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodpairin) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodmempair1) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodmempair) =>
% 132.59/22.92 ((
% 132.59/22.92 (setunionE2) =>
% 132.59/22.92 ((
% 132.59/22.92 (setunionsingleton1) =>
% 132.59/22.92 ((
% 132.59/22.92 (setunionsingleton2) =>
% 132.59/22.92 ((
% 132.59/22.92 (setunionsingleton) =>
% 132.59/22.92 ((
% 132.59/22.92 (singletonprop) =>
% 132.59/22.92 ((
% 132.59/22.92 (ex1E1) =>
% 132.59/22.92 ((
% 132.59/22.92 (ex1I) =>
% 132.59/22.92 ((
% 132.59/22.92 (ex1I2) =>
% 132.59/22.92 ((
% 132.59/22.92 (singletonsuniq) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjL1) =>
% 132.59/22.92 ((
% 132.59/22.92 (kfstsingleton) =>
% 132.59/22.92 ((
% 132.59/22.92 (theprop) =>
% 132.59/22.92 ((
% 132.59/22.92 (kfstpairEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodfstin) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjL2) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjL) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjR11) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjR12) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjR1) =>
% 132.59/22.92 ((
% 132.59/22.92 (upairequniteq) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjR2) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjR) =>
% 132.59/22.92 ((
% 132.59/22.92 (ksndsingleton) =>
% 132.59/22.92 ((
% 132.59/22.92 (ksndpairEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (kpairsurjEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodsndin) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodpairmemEL) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodpairmemER) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodmempaircEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodfstpairEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodsndpairEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodpairsurjEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (dpsetconstrI) =>
% 132.59/22.92 ((
% 132.59/22.92 (dpsetconstrSub) =>
% 132.59/22.92 ((
% 132.59/22.92 (setOfPairsIsBReln) =>
% 132.59/22.92 ((
% 132.59/22.92 (dpsetconstrERa) =>
% 132.59/22.92 ((
% 132.59/22.92 (dpsetconstrEL1) =>
% 132.59/22.92 ((
% 132.59/22.92 (dpsetconstrEL2) =>
% 132.59/22.92 ((
% 132.59/22.92 (dpsetconstrER) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcImageSingleton) =>
% 132.59/22.92 ((
% 132.59/22.92 (apProp) =>
% 132.59/22.92 ((
% 132.59/22.92 (app) =>
% 132.59/22.92 ((
% 132.59/22.92 (infuncsetfunc) =>
% 132.59/22.92 ((
% 132.59/22.92 (ap2p) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcinfuncset) =>
% 132.59/22.92 ((
% 132.59/22.92 (lamProp) =>
% 132.59/22.92 ((
% 132.59/22.92 (lamp) =>
% 132.59/22.92 ((
% 132.59/22.92 (lam2p) =>
% 132.59/22.92 ((
% 132.59/22.92 (brelnall1) =>
% 132.59/22.92 ((
% 132.59/22.92 (brelnall2) =>
% 132.59/22.92 ((
% 132.59/22.92 (ex1E2) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcGraphProp1) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcGraphProp3) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcGraphProp2) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcextLem) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcGraphProp4) =>
% 132.59/22.92 ((
% 132.59/22.92 (subbreln) =>
% 132.59/22.92 ((
% 132.59/22.92 (eqbreln) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcext) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcext2) =>
% 132.59/22.92 ((
% 132.59/22.92 (ap2apEq1) =>
% 132.59/22.92 ((
% 132.59/22.92 (ap2apEq2) =>
% 132.59/22.92 ((
% 132.59/22.92 (beta1) =>
% 132.59/22.92 ((
% 132.59/22.92 (eta1) =>
% 132.59/22.92 ((
% 132.59/22.92 (lam2lamEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (beta2) =>
% 132.59/22.92 ((
% 132.59/22.92 (eta2) =>
% 132.59/22.92 ((
% 132.59/22.92 (iffalseProp1) =>
% 132.59/22.92 ((
% 132.59/22.92 (iffalseProp2) =>
% 132.59/22.92 ((
% 132.59/22.92 (iftrueProp1) =>
% 132.59/22.92 ((
% 132.59/22.92 (iftrueProp2) =>
% 132.59/22.92 ((
% 132.59/22.92 (ifSingleton) =>
% 132.59/22.92 ((
% 132.59/22.92 (ifp) =>
% 132.59/22.92 ((
% 132.59/22.92 (theeq) =>
% 132.59/22.92 ((
% 132.59/22.92 (iftrue) =>
% 132.59/22.92 ((
% 132.59/22.92 (iffalse) =>
% 132.59/22.92 ((
% 132.59/22.92 (iftrueorfalse) =>
% 132.59/22.92 ((
% 132.59/22.92 (binintersectT_lem) =>
% 132.59/22.92 ((
% 132.59/22.92 (binunionT_lem) =>
% 132.59/22.92 ((
% 132.59/22.92 (powersetT_lem) =>
% 132.59/22.92 ((
% 132.59/22.92 (setminusT_lem) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementT_lem) =>
% 132.59/22.92 ((
% 132.59/22.92 (setextT) =>
% 132.59/22.92 ((
% 132.59/22.92 (subsetTI) =>
% 132.59/22.92 ((
% 132.59/22.92 (powersetTI1) =>
% 132.59/22.92 ((
% 132.59/22.92 (powersetTE1) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementTI1) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementTE1) =>
% 132.59/22.92 ((
% 132.59/22.92 (binintersectTELcontra) =>
% 132.59/22.92 ((
% 132.59/22.92 (binintersectTERcontra) =>
% 132.59/22.92 ((
% 132.59/22.92 (contrasubsetT) =>
% 132.59/22.92 ((
% 132.59/22.92 (contrasubsetT1) =>
% 132.59/22.92 ((
% 132.59/22.92 (contrasubsetT2) =>
% 132.59/22.92 ((
% 132.59/22.92 (contrasubsetT3) =>
% 132.59/22.92 ((
% 132.59/22.92 (doubleComplementI1) =>
% 132.59/22.92 ((
% 132.59/22.92 (doubleComplementE1) =>
% 132.59/22.92 ((
% 132.59/22.92 (doubleComplementSub1) =>
% 132.59/22.92 ((
% 132.59/22.92 (doubleComplementSub2) =>
% 132.59/22.92 ((
% 132.59/22.92 (doubleComplementEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementTnotintersectT) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementImpComplementIntersect) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementSubsetComplementIntersect) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementInPowersetComplementIntersect) =>
% 132.59/22.92 ((
% 132.59/22.92 (contraSubsetComplement) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementTcontraSubset) =>
% 132.59/22.92 ((
% 132.59/22.92 (binunionTILcontra) =>
% 132.59/22.92 ((
% 132.59/22.92 (binunionTIRcontra) =>
% 132.59/22.92 ((
% 132.59/22.92 (inIntersectImpInUnion) =>
% 132.59/22.92 ((
% 132.59/22.92 (inIntersectImpInUnion2) =>
% 132.59/22.92 ((
% 132.59/22.92 (inIntersectImpInIntersectUnions) =>
% 132.59/22.92 ((
% 132.59/22.92 (intersectInPowersetIntersectUnions) =>
% 132.59/22.92 ((
% 132.59/22.92 (inComplementUnionImpNotIn1) =>
% 132.59/22.92 ((
% 132.59/22.92 (inComplementUnionImpInComplement1) =>
% 132.59/22.92 ((
% 132.59/22.92 (binunionTE) =>
% 132.59/22.92 ((
% 132.59/22.92 (binunionTEcontra) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan2a1) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementUnionInPowersetComplement) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan2a2) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan1a) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan1b) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan1) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan2a) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan2b2) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan2b) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan2) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz13rule0) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz13rule1) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz13rule2) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz13rule3) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz13rule4) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz1_1) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz1_2) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz1_3) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz1_4) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz1_5) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1all2) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1SetBreln1) =>
% 132.59/22.92 ((
% 132.59/22.92 (choice2fnsingleton) =>
% 132.59/22.92 ((
% 132.59/22.92 (setOfPairsIsBReln1) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1all1) =>
% 132.59/22.92 ((
% 132.59/22.92 (subbreln1) =>
% 132.59/22.92 ((
% 132.59/22.92 (eqbreln1) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1invprop) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1invI) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1invE) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1compprop) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1compI) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1compE) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1compEex) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1unionprop) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1unionIL) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1unionIR) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1unionI) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1unionE) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1unionEcases) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1unionCommutes) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz2Ex) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz2W) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz2A) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz2B) =>
% 132.59/22.92 ((
% 132.59/22.92 (image1Ex) =>
% 132.59/22.92 ((
% 132.59/22.92 (image1Ex1) =>
% 132.59/22.92 ((
% 132.59/22.92 (image1Equiv) =>
% 132.59/22.92 ((
% 132.59/22.92 (image1E) =>
% 132.59/22.92 ((
% 132.59/22.92 (image1I) =>
% 132.59/22.92 ((
% 132.59/22.92 (injFuncInInjFuncSet) =>
% 132.59/22.92 ((
% 132.59/22.92 (injFuncSetFuncIn) =>
% 132.59/22.92 ((
% 132.59/22.92 (injFuncSetFuncInj) =>
% 132.59/22.92 ((
% 132.59/22.92 (surjFuncSetFuncIn) =>
% 132.59/22.92 ((
% 132.59/22.92 (surjFuncSetFuncSurj) =>
% 132.59/22.92 ((
% 132.59/22.92 (leftInvIsSurj) =>
% 132.59/22.92 ((
% 132.59/22.92 (surjCantorThm) =>
% 132.59/22.92 ((
% 132.59/22.92 (foundation2) =>
% 132.59/22.92 ((
% 132.59/22.92 (notinself) =>
% 132.59/22.92 ((
% 132.59/22.92 (notinself2) =>
% 132.59/22.92 ((
% 132.59/22.92 (omegaSp) =>
% 132.59/22.92 ((
% 132.59/22.92 (omegaSclos) =>
% 132.59/22.92 ((
% 132.59/22.92 (peano0notS) =>
% 132.59/22.92 ((
% 132.59/22.92 (peanoSinj) =>
% 132.59/22.92 ((
% 132.59/22.92 (transitivesetOp1) =>
% 132.59/22.92 ((
% 132.59/22.92 (binintTransitive) =>
% 132.59/22.92 ((
% 132.59/22.92 (transitivesetOp2) =>
% 132.59/22.92 ((
% 132.59/22.92 (setunionTransitive) =>
% 132.59/22.92 ((
% 132.59/22.92 (ordinalMinLem1) =>
% 132.59/22.92 ((
% 132.59/22.92 (ordinalTransSet) =>
% 132.59/22.92 ((
% 132.59/22.92 (ordinalTransSet1) =>
% 132.59/22.92 ((
% 132.59/22.92 (setunionOrdinalLem1) =>
% 132.59/22.92 (ordinal @
% 132.59/22.92 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.59/22.92 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl924])).
% 132.59/22.92 thf(zip_derived_cl934, plain,
% 132.59/22.92 (~ (((binunionE) =>
% 132.59/22.92 (((binunionLsub) =>
% 132.59/22.92 (((binunionRsub) =>
% 132.59/22.92 (((binintersectI) =>
% 132.59/22.92 (((binintersectSubset5) =>
% 132.59/22.92 (((binintersectEL) =>
% 132.59/22.92 (((binintersectLsub) =>
% 132.59/22.92 (((binintersectSubset2) =>
% 132.59/22.92 (((binintersectSubset3) =>
% 132.59/22.92 (((binintersectER) =>
% 132.59/22.92 (((disjointsetsI1) =>
% 132.59/22.92 (((binintersectRsub) =>
% 132.59/22.92 (((binintersectSubset4) =>
% 132.59/22.92 (((binintersectSubset1) =>
% 132.59/22.92 (((bs114d) =>
% 132.59/22.92 (((setminusI) =>
% 132.59/22.92 (((setminusEL) =>
% 132.59/22.92 (((setminusER) =>
% 132.59/22.92 (((setminusSubset2) =>
% 132.59/22.92 (((setminusERneg) =>
% 132.59/22.92 (((setminusELneg) =>
% 132.59/22.92 (((setminusILneg) =>
% 132.59/22.92 (((setminusIRneg) =>
% 132.59/22.92 (((setminusLsub) =>
% 132.59/22.92 (((setminusSubset1) =>
% 132.59/22.92 (((symdiffE) =>
% 132.59/22.92 (((symdiffI1) =>
% 132.59/22.92 (((symdiffI2) =>
% 132.59/22.92 (((symdiffIneg1) =>
% 132.59/22.92 (((symdiffIneg2) =>
% 132.59/22.92 ((
% 132.59/22.92 (secondinupair) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairIL) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairIR) =>
% 132.59/22.92 ((
% 132.59/22.92 (kpairiskpair) =>
% 132.59/22.92 ((
% 132.59/22.92 (kpairp) =>
% 132.59/22.92 ((
% 132.59/22.92 (singletonsubset) =>
% 132.59/22.92 ((
% 132.59/22.92 (singletoninpowerset) =>
% 132.59/22.92 ((
% 132.59/22.92 (singletoninpowunion) =>
% 132.59/22.92 ((
% 132.59/22.92 (upairset2E) =>
% 132.59/22.92 ((
% 132.59/22.92 (upairsubunion) =>
% 132.59/22.92 ((
% 132.59/22.92 (upairinpowunion) =>
% 132.59/22.92 ((
% 132.59/22.92 (ubforcartprodlem1) =>
% 132.59/22.92 ((
% 132.59/22.92 (ubforcartprodlem2) =>
% 132.59/22.92 ((
% 132.59/22.92 (ubforcartprodlem3) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodpairin) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodmempair1) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodmempair) =>
% 132.59/22.92 ((
% 132.59/22.92 (setunionE2) =>
% 132.59/22.92 ((
% 132.59/22.92 (setunionsingleton1) =>
% 132.59/22.92 ((
% 132.59/22.92 (setunionsingleton2) =>
% 132.59/22.92 ((
% 132.59/22.92 (setunionsingleton) =>
% 132.59/22.92 ((
% 132.59/22.92 (singletonprop) =>
% 132.59/22.92 ((
% 132.59/22.92 (ex1E1) =>
% 132.59/22.92 ((
% 132.59/22.92 (ex1I) =>
% 132.59/22.92 ((
% 132.59/22.92 (ex1I2) =>
% 132.59/22.92 ((
% 132.59/22.92 (singletonsuniq) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjL1) =>
% 132.59/22.92 ((
% 132.59/22.92 (kfstsingleton) =>
% 132.59/22.92 ((
% 132.59/22.92 (theprop) =>
% 132.59/22.92 ((
% 132.59/22.92 (kfstpairEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodfstin) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjL2) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjL) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjR11) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjR12) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjR1) =>
% 132.59/22.92 ((
% 132.59/22.92 (upairequniteq) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjR2) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjR) =>
% 132.59/22.92 ((
% 132.59/22.92 (ksndsingleton) =>
% 132.59/22.92 ((
% 132.59/22.92 (ksndpairEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (kpairsurjEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodsndin) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodpairmemEL) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodpairmemER) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodmempaircEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodfstpairEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodsndpairEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodpairsurjEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (dpsetconstrI) =>
% 132.59/22.92 ((
% 132.59/22.92 (dpsetconstrSub) =>
% 132.59/22.92 ((
% 132.59/22.92 (setOfPairsIsBReln) =>
% 132.59/22.92 ((
% 132.59/22.92 (dpsetconstrERa) =>
% 132.59/22.92 ((
% 132.59/22.92 (dpsetconstrEL1) =>
% 132.59/22.92 ((
% 132.59/22.92 (dpsetconstrEL2) =>
% 132.59/22.92 ((
% 132.59/22.92 (dpsetconstrER) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcImageSingleton) =>
% 132.59/22.92 ((
% 132.59/22.92 (apProp) =>
% 132.59/22.92 ((
% 132.59/22.92 (app) =>
% 132.59/22.92 ((
% 132.59/22.92 (infuncsetfunc) =>
% 132.59/22.92 ((
% 132.59/22.92 (ap2p) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcinfuncset) =>
% 132.59/22.92 ((
% 132.59/22.92 (lamProp) =>
% 132.59/22.92 ((
% 132.59/22.92 (lamp) =>
% 132.59/22.92 ((
% 132.59/22.92 (lam2p) =>
% 132.59/22.92 ((
% 132.59/22.92 (brelnall1) =>
% 132.59/22.92 ((
% 132.59/22.92 (brelnall2) =>
% 132.59/22.92 ((
% 132.59/22.92 (ex1E2) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcGraphProp1) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcGraphProp3) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcGraphProp2) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcextLem) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcGraphProp4) =>
% 132.59/22.92 ((
% 132.59/22.92 (subbreln) =>
% 132.59/22.92 ((
% 132.59/22.92 (eqbreln) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcext) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcext2) =>
% 132.59/22.92 ((
% 132.59/22.92 (ap2apEq1) =>
% 132.59/22.92 ((
% 132.59/22.92 (ap2apEq2) =>
% 132.59/22.92 ((
% 132.59/22.92 (beta1) =>
% 132.59/22.92 ((
% 132.59/22.92 (eta1) =>
% 132.59/22.92 ((
% 132.59/22.92 (lam2lamEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (beta2) =>
% 132.59/22.92 ((
% 132.59/22.92 (eta2) =>
% 132.59/22.92 ((
% 132.59/22.92 (iffalseProp1) =>
% 132.59/22.92 ((
% 132.59/22.92 (iffalseProp2) =>
% 132.59/22.92 ((
% 132.59/22.92 (iftrueProp1) =>
% 132.59/22.92 ((
% 132.59/22.92 (iftrueProp2) =>
% 132.59/22.92 ((
% 132.59/22.92 (ifSingleton) =>
% 132.59/22.92 ((
% 132.59/22.92 (ifp) =>
% 132.59/22.92 ((
% 132.59/22.92 (theeq) =>
% 132.59/22.92 ((
% 132.59/22.92 (iftrue) =>
% 132.59/22.92 ((
% 132.59/22.92 (iffalse) =>
% 132.59/22.92 ((
% 132.59/22.92 (iftrueorfalse) =>
% 132.59/22.92 ((
% 132.59/22.92 (binintersectT_lem) =>
% 132.59/22.92 ((
% 132.59/22.92 (binunionT_lem) =>
% 132.59/22.92 ((
% 132.59/22.92 (powersetT_lem) =>
% 132.59/22.92 ((
% 132.59/22.92 (setminusT_lem) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementT_lem) =>
% 132.59/22.92 ((
% 132.59/22.92 (setextT) =>
% 132.59/22.92 ((
% 132.59/22.92 (subsetTI) =>
% 132.59/22.92 ((
% 132.59/22.92 (powersetTI1) =>
% 132.59/22.92 ((
% 132.59/22.92 (powersetTE1) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementTI1) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementTE1) =>
% 132.59/22.92 ((
% 132.59/22.92 (binintersectTELcontra) =>
% 132.59/22.92 ((
% 132.59/22.92 (binintersectTERcontra) =>
% 132.59/22.92 ((
% 132.59/22.92 (contrasubsetT) =>
% 132.59/22.92 ((
% 132.59/22.92 (contrasubsetT1) =>
% 132.59/22.92 ((
% 132.59/22.92 (contrasubsetT2) =>
% 132.59/22.92 ((
% 132.59/22.92 (contrasubsetT3) =>
% 132.59/22.92 ((
% 132.59/22.92 (doubleComplementI1) =>
% 132.59/22.92 ((
% 132.59/22.92 (doubleComplementE1) =>
% 132.59/22.92 ((
% 132.59/22.92 (doubleComplementSub1) =>
% 132.59/22.92 ((
% 132.59/22.92 (doubleComplementSub2) =>
% 132.59/22.92 ((
% 132.59/22.92 (doubleComplementEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementTnotintersectT) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementImpComplementIntersect) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementSubsetComplementIntersect) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementInPowersetComplementIntersect) =>
% 132.59/22.92 ((
% 132.59/22.92 (contraSubsetComplement) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementTcontraSubset) =>
% 132.59/22.92 ((
% 132.59/22.92 (binunionTILcontra) =>
% 132.59/22.92 ((
% 132.59/22.92 (binunionTIRcontra) =>
% 132.59/22.92 ((
% 132.59/22.92 (inIntersectImpInUnion) =>
% 132.59/22.92 ((
% 132.59/22.92 (inIntersectImpInUnion2) =>
% 132.59/22.92 ((
% 132.59/22.92 (inIntersectImpInIntersectUnions) =>
% 132.59/22.92 ((
% 132.59/22.92 (intersectInPowersetIntersectUnions) =>
% 132.59/22.92 ((
% 132.59/22.92 (inComplementUnionImpNotIn1) =>
% 132.59/22.92 ((
% 132.59/22.92 (inComplementUnionImpInComplement1) =>
% 132.59/22.92 ((
% 132.59/22.92 (binunionTE) =>
% 132.59/22.92 ((
% 132.59/22.92 (binunionTEcontra) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan2a1) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementUnionInPowersetComplement) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan2a2) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan1a) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan1b) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan1) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan2a) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan2b2) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan2b) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan2) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz13rule0) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz13rule1) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz13rule2) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz13rule3) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz13rule4) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz1_1) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz1_2) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz1_3) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz1_4) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz1_5) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1all2) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1SetBreln1) =>
% 132.59/22.92 ((
% 132.59/22.92 (choice2fnsingleton) =>
% 132.59/22.92 ((
% 132.59/22.92 (setOfPairsIsBReln1) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1all1) =>
% 132.59/22.92 ((
% 132.59/22.92 (subbreln1) =>
% 132.59/22.92 ((
% 132.59/22.92 (eqbreln1) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1invprop) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1invI) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1invE) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1compprop) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1compI) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1compE) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1compEex) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1unionprop) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1unionIL) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1unionIR) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1unionI) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1unionE) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1unionEcases) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1unionCommutes) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz2Ex) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz2W) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz2A) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz2B) =>
% 132.59/22.92 ((
% 132.59/22.92 (image1Ex) =>
% 132.59/22.92 ((
% 132.59/22.92 (image1Ex1) =>
% 132.59/22.92 ((
% 132.59/22.92 (image1Equiv) =>
% 132.59/22.92 ((
% 132.59/22.92 (image1E) =>
% 132.59/22.92 ((
% 132.59/22.92 (image1I) =>
% 132.59/22.92 ((
% 132.59/22.92 (injFuncInInjFuncSet) =>
% 132.59/22.92 ((
% 132.59/22.92 (injFuncSetFuncIn) =>
% 132.59/22.92 ((
% 132.59/22.92 (injFuncSetFuncInj) =>
% 132.59/22.92 ((
% 132.59/22.92 (surjFuncSetFuncIn) =>
% 132.59/22.92 ((
% 132.59/22.92 (surjFuncSetFuncSurj) =>
% 132.59/22.92 ((
% 132.59/22.92 (leftInvIsSurj) =>
% 132.59/22.92 ((
% 132.59/22.92 (surjCantorThm) =>
% 132.59/22.92 ((
% 132.59/22.92 (foundation2) =>
% 132.59/22.92 ((
% 132.59/22.92 (notinself) =>
% 132.59/22.92 ((
% 132.59/22.92 (notinself2) =>
% 132.59/22.92 ((
% 132.59/22.92 (omegaSp) =>
% 132.59/22.92 ((
% 132.59/22.92 (omegaSclos) =>
% 132.59/22.92 ((
% 132.59/22.92 (peano0notS) =>
% 132.59/22.92 ((
% 132.59/22.92 (peanoSinj) =>
% 132.59/22.92 ((
% 132.59/22.92 (transitivesetOp1) =>
% 132.59/22.92 ((
% 132.59/22.92 (binintTransitive) =>
% 132.59/22.92 ((
% 132.59/22.92 (transitivesetOp2) =>
% 132.59/22.92 ((
% 132.59/22.92 (setunionTransitive) =>
% 132.59/22.92 ((
% 132.59/22.92 (ordinalMinLem1) =>
% 132.59/22.92 ((
% 132.59/22.92 (ordinalTransSet) =>
% 132.59/22.92 ((
% 132.59/22.92 (ordinalTransSet1) =>
% 132.59/22.92 ((
% 132.59/22.92 (setunionOrdinalLem1) =>
% 132.59/22.92 (ordinal @
% 132.59/22.92 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.59/22.92 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl929])).
% 132.59/22.92 thf(zip_derived_cl940, plain,
% 132.59/22.92 (~ (((binunionLsub) =>
% 132.59/22.92 (((binunionRsub) =>
% 132.59/22.92 (((binintersectI) =>
% 132.59/22.92 (((binintersectSubset5) =>
% 132.59/22.92 (((binintersectEL) =>
% 132.59/22.92 (((binintersectLsub) =>
% 132.59/22.92 (((binintersectSubset2) =>
% 132.59/22.92 (((binintersectSubset3) =>
% 132.59/22.92 (((binintersectER) =>
% 132.59/22.92 (((disjointsetsI1) =>
% 132.59/22.92 (((binintersectRsub) =>
% 132.59/22.92 (((binintersectSubset4) =>
% 132.59/22.92 (((binintersectSubset1) =>
% 132.59/22.92 (((bs114d) =>
% 132.59/22.92 (((setminusI) =>
% 132.59/22.92 (((setminusEL) =>
% 132.59/22.92 (((setminusER) =>
% 132.59/22.92 (((setminusSubset2) =>
% 132.59/22.92 (((setminusERneg) =>
% 132.59/22.92 (((setminusELneg) =>
% 132.59/22.92 (((setminusILneg) =>
% 132.59/22.92 (((setminusIRneg) =>
% 132.59/22.92 (((setminusLsub) =>
% 132.59/22.92 (((setminusSubset1) =>
% 132.59/22.92 (((symdiffE) =>
% 132.59/22.92 (((symdiffI1) =>
% 132.59/22.92 (((symdiffI2) =>
% 132.59/22.92 (((symdiffIneg1) =>
% 132.59/22.92 (((symdiffIneg2) =>
% 132.59/22.92 (((secondinupair) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairIL) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairIR) =>
% 132.59/22.92 ((
% 132.59/22.92 (kpairiskpair) =>
% 132.59/22.92 ((
% 132.59/22.92 (kpairp) =>
% 132.59/22.92 ((
% 132.59/22.92 (singletonsubset) =>
% 132.59/22.92 ((
% 132.59/22.92 (singletoninpowerset) =>
% 132.59/22.92 ((
% 132.59/22.92 (singletoninpowunion) =>
% 132.59/22.92 ((
% 132.59/22.92 (upairset2E) =>
% 132.59/22.92 ((
% 132.59/22.92 (upairsubunion) =>
% 132.59/22.92 ((
% 132.59/22.92 (upairinpowunion) =>
% 132.59/22.92 ((
% 132.59/22.92 (ubforcartprodlem1) =>
% 132.59/22.92 ((
% 132.59/22.92 (ubforcartprodlem2) =>
% 132.59/22.92 ((
% 132.59/22.92 (ubforcartprodlem3) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodpairin) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodmempair1) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodmempair) =>
% 132.59/22.92 ((
% 132.59/22.92 (setunionE2) =>
% 132.59/22.92 ((
% 132.59/22.92 (setunionsingleton1) =>
% 132.59/22.92 ((
% 132.59/22.92 (setunionsingleton2) =>
% 132.59/22.92 ((
% 132.59/22.92 (setunionsingleton) =>
% 132.59/22.92 ((
% 132.59/22.92 (singletonprop) =>
% 132.59/22.92 ((
% 132.59/22.92 (ex1E1) =>
% 132.59/22.92 ((
% 132.59/22.92 (ex1I) =>
% 132.59/22.92 ((
% 132.59/22.92 (ex1I2) =>
% 132.59/22.92 ((
% 132.59/22.92 (singletonsuniq) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjL1) =>
% 132.59/22.92 ((
% 132.59/22.92 (kfstsingleton) =>
% 132.59/22.92 ((
% 132.59/22.92 (theprop) =>
% 132.59/22.92 ((
% 132.59/22.92 (kfstpairEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodfstin) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjL2) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjL) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjR11) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjR12) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjR1) =>
% 132.59/22.92 ((
% 132.59/22.92 (upairequniteq) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjR2) =>
% 132.59/22.92 ((
% 132.59/22.92 (setukpairinjR) =>
% 132.59/22.92 ((
% 132.59/22.92 (ksndsingleton) =>
% 132.59/22.92 ((
% 132.59/22.92 (ksndpairEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (kpairsurjEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodsndin) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodpairmemEL) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodpairmemER) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodmempaircEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodfstpairEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodsndpairEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (cartprodpairsurjEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (dpsetconstrI) =>
% 132.59/22.92 ((
% 132.59/22.92 (dpsetconstrSub) =>
% 132.59/22.92 ((
% 132.59/22.92 (setOfPairsIsBReln) =>
% 132.59/22.92 ((
% 132.59/22.92 (dpsetconstrERa) =>
% 132.59/22.92 ((
% 132.59/22.92 (dpsetconstrEL1) =>
% 132.59/22.92 ((
% 132.59/22.92 (dpsetconstrEL2) =>
% 132.59/22.92 ((
% 132.59/22.92 (dpsetconstrER) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcImageSingleton) =>
% 132.59/22.92 ((
% 132.59/22.92 (apProp) =>
% 132.59/22.92 ((
% 132.59/22.92 (app) =>
% 132.59/22.92 ((
% 132.59/22.92 (infuncsetfunc) =>
% 132.59/22.92 ((
% 132.59/22.92 (ap2p) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcinfuncset) =>
% 132.59/22.92 ((
% 132.59/22.92 (lamProp) =>
% 132.59/22.92 ((
% 132.59/22.92 (lamp) =>
% 132.59/22.92 ((
% 132.59/22.92 (lam2p) =>
% 132.59/22.92 ((
% 132.59/22.92 (brelnall1) =>
% 132.59/22.92 ((
% 132.59/22.92 (brelnall2) =>
% 132.59/22.92 ((
% 132.59/22.92 (ex1E2) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcGraphProp1) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcGraphProp3) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcGraphProp2) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcextLem) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcGraphProp4) =>
% 132.59/22.92 ((
% 132.59/22.92 (subbreln) =>
% 132.59/22.92 ((
% 132.59/22.92 (eqbreln) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcext) =>
% 132.59/22.92 ((
% 132.59/22.92 (funcext2) =>
% 132.59/22.92 ((
% 132.59/22.92 (ap2apEq1) =>
% 132.59/22.92 ((
% 132.59/22.92 (ap2apEq2) =>
% 132.59/22.92 ((
% 132.59/22.92 (beta1) =>
% 132.59/22.92 ((
% 132.59/22.92 (eta1) =>
% 132.59/22.92 ((
% 132.59/22.92 (lam2lamEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (beta2) =>
% 132.59/22.92 ((
% 132.59/22.92 (eta2) =>
% 132.59/22.92 ((
% 132.59/22.92 (iffalseProp1) =>
% 132.59/22.92 ((
% 132.59/22.92 (iffalseProp2) =>
% 132.59/22.92 ((
% 132.59/22.92 (iftrueProp1) =>
% 132.59/22.92 ((
% 132.59/22.92 (iftrueProp2) =>
% 132.59/22.92 ((
% 132.59/22.92 (ifSingleton) =>
% 132.59/22.92 ((
% 132.59/22.92 (ifp) =>
% 132.59/22.92 ((
% 132.59/22.92 (theeq) =>
% 132.59/22.92 ((
% 132.59/22.92 (iftrue) =>
% 132.59/22.92 ((
% 132.59/22.92 (iffalse) =>
% 132.59/22.92 ((
% 132.59/22.92 (iftrueorfalse) =>
% 132.59/22.92 ((
% 132.59/22.92 (binintersectT_lem) =>
% 132.59/22.92 ((
% 132.59/22.92 (binunionT_lem) =>
% 132.59/22.92 ((
% 132.59/22.92 (powersetT_lem) =>
% 132.59/22.92 ((
% 132.59/22.92 (setminusT_lem) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementT_lem) =>
% 132.59/22.92 ((
% 132.59/22.92 (setextT) =>
% 132.59/22.92 ((
% 132.59/22.92 (subsetTI) =>
% 132.59/22.92 ((
% 132.59/22.92 (powersetTI1) =>
% 132.59/22.92 ((
% 132.59/22.92 (powersetTE1) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementTI1) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementTE1) =>
% 132.59/22.92 ((
% 132.59/22.92 (binintersectTELcontra) =>
% 132.59/22.92 ((
% 132.59/22.92 (binintersectTERcontra) =>
% 132.59/22.92 ((
% 132.59/22.92 (contrasubsetT) =>
% 132.59/22.92 ((
% 132.59/22.92 (contrasubsetT1) =>
% 132.59/22.92 ((
% 132.59/22.92 (contrasubsetT2) =>
% 132.59/22.92 ((
% 132.59/22.92 (contrasubsetT3) =>
% 132.59/22.92 ((
% 132.59/22.92 (doubleComplementI1) =>
% 132.59/22.92 ((
% 132.59/22.92 (doubleComplementE1) =>
% 132.59/22.92 ((
% 132.59/22.92 (doubleComplementSub1) =>
% 132.59/22.92 ((
% 132.59/22.92 (doubleComplementSub2) =>
% 132.59/22.92 ((
% 132.59/22.92 (doubleComplementEq) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementTnotintersectT) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementImpComplementIntersect) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementSubsetComplementIntersect) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementInPowersetComplementIntersect) =>
% 132.59/22.92 ((
% 132.59/22.92 (contraSubsetComplement) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementTcontraSubset) =>
% 132.59/22.92 ((
% 132.59/22.92 (binunionTILcontra) =>
% 132.59/22.92 ((
% 132.59/22.92 (binunionTIRcontra) =>
% 132.59/22.92 ((
% 132.59/22.92 (inIntersectImpInUnion) =>
% 132.59/22.92 ((
% 132.59/22.92 (inIntersectImpInUnion2) =>
% 132.59/22.92 ((
% 132.59/22.92 (inIntersectImpInIntersectUnions) =>
% 132.59/22.92 ((
% 132.59/22.92 (intersectInPowersetIntersectUnions) =>
% 132.59/22.92 ((
% 132.59/22.92 (inComplementUnionImpNotIn1) =>
% 132.59/22.92 ((
% 132.59/22.92 (inComplementUnionImpInComplement1) =>
% 132.59/22.92 ((
% 132.59/22.92 (binunionTE) =>
% 132.59/22.92 ((
% 132.59/22.92 (binunionTEcontra) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan2a1) =>
% 132.59/22.92 ((
% 132.59/22.92 (complementUnionInPowersetComplement) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan2a2) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan1a) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan1b) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan1) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan2a) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan2b2) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan2b) =>
% 132.59/22.92 ((
% 132.59/22.92 (demorgan2) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz13rule0) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz13rule1) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz13rule2) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz13rule3) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz13rule4) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz1_1) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz1_2) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz1_3) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz1_4) =>
% 132.59/22.92 ((
% 132.59/22.92 (woz1_5) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1all2) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1SetBreln1) =>
% 132.59/22.92 ((
% 132.59/22.92 (choice2fnsingleton) =>
% 132.59/22.92 ((
% 132.59/22.92 (setOfPairsIsBReln1) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1all1) =>
% 132.59/22.92 ((
% 132.59/22.92 (subbreln1) =>
% 132.59/22.92 ((
% 132.59/22.92 (eqbreln1) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1invprop) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1invI) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1invE) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1compprop) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1compI) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1compE) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1compEex) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1unionprop) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1unionIL) =>
% 132.59/22.92 ((
% 132.59/22.92 (breln1unionIR) =>
% 132.59/22.92 ((
% 132.59/22.93 (breln1unionI) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1unionE) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1unionEcases) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1unionCommutes) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz2Ex) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz2W) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz2A) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz2B) =>
% 132.59/22.93 ((
% 132.59/22.93 (image1Ex) =>
% 132.59/22.93 ((
% 132.59/22.93 (image1Ex1) =>
% 132.59/22.93 ((
% 132.59/22.93 (image1Equiv) =>
% 132.59/22.93 ((
% 132.59/22.93 (image1E) =>
% 132.59/22.93 ((
% 132.59/22.93 (image1I) =>
% 132.59/22.93 ((
% 132.59/22.93 (injFuncInInjFuncSet) =>
% 132.59/22.93 ((
% 132.59/22.93 (injFuncSetFuncIn) =>
% 132.59/22.93 ((
% 132.59/22.93 (injFuncSetFuncInj) =>
% 132.59/22.93 ((
% 132.59/22.93 (surjFuncSetFuncIn) =>
% 132.59/22.93 ((
% 132.59/22.93 (surjFuncSetFuncSurj) =>
% 132.59/22.93 ((
% 132.59/22.93 (leftInvIsSurj) =>
% 132.59/22.93 ((
% 132.59/22.93 (surjCantorThm) =>
% 132.59/22.93 ((
% 132.59/22.93 (foundation2) =>
% 132.59/22.93 ((
% 132.59/22.93 (notinself) =>
% 132.59/22.93 ((
% 132.59/22.93 (notinself2) =>
% 132.59/22.93 ((
% 132.59/22.93 (omegaSp) =>
% 132.59/22.93 ((
% 132.59/22.93 (omegaSclos) =>
% 132.59/22.93 ((
% 132.59/22.93 (peano0notS) =>
% 132.59/22.93 ((
% 132.59/22.93 (peanoSinj) =>
% 132.59/22.93 ((
% 132.59/22.93 (transitivesetOp1) =>
% 132.59/22.93 ((
% 132.59/22.93 (binintTransitive) =>
% 132.59/22.93 ((
% 132.59/22.93 (transitivesetOp2) =>
% 132.59/22.93 ((
% 132.59/22.93 (setunionTransitive) =>
% 132.59/22.93 ((
% 132.59/22.93 (ordinalMinLem1) =>
% 132.59/22.93 ((
% 132.59/22.93 (ordinalTransSet) =>
% 132.59/22.93 ((
% 132.59/22.93 (ordinalTransSet1) =>
% 132.59/22.93 ((
% 132.59/22.93 (setunionOrdinalLem1) =>
% 132.59/22.93 (ordinal @
% 132.59/22.93 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.59/22.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl934])).
% 132.59/22.93 thf(zip_derived_cl945, plain,
% 132.59/22.93 (~ (((binunionRsub) =>
% 132.59/22.93 (((binintersectI) =>
% 132.59/22.93 (((binintersectSubset5) =>
% 132.59/22.93 (((binintersectEL) =>
% 132.59/22.93 (((binintersectLsub) =>
% 132.59/22.93 (((binintersectSubset2) =>
% 132.59/22.93 (((binintersectSubset3) =>
% 132.59/22.93 (((binintersectER) =>
% 132.59/22.93 (((disjointsetsI1) =>
% 132.59/22.93 (((binintersectRsub) =>
% 132.59/22.93 (((binintersectSubset4) =>
% 132.59/22.93 (((binintersectSubset1) =>
% 132.59/22.93 (((bs114d) =>
% 132.59/22.93 (((setminusI) =>
% 132.59/22.93 (((setminusEL) =>
% 132.59/22.93 (((setminusER) =>
% 132.59/22.93 (((setminusSubset2) =>
% 132.59/22.93 (((setminusERneg) =>
% 132.59/22.93 (((setminusELneg) =>
% 132.59/22.93 (((setminusILneg) =>
% 132.59/22.93 (((setminusIRneg) =>
% 132.59/22.93 (((setminusLsub) =>
% 132.59/22.93 (((setminusSubset1) =>
% 132.59/22.93 (((symdiffE) =>
% 132.59/22.93 (((symdiffI1) =>
% 132.59/22.93 (((symdiffI2) =>
% 132.59/22.93 (((symdiffIneg1) =>
% 132.59/22.93 (((symdiffIneg2) =>
% 132.59/22.93 (((secondinupair) =>
% 132.59/22.93 (((setukpairIL) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairIR) =>
% 132.59/22.93 ((
% 132.59/22.93 (kpairiskpair) =>
% 132.59/22.93 ((
% 132.59/22.93 (kpairp) =>
% 132.59/22.93 ((
% 132.59/22.93 (singletonsubset) =>
% 132.59/22.93 ((
% 132.59/22.93 (singletoninpowerset) =>
% 132.59/22.93 ((
% 132.59/22.93 (singletoninpowunion) =>
% 132.59/22.93 ((
% 132.59/22.93 (upairset2E) =>
% 132.59/22.93 ((
% 132.59/22.93 (upairsubunion) =>
% 132.59/22.93 ((
% 132.59/22.93 (upairinpowunion) =>
% 132.59/22.93 ((
% 132.59/22.93 (ubforcartprodlem1) =>
% 132.59/22.93 ((
% 132.59/22.93 (ubforcartprodlem2) =>
% 132.59/22.93 ((
% 132.59/22.93 (ubforcartprodlem3) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodpairin) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodmempair1) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodmempair) =>
% 132.59/22.93 ((
% 132.59/22.93 (setunionE2) =>
% 132.59/22.93 ((
% 132.59/22.93 (setunionsingleton1) =>
% 132.59/22.93 ((
% 132.59/22.93 (setunionsingleton2) =>
% 132.59/22.93 ((
% 132.59/22.93 (setunionsingleton) =>
% 132.59/22.93 ((
% 132.59/22.93 (singletonprop) =>
% 132.59/22.93 ((
% 132.59/22.93 (ex1E1) =>
% 132.59/22.93 ((
% 132.59/22.93 (ex1I) =>
% 132.59/22.93 ((
% 132.59/22.93 (ex1I2) =>
% 132.59/22.93 ((
% 132.59/22.93 (singletonsuniq) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjL1) =>
% 132.59/22.93 ((
% 132.59/22.93 (kfstsingleton) =>
% 132.59/22.93 ((
% 132.59/22.93 (theprop) =>
% 132.59/22.93 ((
% 132.59/22.93 (kfstpairEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodfstin) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjL2) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjL) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjR11) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjR12) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjR1) =>
% 132.59/22.93 ((
% 132.59/22.93 (upairequniteq) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjR2) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjR) =>
% 132.59/22.93 ((
% 132.59/22.93 (ksndsingleton) =>
% 132.59/22.93 ((
% 132.59/22.93 (ksndpairEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (kpairsurjEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodsndin) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodpairmemEL) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodpairmemER) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodmempaircEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodfstpairEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodsndpairEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodpairsurjEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (dpsetconstrI) =>
% 132.59/22.93 ((
% 132.59/22.93 (dpsetconstrSub) =>
% 132.59/22.93 ((
% 132.59/22.93 (setOfPairsIsBReln) =>
% 132.59/22.93 ((
% 132.59/22.93 (dpsetconstrERa) =>
% 132.59/22.93 ((
% 132.59/22.93 (dpsetconstrEL1) =>
% 132.59/22.93 ((
% 132.59/22.93 (dpsetconstrEL2) =>
% 132.59/22.93 ((
% 132.59/22.93 (dpsetconstrER) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcImageSingleton) =>
% 132.59/22.93 ((
% 132.59/22.93 (apProp) =>
% 132.59/22.93 ((
% 132.59/22.93 (app) =>
% 132.59/22.93 ((
% 132.59/22.93 (infuncsetfunc) =>
% 132.59/22.93 ((
% 132.59/22.93 (ap2p) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcinfuncset) =>
% 132.59/22.93 ((
% 132.59/22.93 (lamProp) =>
% 132.59/22.93 ((
% 132.59/22.93 (lamp) =>
% 132.59/22.93 ((
% 132.59/22.93 (lam2p) =>
% 132.59/22.93 ((
% 132.59/22.93 (brelnall1) =>
% 132.59/22.93 ((
% 132.59/22.93 (brelnall2) =>
% 132.59/22.93 ((
% 132.59/22.93 (ex1E2) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcGraphProp1) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcGraphProp3) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcGraphProp2) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcextLem) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcGraphProp4) =>
% 132.59/22.93 ((
% 132.59/22.93 (subbreln) =>
% 132.59/22.93 ((
% 132.59/22.93 (eqbreln) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcext) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcext2) =>
% 132.59/22.93 ((
% 132.59/22.93 (ap2apEq1) =>
% 132.59/22.93 ((
% 132.59/22.93 (ap2apEq2) =>
% 132.59/22.93 ((
% 132.59/22.93 (beta1) =>
% 132.59/22.93 ((
% 132.59/22.93 (eta1) =>
% 132.59/22.93 ((
% 132.59/22.93 (lam2lamEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (beta2) =>
% 132.59/22.93 ((
% 132.59/22.93 (eta2) =>
% 132.59/22.93 ((
% 132.59/22.93 (iffalseProp1) =>
% 132.59/22.93 ((
% 132.59/22.93 (iffalseProp2) =>
% 132.59/22.93 ((
% 132.59/22.93 (iftrueProp1) =>
% 132.59/22.93 ((
% 132.59/22.93 (iftrueProp2) =>
% 132.59/22.93 ((
% 132.59/22.93 (ifSingleton) =>
% 132.59/22.93 ((
% 132.59/22.93 (ifp) =>
% 132.59/22.93 ((
% 132.59/22.93 (theeq) =>
% 132.59/22.93 ((
% 132.59/22.93 (iftrue) =>
% 132.59/22.93 ((
% 132.59/22.93 (iffalse) =>
% 132.59/22.93 ((
% 132.59/22.93 (iftrueorfalse) =>
% 132.59/22.93 ((
% 132.59/22.93 (binintersectT_lem) =>
% 132.59/22.93 ((
% 132.59/22.93 (binunionT_lem) =>
% 132.59/22.93 ((
% 132.59/22.93 (powersetT_lem) =>
% 132.59/22.93 ((
% 132.59/22.93 (setminusT_lem) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementT_lem) =>
% 132.59/22.93 ((
% 132.59/22.93 (setextT) =>
% 132.59/22.93 ((
% 132.59/22.93 (subsetTI) =>
% 132.59/22.93 ((
% 132.59/22.93 (powersetTI1) =>
% 132.59/22.93 ((
% 132.59/22.93 (powersetTE1) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementTI1) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementTE1) =>
% 132.59/22.93 ((
% 132.59/22.93 (binintersectTELcontra) =>
% 132.59/22.93 ((
% 132.59/22.93 (binintersectTERcontra) =>
% 132.59/22.93 ((
% 132.59/22.93 (contrasubsetT) =>
% 132.59/22.93 ((
% 132.59/22.93 (contrasubsetT1) =>
% 132.59/22.93 ((
% 132.59/22.93 (contrasubsetT2) =>
% 132.59/22.93 ((
% 132.59/22.93 (contrasubsetT3) =>
% 132.59/22.93 ((
% 132.59/22.93 (doubleComplementI1) =>
% 132.59/22.93 ((
% 132.59/22.93 (doubleComplementE1) =>
% 132.59/22.93 ((
% 132.59/22.93 (doubleComplementSub1) =>
% 132.59/22.93 ((
% 132.59/22.93 (doubleComplementSub2) =>
% 132.59/22.93 ((
% 132.59/22.93 (doubleComplementEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementTnotintersectT) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementImpComplementIntersect) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementSubsetComplementIntersect) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementInPowersetComplementIntersect) =>
% 132.59/22.93 ((
% 132.59/22.93 (contraSubsetComplement) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementTcontraSubset) =>
% 132.59/22.93 ((
% 132.59/22.93 (binunionTILcontra) =>
% 132.59/22.93 ((
% 132.59/22.93 (binunionTIRcontra) =>
% 132.59/22.93 ((
% 132.59/22.93 (inIntersectImpInUnion) =>
% 132.59/22.93 ((
% 132.59/22.93 (inIntersectImpInUnion2) =>
% 132.59/22.93 ((
% 132.59/22.93 (inIntersectImpInIntersectUnions) =>
% 132.59/22.93 ((
% 132.59/22.93 (intersectInPowersetIntersectUnions) =>
% 132.59/22.93 ((
% 132.59/22.93 (inComplementUnionImpNotIn1) =>
% 132.59/22.93 ((
% 132.59/22.93 (inComplementUnionImpInComplement1) =>
% 132.59/22.93 ((
% 132.59/22.93 (binunionTE) =>
% 132.59/22.93 ((
% 132.59/22.93 (binunionTEcontra) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan2a1) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementUnionInPowersetComplement) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan2a2) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan1a) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan1b) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan1) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan2a) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan2b2) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan2b) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan2) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz13rule0) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz13rule1) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz13rule2) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz13rule3) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz13rule4) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz1_1) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz1_2) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz1_3) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz1_4) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz1_5) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1all2) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1SetBreln1) =>
% 132.59/22.93 ((
% 132.59/22.93 (choice2fnsingleton) =>
% 132.59/22.93 ((
% 132.59/22.93 (setOfPairsIsBReln1) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1all1) =>
% 132.59/22.93 ((
% 132.59/22.93 (subbreln1) =>
% 132.59/22.93 ((
% 132.59/22.93 (eqbreln1) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1invprop) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1invI) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1invE) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1compprop) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1compI) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1compE) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1compEex) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1unionprop) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1unionIL) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1unionIR) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1unionI) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1unionE) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1unionEcases) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1unionCommutes) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz2Ex) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz2W) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz2A) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz2B) =>
% 132.59/22.93 ((
% 132.59/22.93 (image1Ex) =>
% 132.59/22.93 ((
% 132.59/22.93 (image1Ex1) =>
% 132.59/22.93 ((
% 132.59/22.93 (image1Equiv) =>
% 132.59/22.93 ((
% 132.59/22.93 (image1E) =>
% 132.59/22.93 ((
% 132.59/22.93 (image1I) =>
% 132.59/22.93 ((
% 132.59/22.93 (injFuncInInjFuncSet) =>
% 132.59/22.93 ((
% 132.59/22.93 (injFuncSetFuncIn) =>
% 132.59/22.93 ((
% 132.59/22.93 (injFuncSetFuncInj) =>
% 132.59/22.93 ((
% 132.59/22.93 (surjFuncSetFuncIn) =>
% 132.59/22.93 ((
% 132.59/22.93 (surjFuncSetFuncSurj) =>
% 132.59/22.93 ((
% 132.59/22.93 (leftInvIsSurj) =>
% 132.59/22.93 ((
% 132.59/22.93 (surjCantorThm) =>
% 132.59/22.93 ((
% 132.59/22.93 (foundation2) =>
% 132.59/22.93 ((
% 132.59/22.93 (notinself) =>
% 132.59/22.93 ((
% 132.59/22.93 (notinself2) =>
% 132.59/22.93 ((
% 132.59/22.93 (omegaSp) =>
% 132.59/22.93 ((
% 132.59/22.93 (omegaSclos) =>
% 132.59/22.93 ((
% 132.59/22.93 (peano0notS) =>
% 132.59/22.93 ((
% 132.59/22.93 (peanoSinj) =>
% 132.59/22.93 ((
% 132.59/22.93 (transitivesetOp1) =>
% 132.59/22.93 ((
% 132.59/22.93 (binintTransitive) =>
% 132.59/22.93 ((
% 132.59/22.93 (transitivesetOp2) =>
% 132.59/22.93 ((
% 132.59/22.93 (setunionTransitive) =>
% 132.59/22.93 ((
% 132.59/22.93 (ordinalMinLem1) =>
% 132.59/22.93 ((
% 132.59/22.93 (ordinalTransSet) =>
% 132.59/22.93 ((
% 132.59/22.93 (ordinalTransSet1) =>
% 132.59/22.93 ((
% 132.59/22.93 (setunionOrdinalLem1) =>
% 132.59/22.93 (ordinal @
% 132.59/22.93 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.59/22.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl940])).
% 132.59/22.93 thf(zip_derived_cl951, plain,
% 132.59/22.93 (~ (((binintersectI) =>
% 132.59/22.93 (((binintersectSubset5) =>
% 132.59/22.93 (((binintersectEL) =>
% 132.59/22.93 (((binintersectLsub) =>
% 132.59/22.93 (((binintersectSubset2) =>
% 132.59/22.93 (((binintersectSubset3) =>
% 132.59/22.93 (((binintersectER) =>
% 132.59/22.93 (((disjointsetsI1) =>
% 132.59/22.93 (((binintersectRsub) =>
% 132.59/22.93 (((binintersectSubset4) =>
% 132.59/22.93 (((binintersectSubset1) =>
% 132.59/22.93 (((bs114d) =>
% 132.59/22.93 (((setminusI) =>
% 132.59/22.93 (((setminusEL) =>
% 132.59/22.93 (((setminusER) =>
% 132.59/22.93 (((setminusSubset2) =>
% 132.59/22.93 (((setminusERneg) =>
% 132.59/22.93 (((setminusELneg) =>
% 132.59/22.93 (((setminusILneg) =>
% 132.59/22.93 (((setminusIRneg) =>
% 132.59/22.93 (((setminusLsub) =>
% 132.59/22.93 (((setminusSubset1) =>
% 132.59/22.93 (((symdiffE) =>
% 132.59/22.93 (((symdiffI1) =>
% 132.59/22.93 (((symdiffI2) =>
% 132.59/22.93 (((symdiffIneg1) =>
% 132.59/22.93 (((symdiffIneg2) =>
% 132.59/22.93 (((secondinupair) =>
% 132.59/22.93 (((setukpairIL) =>
% 132.59/22.93 (((setukpairIR) =>
% 132.59/22.93 ((
% 132.59/22.93 (kpairiskpair) =>
% 132.59/22.93 ((
% 132.59/22.93 (kpairp) =>
% 132.59/22.93 ((
% 132.59/22.93 (singletonsubset) =>
% 132.59/22.93 ((
% 132.59/22.93 (singletoninpowerset) =>
% 132.59/22.93 ((
% 132.59/22.93 (singletoninpowunion) =>
% 132.59/22.93 ((
% 132.59/22.93 (upairset2E) =>
% 132.59/22.93 ((
% 132.59/22.93 (upairsubunion) =>
% 132.59/22.93 ((
% 132.59/22.93 (upairinpowunion) =>
% 132.59/22.93 ((
% 132.59/22.93 (ubforcartprodlem1) =>
% 132.59/22.93 ((
% 132.59/22.93 (ubforcartprodlem2) =>
% 132.59/22.93 ((
% 132.59/22.93 (ubforcartprodlem3) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodpairin) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodmempair1) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodmempair) =>
% 132.59/22.93 ((
% 132.59/22.93 (setunionE2) =>
% 132.59/22.93 ((
% 132.59/22.93 (setunionsingleton1) =>
% 132.59/22.93 ((
% 132.59/22.93 (setunionsingleton2) =>
% 132.59/22.93 ((
% 132.59/22.93 (setunionsingleton) =>
% 132.59/22.93 ((
% 132.59/22.93 (singletonprop) =>
% 132.59/22.93 ((
% 132.59/22.93 (ex1E1) =>
% 132.59/22.93 ((
% 132.59/22.93 (ex1I) =>
% 132.59/22.93 ((
% 132.59/22.93 (ex1I2) =>
% 132.59/22.93 ((
% 132.59/22.93 (singletonsuniq) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjL1) =>
% 132.59/22.93 ((
% 132.59/22.93 (kfstsingleton) =>
% 132.59/22.93 ((
% 132.59/22.93 (theprop) =>
% 132.59/22.93 ((
% 132.59/22.93 (kfstpairEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodfstin) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjL2) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjL) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjR11) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjR12) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjR1) =>
% 132.59/22.93 ((
% 132.59/22.93 (upairequniteq) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjR2) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjR) =>
% 132.59/22.93 ((
% 132.59/22.93 (ksndsingleton) =>
% 132.59/22.93 ((
% 132.59/22.93 (ksndpairEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (kpairsurjEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodsndin) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodpairmemEL) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodpairmemER) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodmempaircEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodfstpairEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodsndpairEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodpairsurjEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (dpsetconstrI) =>
% 132.59/22.93 ((
% 132.59/22.93 (dpsetconstrSub) =>
% 132.59/22.93 ((
% 132.59/22.93 (setOfPairsIsBReln) =>
% 132.59/22.93 ((
% 132.59/22.93 (dpsetconstrERa) =>
% 132.59/22.93 ((
% 132.59/22.93 (dpsetconstrEL1) =>
% 132.59/22.93 ((
% 132.59/22.93 (dpsetconstrEL2) =>
% 132.59/22.93 ((
% 132.59/22.93 (dpsetconstrER) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcImageSingleton) =>
% 132.59/22.93 ((
% 132.59/22.93 (apProp) =>
% 132.59/22.93 ((
% 132.59/22.93 (app) =>
% 132.59/22.93 ((
% 132.59/22.93 (infuncsetfunc) =>
% 132.59/22.93 ((
% 132.59/22.93 (ap2p) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcinfuncset) =>
% 132.59/22.93 ((
% 132.59/22.93 (lamProp) =>
% 132.59/22.93 ((
% 132.59/22.93 (lamp) =>
% 132.59/22.93 ((
% 132.59/22.93 (lam2p) =>
% 132.59/22.93 ((
% 132.59/22.93 (brelnall1) =>
% 132.59/22.93 ((
% 132.59/22.93 (brelnall2) =>
% 132.59/22.93 ((
% 132.59/22.93 (ex1E2) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcGraphProp1) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcGraphProp3) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcGraphProp2) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcextLem) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcGraphProp4) =>
% 132.59/22.93 ((
% 132.59/22.93 (subbreln) =>
% 132.59/22.93 ((
% 132.59/22.93 (eqbreln) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcext) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcext2) =>
% 132.59/22.93 ((
% 132.59/22.93 (ap2apEq1) =>
% 132.59/22.93 ((
% 132.59/22.93 (ap2apEq2) =>
% 132.59/22.93 ((
% 132.59/22.93 (beta1) =>
% 132.59/22.93 ((
% 132.59/22.93 (eta1) =>
% 132.59/22.93 ((
% 132.59/22.93 (lam2lamEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (beta2) =>
% 132.59/22.93 ((
% 132.59/22.93 (eta2) =>
% 132.59/22.93 ((
% 132.59/22.93 (iffalseProp1) =>
% 132.59/22.93 ((
% 132.59/22.93 (iffalseProp2) =>
% 132.59/22.93 ((
% 132.59/22.93 (iftrueProp1) =>
% 132.59/22.93 ((
% 132.59/22.93 (iftrueProp2) =>
% 132.59/22.93 ((
% 132.59/22.93 (ifSingleton) =>
% 132.59/22.93 ((
% 132.59/22.93 (ifp) =>
% 132.59/22.93 ((
% 132.59/22.93 (theeq) =>
% 132.59/22.93 ((
% 132.59/22.93 (iftrue) =>
% 132.59/22.93 ((
% 132.59/22.93 (iffalse) =>
% 132.59/22.93 ((
% 132.59/22.93 (iftrueorfalse) =>
% 132.59/22.93 ((
% 132.59/22.93 (binintersectT_lem) =>
% 132.59/22.93 ((
% 132.59/22.93 (binunionT_lem) =>
% 132.59/22.93 ((
% 132.59/22.93 (powersetT_lem) =>
% 132.59/22.93 ((
% 132.59/22.93 (setminusT_lem) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementT_lem) =>
% 132.59/22.93 ((
% 132.59/22.93 (setextT) =>
% 132.59/22.93 ((
% 132.59/22.93 (subsetTI) =>
% 132.59/22.93 ((
% 132.59/22.93 (powersetTI1) =>
% 132.59/22.93 ((
% 132.59/22.93 (powersetTE1) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementTI1) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementTE1) =>
% 132.59/22.93 ((
% 132.59/22.93 (binintersectTELcontra) =>
% 132.59/22.93 ((
% 132.59/22.93 (binintersectTERcontra) =>
% 132.59/22.93 ((
% 132.59/22.93 (contrasubsetT) =>
% 132.59/22.93 ((
% 132.59/22.93 (contrasubsetT1) =>
% 132.59/22.93 ((
% 132.59/22.93 (contrasubsetT2) =>
% 132.59/22.93 ((
% 132.59/22.93 (contrasubsetT3) =>
% 132.59/22.93 ((
% 132.59/22.93 (doubleComplementI1) =>
% 132.59/22.93 ((
% 132.59/22.93 (doubleComplementE1) =>
% 132.59/22.93 ((
% 132.59/22.93 (doubleComplementSub1) =>
% 132.59/22.93 ((
% 132.59/22.93 (doubleComplementSub2) =>
% 132.59/22.93 ((
% 132.59/22.93 (doubleComplementEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementTnotintersectT) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementImpComplementIntersect) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementSubsetComplementIntersect) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementInPowersetComplementIntersect) =>
% 132.59/22.93 ((
% 132.59/22.93 (contraSubsetComplement) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementTcontraSubset) =>
% 132.59/22.93 ((
% 132.59/22.93 (binunionTILcontra) =>
% 132.59/22.93 ((
% 132.59/22.93 (binunionTIRcontra) =>
% 132.59/22.93 ((
% 132.59/22.93 (inIntersectImpInUnion) =>
% 132.59/22.93 ((
% 132.59/22.93 (inIntersectImpInUnion2) =>
% 132.59/22.93 ((
% 132.59/22.93 (inIntersectImpInIntersectUnions) =>
% 132.59/22.93 ((
% 132.59/22.93 (intersectInPowersetIntersectUnions) =>
% 132.59/22.93 ((
% 132.59/22.93 (inComplementUnionImpNotIn1) =>
% 132.59/22.93 ((
% 132.59/22.93 (inComplementUnionImpInComplement1) =>
% 132.59/22.93 ((
% 132.59/22.93 (binunionTE) =>
% 132.59/22.93 ((
% 132.59/22.93 (binunionTEcontra) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan2a1) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementUnionInPowersetComplement) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan2a2) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan1a) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan1b) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan1) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan2a) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan2b2) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan2b) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan2) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz13rule0) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz13rule1) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz13rule2) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz13rule3) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz13rule4) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz1_1) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz1_2) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz1_3) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz1_4) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz1_5) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1all2) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1SetBreln1) =>
% 132.59/22.93 ((
% 132.59/22.93 (choice2fnsingleton) =>
% 132.59/22.93 ((
% 132.59/22.93 (setOfPairsIsBReln1) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1all1) =>
% 132.59/22.93 ((
% 132.59/22.93 (subbreln1) =>
% 132.59/22.93 ((
% 132.59/22.93 (eqbreln1) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1invprop) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1invI) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1invE) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1compprop) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1compI) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1compE) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1compEex) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1unionprop) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1unionIL) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1unionIR) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1unionI) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1unionE) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1unionEcases) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1unionCommutes) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz2Ex) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz2W) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz2A) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz2B) =>
% 132.59/22.93 ((
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% 132.59/22.93 ((
% 132.59/22.93 (image1Ex1) =>
% 132.59/22.93 ((
% 132.59/22.93 (image1Equiv) =>
% 132.59/22.93 ((
% 132.59/22.93 (image1E) =>
% 132.59/22.93 ((
% 132.59/22.93 (image1I) =>
% 132.59/22.93 ((
% 132.59/22.93 (injFuncInInjFuncSet) =>
% 132.59/22.93 ((
% 132.59/22.93 (injFuncSetFuncIn) =>
% 132.59/22.93 ((
% 132.59/22.93 (injFuncSetFuncInj) =>
% 132.59/22.93 ((
% 132.59/22.93 (surjFuncSetFuncIn) =>
% 132.59/22.93 ((
% 132.59/22.93 (surjFuncSetFuncSurj) =>
% 132.59/22.93 ((
% 132.59/22.93 (leftInvIsSurj) =>
% 132.59/22.93 ((
% 132.59/22.93 (surjCantorThm) =>
% 132.59/22.93 ((
% 132.59/22.93 (foundation2) =>
% 132.59/22.93 ((
% 132.59/22.93 (notinself) =>
% 132.59/22.93 ((
% 132.59/22.93 (notinself2) =>
% 132.59/22.93 ((
% 132.59/22.93 (omegaSp) =>
% 132.59/22.93 ((
% 132.59/22.93 (omegaSclos) =>
% 132.59/22.93 ((
% 132.59/22.93 (peano0notS) =>
% 132.59/22.93 ((
% 132.59/22.93 (peanoSinj) =>
% 132.59/22.93 ((
% 132.59/22.93 (transitivesetOp1) =>
% 132.59/22.93 ((
% 132.59/22.93 (binintTransitive) =>
% 132.59/22.93 ((
% 132.59/22.93 (transitivesetOp2) =>
% 132.59/22.93 ((
% 132.59/22.93 (setunionTransitive) =>
% 132.59/22.93 ((
% 132.59/22.93 (ordinalMinLem1) =>
% 132.59/22.93 ((
% 132.59/22.93 (ordinalTransSet) =>
% 132.59/22.93 ((
% 132.59/22.93 (ordinalTransSet1) =>
% 132.59/22.93 ((
% 132.59/22.93 (setunionOrdinalLem1) =>
% 132.59/22.93 (ordinal @
% 132.59/22.93 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.59/22.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl945])).
% 132.59/22.93 thf(zip_derived_cl957, plain,
% 132.59/22.93 (~ (((binintersectSubset5) =>
% 132.59/22.93 (((binintersectEL) =>
% 132.59/22.93 (((binintersectLsub) =>
% 132.59/22.93 (((binintersectSubset2) =>
% 132.59/22.93 (((binintersectSubset3) =>
% 132.59/22.93 (((binintersectER) =>
% 132.59/22.93 (((disjointsetsI1) =>
% 132.59/22.93 (((binintersectRsub) =>
% 132.59/22.93 (((binintersectSubset4) =>
% 132.59/22.93 (((binintersectSubset1) =>
% 132.59/22.93 (((bs114d) =>
% 132.59/22.93 (((setminusI) =>
% 132.59/22.93 (((setminusEL) =>
% 132.59/22.93 (((setminusER) =>
% 132.59/22.93 (((setminusSubset2) =>
% 132.59/22.93 (((setminusERneg) =>
% 132.59/22.93 (((setminusELneg) =>
% 132.59/22.93 (((setminusILneg) =>
% 132.59/22.93 (((setminusIRneg) =>
% 132.59/22.93 (((setminusLsub) =>
% 132.59/22.93 (((setminusSubset1) =>
% 132.59/22.93 (((symdiffE) =>
% 132.59/22.93 (((symdiffI1) =>
% 132.59/22.93 (((symdiffI2) =>
% 132.59/22.93 (((symdiffIneg1) =>
% 132.59/22.93 (((symdiffIneg2) =>
% 132.59/22.93 (((secondinupair) =>
% 132.59/22.93 (((setukpairIL) =>
% 132.59/22.93 (((setukpairIR) =>
% 132.59/22.93 (((kpairiskpair) =>
% 132.59/22.93 ((
% 132.59/22.93 (kpairp) =>
% 132.59/22.93 ((
% 132.59/22.93 (singletonsubset) =>
% 132.59/22.93 ((
% 132.59/22.93 (singletoninpowerset) =>
% 132.59/22.93 ((
% 132.59/22.93 (singletoninpowunion) =>
% 132.59/22.93 ((
% 132.59/22.93 (upairset2E) =>
% 132.59/22.93 ((
% 132.59/22.93 (upairsubunion) =>
% 132.59/22.93 ((
% 132.59/22.93 (upairinpowunion) =>
% 132.59/22.93 ((
% 132.59/22.93 (ubforcartprodlem1) =>
% 132.59/22.93 ((
% 132.59/22.93 (ubforcartprodlem2) =>
% 132.59/22.93 ((
% 132.59/22.93 (ubforcartprodlem3) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodpairin) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodmempair1) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodmempair) =>
% 132.59/22.93 ((
% 132.59/22.93 (setunionE2) =>
% 132.59/22.93 ((
% 132.59/22.93 (setunionsingleton1) =>
% 132.59/22.93 ((
% 132.59/22.93 (setunionsingleton2) =>
% 132.59/22.93 ((
% 132.59/22.93 (setunionsingleton) =>
% 132.59/22.93 ((
% 132.59/22.93 (singletonprop) =>
% 132.59/22.93 ((
% 132.59/22.93 (ex1E1) =>
% 132.59/22.93 ((
% 132.59/22.93 (ex1I) =>
% 132.59/22.93 ((
% 132.59/22.93 (ex1I2) =>
% 132.59/22.93 ((
% 132.59/22.93 (singletonsuniq) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjL1) =>
% 132.59/22.93 ((
% 132.59/22.93 (kfstsingleton) =>
% 132.59/22.93 ((
% 132.59/22.93 (theprop) =>
% 132.59/22.93 ((
% 132.59/22.93 (kfstpairEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodfstin) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjL2) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjL) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjR11) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjR12) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjR1) =>
% 132.59/22.93 ((
% 132.59/22.93 (upairequniteq) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjR2) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjR) =>
% 132.59/22.93 ((
% 132.59/22.93 (ksndsingleton) =>
% 132.59/22.93 ((
% 132.59/22.93 (ksndpairEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (kpairsurjEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodsndin) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodpairmemEL) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodpairmemER) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodmempaircEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodfstpairEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodsndpairEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodpairsurjEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (dpsetconstrI) =>
% 132.59/22.93 ((
% 132.59/22.93 (dpsetconstrSub) =>
% 132.59/22.93 ((
% 132.59/22.93 (setOfPairsIsBReln) =>
% 132.59/22.93 ((
% 132.59/22.93 (dpsetconstrERa) =>
% 132.59/22.93 ((
% 132.59/22.93 (dpsetconstrEL1) =>
% 132.59/22.93 ((
% 132.59/22.93 (dpsetconstrEL2) =>
% 132.59/22.93 ((
% 132.59/22.93 (dpsetconstrER) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcImageSingleton) =>
% 132.59/22.93 ((
% 132.59/22.93 (apProp) =>
% 132.59/22.93 ((
% 132.59/22.93 (app) =>
% 132.59/22.93 ((
% 132.59/22.93 (infuncsetfunc) =>
% 132.59/22.93 ((
% 132.59/22.93 (ap2p) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcinfuncset) =>
% 132.59/22.93 ((
% 132.59/22.93 (lamProp) =>
% 132.59/22.93 ((
% 132.59/22.93 (lamp) =>
% 132.59/22.93 ((
% 132.59/22.93 (lam2p) =>
% 132.59/22.93 ((
% 132.59/22.93 (brelnall1) =>
% 132.59/22.93 ((
% 132.59/22.93 (brelnall2) =>
% 132.59/22.93 ((
% 132.59/22.93 (ex1E2) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcGraphProp1) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcGraphProp3) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcGraphProp2) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcextLem) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcGraphProp4) =>
% 132.59/22.93 ((
% 132.59/22.93 (subbreln) =>
% 132.59/22.93 ((
% 132.59/22.93 (eqbreln) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcext) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcext2) =>
% 132.59/22.93 ((
% 132.59/22.93 (ap2apEq1) =>
% 132.59/22.93 ((
% 132.59/22.93 (ap2apEq2) =>
% 132.59/22.93 ((
% 132.59/22.93 (beta1) =>
% 132.59/22.93 ((
% 132.59/22.93 (eta1) =>
% 132.59/22.93 ((
% 132.59/22.93 (lam2lamEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (beta2) =>
% 132.59/22.93 ((
% 132.59/22.93 (eta2) =>
% 132.59/22.93 ((
% 132.59/22.93 (iffalseProp1) =>
% 132.59/22.93 ((
% 132.59/22.93 (iffalseProp2) =>
% 132.59/22.93 ((
% 132.59/22.93 (iftrueProp1) =>
% 132.59/22.93 ((
% 132.59/22.93 (iftrueProp2) =>
% 132.59/22.93 ((
% 132.59/22.93 (ifSingleton) =>
% 132.59/22.93 ((
% 132.59/22.93 (ifp) =>
% 132.59/22.93 ((
% 132.59/22.93 (theeq) =>
% 132.59/22.93 ((
% 132.59/22.93 (iftrue) =>
% 132.59/22.93 ((
% 132.59/22.93 (iffalse) =>
% 132.59/22.93 ((
% 132.59/22.93 (iftrueorfalse) =>
% 132.59/22.93 ((
% 132.59/22.93 (binintersectT_lem) =>
% 132.59/22.93 ((
% 132.59/22.93 (binunionT_lem) =>
% 132.59/22.93 ((
% 132.59/22.93 (powersetT_lem) =>
% 132.59/22.93 ((
% 132.59/22.93 (setminusT_lem) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementT_lem) =>
% 132.59/22.93 ((
% 132.59/22.93 (setextT) =>
% 132.59/22.93 ((
% 132.59/22.93 (subsetTI) =>
% 132.59/22.93 ((
% 132.59/22.93 (powersetTI1) =>
% 132.59/22.93 ((
% 132.59/22.93 (powersetTE1) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementTI1) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementTE1) =>
% 132.59/22.93 ((
% 132.59/22.93 (binintersectTELcontra) =>
% 132.59/22.93 ((
% 132.59/22.93 (binintersectTERcontra) =>
% 132.59/22.93 ((
% 132.59/22.93 (contrasubsetT) =>
% 132.59/22.93 ((
% 132.59/22.93 (contrasubsetT1) =>
% 132.59/22.93 ((
% 132.59/22.93 (contrasubsetT2) =>
% 132.59/22.93 ((
% 132.59/22.93 (contrasubsetT3) =>
% 132.59/22.93 ((
% 132.59/22.93 (doubleComplementI1) =>
% 132.59/22.93 ((
% 132.59/22.93 (doubleComplementE1) =>
% 132.59/22.93 ((
% 132.59/22.93 (doubleComplementSub1) =>
% 132.59/22.93 ((
% 132.59/22.93 (doubleComplementSub2) =>
% 132.59/22.93 ((
% 132.59/22.93 (doubleComplementEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementTnotintersectT) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementImpComplementIntersect) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementSubsetComplementIntersect) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementInPowersetComplementIntersect) =>
% 132.59/22.93 ((
% 132.59/22.93 (contraSubsetComplement) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementTcontraSubset) =>
% 132.59/22.93 ((
% 132.59/22.93 (binunionTILcontra) =>
% 132.59/22.93 ((
% 132.59/22.93 (binunionTIRcontra) =>
% 132.59/22.93 ((
% 132.59/22.93 (inIntersectImpInUnion) =>
% 132.59/22.93 ((
% 132.59/22.93 (inIntersectImpInUnion2) =>
% 132.59/22.93 ((
% 132.59/22.93 (inIntersectImpInIntersectUnions) =>
% 132.59/22.93 ((
% 132.59/22.93 (intersectInPowersetIntersectUnions) =>
% 132.59/22.93 ((
% 132.59/22.93 (inComplementUnionImpNotIn1) =>
% 132.59/22.93 ((
% 132.59/22.93 (inComplementUnionImpInComplement1) =>
% 132.59/22.93 ((
% 132.59/22.93 (binunionTE) =>
% 132.59/22.93 ((
% 132.59/22.93 (binunionTEcontra) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan2a1) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementUnionInPowersetComplement) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan2a2) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan1a) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan1b) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan1) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan2a) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan2b2) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan2b) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan2) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz13rule0) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz13rule1) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz13rule2) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz13rule3) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz13rule4) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz1_1) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz1_2) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz1_3) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz1_4) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz1_5) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1all2) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1SetBreln1) =>
% 132.59/22.93 ((
% 132.59/22.93 (choice2fnsingleton) =>
% 132.59/22.93 ((
% 132.59/22.93 (setOfPairsIsBReln1) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1all1) =>
% 132.59/22.93 ((
% 132.59/22.93 (subbreln1) =>
% 132.59/22.93 ((
% 132.59/22.93 (eqbreln1) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1invprop) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1invI) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1invE) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1compprop) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1compI) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1compE) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1compEex) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1unionprop) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1unionIL) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1unionIR) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1unionI) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1unionE) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1unionEcases) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1unionCommutes) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz2Ex) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz2W) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz2A) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz2B) =>
% 132.59/22.93 ((
% 132.59/22.93 (image1Ex) =>
% 132.59/22.93 ((
% 132.59/22.93 (image1Ex1) =>
% 132.59/22.93 ((
% 132.59/22.93 (image1Equiv) =>
% 132.59/22.93 ((
% 132.59/22.93 (image1E) =>
% 132.59/22.93 ((
% 132.59/22.93 (image1I) =>
% 132.59/22.93 ((
% 132.59/22.93 (injFuncInInjFuncSet) =>
% 132.59/22.93 ((
% 132.59/22.93 (injFuncSetFuncIn) =>
% 132.59/22.93 ((
% 132.59/22.93 (injFuncSetFuncInj) =>
% 132.59/22.93 ((
% 132.59/22.93 (surjFuncSetFuncIn) =>
% 132.59/22.93 ((
% 132.59/22.93 (surjFuncSetFuncSurj) =>
% 132.59/22.93 ((
% 132.59/22.93 (leftInvIsSurj) =>
% 132.59/22.93 ((
% 132.59/22.93 (surjCantorThm) =>
% 132.59/22.93 ((
% 132.59/22.93 (foundation2) =>
% 132.59/22.93 ((
% 132.59/22.93 (notinself) =>
% 132.59/22.93 ((
% 132.59/22.93 (notinself2) =>
% 132.59/22.93 ((
% 132.59/22.93 (omegaSp) =>
% 132.59/22.93 ((
% 132.59/22.93 (omegaSclos) =>
% 132.59/22.93 ((
% 132.59/22.93 (peano0notS) =>
% 132.59/22.93 ((
% 132.59/22.93 (peanoSinj) =>
% 132.59/22.93 ((
% 132.59/22.93 (transitivesetOp1) =>
% 132.59/22.93 ((
% 132.59/22.93 (binintTransitive) =>
% 132.59/22.93 ((
% 132.59/22.93 (transitivesetOp2) =>
% 132.59/22.93 ((
% 132.59/22.93 (setunionTransitive) =>
% 132.59/22.93 ((
% 132.59/22.93 (ordinalMinLem1) =>
% 132.59/22.93 ((
% 132.59/22.93 (ordinalTransSet) =>
% 132.59/22.93 ((
% 132.59/22.93 (ordinalTransSet1) =>
% 132.59/22.93 ((
% 132.59/22.93 (setunionOrdinalLem1) =>
% 132.59/22.93 (ordinal @
% 132.59/22.93 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.59/22.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl951])).
% 132.59/22.93 thf(zip_derived_cl964, plain,
% 132.59/22.93 (~ (((binintersectEL) =>
% 132.59/22.93 (((binintersectLsub) =>
% 132.59/22.93 (((binintersectSubset2) =>
% 132.59/22.93 (((binintersectSubset3) =>
% 132.59/22.93 (((binintersectER) =>
% 132.59/22.93 (((disjointsetsI1) =>
% 132.59/22.93 (((binintersectRsub) =>
% 132.59/22.93 (((binintersectSubset4) =>
% 132.59/22.93 (((binintersectSubset1) =>
% 132.59/22.93 (((bs114d) =>
% 132.59/22.93 (((setminusI) =>
% 132.59/22.93 (((setminusEL) =>
% 132.59/22.93 (((setminusER) =>
% 132.59/22.93 (((setminusSubset2) =>
% 132.59/22.93 (((setminusERneg) =>
% 132.59/22.93 (((setminusELneg) =>
% 132.59/22.93 (((setminusILneg) =>
% 132.59/22.93 (((setminusIRneg) =>
% 132.59/22.93 (((setminusLsub) =>
% 132.59/22.93 (((setminusSubset1) =>
% 132.59/22.93 (((symdiffE) =>
% 132.59/22.93 (((symdiffI1) =>
% 132.59/22.93 (((symdiffI2) =>
% 132.59/22.93 (((symdiffIneg1) =>
% 132.59/22.93 (((symdiffIneg2) =>
% 132.59/22.93 (((secondinupair) =>
% 132.59/22.93 (((setukpairIL) =>
% 132.59/22.93 (((setukpairIR) =>
% 132.59/22.93 (((kpairiskpair) =>
% 132.59/22.93 (((kpairp) =>
% 132.59/22.93 ((
% 132.59/22.93 (singletonsubset) =>
% 132.59/22.93 ((
% 132.59/22.93 (singletoninpowerset) =>
% 132.59/22.93 ((
% 132.59/22.93 (singletoninpowunion) =>
% 132.59/22.93 ((
% 132.59/22.93 (upairset2E) =>
% 132.59/22.93 ((
% 132.59/22.93 (upairsubunion) =>
% 132.59/22.93 ((
% 132.59/22.93 (upairinpowunion) =>
% 132.59/22.93 ((
% 132.59/22.93 (ubforcartprodlem1) =>
% 132.59/22.93 ((
% 132.59/22.93 (ubforcartprodlem2) =>
% 132.59/22.93 ((
% 132.59/22.93 (ubforcartprodlem3) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodpairin) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodmempair1) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodmempair) =>
% 132.59/22.93 ((
% 132.59/22.93 (setunionE2) =>
% 132.59/22.93 ((
% 132.59/22.93 (setunionsingleton1) =>
% 132.59/22.93 ((
% 132.59/22.93 (setunionsingleton2) =>
% 132.59/22.93 ((
% 132.59/22.93 (setunionsingleton) =>
% 132.59/22.93 ((
% 132.59/22.93 (singletonprop) =>
% 132.59/22.93 ((
% 132.59/22.93 (ex1E1) =>
% 132.59/22.93 ((
% 132.59/22.93 (ex1I) =>
% 132.59/22.93 ((
% 132.59/22.93 (ex1I2) =>
% 132.59/22.93 ((
% 132.59/22.93 (singletonsuniq) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjL1) =>
% 132.59/22.93 ((
% 132.59/22.93 (kfstsingleton) =>
% 132.59/22.93 ((
% 132.59/22.93 (theprop) =>
% 132.59/22.93 ((
% 132.59/22.93 (kfstpairEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodfstin) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjL2) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjL) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjR11) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjR12) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjR1) =>
% 132.59/22.93 ((
% 132.59/22.93 (upairequniteq) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjR2) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjR) =>
% 132.59/22.93 ((
% 132.59/22.93 (ksndsingleton) =>
% 132.59/22.93 ((
% 132.59/22.93 (ksndpairEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (kpairsurjEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodsndin) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodpairmemEL) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodpairmemER) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodmempaircEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodfstpairEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodsndpairEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodpairsurjEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (dpsetconstrI) =>
% 132.59/22.93 ((
% 132.59/22.93 (dpsetconstrSub) =>
% 132.59/22.93 ((
% 132.59/22.93 (setOfPairsIsBReln) =>
% 132.59/22.93 ((
% 132.59/22.93 (dpsetconstrERa) =>
% 132.59/22.93 ((
% 132.59/22.93 (dpsetconstrEL1) =>
% 132.59/22.93 ((
% 132.59/22.93 (dpsetconstrEL2) =>
% 132.59/22.93 ((
% 132.59/22.93 (dpsetconstrER) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcImageSingleton) =>
% 132.59/22.93 ((
% 132.59/22.93 (apProp) =>
% 132.59/22.93 ((
% 132.59/22.93 (app) =>
% 132.59/22.93 ((
% 132.59/22.93 (infuncsetfunc) =>
% 132.59/22.93 ((
% 132.59/22.93 (ap2p) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcinfuncset) =>
% 132.59/22.93 ((
% 132.59/22.93 (lamProp) =>
% 132.59/22.93 ((
% 132.59/22.93 (lamp) =>
% 132.59/22.93 ((
% 132.59/22.93 (lam2p) =>
% 132.59/22.93 ((
% 132.59/22.93 (brelnall1) =>
% 132.59/22.93 ((
% 132.59/22.93 (brelnall2) =>
% 132.59/22.93 ((
% 132.59/22.93 (ex1E2) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcGraphProp1) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcGraphProp3) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcGraphProp2) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcextLem) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcGraphProp4) =>
% 132.59/22.93 ((
% 132.59/22.93 (subbreln) =>
% 132.59/22.93 ((
% 132.59/22.93 (eqbreln) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcext) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcext2) =>
% 132.59/22.93 ((
% 132.59/22.93 (ap2apEq1) =>
% 132.59/22.93 ((
% 132.59/22.93 (ap2apEq2) =>
% 132.59/22.93 ((
% 132.59/22.93 (beta1) =>
% 132.59/22.93 ((
% 132.59/22.93 (eta1) =>
% 132.59/22.93 ((
% 132.59/22.93 (lam2lamEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (beta2) =>
% 132.59/22.93 ((
% 132.59/22.93 (eta2) =>
% 132.59/22.93 ((
% 132.59/22.93 (iffalseProp1) =>
% 132.59/22.93 ((
% 132.59/22.93 (iffalseProp2) =>
% 132.59/22.93 ((
% 132.59/22.93 (iftrueProp1) =>
% 132.59/22.93 ((
% 132.59/22.93 (iftrueProp2) =>
% 132.59/22.93 ((
% 132.59/22.93 (ifSingleton) =>
% 132.59/22.93 ((
% 132.59/22.93 (ifp) =>
% 132.59/22.93 ((
% 132.59/22.93 (theeq) =>
% 132.59/22.93 ((
% 132.59/22.93 (iftrue) =>
% 132.59/22.93 ((
% 132.59/22.93 (iffalse) =>
% 132.59/22.93 ((
% 132.59/22.93 (iftrueorfalse) =>
% 132.59/22.93 ((
% 132.59/22.93 (binintersectT_lem) =>
% 132.59/22.93 ((
% 132.59/22.93 (binunionT_lem) =>
% 132.59/22.93 ((
% 132.59/22.93 (powersetT_lem) =>
% 132.59/22.93 ((
% 132.59/22.93 (setminusT_lem) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementT_lem) =>
% 132.59/22.93 ((
% 132.59/22.93 (setextT) =>
% 132.59/22.93 ((
% 132.59/22.93 (subsetTI) =>
% 132.59/22.93 ((
% 132.59/22.93 (powersetTI1) =>
% 132.59/22.93 ((
% 132.59/22.93 (powersetTE1) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementTI1) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementTE1) =>
% 132.59/22.93 ((
% 132.59/22.93 (binintersectTELcontra) =>
% 132.59/22.93 ((
% 132.59/22.93 (binintersectTERcontra) =>
% 132.59/22.93 ((
% 132.59/22.93 (contrasubsetT) =>
% 132.59/22.93 ((
% 132.59/22.93 (contrasubsetT1) =>
% 132.59/22.93 ((
% 132.59/22.93 (contrasubsetT2) =>
% 132.59/22.93 ((
% 132.59/22.93 (contrasubsetT3) =>
% 132.59/22.93 ((
% 132.59/22.93 (doubleComplementI1) =>
% 132.59/22.93 ((
% 132.59/22.93 (doubleComplementE1) =>
% 132.59/22.93 ((
% 132.59/22.93 (doubleComplementSub1) =>
% 132.59/22.93 ((
% 132.59/22.93 (doubleComplementSub2) =>
% 132.59/22.93 ((
% 132.59/22.93 (doubleComplementEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementTnotintersectT) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementImpComplementIntersect) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementSubsetComplementIntersect) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementInPowersetComplementIntersect) =>
% 132.59/22.93 ((
% 132.59/22.93 (contraSubsetComplement) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementTcontraSubset) =>
% 132.59/22.93 ((
% 132.59/22.93 (binunionTILcontra) =>
% 132.59/22.93 ((
% 132.59/22.93 (binunionTIRcontra) =>
% 132.59/22.93 ((
% 132.59/22.93 (inIntersectImpInUnion) =>
% 132.59/22.93 ((
% 132.59/22.93 (inIntersectImpInUnion2) =>
% 132.59/22.93 ((
% 132.59/22.93 (inIntersectImpInIntersectUnions) =>
% 132.59/22.93 ((
% 132.59/22.93 (intersectInPowersetIntersectUnions) =>
% 132.59/22.93 ((
% 132.59/22.93 (inComplementUnionImpNotIn1) =>
% 132.59/22.93 ((
% 132.59/22.93 (inComplementUnionImpInComplement1) =>
% 132.59/22.93 ((
% 132.59/22.93 (binunionTE) =>
% 132.59/22.93 ((
% 132.59/22.93 (binunionTEcontra) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan2a1) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementUnionInPowersetComplement) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan2a2) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan1a) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan1b) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan1) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan2a) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan2b2) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan2b) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan2) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz13rule0) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz13rule1) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz13rule2) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz13rule3) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz13rule4) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz1_1) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz1_2) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz1_3) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz1_4) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz1_5) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1all2) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1SetBreln1) =>
% 132.59/22.93 ((
% 132.59/22.93 (choice2fnsingleton) =>
% 132.59/22.93 ((
% 132.59/22.93 (setOfPairsIsBReln1) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1all1) =>
% 132.59/22.93 ((
% 132.59/22.93 (subbreln1) =>
% 132.59/22.93 ((
% 132.59/22.93 (eqbreln1) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1invprop) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1invI) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1invE) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1compprop) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1compI) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1compE) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1compEex) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1unionprop) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1unionIL) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1unionIR) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1unionI) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1unionE) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1unionEcases) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1unionCommutes) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz2Ex) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz2W) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz2A) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz2B) =>
% 132.59/22.93 ((
% 132.59/22.93 (image1Ex) =>
% 132.59/22.93 ((
% 132.59/22.93 (image1Ex1) =>
% 132.59/22.93 ((
% 132.59/22.93 (image1Equiv) =>
% 132.59/22.93 ((
% 132.59/22.93 (image1E) =>
% 132.59/22.93 ((
% 132.59/22.93 (image1I) =>
% 132.59/22.93 ((
% 132.59/22.93 (injFuncInInjFuncSet) =>
% 132.59/22.93 ((
% 132.59/22.93 (injFuncSetFuncIn) =>
% 132.59/22.93 ((
% 132.59/22.93 (injFuncSetFuncInj) =>
% 132.59/22.93 ((
% 132.59/22.93 (surjFuncSetFuncIn) =>
% 132.59/22.93 ((
% 132.59/22.93 (surjFuncSetFuncSurj) =>
% 132.59/22.93 ((
% 132.59/22.93 (leftInvIsSurj) =>
% 132.59/22.93 ((
% 132.59/22.93 (surjCantorThm) =>
% 132.59/22.93 ((
% 132.59/22.93 (foundation2) =>
% 132.59/22.93 ((
% 132.59/22.93 (notinself) =>
% 132.59/22.93 ((
% 132.59/22.93 (notinself2) =>
% 132.59/22.93 ((
% 132.59/22.93 (omegaSp) =>
% 132.59/22.93 ((
% 132.59/22.93 (omegaSclos) =>
% 132.59/22.93 ((
% 132.59/22.93 (peano0notS) =>
% 132.59/22.93 ((
% 132.59/22.93 (peanoSinj) =>
% 132.59/22.93 ((
% 132.59/22.93 (transitivesetOp1) =>
% 132.59/22.93 ((
% 132.59/22.93 (binintTransitive) =>
% 132.59/22.93 ((
% 132.59/22.93 (transitivesetOp2) =>
% 132.59/22.93 ((
% 132.59/22.93 (setunionTransitive) =>
% 132.59/22.93 ((
% 132.59/22.93 (ordinalMinLem1) =>
% 132.59/22.93 ((
% 132.59/22.93 (ordinalTransSet) =>
% 132.59/22.93 ((
% 132.59/22.93 (ordinalTransSet1) =>
% 132.59/22.93 ((
% 132.59/22.93 (setunionOrdinalLem1) =>
% 132.59/22.93 (ordinal @
% 132.59/22.93 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.59/22.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl957])).
% 132.59/22.93 thf(zip_derived_cl971, plain,
% 132.59/22.93 (~ (((binintersectLsub) =>
% 132.59/22.93 (((binintersectSubset2) =>
% 132.59/22.93 (((binintersectSubset3) =>
% 132.59/22.93 (((binintersectER) =>
% 132.59/22.93 (((disjointsetsI1) =>
% 132.59/22.93 (((binintersectRsub) =>
% 132.59/22.93 (((binintersectSubset4) =>
% 132.59/22.93 (((binintersectSubset1) =>
% 132.59/22.93 (((bs114d) =>
% 132.59/22.93 (((setminusI) =>
% 132.59/22.93 (((setminusEL) =>
% 132.59/22.93 (((setminusER) =>
% 132.59/22.93 (((setminusSubset2) =>
% 132.59/22.93 (((setminusERneg) =>
% 132.59/22.93 (((setminusELneg) =>
% 132.59/22.93 (((setminusILneg) =>
% 132.59/22.93 (((setminusIRneg) =>
% 132.59/22.93 (((setminusLsub) =>
% 132.59/22.93 (((setminusSubset1) =>
% 132.59/22.93 (((symdiffE) =>
% 132.59/22.93 (((symdiffI1) =>
% 132.59/22.93 (((symdiffI2) =>
% 132.59/22.93 (((symdiffIneg1) =>
% 132.59/22.93 (((symdiffIneg2) =>
% 132.59/22.93 (((secondinupair) =>
% 132.59/22.93 (((setukpairIL) =>
% 132.59/22.93 (((setukpairIR) =>
% 132.59/22.93 (((kpairiskpair) =>
% 132.59/22.93 (((kpairp) =>
% 132.59/22.93 (((singletonsubset) =>
% 132.59/22.93 ((
% 132.59/22.93 (singletoninpowerset) =>
% 132.59/22.93 ((
% 132.59/22.93 (singletoninpowunion) =>
% 132.59/22.93 ((
% 132.59/22.93 (upairset2E) =>
% 132.59/22.93 ((
% 132.59/22.93 (upairsubunion) =>
% 132.59/22.93 ((
% 132.59/22.93 (upairinpowunion) =>
% 132.59/22.93 ((
% 132.59/22.93 (ubforcartprodlem1) =>
% 132.59/22.93 ((
% 132.59/22.93 (ubforcartprodlem2) =>
% 132.59/22.93 ((
% 132.59/22.93 (ubforcartprodlem3) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodpairin) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodmempair1) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodmempair) =>
% 132.59/22.93 ((
% 132.59/22.93 (setunionE2) =>
% 132.59/22.93 ((
% 132.59/22.93 (setunionsingleton1) =>
% 132.59/22.93 ((
% 132.59/22.93 (setunionsingleton2) =>
% 132.59/22.93 ((
% 132.59/22.93 (setunionsingleton) =>
% 132.59/22.93 ((
% 132.59/22.93 (singletonprop) =>
% 132.59/22.93 ((
% 132.59/22.93 (ex1E1) =>
% 132.59/22.93 ((
% 132.59/22.93 (ex1I) =>
% 132.59/22.93 ((
% 132.59/22.93 (ex1I2) =>
% 132.59/22.93 ((
% 132.59/22.93 (singletonsuniq) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjL1) =>
% 132.59/22.93 ((
% 132.59/22.93 (kfstsingleton) =>
% 132.59/22.93 ((
% 132.59/22.93 (theprop) =>
% 132.59/22.93 ((
% 132.59/22.93 (kfstpairEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodfstin) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjL2) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjL) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjR11) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjR12) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjR1) =>
% 132.59/22.93 ((
% 132.59/22.93 (upairequniteq) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjR2) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjR) =>
% 132.59/22.93 ((
% 132.59/22.93 (ksndsingleton) =>
% 132.59/22.93 ((
% 132.59/22.93 (ksndpairEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (kpairsurjEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodsndin) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodpairmemEL) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodpairmemER) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodmempaircEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodfstpairEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodsndpairEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodpairsurjEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (dpsetconstrI) =>
% 132.59/22.93 ((
% 132.59/22.93 (dpsetconstrSub) =>
% 132.59/22.93 ((
% 132.59/22.93 (setOfPairsIsBReln) =>
% 132.59/22.93 ((
% 132.59/22.93 (dpsetconstrERa) =>
% 132.59/22.93 ((
% 132.59/22.93 (dpsetconstrEL1) =>
% 132.59/22.93 ((
% 132.59/22.93 (dpsetconstrEL2) =>
% 132.59/22.93 ((
% 132.59/22.93 (dpsetconstrER) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcImageSingleton) =>
% 132.59/22.93 ((
% 132.59/22.93 (apProp) =>
% 132.59/22.93 ((
% 132.59/22.93 (app) =>
% 132.59/22.93 ((
% 132.59/22.93 (infuncsetfunc) =>
% 132.59/22.93 ((
% 132.59/22.93 (ap2p) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcinfuncset) =>
% 132.59/22.93 ((
% 132.59/22.93 (lamProp) =>
% 132.59/22.93 ((
% 132.59/22.93 (lamp) =>
% 132.59/22.93 ((
% 132.59/22.93 (lam2p) =>
% 132.59/22.93 ((
% 132.59/22.93 (brelnall1) =>
% 132.59/22.93 ((
% 132.59/22.93 (brelnall2) =>
% 132.59/22.93 ((
% 132.59/22.93 (ex1E2) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcGraphProp1) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcGraphProp3) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcGraphProp2) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcextLem) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcGraphProp4) =>
% 132.59/22.93 ((
% 132.59/22.93 (subbreln) =>
% 132.59/22.93 ((
% 132.59/22.93 (eqbreln) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcext) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcext2) =>
% 132.59/22.93 ((
% 132.59/22.93 (ap2apEq1) =>
% 132.59/22.93 ((
% 132.59/22.93 (ap2apEq2) =>
% 132.59/22.93 ((
% 132.59/22.93 (beta1) =>
% 132.59/22.93 ((
% 132.59/22.93 (eta1) =>
% 132.59/22.93 ((
% 132.59/22.93 (lam2lamEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (beta2) =>
% 132.59/22.93 ((
% 132.59/22.93 (eta2) =>
% 132.59/22.93 ((
% 132.59/22.93 (iffalseProp1) =>
% 132.59/22.93 ((
% 132.59/22.93 (iffalseProp2) =>
% 132.59/22.93 ((
% 132.59/22.93 (iftrueProp1) =>
% 132.59/22.93 ((
% 132.59/22.93 (iftrueProp2) =>
% 132.59/22.93 ((
% 132.59/22.93 (ifSingleton) =>
% 132.59/22.93 ((
% 132.59/22.93 (ifp) =>
% 132.59/22.93 ((
% 132.59/22.93 (theeq) =>
% 132.59/22.93 ((
% 132.59/22.93 (iftrue) =>
% 132.59/22.93 ((
% 132.59/22.93 (iffalse) =>
% 132.59/22.93 ((
% 132.59/22.93 (iftrueorfalse) =>
% 132.59/22.93 ((
% 132.59/22.93 (binintersectT_lem) =>
% 132.59/22.93 ((
% 132.59/22.93 (binunionT_lem) =>
% 132.59/22.93 ((
% 132.59/22.93 (powersetT_lem) =>
% 132.59/22.93 ((
% 132.59/22.93 (setminusT_lem) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementT_lem) =>
% 132.59/22.93 ((
% 132.59/22.93 (setextT) =>
% 132.59/22.93 ((
% 132.59/22.93 (subsetTI) =>
% 132.59/22.93 ((
% 132.59/22.93 (powersetTI1) =>
% 132.59/22.93 ((
% 132.59/22.93 (powersetTE1) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementTI1) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementTE1) =>
% 132.59/22.93 ((
% 132.59/22.93 (binintersectTELcontra) =>
% 132.59/22.93 ((
% 132.59/22.93 (binintersectTERcontra) =>
% 132.59/22.93 ((
% 132.59/22.93 (contrasubsetT) =>
% 132.59/22.93 ((
% 132.59/22.93 (contrasubsetT1) =>
% 132.59/22.93 ((
% 132.59/22.93 (contrasubsetT2) =>
% 132.59/22.93 ((
% 132.59/22.93 (contrasubsetT3) =>
% 132.59/22.93 ((
% 132.59/22.93 (doubleComplementI1) =>
% 132.59/22.93 ((
% 132.59/22.93 (doubleComplementE1) =>
% 132.59/22.93 ((
% 132.59/22.93 (doubleComplementSub1) =>
% 132.59/22.93 ((
% 132.59/22.93 (doubleComplementSub2) =>
% 132.59/22.93 ((
% 132.59/22.93 (doubleComplementEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementTnotintersectT) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementImpComplementIntersect) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementSubsetComplementIntersect) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementInPowersetComplementIntersect) =>
% 132.59/22.93 ((
% 132.59/22.93 (contraSubsetComplement) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementTcontraSubset) =>
% 132.59/22.93 ((
% 132.59/22.93 (binunionTILcontra) =>
% 132.59/22.93 ((
% 132.59/22.93 (binunionTIRcontra) =>
% 132.59/22.93 ((
% 132.59/22.93 (inIntersectImpInUnion) =>
% 132.59/22.93 ((
% 132.59/22.93 (inIntersectImpInUnion2) =>
% 132.59/22.93 ((
% 132.59/22.93 (inIntersectImpInIntersectUnions) =>
% 132.59/22.93 ((
% 132.59/22.93 (intersectInPowersetIntersectUnions) =>
% 132.59/22.93 ((
% 132.59/22.93 (inComplementUnionImpNotIn1) =>
% 132.59/22.93 ((
% 132.59/22.93 (inComplementUnionImpInComplement1) =>
% 132.59/22.93 ((
% 132.59/22.93 (binunionTE) =>
% 132.59/22.93 ((
% 132.59/22.93 (binunionTEcontra) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan2a1) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementUnionInPowersetComplement) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan2a2) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan1a) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan1b) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan1) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan2a) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan2b2) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan2b) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan2) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz13rule0) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz13rule1) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz13rule2) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz13rule3) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz13rule4) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz1_1) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz1_2) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz1_3) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz1_4) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz1_5) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1all2) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1SetBreln1) =>
% 132.59/22.93 ((
% 132.59/22.93 (choice2fnsingleton) =>
% 132.59/22.93 ((
% 132.59/22.93 (setOfPairsIsBReln1) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1all1) =>
% 132.59/22.93 ((
% 132.59/22.93 (subbreln1) =>
% 132.59/22.93 ((
% 132.59/22.93 (eqbreln1) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1invprop) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1invI) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1invE) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1compprop) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1compI) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1compE) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1compEex) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1unionprop) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1unionIL) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1unionIR) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1unionI) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1unionE) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1unionEcases) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1unionCommutes) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz2Ex) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz2W) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz2A) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz2B) =>
% 132.59/22.93 ((
% 132.59/22.93 (image1Ex) =>
% 132.59/22.93 ((
% 132.59/22.93 (image1Ex1) =>
% 132.59/22.93 ((
% 132.59/22.93 (image1Equiv) =>
% 132.59/22.93 ((
% 132.59/22.93 (image1E) =>
% 132.59/22.93 ((
% 132.59/22.93 (image1I) =>
% 132.59/22.93 ((
% 132.59/22.93 (injFuncInInjFuncSet) =>
% 132.59/22.93 ((
% 132.59/22.93 (injFuncSetFuncIn) =>
% 132.59/22.93 ((
% 132.59/22.93 (injFuncSetFuncInj) =>
% 132.59/22.93 ((
% 132.59/22.93 (surjFuncSetFuncIn) =>
% 132.59/22.93 ((
% 132.59/22.93 (surjFuncSetFuncSurj) =>
% 132.59/22.93 ((
% 132.59/22.93 (leftInvIsSurj) =>
% 132.59/22.93 ((
% 132.59/22.93 (surjCantorThm) =>
% 132.59/22.93 ((
% 132.59/22.93 (foundation2) =>
% 132.59/22.93 ((
% 132.59/22.93 (notinself) =>
% 132.59/22.93 ((
% 132.59/22.93 (notinself2) =>
% 132.59/22.93 ((
% 132.59/22.93 (omegaSp) =>
% 132.59/22.93 ((
% 132.59/22.93 (omegaSclos) =>
% 132.59/22.93 ((
% 132.59/22.93 (peano0notS) =>
% 132.59/22.93 ((
% 132.59/22.93 (peanoSinj) =>
% 132.59/22.93 ((
% 132.59/22.93 (transitivesetOp1) =>
% 132.59/22.93 ((
% 132.59/22.93 (binintTransitive) =>
% 132.59/22.93 ((
% 132.59/22.93 (transitivesetOp2) =>
% 132.59/22.93 ((
% 132.59/22.93 (setunionTransitive) =>
% 132.59/22.93 ((
% 132.59/22.93 (ordinalMinLem1) =>
% 132.59/22.93 ((
% 132.59/22.93 (ordinalTransSet) =>
% 132.59/22.93 ((
% 132.59/22.93 (ordinalTransSet1) =>
% 132.59/22.93 ((
% 132.59/22.93 (setunionOrdinalLem1) =>
% 132.59/22.93 (ordinal @
% 132.59/22.93 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.59/22.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl964])).
% 132.59/22.93 thf(zip_derived_cl978, plain,
% 132.59/22.93 (~ (((binintersectSubset2) =>
% 132.59/22.93 (((binintersectSubset3) =>
% 132.59/22.93 (((binintersectER) =>
% 132.59/22.93 (((disjointsetsI1) =>
% 132.59/22.93 (((binintersectRsub) =>
% 132.59/22.93 (((binintersectSubset4) =>
% 132.59/22.93 (((binintersectSubset1) =>
% 132.59/22.93 (((bs114d) =>
% 132.59/22.93 (((setminusI) =>
% 132.59/22.93 (((setminusEL) =>
% 132.59/22.93 (((setminusER) =>
% 132.59/22.93 (((setminusSubset2) =>
% 132.59/22.93 (((setminusERneg) =>
% 132.59/22.93 (((setminusELneg) =>
% 132.59/22.93 (((setminusILneg) =>
% 132.59/22.93 (((setminusIRneg) =>
% 132.59/22.93 (((setminusLsub) =>
% 132.59/22.93 (((setminusSubset1) =>
% 132.59/22.93 (((symdiffE) =>
% 132.59/22.93 (((symdiffI1) =>
% 132.59/22.93 (((symdiffI2) =>
% 132.59/22.93 (((symdiffIneg1) =>
% 132.59/22.93 (((symdiffIneg2) =>
% 132.59/22.93 (((secondinupair) =>
% 132.59/22.93 (((setukpairIL) =>
% 132.59/22.93 (((setukpairIR) =>
% 132.59/22.93 (((kpairiskpair) =>
% 132.59/22.93 (((kpairp) =>
% 132.59/22.93 (((singletonsubset) =>
% 132.59/22.93 (((singletoninpowerset) =>
% 132.59/22.93 ((
% 132.59/22.93 (singletoninpowunion) =>
% 132.59/22.93 ((
% 132.59/22.93 (upairset2E) =>
% 132.59/22.93 ((
% 132.59/22.93 (upairsubunion) =>
% 132.59/22.93 ((
% 132.59/22.93 (upairinpowunion) =>
% 132.59/22.93 ((
% 132.59/22.93 (ubforcartprodlem1) =>
% 132.59/22.93 ((
% 132.59/22.93 (ubforcartprodlem2) =>
% 132.59/22.93 ((
% 132.59/22.93 (ubforcartprodlem3) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodpairin) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodmempair1) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodmempair) =>
% 132.59/22.93 ((
% 132.59/22.93 (setunionE2) =>
% 132.59/22.93 ((
% 132.59/22.93 (setunionsingleton1) =>
% 132.59/22.93 ((
% 132.59/22.93 (setunionsingleton2) =>
% 132.59/22.93 ((
% 132.59/22.93 (setunionsingleton) =>
% 132.59/22.93 ((
% 132.59/22.93 (singletonprop) =>
% 132.59/22.93 ((
% 132.59/22.93 (ex1E1) =>
% 132.59/22.93 ((
% 132.59/22.93 (ex1I) =>
% 132.59/22.93 ((
% 132.59/22.93 (ex1I2) =>
% 132.59/22.93 ((
% 132.59/22.93 (singletonsuniq) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjL1) =>
% 132.59/22.93 ((
% 132.59/22.93 (kfstsingleton) =>
% 132.59/22.93 ((
% 132.59/22.93 (theprop) =>
% 132.59/22.93 ((
% 132.59/22.93 (kfstpairEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodfstin) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjL2) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjL) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjR11) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjR12) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjR1) =>
% 132.59/22.93 ((
% 132.59/22.93 (upairequniteq) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjR2) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjR) =>
% 132.59/22.93 ((
% 132.59/22.93 (ksndsingleton) =>
% 132.59/22.93 ((
% 132.59/22.93 (ksndpairEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (kpairsurjEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodsndin) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodpairmemEL) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodpairmemER) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodmempaircEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodfstpairEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodsndpairEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodpairsurjEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (dpsetconstrI) =>
% 132.59/22.93 ((
% 132.59/22.93 (dpsetconstrSub) =>
% 132.59/22.93 ((
% 132.59/22.93 (setOfPairsIsBReln) =>
% 132.59/22.93 ((
% 132.59/22.93 (dpsetconstrERa) =>
% 132.59/22.93 ((
% 132.59/22.93 (dpsetconstrEL1) =>
% 132.59/22.93 ((
% 132.59/22.93 (dpsetconstrEL2) =>
% 132.59/22.93 ((
% 132.59/22.93 (dpsetconstrER) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcImageSingleton) =>
% 132.59/22.93 ((
% 132.59/22.93 (apProp) =>
% 132.59/22.93 ((
% 132.59/22.93 (app) =>
% 132.59/22.93 ((
% 132.59/22.93 (infuncsetfunc) =>
% 132.59/22.93 ((
% 132.59/22.93 (ap2p) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcinfuncset) =>
% 132.59/22.93 ((
% 132.59/22.93 (lamProp) =>
% 132.59/22.93 ((
% 132.59/22.93 (lamp) =>
% 132.59/22.93 ((
% 132.59/22.93 (lam2p) =>
% 132.59/22.93 ((
% 132.59/22.93 (brelnall1) =>
% 132.59/22.93 ((
% 132.59/22.93 (brelnall2) =>
% 132.59/22.93 ((
% 132.59/22.93 (ex1E2) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcGraphProp1) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcGraphProp3) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcGraphProp2) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcextLem) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcGraphProp4) =>
% 132.59/22.93 ((
% 132.59/22.93 (subbreln) =>
% 132.59/22.93 ((
% 132.59/22.93 (eqbreln) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcext) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcext2) =>
% 132.59/22.93 ((
% 132.59/22.93 (ap2apEq1) =>
% 132.59/22.93 ((
% 132.59/22.93 (ap2apEq2) =>
% 132.59/22.93 ((
% 132.59/22.93 (beta1) =>
% 132.59/22.93 ((
% 132.59/22.93 (eta1) =>
% 132.59/22.93 ((
% 132.59/22.93 (lam2lamEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (beta2) =>
% 132.59/22.93 ((
% 132.59/22.93 (eta2) =>
% 132.59/22.93 ((
% 132.59/22.93 (iffalseProp1) =>
% 132.59/22.93 ((
% 132.59/22.93 (iffalseProp2) =>
% 132.59/22.93 ((
% 132.59/22.93 (iftrueProp1) =>
% 132.59/22.93 ((
% 132.59/22.93 (iftrueProp2) =>
% 132.59/22.93 ((
% 132.59/22.93 (ifSingleton) =>
% 132.59/22.93 ((
% 132.59/22.93 (ifp) =>
% 132.59/22.93 ((
% 132.59/22.93 (theeq) =>
% 132.59/22.93 ((
% 132.59/22.93 (iftrue) =>
% 132.59/22.93 ((
% 132.59/22.93 (iffalse) =>
% 132.59/22.93 ((
% 132.59/22.93 (iftrueorfalse) =>
% 132.59/22.93 ((
% 132.59/22.93 (binintersectT_lem) =>
% 132.59/22.93 ((
% 132.59/22.93 (binunionT_lem) =>
% 132.59/22.93 ((
% 132.59/22.93 (powersetT_lem) =>
% 132.59/22.93 ((
% 132.59/22.93 (setminusT_lem) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementT_lem) =>
% 132.59/22.93 ((
% 132.59/22.93 (setextT) =>
% 132.59/22.93 ((
% 132.59/22.93 (subsetTI) =>
% 132.59/22.93 ((
% 132.59/22.93 (powersetTI1) =>
% 132.59/22.93 ((
% 132.59/22.93 (powersetTE1) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementTI1) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementTE1) =>
% 132.59/22.93 ((
% 132.59/22.93 (binintersectTELcontra) =>
% 132.59/22.93 ((
% 132.59/22.93 (binintersectTERcontra) =>
% 132.59/22.93 ((
% 132.59/22.93 (contrasubsetT) =>
% 132.59/22.93 ((
% 132.59/22.93 (contrasubsetT1) =>
% 132.59/22.93 ((
% 132.59/22.93 (contrasubsetT2) =>
% 132.59/22.93 ((
% 132.59/22.93 (contrasubsetT3) =>
% 132.59/22.93 ((
% 132.59/22.93 (doubleComplementI1) =>
% 132.59/22.93 ((
% 132.59/22.93 (doubleComplementE1) =>
% 132.59/22.93 ((
% 132.59/22.93 (doubleComplementSub1) =>
% 132.59/22.93 ((
% 132.59/22.93 (doubleComplementSub2) =>
% 132.59/22.93 ((
% 132.59/22.93 (doubleComplementEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementTnotintersectT) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementImpComplementIntersect) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementSubsetComplementIntersect) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementInPowersetComplementIntersect) =>
% 132.59/22.93 ((
% 132.59/22.93 (contraSubsetComplement) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementTcontraSubset) =>
% 132.59/22.93 ((
% 132.59/22.93 (binunionTILcontra) =>
% 132.59/22.93 ((
% 132.59/22.93 (binunionTIRcontra) =>
% 132.59/22.93 ((
% 132.59/22.93 (inIntersectImpInUnion) =>
% 132.59/22.93 ((
% 132.59/22.93 (inIntersectImpInUnion2) =>
% 132.59/22.93 ((
% 132.59/22.93 (inIntersectImpInIntersectUnions) =>
% 132.59/22.93 ((
% 132.59/22.93 (intersectInPowersetIntersectUnions) =>
% 132.59/22.93 ((
% 132.59/22.93 (inComplementUnionImpNotIn1) =>
% 132.59/22.93 ((
% 132.59/22.93 (inComplementUnionImpInComplement1) =>
% 132.59/22.93 ((
% 132.59/22.93 (binunionTE) =>
% 132.59/22.93 ((
% 132.59/22.93 (binunionTEcontra) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan2a1) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementUnionInPowersetComplement) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan2a2) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan1a) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan1b) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan1) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan2a) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan2b2) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan2b) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan2) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz13rule0) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz13rule1) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz13rule2) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz13rule3) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz13rule4) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz1_1) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz1_2) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz1_3) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz1_4) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz1_5) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1all2) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1SetBreln1) =>
% 132.59/22.93 ((
% 132.59/22.93 (choice2fnsingleton) =>
% 132.59/22.93 ((
% 132.59/22.93 (setOfPairsIsBReln1) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1all1) =>
% 132.59/22.93 ((
% 132.59/22.93 (subbreln1) =>
% 132.59/22.93 ((
% 132.59/22.93 (eqbreln1) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1invprop) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1invI) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1invE) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1compprop) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1compI) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1compE) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1compEex) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1unionprop) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1unionIL) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1unionIR) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1unionI) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1unionE) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1unionEcases) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1unionCommutes) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz2Ex) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz2W) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz2A) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz2B) =>
% 132.59/22.93 ((
% 132.59/22.93 (image1Ex) =>
% 132.59/22.93 ((
% 132.59/22.93 (image1Ex1) =>
% 132.59/22.93 ((
% 132.59/22.93 (image1Equiv) =>
% 132.59/22.93 ((
% 132.59/22.93 (image1E) =>
% 132.59/22.93 ((
% 132.59/22.93 (image1I) =>
% 132.59/22.93 ((
% 132.59/22.93 (injFuncInInjFuncSet) =>
% 132.59/22.93 ((
% 132.59/22.93 (injFuncSetFuncIn) =>
% 132.59/22.93 ((
% 132.59/22.93 (injFuncSetFuncInj) =>
% 132.59/22.93 ((
% 132.59/22.93 (surjFuncSetFuncIn) =>
% 132.59/22.93 ((
% 132.59/22.93 (surjFuncSetFuncSurj) =>
% 132.59/22.93 ((
% 132.59/22.93 (leftInvIsSurj) =>
% 132.59/22.93 ((
% 132.59/22.93 (surjCantorThm) =>
% 132.59/22.93 ((
% 132.59/22.93 (foundation2) =>
% 132.59/22.93 ((
% 132.59/22.93 (notinself) =>
% 132.59/22.93 ((
% 132.59/22.93 (notinself2) =>
% 132.59/22.93 ((
% 132.59/22.93 (omegaSp) =>
% 132.59/22.93 ((
% 132.59/22.93 (omegaSclos) =>
% 132.59/22.93 ((
% 132.59/22.93 (peano0notS) =>
% 132.59/22.93 ((
% 132.59/22.93 (peanoSinj) =>
% 132.59/22.93 ((
% 132.59/22.93 (transitivesetOp1) =>
% 132.59/22.93 ((
% 132.59/22.93 (binintTransitive) =>
% 132.59/22.93 ((
% 132.59/22.93 (transitivesetOp2) =>
% 132.59/22.93 ((
% 132.59/22.93 (setunionTransitive) =>
% 132.59/22.93 ((
% 132.59/22.93 (ordinalMinLem1) =>
% 132.59/22.93 ((
% 132.59/22.93 (ordinalTransSet) =>
% 132.59/22.93 ((
% 132.59/22.93 (ordinalTransSet1) =>
% 132.59/22.93 ((
% 132.59/22.93 (setunionOrdinalLem1) =>
% 132.59/22.93 (ordinal @
% 132.59/22.93 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.59/22.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl971])).
% 132.59/22.93 thf(zip_derived_cl985, plain,
% 132.59/22.93 (~ (((binintersectSubset3) =>
% 132.59/22.93 (((binintersectER) =>
% 132.59/22.93 (((disjointsetsI1) =>
% 132.59/22.93 (((binintersectRsub) =>
% 132.59/22.93 (((binintersectSubset4) =>
% 132.59/22.93 (((binintersectSubset1) =>
% 132.59/22.93 (((bs114d) =>
% 132.59/22.93 (((setminusI) =>
% 132.59/22.93 (((setminusEL) =>
% 132.59/22.93 (((setminusER) =>
% 132.59/22.93 (((setminusSubset2) =>
% 132.59/22.93 (((setminusERneg) =>
% 132.59/22.93 (((setminusELneg) =>
% 132.59/22.93 (((setminusILneg) =>
% 132.59/22.93 (((setminusIRneg) =>
% 132.59/22.93 (((setminusLsub) =>
% 132.59/22.93 (((setminusSubset1) =>
% 132.59/22.93 (((symdiffE) =>
% 132.59/22.93 (((symdiffI1) =>
% 132.59/22.93 (((symdiffI2) =>
% 132.59/22.93 (((symdiffIneg1) =>
% 132.59/22.93 (((symdiffIneg2) =>
% 132.59/22.93 (((secondinupair) =>
% 132.59/22.93 (((setukpairIL) =>
% 132.59/22.93 (((setukpairIR) =>
% 132.59/22.93 (((kpairiskpair) =>
% 132.59/22.93 (((kpairp) =>
% 132.59/22.93 (((singletonsubset) =>
% 132.59/22.93 (((singletoninpowerset) =>
% 132.59/22.93 (((singletoninpowunion) =>
% 132.59/22.93 ((
% 132.59/22.93 (upairset2E) =>
% 132.59/22.93 ((
% 132.59/22.93 (upairsubunion) =>
% 132.59/22.93 ((
% 132.59/22.93 (upairinpowunion) =>
% 132.59/22.93 ((
% 132.59/22.93 (ubforcartprodlem1) =>
% 132.59/22.93 ((
% 132.59/22.93 (ubforcartprodlem2) =>
% 132.59/22.93 ((
% 132.59/22.93 (ubforcartprodlem3) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodpairin) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodmempair1) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodmempair) =>
% 132.59/22.93 ((
% 132.59/22.93 (setunionE2) =>
% 132.59/22.93 ((
% 132.59/22.93 (setunionsingleton1) =>
% 132.59/22.93 ((
% 132.59/22.93 (setunionsingleton2) =>
% 132.59/22.93 ((
% 132.59/22.93 (setunionsingleton) =>
% 132.59/22.93 ((
% 132.59/22.93 (singletonprop) =>
% 132.59/22.93 ((
% 132.59/22.93 (ex1E1) =>
% 132.59/22.93 ((
% 132.59/22.93 (ex1I) =>
% 132.59/22.93 ((
% 132.59/22.93 (ex1I2) =>
% 132.59/22.93 ((
% 132.59/22.93 (singletonsuniq) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjL1) =>
% 132.59/22.93 ((
% 132.59/22.93 (kfstsingleton) =>
% 132.59/22.93 ((
% 132.59/22.93 (theprop) =>
% 132.59/22.93 ((
% 132.59/22.93 (kfstpairEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodfstin) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjL2) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjL) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjR11) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjR12) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjR1) =>
% 132.59/22.93 ((
% 132.59/22.93 (upairequniteq) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjR2) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjR) =>
% 132.59/22.93 ((
% 132.59/22.93 (ksndsingleton) =>
% 132.59/22.93 ((
% 132.59/22.93 (ksndpairEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (kpairsurjEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodsndin) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodpairmemEL) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodpairmemER) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodmempaircEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodfstpairEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodsndpairEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodpairsurjEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (dpsetconstrI) =>
% 132.59/22.93 ((
% 132.59/22.93 (dpsetconstrSub) =>
% 132.59/22.93 ((
% 132.59/22.93 (setOfPairsIsBReln) =>
% 132.59/22.93 ((
% 132.59/22.93 (dpsetconstrERa) =>
% 132.59/22.93 ((
% 132.59/22.93 (dpsetconstrEL1) =>
% 132.59/22.93 ((
% 132.59/22.93 (dpsetconstrEL2) =>
% 132.59/22.93 ((
% 132.59/22.93 (dpsetconstrER) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcImageSingleton) =>
% 132.59/22.93 ((
% 132.59/22.93 (apProp) =>
% 132.59/22.93 ((
% 132.59/22.93 (app) =>
% 132.59/22.93 ((
% 132.59/22.93 (infuncsetfunc) =>
% 132.59/22.93 ((
% 132.59/22.93 (ap2p) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcinfuncset) =>
% 132.59/22.93 ((
% 132.59/22.93 (lamProp) =>
% 132.59/22.93 ((
% 132.59/22.93 (lamp) =>
% 132.59/22.93 ((
% 132.59/22.93 (lam2p) =>
% 132.59/22.93 ((
% 132.59/22.93 (brelnall1) =>
% 132.59/22.93 ((
% 132.59/22.93 (brelnall2) =>
% 132.59/22.93 ((
% 132.59/22.93 (ex1E2) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcGraphProp1) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcGraphProp3) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcGraphProp2) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcextLem) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcGraphProp4) =>
% 132.59/22.93 ((
% 132.59/22.93 (subbreln) =>
% 132.59/22.93 ((
% 132.59/22.93 (eqbreln) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcext) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcext2) =>
% 132.59/22.93 ((
% 132.59/22.93 (ap2apEq1) =>
% 132.59/22.93 ((
% 132.59/22.93 (ap2apEq2) =>
% 132.59/22.93 ((
% 132.59/22.93 (beta1) =>
% 132.59/22.93 ((
% 132.59/22.93 (eta1) =>
% 132.59/22.93 ((
% 132.59/22.93 (lam2lamEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (beta2) =>
% 132.59/22.93 ((
% 132.59/22.93 (eta2) =>
% 132.59/22.93 ((
% 132.59/22.93 (iffalseProp1) =>
% 132.59/22.93 ((
% 132.59/22.93 (iffalseProp2) =>
% 132.59/22.93 ((
% 132.59/22.93 (iftrueProp1) =>
% 132.59/22.93 ((
% 132.59/22.93 (iftrueProp2) =>
% 132.59/22.93 ((
% 132.59/22.93 (ifSingleton) =>
% 132.59/22.93 ((
% 132.59/22.93 (ifp) =>
% 132.59/22.93 ((
% 132.59/22.93 (theeq) =>
% 132.59/22.93 ((
% 132.59/22.93 (iftrue) =>
% 132.59/22.93 ((
% 132.59/22.93 (iffalse) =>
% 132.59/22.93 ((
% 132.59/22.93 (iftrueorfalse) =>
% 132.59/22.93 ((
% 132.59/22.93 (binintersectT_lem) =>
% 132.59/22.93 ((
% 132.59/22.93 (binunionT_lem) =>
% 132.59/22.93 ((
% 132.59/22.93 (powersetT_lem) =>
% 132.59/22.93 ((
% 132.59/22.93 (setminusT_lem) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementT_lem) =>
% 132.59/22.93 ((
% 132.59/22.93 (setextT) =>
% 132.59/22.93 ((
% 132.59/22.93 (subsetTI) =>
% 132.59/22.93 ((
% 132.59/22.93 (powersetTI1) =>
% 132.59/22.93 ((
% 132.59/22.93 (powersetTE1) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementTI1) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementTE1) =>
% 132.59/22.93 ((
% 132.59/22.93 (binintersectTELcontra) =>
% 132.59/22.93 ((
% 132.59/22.93 (binintersectTERcontra) =>
% 132.59/22.93 ((
% 132.59/22.93 (contrasubsetT) =>
% 132.59/22.93 ((
% 132.59/22.93 (contrasubsetT1) =>
% 132.59/22.93 ((
% 132.59/22.93 (contrasubsetT2) =>
% 132.59/22.93 ((
% 132.59/22.93 (contrasubsetT3) =>
% 132.59/22.93 ((
% 132.59/22.93 (doubleComplementI1) =>
% 132.59/22.93 ((
% 132.59/22.93 (doubleComplementE1) =>
% 132.59/22.93 ((
% 132.59/22.93 (doubleComplementSub1) =>
% 132.59/22.93 ((
% 132.59/22.93 (doubleComplementSub2) =>
% 132.59/22.93 ((
% 132.59/22.93 (doubleComplementEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementTnotintersectT) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementImpComplementIntersect) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementSubsetComplementIntersect) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementInPowersetComplementIntersect) =>
% 132.59/22.93 ((
% 132.59/22.93 (contraSubsetComplement) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementTcontraSubset) =>
% 132.59/22.93 ((
% 132.59/22.93 (binunionTILcontra) =>
% 132.59/22.93 ((
% 132.59/22.93 (binunionTIRcontra) =>
% 132.59/22.93 ((
% 132.59/22.93 (inIntersectImpInUnion) =>
% 132.59/22.93 ((
% 132.59/22.93 (inIntersectImpInUnion2) =>
% 132.59/22.93 ((
% 132.59/22.93 (inIntersectImpInIntersectUnions) =>
% 132.59/22.93 ((
% 132.59/22.93 (intersectInPowersetIntersectUnions) =>
% 132.59/22.93 ((
% 132.59/22.93 (inComplementUnionImpNotIn1) =>
% 132.59/22.93 ((
% 132.59/22.93 (inComplementUnionImpInComplement1) =>
% 132.59/22.93 ((
% 132.59/22.93 (binunionTE) =>
% 132.59/22.93 ((
% 132.59/22.93 (binunionTEcontra) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan2a1) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementUnionInPowersetComplement) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan2a2) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan1a) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan1b) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan1) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan2a) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan2b2) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan2b) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan2) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz13rule0) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz13rule1) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz13rule2) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz13rule3) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz13rule4) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz1_1) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz1_2) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz1_3) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz1_4) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz1_5) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1all2) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1SetBreln1) =>
% 132.59/22.93 ((
% 132.59/22.93 (choice2fnsingleton) =>
% 132.59/22.93 ((
% 132.59/22.93 (setOfPairsIsBReln1) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1all1) =>
% 132.59/22.93 ((
% 132.59/22.93 (subbreln1) =>
% 132.59/22.93 ((
% 132.59/22.93 (eqbreln1) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1invprop) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1invI) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1invE) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1compprop) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1compI) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1compE) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1compEex) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1unionprop) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1unionIL) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1unionIR) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1unionI) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1unionE) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1unionEcases) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1unionCommutes) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz2Ex) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz2W) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz2A) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz2B) =>
% 132.59/22.93 ((
% 132.59/22.93 (image1Ex) =>
% 132.59/22.93 ((
% 132.59/22.93 (image1Ex1) =>
% 132.59/22.93 ((
% 132.59/22.93 (image1Equiv) =>
% 132.59/22.93 ((
% 132.59/22.93 (image1E) =>
% 132.59/22.93 ((
% 132.59/22.93 (image1I) =>
% 132.59/22.93 ((
% 132.59/22.93 (injFuncInInjFuncSet) =>
% 132.59/22.93 ((
% 132.59/22.93 (injFuncSetFuncIn) =>
% 132.59/22.93 ((
% 132.59/22.93 (injFuncSetFuncInj) =>
% 132.59/22.93 ((
% 132.59/22.93 (surjFuncSetFuncIn) =>
% 132.59/22.93 ((
% 132.59/22.93 (surjFuncSetFuncSurj) =>
% 132.59/22.93 ((
% 132.59/22.93 (leftInvIsSurj) =>
% 132.59/22.93 ((
% 132.59/22.93 (surjCantorThm) =>
% 132.59/22.93 ((
% 132.59/22.93 (foundation2) =>
% 132.59/22.93 ((
% 132.59/22.93 (notinself) =>
% 132.59/22.93 ((
% 132.59/22.93 (notinself2) =>
% 132.59/22.93 ((
% 132.59/22.93 (omegaSp) =>
% 132.59/22.93 ((
% 132.59/22.93 (omegaSclos) =>
% 132.59/22.93 ((
% 132.59/22.93 (peano0notS) =>
% 132.59/22.93 ((
% 132.59/22.93 (peanoSinj) =>
% 132.59/22.93 ((
% 132.59/22.93 (transitivesetOp1) =>
% 132.59/22.93 ((
% 132.59/22.93 (binintTransitive) =>
% 132.59/22.93 ((
% 132.59/22.93 (transitivesetOp2) =>
% 132.59/22.93 ((
% 132.59/22.93 (setunionTransitive) =>
% 132.59/22.93 ((
% 132.59/22.93 (ordinalMinLem1) =>
% 132.59/22.93 ((
% 132.59/22.93 (ordinalTransSet) =>
% 132.59/22.93 ((
% 132.59/22.93 (ordinalTransSet1) =>
% 132.59/22.93 ((
% 132.59/22.93 (setunionOrdinalLem1) =>
% 132.59/22.93 (ordinal @
% 132.59/22.93 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.59/22.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl978])).
% 132.59/22.93 thf(zip_derived_cl994, plain,
% 132.59/22.93 (~ (((binintersectER) =>
% 132.59/22.93 (((disjointsetsI1) =>
% 132.59/22.93 (((binintersectRsub) =>
% 132.59/22.93 (((binintersectSubset4) =>
% 132.59/22.93 (((binintersectSubset1) =>
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% 132.59/22.93 (((setminusEL) =>
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% 132.59/22.93 (((setminusILneg) =>
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% 132.59/22.93 (((symdiffI1) =>
% 132.59/22.93 (((symdiffI2) =>
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% 132.59/22.93 (((symdiffIneg2) =>
% 132.59/22.93 (((secondinupair) =>
% 132.59/22.93 (((setukpairIL) =>
% 132.59/22.93 (((setukpairIR) =>
% 132.59/22.93 (((kpairiskpair) =>
% 132.59/22.93 (((kpairp) =>
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% 132.59/22.93 (((singletoninpowerset) =>
% 132.59/22.93 (((singletoninpowunion) =>
% 132.59/22.93 (((upairset2E) =>
% 132.59/22.93 ((
% 132.59/22.93 (upairsubunion) =>
% 132.59/22.93 ((
% 132.59/22.93 (upairinpowunion) =>
% 132.59/22.93 ((
% 132.59/22.93 (ubforcartprodlem1) =>
% 132.59/22.93 ((
% 132.59/22.93 (ubforcartprodlem2) =>
% 132.59/22.93 ((
% 132.59/22.93 (ubforcartprodlem3) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodpairin) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodmempair1) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodmempair) =>
% 132.59/22.93 ((
% 132.59/22.93 (setunionE2) =>
% 132.59/22.93 ((
% 132.59/22.93 (setunionsingleton1) =>
% 132.59/22.93 ((
% 132.59/22.93 (setunionsingleton2) =>
% 132.59/22.93 ((
% 132.59/22.93 (setunionsingleton) =>
% 132.59/22.93 ((
% 132.59/22.93 (singletonprop) =>
% 132.59/22.93 ((
% 132.59/22.93 (ex1E1) =>
% 132.59/22.93 ((
% 132.59/22.93 (ex1I) =>
% 132.59/22.93 ((
% 132.59/22.93 (ex1I2) =>
% 132.59/22.93 ((
% 132.59/22.93 (singletonsuniq) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjL1) =>
% 132.59/22.93 ((
% 132.59/22.93 (kfstsingleton) =>
% 132.59/22.93 ((
% 132.59/22.93 (theprop) =>
% 132.59/22.93 ((
% 132.59/22.93 (kfstpairEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodfstin) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjL2) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjL) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjR11) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjR12) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjR1) =>
% 132.59/22.93 ((
% 132.59/22.93 (upairequniteq) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjR2) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjR) =>
% 132.59/22.93 ((
% 132.59/22.93 (ksndsingleton) =>
% 132.59/22.93 ((
% 132.59/22.93 (ksndpairEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (kpairsurjEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodsndin) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodpairmemEL) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodpairmemER) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodmempaircEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodfstpairEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodsndpairEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodpairsurjEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (dpsetconstrI) =>
% 132.59/22.93 ((
% 132.59/22.93 (dpsetconstrSub) =>
% 132.59/22.93 ((
% 132.59/22.93 (setOfPairsIsBReln) =>
% 132.59/22.93 ((
% 132.59/22.93 (dpsetconstrERa) =>
% 132.59/22.93 ((
% 132.59/22.93 (dpsetconstrEL1) =>
% 132.59/22.93 ((
% 132.59/22.93 (dpsetconstrEL2) =>
% 132.59/22.93 ((
% 132.59/22.93 (dpsetconstrER) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcImageSingleton) =>
% 132.59/22.93 ((
% 132.59/22.93 (apProp) =>
% 132.59/22.93 ((
% 132.59/22.93 (app) =>
% 132.59/22.93 ((
% 132.59/22.93 (infuncsetfunc) =>
% 132.59/22.93 ((
% 132.59/22.93 (ap2p) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcinfuncset) =>
% 132.59/22.93 ((
% 132.59/22.93 (lamProp) =>
% 132.59/22.93 ((
% 132.59/22.93 (lamp) =>
% 132.59/22.93 ((
% 132.59/22.93 (lam2p) =>
% 132.59/22.93 ((
% 132.59/22.93 (brelnall1) =>
% 132.59/22.93 ((
% 132.59/22.93 (brelnall2) =>
% 132.59/22.93 ((
% 132.59/22.93 (ex1E2) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcGraphProp1) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcGraphProp3) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcGraphProp2) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcextLem) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcGraphProp4) =>
% 132.59/22.93 ((
% 132.59/22.93 (subbreln) =>
% 132.59/22.93 ((
% 132.59/22.93 (eqbreln) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcext) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcext2) =>
% 132.59/22.93 ((
% 132.59/22.93 (ap2apEq1) =>
% 132.59/22.93 ((
% 132.59/22.93 (ap2apEq2) =>
% 132.59/22.93 ((
% 132.59/22.93 (beta1) =>
% 132.59/22.93 ((
% 132.59/22.93 (eta1) =>
% 132.59/22.93 ((
% 132.59/22.93 (lam2lamEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (beta2) =>
% 132.59/22.93 ((
% 132.59/22.93 (eta2) =>
% 132.59/22.93 ((
% 132.59/22.93 (iffalseProp1) =>
% 132.59/22.93 ((
% 132.59/22.93 (iffalseProp2) =>
% 132.59/22.93 ((
% 132.59/22.93 (iftrueProp1) =>
% 132.59/22.93 ((
% 132.59/22.93 (iftrueProp2) =>
% 132.59/22.93 ((
% 132.59/22.93 (ifSingleton) =>
% 132.59/22.93 ((
% 132.59/22.93 (ifp) =>
% 132.59/22.93 ((
% 132.59/22.93 (theeq) =>
% 132.59/22.93 ((
% 132.59/22.93 (iftrue) =>
% 132.59/22.93 ((
% 132.59/22.93 (iffalse) =>
% 132.59/22.93 ((
% 132.59/22.93 (iftrueorfalse) =>
% 132.59/22.93 ((
% 132.59/22.93 (binintersectT_lem) =>
% 132.59/22.93 ((
% 132.59/22.93 (binunionT_lem) =>
% 132.59/22.93 ((
% 132.59/22.93 (powersetT_lem) =>
% 132.59/22.93 ((
% 132.59/22.93 (setminusT_lem) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementT_lem) =>
% 132.59/22.93 ((
% 132.59/22.93 (setextT) =>
% 132.59/22.93 ((
% 132.59/22.93 (subsetTI) =>
% 132.59/22.93 ((
% 132.59/22.93 (powersetTI1) =>
% 132.59/22.93 ((
% 132.59/22.93 (powersetTE1) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementTI1) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementTE1) =>
% 132.59/22.93 ((
% 132.59/22.93 (binintersectTELcontra) =>
% 132.59/22.93 ((
% 132.59/22.93 (binintersectTERcontra) =>
% 132.59/22.93 ((
% 132.59/22.93 (contrasubsetT) =>
% 132.59/22.93 ((
% 132.59/22.93 (contrasubsetT1) =>
% 132.59/22.93 ((
% 132.59/22.93 (contrasubsetT2) =>
% 132.59/22.93 ((
% 132.59/22.93 (contrasubsetT3) =>
% 132.59/22.93 ((
% 132.59/22.93 (doubleComplementI1) =>
% 132.59/22.93 ((
% 132.59/22.93 (doubleComplementE1) =>
% 132.59/22.93 ((
% 132.59/22.93 (doubleComplementSub1) =>
% 132.59/22.93 ((
% 132.59/22.93 (doubleComplementSub2) =>
% 132.59/22.93 ((
% 132.59/22.93 (doubleComplementEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementTnotintersectT) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementImpComplementIntersect) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementSubsetComplementIntersect) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementInPowersetComplementIntersect) =>
% 132.59/22.93 ((
% 132.59/22.93 (contraSubsetComplement) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementTcontraSubset) =>
% 132.59/22.93 ((
% 132.59/22.93 (binunionTILcontra) =>
% 132.59/22.93 ((
% 132.59/22.93 (binunionTIRcontra) =>
% 132.59/22.93 ((
% 132.59/22.93 (inIntersectImpInUnion) =>
% 132.59/22.93 ((
% 132.59/22.93 (inIntersectImpInUnion2) =>
% 132.59/22.93 ((
% 132.59/22.93 (inIntersectImpInIntersectUnions) =>
% 132.59/22.93 ((
% 132.59/22.93 (intersectInPowersetIntersectUnions) =>
% 132.59/22.93 ((
% 132.59/22.93 (inComplementUnionImpNotIn1) =>
% 132.59/22.93 ((
% 132.59/22.93 (inComplementUnionImpInComplement1) =>
% 132.59/22.93 ((
% 132.59/22.93 (binunionTE) =>
% 132.59/22.93 ((
% 132.59/22.93 (binunionTEcontra) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan2a1) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementUnionInPowersetComplement) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan2a2) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan1a) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan1b) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan1) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan2a) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan2b2) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan2b) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan2) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz13rule0) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz13rule1) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz13rule2) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz13rule3) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz13rule4) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz1_1) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz1_2) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz1_3) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz1_4) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz1_5) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1all2) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1SetBreln1) =>
% 132.59/22.93 ((
% 132.59/22.93 (choice2fnsingleton) =>
% 132.59/22.93 ((
% 132.59/22.93 (setOfPairsIsBReln1) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1all1) =>
% 132.59/22.93 ((
% 132.59/22.93 (subbreln1) =>
% 132.59/22.93 ((
% 132.59/22.93 (eqbreln1) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1invprop) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1invI) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1invE) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1compprop) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1compI) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1compE) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1compEex) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1unionprop) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1unionIL) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1unionIR) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1unionI) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1unionE) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1unionEcases) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1unionCommutes) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz2Ex) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz2W) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz2A) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz2B) =>
% 132.59/22.93 ((
% 132.59/22.93 (image1Ex) =>
% 132.59/22.93 ((
% 132.59/22.93 (image1Ex1) =>
% 132.59/22.93 ((
% 132.59/22.93 (image1Equiv) =>
% 132.59/22.93 ((
% 132.59/22.93 (image1E) =>
% 132.59/22.93 ((
% 132.59/22.93 (image1I) =>
% 132.59/22.93 ((
% 132.59/22.93 (injFuncInInjFuncSet) =>
% 132.59/22.93 ((
% 132.59/22.93 (injFuncSetFuncIn) =>
% 132.59/22.93 ((
% 132.59/22.93 (injFuncSetFuncInj) =>
% 132.59/22.93 ((
% 132.59/22.93 (surjFuncSetFuncIn) =>
% 132.59/22.93 ((
% 132.59/22.93 (surjFuncSetFuncSurj) =>
% 132.59/22.93 ((
% 132.59/22.93 (leftInvIsSurj) =>
% 132.59/22.93 ((
% 132.59/22.93 (surjCantorThm) =>
% 132.59/22.93 ((
% 132.59/22.93 (foundation2) =>
% 132.59/22.93 ((
% 132.59/22.93 (notinself) =>
% 132.59/22.93 ((
% 132.59/22.93 (notinself2) =>
% 132.59/22.93 ((
% 132.59/22.93 (omegaSp) =>
% 132.59/22.93 ((
% 132.59/22.93 (omegaSclos) =>
% 132.59/22.93 ((
% 132.59/22.93 (peano0notS) =>
% 132.59/22.93 ((
% 132.59/22.93 (peanoSinj) =>
% 132.59/22.93 ((
% 132.59/22.93 (transitivesetOp1) =>
% 132.59/22.93 ((
% 132.59/22.93 (binintTransitive) =>
% 132.59/22.93 ((
% 132.59/22.93 (transitivesetOp2) =>
% 132.59/22.93 ((
% 132.59/22.93 (setunionTransitive) =>
% 132.59/22.93 ((
% 132.59/22.93 (ordinalMinLem1) =>
% 132.59/22.93 ((
% 132.59/22.93 (ordinalTransSet) =>
% 132.59/22.93 ((
% 132.59/22.93 (ordinalTransSet1) =>
% 132.59/22.93 ((
% 132.59/22.93 (setunionOrdinalLem1) =>
% 132.59/22.93 (ordinal @
% 132.59/22.93 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.59/22.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl985])).
% 132.59/22.93 thf(zip_derived_cl1002, plain,
% 132.59/22.93 (~ (((disjointsetsI1) =>
% 132.59/22.93 (((binintersectRsub) =>
% 132.59/22.93 (((binintersectSubset4) =>
% 132.59/22.93 (((binintersectSubset1) =>
% 132.59/22.93 (((bs114d) =>
% 132.59/22.93 (((setminusI) =>
% 132.59/22.93 (((setminusEL) =>
% 132.59/22.93 (((setminusER) =>
% 132.59/22.93 (((setminusSubset2) =>
% 132.59/22.93 (((setminusERneg) =>
% 132.59/22.93 (((setminusELneg) =>
% 132.59/22.93 (((setminusILneg) =>
% 132.59/22.93 (((setminusIRneg) =>
% 132.59/22.93 (((setminusLsub) =>
% 132.59/22.93 (((setminusSubset1) =>
% 132.59/22.93 (((symdiffE) =>
% 132.59/22.93 (((symdiffI1) =>
% 132.59/22.93 (((symdiffI2) =>
% 132.59/22.93 (((symdiffIneg1) =>
% 132.59/22.93 (((symdiffIneg2) =>
% 132.59/22.93 (((secondinupair) =>
% 132.59/22.93 (((setukpairIL) =>
% 132.59/22.93 (((setukpairIR) =>
% 132.59/22.93 (((kpairiskpair) =>
% 132.59/22.93 (((kpairp) =>
% 132.59/22.93 (((singletonsubset) =>
% 132.59/22.93 (((singletoninpowerset) =>
% 132.59/22.93 (((singletoninpowunion) =>
% 132.59/22.93 (((upairset2E) =>
% 132.59/22.93 (((upairsubunion) =>
% 132.59/22.93 ((
% 132.59/22.93 (upairinpowunion) =>
% 132.59/22.93 ((
% 132.59/22.93 (ubforcartprodlem1) =>
% 132.59/22.93 ((
% 132.59/22.93 (ubforcartprodlem2) =>
% 132.59/22.93 ((
% 132.59/22.93 (ubforcartprodlem3) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodpairin) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodmempair1) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodmempair) =>
% 132.59/22.93 ((
% 132.59/22.93 (setunionE2) =>
% 132.59/22.93 ((
% 132.59/22.93 (setunionsingleton1) =>
% 132.59/22.93 ((
% 132.59/22.93 (setunionsingleton2) =>
% 132.59/22.93 ((
% 132.59/22.93 (setunionsingleton) =>
% 132.59/22.93 ((
% 132.59/22.93 (singletonprop) =>
% 132.59/22.93 ((
% 132.59/22.93 (ex1E1) =>
% 132.59/22.93 ((
% 132.59/22.93 (ex1I) =>
% 132.59/22.93 ((
% 132.59/22.93 (ex1I2) =>
% 132.59/22.93 ((
% 132.59/22.93 (singletonsuniq) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjL1) =>
% 132.59/22.93 ((
% 132.59/22.93 (kfstsingleton) =>
% 132.59/22.93 ((
% 132.59/22.93 (theprop) =>
% 132.59/22.93 ((
% 132.59/22.93 (kfstpairEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodfstin) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjL2) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjL) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjR11) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjR12) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjR1) =>
% 132.59/22.93 ((
% 132.59/22.93 (upairequniteq) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjR2) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjR) =>
% 132.59/22.93 ((
% 132.59/22.93 (ksndsingleton) =>
% 132.59/22.93 ((
% 132.59/22.93 (ksndpairEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (kpairsurjEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodsndin) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodpairmemEL) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodpairmemER) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodmempaircEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodfstpairEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodsndpairEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodpairsurjEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (dpsetconstrI) =>
% 132.59/22.93 ((
% 132.59/22.93 (dpsetconstrSub) =>
% 132.59/22.93 ((
% 132.59/22.93 (setOfPairsIsBReln) =>
% 132.59/22.93 ((
% 132.59/22.93 (dpsetconstrERa) =>
% 132.59/22.93 ((
% 132.59/22.93 (dpsetconstrEL1) =>
% 132.59/22.93 ((
% 132.59/22.93 (dpsetconstrEL2) =>
% 132.59/22.93 ((
% 132.59/22.93 (dpsetconstrER) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcImageSingleton) =>
% 132.59/22.93 ((
% 132.59/22.93 (apProp) =>
% 132.59/22.93 ((
% 132.59/22.93 (app) =>
% 132.59/22.93 ((
% 132.59/22.93 (infuncsetfunc) =>
% 132.59/22.93 ((
% 132.59/22.93 (ap2p) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcinfuncset) =>
% 132.59/22.93 ((
% 132.59/22.93 (lamProp) =>
% 132.59/22.93 ((
% 132.59/22.93 (lamp) =>
% 132.59/22.93 ((
% 132.59/22.93 (lam2p) =>
% 132.59/22.93 ((
% 132.59/22.93 (brelnall1) =>
% 132.59/22.93 ((
% 132.59/22.93 (brelnall2) =>
% 132.59/22.93 ((
% 132.59/22.93 (ex1E2) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcGraphProp1) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcGraphProp3) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcGraphProp2) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcextLem) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcGraphProp4) =>
% 132.59/22.93 ((
% 132.59/22.93 (subbreln) =>
% 132.59/22.93 ((
% 132.59/22.93 (eqbreln) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcext) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcext2) =>
% 132.59/22.93 ((
% 132.59/22.93 (ap2apEq1) =>
% 132.59/22.93 ((
% 132.59/22.93 (ap2apEq2) =>
% 132.59/22.93 ((
% 132.59/22.93 (beta1) =>
% 132.59/22.93 ((
% 132.59/22.93 (eta1) =>
% 132.59/22.93 ((
% 132.59/22.93 (lam2lamEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (beta2) =>
% 132.59/22.93 ((
% 132.59/22.93 (eta2) =>
% 132.59/22.93 ((
% 132.59/22.93 (iffalseProp1) =>
% 132.59/22.93 ((
% 132.59/22.93 (iffalseProp2) =>
% 132.59/22.93 ((
% 132.59/22.93 (iftrueProp1) =>
% 132.59/22.93 ((
% 132.59/22.93 (iftrueProp2) =>
% 132.59/22.93 ((
% 132.59/22.93 (ifSingleton) =>
% 132.59/22.93 ((
% 132.59/22.93 (ifp) =>
% 132.59/22.93 ((
% 132.59/22.93 (theeq) =>
% 132.59/22.93 ((
% 132.59/22.93 (iftrue) =>
% 132.59/22.93 ((
% 132.59/22.93 (iffalse) =>
% 132.59/22.93 ((
% 132.59/22.93 (iftrueorfalse) =>
% 132.59/22.93 ((
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% 132.59/22.93 ((
% 132.59/22.93 (binunionT_lem) =>
% 132.59/22.93 ((
% 132.59/22.93 (powersetT_lem) =>
% 132.59/22.93 ((
% 132.59/22.93 (setminusT_lem) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementT_lem) =>
% 132.59/22.93 ((
% 132.59/22.93 (setextT) =>
% 132.59/22.93 ((
% 132.59/22.93 (subsetTI) =>
% 132.59/22.93 ((
% 132.59/22.93 (powersetTI1) =>
% 132.59/22.93 ((
% 132.59/22.93 (powersetTE1) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementTI1) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementTE1) =>
% 132.59/22.93 ((
% 132.59/22.93 (binintersectTELcontra) =>
% 132.59/22.93 ((
% 132.59/22.93 (binintersectTERcontra) =>
% 132.59/22.93 ((
% 132.59/22.93 (contrasubsetT) =>
% 132.59/22.93 ((
% 132.59/22.93 (contrasubsetT1) =>
% 132.59/22.93 ((
% 132.59/22.93 (contrasubsetT2) =>
% 132.59/22.93 ((
% 132.59/22.93 (contrasubsetT3) =>
% 132.59/22.93 ((
% 132.59/22.93 (doubleComplementI1) =>
% 132.59/22.93 ((
% 132.59/22.93 (doubleComplementE1) =>
% 132.59/22.93 ((
% 132.59/22.93 (doubleComplementSub1) =>
% 132.59/22.93 ((
% 132.59/22.93 (doubleComplementSub2) =>
% 132.59/22.93 ((
% 132.59/22.93 (doubleComplementEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementTnotintersectT) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementImpComplementIntersect) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementSubsetComplementIntersect) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementInPowersetComplementIntersect) =>
% 132.59/22.93 ((
% 132.59/22.93 (contraSubsetComplement) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementTcontraSubset) =>
% 132.59/22.93 ((
% 132.59/22.93 (binunionTILcontra) =>
% 132.59/22.93 ((
% 132.59/22.93 (binunionTIRcontra) =>
% 132.59/22.93 ((
% 132.59/22.93 (inIntersectImpInUnion) =>
% 132.59/22.93 ((
% 132.59/22.93 (inIntersectImpInUnion2) =>
% 132.59/22.93 ((
% 132.59/22.93 (inIntersectImpInIntersectUnions) =>
% 132.59/22.93 ((
% 132.59/22.93 (intersectInPowersetIntersectUnions) =>
% 132.59/22.93 ((
% 132.59/22.93 (inComplementUnionImpNotIn1) =>
% 132.59/22.93 ((
% 132.59/22.93 (inComplementUnionImpInComplement1) =>
% 132.59/22.93 ((
% 132.59/22.93 (binunionTE) =>
% 132.59/22.93 ((
% 132.59/22.93 (binunionTEcontra) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan2a1) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementUnionInPowersetComplement) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan2a2) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan1a) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan1b) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan1) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan2a) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan2b2) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan2b) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan2) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz13rule0) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz13rule1) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz13rule2) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz13rule3) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz13rule4) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz1_1) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz1_2) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz1_3) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz1_4) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz1_5) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1all2) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1SetBreln1) =>
% 132.59/22.93 ((
% 132.59/22.93 (choice2fnsingleton) =>
% 132.59/22.93 ((
% 132.59/22.93 (setOfPairsIsBReln1) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1all1) =>
% 132.59/22.93 ((
% 132.59/22.93 (subbreln1) =>
% 132.59/22.93 ((
% 132.59/22.93 (eqbreln1) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1invprop) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1invI) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1invE) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1compprop) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1compI) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1compE) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1compEex) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1unionprop) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1unionIL) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1unionIR) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1unionI) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1unionE) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1unionEcases) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1unionCommutes) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz2Ex) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz2W) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz2A) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz2B) =>
% 132.59/22.93 ((
% 132.59/22.93 (image1Ex) =>
% 132.59/22.93 ((
% 132.59/22.93 (image1Ex1) =>
% 132.59/22.93 ((
% 132.59/22.93 (image1Equiv) =>
% 132.59/22.93 ((
% 132.59/22.93 (image1E) =>
% 132.59/22.93 ((
% 132.59/22.93 (image1I) =>
% 132.59/22.93 ((
% 132.59/22.93 (injFuncInInjFuncSet) =>
% 132.59/22.93 ((
% 132.59/22.93 (injFuncSetFuncIn) =>
% 132.59/22.93 ((
% 132.59/22.93 (injFuncSetFuncInj) =>
% 132.59/22.93 ((
% 132.59/22.93 (surjFuncSetFuncIn) =>
% 132.59/22.93 ((
% 132.59/22.93 (surjFuncSetFuncSurj) =>
% 132.59/22.93 ((
% 132.59/22.93 (leftInvIsSurj) =>
% 132.59/22.93 ((
% 132.59/22.93 (surjCantorThm) =>
% 132.59/22.93 ((
% 132.59/22.93 (foundation2) =>
% 132.59/22.93 ((
% 132.59/22.93 (notinself) =>
% 132.59/22.93 ((
% 132.59/22.93 (notinself2) =>
% 132.59/22.93 ((
% 132.59/22.93 (omegaSp) =>
% 132.59/22.93 ((
% 132.59/22.93 (omegaSclos) =>
% 132.59/22.93 ((
% 132.59/22.93 (peano0notS) =>
% 132.59/22.93 ((
% 132.59/22.93 (peanoSinj) =>
% 132.59/22.93 ((
% 132.59/22.93 (transitivesetOp1) =>
% 132.59/22.93 ((
% 132.59/22.93 (binintTransitive) =>
% 132.59/22.93 ((
% 132.59/22.93 (transitivesetOp2) =>
% 132.59/22.93 ((
% 132.59/22.93 (setunionTransitive) =>
% 132.59/22.93 ((
% 132.59/22.93 (ordinalMinLem1) =>
% 132.59/22.93 ((
% 132.59/22.93 (ordinalTransSet) =>
% 132.59/22.93 ((
% 132.59/22.93 (ordinalTransSet1) =>
% 132.59/22.93 ((
% 132.59/22.93 (setunionOrdinalLem1) =>
% 132.59/22.93 (ordinal @
% 132.59/22.93 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.59/22.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl994])).
% 132.59/22.93 thf(zip_derived_cl1008, plain,
% 132.59/22.93 (~ (((binintersectRsub) =>
% 132.59/22.93 (((binintersectSubset4) =>
% 132.59/22.93 (((binintersectSubset1) =>
% 132.59/22.93 (((bs114d) =>
% 132.59/22.93 (((setminusI) =>
% 132.59/22.93 (((setminusEL) =>
% 132.59/22.93 (((setminusER) =>
% 132.59/22.93 (((setminusSubset2) =>
% 132.59/22.93 (((setminusERneg) =>
% 132.59/22.93 (((setminusELneg) =>
% 132.59/22.93 (((setminusILneg) =>
% 132.59/22.93 (((setminusIRneg) =>
% 132.59/22.93 (((setminusLsub) =>
% 132.59/22.93 (((setminusSubset1) =>
% 132.59/22.93 (((symdiffE) =>
% 132.59/22.93 (((symdiffI1) =>
% 132.59/22.93 (((symdiffI2) =>
% 132.59/22.93 (((symdiffIneg1) =>
% 132.59/22.93 (((symdiffIneg2) =>
% 132.59/22.93 (((secondinupair) =>
% 132.59/22.93 (((setukpairIL) =>
% 132.59/22.93 (((setukpairIR) =>
% 132.59/22.93 (((kpairiskpair) =>
% 132.59/22.93 (((kpairp) =>
% 132.59/22.93 (((singletonsubset) =>
% 132.59/22.93 (((singletoninpowerset) =>
% 132.59/22.93 (((singletoninpowunion) =>
% 132.59/22.93 (((upairset2E) =>
% 132.59/22.93 (((upairsubunion) =>
% 132.59/22.93 (((upairinpowunion) =>
% 132.59/22.93 ((
% 132.59/22.93 (ubforcartprodlem1) =>
% 132.59/22.93 ((
% 132.59/22.93 (ubforcartprodlem2) =>
% 132.59/22.93 ((
% 132.59/22.93 (ubforcartprodlem3) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodpairin) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodmempair1) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodmempair) =>
% 132.59/22.93 ((
% 132.59/22.93 (setunionE2) =>
% 132.59/22.93 ((
% 132.59/22.93 (setunionsingleton1) =>
% 132.59/22.93 ((
% 132.59/22.93 (setunionsingleton2) =>
% 132.59/22.93 ((
% 132.59/22.93 (setunionsingleton) =>
% 132.59/22.93 ((
% 132.59/22.93 (singletonprop) =>
% 132.59/22.93 ((
% 132.59/22.93 (ex1E1) =>
% 132.59/22.93 ((
% 132.59/22.93 (ex1I) =>
% 132.59/22.93 ((
% 132.59/22.93 (ex1I2) =>
% 132.59/22.93 ((
% 132.59/22.93 (singletonsuniq) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjL1) =>
% 132.59/22.93 ((
% 132.59/22.93 (kfstsingleton) =>
% 132.59/22.93 ((
% 132.59/22.93 (theprop) =>
% 132.59/22.93 ((
% 132.59/22.93 (kfstpairEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodfstin) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjL2) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjL) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjR11) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjR12) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjR1) =>
% 132.59/22.93 ((
% 132.59/22.93 (upairequniteq) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjR2) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjR) =>
% 132.59/22.93 ((
% 132.59/22.93 (ksndsingleton) =>
% 132.59/22.93 ((
% 132.59/22.93 (ksndpairEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (kpairsurjEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodsndin) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodpairmemEL) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodpairmemER) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodmempaircEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodfstpairEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodsndpairEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodpairsurjEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (dpsetconstrI) =>
% 132.59/22.93 ((
% 132.59/22.93 (dpsetconstrSub) =>
% 132.59/22.93 ((
% 132.59/22.93 (setOfPairsIsBReln) =>
% 132.59/22.93 ((
% 132.59/22.93 (dpsetconstrERa) =>
% 132.59/22.93 ((
% 132.59/22.93 (dpsetconstrEL1) =>
% 132.59/22.93 ((
% 132.59/22.93 (dpsetconstrEL2) =>
% 132.59/22.93 ((
% 132.59/22.93 (dpsetconstrER) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcImageSingleton) =>
% 132.59/22.93 ((
% 132.59/22.93 (apProp) =>
% 132.59/22.93 ((
% 132.59/22.93 (app) =>
% 132.59/22.93 ((
% 132.59/22.93 (infuncsetfunc) =>
% 132.59/22.93 ((
% 132.59/22.93 (ap2p) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcinfuncset) =>
% 132.59/22.93 ((
% 132.59/22.93 (lamProp) =>
% 132.59/22.93 ((
% 132.59/22.93 (lamp) =>
% 132.59/22.93 ((
% 132.59/22.93 (lam2p) =>
% 132.59/22.93 ((
% 132.59/22.93 (brelnall1) =>
% 132.59/22.93 ((
% 132.59/22.93 (brelnall2) =>
% 132.59/22.93 ((
% 132.59/22.93 (ex1E2) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcGraphProp1) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcGraphProp3) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcGraphProp2) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcextLem) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcGraphProp4) =>
% 132.59/22.93 ((
% 132.59/22.93 (subbreln) =>
% 132.59/22.93 ((
% 132.59/22.93 (eqbreln) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcext) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcext2) =>
% 132.59/22.93 ((
% 132.59/22.93 (ap2apEq1) =>
% 132.59/22.93 ((
% 132.59/22.93 (ap2apEq2) =>
% 132.59/22.93 ((
% 132.59/22.93 (beta1) =>
% 132.59/22.93 ((
% 132.59/22.93 (eta1) =>
% 132.59/22.93 ((
% 132.59/22.93 (lam2lamEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (beta2) =>
% 132.59/22.93 ((
% 132.59/22.93 (eta2) =>
% 132.59/22.93 ((
% 132.59/22.93 (iffalseProp1) =>
% 132.59/22.93 ((
% 132.59/22.93 (iffalseProp2) =>
% 132.59/22.93 ((
% 132.59/22.93 (iftrueProp1) =>
% 132.59/22.93 ((
% 132.59/22.93 (iftrueProp2) =>
% 132.59/22.93 ((
% 132.59/22.93 (ifSingleton) =>
% 132.59/22.93 ((
% 132.59/22.93 (ifp) =>
% 132.59/22.93 ((
% 132.59/22.93 (theeq) =>
% 132.59/22.93 ((
% 132.59/22.93 (iftrue) =>
% 132.59/22.93 ((
% 132.59/22.93 (iffalse) =>
% 132.59/22.93 ((
% 132.59/22.93 (iftrueorfalse) =>
% 132.59/22.93 ((
% 132.59/22.93 (binintersectT_lem) =>
% 132.59/22.93 ((
% 132.59/22.93 (binunionT_lem) =>
% 132.59/22.93 ((
% 132.59/22.93 (powersetT_lem) =>
% 132.59/22.93 ((
% 132.59/22.93 (setminusT_lem) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementT_lem) =>
% 132.59/22.93 ((
% 132.59/22.93 (setextT) =>
% 132.59/22.93 ((
% 132.59/22.93 (subsetTI) =>
% 132.59/22.93 ((
% 132.59/22.93 (powersetTI1) =>
% 132.59/22.93 ((
% 132.59/22.93 (powersetTE1) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementTI1) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementTE1) =>
% 132.59/22.93 ((
% 132.59/22.93 (binintersectTELcontra) =>
% 132.59/22.93 ((
% 132.59/22.93 (binintersectTERcontra) =>
% 132.59/22.93 ((
% 132.59/22.93 (contrasubsetT) =>
% 132.59/22.93 ((
% 132.59/22.93 (contrasubsetT1) =>
% 132.59/22.93 ((
% 132.59/22.93 (contrasubsetT2) =>
% 132.59/22.93 ((
% 132.59/22.93 (contrasubsetT3) =>
% 132.59/22.93 ((
% 132.59/22.93 (doubleComplementI1) =>
% 132.59/22.93 ((
% 132.59/22.93 (doubleComplementE1) =>
% 132.59/22.93 ((
% 132.59/22.93 (doubleComplementSub1) =>
% 132.59/22.93 ((
% 132.59/22.93 (doubleComplementSub2) =>
% 132.59/22.93 ((
% 132.59/22.93 (doubleComplementEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementTnotintersectT) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementImpComplementIntersect) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementSubsetComplementIntersect) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementInPowersetComplementIntersect) =>
% 132.59/22.93 ((
% 132.59/22.93 (contraSubsetComplement) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementTcontraSubset) =>
% 132.59/22.93 ((
% 132.59/22.93 (binunionTILcontra) =>
% 132.59/22.93 ((
% 132.59/22.93 (binunionTIRcontra) =>
% 132.59/22.93 ((
% 132.59/22.93 (inIntersectImpInUnion) =>
% 132.59/22.93 ((
% 132.59/22.93 (inIntersectImpInUnion2) =>
% 132.59/22.93 ((
% 132.59/22.93 (inIntersectImpInIntersectUnions) =>
% 132.59/22.93 ((
% 132.59/22.93 (intersectInPowersetIntersectUnions) =>
% 132.59/22.93 ((
% 132.59/22.93 (inComplementUnionImpNotIn1) =>
% 132.59/22.93 ((
% 132.59/22.93 (inComplementUnionImpInComplement1) =>
% 132.59/22.93 ((
% 132.59/22.93 (binunionTE) =>
% 132.59/22.93 ((
% 132.59/22.93 (binunionTEcontra) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan2a1) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementUnionInPowersetComplement) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan2a2) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan1a) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan1b) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan1) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan2a) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan2b2) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan2b) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan2) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz13rule0) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz13rule1) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz13rule2) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz13rule3) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz13rule4) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz1_1) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz1_2) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz1_3) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz1_4) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz1_5) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1all2) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1SetBreln1) =>
% 132.59/22.93 ((
% 132.59/22.93 (choice2fnsingleton) =>
% 132.59/22.93 ((
% 132.59/22.93 (setOfPairsIsBReln1) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1all1) =>
% 132.59/22.93 ((
% 132.59/22.93 (subbreln1) =>
% 132.59/22.93 ((
% 132.59/22.93 (eqbreln1) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1invprop) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1invI) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1invE) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1compprop) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1compI) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1compE) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1compEex) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1unionprop) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1unionIL) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1unionIR) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1unionI) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1unionE) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1unionEcases) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1unionCommutes) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz2Ex) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz2W) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz2A) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz2B) =>
% 132.59/22.93 ((
% 132.59/22.93 (image1Ex) =>
% 132.59/22.93 ((
% 132.59/22.93 (image1Ex1) =>
% 132.59/22.93 ((
% 132.59/22.93 (image1Equiv) =>
% 132.59/22.93 ((
% 132.59/22.93 (image1E) =>
% 132.59/22.93 ((
% 132.59/22.93 (image1I) =>
% 132.59/22.93 ((
% 132.59/22.93 (injFuncInInjFuncSet) =>
% 132.59/22.93 ((
% 132.59/22.93 (injFuncSetFuncIn) =>
% 132.59/22.93 ((
% 132.59/22.93 (injFuncSetFuncInj) =>
% 132.59/22.93 ((
% 132.59/22.93 (surjFuncSetFuncIn) =>
% 132.59/22.93 ((
% 132.59/22.93 (surjFuncSetFuncSurj) =>
% 132.59/22.93 ((
% 132.59/22.93 (leftInvIsSurj) =>
% 132.59/22.93 ((
% 132.59/22.93 (surjCantorThm) =>
% 132.59/22.93 ((
% 132.59/22.93 (foundation2) =>
% 132.59/22.93 ((
% 132.59/22.93 (notinself) =>
% 132.59/22.93 ((
% 132.59/22.93 (notinself2) =>
% 132.59/22.93 ((
% 132.59/22.93 (omegaSp) =>
% 132.59/22.93 ((
% 132.59/22.93 (omegaSclos) =>
% 132.59/22.93 ((
% 132.59/22.93 (peano0notS) =>
% 132.59/22.93 ((
% 132.59/22.93 (peanoSinj) =>
% 132.59/22.93 ((
% 132.59/22.93 (transitivesetOp1) =>
% 132.59/22.93 ((
% 132.59/22.93 (binintTransitive) =>
% 132.59/22.93 ((
% 132.59/22.93 (transitivesetOp2) =>
% 132.59/22.93 ((
% 132.59/22.93 (setunionTransitive) =>
% 132.59/22.93 ((
% 132.59/22.93 (ordinalMinLem1) =>
% 132.59/22.93 ((
% 132.59/22.93 (ordinalTransSet) =>
% 132.59/22.93 ((
% 132.59/22.93 (ordinalTransSet1) =>
% 132.59/22.93 ((
% 132.59/22.93 (setunionOrdinalLem1) =>
% 132.59/22.93 (ordinal @
% 132.59/22.93 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.59/22.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1002])).
% 132.59/22.93 thf(zip_derived_cl1014, plain,
% 132.59/22.93 (~ (((binintersectSubset4) =>
% 132.59/22.93 (((binintersectSubset1) =>
% 132.59/22.93 (((bs114d) =>
% 132.59/22.93 (((setminusI) =>
% 132.59/22.93 (((setminusEL) =>
% 132.59/22.93 (((setminusER) =>
% 132.59/22.93 (((setminusSubset2) =>
% 132.59/22.93 (((setminusERneg) =>
% 132.59/22.93 (((setminusELneg) =>
% 132.59/22.93 (((setminusILneg) =>
% 132.59/22.93 (((setminusIRneg) =>
% 132.59/22.93 (((setminusLsub) =>
% 132.59/22.93 (((setminusSubset1) =>
% 132.59/22.93 (((symdiffE) =>
% 132.59/22.93 (((symdiffI1) =>
% 132.59/22.93 (((symdiffI2) =>
% 132.59/22.93 (((symdiffIneg1) =>
% 132.59/22.93 (((symdiffIneg2) =>
% 132.59/22.93 (((secondinupair) =>
% 132.59/22.93 (((setukpairIL) =>
% 132.59/22.93 (((setukpairIR) =>
% 132.59/22.93 (((kpairiskpair) =>
% 132.59/22.93 (((kpairp) =>
% 132.59/22.93 (((singletonsubset) =>
% 132.59/22.93 (((singletoninpowerset) =>
% 132.59/22.93 (((singletoninpowunion) =>
% 132.59/22.93 (((upairset2E) =>
% 132.59/22.93 (((upairsubunion) =>
% 132.59/22.93 (((upairinpowunion) =>
% 132.59/22.93 (((ubforcartprodlem1) =>
% 132.59/22.93 ((
% 132.59/22.93 (ubforcartprodlem2) =>
% 132.59/22.93 ((
% 132.59/22.93 (ubforcartprodlem3) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodpairin) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodmempair1) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodmempair) =>
% 132.59/22.93 ((
% 132.59/22.93 (setunionE2) =>
% 132.59/22.93 ((
% 132.59/22.93 (setunionsingleton1) =>
% 132.59/22.93 ((
% 132.59/22.93 (setunionsingleton2) =>
% 132.59/22.93 ((
% 132.59/22.93 (setunionsingleton) =>
% 132.59/22.93 ((
% 132.59/22.93 (singletonprop) =>
% 132.59/22.93 ((
% 132.59/22.93 (ex1E1) =>
% 132.59/22.93 ((
% 132.59/22.93 (ex1I) =>
% 132.59/22.93 ((
% 132.59/22.93 (ex1I2) =>
% 132.59/22.93 ((
% 132.59/22.93 (singletonsuniq) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjL1) =>
% 132.59/22.93 ((
% 132.59/22.93 (kfstsingleton) =>
% 132.59/22.93 ((
% 132.59/22.93 (theprop) =>
% 132.59/22.93 ((
% 132.59/22.93 (kfstpairEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodfstin) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjL2) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjL) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjR11) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjR12) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjR1) =>
% 132.59/22.93 ((
% 132.59/22.93 (upairequniteq) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjR2) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjR) =>
% 132.59/22.93 ((
% 132.59/22.93 (ksndsingleton) =>
% 132.59/22.93 ((
% 132.59/22.93 (ksndpairEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (kpairsurjEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodsndin) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodpairmemEL) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodpairmemER) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodmempaircEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodfstpairEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodsndpairEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodpairsurjEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (dpsetconstrI) =>
% 132.59/22.93 ((
% 132.59/22.93 (dpsetconstrSub) =>
% 132.59/22.93 ((
% 132.59/22.93 (setOfPairsIsBReln) =>
% 132.59/22.93 ((
% 132.59/22.93 (dpsetconstrERa) =>
% 132.59/22.93 ((
% 132.59/22.93 (dpsetconstrEL1) =>
% 132.59/22.93 ((
% 132.59/22.93 (dpsetconstrEL2) =>
% 132.59/22.93 ((
% 132.59/22.93 (dpsetconstrER) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcImageSingleton) =>
% 132.59/22.93 ((
% 132.59/22.93 (apProp) =>
% 132.59/22.93 ((
% 132.59/22.93 (app) =>
% 132.59/22.93 ((
% 132.59/22.93 (infuncsetfunc) =>
% 132.59/22.93 ((
% 132.59/22.93 (ap2p) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcinfuncset) =>
% 132.59/22.93 ((
% 132.59/22.93 (lamProp) =>
% 132.59/22.93 ((
% 132.59/22.93 (lamp) =>
% 132.59/22.93 ((
% 132.59/22.93 (lam2p) =>
% 132.59/22.93 ((
% 132.59/22.93 (brelnall1) =>
% 132.59/22.93 ((
% 132.59/22.93 (brelnall2) =>
% 132.59/22.93 ((
% 132.59/22.93 (ex1E2) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcGraphProp1) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcGraphProp3) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcGraphProp2) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcextLem) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcGraphProp4) =>
% 132.59/22.93 ((
% 132.59/22.93 (subbreln) =>
% 132.59/22.93 ((
% 132.59/22.93 (eqbreln) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcext) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcext2) =>
% 132.59/22.93 ((
% 132.59/22.93 (ap2apEq1) =>
% 132.59/22.93 ((
% 132.59/22.93 (ap2apEq2) =>
% 132.59/22.93 ((
% 132.59/22.93 (beta1) =>
% 132.59/22.93 ((
% 132.59/22.93 (eta1) =>
% 132.59/22.93 ((
% 132.59/22.93 (lam2lamEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (beta2) =>
% 132.59/22.93 ((
% 132.59/22.93 (eta2) =>
% 132.59/22.93 ((
% 132.59/22.93 (iffalseProp1) =>
% 132.59/22.93 ((
% 132.59/22.93 (iffalseProp2) =>
% 132.59/22.93 ((
% 132.59/22.93 (iftrueProp1) =>
% 132.59/22.93 ((
% 132.59/22.93 (iftrueProp2) =>
% 132.59/22.93 ((
% 132.59/22.93 (ifSingleton) =>
% 132.59/22.93 ((
% 132.59/22.93 (ifp) =>
% 132.59/22.93 ((
% 132.59/22.93 (theeq) =>
% 132.59/22.93 ((
% 132.59/22.93 (iftrue) =>
% 132.59/22.93 ((
% 132.59/22.93 (iffalse) =>
% 132.59/22.93 ((
% 132.59/22.93 (iftrueorfalse) =>
% 132.59/22.93 ((
% 132.59/22.93 (binintersectT_lem) =>
% 132.59/22.93 ((
% 132.59/22.93 (binunionT_lem) =>
% 132.59/22.93 ((
% 132.59/22.93 (powersetT_lem) =>
% 132.59/22.93 ((
% 132.59/22.93 (setminusT_lem) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementT_lem) =>
% 132.59/22.93 ((
% 132.59/22.93 (setextT) =>
% 132.59/22.93 ((
% 132.59/22.93 (subsetTI) =>
% 132.59/22.93 ((
% 132.59/22.93 (powersetTI1) =>
% 132.59/22.93 ((
% 132.59/22.93 (powersetTE1) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementTI1) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementTE1) =>
% 132.59/22.93 ((
% 132.59/22.93 (binintersectTELcontra) =>
% 132.59/22.93 ((
% 132.59/22.93 (binintersectTERcontra) =>
% 132.59/22.93 ((
% 132.59/22.93 (contrasubsetT) =>
% 132.59/22.93 ((
% 132.59/22.93 (contrasubsetT1) =>
% 132.59/22.93 ((
% 132.59/22.93 (contrasubsetT2) =>
% 132.59/22.93 ((
% 132.59/22.93 (contrasubsetT3) =>
% 132.59/22.93 ((
% 132.59/22.93 (doubleComplementI1) =>
% 132.59/22.93 ((
% 132.59/22.93 (doubleComplementE1) =>
% 132.59/22.93 ((
% 132.59/22.93 (doubleComplementSub1) =>
% 132.59/22.93 ((
% 132.59/22.93 (doubleComplementSub2) =>
% 132.59/22.93 ((
% 132.59/22.93 (doubleComplementEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementTnotintersectT) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementImpComplementIntersect) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementSubsetComplementIntersect) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementInPowersetComplementIntersect) =>
% 132.59/22.93 ((
% 132.59/22.93 (contraSubsetComplement) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementTcontraSubset) =>
% 132.59/22.93 ((
% 132.59/22.93 (binunionTILcontra) =>
% 132.59/22.93 ((
% 132.59/22.93 (binunionTIRcontra) =>
% 132.59/22.93 ((
% 132.59/22.93 (inIntersectImpInUnion) =>
% 132.59/22.93 ((
% 132.59/22.93 (inIntersectImpInUnion2) =>
% 132.59/22.93 ((
% 132.59/22.93 (inIntersectImpInIntersectUnions) =>
% 132.59/22.93 ((
% 132.59/22.93 (intersectInPowersetIntersectUnions) =>
% 132.59/22.93 ((
% 132.59/22.93 (inComplementUnionImpNotIn1) =>
% 132.59/22.93 ((
% 132.59/22.93 (inComplementUnionImpInComplement1) =>
% 132.59/22.93 ((
% 132.59/22.93 (binunionTE) =>
% 132.59/22.93 ((
% 132.59/22.93 (binunionTEcontra) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan2a1) =>
% 132.59/22.93 ((
% 132.59/22.93 (complementUnionInPowersetComplement) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan2a2) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan1a) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan1b) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan1) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan2a) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan2b2) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan2b) =>
% 132.59/22.93 ((
% 132.59/22.93 (demorgan2) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz13rule0) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz13rule1) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz13rule2) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz13rule3) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz13rule4) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz1_1) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz1_2) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz1_3) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz1_4) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz1_5) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1all2) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1SetBreln1) =>
% 132.59/22.93 ((
% 132.59/22.93 (choice2fnsingleton) =>
% 132.59/22.93 ((
% 132.59/22.93 (setOfPairsIsBReln1) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1all1) =>
% 132.59/22.93 ((
% 132.59/22.93 (subbreln1) =>
% 132.59/22.93 ((
% 132.59/22.93 (eqbreln1) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1invprop) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1invI) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1invE) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1compprop) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1compI) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1compE) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1compEex) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1unionprop) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1unionIL) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1unionIR) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1unionI) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1unionE) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1unionEcases) =>
% 132.59/22.93 ((
% 132.59/22.93 (breln1unionCommutes) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz2Ex) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz2W) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz2A) =>
% 132.59/22.93 ((
% 132.59/22.93 (woz2B) =>
% 132.59/22.93 ((
% 132.59/22.93 (image1Ex) =>
% 132.59/22.93 ((
% 132.59/22.93 (image1Ex1) =>
% 132.59/22.93 ((
% 132.59/22.93 (image1Equiv) =>
% 132.59/22.93 ((
% 132.59/22.93 (image1E) =>
% 132.59/22.93 ((
% 132.59/22.93 (image1I) =>
% 132.59/22.93 ((
% 132.59/22.93 (injFuncInInjFuncSet) =>
% 132.59/22.93 ((
% 132.59/22.93 (injFuncSetFuncIn) =>
% 132.59/22.93 ((
% 132.59/22.93 (injFuncSetFuncInj) =>
% 132.59/22.93 ((
% 132.59/22.93 (surjFuncSetFuncIn) =>
% 132.59/22.93 ((
% 132.59/22.93 (surjFuncSetFuncSurj) =>
% 132.59/22.93 ((
% 132.59/22.93 (leftInvIsSurj) =>
% 132.59/22.93 ((
% 132.59/22.93 (surjCantorThm) =>
% 132.59/22.93 ((
% 132.59/22.93 (foundation2) =>
% 132.59/22.93 ((
% 132.59/22.93 (notinself) =>
% 132.59/22.93 ((
% 132.59/22.93 (notinself2) =>
% 132.59/22.93 ((
% 132.59/22.93 (omegaSp) =>
% 132.59/22.93 ((
% 132.59/22.93 (omegaSclos) =>
% 132.59/22.93 ((
% 132.59/22.93 (peano0notS) =>
% 132.59/22.93 ((
% 132.59/22.93 (peanoSinj) =>
% 132.59/22.93 ((
% 132.59/22.93 (transitivesetOp1) =>
% 132.59/22.93 ((
% 132.59/22.93 (binintTransitive) =>
% 132.59/22.93 ((
% 132.59/22.93 (transitivesetOp2) =>
% 132.59/22.93 ((
% 132.59/22.93 (setunionTransitive) =>
% 132.59/22.93 ((
% 132.59/22.93 (ordinalMinLem1) =>
% 132.59/22.93 ((
% 132.59/22.93 (ordinalTransSet) =>
% 132.59/22.93 ((
% 132.59/22.93 (ordinalTransSet1) =>
% 132.59/22.93 ((
% 132.59/22.93 (setunionOrdinalLem1) =>
% 132.59/22.93 (ordinal @
% 132.59/22.93 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.59/22.93 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1008])).
% 132.59/22.93 thf(zip_derived_cl1021, plain,
% 132.59/22.93 (~ (((binintersectSubset1) =>
% 132.59/22.93 (((bs114d) =>
% 132.59/22.93 (((setminusI) =>
% 132.59/22.93 (((setminusEL) =>
% 132.59/22.93 (((setminusER) =>
% 132.59/22.93 (((setminusSubset2) =>
% 132.59/22.93 (((setminusERneg) =>
% 132.59/22.93 (((setminusELneg) =>
% 132.59/22.93 (((setminusILneg) =>
% 132.59/22.93 (((setminusIRneg) =>
% 132.59/22.93 (((setminusLsub) =>
% 132.59/22.93 (((setminusSubset1) =>
% 132.59/22.93 (((symdiffE) =>
% 132.59/22.93 (((symdiffI1) =>
% 132.59/22.93 (((symdiffI2) =>
% 132.59/22.93 (((symdiffIneg1) =>
% 132.59/22.93 (((symdiffIneg2) =>
% 132.59/22.93 (((secondinupair) =>
% 132.59/22.93 (((setukpairIL) =>
% 132.59/22.93 (((setukpairIR) =>
% 132.59/22.93 (((kpairiskpair) =>
% 132.59/22.93 (((kpairp) =>
% 132.59/22.93 (((singletonsubset) =>
% 132.59/22.93 (((singletoninpowerset) =>
% 132.59/22.93 (((singletoninpowunion) =>
% 132.59/22.93 (((upairset2E) =>
% 132.59/22.93 (((upairsubunion) =>
% 132.59/22.93 (((upairinpowunion) =>
% 132.59/22.93 (((ubforcartprodlem1) =>
% 132.59/22.93 (((ubforcartprodlem2) =>
% 132.59/22.93 ((
% 132.59/22.93 (ubforcartprodlem3) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodpairin) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodmempair1) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodmempair) =>
% 132.59/22.93 ((
% 132.59/22.93 (setunionE2) =>
% 132.59/22.93 ((
% 132.59/22.93 (setunionsingleton1) =>
% 132.59/22.93 ((
% 132.59/22.93 (setunionsingleton2) =>
% 132.59/22.93 ((
% 132.59/22.93 (setunionsingleton) =>
% 132.59/22.93 ((
% 132.59/22.93 (singletonprop) =>
% 132.59/22.93 ((
% 132.59/22.93 (ex1E1) =>
% 132.59/22.93 ((
% 132.59/22.93 (ex1I) =>
% 132.59/22.93 ((
% 132.59/22.93 (ex1I2) =>
% 132.59/22.93 ((
% 132.59/22.93 (singletonsuniq) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjL1) =>
% 132.59/22.93 ((
% 132.59/22.93 (kfstsingleton) =>
% 132.59/22.93 ((
% 132.59/22.93 (theprop) =>
% 132.59/22.93 ((
% 132.59/22.93 (kfstpairEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodfstin) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjL2) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjL) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjR11) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjR12) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjR1) =>
% 132.59/22.93 ((
% 132.59/22.93 (upairequniteq) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjR2) =>
% 132.59/22.93 ((
% 132.59/22.93 (setukpairinjR) =>
% 132.59/22.93 ((
% 132.59/22.93 (ksndsingleton) =>
% 132.59/22.93 ((
% 132.59/22.93 (ksndpairEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (kpairsurjEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodsndin) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodpairmemEL) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodpairmemER) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodmempaircEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodfstpairEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodsndpairEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (cartprodpairsurjEq) =>
% 132.59/22.93 ((
% 132.59/22.93 (dpsetconstrI) =>
% 132.59/22.93 ((
% 132.59/22.93 (dpsetconstrSub) =>
% 132.59/22.93 ((
% 132.59/22.93 (setOfPairsIsBReln) =>
% 132.59/22.93 ((
% 132.59/22.93 (dpsetconstrERa) =>
% 132.59/22.93 ((
% 132.59/22.93 (dpsetconstrEL1) =>
% 132.59/22.93 ((
% 132.59/22.93 (dpsetconstrEL2) =>
% 132.59/22.93 ((
% 132.59/22.93 (dpsetconstrER) =>
% 132.59/22.93 ((
% 132.59/22.93 (funcImageSingleton) =>
% 132.59/22.93 ((
% 132.59/22.93 (apProp) =>
% 132.59/22.93 ((
% 132.59/22.93 (app) =>
% 132.59/22.93 ((
% 132.59/22.93 (infuncsetfunc) =>
% 132.59/22.94 ((
% 132.59/22.94 (ap2p) =>
% 132.59/22.94 ((
% 132.59/22.94 (funcinfuncset) =>
% 132.59/22.94 ((
% 132.59/22.94 (lamProp) =>
% 132.59/22.94 ((
% 132.59/22.94 (lamp) =>
% 132.59/22.94 ((
% 132.59/22.94 (lam2p) =>
% 132.59/22.94 ((
% 132.59/22.94 (brelnall1) =>
% 132.59/22.94 ((
% 132.59/22.94 (brelnall2) =>
% 132.59/22.94 ((
% 132.59/22.94 (ex1E2) =>
% 132.59/22.94 ((
% 132.59/22.94 (funcGraphProp1) =>
% 132.59/22.94 ((
% 132.59/22.94 (funcGraphProp3) =>
% 132.59/22.94 ((
% 132.59/22.94 (funcGraphProp2) =>
% 132.59/22.94 ((
% 132.59/22.94 (funcextLem) =>
% 132.59/22.94 ((
% 132.59/22.94 (funcGraphProp4) =>
% 132.59/22.94 ((
% 132.59/22.94 (subbreln) =>
% 132.59/22.94 ((
% 132.59/22.94 (eqbreln) =>
% 132.59/22.94 ((
% 132.59/22.94 (funcext) =>
% 132.59/22.94 ((
% 132.59/22.94 (funcext2) =>
% 132.59/22.94 ((
% 132.59/22.94 (ap2apEq1) =>
% 132.59/22.94 ((
% 132.59/22.94 (ap2apEq2) =>
% 132.59/22.94 ((
% 132.59/22.94 (beta1) =>
% 132.59/22.94 ((
% 132.59/22.94 (eta1) =>
% 132.59/22.94 ((
% 132.59/22.94 (lam2lamEq) =>
% 132.59/22.94 ((
% 132.59/22.94 (beta2) =>
% 132.59/22.94 ((
% 132.59/22.94 (eta2) =>
% 132.59/22.94 ((
% 132.59/22.94 (iffalseProp1) =>
% 132.59/22.94 ((
% 132.59/22.94 (iffalseProp2) =>
% 132.59/22.94 ((
% 132.59/22.94 (iftrueProp1) =>
% 132.59/22.94 ((
% 132.59/22.94 (iftrueProp2) =>
% 132.59/22.94 ((
% 132.59/22.94 (ifSingleton) =>
% 132.59/22.94 ((
% 132.59/22.94 (ifp) =>
% 132.59/22.94 ((
% 132.59/22.94 (theeq) =>
% 132.59/22.94 ((
% 132.59/22.94 (iftrue) =>
% 132.59/22.94 ((
% 132.59/22.94 (iffalse) =>
% 132.59/22.94 ((
% 132.59/22.94 (iftrueorfalse) =>
% 132.59/22.94 ((
% 132.59/22.94 (binintersectT_lem) =>
% 132.59/22.94 ((
% 132.59/22.94 (binunionT_lem) =>
% 132.59/22.94 ((
% 132.59/22.94 (powersetT_lem) =>
% 132.59/22.94 ((
% 132.59/22.94 (setminusT_lem) =>
% 132.59/22.94 ((
% 132.59/22.94 (complementT_lem) =>
% 132.59/22.94 ((
% 132.59/22.94 (setextT) =>
% 132.59/22.94 ((
% 132.59/22.94 (subsetTI) =>
% 132.59/22.94 ((
% 132.59/22.94 (powersetTI1) =>
% 132.59/22.94 ((
% 132.59/22.94 (powersetTE1) =>
% 132.59/22.94 ((
% 132.59/22.94 (complementTI1) =>
% 132.59/22.94 ((
% 132.59/22.94 (complementTE1) =>
% 132.59/22.94 ((
% 132.59/22.94 (binintersectTELcontra) =>
% 132.59/22.94 ((
% 132.59/22.94 (binintersectTERcontra) =>
% 132.59/22.94 ((
% 132.59/22.94 (contrasubsetT) =>
% 132.59/22.94 ((
% 132.59/22.94 (contrasubsetT1) =>
% 132.59/22.94 ((
% 132.59/22.94 (contrasubsetT2) =>
% 132.59/22.94 ((
% 132.59/22.94 (contrasubsetT3) =>
% 132.59/22.94 ((
% 132.59/22.94 (doubleComplementI1) =>
% 132.59/22.94 ((
% 132.59/22.94 (doubleComplementE1) =>
% 132.59/22.94 ((
% 132.59/22.94 (doubleComplementSub1) =>
% 132.59/22.94 ((
% 132.59/22.94 (doubleComplementSub2) =>
% 132.59/22.94 ((
% 132.59/22.94 (doubleComplementEq) =>
% 132.59/22.94 ((
% 132.59/22.94 (complementTnotintersectT) =>
% 132.59/22.94 ((
% 132.59/22.94 (complementImpComplementIntersect) =>
% 132.59/22.94 ((
% 132.59/22.94 (complementSubsetComplementIntersect) =>
% 132.59/22.94 ((
% 132.59/22.94 (complementInPowersetComplementIntersect) =>
% 132.59/22.94 ((
% 132.59/22.94 (contraSubsetComplement) =>
% 132.59/22.94 ((
% 132.59/22.94 (complementTcontraSubset) =>
% 132.59/22.94 ((
% 132.59/22.94 (binunionTILcontra) =>
% 132.59/22.94 ((
% 132.59/22.94 (binunionTIRcontra) =>
% 132.59/22.94 ((
% 132.59/22.94 (inIntersectImpInUnion) =>
% 132.59/22.94 ((
% 132.59/22.94 (inIntersectImpInUnion2) =>
% 132.59/22.94 ((
% 132.59/22.94 (inIntersectImpInIntersectUnions) =>
% 132.59/22.94 ((
% 132.59/22.94 (intersectInPowersetIntersectUnions) =>
% 132.59/22.94 ((
% 132.59/22.94 (inComplementUnionImpNotIn1) =>
% 132.59/22.94 ((
% 132.59/22.94 (inComplementUnionImpInComplement1) =>
% 132.59/22.94 ((
% 132.59/22.94 (binunionTE) =>
% 132.59/22.94 ((
% 132.59/22.94 (binunionTEcontra) =>
% 132.59/22.94 ((
% 132.59/22.94 (demorgan2a1) =>
% 132.59/22.94 ((
% 132.59/22.94 (complementUnionInPowersetComplement) =>
% 132.59/22.94 ((
% 132.59/22.94 (demorgan2a2) =>
% 132.59/22.94 ((
% 132.59/22.94 (demorgan1a) =>
% 132.59/22.94 ((
% 132.59/22.94 (demorgan1b) =>
% 132.59/22.94 ((
% 132.59/22.94 (demorgan1) =>
% 132.59/22.94 ((
% 132.59/22.94 (demorgan2a) =>
% 132.59/22.94 ((
% 132.59/22.94 (demorgan2b2) =>
% 132.59/22.94 ((
% 132.59/22.94 (demorgan2b) =>
% 132.59/22.94 ((
% 132.59/22.94 (demorgan2) =>
% 132.59/22.94 ((
% 132.59/22.94 (woz13rule0) =>
% 132.59/22.94 ((
% 132.59/22.94 (woz13rule1) =>
% 132.59/22.94 ((
% 132.59/22.94 (woz13rule2) =>
% 132.59/22.94 ((
% 132.59/22.94 (woz13rule3) =>
% 132.59/22.94 ((
% 132.59/22.94 (woz13rule4) =>
% 132.59/22.94 ((
% 132.59/22.94 (woz1_1) =>
% 132.59/22.94 ((
% 132.59/22.94 (woz1_2) =>
% 132.59/22.94 ((
% 132.59/22.94 (woz1_3) =>
% 132.59/22.94 ((
% 132.59/22.94 (woz1_4) =>
% 132.59/22.94 ((
% 132.59/22.94 (woz1_5) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1all2) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1SetBreln1) =>
% 132.59/22.94 ((
% 132.59/22.94 (choice2fnsingleton) =>
% 132.59/22.94 ((
% 132.59/22.94 (setOfPairsIsBReln1) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1all1) =>
% 132.59/22.94 ((
% 132.59/22.94 (subbreln1) =>
% 132.59/22.94 ((
% 132.59/22.94 (eqbreln1) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1invprop) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1invI) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1invE) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1compprop) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1compI) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1compE) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1compEex) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1unionprop) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1unionIL) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1unionIR) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1unionI) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1unionE) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1unionEcases) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1unionCommutes) =>
% 132.59/22.94 ((
% 132.59/22.94 (woz2Ex) =>
% 132.59/22.94 ((
% 132.59/22.94 (woz2W) =>
% 132.59/22.94 ((
% 132.59/22.94 (woz2A) =>
% 132.59/22.94 ((
% 132.59/22.94 (woz2B) =>
% 132.59/22.94 ((
% 132.59/22.94 (image1Ex) =>
% 132.59/22.94 ((
% 132.59/22.94 (image1Ex1) =>
% 132.59/22.94 ((
% 132.59/22.94 (image1Equiv) =>
% 132.59/22.94 ((
% 132.59/22.94 (image1E) =>
% 132.59/22.94 ((
% 132.59/22.94 (image1I) =>
% 132.59/22.94 ((
% 132.59/22.94 (injFuncInInjFuncSet) =>
% 132.59/22.94 ((
% 132.59/22.94 (injFuncSetFuncIn) =>
% 132.59/22.94 ((
% 132.59/22.94 (injFuncSetFuncInj) =>
% 132.59/22.94 ((
% 132.59/22.94 (surjFuncSetFuncIn) =>
% 132.59/22.94 ((
% 132.59/22.94 (surjFuncSetFuncSurj) =>
% 132.59/22.94 ((
% 132.59/22.94 (leftInvIsSurj) =>
% 132.59/22.94 ((
% 132.59/22.94 (surjCantorThm) =>
% 132.59/22.94 ((
% 132.59/22.94 (foundation2) =>
% 132.59/22.94 ((
% 132.59/22.94 (notinself) =>
% 132.59/22.94 ((
% 132.59/22.94 (notinself2) =>
% 132.59/22.94 ((
% 132.59/22.94 (omegaSp) =>
% 132.59/22.94 ((
% 132.59/22.94 (omegaSclos) =>
% 132.59/22.94 ((
% 132.59/22.94 (peano0notS) =>
% 132.59/22.94 ((
% 132.59/22.94 (peanoSinj) =>
% 132.59/22.94 ((
% 132.59/22.94 (transitivesetOp1) =>
% 132.59/22.94 ((
% 132.59/22.94 (binintTransitive) =>
% 132.59/22.94 ((
% 132.59/22.94 (transitivesetOp2) =>
% 132.59/22.94 ((
% 132.59/22.94 (setunionTransitive) =>
% 132.59/22.94 ((
% 132.59/22.94 (ordinalMinLem1) =>
% 132.59/22.94 ((
% 132.59/22.94 (ordinalTransSet) =>
% 132.59/22.94 ((
% 132.59/22.94 (ordinalTransSet1) =>
% 132.59/22.94 ((
% 132.59/22.94 (setunionOrdinalLem1) =>
% 132.59/22.94 (ordinal @
% 132.59/22.94 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.59/22.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1014])).
% 132.59/22.94 thf(zip_derived_cl1028, plain,
% 132.59/22.94 (~ (((bs114d) =>
% 132.59/22.94 (((setminusI) =>
% 132.59/22.94 (((setminusEL) =>
% 132.59/22.94 (((setminusER) =>
% 132.59/22.94 (((setminusSubset2) =>
% 132.59/22.94 (((setminusERneg) =>
% 132.59/22.94 (((setminusELneg) =>
% 132.59/22.94 (((setminusILneg) =>
% 132.59/22.94 (((setminusIRneg) =>
% 132.59/22.94 (((setminusLsub) =>
% 132.59/22.94 (((setminusSubset1) =>
% 132.59/22.94 (((symdiffE) =>
% 132.59/22.94 (((symdiffI1) =>
% 132.59/22.94 (((symdiffI2) =>
% 132.59/22.94 (((symdiffIneg1) =>
% 132.59/22.94 (((symdiffIneg2) =>
% 132.59/22.94 (((secondinupair) =>
% 132.59/22.94 (((setukpairIL) =>
% 132.59/22.94 (((setukpairIR) =>
% 132.59/22.94 (((kpairiskpair) =>
% 132.59/22.94 (((kpairp) =>
% 132.59/22.94 (((singletonsubset) =>
% 132.59/22.94 (((singletoninpowerset) =>
% 132.59/22.94 (((singletoninpowunion) =>
% 132.59/22.94 (((upairset2E) =>
% 132.59/22.94 (((upairsubunion) =>
% 132.59/22.94 (((upairinpowunion) =>
% 132.59/22.94 (((ubforcartprodlem1) =>
% 132.59/22.94 (((ubforcartprodlem2) =>
% 132.59/22.94 (((ubforcartprodlem3) =>
% 132.59/22.94 ((
% 132.59/22.94 (cartprodpairin) =>
% 132.59/22.94 ((
% 132.59/22.94 (cartprodmempair1) =>
% 132.59/22.94 ((
% 132.59/22.94 (cartprodmempair) =>
% 132.59/22.94 ((
% 132.59/22.94 (setunionE2) =>
% 132.59/22.94 ((
% 132.59/22.94 (setunionsingleton1) =>
% 132.59/22.94 ((
% 132.59/22.94 (setunionsingleton2) =>
% 132.59/22.94 ((
% 132.59/22.94 (setunionsingleton) =>
% 132.59/22.94 ((
% 132.59/22.94 (singletonprop) =>
% 132.59/22.94 ((
% 132.59/22.94 (ex1E1) =>
% 132.59/22.94 ((
% 132.59/22.94 (ex1I) =>
% 132.59/22.94 ((
% 132.59/22.94 (ex1I2) =>
% 132.59/22.94 ((
% 132.59/22.94 (singletonsuniq) =>
% 132.59/22.94 ((
% 132.59/22.94 (setukpairinjL1) =>
% 132.59/22.94 ((
% 132.59/22.94 (kfstsingleton) =>
% 132.59/22.94 ((
% 132.59/22.94 (theprop) =>
% 132.59/22.94 ((
% 132.59/22.94 (kfstpairEq) =>
% 132.59/22.94 ((
% 132.59/22.94 (cartprodfstin) =>
% 132.59/22.94 ((
% 132.59/22.94 (setukpairinjL2) =>
% 132.59/22.94 ((
% 132.59/22.94 (setukpairinjL) =>
% 132.59/22.94 ((
% 132.59/22.94 (setukpairinjR11) =>
% 132.59/22.94 ((
% 132.59/22.94 (setukpairinjR12) =>
% 132.59/22.94 ((
% 132.59/22.94 (setukpairinjR1) =>
% 132.59/22.94 ((
% 132.59/22.94 (upairequniteq) =>
% 132.59/22.94 ((
% 132.59/22.94 (setukpairinjR2) =>
% 132.59/22.94 ((
% 132.59/22.94 (setukpairinjR) =>
% 132.59/22.94 ((
% 132.59/22.94 (ksndsingleton) =>
% 132.59/22.94 ((
% 132.59/22.94 (ksndpairEq) =>
% 132.59/22.94 ((
% 132.59/22.94 (kpairsurjEq) =>
% 132.59/22.94 ((
% 132.59/22.94 (cartprodsndin) =>
% 132.59/22.94 ((
% 132.59/22.94 (cartprodpairmemEL) =>
% 132.59/22.94 ((
% 132.59/22.94 (cartprodpairmemER) =>
% 132.59/22.94 ((
% 132.59/22.94 (cartprodmempaircEq) =>
% 132.59/22.94 ((
% 132.59/22.94 (cartprodfstpairEq) =>
% 132.59/22.94 ((
% 132.59/22.94 (cartprodsndpairEq) =>
% 132.59/22.94 ((
% 132.59/22.94 (cartprodpairsurjEq) =>
% 132.59/22.94 ((
% 132.59/22.94 (dpsetconstrI) =>
% 132.59/22.94 ((
% 132.59/22.94 (dpsetconstrSub) =>
% 132.59/22.94 ((
% 132.59/22.94 (setOfPairsIsBReln) =>
% 132.59/22.94 ((
% 132.59/22.94 (dpsetconstrERa) =>
% 132.59/22.94 ((
% 132.59/22.94 (dpsetconstrEL1) =>
% 132.59/22.94 ((
% 132.59/22.94 (dpsetconstrEL2) =>
% 132.59/22.94 ((
% 132.59/22.94 (dpsetconstrER) =>
% 132.59/22.94 ((
% 132.59/22.94 (funcImageSingleton) =>
% 132.59/22.94 ((
% 132.59/22.94 (apProp) =>
% 132.59/22.94 ((
% 132.59/22.94 (app) =>
% 132.59/22.94 ((
% 132.59/22.94 (infuncsetfunc) =>
% 132.59/22.94 ((
% 132.59/22.94 (ap2p) =>
% 132.59/22.94 ((
% 132.59/22.94 (funcinfuncset) =>
% 132.59/22.94 ((
% 132.59/22.94 (lamProp) =>
% 132.59/22.94 ((
% 132.59/22.94 (lamp) =>
% 132.59/22.94 ((
% 132.59/22.94 (lam2p) =>
% 132.59/22.94 ((
% 132.59/22.94 (brelnall1) =>
% 132.59/22.94 ((
% 132.59/22.94 (brelnall2) =>
% 132.59/22.94 ((
% 132.59/22.94 (ex1E2) =>
% 132.59/22.94 ((
% 132.59/22.94 (funcGraphProp1) =>
% 132.59/22.94 ((
% 132.59/22.94 (funcGraphProp3) =>
% 132.59/22.94 ((
% 132.59/22.94 (funcGraphProp2) =>
% 132.59/22.94 ((
% 132.59/22.94 (funcextLem) =>
% 132.59/22.94 ((
% 132.59/22.94 (funcGraphProp4) =>
% 132.59/22.94 ((
% 132.59/22.94 (subbreln) =>
% 132.59/22.94 ((
% 132.59/22.94 (eqbreln) =>
% 132.59/22.94 ((
% 132.59/22.94 (funcext) =>
% 132.59/22.94 ((
% 132.59/22.94 (funcext2) =>
% 132.59/22.94 ((
% 132.59/22.94 (ap2apEq1) =>
% 132.59/22.94 ((
% 132.59/22.94 (ap2apEq2) =>
% 132.59/22.94 ((
% 132.59/22.94 (beta1) =>
% 132.59/22.94 ((
% 132.59/22.94 (eta1) =>
% 132.59/22.94 ((
% 132.59/22.94 (lam2lamEq) =>
% 132.59/22.94 ((
% 132.59/22.94 (beta2) =>
% 132.59/22.94 ((
% 132.59/22.94 (eta2) =>
% 132.59/22.94 ((
% 132.59/22.94 (iffalseProp1) =>
% 132.59/22.94 ((
% 132.59/22.94 (iffalseProp2) =>
% 132.59/22.94 ((
% 132.59/22.94 (iftrueProp1) =>
% 132.59/22.94 ((
% 132.59/22.94 (iftrueProp2) =>
% 132.59/22.94 ((
% 132.59/22.94 (ifSingleton) =>
% 132.59/22.94 ((
% 132.59/22.94 (ifp) =>
% 132.59/22.94 ((
% 132.59/22.94 (theeq) =>
% 132.59/22.94 ((
% 132.59/22.94 (iftrue) =>
% 132.59/22.94 ((
% 132.59/22.94 (iffalse) =>
% 132.59/22.94 ((
% 132.59/22.94 (iftrueorfalse) =>
% 132.59/22.94 ((
% 132.59/22.94 (binintersectT_lem) =>
% 132.59/22.94 ((
% 132.59/22.94 (binunionT_lem) =>
% 132.59/22.94 ((
% 132.59/22.94 (powersetT_lem) =>
% 132.59/22.94 ((
% 132.59/22.94 (setminusT_lem) =>
% 132.59/22.94 ((
% 132.59/22.94 (complementT_lem) =>
% 132.59/22.94 ((
% 132.59/22.94 (setextT) =>
% 132.59/22.94 ((
% 132.59/22.94 (subsetTI) =>
% 132.59/22.94 ((
% 132.59/22.94 (powersetTI1) =>
% 132.59/22.94 ((
% 132.59/22.94 (powersetTE1) =>
% 132.59/22.94 ((
% 132.59/22.94 (complementTI1) =>
% 132.59/22.94 ((
% 132.59/22.94 (complementTE1) =>
% 132.59/22.94 ((
% 132.59/22.94 (binintersectTELcontra) =>
% 132.59/22.94 ((
% 132.59/22.94 (binintersectTERcontra) =>
% 132.59/22.94 ((
% 132.59/22.94 (contrasubsetT) =>
% 132.59/22.94 ((
% 132.59/22.94 (contrasubsetT1) =>
% 132.59/22.94 ((
% 132.59/22.94 (contrasubsetT2) =>
% 132.59/22.94 ((
% 132.59/22.94 (contrasubsetT3) =>
% 132.59/22.94 ((
% 132.59/22.94 (doubleComplementI1) =>
% 132.59/22.94 ((
% 132.59/22.94 (doubleComplementE1) =>
% 132.59/22.94 ((
% 132.59/22.94 (doubleComplementSub1) =>
% 132.59/22.94 ((
% 132.59/22.94 (doubleComplementSub2) =>
% 132.59/22.94 ((
% 132.59/22.94 (doubleComplementEq) =>
% 132.59/22.94 ((
% 132.59/22.94 (complementTnotintersectT) =>
% 132.59/22.94 ((
% 132.59/22.94 (complementImpComplementIntersect) =>
% 132.59/22.94 ((
% 132.59/22.94 (complementSubsetComplementIntersect) =>
% 132.59/22.94 ((
% 132.59/22.94 (complementInPowersetComplementIntersect) =>
% 132.59/22.94 ((
% 132.59/22.94 (contraSubsetComplement) =>
% 132.59/22.94 ((
% 132.59/22.94 (complementTcontraSubset) =>
% 132.59/22.94 ((
% 132.59/22.94 (binunionTILcontra) =>
% 132.59/22.94 ((
% 132.59/22.94 (binunionTIRcontra) =>
% 132.59/22.94 ((
% 132.59/22.94 (inIntersectImpInUnion) =>
% 132.59/22.94 ((
% 132.59/22.94 (inIntersectImpInUnion2) =>
% 132.59/22.94 ((
% 132.59/22.94 (inIntersectImpInIntersectUnions) =>
% 132.59/22.94 ((
% 132.59/22.94 (intersectInPowersetIntersectUnions) =>
% 132.59/22.94 ((
% 132.59/22.94 (inComplementUnionImpNotIn1) =>
% 132.59/22.94 ((
% 132.59/22.94 (inComplementUnionImpInComplement1) =>
% 132.59/22.94 ((
% 132.59/22.94 (binunionTE) =>
% 132.59/22.94 ((
% 132.59/22.94 (binunionTEcontra) =>
% 132.59/22.94 ((
% 132.59/22.94 (demorgan2a1) =>
% 132.59/22.94 ((
% 132.59/22.94 (complementUnionInPowersetComplement) =>
% 132.59/22.94 ((
% 132.59/22.94 (demorgan2a2) =>
% 132.59/22.94 ((
% 132.59/22.94 (demorgan1a) =>
% 132.59/22.94 ((
% 132.59/22.94 (demorgan1b) =>
% 132.59/22.94 ((
% 132.59/22.94 (demorgan1) =>
% 132.59/22.94 ((
% 132.59/22.94 (demorgan2a) =>
% 132.59/22.94 ((
% 132.59/22.94 (demorgan2b2) =>
% 132.59/22.94 ((
% 132.59/22.94 (demorgan2b) =>
% 132.59/22.94 ((
% 132.59/22.94 (demorgan2) =>
% 132.59/22.94 ((
% 132.59/22.94 (woz13rule0) =>
% 132.59/22.94 ((
% 132.59/22.94 (woz13rule1) =>
% 132.59/22.94 ((
% 132.59/22.94 (woz13rule2) =>
% 132.59/22.94 ((
% 132.59/22.94 (woz13rule3) =>
% 132.59/22.94 ((
% 132.59/22.94 (woz13rule4) =>
% 132.59/22.94 ((
% 132.59/22.94 (woz1_1) =>
% 132.59/22.94 ((
% 132.59/22.94 (woz1_2) =>
% 132.59/22.94 ((
% 132.59/22.94 (woz1_3) =>
% 132.59/22.94 ((
% 132.59/22.94 (woz1_4) =>
% 132.59/22.94 ((
% 132.59/22.94 (woz1_5) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1all2) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1SetBreln1) =>
% 132.59/22.94 ((
% 132.59/22.94 (choice2fnsingleton) =>
% 132.59/22.94 ((
% 132.59/22.94 (setOfPairsIsBReln1) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1all1) =>
% 132.59/22.94 ((
% 132.59/22.94 (subbreln1) =>
% 132.59/22.94 ((
% 132.59/22.94 (eqbreln1) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1invprop) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1invI) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1invE) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1compprop) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1compI) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1compE) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1compEex) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1unionprop) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1unionIL) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1unionIR) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1unionI) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1unionE) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1unionEcases) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1unionCommutes) =>
% 132.59/22.94 ((
% 132.59/22.94 (woz2Ex) =>
% 132.59/22.94 ((
% 132.59/22.94 (woz2W) =>
% 132.59/22.94 ((
% 132.59/22.94 (woz2A) =>
% 132.59/22.94 ((
% 132.59/22.94 (woz2B) =>
% 132.59/22.94 ((
% 132.59/22.94 (image1Ex) =>
% 132.59/22.94 ((
% 132.59/22.94 (image1Ex1) =>
% 132.59/22.94 ((
% 132.59/22.94 (image1Equiv) =>
% 132.59/22.94 ((
% 132.59/22.94 (image1E) =>
% 132.59/22.94 ((
% 132.59/22.94 (image1I) =>
% 132.59/22.94 ((
% 132.59/22.94 (injFuncInInjFuncSet) =>
% 132.59/22.94 ((
% 132.59/22.94 (injFuncSetFuncIn) =>
% 132.59/22.94 ((
% 132.59/22.94 (injFuncSetFuncInj) =>
% 132.59/22.94 ((
% 132.59/22.94 (surjFuncSetFuncIn) =>
% 132.59/22.94 ((
% 132.59/22.94 (surjFuncSetFuncSurj) =>
% 132.59/22.94 ((
% 132.59/22.94 (leftInvIsSurj) =>
% 132.59/22.94 ((
% 132.59/22.94 (surjCantorThm) =>
% 132.59/22.94 ((
% 132.59/22.94 (foundation2) =>
% 132.59/22.94 ((
% 132.59/22.94 (notinself) =>
% 132.59/22.94 ((
% 132.59/22.94 (notinself2) =>
% 132.59/22.94 ((
% 132.59/22.94 (omegaSp) =>
% 132.59/22.94 ((
% 132.59/22.94 (omegaSclos) =>
% 132.59/22.94 ((
% 132.59/22.94 (peano0notS) =>
% 132.59/22.94 ((
% 132.59/22.94 (peanoSinj) =>
% 132.59/22.94 ((
% 132.59/22.94 (transitivesetOp1) =>
% 132.59/22.94 ((
% 132.59/22.94 (binintTransitive) =>
% 132.59/22.94 ((
% 132.59/22.94 (transitivesetOp2) =>
% 132.59/22.94 ((
% 132.59/22.94 (setunionTransitive) =>
% 132.59/22.94 ((
% 132.59/22.94 (ordinalMinLem1) =>
% 132.59/22.94 ((
% 132.59/22.94 (ordinalTransSet) =>
% 132.59/22.94 ((
% 132.59/22.94 (ordinalTransSet1) =>
% 132.59/22.94 ((
% 132.59/22.94 (setunionOrdinalLem1) =>
% 132.59/22.94 (ordinal @
% 132.59/22.94 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.59/22.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1021])).
% 132.59/22.94 thf(zip_derived_cl1034, plain,
% 132.59/22.94 (~ (((setminusI) =>
% 132.59/22.94 (((setminusEL) =>
% 132.59/22.94 (((setminusER) =>
% 132.59/22.94 (((setminusSubset2) =>
% 132.59/22.94 (((setminusERneg) =>
% 132.59/22.94 (((setminusELneg) =>
% 132.59/22.94 (((setminusILneg) =>
% 132.59/22.94 (((setminusIRneg) =>
% 132.59/22.94 (((setminusLsub) =>
% 132.59/22.94 (((setminusSubset1) =>
% 132.59/22.94 (((symdiffE) =>
% 132.59/22.94 (((symdiffI1) =>
% 132.59/22.94 (((symdiffI2) =>
% 132.59/22.94 (((symdiffIneg1) =>
% 132.59/22.94 (((symdiffIneg2) =>
% 132.59/22.94 (((secondinupair) =>
% 132.59/22.94 (((setukpairIL) =>
% 132.59/22.94 (((setukpairIR) =>
% 132.59/22.94 (((kpairiskpair) =>
% 132.59/22.94 (((kpairp) =>
% 132.59/22.94 (((singletonsubset) =>
% 132.59/22.94 (((singletoninpowerset) =>
% 132.59/22.94 (((singletoninpowunion) =>
% 132.59/22.94 (((upairset2E) =>
% 132.59/22.94 (((upairsubunion) =>
% 132.59/22.94 (((upairinpowunion) =>
% 132.59/22.94 (((ubforcartprodlem1) =>
% 132.59/22.94 (((ubforcartprodlem2) =>
% 132.59/22.94 (((ubforcartprodlem3) =>
% 132.59/22.94 (((cartprodpairin) =>
% 132.59/22.94 ((
% 132.59/22.94 (cartprodmempair1) =>
% 132.59/22.94 ((
% 132.59/22.94 (cartprodmempair) =>
% 132.59/22.94 ((
% 132.59/22.94 (setunionE2) =>
% 132.59/22.94 ((
% 132.59/22.94 (setunionsingleton1) =>
% 132.59/22.94 ((
% 132.59/22.94 (setunionsingleton2) =>
% 132.59/22.94 ((
% 132.59/22.94 (setunionsingleton) =>
% 132.59/22.94 ((
% 132.59/22.94 (singletonprop) =>
% 132.59/22.94 ((
% 132.59/22.94 (ex1E1) =>
% 132.59/22.94 ((
% 132.59/22.94 (ex1I) =>
% 132.59/22.94 ((
% 132.59/22.94 (ex1I2) =>
% 132.59/22.94 ((
% 132.59/22.94 (singletonsuniq) =>
% 132.59/22.94 ((
% 132.59/22.94 (setukpairinjL1) =>
% 132.59/22.94 ((
% 132.59/22.94 (kfstsingleton) =>
% 132.59/22.94 ((
% 132.59/22.94 (theprop) =>
% 132.59/22.94 ((
% 132.59/22.94 (kfstpairEq) =>
% 132.59/22.94 ((
% 132.59/22.94 (cartprodfstin) =>
% 132.59/22.94 ((
% 132.59/22.94 (setukpairinjL2) =>
% 132.59/22.94 ((
% 132.59/22.94 (setukpairinjL) =>
% 132.59/22.94 ((
% 132.59/22.94 (setukpairinjR11) =>
% 132.59/22.94 ((
% 132.59/22.94 (setukpairinjR12) =>
% 132.59/22.94 ((
% 132.59/22.94 (setukpairinjR1) =>
% 132.59/22.94 ((
% 132.59/22.94 (upairequniteq) =>
% 132.59/22.94 ((
% 132.59/22.94 (setukpairinjR2) =>
% 132.59/22.94 ((
% 132.59/22.94 (setukpairinjR) =>
% 132.59/22.94 ((
% 132.59/22.94 (ksndsingleton) =>
% 132.59/22.94 ((
% 132.59/22.94 (ksndpairEq) =>
% 132.59/22.94 ((
% 132.59/22.94 (kpairsurjEq) =>
% 132.59/22.94 ((
% 132.59/22.94 (cartprodsndin) =>
% 132.59/22.94 ((
% 132.59/22.94 (cartprodpairmemEL) =>
% 132.59/22.94 ((
% 132.59/22.94 (cartprodpairmemER) =>
% 132.59/22.94 ((
% 132.59/22.94 (cartprodmempaircEq) =>
% 132.59/22.94 ((
% 132.59/22.94 (cartprodfstpairEq) =>
% 132.59/22.94 ((
% 132.59/22.94 (cartprodsndpairEq) =>
% 132.59/22.94 ((
% 132.59/22.94 (cartprodpairsurjEq) =>
% 132.59/22.94 ((
% 132.59/22.94 (dpsetconstrI) =>
% 132.59/22.94 ((
% 132.59/22.94 (dpsetconstrSub) =>
% 132.59/22.94 ((
% 132.59/22.94 (setOfPairsIsBReln) =>
% 132.59/22.94 ((
% 132.59/22.94 (dpsetconstrERa) =>
% 132.59/22.94 ((
% 132.59/22.94 (dpsetconstrEL1) =>
% 132.59/22.94 ((
% 132.59/22.94 (dpsetconstrEL2) =>
% 132.59/22.94 ((
% 132.59/22.94 (dpsetconstrER) =>
% 132.59/22.94 ((
% 132.59/22.94 (funcImageSingleton) =>
% 132.59/22.94 ((
% 132.59/22.94 (apProp) =>
% 132.59/22.94 ((
% 132.59/22.94 (app) =>
% 132.59/22.94 ((
% 132.59/22.94 (infuncsetfunc) =>
% 132.59/22.94 ((
% 132.59/22.94 (ap2p) =>
% 132.59/22.94 ((
% 132.59/22.94 (funcinfuncset) =>
% 132.59/22.94 ((
% 132.59/22.94 (lamProp) =>
% 132.59/22.94 ((
% 132.59/22.94 (lamp) =>
% 132.59/22.94 ((
% 132.59/22.94 (lam2p) =>
% 132.59/22.94 ((
% 132.59/22.94 (brelnall1) =>
% 132.59/22.94 ((
% 132.59/22.94 (brelnall2) =>
% 132.59/22.94 ((
% 132.59/22.94 (ex1E2) =>
% 132.59/22.94 ((
% 132.59/22.94 (funcGraphProp1) =>
% 132.59/22.94 ((
% 132.59/22.94 (funcGraphProp3) =>
% 132.59/22.94 ((
% 132.59/22.94 (funcGraphProp2) =>
% 132.59/22.94 ((
% 132.59/22.94 (funcextLem) =>
% 132.59/22.94 ((
% 132.59/22.94 (funcGraphProp4) =>
% 132.59/22.94 ((
% 132.59/22.94 (subbreln) =>
% 132.59/22.94 ((
% 132.59/22.94 (eqbreln) =>
% 132.59/22.94 ((
% 132.59/22.94 (funcext) =>
% 132.59/22.94 ((
% 132.59/22.94 (funcext2) =>
% 132.59/22.94 ((
% 132.59/22.94 (ap2apEq1) =>
% 132.59/22.94 ((
% 132.59/22.94 (ap2apEq2) =>
% 132.59/22.94 ((
% 132.59/22.94 (beta1) =>
% 132.59/22.94 ((
% 132.59/22.94 (eta1) =>
% 132.59/22.94 ((
% 132.59/22.94 (lam2lamEq) =>
% 132.59/22.94 ((
% 132.59/22.94 (beta2) =>
% 132.59/22.94 ((
% 132.59/22.94 (eta2) =>
% 132.59/22.94 ((
% 132.59/22.94 (iffalseProp1) =>
% 132.59/22.94 ((
% 132.59/22.94 (iffalseProp2) =>
% 132.59/22.94 ((
% 132.59/22.94 (iftrueProp1) =>
% 132.59/22.94 ((
% 132.59/22.94 (iftrueProp2) =>
% 132.59/22.94 ((
% 132.59/22.94 (ifSingleton) =>
% 132.59/22.94 ((
% 132.59/22.94 (ifp) =>
% 132.59/22.94 ((
% 132.59/22.94 (theeq) =>
% 132.59/22.94 ((
% 132.59/22.94 (iftrue) =>
% 132.59/22.94 ((
% 132.59/22.94 (iffalse) =>
% 132.59/22.94 ((
% 132.59/22.94 (iftrueorfalse) =>
% 132.59/22.94 ((
% 132.59/22.94 (binintersectT_lem) =>
% 132.59/22.94 ((
% 132.59/22.94 (binunionT_lem) =>
% 132.59/22.94 ((
% 132.59/22.94 (powersetT_lem) =>
% 132.59/22.94 ((
% 132.59/22.94 (setminusT_lem) =>
% 132.59/22.94 ((
% 132.59/22.94 (complementT_lem) =>
% 132.59/22.94 ((
% 132.59/22.94 (setextT) =>
% 132.59/22.94 ((
% 132.59/22.94 (subsetTI) =>
% 132.59/22.94 ((
% 132.59/22.94 (powersetTI1) =>
% 132.59/22.94 ((
% 132.59/22.94 (powersetTE1) =>
% 132.59/22.94 ((
% 132.59/22.94 (complementTI1) =>
% 132.59/22.94 ((
% 132.59/22.94 (complementTE1) =>
% 132.59/22.94 ((
% 132.59/22.94 (binintersectTELcontra) =>
% 132.59/22.94 ((
% 132.59/22.94 (binintersectTERcontra) =>
% 132.59/22.94 ((
% 132.59/22.94 (contrasubsetT) =>
% 132.59/22.94 ((
% 132.59/22.94 (contrasubsetT1) =>
% 132.59/22.94 ((
% 132.59/22.94 (contrasubsetT2) =>
% 132.59/22.94 ((
% 132.59/22.94 (contrasubsetT3) =>
% 132.59/22.94 ((
% 132.59/22.94 (doubleComplementI1) =>
% 132.59/22.94 ((
% 132.59/22.94 (doubleComplementE1) =>
% 132.59/22.94 ((
% 132.59/22.94 (doubleComplementSub1) =>
% 132.59/22.94 ((
% 132.59/22.94 (doubleComplementSub2) =>
% 132.59/22.94 ((
% 132.59/22.94 (doubleComplementEq) =>
% 132.59/22.94 ((
% 132.59/22.94 (complementTnotintersectT) =>
% 132.59/22.94 ((
% 132.59/22.94 (complementImpComplementIntersect) =>
% 132.59/22.94 ((
% 132.59/22.94 (complementSubsetComplementIntersect) =>
% 132.59/22.94 ((
% 132.59/22.94 (complementInPowersetComplementIntersect) =>
% 132.59/22.94 ((
% 132.59/22.94 (contraSubsetComplement) =>
% 132.59/22.94 ((
% 132.59/22.94 (complementTcontraSubset) =>
% 132.59/22.94 ((
% 132.59/22.94 (binunionTILcontra) =>
% 132.59/22.94 ((
% 132.59/22.94 (binunionTIRcontra) =>
% 132.59/22.94 ((
% 132.59/22.94 (inIntersectImpInUnion) =>
% 132.59/22.94 ((
% 132.59/22.94 (inIntersectImpInUnion2) =>
% 132.59/22.94 ((
% 132.59/22.94 (inIntersectImpInIntersectUnions) =>
% 132.59/22.94 ((
% 132.59/22.94 (intersectInPowersetIntersectUnions) =>
% 132.59/22.94 ((
% 132.59/22.94 (inComplementUnionImpNotIn1) =>
% 132.59/22.94 ((
% 132.59/22.94 (inComplementUnionImpInComplement1) =>
% 132.59/22.94 ((
% 132.59/22.94 (binunionTE) =>
% 132.59/22.94 ((
% 132.59/22.94 (binunionTEcontra) =>
% 132.59/22.94 ((
% 132.59/22.94 (demorgan2a1) =>
% 132.59/22.94 ((
% 132.59/22.94 (complementUnionInPowersetComplement) =>
% 132.59/22.94 ((
% 132.59/22.94 (demorgan2a2) =>
% 132.59/22.94 ((
% 132.59/22.94 (demorgan1a) =>
% 132.59/22.94 ((
% 132.59/22.94 (demorgan1b) =>
% 132.59/22.94 ((
% 132.59/22.94 (demorgan1) =>
% 132.59/22.94 ((
% 132.59/22.94 (demorgan2a) =>
% 132.59/22.94 ((
% 132.59/22.94 (demorgan2b2) =>
% 132.59/22.94 ((
% 132.59/22.94 (demorgan2b) =>
% 132.59/22.94 ((
% 132.59/22.94 (demorgan2) =>
% 132.59/22.94 ((
% 132.59/22.94 (woz13rule0) =>
% 132.59/22.94 ((
% 132.59/22.94 (woz13rule1) =>
% 132.59/22.94 ((
% 132.59/22.94 (woz13rule2) =>
% 132.59/22.94 ((
% 132.59/22.94 (woz13rule3) =>
% 132.59/22.94 ((
% 132.59/22.94 (woz13rule4) =>
% 132.59/22.94 ((
% 132.59/22.94 (woz1_1) =>
% 132.59/22.94 ((
% 132.59/22.94 (woz1_2) =>
% 132.59/22.94 ((
% 132.59/22.94 (woz1_3) =>
% 132.59/22.94 ((
% 132.59/22.94 (woz1_4) =>
% 132.59/22.94 ((
% 132.59/22.94 (woz1_5) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1all2) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1SetBreln1) =>
% 132.59/22.94 ((
% 132.59/22.94 (choice2fnsingleton) =>
% 132.59/22.94 ((
% 132.59/22.94 (setOfPairsIsBReln1) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1all1) =>
% 132.59/22.94 ((
% 132.59/22.94 (subbreln1) =>
% 132.59/22.94 ((
% 132.59/22.94 (eqbreln1) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1invprop) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1invI) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1invE) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1compprop) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1compI) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1compE) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1compEex) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1unionprop) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1unionIL) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1unionIR) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1unionI) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1unionE) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1unionEcases) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1unionCommutes) =>
% 132.59/22.94 ((
% 132.59/22.94 (woz2Ex) =>
% 132.59/22.94 ((
% 132.59/22.94 (woz2W) =>
% 132.59/22.94 ((
% 132.59/22.94 (woz2A) =>
% 132.59/22.94 ((
% 132.59/22.94 (woz2B) =>
% 132.59/22.94 ((
% 132.59/22.94 (image1Ex) =>
% 132.59/22.94 ((
% 132.59/22.94 (image1Ex1) =>
% 132.59/22.94 ((
% 132.59/22.94 (image1Equiv) =>
% 132.59/22.94 ((
% 132.59/22.94 (image1E) =>
% 132.59/22.94 ((
% 132.59/22.94 (image1I) =>
% 132.59/22.94 ((
% 132.59/22.94 (injFuncInInjFuncSet) =>
% 132.59/22.94 ((
% 132.59/22.94 (injFuncSetFuncIn) =>
% 132.59/22.94 ((
% 132.59/22.94 (injFuncSetFuncInj) =>
% 132.59/22.94 ((
% 132.59/22.94 (surjFuncSetFuncIn) =>
% 132.59/22.94 ((
% 132.59/22.94 (surjFuncSetFuncSurj) =>
% 132.59/22.94 ((
% 132.59/22.94 (leftInvIsSurj) =>
% 132.59/22.94 ((
% 132.59/22.94 (surjCantorThm) =>
% 132.59/22.94 ((
% 132.59/22.94 (foundation2) =>
% 132.59/22.94 ((
% 132.59/22.94 (notinself) =>
% 132.59/22.94 ((
% 132.59/22.94 (notinself2) =>
% 132.59/22.94 ((
% 132.59/22.94 (omegaSp) =>
% 132.59/22.94 ((
% 132.59/22.94 (omegaSclos) =>
% 132.59/22.94 ((
% 132.59/22.94 (peano0notS) =>
% 132.59/22.94 ((
% 132.59/22.94 (peanoSinj) =>
% 132.59/22.94 ((
% 132.59/22.94 (transitivesetOp1) =>
% 132.59/22.94 ((
% 132.59/22.94 (binintTransitive) =>
% 132.59/22.94 ((
% 132.59/22.94 (transitivesetOp2) =>
% 132.59/22.94 ((
% 132.59/22.94 (setunionTransitive) =>
% 132.59/22.94 ((
% 132.59/22.94 (ordinalMinLem1) =>
% 132.59/22.94 ((
% 132.59/22.94 (ordinalTransSet) =>
% 132.59/22.94 ((
% 132.59/22.94 (ordinalTransSet1) =>
% 132.59/22.94 ((
% 132.59/22.94 (setunionOrdinalLem1) =>
% 132.59/22.94 (ordinal @
% 132.59/22.94 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.59/22.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1028])).
% 132.59/22.94 thf(zip_derived_cl1041, plain,
% 132.59/22.94 (~ (((setminusEL) =>
% 132.59/22.94 (((setminusER) =>
% 132.59/22.94 (((setminusSubset2) =>
% 132.59/22.94 (((setminusERneg) =>
% 132.59/22.94 (((setminusELneg) =>
% 132.59/22.94 (((setminusILneg) =>
% 132.59/22.94 (((setminusIRneg) =>
% 132.59/22.94 (((setminusLsub) =>
% 132.59/22.94 (((setminusSubset1) =>
% 132.59/22.94 (((symdiffE) =>
% 132.59/22.94 (((symdiffI1) =>
% 132.59/22.94 (((symdiffI2) =>
% 132.59/22.94 (((symdiffIneg1) =>
% 132.59/22.94 (((symdiffIneg2) =>
% 132.59/22.94 (((secondinupair) =>
% 132.59/22.94 (((setukpairIL) =>
% 132.59/22.94 (((setukpairIR) =>
% 132.59/22.94 (((kpairiskpair) =>
% 132.59/22.94 (((kpairp) =>
% 132.59/22.94 (((singletonsubset) =>
% 132.59/22.94 (((singletoninpowerset) =>
% 132.59/22.94 (((singletoninpowunion) =>
% 132.59/22.94 (((upairset2E) =>
% 132.59/22.94 (((upairsubunion) =>
% 132.59/22.94 (((upairinpowunion) =>
% 132.59/22.94 (((ubforcartprodlem1) =>
% 132.59/22.94 (((ubforcartprodlem2) =>
% 132.59/22.94 (((ubforcartprodlem3) =>
% 132.59/22.94 (((cartprodpairin) =>
% 132.59/22.94 (((cartprodmempair1) =>
% 132.59/22.94 ((
% 132.59/22.94 (cartprodmempair) =>
% 132.59/22.94 ((
% 132.59/22.94 (setunionE2) =>
% 132.59/22.94 ((
% 132.59/22.94 (setunionsingleton1) =>
% 132.59/22.94 ((
% 132.59/22.94 (setunionsingleton2) =>
% 132.59/22.94 ((
% 132.59/22.94 (setunionsingleton) =>
% 132.59/22.94 ((
% 132.59/22.94 (singletonprop) =>
% 132.59/22.94 ((
% 132.59/22.94 (ex1E1) =>
% 132.59/22.94 ((
% 132.59/22.94 (ex1I) =>
% 132.59/22.94 ((
% 132.59/22.94 (ex1I2) =>
% 132.59/22.94 ((
% 132.59/22.94 (singletonsuniq) =>
% 132.59/22.94 ((
% 132.59/22.94 (setukpairinjL1) =>
% 132.59/22.94 ((
% 132.59/22.94 (kfstsingleton) =>
% 132.59/22.94 ((
% 132.59/22.94 (theprop) =>
% 132.59/22.94 ((
% 132.59/22.94 (kfstpairEq) =>
% 132.59/22.94 ((
% 132.59/22.94 (cartprodfstin) =>
% 132.59/22.94 ((
% 132.59/22.94 (setukpairinjL2) =>
% 132.59/22.94 ((
% 132.59/22.94 (setukpairinjL) =>
% 132.59/22.94 ((
% 132.59/22.94 (setukpairinjR11) =>
% 132.59/22.94 ((
% 132.59/22.94 (setukpairinjR12) =>
% 132.59/22.94 ((
% 132.59/22.94 (setukpairinjR1) =>
% 132.59/22.94 ((
% 132.59/22.94 (upairequniteq) =>
% 132.59/22.94 ((
% 132.59/22.94 (setukpairinjR2) =>
% 132.59/22.94 ((
% 132.59/22.94 (setukpairinjR) =>
% 132.59/22.94 ((
% 132.59/22.94 (ksndsingleton) =>
% 132.59/22.94 ((
% 132.59/22.94 (ksndpairEq) =>
% 132.59/22.94 ((
% 132.59/22.94 (kpairsurjEq) =>
% 132.59/22.94 ((
% 132.59/22.94 (cartprodsndin) =>
% 132.59/22.94 ((
% 132.59/22.94 (cartprodpairmemEL) =>
% 132.59/22.94 ((
% 132.59/22.94 (cartprodpairmemER) =>
% 132.59/22.94 ((
% 132.59/22.94 (cartprodmempaircEq) =>
% 132.59/22.94 ((
% 132.59/22.94 (cartprodfstpairEq) =>
% 132.59/22.94 ((
% 132.59/22.94 (cartprodsndpairEq) =>
% 132.59/22.94 ((
% 132.59/22.94 (cartprodpairsurjEq) =>
% 132.59/22.94 ((
% 132.59/22.94 (dpsetconstrI) =>
% 132.59/22.94 ((
% 132.59/22.94 (dpsetconstrSub) =>
% 132.59/22.94 ((
% 132.59/22.94 (setOfPairsIsBReln) =>
% 132.59/22.94 ((
% 132.59/22.94 (dpsetconstrERa) =>
% 132.59/22.94 ((
% 132.59/22.94 (dpsetconstrEL1) =>
% 132.59/22.94 ((
% 132.59/22.94 (dpsetconstrEL2) =>
% 132.59/22.94 ((
% 132.59/22.94 (dpsetconstrER) =>
% 132.59/22.94 ((
% 132.59/22.94 (funcImageSingleton) =>
% 132.59/22.94 ((
% 132.59/22.94 (apProp) =>
% 132.59/22.94 ((
% 132.59/22.94 (app) =>
% 132.59/22.94 ((
% 132.59/22.94 (infuncsetfunc) =>
% 132.59/22.94 ((
% 132.59/22.94 (ap2p) =>
% 132.59/22.94 ((
% 132.59/22.94 (funcinfuncset) =>
% 132.59/22.94 ((
% 132.59/22.94 (lamProp) =>
% 132.59/22.94 ((
% 132.59/22.94 (lamp) =>
% 132.59/22.94 ((
% 132.59/22.94 (lam2p) =>
% 132.59/22.94 ((
% 132.59/22.94 (brelnall1) =>
% 132.59/22.94 ((
% 132.59/22.94 (brelnall2) =>
% 132.59/22.94 ((
% 132.59/22.94 (ex1E2) =>
% 132.59/22.94 ((
% 132.59/22.94 (funcGraphProp1) =>
% 132.59/22.94 ((
% 132.59/22.94 (funcGraphProp3) =>
% 132.59/22.94 ((
% 132.59/22.94 (funcGraphProp2) =>
% 132.59/22.94 ((
% 132.59/22.94 (funcextLem) =>
% 132.59/22.94 ((
% 132.59/22.94 (funcGraphProp4) =>
% 132.59/22.94 ((
% 132.59/22.94 (subbreln) =>
% 132.59/22.94 ((
% 132.59/22.94 (eqbreln) =>
% 132.59/22.94 ((
% 132.59/22.94 (funcext) =>
% 132.59/22.94 ((
% 132.59/22.94 (funcext2) =>
% 132.59/22.94 ((
% 132.59/22.94 (ap2apEq1) =>
% 132.59/22.94 ((
% 132.59/22.94 (ap2apEq2) =>
% 132.59/22.94 ((
% 132.59/22.94 (beta1) =>
% 132.59/22.94 ((
% 132.59/22.94 (eta1) =>
% 132.59/22.94 ((
% 132.59/22.94 (lam2lamEq) =>
% 132.59/22.94 ((
% 132.59/22.94 (beta2) =>
% 132.59/22.94 ((
% 132.59/22.94 (eta2) =>
% 132.59/22.94 ((
% 132.59/22.94 (iffalseProp1) =>
% 132.59/22.94 ((
% 132.59/22.94 (iffalseProp2) =>
% 132.59/22.94 ((
% 132.59/22.94 (iftrueProp1) =>
% 132.59/22.94 ((
% 132.59/22.94 (iftrueProp2) =>
% 132.59/22.94 ((
% 132.59/22.94 (ifSingleton) =>
% 132.59/22.94 ((
% 132.59/22.94 (ifp) =>
% 132.59/22.94 ((
% 132.59/22.94 (theeq) =>
% 132.59/22.94 ((
% 132.59/22.94 (iftrue) =>
% 132.59/22.94 ((
% 132.59/22.94 (iffalse) =>
% 132.59/22.94 ((
% 132.59/22.94 (iftrueorfalse) =>
% 132.59/22.94 ((
% 132.59/22.94 (binintersectT_lem) =>
% 132.59/22.94 ((
% 132.59/22.94 (binunionT_lem) =>
% 132.59/22.94 ((
% 132.59/22.94 (powersetT_lem) =>
% 132.59/22.94 ((
% 132.59/22.94 (setminusT_lem) =>
% 132.59/22.94 ((
% 132.59/22.94 (complementT_lem) =>
% 132.59/22.94 ((
% 132.59/22.94 (setextT) =>
% 132.59/22.94 ((
% 132.59/22.94 (subsetTI) =>
% 132.59/22.94 ((
% 132.59/22.94 (powersetTI1) =>
% 132.59/22.94 ((
% 132.59/22.94 (powersetTE1) =>
% 132.59/22.94 ((
% 132.59/22.94 (complementTI1) =>
% 132.59/22.94 ((
% 132.59/22.94 (complementTE1) =>
% 132.59/22.94 ((
% 132.59/22.94 (binintersectTELcontra) =>
% 132.59/22.94 ((
% 132.59/22.94 (binintersectTERcontra) =>
% 132.59/22.94 ((
% 132.59/22.94 (contrasubsetT) =>
% 132.59/22.94 ((
% 132.59/22.94 (contrasubsetT1) =>
% 132.59/22.94 ((
% 132.59/22.94 (contrasubsetT2) =>
% 132.59/22.94 ((
% 132.59/22.94 (contrasubsetT3) =>
% 132.59/22.94 ((
% 132.59/22.94 (doubleComplementI1) =>
% 132.59/22.94 ((
% 132.59/22.94 (doubleComplementE1) =>
% 132.59/22.94 ((
% 132.59/22.94 (doubleComplementSub1) =>
% 132.59/22.94 ((
% 132.59/22.94 (doubleComplementSub2) =>
% 132.59/22.94 ((
% 132.59/22.94 (doubleComplementEq) =>
% 132.59/22.94 ((
% 132.59/22.94 (complementTnotintersectT) =>
% 132.59/22.94 ((
% 132.59/22.94 (complementImpComplementIntersect) =>
% 132.59/22.94 ((
% 132.59/22.94 (complementSubsetComplementIntersect) =>
% 132.59/22.94 ((
% 132.59/22.94 (complementInPowersetComplementIntersect) =>
% 132.59/22.94 ((
% 132.59/22.94 (contraSubsetComplement) =>
% 132.59/22.94 ((
% 132.59/22.94 (complementTcontraSubset) =>
% 132.59/22.94 ((
% 132.59/22.94 (binunionTILcontra) =>
% 132.59/22.94 ((
% 132.59/22.94 (binunionTIRcontra) =>
% 132.59/22.94 ((
% 132.59/22.94 (inIntersectImpInUnion) =>
% 132.59/22.94 ((
% 132.59/22.94 (inIntersectImpInUnion2) =>
% 132.59/22.94 ((
% 132.59/22.94 (inIntersectImpInIntersectUnions) =>
% 132.59/22.94 ((
% 132.59/22.94 (intersectInPowersetIntersectUnions) =>
% 132.59/22.94 ((
% 132.59/22.94 (inComplementUnionImpNotIn1) =>
% 132.59/22.94 ((
% 132.59/22.94 (inComplementUnionImpInComplement1) =>
% 132.59/22.94 ((
% 132.59/22.94 (binunionTE) =>
% 132.59/22.94 ((
% 132.59/22.94 (binunionTEcontra) =>
% 132.59/22.94 ((
% 132.59/22.94 (demorgan2a1) =>
% 132.59/22.94 ((
% 132.59/22.94 (complementUnionInPowersetComplement) =>
% 132.59/22.94 ((
% 132.59/22.94 (demorgan2a2) =>
% 132.59/22.94 ((
% 132.59/22.94 (demorgan1a) =>
% 132.59/22.94 ((
% 132.59/22.94 (demorgan1b) =>
% 132.59/22.94 ((
% 132.59/22.94 (demorgan1) =>
% 132.59/22.94 ((
% 132.59/22.94 (demorgan2a) =>
% 132.59/22.94 ((
% 132.59/22.94 (demorgan2b2) =>
% 132.59/22.94 ((
% 132.59/22.94 (demorgan2b) =>
% 132.59/22.94 ((
% 132.59/22.94 (demorgan2) =>
% 132.59/22.94 ((
% 132.59/22.94 (woz13rule0) =>
% 132.59/22.94 ((
% 132.59/22.94 (woz13rule1) =>
% 132.59/22.94 ((
% 132.59/22.94 (woz13rule2) =>
% 132.59/22.94 ((
% 132.59/22.94 (woz13rule3) =>
% 132.59/22.94 ((
% 132.59/22.94 (woz13rule4) =>
% 132.59/22.94 ((
% 132.59/22.94 (woz1_1) =>
% 132.59/22.94 ((
% 132.59/22.94 (woz1_2) =>
% 132.59/22.94 ((
% 132.59/22.94 (woz1_3) =>
% 132.59/22.94 ((
% 132.59/22.94 (woz1_4) =>
% 132.59/22.94 ((
% 132.59/22.94 (woz1_5) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1all2) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1SetBreln1) =>
% 132.59/22.94 ((
% 132.59/22.94 (choice2fnsingleton) =>
% 132.59/22.94 ((
% 132.59/22.94 (setOfPairsIsBReln1) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1all1) =>
% 132.59/22.94 ((
% 132.59/22.94 (subbreln1) =>
% 132.59/22.94 ((
% 132.59/22.94 (eqbreln1) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1invprop) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1invI) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1invE) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1compprop) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1compI) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1compE) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1compEex) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1unionprop) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1unionIL) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1unionIR) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1unionI) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1unionE) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1unionEcases) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1unionCommutes) =>
% 132.59/22.94 ((
% 132.59/22.94 (woz2Ex) =>
% 132.59/22.94 ((
% 132.59/22.94 (woz2W) =>
% 132.59/22.94 ((
% 132.59/22.94 (woz2A) =>
% 132.59/22.94 ((
% 132.59/22.94 (woz2B) =>
% 132.59/22.94 ((
% 132.59/22.94 (image1Ex) =>
% 132.59/22.94 ((
% 132.59/22.94 (image1Ex1) =>
% 132.59/22.94 ((
% 132.59/22.94 (image1Equiv) =>
% 132.59/22.94 ((
% 132.59/22.94 (image1E) =>
% 132.59/22.94 ((
% 132.59/22.94 (image1I) =>
% 132.59/22.94 ((
% 132.59/22.94 (injFuncInInjFuncSet) =>
% 132.59/22.94 ((
% 132.59/22.94 (injFuncSetFuncIn) =>
% 132.59/22.94 ((
% 132.59/22.94 (injFuncSetFuncInj) =>
% 132.59/22.94 ((
% 132.59/22.94 (surjFuncSetFuncIn) =>
% 132.59/22.94 ((
% 132.59/22.94 (surjFuncSetFuncSurj) =>
% 132.59/22.94 ((
% 132.59/22.94 (leftInvIsSurj) =>
% 132.59/22.94 ((
% 132.59/22.94 (surjCantorThm) =>
% 132.59/22.94 ((
% 132.59/22.94 (foundation2) =>
% 132.59/22.94 ((
% 132.59/22.94 (notinself) =>
% 132.59/22.94 ((
% 132.59/22.94 (notinself2) =>
% 132.59/22.94 ((
% 132.59/22.94 (omegaSp) =>
% 132.59/22.94 ((
% 132.59/22.94 (omegaSclos) =>
% 132.59/22.94 ((
% 132.59/22.94 (peano0notS) =>
% 132.59/22.94 ((
% 132.59/22.94 (peanoSinj) =>
% 132.59/22.94 ((
% 132.59/22.94 (transitivesetOp1) =>
% 132.59/22.94 ((
% 132.59/22.94 (binintTransitive) =>
% 132.59/22.94 ((
% 132.59/22.94 (transitivesetOp2) =>
% 132.59/22.94 ((
% 132.59/22.94 (setunionTransitive) =>
% 132.59/22.94 ((
% 132.59/22.94 (ordinalMinLem1) =>
% 132.59/22.94 ((
% 132.59/22.94 (ordinalTransSet) =>
% 132.59/22.94 ((
% 132.59/22.94 (ordinalTransSet1) =>
% 132.59/22.94 ((
% 132.59/22.94 (setunionOrdinalLem1) =>
% 132.59/22.94 (ordinal @
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% 132.59/22.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1034])).
% 132.59/22.94 thf(zip_derived_cl1047, plain,
% 132.59/22.94 (~ (((setminusER) =>
% 132.59/22.94 (((setminusSubset2) =>
% 132.59/22.94 (((setminusERneg) =>
% 132.59/22.94 (((setminusELneg) =>
% 132.59/22.94 (((setminusILneg) =>
% 132.59/22.94 (((setminusIRneg) =>
% 132.59/22.94 (((setminusLsub) =>
% 132.59/22.94 (((setminusSubset1) =>
% 132.59/22.94 (((symdiffE) =>
% 132.59/22.94 (((symdiffI1) =>
% 132.59/22.94 (((symdiffI2) =>
% 132.59/22.94 (((symdiffIneg1) =>
% 132.59/22.94 (((symdiffIneg2) =>
% 132.59/22.94 (((secondinupair) =>
% 132.59/22.94 (((setukpairIL) =>
% 132.59/22.94 (((setukpairIR) =>
% 132.59/22.94 (((kpairiskpair) =>
% 132.59/22.94 (((kpairp) =>
% 132.59/22.94 (((singletonsubset) =>
% 132.59/22.94 (((singletoninpowerset) =>
% 132.59/22.94 (((singletoninpowunion) =>
% 132.59/22.94 (((upairset2E) =>
% 132.59/22.94 (((upairsubunion) =>
% 132.59/22.94 (((upairinpowunion) =>
% 132.59/22.94 (((ubforcartprodlem1) =>
% 132.59/22.94 (((ubforcartprodlem2) =>
% 132.59/22.94 (((ubforcartprodlem3) =>
% 132.59/22.94 (((cartprodpairin) =>
% 132.59/22.94 (((cartprodmempair1) =>
% 132.59/22.94 (((cartprodmempair) =>
% 132.59/22.94 ((
% 132.59/22.94 (setunionE2) =>
% 132.59/22.94 ((
% 132.59/22.94 (setunionsingleton1) =>
% 132.59/22.94 ((
% 132.59/22.94 (setunionsingleton2) =>
% 132.59/22.94 ((
% 132.59/22.94 (setunionsingleton) =>
% 132.59/22.94 ((
% 132.59/22.94 (singletonprop) =>
% 132.59/22.94 ((
% 132.59/22.94 (ex1E1) =>
% 132.59/22.94 ((
% 132.59/22.94 (ex1I) =>
% 132.59/22.94 ((
% 132.59/22.94 (ex1I2) =>
% 132.59/22.94 ((
% 132.59/22.94 (singletonsuniq) =>
% 132.59/22.94 ((
% 132.59/22.94 (setukpairinjL1) =>
% 132.59/22.94 ((
% 132.59/22.94 (kfstsingleton) =>
% 132.59/22.94 ((
% 132.59/22.94 (theprop) =>
% 132.59/22.94 ((
% 132.59/22.94 (kfstpairEq) =>
% 132.59/22.94 ((
% 132.59/22.94 (cartprodfstin) =>
% 132.59/22.94 ((
% 132.59/22.94 (setukpairinjL2) =>
% 132.59/22.94 ((
% 132.59/22.94 (setukpairinjL) =>
% 132.59/22.94 ((
% 132.59/22.94 (setukpairinjR11) =>
% 132.59/22.94 ((
% 132.59/22.94 (setukpairinjR12) =>
% 132.59/22.94 ((
% 132.59/22.94 (setukpairinjR1) =>
% 132.59/22.94 ((
% 132.59/22.94 (upairequniteq) =>
% 132.59/22.94 ((
% 132.59/22.94 (setukpairinjR2) =>
% 132.59/22.94 ((
% 132.59/22.94 (setukpairinjR) =>
% 132.59/22.94 ((
% 132.59/22.94 (ksndsingleton) =>
% 132.59/22.94 ((
% 132.59/22.94 (ksndpairEq) =>
% 132.59/22.94 ((
% 132.59/22.94 (kpairsurjEq) =>
% 132.59/22.94 ((
% 132.59/22.94 (cartprodsndin) =>
% 132.59/22.94 ((
% 132.59/22.94 (cartprodpairmemEL) =>
% 132.59/22.94 ((
% 132.59/22.94 (cartprodpairmemER) =>
% 132.59/22.94 ((
% 132.59/22.94 (cartprodmempaircEq) =>
% 132.59/22.94 ((
% 132.59/22.94 (cartprodfstpairEq) =>
% 132.59/22.94 ((
% 132.59/22.94 (cartprodsndpairEq) =>
% 132.59/22.94 ((
% 132.59/22.94 (cartprodpairsurjEq) =>
% 132.59/22.94 ((
% 132.59/22.94 (dpsetconstrI) =>
% 132.59/22.94 ((
% 132.59/22.94 (dpsetconstrSub) =>
% 132.59/22.94 ((
% 132.59/22.94 (setOfPairsIsBReln) =>
% 132.59/22.94 ((
% 132.59/22.94 (dpsetconstrERa) =>
% 132.59/22.94 ((
% 132.59/22.94 (dpsetconstrEL1) =>
% 132.59/22.94 ((
% 132.59/22.94 (dpsetconstrEL2) =>
% 132.59/22.94 ((
% 132.59/22.94 (dpsetconstrER) =>
% 132.59/22.94 ((
% 132.59/22.94 (funcImageSingleton) =>
% 132.59/22.94 ((
% 132.59/22.94 (apProp) =>
% 132.59/22.94 ((
% 132.59/22.94 (app) =>
% 132.59/22.94 ((
% 132.59/22.94 (infuncsetfunc) =>
% 132.59/22.94 ((
% 132.59/22.94 (ap2p) =>
% 132.59/22.94 ((
% 132.59/22.94 (funcinfuncset) =>
% 132.59/22.94 ((
% 132.59/22.94 (lamProp) =>
% 132.59/22.94 ((
% 132.59/22.94 (lamp) =>
% 132.59/22.94 ((
% 132.59/22.94 (lam2p) =>
% 132.59/22.94 ((
% 132.59/22.94 (brelnall1) =>
% 132.59/22.94 ((
% 132.59/22.94 (brelnall2) =>
% 132.59/22.94 ((
% 132.59/22.94 (ex1E2) =>
% 132.59/22.94 ((
% 132.59/22.94 (funcGraphProp1) =>
% 132.59/22.94 ((
% 132.59/22.94 (funcGraphProp3) =>
% 132.59/22.94 ((
% 132.59/22.94 (funcGraphProp2) =>
% 132.59/22.94 ((
% 132.59/22.94 (funcextLem) =>
% 132.59/22.94 ((
% 132.59/22.94 (funcGraphProp4) =>
% 132.59/22.94 ((
% 132.59/22.94 (subbreln) =>
% 132.59/22.94 ((
% 132.59/22.94 (eqbreln) =>
% 132.59/22.94 ((
% 132.59/22.94 (funcext) =>
% 132.59/22.94 ((
% 132.59/22.94 (funcext2) =>
% 132.59/22.94 ((
% 132.59/22.94 (ap2apEq1) =>
% 132.59/22.94 ((
% 132.59/22.94 (ap2apEq2) =>
% 132.59/22.94 ((
% 132.59/22.94 (beta1) =>
% 132.59/22.94 ((
% 132.59/22.94 (eta1) =>
% 132.59/22.94 ((
% 132.59/22.94 (lam2lamEq) =>
% 132.59/22.94 ((
% 132.59/22.94 (beta2) =>
% 132.59/22.94 ((
% 132.59/22.94 (eta2) =>
% 132.59/22.94 ((
% 132.59/22.94 (iffalseProp1) =>
% 132.59/22.94 ((
% 132.59/22.94 (iffalseProp2) =>
% 132.59/22.94 ((
% 132.59/22.94 (iftrueProp1) =>
% 132.59/22.94 ((
% 132.59/22.94 (iftrueProp2) =>
% 132.59/22.94 ((
% 132.59/22.94 (ifSingleton) =>
% 132.59/22.94 ((
% 132.59/22.94 (ifp) =>
% 132.59/22.94 ((
% 132.59/22.94 (theeq) =>
% 132.59/22.94 ((
% 132.59/22.94 (iftrue) =>
% 132.59/22.94 ((
% 132.59/22.94 (iffalse) =>
% 132.59/22.94 ((
% 132.59/22.94 (iftrueorfalse) =>
% 132.59/22.94 ((
% 132.59/22.94 (binintersectT_lem) =>
% 132.59/22.94 ((
% 132.59/22.94 (binunionT_lem) =>
% 132.59/22.94 ((
% 132.59/22.94 (powersetT_lem) =>
% 132.59/22.94 ((
% 132.59/22.94 (setminusT_lem) =>
% 132.59/22.94 ((
% 132.59/22.94 (complementT_lem) =>
% 132.59/22.94 ((
% 132.59/22.94 (setextT) =>
% 132.59/22.94 ((
% 132.59/22.94 (subsetTI) =>
% 132.59/22.94 ((
% 132.59/22.94 (powersetTI1) =>
% 132.59/22.94 ((
% 132.59/22.94 (powersetTE1) =>
% 132.59/22.94 ((
% 132.59/22.94 (complementTI1) =>
% 132.59/22.94 ((
% 132.59/22.94 (complementTE1) =>
% 132.59/22.94 ((
% 132.59/22.94 (binintersectTELcontra) =>
% 132.59/22.94 ((
% 132.59/22.94 (binintersectTERcontra) =>
% 132.59/22.94 ((
% 132.59/22.94 (contrasubsetT) =>
% 132.59/22.94 ((
% 132.59/22.94 (contrasubsetT1) =>
% 132.59/22.94 ((
% 132.59/22.94 (contrasubsetT2) =>
% 132.59/22.94 ((
% 132.59/22.94 (contrasubsetT3) =>
% 132.59/22.94 ((
% 132.59/22.94 (doubleComplementI1) =>
% 132.59/22.94 ((
% 132.59/22.94 (doubleComplementE1) =>
% 132.59/22.94 ((
% 132.59/22.94 (doubleComplementSub1) =>
% 132.59/22.94 ((
% 132.59/22.94 (doubleComplementSub2) =>
% 132.59/22.94 ((
% 132.59/22.94 (doubleComplementEq) =>
% 132.59/22.94 ((
% 132.59/22.94 (complementTnotintersectT) =>
% 132.59/22.94 ((
% 132.59/22.94 (complementImpComplementIntersect) =>
% 132.59/22.94 ((
% 132.59/22.94 (complementSubsetComplementIntersect) =>
% 132.59/22.94 ((
% 132.59/22.94 (complementInPowersetComplementIntersect) =>
% 132.59/22.94 ((
% 132.59/22.94 (contraSubsetComplement) =>
% 132.59/22.94 ((
% 132.59/22.94 (complementTcontraSubset) =>
% 132.59/22.94 ((
% 132.59/22.94 (binunionTILcontra) =>
% 132.59/22.94 ((
% 132.59/22.94 (binunionTIRcontra) =>
% 132.59/22.94 ((
% 132.59/22.94 (inIntersectImpInUnion) =>
% 132.59/22.94 ((
% 132.59/22.94 (inIntersectImpInUnion2) =>
% 132.59/22.94 ((
% 132.59/22.94 (inIntersectImpInIntersectUnions) =>
% 132.59/22.94 ((
% 132.59/22.94 (intersectInPowersetIntersectUnions) =>
% 132.59/22.94 ((
% 132.59/22.94 (inComplementUnionImpNotIn1) =>
% 132.59/22.94 ((
% 132.59/22.94 (inComplementUnionImpInComplement1) =>
% 132.59/22.94 ((
% 132.59/22.94 (binunionTE) =>
% 132.59/22.94 ((
% 132.59/22.94 (binunionTEcontra) =>
% 132.59/22.94 ((
% 132.59/22.94 (demorgan2a1) =>
% 132.59/22.94 ((
% 132.59/22.94 (complementUnionInPowersetComplement) =>
% 132.59/22.94 ((
% 132.59/22.94 (demorgan2a2) =>
% 132.59/22.94 ((
% 132.59/22.94 (demorgan1a) =>
% 132.59/22.94 ((
% 132.59/22.94 (demorgan1b) =>
% 132.59/22.94 ((
% 132.59/22.94 (demorgan1) =>
% 132.59/22.94 ((
% 132.59/22.94 (demorgan2a) =>
% 132.59/22.94 ((
% 132.59/22.94 (demorgan2b2) =>
% 132.59/22.94 ((
% 132.59/22.94 (demorgan2b) =>
% 132.59/22.94 ((
% 132.59/22.94 (demorgan2) =>
% 132.59/22.94 ((
% 132.59/22.94 (woz13rule0) =>
% 132.59/22.94 ((
% 132.59/22.94 (woz13rule1) =>
% 132.59/22.94 ((
% 132.59/22.94 (woz13rule2) =>
% 132.59/22.94 ((
% 132.59/22.94 (woz13rule3) =>
% 132.59/22.94 ((
% 132.59/22.94 (woz13rule4) =>
% 132.59/22.94 ((
% 132.59/22.94 (woz1_1) =>
% 132.59/22.94 ((
% 132.59/22.94 (woz1_2) =>
% 132.59/22.94 ((
% 132.59/22.94 (woz1_3) =>
% 132.59/22.94 ((
% 132.59/22.94 (woz1_4) =>
% 132.59/22.94 ((
% 132.59/22.94 (woz1_5) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1all2) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1SetBreln1) =>
% 132.59/22.94 ((
% 132.59/22.94 (choice2fnsingleton) =>
% 132.59/22.94 ((
% 132.59/22.94 (setOfPairsIsBReln1) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1all1) =>
% 132.59/22.94 ((
% 132.59/22.94 (subbreln1) =>
% 132.59/22.94 ((
% 132.59/22.94 (eqbreln1) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1invprop) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1invI) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1invE) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1compprop) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1compI) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1compE) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1compEex) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1unionprop) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1unionIL) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1unionIR) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1unionI) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1unionE) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1unionEcases) =>
% 132.59/22.94 ((
% 132.59/22.94 (breln1unionCommutes) =>
% 132.59/22.94 ((
% 132.59/22.94 (woz2Ex) =>
% 132.59/22.94 ((
% 132.59/22.94 (woz2W) =>
% 132.59/22.94 ((
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% 132.59/22.94 ((
% 132.59/22.94 (woz2B) =>
% 132.59/22.94 ((
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% 132.59/22.94 ((
% 132.59/22.94 (image1Ex1) =>
% 132.59/22.94 ((
% 132.59/22.94 (image1Equiv) =>
% 132.59/22.94 ((
% 132.59/22.94 (image1E) =>
% 132.59/22.94 ((
% 132.59/22.94 (image1I) =>
% 132.59/22.94 ((
% 132.59/22.94 (injFuncInInjFuncSet) =>
% 132.59/22.94 ((
% 132.59/22.94 (injFuncSetFuncIn) =>
% 132.59/22.94 ((
% 132.59/22.94 (injFuncSetFuncInj) =>
% 132.59/22.94 ((
% 132.59/22.94 (surjFuncSetFuncIn) =>
% 132.59/22.94 ((
% 132.59/22.94 (surjFuncSetFuncSurj) =>
% 132.59/22.94 ((
% 132.59/22.94 (leftInvIsSurj) =>
% 132.59/22.94 ((
% 132.59/22.94 (surjCantorThm) =>
% 132.59/22.94 ((
% 132.59/22.94 (foundation2) =>
% 132.59/22.94 ((
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% 132.59/22.94 ((
% 132.59/22.94 (notinself2) =>
% 132.59/22.94 ((
% 132.59/22.94 (omegaSp) =>
% 132.59/22.94 ((
% 132.59/22.94 (omegaSclos) =>
% 132.59/22.94 ((
% 132.59/22.94 (peano0notS) =>
% 132.59/22.94 ((
% 132.59/22.94 (peanoSinj) =>
% 132.59/22.94 ((
% 132.59/22.94 (transitivesetOp1) =>
% 132.59/22.94 ((
% 132.59/22.94 (binintTransitive) =>
% 132.59/22.94 ((
% 132.59/22.94 (transitivesetOp2) =>
% 132.59/22.94 ((
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% 132.59/22.94 ((
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% 132.59/22.94 ((
% 132.59/22.94 (ordinalTransSet) =>
% 132.59/22.94 ((
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% 132.59/22.94 ((
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% 132.59/22.94 (ordinal @
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% 132.59/22.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1041])).
% 132.59/22.94 thf(zip_derived_cl1054, plain,
% 132.59/22.94 (~ (((setminusSubset2) =>
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% 132.59/22.94 (((setminusILneg) =>
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% 132.59/22.94 (((setukpairIR) =>
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% 132.59/22.94 (((singletoninpowunion) =>
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% 132.59/22.94 (((upairinpowunion) =>
% 132.59/22.94 (((ubforcartprodlem1) =>
% 132.59/22.94 (((ubforcartprodlem2) =>
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% 132.59/22.94 ((
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% 132.59/22.94 ((
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% 132.79/22.94 ((
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% 132.79/22.94 ((
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% 132.79/22.94 ((
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% 132.79/22.94 ((
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% 132.79/22.94 ((
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% 132.79/22.94 ((
% 132.79/22.94 (setukpairinjL) =>
% 132.79/22.94 ((
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% 132.79/22.94 ((
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% 132.79/22.94 ((
% 132.79/22.94 (setukpairinjR1) =>
% 132.79/22.94 ((
% 132.79/22.94 (upairequniteq) =>
% 132.79/22.94 ((
% 132.79/22.94 (setukpairinjR2) =>
% 132.79/22.94 ((
% 132.79/22.94 (setukpairinjR) =>
% 132.79/22.94 ((
% 132.79/22.94 (ksndsingleton) =>
% 132.79/22.94 ((
% 132.79/22.94 (ksndpairEq) =>
% 132.79/22.94 ((
% 132.79/22.94 (kpairsurjEq) =>
% 132.79/22.94 ((
% 132.79/22.94 (cartprodsndin) =>
% 132.79/22.94 ((
% 132.79/22.94 (cartprodpairmemEL) =>
% 132.79/22.94 ((
% 132.79/22.94 (cartprodpairmemER) =>
% 132.79/22.94 ((
% 132.79/22.94 (cartprodmempaircEq) =>
% 132.79/22.94 ((
% 132.79/22.94 (cartprodfstpairEq) =>
% 132.79/22.94 ((
% 132.79/22.94 (cartprodsndpairEq) =>
% 132.79/22.94 ((
% 132.79/22.94 (cartprodpairsurjEq) =>
% 132.79/22.94 ((
% 132.79/22.94 (dpsetconstrI) =>
% 132.79/22.94 ((
% 132.79/22.94 (dpsetconstrSub) =>
% 132.79/22.94 ((
% 132.79/22.94 (setOfPairsIsBReln) =>
% 132.79/22.94 ((
% 132.79/22.94 (dpsetconstrERa) =>
% 132.79/22.94 ((
% 132.79/22.94 (dpsetconstrEL1) =>
% 132.79/22.94 ((
% 132.79/22.94 (dpsetconstrEL2) =>
% 132.79/22.94 ((
% 132.79/22.94 (dpsetconstrER) =>
% 132.79/22.94 ((
% 132.79/22.94 (funcImageSingleton) =>
% 132.79/22.94 ((
% 132.79/22.94 (apProp) =>
% 132.79/22.94 ((
% 132.79/22.94 (app) =>
% 132.79/22.94 ((
% 132.79/22.94 (infuncsetfunc) =>
% 132.79/22.94 ((
% 132.79/22.94 (ap2p) =>
% 132.79/22.94 ((
% 132.79/22.94 (funcinfuncset) =>
% 132.79/22.94 ((
% 132.79/22.94 (lamProp) =>
% 132.79/22.94 ((
% 132.79/22.94 (lamp) =>
% 132.79/22.94 ((
% 132.79/22.94 (lam2p) =>
% 132.79/22.94 ((
% 132.79/22.94 (brelnall1) =>
% 132.79/22.94 ((
% 132.79/22.94 (brelnall2) =>
% 132.79/22.94 ((
% 132.79/22.94 (ex1E2) =>
% 132.79/22.94 ((
% 132.79/22.94 (funcGraphProp1) =>
% 132.79/22.94 ((
% 132.79/22.94 (funcGraphProp3) =>
% 132.79/22.94 ((
% 132.79/22.94 (funcGraphProp2) =>
% 132.79/22.94 ((
% 132.79/22.94 (funcextLem) =>
% 132.79/22.94 ((
% 132.79/22.94 (funcGraphProp4) =>
% 132.79/22.94 ((
% 132.79/22.94 (subbreln) =>
% 132.79/22.94 ((
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% 132.79/22.94 ((
% 132.79/22.94 (funcext) =>
% 132.79/22.94 ((
% 132.79/22.94 (funcext2) =>
% 132.79/22.94 ((
% 132.79/22.94 (ap2apEq1) =>
% 132.79/22.94 ((
% 132.79/22.94 (ap2apEq2) =>
% 132.79/22.94 ((
% 132.79/22.94 (beta1) =>
% 132.79/22.94 ((
% 132.79/22.94 (eta1) =>
% 132.79/22.94 ((
% 132.79/22.94 (lam2lamEq) =>
% 132.79/22.94 ((
% 132.79/22.94 (beta2) =>
% 132.79/22.94 ((
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% 132.79/22.94 ((
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% 132.79/22.94 ((
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% 132.79/22.94 (iftrueProp2) =>
% 132.79/22.94 ((
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% 132.79/22.94 ((
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% 132.79/22.94 ((
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% 132.79/22.94 ((
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% 132.79/22.94 ((
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% 132.79/22.94 ((
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% 132.79/22.94 ((
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% 132.79/22.94 ((
% 132.79/22.94 (powersetTI1) =>
% 132.79/22.94 ((
% 132.79/22.94 (powersetTE1) =>
% 132.79/22.94 ((
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% 132.79/22.94 ((
% 132.79/22.94 (complementTE1) =>
% 132.79/22.94 ((
% 132.79/22.94 (binintersectTELcontra) =>
% 132.79/22.94 ((
% 132.79/22.94 (binintersectTERcontra) =>
% 132.79/22.94 ((
% 132.79/22.94 (contrasubsetT) =>
% 132.79/22.94 ((
% 132.79/22.94 (contrasubsetT1) =>
% 132.79/22.94 ((
% 132.79/22.94 (contrasubsetT2) =>
% 132.79/22.94 ((
% 132.79/22.94 (contrasubsetT3) =>
% 132.79/22.94 ((
% 132.79/22.94 (doubleComplementI1) =>
% 132.79/22.94 ((
% 132.79/22.94 (doubleComplementE1) =>
% 132.79/22.94 ((
% 132.79/22.94 (doubleComplementSub1) =>
% 132.79/22.94 ((
% 132.79/22.94 (doubleComplementSub2) =>
% 132.79/22.94 ((
% 132.79/22.94 (doubleComplementEq) =>
% 132.79/22.94 ((
% 132.79/22.94 (complementTnotintersectT) =>
% 132.79/22.94 ((
% 132.79/22.94 (complementImpComplementIntersect) =>
% 132.79/22.94 ((
% 132.79/22.94 (complementSubsetComplementIntersect) =>
% 132.79/22.94 ((
% 132.79/22.94 (complementInPowersetComplementIntersect) =>
% 132.79/22.94 ((
% 132.79/22.94 (contraSubsetComplement) =>
% 132.79/22.94 ((
% 132.79/22.94 (complementTcontraSubset) =>
% 132.79/22.94 ((
% 132.79/22.94 (binunionTILcontra) =>
% 132.79/22.94 ((
% 132.79/22.94 (binunionTIRcontra) =>
% 132.79/22.94 ((
% 132.79/22.94 (inIntersectImpInUnion) =>
% 132.79/22.94 ((
% 132.79/22.94 (inIntersectImpInUnion2) =>
% 132.79/22.94 ((
% 132.79/22.94 (inIntersectImpInIntersectUnions) =>
% 132.79/22.94 ((
% 132.79/22.94 (intersectInPowersetIntersectUnions) =>
% 132.79/22.94 ((
% 132.79/22.94 (inComplementUnionImpNotIn1) =>
% 132.79/22.94 ((
% 132.79/22.94 (inComplementUnionImpInComplement1) =>
% 132.79/22.94 ((
% 132.79/22.94 (binunionTE) =>
% 132.79/22.94 ((
% 132.79/22.94 (binunionTEcontra) =>
% 132.79/22.94 ((
% 132.79/22.94 (demorgan2a1) =>
% 132.79/22.94 ((
% 132.79/22.94 (complementUnionInPowersetComplement) =>
% 132.79/22.94 ((
% 132.79/22.94 (demorgan2a2) =>
% 132.79/22.94 ((
% 132.79/22.94 (demorgan1a) =>
% 132.79/22.94 ((
% 132.79/22.94 (demorgan1b) =>
% 132.79/22.94 ((
% 132.79/22.94 (demorgan1) =>
% 132.79/22.94 ((
% 132.79/22.94 (demorgan2a) =>
% 132.79/22.94 ((
% 132.79/22.94 (demorgan2b2) =>
% 132.79/22.94 ((
% 132.79/22.94 (demorgan2b) =>
% 132.79/22.94 ((
% 132.79/22.94 (demorgan2) =>
% 132.79/22.94 ((
% 132.79/22.94 (woz13rule0) =>
% 132.79/22.94 ((
% 132.79/22.94 (woz13rule1) =>
% 132.79/22.94 ((
% 132.79/22.94 (woz13rule2) =>
% 132.79/22.94 ((
% 132.79/22.94 (woz13rule3) =>
% 132.79/22.94 ((
% 132.79/22.94 (woz13rule4) =>
% 132.79/22.94 ((
% 132.79/22.94 (woz1_1) =>
% 132.79/22.94 ((
% 132.79/22.94 (woz1_2) =>
% 132.79/22.94 ((
% 132.79/22.94 (woz1_3) =>
% 132.79/22.94 ((
% 132.79/22.94 (woz1_4) =>
% 132.79/22.94 ((
% 132.79/22.94 (woz1_5) =>
% 132.79/22.94 ((
% 132.79/22.94 (breln1all2) =>
% 132.79/22.94 ((
% 132.79/22.94 (breln1SetBreln1) =>
% 132.79/22.94 ((
% 132.79/22.94 (choice2fnsingleton) =>
% 132.79/22.94 ((
% 132.79/22.94 (setOfPairsIsBReln1) =>
% 132.79/22.94 ((
% 132.79/22.94 (breln1all1) =>
% 132.79/22.94 ((
% 132.79/22.94 (subbreln1) =>
% 132.79/22.94 ((
% 132.79/22.94 (eqbreln1) =>
% 132.79/22.94 ((
% 132.79/22.94 (breln1invprop) =>
% 132.79/22.94 ((
% 132.79/22.94 (breln1invI) =>
% 132.79/22.94 ((
% 132.79/22.94 (breln1invE) =>
% 132.79/22.94 ((
% 132.79/22.94 (breln1compprop) =>
% 132.79/22.94 ((
% 132.79/22.94 (breln1compI) =>
% 132.79/22.94 ((
% 132.79/22.94 (breln1compE) =>
% 132.79/22.94 ((
% 132.79/22.94 (breln1compEex) =>
% 132.79/22.94 ((
% 132.79/22.94 (breln1unionprop) =>
% 132.79/22.94 ((
% 132.79/22.94 (breln1unionIL) =>
% 132.79/22.94 ((
% 132.79/22.94 (breln1unionIR) =>
% 132.79/22.94 ((
% 132.79/22.94 (breln1unionI) =>
% 132.79/22.94 ((
% 132.79/22.94 (breln1unionE) =>
% 132.79/22.94 ((
% 132.79/22.94 (breln1unionEcases) =>
% 132.79/22.94 ((
% 132.79/22.94 (breln1unionCommutes) =>
% 132.79/22.94 ((
% 132.79/22.94 (woz2Ex) =>
% 132.79/22.94 ((
% 132.79/22.94 (woz2W) =>
% 132.79/22.94 ((
% 132.79/22.94 (woz2A) =>
% 132.79/22.94 ((
% 132.79/22.94 (woz2B) =>
% 132.79/22.94 ((
% 132.79/22.94 (image1Ex) =>
% 132.79/22.94 ((
% 132.79/22.94 (image1Ex1) =>
% 132.79/22.94 ((
% 132.79/22.94 (image1Equiv) =>
% 132.79/22.94 ((
% 132.79/22.94 (image1E) =>
% 132.79/22.94 ((
% 132.79/22.94 (image1I) =>
% 132.79/22.94 ((
% 132.79/22.94 (injFuncInInjFuncSet) =>
% 132.79/22.94 ((
% 132.79/22.94 (injFuncSetFuncIn) =>
% 132.79/22.94 ((
% 132.79/22.94 (injFuncSetFuncInj) =>
% 132.79/22.94 ((
% 132.79/22.94 (surjFuncSetFuncIn) =>
% 132.79/22.94 ((
% 132.79/22.94 (surjFuncSetFuncSurj) =>
% 132.79/22.94 ((
% 132.79/22.94 (leftInvIsSurj) =>
% 132.79/22.94 ((
% 132.79/22.94 (surjCantorThm) =>
% 132.79/22.94 ((
% 132.79/22.94 (foundation2) =>
% 132.79/22.94 ((
% 132.79/22.94 (notinself) =>
% 132.79/22.94 ((
% 132.79/22.94 (notinself2) =>
% 132.79/22.94 ((
% 132.79/22.94 (omegaSp) =>
% 132.79/22.94 ((
% 132.79/22.94 (omegaSclos) =>
% 132.79/22.94 ((
% 132.79/22.94 (peano0notS) =>
% 132.79/22.94 ((
% 132.79/22.94 (peanoSinj) =>
% 132.79/22.94 ((
% 132.79/22.94 (transitivesetOp1) =>
% 132.79/22.94 ((
% 132.79/22.94 (binintTransitive) =>
% 132.79/22.94 ((
% 132.79/22.94 (transitivesetOp2) =>
% 132.79/22.94 ((
% 132.79/22.94 (setunionTransitive) =>
% 132.79/22.94 ((
% 132.79/22.94 (ordinalMinLem1) =>
% 132.79/22.94 ((
% 132.79/22.94 (ordinalTransSet) =>
% 132.79/22.94 ((
% 132.79/22.94 (ordinalTransSet1) =>
% 132.79/22.94 ((
% 132.79/22.94 (setunionOrdinalLem1) =>
% 132.79/22.94 (ordinal @
% 132.79/22.94 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/22.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1047])).
% 132.79/22.94 thf(zip_derived_cl1061, plain,
% 132.79/22.94 (~ (((setminusERneg) =>
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% 132.79/22.94 (((setminusILneg) =>
% 132.79/22.94 (((setminusIRneg) =>
% 132.79/22.94 (((setminusLsub) =>
% 132.79/22.94 (((setminusSubset1) =>
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% 132.79/22.94 (((symdiffI1) =>
% 132.79/22.94 (((symdiffI2) =>
% 132.79/22.94 (((symdiffIneg1) =>
% 132.79/22.94 (((symdiffIneg2) =>
% 132.79/22.94 (((secondinupair) =>
% 132.79/22.94 (((setukpairIL) =>
% 132.79/22.94 (((setukpairIR) =>
% 132.79/22.94 (((kpairiskpair) =>
% 132.79/22.94 (((kpairp) =>
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% 132.79/22.94 (((singletoninpowerset) =>
% 132.79/22.94 (((singletoninpowunion) =>
% 132.79/22.94 (((upairset2E) =>
% 132.79/22.94 (((upairsubunion) =>
% 132.79/22.94 (((upairinpowunion) =>
% 132.79/22.94 (((ubforcartprodlem1) =>
% 132.79/22.94 (((ubforcartprodlem2) =>
% 132.79/22.94 (((ubforcartprodlem3) =>
% 132.79/22.94 (((cartprodpairin) =>
% 132.79/22.94 (((cartprodmempair1) =>
% 132.79/22.94 (((cartprodmempair) =>
% 132.79/22.94 (((setunionE2) =>
% 132.79/22.94 (((setunionsingleton1) =>
% 132.79/22.94 ((
% 132.79/22.94 (setunionsingleton2) =>
% 132.79/22.94 ((
% 132.79/22.94 (setunionsingleton) =>
% 132.79/22.94 ((
% 132.79/22.94 (singletonprop) =>
% 132.79/22.94 ((
% 132.79/22.94 (ex1E1) =>
% 132.79/22.94 ((
% 132.79/22.94 (ex1I) =>
% 132.79/22.94 ((
% 132.79/22.94 (ex1I2) =>
% 132.79/22.94 ((
% 132.79/22.94 (singletonsuniq) =>
% 132.79/22.94 ((
% 132.79/22.94 (setukpairinjL1) =>
% 132.79/22.94 ((
% 132.79/22.94 (kfstsingleton) =>
% 132.79/22.94 ((
% 132.79/22.94 (theprop) =>
% 132.79/22.94 ((
% 132.79/22.94 (kfstpairEq) =>
% 132.79/22.94 ((
% 132.79/22.94 (cartprodfstin) =>
% 132.79/22.94 ((
% 132.79/22.94 (setukpairinjL2) =>
% 132.79/22.94 ((
% 132.79/22.94 (setukpairinjL) =>
% 132.79/22.94 ((
% 132.79/22.94 (setukpairinjR11) =>
% 132.79/22.94 ((
% 132.79/22.94 (setukpairinjR12) =>
% 132.79/22.94 ((
% 132.79/22.94 (setukpairinjR1) =>
% 132.79/22.94 ((
% 132.79/22.94 (upairequniteq) =>
% 132.79/22.94 ((
% 132.79/22.94 (setukpairinjR2) =>
% 132.79/22.94 ((
% 132.79/22.94 (setukpairinjR) =>
% 132.79/22.94 ((
% 132.79/22.94 (ksndsingleton) =>
% 132.79/22.94 ((
% 132.79/22.94 (ksndpairEq) =>
% 132.79/22.94 ((
% 132.79/22.94 (kpairsurjEq) =>
% 132.79/22.94 ((
% 132.79/22.94 (cartprodsndin) =>
% 132.79/22.94 ((
% 132.79/22.94 (cartprodpairmemEL) =>
% 132.79/22.94 ((
% 132.79/22.94 (cartprodpairmemER) =>
% 132.79/22.94 ((
% 132.79/22.94 (cartprodmempaircEq) =>
% 132.79/22.94 ((
% 132.79/22.94 (cartprodfstpairEq) =>
% 132.79/22.94 ((
% 132.79/22.94 (cartprodsndpairEq) =>
% 132.79/22.94 ((
% 132.79/22.94 (cartprodpairsurjEq) =>
% 132.79/22.94 ((
% 132.79/22.94 (dpsetconstrI) =>
% 132.79/22.94 ((
% 132.79/22.94 (dpsetconstrSub) =>
% 132.79/22.94 ((
% 132.79/22.94 (setOfPairsIsBReln) =>
% 132.79/22.94 ((
% 132.79/22.94 (dpsetconstrERa) =>
% 132.79/22.94 ((
% 132.79/22.94 (dpsetconstrEL1) =>
% 132.79/22.94 ((
% 132.79/22.94 (dpsetconstrEL2) =>
% 132.79/22.94 ((
% 132.79/22.94 (dpsetconstrER) =>
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% 132.79/22.94 ((
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% 132.79/22.94 ((
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% 132.79/22.94 ((
% 132.79/22.94 (infuncsetfunc) =>
% 132.79/22.94 ((
% 132.79/22.94 (ap2p) =>
% 132.79/22.94 ((
% 132.79/22.94 (funcinfuncset) =>
% 132.79/22.94 ((
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% 132.79/22.94 ((
% 132.79/22.94 (lamp) =>
% 132.79/22.94 ((
% 132.79/22.94 (lam2p) =>
% 132.79/22.94 ((
% 132.79/22.94 (brelnall1) =>
% 132.79/22.94 ((
% 132.79/22.94 (brelnall2) =>
% 132.79/22.94 ((
% 132.79/22.94 (ex1E2) =>
% 132.79/22.94 ((
% 132.79/22.94 (funcGraphProp1) =>
% 132.79/22.94 ((
% 132.79/22.94 (funcGraphProp3) =>
% 132.79/22.94 ((
% 132.79/22.94 (funcGraphProp2) =>
% 132.79/22.94 ((
% 132.79/22.94 (funcextLem) =>
% 132.79/22.94 ((
% 132.79/22.94 (funcGraphProp4) =>
% 132.79/22.94 ((
% 132.79/22.94 (subbreln) =>
% 132.79/22.94 ((
% 132.79/22.94 (eqbreln) =>
% 132.79/22.94 ((
% 132.79/22.94 (funcext) =>
% 132.79/22.94 ((
% 132.79/22.94 (funcext2) =>
% 132.79/22.94 ((
% 132.79/22.94 (ap2apEq1) =>
% 132.79/22.94 ((
% 132.79/22.94 (ap2apEq2) =>
% 132.79/22.94 ((
% 132.79/22.94 (beta1) =>
% 132.79/22.94 ((
% 132.79/22.94 (eta1) =>
% 132.79/22.94 ((
% 132.79/22.94 (lam2lamEq) =>
% 132.79/22.94 ((
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% 132.79/22.94 ((
% 132.79/22.94 (eta2) =>
% 132.79/22.94 ((
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% 132.79/22.94 ((
% 132.79/22.94 (iffalseProp2) =>
% 132.79/22.94 ((
% 132.79/22.94 (iftrueProp1) =>
% 132.79/22.94 ((
% 132.79/22.94 (iftrueProp2) =>
% 132.79/22.94 ((
% 132.79/22.94 (ifSingleton) =>
% 132.79/22.94 ((
% 132.79/22.94 (ifp) =>
% 132.79/22.94 ((
% 132.79/22.94 (theeq) =>
% 132.79/22.94 ((
% 132.79/22.94 (iftrue) =>
% 132.79/22.94 ((
% 132.79/22.94 (iffalse) =>
% 132.79/22.94 ((
% 132.79/22.94 (iftrueorfalse) =>
% 132.79/22.94 ((
% 132.79/22.94 (binintersectT_lem) =>
% 132.79/22.94 ((
% 132.79/22.94 (binunionT_lem) =>
% 132.79/22.94 ((
% 132.79/22.94 (powersetT_lem) =>
% 132.79/22.94 ((
% 132.79/22.94 (setminusT_lem) =>
% 132.79/22.94 ((
% 132.79/22.94 (complementT_lem) =>
% 132.79/22.94 ((
% 132.79/22.94 (setextT) =>
% 132.79/22.94 ((
% 132.79/22.94 (subsetTI) =>
% 132.79/22.94 ((
% 132.79/22.94 (powersetTI1) =>
% 132.79/22.94 ((
% 132.79/22.94 (powersetTE1) =>
% 132.79/22.94 ((
% 132.79/22.94 (complementTI1) =>
% 132.79/22.94 ((
% 132.79/22.94 (complementTE1) =>
% 132.79/22.94 ((
% 132.79/22.94 (binintersectTELcontra) =>
% 132.79/22.94 ((
% 132.79/22.94 (binintersectTERcontra) =>
% 132.79/22.94 ((
% 132.79/22.94 (contrasubsetT) =>
% 132.79/22.94 ((
% 132.79/22.94 (contrasubsetT1) =>
% 132.79/22.94 ((
% 132.79/22.94 (contrasubsetT2) =>
% 132.79/22.94 ((
% 132.79/22.94 (contrasubsetT3) =>
% 132.79/22.94 ((
% 132.79/22.94 (doubleComplementI1) =>
% 132.79/22.94 ((
% 132.79/22.94 (doubleComplementE1) =>
% 132.79/22.94 ((
% 132.79/22.94 (doubleComplementSub1) =>
% 132.79/22.94 ((
% 132.79/22.94 (doubleComplementSub2) =>
% 132.79/22.94 ((
% 132.79/22.94 (doubleComplementEq) =>
% 132.79/22.94 ((
% 132.79/22.94 (complementTnotintersectT) =>
% 132.79/22.94 ((
% 132.79/22.94 (complementImpComplementIntersect) =>
% 132.79/22.94 ((
% 132.79/22.94 (complementSubsetComplementIntersect) =>
% 132.79/22.94 ((
% 132.79/22.94 (complementInPowersetComplementIntersect) =>
% 132.79/22.94 ((
% 132.79/22.94 (contraSubsetComplement) =>
% 132.79/22.94 ((
% 132.79/22.94 (complementTcontraSubset) =>
% 132.79/22.94 ((
% 132.79/22.94 (binunionTILcontra) =>
% 132.79/22.94 ((
% 132.79/22.94 (binunionTIRcontra) =>
% 132.79/22.94 ((
% 132.79/22.94 (inIntersectImpInUnion) =>
% 132.79/22.94 ((
% 132.79/22.94 (inIntersectImpInUnion2) =>
% 132.79/22.94 ((
% 132.79/22.94 (inIntersectImpInIntersectUnions) =>
% 132.79/22.94 ((
% 132.79/22.94 (intersectInPowersetIntersectUnions) =>
% 132.79/22.94 ((
% 132.79/22.94 (inComplementUnionImpNotIn1) =>
% 132.79/22.94 ((
% 132.79/22.94 (inComplementUnionImpInComplement1) =>
% 132.79/22.94 ((
% 132.79/22.94 (binunionTE) =>
% 132.79/22.94 ((
% 132.79/22.94 (binunionTEcontra) =>
% 132.79/22.94 ((
% 132.79/22.94 (demorgan2a1) =>
% 132.79/22.94 ((
% 132.79/22.94 (complementUnionInPowersetComplement) =>
% 132.79/22.94 ((
% 132.79/22.94 (demorgan2a2) =>
% 132.79/22.94 ((
% 132.79/22.94 (demorgan1a) =>
% 132.79/22.94 ((
% 132.79/22.94 (demorgan1b) =>
% 132.79/22.94 ((
% 132.79/22.94 (demorgan1) =>
% 132.79/22.94 ((
% 132.79/22.94 (demorgan2a) =>
% 132.79/22.94 ((
% 132.79/22.94 (demorgan2b2) =>
% 132.79/22.94 ((
% 132.79/22.94 (demorgan2b) =>
% 132.79/22.94 ((
% 132.79/22.94 (demorgan2) =>
% 132.79/22.94 ((
% 132.79/22.94 (woz13rule0) =>
% 132.79/22.94 ((
% 132.79/22.94 (woz13rule1) =>
% 132.79/22.94 ((
% 132.79/22.94 (woz13rule2) =>
% 132.79/22.94 ((
% 132.79/22.94 (woz13rule3) =>
% 132.79/22.94 ((
% 132.79/22.94 (woz13rule4) =>
% 132.79/22.94 ((
% 132.79/22.94 (woz1_1) =>
% 132.79/22.94 ((
% 132.79/22.94 (woz1_2) =>
% 132.79/22.94 ((
% 132.79/22.94 (woz1_3) =>
% 132.79/22.94 ((
% 132.79/22.94 (woz1_4) =>
% 132.79/22.94 ((
% 132.79/22.94 (woz1_5) =>
% 132.79/22.94 ((
% 132.79/22.94 (breln1all2) =>
% 132.79/22.94 ((
% 132.79/22.94 (breln1SetBreln1) =>
% 132.79/22.94 ((
% 132.79/22.94 (choice2fnsingleton) =>
% 132.79/22.94 ((
% 132.79/22.94 (setOfPairsIsBReln1) =>
% 132.79/22.94 ((
% 132.79/22.94 (breln1all1) =>
% 132.79/22.94 ((
% 132.79/22.94 (subbreln1) =>
% 132.79/22.94 ((
% 132.79/22.94 (eqbreln1) =>
% 132.79/22.94 ((
% 132.79/22.94 (breln1invprop) =>
% 132.79/22.94 ((
% 132.79/22.94 (breln1invI) =>
% 132.79/22.94 ((
% 132.79/22.94 (breln1invE) =>
% 132.79/22.94 ((
% 132.79/22.94 (breln1compprop) =>
% 132.79/22.94 ((
% 132.79/22.94 (breln1compI) =>
% 132.79/22.94 ((
% 132.79/22.94 (breln1compE) =>
% 132.79/22.94 ((
% 132.79/22.94 (breln1compEex) =>
% 132.79/22.94 ((
% 132.79/22.94 (breln1unionprop) =>
% 132.79/22.94 ((
% 132.79/22.94 (breln1unionIL) =>
% 132.79/22.94 ((
% 132.79/22.94 (breln1unionIR) =>
% 132.79/22.94 ((
% 132.79/22.94 (breln1unionI) =>
% 132.79/22.94 ((
% 132.79/22.94 (breln1unionE) =>
% 132.79/22.94 ((
% 132.79/22.94 (breln1unionEcases) =>
% 132.79/22.94 ((
% 132.79/22.94 (breln1unionCommutes) =>
% 132.79/22.94 ((
% 132.79/22.94 (woz2Ex) =>
% 132.79/22.94 ((
% 132.79/22.94 (woz2W) =>
% 132.79/22.94 ((
% 132.79/22.94 (woz2A) =>
% 132.79/22.94 ((
% 132.79/22.94 (woz2B) =>
% 132.79/22.94 ((
% 132.79/22.94 (image1Ex) =>
% 132.79/22.94 ((
% 132.79/22.94 (image1Ex1) =>
% 132.79/22.94 ((
% 132.79/22.94 (image1Equiv) =>
% 132.79/22.94 ((
% 132.79/22.94 (image1E) =>
% 132.79/22.94 ((
% 132.79/22.94 (image1I) =>
% 132.79/22.94 ((
% 132.79/22.94 (injFuncInInjFuncSet) =>
% 132.79/22.94 ((
% 132.79/22.94 (injFuncSetFuncIn) =>
% 132.79/22.94 ((
% 132.79/22.94 (injFuncSetFuncInj) =>
% 132.79/22.94 ((
% 132.79/22.94 (surjFuncSetFuncIn) =>
% 132.79/22.94 ((
% 132.79/22.94 (surjFuncSetFuncSurj) =>
% 132.79/22.94 ((
% 132.79/22.94 (leftInvIsSurj) =>
% 132.79/22.94 ((
% 132.79/22.94 (surjCantorThm) =>
% 132.79/22.94 ((
% 132.79/22.94 (foundation2) =>
% 132.79/22.94 ((
% 132.79/22.94 (notinself) =>
% 132.79/22.94 ((
% 132.79/22.94 (notinself2) =>
% 132.79/22.94 ((
% 132.79/22.94 (omegaSp) =>
% 132.79/22.94 ((
% 132.79/22.94 (omegaSclos) =>
% 132.79/22.94 ((
% 132.79/22.94 (peano0notS) =>
% 132.79/22.94 ((
% 132.79/22.94 (peanoSinj) =>
% 132.79/22.94 ((
% 132.79/22.94 (transitivesetOp1) =>
% 132.79/22.94 ((
% 132.79/22.94 (binintTransitive) =>
% 132.79/22.94 ((
% 132.79/22.94 (transitivesetOp2) =>
% 132.79/22.94 ((
% 132.79/22.94 (setunionTransitive) =>
% 132.79/22.94 ((
% 132.79/22.94 (ordinalMinLem1) =>
% 132.79/22.94 ((
% 132.79/22.94 (ordinalTransSet) =>
% 132.79/22.94 ((
% 132.79/22.94 (ordinalTransSet1) =>
% 132.79/22.94 ((
% 132.79/22.94 (setunionOrdinalLem1) =>
% 132.79/22.94 (ordinal @
% 132.79/22.94 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/22.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1054])).
% 132.79/22.94 thf(zip_derived_cl1068, plain,
% 132.79/22.94 (~ (((setminusELneg) =>
% 132.79/22.94 (((setminusILneg) =>
% 132.79/22.94 (((setminusIRneg) =>
% 132.79/22.94 (((setminusLsub) =>
% 132.79/22.94 (((setminusSubset1) =>
% 132.79/22.94 (((symdiffE) =>
% 132.79/22.94 (((symdiffI1) =>
% 132.79/22.94 (((symdiffI2) =>
% 132.79/22.94 (((symdiffIneg1) =>
% 132.79/22.94 (((symdiffIneg2) =>
% 132.79/22.94 (((secondinupair) =>
% 132.79/22.94 (((setukpairIL) =>
% 132.79/22.94 (((setukpairIR) =>
% 132.79/22.94 (((kpairiskpair) =>
% 132.79/22.94 (((kpairp) =>
% 132.79/22.94 (((singletonsubset) =>
% 132.79/22.94 (((singletoninpowerset) =>
% 132.79/22.94 (((singletoninpowunion) =>
% 132.79/22.94 (((upairset2E) =>
% 132.79/22.94 (((upairsubunion) =>
% 132.79/22.94 (((upairinpowunion) =>
% 132.79/22.94 (((ubforcartprodlem1) =>
% 132.79/22.94 (((ubforcartprodlem2) =>
% 132.79/22.94 (((ubforcartprodlem3) =>
% 132.79/22.94 (((cartprodpairin) =>
% 132.79/22.94 (((cartprodmempair1) =>
% 132.79/22.94 (((cartprodmempair) =>
% 132.79/22.94 (((setunionE2) =>
% 132.79/22.94 (((setunionsingleton1) =>
% 132.79/22.94 (((setunionsingleton2) =>
% 132.79/22.94 ((
% 132.79/22.94 (setunionsingleton) =>
% 132.79/22.94 ((
% 132.79/22.94 (singletonprop) =>
% 132.79/22.94 ((
% 132.79/22.94 (ex1E1) =>
% 132.79/22.94 ((
% 132.79/22.94 (ex1I) =>
% 132.79/22.94 ((
% 132.79/22.94 (ex1I2) =>
% 132.79/22.94 ((
% 132.79/22.94 (singletonsuniq) =>
% 132.79/22.94 ((
% 132.79/22.94 (setukpairinjL1) =>
% 132.79/22.94 ((
% 132.79/22.94 (kfstsingleton) =>
% 132.79/22.94 ((
% 132.79/22.94 (theprop) =>
% 132.79/22.94 ((
% 132.79/22.94 (kfstpairEq) =>
% 132.79/22.94 ((
% 132.79/22.94 (cartprodfstin) =>
% 132.79/22.94 ((
% 132.79/22.94 (setukpairinjL2) =>
% 132.79/22.94 ((
% 132.79/22.94 (setukpairinjL) =>
% 132.79/22.94 ((
% 132.79/22.94 (setukpairinjR11) =>
% 132.79/22.94 ((
% 132.79/22.94 (setukpairinjR12) =>
% 132.79/22.94 ((
% 132.79/22.94 (setukpairinjR1) =>
% 132.79/22.94 ((
% 132.79/22.94 (upairequniteq) =>
% 132.79/22.94 ((
% 132.79/22.94 (setukpairinjR2) =>
% 132.79/22.94 ((
% 132.79/22.94 (setukpairinjR) =>
% 132.79/22.94 ((
% 132.79/22.94 (ksndsingleton) =>
% 132.79/22.94 ((
% 132.79/22.94 (ksndpairEq) =>
% 132.79/22.94 ((
% 132.79/22.94 (kpairsurjEq) =>
% 132.79/22.94 ((
% 132.79/22.94 (cartprodsndin) =>
% 132.79/22.94 ((
% 132.79/22.94 (cartprodpairmemEL) =>
% 132.79/22.94 ((
% 132.79/22.94 (cartprodpairmemER) =>
% 132.79/22.94 ((
% 132.79/22.94 (cartprodmempaircEq) =>
% 132.79/22.94 ((
% 132.79/22.94 (cartprodfstpairEq) =>
% 132.79/22.94 ((
% 132.79/22.94 (cartprodsndpairEq) =>
% 132.79/22.94 ((
% 132.79/22.94 (cartprodpairsurjEq) =>
% 132.79/22.94 ((
% 132.79/22.94 (dpsetconstrI) =>
% 132.79/22.94 ((
% 132.79/22.94 (dpsetconstrSub) =>
% 132.79/22.94 ((
% 132.79/22.94 (setOfPairsIsBReln) =>
% 132.79/22.94 ((
% 132.79/22.94 (dpsetconstrERa) =>
% 132.79/22.94 ((
% 132.79/22.94 (dpsetconstrEL1) =>
% 132.79/22.94 ((
% 132.79/22.94 (dpsetconstrEL2) =>
% 132.79/22.94 ((
% 132.79/22.94 (dpsetconstrER) =>
% 132.79/22.94 ((
% 132.79/22.94 (funcImageSingleton) =>
% 132.79/22.94 ((
% 132.79/22.94 (apProp) =>
% 132.79/22.94 ((
% 132.79/22.94 (app) =>
% 132.79/22.94 ((
% 132.79/22.94 (infuncsetfunc) =>
% 132.79/22.94 ((
% 132.79/22.94 (ap2p) =>
% 132.79/22.94 ((
% 132.79/22.94 (funcinfuncset) =>
% 132.79/22.94 ((
% 132.79/22.94 (lamProp) =>
% 132.79/22.94 ((
% 132.79/22.94 (lamp) =>
% 132.79/22.94 ((
% 132.79/22.94 (lam2p) =>
% 132.79/22.94 ((
% 132.79/22.94 (brelnall1) =>
% 132.79/22.94 ((
% 132.79/22.94 (brelnall2) =>
% 132.79/22.94 ((
% 132.79/22.94 (ex1E2) =>
% 132.79/22.94 ((
% 132.79/22.94 (funcGraphProp1) =>
% 132.79/22.94 ((
% 132.79/22.94 (funcGraphProp3) =>
% 132.79/22.94 ((
% 132.79/22.94 (funcGraphProp2) =>
% 132.79/22.94 ((
% 132.79/22.94 (funcextLem) =>
% 132.79/22.94 ((
% 132.79/22.94 (funcGraphProp4) =>
% 132.79/22.94 ((
% 132.79/22.94 (subbreln) =>
% 132.79/22.94 ((
% 132.79/22.94 (eqbreln) =>
% 132.79/22.94 ((
% 132.79/22.94 (funcext) =>
% 132.79/22.94 ((
% 132.79/22.94 (funcext2) =>
% 132.79/22.94 ((
% 132.79/22.94 (ap2apEq1) =>
% 132.79/22.94 ((
% 132.79/22.94 (ap2apEq2) =>
% 132.79/22.94 ((
% 132.79/22.94 (beta1) =>
% 132.79/22.94 ((
% 132.79/22.94 (eta1) =>
% 132.79/22.94 ((
% 132.79/22.94 (lam2lamEq) =>
% 132.79/22.94 ((
% 132.79/22.94 (beta2) =>
% 132.79/22.94 ((
% 132.79/22.94 (eta2) =>
% 132.79/22.94 ((
% 132.79/22.94 (iffalseProp1) =>
% 132.79/22.94 ((
% 132.79/22.94 (iffalseProp2) =>
% 132.79/22.94 ((
% 132.79/22.94 (iftrueProp1) =>
% 132.79/22.94 ((
% 132.79/22.94 (iftrueProp2) =>
% 132.79/22.94 ((
% 132.79/22.94 (ifSingleton) =>
% 132.79/22.94 ((
% 132.79/22.94 (ifp) =>
% 132.79/22.94 ((
% 132.79/22.94 (theeq) =>
% 132.79/22.94 ((
% 132.79/22.94 (iftrue) =>
% 132.79/22.94 ((
% 132.79/22.94 (iffalse) =>
% 132.79/22.94 ((
% 132.79/22.94 (iftrueorfalse) =>
% 132.79/22.94 ((
% 132.79/22.94 (binintersectT_lem) =>
% 132.79/22.94 ((
% 132.79/22.94 (binunionT_lem) =>
% 132.79/22.94 ((
% 132.79/22.94 (powersetT_lem) =>
% 132.79/22.94 ((
% 132.79/22.94 (setminusT_lem) =>
% 132.79/22.94 ((
% 132.79/22.94 (complementT_lem) =>
% 132.79/22.94 ((
% 132.79/22.94 (setextT) =>
% 132.79/22.94 ((
% 132.79/22.94 (subsetTI) =>
% 132.79/22.94 ((
% 132.79/22.94 (powersetTI1) =>
% 132.79/22.94 ((
% 132.79/22.94 (powersetTE1) =>
% 132.79/22.94 ((
% 132.79/22.94 (complementTI1) =>
% 132.79/22.94 ((
% 132.79/22.94 (complementTE1) =>
% 132.79/22.94 ((
% 132.79/22.94 (binintersectTELcontra) =>
% 132.79/22.94 ((
% 132.79/22.94 (binintersectTERcontra) =>
% 132.79/22.94 ((
% 132.79/22.94 (contrasubsetT) =>
% 132.79/22.94 ((
% 132.79/22.94 (contrasubsetT1) =>
% 132.79/22.94 ((
% 132.79/22.94 (contrasubsetT2) =>
% 132.79/22.94 ((
% 132.79/22.94 (contrasubsetT3) =>
% 132.79/22.94 ((
% 132.79/22.94 (doubleComplementI1) =>
% 132.79/22.94 ((
% 132.79/22.94 (doubleComplementE1) =>
% 132.79/22.94 ((
% 132.79/22.94 (doubleComplementSub1) =>
% 132.79/22.94 ((
% 132.79/22.94 (doubleComplementSub2) =>
% 132.79/22.94 ((
% 132.79/22.94 (doubleComplementEq) =>
% 132.79/22.94 ((
% 132.79/22.94 (complementTnotintersectT) =>
% 132.79/22.94 ((
% 132.79/22.94 (complementImpComplementIntersect) =>
% 132.79/22.94 ((
% 132.79/22.94 (complementSubsetComplementIntersect) =>
% 132.79/22.94 ((
% 132.79/22.94 (complementInPowersetComplementIntersect) =>
% 132.79/22.94 ((
% 132.79/22.94 (contraSubsetComplement) =>
% 132.79/22.94 ((
% 132.79/22.94 (complementTcontraSubset) =>
% 132.79/22.94 ((
% 132.79/22.94 (binunionTILcontra) =>
% 132.79/22.94 ((
% 132.79/22.94 (binunionTIRcontra) =>
% 132.79/22.94 ((
% 132.79/22.94 (inIntersectImpInUnion) =>
% 132.79/22.94 ((
% 132.79/22.94 (inIntersectImpInUnion2) =>
% 132.79/22.94 ((
% 132.79/22.94 (inIntersectImpInIntersectUnions) =>
% 132.79/22.94 ((
% 132.79/22.94 (intersectInPowersetIntersectUnions) =>
% 132.79/22.94 ((
% 132.79/22.94 (inComplementUnionImpNotIn1) =>
% 132.79/22.94 ((
% 132.79/22.94 (inComplementUnionImpInComplement1) =>
% 132.79/22.94 ((
% 132.79/22.94 (binunionTE) =>
% 132.79/22.94 ((
% 132.79/22.94 (binunionTEcontra) =>
% 132.79/22.94 ((
% 132.79/22.94 (demorgan2a1) =>
% 132.79/22.94 ((
% 132.79/22.94 (complementUnionInPowersetComplement) =>
% 132.79/22.94 ((
% 132.79/22.94 (demorgan2a2) =>
% 132.79/22.94 ((
% 132.79/22.94 (demorgan1a) =>
% 132.79/22.94 ((
% 132.79/22.94 (demorgan1b) =>
% 132.79/22.94 ((
% 132.79/22.94 (demorgan1) =>
% 132.79/22.94 ((
% 132.79/22.94 (demorgan2a) =>
% 132.79/22.94 ((
% 132.79/22.94 (demorgan2b2) =>
% 132.79/22.94 ((
% 132.79/22.94 (demorgan2b) =>
% 132.79/22.94 ((
% 132.79/22.94 (demorgan2) =>
% 132.79/22.94 ((
% 132.79/22.94 (woz13rule0) =>
% 132.79/22.94 ((
% 132.79/22.94 (woz13rule1) =>
% 132.79/22.94 ((
% 132.79/22.94 (woz13rule2) =>
% 132.79/22.94 ((
% 132.79/22.94 (woz13rule3) =>
% 132.79/22.94 ((
% 132.79/22.94 (woz13rule4) =>
% 132.79/22.94 ((
% 132.79/22.94 (woz1_1) =>
% 132.79/22.94 ((
% 132.79/22.94 (woz1_2) =>
% 132.79/22.94 ((
% 132.79/22.94 (woz1_3) =>
% 132.79/22.94 ((
% 132.79/22.94 (woz1_4) =>
% 132.79/22.94 ((
% 132.79/22.94 (woz1_5) =>
% 132.79/22.94 ((
% 132.79/22.94 (breln1all2) =>
% 132.79/22.94 ((
% 132.79/22.94 (breln1SetBreln1) =>
% 132.79/22.94 ((
% 132.79/22.94 (choice2fnsingleton) =>
% 132.79/22.94 ((
% 132.79/22.94 (setOfPairsIsBReln1) =>
% 132.79/22.94 ((
% 132.79/22.94 (breln1all1) =>
% 132.79/22.94 ((
% 132.79/22.94 (subbreln1) =>
% 132.79/22.94 ((
% 132.79/22.94 (eqbreln1) =>
% 132.79/22.94 ((
% 132.79/22.94 (breln1invprop) =>
% 132.79/22.94 ((
% 132.79/22.94 (breln1invI) =>
% 132.79/22.94 ((
% 132.79/22.94 (breln1invE) =>
% 132.79/22.94 ((
% 132.79/22.94 (breln1compprop) =>
% 132.79/22.94 ((
% 132.79/22.94 (breln1compI) =>
% 132.79/22.94 ((
% 132.79/22.94 (breln1compE) =>
% 132.79/22.94 ((
% 132.79/22.94 (breln1compEex) =>
% 132.79/22.94 ((
% 132.79/22.94 (breln1unionprop) =>
% 132.79/22.94 ((
% 132.79/22.94 (breln1unionIL) =>
% 132.79/22.94 ((
% 132.79/22.94 (breln1unionIR) =>
% 132.79/22.94 ((
% 132.79/22.94 (breln1unionI) =>
% 132.79/22.94 ((
% 132.79/22.94 (breln1unionE) =>
% 132.79/22.94 ((
% 132.79/22.94 (breln1unionEcases) =>
% 132.79/22.94 ((
% 132.79/22.94 (breln1unionCommutes) =>
% 132.79/22.94 ((
% 132.79/22.94 (woz2Ex) =>
% 132.79/22.94 ((
% 132.79/22.94 (woz2W) =>
% 132.79/22.94 ((
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% 132.79/22.94 ((
% 132.79/22.94 (woz2B) =>
% 132.79/22.94 ((
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% 132.79/22.94 ((
% 132.79/22.94 (image1Ex1) =>
% 132.79/22.94 ((
% 132.79/22.94 (image1Equiv) =>
% 132.79/22.94 ((
% 132.79/22.94 (image1E) =>
% 132.79/22.94 ((
% 132.79/22.94 (image1I) =>
% 132.79/22.94 ((
% 132.79/22.94 (injFuncInInjFuncSet) =>
% 132.79/22.94 ((
% 132.79/22.94 (injFuncSetFuncIn) =>
% 132.79/22.94 ((
% 132.79/22.94 (injFuncSetFuncInj) =>
% 132.79/22.94 ((
% 132.79/22.94 (surjFuncSetFuncIn) =>
% 132.79/22.94 ((
% 132.79/22.94 (surjFuncSetFuncSurj) =>
% 132.79/22.94 ((
% 132.79/22.94 (leftInvIsSurj) =>
% 132.79/22.94 ((
% 132.79/22.94 (surjCantorThm) =>
% 132.79/22.94 ((
% 132.79/22.94 (foundation2) =>
% 132.79/22.94 ((
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% 132.79/22.94 ((
% 132.79/22.94 (notinself2) =>
% 132.79/22.94 ((
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% 132.79/22.94 ((
% 132.79/22.94 (omegaSclos) =>
% 132.79/22.94 ((
% 132.79/22.94 (peano0notS) =>
% 132.79/22.94 ((
% 132.79/22.94 (peanoSinj) =>
% 132.79/22.94 ((
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% 132.79/22.94 ((
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% 132.79/22.94 ((
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% 132.79/22.94 ((
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% 132.79/22.94 ((
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% 132.79/22.94 ((
% 132.79/22.94 (ordinalTransSet) =>
% 132.79/22.94 ((
% 132.79/22.94 (ordinalTransSet1) =>
% 132.79/22.94 ((
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% 132.79/22.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1061])).
% 132.79/22.94 thf(zip_derived_cl1075, plain,
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% 132.79/22.94 (((upairinpowunion) =>
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% 132.79/22.94 (((ubforcartprodlem3) =>
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% 132.79/22.94 (((cartprodmempair) =>
% 132.79/22.94 (((setunionE2) =>
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% 132.79/22.94 (((setunionsingleton2) =>
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% 132.79/22.94 ((
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% 132.79/22.94 ((
% 132.79/22.94 (singletonsuniq) =>
% 132.79/22.94 ((
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% 132.79/22.94 ((
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% 132.79/22.94 ((
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% 132.79/22.94 ((
% 132.79/22.94 (kfstpairEq) =>
% 132.79/22.94 ((
% 132.79/22.94 (cartprodfstin) =>
% 132.79/22.94 ((
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% 132.79/22.94 ((
% 132.79/22.94 (setukpairinjL) =>
% 132.79/22.94 ((
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% 132.79/22.94 ((
% 132.79/22.94 (setukpairinjR12) =>
% 132.79/22.94 ((
% 132.79/22.94 (setukpairinjR1) =>
% 132.79/22.94 ((
% 132.79/22.94 (upairequniteq) =>
% 132.79/22.94 ((
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% 132.79/22.94 ((
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% 132.79/22.94 ((
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% 132.79/22.94 ((
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% 132.79/22.94 ((
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% 132.79/22.94 ((
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% 132.79/22.94 ((
% 132.79/22.94 (cartprodmempaircEq) =>
% 132.79/22.94 ((
% 132.79/22.94 (cartprodfstpairEq) =>
% 132.79/22.94 ((
% 132.79/22.94 (cartprodsndpairEq) =>
% 132.79/22.94 ((
% 132.79/22.94 (cartprodpairsurjEq) =>
% 132.79/22.94 ((
% 132.79/22.94 (dpsetconstrI) =>
% 132.79/22.94 ((
% 132.79/22.94 (dpsetconstrSub) =>
% 132.79/22.94 ((
% 132.79/22.94 (setOfPairsIsBReln) =>
% 132.79/22.94 ((
% 132.79/22.94 (dpsetconstrERa) =>
% 132.79/22.94 ((
% 132.79/22.94 (dpsetconstrEL1) =>
% 132.79/22.94 ((
% 132.79/22.94 (dpsetconstrEL2) =>
% 132.79/22.94 ((
% 132.79/22.94 (dpsetconstrER) =>
% 132.79/22.94 ((
% 132.79/22.94 (funcImageSingleton) =>
% 132.79/22.94 ((
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% 132.79/22.94 ((
% 132.79/22.94 (app) =>
% 132.79/22.94 ((
% 132.79/22.94 (infuncsetfunc) =>
% 132.79/22.94 ((
% 132.79/22.94 (ap2p) =>
% 132.79/22.94 ((
% 132.79/22.94 (funcinfuncset) =>
% 132.79/22.94 ((
% 132.79/22.94 (lamProp) =>
% 132.79/22.94 ((
% 132.79/22.94 (lamp) =>
% 132.79/22.94 ((
% 132.79/22.94 (lam2p) =>
% 132.79/22.94 ((
% 132.79/22.94 (brelnall1) =>
% 132.79/22.94 ((
% 132.79/22.94 (brelnall2) =>
% 132.79/22.94 ((
% 132.79/22.94 (ex1E2) =>
% 132.79/22.94 ((
% 132.79/22.94 (funcGraphProp1) =>
% 132.79/22.94 ((
% 132.79/22.94 (funcGraphProp3) =>
% 132.79/22.94 ((
% 132.79/22.94 (funcGraphProp2) =>
% 132.79/22.94 ((
% 132.79/22.94 (funcextLem) =>
% 132.79/22.94 ((
% 132.79/22.94 (funcGraphProp4) =>
% 132.79/22.94 ((
% 132.79/22.94 (subbreln) =>
% 132.79/22.94 ((
% 132.79/22.94 (eqbreln) =>
% 132.79/22.94 ((
% 132.79/22.94 (funcext) =>
% 132.79/22.94 ((
% 132.79/22.94 (funcext2) =>
% 132.79/22.94 ((
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% 132.79/22.94 ((
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% 132.79/22.94 ((
% 132.79/22.94 (eta1) =>
% 132.79/22.94 ((
% 132.79/22.94 (lam2lamEq) =>
% 132.79/22.94 ((
% 132.79/22.94 (beta2) =>
% 132.79/22.94 ((
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% 132.79/22.94 ((
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% 132.79/22.94 ((
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% 132.79/22.94 (iftrueProp2) =>
% 132.79/22.94 ((
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% 132.79/22.94 ((
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% 132.79/22.94 ((
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% 132.79/22.94 ((
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% 132.79/22.94 ((
% 132.79/22.94 (iftrueorfalse) =>
% 132.79/22.94 ((
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% 132.79/22.94 ((
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% 132.79/22.94 ((
% 132.79/22.94 (powersetT_lem) =>
% 132.79/22.94 ((
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% 132.79/22.94 ((
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% 132.79/22.94 ((
% 132.79/22.94 (setextT) =>
% 132.79/22.94 ((
% 132.79/22.94 (subsetTI) =>
% 132.79/22.94 ((
% 132.79/22.94 (powersetTI1) =>
% 132.79/22.94 ((
% 132.79/22.94 (powersetTE1) =>
% 132.79/22.94 ((
% 132.79/22.94 (complementTI1) =>
% 132.79/22.94 ((
% 132.79/22.94 (complementTE1) =>
% 132.79/22.94 ((
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% 132.79/22.94 ((
% 132.79/22.94 (binintersectTERcontra) =>
% 132.79/22.94 ((
% 132.79/22.94 (contrasubsetT) =>
% 132.79/22.94 ((
% 132.79/22.94 (contrasubsetT1) =>
% 132.79/22.94 ((
% 132.79/22.94 (contrasubsetT2) =>
% 132.79/22.94 ((
% 132.79/22.94 (contrasubsetT3) =>
% 132.79/22.94 ((
% 132.79/22.94 (doubleComplementI1) =>
% 132.79/22.94 ((
% 132.79/22.94 (doubleComplementE1) =>
% 132.79/22.94 ((
% 132.79/22.94 (doubleComplementSub1) =>
% 132.79/22.94 ((
% 132.79/22.94 (doubleComplementSub2) =>
% 132.79/22.94 ((
% 132.79/22.94 (doubleComplementEq) =>
% 132.79/22.94 ((
% 132.79/22.94 (complementTnotintersectT) =>
% 132.79/22.94 ((
% 132.79/22.94 (complementImpComplementIntersect) =>
% 132.79/22.94 ((
% 132.79/22.94 (complementSubsetComplementIntersect) =>
% 132.79/22.94 ((
% 132.79/22.94 (complementInPowersetComplementIntersect) =>
% 132.79/22.94 ((
% 132.79/22.94 (contraSubsetComplement) =>
% 132.79/22.94 ((
% 132.79/22.94 (complementTcontraSubset) =>
% 132.79/22.94 ((
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% 132.79/22.94 ((
% 132.79/22.94 (binunionTIRcontra) =>
% 132.79/22.94 ((
% 132.79/22.94 (inIntersectImpInUnion) =>
% 132.79/22.94 ((
% 132.79/22.94 (inIntersectImpInUnion2) =>
% 132.79/22.94 ((
% 132.79/22.94 (inIntersectImpInIntersectUnions) =>
% 132.79/22.94 ((
% 132.79/22.94 (intersectInPowersetIntersectUnions) =>
% 132.79/22.94 ((
% 132.79/22.94 (inComplementUnionImpNotIn1) =>
% 132.79/22.94 ((
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% 132.79/22.94 ((
% 132.79/22.94 (binunionTE) =>
% 132.79/22.94 ((
% 132.79/22.94 (binunionTEcontra) =>
% 132.79/22.94 ((
% 132.79/22.94 (demorgan2a1) =>
% 132.79/22.94 ((
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% 132.79/22.94 ((
% 132.79/22.94 (demorgan2a2) =>
% 132.79/22.94 ((
% 132.79/22.94 (demorgan1a) =>
% 132.79/22.94 ((
% 132.79/22.94 (demorgan1b) =>
% 132.79/22.94 ((
% 132.79/22.94 (demorgan1) =>
% 132.79/22.94 ((
% 132.79/22.94 (demorgan2a) =>
% 132.79/22.94 ((
% 132.79/22.94 (demorgan2b2) =>
% 132.79/22.94 ((
% 132.79/22.94 (demorgan2b) =>
% 132.79/22.94 ((
% 132.79/22.94 (demorgan2) =>
% 132.79/22.94 ((
% 132.79/22.94 (woz13rule0) =>
% 132.79/22.94 ((
% 132.79/22.94 (woz13rule1) =>
% 132.79/22.94 ((
% 132.79/22.94 (woz13rule2) =>
% 132.79/22.94 ((
% 132.79/22.94 (woz13rule3) =>
% 132.79/22.94 ((
% 132.79/22.94 (woz13rule4) =>
% 132.79/22.94 ((
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% 132.79/22.94 ((
% 132.79/22.94 (woz1_2) =>
% 132.79/22.94 ((
% 132.79/22.94 (woz1_3) =>
% 132.79/22.94 ((
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% 132.79/22.94 ((
% 132.79/22.94 (woz1_5) =>
% 132.79/22.94 ((
% 132.79/22.94 (breln1all2) =>
% 132.79/22.94 ((
% 132.79/22.94 (breln1SetBreln1) =>
% 132.79/22.94 ((
% 132.79/22.94 (choice2fnsingleton) =>
% 132.79/22.94 ((
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% 132.79/22.94 ((
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% 132.79/22.94 ((
% 132.79/22.94 (breln1invI) =>
% 132.79/22.94 ((
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% 132.79/22.94 ((
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% 132.79/22.94 ((
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% 132.79/22.94 ((
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% 132.79/22.94 ((
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% 132.79/22.94 ((
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% 132.79/22.94 ((
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% 132.79/22.94 (breln1unionCommutes) =>
% 132.79/22.94 ((
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% 132.79/22.94 ((
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% 132.79/22.94 ((
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% 132.79/22.94 ((
% 132.79/22.94 (image1E) =>
% 132.79/22.94 ((
% 132.79/22.94 (image1I) =>
% 132.79/22.94 ((
% 132.79/22.94 (injFuncInInjFuncSet) =>
% 132.79/22.94 ((
% 132.79/22.94 (injFuncSetFuncIn) =>
% 132.79/22.94 ((
% 132.79/22.94 (injFuncSetFuncInj) =>
% 132.79/22.94 ((
% 132.79/22.94 (surjFuncSetFuncIn) =>
% 132.79/22.94 ((
% 132.79/22.94 (surjFuncSetFuncSurj) =>
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% 132.79/22.94 ((
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% 132.79/22.94 ((
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% 132.79/22.94 ((
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% 132.79/22.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1068])).
% 132.79/22.94 thf(zip_derived_cl1082, plain,
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% 132.79/22.94 ((
% 132.79/22.94 (dpsetconstrI) =>
% 132.79/22.94 ((
% 132.79/22.94 (dpsetconstrSub) =>
% 132.79/22.94 ((
% 132.79/22.94 (setOfPairsIsBReln) =>
% 132.79/22.94 ((
% 132.79/22.94 (dpsetconstrERa) =>
% 132.79/22.94 ((
% 132.79/22.94 (dpsetconstrEL1) =>
% 132.79/22.94 ((
% 132.79/22.94 (dpsetconstrEL2) =>
% 132.79/22.94 ((
% 132.79/22.94 (dpsetconstrER) =>
% 132.79/22.94 ((
% 132.79/22.94 (funcImageSingleton) =>
% 132.79/22.94 ((
% 132.79/22.94 (apProp) =>
% 132.79/22.94 ((
% 132.79/22.94 (app) =>
% 132.79/22.94 ((
% 132.79/22.94 (infuncsetfunc) =>
% 132.79/22.94 ((
% 132.79/22.94 (ap2p) =>
% 132.79/22.94 ((
% 132.79/22.94 (funcinfuncset) =>
% 132.79/22.94 ((
% 132.79/22.94 (lamProp) =>
% 132.79/22.94 ((
% 132.79/22.94 (lamp) =>
% 132.79/22.94 ((
% 132.79/22.94 (lam2p) =>
% 132.79/22.94 ((
% 132.79/22.94 (brelnall1) =>
% 132.79/22.94 ((
% 132.79/22.94 (brelnall2) =>
% 132.79/22.94 ((
% 132.79/22.94 (ex1E2) =>
% 132.79/22.94 ((
% 132.79/22.94 (funcGraphProp1) =>
% 132.79/22.94 ((
% 132.79/22.94 (funcGraphProp3) =>
% 132.79/22.94 ((
% 132.79/22.94 (funcGraphProp2) =>
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% 132.79/22.94 ((
% 132.79/22.94 (funcGraphProp4) =>
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% 132.79/22.94 ((
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% 132.79/22.94 ((
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% 132.79/22.94 ((
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% 132.79/22.94 ((
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% 132.79/22.94 ((
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% 132.79/22.94 ((
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% 132.79/22.94 ((
% 132.79/22.94 (binintersectTERcontra) =>
% 132.79/22.94 ((
% 132.79/22.94 (contrasubsetT) =>
% 132.79/22.94 ((
% 132.79/22.94 (contrasubsetT1) =>
% 132.79/22.94 ((
% 132.79/22.94 (contrasubsetT2) =>
% 132.79/22.94 ((
% 132.79/22.94 (contrasubsetT3) =>
% 132.79/22.94 ((
% 132.79/22.94 (doubleComplementI1) =>
% 132.79/22.94 ((
% 132.79/22.94 (doubleComplementE1) =>
% 132.79/22.94 ((
% 132.79/22.94 (doubleComplementSub1) =>
% 132.79/22.94 ((
% 132.79/22.94 (doubleComplementSub2) =>
% 132.79/22.94 ((
% 132.79/22.94 (doubleComplementEq) =>
% 132.79/22.94 ((
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% 132.79/22.94 ((
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% 132.79/22.94 ((
% 132.79/22.94 (complementInPowersetComplementIntersect) =>
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% 132.79/22.94 (contraSubsetComplement) =>
% 132.79/22.94 ((
% 132.79/22.94 (complementTcontraSubset) =>
% 132.79/22.94 ((
% 132.79/22.94 (binunionTILcontra) =>
% 132.79/22.94 ((
% 132.79/22.94 (binunionTIRcontra) =>
% 132.79/22.94 ((
% 132.79/22.94 (inIntersectImpInUnion) =>
% 132.79/22.94 ((
% 132.79/22.94 (inIntersectImpInUnion2) =>
% 132.79/22.94 ((
% 132.79/22.94 (inIntersectImpInIntersectUnions) =>
% 132.79/22.94 ((
% 132.79/22.94 (intersectInPowersetIntersectUnions) =>
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% 132.79/22.94 (inComplementUnionImpNotIn1) =>
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% 132.79/22.94 ((
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% 132.79/22.94 ((
% 132.79/22.94 (demorgan2a1) =>
% 132.79/22.94 ((
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% 132.79/22.94 ((
% 132.79/22.94 (demorgan2a2) =>
% 132.79/22.94 ((
% 132.79/22.94 (demorgan1a) =>
% 132.79/22.94 ((
% 132.79/22.94 (demorgan1b) =>
% 132.79/22.94 ((
% 132.79/22.94 (demorgan1) =>
% 132.79/22.94 ((
% 132.79/22.94 (demorgan2a) =>
% 132.79/22.94 ((
% 132.79/22.94 (demorgan2b2) =>
% 132.79/22.94 ((
% 132.79/22.94 (demorgan2b) =>
% 132.79/22.94 ((
% 132.79/22.94 (demorgan2) =>
% 132.79/22.94 ((
% 132.79/22.94 (woz13rule0) =>
% 132.79/22.94 ((
% 132.79/22.94 (woz13rule1) =>
% 132.79/22.94 ((
% 132.79/22.94 (woz13rule2) =>
% 132.79/22.94 ((
% 132.79/22.94 (woz13rule3) =>
% 132.79/22.94 ((
% 132.79/22.94 (woz13rule4) =>
% 132.79/22.94 ((
% 132.79/22.94 (woz1_1) =>
% 132.79/22.94 ((
% 132.79/22.94 (woz1_2) =>
% 132.79/22.94 ((
% 132.79/22.94 (woz1_3) =>
% 132.79/22.94 ((
% 132.79/22.94 (woz1_4) =>
% 132.79/22.94 ((
% 132.79/22.94 (woz1_5) =>
% 132.79/22.94 ((
% 132.79/22.94 (breln1all2) =>
% 132.79/22.94 ((
% 132.79/22.94 (breln1SetBreln1) =>
% 132.79/22.94 ((
% 132.79/22.94 (choice2fnsingleton) =>
% 132.79/22.94 ((
% 132.79/22.94 (setOfPairsIsBReln1) =>
% 132.79/22.94 ((
% 132.79/22.94 (breln1all1) =>
% 132.79/22.94 ((
% 132.79/22.94 (subbreln1) =>
% 132.79/22.94 ((
% 132.79/22.94 (eqbreln1) =>
% 132.79/22.94 ((
% 132.79/22.94 (breln1invprop) =>
% 132.79/22.94 ((
% 132.79/22.94 (breln1invI) =>
% 132.79/22.94 ((
% 132.79/22.94 (breln1invE) =>
% 132.79/22.94 ((
% 132.79/22.94 (breln1compprop) =>
% 132.79/22.94 ((
% 132.79/22.94 (breln1compI) =>
% 132.79/22.94 ((
% 132.79/22.94 (breln1compE) =>
% 132.79/22.94 ((
% 132.79/22.94 (breln1compEex) =>
% 132.79/22.94 ((
% 132.79/22.94 (breln1unionprop) =>
% 132.79/22.94 ((
% 132.79/22.94 (breln1unionIL) =>
% 132.79/22.94 ((
% 132.79/22.94 (breln1unionIR) =>
% 132.79/22.94 ((
% 132.79/22.94 (breln1unionI) =>
% 132.79/22.94 ((
% 132.79/22.94 (breln1unionE) =>
% 132.79/22.94 ((
% 132.79/22.94 (breln1unionEcases) =>
% 132.79/22.94 ((
% 132.79/22.94 (breln1unionCommutes) =>
% 132.79/22.94 ((
% 132.79/22.94 (woz2Ex) =>
% 132.79/22.94 ((
% 132.79/22.94 (woz2W) =>
% 132.79/22.94 ((
% 132.79/22.94 (woz2A) =>
% 132.79/22.94 ((
% 132.79/22.94 (woz2B) =>
% 132.79/22.94 ((
% 132.79/22.94 (image1Ex) =>
% 132.79/22.94 ((
% 132.79/22.94 (image1Ex1) =>
% 132.79/22.94 ((
% 132.79/22.94 (image1Equiv) =>
% 132.79/22.94 ((
% 132.79/22.94 (image1E) =>
% 132.79/22.94 ((
% 132.79/22.94 (image1I) =>
% 132.79/22.94 ((
% 132.79/22.94 (injFuncInInjFuncSet) =>
% 132.79/22.94 ((
% 132.79/22.94 (injFuncSetFuncIn) =>
% 132.79/22.94 ((
% 132.79/22.94 (injFuncSetFuncInj) =>
% 132.79/22.94 ((
% 132.79/22.94 (surjFuncSetFuncIn) =>
% 132.79/22.94 ((
% 132.79/22.94 (surjFuncSetFuncSurj) =>
% 132.79/22.94 ((
% 132.79/22.94 (leftInvIsSurj) =>
% 132.79/22.94 ((
% 132.79/22.94 (surjCantorThm) =>
% 132.79/22.94 ((
% 132.79/22.94 (foundation2) =>
% 132.79/22.94 ((
% 132.79/22.94 (notinself) =>
% 132.79/22.94 ((
% 132.79/22.94 (notinself2) =>
% 132.79/22.94 ((
% 132.79/22.94 (omegaSp) =>
% 132.79/22.94 ((
% 132.79/22.94 (omegaSclos) =>
% 132.79/22.94 ((
% 132.79/22.94 (peano0notS) =>
% 132.79/22.94 ((
% 132.79/22.94 (peanoSinj) =>
% 132.79/22.94 ((
% 132.79/22.94 (transitivesetOp1) =>
% 132.79/22.94 ((
% 132.79/22.94 (binintTransitive) =>
% 132.79/22.94 ((
% 132.79/22.94 (transitivesetOp2) =>
% 132.79/22.94 ((
% 132.79/22.94 (setunionTransitive) =>
% 132.79/22.94 ((
% 132.79/22.94 (ordinalMinLem1) =>
% 132.79/22.94 ((
% 132.79/22.94 (ordinalTransSet) =>
% 132.79/22.94 ((
% 132.79/22.94 (ordinalTransSet1) =>
% 132.79/22.94 ((
% 132.79/22.94 (setunionOrdinalLem1) =>
% 132.79/22.94 (ordinal @
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% 132.79/22.94 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1075])).
% 132.79/22.94 thf(zip_derived_cl1089, plain,
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% 132.79/22.94 (((symdiffIneg2) =>
% 132.79/22.94 (((secondinupair) =>
% 132.79/22.94 (((setukpairIL) =>
% 132.79/22.94 (((setukpairIR) =>
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% 132.79/22.94 (((singletoninpowerset) =>
% 132.79/22.94 (((singletoninpowunion) =>
% 132.79/22.94 (((upairset2E) =>
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% 132.79/22.94 (((upairinpowunion) =>
% 132.79/22.94 (((ubforcartprodlem1) =>
% 132.79/22.94 (((ubforcartprodlem2) =>
% 132.79/22.94 (((ubforcartprodlem3) =>
% 132.79/22.94 (((cartprodpairin) =>
% 132.79/22.94 (((cartprodmempair1) =>
% 132.79/22.94 (((cartprodmempair) =>
% 132.79/22.94 (((setunionE2) =>
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% 132.79/22.94 (((setunionsingleton2) =>
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% 132.79/22.94 ((
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% 132.79/22.94 ((
% 132.79/22.94 (ex1I2) =>
% 132.79/22.94 ((
% 132.79/22.94 (singletonsuniq) =>
% 132.79/22.94 ((
% 132.79/22.94 (setukpairinjL1) =>
% 132.79/22.94 ((
% 132.79/22.94 (kfstsingleton) =>
% 132.79/22.94 ((
% 132.79/22.94 (theprop) =>
% 132.79/22.94 ((
% 132.79/22.94 (kfstpairEq) =>
% 132.79/22.94 ((
% 132.79/22.94 (cartprodfstin) =>
% 132.79/22.94 ((
% 132.79/22.94 (setukpairinjL2) =>
% 132.79/22.94 ((
% 132.79/22.94 (setukpairinjL) =>
% 132.79/22.94 ((
% 132.79/22.94 (setukpairinjR11) =>
% 132.79/22.94 ((
% 132.79/22.94 (setukpairinjR12) =>
% 132.79/22.94 ((
% 132.79/22.94 (setukpairinjR1) =>
% 132.79/22.94 ((
% 132.79/22.94 (upairequniteq) =>
% 132.79/22.94 ((
% 132.79/22.94 (setukpairinjR2) =>
% 132.79/22.94 ((
% 132.79/22.94 (setukpairinjR) =>
% 132.79/22.94 ((
% 132.79/22.94 (ksndsingleton) =>
% 132.79/22.94 ((
% 132.79/22.94 (ksndpairEq) =>
% 132.79/22.94 ((
% 132.79/22.94 (kpairsurjEq) =>
% 132.79/22.94 ((
% 132.79/22.94 (cartprodsndin) =>
% 132.79/22.94 ((
% 132.79/22.94 (cartprodpairmemEL) =>
% 132.79/22.94 ((
% 132.79/22.94 (cartprodpairmemER) =>
% 132.79/22.94 ((
% 132.79/22.94 (cartprodmempaircEq) =>
% 132.79/22.94 ((
% 132.79/22.94 (cartprodfstpairEq) =>
% 132.79/22.94 ((
% 132.79/22.94 (cartprodsndpairEq) =>
% 132.79/22.94 ((
% 132.79/22.94 (cartprodpairsurjEq) =>
% 132.79/22.94 ((
% 132.79/22.94 (dpsetconstrI) =>
% 132.79/22.94 ((
% 132.79/22.94 (dpsetconstrSub) =>
% 132.79/22.94 ((
% 132.79/22.94 (setOfPairsIsBReln) =>
% 132.79/22.94 ((
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% 132.79/22.94 ((
% 132.79/22.94 (dpsetconstrEL1) =>
% 132.79/22.94 ((
% 132.79/22.94 (dpsetconstrEL2) =>
% 132.79/22.94 ((
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% 132.79/22.94 ((
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% 132.79/22.94 ((
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% 132.79/22.94 ((
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% 132.79/22.94 ((
% 132.79/22.94 (lamp) =>
% 132.79/22.94 ((
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% 132.79/22.94 ((
% 132.79/22.94 (brelnall1) =>
% 132.79/22.94 ((
% 132.79/22.94 (brelnall2) =>
% 132.79/22.94 ((
% 132.79/22.94 (ex1E2) =>
% 132.79/22.94 ((
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% 132.79/22.94 ((
% 132.79/22.94 (funcGraphProp3) =>
% 132.79/22.94 ((
% 132.79/22.94 (funcGraphProp2) =>
% 132.79/22.94 ((
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% 132.79/22.94 ((
% 132.79/22.94 (funcGraphProp4) =>
% 132.79/22.94 ((
% 132.79/22.94 (subbreln) =>
% 132.79/22.94 ((
% 132.79/22.94 (eqbreln) =>
% 132.79/22.94 ((
% 132.79/22.94 (funcext) =>
% 132.79/22.94 ((
% 132.79/22.94 (funcext2) =>
% 132.79/22.94 ((
% 132.79/22.94 (ap2apEq1) =>
% 132.79/22.94 ((
% 132.79/22.94 (ap2apEq2) =>
% 132.79/22.94 ((
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% 132.79/22.94 ((
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% 132.79/22.94 ((
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% 132.79/22.94 ((
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% 132.79/22.94 ((
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% 132.79/22.94 ((
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% 132.79/22.95 ((
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% 132.79/22.95 (ifSingleton) =>
% 132.79/22.95 ((
% 132.79/22.95 (ifp) =>
% 132.79/22.95 ((
% 132.79/22.95 (theeq) =>
% 132.79/22.95 ((
% 132.79/22.95 (iftrue) =>
% 132.79/22.95 ((
% 132.79/22.95 (iffalse) =>
% 132.79/22.95 ((
% 132.79/22.95 (iftrueorfalse) =>
% 132.79/22.95 ((
% 132.79/22.95 (binintersectT_lem) =>
% 132.79/22.95 ((
% 132.79/22.95 (binunionT_lem) =>
% 132.79/22.95 ((
% 132.79/22.95 (powersetT_lem) =>
% 132.79/22.95 ((
% 132.79/22.95 (setminusT_lem) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementT_lem) =>
% 132.79/22.95 ((
% 132.79/22.95 (setextT) =>
% 132.79/22.95 ((
% 132.79/22.95 (subsetTI) =>
% 132.79/22.95 ((
% 132.79/22.95 (powersetTI1) =>
% 132.79/22.95 ((
% 132.79/22.95 (powersetTE1) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementTI1) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementTE1) =>
% 132.79/22.95 ((
% 132.79/22.95 (binintersectTELcontra) =>
% 132.79/22.95 ((
% 132.79/22.95 (binintersectTERcontra) =>
% 132.79/22.95 ((
% 132.79/22.95 (contrasubsetT) =>
% 132.79/22.95 ((
% 132.79/22.95 (contrasubsetT1) =>
% 132.79/22.95 ((
% 132.79/22.95 (contrasubsetT2) =>
% 132.79/22.95 ((
% 132.79/22.95 (contrasubsetT3) =>
% 132.79/22.95 ((
% 132.79/22.95 (doubleComplementI1) =>
% 132.79/22.95 ((
% 132.79/22.95 (doubleComplementE1) =>
% 132.79/22.95 ((
% 132.79/22.95 (doubleComplementSub1) =>
% 132.79/22.95 ((
% 132.79/22.95 (doubleComplementSub2) =>
% 132.79/22.95 ((
% 132.79/22.95 (doubleComplementEq) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementTnotintersectT) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementImpComplementIntersect) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementSubsetComplementIntersect) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementInPowersetComplementIntersect) =>
% 132.79/22.95 ((
% 132.79/22.95 (contraSubsetComplement) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementTcontraSubset) =>
% 132.79/22.95 ((
% 132.79/22.95 (binunionTILcontra) =>
% 132.79/22.95 ((
% 132.79/22.95 (binunionTIRcontra) =>
% 132.79/22.95 ((
% 132.79/22.95 (inIntersectImpInUnion) =>
% 132.79/22.95 ((
% 132.79/22.95 (inIntersectImpInUnion2) =>
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% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1089])).
% 132.79/22.95 thf(zip_derived_cl1103, plain,
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% 132.79/22.95 (((upairinpowunion) =>
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% 132.79/22.95 (((ubforcartprodlem3) =>
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% 132.79/22.95 (((cartprodmempair) =>
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% 132.79/22.95 (((setunionsingleton1) =>
% 132.79/22.95 (((setunionsingleton2) =>
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% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (kfstpairEq) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (setukpairinjL) =>
% 132.79/22.95 ((
% 132.79/22.95 (setukpairinjR11) =>
% 132.79/22.95 ((
% 132.79/22.95 (setukpairinjR12) =>
% 132.79/22.95 ((
% 132.79/22.95 (setukpairinjR1) =>
% 132.79/22.95 ((
% 132.79/22.95 (upairequniteq) =>
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% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (cartprodfstpairEq) =>
% 132.79/22.95 ((
% 132.79/22.95 (cartprodsndpairEq) =>
% 132.79/22.95 ((
% 132.79/22.95 (cartprodpairsurjEq) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (dpsetconstrEL2) =>
% 132.79/22.95 ((
% 132.79/22.95 (dpsetconstrER) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (ap2p) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (brelnall2) =>
% 132.79/22.95 ((
% 132.79/22.95 (ex1E2) =>
% 132.79/22.95 ((
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% 132.79/22.95 (funcext2) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (ap2apEq2) =>
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% 132.79/22.95 ((
% 132.79/22.95 (powersetT_lem) =>
% 132.79/22.95 ((
% 132.79/22.95 (setminusT_lem) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementT_lem) =>
% 132.79/22.95 ((
% 132.79/22.95 (setextT) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (powersetTI1) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (complementTE1) =>
% 132.79/22.95 ((
% 132.79/22.95 (binintersectTELcontra) =>
% 132.79/22.95 ((
% 132.79/22.95 (binintersectTERcontra) =>
% 132.79/22.95 ((
% 132.79/22.95 (contrasubsetT) =>
% 132.79/22.95 ((
% 132.79/22.95 (contrasubsetT1) =>
% 132.79/22.95 ((
% 132.79/22.95 (contrasubsetT2) =>
% 132.79/22.95 ((
% 132.79/22.95 (contrasubsetT3) =>
% 132.79/22.95 ((
% 132.79/22.95 (doubleComplementI1) =>
% 132.79/22.95 ((
% 132.79/22.95 (doubleComplementE1) =>
% 132.79/22.95 ((
% 132.79/22.95 (doubleComplementSub1) =>
% 132.79/22.95 ((
% 132.79/22.95 (doubleComplementSub2) =>
% 132.79/22.95 ((
% 132.79/22.95 (doubleComplementEq) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementTnotintersectT) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementImpComplementIntersect) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementSubsetComplementIntersect) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementInPowersetComplementIntersect) =>
% 132.79/22.95 ((
% 132.79/22.95 (contraSubsetComplement) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementTcontraSubset) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (binunionTIRcontra) =>
% 132.79/22.95 ((
% 132.79/22.95 (inIntersectImpInUnion) =>
% 132.79/22.95 ((
% 132.79/22.95 (inIntersectImpInUnion2) =>
% 132.79/22.95 ((
% 132.79/22.95 (inIntersectImpInIntersectUnions) =>
% 132.79/22.95 ((
% 132.79/22.95 (intersectInPowersetIntersectUnions) =>
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% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (binunionTEcontra) =>
% 132.79/22.95 ((
% 132.79/22.95 (demorgan2a1) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (demorgan2a2) =>
% 132.79/22.95 ((
% 132.79/22.95 (demorgan1a) =>
% 132.79/22.95 ((
% 132.79/22.95 (demorgan1b) =>
% 132.79/22.95 ((
% 132.79/22.95 (demorgan1) =>
% 132.79/22.95 ((
% 132.79/22.95 (demorgan2a) =>
% 132.79/22.95 ((
% 132.79/22.95 (demorgan2b2) =>
% 132.79/22.95 ((
% 132.79/22.95 (demorgan2b) =>
% 132.79/22.95 ((
% 132.79/22.95 (demorgan2) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz13rule0) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz13rule1) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz13rule2) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz13rule3) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz13rule4) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (woz1_2) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz1_3) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz1_4) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz1_5) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1all2) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1SetBreln1) =>
% 132.79/22.95 ((
% 132.79/22.95 (choice2fnsingleton) =>
% 132.79/22.95 ((
% 132.79/22.95 (setOfPairsIsBReln1) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (subbreln1) =>
% 132.79/22.95 ((
% 132.79/22.95 (eqbreln1) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1invprop) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1invI) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1invE) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1compprop) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1compI) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1compE) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (breln1unionprop) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1unionIL) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1unionIR) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1unionI) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1unionE) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (breln1unionCommutes) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (woz2W) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (woz2B) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (image1Ex1) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (image1E) =>
% 132.79/22.95 ((
% 132.79/22.95 (image1I) =>
% 132.79/22.95 ((
% 132.79/22.95 (injFuncInInjFuncSet) =>
% 132.79/22.95 ((
% 132.79/22.95 (injFuncSetFuncIn) =>
% 132.79/22.95 ((
% 132.79/22.95 (injFuncSetFuncInj) =>
% 132.79/22.95 ((
% 132.79/22.95 (surjFuncSetFuncIn) =>
% 132.79/22.95 ((
% 132.79/22.95 (surjFuncSetFuncSurj) =>
% 132.79/22.95 ((
% 132.79/22.95 (leftInvIsSurj) =>
% 132.79/22.95 ((
% 132.79/22.95 (surjCantorThm) =>
% 132.79/22.95 ((
% 132.79/22.95 (foundation2) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (notinself2) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (omegaSclos) =>
% 132.79/22.95 ((
% 132.79/22.95 (peano0notS) =>
% 132.79/22.95 ((
% 132.79/22.95 (peanoSinj) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1096])).
% 132.79/22.95 thf(zip_derived_cl1111, plain,
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% 132.79/22.95 ((
% 132.79/22.95 (ap2apEq1) =>
% 132.79/22.95 ((
% 132.79/22.95 (ap2apEq2) =>
% 132.79/22.95 ((
% 132.79/22.95 (beta1) =>
% 132.79/22.95 ((
% 132.79/22.95 (eta1) =>
% 132.79/22.95 ((
% 132.79/22.95 (lam2lamEq) =>
% 132.79/22.95 ((
% 132.79/22.95 (beta2) =>
% 132.79/22.95 ((
% 132.79/22.95 (eta2) =>
% 132.79/22.95 ((
% 132.79/22.95 (iffalseProp1) =>
% 132.79/22.95 ((
% 132.79/22.95 (iffalseProp2) =>
% 132.79/22.95 ((
% 132.79/22.95 (iftrueProp1) =>
% 132.79/22.95 ((
% 132.79/22.95 (iftrueProp2) =>
% 132.79/22.95 ((
% 132.79/22.95 (ifSingleton) =>
% 132.79/22.95 ((
% 132.79/22.95 (ifp) =>
% 132.79/22.95 ((
% 132.79/22.95 (theeq) =>
% 132.79/22.95 ((
% 132.79/22.95 (iftrue) =>
% 132.79/22.95 ((
% 132.79/22.95 (iffalse) =>
% 132.79/22.95 ((
% 132.79/22.95 (iftrueorfalse) =>
% 132.79/22.95 ((
% 132.79/22.95 (binintersectT_lem) =>
% 132.79/22.95 ((
% 132.79/22.95 (binunionT_lem) =>
% 132.79/22.95 ((
% 132.79/22.95 (powersetT_lem) =>
% 132.79/22.95 ((
% 132.79/22.95 (setminusT_lem) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementT_lem) =>
% 132.79/22.95 ((
% 132.79/22.95 (setextT) =>
% 132.79/22.95 ((
% 132.79/22.95 (subsetTI) =>
% 132.79/22.95 ((
% 132.79/22.95 (powersetTI1) =>
% 132.79/22.95 ((
% 132.79/22.95 (powersetTE1) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementTI1) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementTE1) =>
% 132.79/22.95 ((
% 132.79/22.95 (binintersectTELcontra) =>
% 132.79/22.95 ((
% 132.79/22.95 (binintersectTERcontra) =>
% 132.79/22.95 ((
% 132.79/22.95 (contrasubsetT) =>
% 132.79/22.95 ((
% 132.79/22.95 (contrasubsetT1) =>
% 132.79/22.95 ((
% 132.79/22.95 (contrasubsetT2) =>
% 132.79/22.95 ((
% 132.79/22.95 (contrasubsetT3) =>
% 132.79/22.95 ((
% 132.79/22.95 (doubleComplementI1) =>
% 132.79/22.95 ((
% 132.79/22.95 (doubleComplementE1) =>
% 132.79/22.95 ((
% 132.79/22.95 (doubleComplementSub1) =>
% 132.79/22.95 ((
% 132.79/22.95 (doubleComplementSub2) =>
% 132.79/22.95 ((
% 132.79/22.95 (doubleComplementEq) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementTnotintersectT) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementImpComplementIntersect) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementSubsetComplementIntersect) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementInPowersetComplementIntersect) =>
% 132.79/22.95 ((
% 132.79/22.95 (contraSubsetComplement) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementTcontraSubset) =>
% 132.79/22.95 ((
% 132.79/22.95 (binunionTILcontra) =>
% 132.79/22.95 ((
% 132.79/22.95 (binunionTIRcontra) =>
% 132.79/22.95 ((
% 132.79/22.95 (inIntersectImpInUnion) =>
% 132.79/22.95 ((
% 132.79/22.95 (inIntersectImpInUnion2) =>
% 132.79/22.95 ((
% 132.79/22.95 (inIntersectImpInIntersectUnions) =>
% 132.79/22.95 ((
% 132.79/22.95 (intersectInPowersetIntersectUnions) =>
% 132.79/22.95 ((
% 132.79/22.95 (inComplementUnionImpNotIn1) =>
% 132.79/22.95 ((
% 132.79/22.95 (inComplementUnionImpInComplement1) =>
% 132.79/22.95 ((
% 132.79/22.95 (binunionTE) =>
% 132.79/22.95 ((
% 132.79/22.95 (binunionTEcontra) =>
% 132.79/22.95 ((
% 132.79/22.95 (demorgan2a1) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementUnionInPowersetComplement) =>
% 132.79/22.95 ((
% 132.79/22.95 (demorgan2a2) =>
% 132.79/22.95 ((
% 132.79/22.95 (demorgan1a) =>
% 132.79/22.95 ((
% 132.79/22.95 (demorgan1b) =>
% 132.79/22.95 ((
% 132.79/22.95 (demorgan1) =>
% 132.79/22.95 ((
% 132.79/22.95 (demorgan2a) =>
% 132.79/22.95 ((
% 132.79/22.95 (demorgan2b2) =>
% 132.79/22.95 ((
% 132.79/22.95 (demorgan2b) =>
% 132.79/22.95 ((
% 132.79/22.95 (demorgan2) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz13rule0) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz13rule1) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz13rule2) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz13rule3) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz13rule4) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz1_1) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz1_2) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz1_3) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz1_4) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz1_5) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1all2) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1SetBreln1) =>
% 132.79/22.95 ((
% 132.79/22.95 (choice2fnsingleton) =>
% 132.79/22.95 ((
% 132.79/22.95 (setOfPairsIsBReln1) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1all1) =>
% 132.79/22.95 ((
% 132.79/22.95 (subbreln1) =>
% 132.79/22.95 ((
% 132.79/22.95 (eqbreln1) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1invprop) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1invI) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1invE) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1compprop) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1compI) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1compE) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1compEex) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1unionprop) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1unionIL) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1unionIR) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1unionI) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1unionE) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1unionEcases) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1unionCommutes) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz2Ex) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz2W) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz2A) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz2B) =>
% 132.79/22.95 ((
% 132.79/22.95 (image1Ex) =>
% 132.79/22.95 ((
% 132.79/22.95 (image1Ex1) =>
% 132.79/22.95 ((
% 132.79/22.95 (image1Equiv) =>
% 132.79/22.95 ((
% 132.79/22.95 (image1E) =>
% 132.79/22.95 ((
% 132.79/22.95 (image1I) =>
% 132.79/22.95 ((
% 132.79/22.95 (injFuncInInjFuncSet) =>
% 132.79/22.95 ((
% 132.79/22.95 (injFuncSetFuncIn) =>
% 132.79/22.95 ((
% 132.79/22.95 (injFuncSetFuncInj) =>
% 132.79/22.95 ((
% 132.79/22.95 (surjFuncSetFuncIn) =>
% 132.79/22.95 ((
% 132.79/22.95 (surjFuncSetFuncSurj) =>
% 132.79/22.95 ((
% 132.79/22.95 (leftInvIsSurj) =>
% 132.79/22.95 ((
% 132.79/22.95 (surjCantorThm) =>
% 132.79/22.95 ((
% 132.79/22.95 (foundation2) =>
% 132.79/22.95 ((
% 132.79/22.95 (notinself) =>
% 132.79/22.95 ((
% 132.79/22.95 (notinself2) =>
% 132.79/22.95 ((
% 132.79/22.95 (omegaSp) =>
% 132.79/22.95 ((
% 132.79/22.95 (omegaSclos) =>
% 132.79/22.95 ((
% 132.79/22.95 (peano0notS) =>
% 132.79/22.95 ((
% 132.79/22.95 (peanoSinj) =>
% 132.79/22.95 ((
% 132.79/22.95 (transitivesetOp1) =>
% 132.79/22.95 ((
% 132.79/22.95 (binintTransitive) =>
% 132.79/22.95 ((
% 132.79/22.95 (transitivesetOp2) =>
% 132.79/22.95 ((
% 132.79/22.95 (setunionTransitive) =>
% 132.79/22.95 ((
% 132.79/22.95 (ordinalMinLem1) =>
% 132.79/22.95 ((
% 132.79/22.95 (ordinalTransSet) =>
% 132.79/22.95 ((
% 132.79/22.95 (ordinalTransSet1) =>
% 132.79/22.95 ((
% 132.79/22.95 (setunionOrdinalLem1) =>
% 132.79/22.95 (ordinal @
% 132.79/22.95 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/22.95 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1103])).
% 132.79/22.95 thf(zip_derived_cl1119, plain,
% 132.79/22.95 (~ (((symdiffI2) =>
% 132.79/22.95 (((symdiffIneg1) =>
% 132.79/22.95 (((symdiffIneg2) =>
% 132.79/22.95 (((secondinupair) =>
% 132.79/22.95 (((setukpairIL) =>
% 132.79/22.95 (((setukpairIR) =>
% 132.79/22.95 (((kpairiskpair) =>
% 132.79/22.95 (((kpairp) =>
% 132.79/22.95 (((singletonsubset) =>
% 132.79/22.95 (((singletoninpowerset) =>
% 132.79/22.95 (((singletoninpowunion) =>
% 132.79/22.95 (((upairset2E) =>
% 132.79/22.95 (((upairsubunion) =>
% 132.79/22.95 (((upairinpowunion) =>
% 132.79/22.95 (((ubforcartprodlem1) =>
% 132.79/22.95 (((ubforcartprodlem2) =>
% 132.79/22.95 (((ubforcartprodlem3) =>
% 132.79/22.95 (((cartprodpairin) =>
% 132.79/22.95 (((cartprodmempair1) =>
% 132.79/22.95 (((cartprodmempair) =>
% 132.79/22.95 (((setunionE2) =>
% 132.79/22.95 (((setunionsingleton1) =>
% 132.79/22.95 (((setunionsingleton2) =>
% 132.79/22.95 (((setunionsingleton) =>
% 132.79/22.95 (((singletonprop) =>
% 132.79/22.95 (((ex1E1) =>
% 132.79/22.95 (((ex1I) =>
% 132.79/22.95 (((ex1I2) =>
% 132.79/22.95 (((singletonsuniq) =>
% 132.79/22.95 (((setukpairinjL1) =>
% 132.79/22.95 ((
% 132.79/22.95 (kfstsingleton) =>
% 132.79/22.95 ((
% 132.79/22.95 (theprop) =>
% 132.79/22.95 ((
% 132.79/22.95 (kfstpairEq) =>
% 132.79/22.95 ((
% 132.79/22.95 (cartprodfstin) =>
% 132.79/22.95 ((
% 132.79/22.95 (setukpairinjL2) =>
% 132.79/22.95 ((
% 132.79/22.95 (setukpairinjL) =>
% 132.79/22.95 ((
% 132.79/22.95 (setukpairinjR11) =>
% 132.79/22.95 ((
% 132.79/22.95 (setukpairinjR12) =>
% 132.79/22.95 ((
% 132.79/22.95 (setukpairinjR1) =>
% 132.79/22.95 ((
% 132.79/22.95 (upairequniteq) =>
% 132.79/22.95 ((
% 132.79/22.95 (setukpairinjR2) =>
% 132.79/22.95 ((
% 132.79/22.95 (setukpairinjR) =>
% 132.79/22.95 ((
% 132.79/22.95 (ksndsingleton) =>
% 132.79/22.95 ((
% 132.79/22.95 (ksndpairEq) =>
% 132.79/22.95 ((
% 132.79/22.95 (kpairsurjEq) =>
% 132.79/22.95 ((
% 132.79/22.95 (cartprodsndin) =>
% 132.79/22.95 ((
% 132.79/22.95 (cartprodpairmemEL) =>
% 132.79/22.95 ((
% 132.79/22.95 (cartprodpairmemER) =>
% 132.79/22.95 ((
% 132.79/22.95 (cartprodmempaircEq) =>
% 132.79/22.95 ((
% 132.79/22.95 (cartprodfstpairEq) =>
% 132.79/22.95 ((
% 132.79/22.95 (cartprodsndpairEq) =>
% 132.79/22.95 ((
% 132.79/22.95 (cartprodpairsurjEq) =>
% 132.79/22.95 ((
% 132.79/22.95 (dpsetconstrI) =>
% 132.79/22.95 ((
% 132.79/22.95 (dpsetconstrSub) =>
% 132.79/22.95 ((
% 132.79/22.95 (setOfPairsIsBReln) =>
% 132.79/22.95 ((
% 132.79/22.95 (dpsetconstrERa) =>
% 132.79/22.95 ((
% 132.79/22.95 (dpsetconstrEL1) =>
% 132.79/22.95 ((
% 132.79/22.95 (dpsetconstrEL2) =>
% 132.79/22.95 ((
% 132.79/22.95 (dpsetconstrER) =>
% 132.79/22.95 ((
% 132.79/22.95 (funcImageSingleton) =>
% 132.79/22.95 ((
% 132.79/22.95 (apProp) =>
% 132.79/22.95 ((
% 132.79/22.95 (app) =>
% 132.79/22.95 ((
% 132.79/22.95 (infuncsetfunc) =>
% 132.79/22.95 ((
% 132.79/22.95 (ap2p) =>
% 132.79/22.95 ((
% 132.79/22.95 (funcinfuncset) =>
% 132.79/22.95 ((
% 132.79/22.95 (lamProp) =>
% 132.79/22.95 ((
% 132.79/22.95 (lamp) =>
% 132.79/22.95 ((
% 132.79/22.95 (lam2p) =>
% 132.79/22.95 ((
% 132.79/22.95 (brelnall1) =>
% 132.79/22.95 ((
% 132.79/22.95 (brelnall2) =>
% 132.79/22.95 ((
% 132.79/22.95 (ex1E2) =>
% 132.79/22.95 ((
% 132.79/22.95 (funcGraphProp1) =>
% 132.79/22.95 ((
% 132.79/22.95 (funcGraphProp3) =>
% 132.79/22.95 ((
% 132.79/22.95 (funcGraphProp2) =>
% 132.79/22.95 ((
% 132.79/22.95 (funcextLem) =>
% 132.79/22.95 ((
% 132.79/22.95 (funcGraphProp4) =>
% 132.79/22.95 ((
% 132.79/22.95 (subbreln) =>
% 132.79/22.95 ((
% 132.79/22.95 (eqbreln) =>
% 132.79/22.95 ((
% 132.79/22.95 (funcext) =>
% 132.79/22.95 ((
% 132.79/22.95 (funcext2) =>
% 132.79/22.95 ((
% 132.79/22.95 (ap2apEq1) =>
% 132.79/22.95 ((
% 132.79/22.95 (ap2apEq2) =>
% 132.79/22.95 ((
% 132.79/22.95 (beta1) =>
% 132.79/22.95 ((
% 132.79/22.95 (eta1) =>
% 132.79/22.95 ((
% 132.79/22.95 (lam2lamEq) =>
% 132.79/22.95 ((
% 132.79/22.95 (beta2) =>
% 132.79/22.95 ((
% 132.79/22.95 (eta2) =>
% 132.79/22.95 ((
% 132.79/22.95 (iffalseProp1) =>
% 132.79/22.95 ((
% 132.79/22.95 (iffalseProp2) =>
% 132.79/22.95 ((
% 132.79/22.95 (iftrueProp1) =>
% 132.79/22.95 ((
% 132.79/22.95 (iftrueProp2) =>
% 132.79/22.95 ((
% 132.79/22.95 (ifSingleton) =>
% 132.79/22.95 ((
% 132.79/22.95 (ifp) =>
% 132.79/22.95 ((
% 132.79/22.95 (theeq) =>
% 132.79/22.95 ((
% 132.79/22.95 (iftrue) =>
% 132.79/22.95 ((
% 132.79/22.95 (iffalse) =>
% 132.79/22.95 ((
% 132.79/22.95 (iftrueorfalse) =>
% 132.79/22.95 ((
% 132.79/22.95 (binintersectT_lem) =>
% 132.79/22.95 ((
% 132.79/22.95 (binunionT_lem) =>
% 132.79/22.95 ((
% 132.79/22.95 (powersetT_lem) =>
% 132.79/22.95 ((
% 132.79/22.95 (setminusT_lem) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementT_lem) =>
% 132.79/22.95 ((
% 132.79/22.95 (setextT) =>
% 132.79/22.95 ((
% 132.79/22.95 (subsetTI) =>
% 132.79/22.95 ((
% 132.79/22.95 (powersetTI1) =>
% 132.79/22.95 ((
% 132.79/22.95 (powersetTE1) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementTI1) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementTE1) =>
% 132.79/22.95 ((
% 132.79/22.95 (binintersectTELcontra) =>
% 132.79/22.95 ((
% 132.79/22.95 (binintersectTERcontra) =>
% 132.79/22.95 ((
% 132.79/22.95 (contrasubsetT) =>
% 132.79/22.95 ((
% 132.79/22.95 (contrasubsetT1) =>
% 132.79/22.95 ((
% 132.79/22.95 (contrasubsetT2) =>
% 132.79/22.95 ((
% 132.79/22.95 (contrasubsetT3) =>
% 132.79/22.95 ((
% 132.79/22.95 (doubleComplementI1) =>
% 132.79/22.95 ((
% 132.79/22.95 (doubleComplementE1) =>
% 132.79/22.95 ((
% 132.79/22.95 (doubleComplementSub1) =>
% 132.79/22.95 ((
% 132.79/22.95 (doubleComplementSub2) =>
% 132.79/22.95 ((
% 132.79/22.95 (doubleComplementEq) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementTnotintersectT) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementImpComplementIntersect) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementSubsetComplementIntersect) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementInPowersetComplementIntersect) =>
% 132.79/22.95 ((
% 132.79/22.95 (contraSubsetComplement) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementTcontraSubset) =>
% 132.79/22.95 ((
% 132.79/22.95 (binunionTILcontra) =>
% 132.79/22.95 ((
% 132.79/22.95 (binunionTIRcontra) =>
% 132.79/22.95 ((
% 132.79/22.95 (inIntersectImpInUnion) =>
% 132.79/22.95 ((
% 132.79/22.95 (inIntersectImpInUnion2) =>
% 132.79/22.95 ((
% 132.79/22.95 (inIntersectImpInIntersectUnions) =>
% 132.79/22.95 ((
% 132.79/22.95 (intersectInPowersetIntersectUnions) =>
% 132.79/22.95 ((
% 132.79/22.95 (inComplementUnionImpNotIn1) =>
% 132.79/22.95 ((
% 132.79/22.95 (inComplementUnionImpInComplement1) =>
% 132.79/22.95 ((
% 132.79/22.95 (binunionTE) =>
% 132.79/22.95 ((
% 132.79/22.95 (binunionTEcontra) =>
% 132.79/22.95 ((
% 132.79/22.95 (demorgan2a1) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementUnionInPowersetComplement) =>
% 132.79/22.95 ((
% 132.79/22.95 (demorgan2a2) =>
% 132.79/22.95 ((
% 132.79/22.95 (demorgan1a) =>
% 132.79/22.95 ((
% 132.79/22.95 (demorgan1b) =>
% 132.79/22.95 ((
% 132.79/22.95 (demorgan1) =>
% 132.79/22.95 ((
% 132.79/22.95 (demorgan2a) =>
% 132.79/22.95 ((
% 132.79/22.95 (demorgan2b2) =>
% 132.79/22.95 ((
% 132.79/22.95 (demorgan2b) =>
% 132.79/22.95 ((
% 132.79/22.95 (demorgan2) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz13rule0) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz13rule1) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz13rule2) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz13rule3) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz13rule4) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz1_1) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz1_2) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz1_3) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz1_4) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz1_5) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1all2) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1SetBreln1) =>
% 132.79/22.95 ((
% 132.79/22.95 (choice2fnsingleton) =>
% 132.79/22.95 ((
% 132.79/22.95 (setOfPairsIsBReln1) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1all1) =>
% 132.79/22.95 ((
% 132.79/22.95 (subbreln1) =>
% 132.79/22.95 ((
% 132.79/22.95 (eqbreln1) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1invprop) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1invI) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1invE) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1compprop) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1compI) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1compE) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1compEex) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1unionprop) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1unionIL) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1unionIR) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1unionI) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1unionE) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1unionEcases) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1unionCommutes) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz2Ex) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz2W) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz2A) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz2B) =>
% 132.79/22.95 ((
% 132.79/22.95 (image1Ex) =>
% 132.79/22.95 ((
% 132.79/22.95 (image1Ex1) =>
% 132.79/22.95 ((
% 132.79/22.95 (image1Equiv) =>
% 132.79/22.95 ((
% 132.79/22.95 (image1E) =>
% 132.79/22.95 ((
% 132.79/22.95 (image1I) =>
% 132.79/22.95 ((
% 132.79/22.95 (injFuncInInjFuncSet) =>
% 132.79/22.95 ((
% 132.79/22.95 (injFuncSetFuncIn) =>
% 132.79/22.95 ((
% 132.79/22.95 (injFuncSetFuncInj) =>
% 132.79/22.95 ((
% 132.79/22.95 (surjFuncSetFuncIn) =>
% 132.79/22.95 ((
% 132.79/22.95 (surjFuncSetFuncSurj) =>
% 132.79/22.95 ((
% 132.79/22.95 (leftInvIsSurj) =>
% 132.79/22.95 ((
% 132.79/22.95 (surjCantorThm) =>
% 132.79/22.95 ((
% 132.79/22.95 (foundation2) =>
% 132.79/22.95 ((
% 132.79/22.95 (notinself) =>
% 132.79/22.95 ((
% 132.79/22.95 (notinself2) =>
% 132.79/22.95 ((
% 132.79/22.95 (omegaSp) =>
% 132.79/22.95 ((
% 132.79/22.95 (omegaSclos) =>
% 132.79/22.95 ((
% 132.79/22.95 (peano0notS) =>
% 132.79/22.95 ((
% 132.79/22.95 (peanoSinj) =>
% 132.79/22.95 ((
% 132.79/22.95 (transitivesetOp1) =>
% 132.79/22.95 ((
% 132.79/22.95 (binintTransitive) =>
% 132.79/22.95 ((
% 132.79/22.95 (transitivesetOp2) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (ordinalMinLem1) =>
% 132.79/22.95 ((
% 132.79/22.95 (ordinalTransSet) =>
% 132.79/22.95 ((
% 132.79/22.95 (ordinalTransSet1) =>
% 132.79/22.95 ((
% 132.79/22.95 (setunionOrdinalLem1) =>
% 132.79/22.95 (ordinal @
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% 132.79/22.95 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1111])).
% 132.79/22.95 thf(zip_derived_cl1125, plain,
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% 132.79/22.95 (((singletoninpowunion) =>
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% 132.79/22.95 (((upairsubunion) =>
% 132.79/22.95 (((upairinpowunion) =>
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% 132.79/22.95 (((ubforcartprodlem2) =>
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% 132.79/22.95 (((kfstsingleton) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (kfstpairEq) =>
% 132.79/22.95 ((
% 132.79/22.95 (cartprodfstin) =>
% 132.79/22.95 ((
% 132.79/22.95 (setukpairinjL2) =>
% 132.79/22.95 ((
% 132.79/22.95 (setukpairinjL) =>
% 132.79/22.95 ((
% 132.79/22.95 (setukpairinjR11) =>
% 132.79/22.95 ((
% 132.79/22.95 (setukpairinjR12) =>
% 132.79/22.95 ((
% 132.79/22.95 (setukpairinjR1) =>
% 132.79/22.95 ((
% 132.79/22.95 (upairequniteq) =>
% 132.79/22.95 ((
% 132.79/22.95 (setukpairinjR2) =>
% 132.79/22.95 ((
% 132.79/22.95 (setukpairinjR) =>
% 132.79/22.95 ((
% 132.79/22.95 (ksndsingleton) =>
% 132.79/22.95 ((
% 132.79/22.95 (ksndpairEq) =>
% 132.79/22.95 ((
% 132.79/22.95 (kpairsurjEq) =>
% 132.79/22.95 ((
% 132.79/22.95 (cartprodsndin) =>
% 132.79/22.95 ((
% 132.79/22.95 (cartprodpairmemEL) =>
% 132.79/22.95 ((
% 132.79/22.95 (cartprodpairmemER) =>
% 132.79/22.95 ((
% 132.79/22.95 (cartprodmempaircEq) =>
% 132.79/22.95 ((
% 132.79/22.95 (cartprodfstpairEq) =>
% 132.79/22.95 ((
% 132.79/22.95 (cartprodsndpairEq) =>
% 132.79/22.95 ((
% 132.79/22.95 (cartprodpairsurjEq) =>
% 132.79/22.95 ((
% 132.79/22.95 (dpsetconstrI) =>
% 132.79/22.95 ((
% 132.79/22.95 (dpsetconstrSub) =>
% 132.79/22.95 ((
% 132.79/22.95 (setOfPairsIsBReln) =>
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% 132.79/22.95 (dpsetconstrERa) =>
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% 132.79/22.95 ((
% 132.79/22.95 (dpsetconstrEL2) =>
% 132.79/22.95 ((
% 132.79/22.95 (dpsetconstrER) =>
% 132.79/22.95 ((
% 132.79/22.95 (funcImageSingleton) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (app) =>
% 132.79/22.95 ((
% 132.79/22.95 (infuncsetfunc) =>
% 132.79/22.95 ((
% 132.79/22.95 (ap2p) =>
% 132.79/22.95 ((
% 132.79/22.95 (funcinfuncset) =>
% 132.79/22.95 ((
% 132.79/22.95 (lamProp) =>
% 132.79/22.95 ((
% 132.79/22.95 (lamp) =>
% 132.79/22.95 ((
% 132.79/22.95 (lam2p) =>
% 132.79/22.95 ((
% 132.79/22.95 (brelnall1) =>
% 132.79/22.95 ((
% 132.79/22.95 (brelnall2) =>
% 132.79/22.95 ((
% 132.79/22.95 (ex1E2) =>
% 132.79/22.95 ((
% 132.79/22.95 (funcGraphProp1) =>
% 132.79/22.95 ((
% 132.79/22.95 (funcGraphProp3) =>
% 132.79/22.95 ((
% 132.79/22.95 (funcGraphProp2) =>
% 132.79/22.95 ((
% 132.79/22.95 (funcextLem) =>
% 132.79/22.95 ((
% 132.79/22.95 (funcGraphProp4) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (eqbreln) =>
% 132.79/22.95 ((
% 132.79/22.95 (funcext) =>
% 132.79/22.95 ((
% 132.79/22.95 (funcext2) =>
% 132.79/22.95 ((
% 132.79/22.95 (ap2apEq1) =>
% 132.79/22.95 ((
% 132.79/22.95 (ap2apEq2) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (eta1) =>
% 132.79/22.95 ((
% 132.79/22.95 (lam2lamEq) =>
% 132.79/22.95 ((
% 132.79/22.95 (beta2) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (iftrueProp2) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (ifp) =>
% 132.79/22.95 ((
% 132.79/22.95 (theeq) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (powersetT_lem) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (complementT_lem) =>
% 132.79/22.95 ((
% 132.79/22.95 (setextT) =>
% 132.79/22.95 ((
% 132.79/22.95 (subsetTI) =>
% 132.79/22.95 ((
% 132.79/22.95 (powersetTI1) =>
% 132.79/22.95 ((
% 132.79/22.95 (powersetTE1) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementTI1) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementTE1) =>
% 132.79/22.95 ((
% 132.79/22.95 (binintersectTELcontra) =>
% 132.79/22.95 ((
% 132.79/22.95 (binintersectTERcontra) =>
% 132.79/22.95 ((
% 132.79/22.95 (contrasubsetT) =>
% 132.79/22.95 ((
% 132.79/22.95 (contrasubsetT1) =>
% 132.79/22.95 ((
% 132.79/22.95 (contrasubsetT2) =>
% 132.79/22.95 ((
% 132.79/22.95 (contrasubsetT3) =>
% 132.79/22.95 ((
% 132.79/22.95 (doubleComplementI1) =>
% 132.79/22.95 ((
% 132.79/22.95 (doubleComplementE1) =>
% 132.79/22.95 ((
% 132.79/22.95 (doubleComplementSub1) =>
% 132.79/22.95 ((
% 132.79/22.95 (doubleComplementSub2) =>
% 132.79/22.95 ((
% 132.79/22.95 (doubleComplementEq) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementTnotintersectT) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementImpComplementIntersect) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementSubsetComplementIntersect) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementInPowersetComplementIntersect) =>
% 132.79/22.95 ((
% 132.79/22.95 (contraSubsetComplement) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementTcontraSubset) =>
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% 132.79/22.95 ((
% 132.79/22.95 (binunionTIRcontra) =>
% 132.79/22.95 ((
% 132.79/22.95 (inIntersectImpInUnion) =>
% 132.79/22.95 ((
% 132.79/22.95 (inIntersectImpInUnion2) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (demorgan2a1) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (demorgan2a2) =>
% 132.79/22.95 ((
% 132.79/22.95 (demorgan1a) =>
% 132.79/22.95 ((
% 132.79/22.95 (demorgan1b) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (demorgan2a) =>
% 132.79/22.95 ((
% 132.79/22.95 (demorgan2b2) =>
% 132.79/22.95 ((
% 132.79/22.95 (demorgan2b) =>
% 132.79/22.95 ((
% 132.79/22.95 (demorgan2) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz13rule0) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz13rule1) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz13rule2) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz13rule3) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz13rule4) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (woz1_4) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz1_5) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1all2) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1SetBreln1) =>
% 132.79/22.95 ((
% 132.79/22.95 (choice2fnsingleton) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (breln1invE) =>
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% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (image1I) =>
% 132.79/22.95 ((
% 132.79/22.95 (injFuncInInjFuncSet) =>
% 132.79/22.95 ((
% 132.79/22.95 (injFuncSetFuncIn) =>
% 132.79/22.95 ((
% 132.79/22.95 (injFuncSetFuncInj) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1119])).
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% 132.79/22.95 ((
% 132.79/22.95 (setukpairinjR2) =>
% 132.79/22.95 ((
% 132.79/22.95 (setukpairinjR) =>
% 132.79/22.95 ((
% 132.79/22.95 (ksndsingleton) =>
% 132.79/22.95 ((
% 132.79/22.95 (ksndpairEq) =>
% 132.79/22.95 ((
% 132.79/22.95 (kpairsurjEq) =>
% 132.79/22.95 ((
% 132.79/22.95 (cartprodsndin) =>
% 132.79/22.95 ((
% 132.79/22.95 (cartprodpairmemEL) =>
% 132.79/22.95 ((
% 132.79/22.95 (cartprodpairmemER) =>
% 132.79/22.95 ((
% 132.79/22.95 (cartprodmempaircEq) =>
% 132.79/22.95 ((
% 132.79/22.95 (cartprodfstpairEq) =>
% 132.79/22.95 ((
% 132.79/22.95 (cartprodsndpairEq) =>
% 132.79/22.95 ((
% 132.79/22.95 (cartprodpairsurjEq) =>
% 132.79/22.95 ((
% 132.79/22.95 (dpsetconstrI) =>
% 132.79/22.95 ((
% 132.79/22.95 (dpsetconstrSub) =>
% 132.79/22.95 ((
% 132.79/22.95 (setOfPairsIsBReln) =>
% 132.79/22.95 ((
% 132.79/22.95 (dpsetconstrERa) =>
% 132.79/22.95 ((
% 132.79/22.95 (dpsetconstrEL1) =>
% 132.79/22.95 ((
% 132.79/22.95 (dpsetconstrEL2) =>
% 132.79/22.95 ((
% 132.79/22.95 (dpsetconstrER) =>
% 132.79/22.95 ((
% 132.79/22.95 (funcImageSingleton) =>
% 132.79/22.95 ((
% 132.79/22.95 (apProp) =>
% 132.79/22.95 ((
% 132.79/22.95 (app) =>
% 132.79/22.95 ((
% 132.79/22.95 (infuncsetfunc) =>
% 132.79/22.95 ((
% 132.79/22.95 (ap2p) =>
% 132.79/22.95 ((
% 132.79/22.95 (funcinfuncset) =>
% 132.79/22.95 ((
% 132.79/22.95 (lamProp) =>
% 132.79/22.95 ((
% 132.79/22.95 (lamp) =>
% 132.79/22.95 ((
% 132.79/22.95 (lam2p) =>
% 132.79/22.95 ((
% 132.79/22.95 (brelnall1) =>
% 132.79/22.95 ((
% 132.79/22.95 (brelnall2) =>
% 132.79/22.95 ((
% 132.79/22.95 (ex1E2) =>
% 132.79/22.95 ((
% 132.79/22.95 (funcGraphProp1) =>
% 132.79/22.95 ((
% 132.79/22.95 (funcGraphProp3) =>
% 132.79/22.95 ((
% 132.79/22.95 (funcGraphProp2) =>
% 132.79/22.95 ((
% 132.79/22.95 (funcextLem) =>
% 132.79/22.95 ((
% 132.79/22.95 (funcGraphProp4) =>
% 132.79/22.95 ((
% 132.79/22.95 (subbreln) =>
% 132.79/22.95 ((
% 132.79/22.95 (eqbreln) =>
% 132.79/22.95 ((
% 132.79/22.95 (funcext) =>
% 132.79/22.95 ((
% 132.79/22.95 (funcext2) =>
% 132.79/22.95 ((
% 132.79/22.95 (ap2apEq1) =>
% 132.79/22.95 ((
% 132.79/22.95 (ap2apEq2) =>
% 132.79/22.95 ((
% 132.79/22.95 (beta1) =>
% 132.79/22.95 ((
% 132.79/22.95 (eta1) =>
% 132.79/22.95 ((
% 132.79/22.95 (lam2lamEq) =>
% 132.79/22.95 ((
% 132.79/22.95 (beta2) =>
% 132.79/22.95 ((
% 132.79/22.95 (eta2) =>
% 132.79/22.95 ((
% 132.79/22.95 (iffalseProp1) =>
% 132.79/22.95 ((
% 132.79/22.95 (iffalseProp2) =>
% 132.79/22.95 ((
% 132.79/22.95 (iftrueProp1) =>
% 132.79/22.95 ((
% 132.79/22.95 (iftrueProp2) =>
% 132.79/22.95 ((
% 132.79/22.95 (ifSingleton) =>
% 132.79/22.95 ((
% 132.79/22.95 (ifp) =>
% 132.79/22.95 ((
% 132.79/22.95 (theeq) =>
% 132.79/22.95 ((
% 132.79/22.95 (iftrue) =>
% 132.79/22.95 ((
% 132.79/22.95 (iffalse) =>
% 132.79/22.95 ((
% 132.79/22.95 (iftrueorfalse) =>
% 132.79/22.95 ((
% 132.79/22.95 (binintersectT_lem) =>
% 132.79/22.95 ((
% 132.79/22.95 (binunionT_lem) =>
% 132.79/22.95 ((
% 132.79/22.95 (powersetT_lem) =>
% 132.79/22.95 ((
% 132.79/22.95 (setminusT_lem) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementT_lem) =>
% 132.79/22.95 ((
% 132.79/22.95 (setextT) =>
% 132.79/22.95 ((
% 132.79/22.95 (subsetTI) =>
% 132.79/22.95 ((
% 132.79/22.95 (powersetTI1) =>
% 132.79/22.95 ((
% 132.79/22.95 (powersetTE1) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementTI1) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementTE1) =>
% 132.79/22.95 ((
% 132.79/22.95 (binintersectTELcontra) =>
% 132.79/22.95 ((
% 132.79/22.95 (binintersectTERcontra) =>
% 132.79/22.95 ((
% 132.79/22.95 (contrasubsetT) =>
% 132.79/22.95 ((
% 132.79/22.95 (contrasubsetT1) =>
% 132.79/22.95 ((
% 132.79/22.95 (contrasubsetT2) =>
% 132.79/22.95 ((
% 132.79/22.95 (contrasubsetT3) =>
% 132.79/22.95 ((
% 132.79/22.95 (doubleComplementI1) =>
% 132.79/22.95 ((
% 132.79/22.95 (doubleComplementE1) =>
% 132.79/22.95 ((
% 132.79/22.95 (doubleComplementSub1) =>
% 132.79/22.95 ((
% 132.79/22.95 (doubleComplementSub2) =>
% 132.79/22.95 ((
% 132.79/22.95 (doubleComplementEq) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementTnotintersectT) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementImpComplementIntersect) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementSubsetComplementIntersect) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementInPowersetComplementIntersect) =>
% 132.79/22.95 ((
% 132.79/22.95 (contraSubsetComplement) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementTcontraSubset) =>
% 132.79/22.95 ((
% 132.79/22.95 (binunionTILcontra) =>
% 132.79/22.95 ((
% 132.79/22.95 (binunionTIRcontra) =>
% 132.79/22.95 ((
% 132.79/22.95 (inIntersectImpInUnion) =>
% 132.79/22.95 ((
% 132.79/22.95 (inIntersectImpInUnion2) =>
% 132.79/22.95 ((
% 132.79/22.95 (inIntersectImpInIntersectUnions) =>
% 132.79/22.95 ((
% 132.79/22.95 (intersectInPowersetIntersectUnions) =>
% 132.79/22.95 ((
% 132.79/22.95 (inComplementUnionImpNotIn1) =>
% 132.79/22.95 ((
% 132.79/22.95 (inComplementUnionImpInComplement1) =>
% 132.79/22.95 ((
% 132.79/22.95 (binunionTE) =>
% 132.79/22.95 ((
% 132.79/22.95 (binunionTEcontra) =>
% 132.79/22.95 ((
% 132.79/22.95 (demorgan2a1) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementUnionInPowersetComplement) =>
% 132.79/22.95 ((
% 132.79/22.95 (demorgan2a2) =>
% 132.79/22.95 ((
% 132.79/22.95 (demorgan1a) =>
% 132.79/22.95 ((
% 132.79/22.95 (demorgan1b) =>
% 132.79/22.95 ((
% 132.79/22.95 (demorgan1) =>
% 132.79/22.95 ((
% 132.79/22.95 (demorgan2a) =>
% 132.79/22.95 ((
% 132.79/22.95 (demorgan2b2) =>
% 132.79/22.95 ((
% 132.79/22.95 (demorgan2b) =>
% 132.79/22.95 ((
% 132.79/22.95 (demorgan2) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz13rule0) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz13rule1) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz13rule2) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz13rule3) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz13rule4) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz1_1) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz1_2) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz1_3) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz1_4) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz1_5) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1all2) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1SetBreln1) =>
% 132.79/22.95 ((
% 132.79/22.95 (choice2fnsingleton) =>
% 132.79/22.95 ((
% 132.79/22.95 (setOfPairsIsBReln1) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1all1) =>
% 132.79/22.95 ((
% 132.79/22.95 (subbreln1) =>
% 132.79/22.95 ((
% 132.79/22.95 (eqbreln1) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1invprop) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1invI) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1invE) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1compprop) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1compI) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1compE) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1compEex) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1unionprop) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1unionIL) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1unionIR) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1unionI) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1unionE) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1unionEcases) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1unionCommutes) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz2Ex) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz2W) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz2A) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz2B) =>
% 132.79/22.95 ((
% 132.79/22.95 (image1Ex) =>
% 132.79/22.95 ((
% 132.79/22.95 (image1Ex1) =>
% 132.79/22.95 ((
% 132.79/22.95 (image1Equiv) =>
% 132.79/22.95 ((
% 132.79/22.95 (image1E) =>
% 132.79/22.95 ((
% 132.79/22.95 (image1I) =>
% 132.79/22.95 ((
% 132.79/22.95 (injFuncInInjFuncSet) =>
% 132.79/22.95 ((
% 132.79/22.95 (injFuncSetFuncIn) =>
% 132.79/22.95 ((
% 132.79/22.95 (injFuncSetFuncInj) =>
% 132.79/22.95 ((
% 132.79/22.95 (surjFuncSetFuncIn) =>
% 132.79/22.95 ((
% 132.79/22.95 (surjFuncSetFuncSurj) =>
% 132.79/22.95 ((
% 132.79/22.95 (leftInvIsSurj) =>
% 132.79/22.95 ((
% 132.79/22.95 (surjCantorThm) =>
% 132.79/22.95 ((
% 132.79/22.95 (foundation2) =>
% 132.79/22.95 ((
% 132.79/22.95 (notinself) =>
% 132.79/22.95 ((
% 132.79/22.95 (notinself2) =>
% 132.79/22.95 ((
% 132.79/22.95 (omegaSp) =>
% 132.79/22.95 ((
% 132.79/22.95 (omegaSclos) =>
% 132.79/22.95 ((
% 132.79/22.95 (peano0notS) =>
% 132.79/22.95 ((
% 132.79/22.95 (peanoSinj) =>
% 132.79/22.95 ((
% 132.79/22.95 (transitivesetOp1) =>
% 132.79/22.95 ((
% 132.79/22.95 (binintTransitive) =>
% 132.79/22.95 ((
% 132.79/22.95 (transitivesetOp2) =>
% 132.79/22.95 ((
% 132.79/22.95 (setunionTransitive) =>
% 132.79/22.95 ((
% 132.79/22.95 (ordinalMinLem1) =>
% 132.79/22.95 ((
% 132.79/22.95 (ordinalTransSet) =>
% 132.79/22.95 ((
% 132.79/22.95 (ordinalTransSet1) =>
% 132.79/22.95 ((
% 132.79/22.95 (setunionOrdinalLem1) =>
% 132.79/22.95 (ordinal @
% 132.79/22.95 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/22.95 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1125])).
% 132.79/22.95 thf(zip_derived_cl1138, plain,
% 132.79/22.95 (~ (((secondinupair) =>
% 132.79/22.95 (((setukpairIL) =>
% 132.79/22.95 (((setukpairIR) =>
% 132.79/22.95 (((kpairiskpair) =>
% 132.79/22.95 (((kpairp) =>
% 132.79/22.95 (((singletonsubset) =>
% 132.79/22.95 (((singletoninpowerset) =>
% 132.79/22.95 (((singletoninpowunion) =>
% 132.79/22.95 (((upairset2E) =>
% 132.79/22.95 (((upairsubunion) =>
% 132.79/22.95 (((upairinpowunion) =>
% 132.79/22.95 (((ubforcartprodlem1) =>
% 132.79/22.95 (((ubforcartprodlem2) =>
% 132.79/22.95 (((ubforcartprodlem3) =>
% 132.79/22.95 (((cartprodpairin) =>
% 132.79/22.95 (((cartprodmempair1) =>
% 132.79/22.95 (((cartprodmempair) =>
% 132.79/22.95 (((setunionE2) =>
% 132.79/22.95 (((setunionsingleton1) =>
% 132.79/22.95 (((setunionsingleton2) =>
% 132.79/22.95 (((setunionsingleton) =>
% 132.79/22.95 (((singletonprop) =>
% 132.79/22.95 (((ex1E1) =>
% 132.79/22.95 (((ex1I) =>
% 132.79/22.95 (((ex1I2) =>
% 132.79/22.95 (((singletonsuniq) =>
% 132.79/22.95 (((setukpairinjL1) =>
% 132.79/22.95 (((kfstsingleton) =>
% 132.79/22.95 (((theprop) =>
% 132.79/22.95 (((kfstpairEq) =>
% 132.79/22.95 ((
% 132.79/22.95 (cartprodfstin) =>
% 132.79/22.95 ((
% 132.79/22.95 (setukpairinjL2) =>
% 132.79/22.95 ((
% 132.79/22.95 (setukpairinjL) =>
% 132.79/22.95 ((
% 132.79/22.95 (setukpairinjR11) =>
% 132.79/22.95 ((
% 132.79/22.95 (setukpairinjR12) =>
% 132.79/22.95 ((
% 132.79/22.95 (setukpairinjR1) =>
% 132.79/22.95 ((
% 132.79/22.95 (upairequniteq) =>
% 132.79/22.95 ((
% 132.79/22.95 (setukpairinjR2) =>
% 132.79/22.95 ((
% 132.79/22.95 (setukpairinjR) =>
% 132.79/22.95 ((
% 132.79/22.95 (ksndsingleton) =>
% 132.79/22.95 ((
% 132.79/22.95 (ksndpairEq) =>
% 132.79/22.95 ((
% 132.79/22.95 (kpairsurjEq) =>
% 132.79/22.95 ((
% 132.79/22.95 (cartprodsndin) =>
% 132.79/22.95 ((
% 132.79/22.95 (cartprodpairmemEL) =>
% 132.79/22.95 ((
% 132.79/22.95 (cartprodpairmemER) =>
% 132.79/22.95 ((
% 132.79/22.95 (cartprodmempaircEq) =>
% 132.79/22.95 ((
% 132.79/22.95 (cartprodfstpairEq) =>
% 132.79/22.95 ((
% 132.79/22.95 (cartprodsndpairEq) =>
% 132.79/22.95 ((
% 132.79/22.95 (cartprodpairsurjEq) =>
% 132.79/22.95 ((
% 132.79/22.95 (dpsetconstrI) =>
% 132.79/22.95 ((
% 132.79/22.95 (dpsetconstrSub) =>
% 132.79/22.95 ((
% 132.79/22.95 (setOfPairsIsBReln) =>
% 132.79/22.95 ((
% 132.79/22.95 (dpsetconstrERa) =>
% 132.79/22.95 ((
% 132.79/22.95 (dpsetconstrEL1) =>
% 132.79/22.95 ((
% 132.79/22.95 (dpsetconstrEL2) =>
% 132.79/22.95 ((
% 132.79/22.95 (dpsetconstrER) =>
% 132.79/22.95 ((
% 132.79/22.95 (funcImageSingleton) =>
% 132.79/22.95 ((
% 132.79/22.95 (apProp) =>
% 132.79/22.95 ((
% 132.79/22.95 (app) =>
% 132.79/22.95 ((
% 132.79/22.95 (infuncsetfunc) =>
% 132.79/22.95 ((
% 132.79/22.95 (ap2p) =>
% 132.79/22.95 ((
% 132.79/22.95 (funcinfuncset) =>
% 132.79/22.95 ((
% 132.79/22.95 (lamProp) =>
% 132.79/22.95 ((
% 132.79/22.95 (lamp) =>
% 132.79/22.95 ((
% 132.79/22.95 (lam2p) =>
% 132.79/22.95 ((
% 132.79/22.95 (brelnall1) =>
% 132.79/22.95 ((
% 132.79/22.95 (brelnall2) =>
% 132.79/22.95 ((
% 132.79/22.95 (ex1E2) =>
% 132.79/22.95 ((
% 132.79/22.95 (funcGraphProp1) =>
% 132.79/22.95 ((
% 132.79/22.95 (funcGraphProp3) =>
% 132.79/22.95 ((
% 132.79/22.95 (funcGraphProp2) =>
% 132.79/22.95 ((
% 132.79/22.95 (funcextLem) =>
% 132.79/22.95 ((
% 132.79/22.95 (funcGraphProp4) =>
% 132.79/22.95 ((
% 132.79/22.95 (subbreln) =>
% 132.79/22.95 ((
% 132.79/22.95 (eqbreln) =>
% 132.79/22.95 ((
% 132.79/22.95 (funcext) =>
% 132.79/22.95 ((
% 132.79/22.95 (funcext2) =>
% 132.79/22.95 ((
% 132.79/22.95 (ap2apEq1) =>
% 132.79/22.95 ((
% 132.79/22.95 (ap2apEq2) =>
% 132.79/22.95 ((
% 132.79/22.95 (beta1) =>
% 132.79/22.95 ((
% 132.79/22.95 (eta1) =>
% 132.79/22.95 ((
% 132.79/22.95 (lam2lamEq) =>
% 132.79/22.95 ((
% 132.79/22.95 (beta2) =>
% 132.79/22.95 ((
% 132.79/22.95 (eta2) =>
% 132.79/22.95 ((
% 132.79/22.95 (iffalseProp1) =>
% 132.79/22.95 ((
% 132.79/22.95 (iffalseProp2) =>
% 132.79/22.95 ((
% 132.79/22.95 (iftrueProp1) =>
% 132.79/22.95 ((
% 132.79/22.95 (iftrueProp2) =>
% 132.79/22.95 ((
% 132.79/22.95 (ifSingleton) =>
% 132.79/22.95 ((
% 132.79/22.95 (ifp) =>
% 132.79/22.95 ((
% 132.79/22.95 (theeq) =>
% 132.79/22.95 ((
% 132.79/22.95 (iftrue) =>
% 132.79/22.95 ((
% 132.79/22.95 (iffalse) =>
% 132.79/22.95 ((
% 132.79/22.95 (iftrueorfalse) =>
% 132.79/22.95 ((
% 132.79/22.95 (binintersectT_lem) =>
% 132.79/22.95 ((
% 132.79/22.95 (binunionT_lem) =>
% 132.79/22.95 ((
% 132.79/22.95 (powersetT_lem) =>
% 132.79/22.95 ((
% 132.79/22.95 (setminusT_lem) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementT_lem) =>
% 132.79/22.95 ((
% 132.79/22.95 (setextT) =>
% 132.79/22.95 ((
% 132.79/22.95 (subsetTI) =>
% 132.79/22.95 ((
% 132.79/22.95 (powersetTI1) =>
% 132.79/22.95 ((
% 132.79/22.95 (powersetTE1) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementTI1) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementTE1) =>
% 132.79/22.95 ((
% 132.79/22.95 (binintersectTELcontra) =>
% 132.79/22.95 ((
% 132.79/22.95 (binintersectTERcontra) =>
% 132.79/22.95 ((
% 132.79/22.95 (contrasubsetT) =>
% 132.79/22.95 ((
% 132.79/22.95 (contrasubsetT1) =>
% 132.79/22.95 ((
% 132.79/22.95 (contrasubsetT2) =>
% 132.79/22.95 ((
% 132.79/22.95 (contrasubsetT3) =>
% 132.79/22.95 ((
% 132.79/22.95 (doubleComplementI1) =>
% 132.79/22.95 ((
% 132.79/22.95 (doubleComplementE1) =>
% 132.79/22.95 ((
% 132.79/22.95 (doubleComplementSub1) =>
% 132.79/22.95 ((
% 132.79/22.95 (doubleComplementSub2) =>
% 132.79/22.95 ((
% 132.79/22.95 (doubleComplementEq) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementTnotintersectT) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementImpComplementIntersect) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementSubsetComplementIntersect) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementInPowersetComplementIntersect) =>
% 132.79/22.95 ((
% 132.79/22.95 (contraSubsetComplement) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementTcontraSubset) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (binunionTIRcontra) =>
% 132.79/22.95 ((
% 132.79/22.95 (inIntersectImpInUnion) =>
% 132.79/22.95 ((
% 132.79/22.95 (inIntersectImpInUnion2) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (demorgan2a) =>
% 132.79/22.95 ((
% 132.79/22.95 (demorgan2b2) =>
% 132.79/22.95 ((
% 132.79/22.95 (demorgan2b) =>
% 132.79/22.95 ((
% 132.79/22.95 (demorgan2) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz13rule0) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz13rule1) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz13rule2) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz13rule3) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz13rule4) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (woz1_2) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz1_3) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz1_4) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (breln1all2) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (eqbreln1) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1invprop) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1invI) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1invE) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1compprop) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1compI) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1compE) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1compEex) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1unionprop) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1unionIL) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1unionIR) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1unionI) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1unionE) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1unionEcases) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1unionCommutes) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (woz2W) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (woz2B) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (image1Ex1) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (image1E) =>
% 132.79/22.95 ((
% 132.79/22.95 (image1I) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (injFuncSetFuncIn) =>
% 132.79/22.95 ((
% 132.79/22.95 (injFuncSetFuncInj) =>
% 132.79/22.95 ((
% 132.79/22.95 (surjFuncSetFuncIn) =>
% 132.79/22.95 ((
% 132.79/22.95 (surjFuncSetFuncSurj) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1131])).
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% 132.79/22.95 (upairequniteq) =>
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% 132.79/22.95 (ksndpairEq) =>
% 132.79/22.95 ((
% 132.79/22.95 (kpairsurjEq) =>
% 132.79/22.95 ((
% 132.79/22.95 (cartprodsndin) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (cartprodpairmemER) =>
% 132.79/22.95 ((
% 132.79/22.95 (cartprodmempaircEq) =>
% 132.79/22.95 ((
% 132.79/22.95 (cartprodfstpairEq) =>
% 132.79/22.95 ((
% 132.79/22.95 (cartprodsndpairEq) =>
% 132.79/22.95 ((
% 132.79/22.95 (cartprodpairsurjEq) =>
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% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (lam2p) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 (setextT) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (powersetTI1) =>
% 132.79/22.95 ((
% 132.79/22.95 (powersetTE1) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementTI1) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementTE1) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (binintersectTERcontra) =>
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% 132.79/22.95 ((
% 132.79/22.95 (contrasubsetT2) =>
% 132.79/22.95 ((
% 132.79/22.95 (contrasubsetT3) =>
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% 132.79/22.95 (doubleComplementI1) =>
% 132.79/22.95 ((
% 132.79/22.95 (doubleComplementE1) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (doubleComplementSub2) =>
% 132.79/22.95 ((
% 132.79/22.95 (doubleComplementEq) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementTnotintersectT) =>
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% 132.79/22.95 (complementImpComplementIntersect) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementSubsetComplementIntersect) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementInPowersetComplementIntersect) =>
% 132.79/22.95 ((
% 132.79/22.95 (contraSubsetComplement) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (binunionTIRcontra) =>
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% 132.79/22.95 (intersectInPowersetIntersectUnions) =>
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% 132.79/22.95 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1138])).
% 132.79/22.95 thf(zip_derived_cl1153, plain,
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% 132.79/22.95 (((upairinpowunion) =>
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% 132.79/22.95 (((ubforcartprodlem2) =>
% 132.79/22.95 (((ubforcartprodlem3) =>
% 132.79/22.95 (((cartprodpairin) =>
% 132.79/22.95 (((cartprodmempair1) =>
% 132.79/22.95 (((cartprodmempair) =>
% 132.79/22.95 (((setunionE2) =>
% 132.79/22.95 (((setunionsingleton1) =>
% 132.79/22.95 (((setunionsingleton2) =>
% 132.79/22.95 (((setunionsingleton) =>
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% 132.79/22.95 (((singletonsuniq) =>
% 132.79/22.95 (((setukpairinjL1) =>
% 132.79/22.95 (((kfstsingleton) =>
% 132.79/22.95 (((theprop) =>
% 132.79/22.95 (((kfstpairEq) =>
% 132.79/22.95 (((cartprodfstin) =>
% 132.79/22.95 (((setukpairinjL2) =>
% 132.79/22.95 ((
% 132.79/22.95 (setukpairinjL) =>
% 132.79/22.95 ((
% 132.79/22.95 (setukpairinjR11) =>
% 132.79/22.95 ((
% 132.79/22.95 (setukpairinjR12) =>
% 132.79/22.95 ((
% 132.79/22.95 (setukpairinjR1) =>
% 132.79/22.95 ((
% 132.79/22.95 (upairequniteq) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (kpairsurjEq) =>
% 132.79/22.95 ((
% 132.79/22.95 (cartprodsndin) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (cartprodpairmemER) =>
% 132.79/22.95 ((
% 132.79/22.95 (cartprodmempaircEq) =>
% 132.79/22.95 ((
% 132.79/22.95 (cartprodfstpairEq) =>
% 132.79/22.95 ((
% 132.79/22.95 (cartprodsndpairEq) =>
% 132.79/22.95 ((
% 132.79/22.95 (cartprodpairsurjEq) =>
% 132.79/22.95 ((
% 132.79/22.95 (dpsetconstrI) =>
% 132.79/22.95 ((
% 132.79/22.95 (dpsetconstrSub) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (dpsetconstrER) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (infuncsetfunc) =>
% 132.79/22.95 ((
% 132.79/22.95 (ap2p) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (lam2p) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (brelnall2) =>
% 132.79/22.95 ((
% 132.79/22.95 (ex1E2) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 (iffalseProp2) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (iftrueProp2) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (powersetTI1) =>
% 132.79/22.95 ((
% 132.79/22.95 (powersetTE1) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementTI1) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementTE1) =>
% 132.79/22.95 ((
% 132.79/22.95 (binintersectTELcontra) =>
% 132.79/22.95 ((
% 132.79/22.95 (binintersectTERcontra) =>
% 132.79/22.95 ((
% 132.79/22.95 (contrasubsetT) =>
% 132.79/22.95 ((
% 132.79/22.95 (contrasubsetT1) =>
% 132.79/22.95 ((
% 132.79/22.95 (contrasubsetT2) =>
% 132.79/22.95 ((
% 132.79/22.95 (contrasubsetT3) =>
% 132.79/22.95 ((
% 132.79/22.95 (doubleComplementI1) =>
% 132.79/22.95 ((
% 132.79/22.95 (doubleComplementE1) =>
% 132.79/22.95 ((
% 132.79/22.95 (doubleComplementSub1) =>
% 132.79/22.95 ((
% 132.79/22.95 (doubleComplementSub2) =>
% 132.79/22.95 ((
% 132.79/22.95 (doubleComplementEq) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementTnotintersectT) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementImpComplementIntersect) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementSubsetComplementIntersect) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementInPowersetComplementIntersect) =>
% 132.79/22.95 ((
% 132.79/22.95 (contraSubsetComplement) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementTcontraSubset) =>
% 132.79/22.95 ((
% 132.79/22.95 (binunionTILcontra) =>
% 132.79/22.95 ((
% 132.79/22.95 (binunionTIRcontra) =>
% 132.79/22.95 ((
% 132.79/22.95 (inIntersectImpInUnion) =>
% 132.79/22.95 ((
% 132.79/22.95 (inIntersectImpInUnion2) =>
% 132.79/22.95 ((
% 132.79/22.95 (inIntersectImpInIntersectUnions) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (inComplementUnionImpInComplement1) =>
% 132.79/22.95 ((
% 132.79/22.95 (binunionTE) =>
% 132.79/22.95 ((
% 132.79/22.95 (binunionTEcontra) =>
% 132.79/22.95 ((
% 132.79/22.95 (demorgan2a1) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (demorgan2a2) =>
% 132.79/22.95 ((
% 132.79/22.95 (demorgan1a) =>
% 132.79/22.95 ((
% 132.79/22.95 (demorgan1b) =>
% 132.79/22.95 ((
% 132.79/22.95 (demorgan1) =>
% 132.79/22.95 ((
% 132.79/22.95 (demorgan2a) =>
% 132.79/22.95 ((
% 132.79/22.95 (demorgan2b2) =>
% 132.79/22.95 ((
% 132.79/22.95 (demorgan2b) =>
% 132.79/22.95 ((
% 132.79/22.95 (demorgan2) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz13rule0) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz13rule1) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz13rule2) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz13rule3) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz13rule4) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz1_1) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz1_2) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz1_3) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz1_4) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz1_5) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1all2) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1SetBreln1) =>
% 132.79/22.95 ((
% 132.79/22.95 (choice2fnsingleton) =>
% 132.79/22.95 ((
% 132.79/22.95 (setOfPairsIsBReln1) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1all1) =>
% 132.79/22.95 ((
% 132.79/22.95 (subbreln1) =>
% 132.79/22.95 ((
% 132.79/22.95 (eqbreln1) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1invprop) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1invI) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1invE) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1compprop) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1compI) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1compE) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1compEex) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1unionprop) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1unionIL) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1unionIR) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1unionI) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1unionE) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1unionEcases) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1unionCommutes) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz2Ex) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (woz2B) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (image1Ex1) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (image1E) =>
% 132.79/22.95 ((
% 132.79/22.95 (image1I) =>
% 132.79/22.95 ((
% 132.79/22.95 (injFuncInInjFuncSet) =>
% 132.79/22.95 ((
% 132.79/22.95 (injFuncSetFuncIn) =>
% 132.79/22.95 ((
% 132.79/22.95 (injFuncSetFuncInj) =>
% 132.79/22.95 ((
% 132.79/22.95 (surjFuncSetFuncIn) =>
% 132.79/22.95 ((
% 132.79/22.95 (surjFuncSetFuncSurj) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (surjCantorThm) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (notinself2) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (omegaSclos) =>
% 132.79/22.95 ((
% 132.79/22.95 (peano0notS) =>
% 132.79/22.95 ((
% 132.79/22.95 (peanoSinj) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1145])).
% 132.79/22.95 thf(zip_derived_cl1162, plain,
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% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (complementT_lem) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (complementTE1) =>
% 132.79/22.95 ((
% 132.79/22.95 (binintersectTELcontra) =>
% 132.79/22.95 ((
% 132.79/22.95 (binintersectTERcontra) =>
% 132.79/22.95 ((
% 132.79/22.95 (contrasubsetT) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (contrasubsetT2) =>
% 132.79/22.95 ((
% 132.79/22.95 (contrasubsetT3) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (doubleComplementE1) =>
% 132.79/22.95 ((
% 132.79/22.95 (doubleComplementSub1) =>
% 132.79/22.95 ((
% 132.79/22.95 (doubleComplementSub2) =>
% 132.79/22.95 ((
% 132.79/22.95 (doubleComplementEq) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (complementSubsetComplementIntersect) =>
% 132.79/22.95 ((
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% 132.79/22.95 (contraSubsetComplement) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementTcontraSubset) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (binunionTIRcontra) =>
% 132.79/22.95 ((
% 132.79/22.95 (inIntersectImpInUnion) =>
% 132.79/22.95 ((
% 132.79/22.95 (inIntersectImpInUnion2) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (demorgan1a) =>
% 132.79/22.95 ((
% 132.79/22.95 (demorgan1b) =>
% 132.79/22.95 ((
% 132.79/22.95 (demorgan1) =>
% 132.79/22.95 ((
% 132.79/22.95 (demorgan2a) =>
% 132.79/22.95 ((
% 132.79/22.95 (demorgan2b2) =>
% 132.79/22.95 ((
% 132.79/22.95 (demorgan2b) =>
% 132.79/22.95 ((
% 132.79/22.95 (demorgan2) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz13rule0) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz13rule1) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz13rule2) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz13rule3) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz13rule4) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (woz1_2) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz1_3) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz1_4) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz1_5) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1all2) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1SetBreln1) =>
% 132.79/22.95 ((
% 132.79/22.95 (choice2fnsingleton) =>
% 132.79/22.95 ((
% 132.79/22.95 (setOfPairsIsBReln1) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1all1) =>
% 132.79/22.95 ((
% 132.79/22.95 (subbreln1) =>
% 132.79/22.95 ((
% 132.79/22.95 (eqbreln1) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1invprop) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1invI) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1invE) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1compprop) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1compI) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1compE) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1compEex) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1unionprop) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1unionIL) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1unionIR) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1unionI) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1unionE) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1unionEcases) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1unionCommutes) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz2Ex) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz2W) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz2A) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz2B) =>
% 132.79/22.95 ((
% 132.79/22.95 (image1Ex) =>
% 132.79/22.95 ((
% 132.79/22.95 (image1Ex1) =>
% 132.79/22.95 ((
% 132.79/22.95 (image1Equiv) =>
% 132.79/22.95 ((
% 132.79/22.95 (image1E) =>
% 132.79/22.95 ((
% 132.79/22.95 (image1I) =>
% 132.79/22.95 ((
% 132.79/22.95 (injFuncInInjFuncSet) =>
% 132.79/22.95 ((
% 132.79/22.95 (injFuncSetFuncIn) =>
% 132.79/22.95 ((
% 132.79/22.95 (injFuncSetFuncInj) =>
% 132.79/22.95 ((
% 132.79/22.95 (surjFuncSetFuncIn) =>
% 132.79/22.95 ((
% 132.79/22.95 (surjFuncSetFuncSurj) =>
% 132.79/22.95 ((
% 132.79/22.95 (leftInvIsSurj) =>
% 132.79/22.95 ((
% 132.79/22.95 (surjCantorThm) =>
% 132.79/22.95 ((
% 132.79/22.95 (foundation2) =>
% 132.79/22.95 ((
% 132.79/22.95 (notinself) =>
% 132.79/22.95 ((
% 132.79/22.95 (notinself2) =>
% 132.79/22.95 ((
% 132.79/22.95 (omegaSp) =>
% 132.79/22.95 ((
% 132.79/22.95 (omegaSclos) =>
% 132.79/22.95 ((
% 132.79/22.95 (peano0notS) =>
% 132.79/22.95 ((
% 132.79/22.95 (peanoSinj) =>
% 132.79/22.95 ((
% 132.79/22.95 (transitivesetOp1) =>
% 132.79/22.95 ((
% 132.79/22.95 (binintTransitive) =>
% 132.79/22.95 ((
% 132.79/22.95 (transitivesetOp2) =>
% 132.79/22.95 ((
% 132.79/22.95 (setunionTransitive) =>
% 132.79/22.95 ((
% 132.79/22.95 (ordinalMinLem1) =>
% 132.79/22.95 ((
% 132.79/22.95 (ordinalTransSet) =>
% 132.79/22.95 ((
% 132.79/22.95 (ordinalTransSet1) =>
% 132.79/22.95 ((
% 132.79/22.95 (setunionOrdinalLem1) =>
% 132.79/22.95 (ordinal @
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% 132.79/22.95 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1153])).
% 132.79/22.95 thf(zip_derived_cl1172, plain,
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% 132.79/22.95 (((upairset2E) =>
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% 132.79/22.95 (((upairinpowunion) =>
% 132.79/22.95 (((ubforcartprodlem1) =>
% 132.79/22.95 (((ubforcartprodlem2) =>
% 132.79/22.95 (((ubforcartprodlem3) =>
% 132.79/22.95 (((cartprodpairin) =>
% 132.79/22.95 (((cartprodmempair1) =>
% 132.79/22.95 (((cartprodmempair) =>
% 132.79/22.95 (((setunionE2) =>
% 132.79/22.95 (((setunionsingleton1) =>
% 132.79/22.95 (((setunionsingleton2) =>
% 132.79/22.95 (((setunionsingleton) =>
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% 132.79/22.95 (((kfstsingleton) =>
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% 132.79/22.95 (((kfstpairEq) =>
% 132.79/22.95 (((cartprodfstin) =>
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% 132.79/22.95 (((setukpairinjL) =>
% 132.79/22.95 (((setukpairinjR11) =>
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% 132.79/22.95 (setukpairinjR12) =>
% 132.79/22.95 ((
% 132.79/22.95 (setukpairinjR1) =>
% 132.79/22.95 ((
% 132.79/22.95 (upairequniteq) =>
% 132.79/22.95 ((
% 132.79/22.95 (setukpairinjR2) =>
% 132.79/22.95 ((
% 132.79/22.95 (setukpairinjR) =>
% 132.79/22.95 ((
% 132.79/22.95 (ksndsingleton) =>
% 132.79/22.95 ((
% 132.79/22.95 (ksndpairEq) =>
% 132.79/22.95 ((
% 132.79/22.95 (kpairsurjEq) =>
% 132.79/22.95 ((
% 132.79/22.95 (cartprodsndin) =>
% 132.79/22.95 ((
% 132.79/22.95 (cartprodpairmemEL) =>
% 132.79/22.95 ((
% 132.79/22.95 (cartprodpairmemER) =>
% 132.79/22.95 ((
% 132.79/22.95 (cartprodmempaircEq) =>
% 132.79/22.95 ((
% 132.79/22.95 (cartprodfstpairEq) =>
% 132.79/22.95 ((
% 132.79/22.95 (cartprodsndpairEq) =>
% 132.79/22.95 ((
% 132.79/22.95 (cartprodpairsurjEq) =>
% 132.79/22.95 ((
% 132.79/22.95 (dpsetconstrI) =>
% 132.79/22.95 ((
% 132.79/22.95 (dpsetconstrSub) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (app) =>
% 132.79/22.95 ((
% 132.79/22.95 (infuncsetfunc) =>
% 132.79/22.95 ((
% 132.79/22.95 (ap2p) =>
% 132.79/22.95 ((
% 132.79/22.95 (funcinfuncset) =>
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% 132.79/22.95 (lamProp) =>
% 132.79/22.95 ((
% 132.79/22.95 (lamp) =>
% 132.79/22.95 ((
% 132.79/22.95 (lam2p) =>
% 132.79/22.95 ((
% 132.79/22.95 (brelnall1) =>
% 132.79/22.95 ((
% 132.79/22.95 (brelnall2) =>
% 132.79/22.95 ((
% 132.79/22.95 (ex1E2) =>
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% 132.79/22.95 ((
% 132.79/22.95 (funcGraphProp3) =>
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% 132.79/22.95 (eqbreln) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (funcext2) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (ap2apEq2) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (eta1) =>
% 132.79/22.95 ((
% 132.79/22.95 (lam2lamEq) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (iffalseProp2) =>
% 132.79/22.95 ((
% 132.79/22.95 (iftrueProp1) =>
% 132.79/22.95 ((
% 132.79/22.95 (iftrueProp2) =>
% 132.79/22.95 ((
% 132.79/22.95 (ifSingleton) =>
% 132.79/22.95 ((
% 132.79/22.95 (ifp) =>
% 132.79/22.95 ((
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% 132.79/22.95 (iftrue) =>
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% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (complementTE1) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (binintersectTERcontra) =>
% 132.79/22.95 ((
% 132.79/22.95 (contrasubsetT) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (contrasubsetT2) =>
% 132.79/22.95 ((
% 132.79/22.95 (contrasubsetT3) =>
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% 132.79/22.95 ((
% 132.79/22.95 (doubleComplementE1) =>
% 132.79/22.95 ((
% 132.79/22.95 (doubleComplementSub1) =>
% 132.79/22.95 ((
% 132.79/22.95 (doubleComplementSub2) =>
% 132.79/22.95 ((
% 132.79/22.95 (doubleComplementEq) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementTnotintersectT) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementImpComplementIntersect) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementSubsetComplementIntersect) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementInPowersetComplementIntersect) =>
% 132.79/22.95 ((
% 132.79/22.95 (contraSubsetComplement) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementTcontraSubset) =>
% 132.79/22.95 ((
% 132.79/22.95 (binunionTILcontra) =>
% 132.79/22.95 ((
% 132.79/22.95 (binunionTIRcontra) =>
% 132.79/22.95 ((
% 132.79/22.95 (inIntersectImpInUnion) =>
% 132.79/22.95 ((
% 132.79/22.95 (inIntersectImpInUnion2) =>
% 132.79/22.95 ((
% 132.79/22.95 (inIntersectImpInIntersectUnions) =>
% 132.79/22.95 ((
% 132.79/22.95 (intersectInPowersetIntersectUnions) =>
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% 132.79/22.95 (inComplementUnionImpInComplement1) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (binunionTEcontra) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (demorgan2) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 ((
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% 132.79/22.95 (eqbreln) =>
% 132.79/22.95 ((
% 132.79/22.95 (funcext) =>
% 132.79/22.95 ((
% 132.79/22.95 (funcext2) =>
% 132.79/22.95 ((
% 132.79/22.95 (ap2apEq1) =>
% 132.79/22.95 ((
% 132.79/22.95 (ap2apEq2) =>
% 132.79/22.95 ((
% 132.79/22.95 (beta1) =>
% 132.79/22.95 ((
% 132.79/22.95 (eta1) =>
% 132.79/22.95 ((
% 132.79/22.95 (lam2lamEq) =>
% 132.79/22.95 ((
% 132.79/22.95 (beta2) =>
% 132.79/22.95 ((
% 132.79/22.95 (eta2) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (iffalseProp2) =>
% 132.79/22.95 ((
% 132.79/22.95 (iftrueProp1) =>
% 132.79/22.95 ((
% 132.79/22.95 (iftrueProp2) =>
% 132.79/22.95 ((
% 132.79/22.95 (ifSingleton) =>
% 132.79/22.95 ((
% 132.79/22.95 (ifp) =>
% 132.79/22.95 ((
% 132.79/22.95 (theeq) =>
% 132.79/22.95 ((
% 132.79/22.95 (iftrue) =>
% 132.79/22.95 ((
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% 132.79/22.95 ((
% 132.79/22.95 (iftrueorfalse) =>
% 132.79/22.95 ((
% 132.79/22.95 (binintersectT_lem) =>
% 132.79/22.95 ((
% 132.79/22.95 (binunionT_lem) =>
% 132.79/22.95 ((
% 132.79/22.95 (powersetT_lem) =>
% 132.79/22.95 ((
% 132.79/22.95 (setminusT_lem) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementT_lem) =>
% 132.79/22.95 ((
% 132.79/22.95 (setextT) =>
% 132.79/22.95 ((
% 132.79/22.95 (subsetTI) =>
% 132.79/22.95 ((
% 132.79/22.95 (powersetTI1) =>
% 132.79/22.95 ((
% 132.79/22.95 (powersetTE1) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementTI1) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementTE1) =>
% 132.79/22.95 ((
% 132.79/22.95 (binintersectTELcontra) =>
% 132.79/22.95 ((
% 132.79/22.95 (binintersectTERcontra) =>
% 132.79/22.95 ((
% 132.79/22.95 (contrasubsetT) =>
% 132.79/22.95 ((
% 132.79/22.95 (contrasubsetT1) =>
% 132.79/22.95 ((
% 132.79/22.95 (contrasubsetT2) =>
% 132.79/22.95 ((
% 132.79/22.95 (contrasubsetT3) =>
% 132.79/22.95 ((
% 132.79/22.95 (doubleComplementI1) =>
% 132.79/22.95 ((
% 132.79/22.95 (doubleComplementE1) =>
% 132.79/22.95 ((
% 132.79/22.95 (doubleComplementSub1) =>
% 132.79/22.95 ((
% 132.79/22.95 (doubleComplementSub2) =>
% 132.79/22.95 ((
% 132.79/22.95 (doubleComplementEq) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementTnotintersectT) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementImpComplementIntersect) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementSubsetComplementIntersect) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementInPowersetComplementIntersect) =>
% 132.79/22.95 ((
% 132.79/22.95 (contraSubsetComplement) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementTcontraSubset) =>
% 132.79/22.95 ((
% 132.79/22.95 (binunionTILcontra) =>
% 132.79/22.95 ((
% 132.79/22.95 (binunionTIRcontra) =>
% 132.79/22.95 ((
% 132.79/22.95 (inIntersectImpInUnion) =>
% 132.79/22.95 ((
% 132.79/22.95 (inIntersectImpInUnion2) =>
% 132.79/22.95 ((
% 132.79/22.95 (inIntersectImpInIntersectUnions) =>
% 132.79/22.95 ((
% 132.79/22.95 (intersectInPowersetIntersectUnions) =>
% 132.79/22.95 ((
% 132.79/22.95 (inComplementUnionImpNotIn1) =>
% 132.79/22.95 ((
% 132.79/22.95 (inComplementUnionImpInComplement1) =>
% 132.79/22.95 ((
% 132.79/22.95 (binunionTE) =>
% 132.79/22.95 ((
% 132.79/22.95 (binunionTEcontra) =>
% 132.79/22.95 ((
% 132.79/22.95 (demorgan2a1) =>
% 132.79/22.95 ((
% 132.79/22.95 (complementUnionInPowersetComplement) =>
% 132.79/22.95 ((
% 132.79/22.95 (demorgan2a2) =>
% 132.79/22.95 ((
% 132.79/22.95 (demorgan1a) =>
% 132.79/22.95 ((
% 132.79/22.95 (demorgan1b) =>
% 132.79/22.95 ((
% 132.79/22.95 (demorgan1) =>
% 132.79/22.95 ((
% 132.79/22.95 (demorgan2a) =>
% 132.79/22.95 ((
% 132.79/22.95 (demorgan2b2) =>
% 132.79/22.95 ((
% 132.79/22.95 (demorgan2b) =>
% 132.79/22.95 ((
% 132.79/22.95 (demorgan2) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz13rule0) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz13rule1) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz13rule2) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz13rule3) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz13rule4) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz1_1) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz1_2) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz1_3) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz1_4) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz1_5) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1all2) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1SetBreln1) =>
% 132.79/22.95 ((
% 132.79/22.95 (choice2fnsingleton) =>
% 132.79/22.95 ((
% 132.79/22.95 (setOfPairsIsBReln1) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1all1) =>
% 132.79/22.95 ((
% 132.79/22.95 (subbreln1) =>
% 132.79/22.95 ((
% 132.79/22.95 (eqbreln1) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1invprop) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1invI) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1invE) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1compprop) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1compI) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1compE) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1compEex) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1unionprop) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1unionIL) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1unionIR) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1unionI) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1unionE) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1unionEcases) =>
% 132.79/22.95 ((
% 132.79/22.95 (breln1unionCommutes) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz2Ex) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz2W) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz2A) =>
% 132.79/22.95 ((
% 132.79/22.95 (woz2B) =>
% 132.79/22.95 ((
% 132.79/22.95 (image1Ex) =>
% 132.79/22.95 ((
% 132.79/22.95 (image1Ex1) =>
% 132.79/22.95 ((
% 132.79/22.95 (image1Equiv) =>
% 132.79/22.95 ((
% 132.79/22.95 (image1E) =>
% 132.79/22.95 ((
% 132.79/22.95 (image1I) =>
% 132.79/22.95 ((
% 132.79/22.95 (injFuncInInjFuncSet) =>
% 132.79/22.95 ((
% 132.79/22.95 (injFuncSetFuncIn) =>
% 132.79/22.95 ((
% 132.79/22.95 (injFuncSetFuncInj) =>
% 132.79/22.95 ((
% 132.79/22.95 (surjFuncSetFuncIn) =>
% 132.79/22.95 ((
% 132.79/22.95 (surjFuncSetFuncSurj) =>
% 132.79/22.95 ((
% 132.79/22.95 (leftInvIsSurj) =>
% 132.79/22.95 ((
% 132.79/22.95 (surjCantorThm) =>
% 132.79/22.95 ((
% 132.79/22.95 (foundation2) =>
% 132.79/22.95 ((
% 132.79/22.95 (notinself) =>
% 132.79/22.95 ((
% 132.79/22.95 (notinself2) =>
% 132.79/22.95 ((
% 132.79/22.95 (omegaSp) =>
% 132.79/22.95 ((
% 132.79/22.95 (omegaSclos) =>
% 132.79/22.95 ((
% 132.79/22.95 (peano0notS) =>
% 132.79/22.95 ((
% 132.79/22.95 (peanoSinj) =>
% 132.79/22.95 ((
% 132.79/22.95 (transitivesetOp1) =>
% 132.79/22.95 ((
% 132.79/22.95 (binintTransitive) =>
% 132.79/22.95 ((
% 132.79/22.95 (transitivesetOp2) =>
% 132.79/22.95 ((
% 132.79/22.95 (setunionTransitive) =>
% 132.79/22.95 ((
% 132.79/22.95 (ordinalMinLem1) =>
% 132.79/22.95 ((
% 132.79/22.95 (ordinalTransSet) =>
% 132.79/22.95 ((
% 132.79/22.95 (ordinalTransSet1) =>
% 132.79/22.95 ((
% 132.79/22.95 (setunionOrdinalLem1) =>
% 132.79/22.95 (ordinal @
% 132.79/22.95 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/22.95 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1185])).
% 132.79/22.95 thf(zip_derived_cl1202, plain,
% 132.79/22.95 (~ (((singletoninpowunion) =>
% 132.79/22.95 (((upairset2E) =>
% 132.79/22.95 (((upairsubunion) =>
% 132.79/22.95 (((upairinpowunion) =>
% 132.79/22.95 (((ubforcartprodlem1) =>
% 132.79/22.95 (((ubforcartprodlem2) =>
% 132.79/22.95 (((ubforcartprodlem3) =>
% 132.79/22.95 (((cartprodpairin) =>
% 132.79/22.95 (((cartprodmempair1) =>
% 132.79/22.95 (((cartprodmempair) =>
% 132.79/22.95 (((setunionE2) =>
% 132.79/22.95 (((setunionsingleton1) =>
% 132.79/22.95 (((setunionsingleton2) =>
% 132.79/22.95 (((setunionsingleton) =>
% 132.79/22.95 (((singletonprop) =>
% 132.79/22.95 (((ex1E1) =>
% 132.79/22.95 (((ex1I) =>
% 132.79/22.95 (((ex1I2) =>
% 132.79/22.95 (((singletonsuniq) =>
% 132.79/22.95 (((setukpairinjL1) =>
% 132.79/22.95 (((kfstsingleton) =>
% 132.79/22.95 (((theprop) =>
% 132.79/22.95 (((kfstpairEq) =>
% 132.79/22.95 (((cartprodfstin) =>
% 132.79/22.95 (((setukpairinjL2) =>
% 132.79/22.95 (((setukpairinjL) =>
% 132.79/22.95 (((setukpairinjR11) =>
% 132.79/22.95 (((setukpairinjR12) =>
% 132.79/22.95 (((setukpairinjR1) =>
% 132.79/22.95 (((upairequniteq) =>
% 132.79/22.95 ((
% 132.79/22.95 (setukpairinjR2) =>
% 132.79/22.95 ((
% 132.79/22.95 (setukpairinjR) =>
% 132.79/22.95 ((
% 132.79/22.95 (ksndsingleton) =>
% 132.79/22.95 ((
% 132.79/22.95 (ksndpairEq) =>
% 132.79/22.95 ((
% 132.79/22.95 (kpairsurjEq) =>
% 132.79/22.95 ((
% 132.79/22.95 (cartprodsndin) =>
% 132.79/22.95 ((
% 132.79/22.95 (cartprodpairmemEL) =>
% 132.79/22.95 ((
% 132.79/22.95 (cartprodpairmemER) =>
% 132.79/22.95 ((
% 132.79/22.95 (cartprodmempaircEq) =>
% 132.79/22.95 ((
% 132.79/22.95 (cartprodfstpairEq) =>
% 132.79/22.95 ((
% 132.79/22.95 (cartprodsndpairEq) =>
% 132.79/22.95 ((
% 132.79/22.95 (cartprodpairsurjEq) =>
% 132.79/22.95 ((
% 132.79/22.95 (dpsetconstrI) =>
% 132.79/22.95 ((
% 132.79/22.95 (dpsetconstrSub) =>
% 132.79/22.95 ((
% 132.79/22.95 (setOfPairsIsBReln) =>
% 132.79/22.95 ((
% 132.79/22.95 (dpsetconstrERa) =>
% 132.79/22.95 ((
% 132.79/22.95 (dpsetconstrEL1) =>
% 132.79/22.95 ((
% 132.79/22.95 (dpsetconstrEL2) =>
% 132.79/22.95 ((
% 132.79/22.95 (dpsetconstrER) =>
% 132.79/22.95 ((
% 132.79/22.95 (funcImageSingleton) =>
% 132.79/22.95 ((
% 132.79/22.95 (apProp) =>
% 132.79/22.95 ((
% 132.79/22.95 (app) =>
% 132.79/22.95 ((
% 132.79/22.95 (infuncsetfunc) =>
% 132.79/22.95 ((
% 132.79/22.95 (ap2p) =>
% 132.79/22.95 ((
% 132.79/22.95 (funcinfuncset) =>
% 132.79/22.95 ((
% 132.79/22.95 (lamProp) =>
% 132.79/22.95 ((
% 132.79/22.95 (lamp) =>
% 132.79/22.95 ((
% 132.79/22.95 (lam2p) =>
% 132.79/22.95 ((
% 132.79/22.95 (brelnall1) =>
% 132.79/22.95 ((
% 132.79/22.95 (brelnall2) =>
% 132.79/22.95 ((
% 132.79/22.95 (ex1E2) =>
% 132.79/22.95 ((
% 132.79/22.96 (funcGraphProp1) =>
% 132.79/22.96 ((
% 132.79/22.96 (funcGraphProp3) =>
% 132.79/22.96 ((
% 132.79/22.96 (funcGraphProp2) =>
% 132.79/22.96 ((
% 132.79/22.96 (funcextLem) =>
% 132.79/22.96 ((
% 132.79/22.96 (funcGraphProp4) =>
% 132.79/22.96 ((
% 132.79/22.96 (subbreln) =>
% 132.79/22.96 ((
% 132.79/22.96 (eqbreln) =>
% 132.79/22.96 ((
% 132.79/22.96 (funcext) =>
% 132.79/22.96 ((
% 132.79/22.96 (funcext2) =>
% 132.79/22.96 ((
% 132.79/22.96 (ap2apEq1) =>
% 132.79/22.96 ((
% 132.79/22.96 (ap2apEq2) =>
% 132.79/22.96 ((
% 132.79/22.96 (beta1) =>
% 132.79/22.96 ((
% 132.79/22.96 (eta1) =>
% 132.79/22.96 ((
% 132.79/22.96 (lam2lamEq) =>
% 132.79/22.96 ((
% 132.79/22.96 (beta2) =>
% 132.79/22.96 ((
% 132.79/22.96 (eta2) =>
% 132.79/22.96 ((
% 132.79/22.96 (iffalseProp1) =>
% 132.79/22.96 ((
% 132.79/22.96 (iffalseProp2) =>
% 132.79/22.96 ((
% 132.79/22.96 (iftrueProp1) =>
% 132.79/22.96 ((
% 132.79/22.96 (iftrueProp2) =>
% 132.79/22.96 ((
% 132.79/22.96 (ifSingleton) =>
% 132.79/22.96 ((
% 132.79/22.96 (ifp) =>
% 132.79/22.96 ((
% 132.79/22.96 (theeq) =>
% 132.79/22.96 ((
% 132.79/22.96 (iftrue) =>
% 132.79/22.96 ((
% 132.79/22.96 (iffalse) =>
% 132.79/22.96 ((
% 132.79/22.96 (iftrueorfalse) =>
% 132.79/22.96 ((
% 132.79/22.96 (binintersectT_lem) =>
% 132.79/22.96 ((
% 132.79/22.96 (binunionT_lem) =>
% 132.79/22.96 ((
% 132.79/22.96 (powersetT_lem) =>
% 132.79/22.96 ((
% 132.79/22.96 (setminusT_lem) =>
% 132.79/22.96 ((
% 132.79/22.96 (complementT_lem) =>
% 132.79/22.96 ((
% 132.79/22.96 (setextT) =>
% 132.79/22.96 ((
% 132.79/22.96 (subsetTI) =>
% 132.79/22.96 ((
% 132.79/22.96 (powersetTI1) =>
% 132.79/22.96 ((
% 132.79/22.96 (powersetTE1) =>
% 132.79/22.96 ((
% 132.79/22.96 (complementTI1) =>
% 132.79/22.96 ((
% 132.79/22.96 (complementTE1) =>
% 132.79/22.96 ((
% 132.79/22.96 (binintersectTELcontra) =>
% 132.79/22.96 ((
% 132.79/22.96 (binintersectTERcontra) =>
% 132.79/22.96 ((
% 132.79/22.96 (contrasubsetT) =>
% 132.79/22.96 ((
% 132.79/22.96 (contrasubsetT1) =>
% 132.79/22.96 ((
% 132.79/22.96 (contrasubsetT2) =>
% 132.79/22.96 ((
% 132.79/22.96 (contrasubsetT3) =>
% 132.79/22.96 ((
% 132.79/22.96 (doubleComplementI1) =>
% 132.79/22.96 ((
% 132.79/22.96 (doubleComplementE1) =>
% 132.79/22.96 ((
% 132.79/22.96 (doubleComplementSub1) =>
% 132.79/22.96 ((
% 132.79/22.96 (doubleComplementSub2) =>
% 132.79/22.96 ((
% 132.79/22.96 (doubleComplementEq) =>
% 132.79/22.96 ((
% 132.79/22.96 (complementTnotintersectT) =>
% 132.79/22.96 ((
% 132.79/22.96 (complementImpComplementIntersect) =>
% 132.79/22.96 ((
% 132.79/22.96 (complementSubsetComplementIntersect) =>
% 132.79/22.96 ((
% 132.79/22.96 (complementInPowersetComplementIntersect) =>
% 132.79/22.96 ((
% 132.79/22.96 (contraSubsetComplement) =>
% 132.79/22.96 ((
% 132.79/22.96 (complementTcontraSubset) =>
% 132.79/22.96 ((
% 132.79/22.96 (binunionTILcontra) =>
% 132.79/22.96 ((
% 132.79/22.96 (binunionTIRcontra) =>
% 132.79/22.96 ((
% 132.79/22.96 (inIntersectImpInUnion) =>
% 132.79/22.96 ((
% 132.79/22.96 (inIntersectImpInUnion2) =>
% 132.79/22.96 ((
% 132.79/22.96 (inIntersectImpInIntersectUnions) =>
% 132.79/22.96 ((
% 132.79/22.96 (intersectInPowersetIntersectUnions) =>
% 132.79/22.96 ((
% 132.79/22.96 (inComplementUnionImpNotIn1) =>
% 132.79/22.96 ((
% 132.79/22.96 (inComplementUnionImpInComplement1) =>
% 132.79/22.96 ((
% 132.79/22.96 (binunionTE) =>
% 132.79/22.96 ((
% 132.79/22.96 (binunionTEcontra) =>
% 132.79/22.96 ((
% 132.79/22.96 (demorgan2a1) =>
% 132.79/22.96 ((
% 132.79/22.96 (complementUnionInPowersetComplement) =>
% 132.79/22.96 ((
% 132.79/22.96 (demorgan2a2) =>
% 132.79/22.96 ((
% 132.79/22.96 (demorgan1a) =>
% 132.79/22.96 ((
% 132.79/22.96 (demorgan1b) =>
% 132.79/22.96 ((
% 132.79/22.96 (demorgan1) =>
% 132.79/22.96 ((
% 132.79/22.96 (demorgan2a) =>
% 132.79/22.96 ((
% 132.79/22.96 (demorgan2b2) =>
% 132.79/22.96 ((
% 132.79/22.96 (demorgan2b) =>
% 132.79/22.96 ((
% 132.79/22.96 (demorgan2) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz13rule0) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz13rule1) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz13rule2) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz13rule3) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz13rule4) =>
% 132.79/22.96 ((
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% 132.79/22.96 ((
% 132.79/22.96 (woz1_2) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz1_3) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz1_4) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz1_5) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1all2) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1SetBreln1) =>
% 132.79/22.96 ((
% 132.79/22.96 (choice2fnsingleton) =>
% 132.79/22.96 ((
% 132.79/22.96 (setOfPairsIsBReln1) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1all1) =>
% 132.79/22.96 ((
% 132.79/22.96 (subbreln1) =>
% 132.79/22.96 ((
% 132.79/22.96 (eqbreln1) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1invprop) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1invI) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1invE) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1compprop) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1compI) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1compE) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1compEex) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1unionprop) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1unionIL) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1unionIR) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1unionI) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1unionE) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1unionEcases) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1unionCommutes) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz2Ex) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz2W) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz2A) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz2B) =>
% 132.79/22.96 ((
% 132.79/22.96 (image1Ex) =>
% 132.79/22.96 ((
% 132.79/22.96 (image1Ex1) =>
% 132.79/22.96 ((
% 132.79/22.96 (image1Equiv) =>
% 132.79/22.96 ((
% 132.79/22.96 (image1E) =>
% 132.79/22.96 ((
% 132.79/22.96 (image1I) =>
% 132.79/22.96 ((
% 132.79/22.96 (injFuncInInjFuncSet) =>
% 132.79/22.96 ((
% 132.79/22.96 (injFuncSetFuncIn) =>
% 132.79/22.96 ((
% 132.79/22.96 (injFuncSetFuncInj) =>
% 132.79/22.96 ((
% 132.79/22.96 (surjFuncSetFuncIn) =>
% 132.79/22.96 ((
% 132.79/22.96 (surjFuncSetFuncSurj) =>
% 132.79/22.96 ((
% 132.79/22.96 (leftInvIsSurj) =>
% 132.79/22.96 ((
% 132.79/22.96 (surjCantorThm) =>
% 132.79/22.96 ((
% 132.79/22.96 (foundation2) =>
% 132.79/22.96 ((
% 132.79/22.96 (notinself) =>
% 132.79/22.96 ((
% 132.79/22.96 (notinself2) =>
% 132.79/22.96 ((
% 132.79/22.96 (omegaSp) =>
% 132.79/22.96 ((
% 132.79/22.96 (omegaSclos) =>
% 132.79/22.96 ((
% 132.79/22.96 (peano0notS) =>
% 132.79/22.96 ((
% 132.79/22.96 (peanoSinj) =>
% 132.79/22.96 ((
% 132.79/22.96 (transitivesetOp1) =>
% 132.79/22.96 ((
% 132.79/22.96 (binintTransitive) =>
% 132.79/22.96 ((
% 132.79/22.96 (transitivesetOp2) =>
% 132.79/22.96 ((
% 132.79/22.96 (setunionTransitive) =>
% 132.79/22.96 ((
% 132.79/22.96 (ordinalMinLem1) =>
% 132.79/22.96 ((
% 132.79/22.96 (ordinalTransSet) =>
% 132.79/22.96 ((
% 132.79/22.96 (ordinalTransSet1) =>
% 132.79/22.96 ((
% 132.79/22.96 (setunionOrdinalLem1) =>
% 132.79/22.96 (ordinal @
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% 132.79/22.96 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1195])).
% 132.79/22.96 thf(zip_derived_cl1207, plain,
% 132.79/22.96 (~ (((upairset2E) =>
% 132.79/22.96 (((upairsubunion) =>
% 132.79/22.96 (((upairinpowunion) =>
% 132.79/22.96 (((ubforcartprodlem1) =>
% 132.79/22.96 (((ubforcartprodlem2) =>
% 132.79/22.96 (((ubforcartprodlem3) =>
% 132.79/22.96 (((cartprodpairin) =>
% 132.79/22.96 (((cartprodmempair1) =>
% 132.79/22.96 (((cartprodmempair) =>
% 132.79/22.96 (((setunionE2) =>
% 132.79/22.96 (((setunionsingleton1) =>
% 132.79/22.96 (((setunionsingleton2) =>
% 132.79/22.96 (((setunionsingleton) =>
% 132.79/22.96 (((singletonprop) =>
% 132.79/22.96 (((ex1E1) =>
% 132.79/22.96 (((ex1I) =>
% 132.79/22.96 (((ex1I2) =>
% 132.79/22.96 (((singletonsuniq) =>
% 132.79/22.96 (((setukpairinjL1) =>
% 132.79/22.96 (((kfstsingleton) =>
% 132.79/22.96 (((theprop) =>
% 132.79/22.96 (((kfstpairEq) =>
% 132.79/22.96 (((cartprodfstin) =>
% 132.79/22.96 (((setukpairinjL2) =>
% 132.79/22.96 (((setukpairinjL) =>
% 132.79/22.96 (((setukpairinjR11) =>
% 132.79/22.96 (((setukpairinjR12) =>
% 132.79/22.96 (((setukpairinjR1) =>
% 132.79/22.96 (((upairequniteq) =>
% 132.79/22.96 (((setukpairinjR2) =>
% 132.79/22.96 ((
% 132.79/22.96 (setukpairinjR) =>
% 132.79/22.96 ((
% 132.79/22.96 (ksndsingleton) =>
% 132.79/22.96 ((
% 132.79/22.96 (ksndpairEq) =>
% 132.79/22.96 ((
% 132.79/22.96 (kpairsurjEq) =>
% 132.79/22.96 ((
% 132.79/22.96 (cartprodsndin) =>
% 132.79/22.96 ((
% 132.79/22.96 (cartprodpairmemEL) =>
% 132.79/22.96 ((
% 132.79/22.96 (cartprodpairmemER) =>
% 132.79/22.96 ((
% 132.79/22.96 (cartprodmempaircEq) =>
% 132.79/22.96 ((
% 132.79/22.96 (cartprodfstpairEq) =>
% 132.79/22.96 ((
% 132.79/22.96 (cartprodsndpairEq) =>
% 132.79/22.96 ((
% 132.79/22.96 (cartprodpairsurjEq) =>
% 132.79/22.96 ((
% 132.79/22.96 (dpsetconstrI) =>
% 132.79/22.96 ((
% 132.79/22.96 (dpsetconstrSub) =>
% 132.79/22.96 ((
% 132.79/22.96 (setOfPairsIsBReln) =>
% 132.79/22.96 ((
% 132.79/22.96 (dpsetconstrERa) =>
% 132.79/22.96 ((
% 132.79/22.96 (dpsetconstrEL1) =>
% 132.79/22.96 ((
% 132.79/22.96 (dpsetconstrEL2) =>
% 132.79/22.96 ((
% 132.79/22.96 (dpsetconstrER) =>
% 132.79/22.96 ((
% 132.79/22.96 (funcImageSingleton) =>
% 132.79/22.96 ((
% 132.79/22.96 (apProp) =>
% 132.79/22.96 ((
% 132.79/22.96 (app) =>
% 132.79/22.96 ((
% 132.79/22.96 (infuncsetfunc) =>
% 132.79/22.96 ((
% 132.79/22.96 (ap2p) =>
% 132.79/22.96 ((
% 132.79/22.96 (funcinfuncset) =>
% 132.79/22.96 ((
% 132.79/22.96 (lamProp) =>
% 132.79/22.96 ((
% 132.79/22.96 (lamp) =>
% 132.79/22.96 ((
% 132.79/22.96 (lam2p) =>
% 132.79/22.96 ((
% 132.79/22.96 (brelnall1) =>
% 132.79/22.96 ((
% 132.79/22.96 (brelnall2) =>
% 132.79/22.96 ((
% 132.79/22.96 (ex1E2) =>
% 132.79/22.96 ((
% 132.79/22.96 (funcGraphProp1) =>
% 132.79/22.96 ((
% 132.79/22.96 (funcGraphProp3) =>
% 132.79/22.96 ((
% 132.79/22.96 (funcGraphProp2) =>
% 132.79/22.96 ((
% 132.79/22.96 (funcextLem) =>
% 132.79/22.96 ((
% 132.79/22.96 (funcGraphProp4) =>
% 132.79/22.96 ((
% 132.79/22.96 (subbreln) =>
% 132.79/22.96 ((
% 132.79/22.96 (eqbreln) =>
% 132.79/22.96 ((
% 132.79/22.96 (funcext) =>
% 132.79/22.96 ((
% 132.79/22.96 (funcext2) =>
% 132.79/22.96 ((
% 132.79/22.96 (ap2apEq1) =>
% 132.79/22.96 ((
% 132.79/22.96 (ap2apEq2) =>
% 132.79/22.96 ((
% 132.79/22.96 (beta1) =>
% 132.79/22.96 ((
% 132.79/22.96 (eta1) =>
% 132.79/22.96 ((
% 132.79/22.96 (lam2lamEq) =>
% 132.79/22.96 ((
% 132.79/22.96 (beta2) =>
% 132.79/22.96 ((
% 132.79/22.96 (eta2) =>
% 132.79/22.96 ((
% 132.79/22.96 (iffalseProp1) =>
% 132.79/22.96 ((
% 132.79/22.96 (iffalseProp2) =>
% 132.79/22.96 ((
% 132.79/22.96 (iftrueProp1) =>
% 132.79/22.96 ((
% 132.79/22.96 (iftrueProp2) =>
% 132.79/22.96 ((
% 132.79/22.96 (ifSingleton) =>
% 132.79/22.96 ((
% 132.79/22.96 (ifp) =>
% 132.79/22.96 ((
% 132.79/22.96 (theeq) =>
% 132.79/22.96 ((
% 132.79/22.96 (iftrue) =>
% 132.79/22.96 ((
% 132.79/22.96 (iffalse) =>
% 132.79/22.96 ((
% 132.79/22.96 (iftrueorfalse) =>
% 132.79/22.96 ((
% 132.79/22.96 (binintersectT_lem) =>
% 132.79/22.96 ((
% 132.79/22.96 (binunionT_lem) =>
% 132.79/22.96 ((
% 132.79/22.96 (powersetT_lem) =>
% 132.79/22.96 ((
% 132.79/22.96 (setminusT_lem) =>
% 132.79/22.96 ((
% 132.79/22.96 (complementT_lem) =>
% 132.79/22.96 ((
% 132.79/22.96 (setextT) =>
% 132.79/22.96 ((
% 132.79/22.96 (subsetTI) =>
% 132.79/22.96 ((
% 132.79/22.96 (powersetTI1) =>
% 132.79/22.96 ((
% 132.79/22.96 (powersetTE1) =>
% 132.79/22.96 ((
% 132.79/22.96 (complementTI1) =>
% 132.79/22.96 ((
% 132.79/22.96 (complementTE1) =>
% 132.79/22.96 ((
% 132.79/22.96 (binintersectTELcontra) =>
% 132.79/22.96 ((
% 132.79/22.96 (binintersectTERcontra) =>
% 132.79/22.96 ((
% 132.79/22.96 (contrasubsetT) =>
% 132.79/22.96 ((
% 132.79/22.96 (contrasubsetT1) =>
% 132.79/22.96 ((
% 132.79/22.96 (contrasubsetT2) =>
% 132.79/22.96 ((
% 132.79/22.96 (contrasubsetT3) =>
% 132.79/22.96 ((
% 132.79/22.96 (doubleComplementI1) =>
% 132.79/22.96 ((
% 132.79/22.96 (doubleComplementE1) =>
% 132.79/22.96 ((
% 132.79/22.96 (doubleComplementSub1) =>
% 132.79/22.96 ((
% 132.79/22.96 (doubleComplementSub2) =>
% 132.79/22.96 ((
% 132.79/22.96 (doubleComplementEq) =>
% 132.79/22.96 ((
% 132.79/22.96 (complementTnotintersectT) =>
% 132.79/22.96 ((
% 132.79/22.96 (complementImpComplementIntersect) =>
% 132.79/22.96 ((
% 132.79/22.96 (complementSubsetComplementIntersect) =>
% 132.79/22.96 ((
% 132.79/22.96 (complementInPowersetComplementIntersect) =>
% 132.79/22.96 ((
% 132.79/22.96 (contraSubsetComplement) =>
% 132.79/22.96 ((
% 132.79/22.96 (complementTcontraSubset) =>
% 132.79/22.96 ((
% 132.79/22.96 (binunionTILcontra) =>
% 132.79/22.96 ((
% 132.79/22.96 (binunionTIRcontra) =>
% 132.79/22.96 ((
% 132.79/22.96 (inIntersectImpInUnion) =>
% 132.79/22.96 ((
% 132.79/22.96 (inIntersectImpInUnion2) =>
% 132.79/22.96 ((
% 132.79/22.96 (inIntersectImpInIntersectUnions) =>
% 132.79/22.96 ((
% 132.79/22.96 (intersectInPowersetIntersectUnions) =>
% 132.79/22.96 ((
% 132.79/22.96 (inComplementUnionImpNotIn1) =>
% 132.79/22.96 ((
% 132.79/22.96 (inComplementUnionImpInComplement1) =>
% 132.79/22.96 ((
% 132.79/22.96 (binunionTE) =>
% 132.79/22.96 ((
% 132.79/22.96 (binunionTEcontra) =>
% 132.79/22.96 ((
% 132.79/22.96 (demorgan2a1) =>
% 132.79/22.96 ((
% 132.79/22.96 (complementUnionInPowersetComplement) =>
% 132.79/22.96 ((
% 132.79/22.96 (demorgan2a2) =>
% 132.79/22.96 ((
% 132.79/22.96 (demorgan1a) =>
% 132.79/22.96 ((
% 132.79/22.96 (demorgan1b) =>
% 132.79/22.96 ((
% 132.79/22.96 (demorgan1) =>
% 132.79/22.96 ((
% 132.79/22.96 (demorgan2a) =>
% 132.79/22.96 ((
% 132.79/22.96 (demorgan2b2) =>
% 132.79/22.96 ((
% 132.79/22.96 (demorgan2b) =>
% 132.79/22.96 ((
% 132.79/22.96 (demorgan2) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz13rule0) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz13rule1) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz13rule2) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz13rule3) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz13rule4) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz1_1) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz1_2) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz1_3) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz1_4) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz1_5) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1all2) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1SetBreln1) =>
% 132.79/22.96 ((
% 132.79/22.96 (choice2fnsingleton) =>
% 132.79/22.96 ((
% 132.79/22.96 (setOfPairsIsBReln1) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1all1) =>
% 132.79/22.96 ((
% 132.79/22.96 (subbreln1) =>
% 132.79/22.96 ((
% 132.79/22.96 (eqbreln1) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1invprop) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1invI) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1invE) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1compprop) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1compI) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1compE) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1compEex) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1unionprop) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1unionIL) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1unionIR) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1unionI) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1unionE) =>
% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
% 132.79/22.96 (woz2Ex) =>
% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
% 132.79/22.96 (woz2B) =>
% 132.79/22.96 ((
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% 132.79/22.96 ((
% 132.79/22.96 (image1Ex1) =>
% 132.79/22.96 ((
% 132.79/22.96 (image1Equiv) =>
% 132.79/22.96 ((
% 132.79/22.96 (image1E) =>
% 132.79/22.96 ((
% 132.79/22.96 (image1I) =>
% 132.79/22.96 ((
% 132.79/22.96 (injFuncInInjFuncSet) =>
% 132.79/22.96 ((
% 132.79/22.96 (injFuncSetFuncIn) =>
% 132.79/22.96 ((
% 132.79/22.96 (injFuncSetFuncInj) =>
% 132.79/22.96 ((
% 132.79/22.96 (surjFuncSetFuncIn) =>
% 132.79/22.96 ((
% 132.79/22.96 (surjFuncSetFuncSurj) =>
% 132.79/22.96 ((
% 132.79/22.96 (leftInvIsSurj) =>
% 132.79/22.96 ((
% 132.79/22.96 (surjCantorThm) =>
% 132.79/22.96 ((
% 132.79/22.96 (foundation2) =>
% 132.79/22.96 ((
% 132.79/22.96 (notinself) =>
% 132.79/22.96 ((
% 132.79/22.96 (notinself2) =>
% 132.79/22.96 ((
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% 132.79/22.96 ((
% 132.79/22.96 (omegaSclos) =>
% 132.79/22.96 ((
% 132.79/22.96 (peano0notS) =>
% 132.79/22.96 ((
% 132.79/22.96 (peanoSinj) =>
% 132.79/22.96 ((
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% 132.79/22.96 ((
% 132.79/22.96 (binintTransitive) =>
% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
% 132.79/22.96 (ordinalTransSet1) =>
% 132.79/22.96 ((
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% 132.79/22.96 (ordinal @
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% 132.79/22.96 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1202])).
% 132.79/22.96 thf(zip_derived_cl1212, plain,
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% 132.79/22.96 (((ubforcartprodlem1) =>
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% 132.79/22.96 (((setunionsingleton2) =>
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% 132.79/22.96 (((kfstsingleton) =>
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% 132.79/22.96 (((setukpairinjL) =>
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% 132.79/22.96 (((setukpairinjR12) =>
% 132.79/22.96 (((setukpairinjR1) =>
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% 132.79/22.96 ((
% 132.79/22.96 (ksndpairEq) =>
% 132.79/22.96 ((
% 132.79/22.96 (kpairsurjEq) =>
% 132.79/22.96 ((
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% 132.79/22.96 ((
% 132.79/22.96 (cartprodpairmemEL) =>
% 132.79/22.96 ((
% 132.79/22.96 (cartprodpairmemER) =>
% 132.79/22.96 ((
% 132.79/22.96 (cartprodmempaircEq) =>
% 132.79/22.96 ((
% 132.79/22.96 (cartprodfstpairEq) =>
% 132.79/22.96 ((
% 132.79/22.96 (cartprodsndpairEq) =>
% 132.79/22.96 ((
% 132.79/22.96 (cartprodpairsurjEq) =>
% 132.79/22.96 ((
% 132.79/22.96 (dpsetconstrI) =>
% 132.79/22.96 ((
% 132.79/22.96 (dpsetconstrSub) =>
% 132.79/22.96 ((
% 132.79/22.96 (setOfPairsIsBReln) =>
% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
% 132.79/22.96 (dpsetconstrEL2) =>
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% 132.79/22.96 ((
% 132.79/22.96 (lam2p) =>
% 132.79/22.96 ((
% 132.79/22.96 (brelnall1) =>
% 132.79/22.96 ((
% 132.79/22.96 (brelnall2) =>
% 132.79/22.96 ((
% 132.79/22.96 (ex1E2) =>
% 132.79/22.96 ((
% 132.79/22.96 (funcGraphProp1) =>
% 132.79/22.96 ((
% 132.79/22.96 (funcGraphProp3) =>
% 132.79/22.96 ((
% 132.79/22.96 (funcGraphProp2) =>
% 132.79/22.96 ((
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% 132.79/22.96 ((
% 132.79/22.96 (funcGraphProp4) =>
% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
% 132.79/22.96 (funcext2) =>
% 132.79/22.96 ((
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% 132.79/22.96 ((
% 132.79/22.96 (ap2apEq2) =>
% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
% 132.79/22.96 (lam2lamEq) =>
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% 132.79/22.96 ((
% 132.79/22.96 (iffalseProp2) =>
% 132.79/22.96 ((
% 132.79/22.96 (iftrueProp1) =>
% 132.79/22.96 ((
% 132.79/22.96 (iftrueProp2) =>
% 132.79/22.96 ((
% 132.79/22.96 (ifSingleton) =>
% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
% 132.79/22.96 (iftrue) =>
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% 132.79/22.96 ((
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% 132.79/22.96 (powersetT_lem) =>
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
% 132.79/22.96 (subsetTI) =>
% 132.79/22.96 ((
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% 132.79/22.96 ((
% 132.79/22.96 (powersetTE1) =>
% 132.79/22.96 ((
% 132.79/22.96 (complementTI1) =>
% 132.79/22.96 ((
% 132.79/22.96 (complementTE1) =>
% 132.79/22.96 ((
% 132.79/22.96 (binintersectTELcontra) =>
% 132.79/22.96 ((
% 132.79/22.96 (binintersectTERcontra) =>
% 132.79/22.96 ((
% 132.79/22.96 (contrasubsetT) =>
% 132.79/22.96 ((
% 132.79/22.96 (contrasubsetT1) =>
% 132.79/22.96 ((
% 132.79/22.96 (contrasubsetT2) =>
% 132.79/22.96 ((
% 132.79/22.96 (contrasubsetT3) =>
% 132.79/22.96 ((
% 132.79/22.96 (doubleComplementI1) =>
% 132.79/22.96 ((
% 132.79/22.96 (doubleComplementE1) =>
% 132.79/22.96 ((
% 132.79/22.96 (doubleComplementSub1) =>
% 132.79/22.96 ((
% 132.79/22.96 (doubleComplementSub2) =>
% 132.79/22.96 ((
% 132.79/22.96 (doubleComplementEq) =>
% 132.79/22.96 ((
% 132.79/22.96 (complementTnotintersectT) =>
% 132.79/22.96 ((
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% 132.79/22.96 ((
% 132.79/22.96 (complementSubsetComplementIntersect) =>
% 132.79/22.96 ((
% 132.79/22.96 (complementInPowersetComplementIntersect) =>
% 132.79/22.96 ((
% 132.79/22.96 (contraSubsetComplement) =>
% 132.79/22.96 ((
% 132.79/22.96 (complementTcontraSubset) =>
% 132.79/22.96 ((
% 132.79/22.96 (binunionTILcontra) =>
% 132.79/22.96 ((
% 132.79/22.96 (binunionTIRcontra) =>
% 132.79/22.96 ((
% 132.79/22.96 (inIntersectImpInUnion) =>
% 132.79/22.96 ((
% 132.79/22.96 (inIntersectImpInUnion2) =>
% 132.79/22.96 ((
% 132.79/22.96 (inIntersectImpInIntersectUnions) =>
% 132.79/22.96 ((
% 132.79/22.96 (intersectInPowersetIntersectUnions) =>
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% 132.79/22.96 (inComplementUnionImpNotIn1) =>
% 132.79/22.96 ((
% 132.79/22.96 (inComplementUnionImpInComplement1) =>
% 132.79/22.96 ((
% 132.79/22.96 (binunionTE) =>
% 132.79/22.96 ((
% 132.79/22.96 (binunionTEcontra) =>
% 132.79/22.96 ((
% 132.79/22.96 (demorgan2a1) =>
% 132.79/22.96 ((
% 132.79/22.96 (complementUnionInPowersetComplement) =>
% 132.79/22.96 ((
% 132.79/22.96 (demorgan2a2) =>
% 132.79/22.96 ((
% 132.79/22.96 (demorgan1a) =>
% 132.79/22.96 ((
% 132.79/22.96 (demorgan1b) =>
% 132.79/22.96 ((
% 132.79/22.96 (demorgan1) =>
% 132.79/22.96 ((
% 132.79/22.96 (demorgan2a) =>
% 132.79/22.96 ((
% 132.79/22.96 (demorgan2b2) =>
% 132.79/22.96 ((
% 132.79/22.96 (demorgan2b) =>
% 132.79/22.96 ((
% 132.79/22.96 (demorgan2) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz13rule0) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz13rule1) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz13rule2) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz13rule3) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz13rule4) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz1_1) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz1_2) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz1_3) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz1_4) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz1_5) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1all2) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1SetBreln1) =>
% 132.79/22.96 ((
% 132.79/22.96 (choice2fnsingleton) =>
% 132.79/22.96 ((
% 132.79/22.96 (setOfPairsIsBReln1) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1all1) =>
% 132.79/22.96 ((
% 132.79/22.96 (subbreln1) =>
% 132.79/22.96 ((
% 132.79/22.96 (eqbreln1) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1invprop) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1invI) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1invE) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1compprop) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1compI) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1compE) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1compEex) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1unionprop) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1unionIL) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1unionIR) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1unionI) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1unionE) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1unionEcases) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1unionCommutes) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz2Ex) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz2W) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz2A) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz2B) =>
% 132.79/22.96 ((
% 132.79/22.96 (image1Ex) =>
% 132.79/22.96 ((
% 132.79/22.96 (image1Ex1) =>
% 132.79/22.96 ((
% 132.79/22.96 (image1Equiv) =>
% 132.79/22.96 ((
% 132.79/22.96 (image1E) =>
% 132.79/22.96 ((
% 132.79/22.96 (image1I) =>
% 132.79/22.96 ((
% 132.79/22.96 (injFuncInInjFuncSet) =>
% 132.79/22.96 ((
% 132.79/22.96 (injFuncSetFuncIn) =>
% 132.79/22.96 ((
% 132.79/22.96 (injFuncSetFuncInj) =>
% 132.79/22.96 ((
% 132.79/22.96 (surjFuncSetFuncIn) =>
% 132.79/22.96 ((
% 132.79/22.96 (surjFuncSetFuncSurj) =>
% 132.79/22.96 ((
% 132.79/22.96 (leftInvIsSurj) =>
% 132.79/22.96 ((
% 132.79/22.96 (surjCantorThm) =>
% 132.79/22.96 ((
% 132.79/22.96 (foundation2) =>
% 132.79/22.96 ((
% 132.79/22.96 (notinself) =>
% 132.79/22.96 ((
% 132.79/22.96 (notinself2) =>
% 132.79/22.96 ((
% 132.79/22.96 (omegaSp) =>
% 132.79/22.96 ((
% 132.79/22.96 (omegaSclos) =>
% 132.79/22.96 ((
% 132.79/22.96 (peano0notS) =>
% 132.79/22.96 ((
% 132.79/22.96 (peanoSinj) =>
% 132.79/22.96 ((
% 132.79/22.96 (transitivesetOp1) =>
% 132.79/22.96 ((
% 132.79/22.96 (binintTransitive) =>
% 132.79/22.96 ((
% 132.79/22.96 (transitivesetOp2) =>
% 132.79/22.96 ((
% 132.79/22.96 (setunionTransitive) =>
% 132.79/22.96 ((
% 132.79/22.96 (ordinalMinLem1) =>
% 132.79/22.96 ((
% 132.79/22.96 (ordinalTransSet) =>
% 132.79/22.96 ((
% 132.79/22.96 (ordinalTransSet1) =>
% 132.79/22.96 ((
% 132.79/22.96 (setunionOrdinalLem1) =>
% 132.79/22.96 (ordinal @
% 132.79/22.96 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/22.96 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1207])).
% 132.79/22.96 thf(zip_derived_cl1218, plain,
% 132.79/22.96 (~ (((upairinpowunion) =>
% 132.79/22.96 (((ubforcartprodlem1) =>
% 132.79/22.96 (((ubforcartprodlem2) =>
% 132.79/22.96 (((ubforcartprodlem3) =>
% 132.79/22.96 (((cartprodpairin) =>
% 132.79/22.96 (((cartprodmempair1) =>
% 132.79/22.96 (((cartprodmempair) =>
% 132.79/22.96 (((setunionE2) =>
% 132.79/22.96 (((setunionsingleton1) =>
% 132.79/22.96 (((setunionsingleton2) =>
% 132.79/22.96 (((setunionsingleton) =>
% 132.79/22.96 (((singletonprop) =>
% 132.79/22.96 (((ex1E1) =>
% 132.79/22.96 (((ex1I) =>
% 132.79/22.96 (((ex1I2) =>
% 132.79/22.96 (((singletonsuniq) =>
% 132.79/22.96 (((setukpairinjL1) =>
% 132.79/22.96 (((kfstsingleton) =>
% 132.79/22.96 (((theprop) =>
% 132.79/22.96 (((kfstpairEq) =>
% 132.79/22.96 (((cartprodfstin) =>
% 132.79/22.96 (((setukpairinjL2) =>
% 132.79/22.96 (((setukpairinjL) =>
% 132.79/22.96 (((setukpairinjR11) =>
% 132.79/22.96 (((setukpairinjR12) =>
% 132.79/22.96 (((setukpairinjR1) =>
% 132.79/22.96 (((upairequniteq) =>
% 132.79/22.96 (((setukpairinjR2) =>
% 132.79/22.96 (((setukpairinjR) =>
% 132.79/22.96 (((ksndsingleton) =>
% 132.79/22.96 ((
% 132.79/22.96 (ksndpairEq) =>
% 132.79/22.96 ((
% 132.79/22.96 (kpairsurjEq) =>
% 132.79/22.96 ((
% 132.79/22.96 (cartprodsndin) =>
% 132.79/22.96 ((
% 132.79/22.96 (cartprodpairmemEL) =>
% 132.79/22.96 ((
% 132.79/22.96 (cartprodpairmemER) =>
% 132.79/22.96 ((
% 132.79/22.96 (cartprodmempaircEq) =>
% 132.79/22.96 ((
% 132.79/22.96 (cartprodfstpairEq) =>
% 132.79/22.96 ((
% 132.79/22.96 (cartprodsndpairEq) =>
% 132.79/22.96 ((
% 132.79/22.96 (cartprodpairsurjEq) =>
% 132.79/22.96 ((
% 132.79/22.96 (dpsetconstrI) =>
% 132.79/22.96 ((
% 132.79/22.96 (dpsetconstrSub) =>
% 132.79/22.96 ((
% 132.79/22.96 (setOfPairsIsBReln) =>
% 132.79/22.96 ((
% 132.79/22.96 (dpsetconstrERa) =>
% 132.79/22.96 ((
% 132.79/22.96 (dpsetconstrEL1) =>
% 132.79/22.96 ((
% 132.79/22.96 (dpsetconstrEL2) =>
% 132.79/22.96 ((
% 132.79/22.96 (dpsetconstrER) =>
% 132.79/22.96 ((
% 132.79/22.96 (funcImageSingleton) =>
% 132.79/22.96 ((
% 132.79/22.96 (apProp) =>
% 132.79/22.96 ((
% 132.79/22.96 (app) =>
% 132.79/22.96 ((
% 132.79/22.96 (infuncsetfunc) =>
% 132.79/22.96 ((
% 132.79/22.96 (ap2p) =>
% 132.79/22.96 ((
% 132.79/22.96 (funcinfuncset) =>
% 132.79/22.96 ((
% 132.79/22.96 (lamProp) =>
% 132.79/22.96 ((
% 132.79/22.96 (lamp) =>
% 132.79/22.96 ((
% 132.79/22.96 (lam2p) =>
% 132.79/22.96 ((
% 132.79/22.96 (brelnall1) =>
% 132.79/22.96 ((
% 132.79/22.96 (brelnall2) =>
% 132.79/22.96 ((
% 132.79/22.96 (ex1E2) =>
% 132.79/22.96 ((
% 132.79/22.96 (funcGraphProp1) =>
% 132.79/22.96 ((
% 132.79/22.96 (funcGraphProp3) =>
% 132.79/22.96 ((
% 132.79/22.96 (funcGraphProp2) =>
% 132.79/22.96 ((
% 132.79/22.96 (funcextLem) =>
% 132.79/22.96 ((
% 132.79/22.96 (funcGraphProp4) =>
% 132.79/22.96 ((
% 132.79/22.96 (subbreln) =>
% 132.79/22.96 ((
% 132.79/22.96 (eqbreln) =>
% 132.79/22.96 ((
% 132.79/22.96 (funcext) =>
% 132.79/22.96 ((
% 132.79/22.96 (funcext2) =>
% 132.79/22.96 ((
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% 132.79/22.96 ((
% 132.79/22.96 (ap2apEq2) =>
% 132.79/22.96 ((
% 132.79/22.96 (beta1) =>
% 132.79/22.96 ((
% 132.79/22.96 (eta1) =>
% 132.79/22.96 ((
% 132.79/22.96 (lam2lamEq) =>
% 132.79/22.96 ((
% 132.79/22.96 (beta2) =>
% 132.79/22.96 ((
% 132.79/22.96 (eta2) =>
% 132.79/22.96 ((
% 132.79/22.96 (iffalseProp1) =>
% 132.79/22.96 ((
% 132.79/22.96 (iffalseProp2) =>
% 132.79/22.96 ((
% 132.79/22.96 (iftrueProp1) =>
% 132.79/22.96 ((
% 132.79/22.96 (iftrueProp2) =>
% 132.79/22.96 ((
% 132.79/22.96 (ifSingleton) =>
% 132.79/22.96 ((
% 132.79/22.96 (ifp) =>
% 132.79/22.96 ((
% 132.79/22.96 (theeq) =>
% 132.79/22.96 ((
% 132.79/22.96 (iftrue) =>
% 132.79/22.96 ((
% 132.79/22.96 (iffalse) =>
% 132.79/22.96 ((
% 132.79/22.96 (iftrueorfalse) =>
% 132.79/22.96 ((
% 132.79/22.96 (binintersectT_lem) =>
% 132.79/22.96 ((
% 132.79/22.96 (binunionT_lem) =>
% 132.79/22.96 ((
% 132.79/22.96 (powersetT_lem) =>
% 132.79/22.96 ((
% 132.79/22.96 (setminusT_lem) =>
% 132.79/22.96 ((
% 132.79/22.96 (complementT_lem) =>
% 132.79/22.96 ((
% 132.79/22.96 (setextT) =>
% 132.79/22.96 ((
% 132.79/22.96 (subsetTI) =>
% 132.79/22.96 ((
% 132.79/22.96 (powersetTI1) =>
% 132.79/22.96 ((
% 132.79/22.96 (powersetTE1) =>
% 132.79/22.96 ((
% 132.79/22.96 (complementTI1) =>
% 132.79/22.96 ((
% 132.79/22.96 (complementTE1) =>
% 132.79/22.96 ((
% 132.79/22.96 (binintersectTELcontra) =>
% 132.79/22.96 ((
% 132.79/22.96 (binintersectTERcontra) =>
% 132.79/22.96 ((
% 132.79/22.96 (contrasubsetT) =>
% 132.79/22.96 ((
% 132.79/22.96 (contrasubsetT1) =>
% 132.79/22.96 ((
% 132.79/22.96 (contrasubsetT2) =>
% 132.79/22.96 ((
% 132.79/22.96 (contrasubsetT3) =>
% 132.79/22.96 ((
% 132.79/22.96 (doubleComplementI1) =>
% 132.79/22.96 ((
% 132.79/22.96 (doubleComplementE1) =>
% 132.79/22.96 ((
% 132.79/22.96 (doubleComplementSub1) =>
% 132.79/22.96 ((
% 132.79/22.96 (doubleComplementSub2) =>
% 132.79/22.96 ((
% 132.79/22.96 (doubleComplementEq) =>
% 132.79/22.96 ((
% 132.79/22.96 (complementTnotintersectT) =>
% 132.79/22.96 ((
% 132.79/22.96 (complementImpComplementIntersect) =>
% 132.79/22.96 ((
% 132.79/22.96 (complementSubsetComplementIntersect) =>
% 132.79/22.96 ((
% 132.79/22.96 (complementInPowersetComplementIntersect) =>
% 132.79/22.96 ((
% 132.79/22.96 (contraSubsetComplement) =>
% 132.79/22.96 ((
% 132.79/22.96 (complementTcontraSubset) =>
% 132.79/22.96 ((
% 132.79/22.96 (binunionTILcontra) =>
% 132.79/22.96 ((
% 132.79/22.96 (binunionTIRcontra) =>
% 132.79/22.96 ((
% 132.79/22.96 (inIntersectImpInUnion) =>
% 132.79/22.96 ((
% 132.79/22.96 (inIntersectImpInUnion2) =>
% 132.79/22.96 ((
% 132.79/22.96 (inIntersectImpInIntersectUnions) =>
% 132.79/22.96 ((
% 132.79/22.96 (intersectInPowersetIntersectUnions) =>
% 132.79/22.96 ((
% 132.79/22.96 (inComplementUnionImpNotIn1) =>
% 132.79/22.96 ((
% 132.79/22.96 (inComplementUnionImpInComplement1) =>
% 132.79/22.96 ((
% 132.79/22.96 (binunionTE) =>
% 132.79/22.96 ((
% 132.79/22.96 (binunionTEcontra) =>
% 132.79/22.96 ((
% 132.79/22.96 (demorgan2a1) =>
% 132.79/22.96 ((
% 132.79/22.96 (complementUnionInPowersetComplement) =>
% 132.79/22.96 ((
% 132.79/22.96 (demorgan2a2) =>
% 132.79/22.96 ((
% 132.79/22.96 (demorgan1a) =>
% 132.79/22.96 ((
% 132.79/22.96 (demorgan1b) =>
% 132.79/22.96 ((
% 132.79/22.96 (demorgan1) =>
% 132.79/22.96 ((
% 132.79/22.96 (demorgan2a) =>
% 132.79/22.96 ((
% 132.79/22.96 (demorgan2b2) =>
% 132.79/22.96 ((
% 132.79/22.96 (demorgan2b) =>
% 132.79/22.96 ((
% 132.79/22.96 (demorgan2) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz13rule0) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz13rule1) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz13rule2) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz13rule3) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz13rule4) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz1_1) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz1_2) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz1_3) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz1_4) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz1_5) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1all2) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1SetBreln1) =>
% 132.79/22.96 ((
% 132.79/22.96 (choice2fnsingleton) =>
% 132.79/22.96 ((
% 132.79/22.96 (setOfPairsIsBReln1) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1all1) =>
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% 132.79/22.96 (subbreln1) =>
% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
% 132.79/22.96 (breln1invI) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1invE) =>
% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
% 132.79/22.96 (breln1unionIR) =>
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% 132.79/22.96 (breln1unionE) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1unionEcases) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1unionCommutes) =>
% 132.79/22.96 ((
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% 132.79/22.96 ((
% 132.79/22.96 (woz2W) =>
% 132.79/22.96 ((
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% 132.79/22.96 ((
% 132.79/22.96 (woz2B) =>
% 132.79/22.96 ((
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% 132.79/22.96 ((
% 132.79/22.96 (image1Ex1) =>
% 132.79/22.96 ((
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% 132.79/22.96 ((
% 132.79/22.96 (image1E) =>
% 132.79/22.96 ((
% 132.79/22.96 (image1I) =>
% 132.79/22.96 ((
% 132.79/22.96 (injFuncInInjFuncSet) =>
% 132.79/22.96 ((
% 132.79/22.96 (injFuncSetFuncIn) =>
% 132.79/22.96 ((
% 132.79/22.96 (injFuncSetFuncInj) =>
% 132.79/22.96 ((
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% 132.79/22.96 ((
% 132.79/22.96 (surjFuncSetFuncSurj) =>
% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1212])).
% 132.79/22.96 thf(zip_derived_cl1224, plain,
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% 132.79/22.96 ((
% 132.79/22.96 (cartprodpairmemER) =>
% 132.79/22.96 ((
% 132.79/22.96 (cartprodmempaircEq) =>
% 132.79/22.96 ((
% 132.79/22.96 (cartprodfstpairEq) =>
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% 132.79/22.96 (cartprodsndpairEq) =>
% 132.79/22.96 ((
% 132.79/22.96 (cartprodpairsurjEq) =>
% 132.79/22.96 ((
% 132.79/22.96 (dpsetconstrI) =>
% 132.79/22.96 ((
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% 132.79/22.96 ((
% 132.79/22.96 (doubleComplementE1) =>
% 132.79/22.96 ((
% 132.79/22.96 (doubleComplementSub1) =>
% 132.79/22.96 ((
% 132.79/22.96 (doubleComplementSub2) =>
% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
% 132.79/22.96 (complementInPowersetComplementIntersect) =>
% 132.79/22.96 ((
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% 132.79/22.96 ((
% 132.79/22.96 (complementTcontraSubset) =>
% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
% 132.79/22.96 (demorgan2a) =>
% 132.79/22.96 ((
% 132.79/22.96 (demorgan2b2) =>
% 132.79/22.96 ((
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% 132.79/22.96 ((
% 132.79/22.96 (demorgan2) =>
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
% 132.79/22.96 (brelnall1) =>
% 132.79/22.96 ((
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% 132.79/22.96 ((
% 132.79/22.96 (binintersectTERcontra) =>
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% 132.79/22.96 (contrasubsetT3) =>
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% 132.79/22.96 (doubleComplementE1) =>
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
% 132.79/22.96 (demorgan1b) =>
% 132.79/22.96 ((
% 132.79/22.96 (demorgan1) =>
% 132.79/22.96 ((
% 132.79/22.96 (demorgan2a) =>
% 132.79/22.96 ((
% 132.79/22.96 (demorgan2b2) =>
% 132.79/22.96 ((
% 132.79/22.96 (demorgan2b) =>
% 132.79/22.96 ((
% 132.79/22.96 (demorgan2) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz13rule0) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz13rule1) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz13rule2) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz13rule3) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz13rule4) =>
% 132.79/22.96 ((
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% 132.79/22.96 ((
% 132.79/22.96 (woz1_2) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz1_3) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz1_4) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz1_5) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1all2) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1SetBreln1) =>
% 132.79/22.96 ((
% 132.79/22.96 (choice2fnsingleton) =>
% 132.79/22.96 ((
% 132.79/22.96 (setOfPairsIsBReln1) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1all1) =>
% 132.79/22.96 ((
% 132.79/22.96 (subbreln1) =>
% 132.79/22.96 ((
% 132.79/22.96 (eqbreln1) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1invprop) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1invI) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1invE) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1compprop) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1compI) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1compE) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1compEex) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1unionprop) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1unionIL) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1unionIR) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1unionI) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1unionE) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1unionEcases) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1unionCommutes) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz2Ex) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz2W) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz2A) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz2B) =>
% 132.79/22.96 ((
% 132.79/22.96 (image1Ex) =>
% 132.79/22.96 ((
% 132.79/22.96 (image1Ex1) =>
% 132.79/22.96 ((
% 132.79/22.96 (image1Equiv) =>
% 132.79/22.96 ((
% 132.79/22.96 (image1E) =>
% 132.79/22.96 ((
% 132.79/22.96 (image1I) =>
% 132.79/22.96 ((
% 132.79/22.96 (injFuncInInjFuncSet) =>
% 132.79/22.96 ((
% 132.79/22.96 (injFuncSetFuncIn) =>
% 132.79/22.96 ((
% 132.79/22.96 (injFuncSetFuncInj) =>
% 132.79/22.96 ((
% 132.79/22.96 (surjFuncSetFuncIn) =>
% 132.79/22.96 ((
% 132.79/22.96 (surjFuncSetFuncSurj) =>
% 132.79/22.96 ((
% 132.79/22.96 (leftInvIsSurj) =>
% 132.79/22.96 ((
% 132.79/22.96 (surjCantorThm) =>
% 132.79/22.96 ((
% 132.79/22.96 (foundation2) =>
% 132.79/22.96 ((
% 132.79/22.96 (notinself) =>
% 132.79/22.96 ((
% 132.79/22.96 (notinself2) =>
% 132.79/22.96 ((
% 132.79/22.96 (omegaSp) =>
% 132.79/22.96 ((
% 132.79/22.96 (omegaSclos) =>
% 132.79/22.96 ((
% 132.79/22.96 (peano0notS) =>
% 132.79/22.96 ((
% 132.79/22.96 (peanoSinj) =>
% 132.79/22.96 ((
% 132.79/22.96 (transitivesetOp1) =>
% 132.79/22.96 ((
% 132.79/22.96 (binintTransitive) =>
% 132.79/22.96 ((
% 132.79/22.96 (transitivesetOp2) =>
% 132.79/22.96 ((
% 132.79/22.96 (setunionTransitive) =>
% 132.79/22.96 ((
% 132.79/22.96 (ordinalMinLem1) =>
% 132.79/22.96 ((
% 132.79/22.96 (ordinalTransSet) =>
% 132.79/22.96 ((
% 132.79/22.96 (ordinalTransSet1) =>
% 132.79/22.96 ((
% 132.79/22.96 (setunionOrdinalLem1) =>
% 132.79/22.96 (ordinal @
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% 132.79/22.96 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1224])).
% 132.79/22.96 thf(zip_derived_cl1237, plain,
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% 132.79/22.96 (((setunionE2) =>
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% 132.79/22.96 (((setunionsingleton) =>
% 132.79/22.96 (((singletonprop) =>
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% 132.79/22.96 (((ex1I2) =>
% 132.79/22.96 (((singletonsuniq) =>
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% 132.79/22.96 (((kfstsingleton) =>
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% 132.79/22.96 (((setukpairinjR12) =>
% 132.79/22.96 (((setukpairinjR1) =>
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% 132.79/22.96 (((kpairsurjEq) =>
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% 132.79/22.96 ((
% 132.79/22.96 (cartprodpairmemEL) =>
% 132.79/22.96 ((
% 132.79/22.96 (cartprodpairmemER) =>
% 132.79/22.96 ((
% 132.79/22.96 (cartprodmempaircEq) =>
% 132.79/22.96 ((
% 132.79/22.96 (cartprodfstpairEq) =>
% 132.79/22.96 ((
% 132.79/22.96 (cartprodsndpairEq) =>
% 132.79/22.96 ((
% 132.79/22.96 (cartprodpairsurjEq) =>
% 132.79/22.96 ((
% 132.79/22.96 (dpsetconstrI) =>
% 132.79/22.96 ((
% 132.79/22.96 (dpsetconstrSub) =>
% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
% 132.79/22.96 (dpsetconstrEL2) =>
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% 132.79/22.96 (dpsetconstrER) =>
% 132.79/22.96 ((
% 132.79/22.96 (funcImageSingleton) =>
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 (ap2apEq2) =>
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% 132.79/22.96 ((
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% 132.79/22.96 ((
% 132.79/22.96 (powersetT_lem) =>
% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 (contrasubsetT3) =>
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% 132.79/22.96 (doubleComplementI1) =>
% 132.79/22.96 ((
% 132.79/22.96 (doubleComplementE1) =>
% 132.79/22.96 ((
% 132.79/22.96 (doubleComplementSub1) =>
% 132.79/22.96 ((
% 132.79/22.96 (doubleComplementSub2) =>
% 132.79/22.96 ((
% 132.79/22.96 (doubleComplementEq) =>
% 132.79/22.96 ((
% 132.79/22.96 (complementTnotintersectT) =>
% 132.79/22.96 ((
% 132.79/22.96 (complementImpComplementIntersect) =>
% 132.79/22.96 ((
% 132.79/22.96 (complementSubsetComplementIntersect) =>
% 132.79/22.96 ((
% 132.79/22.96 (complementInPowersetComplementIntersect) =>
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% 132.79/22.96 (contraSubsetComplement) =>
% 132.79/22.96 ((
% 132.79/22.96 (complementTcontraSubset) =>
% 132.79/22.96 ((
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% 132.79/22.96 ((
% 132.79/22.96 (binunionTIRcontra) =>
% 132.79/22.96 ((
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% 132.79/22.96 ((
% 132.79/22.96 (inIntersectImpInUnion2) =>
% 132.79/22.96 ((
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% 132.79/22.96 ((
% 132.79/22.96 (intersectInPowersetIntersectUnions) =>
% 132.79/22.96 ((
% 132.79/22.96 (inComplementUnionImpNotIn1) =>
% 132.79/22.96 ((
% 132.79/22.96 (inComplementUnionImpInComplement1) =>
% 132.79/22.96 ((
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% 132.79/22.96 ((
% 132.79/22.96 (binunionTEcontra) =>
% 132.79/22.96 ((
% 132.79/22.96 (demorgan2a1) =>
% 132.79/22.96 ((
% 132.79/22.96 (complementUnionInPowersetComplement) =>
% 132.79/22.96 ((
% 132.79/22.96 (demorgan2a2) =>
% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 (demorgan2b) =>
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% 132.79/22.96 (woz1_5) =>
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% 132.79/22.96 ((
% 132.79/22.96 (breln1invE) =>
% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
% 132.79/22.96 (breln1compE) =>
% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
% 132.79/22.96 (breln1unionIR) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1unionI) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1unionE) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1unionEcases) =>
% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
% 132.79/22.96 (image1E) =>
% 132.79/22.96 ((
% 132.79/22.96 (image1I) =>
% 132.79/22.96 ((
% 132.79/22.96 (injFuncInInjFuncSet) =>
% 132.79/22.96 ((
% 132.79/22.96 (injFuncSetFuncIn) =>
% 132.79/22.96 ((
% 132.79/22.96 (injFuncSetFuncInj) =>
% 132.79/22.96 ((
% 132.79/22.96 (surjFuncSetFuncIn) =>
% 132.79/22.96 ((
% 132.79/22.96 (surjFuncSetFuncSurj) =>
% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1230])).
% 132.79/22.96 thf(zip_derived_cl1244, plain,
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% 132.79/22.96 (cartprodmempaircEq) =>
% 132.79/22.96 ((
% 132.79/22.96 (cartprodfstpairEq) =>
% 132.79/22.96 ((
% 132.79/22.96 (cartprodsndpairEq) =>
% 132.79/22.96 ((
% 132.79/22.96 (cartprodpairsurjEq) =>
% 132.79/22.96 ((
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% 132.79/22.96 ((
% 132.79/22.96 (dpsetconstrSub) =>
% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
% 132.79/22.96 (binintersectTERcontra) =>
% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 (contrasubsetT2) =>
% 132.79/22.96 ((
% 132.79/22.96 (contrasubsetT3) =>
% 132.79/22.96 ((
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% 132.79/22.96 ((
% 132.79/22.96 (doubleComplementE1) =>
% 132.79/22.96 ((
% 132.79/22.96 (doubleComplementSub1) =>
% 132.79/22.96 ((
% 132.79/22.96 (doubleComplementSub2) =>
% 132.79/22.96 ((
% 132.79/22.96 (doubleComplementEq) =>
% 132.79/22.96 ((
% 132.79/22.96 (complementTnotintersectT) =>
% 132.79/22.96 ((
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% 132.79/22.96 ((
% 132.79/22.96 (complementSubsetComplementIntersect) =>
% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
% 132.79/22.96 (binunionTIRcontra) =>
% 132.79/22.96 ((
% 132.79/22.96 (inIntersectImpInUnion) =>
% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
% 132.79/22.96 (inComplementUnionImpInComplement1) =>
% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
% 132.79/22.96 (complementUnionInPowersetComplement) =>
% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
% 132.79/22.96 (demorgan2b2) =>
% 132.79/22.96 ((
% 132.79/22.96 (demorgan2b) =>
% 132.79/22.96 ((
% 132.79/22.96 (demorgan2) =>
% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 (contrasubsetT3) =>
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
% 132.79/22.96 (demorgan1b) =>
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% 132.79/22.96 ((
% 132.79/22.96 (demorgan2a) =>
% 132.79/22.96 ((
% 132.79/22.96 (demorgan2b2) =>
% 132.79/22.96 ((
% 132.79/22.96 (demorgan2b) =>
% 132.79/22.96 ((
% 132.79/22.96 (demorgan2) =>
% 132.79/22.96 ((
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% 132.79/22.96 ((
% 132.79/22.96 (woz13rule1) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz13rule2) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz13rule3) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz13rule4) =>
% 132.79/22.96 ((
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% 132.79/22.96 ((
% 132.79/22.96 (woz1_2) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz1_3) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz1_4) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz1_5) =>
% 132.79/22.96 ((
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% 132.79/22.96 ((
% 132.79/22.96 (breln1SetBreln1) =>
% 132.79/22.96 ((
% 132.79/22.96 (choice2fnsingleton) =>
% 132.79/22.96 ((
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% 132.79/22.96 ((
% 132.79/22.96 (breln1all1) =>
% 132.79/22.96 ((
% 132.79/22.96 (subbreln1) =>
% 132.79/22.96 ((
% 132.79/22.96 (eqbreln1) =>
% 132.79/22.96 ((
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% 132.79/22.96 ((
% 132.79/22.96 (breln1invI) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1invE) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1compprop) =>
% 132.79/22.96 ((
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% 132.79/22.96 ((
% 132.79/22.96 (breln1compE) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1compEex) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1unionprop) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1unionIL) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1unionIR) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1unionI) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1unionE) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1unionEcases) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1unionCommutes) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz2Ex) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz2W) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz2A) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz2B) =>
% 132.79/22.96 ((
% 132.79/22.96 (image1Ex) =>
% 132.79/22.96 ((
% 132.79/22.96 (image1Ex1) =>
% 132.79/22.96 ((
% 132.79/22.96 (image1Equiv) =>
% 132.79/22.96 ((
% 132.79/22.96 (image1E) =>
% 132.79/22.96 ((
% 132.79/22.96 (image1I) =>
% 132.79/22.96 ((
% 132.79/22.96 (injFuncInInjFuncSet) =>
% 132.79/22.96 ((
% 132.79/22.96 (injFuncSetFuncIn) =>
% 132.79/22.96 ((
% 132.79/22.96 (injFuncSetFuncInj) =>
% 132.79/22.96 ((
% 132.79/22.96 (surjFuncSetFuncIn) =>
% 132.79/22.96 ((
% 132.79/22.96 (surjFuncSetFuncSurj) =>
% 132.79/22.96 ((
% 132.79/22.96 (leftInvIsSurj) =>
% 132.79/22.96 ((
% 132.79/22.96 (surjCantorThm) =>
% 132.79/22.96 ((
% 132.79/22.96 (foundation2) =>
% 132.79/22.96 ((
% 132.79/22.96 (notinself) =>
% 132.79/22.96 ((
% 132.79/22.96 (notinself2) =>
% 132.79/22.96 ((
% 132.79/22.96 (omegaSp) =>
% 132.79/22.96 ((
% 132.79/22.96 (omegaSclos) =>
% 132.79/22.96 ((
% 132.79/22.96 (peano0notS) =>
% 132.79/22.96 ((
% 132.79/22.96 (peanoSinj) =>
% 132.79/22.96 ((
% 132.79/22.96 (transitivesetOp1) =>
% 132.79/22.96 ((
% 132.79/22.96 (binintTransitive) =>
% 132.79/22.96 ((
% 132.79/22.96 (transitivesetOp2) =>
% 132.79/22.96 ((
% 132.79/22.96 (setunionTransitive) =>
% 132.79/22.96 ((
% 132.79/22.96 (ordinalMinLem1) =>
% 132.79/22.96 ((
% 132.79/22.96 (ordinalTransSet) =>
% 132.79/22.96 ((
% 132.79/22.96 (ordinalTransSet1) =>
% 132.79/22.96 ((
% 132.79/22.96 (setunionOrdinalLem1) =>
% 132.79/22.96 (ordinal @
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% 132.79/22.96 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1244])).
% 132.79/22.96 thf(zip_derived_cl1261, plain,
% 132.79/22.96 (~ (((cartprodmempair) =>
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% 132.79/22.96 (((ex1I2) =>
% 132.79/22.96 (((singletonsuniq) =>
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% 132.79/22.96 (((cartprodfstin) =>
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% 132.79/22.96 (((setukpairinjR1) =>
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% 132.79/22.96 (((setukpairinjR) =>
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% 132.79/22.96 (((kpairsurjEq) =>
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% 132.79/22.96 (((cartprodpairmemER) =>
% 132.79/22.96 (((cartprodmempaircEq) =>
% 132.79/22.96 ((
% 132.79/22.96 (cartprodfstpairEq) =>
% 132.79/22.96 ((
% 132.79/22.96 (cartprodsndpairEq) =>
% 132.79/22.96 ((
% 132.79/22.96 (cartprodpairsurjEq) =>
% 132.79/22.96 ((
% 132.79/22.96 (dpsetconstrI) =>
% 132.79/22.96 ((
% 132.79/22.96 (dpsetconstrSub) =>
% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 (funcImageSingleton) =>
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% 132.79/22.96 (apProp) =>
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% 132.79/22.96 ((
% 132.79/22.96 (infuncsetfunc) =>
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% 132.79/22.96 ((
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% 132.79/22.96 (doubleComplementSub2) =>
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% 132.79/22.96 ((
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% 132.79/22.96 ((
% 132.79/22.96 (complementSubsetComplementIntersect) =>
% 132.79/22.96 ((
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% 132.79/22.96 ((
% 132.79/22.96 (contraSubsetComplement) =>
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% 132.79/22.96 ((
% 132.79/22.96 (inIntersectImpInUnion2) =>
% 132.79/22.96 ((
% 132.79/22.96 (inIntersectImpInIntersectUnions) =>
% 132.79/22.96 ((
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% 132.79/22.96 (inComplementUnionImpInComplement1) =>
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% 132.79/22.96 ((
% 132.79/22.96 (binunionTEcontra) =>
% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 thf(zip_derived_cl1270, plain,
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
% 132.79/22.96 (demorgan1b) =>
% 132.79/22.96 ((
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% 132.79/22.96 ((
% 132.79/22.96 (demorgan2a) =>
% 132.79/22.96 ((
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% 132.79/22.96 ((
% 132.79/22.96 (demorgan2b) =>
% 132.79/22.96 ((
% 132.79/22.96 (demorgan2) =>
% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
% 132.79/22.96 (image1E) =>
% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
% 132.79/22.96 (injFuncSetFuncInj) =>
% 132.79/22.96 ((
% 132.79/22.96 (surjFuncSetFuncIn) =>
% 132.79/22.96 ((
% 132.79/22.96 (surjFuncSetFuncSurj) =>
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
% 132.79/22.96 (peano0notS) =>
% 132.79/22.96 ((
% 132.79/22.96 (peanoSinj) =>
% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
% 132.79/22.96 (setunionTransitive) =>
% 132.79/22.96 ((
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% 132.79/22.96 ((
% 132.79/22.96 (ordinalTransSet) =>
% 132.79/22.96 ((
% 132.79/22.96 (ordinalTransSet1) =>
% 132.79/22.96 ((
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% 132.79/22.96 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1279])).
% 132.79/22.96 thf(zip_derived_cl1297, plain,
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% 132.79/22.96 (((kfstsingleton) =>
% 132.79/22.96 (((theprop) =>
% 132.79/22.96 (((kfstpairEq) =>
% 132.79/22.96 (((cartprodfstin) =>
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% 132.79/22.96 (((setukpairinjL) =>
% 132.79/22.96 (((setukpairinjR11) =>
% 132.79/22.96 (((setukpairinjR12) =>
% 132.79/22.96 (((setukpairinjR1) =>
% 132.79/22.96 (((upairequniteq) =>
% 132.79/22.96 (((setukpairinjR2) =>
% 132.79/22.96 (((setukpairinjR) =>
% 132.79/22.96 (((ksndsingleton) =>
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% 132.79/22.96 (((kpairsurjEq) =>
% 132.79/22.96 (((cartprodsndin) =>
% 132.79/22.96 (((cartprodpairmemEL) =>
% 132.79/22.96 (((cartprodpairmemER) =>
% 132.79/22.96 (((cartprodmempaircEq) =>
% 132.79/22.96 (((cartprodfstpairEq) =>
% 132.79/22.96 (((cartprodsndpairEq) =>
% 132.79/22.96 (((cartprodpairsurjEq) =>
% 132.79/22.96 (((dpsetconstrI) =>
% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
% 132.79/22.96 (ap2p) =>
% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
% 132.79/22.96 (lam2p) =>
% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
% 132.79/22.96 (iftrue) =>
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
% 132.79/22.96 (complementTE1) =>
% 132.79/22.96 ((
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% 132.79/22.96 ((
% 132.79/22.96 (binintersectTERcontra) =>
% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
% 132.79/22.96 (contrasubsetT3) =>
% 132.79/22.96 ((
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% 132.79/22.96 ((
% 132.79/22.96 (doubleComplementE1) =>
% 132.79/22.96 ((
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% 132.79/22.96 ((
% 132.79/22.96 (doubleComplementSub2) =>
% 132.79/22.96 ((
% 132.79/22.96 (doubleComplementEq) =>
% 132.79/22.96 ((
% 132.79/22.96 (complementTnotintersectT) =>
% 132.79/22.96 ((
% 132.79/22.96 (complementImpComplementIntersect) =>
% 132.79/22.96 ((
% 132.79/22.96 (complementSubsetComplementIntersect) =>
% 132.79/22.96 ((
% 132.79/22.96 (complementInPowersetComplementIntersect) =>
% 132.79/22.96 ((
% 132.79/22.96 (contraSubsetComplement) =>
% 132.79/22.96 ((
% 132.79/22.96 (complementTcontraSubset) =>
% 132.79/22.96 ((
% 132.79/22.96 (binunionTILcontra) =>
% 132.79/22.96 ((
% 132.79/22.96 (binunionTIRcontra) =>
% 132.79/22.96 ((
% 132.79/22.96 (inIntersectImpInUnion) =>
% 132.79/22.96 ((
% 132.79/22.96 (inIntersectImpInUnion2) =>
% 132.79/22.96 ((
% 132.79/22.96 (inIntersectImpInIntersectUnions) =>
% 132.79/22.96 ((
% 132.79/22.96 (intersectInPowersetIntersectUnions) =>
% 132.79/22.96 ((
% 132.79/22.96 (inComplementUnionImpNotIn1) =>
% 132.79/22.96 ((
% 132.79/22.96 (inComplementUnionImpInComplement1) =>
% 132.79/22.96 ((
% 132.79/22.96 (binunionTE) =>
% 132.79/22.96 ((
% 132.79/22.96 (binunionTEcontra) =>
% 132.79/22.96 ((
% 132.79/22.96 (demorgan2a1) =>
% 132.79/22.96 ((
% 132.79/22.96 (complementUnionInPowersetComplement) =>
% 132.79/22.96 ((
% 132.79/22.96 (demorgan2a2) =>
% 132.79/22.96 ((
% 132.79/22.96 (demorgan1a) =>
% 132.79/22.96 ((
% 132.79/22.96 (demorgan1b) =>
% 132.79/22.96 ((
% 132.79/22.96 (demorgan1) =>
% 132.79/22.96 ((
% 132.79/22.96 (demorgan2a) =>
% 132.79/22.96 ((
% 132.79/22.96 (demorgan2b2) =>
% 132.79/22.96 ((
% 132.79/22.96 (demorgan2b) =>
% 132.79/22.96 ((
% 132.79/22.96 (demorgan2) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz13rule0) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz13rule1) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz13rule2) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz13rule3) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz13rule4) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz1_1) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz1_2) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz1_3) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz1_4) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz1_5) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1all2) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1SetBreln1) =>
% 132.79/22.96 ((
% 132.79/22.96 (choice2fnsingleton) =>
% 132.79/22.96 ((
% 132.79/22.96 (setOfPairsIsBReln1) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1all1) =>
% 132.79/22.96 ((
% 132.79/22.96 (subbreln1) =>
% 132.79/22.96 ((
% 132.79/22.96 (eqbreln1) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1invprop) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1invI) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1invE) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1compprop) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1compI) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1compE) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1compEex) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1unionprop) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1unionIL) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1unionIR) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1unionI) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1unionE) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1unionEcases) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1unionCommutes) =>
% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
% 132.79/22.96 (image1E) =>
% 132.79/22.96 ((
% 132.79/22.96 (image1I) =>
% 132.79/22.96 ((
% 132.79/22.96 (injFuncInInjFuncSet) =>
% 132.79/22.96 ((
% 132.79/22.96 (injFuncSetFuncIn) =>
% 132.79/22.96 ((
% 132.79/22.96 (injFuncSetFuncInj) =>
% 132.79/22.96 ((
% 132.79/22.96 (surjFuncSetFuncIn) =>
% 132.79/22.96 ((
% 132.79/22.96 (surjFuncSetFuncSurj) =>
% 132.79/22.96 ((
% 132.79/22.96 (leftInvIsSurj) =>
% 132.79/22.96 ((
% 132.79/22.96 (surjCantorThm) =>
% 132.79/22.96 ((
% 132.79/22.96 (foundation2) =>
% 132.79/22.96 ((
% 132.79/22.96 (notinself) =>
% 132.79/22.96 ((
% 132.79/22.96 (notinself2) =>
% 132.79/22.96 ((
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% 132.79/22.96 ((
% 132.79/22.96 (omegaSclos) =>
% 132.79/22.96 ((
% 132.79/22.96 (peano0notS) =>
% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 ((
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% 132.79/22.96 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1288])).
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% 132.79/22.96 (complementInPowersetComplementIntersect) =>
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% 132.79/22.96 (contraSubsetComplement) =>
% 132.79/22.96 ((
% 132.79/22.96 (complementTcontraSubset) =>
% 132.79/22.96 ((
% 132.79/22.96 (binunionTILcontra) =>
% 132.79/22.96 ((
% 132.79/22.96 (binunionTIRcontra) =>
% 132.79/22.96 ((
% 132.79/22.96 (inIntersectImpInUnion) =>
% 132.79/22.96 ((
% 132.79/22.96 (inIntersectImpInUnion2) =>
% 132.79/22.96 ((
% 132.79/22.96 (inIntersectImpInIntersectUnions) =>
% 132.79/22.96 ((
% 132.79/22.96 (intersectInPowersetIntersectUnions) =>
% 132.79/22.96 ((
% 132.79/22.96 (inComplementUnionImpNotIn1) =>
% 132.79/22.96 ((
% 132.79/22.96 (inComplementUnionImpInComplement1) =>
% 132.79/22.96 ((
% 132.79/22.96 (binunionTE) =>
% 132.79/22.96 ((
% 132.79/22.96 (binunionTEcontra) =>
% 132.79/22.96 ((
% 132.79/22.96 (demorgan2a1) =>
% 132.79/22.96 ((
% 132.79/22.96 (complementUnionInPowersetComplement) =>
% 132.79/22.96 ((
% 132.79/22.96 (demorgan2a2) =>
% 132.79/22.96 ((
% 132.79/22.96 (demorgan1a) =>
% 132.79/22.96 ((
% 132.79/22.96 (demorgan1b) =>
% 132.79/22.96 ((
% 132.79/22.96 (demorgan1) =>
% 132.79/22.96 ((
% 132.79/22.96 (demorgan2a) =>
% 132.79/22.96 ((
% 132.79/22.96 (demorgan2b2) =>
% 132.79/22.96 ((
% 132.79/22.96 (demorgan2b) =>
% 132.79/22.96 ((
% 132.79/22.96 (demorgan2) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz13rule0) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz13rule1) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz13rule2) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz13rule3) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz13rule4) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz1_1) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz1_2) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz1_3) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz1_4) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz1_5) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1all2) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1SetBreln1) =>
% 132.79/22.96 ((
% 132.79/22.96 (choice2fnsingleton) =>
% 132.79/22.96 ((
% 132.79/22.96 (setOfPairsIsBReln1) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1all1) =>
% 132.79/22.96 ((
% 132.79/22.96 (subbreln1) =>
% 132.79/22.96 ((
% 132.79/22.96 (eqbreln1) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1invprop) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1invI) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1invE) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1compprop) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1compI) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1compE) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1compEex) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1unionprop) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1unionIL) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1unionIR) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1unionI) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1unionE) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1unionEcases) =>
% 132.79/22.96 ((
% 132.79/22.96 (breln1unionCommutes) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz2Ex) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz2W) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz2A) =>
% 132.79/22.96 ((
% 132.79/22.96 (woz2B) =>
% 132.79/22.96 ((
% 132.79/22.96 (image1Ex) =>
% 132.79/22.96 ((
% 132.79/22.96 (image1Ex1) =>
% 132.79/22.96 ((
% 132.79/22.96 (image1Equiv) =>
% 132.79/22.96 ((
% 132.79/22.96 (image1E) =>
% 132.79/22.96 ((
% 132.79/22.96 (image1I) =>
% 132.79/22.96 ((
% 132.79/22.96 (injFuncInInjFuncSet) =>
% 132.79/22.96 ((
% 132.79/22.96 (injFuncSetFuncIn) =>
% 132.79/22.96 ((
% 132.79/22.96 (injFuncSetFuncInj) =>
% 132.79/22.96 ((
% 132.79/22.96 (surjFuncSetFuncIn) =>
% 132.79/22.96 ((
% 132.79/22.96 (surjFuncSetFuncSurj) =>
% 132.79/22.96 ((
% 132.79/22.96 (leftInvIsSurj) =>
% 132.79/22.96 ((
% 132.79/22.96 (surjCantorThm) =>
% 132.79/22.96 ((
% 132.79/22.96 (foundation2) =>
% 132.79/22.96 ((
% 132.79/22.96 (notinself) =>
% 132.79/22.96 ((
% 132.79/22.96 (notinself2) =>
% 132.79/22.96 ((
% 132.79/22.96 (omegaSp) =>
% 132.79/22.96 ((
% 132.79/22.96 (omegaSclos) =>
% 132.79/22.96 ((
% 132.79/22.96 (peano0notS) =>
% 132.79/22.96 ((
% 132.79/22.96 (peanoSinj) =>
% 132.79/22.96 ((
% 132.79/22.96 (transitivesetOp1) =>
% 132.79/22.96 ((
% 132.79/22.96 (binintTransitive) =>
% 132.79/22.96 ((
% 132.79/22.96 (transitivesetOp2) =>
% 132.79/22.96 ((
% 132.79/22.96 (setunionTransitive) =>
% 132.79/22.96 ((
% 132.79/22.96 (ordinalMinLem1) =>
% 132.79/22.96 ((
% 132.79/22.96 (ordinalTransSet) =>
% 132.79/22.96 ((
% 132.79/22.96 (ordinalTransSet1) =>
% 132.79/22.96 ((
% 132.79/22.96 (setunionOrdinalLem1) =>
% 132.79/22.96 (ordinal @
% 132.79/22.96 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/22.96 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1297])).
% 132.79/22.96 thf(zip_derived_cl1314, plain,
% 132.79/22.96 (~ (((ex1E1) =>
% 132.79/22.96 (((ex1I) =>
% 132.79/22.96 (((ex1I2) =>
% 132.79/22.96 (((singletonsuniq) =>
% 132.79/22.96 (((setukpairinjL1) =>
% 132.79/22.96 (((kfstsingleton) =>
% 132.79/22.96 (((theprop) =>
% 132.79/22.96 (((kfstpairEq) =>
% 132.79/22.96 (((cartprodfstin) =>
% 132.79/22.96 (((setukpairinjL2) =>
% 132.79/22.96 (((setukpairinjL) =>
% 132.79/22.96 (((setukpairinjR11) =>
% 132.79/22.96 (((setukpairinjR12) =>
% 132.79/22.96 (((setukpairinjR1) =>
% 132.79/22.96 (((upairequniteq) =>
% 132.79/22.96 (((setukpairinjR2) =>
% 132.79/22.96 (((setukpairinjR) =>
% 132.79/22.96 (((ksndsingleton) =>
% 132.79/22.96 (((ksndpairEq) =>
% 132.79/22.96 (((kpairsurjEq) =>
% 132.79/22.96 (((cartprodsndin) =>
% 132.79/22.96 (((cartprodpairmemEL) =>
% 132.79/22.96 (((cartprodpairmemER) =>
% 132.79/22.96 (((cartprodmempaircEq) =>
% 132.79/22.96 (((cartprodfstpairEq) =>
% 132.79/22.96 (((cartprodsndpairEq) =>
% 132.79/22.96 (((cartprodpairsurjEq) =>
% 132.79/22.96 (((dpsetconstrI) =>
% 132.79/22.96 (((dpsetconstrSub) =>
% 132.79/22.96 (((setOfPairsIsBReln) =>
% 132.79/22.96 ((
% 132.79/22.96 (dpsetconstrERa) =>
% 132.79/22.96 ((
% 132.79/22.96 (dpsetconstrEL1) =>
% 132.79/22.96 ((
% 132.79/22.96 (dpsetconstrEL2) =>
% 132.79/22.96 ((
% 132.79/22.96 (dpsetconstrER) =>
% 132.79/22.96 ((
% 132.79/22.96 (funcImageSingleton) =>
% 132.79/22.96 ((
% 132.79/22.96 (apProp) =>
% 132.79/22.96 ((
% 132.79/22.96 (app) =>
% 132.79/22.96 ((
% 132.79/22.96 (infuncsetfunc) =>
% 132.79/22.96 ((
% 132.79/22.96 (ap2p) =>
% 132.79/22.96 ((
% 132.79/22.96 (funcinfuncset) =>
% 132.79/22.96 ((
% 132.79/22.96 (lamProp) =>
% 132.79/22.96 ((
% 132.79/22.96 (lamp) =>
% 132.79/22.96 ((
% 132.79/22.96 (lam2p) =>
% 132.79/22.96 ((
% 132.79/22.96 (brelnall1) =>
% 132.79/22.96 ((
% 132.79/22.96 (brelnall2) =>
% 132.79/22.96 ((
% 132.79/22.96 (ex1E2) =>
% 132.79/22.96 ((
% 132.79/22.96 (funcGraphProp1) =>
% 132.79/22.96 ((
% 132.79/22.96 (funcGraphProp3) =>
% 132.79/22.96 ((
% 132.79/22.96 (funcGraphProp2) =>
% 132.79/22.96 ((
% 132.79/22.96 (funcextLem) =>
% 132.79/22.96 ((
% 132.79/22.96 (funcGraphProp4) =>
% 132.79/22.96 ((
% 132.79/22.96 (subbreln) =>
% 132.79/22.96 ((
% 132.79/22.96 (eqbreln) =>
% 132.79/22.96 ((
% 132.79/22.96 (funcext) =>
% 132.79/22.96 ((
% 132.79/22.96 (funcext2) =>
% 132.79/22.96 ((
% 132.79/22.96 (ap2apEq1) =>
% 132.79/22.96 ((
% 132.79/22.96 (ap2apEq2) =>
% 132.79/22.96 ((
% 132.79/22.96 (beta1) =>
% 132.79/22.96 ((
% 132.79/22.96 (eta1) =>
% 132.79/22.96 ((
% 132.79/22.96 (lam2lamEq) =>
% 132.79/22.96 ((
% 132.79/22.96 (beta2) =>
% 132.79/22.96 ((
% 132.79/22.96 (eta2) =>
% 132.79/22.96 ((
% 132.79/22.96 (iffalseProp1) =>
% 132.79/22.96 ((
% 132.79/22.96 (iffalseProp2) =>
% 132.79/22.96 ((
% 132.79/22.96 (iftrueProp1) =>
% 132.79/22.96 ((
% 132.79/22.96 (iftrueProp2) =>
% 132.79/22.96 ((
% 132.79/22.96 (ifSingleton) =>
% 132.79/22.96 ((
% 132.79/22.96 (ifp) =>
% 132.79/22.96 ((
% 132.79/22.97 (theeq) =>
% 132.79/22.97 ((
% 132.79/22.97 (iftrue) =>
% 132.79/22.97 ((
% 132.79/22.97 (iffalse) =>
% 132.79/22.97 ((
% 132.79/22.97 (iftrueorfalse) =>
% 132.79/22.97 ((
% 132.79/22.97 (binintersectT_lem) =>
% 132.79/22.97 ((
% 132.79/22.97 (binunionT_lem) =>
% 132.79/22.97 ((
% 132.79/22.97 (powersetT_lem) =>
% 132.79/22.97 ((
% 132.79/22.97 (setminusT_lem) =>
% 132.79/22.97 ((
% 132.79/22.97 (complementT_lem) =>
% 132.79/22.97 ((
% 132.79/22.97 (setextT) =>
% 132.79/22.97 ((
% 132.79/22.97 (subsetTI) =>
% 132.79/22.97 ((
% 132.79/22.97 (powersetTI1) =>
% 132.79/22.97 ((
% 132.79/22.97 (powersetTE1) =>
% 132.79/22.97 ((
% 132.79/22.97 (complementTI1) =>
% 132.79/22.97 ((
% 132.79/22.97 (complementTE1) =>
% 132.79/22.97 ((
% 132.79/22.97 (binintersectTELcontra) =>
% 132.79/22.97 ((
% 132.79/22.97 (binintersectTERcontra) =>
% 132.79/22.97 ((
% 132.79/22.97 (contrasubsetT) =>
% 132.79/22.97 ((
% 132.79/22.97 (contrasubsetT1) =>
% 132.79/22.97 ((
% 132.79/22.97 (contrasubsetT2) =>
% 132.79/22.97 ((
% 132.79/22.97 (contrasubsetT3) =>
% 132.79/22.97 ((
% 132.79/22.97 (doubleComplementI1) =>
% 132.79/22.97 ((
% 132.79/22.97 (doubleComplementE1) =>
% 132.79/22.97 ((
% 132.79/22.97 (doubleComplementSub1) =>
% 132.79/22.97 ((
% 132.79/22.97 (doubleComplementSub2) =>
% 132.79/22.97 ((
% 132.79/22.97 (doubleComplementEq) =>
% 132.79/22.97 ((
% 132.79/22.97 (complementTnotintersectT) =>
% 132.79/22.97 ((
% 132.79/22.97 (complementImpComplementIntersect) =>
% 132.79/22.97 ((
% 132.79/22.97 (complementSubsetComplementIntersect) =>
% 132.79/22.97 ((
% 132.79/22.97 (complementInPowersetComplementIntersect) =>
% 132.79/22.97 ((
% 132.79/22.97 (contraSubsetComplement) =>
% 132.79/22.97 ((
% 132.79/22.97 (complementTcontraSubset) =>
% 132.79/22.97 ((
% 132.79/22.97 (binunionTILcontra) =>
% 132.79/22.97 ((
% 132.79/22.97 (binunionTIRcontra) =>
% 132.79/22.97 ((
% 132.79/22.97 (inIntersectImpInUnion) =>
% 132.79/22.97 ((
% 132.79/22.97 (inIntersectImpInUnion2) =>
% 132.79/22.97 ((
% 132.79/22.97 (inIntersectImpInIntersectUnions) =>
% 132.79/22.97 ((
% 132.79/22.97 (intersectInPowersetIntersectUnions) =>
% 132.79/22.97 ((
% 132.79/22.97 (inComplementUnionImpNotIn1) =>
% 132.79/22.97 ((
% 132.79/22.97 (inComplementUnionImpInComplement1) =>
% 132.79/22.97 ((
% 132.79/22.97 (binunionTE) =>
% 132.79/22.97 ((
% 132.79/22.97 (binunionTEcontra) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan2a1) =>
% 132.79/22.97 ((
% 132.79/22.97 (complementUnionInPowersetComplement) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan2a2) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan1a) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan1b) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan1) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan2a) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan2b2) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan2b) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan2) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz13rule0) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz13rule1) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz13rule2) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz13rule3) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz13rule4) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz1_1) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz1_2) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz1_3) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz1_4) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz1_5) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1all2) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1SetBreln1) =>
% 132.79/22.97 ((
% 132.79/22.97 (choice2fnsingleton) =>
% 132.79/22.97 ((
% 132.79/22.97 (setOfPairsIsBReln1) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1all1) =>
% 132.79/22.97 ((
% 132.79/22.97 (subbreln1) =>
% 132.79/22.97 ((
% 132.79/22.97 (eqbreln1) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1invprop) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1invI) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1invE) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1compprop) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1compI) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1compE) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1compEex) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionprop) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionIL) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionIR) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionI) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionE) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionEcases) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionCommutes) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz2Ex) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz2W) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz2A) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz2B) =>
% 132.79/22.97 ((
% 132.79/22.97 (image1Ex) =>
% 132.79/22.97 ((
% 132.79/22.97 (image1Ex1) =>
% 132.79/22.97 ((
% 132.79/22.97 (image1Equiv) =>
% 132.79/22.97 ((
% 132.79/22.97 (image1E) =>
% 132.79/22.97 ((
% 132.79/22.97 (image1I) =>
% 132.79/22.97 ((
% 132.79/22.97 (injFuncInInjFuncSet) =>
% 132.79/22.97 ((
% 132.79/22.97 (injFuncSetFuncIn) =>
% 132.79/22.97 ((
% 132.79/22.97 (injFuncSetFuncInj) =>
% 132.79/22.97 ((
% 132.79/22.97 (surjFuncSetFuncIn) =>
% 132.79/22.97 ((
% 132.79/22.97 (surjFuncSetFuncSurj) =>
% 132.79/22.97 ((
% 132.79/22.97 (leftInvIsSurj) =>
% 132.79/22.97 ((
% 132.79/22.97 (surjCantorThm) =>
% 132.79/22.97 ((
% 132.79/22.97 (foundation2) =>
% 132.79/22.97 ((
% 132.79/22.97 (notinself) =>
% 132.79/22.97 ((
% 132.79/22.97 (notinself2) =>
% 132.79/22.97 ((
% 132.79/22.97 (omegaSp) =>
% 132.79/22.97 ((
% 132.79/22.97 (omegaSclos) =>
% 132.79/22.97 ((
% 132.79/22.97 (peano0notS) =>
% 132.79/22.97 ((
% 132.79/22.97 (peanoSinj) =>
% 132.79/22.97 ((
% 132.79/22.97 (transitivesetOp1) =>
% 132.79/22.97 ((
% 132.79/22.97 (binintTransitive) =>
% 132.79/22.97 ((
% 132.79/22.97 (transitivesetOp2) =>
% 132.79/22.97 ((
% 132.79/22.97 (setunionTransitive) =>
% 132.79/22.97 ((
% 132.79/22.97 (ordinalMinLem1) =>
% 132.79/22.97 ((
% 132.79/22.97 (ordinalTransSet) =>
% 132.79/22.97 ((
% 132.79/22.97 (ordinalTransSet1) =>
% 132.79/22.97 ((
% 132.79/22.97 (setunionOrdinalLem1) =>
% 132.79/22.97 (ordinal @
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% 132.79/22.97 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1306])).
% 132.79/22.97 thf(zip_derived_cl1321, plain,
% 132.79/22.97 (~ (((ex1I) =>
% 132.79/22.97 (((ex1I2) =>
% 132.79/22.97 (((singletonsuniq) =>
% 132.79/22.97 (((setukpairinjL1) =>
% 132.79/22.97 (((kfstsingleton) =>
% 132.79/22.97 (((theprop) =>
% 132.79/22.97 (((kfstpairEq) =>
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% 132.79/22.97 (((setukpairinjL2) =>
% 132.79/22.97 (((setukpairinjL) =>
% 132.79/22.97 (((setukpairinjR11) =>
% 132.79/22.97 (((setukpairinjR12) =>
% 132.79/22.97 (((setukpairinjR1) =>
% 132.79/22.97 (((upairequniteq) =>
% 132.79/22.97 (((setukpairinjR2) =>
% 132.79/22.97 (((setukpairinjR) =>
% 132.79/22.97 (((ksndsingleton) =>
% 132.79/22.97 (((ksndpairEq) =>
% 132.79/22.97 (((kpairsurjEq) =>
% 132.79/22.97 (((cartprodsndin) =>
% 132.79/22.97 (((cartprodpairmemEL) =>
% 132.79/22.97 (((cartprodpairmemER) =>
% 132.79/22.97 (((cartprodmempaircEq) =>
% 132.79/22.97 (((cartprodfstpairEq) =>
% 132.79/22.97 (((cartprodsndpairEq) =>
% 132.79/22.97 (((cartprodpairsurjEq) =>
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% 132.79/22.97 (dpsetconstrEL2) =>
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% 132.79/22.97 (dpsetconstrER) =>
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% 132.79/22.97 ((
% 132.79/22.97 (ap2p) =>
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% 132.79/22.97 (lam2p) =>
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% 132.79/22.97 ((
% 132.79/22.97 (brelnall2) =>
% 132.79/22.97 ((
% 132.79/22.97 (ex1E2) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (funcGraphProp3) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (complementTE1) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (binintersectTERcontra) =>
% 132.79/22.97 ((
% 132.79/22.97 (contrasubsetT) =>
% 132.79/22.97 ((
% 132.79/22.97 (contrasubsetT1) =>
% 132.79/22.97 ((
% 132.79/22.97 (contrasubsetT2) =>
% 132.79/22.97 ((
% 132.79/22.97 (contrasubsetT3) =>
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% 132.79/22.97 ((
% 132.79/22.97 (doubleComplementE1) =>
% 132.79/22.97 ((
% 132.79/22.97 (doubleComplementSub1) =>
% 132.79/22.97 ((
% 132.79/22.97 (doubleComplementSub2) =>
% 132.79/22.97 ((
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% 132.79/22.97 (complementSubsetComplementIntersect) =>
% 132.79/22.97 ((
% 132.79/22.97 (complementInPowersetComplementIntersect) =>
% 132.79/22.97 ((
% 132.79/22.97 (contraSubsetComplement) =>
% 132.79/22.97 ((
% 132.79/22.97 (complementTcontraSubset) =>
% 132.79/22.97 ((
% 132.79/22.97 (binunionTILcontra) =>
% 132.79/22.97 ((
% 132.79/22.97 (binunionTIRcontra) =>
% 132.79/22.97 ((
% 132.79/22.97 (inIntersectImpInUnion) =>
% 132.79/22.97 ((
% 132.79/22.97 (inIntersectImpInUnion2) =>
% 132.79/22.97 ((
% 132.79/22.97 (inIntersectImpInIntersectUnions) =>
% 132.79/22.97 ((
% 132.79/22.97 (intersectInPowersetIntersectUnions) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (inComplementUnionImpInComplement1) =>
% 132.79/22.97 ((
% 132.79/22.97 (binunionTE) =>
% 132.79/22.97 ((
% 132.79/22.97 (binunionTEcontra) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan2a1) =>
% 132.79/22.97 ((
% 132.79/22.97 (complementUnionInPowersetComplement) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan2a2) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan1a) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan1b) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan1) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan2a) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan2b2) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan2b) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan2) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz13rule0) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz13rule1) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz13rule2) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz13rule3) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz13rule4) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz1_1) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz1_2) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz1_3) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz1_4) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz1_5) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1all2) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1SetBreln1) =>
% 132.79/22.97 ((
% 132.79/22.97 (choice2fnsingleton) =>
% 132.79/22.97 ((
% 132.79/22.97 (setOfPairsIsBReln1) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1all1) =>
% 132.79/22.97 ((
% 132.79/22.97 (subbreln1) =>
% 132.79/22.97 ((
% 132.79/22.97 (eqbreln1) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1invprop) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1invI) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1invE) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1compprop) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1compI) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1compE) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1compEex) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionprop) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionIL) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionIR) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionI) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionE) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionEcases) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionCommutes) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz2Ex) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz2W) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz2A) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz2B) =>
% 132.79/22.97 ((
% 132.79/22.97 (image1Ex) =>
% 132.79/22.97 ((
% 132.79/22.97 (image1Ex1) =>
% 132.79/22.97 ((
% 132.79/22.97 (image1Equiv) =>
% 132.79/22.97 ((
% 132.79/22.97 (image1E) =>
% 132.79/22.97 ((
% 132.79/22.97 (image1I) =>
% 132.79/22.97 ((
% 132.79/22.97 (injFuncInInjFuncSet) =>
% 132.79/22.97 ((
% 132.79/22.97 (injFuncSetFuncIn) =>
% 132.79/22.97 ((
% 132.79/22.97 (injFuncSetFuncInj) =>
% 132.79/22.97 ((
% 132.79/22.97 (surjFuncSetFuncIn) =>
% 132.79/22.97 ((
% 132.79/22.97 (surjFuncSetFuncSurj) =>
% 132.79/22.97 ((
% 132.79/22.97 (leftInvIsSurj) =>
% 132.79/22.97 ((
% 132.79/22.97 (surjCantorThm) =>
% 132.79/22.97 ((
% 132.79/22.97 (foundation2) =>
% 132.79/22.97 ((
% 132.79/22.97 (notinself) =>
% 132.79/22.97 ((
% 132.79/22.97 (notinself2) =>
% 132.79/22.97 ((
% 132.79/22.97 (omegaSp) =>
% 132.79/22.97 ((
% 132.79/22.97 (omegaSclos) =>
% 132.79/22.97 ((
% 132.79/22.97 (peano0notS) =>
% 132.79/22.97 ((
% 132.79/22.97 (peanoSinj) =>
% 132.79/22.97 ((
% 132.79/22.97 (transitivesetOp1) =>
% 132.79/22.97 ((
% 132.79/22.97 (binintTransitive) =>
% 132.79/22.97 ((
% 132.79/22.97 (transitivesetOp2) =>
% 132.79/22.97 ((
% 132.79/22.97 (setunionTransitive) =>
% 132.79/22.97 ((
% 132.79/22.97 (ordinalMinLem1) =>
% 132.79/22.97 ((
% 132.79/22.97 (ordinalTransSet) =>
% 132.79/22.97 ((
% 132.79/22.97 (ordinalTransSet1) =>
% 132.79/22.97 ((
% 132.79/22.97 (setunionOrdinalLem1) =>
% 132.79/22.97 (ordinal @
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% 132.79/22.97 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1314])).
% 132.79/22.97 thf(zip_derived_cl1328, plain,
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% 132.79/22.97 (((theprop) =>
% 132.79/22.97 (((kfstpairEq) =>
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% 132.79/22.97 (((setukpairinjL) =>
% 132.79/22.97 (((setukpairinjR11) =>
% 132.79/22.97 (((setukpairinjR12) =>
% 132.79/22.97 (((setukpairinjR1) =>
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% 132.79/22.97 (((setukpairinjR) =>
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% 132.79/22.97 (((kpairsurjEq) =>
% 132.79/22.97 (((cartprodsndin) =>
% 132.79/22.97 (((cartprodpairmemEL) =>
% 132.79/22.97 (((cartprodpairmemER) =>
% 132.79/22.97 (((cartprodmempaircEq) =>
% 132.79/22.97 (((cartprodfstpairEq) =>
% 132.79/22.97 (((cartprodsndpairEq) =>
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% 132.79/22.97 (dpsetconstrEL2) =>
% 132.79/22.97 ((
% 132.79/22.97 (dpsetconstrER) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (lam2p) =>
% 132.79/22.97 ((
% 132.79/22.97 (brelnall1) =>
% 132.79/22.97 ((
% 132.79/22.97 (brelnall2) =>
% 132.79/22.97 ((
% 132.79/22.97 (ex1E2) =>
% 132.79/22.97 ((
% 132.79/22.97 (funcGraphProp1) =>
% 132.79/22.97 ((
% 132.79/22.97 (funcGraphProp3) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (funcext2) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (eta1) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (binunionT_lem) =>
% 132.79/22.97 ((
% 132.79/22.97 (powersetT_lem) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (setextT) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (powersetTI1) =>
% 132.79/22.97 ((
% 132.79/22.97 (powersetTE1) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (complementTE1) =>
% 132.79/22.97 ((
% 132.79/22.97 (binintersectTELcontra) =>
% 132.79/22.97 ((
% 132.79/22.97 (binintersectTERcontra) =>
% 132.79/22.97 ((
% 132.79/22.97 (contrasubsetT) =>
% 132.79/22.97 ((
% 132.79/22.97 (contrasubsetT1) =>
% 132.79/22.97 ((
% 132.79/22.97 (contrasubsetT2) =>
% 132.79/22.97 ((
% 132.79/22.97 (contrasubsetT3) =>
% 132.79/22.97 ((
% 132.79/22.97 (doubleComplementI1) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (doubleComplementSub1) =>
% 132.79/22.97 ((
% 132.79/22.97 (doubleComplementSub2) =>
% 132.79/22.97 ((
% 132.79/22.97 (doubleComplementEq) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (complementSubsetComplementIntersect) =>
% 132.79/22.97 ((
% 132.79/22.97 (complementInPowersetComplementIntersect) =>
% 132.79/22.97 ((
% 132.79/22.97 (contraSubsetComplement) =>
% 132.79/22.97 ((
% 132.79/22.97 (complementTcontraSubset) =>
% 132.79/22.97 ((
% 132.79/22.97 (binunionTILcontra) =>
% 132.79/22.97 ((
% 132.79/22.97 (binunionTIRcontra) =>
% 132.79/22.97 ((
% 132.79/22.97 (inIntersectImpInUnion) =>
% 132.79/22.97 ((
% 132.79/22.97 (inIntersectImpInUnion2) =>
% 132.79/22.97 ((
% 132.79/22.97 (inIntersectImpInIntersectUnions) =>
% 132.79/22.97 ((
% 132.79/22.97 (intersectInPowersetIntersectUnions) =>
% 132.79/22.97 ((
% 132.79/22.97 (inComplementUnionImpNotIn1) =>
% 132.79/22.97 ((
% 132.79/22.97 (inComplementUnionImpInComplement1) =>
% 132.79/22.97 ((
% 132.79/22.97 (binunionTE) =>
% 132.79/22.97 ((
% 132.79/22.97 (binunionTEcontra) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan2a1) =>
% 132.79/22.97 ((
% 132.79/22.97 (complementUnionInPowersetComplement) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan2a2) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan1a) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan1b) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan1) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan2a) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan2b2) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan2b) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan2) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz13rule0) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz13rule1) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz13rule2) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz13rule3) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz13rule4) =>
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% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (woz1_3) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (woz1_5) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1all2) =>
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% 132.79/22.97 ((
% 132.79/22.97 (choice2fnsingleton) =>
% 132.79/22.97 ((
% 132.79/22.97 (setOfPairsIsBReln1) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1all1) =>
% 132.79/22.97 ((
% 132.79/22.97 (subbreln1) =>
% 132.79/22.97 ((
% 132.79/22.97 (eqbreln1) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1invprop) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1invI) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1invE) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1compprop) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1compI) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1compE) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1compEex) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionprop) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionIL) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionIR) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionI) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionE) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionEcases) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionCommutes) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz2Ex) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz2W) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz2A) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz2B) =>
% 132.79/22.97 ((
% 132.79/22.97 (image1Ex) =>
% 132.79/22.97 ((
% 132.79/22.97 (image1Ex1) =>
% 132.79/22.97 ((
% 132.79/22.97 (image1Equiv) =>
% 132.79/22.97 ((
% 132.79/22.97 (image1E) =>
% 132.79/22.97 ((
% 132.79/22.97 (image1I) =>
% 132.79/22.97 ((
% 132.79/22.97 (injFuncInInjFuncSet) =>
% 132.79/22.97 ((
% 132.79/22.97 (injFuncSetFuncIn) =>
% 132.79/22.97 ((
% 132.79/22.97 (injFuncSetFuncInj) =>
% 132.79/22.97 ((
% 132.79/22.97 (surjFuncSetFuncIn) =>
% 132.79/22.97 ((
% 132.79/22.97 (surjFuncSetFuncSurj) =>
% 132.79/22.97 ((
% 132.79/22.97 (leftInvIsSurj) =>
% 132.79/22.97 ((
% 132.79/22.97 (surjCantorThm) =>
% 132.79/22.97 ((
% 132.79/22.97 (foundation2) =>
% 132.79/22.97 ((
% 132.79/22.97 (notinself) =>
% 132.79/22.97 ((
% 132.79/22.97 (notinself2) =>
% 132.79/22.97 ((
% 132.79/22.97 (omegaSp) =>
% 132.79/22.97 ((
% 132.79/22.97 (omegaSclos) =>
% 132.79/22.97 ((
% 132.79/22.97 (peano0notS) =>
% 132.79/22.97 ((
% 132.79/22.97 (peanoSinj) =>
% 132.79/22.97 ((
% 132.79/22.97 (transitivesetOp1) =>
% 132.79/22.97 ((
% 132.79/22.97 (binintTransitive) =>
% 132.79/22.97 ((
% 132.79/22.97 (transitivesetOp2) =>
% 132.79/22.97 ((
% 132.79/22.97 (setunionTransitive) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (ordinalTransSet) =>
% 132.79/22.97 ((
% 132.79/22.97 (ordinalTransSet1) =>
% 132.79/22.97 ((
% 132.79/22.97 (setunionOrdinalLem1) =>
% 132.79/22.97 (ordinal @
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% 132.79/22.97 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1321])).
% 132.79/22.97 thf(zip_derived_cl1336, plain,
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% 132.79/22.97 (((kfstsingleton) =>
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% 132.79/22.97 (((kfstpairEq) =>
% 132.79/22.97 (((cartprodfstin) =>
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% 132.79/22.97 (((setukpairinjL) =>
% 132.79/22.97 (((setukpairinjR11) =>
% 132.79/22.97 (((setukpairinjR12) =>
% 132.79/22.97 (((setukpairinjR1) =>
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% 132.79/22.97 (((setukpairinjR2) =>
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% 132.79/22.97 (((ksndsingleton) =>
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% 132.79/22.97 (((cartprodpairmemER) =>
% 132.79/22.97 (((cartprodmempaircEq) =>
% 132.79/22.97 (((cartprodfstpairEq) =>
% 132.79/22.97 (((cartprodsndpairEq) =>
% 132.79/22.97 (((cartprodpairsurjEq) =>
% 132.79/22.97 (((dpsetconstrI) =>
% 132.79/22.97 (((dpsetconstrSub) =>
% 132.79/22.97 (((setOfPairsIsBReln) =>
% 132.79/22.97 (((dpsetconstrERa) =>
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% 132.79/22.97 (((dpsetconstrEL2) =>
% 132.79/22.97 ((
% 132.79/22.97 (dpsetconstrER) =>
% 132.79/22.97 ((
% 132.79/22.97 (funcImageSingleton) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (app) =>
% 132.79/22.97 ((
% 132.79/22.97 (infuncsetfunc) =>
% 132.79/22.97 ((
% 132.79/22.97 (ap2p) =>
% 132.79/22.97 ((
% 132.79/22.97 (funcinfuncset) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (lamp) =>
% 132.79/22.97 ((
% 132.79/22.97 (lam2p) =>
% 132.79/22.97 ((
% 132.79/22.97 (brelnall1) =>
% 132.79/22.97 ((
% 132.79/22.97 (brelnall2) =>
% 132.79/22.97 ((
% 132.79/22.97 (ex1E2) =>
% 132.79/22.97 ((
% 132.79/22.97 (funcGraphProp1) =>
% 132.79/22.97 ((
% 132.79/22.97 (funcGraphProp3) =>
% 132.79/22.97 ((
% 132.79/22.97 (funcGraphProp2) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (funcGraphProp4) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (ap2apEq2) =>
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (powersetT_lem) =>
% 132.79/22.97 ((
% 132.79/22.97 (setminusT_lem) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (powersetTE1) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (complementTE1) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (binintersectTERcontra) =>
% 132.79/22.97 ((
% 132.79/22.97 (contrasubsetT) =>
% 132.79/22.97 ((
% 132.79/22.97 (contrasubsetT1) =>
% 132.79/22.97 ((
% 132.79/22.97 (contrasubsetT2) =>
% 132.79/22.97 ((
% 132.79/22.97 (contrasubsetT3) =>
% 132.79/22.97 ((
% 132.79/22.97 (doubleComplementI1) =>
% 132.79/22.97 ((
% 132.79/22.97 (doubleComplementE1) =>
% 132.79/22.97 ((
% 132.79/22.97 (doubleComplementSub1) =>
% 132.79/22.97 ((
% 132.79/22.97 (doubleComplementSub2) =>
% 132.79/22.97 ((
% 132.79/22.97 (doubleComplementEq) =>
% 132.79/22.97 ((
% 132.79/22.97 (complementTnotintersectT) =>
% 132.79/22.97 ((
% 132.79/22.97 (complementImpComplementIntersect) =>
% 132.79/22.97 ((
% 132.79/22.97 (complementSubsetComplementIntersect) =>
% 132.79/22.97 ((
% 132.79/22.97 (complementInPowersetComplementIntersect) =>
% 132.79/22.97 ((
% 132.79/22.97 (contraSubsetComplement) =>
% 132.79/22.97 ((
% 132.79/22.97 (complementTcontraSubset) =>
% 132.79/22.97 ((
% 132.79/22.97 (binunionTILcontra) =>
% 132.79/22.97 ((
% 132.79/22.97 (binunionTIRcontra) =>
% 132.79/22.97 ((
% 132.79/22.97 (inIntersectImpInUnion) =>
% 132.79/22.97 ((
% 132.79/22.97 (inIntersectImpInUnion2) =>
% 132.79/22.97 ((
% 132.79/22.97 (inIntersectImpInIntersectUnions) =>
% 132.79/22.97 ((
% 132.79/22.97 (intersectInPowersetIntersectUnions) =>
% 132.79/22.97 ((
% 132.79/22.97 (inComplementUnionImpNotIn1) =>
% 132.79/22.97 ((
% 132.79/22.97 (inComplementUnionImpInComplement1) =>
% 132.79/22.97 ((
% 132.79/22.97 (binunionTE) =>
% 132.79/22.97 ((
% 132.79/22.97 (binunionTEcontra) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan2a1) =>
% 132.79/22.97 ((
% 132.79/22.97 (complementUnionInPowersetComplement) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan2a2) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan1a) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan1b) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan1) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan2a) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan2b2) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan2b) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan2) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz13rule0) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz13rule1) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz13rule2) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz13rule3) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz13rule4) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz1_1) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz1_2) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz1_3) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz1_4) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz1_5) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1all2) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1SetBreln1) =>
% 132.79/22.97 ((
% 132.79/22.97 (choice2fnsingleton) =>
% 132.79/22.97 ((
% 132.79/22.97 (setOfPairsIsBReln1) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1all1) =>
% 132.79/22.97 ((
% 132.79/22.97 (subbreln1) =>
% 132.79/22.97 ((
% 132.79/22.97 (eqbreln1) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1invprop) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1invI) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1invE) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1compprop) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1compI) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1compE) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1compEex) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionprop) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionIL) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionIR) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionI) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionE) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (image1I) =>
% 132.79/22.97 ((
% 132.79/22.97 (injFuncInInjFuncSet) =>
% 132.79/22.97 ((
% 132.79/22.97 (injFuncSetFuncIn) =>
% 132.79/22.97 ((
% 132.79/22.97 (injFuncSetFuncInj) =>
% 132.79/22.97 ((
% 132.79/22.97 (surjFuncSetFuncIn) =>
% 132.79/22.97 ((
% 132.79/22.97 (surjFuncSetFuncSurj) =>
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% 132.79/22.97 (leftInvIsSurj) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (notinself2) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1328])).
% 132.79/22.97 thf(zip_derived_cl1344, plain,
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% 132.79/22.97 (complementTE1) =>
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% 132.79/22.97 (binintersectTERcontra) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 (contrasubsetT3) =>
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (inIntersectImpInUnion) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (demorgan1a) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan1b) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan1) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan2a) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan2b2) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan2b) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan2) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz13rule0) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz13rule1) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz13rule2) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz13rule3) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz13rule4) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz1_1) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz1_2) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz1_3) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz1_4) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz1_5) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1all2) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1SetBreln1) =>
% 132.79/22.97 ((
% 132.79/22.97 (choice2fnsingleton) =>
% 132.79/22.97 ((
% 132.79/22.97 (setOfPairsIsBReln1) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1all1) =>
% 132.79/22.97 ((
% 132.79/22.97 (subbreln1) =>
% 132.79/22.97 ((
% 132.79/22.97 (eqbreln1) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1invprop) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1invI) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1invE) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1compprop) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1compI) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1compE) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1compEex) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionprop) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionIL) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionIR) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionI) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionE) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionEcases) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionCommutes) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz2Ex) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz2W) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz2A) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz2B) =>
% 132.79/22.97 ((
% 132.79/22.97 (image1Ex) =>
% 132.79/22.97 ((
% 132.79/22.97 (image1Ex1) =>
% 132.79/22.97 ((
% 132.79/22.97 (image1Equiv) =>
% 132.79/22.97 ((
% 132.79/22.97 (image1E) =>
% 132.79/22.97 ((
% 132.79/22.97 (image1I) =>
% 132.79/22.97 ((
% 132.79/22.97 (injFuncInInjFuncSet) =>
% 132.79/22.97 ((
% 132.79/22.97 (injFuncSetFuncIn) =>
% 132.79/22.97 ((
% 132.79/22.97 (injFuncSetFuncInj) =>
% 132.79/22.97 ((
% 132.79/22.97 (surjFuncSetFuncIn) =>
% 132.79/22.97 ((
% 132.79/22.97 (surjFuncSetFuncSurj) =>
% 132.79/22.97 ((
% 132.79/22.97 (leftInvIsSurj) =>
% 132.79/22.97 ((
% 132.79/22.97 (surjCantorThm) =>
% 132.79/22.97 ((
% 132.79/22.97 (foundation2) =>
% 132.79/22.97 ((
% 132.79/22.97 (notinself) =>
% 132.79/22.97 ((
% 132.79/22.97 (notinself2) =>
% 132.79/22.97 ((
% 132.79/22.97 (omegaSp) =>
% 132.79/22.97 ((
% 132.79/22.97 (omegaSclos) =>
% 132.79/22.97 ((
% 132.79/22.97 (peano0notS) =>
% 132.79/22.97 ((
% 132.79/22.97 (peanoSinj) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (binintTransitive) =>
% 132.79/22.97 ((
% 132.79/22.97 (transitivesetOp2) =>
% 132.79/22.97 ((
% 132.79/22.97 (setunionTransitive) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (ordinalTransSet) =>
% 132.79/22.97 ((
% 132.79/22.97 (ordinalTransSet1) =>
% 132.79/22.97 ((
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% 132.79/22.97 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1336])).
% 132.79/22.97 thf(zip_derived_cl1352, plain,
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% 132.79/22.97 (((setukpairinjR12) =>
% 132.79/22.97 (((setukpairinjR1) =>
% 132.79/22.97 (((upairequniteq) =>
% 132.79/22.97 (((setukpairinjR2) =>
% 132.79/22.97 (((setukpairinjR) =>
% 132.79/22.97 (((ksndsingleton) =>
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% 132.79/22.97 (((kpairsurjEq) =>
% 132.79/22.97 (((cartprodsndin) =>
% 132.79/22.97 (((cartprodpairmemEL) =>
% 132.79/22.97 (((cartprodpairmemER) =>
% 132.79/22.97 (((cartprodmempaircEq) =>
% 132.79/22.97 (((cartprodfstpairEq) =>
% 132.79/22.97 (((cartprodsndpairEq) =>
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% 132.79/22.97 ((
% 132.79/22.97 (app) =>
% 132.79/22.97 ((
% 132.79/22.97 (infuncsetfunc) =>
% 132.79/22.97 ((
% 132.79/22.97 (ap2p) =>
% 132.79/22.97 ((
% 132.79/22.97 (funcinfuncset) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (lamp) =>
% 132.79/22.97 ((
% 132.79/22.97 (lam2p) =>
% 132.79/22.97 ((
% 132.79/22.97 (brelnall1) =>
% 132.79/22.97 ((
% 132.79/22.97 (brelnall2) =>
% 132.79/22.97 ((
% 132.79/22.97 (ex1E2) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (funcGraphProp3) =>
% 132.79/22.97 ((
% 132.79/22.97 (funcGraphProp2) =>
% 132.79/22.97 ((
% 132.79/22.97 (funcextLem) =>
% 132.79/22.97 ((
% 132.79/22.97 (funcGraphProp4) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (eqbreln) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (funcext2) =>
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% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (eta1) =>
% 132.79/22.97 ((
% 132.79/22.97 (lam2lamEq) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (eta2) =>
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (complementTE1) =>
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% 132.79/22.97 ((
% 132.79/22.97 (binintersectTERcontra) =>
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% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (contrasubsetT2) =>
% 132.79/22.97 ((
% 132.79/22.97 (contrasubsetT3) =>
% 132.79/22.97 ((
% 132.79/22.97 (doubleComplementI1) =>
% 132.79/22.97 ((
% 132.79/22.97 (doubleComplementE1) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (doubleComplementSub2) =>
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% 132.79/22.97 ((
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% 132.79/22.97 (complementSubsetComplementIntersect) =>
% 132.79/22.97 ((
% 132.79/22.97 (complementInPowersetComplementIntersect) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (binunionTIRcontra) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (inIntersectImpInUnion2) =>
% 132.79/22.97 ((
% 132.79/22.97 (inIntersectImpInIntersectUnions) =>
% 132.79/22.97 ((
% 132.79/22.97 (intersectInPowersetIntersectUnions) =>
% 132.79/22.97 ((
% 132.79/22.97 (inComplementUnionImpNotIn1) =>
% 132.79/22.97 ((
% 132.79/22.97 (inComplementUnionImpInComplement1) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (binunionTEcontra) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (demorgan2a2) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (demorgan2b2) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan2b) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan2) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (woz13rule2) =>
% 132.79/22.97 ((
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% 132.79/22.97 (woz1_2) =>
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% 132.79/22.97 ((
% 132.79/22.97 (setunionTransitive) =>
% 132.79/22.97 ((
% 132.79/22.97 (ordinalMinLem1) =>
% 132.79/22.97 ((
% 132.79/22.97 (ordinalTransSet) =>
% 132.79/22.97 ((
% 132.79/22.97 (ordinalTransSet1) =>
% 132.79/22.97 ((
% 132.79/22.97 (setunionOrdinalLem1) =>
% 132.79/22.97 (ordinal @
% 132.79/22.97 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/22.97 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1344])).
% 132.79/22.97 thf(zip_derived_cl1361, plain,
% 132.79/22.97 (~ (((theprop) =>
% 132.79/22.97 (((kfstpairEq) =>
% 132.79/22.97 (((cartprodfstin) =>
% 132.79/22.97 (((setukpairinjL2) =>
% 132.79/22.97 (((setukpairinjL) =>
% 132.79/22.97 (((setukpairinjR11) =>
% 132.79/22.97 (((setukpairinjR12) =>
% 132.79/22.97 (((setukpairinjR1) =>
% 132.79/22.97 (((upairequniteq) =>
% 132.79/22.97 (((setukpairinjR2) =>
% 132.79/22.97 (((setukpairinjR) =>
% 132.79/22.97 (((ksndsingleton) =>
% 132.79/22.97 (((ksndpairEq) =>
% 132.79/22.97 (((kpairsurjEq) =>
% 132.79/22.97 (((cartprodsndin) =>
% 132.79/22.97 (((cartprodpairmemEL) =>
% 132.79/22.97 (((cartprodpairmemER) =>
% 132.79/22.97 (((cartprodmempaircEq) =>
% 132.79/22.97 (((cartprodfstpairEq) =>
% 132.79/22.97 (((cartprodsndpairEq) =>
% 132.79/22.97 (((cartprodpairsurjEq) =>
% 132.79/22.97 (((dpsetconstrI) =>
% 132.79/22.97 (((dpsetconstrSub) =>
% 132.79/22.97 (((setOfPairsIsBReln) =>
% 132.79/22.97 (((dpsetconstrERa) =>
% 132.79/22.97 (((dpsetconstrEL1) =>
% 132.79/22.97 (((dpsetconstrEL2) =>
% 132.79/22.97 (((dpsetconstrER) =>
% 132.79/22.97 (((funcImageSingleton) =>
% 132.79/22.97 (((apProp) =>
% 132.79/22.97 ((
% 132.79/22.97 (app) =>
% 132.79/22.97 ((
% 132.79/22.97 (infuncsetfunc) =>
% 132.79/22.97 ((
% 132.79/22.97 (ap2p) =>
% 132.79/22.97 ((
% 132.79/22.97 (funcinfuncset) =>
% 132.79/22.97 ((
% 132.79/22.97 (lamProp) =>
% 132.79/22.97 ((
% 132.79/22.97 (lamp) =>
% 132.79/22.97 ((
% 132.79/22.97 (lam2p) =>
% 132.79/22.97 ((
% 132.79/22.97 (brelnall1) =>
% 132.79/22.97 ((
% 132.79/22.97 (brelnall2) =>
% 132.79/22.97 ((
% 132.79/22.97 (ex1E2) =>
% 132.79/22.97 ((
% 132.79/22.97 (funcGraphProp1) =>
% 132.79/22.97 ((
% 132.79/22.97 (funcGraphProp3) =>
% 132.79/22.97 ((
% 132.79/22.97 (funcGraphProp2) =>
% 132.79/22.97 ((
% 132.79/22.97 (funcextLem) =>
% 132.79/22.97 ((
% 132.79/22.97 (funcGraphProp4) =>
% 132.79/22.97 ((
% 132.79/22.97 (subbreln) =>
% 132.79/22.97 ((
% 132.79/22.97 (eqbreln) =>
% 132.79/22.97 ((
% 132.79/22.97 (funcext) =>
% 132.79/22.97 ((
% 132.79/22.97 (funcext2) =>
% 132.79/22.97 ((
% 132.79/22.97 (ap2apEq1) =>
% 132.79/22.97 ((
% 132.79/22.97 (ap2apEq2) =>
% 132.79/22.97 ((
% 132.79/22.97 (beta1) =>
% 132.79/22.97 ((
% 132.79/22.97 (eta1) =>
% 132.79/22.97 ((
% 132.79/22.97 (lam2lamEq) =>
% 132.79/22.97 ((
% 132.79/22.97 (beta2) =>
% 132.79/22.97 ((
% 132.79/22.97 (eta2) =>
% 132.79/22.97 ((
% 132.79/22.97 (iffalseProp1) =>
% 132.79/22.97 ((
% 132.79/22.97 (iffalseProp2) =>
% 132.79/22.97 ((
% 132.79/22.97 (iftrueProp1) =>
% 132.79/22.97 ((
% 132.79/22.97 (iftrueProp2) =>
% 132.79/22.97 ((
% 132.79/22.97 (ifSingleton) =>
% 132.79/22.97 ((
% 132.79/22.97 (ifp) =>
% 132.79/22.97 ((
% 132.79/22.97 (theeq) =>
% 132.79/22.97 ((
% 132.79/22.97 (iftrue) =>
% 132.79/22.97 ((
% 132.79/22.97 (iffalse) =>
% 132.79/22.97 ((
% 132.79/22.97 (iftrueorfalse) =>
% 132.79/22.97 ((
% 132.79/22.97 (binintersectT_lem) =>
% 132.79/22.97 ((
% 132.79/22.97 (binunionT_lem) =>
% 132.79/22.97 ((
% 132.79/22.97 (powersetT_lem) =>
% 132.79/22.97 ((
% 132.79/22.97 (setminusT_lem) =>
% 132.79/22.97 ((
% 132.79/22.97 (complementT_lem) =>
% 132.79/22.97 ((
% 132.79/22.97 (setextT) =>
% 132.79/22.97 ((
% 132.79/22.97 (subsetTI) =>
% 132.79/22.97 ((
% 132.79/22.97 (powersetTI1) =>
% 132.79/22.97 ((
% 132.79/22.97 (powersetTE1) =>
% 132.79/22.97 ((
% 132.79/22.97 (complementTI1) =>
% 132.79/22.97 ((
% 132.79/22.97 (complementTE1) =>
% 132.79/22.97 ((
% 132.79/22.97 (binintersectTELcontra) =>
% 132.79/22.97 ((
% 132.79/22.97 (binintersectTERcontra) =>
% 132.79/22.97 ((
% 132.79/22.97 (contrasubsetT) =>
% 132.79/22.97 ((
% 132.79/22.97 (contrasubsetT1) =>
% 132.79/22.97 ((
% 132.79/22.97 (contrasubsetT2) =>
% 132.79/22.97 ((
% 132.79/22.97 (contrasubsetT3) =>
% 132.79/22.97 ((
% 132.79/22.97 (doubleComplementI1) =>
% 132.79/22.97 ((
% 132.79/22.97 (doubleComplementE1) =>
% 132.79/22.97 ((
% 132.79/22.97 (doubleComplementSub1) =>
% 132.79/22.97 ((
% 132.79/22.97 (doubleComplementSub2) =>
% 132.79/22.97 ((
% 132.79/22.97 (doubleComplementEq) =>
% 132.79/22.97 ((
% 132.79/22.97 (complementTnotintersectT) =>
% 132.79/22.97 ((
% 132.79/22.97 (complementImpComplementIntersect) =>
% 132.79/22.97 ((
% 132.79/22.97 (complementSubsetComplementIntersect) =>
% 132.79/22.97 ((
% 132.79/22.97 (complementInPowersetComplementIntersect) =>
% 132.79/22.97 ((
% 132.79/22.97 (contraSubsetComplement) =>
% 132.79/22.97 ((
% 132.79/22.97 (complementTcontraSubset) =>
% 132.79/22.97 ((
% 132.79/22.97 (binunionTILcontra) =>
% 132.79/22.97 ((
% 132.79/22.97 (binunionTIRcontra) =>
% 132.79/22.97 ((
% 132.79/22.97 (inIntersectImpInUnion) =>
% 132.79/22.97 ((
% 132.79/22.97 (inIntersectImpInUnion2) =>
% 132.79/22.97 ((
% 132.79/22.97 (inIntersectImpInIntersectUnions) =>
% 132.79/22.97 ((
% 132.79/22.97 (intersectInPowersetIntersectUnions) =>
% 132.79/22.97 ((
% 132.79/22.97 (inComplementUnionImpNotIn1) =>
% 132.79/22.97 ((
% 132.79/22.97 (inComplementUnionImpInComplement1) =>
% 132.79/22.97 ((
% 132.79/22.97 (binunionTE) =>
% 132.79/22.97 ((
% 132.79/22.97 (binunionTEcontra) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan2a1) =>
% 132.79/22.97 ((
% 132.79/22.97 (complementUnionInPowersetComplement) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan2a2) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan1a) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan1b) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan1) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan2a) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan2b2) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan2b) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan2) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz13rule0) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz13rule1) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz13rule2) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz13rule3) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz13rule4) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz1_1) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz1_2) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz1_3) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz1_4) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz1_5) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1all2) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1SetBreln1) =>
% 132.79/22.97 ((
% 132.79/22.97 (choice2fnsingleton) =>
% 132.79/22.97 ((
% 132.79/22.97 (setOfPairsIsBReln1) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1all1) =>
% 132.79/22.97 ((
% 132.79/22.97 (subbreln1) =>
% 132.79/22.97 ((
% 132.79/22.97 (eqbreln1) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1invprop) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1invI) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1invE) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1compprop) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1compI) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1compE) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1compEex) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionprop) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionIL) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionIR) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionI) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionE) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionEcases) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionCommutes) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz2Ex) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz2W) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz2A) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz2B) =>
% 132.79/22.97 ((
% 132.79/22.97 (image1Ex) =>
% 132.79/22.97 ((
% 132.79/22.97 (image1Ex1) =>
% 132.79/22.97 ((
% 132.79/22.97 (image1Equiv) =>
% 132.79/22.97 ((
% 132.79/22.97 (image1E) =>
% 132.79/22.97 ((
% 132.79/22.97 (image1I) =>
% 132.79/22.97 ((
% 132.79/22.97 (injFuncInInjFuncSet) =>
% 132.79/22.97 ((
% 132.79/22.97 (injFuncSetFuncIn) =>
% 132.79/22.97 ((
% 132.79/22.97 (injFuncSetFuncInj) =>
% 132.79/22.97 ((
% 132.79/22.97 (surjFuncSetFuncIn) =>
% 132.79/22.97 ((
% 132.79/22.97 (surjFuncSetFuncSurj) =>
% 132.79/22.97 ((
% 132.79/22.97 (leftInvIsSurj) =>
% 132.79/22.97 ((
% 132.79/22.97 (surjCantorThm) =>
% 132.79/22.97 ((
% 132.79/22.97 (foundation2) =>
% 132.79/22.97 ((
% 132.79/22.97 (notinself) =>
% 132.79/22.97 ((
% 132.79/22.97 (notinself2) =>
% 132.79/22.97 ((
% 132.79/22.97 (omegaSp) =>
% 132.79/22.97 ((
% 132.79/22.97 (omegaSclos) =>
% 132.79/22.97 ((
% 132.79/22.97 (peano0notS) =>
% 132.79/22.97 ((
% 132.79/22.97 (peanoSinj) =>
% 132.79/22.97 ((
% 132.79/22.97 (transitivesetOp1) =>
% 132.79/22.97 ((
% 132.79/22.97 (binintTransitive) =>
% 132.79/22.97 ((
% 132.79/22.97 (transitivesetOp2) =>
% 132.79/22.97 ((
% 132.79/22.97 (setunionTransitive) =>
% 132.79/22.97 ((
% 132.79/22.97 (ordinalMinLem1) =>
% 132.79/22.97 ((
% 132.79/22.97 (ordinalTransSet) =>
% 132.79/22.97 ((
% 132.79/22.97 (ordinalTransSet1) =>
% 132.79/22.97 ((
% 132.79/22.97 (setunionOrdinalLem1) =>
% 132.79/22.97 (ordinal @
% 132.79/22.97 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/22.97 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1352])).
% 132.79/22.97 thf(zip_derived_cl1371, plain,
% 132.79/22.97 (~ (((kfstpairEq) =>
% 132.79/22.97 (((cartprodfstin) =>
% 132.79/22.97 (((setukpairinjL2) =>
% 132.79/22.97 (((setukpairinjL) =>
% 132.79/22.97 (((setukpairinjR11) =>
% 132.79/22.97 (((setukpairinjR12) =>
% 132.79/22.97 (((setukpairinjR1) =>
% 132.79/22.97 (((upairequniteq) =>
% 132.79/22.97 (((setukpairinjR2) =>
% 132.79/22.97 (((setukpairinjR) =>
% 132.79/22.97 (((ksndsingleton) =>
% 132.79/22.97 (((ksndpairEq) =>
% 132.79/22.97 (((kpairsurjEq) =>
% 132.79/22.97 (((cartprodsndin) =>
% 132.79/22.97 (((cartprodpairmemEL) =>
% 132.79/22.97 (((cartprodpairmemER) =>
% 132.79/22.97 (((cartprodmempaircEq) =>
% 132.79/22.97 (((cartprodfstpairEq) =>
% 132.79/22.97 (((cartprodsndpairEq) =>
% 132.79/22.97 (((cartprodpairsurjEq) =>
% 132.79/22.97 (((dpsetconstrI) =>
% 132.79/22.97 (((dpsetconstrSub) =>
% 132.79/22.97 (((setOfPairsIsBReln) =>
% 132.79/22.97 (((dpsetconstrERa) =>
% 132.79/22.97 (((dpsetconstrEL1) =>
% 132.79/22.97 (((dpsetconstrEL2) =>
% 132.79/22.97 (((dpsetconstrER) =>
% 132.79/22.97 (((funcImageSingleton) =>
% 132.79/22.97 (((apProp) =>
% 132.79/22.97 (((app) =>
% 132.79/22.97 ((
% 132.79/22.97 (infuncsetfunc) =>
% 132.79/22.97 ((
% 132.79/22.97 (ap2p) =>
% 132.79/22.97 ((
% 132.79/22.97 (funcinfuncset) =>
% 132.79/22.97 ((
% 132.79/22.97 (lamProp) =>
% 132.79/22.97 ((
% 132.79/22.97 (lamp) =>
% 132.79/22.97 ((
% 132.79/22.97 (lam2p) =>
% 132.79/22.97 ((
% 132.79/22.97 (brelnall1) =>
% 132.79/22.97 ((
% 132.79/22.97 (brelnall2) =>
% 132.79/22.97 ((
% 132.79/22.97 (ex1E2) =>
% 132.79/22.97 ((
% 132.79/22.97 (funcGraphProp1) =>
% 132.79/22.97 ((
% 132.79/22.97 (funcGraphProp3) =>
% 132.79/22.97 ((
% 132.79/22.97 (funcGraphProp2) =>
% 132.79/22.97 ((
% 132.79/22.97 (funcextLem) =>
% 132.79/22.97 ((
% 132.79/22.97 (funcGraphProp4) =>
% 132.79/22.97 ((
% 132.79/22.97 (subbreln) =>
% 132.79/22.97 ((
% 132.79/22.97 (eqbreln) =>
% 132.79/22.97 ((
% 132.79/22.97 (funcext) =>
% 132.79/22.97 ((
% 132.79/22.97 (funcext2) =>
% 132.79/22.97 ((
% 132.79/22.97 (ap2apEq1) =>
% 132.79/22.97 ((
% 132.79/22.97 (ap2apEq2) =>
% 132.79/22.97 ((
% 132.79/22.97 (beta1) =>
% 132.79/22.97 ((
% 132.79/22.97 (eta1) =>
% 132.79/22.97 ((
% 132.79/22.97 (lam2lamEq) =>
% 132.79/22.97 ((
% 132.79/22.97 (beta2) =>
% 132.79/22.97 ((
% 132.79/22.97 (eta2) =>
% 132.79/22.97 ((
% 132.79/22.97 (iffalseProp1) =>
% 132.79/22.97 ((
% 132.79/22.97 (iffalseProp2) =>
% 132.79/22.97 ((
% 132.79/22.97 (iftrueProp1) =>
% 132.79/22.97 ((
% 132.79/22.97 (iftrueProp2) =>
% 132.79/22.97 ((
% 132.79/22.97 (ifSingleton) =>
% 132.79/22.97 ((
% 132.79/22.97 (ifp) =>
% 132.79/22.97 ((
% 132.79/22.97 (theeq) =>
% 132.79/22.97 ((
% 132.79/22.97 (iftrue) =>
% 132.79/22.97 ((
% 132.79/22.97 (iffalse) =>
% 132.79/22.97 ((
% 132.79/22.97 (iftrueorfalse) =>
% 132.79/22.97 ((
% 132.79/22.97 (binintersectT_lem) =>
% 132.79/22.97 ((
% 132.79/22.97 (binunionT_lem) =>
% 132.79/22.97 ((
% 132.79/22.97 (powersetT_lem) =>
% 132.79/22.97 ((
% 132.79/22.97 (setminusT_lem) =>
% 132.79/22.97 ((
% 132.79/22.97 (complementT_lem) =>
% 132.79/22.97 ((
% 132.79/22.97 (setextT) =>
% 132.79/22.97 ((
% 132.79/22.97 (subsetTI) =>
% 132.79/22.97 ((
% 132.79/22.97 (powersetTI1) =>
% 132.79/22.97 ((
% 132.79/22.97 (powersetTE1) =>
% 132.79/22.97 ((
% 132.79/22.97 (complementTI1) =>
% 132.79/22.97 ((
% 132.79/22.97 (complementTE1) =>
% 132.79/22.97 ((
% 132.79/22.97 (binintersectTELcontra) =>
% 132.79/22.97 ((
% 132.79/22.97 (binintersectTERcontra) =>
% 132.79/22.97 ((
% 132.79/22.97 (contrasubsetT) =>
% 132.79/22.97 ((
% 132.79/22.97 (contrasubsetT1) =>
% 132.79/22.97 ((
% 132.79/22.97 (contrasubsetT2) =>
% 132.79/22.97 ((
% 132.79/22.97 (contrasubsetT3) =>
% 132.79/22.97 ((
% 132.79/22.97 (doubleComplementI1) =>
% 132.79/22.97 ((
% 132.79/22.97 (doubleComplementE1) =>
% 132.79/22.97 ((
% 132.79/22.97 (doubleComplementSub1) =>
% 132.79/22.97 ((
% 132.79/22.97 (doubleComplementSub2) =>
% 132.79/22.97 ((
% 132.79/22.97 (doubleComplementEq) =>
% 132.79/22.97 ((
% 132.79/22.97 (complementTnotintersectT) =>
% 132.79/22.97 ((
% 132.79/22.97 (complementImpComplementIntersect) =>
% 132.79/22.97 ((
% 132.79/22.97 (complementSubsetComplementIntersect) =>
% 132.79/22.97 ((
% 132.79/22.97 (complementInPowersetComplementIntersect) =>
% 132.79/22.97 ((
% 132.79/22.97 (contraSubsetComplement) =>
% 132.79/22.97 ((
% 132.79/22.97 (complementTcontraSubset) =>
% 132.79/22.97 ((
% 132.79/22.97 (binunionTILcontra) =>
% 132.79/22.97 ((
% 132.79/22.97 (binunionTIRcontra) =>
% 132.79/22.97 ((
% 132.79/22.97 (inIntersectImpInUnion) =>
% 132.79/22.97 ((
% 132.79/22.97 (inIntersectImpInUnion2) =>
% 132.79/22.97 ((
% 132.79/22.97 (inIntersectImpInIntersectUnions) =>
% 132.79/22.97 ((
% 132.79/22.97 (intersectInPowersetIntersectUnions) =>
% 132.79/22.97 ((
% 132.79/22.97 (inComplementUnionImpNotIn1) =>
% 132.79/22.97 ((
% 132.79/22.97 (inComplementUnionImpInComplement1) =>
% 132.79/22.97 ((
% 132.79/22.97 (binunionTE) =>
% 132.79/22.97 ((
% 132.79/22.97 (binunionTEcontra) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan2a1) =>
% 132.79/22.97 ((
% 132.79/22.97 (complementUnionInPowersetComplement) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan2a2) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan1a) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan1b) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan1) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan2a) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan2b2) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan2b) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan2) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz13rule0) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz13rule1) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz13rule2) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz13rule3) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz13rule4) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz1_1) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz1_2) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz1_3) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz1_4) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz1_5) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1all2) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1SetBreln1) =>
% 132.79/22.97 ((
% 132.79/22.97 (choice2fnsingleton) =>
% 132.79/22.97 ((
% 132.79/22.97 (setOfPairsIsBReln1) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1all1) =>
% 132.79/22.97 ((
% 132.79/22.97 (subbreln1) =>
% 132.79/22.97 ((
% 132.79/22.97 (eqbreln1) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1invprop) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1invI) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1invE) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1compprop) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1compI) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1compE) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1compEex) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionprop) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionIL) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionIR) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionI) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionE) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionEcases) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionCommutes) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz2Ex) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz2W) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz2A) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz2B) =>
% 132.79/22.97 ((
% 132.79/22.97 (image1Ex) =>
% 132.79/22.97 ((
% 132.79/22.97 (image1Ex1) =>
% 132.79/22.97 ((
% 132.79/22.97 (image1Equiv) =>
% 132.79/22.97 ((
% 132.79/22.97 (image1E) =>
% 132.79/22.97 ((
% 132.79/22.97 (image1I) =>
% 132.79/22.97 ((
% 132.79/22.97 (injFuncInInjFuncSet) =>
% 132.79/22.97 ((
% 132.79/22.97 (injFuncSetFuncIn) =>
% 132.79/22.97 ((
% 132.79/22.97 (injFuncSetFuncInj) =>
% 132.79/22.97 ((
% 132.79/22.97 (surjFuncSetFuncIn) =>
% 132.79/22.97 ((
% 132.79/22.97 (surjFuncSetFuncSurj) =>
% 132.79/22.97 ((
% 132.79/22.97 (leftInvIsSurj) =>
% 132.79/22.97 ((
% 132.79/22.97 (surjCantorThm) =>
% 132.79/22.97 ((
% 132.79/22.97 (foundation2) =>
% 132.79/22.97 ((
% 132.79/22.97 (notinself) =>
% 132.79/22.97 ((
% 132.79/22.97 (notinself2) =>
% 132.79/22.97 ((
% 132.79/22.97 (omegaSp) =>
% 132.79/22.97 ((
% 132.79/22.97 (omegaSclos) =>
% 132.79/22.97 ((
% 132.79/22.97 (peano0notS) =>
% 132.79/22.97 ((
% 132.79/22.97 (peanoSinj) =>
% 132.79/22.97 ((
% 132.79/22.97 (transitivesetOp1) =>
% 132.79/22.97 ((
% 132.79/22.97 (binintTransitive) =>
% 132.79/22.97 ((
% 132.79/22.97 (transitivesetOp2) =>
% 132.79/22.97 ((
% 132.79/22.97 (setunionTransitive) =>
% 132.79/22.97 ((
% 132.79/22.97 (ordinalMinLem1) =>
% 132.79/22.97 ((
% 132.79/22.97 (ordinalTransSet) =>
% 132.79/22.97 ((
% 132.79/22.97 (ordinalTransSet1) =>
% 132.79/22.97 ((
% 132.79/22.97 (setunionOrdinalLem1) =>
% 132.79/22.97 (ordinal @
% 132.79/22.97 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/22.97 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1361])).
% 132.79/22.97 thf(zip_derived_cl1382, plain,
% 132.79/22.97 (~ (((cartprodfstin) =>
% 132.79/22.97 (((setukpairinjL2) =>
% 132.79/22.97 (((setukpairinjL) =>
% 132.79/22.97 (((setukpairinjR11) =>
% 132.79/22.97 (((setukpairinjR12) =>
% 132.79/22.97 (((setukpairinjR1) =>
% 132.79/22.97 (((upairequniteq) =>
% 132.79/22.97 (((setukpairinjR2) =>
% 132.79/22.97 (((setukpairinjR) =>
% 132.79/22.97 (((ksndsingleton) =>
% 132.79/22.97 (((ksndpairEq) =>
% 132.79/22.97 (((kpairsurjEq) =>
% 132.79/22.97 (((cartprodsndin) =>
% 132.79/22.97 (((cartprodpairmemEL) =>
% 132.79/22.97 (((cartprodpairmemER) =>
% 132.79/22.97 (((cartprodmempaircEq) =>
% 132.79/22.97 (((cartprodfstpairEq) =>
% 132.79/22.97 (((cartprodsndpairEq) =>
% 132.79/22.97 (((cartprodpairsurjEq) =>
% 132.79/22.97 (((dpsetconstrI) =>
% 132.79/22.97 (((dpsetconstrSub) =>
% 132.79/22.97 (((setOfPairsIsBReln) =>
% 132.79/22.97 (((dpsetconstrERa) =>
% 132.79/22.97 (((dpsetconstrEL1) =>
% 132.79/22.97 (((dpsetconstrEL2) =>
% 132.79/22.97 (((dpsetconstrER) =>
% 132.79/22.97 (((funcImageSingleton) =>
% 132.79/22.97 (((apProp) =>
% 132.79/22.97 (((app) =>
% 132.79/22.97 (((infuncsetfunc) =>
% 132.79/22.97 ((
% 132.79/22.97 (ap2p) =>
% 132.79/22.97 ((
% 132.79/22.97 (funcinfuncset) =>
% 132.79/22.97 ((
% 132.79/22.97 (lamProp) =>
% 132.79/22.97 ((
% 132.79/22.97 (lamp) =>
% 132.79/22.97 ((
% 132.79/22.97 (lam2p) =>
% 132.79/22.97 ((
% 132.79/22.97 (brelnall1) =>
% 132.79/22.97 ((
% 132.79/22.97 (brelnall2) =>
% 132.79/22.97 ((
% 132.79/22.97 (ex1E2) =>
% 132.79/22.97 ((
% 132.79/22.97 (funcGraphProp1) =>
% 132.79/22.97 ((
% 132.79/22.97 (funcGraphProp3) =>
% 132.79/22.97 ((
% 132.79/22.97 (funcGraphProp2) =>
% 132.79/22.97 ((
% 132.79/22.97 (funcextLem) =>
% 132.79/22.97 ((
% 132.79/22.97 (funcGraphProp4) =>
% 132.79/22.97 ((
% 132.79/22.97 (subbreln) =>
% 132.79/22.97 ((
% 132.79/22.97 (eqbreln) =>
% 132.79/22.97 ((
% 132.79/22.97 (funcext) =>
% 132.79/22.97 ((
% 132.79/22.97 (funcext2) =>
% 132.79/22.97 ((
% 132.79/22.97 (ap2apEq1) =>
% 132.79/22.97 ((
% 132.79/22.97 (ap2apEq2) =>
% 132.79/22.97 ((
% 132.79/22.97 (beta1) =>
% 132.79/22.97 ((
% 132.79/22.97 (eta1) =>
% 132.79/22.97 ((
% 132.79/22.97 (lam2lamEq) =>
% 132.79/22.97 ((
% 132.79/22.97 (beta2) =>
% 132.79/22.97 ((
% 132.79/22.97 (eta2) =>
% 132.79/22.97 ((
% 132.79/22.97 (iffalseProp1) =>
% 132.79/22.97 ((
% 132.79/22.97 (iffalseProp2) =>
% 132.79/22.97 ((
% 132.79/22.97 (iftrueProp1) =>
% 132.79/22.97 ((
% 132.79/22.97 (iftrueProp2) =>
% 132.79/22.97 ((
% 132.79/22.97 (ifSingleton) =>
% 132.79/22.97 ((
% 132.79/22.97 (ifp) =>
% 132.79/22.97 ((
% 132.79/22.97 (theeq) =>
% 132.79/22.97 ((
% 132.79/22.97 (iftrue) =>
% 132.79/22.97 ((
% 132.79/22.97 (iffalse) =>
% 132.79/22.97 ((
% 132.79/22.97 (iftrueorfalse) =>
% 132.79/22.97 ((
% 132.79/22.97 (binintersectT_lem) =>
% 132.79/22.97 ((
% 132.79/22.97 (binunionT_lem) =>
% 132.79/22.97 ((
% 132.79/22.97 (powersetT_lem) =>
% 132.79/22.97 ((
% 132.79/22.97 (setminusT_lem) =>
% 132.79/22.97 ((
% 132.79/22.97 (complementT_lem) =>
% 132.79/22.97 ((
% 132.79/22.97 (setextT) =>
% 132.79/22.97 ((
% 132.79/22.97 (subsetTI) =>
% 132.79/22.97 ((
% 132.79/22.97 (powersetTI1) =>
% 132.79/22.97 ((
% 132.79/22.97 (powersetTE1) =>
% 132.79/22.97 ((
% 132.79/22.97 (complementTI1) =>
% 132.79/22.97 ((
% 132.79/22.97 (complementTE1) =>
% 132.79/22.97 ((
% 132.79/22.97 (binintersectTELcontra) =>
% 132.79/22.97 ((
% 132.79/22.97 (binintersectTERcontra) =>
% 132.79/22.97 ((
% 132.79/22.97 (contrasubsetT) =>
% 132.79/22.97 ((
% 132.79/22.97 (contrasubsetT1) =>
% 132.79/22.97 ((
% 132.79/22.97 (contrasubsetT2) =>
% 132.79/22.97 ((
% 132.79/22.97 (contrasubsetT3) =>
% 132.79/22.97 ((
% 132.79/22.97 (doubleComplementI1) =>
% 132.79/22.97 ((
% 132.79/22.97 (doubleComplementE1) =>
% 132.79/22.97 ((
% 132.79/22.97 (doubleComplementSub1) =>
% 132.79/22.97 ((
% 132.79/22.97 (doubleComplementSub2) =>
% 132.79/22.97 ((
% 132.79/22.97 (doubleComplementEq) =>
% 132.79/22.97 ((
% 132.79/22.97 (complementTnotintersectT) =>
% 132.79/22.97 ((
% 132.79/22.97 (complementImpComplementIntersect) =>
% 132.79/22.97 ((
% 132.79/22.97 (complementSubsetComplementIntersect) =>
% 132.79/22.97 ((
% 132.79/22.97 (complementInPowersetComplementIntersect) =>
% 132.79/22.97 ((
% 132.79/22.97 (contraSubsetComplement) =>
% 132.79/22.97 ((
% 132.79/22.97 (complementTcontraSubset) =>
% 132.79/22.97 ((
% 132.79/22.97 (binunionTILcontra) =>
% 132.79/22.97 ((
% 132.79/22.97 (binunionTIRcontra) =>
% 132.79/22.97 ((
% 132.79/22.97 (inIntersectImpInUnion) =>
% 132.79/22.97 ((
% 132.79/22.97 (inIntersectImpInUnion2) =>
% 132.79/22.97 ((
% 132.79/22.97 (inIntersectImpInIntersectUnions) =>
% 132.79/22.97 ((
% 132.79/22.97 (intersectInPowersetIntersectUnions) =>
% 132.79/22.97 ((
% 132.79/22.97 (inComplementUnionImpNotIn1) =>
% 132.79/22.97 ((
% 132.79/22.97 (inComplementUnionImpInComplement1) =>
% 132.79/22.97 ((
% 132.79/22.97 (binunionTE) =>
% 132.79/22.97 ((
% 132.79/22.97 (binunionTEcontra) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan2a1) =>
% 132.79/22.97 ((
% 132.79/22.97 (complementUnionInPowersetComplement) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan2a2) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan1a) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan1b) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan1) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan2a) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan2b2) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan2b) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan2) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz13rule0) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz13rule1) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz13rule2) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz13rule3) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz13rule4) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz1_1) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz1_2) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz1_3) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz1_4) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz1_5) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1all2) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1SetBreln1) =>
% 132.79/22.97 ((
% 132.79/22.97 (choice2fnsingleton) =>
% 132.79/22.97 ((
% 132.79/22.97 (setOfPairsIsBReln1) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1all1) =>
% 132.79/22.97 ((
% 132.79/22.97 (subbreln1) =>
% 132.79/22.97 ((
% 132.79/22.97 (eqbreln1) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1invprop) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1invI) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1invE) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1compprop) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1compI) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1compE) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1compEex) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionprop) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionIL) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionIR) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionI) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionE) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionEcases) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionCommutes) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz2Ex) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz2W) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz2A) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz2B) =>
% 132.79/22.97 ((
% 132.79/22.97 (image1Ex) =>
% 132.79/22.97 ((
% 132.79/22.97 (image1Ex1) =>
% 132.79/22.97 ((
% 132.79/22.97 (image1Equiv) =>
% 132.79/22.97 ((
% 132.79/22.97 (image1E) =>
% 132.79/22.97 ((
% 132.79/22.97 (image1I) =>
% 132.79/22.97 ((
% 132.79/22.97 (injFuncInInjFuncSet) =>
% 132.79/22.97 ((
% 132.79/22.97 (injFuncSetFuncIn) =>
% 132.79/22.97 ((
% 132.79/22.97 (injFuncSetFuncInj) =>
% 132.79/22.97 ((
% 132.79/22.97 (surjFuncSetFuncIn) =>
% 132.79/22.97 ((
% 132.79/22.97 (surjFuncSetFuncSurj) =>
% 132.79/22.97 ((
% 132.79/22.97 (leftInvIsSurj) =>
% 132.79/22.97 ((
% 132.79/22.97 (surjCantorThm) =>
% 132.79/22.97 ((
% 132.79/22.97 (foundation2) =>
% 132.79/22.97 ((
% 132.79/22.97 (notinself) =>
% 132.79/22.97 ((
% 132.79/22.97 (notinself2) =>
% 132.79/22.97 ((
% 132.79/22.97 (omegaSp) =>
% 132.79/22.97 ((
% 132.79/22.97 (omegaSclos) =>
% 132.79/22.97 ((
% 132.79/22.97 (peano0notS) =>
% 132.79/22.97 ((
% 132.79/22.97 (peanoSinj) =>
% 132.79/22.97 ((
% 132.79/22.97 (transitivesetOp1) =>
% 132.79/22.97 ((
% 132.79/22.97 (binintTransitive) =>
% 132.79/22.97 ((
% 132.79/22.97 (transitivesetOp2) =>
% 132.79/22.97 ((
% 132.79/22.97 (setunionTransitive) =>
% 132.79/22.97 ((
% 132.79/22.97 (ordinalMinLem1) =>
% 132.79/22.97 ((
% 132.79/22.97 (ordinalTransSet) =>
% 132.79/22.97 ((
% 132.79/22.97 (ordinalTransSet1) =>
% 132.79/22.97 ((
% 132.79/22.97 (setunionOrdinalLem1) =>
% 132.79/22.97 (ordinal @
% 132.79/22.97 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/22.97 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1371])).
% 132.79/22.97 thf(zip_derived_cl1396, plain,
% 132.79/22.97 (~ (((setukpairinjL2) =>
% 132.79/22.97 (((setukpairinjL) =>
% 132.79/22.97 (((setukpairinjR11) =>
% 132.79/22.97 (((setukpairinjR12) =>
% 132.79/22.97 (((setukpairinjR1) =>
% 132.79/22.97 (((upairequniteq) =>
% 132.79/22.97 (((setukpairinjR2) =>
% 132.79/22.97 (((setukpairinjR) =>
% 132.79/22.97 (((ksndsingleton) =>
% 132.79/22.97 (((ksndpairEq) =>
% 132.79/22.97 (((kpairsurjEq) =>
% 132.79/22.97 (((cartprodsndin) =>
% 132.79/22.97 (((cartprodpairmemEL) =>
% 132.79/22.97 (((cartprodpairmemER) =>
% 132.79/22.97 (((cartprodmempaircEq) =>
% 132.79/22.97 (((cartprodfstpairEq) =>
% 132.79/22.97 (((cartprodsndpairEq) =>
% 132.79/22.97 (((cartprodpairsurjEq) =>
% 132.79/22.97 (((dpsetconstrI) =>
% 132.79/22.97 (((dpsetconstrSub) =>
% 132.79/22.97 (((setOfPairsIsBReln) =>
% 132.79/22.97 (((dpsetconstrERa) =>
% 132.79/22.97 (((dpsetconstrEL1) =>
% 132.79/22.97 (((dpsetconstrEL2) =>
% 132.79/22.97 (((dpsetconstrER) =>
% 132.79/22.97 (((funcImageSingleton) =>
% 132.79/22.97 (((apProp) =>
% 132.79/22.97 (((app) =>
% 132.79/22.97 (((infuncsetfunc) =>
% 132.79/22.97 (((ap2p) =>
% 132.79/22.97 ((
% 132.79/22.97 (funcinfuncset) =>
% 132.79/22.97 ((
% 132.79/22.97 (lamProp) =>
% 132.79/22.97 ((
% 132.79/22.97 (lamp) =>
% 132.79/22.97 ((
% 132.79/22.97 (lam2p) =>
% 132.79/22.97 ((
% 132.79/22.97 (brelnall1) =>
% 132.79/22.97 ((
% 132.79/22.97 (brelnall2) =>
% 132.79/22.97 ((
% 132.79/22.97 (ex1E2) =>
% 132.79/22.97 ((
% 132.79/22.97 (funcGraphProp1) =>
% 132.79/22.97 ((
% 132.79/22.97 (funcGraphProp3) =>
% 132.79/22.97 ((
% 132.79/22.97 (funcGraphProp2) =>
% 132.79/22.97 ((
% 132.79/22.97 (funcextLem) =>
% 132.79/22.97 ((
% 132.79/22.97 (funcGraphProp4) =>
% 132.79/22.97 ((
% 132.79/22.97 (subbreln) =>
% 132.79/22.97 ((
% 132.79/22.97 (eqbreln) =>
% 132.79/22.97 ((
% 132.79/22.97 (funcext) =>
% 132.79/22.97 ((
% 132.79/22.97 (funcext2) =>
% 132.79/22.97 ((
% 132.79/22.97 (ap2apEq1) =>
% 132.79/22.97 ((
% 132.79/22.97 (ap2apEq2) =>
% 132.79/22.97 ((
% 132.79/22.97 (beta1) =>
% 132.79/22.97 ((
% 132.79/22.97 (eta1) =>
% 132.79/22.97 ((
% 132.79/22.97 (lam2lamEq) =>
% 132.79/22.97 ((
% 132.79/22.97 (beta2) =>
% 132.79/22.97 ((
% 132.79/22.97 (eta2) =>
% 132.79/22.97 ((
% 132.79/22.97 (iffalseProp1) =>
% 132.79/22.97 ((
% 132.79/22.97 (iffalseProp2) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 (demorgan2b) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan2) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (woz13rule2) =>
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% 132.79/22.97 (eqbreln1) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (breln1unionE) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (injFuncSetFuncIn) =>
% 132.79/22.97 ((
% 132.79/22.97 (injFuncSetFuncInj) =>
% 132.79/22.97 ((
% 132.79/22.97 (surjFuncSetFuncIn) =>
% 132.79/22.97 ((
% 132.79/22.97 (surjFuncSetFuncSurj) =>
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% 132.79/22.97 (leftInvIsSurj) =>
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1382])).
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (ordinalTransSet) =>
% 132.79/22.97 ((
% 132.79/22.97 (ordinalTransSet1) =>
% 132.79/22.97 ((
% 132.79/22.97 (setunionOrdinalLem1) =>
% 132.79/22.97 (ordinal @
% 132.79/22.97 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/22.97 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1396])).
% 132.79/22.97 thf(zip_derived_cl1425, plain,
% 132.79/22.97 (~ (((setukpairinjR11) =>
% 132.79/22.97 (((setukpairinjR12) =>
% 132.79/22.97 (((setukpairinjR1) =>
% 132.79/22.97 (((upairequniteq) =>
% 132.79/22.97 (((setukpairinjR2) =>
% 132.79/22.97 (((setukpairinjR) =>
% 132.79/22.97 (((ksndsingleton) =>
% 132.79/22.97 (((ksndpairEq) =>
% 132.79/22.97 (((kpairsurjEq) =>
% 132.79/22.97 (((cartprodsndin) =>
% 132.79/22.97 (((cartprodpairmemEL) =>
% 132.79/22.97 (((cartprodpairmemER) =>
% 132.79/22.97 (((cartprodmempaircEq) =>
% 132.79/22.97 (((cartprodfstpairEq) =>
% 132.79/22.97 (((cartprodsndpairEq) =>
% 132.79/22.97 (((cartprodpairsurjEq) =>
% 132.79/22.97 (((dpsetconstrI) =>
% 132.79/22.97 (((dpsetconstrSub) =>
% 132.79/22.97 (((setOfPairsIsBReln) =>
% 132.79/22.97 (((dpsetconstrERa) =>
% 132.79/22.97 (((dpsetconstrEL1) =>
% 132.79/22.97 (((dpsetconstrEL2) =>
% 132.79/22.97 (((dpsetconstrER) =>
% 132.79/22.97 (((funcImageSingleton) =>
% 132.79/22.97 (((apProp) =>
% 132.79/22.97 (((app) =>
% 132.79/22.97 (((infuncsetfunc) =>
% 132.79/22.97 (((ap2p) =>
% 132.79/22.97 (((funcinfuncset) =>
% 132.79/22.97 (((lamProp) =>
% 132.79/22.97 ((
% 132.79/22.97 (lamp) =>
% 132.79/22.97 ((
% 132.79/22.97 (lam2p) =>
% 132.79/22.97 ((
% 132.79/22.97 (brelnall1) =>
% 132.79/22.97 ((
% 132.79/22.97 (brelnall2) =>
% 132.79/22.97 ((
% 132.79/22.97 (ex1E2) =>
% 132.79/22.97 ((
% 132.79/22.97 (funcGraphProp1) =>
% 132.79/22.97 ((
% 132.79/22.97 (funcGraphProp3) =>
% 132.79/22.97 ((
% 132.79/22.97 (funcGraphProp2) =>
% 132.79/22.97 ((
% 132.79/22.97 (funcextLem) =>
% 132.79/22.97 ((
% 132.79/22.97 (funcGraphProp4) =>
% 132.79/22.97 ((
% 132.79/22.97 (subbreln) =>
% 132.79/22.97 ((
% 132.79/22.97 (eqbreln) =>
% 132.79/22.97 ((
% 132.79/22.97 (funcext) =>
% 132.79/22.97 ((
% 132.79/22.97 (funcext2) =>
% 132.79/22.97 ((
% 132.79/22.97 (ap2apEq1) =>
% 132.79/22.97 ((
% 132.79/22.97 (ap2apEq2) =>
% 132.79/22.97 ((
% 132.79/22.97 (beta1) =>
% 132.79/22.97 ((
% 132.79/22.97 (eta1) =>
% 132.79/22.97 ((
% 132.79/22.97 (lam2lamEq) =>
% 132.79/22.97 ((
% 132.79/22.97 (beta2) =>
% 132.79/22.97 ((
% 132.79/22.97 (eta2) =>
% 132.79/22.97 ((
% 132.79/22.97 (iffalseProp1) =>
% 132.79/22.97 ((
% 132.79/22.97 (iffalseProp2) =>
% 132.79/22.97 ((
% 132.79/22.97 (iftrueProp1) =>
% 132.79/22.97 ((
% 132.79/22.97 (iftrueProp2) =>
% 132.79/22.97 ((
% 132.79/22.97 (ifSingleton) =>
% 132.79/22.97 ((
% 132.79/22.97 (ifp) =>
% 132.79/22.97 ((
% 132.79/22.97 (theeq) =>
% 132.79/22.97 ((
% 132.79/22.97 (iftrue) =>
% 132.79/22.97 ((
% 132.79/22.97 (iffalse) =>
% 132.79/22.97 ((
% 132.79/22.97 (iftrueorfalse) =>
% 132.79/22.97 ((
% 132.79/22.97 (binintersectT_lem) =>
% 132.79/22.97 ((
% 132.79/22.97 (binunionT_lem) =>
% 132.79/22.97 ((
% 132.79/22.97 (powersetT_lem) =>
% 132.79/22.97 ((
% 132.79/22.97 (setminusT_lem) =>
% 132.79/22.97 ((
% 132.79/22.97 (complementT_lem) =>
% 132.79/22.97 ((
% 132.79/22.97 (setextT) =>
% 132.79/22.97 ((
% 132.79/22.97 (subsetTI) =>
% 132.79/22.97 ((
% 132.79/22.97 (powersetTI1) =>
% 132.79/22.97 ((
% 132.79/22.97 (powersetTE1) =>
% 132.79/22.97 ((
% 132.79/22.97 (complementTI1) =>
% 132.79/22.97 ((
% 132.79/22.97 (complementTE1) =>
% 132.79/22.97 ((
% 132.79/22.97 (binintersectTELcontra) =>
% 132.79/22.97 ((
% 132.79/22.97 (binintersectTERcontra) =>
% 132.79/22.97 ((
% 132.79/22.97 (contrasubsetT) =>
% 132.79/22.97 ((
% 132.79/22.97 (contrasubsetT1) =>
% 132.79/22.97 ((
% 132.79/22.97 (contrasubsetT2) =>
% 132.79/22.97 ((
% 132.79/22.97 (contrasubsetT3) =>
% 132.79/22.97 ((
% 132.79/22.97 (doubleComplementI1) =>
% 132.79/22.97 ((
% 132.79/22.97 (doubleComplementE1) =>
% 132.79/22.97 ((
% 132.79/22.97 (doubleComplementSub1) =>
% 132.79/22.97 ((
% 132.79/22.97 (doubleComplementSub2) =>
% 132.79/22.97 ((
% 132.79/22.97 (doubleComplementEq) =>
% 132.79/22.97 ((
% 132.79/22.97 (complementTnotintersectT) =>
% 132.79/22.97 ((
% 132.79/22.97 (complementImpComplementIntersect) =>
% 132.79/22.97 ((
% 132.79/22.97 (complementSubsetComplementIntersect) =>
% 132.79/22.97 ((
% 132.79/22.97 (complementInPowersetComplementIntersect) =>
% 132.79/22.97 ((
% 132.79/22.97 (contraSubsetComplement) =>
% 132.79/22.97 ((
% 132.79/22.97 (complementTcontraSubset) =>
% 132.79/22.97 ((
% 132.79/22.97 (binunionTILcontra) =>
% 132.79/22.97 ((
% 132.79/22.97 (binunionTIRcontra) =>
% 132.79/22.97 ((
% 132.79/22.97 (inIntersectImpInUnion) =>
% 132.79/22.97 ((
% 132.79/22.97 (inIntersectImpInUnion2) =>
% 132.79/22.97 ((
% 132.79/22.97 (inIntersectImpInIntersectUnions) =>
% 132.79/22.97 ((
% 132.79/22.97 (intersectInPowersetIntersectUnions) =>
% 132.79/22.97 ((
% 132.79/22.97 (inComplementUnionImpNotIn1) =>
% 132.79/22.97 ((
% 132.79/22.97 (inComplementUnionImpInComplement1) =>
% 132.79/22.97 ((
% 132.79/22.97 (binunionTE) =>
% 132.79/22.97 ((
% 132.79/22.97 (binunionTEcontra) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan2a1) =>
% 132.79/22.97 ((
% 132.79/22.97 (complementUnionInPowersetComplement) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan2a2) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan1a) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan1b) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan1) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan2a) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan2b2) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan2b) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan2) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz13rule0) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz13rule1) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz13rule2) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz13rule3) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz13rule4) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz1_1) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz1_2) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz1_3) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz1_4) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz1_5) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1all2) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1SetBreln1) =>
% 132.79/22.97 ((
% 132.79/22.97 (choice2fnsingleton) =>
% 132.79/22.97 ((
% 132.79/22.97 (setOfPairsIsBReln1) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1all1) =>
% 132.79/22.97 ((
% 132.79/22.97 (subbreln1) =>
% 132.79/22.97 ((
% 132.79/22.97 (eqbreln1) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1invprop) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1invI) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1invE) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1compprop) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1compI) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1compE) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1compEex) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionprop) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionIL) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionIR) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionI) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionE) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionEcases) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionCommutes) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz2Ex) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz2W) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz2A) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz2B) =>
% 132.79/22.97 ((
% 132.79/22.97 (image1Ex) =>
% 132.79/22.97 ((
% 132.79/22.97 (image1Ex1) =>
% 132.79/22.97 ((
% 132.79/22.97 (image1Equiv) =>
% 132.79/22.97 ((
% 132.79/22.97 (image1E) =>
% 132.79/22.97 ((
% 132.79/22.97 (image1I) =>
% 132.79/22.97 ((
% 132.79/22.97 (injFuncInInjFuncSet) =>
% 132.79/22.97 ((
% 132.79/22.97 (injFuncSetFuncIn) =>
% 132.79/22.97 ((
% 132.79/22.97 (injFuncSetFuncInj) =>
% 132.79/22.97 ((
% 132.79/22.97 (surjFuncSetFuncIn) =>
% 132.79/22.97 ((
% 132.79/22.97 (surjFuncSetFuncSurj) =>
% 132.79/22.97 ((
% 132.79/22.97 (leftInvIsSurj) =>
% 132.79/22.97 ((
% 132.79/22.97 (surjCantorThm) =>
% 132.79/22.97 ((
% 132.79/22.97 (foundation2) =>
% 132.79/22.97 ((
% 132.79/22.97 (notinself) =>
% 132.79/22.97 ((
% 132.79/22.97 (notinself2) =>
% 132.79/22.97 ((
% 132.79/22.97 (omegaSp) =>
% 132.79/22.97 ((
% 132.79/22.97 (omegaSclos) =>
% 132.79/22.97 ((
% 132.79/22.97 (peano0notS) =>
% 132.79/22.97 ((
% 132.79/22.97 (peanoSinj) =>
% 132.79/22.97 ((
% 132.79/22.97 (transitivesetOp1) =>
% 132.79/22.97 ((
% 132.79/22.97 (binintTransitive) =>
% 132.79/22.97 ((
% 132.79/22.97 (transitivesetOp2) =>
% 132.79/22.97 ((
% 132.79/22.97 (setunionTransitive) =>
% 132.79/22.97 ((
% 132.79/22.97 (ordinalMinLem1) =>
% 132.79/22.97 ((
% 132.79/22.97 (ordinalTransSet) =>
% 132.79/22.97 ((
% 132.79/22.97 (ordinalTransSet1) =>
% 132.79/22.97 ((
% 132.79/22.97 (setunionOrdinalLem1) =>
% 132.79/22.97 (ordinal @
% 132.79/22.97 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/22.97 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1409])).
% 132.79/22.97 thf(zip_derived_cl1440, plain,
% 132.79/22.97 (~ (((setukpairinjR12) =>
% 132.79/22.97 (((setukpairinjR1) =>
% 132.79/22.97 (((upairequniteq) =>
% 132.79/22.97 (((setukpairinjR2) =>
% 132.79/22.97 (((setukpairinjR) =>
% 132.79/22.97 (((ksndsingleton) =>
% 132.79/22.97 (((ksndpairEq) =>
% 132.79/22.97 (((kpairsurjEq) =>
% 132.79/22.97 (((cartprodsndin) =>
% 132.79/22.97 (((cartprodpairmemEL) =>
% 132.79/22.97 (((cartprodpairmemER) =>
% 132.79/22.97 (((cartprodmempaircEq) =>
% 132.79/22.97 (((cartprodfstpairEq) =>
% 132.79/22.97 (((cartprodsndpairEq) =>
% 132.79/22.97 (((cartprodpairsurjEq) =>
% 132.79/22.97 (((dpsetconstrI) =>
% 132.79/22.97 (((dpsetconstrSub) =>
% 132.79/22.97 (((setOfPairsIsBReln) =>
% 132.79/22.97 (((dpsetconstrERa) =>
% 132.79/22.97 (((dpsetconstrEL1) =>
% 132.79/22.97 (((dpsetconstrEL2) =>
% 132.79/22.97 (((dpsetconstrER) =>
% 132.79/22.97 (((funcImageSingleton) =>
% 132.79/22.97 (((apProp) =>
% 132.79/22.97 (((app) =>
% 132.79/22.97 (((infuncsetfunc) =>
% 132.79/22.97 (((ap2p) =>
% 132.79/22.97 (((funcinfuncset) =>
% 132.79/22.97 (((lamProp) =>
% 132.79/22.97 (((lamp) =>
% 132.79/22.97 ((
% 132.79/22.97 (lam2p) =>
% 132.79/22.97 ((
% 132.79/22.97 (brelnall1) =>
% 132.79/22.97 ((
% 132.79/22.97 (brelnall2) =>
% 132.79/22.97 ((
% 132.79/22.97 (ex1E2) =>
% 132.79/22.97 ((
% 132.79/22.97 (funcGraphProp1) =>
% 132.79/22.97 ((
% 132.79/22.97 (funcGraphProp3) =>
% 132.79/22.97 ((
% 132.79/22.97 (funcGraphProp2) =>
% 132.79/22.97 ((
% 132.79/22.97 (funcextLem) =>
% 132.79/22.97 ((
% 132.79/22.97 (funcGraphProp4) =>
% 132.79/22.97 ((
% 132.79/22.97 (subbreln) =>
% 132.79/22.97 ((
% 132.79/22.97 (eqbreln) =>
% 132.79/22.97 ((
% 132.79/22.97 (funcext) =>
% 132.79/22.97 ((
% 132.79/22.97 (funcext2) =>
% 132.79/22.97 ((
% 132.79/22.97 (ap2apEq1) =>
% 132.79/22.97 ((
% 132.79/22.97 (ap2apEq2) =>
% 132.79/22.97 ((
% 132.79/22.97 (beta1) =>
% 132.79/22.97 ((
% 132.79/22.97 (eta1) =>
% 132.79/22.97 ((
% 132.79/22.97 (lam2lamEq) =>
% 132.79/22.97 ((
% 132.79/22.97 (beta2) =>
% 132.79/22.97 ((
% 132.79/22.97 (eta2) =>
% 132.79/22.97 ((
% 132.79/22.97 (iffalseProp1) =>
% 132.79/22.97 ((
% 132.79/22.97 (iffalseProp2) =>
% 132.79/22.97 ((
% 132.79/22.97 (iftrueProp1) =>
% 132.79/22.97 ((
% 132.79/22.97 (iftrueProp2) =>
% 132.79/22.97 ((
% 132.79/22.97 (ifSingleton) =>
% 132.79/22.97 ((
% 132.79/22.97 (ifp) =>
% 132.79/22.97 ((
% 132.79/22.97 (theeq) =>
% 132.79/22.97 ((
% 132.79/22.97 (iftrue) =>
% 132.79/22.97 ((
% 132.79/22.97 (iffalse) =>
% 132.79/22.97 ((
% 132.79/22.97 (iftrueorfalse) =>
% 132.79/22.97 ((
% 132.79/22.97 (binintersectT_lem) =>
% 132.79/22.97 ((
% 132.79/22.97 (binunionT_lem) =>
% 132.79/22.97 ((
% 132.79/22.97 (powersetT_lem) =>
% 132.79/22.97 ((
% 132.79/22.97 (setminusT_lem) =>
% 132.79/22.97 ((
% 132.79/22.97 (complementT_lem) =>
% 132.79/22.97 ((
% 132.79/22.97 (setextT) =>
% 132.79/22.97 ((
% 132.79/22.97 (subsetTI) =>
% 132.79/22.97 ((
% 132.79/22.97 (powersetTI1) =>
% 132.79/22.97 ((
% 132.79/22.97 (powersetTE1) =>
% 132.79/22.97 ((
% 132.79/22.97 (complementTI1) =>
% 132.79/22.97 ((
% 132.79/22.97 (complementTE1) =>
% 132.79/22.97 ((
% 132.79/22.97 (binintersectTELcontra) =>
% 132.79/22.97 ((
% 132.79/22.97 (binintersectTERcontra) =>
% 132.79/22.97 ((
% 132.79/22.97 (contrasubsetT) =>
% 132.79/22.97 ((
% 132.79/22.97 (contrasubsetT1) =>
% 132.79/22.97 ((
% 132.79/22.97 (contrasubsetT2) =>
% 132.79/22.97 ((
% 132.79/22.97 (contrasubsetT3) =>
% 132.79/22.97 ((
% 132.79/22.97 (doubleComplementI1) =>
% 132.79/22.97 ((
% 132.79/22.97 (doubleComplementE1) =>
% 132.79/22.97 ((
% 132.79/22.97 (doubleComplementSub1) =>
% 132.79/22.97 ((
% 132.79/22.97 (doubleComplementSub2) =>
% 132.79/22.97 ((
% 132.79/22.97 (doubleComplementEq) =>
% 132.79/22.97 ((
% 132.79/22.97 (complementTnotintersectT) =>
% 132.79/22.97 ((
% 132.79/22.97 (complementImpComplementIntersect) =>
% 132.79/22.97 ((
% 132.79/22.97 (complementSubsetComplementIntersect) =>
% 132.79/22.97 ((
% 132.79/22.97 (complementInPowersetComplementIntersect) =>
% 132.79/22.97 ((
% 132.79/22.97 (contraSubsetComplement) =>
% 132.79/22.97 ((
% 132.79/22.97 (complementTcontraSubset) =>
% 132.79/22.97 ((
% 132.79/22.97 (binunionTILcontra) =>
% 132.79/22.97 ((
% 132.79/22.97 (binunionTIRcontra) =>
% 132.79/22.97 ((
% 132.79/22.97 (inIntersectImpInUnion) =>
% 132.79/22.97 ((
% 132.79/22.97 (inIntersectImpInUnion2) =>
% 132.79/22.97 ((
% 132.79/22.97 (inIntersectImpInIntersectUnions) =>
% 132.79/22.97 ((
% 132.79/22.97 (intersectInPowersetIntersectUnions) =>
% 132.79/22.97 ((
% 132.79/22.97 (inComplementUnionImpNotIn1) =>
% 132.79/22.97 ((
% 132.79/22.97 (inComplementUnionImpInComplement1) =>
% 132.79/22.97 ((
% 132.79/22.97 (binunionTE) =>
% 132.79/22.97 ((
% 132.79/22.97 (binunionTEcontra) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan2a1) =>
% 132.79/22.97 ((
% 132.79/22.97 (complementUnionInPowersetComplement) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan2a2) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan1a) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan1b) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan1) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan2a) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan2b2) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan2b) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan2) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz13rule0) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz13rule1) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz13rule2) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz13rule3) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz13rule4) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz1_1) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz1_2) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz1_3) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz1_4) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz1_5) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1all2) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1SetBreln1) =>
% 132.79/22.97 ((
% 132.79/22.97 (choice2fnsingleton) =>
% 132.79/22.97 ((
% 132.79/22.97 (setOfPairsIsBReln1) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1all1) =>
% 132.79/22.97 ((
% 132.79/22.97 (subbreln1) =>
% 132.79/22.97 ((
% 132.79/22.97 (eqbreln1) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1invprop) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1invI) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1invE) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1compprop) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1compI) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1compE) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1compEex) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionprop) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionIL) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionIR) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionI) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionE) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionEcases) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionCommutes) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz2Ex) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz2W) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz2A) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz2B) =>
% 132.79/22.97 ((
% 132.79/22.97 (image1Ex) =>
% 132.79/22.97 ((
% 132.79/22.97 (image1Ex1) =>
% 132.79/22.97 ((
% 132.79/22.97 (image1Equiv) =>
% 132.79/22.97 ((
% 132.79/22.97 (image1E) =>
% 132.79/22.97 ((
% 132.79/22.97 (image1I) =>
% 132.79/22.97 ((
% 132.79/22.97 (injFuncInInjFuncSet) =>
% 132.79/22.97 ((
% 132.79/22.97 (injFuncSetFuncIn) =>
% 132.79/22.97 ((
% 132.79/22.97 (injFuncSetFuncInj) =>
% 132.79/22.97 ((
% 132.79/22.97 (surjFuncSetFuncIn) =>
% 132.79/22.97 ((
% 132.79/22.97 (surjFuncSetFuncSurj) =>
% 132.79/22.97 ((
% 132.79/22.97 (leftInvIsSurj) =>
% 132.79/22.97 ((
% 132.79/22.97 (surjCantorThm) =>
% 132.79/22.97 ((
% 132.79/22.97 (foundation2) =>
% 132.79/22.97 ((
% 132.79/22.97 (notinself) =>
% 132.79/22.97 ((
% 132.79/22.97 (notinself2) =>
% 132.79/22.97 ((
% 132.79/22.97 (omegaSp) =>
% 132.79/22.97 ((
% 132.79/22.97 (omegaSclos) =>
% 132.79/22.97 ((
% 132.79/22.97 (peano0notS) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1425])).
% 132.79/22.97 thf(zip_derived_cl1453, plain,
% 132.79/22.97 (~ (((setukpairinjR1) =>
% 132.79/22.97 (((upairequniteq) =>
% 132.79/22.97 (((setukpairinjR2) =>
% 132.79/22.97 (((setukpairinjR) =>
% 132.79/22.97 (((ksndsingleton) =>
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% 132.79/22.97 (((kpairsurjEq) =>
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% 132.79/22.97 (((cartprodpairmemER) =>
% 132.79/22.97 (((cartprodmempaircEq) =>
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% 132.79/22.97 (((cartprodsndpairEq) =>
% 132.79/22.97 (((cartprodpairsurjEq) =>
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% 132.79/22.97 (((dpsetconstrEL2) =>
% 132.79/22.97 (((dpsetconstrER) =>
% 132.79/22.97 (((funcImageSingleton) =>
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% 132.79/22.97 (((app) =>
% 132.79/22.97 (((infuncsetfunc) =>
% 132.79/22.97 (((ap2p) =>
% 132.79/22.97 (((funcinfuncset) =>
% 132.79/22.97 (((lamProp) =>
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% 132.79/22.97 (((lam2p) =>
% 132.79/22.97 ((
% 132.79/22.97 (brelnall1) =>
% 132.79/22.97 ((
% 132.79/22.97 (brelnall2) =>
% 132.79/22.97 ((
% 132.79/22.97 (ex1E2) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (funcGraphProp2) =>
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% 132.79/22.97 ((
% 132.79/22.97 (funcGraphProp4) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (funcext2) =>
% 132.79/22.97 ((
% 132.79/22.97 (ap2apEq1) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (contrasubsetT2) =>
% 132.79/22.97 ((
% 132.79/22.97 (contrasubsetT3) =>
% 132.79/22.97 ((
% 132.79/22.97 (doubleComplementI1) =>
% 132.79/22.97 ((
% 132.79/22.97 (doubleComplementE1) =>
% 132.79/22.97 ((
% 132.79/22.97 (doubleComplementSub1) =>
% 132.79/22.97 ((
% 132.79/22.97 (doubleComplementSub2) =>
% 132.79/22.97 ((
% 132.79/22.97 (doubleComplementEq) =>
% 132.79/22.97 ((
% 132.79/22.97 (complementTnotintersectT) =>
% 132.79/22.97 ((
% 132.79/22.97 (complementImpComplementIntersect) =>
% 132.79/22.97 ((
% 132.79/22.97 (complementSubsetComplementIntersect) =>
% 132.79/22.97 ((
% 132.79/22.97 (complementInPowersetComplementIntersect) =>
% 132.79/22.97 ((
% 132.79/22.97 (contraSubsetComplement) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (binunionTIRcontra) =>
% 132.79/22.97 ((
% 132.79/22.97 (inIntersectImpInUnion) =>
% 132.79/22.97 ((
% 132.79/22.97 (inIntersectImpInUnion2) =>
% 132.79/22.97 ((
% 132.79/22.97 (inIntersectImpInIntersectUnions) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (binunionTE) =>
% 132.79/22.97 ((
% 132.79/22.97 (binunionTEcontra) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan2a1) =>
% 132.79/22.97 ((
% 132.79/22.97 (complementUnionInPowersetComplement) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan2a2) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan1a) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan1b) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan1) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan2a) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan2b2) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan2b) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan2) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz13rule0) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz13rule1) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz13rule2) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz13rule3) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz13rule4) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (woz1_2) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz1_3) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz1_4) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz1_5) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1all2) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1SetBreln1) =>
% 132.79/22.97 ((
% 132.79/22.97 (choice2fnsingleton) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (breln1all1) =>
% 132.79/22.97 ((
% 132.79/22.97 (subbreln1) =>
% 132.79/22.97 ((
% 132.79/22.97 (eqbreln1) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (breln1invE) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (breln1unionprop) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionIL) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionIR) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionI) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionE) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (image1E) =>
% 132.79/22.97 ((
% 132.79/22.97 (image1I) =>
% 132.79/22.97 ((
% 132.79/22.97 (injFuncInInjFuncSet) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1440])).
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% 132.79/22.97 ((
% 132.79/22.97 (contrasubsetT2) =>
% 132.79/22.97 ((
% 132.79/22.97 (contrasubsetT3) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (doubleComplementE1) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (doubleComplementSub2) =>
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (inIntersectImpInUnion) =>
% 132.79/22.97 ((
% 132.79/22.97 (inIntersectImpInUnion2) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (binunionTEcontra) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan2a1) =>
% 132.79/22.97 ((
% 132.79/22.97 (complementUnionInPowersetComplement) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan2a2) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan1a) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan1b) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan1) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan2a) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan2b2) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan2b) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan2) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (woz13rule1) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz13rule2) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz13rule3) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz13rule4) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (woz1_2) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz1_3) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz1_4) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz1_5) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1all2) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1SetBreln1) =>
% 132.79/22.97 ((
% 132.79/22.97 (choice2fnsingleton) =>
% 132.79/22.97 ((
% 132.79/22.97 (setOfPairsIsBReln1) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1all1) =>
% 132.79/22.97 ((
% 132.79/22.97 (subbreln1) =>
% 132.79/22.97 ((
% 132.79/22.97 (eqbreln1) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (breln1invI) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1invE) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1compprop) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1compI) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1compE) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1compEex) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionprop) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionIL) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionIR) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionI) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionE) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionEcases) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionCommutes) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz2Ex) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz2W) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (woz2B) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (image1Equiv) =>
% 132.79/22.97 ((
% 132.79/22.97 (image1E) =>
% 132.79/22.97 ((
% 132.79/22.97 (image1I) =>
% 132.79/22.97 ((
% 132.79/22.97 (injFuncInInjFuncSet) =>
% 132.79/22.97 ((
% 132.79/22.97 (injFuncSetFuncIn) =>
% 132.79/22.97 ((
% 132.79/22.97 (injFuncSetFuncInj) =>
% 132.79/22.97 ((
% 132.79/22.97 (surjFuncSetFuncIn) =>
% 132.79/22.97 ((
% 132.79/22.97 (surjFuncSetFuncSurj) =>
% 132.79/22.97 ((
% 132.79/22.97 (leftInvIsSurj) =>
% 132.79/22.97 ((
% 132.79/22.97 (surjCantorThm) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (notinself2) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (omegaSclos) =>
% 132.79/22.97 ((
% 132.79/22.97 (peano0notS) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1453])).
% 132.79/22.97 thf(zip_derived_cl1475, plain,
% 132.79/22.97 (~ (((setukpairinjR2) =>
% 132.79/22.97 (((setukpairinjR) =>
% 132.79/22.97 (((ksndsingleton) =>
% 132.79/22.97 (((ksndpairEq) =>
% 132.79/22.97 (((kpairsurjEq) =>
% 132.79/22.97 (((cartprodsndin) =>
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% 132.79/22.97 (((cartprodpairmemER) =>
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% 132.79/22.97 (((dpsetconstrSub) =>
% 132.79/22.97 (((setOfPairsIsBReln) =>
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% 132.79/22.97 (((dpsetconstrEL2) =>
% 132.79/22.97 (((dpsetconstrER) =>
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% 132.79/22.97 (((infuncsetfunc) =>
% 132.79/22.97 (((ap2p) =>
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% 132.79/22.97 (((lam2p) =>
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% 132.79/22.97 (((brelnall2) =>
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (funcext2) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (ap2apEq2) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (eta1) =>
% 132.79/22.97 ((
% 132.79/22.97 (lam2lamEq) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (iftrueProp2) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (theeq) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (powersetT_lem) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (complementTE1) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (binintersectTERcontra) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (contrasubsetT3) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (doubleComplementE1) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (doubleComplementSub2) =>
% 132.79/22.97 ((
% 132.79/22.97 (doubleComplementEq) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (demorgan2a) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 (((brelnall2) =>
% 132.79/22.97 (((ex1E2) =>
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% 132.79/22.97 (funcGraphProp1) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (doubleComplementE1) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (demorgan2a) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (demorgan2b) =>
% 132.79/22.97 ((
% 132.79/22.97 (demorgan2) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz13rule0) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz13rule1) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz13rule2) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz13rule3) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz13rule4) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz1_1) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz1_2) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz1_3) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz1_4) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz1_5) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1all2) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1SetBreln1) =>
% 132.79/22.97 ((
% 132.79/22.97 (choice2fnsingleton) =>
% 132.79/22.97 ((
% 132.79/22.97 (setOfPairsIsBReln1) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1all1) =>
% 132.79/22.97 ((
% 132.79/22.97 (subbreln1) =>
% 132.79/22.97 ((
% 132.79/22.97 (eqbreln1) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1invprop) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1invI) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1invE) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1compprop) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1compI) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1compE) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1compEex) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionprop) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionIL) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionIR) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionI) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionE) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionEcases) =>
% 132.79/22.97 ((
% 132.79/22.97 (breln1unionCommutes) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz2Ex) =>
% 132.79/22.97 ((
% 132.79/22.97 (woz2W) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (woz2B) =>
% 132.79/22.97 ((
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% 132.79/22.97 ((
% 132.79/22.97 (image1Ex1) =>
% 132.79/22.97 ((
% 132.79/22.97 (image1Equiv) =>
% 132.79/22.97 ((
% 132.79/22.98 (image1E) =>
% 132.79/22.98 ((
% 132.79/22.98 (image1I) =>
% 132.79/22.98 ((
% 132.79/22.98 (injFuncInInjFuncSet) =>
% 132.79/22.98 ((
% 132.79/22.98 (injFuncSetFuncIn) =>
% 132.79/22.98 ((
% 132.79/22.98 (injFuncSetFuncInj) =>
% 132.79/22.98 ((
% 132.79/22.98 (surjFuncSetFuncIn) =>
% 132.79/22.98 ((
% 132.79/22.98 (surjFuncSetFuncSurj) =>
% 132.79/22.98 ((
% 132.79/22.98 (leftInvIsSurj) =>
% 132.79/22.98 ((
% 132.79/22.98 (surjCantorThm) =>
% 132.79/22.98 ((
% 132.79/22.98 (foundation2) =>
% 132.79/22.98 ((
% 132.79/22.98 (notinself) =>
% 132.79/22.98 ((
% 132.79/22.98 (notinself2) =>
% 132.79/22.98 ((
% 132.79/22.98 (omegaSp) =>
% 132.79/22.98 ((
% 132.79/22.98 (omegaSclos) =>
% 132.79/22.98 ((
% 132.79/22.98 (peano0notS) =>
% 132.79/22.98 ((
% 132.79/22.98 (peanoSinj) =>
% 132.79/22.98 ((
% 132.79/22.98 (transitivesetOp1) =>
% 132.79/22.98 ((
% 132.79/22.98 (binintTransitive) =>
% 132.79/22.98 ((
% 132.79/22.98 (transitivesetOp2) =>
% 132.79/22.98 ((
% 132.79/22.98 (setunionTransitive) =>
% 132.79/22.98 ((
% 132.79/22.98 (ordinalMinLem1) =>
% 132.79/22.98 ((
% 132.79/22.98 (ordinalTransSet) =>
% 132.79/22.98 ((
% 132.79/22.98 (ordinalTransSet1) =>
% 132.79/22.98 ((
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% 132.79/22.98 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1475])).
% 132.79/22.98 thf(zip_derived_cl1495, plain,
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% 132.79/22.98 (((ksndpairEq) =>
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% 132.79/22.98 (((cartprodpairmemER) =>
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% 132.79/22.98 (((cartprodsndpairEq) =>
% 132.79/22.98 (((cartprodpairsurjEq) =>
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% 132.79/22.98 (((dpsetconstrSub) =>
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
% 132.79/22.98 (doubleComplementSub2) =>
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
% 132.79/22.98 (contraSubsetComplement) =>
% 132.79/22.98 ((
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% 132.79/22.98 ((
% 132.79/22.98 (binunionTILcontra) =>
% 132.79/22.98 ((
% 132.79/22.98 (binunionTIRcontra) =>
% 132.79/22.98 ((
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% 132.79/22.98 ((
% 132.79/22.98 (inIntersectImpInUnion2) =>
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% 132.79/22.98 (inComplementUnionImpNotIn1) =>
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
% 132.79/22.98 (demorgan2b2) =>
% 132.79/22.98 ((
% 132.79/22.98 (demorgan2b) =>
% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 (woz13rule4) =>
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% 132.79/22.98 ((
% 132.79/22.98 (woz1_2) =>
% 132.79/22.98 ((
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% 132.79/22.98 (woz1_4) =>
% 132.79/22.98 ((
% 132.79/22.98 (woz1_5) =>
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% 132.79/22.98 (breln1all2) =>
% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 (image1E) =>
% 132.79/22.98 ((
% 132.79/22.98 (image1I) =>
% 132.79/22.98 ((
% 132.79/22.98 (injFuncInInjFuncSet) =>
% 132.79/22.98 ((
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% 132.79/22.98 ((
% 132.79/22.98 (injFuncSetFuncInj) =>
% 132.79/22.98 ((
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% 132.79/22.98 (surjFuncSetFuncSurj) =>
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% 132.79/22.98 (leftInvIsSurj) =>
% 132.79/22.98 ((
% 132.79/22.98 (surjCantorThm) =>
% 132.79/22.98 ((
% 132.79/22.98 (foundation2) =>
% 132.79/22.98 ((
% 132.79/22.98 (notinself) =>
% 132.79/22.98 ((
% 132.79/22.98 (notinself2) =>
% 132.79/22.98 ((
% 132.79/22.98 (omegaSp) =>
% 132.79/22.98 ((
% 132.79/22.98 (omegaSclos) =>
% 132.79/22.98 ((
% 132.79/22.98 (peano0notS) =>
% 132.79/22.98 ((
% 132.79/22.98 (peanoSinj) =>
% 132.79/22.98 ((
% 132.79/22.98 (transitivesetOp1) =>
% 132.79/22.98 ((
% 132.79/22.98 (binintTransitive) =>
% 132.79/22.98 ((
% 132.79/22.98 (transitivesetOp2) =>
% 132.79/22.98 ((
% 132.79/22.98 (setunionTransitive) =>
% 132.79/22.98 ((
% 132.79/22.98 (ordinalMinLem1) =>
% 132.79/22.98 ((
% 132.79/22.98 (ordinalTransSet) =>
% 132.79/22.98 ((
% 132.79/22.98 (ordinalTransSet1) =>
% 132.79/22.98 ((
% 132.79/22.98 (setunionOrdinalLem1) =>
% 132.79/22.98 (ordinal @
% 132.79/22.98 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/22.98 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1485])).
% 132.79/22.98 thf(zip_derived_cl1504, plain,
% 132.79/22.98 (~ (((ksndpairEq) =>
% 132.79/22.98 (((kpairsurjEq) =>
% 132.79/22.98 (((cartprodsndin) =>
% 132.79/22.98 (((cartprodpairmemEL) =>
% 132.79/22.98 (((cartprodpairmemER) =>
% 132.79/22.98 (((cartprodmempaircEq) =>
% 132.79/22.98 (((cartprodfstpairEq) =>
% 132.79/22.98 (((cartprodsndpairEq) =>
% 132.79/22.98 (((cartprodpairsurjEq) =>
% 132.79/22.98 (((dpsetconstrI) =>
% 132.79/22.98 (((dpsetconstrSub) =>
% 132.79/22.98 (((setOfPairsIsBReln) =>
% 132.79/22.98 (((dpsetconstrERa) =>
% 132.79/22.98 (((dpsetconstrEL1) =>
% 132.79/22.98 (((dpsetconstrEL2) =>
% 132.79/22.98 (((dpsetconstrER) =>
% 132.79/22.98 (((funcImageSingleton) =>
% 132.79/22.98 (((apProp) =>
% 132.79/22.98 (((app) =>
% 132.79/22.98 (((infuncsetfunc) =>
% 132.79/22.98 (((ap2p) =>
% 132.79/22.98 (((funcinfuncset) =>
% 132.79/22.98 (((lamProp) =>
% 132.79/22.98 (((lamp) =>
% 132.79/22.98 (((lam2p) =>
% 132.79/22.98 (((brelnall1) =>
% 132.79/22.98 (((brelnall2) =>
% 132.79/22.98 (((ex1E2) =>
% 132.79/22.98 (((funcGraphProp1) =>
% 132.79/22.98 (((funcGraphProp3) =>
% 132.79/22.98 ((
% 132.79/22.98 (funcGraphProp2) =>
% 132.79/22.98 ((
% 132.79/22.98 (funcextLem) =>
% 132.79/22.98 ((
% 132.79/22.98 (funcGraphProp4) =>
% 132.79/22.98 ((
% 132.79/22.98 (subbreln) =>
% 132.79/22.98 ((
% 132.79/22.98 (eqbreln) =>
% 132.79/22.98 ((
% 132.79/22.98 (funcext) =>
% 132.79/22.98 ((
% 132.79/22.98 (funcext2) =>
% 132.79/22.98 ((
% 132.79/22.98 (ap2apEq1) =>
% 132.79/22.98 ((
% 132.79/22.98 (ap2apEq2) =>
% 132.79/22.98 ((
% 132.79/22.98 (beta1) =>
% 132.79/22.98 ((
% 132.79/22.98 (eta1) =>
% 132.79/22.98 ((
% 132.79/22.98 (lam2lamEq) =>
% 132.79/22.98 ((
% 132.79/22.98 (beta2) =>
% 132.79/22.98 ((
% 132.79/22.98 (eta2) =>
% 132.79/22.98 ((
% 132.79/22.98 (iffalseProp1) =>
% 132.79/22.98 ((
% 132.79/22.98 (iffalseProp2) =>
% 132.79/22.98 ((
% 132.79/22.98 (iftrueProp1) =>
% 132.79/22.98 ((
% 132.79/22.98 (iftrueProp2) =>
% 132.79/22.98 ((
% 132.79/22.98 (ifSingleton) =>
% 132.79/22.98 ((
% 132.79/22.98 (ifp) =>
% 132.79/22.98 ((
% 132.79/22.98 (theeq) =>
% 132.79/22.98 ((
% 132.79/22.98 (iftrue) =>
% 132.79/22.98 ((
% 132.79/22.98 (iffalse) =>
% 132.79/22.98 ((
% 132.79/22.98 (iftrueorfalse) =>
% 132.79/22.98 ((
% 132.79/22.98 (binintersectT_lem) =>
% 132.79/22.98 ((
% 132.79/22.98 (binunionT_lem) =>
% 132.79/22.98 ((
% 132.79/22.98 (powersetT_lem) =>
% 132.79/22.98 ((
% 132.79/22.98 (setminusT_lem) =>
% 132.79/22.98 ((
% 132.79/22.98 (complementT_lem) =>
% 132.79/22.98 ((
% 132.79/22.98 (setextT) =>
% 132.79/22.98 ((
% 132.79/22.98 (subsetTI) =>
% 132.79/22.98 ((
% 132.79/22.98 (powersetTI1) =>
% 132.79/22.98 ((
% 132.79/22.98 (powersetTE1) =>
% 132.79/22.98 ((
% 132.79/22.98 (complementTI1) =>
% 132.79/22.98 ((
% 132.79/22.98 (complementTE1) =>
% 132.79/22.98 ((
% 132.79/22.98 (binintersectTELcontra) =>
% 132.79/22.98 ((
% 132.79/22.98 (binintersectTERcontra) =>
% 132.79/22.98 ((
% 132.79/22.98 (contrasubsetT) =>
% 132.79/22.98 ((
% 132.79/22.98 (contrasubsetT1) =>
% 132.79/22.98 ((
% 132.79/22.98 (contrasubsetT2) =>
% 132.79/22.98 ((
% 132.79/22.98 (contrasubsetT3) =>
% 132.79/22.98 ((
% 132.79/22.98 (doubleComplementI1) =>
% 132.79/22.98 ((
% 132.79/22.98 (doubleComplementE1) =>
% 132.79/22.98 ((
% 132.79/22.98 (doubleComplementSub1) =>
% 132.79/22.98 ((
% 132.79/22.98 (doubleComplementSub2) =>
% 132.79/22.98 ((
% 132.79/22.98 (doubleComplementEq) =>
% 132.79/22.98 ((
% 132.79/22.98 (complementTnotintersectT) =>
% 132.79/22.98 ((
% 132.79/22.98 (complementImpComplementIntersect) =>
% 132.79/22.98 ((
% 132.79/22.98 (complementSubsetComplementIntersect) =>
% 132.79/22.98 ((
% 132.79/22.98 (complementInPowersetComplementIntersect) =>
% 132.79/22.98 ((
% 132.79/22.98 (contraSubsetComplement) =>
% 132.79/22.98 ((
% 132.79/22.98 (complementTcontraSubset) =>
% 132.79/22.98 ((
% 132.79/22.98 (binunionTILcontra) =>
% 132.79/22.98 ((
% 132.79/22.98 (binunionTIRcontra) =>
% 132.79/22.98 ((
% 132.79/22.98 (inIntersectImpInUnion) =>
% 132.79/22.98 ((
% 132.79/22.98 (inIntersectImpInUnion2) =>
% 132.79/22.98 ((
% 132.79/22.98 (inIntersectImpInIntersectUnions) =>
% 132.79/22.98 ((
% 132.79/22.98 (intersectInPowersetIntersectUnions) =>
% 132.79/22.98 ((
% 132.79/22.98 (inComplementUnionImpNotIn1) =>
% 132.79/22.98 ((
% 132.79/22.98 (inComplementUnionImpInComplement1) =>
% 132.79/22.98 ((
% 132.79/22.98 (binunionTE) =>
% 132.79/22.98 ((
% 132.79/22.98 (binunionTEcontra) =>
% 132.79/22.98 ((
% 132.79/22.98 (demorgan2a1) =>
% 132.79/22.98 ((
% 132.79/22.98 (complementUnionInPowersetComplement) =>
% 132.79/22.98 ((
% 132.79/22.98 (demorgan2a2) =>
% 132.79/22.98 ((
% 132.79/22.98 (demorgan1a) =>
% 132.79/22.98 ((
% 132.79/22.98 (demorgan1b) =>
% 132.79/22.98 ((
% 132.79/22.98 (demorgan1) =>
% 132.79/22.98 ((
% 132.79/22.98 (demorgan2a) =>
% 132.79/22.98 ((
% 132.79/22.98 (demorgan2b2) =>
% 132.79/22.98 ((
% 132.79/22.98 (demorgan2b) =>
% 132.79/22.98 ((
% 132.79/22.98 (demorgan2) =>
% 132.79/22.98 ((
% 132.79/22.98 (woz13rule0) =>
% 132.79/22.98 ((
% 132.79/22.98 (woz13rule1) =>
% 132.79/22.98 ((
% 132.79/22.98 (woz13rule2) =>
% 132.79/22.98 ((
% 132.79/22.98 (woz13rule3) =>
% 132.79/22.98 ((
% 132.79/22.98 (woz13rule4) =>
% 132.79/22.98 ((
% 132.79/22.98 (woz1_1) =>
% 132.79/22.98 ((
% 132.79/22.98 (woz1_2) =>
% 132.79/22.98 ((
% 132.79/22.98 (woz1_3) =>
% 132.79/22.98 ((
% 132.79/22.98 (woz1_4) =>
% 132.79/22.98 ((
% 132.79/22.98 (woz1_5) =>
% 132.79/22.98 ((
% 132.79/22.98 (breln1all2) =>
% 132.79/22.98 ((
% 132.79/22.98 (breln1SetBreln1) =>
% 132.79/22.98 ((
% 132.79/22.98 (choice2fnsingleton) =>
% 132.79/22.98 ((
% 132.79/22.98 (setOfPairsIsBReln1) =>
% 132.79/22.98 ((
% 132.79/22.98 (breln1all1) =>
% 132.79/22.98 ((
% 132.79/22.98 (subbreln1) =>
% 132.79/22.98 ((
% 132.79/22.98 (eqbreln1) =>
% 132.79/22.98 ((
% 132.79/22.98 (breln1invprop) =>
% 132.79/22.98 ((
% 132.79/22.98 (breln1invI) =>
% 132.79/22.98 ((
% 132.79/22.98 (breln1invE) =>
% 132.79/22.98 ((
% 132.79/22.98 (breln1compprop) =>
% 132.79/22.98 ((
% 132.79/22.98 (breln1compI) =>
% 132.79/22.98 ((
% 132.79/22.98 (breln1compE) =>
% 132.79/22.98 ((
% 132.79/22.98 (breln1compEex) =>
% 132.79/22.98 ((
% 132.79/22.98 (breln1unionprop) =>
% 132.79/22.98 ((
% 132.79/22.98 (breln1unionIL) =>
% 132.79/22.98 ((
% 132.79/22.98 (breln1unionIR) =>
% 132.79/22.98 ((
% 132.79/22.98 (breln1unionI) =>
% 132.79/22.98 ((
% 132.79/22.98 (breln1unionE) =>
% 132.79/22.98 ((
% 132.79/22.98 (breln1unionEcases) =>
% 132.79/22.98 ((
% 132.79/22.98 (breln1unionCommutes) =>
% 132.79/22.98 ((
% 132.79/22.98 (woz2Ex) =>
% 132.79/22.98 ((
% 132.79/22.98 (woz2W) =>
% 132.79/22.98 ((
% 132.79/22.98 (woz2A) =>
% 132.79/22.98 ((
% 132.79/22.98 (woz2B) =>
% 132.79/22.98 ((
% 132.79/22.98 (image1Ex) =>
% 132.79/22.98 ((
% 132.79/22.98 (image1Ex1) =>
% 132.79/22.98 ((
% 132.79/22.98 (image1Equiv) =>
% 132.79/22.98 ((
% 132.79/22.98 (image1E) =>
% 132.79/22.98 ((
% 132.79/22.98 (image1I) =>
% 132.79/22.98 ((
% 132.79/22.98 (injFuncInInjFuncSet) =>
% 132.79/22.98 ((
% 132.79/22.98 (injFuncSetFuncIn) =>
% 132.79/22.98 ((
% 132.79/22.98 (injFuncSetFuncInj) =>
% 132.79/22.98 ((
% 132.79/22.98 (surjFuncSetFuncIn) =>
% 132.79/22.98 ((
% 132.79/22.98 (surjFuncSetFuncSurj) =>
% 132.79/22.98 ((
% 132.79/22.98 (leftInvIsSurj) =>
% 132.79/22.98 ((
% 132.79/22.98 (surjCantorThm) =>
% 132.79/22.98 ((
% 132.79/22.98 (foundation2) =>
% 132.79/22.98 ((
% 132.79/22.98 (notinself) =>
% 132.79/22.98 ((
% 132.79/22.98 (notinself2) =>
% 132.79/22.98 ((
% 132.79/22.98 (omegaSp) =>
% 132.79/22.98 ((
% 132.79/22.98 (omegaSclos) =>
% 132.79/22.98 ((
% 132.79/22.98 (peano0notS) =>
% 132.79/22.98 ((
% 132.79/22.98 (peanoSinj) =>
% 132.79/22.98 ((
% 132.79/22.98 (transitivesetOp1) =>
% 132.79/22.98 ((
% 132.79/22.98 (binintTransitive) =>
% 132.79/22.98 ((
% 132.79/22.98 (transitivesetOp2) =>
% 132.79/22.98 ((
% 132.79/22.98 (setunionTransitive) =>
% 132.79/22.98 ((
% 132.79/22.98 (ordinalMinLem1) =>
% 132.79/22.98 ((
% 132.79/22.98 (ordinalTransSet) =>
% 132.79/22.98 ((
% 132.79/22.98 (ordinalTransSet1) =>
% 132.79/22.98 ((
% 132.79/22.98 (setunionOrdinalLem1) =>
% 132.79/22.98 (ordinal @
% 132.79/22.98 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/22.98 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1495])).
% 132.79/22.98 thf(zip_derived_cl1511, plain,
% 132.79/22.98 (~ (((kpairsurjEq) =>
% 132.79/22.98 (((cartprodsndin) =>
% 132.79/22.98 (((cartprodpairmemEL) =>
% 132.79/22.98 (((cartprodpairmemER) =>
% 132.79/22.98 (((cartprodmempaircEq) =>
% 132.79/22.98 (((cartprodfstpairEq) =>
% 132.79/22.98 (((cartprodsndpairEq) =>
% 132.79/22.98 (((cartprodpairsurjEq) =>
% 132.79/22.98 (((dpsetconstrI) =>
% 132.79/22.98 (((dpsetconstrSub) =>
% 132.79/22.98 (((setOfPairsIsBReln) =>
% 132.79/22.98 (((dpsetconstrERa) =>
% 132.79/22.98 (((dpsetconstrEL1) =>
% 132.79/22.98 (((dpsetconstrEL2) =>
% 132.79/22.98 (((dpsetconstrER) =>
% 132.79/22.98 (((funcImageSingleton) =>
% 132.79/22.98 (((apProp) =>
% 132.79/22.98 (((app) =>
% 132.79/22.98 (((infuncsetfunc) =>
% 132.79/22.98 (((ap2p) =>
% 132.79/22.98 (((funcinfuncset) =>
% 132.79/22.98 (((lamProp) =>
% 132.79/22.98 (((lamp) =>
% 132.79/22.98 (((lam2p) =>
% 132.79/22.98 (((brelnall1) =>
% 132.79/22.98 (((brelnall2) =>
% 132.79/22.98 (((ex1E2) =>
% 132.79/22.98 (((funcGraphProp1) =>
% 132.79/22.98 (((funcGraphProp3) =>
% 132.79/22.98 (((funcGraphProp2) =>
% 132.79/22.98 ((
% 132.79/22.98 (funcextLem) =>
% 132.79/22.98 ((
% 132.79/22.98 (funcGraphProp4) =>
% 132.79/22.98 ((
% 132.79/22.98 (subbreln) =>
% 132.79/22.98 ((
% 132.79/22.98 (eqbreln) =>
% 132.79/22.98 ((
% 132.79/22.98 (funcext) =>
% 132.79/22.98 ((
% 132.79/22.98 (funcext2) =>
% 132.79/22.98 ((
% 132.79/22.98 (ap2apEq1) =>
% 132.79/22.98 ((
% 132.79/22.98 (ap2apEq2) =>
% 132.79/22.98 ((
% 132.79/22.98 (beta1) =>
% 132.79/22.98 ((
% 132.79/22.98 (eta1) =>
% 132.79/22.98 ((
% 132.79/22.98 (lam2lamEq) =>
% 132.79/22.98 ((
% 132.79/22.98 (beta2) =>
% 132.79/22.98 ((
% 132.79/22.98 (eta2) =>
% 132.79/22.98 ((
% 132.79/22.98 (iffalseProp1) =>
% 132.79/22.98 ((
% 132.79/22.98 (iffalseProp2) =>
% 132.79/22.98 ((
% 132.79/22.98 (iftrueProp1) =>
% 132.79/22.98 ((
% 132.79/22.98 (iftrueProp2) =>
% 132.79/22.98 ((
% 132.79/22.98 (ifSingleton) =>
% 132.79/22.98 ((
% 132.79/22.98 (ifp) =>
% 132.79/22.98 ((
% 132.79/22.98 (theeq) =>
% 132.79/22.98 ((
% 132.79/22.98 (iftrue) =>
% 132.79/22.98 ((
% 132.79/22.98 (iffalse) =>
% 132.79/22.98 ((
% 132.79/22.98 (iftrueorfalse) =>
% 132.79/22.98 ((
% 132.79/22.98 (binintersectT_lem) =>
% 132.79/22.98 ((
% 132.79/22.98 (binunionT_lem) =>
% 132.79/22.98 ((
% 132.79/22.98 (powersetT_lem) =>
% 132.79/22.98 ((
% 132.79/22.98 (setminusT_lem) =>
% 132.79/22.98 ((
% 132.79/22.98 (complementT_lem) =>
% 132.79/22.98 ((
% 132.79/22.98 (setextT) =>
% 132.79/22.98 ((
% 132.79/22.98 (subsetTI) =>
% 132.79/22.98 ((
% 132.79/22.98 (powersetTI1) =>
% 132.79/22.98 ((
% 132.79/22.98 (powersetTE1) =>
% 132.79/22.98 ((
% 132.79/22.98 (complementTI1) =>
% 132.79/22.98 ((
% 132.79/22.98 (complementTE1) =>
% 132.79/22.98 ((
% 132.79/22.98 (binintersectTELcontra) =>
% 132.79/22.98 ((
% 132.79/22.98 (binintersectTERcontra) =>
% 132.79/22.98 ((
% 132.79/22.98 (contrasubsetT) =>
% 132.79/22.98 ((
% 132.79/22.98 (contrasubsetT1) =>
% 132.79/22.98 ((
% 132.79/22.98 (contrasubsetT2) =>
% 132.79/22.98 ((
% 132.79/22.98 (contrasubsetT3) =>
% 132.79/22.98 ((
% 132.79/22.98 (doubleComplementI1) =>
% 132.79/22.98 ((
% 132.79/22.98 (doubleComplementE1) =>
% 132.79/22.98 ((
% 132.79/22.98 (doubleComplementSub1) =>
% 132.79/22.98 ((
% 132.79/22.98 (doubleComplementSub2) =>
% 132.79/22.98 ((
% 132.79/22.98 (doubleComplementEq) =>
% 132.79/22.98 ((
% 132.79/22.98 (complementTnotintersectT) =>
% 132.79/22.98 ((
% 132.79/22.98 (complementImpComplementIntersect) =>
% 132.79/22.98 ((
% 132.79/22.98 (complementSubsetComplementIntersect) =>
% 132.79/22.98 ((
% 132.79/22.98 (complementInPowersetComplementIntersect) =>
% 132.79/22.98 ((
% 132.79/22.98 (contraSubsetComplement) =>
% 132.79/22.98 ((
% 132.79/22.98 (complementTcontraSubset) =>
% 132.79/22.98 ((
% 132.79/22.98 (binunionTILcontra) =>
% 132.79/22.98 ((
% 132.79/22.98 (binunionTIRcontra) =>
% 132.79/22.98 ((
% 132.79/22.98 (inIntersectImpInUnion) =>
% 132.79/22.98 ((
% 132.79/22.98 (inIntersectImpInUnion2) =>
% 132.79/22.98 ((
% 132.79/22.98 (inIntersectImpInIntersectUnions) =>
% 132.79/22.98 ((
% 132.79/22.98 (intersectInPowersetIntersectUnions) =>
% 132.79/22.98 ((
% 132.79/22.98 (inComplementUnionImpNotIn1) =>
% 132.79/22.98 ((
% 132.79/22.98 (inComplementUnionImpInComplement1) =>
% 132.79/22.98 ((
% 132.79/22.98 (binunionTE) =>
% 132.79/22.98 ((
% 132.79/22.98 (binunionTEcontra) =>
% 132.79/22.98 ((
% 132.79/22.98 (demorgan2a1) =>
% 132.79/22.98 ((
% 132.79/22.98 (complementUnionInPowersetComplement) =>
% 132.79/22.98 ((
% 132.79/22.98 (demorgan2a2) =>
% 132.79/22.98 ((
% 132.79/22.98 (demorgan1a) =>
% 132.79/22.98 ((
% 132.79/22.98 (demorgan1b) =>
% 132.79/22.98 ((
% 132.79/22.98 (demorgan1) =>
% 132.79/22.98 ((
% 132.79/22.98 (demorgan2a) =>
% 132.79/22.98 ((
% 132.79/22.98 (demorgan2b2) =>
% 132.79/22.98 ((
% 132.79/22.98 (demorgan2b) =>
% 132.79/22.98 ((
% 132.79/22.98 (demorgan2) =>
% 132.79/22.98 ((
% 132.79/22.98 (woz13rule0) =>
% 132.79/22.98 ((
% 132.79/22.98 (woz13rule1) =>
% 132.79/22.98 ((
% 132.79/22.98 (woz13rule2) =>
% 132.79/22.98 ((
% 132.79/22.98 (woz13rule3) =>
% 132.79/22.98 ((
% 132.79/22.98 (woz13rule4) =>
% 132.79/22.98 ((
% 132.79/22.98 (woz1_1) =>
% 132.79/22.98 ((
% 132.79/22.98 (woz1_2) =>
% 132.79/22.98 ((
% 132.79/22.98 (woz1_3) =>
% 132.79/22.98 ((
% 132.79/22.98 (woz1_4) =>
% 132.79/22.98 ((
% 132.79/22.98 (woz1_5) =>
% 132.79/22.98 ((
% 132.79/22.98 (breln1all2) =>
% 132.79/22.98 ((
% 132.79/22.98 (breln1SetBreln1) =>
% 132.79/22.98 ((
% 132.79/22.98 (choice2fnsingleton) =>
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 (image1E) =>
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1504])).
% 132.79/22.98 thf(zip_derived_cl1519, plain,
% 132.79/22.98 (~ (((cartprodsndin) =>
% 132.79/22.98 (((cartprodpairmemEL) =>
% 132.79/22.98 (((cartprodpairmemER) =>
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% 132.79/22.98 (((dpsetconstrSub) =>
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1511])).
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% 132.79/22.98 (inIntersectImpInUnion2) =>
% 132.79/22.98 ((
% 132.79/22.98 (inIntersectImpInIntersectUnions) =>
% 132.79/22.98 ((
% 132.79/22.98 (intersectInPowersetIntersectUnions) =>
% 132.79/22.98 ((
% 132.79/22.98 (inComplementUnionImpNotIn1) =>
% 132.79/22.98 ((
% 132.79/22.98 (inComplementUnionImpInComplement1) =>
% 132.79/22.98 ((
% 132.79/22.98 (binunionTE) =>
% 132.79/22.98 ((
% 132.79/22.98 (binunionTEcontra) =>
% 132.79/22.98 ((
% 132.79/22.98 (demorgan2a1) =>
% 132.79/22.98 ((
% 132.79/22.98 (complementUnionInPowersetComplement) =>
% 132.79/22.98 ((
% 132.79/22.98 (demorgan2a2) =>
% 132.79/22.98 ((
% 132.79/22.98 (demorgan1a) =>
% 132.79/22.98 ((
% 132.79/22.98 (demorgan1b) =>
% 132.79/22.98 ((
% 132.79/22.98 (demorgan1) =>
% 132.79/22.98 ((
% 132.79/22.98 (demorgan2a) =>
% 132.79/22.98 ((
% 132.79/22.98 (demorgan2b2) =>
% 132.79/22.98 ((
% 132.79/22.98 (demorgan2b) =>
% 132.79/22.98 ((
% 132.79/22.98 (demorgan2) =>
% 132.79/22.98 ((
% 132.79/22.98 (woz13rule0) =>
% 132.79/22.98 ((
% 132.79/22.98 (woz13rule1) =>
% 132.79/22.98 ((
% 132.79/22.98 (woz13rule2) =>
% 132.79/22.98 ((
% 132.79/22.98 (woz13rule3) =>
% 132.79/22.98 ((
% 132.79/22.98 (woz13rule4) =>
% 132.79/22.98 ((
% 132.79/22.98 (woz1_1) =>
% 132.79/22.98 ((
% 132.79/22.98 (woz1_2) =>
% 132.79/22.98 ((
% 132.79/22.98 (woz1_3) =>
% 132.79/22.98 ((
% 132.79/22.98 (woz1_4) =>
% 132.79/22.98 ((
% 132.79/22.98 (woz1_5) =>
% 132.79/22.98 ((
% 132.79/22.98 (breln1all2) =>
% 132.79/22.98 ((
% 132.79/22.98 (breln1SetBreln1) =>
% 132.79/22.98 ((
% 132.79/22.98 (choice2fnsingleton) =>
% 132.79/22.98 ((
% 132.79/22.98 (setOfPairsIsBReln1) =>
% 132.79/22.98 ((
% 132.79/22.98 (breln1all1) =>
% 132.79/22.98 ((
% 132.79/22.98 (subbreln1) =>
% 132.79/22.98 ((
% 132.79/22.98 (eqbreln1) =>
% 132.79/22.98 ((
% 132.79/22.98 (breln1invprop) =>
% 132.79/22.98 ((
% 132.79/22.98 (breln1invI) =>
% 132.79/22.98 ((
% 132.79/22.98 (breln1invE) =>
% 132.79/22.98 ((
% 132.79/22.98 (breln1compprop) =>
% 132.79/22.98 ((
% 132.79/22.98 (breln1compI) =>
% 132.79/22.98 ((
% 132.79/22.98 (breln1compE) =>
% 132.79/22.98 ((
% 132.79/22.98 (breln1compEex) =>
% 132.79/22.98 ((
% 132.79/22.98 (breln1unionprop) =>
% 132.79/22.98 ((
% 132.79/22.98 (breln1unionIL) =>
% 132.79/22.98 ((
% 132.79/22.98 (breln1unionIR) =>
% 132.79/22.98 ((
% 132.79/22.98 (breln1unionI) =>
% 132.79/22.98 ((
% 132.79/22.98 (breln1unionE) =>
% 132.79/22.98 ((
% 132.79/22.98 (breln1unionEcases) =>
% 132.79/22.98 ((
% 132.79/22.98 (breln1unionCommutes) =>
% 132.79/22.98 ((
% 132.79/22.98 (woz2Ex) =>
% 132.79/22.98 ((
% 132.79/22.98 (woz2W) =>
% 132.79/22.98 ((
% 132.79/22.98 (woz2A) =>
% 132.79/22.98 ((
% 132.79/22.98 (woz2B) =>
% 132.79/22.98 ((
% 132.79/22.98 (image1Ex) =>
% 132.79/22.98 ((
% 132.79/22.98 (image1Ex1) =>
% 132.79/22.98 ((
% 132.79/22.98 (image1Equiv) =>
% 132.79/22.98 ((
% 132.79/22.98 (image1E) =>
% 132.79/22.98 ((
% 132.79/22.98 (image1I) =>
% 132.79/22.98 ((
% 132.79/22.98 (injFuncInInjFuncSet) =>
% 132.79/22.98 ((
% 132.79/22.98 (injFuncSetFuncIn) =>
% 132.79/22.98 ((
% 132.79/22.98 (injFuncSetFuncInj) =>
% 132.79/22.98 ((
% 132.79/22.98 (surjFuncSetFuncIn) =>
% 132.79/22.98 ((
% 132.79/22.98 (surjFuncSetFuncSurj) =>
% 132.79/22.98 ((
% 132.79/22.98 (leftInvIsSurj) =>
% 132.79/22.98 ((
% 132.79/22.98 (surjCantorThm) =>
% 132.79/22.98 ((
% 132.79/22.98 (foundation2) =>
% 132.79/22.98 ((
% 132.79/22.98 (notinself) =>
% 132.79/22.98 ((
% 132.79/22.98 (notinself2) =>
% 132.79/22.98 ((
% 132.79/22.98 (omegaSp) =>
% 132.79/22.98 ((
% 132.79/22.98 (omegaSclos) =>
% 132.79/22.98 ((
% 132.79/22.98 (peano0notS) =>
% 132.79/22.98 ((
% 132.79/22.98 (peanoSinj) =>
% 132.79/22.98 ((
% 132.79/22.98 (transitivesetOp1) =>
% 132.79/22.98 ((
% 132.79/22.98 (binintTransitive) =>
% 132.79/22.98 ((
% 132.79/22.98 (transitivesetOp2) =>
% 132.79/22.98 ((
% 132.79/22.98 (setunionTransitive) =>
% 132.79/22.98 ((
% 132.79/22.98 (ordinalMinLem1) =>
% 132.79/22.98 ((
% 132.79/22.98 (ordinalTransSet) =>
% 132.79/22.98 ((
% 132.79/22.98 (ordinalTransSet1) =>
% 132.79/22.98 ((
% 132.79/22.98 (setunionOrdinalLem1) =>
% 132.79/22.98 (ordinal @
% 132.79/22.98 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/22.98 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1519])).
% 132.79/22.98 thf(zip_derived_cl1538, plain,
% 132.79/22.98 (~ (((cartprodpairmemER) =>
% 132.79/22.98 (((cartprodmempaircEq) =>
% 132.79/22.98 (((cartprodfstpairEq) =>
% 132.79/22.98 (((cartprodsndpairEq) =>
% 132.79/22.98 (((cartprodpairsurjEq) =>
% 132.79/22.98 (((dpsetconstrI) =>
% 132.79/22.98 (((dpsetconstrSub) =>
% 132.79/22.98 (((setOfPairsIsBReln) =>
% 132.79/22.98 (((dpsetconstrERa) =>
% 132.79/22.98 (((dpsetconstrEL1) =>
% 132.79/22.98 (((dpsetconstrEL2) =>
% 132.79/22.98 (((dpsetconstrER) =>
% 132.79/22.98 (((funcImageSingleton) =>
% 132.79/22.98 (((apProp) =>
% 132.79/22.98 (((app) =>
% 132.79/22.98 (((infuncsetfunc) =>
% 132.79/22.98 (((ap2p) =>
% 132.79/22.98 (((funcinfuncset) =>
% 132.79/22.98 (((lamProp) =>
% 132.79/22.98 (((lamp) =>
% 132.79/22.98 (((lam2p) =>
% 132.79/22.98 (((brelnall1) =>
% 132.79/22.98 (((brelnall2) =>
% 132.79/22.98 (((ex1E2) =>
% 132.79/22.98 (((funcGraphProp1) =>
% 132.79/22.98 (((funcGraphProp3) =>
% 132.79/22.98 (((funcGraphProp2) =>
% 132.79/22.98 (((funcextLem) =>
% 132.79/22.98 (((funcGraphProp4) =>
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% 132.79/22.98 ((
% 132.79/22.98 (funcext) =>
% 132.79/22.98 ((
% 132.79/22.98 (funcext2) =>
% 132.79/22.98 ((
% 132.79/22.98 (ap2apEq1) =>
% 132.79/22.98 ((
% 132.79/22.98 (ap2apEq2) =>
% 132.79/22.98 ((
% 132.79/22.98 (beta1) =>
% 132.79/22.98 ((
% 132.79/22.98 (eta1) =>
% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
% 132.79/22.98 (iffalseProp2) =>
% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
% 132.79/22.98 (powersetTE1) =>
% 132.79/22.98 ((
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% 132.79/22.98 ((
% 132.79/22.98 (complementTE1) =>
% 132.79/22.98 ((
% 132.79/22.98 (binintersectTELcontra) =>
% 132.79/22.98 ((
% 132.79/22.98 (binintersectTERcontra) =>
% 132.79/22.98 ((
% 132.79/22.98 (contrasubsetT) =>
% 132.79/22.98 ((
% 132.79/22.98 (contrasubsetT1) =>
% 132.79/22.98 ((
% 132.79/22.98 (contrasubsetT2) =>
% 132.79/22.98 ((
% 132.79/22.98 (contrasubsetT3) =>
% 132.79/22.98 ((
% 132.79/22.98 (doubleComplementI1) =>
% 132.79/22.98 ((
% 132.79/22.98 (doubleComplementE1) =>
% 132.79/22.98 ((
% 132.79/22.98 (doubleComplementSub1) =>
% 132.79/22.98 ((
% 132.79/22.98 (doubleComplementSub2) =>
% 132.79/22.98 ((
% 132.79/22.98 (doubleComplementEq) =>
% 132.79/22.98 ((
% 132.79/22.98 (complementTnotintersectT) =>
% 132.79/22.98 ((
% 132.79/22.98 (complementImpComplementIntersect) =>
% 132.79/22.98 ((
% 132.79/22.98 (complementSubsetComplementIntersect) =>
% 132.79/22.98 ((
% 132.79/22.98 (complementInPowersetComplementIntersect) =>
% 132.79/22.98 ((
% 132.79/22.98 (contraSubsetComplement) =>
% 132.79/22.98 ((
% 132.79/22.98 (complementTcontraSubset) =>
% 132.79/22.98 ((
% 132.79/22.98 (binunionTILcontra) =>
% 132.79/22.98 ((
% 132.79/22.98 (binunionTIRcontra) =>
% 132.79/22.98 ((
% 132.79/22.98 (inIntersectImpInUnion) =>
% 132.79/22.98 ((
% 132.79/22.98 (inIntersectImpInUnion2) =>
% 132.79/22.98 ((
% 132.79/22.98 (inIntersectImpInIntersectUnions) =>
% 132.79/22.98 ((
% 132.79/22.98 (intersectInPowersetIntersectUnions) =>
% 132.79/22.98 ((
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% 132.79/22.98 ((
% 132.79/22.98 (inComplementUnionImpInComplement1) =>
% 132.79/22.98 ((
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% 132.79/22.98 ((
% 132.79/22.98 (binunionTEcontra) =>
% 132.79/22.98 ((
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% 132.79/22.98 ((
% 132.79/22.98 (complementUnionInPowersetComplement) =>
% 132.79/22.98 ((
% 132.79/22.98 (demorgan2a2) =>
% 132.79/22.98 ((
% 132.79/22.98 (demorgan1a) =>
% 132.79/22.98 ((
% 132.79/22.98 (demorgan1b) =>
% 132.79/22.98 ((
% 132.79/22.98 (demorgan1) =>
% 132.79/22.98 ((
% 132.79/22.98 (demorgan2a) =>
% 132.79/22.98 ((
% 132.79/22.98 (demorgan2b2) =>
% 132.79/22.98 ((
% 132.79/22.98 (demorgan2b) =>
% 132.79/22.98 ((
% 132.79/22.98 (demorgan2) =>
% 132.79/22.98 ((
% 132.79/22.98 (woz13rule0) =>
% 132.79/22.98 ((
% 132.79/22.98 (woz13rule1) =>
% 132.79/22.98 ((
% 132.79/22.98 (woz13rule2) =>
% 132.79/22.98 ((
% 132.79/22.98 (woz13rule3) =>
% 132.79/22.98 ((
% 132.79/22.98 (woz13rule4) =>
% 132.79/22.98 ((
% 132.79/22.98 (woz1_1) =>
% 132.79/22.98 ((
% 132.79/22.98 (woz1_2) =>
% 132.79/22.98 ((
% 132.79/22.98 (woz1_3) =>
% 132.79/22.98 ((
% 132.79/22.98 (woz1_4) =>
% 132.79/22.98 ((
% 132.79/22.98 (woz1_5) =>
% 132.79/22.98 ((
% 132.79/22.98 (breln1all2) =>
% 132.79/22.98 ((
% 132.79/22.98 (breln1SetBreln1) =>
% 132.79/22.98 ((
% 132.79/22.98 (choice2fnsingleton) =>
% 132.79/22.98 ((
% 132.79/22.98 (setOfPairsIsBReln1) =>
% 132.79/22.98 ((
% 132.79/22.98 (breln1all1) =>
% 132.79/22.98 ((
% 132.79/22.98 (subbreln1) =>
% 132.79/22.98 ((
% 132.79/22.98 (eqbreln1) =>
% 132.79/22.98 ((
% 132.79/22.98 (breln1invprop) =>
% 132.79/22.98 ((
% 132.79/22.98 (breln1invI) =>
% 132.79/22.98 ((
% 132.79/22.98 (breln1invE) =>
% 132.79/22.98 ((
% 132.79/22.98 (breln1compprop) =>
% 132.79/22.98 ((
% 132.79/22.98 (breln1compI) =>
% 132.79/22.98 ((
% 132.79/22.98 (breln1compE) =>
% 132.79/22.98 ((
% 132.79/22.98 (breln1compEex) =>
% 132.79/22.98 ((
% 132.79/22.98 (breln1unionprop) =>
% 132.79/22.98 ((
% 132.79/22.98 (breln1unionIL) =>
% 132.79/22.98 ((
% 132.79/22.98 (breln1unionIR) =>
% 132.79/22.98 ((
% 132.79/22.98 (breln1unionI) =>
% 132.79/22.98 ((
% 132.79/22.98 (breln1unionE) =>
% 132.79/22.98 ((
% 132.79/22.98 (breln1unionEcases) =>
% 132.79/22.98 ((
% 132.79/22.98 (breln1unionCommutes) =>
% 132.79/22.98 ((
% 132.79/22.98 (woz2Ex) =>
% 132.79/22.98 ((
% 132.79/22.98 (woz2W) =>
% 132.79/22.98 ((
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% 132.79/22.98 ((
% 132.79/22.98 (woz2B) =>
% 132.79/22.98 ((
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% 132.79/22.98 ((
% 132.79/22.98 (image1Ex1) =>
% 132.79/22.98 ((
% 132.79/22.98 (image1Equiv) =>
% 132.79/22.98 ((
% 132.79/22.98 (image1E) =>
% 132.79/22.98 ((
% 132.79/22.98 (image1I) =>
% 132.79/22.98 ((
% 132.79/22.98 (injFuncInInjFuncSet) =>
% 132.79/22.98 ((
% 132.79/22.98 (injFuncSetFuncIn) =>
% 132.79/22.98 ((
% 132.79/22.98 (injFuncSetFuncInj) =>
% 132.79/22.98 ((
% 132.79/22.98 (surjFuncSetFuncIn) =>
% 132.79/22.98 ((
% 132.79/22.98 (surjFuncSetFuncSurj) =>
% 132.79/22.98 ((
% 132.79/22.98 (leftInvIsSurj) =>
% 132.79/22.98 ((
% 132.79/22.98 (surjCantorThm) =>
% 132.79/22.98 ((
% 132.79/22.98 (foundation2) =>
% 132.79/22.98 ((
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% 132.79/22.98 ((
% 132.79/22.98 (notinself2) =>
% 132.79/22.98 ((
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% 132.79/22.98 ((
% 132.79/22.98 (omegaSclos) =>
% 132.79/22.98 ((
% 132.79/22.98 (peano0notS) =>
% 132.79/22.98 ((
% 132.79/22.98 (peanoSinj) =>
% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1529])).
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% 132.79/22.98 (((dpsetconstrEL1) =>
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
% 132.79/22.98 (complementTE1) =>
% 132.79/22.98 ((
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% 132.79/22.98 ((
% 132.79/22.98 (binintersectTERcontra) =>
% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
% 132.79/22.98 (contrasubsetT3) =>
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
% 132.79/22.98 (contraSubsetComplement) =>
% 132.79/22.98 ((
% 132.79/22.98 (complementTcontraSubset) =>
% 132.79/22.98 ((
% 132.79/22.98 (binunionTILcontra) =>
% 132.79/22.98 ((
% 132.79/22.98 (binunionTIRcontra) =>
% 132.79/22.98 ((
% 132.79/22.98 (inIntersectImpInUnion) =>
% 132.79/22.98 ((
% 132.79/22.98 (inIntersectImpInUnion2) =>
% 132.79/22.98 ((
% 132.79/22.98 (inIntersectImpInIntersectUnions) =>
% 132.79/22.98 ((
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% 132.79/22.98 ((
% 132.79/22.98 (inComplementUnionImpInComplement1) =>
% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
% 132.79/22.98 (demorgan2a2) =>
% 132.79/22.98 ((
% 132.79/22.98 (demorgan1a) =>
% 132.79/22.98 ((
% 132.79/22.98 (demorgan1b) =>
% 132.79/22.98 ((
% 132.79/22.98 (demorgan1) =>
% 132.79/22.98 ((
% 132.79/22.98 (demorgan2a) =>
% 132.79/22.98 ((
% 132.79/22.98 (demorgan2b2) =>
% 132.79/22.98 ((
% 132.79/22.98 (demorgan2b) =>
% 132.79/22.98 ((
% 132.79/22.98 (demorgan2) =>
% 132.79/22.98 ((
% 132.79/22.98 (woz13rule0) =>
% 132.79/22.98 ((
% 132.79/22.98 (woz13rule1) =>
% 132.79/22.98 ((
% 132.79/22.98 (woz13rule2) =>
% 132.79/22.98 ((
% 132.79/22.98 (woz13rule3) =>
% 132.79/22.98 ((
% 132.79/22.98 (woz13rule4) =>
% 132.79/22.98 ((
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% 132.79/22.98 ((
% 132.79/22.98 (woz1_2) =>
% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
% 132.79/22.98 (breln1all1) =>
% 132.79/22.98 ((
% 132.79/22.98 (subbreln1) =>
% 132.79/22.98 ((
% 132.79/22.98 (eqbreln1) =>
% 132.79/22.98 ((
% 132.79/22.98 (breln1invprop) =>
% 132.79/22.98 ((
% 132.79/22.98 (breln1invI) =>
% 132.79/22.98 ((
% 132.79/22.98 (breln1invE) =>
% 132.79/22.98 ((
% 132.79/22.98 (breln1compprop) =>
% 132.79/22.98 ((
% 132.79/22.98 (breln1compI) =>
% 132.79/22.98 ((
% 132.79/22.98 (breln1compE) =>
% 132.79/22.98 ((
% 132.79/22.98 (breln1compEex) =>
% 132.79/22.98 ((
% 132.79/22.98 (breln1unionprop) =>
% 132.79/22.98 ((
% 132.79/22.98 (breln1unionIL) =>
% 132.79/22.98 ((
% 132.79/22.98 (breln1unionIR) =>
% 132.79/22.98 ((
% 132.79/22.98 (breln1unionI) =>
% 132.79/22.98 ((
% 132.79/22.98 (breln1unionE) =>
% 132.79/22.98 ((
% 132.79/22.98 (breln1unionEcases) =>
% 132.79/22.98 ((
% 132.79/22.98 (breln1unionCommutes) =>
% 132.79/22.98 ((
% 132.79/22.98 (woz2Ex) =>
% 132.79/22.98 ((
% 132.79/22.98 (woz2W) =>
% 132.79/22.98 ((
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% 132.79/22.98 ((
% 132.79/22.98 (woz2B) =>
% 132.79/22.98 ((
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% 132.79/22.98 ((
% 132.79/22.98 (image1Ex1) =>
% 132.79/22.98 ((
% 132.79/22.98 (image1Equiv) =>
% 132.79/22.98 ((
% 132.79/22.98 (image1E) =>
% 132.79/22.98 ((
% 132.79/22.98 (image1I) =>
% 132.79/22.98 ((
% 132.79/22.98 (injFuncInInjFuncSet) =>
% 132.79/22.98 ((
% 132.79/22.98 (injFuncSetFuncIn) =>
% 132.79/22.98 ((
% 132.79/22.98 (injFuncSetFuncInj) =>
% 132.79/22.98 ((
% 132.79/22.98 (surjFuncSetFuncIn) =>
% 132.79/22.98 ((
% 132.79/22.98 (surjFuncSetFuncSurj) =>
% 132.79/22.98 ((
% 132.79/22.98 (leftInvIsSurj) =>
% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
% 132.79/22.98 (notinself2) =>
% 132.79/22.98 ((
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% 132.79/22.98 ((
% 132.79/22.98 (omegaSclos) =>
% 132.79/22.98 ((
% 132.79/22.98 (peano0notS) =>
% 132.79/22.98 ((
% 132.79/22.98 (peanoSinj) =>
% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
% 132.79/22.98 (transitivesetOp2) =>
% 132.79/22.98 ((
% 132.79/22.98 (setunionTransitive) =>
% 132.79/22.98 ((
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% 132.79/22.98 ((
% 132.79/22.98 (ordinalTransSet) =>
% 132.79/22.98 ((
% 132.79/22.98 (ordinalTransSet1) =>
% 132.79/22.98 ((
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% 132.79/22.98 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1538])).
% 132.79/22.98 thf(zip_derived_cl1553, plain,
% 132.79/22.98 (~ (((cartprodfstpairEq) =>
% 132.79/22.98 (((cartprodsndpairEq) =>
% 132.79/22.98 (((cartprodpairsurjEq) =>
% 132.79/22.98 (((dpsetconstrI) =>
% 132.79/22.98 (((dpsetconstrSub) =>
% 132.79/22.98 (((setOfPairsIsBReln) =>
% 132.79/22.98 (((dpsetconstrERa) =>
% 132.79/22.98 (((dpsetconstrEL1) =>
% 132.79/22.98 (((dpsetconstrEL2) =>
% 132.79/22.98 (((dpsetconstrER) =>
% 132.79/22.98 (((funcImageSingleton) =>
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% 132.79/22.98 (((app) =>
% 132.79/22.98 (((infuncsetfunc) =>
% 132.79/22.98 (((ap2p) =>
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% 132.79/22.98 (((lamp) =>
% 132.79/22.98 (((lam2p) =>
% 132.79/22.98 (((brelnall1) =>
% 132.79/22.98 (((brelnall2) =>
% 132.79/22.98 (((ex1E2) =>
% 132.79/22.98 (((funcGraphProp1) =>
% 132.79/22.98 (((funcGraphProp3) =>
% 132.79/22.98 (((funcGraphProp2) =>
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% 132.79/22.98 (((funcGraphProp4) =>
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% 132.79/22.98 (funcext2) =>
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% 132.79/22.98 ((
% 132.79/22.98 (ap2apEq2) =>
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
% 132.79/22.98 (image1E) =>
% 132.79/22.98 ((
% 132.79/22.98 (image1I) =>
% 132.79/22.98 ((
% 132.79/22.98 (injFuncInInjFuncSet) =>
% 132.79/22.98 ((
% 132.79/22.98 (injFuncSetFuncIn) =>
% 132.79/22.98 ((
% 132.79/22.98 (injFuncSetFuncInj) =>
% 132.79/22.98 ((
% 132.79/22.98 (surjFuncSetFuncIn) =>
% 132.79/22.98 ((
% 132.79/22.98 (surjFuncSetFuncSurj) =>
% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1546])).
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% 132.79/22.98 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1559])).
% 132.79/22.98 thf(zip_derived_cl1572, plain,
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% 132.79/22.98 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1566])).
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% 132.79/22.98 ((
% 132.79/22.98 (foundation2) =>
% 132.79/22.98 ((
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% 132.79/22.98 ((
% 132.79/22.98 (notinself2) =>
% 132.79/22.98 ((
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% 132.79/22.98 ((
% 132.79/22.98 (omegaSclos) =>
% 132.79/22.98 ((
% 132.79/22.98 (peano0notS) =>
% 132.79/22.98 ((
% 132.79/22.98 (peanoSinj) =>
% 132.79/22.98 ((
% 132.79/22.98 (transitivesetOp1) =>
% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 (ordinal @
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% 132.79/22.98 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1572])).
% 132.79/22.98 thf(zip_derived_cl1586, plain,
% 132.79/22.98 (~ (((setOfPairsIsBReln) =>
% 132.79/22.98 (((dpsetconstrERa) =>
% 132.79/22.98 (((dpsetconstrEL1) =>
% 132.79/22.98 (((dpsetconstrEL2) =>
% 132.79/22.98 (((dpsetconstrER) =>
% 132.79/22.98 (((funcImageSingleton) =>
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% 132.79/22.98 (((app) =>
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
% 132.79/22.98 (binunionTIRcontra) =>
% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
% 132.79/22.98 (binunionTEcontra) =>
% 132.79/22.98 ((
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% 132.79/22.98 ((
% 132.79/22.98 (complementUnionInPowersetComplement) =>
% 132.79/22.98 ((
% 132.79/22.98 (demorgan2a2) =>
% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
% 132.79/22.98 (demorgan2a) =>
% 132.79/22.98 ((
% 132.79/22.98 (demorgan2b2) =>
% 132.79/22.98 ((
% 132.79/22.98 (demorgan2b) =>
% 132.79/22.98 ((
% 132.79/22.98 (demorgan2) =>
% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
% 132.79/22.98 (woz13rule3) =>
% 132.79/22.98 ((
% 132.79/22.98 (woz13rule4) =>
% 132.79/22.98 ((
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% 132.79/22.98 ((
% 132.79/22.98 (woz1_2) =>
% 132.79/22.98 ((
% 132.79/22.98 (woz1_3) =>
% 132.79/22.98 ((
% 132.79/22.98 (woz1_4) =>
% 132.79/22.98 ((
% 132.79/22.98 (woz1_5) =>
% 132.79/22.98 ((
% 132.79/22.98 (breln1all2) =>
% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
% 132.79/22.98 (breln1all1) =>
% 132.79/22.98 ((
% 132.79/22.98 (subbreln1) =>
% 132.79/22.98 ((
% 132.79/22.98 (eqbreln1) =>
% 132.79/22.98 ((
% 132.79/22.98 (breln1invprop) =>
% 132.79/22.98 ((
% 132.79/22.98 (breln1invI) =>
% 132.79/22.98 ((
% 132.79/22.98 (breln1invE) =>
% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
% 132.79/22.98 (breln1compE) =>
% 132.79/22.98 ((
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% 132.79/22.98 ((
% 132.79/22.98 (breln1unionprop) =>
% 132.79/22.98 ((
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% 132.79/22.98 ((
% 132.79/22.98 (breln1unionIR) =>
% 132.79/22.98 ((
% 132.79/22.98 (breln1unionI) =>
% 132.79/22.98 ((
% 132.79/22.98 (breln1unionE) =>
% 132.79/22.98 ((
% 132.79/22.98 (breln1unionEcases) =>
% 132.79/22.98 ((
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% 132.79/22.98 ((
% 132.79/22.98 (woz2Ex) =>
% 132.79/22.98 ((
% 132.79/22.98 (woz2W) =>
% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
% 132.79/22.98 (image1E) =>
% 132.79/22.98 ((
% 132.79/22.98 (image1I) =>
% 132.79/22.98 ((
% 132.79/22.98 (injFuncInInjFuncSet) =>
% 132.79/22.98 ((
% 132.79/22.98 (injFuncSetFuncIn) =>
% 132.79/22.98 ((
% 132.79/22.98 (injFuncSetFuncInj) =>
% 132.79/22.98 ((
% 132.79/22.98 (surjFuncSetFuncIn) =>
% 132.79/22.98 ((
% 132.79/22.98 (surjFuncSetFuncSurj) =>
% 132.79/22.98 ((
% 132.79/22.98 (leftInvIsSurj) =>
% 132.79/22.98 ((
% 132.79/22.98 (surjCantorThm) =>
% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
% 132.79/22.98 (notinself2) =>
% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 ((
% 132.79/22.98 (peano0notS) =>
% 132.79/22.98 ((
% 132.79/22.98 (peanoSinj) =>
% 132.79/22.98 ((
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% 132.79/22.98 ((
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% 132.79/22.98 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1579])).
% 132.79/22.98 thf(zip_derived_cl1594, plain,
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% 132.79/22.98 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1603])).
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% 132.79/22.98 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1624])).
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% 132.79/22.99 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1633])).
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% 132.79/22.99 ((
% 132.79/22.99 (surjFuncSetFuncSurj) =>
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% 132.79/22.99 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1641])).
% 132.79/22.99 thf(zip_derived_cl1659, plain,
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% 132.79/22.99 ((
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% 132.79/22.99 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1650])).
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% 132.79/22.99 (injFuncSetFuncInj) =>
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% 132.79/22.99 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1678])).
% 132.79/22.99 thf(zip_derived_cl1697, plain,
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% 132.79/22.99 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1688])).
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% 132.79/22.99 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1706])).
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% 132.79/22.99 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1742])).
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% 132.79/22.99 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1750])).
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% 132.79/22.99 ((
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% 132.79/22.99 ((
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% 132.79/22.99 ((
% 132.79/22.99 (demorgan2a2) =>
% 132.79/22.99 ((
% 132.79/22.99 (demorgan1a) =>
% 132.79/22.99 ((
% 132.79/22.99 (demorgan1b) =>
% 132.79/22.99 ((
% 132.79/22.99 (demorgan1) =>
% 132.79/22.99 ((
% 132.79/22.99 (demorgan2a) =>
% 132.79/22.99 ((
% 132.79/22.99 (demorgan2b2) =>
% 132.79/22.99 ((
% 132.79/22.99 (demorgan2b) =>
% 132.79/22.99 ((
% 132.79/22.99 (demorgan2) =>
% 132.79/22.99 ((
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% 132.79/22.99 ((
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% 132.79/22.99 ((
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% 132.79/22.99 ((
% 132.79/22.99 (woz13rule3) =>
% 132.79/22.99 ((
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% 132.79/22.99 ((
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% 132.79/22.99 ((
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% 132.79/22.99 ((
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% 132.79/22.99 ((
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% 132.79/22.99 ((
% 132.79/22.99 (subbreln1) =>
% 132.79/22.99 ((
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% 132.79/22.99 ((
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% 132.79/22.99 ((
% 132.79/22.99 (breln1invI) =>
% 132.79/22.99 ((
% 132.79/22.99 (breln1invE) =>
% 132.79/22.99 ((
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% 132.79/22.99 ((
% 132.79/22.99 (breln1compI) =>
% 132.79/22.99 ((
% 132.79/22.99 (breln1compE) =>
% 132.79/22.99 ((
% 132.79/22.99 (breln1compEex) =>
% 132.79/22.99 ((
% 132.79/22.99 (breln1unionprop) =>
% 132.79/22.99 ((
% 132.79/22.99 (breln1unionIL) =>
% 132.79/22.99 ((
% 132.79/22.99 (breln1unionIR) =>
% 132.79/22.99 ((
% 132.79/22.99 (breln1unionI) =>
% 132.79/22.99 ((
% 132.79/22.99 (breln1unionE) =>
% 132.79/22.99 ((
% 132.79/22.99 (breln1unionEcases) =>
% 132.79/22.99 ((
% 132.79/22.99 (breln1unionCommutes) =>
% 132.79/22.99 ((
% 132.79/22.99 (woz2Ex) =>
% 132.79/22.99 ((
% 132.79/22.99 (woz2W) =>
% 132.79/22.99 ((
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% 132.79/22.99 ((
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% 132.79/22.99 ((
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% 132.79/22.99 ((
% 132.79/22.99 (image1Equiv) =>
% 132.79/22.99 ((
% 132.79/22.99 (image1E) =>
% 132.79/22.99 ((
% 132.79/22.99 (image1I) =>
% 132.79/22.99 ((
% 132.79/22.99 (injFuncInInjFuncSet) =>
% 132.79/22.99 ((
% 132.79/22.99 (injFuncSetFuncIn) =>
% 132.79/22.99 ((
% 132.79/22.99 (injFuncSetFuncInj) =>
% 132.79/22.99 ((
% 132.79/22.99 (surjFuncSetFuncIn) =>
% 132.79/22.99 ((
% 132.79/22.99 (surjFuncSetFuncSurj) =>
% 132.79/22.99 ((
% 132.79/22.99 (leftInvIsSurj) =>
% 132.79/22.99 ((
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% 132.79/22.99 ((
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% 132.79/22.99 ((
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% 132.79/22.99 ((
% 132.79/22.99 (notinself2) =>
% 132.79/22.99 ((
% 132.79/22.99 (omegaSp) =>
% 132.79/22.99 ((
% 132.79/22.99 (omegaSclos) =>
% 132.79/22.99 ((
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% 132.79/22.99 ((
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% 132.79/22.99 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1761])).
% 132.79/22.99 thf(zip_derived_cl1781, plain,
% 132.79/22.99 (~ (((funcGraphProp4) =>
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% 132.79/22.99 ((
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% 132.79/22.99 ((
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% 132.79/22.99 ((
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% 132.79/22.99 ((
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% 132.79/22.99 ((
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% 132.79/22.99 ((
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% 132.79/22.99 ((
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% 132.79/22.99 ((
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% 132.79/22.99 ((
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% 132.79/22.99 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1771])).
% 132.79/22.99 thf(zip_derived_cl1790, plain,
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% 132.79/22.99 ((
% 132.79/22.99 (breln1invE) =>
% 132.79/22.99 ((
% 132.79/22.99 (breln1compprop) =>
% 132.79/22.99 ((
% 132.79/22.99 (breln1compI) =>
% 132.79/22.99 ((
% 132.79/22.99 (breln1compE) =>
% 132.79/22.99 ((
% 132.79/22.99 (breln1compEex) =>
% 132.79/22.99 ((
% 132.79/22.99 (breln1unionprop) =>
% 132.79/22.99 ((
% 132.79/22.99 (breln1unionIL) =>
% 132.79/22.99 ((
% 132.79/22.99 (breln1unionIR) =>
% 132.79/22.99 ((
% 132.79/22.99 (breln1unionI) =>
% 132.79/22.99 ((
% 132.79/22.99 (breln1unionE) =>
% 132.79/22.99 ((
% 132.79/22.99 (breln1unionEcases) =>
% 132.79/22.99 ((
% 132.79/22.99 (breln1unionCommutes) =>
% 132.79/22.99 ((
% 132.79/22.99 (woz2Ex) =>
% 132.79/22.99 ((
% 132.79/22.99 (woz2W) =>
% 132.79/22.99 ((
% 132.79/22.99 (woz2A) =>
% 132.79/22.99 ((
% 132.79/22.99 (woz2B) =>
% 132.79/22.99 ((
% 132.79/22.99 (image1Ex) =>
% 132.79/22.99 ((
% 132.79/22.99 (image1Ex1) =>
% 132.79/22.99 ((
% 132.79/22.99 (image1Equiv) =>
% 132.79/22.99 ((
% 132.79/22.99 (image1E) =>
% 132.79/22.99 ((
% 132.79/22.99 (image1I) =>
% 132.79/22.99 ((
% 132.79/22.99 (injFuncInInjFuncSet) =>
% 132.79/22.99 ((
% 132.79/22.99 (injFuncSetFuncIn) =>
% 132.79/22.99 ((
% 132.79/22.99 (injFuncSetFuncInj) =>
% 132.79/22.99 ((
% 132.79/22.99 (surjFuncSetFuncIn) =>
% 132.79/22.99 ((
% 132.79/22.99 (surjFuncSetFuncSurj) =>
% 132.79/22.99 ((
% 132.79/22.99 (leftInvIsSurj) =>
% 132.79/22.99 ((
% 132.79/22.99 (surjCantorThm) =>
% 132.79/22.99 ((
% 132.79/22.99 (foundation2) =>
% 132.79/22.99 ((
% 132.79/22.99 (notinself) =>
% 132.79/22.99 ((
% 132.79/22.99 (notinself2) =>
% 132.79/22.99 ((
% 132.79/22.99 (omegaSp) =>
% 132.79/22.99 ((
% 132.79/22.99 (omegaSclos) =>
% 132.79/22.99 ((
% 132.79/22.99 (peano0notS) =>
% 132.79/22.99 ((
% 132.79/22.99 (peanoSinj) =>
% 132.79/22.99 ((
% 132.79/22.99 (transitivesetOp1) =>
% 132.79/22.99 ((
% 132.79/22.99 (binintTransitive) =>
% 132.79/22.99 ((
% 132.79/22.99 (transitivesetOp2) =>
% 132.79/22.99 ((
% 132.79/22.99 (setunionTransitive) =>
% 132.79/22.99 ((
% 132.79/22.99 (ordinalMinLem1) =>
% 132.79/22.99 ((
% 132.79/22.99 (ordinalTransSet) =>
% 132.79/22.99 ((
% 132.79/22.99 (ordinalTransSet1) =>
% 132.79/22.99 ((
% 132.79/22.99 (setunionOrdinalLem1) =>
% 132.79/22.99 (ordinal @
% 132.79/22.99 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/22.99 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1781])).
% 132.79/22.99 thf(zip_derived_cl1800, plain,
% 132.79/22.99 (~ (((eqbreln) =>
% 132.79/22.99 (((funcext) =>
% 132.79/22.99 (((funcext2) =>
% 132.79/22.99 (((ap2apEq1) =>
% 132.79/22.99 (((ap2apEq2) =>
% 132.79/22.99 (((beta1) =>
% 132.79/22.99 (((eta1) =>
% 132.79/22.99 (((lam2lamEq) =>
% 132.79/22.99 (((beta2) =>
% 132.79/22.99 (((eta2) =>
% 132.79/22.99 (((iffalseProp1) =>
% 132.79/22.99 (((iffalseProp2) =>
% 132.79/22.99 (((iftrueProp1) =>
% 132.79/22.99 (((iftrueProp2) =>
% 132.79/22.99 (((ifSingleton) =>
% 132.79/22.99 (((ifp) =>
% 132.79/22.99 (((theeq) =>
% 132.79/22.99 (((iftrue) =>
% 132.79/22.99 (((iffalse) =>
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% 132.79/22.99 (((binintersectT_lem) =>
% 132.79/22.99 (((binunionT_lem) =>
% 132.79/22.99 (((powersetT_lem) =>
% 132.79/22.99 (((setminusT_lem) =>
% 132.79/22.99 (((complementT_lem) =>
% 132.79/22.99 (((setextT) =>
% 132.79/22.99 (((subsetTI) =>
% 132.79/22.99 (((powersetTI1) =>
% 132.79/22.99 (((powersetTE1) =>
% 132.79/22.99 (((complementTI1) =>
% 132.79/22.99 ((
% 132.79/22.99 (complementTE1) =>
% 132.79/22.99 ((
% 132.79/22.99 (binintersectTELcontra) =>
% 132.79/22.99 ((
% 132.79/22.99 (binintersectTERcontra) =>
% 132.79/22.99 ((
% 132.79/22.99 (contrasubsetT) =>
% 132.79/22.99 ((
% 132.79/22.99 (contrasubsetT1) =>
% 132.79/22.99 ((
% 132.79/22.99 (contrasubsetT2) =>
% 132.79/22.99 ((
% 132.79/22.99 (contrasubsetT3) =>
% 132.79/22.99 ((
% 132.79/22.99 (doubleComplementI1) =>
% 132.79/22.99 ((
% 132.79/22.99 (doubleComplementE1) =>
% 132.79/22.99 ((
% 132.79/22.99 (doubleComplementSub1) =>
% 132.79/22.99 ((
% 132.79/22.99 (doubleComplementSub2) =>
% 132.79/22.99 ((
% 132.79/22.99 (doubleComplementEq) =>
% 132.79/22.99 ((
% 132.79/22.99 (complementTnotintersectT) =>
% 132.79/22.99 ((
% 132.79/22.99 (complementImpComplementIntersect) =>
% 132.79/22.99 ((
% 132.79/22.99 (complementSubsetComplementIntersect) =>
% 132.79/22.99 ((
% 132.79/22.99 (complementInPowersetComplementIntersect) =>
% 132.79/22.99 ((
% 132.79/22.99 (contraSubsetComplement) =>
% 132.79/22.99 ((
% 132.79/22.99 (complementTcontraSubset) =>
% 132.79/22.99 ((
% 132.79/22.99 (binunionTILcontra) =>
% 132.79/22.99 ((
% 132.79/22.99 (binunionTIRcontra) =>
% 132.79/22.99 ((
% 132.79/22.99 (inIntersectImpInUnion) =>
% 132.79/22.99 ((
% 132.79/22.99 (inIntersectImpInUnion2) =>
% 132.79/22.99 ((
% 132.79/22.99 (inIntersectImpInIntersectUnions) =>
% 132.79/22.99 ((
% 132.79/22.99 (intersectInPowersetIntersectUnions) =>
% 132.79/22.99 ((
% 132.79/22.99 (inComplementUnionImpNotIn1) =>
% 132.79/22.99 ((
% 132.79/22.99 (inComplementUnionImpInComplement1) =>
% 132.79/22.99 ((
% 132.79/22.99 (binunionTE) =>
% 132.79/22.99 ((
% 132.79/22.99 (binunionTEcontra) =>
% 132.79/22.99 ((
% 132.79/22.99 (demorgan2a1) =>
% 132.79/22.99 ((
% 132.79/22.99 (complementUnionInPowersetComplement) =>
% 132.79/22.99 ((
% 132.79/22.99 (demorgan2a2) =>
% 132.79/22.99 ((
% 132.79/22.99 (demorgan1a) =>
% 132.79/22.99 ((
% 132.79/22.99 (demorgan1b) =>
% 132.79/22.99 ((
% 132.79/22.99 (demorgan1) =>
% 132.79/22.99 ((
% 132.79/22.99 (demorgan2a) =>
% 132.79/22.99 ((
% 132.79/22.99 (demorgan2b2) =>
% 132.79/22.99 ((
% 132.79/22.99 (demorgan2b) =>
% 132.79/22.99 ((
% 132.79/22.99 (demorgan2) =>
% 132.79/22.99 ((
% 132.79/22.99 (woz13rule0) =>
% 132.79/22.99 ((
% 132.79/22.99 (woz13rule1) =>
% 132.79/22.99 ((
% 132.79/22.99 (woz13rule2) =>
% 132.79/22.99 ((
% 132.79/22.99 (woz13rule3) =>
% 132.79/22.99 ((
% 132.79/22.99 (woz13rule4) =>
% 132.79/22.99 ((
% 132.79/22.99 (woz1_1) =>
% 132.79/22.99 ((
% 132.79/22.99 (woz1_2) =>
% 132.79/22.99 ((
% 132.79/22.99 (woz1_3) =>
% 132.79/22.99 ((
% 132.79/22.99 (woz1_4) =>
% 132.79/22.99 ((
% 132.79/22.99 (woz1_5) =>
% 132.79/22.99 ((
% 132.79/22.99 (breln1all2) =>
% 132.79/22.99 ((
% 132.79/22.99 (breln1SetBreln1) =>
% 132.79/22.99 ((
% 132.79/22.99 (choice2fnsingleton) =>
% 132.79/22.99 ((
% 132.79/22.99 (setOfPairsIsBReln1) =>
% 132.79/22.99 ((
% 132.79/22.99 (breln1all1) =>
% 132.79/22.99 ((
% 132.79/22.99 (subbreln1) =>
% 132.79/22.99 ((
% 132.79/22.99 (eqbreln1) =>
% 132.79/22.99 ((
% 132.79/22.99 (breln1invprop) =>
% 132.79/22.99 ((
% 132.79/22.99 (breln1invI) =>
% 132.79/22.99 ((
% 132.79/22.99 (breln1invE) =>
% 132.79/22.99 ((
% 132.79/22.99 (breln1compprop) =>
% 132.79/22.99 ((
% 132.79/22.99 (breln1compI) =>
% 132.79/22.99 ((
% 132.79/22.99 (breln1compE) =>
% 132.79/22.99 ((
% 132.79/22.99 (breln1compEex) =>
% 132.79/22.99 ((
% 132.79/22.99 (breln1unionprop) =>
% 132.79/22.99 ((
% 132.79/22.99 (breln1unionIL) =>
% 132.79/22.99 ((
% 132.79/22.99 (breln1unionIR) =>
% 132.79/22.99 ((
% 132.79/22.99 (breln1unionI) =>
% 132.79/22.99 ((
% 132.79/22.99 (breln1unionE) =>
% 132.79/22.99 ((
% 132.79/22.99 (breln1unionEcases) =>
% 132.79/22.99 ((
% 132.79/22.99 (breln1unionCommutes) =>
% 132.79/22.99 ((
% 132.79/22.99 (woz2Ex) =>
% 132.79/22.99 ((
% 132.79/22.99 (woz2W) =>
% 132.79/22.99 ((
% 132.79/22.99 (woz2A) =>
% 132.79/22.99 ((
% 132.79/22.99 (woz2B) =>
% 132.79/22.99 ((
% 132.79/22.99 (image1Ex) =>
% 132.79/22.99 ((
% 132.79/22.99 (image1Ex1) =>
% 132.79/22.99 ((
% 132.79/22.99 (image1Equiv) =>
% 132.79/22.99 ((
% 132.79/22.99 (image1E) =>
% 132.79/22.99 ((
% 132.79/22.99 (image1I) =>
% 132.79/22.99 ((
% 132.79/22.99 (injFuncInInjFuncSet) =>
% 132.79/22.99 ((
% 132.79/22.99 (injFuncSetFuncIn) =>
% 132.79/22.99 ((
% 132.79/22.99 (injFuncSetFuncInj) =>
% 132.79/22.99 ((
% 132.79/22.99 (surjFuncSetFuncIn) =>
% 132.79/22.99 ((
% 132.79/22.99 (surjFuncSetFuncSurj) =>
% 132.79/22.99 ((
% 132.79/22.99 (leftInvIsSurj) =>
% 132.79/22.99 ((
% 132.79/22.99 (surjCantorThm) =>
% 132.79/22.99 ((
% 132.79/22.99 (foundation2) =>
% 132.79/22.99 ((
% 132.79/22.99 (notinself) =>
% 132.79/22.99 ((
% 132.79/22.99 (notinself2) =>
% 132.79/22.99 ((
% 132.79/22.99 (omegaSp) =>
% 132.79/22.99 ((
% 132.79/22.99 (omegaSclos) =>
% 132.79/22.99 ((
% 132.79/22.99 (peano0notS) =>
% 132.79/22.99 ((
% 132.79/22.99 (peanoSinj) =>
% 132.79/22.99 ((
% 132.79/22.99 (transitivesetOp1) =>
% 132.79/22.99 ((
% 132.79/22.99 (binintTransitive) =>
% 132.79/22.99 ((
% 132.79/22.99 (transitivesetOp2) =>
% 132.79/22.99 ((
% 132.79/22.99 (setunionTransitive) =>
% 132.79/22.99 ((
% 132.79/22.99 (ordinalMinLem1) =>
% 132.79/22.99 ((
% 132.79/22.99 (ordinalTransSet) =>
% 132.79/22.99 ((
% 132.79/22.99 (ordinalTransSet1) =>
% 132.79/22.99 ((
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% 132.79/22.99 (ordinal @
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% 132.79/22.99 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1790])).
% 132.79/22.99 thf(zip_derived_cl1812, plain,
% 132.79/22.99 (~ (((funcext) =>
% 132.79/22.99 (((funcext2) =>
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% 132.79/22.99 (((lam2lamEq) =>
% 132.79/22.99 (((beta2) =>
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% 132.79/22.99 (((iffalseProp2) =>
% 132.79/22.99 (((iftrueProp1) =>
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% 132.79/22.99 (((ifp) =>
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% 132.79/22.99 (((binunionT_lem) =>
% 132.79/22.99 (((powersetT_lem) =>
% 132.79/22.99 (((setminusT_lem) =>
% 132.79/22.99 (((complementT_lem) =>
% 132.79/22.99 (((setextT) =>
% 132.79/22.99 (((subsetTI) =>
% 132.79/22.99 (((powersetTI1) =>
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% 132.79/22.99 (((complementTE1) =>
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% 132.79/22.99 ((
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% 132.79/22.99 ((
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% 132.79/22.99 ((
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% 132.79/22.99 ((
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% 132.79/22.99 ((
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% 132.79/22.99 ((
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% 132.79/22.99 ((
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% 132.79/22.99 ((
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% 132.79/22.99 ((
% 132.79/22.99 (complementInPowersetComplementIntersect) =>
% 132.79/22.99 ((
% 132.79/22.99 (contraSubsetComplement) =>
% 132.79/22.99 ((
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% 132.79/22.99 ((
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% 132.79/22.99 ((
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% 132.79/22.99 ((
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% 132.79/22.99 ((
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% 132.79/22.99 ((
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% 132.79/22.99 ((
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% 132.79/22.99 ((
% 132.79/22.99 (inComplementUnionImpInComplement1) =>
% 132.79/22.99 ((
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% 132.79/22.99 ((
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% 132.79/22.99 ((
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% 132.79/22.99 ((
% 132.79/22.99 (complementUnionInPowersetComplement) =>
% 132.79/22.99 ((
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% 132.79/22.99 ((
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% 132.79/22.99 ((
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% 132.79/22.99 ((
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% 132.79/22.99 ((
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% 132.79/22.99 ((
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% 132.79/22.99 ((
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% 132.79/22.99 ((
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% 132.79/22.99 ((
% 132.79/22.99 (image1I) =>
% 132.79/22.99 ((
% 132.79/22.99 (injFuncInInjFuncSet) =>
% 132.79/22.99 ((
% 132.79/22.99 (injFuncSetFuncIn) =>
% 132.79/22.99 ((
% 132.79/22.99 (injFuncSetFuncInj) =>
% 132.79/22.99 ((
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% 132.79/22.99 ((
% 132.79/22.99 (surjFuncSetFuncSurj) =>
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% 132.79/22.99 ((
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% 132.79/22.99 ((
% 132.79/22.99 (peanoSinj) =>
% 132.79/22.99 ((
% 132.79/22.99 (transitivesetOp1) =>
% 132.79/22.99 ((
% 132.79/22.99 (binintTransitive) =>
% 132.79/22.99 ((
% 132.79/22.99 (transitivesetOp2) =>
% 132.79/22.99 ((
% 132.79/22.99 (setunionTransitive) =>
% 132.79/22.99 ((
% 132.79/22.99 (ordinalMinLem1) =>
% 132.79/22.99 ((
% 132.79/22.99 (ordinalTransSet) =>
% 132.79/22.99 ((
% 132.79/22.99 (ordinalTransSet1) =>
% 132.79/22.99 ((
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% 132.79/22.99 (ordinal @
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% 132.79/22.99 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1800])).
% 132.79/22.99 thf(zip_derived_cl1826, plain,
% 132.79/22.99 (~ (((funcext2) =>
% 132.79/22.99 (((ap2apEq1) =>
% 132.79/22.99 (((ap2apEq2) =>
% 132.79/22.99 (((beta1) =>
% 132.79/22.99 (((eta1) =>
% 132.79/22.99 (((lam2lamEq) =>
% 132.79/22.99 (((beta2) =>
% 132.79/22.99 (((eta2) =>
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% 132.79/22.99 (((iffalseProp2) =>
% 132.79/22.99 (((iftrueProp1) =>
% 132.79/22.99 (((iftrueProp2) =>
% 132.79/22.99 (((ifSingleton) =>
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% 132.79/22.99 (((theeq) =>
% 132.79/22.99 (((iftrue) =>
% 132.79/22.99 (((iffalse) =>
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% 132.79/22.99 (((binunionT_lem) =>
% 132.79/22.99 (((powersetT_lem) =>
% 132.79/22.99 (((setminusT_lem) =>
% 132.79/22.99 (((complementT_lem) =>
% 132.79/22.99 (((setextT) =>
% 132.79/22.99 (((subsetTI) =>
% 132.79/22.99 (((powersetTI1) =>
% 132.79/22.99 (((powersetTE1) =>
% 132.79/22.99 (((complementTI1) =>
% 132.79/22.99 (((complementTE1) =>
% 132.79/22.99 (((binintersectTELcontra) =>
% 132.79/22.99 ((
% 132.79/22.99 (binintersectTERcontra) =>
% 132.79/22.99 ((
% 132.79/22.99 (contrasubsetT) =>
% 132.79/22.99 ((
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% 132.79/22.99 ((
% 132.79/22.99 (contrasubsetT2) =>
% 132.79/22.99 ((
% 132.79/22.99 (contrasubsetT3) =>
% 132.79/22.99 ((
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% 132.79/22.99 ((
% 132.79/22.99 (doubleComplementE1) =>
% 132.79/22.99 ((
% 132.79/22.99 (doubleComplementSub1) =>
% 132.79/22.99 ((
% 132.79/22.99 (doubleComplementSub2) =>
% 132.79/22.99 ((
% 132.79/22.99 (doubleComplementEq) =>
% 132.79/22.99 ((
% 132.79/22.99 (complementTnotintersectT) =>
% 132.79/22.99 ((
% 132.79/22.99 (complementImpComplementIntersect) =>
% 132.79/22.99 ((
% 132.79/22.99 (complementSubsetComplementIntersect) =>
% 132.79/22.99 ((
% 132.79/22.99 (complementInPowersetComplementIntersect) =>
% 132.79/22.99 ((
% 132.79/22.99 (contraSubsetComplement) =>
% 132.79/22.99 ((
% 132.79/22.99 (complementTcontraSubset) =>
% 132.79/22.99 ((
% 132.79/22.99 (binunionTILcontra) =>
% 132.79/22.99 ((
% 132.79/22.99 (binunionTIRcontra) =>
% 132.79/22.99 ((
% 132.79/22.99 (inIntersectImpInUnion) =>
% 132.79/22.99 ((
% 132.79/22.99 (inIntersectImpInUnion2) =>
% 132.79/22.99 ((
% 132.79/22.99 (inIntersectImpInIntersectUnions) =>
% 132.79/22.99 ((
% 132.79/22.99 (intersectInPowersetIntersectUnions) =>
% 132.79/22.99 ((
% 132.79/22.99 (inComplementUnionImpNotIn1) =>
% 132.79/22.99 ((
% 132.79/22.99 (inComplementUnionImpInComplement1) =>
% 132.79/22.99 ((
% 132.79/22.99 (binunionTE) =>
% 132.79/22.99 ((
% 132.79/22.99 (binunionTEcontra) =>
% 132.79/22.99 ((
% 132.79/22.99 (demorgan2a1) =>
% 132.79/22.99 ((
% 132.79/22.99 (complementUnionInPowersetComplement) =>
% 132.79/22.99 ((
% 132.79/22.99 (demorgan2a2) =>
% 132.79/22.99 ((
% 132.79/22.99 (demorgan1a) =>
% 132.79/22.99 ((
% 132.79/22.99 (demorgan1b) =>
% 132.79/22.99 ((
% 132.79/22.99 (demorgan1) =>
% 132.79/22.99 ((
% 132.79/22.99 (demorgan2a) =>
% 132.79/22.99 ((
% 132.79/22.99 (demorgan2b2) =>
% 132.79/22.99 ((
% 132.79/22.99 (demorgan2b) =>
% 132.79/22.99 ((
% 132.79/22.99 (demorgan2) =>
% 132.79/22.99 ((
% 132.79/22.99 (woz13rule0) =>
% 132.79/22.99 ((
% 132.79/22.99 (woz13rule1) =>
% 132.79/22.99 ((
% 132.79/22.99 (woz13rule2) =>
% 132.79/22.99 ((
% 132.79/22.99 (woz13rule3) =>
% 132.79/22.99 ((
% 132.79/22.99 (woz13rule4) =>
% 132.79/22.99 ((
% 132.79/22.99 (woz1_1) =>
% 132.79/22.99 ((
% 132.79/22.99 (woz1_2) =>
% 132.79/22.99 ((
% 132.79/22.99 (woz1_3) =>
% 132.79/22.99 ((
% 132.79/22.99 (woz1_4) =>
% 132.79/22.99 ((
% 132.79/22.99 (woz1_5) =>
% 132.79/22.99 ((
% 132.79/22.99 (breln1all2) =>
% 132.79/22.99 ((
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% 132.79/22.99 ((
% 132.79/22.99 (choice2fnsingleton) =>
% 132.79/22.99 ((
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% 132.79/22.99 ((
% 132.79/22.99 (breln1all1) =>
% 132.79/22.99 ((
% 132.79/22.99 (subbreln1) =>
% 132.79/22.99 ((
% 132.79/22.99 (eqbreln1) =>
% 132.79/22.99 ((
% 132.79/22.99 (breln1invprop) =>
% 132.79/22.99 ((
% 132.79/22.99 (breln1invI) =>
% 132.79/22.99 ((
% 132.79/22.99 (breln1invE) =>
% 132.79/22.99 ((
% 132.79/22.99 (breln1compprop) =>
% 132.79/22.99 ((
% 132.79/22.99 (breln1compI) =>
% 132.79/22.99 ((
% 132.79/22.99 (breln1compE) =>
% 132.79/22.99 ((
% 132.79/22.99 (breln1compEex) =>
% 132.79/22.99 ((
% 132.79/22.99 (breln1unionprop) =>
% 132.79/22.99 ((
% 132.79/22.99 (breln1unionIL) =>
% 132.79/22.99 ((
% 132.79/22.99 (breln1unionIR) =>
% 132.79/22.99 ((
% 132.79/22.99 (breln1unionI) =>
% 132.79/22.99 ((
% 132.79/22.99 (breln1unionE) =>
% 132.79/22.99 ((
% 132.79/22.99 (breln1unionEcases) =>
% 132.79/22.99 ((
% 132.79/22.99 (breln1unionCommutes) =>
% 132.79/22.99 ((
% 132.79/22.99 (woz2Ex) =>
% 132.79/22.99 ((
% 132.79/22.99 (woz2W) =>
% 132.79/22.99 ((
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% 132.79/22.99 ((
% 132.79/22.99 (woz2B) =>
% 132.79/22.99 ((
% 132.79/22.99 (image1Ex) =>
% 132.79/22.99 ((
% 132.79/22.99 (image1Ex1) =>
% 132.79/22.99 ((
% 132.79/22.99 (image1Equiv) =>
% 132.79/22.99 ((
% 132.79/22.99 (image1E) =>
% 132.79/22.99 ((
% 132.79/22.99 (image1I) =>
% 132.79/22.99 ((
% 132.79/22.99 (injFuncInInjFuncSet) =>
% 132.79/22.99 ((
% 132.79/22.99 (injFuncSetFuncIn) =>
% 132.79/22.99 ((
% 132.79/22.99 (injFuncSetFuncInj) =>
% 132.79/22.99 ((
% 132.79/22.99 (surjFuncSetFuncIn) =>
% 132.79/22.99 ((
% 132.79/22.99 (surjFuncSetFuncSurj) =>
% 132.79/22.99 ((
% 132.79/22.99 (leftInvIsSurj) =>
% 132.79/22.99 ((
% 132.79/22.99 (surjCantorThm) =>
% 132.79/22.99 ((
% 132.79/22.99 (foundation2) =>
% 132.79/22.99 ((
% 132.79/22.99 (notinself) =>
% 132.79/22.99 ((
% 132.79/22.99 (notinself2) =>
% 132.79/22.99 ((
% 132.79/22.99 (omegaSp) =>
% 132.79/22.99 ((
% 132.79/22.99 (omegaSclos) =>
% 132.79/22.99 ((
% 132.79/22.99 (peano0notS) =>
% 132.79/22.99 ((
% 132.79/22.99 (peanoSinj) =>
% 132.79/22.99 ((
% 132.79/22.99 (transitivesetOp1) =>
% 132.79/22.99 ((
% 132.79/22.99 (binintTransitive) =>
% 132.79/22.99 ((
% 132.79/22.99 (transitivesetOp2) =>
% 132.79/22.99 ((
% 132.79/22.99 (setunionTransitive) =>
% 132.79/22.99 ((
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% 132.79/22.99 ((
% 132.79/22.99 (ordinalTransSet) =>
% 132.79/22.99 ((
% 132.79/22.99 (ordinalTransSet1) =>
% 132.79/22.99 ((
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% 132.79/22.99 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1812])).
% 132.79/22.99 thf(zip_derived_cl1841, plain,
% 132.79/22.99 (~ (((ap2apEq1) =>
% 132.79/22.99 (((ap2apEq2) =>
% 132.79/22.99 (((beta1) =>
% 132.79/22.99 (((eta1) =>
% 132.79/22.99 (((lam2lamEq) =>
% 132.79/22.99 (((beta2) =>
% 132.79/22.99 (((eta2) =>
% 132.79/22.99 (((iffalseProp1) =>
% 132.79/22.99 (((iffalseProp2) =>
% 132.79/22.99 (((iftrueProp1) =>
% 132.79/22.99 (((iftrueProp2) =>
% 132.79/22.99 (((ifSingleton) =>
% 132.79/22.99 (((ifp) =>
% 132.79/22.99 (((theeq) =>
% 132.79/22.99 (((iftrue) =>
% 132.79/22.99 (((iffalse) =>
% 132.79/22.99 (((iftrueorfalse) =>
% 132.79/22.99 (((binintersectT_lem) =>
% 132.79/22.99 (((binunionT_lem) =>
% 132.79/22.99 (((powersetT_lem) =>
% 132.79/22.99 (((setminusT_lem) =>
% 132.79/22.99 (((complementT_lem) =>
% 132.79/22.99 (((setextT) =>
% 132.79/22.99 (((subsetTI) =>
% 132.79/22.99 (((powersetTI1) =>
% 132.79/22.99 (((powersetTE1) =>
% 132.79/22.99 (((complementTI1) =>
% 132.79/22.99 (((complementTE1) =>
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% 132.79/22.99 (((binintersectTERcontra) =>
% 132.79/22.99 ((
% 132.79/22.99 (contrasubsetT) =>
% 132.79/22.99 ((
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% 132.79/22.99 ((
% 132.79/22.99 (contrasubsetT2) =>
% 132.79/22.99 ((
% 132.79/22.99 (contrasubsetT3) =>
% 132.79/22.99 ((
% 132.79/22.99 (doubleComplementI1) =>
% 132.79/22.99 ((
% 132.79/22.99 (doubleComplementE1) =>
% 132.79/22.99 ((
% 132.79/22.99 (doubleComplementSub1) =>
% 132.79/22.99 ((
% 132.79/22.99 (doubleComplementSub2) =>
% 132.79/22.99 ((
% 132.79/22.99 (doubleComplementEq) =>
% 132.79/22.99 ((
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% 132.79/22.99 ((
% 132.79/22.99 (complementImpComplementIntersect) =>
% 132.79/22.99 ((
% 132.79/22.99 (complementSubsetComplementIntersect) =>
% 132.79/22.99 ((
% 132.79/22.99 (complementInPowersetComplementIntersect) =>
% 132.79/22.99 ((
% 132.79/22.99 (contraSubsetComplement) =>
% 132.79/22.99 ((
% 132.79/22.99 (complementTcontraSubset) =>
% 132.79/22.99 ((
% 132.79/22.99 (binunionTILcontra) =>
% 132.79/22.99 ((
% 132.79/22.99 (binunionTIRcontra) =>
% 132.79/22.99 ((
% 132.79/22.99 (inIntersectImpInUnion) =>
% 132.79/22.99 ((
% 132.79/22.99 (inIntersectImpInUnion2) =>
% 132.79/22.99 ((
% 132.79/22.99 (inIntersectImpInIntersectUnions) =>
% 132.79/22.99 ((
% 132.79/22.99 (intersectInPowersetIntersectUnions) =>
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% 132.79/22.99 (inComplementUnionImpNotIn1) =>
% 132.79/22.99 ((
% 132.79/22.99 (inComplementUnionImpInComplement1) =>
% 132.79/22.99 ((
% 132.79/22.99 (binunionTE) =>
% 132.79/22.99 ((
% 132.79/22.99 (binunionTEcontra) =>
% 132.79/22.99 ((
% 132.79/22.99 (demorgan2a1) =>
% 132.79/22.99 ((
% 132.79/22.99 (complementUnionInPowersetComplement) =>
% 132.79/22.99 ((
% 132.79/22.99 (demorgan2a2) =>
% 132.79/22.99 ((
% 132.79/22.99 (demorgan1a) =>
% 132.79/22.99 ((
% 132.79/22.99 (demorgan1b) =>
% 132.79/22.99 ((
% 132.79/22.99 (demorgan1) =>
% 132.79/22.99 ((
% 132.79/22.99 (demorgan2a) =>
% 132.79/22.99 ((
% 132.79/22.99 (demorgan2b2) =>
% 132.79/22.99 ((
% 132.79/22.99 (demorgan2b) =>
% 132.79/22.99 ((
% 132.79/22.99 (demorgan2) =>
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% 132.79/22.99 ((
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% 132.79/22.99 ((
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% 132.79/22.99 ((
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% 132.79/22.99 ((
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% 132.79/22.99 ((
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% 132.79/22.99 ((
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% 132.79/22.99 ((
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% 132.79/22.99 ((
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% 132.79/22.99 ((
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% 132.79/22.99 ((
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% 132.79/22.99 ((
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% 132.79/22.99 ((
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% 132.79/22.99 ((
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% 132.79/22.99 ((
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% 132.79/22.99 ((
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% 132.79/22.99 ((
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% 132.79/22.99 ((
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% 132.79/22.99 ((
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% 132.79/22.99 ((
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% 132.79/22.99 ((
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% 132.79/22.99 ((
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% 132.79/22.99 ((
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% 132.79/22.99 ((
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% 132.79/22.99 ((
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% 132.79/22.99 ((
% 132.79/22.99 (injFuncInInjFuncSet) =>
% 132.79/22.99 ((
% 132.79/22.99 (injFuncSetFuncIn) =>
% 132.79/22.99 ((
% 132.79/22.99 (injFuncSetFuncInj) =>
% 132.79/22.99 ((
% 132.79/22.99 (surjFuncSetFuncIn) =>
% 132.79/22.99 ((
% 132.79/22.99 (surjFuncSetFuncSurj) =>
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% 132.79/22.99 (leftInvIsSurj) =>
% 132.79/22.99 ((
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% 132.79/22.99 ((
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% 132.79/22.99 ((
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% 132.79/22.99 ((
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% 132.79/22.99 ((
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% 132.79/22.99 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1826])).
% 132.79/22.99 thf(zip_derived_cl1857, plain,
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% 132.79/22.99 ((
% 132.79/22.99 (doubleComplementEq) =>
% 132.79/22.99 ((
% 132.79/22.99 (complementTnotintersectT) =>
% 132.79/22.99 ((
% 132.79/22.99 (complementImpComplementIntersect) =>
% 132.79/22.99 ((
% 132.79/22.99 (complementSubsetComplementIntersect) =>
% 132.79/22.99 ((
% 132.79/22.99 (complementInPowersetComplementIntersect) =>
% 132.79/22.99 ((
% 132.79/22.99 (contraSubsetComplement) =>
% 132.79/22.99 ((
% 132.79/22.99 (complementTcontraSubset) =>
% 132.79/22.99 ((
% 132.79/22.99 (binunionTILcontra) =>
% 132.79/22.99 ((
% 132.79/22.99 (binunionTIRcontra) =>
% 132.79/22.99 ((
% 132.79/22.99 (inIntersectImpInUnion) =>
% 132.79/22.99 ((
% 132.79/22.99 (inIntersectImpInUnion2) =>
% 132.79/22.99 ((
% 132.79/22.99 (inIntersectImpInIntersectUnions) =>
% 132.79/22.99 ((
% 132.79/22.99 (intersectInPowersetIntersectUnions) =>
% 132.79/22.99 ((
% 132.79/22.99 (inComplementUnionImpNotIn1) =>
% 132.79/22.99 ((
% 132.79/22.99 (inComplementUnionImpInComplement1) =>
% 132.79/22.99 ((
% 132.79/22.99 (binunionTE) =>
% 132.79/22.99 ((
% 132.79/22.99 (binunionTEcontra) =>
% 132.79/22.99 ((
% 132.79/22.99 (demorgan2a1) =>
% 132.79/22.99 ((
% 132.79/22.99 (complementUnionInPowersetComplement) =>
% 132.79/22.99 ((
% 132.79/22.99 (demorgan2a2) =>
% 132.79/22.99 ((
% 132.79/22.99 (demorgan1a) =>
% 132.79/22.99 ((
% 132.79/22.99 (demorgan1b) =>
% 132.79/22.99 ((
% 132.79/22.99 (demorgan1) =>
% 132.79/22.99 ((
% 132.79/22.99 (demorgan2a) =>
% 132.79/22.99 ((
% 132.79/22.99 (demorgan2b2) =>
% 132.79/22.99 ((
% 132.79/22.99 (demorgan2b) =>
% 132.79/22.99 ((
% 132.79/22.99 (demorgan2) =>
% 132.79/22.99 ((
% 132.79/22.99 (woz13rule0) =>
% 132.79/22.99 ((
% 132.79/22.99 (woz13rule1) =>
% 132.79/22.99 ((
% 132.79/22.99 (woz13rule2) =>
% 132.79/22.99 ((
% 132.79/22.99 (woz13rule3) =>
% 132.79/22.99 ((
% 132.79/22.99 (woz13rule4) =>
% 132.79/22.99 ((
% 132.79/22.99 (woz1_1) =>
% 132.79/22.99 ((
% 132.79/22.99 (woz1_2) =>
% 132.79/22.99 ((
% 132.79/22.99 (woz1_3) =>
% 132.79/22.99 ((
% 132.79/22.99 (woz1_4) =>
% 132.79/22.99 ((
% 132.79/22.99 (woz1_5) =>
% 132.79/22.99 ((
% 132.79/22.99 (breln1all2) =>
% 132.79/22.99 ((
% 132.79/22.99 (breln1SetBreln1) =>
% 132.79/22.99 ((
% 132.79/22.99 (choice2fnsingleton) =>
% 132.79/22.99 ((
% 132.79/22.99 (setOfPairsIsBReln1) =>
% 132.79/22.99 ((
% 132.79/22.99 (breln1all1) =>
% 132.79/22.99 ((
% 132.79/22.99 (subbreln1) =>
% 132.79/22.99 ((
% 132.79/22.99 (eqbreln1) =>
% 132.79/22.99 ((
% 132.79/22.99 (breln1invprop) =>
% 132.79/22.99 ((
% 132.79/22.99 (breln1invI) =>
% 132.79/22.99 ((
% 132.79/22.99 (breln1invE) =>
% 132.79/22.99 ((
% 132.79/22.99 (breln1compprop) =>
% 132.79/22.99 ((
% 132.79/22.99 (breln1compI) =>
% 132.79/22.99 ((
% 132.79/22.99 (breln1compE) =>
% 132.79/22.99 ((
% 132.79/22.99 (breln1compEex) =>
% 132.79/22.99 ((
% 132.79/22.99 (breln1unionprop) =>
% 132.79/22.99 ((
% 132.79/22.99 (breln1unionIL) =>
% 132.79/22.99 ((
% 132.79/22.99 (breln1unionIR) =>
% 132.79/22.99 ((
% 132.79/22.99 (breln1unionI) =>
% 132.79/22.99 ((
% 132.79/22.99 (breln1unionE) =>
% 132.79/22.99 ((
% 132.79/22.99 (breln1unionEcases) =>
% 132.79/22.99 ((
% 132.79/22.99 (breln1unionCommutes) =>
% 132.79/22.99 ((
% 132.79/22.99 (woz2Ex) =>
% 132.79/22.99 ((
% 132.79/22.99 (woz2W) =>
% 132.79/22.99 ((
% 132.79/22.99 (woz2A) =>
% 132.79/22.99 ((
% 132.79/22.99 (woz2B) =>
% 132.79/22.99 ((
% 132.79/22.99 (image1Ex) =>
% 132.79/22.99 ((
% 132.79/22.99 (image1Ex1) =>
% 132.79/22.99 ((
% 132.79/22.99 (image1Equiv) =>
% 132.79/22.99 ((
% 132.79/22.99 (image1E) =>
% 132.79/22.99 ((
% 132.79/22.99 (image1I) =>
% 132.79/22.99 ((
% 132.79/22.99 (injFuncInInjFuncSet) =>
% 132.79/22.99 ((
% 132.79/22.99 (injFuncSetFuncIn) =>
% 132.79/22.99 ((
% 132.79/22.99 (injFuncSetFuncInj) =>
% 132.79/22.99 ((
% 132.79/22.99 (surjFuncSetFuncIn) =>
% 132.79/22.99 ((
% 132.79/22.99 (surjFuncSetFuncSurj) =>
% 132.79/22.99 ((
% 132.79/22.99 (leftInvIsSurj) =>
% 132.79/22.99 ((
% 132.79/22.99 (surjCantorThm) =>
% 132.79/22.99 ((
% 132.79/22.99 (foundation2) =>
% 132.79/22.99 ((
% 132.79/22.99 (notinself) =>
% 132.79/22.99 ((
% 132.79/22.99 (notinself2) =>
% 132.79/22.99 ((
% 132.79/22.99 (omegaSp) =>
% 132.79/22.99 ((
% 132.79/22.99 (omegaSclos) =>
% 132.79/22.99 ((
% 132.79/22.99 (peano0notS) =>
% 132.79/22.99 ((
% 132.79/22.99 (peanoSinj) =>
% 132.79/22.99 ((
% 132.79/22.99 (transitivesetOp1) =>
% 132.79/22.99 ((
% 132.79/22.99 (binintTransitive) =>
% 132.79/22.99 ((
% 132.79/22.99 (transitivesetOp2) =>
% 132.79/22.99 ((
% 132.79/22.99 (setunionTransitive) =>
% 132.79/22.99 ((
% 132.79/22.99 (ordinalMinLem1) =>
% 132.79/22.99 ((
% 132.79/22.99 (ordinalTransSet) =>
% 132.79/22.99 ((
% 132.79/23.00 (ordinalTransSet1) =>
% 132.79/23.00 ((
% 132.79/23.00 (setunionOrdinalLem1) =>
% 132.79/23.00 (ordinal @
% 132.79/23.00 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/23.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1841])).
% 132.79/23.00 thf(zip_derived_cl1874, plain,
% 132.79/23.00 (~ (((beta1) =>
% 132.79/23.00 (((eta1) =>
% 132.79/23.00 (((lam2lamEq) =>
% 132.79/23.00 (((beta2) =>
% 132.79/23.00 (((eta2) =>
% 132.79/23.00 (((iffalseProp1) =>
% 132.79/23.00 (((iffalseProp2) =>
% 132.79/23.00 (((iftrueProp1) =>
% 132.79/23.00 (((iftrueProp2) =>
% 132.79/23.00 (((ifSingleton) =>
% 132.79/23.00 (((ifp) =>
% 132.79/23.00 (((theeq) =>
% 132.79/23.00 (((iftrue) =>
% 132.79/23.00 (((iffalse) =>
% 132.79/23.00 (((iftrueorfalse) =>
% 132.79/23.00 (((binintersectT_lem) =>
% 132.79/23.00 (((binunionT_lem) =>
% 132.79/23.00 (((powersetT_lem) =>
% 132.79/23.00 (((setminusT_lem) =>
% 132.79/23.00 (((complementT_lem) =>
% 132.79/23.00 (((setextT) =>
% 132.79/23.00 (((subsetTI) =>
% 132.79/23.00 (((powersetTI1) =>
% 132.79/23.00 (((powersetTE1) =>
% 132.79/23.00 (((complementTI1) =>
% 132.79/23.00 (((complementTE1) =>
% 132.79/23.00 (((binintersectTELcontra) =>
% 132.79/23.00 (((binintersectTERcontra) =>
% 132.79/23.00 (((contrasubsetT) =>
% 132.79/23.00 (((contrasubsetT1) =>
% 132.79/23.00 ((
% 132.79/23.00 (contrasubsetT2) =>
% 132.79/23.00 ((
% 132.79/23.00 (contrasubsetT3) =>
% 132.79/23.00 ((
% 132.79/23.00 (doubleComplementI1) =>
% 132.79/23.00 ((
% 132.79/23.00 (doubleComplementE1) =>
% 132.79/23.00 ((
% 132.79/23.00 (doubleComplementSub1) =>
% 132.79/23.00 ((
% 132.79/23.00 (doubleComplementSub2) =>
% 132.79/23.00 ((
% 132.79/23.00 (doubleComplementEq) =>
% 132.79/23.00 ((
% 132.79/23.00 (complementTnotintersectT) =>
% 132.79/23.00 ((
% 132.79/23.00 (complementImpComplementIntersect) =>
% 132.79/23.00 ((
% 132.79/23.00 (complementSubsetComplementIntersect) =>
% 132.79/23.00 ((
% 132.79/23.00 (complementInPowersetComplementIntersect) =>
% 132.79/23.00 ((
% 132.79/23.00 (contraSubsetComplement) =>
% 132.79/23.00 ((
% 132.79/23.00 (complementTcontraSubset) =>
% 132.79/23.00 ((
% 132.79/23.00 (binunionTILcontra) =>
% 132.79/23.00 ((
% 132.79/23.00 (binunionTIRcontra) =>
% 132.79/23.00 ((
% 132.79/23.00 (inIntersectImpInUnion) =>
% 132.79/23.00 ((
% 132.79/23.00 (inIntersectImpInUnion2) =>
% 132.79/23.00 ((
% 132.79/23.00 (inIntersectImpInIntersectUnions) =>
% 132.79/23.00 ((
% 132.79/23.00 (intersectInPowersetIntersectUnions) =>
% 132.79/23.00 ((
% 132.79/23.00 (inComplementUnionImpNotIn1) =>
% 132.79/23.00 ((
% 132.79/23.00 (inComplementUnionImpInComplement1) =>
% 132.79/23.00 ((
% 132.79/23.00 (binunionTE) =>
% 132.79/23.00 ((
% 132.79/23.00 (binunionTEcontra) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2a1) =>
% 132.79/23.00 ((
% 132.79/23.00 (complementUnionInPowersetComplement) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2a2) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan1a) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan1b) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan1) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2a) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2b2) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2b) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule0) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule1) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule2) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule3) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule4) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_1) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_2) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_3) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_4) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_5) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1all2) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1SetBreln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (choice2fnsingleton) =>
% 132.79/23.00 ((
% 132.79/23.00 (setOfPairsIsBReln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1all1) =>
% 132.79/23.00 ((
% 132.79/23.00 (subbreln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (eqbreln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1invprop) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1invI) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1invE) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compprop) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compI) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compE) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compEex) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionprop) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionIL) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionIR) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionI) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionE) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionEcases) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionCommutes) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2Ex) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2W) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2A) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2B) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1Ex) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1Ex1) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1Equiv) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1E) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1I) =>
% 132.79/23.00 ((
% 132.79/23.00 (injFuncInInjFuncSet) =>
% 132.79/23.00 ((
% 132.79/23.00 (injFuncSetFuncIn) =>
% 132.79/23.00 ((
% 132.79/23.00 (injFuncSetFuncInj) =>
% 132.79/23.00 ((
% 132.79/23.00 (surjFuncSetFuncIn) =>
% 132.79/23.00 ((
% 132.79/23.00 (surjFuncSetFuncSurj) =>
% 132.79/23.00 ((
% 132.79/23.00 (leftInvIsSurj) =>
% 132.79/23.00 ((
% 132.79/23.00 (surjCantorThm) =>
% 132.79/23.00 ((
% 132.79/23.00 (foundation2) =>
% 132.79/23.00 ((
% 132.79/23.00 (notinself) =>
% 132.79/23.00 ((
% 132.79/23.00 (notinself2) =>
% 132.79/23.00 ((
% 132.79/23.00 (omegaSp) =>
% 132.79/23.00 ((
% 132.79/23.00 (omegaSclos) =>
% 132.79/23.00 ((
% 132.79/23.00 (peano0notS) =>
% 132.79/23.00 ((
% 132.79/23.00 (peanoSinj) =>
% 132.79/23.00 ((
% 132.79/23.00 (transitivesetOp1) =>
% 132.79/23.00 ((
% 132.79/23.00 (binintTransitive) =>
% 132.79/23.00 ((
% 132.79/23.00 (transitivesetOp2) =>
% 132.79/23.00 ((
% 132.79/23.00 (setunionTransitive) =>
% 132.79/23.00 ((
% 132.79/23.00 (ordinalMinLem1) =>
% 132.79/23.00 ((
% 132.79/23.00 (ordinalTransSet) =>
% 132.79/23.00 ((
% 132.79/23.00 (ordinalTransSet1) =>
% 132.79/23.00 ((
% 132.79/23.00 (setunionOrdinalLem1) =>
% 132.79/23.00 (ordinal @
% 132.79/23.00 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/23.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1857])).
% 132.79/23.00 thf(zip_derived_cl1890, plain,
% 132.79/23.00 (~ (((eta1) =>
% 132.79/23.00 (((lam2lamEq) =>
% 132.79/23.00 (((beta2) =>
% 132.79/23.00 (((eta2) =>
% 132.79/23.00 (((iffalseProp1) =>
% 132.79/23.00 (((iffalseProp2) =>
% 132.79/23.00 (((iftrueProp1) =>
% 132.79/23.00 (((iftrueProp2) =>
% 132.79/23.00 (((ifSingleton) =>
% 132.79/23.00 (((ifp) =>
% 132.79/23.00 (((theeq) =>
% 132.79/23.00 (((iftrue) =>
% 132.79/23.00 (((iffalse) =>
% 132.79/23.00 (((iftrueorfalse) =>
% 132.79/23.00 (((binintersectT_lem) =>
% 132.79/23.00 (((binunionT_lem) =>
% 132.79/23.00 (((powersetT_lem) =>
% 132.79/23.00 (((setminusT_lem) =>
% 132.79/23.00 (((complementT_lem) =>
% 132.79/23.00 (((setextT) =>
% 132.79/23.00 (((subsetTI) =>
% 132.79/23.00 (((powersetTI1) =>
% 132.79/23.00 (((powersetTE1) =>
% 132.79/23.00 (((complementTI1) =>
% 132.79/23.00 (((complementTE1) =>
% 132.79/23.00 (((binintersectTELcontra) =>
% 132.79/23.00 (((binintersectTERcontra) =>
% 132.79/23.00 (((contrasubsetT) =>
% 132.79/23.00 (((contrasubsetT1) =>
% 132.79/23.00 (((contrasubsetT2) =>
% 132.79/23.00 ((
% 132.79/23.00 (contrasubsetT3) =>
% 132.79/23.00 ((
% 132.79/23.00 (doubleComplementI1) =>
% 132.79/23.00 ((
% 132.79/23.00 (doubleComplementE1) =>
% 132.79/23.00 ((
% 132.79/23.00 (doubleComplementSub1) =>
% 132.79/23.00 ((
% 132.79/23.00 (doubleComplementSub2) =>
% 132.79/23.00 ((
% 132.79/23.00 (doubleComplementEq) =>
% 132.79/23.00 ((
% 132.79/23.00 (complementTnotintersectT) =>
% 132.79/23.00 ((
% 132.79/23.00 (complementImpComplementIntersect) =>
% 132.79/23.00 ((
% 132.79/23.00 (complementSubsetComplementIntersect) =>
% 132.79/23.00 ((
% 132.79/23.00 (complementInPowersetComplementIntersect) =>
% 132.79/23.00 ((
% 132.79/23.00 (contraSubsetComplement) =>
% 132.79/23.00 ((
% 132.79/23.00 (complementTcontraSubset) =>
% 132.79/23.00 ((
% 132.79/23.00 (binunionTILcontra) =>
% 132.79/23.00 ((
% 132.79/23.00 (binunionTIRcontra) =>
% 132.79/23.00 ((
% 132.79/23.00 (inIntersectImpInUnion) =>
% 132.79/23.00 ((
% 132.79/23.00 (inIntersectImpInUnion2) =>
% 132.79/23.00 ((
% 132.79/23.00 (inIntersectImpInIntersectUnions) =>
% 132.79/23.00 ((
% 132.79/23.00 (intersectInPowersetIntersectUnions) =>
% 132.79/23.00 ((
% 132.79/23.00 (inComplementUnionImpNotIn1) =>
% 132.79/23.00 ((
% 132.79/23.00 (inComplementUnionImpInComplement1) =>
% 132.79/23.00 ((
% 132.79/23.00 (binunionTE) =>
% 132.79/23.00 ((
% 132.79/23.00 (binunionTEcontra) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2a1) =>
% 132.79/23.00 ((
% 132.79/23.00 (complementUnionInPowersetComplement) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2a2) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan1a) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan1b) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan1) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2a) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2b2) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2b) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule0) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule1) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule2) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule3) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule4) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_1) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_2) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_3) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_4) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_5) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1all2) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1SetBreln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (choice2fnsingleton) =>
% 132.79/23.00 ((
% 132.79/23.00 (setOfPairsIsBReln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1all1) =>
% 132.79/23.00 ((
% 132.79/23.00 (subbreln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (eqbreln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1invprop) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1invI) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1invE) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compprop) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compI) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compE) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compEex) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionprop) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionIL) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionIR) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionI) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionE) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionEcases) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionCommutes) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2Ex) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2W) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2A) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2B) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1Ex) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1Ex1) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1Equiv) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1E) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1I) =>
% 132.79/23.00 ((
% 132.79/23.00 (injFuncInInjFuncSet) =>
% 132.79/23.00 ((
% 132.79/23.00 (injFuncSetFuncIn) =>
% 132.79/23.00 ((
% 132.79/23.00 (injFuncSetFuncInj) =>
% 132.79/23.00 ((
% 132.79/23.00 (surjFuncSetFuncIn) =>
% 132.79/23.00 ((
% 132.79/23.00 (surjFuncSetFuncSurj) =>
% 132.79/23.00 ((
% 132.79/23.00 (leftInvIsSurj) =>
% 132.79/23.00 ((
% 132.79/23.00 (surjCantorThm) =>
% 132.79/23.00 ((
% 132.79/23.00 (foundation2) =>
% 132.79/23.00 ((
% 132.79/23.00 (notinself) =>
% 132.79/23.00 ((
% 132.79/23.00 (notinself2) =>
% 132.79/23.00 ((
% 132.79/23.00 (omegaSp) =>
% 132.79/23.00 ((
% 132.79/23.00 (omegaSclos) =>
% 132.79/23.00 ((
% 132.79/23.00 (peano0notS) =>
% 132.79/23.00 ((
% 132.79/23.00 (peanoSinj) =>
% 132.79/23.00 ((
% 132.79/23.00 (transitivesetOp1) =>
% 132.79/23.00 ((
% 132.79/23.00 (binintTransitive) =>
% 132.79/23.00 ((
% 132.79/23.00 (transitivesetOp2) =>
% 132.79/23.00 ((
% 132.79/23.00 (setunionTransitive) =>
% 132.79/23.00 ((
% 132.79/23.00 (ordinalMinLem1) =>
% 132.79/23.00 ((
% 132.79/23.00 (ordinalTransSet) =>
% 132.79/23.00 ((
% 132.79/23.00 (ordinalTransSet1) =>
% 132.79/23.00 ((
% 132.79/23.00 (setunionOrdinalLem1) =>
% 132.79/23.00 (ordinal @
% 132.79/23.00 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/23.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1874])).
% 132.79/23.00 thf(zip_derived_cl1903, plain,
% 132.79/23.00 (~ (((lam2lamEq) =>
% 132.79/23.00 (((beta2) =>
% 132.79/23.00 (((eta2) =>
% 132.79/23.00 (((iffalseProp1) =>
% 132.79/23.00 (((iffalseProp2) =>
% 132.79/23.00 (((iftrueProp1) =>
% 132.79/23.00 (((iftrueProp2) =>
% 132.79/23.00 (((ifSingleton) =>
% 132.79/23.00 (((ifp) =>
% 132.79/23.00 (((theeq) =>
% 132.79/23.00 (((iftrue) =>
% 132.79/23.00 (((iffalse) =>
% 132.79/23.00 (((iftrueorfalse) =>
% 132.79/23.00 (((binintersectT_lem) =>
% 132.79/23.00 (((binunionT_lem) =>
% 132.79/23.00 (((powersetT_lem) =>
% 132.79/23.00 (((setminusT_lem) =>
% 132.79/23.00 (((complementT_lem) =>
% 132.79/23.00 (((setextT) =>
% 132.79/23.00 (((subsetTI) =>
% 132.79/23.00 (((powersetTI1) =>
% 132.79/23.00 (((powersetTE1) =>
% 132.79/23.00 (((complementTI1) =>
% 132.79/23.00 (((complementTE1) =>
% 132.79/23.00 (((binintersectTELcontra) =>
% 132.79/23.00 (((binintersectTERcontra) =>
% 132.79/23.00 (((contrasubsetT) =>
% 132.79/23.00 (((contrasubsetT1) =>
% 132.79/23.00 (((contrasubsetT2) =>
% 132.79/23.00 (((contrasubsetT3) =>
% 132.79/23.00 ((
% 132.79/23.00 (doubleComplementI1) =>
% 132.79/23.00 ((
% 132.79/23.00 (doubleComplementE1) =>
% 132.79/23.00 ((
% 132.79/23.00 (doubleComplementSub1) =>
% 132.79/23.00 ((
% 132.79/23.00 (doubleComplementSub2) =>
% 132.79/23.00 ((
% 132.79/23.00 (doubleComplementEq) =>
% 132.79/23.00 ((
% 132.79/23.00 (complementTnotintersectT) =>
% 132.79/23.00 ((
% 132.79/23.00 (complementImpComplementIntersect) =>
% 132.79/23.00 ((
% 132.79/23.00 (complementSubsetComplementIntersect) =>
% 132.79/23.00 ((
% 132.79/23.00 (complementInPowersetComplementIntersect) =>
% 132.79/23.00 ((
% 132.79/23.00 (contraSubsetComplement) =>
% 132.79/23.00 ((
% 132.79/23.00 (complementTcontraSubset) =>
% 132.79/23.00 ((
% 132.79/23.00 (binunionTILcontra) =>
% 132.79/23.00 ((
% 132.79/23.00 (binunionTIRcontra) =>
% 132.79/23.00 ((
% 132.79/23.00 (inIntersectImpInUnion) =>
% 132.79/23.00 ((
% 132.79/23.00 (inIntersectImpInUnion2) =>
% 132.79/23.00 ((
% 132.79/23.00 (inIntersectImpInIntersectUnions) =>
% 132.79/23.00 ((
% 132.79/23.00 (intersectInPowersetIntersectUnions) =>
% 132.79/23.00 ((
% 132.79/23.00 (inComplementUnionImpNotIn1) =>
% 132.79/23.00 ((
% 132.79/23.00 (inComplementUnionImpInComplement1) =>
% 132.79/23.00 ((
% 132.79/23.00 (binunionTE) =>
% 132.79/23.00 ((
% 132.79/23.00 (binunionTEcontra) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2a1) =>
% 132.79/23.00 ((
% 132.79/23.00 (complementUnionInPowersetComplement) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2a2) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan1a) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan1b) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan1) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2a) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2b2) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2b) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule0) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule1) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule2) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule3) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule4) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_1) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_2) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_3) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_4) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_5) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1all2) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1SetBreln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (choice2fnsingleton) =>
% 132.79/23.00 ((
% 132.79/23.00 (setOfPairsIsBReln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1all1) =>
% 132.79/23.00 ((
% 132.79/23.00 (subbreln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (eqbreln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1invprop) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1invI) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1invE) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compprop) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compI) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compE) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compEex) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionprop) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionIL) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionIR) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionI) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionE) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionEcases) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionCommutes) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2Ex) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2W) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2A) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2B) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1Ex) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1Ex1) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1Equiv) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1E) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1I) =>
% 132.79/23.00 ((
% 132.79/23.00 (injFuncInInjFuncSet) =>
% 132.79/23.00 ((
% 132.79/23.00 (injFuncSetFuncIn) =>
% 132.79/23.00 ((
% 132.79/23.00 (injFuncSetFuncInj) =>
% 132.79/23.00 ((
% 132.79/23.00 (surjFuncSetFuncIn) =>
% 132.79/23.00 ((
% 132.79/23.00 (surjFuncSetFuncSurj) =>
% 132.79/23.00 ((
% 132.79/23.00 (leftInvIsSurj) =>
% 132.79/23.00 ((
% 132.79/23.00 (surjCantorThm) =>
% 132.79/23.00 ((
% 132.79/23.00 (foundation2) =>
% 132.79/23.00 ((
% 132.79/23.00 (notinself) =>
% 132.79/23.00 ((
% 132.79/23.00 (notinself2) =>
% 132.79/23.00 ((
% 132.79/23.00 (omegaSp) =>
% 132.79/23.00 ((
% 132.79/23.00 (omegaSclos) =>
% 132.79/23.00 ((
% 132.79/23.00 (peano0notS) =>
% 132.79/23.00 ((
% 132.79/23.00 (peanoSinj) =>
% 132.79/23.00 ((
% 132.79/23.00 (transitivesetOp1) =>
% 132.79/23.00 ((
% 132.79/23.00 (binintTransitive) =>
% 132.79/23.00 ((
% 132.79/23.00 (transitivesetOp2) =>
% 132.79/23.00 ((
% 132.79/23.00 (setunionTransitive) =>
% 132.79/23.00 ((
% 132.79/23.00 (ordinalMinLem1) =>
% 132.79/23.00 ((
% 132.79/23.00 (ordinalTransSet) =>
% 132.79/23.00 ((
% 132.79/23.00 (ordinalTransSet1) =>
% 132.79/23.00 ((
% 132.79/23.00 (setunionOrdinalLem1) =>
% 132.79/23.00 (ordinal @
% 132.79/23.00 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/23.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1890])).
% 132.79/23.00 thf(zip_derived_cl1916, plain,
% 132.79/23.00 (~ (((beta2) =>
% 132.79/23.00 (((eta2) =>
% 132.79/23.00 (((iffalseProp1) =>
% 132.79/23.00 (((iffalseProp2) =>
% 132.79/23.00 (((iftrueProp1) =>
% 132.79/23.00 (((iftrueProp2) =>
% 132.79/23.00 (((ifSingleton) =>
% 132.79/23.00 (((ifp) =>
% 132.79/23.00 (((theeq) =>
% 132.79/23.00 (((iftrue) =>
% 132.79/23.00 (((iffalse) =>
% 132.79/23.00 (((iftrueorfalse) =>
% 132.79/23.00 (((binintersectT_lem) =>
% 132.79/23.00 (((binunionT_lem) =>
% 132.79/23.00 (((powersetT_lem) =>
% 132.79/23.00 (((setminusT_lem) =>
% 132.79/23.00 (((complementT_lem) =>
% 132.79/23.00 (((setextT) =>
% 132.79/23.00 (((subsetTI) =>
% 132.79/23.00 (((powersetTI1) =>
% 132.79/23.00 (((powersetTE1) =>
% 132.79/23.00 (((complementTI1) =>
% 132.79/23.00 (((complementTE1) =>
% 132.79/23.00 (((binintersectTELcontra) =>
% 132.79/23.00 (((binintersectTERcontra) =>
% 132.79/23.00 (((contrasubsetT) =>
% 132.79/23.00 (((contrasubsetT1) =>
% 132.79/23.00 (((contrasubsetT2) =>
% 132.79/23.00 (((contrasubsetT3) =>
% 132.79/23.00 (((doubleComplementI1) =>
% 132.79/23.00 ((
% 132.79/23.00 (doubleComplementE1) =>
% 132.79/23.00 ((
% 132.79/23.00 (doubleComplementSub1) =>
% 132.79/23.00 ((
% 132.79/23.00 (doubleComplementSub2) =>
% 132.79/23.00 ((
% 132.79/23.00 (doubleComplementEq) =>
% 132.79/23.00 ((
% 132.79/23.00 (complementTnotintersectT) =>
% 132.79/23.00 ((
% 132.79/23.00 (complementImpComplementIntersect) =>
% 132.79/23.00 ((
% 132.79/23.00 (complementSubsetComplementIntersect) =>
% 132.79/23.00 ((
% 132.79/23.00 (complementInPowersetComplementIntersect) =>
% 132.79/23.00 ((
% 132.79/23.00 (contraSubsetComplement) =>
% 132.79/23.00 ((
% 132.79/23.00 (complementTcontraSubset) =>
% 132.79/23.00 ((
% 132.79/23.00 (binunionTILcontra) =>
% 132.79/23.00 ((
% 132.79/23.00 (binunionTIRcontra) =>
% 132.79/23.00 ((
% 132.79/23.00 (inIntersectImpInUnion) =>
% 132.79/23.00 ((
% 132.79/23.00 (inIntersectImpInUnion2) =>
% 132.79/23.00 ((
% 132.79/23.00 (inIntersectImpInIntersectUnions) =>
% 132.79/23.00 ((
% 132.79/23.00 (intersectInPowersetIntersectUnions) =>
% 132.79/23.00 ((
% 132.79/23.00 (inComplementUnionImpNotIn1) =>
% 132.79/23.00 ((
% 132.79/23.00 (inComplementUnionImpInComplement1) =>
% 132.79/23.00 ((
% 132.79/23.00 (binunionTE) =>
% 132.79/23.00 ((
% 132.79/23.00 (binunionTEcontra) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2a1) =>
% 132.79/23.00 ((
% 132.79/23.00 (complementUnionInPowersetComplement) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2a2) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan1a) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan1b) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan1) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2a) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2b2) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2b) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule0) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule1) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule2) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule3) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule4) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_1) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_2) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_3) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_4) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_5) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1all2) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1SetBreln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (choice2fnsingleton) =>
% 132.79/23.00 ((
% 132.79/23.00 (setOfPairsIsBReln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1all1) =>
% 132.79/23.00 ((
% 132.79/23.00 (subbreln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (eqbreln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1invprop) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1invI) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1invE) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compprop) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compI) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compE) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compEex) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionprop) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionIL) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionIR) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionI) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionE) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionEcases) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionCommutes) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2Ex) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2W) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2A) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2B) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1Ex) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1Ex1) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1Equiv) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1E) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1I) =>
% 132.79/23.00 ((
% 132.79/23.00 (injFuncInInjFuncSet) =>
% 132.79/23.00 ((
% 132.79/23.00 (injFuncSetFuncIn) =>
% 132.79/23.00 ((
% 132.79/23.00 (injFuncSetFuncInj) =>
% 132.79/23.00 ((
% 132.79/23.00 (surjFuncSetFuncIn) =>
% 132.79/23.00 ((
% 132.79/23.00 (surjFuncSetFuncSurj) =>
% 132.79/23.00 ((
% 132.79/23.00 (leftInvIsSurj) =>
% 132.79/23.00 ((
% 132.79/23.00 (surjCantorThm) =>
% 132.79/23.00 ((
% 132.79/23.00 (foundation2) =>
% 132.79/23.00 ((
% 132.79/23.00 (notinself) =>
% 132.79/23.00 ((
% 132.79/23.00 (notinself2) =>
% 132.79/23.00 ((
% 132.79/23.00 (omegaSp) =>
% 132.79/23.00 ((
% 132.79/23.00 (omegaSclos) =>
% 132.79/23.00 ((
% 132.79/23.00 (peano0notS) =>
% 132.79/23.00 ((
% 132.79/23.00 (peanoSinj) =>
% 132.79/23.00 ((
% 132.79/23.00 (transitivesetOp1) =>
% 132.79/23.00 ((
% 132.79/23.00 (binintTransitive) =>
% 132.79/23.00 ((
% 132.79/23.00 (transitivesetOp2) =>
% 132.79/23.00 ((
% 132.79/23.00 (setunionTransitive) =>
% 132.79/23.00 ((
% 132.79/23.00 (ordinalMinLem1) =>
% 132.79/23.00 ((
% 132.79/23.00 (ordinalTransSet) =>
% 132.79/23.00 ((
% 132.79/23.00 (ordinalTransSet1) =>
% 132.79/23.00 ((
% 132.79/23.00 (setunionOrdinalLem1) =>
% 132.79/23.00 (ordinal @
% 132.79/23.00 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/23.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1903])).
% 132.79/23.00 thf(zip_derived_cl1930, plain,
% 132.79/23.00 (~ (((eta2) =>
% 132.79/23.00 (((iffalseProp1) =>
% 132.79/23.00 (((iffalseProp2) =>
% 132.79/23.00 (((iftrueProp1) =>
% 132.79/23.00 (((iftrueProp2) =>
% 132.79/23.00 (((ifSingleton) =>
% 132.79/23.00 (((ifp) =>
% 132.79/23.00 (((theeq) =>
% 132.79/23.00 (((iftrue) =>
% 132.79/23.00 (((iffalse) =>
% 132.79/23.00 (((iftrueorfalse) =>
% 132.79/23.00 (((binintersectT_lem) =>
% 132.79/23.00 (((binunionT_lem) =>
% 132.79/23.00 (((powersetT_lem) =>
% 132.79/23.00 (((setminusT_lem) =>
% 132.79/23.00 (((complementT_lem) =>
% 132.79/23.00 (((setextT) =>
% 132.79/23.00 (((subsetTI) =>
% 132.79/23.00 (((powersetTI1) =>
% 132.79/23.00 (((powersetTE1) =>
% 132.79/23.00 (((complementTI1) =>
% 132.79/23.00 (((complementTE1) =>
% 132.79/23.00 (((binintersectTELcontra) =>
% 132.79/23.00 (((binintersectTERcontra) =>
% 132.79/23.00 (((contrasubsetT) =>
% 132.79/23.00 (((contrasubsetT1) =>
% 132.79/23.00 (((contrasubsetT2) =>
% 132.79/23.00 (((contrasubsetT3) =>
% 132.79/23.00 (((doubleComplementI1) =>
% 132.79/23.00 (((doubleComplementE1) =>
% 132.79/23.00 ((
% 132.79/23.00 (doubleComplementSub1) =>
% 132.79/23.00 ((
% 132.79/23.00 (doubleComplementSub2) =>
% 132.79/23.00 ((
% 132.79/23.00 (doubleComplementEq) =>
% 132.79/23.00 ((
% 132.79/23.00 (complementTnotintersectT) =>
% 132.79/23.00 ((
% 132.79/23.00 (complementImpComplementIntersect) =>
% 132.79/23.00 ((
% 132.79/23.00 (complementSubsetComplementIntersect) =>
% 132.79/23.00 ((
% 132.79/23.00 (complementInPowersetComplementIntersect) =>
% 132.79/23.00 ((
% 132.79/23.00 (contraSubsetComplement) =>
% 132.79/23.00 ((
% 132.79/23.00 (complementTcontraSubset) =>
% 132.79/23.00 ((
% 132.79/23.00 (binunionTILcontra) =>
% 132.79/23.00 ((
% 132.79/23.00 (binunionTIRcontra) =>
% 132.79/23.00 ((
% 132.79/23.00 (inIntersectImpInUnion) =>
% 132.79/23.00 ((
% 132.79/23.00 (inIntersectImpInUnion2) =>
% 132.79/23.00 ((
% 132.79/23.00 (inIntersectImpInIntersectUnions) =>
% 132.79/23.00 ((
% 132.79/23.00 (intersectInPowersetIntersectUnions) =>
% 132.79/23.00 ((
% 132.79/23.00 (inComplementUnionImpNotIn1) =>
% 132.79/23.00 ((
% 132.79/23.00 (inComplementUnionImpInComplement1) =>
% 132.79/23.00 ((
% 132.79/23.00 (binunionTE) =>
% 132.79/23.00 ((
% 132.79/23.00 (binunionTEcontra) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2a1) =>
% 132.79/23.00 ((
% 132.79/23.00 (complementUnionInPowersetComplement) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2a2) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan1a) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan1b) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan1) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2a) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2b2) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2b) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule0) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule1) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule2) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule3) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule4) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_1) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_2) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_3) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_4) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_5) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1all2) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1SetBreln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (choice2fnsingleton) =>
% 132.79/23.00 ((
% 132.79/23.00 (setOfPairsIsBReln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1all1) =>
% 132.79/23.00 ((
% 132.79/23.00 (subbreln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (eqbreln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1invprop) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1invI) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1invE) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compprop) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compI) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compE) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compEex) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionprop) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionIL) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionIR) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionI) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionE) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionEcases) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionCommutes) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2Ex) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2W) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2A) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2B) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1Ex) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1Ex1) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1Equiv) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1E) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1I) =>
% 132.79/23.00 ((
% 132.79/23.00 (injFuncInInjFuncSet) =>
% 132.79/23.00 ((
% 132.79/23.00 (injFuncSetFuncIn) =>
% 132.79/23.00 ((
% 132.79/23.00 (injFuncSetFuncInj) =>
% 132.79/23.00 ((
% 132.79/23.00 (surjFuncSetFuncIn) =>
% 132.79/23.00 ((
% 132.79/23.00 (surjFuncSetFuncSurj) =>
% 132.79/23.00 ((
% 132.79/23.00 (leftInvIsSurj) =>
% 132.79/23.00 ((
% 132.79/23.00 (surjCantorThm) =>
% 132.79/23.00 ((
% 132.79/23.00 (foundation2) =>
% 132.79/23.00 ((
% 132.79/23.00 (notinself) =>
% 132.79/23.00 ((
% 132.79/23.00 (notinself2) =>
% 132.79/23.00 ((
% 132.79/23.00 (omegaSp) =>
% 132.79/23.00 ((
% 132.79/23.00 (omegaSclos) =>
% 132.79/23.00 ((
% 132.79/23.00 (peano0notS) =>
% 132.79/23.00 ((
% 132.79/23.00 (peanoSinj) =>
% 132.79/23.00 ((
% 132.79/23.00 (transitivesetOp1) =>
% 132.79/23.00 ((
% 132.79/23.00 (binintTransitive) =>
% 132.79/23.00 ((
% 132.79/23.00 (transitivesetOp2) =>
% 132.79/23.00 ((
% 132.79/23.00 (setunionTransitive) =>
% 132.79/23.00 ((
% 132.79/23.00 (ordinalMinLem1) =>
% 132.79/23.00 ((
% 132.79/23.00 (ordinalTransSet) =>
% 132.79/23.00 ((
% 132.79/23.00 (ordinalTransSet1) =>
% 132.79/23.00 ((
% 132.79/23.00 (setunionOrdinalLem1) =>
% 132.79/23.00 (ordinal @
% 132.79/23.00 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/23.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1916])).
% 132.79/23.00 thf(zip_derived_cl1945, plain,
% 132.79/23.00 (~ (((iffalseProp1) =>
% 132.79/23.00 (((iffalseProp2) =>
% 132.79/23.00 (((iftrueProp1) =>
% 132.79/23.00 (((iftrueProp2) =>
% 132.79/23.00 (((ifSingleton) =>
% 132.79/23.00 (((ifp) =>
% 132.79/23.00 (((theeq) =>
% 132.79/23.00 (((iftrue) =>
% 132.79/23.00 (((iffalse) =>
% 132.79/23.00 (((iftrueorfalse) =>
% 132.79/23.00 (((binintersectT_lem) =>
% 132.79/23.00 (((binunionT_lem) =>
% 132.79/23.00 (((powersetT_lem) =>
% 132.79/23.00 (((setminusT_lem) =>
% 132.79/23.00 (((complementT_lem) =>
% 132.79/23.00 (((setextT) =>
% 132.79/23.00 (((subsetTI) =>
% 132.79/23.00 (((powersetTI1) =>
% 132.79/23.00 (((powersetTE1) =>
% 132.79/23.00 (((complementTI1) =>
% 132.79/23.00 (((complementTE1) =>
% 132.79/23.00 (((binintersectTELcontra) =>
% 132.79/23.00 (((binintersectTERcontra) =>
% 132.79/23.00 (((contrasubsetT) =>
% 132.79/23.00 (((contrasubsetT1) =>
% 132.79/23.00 (((contrasubsetT2) =>
% 132.79/23.00 (((contrasubsetT3) =>
% 132.79/23.00 (((doubleComplementI1) =>
% 132.79/23.00 (((doubleComplementE1) =>
% 132.79/23.00 (((doubleComplementSub1) =>
% 132.79/23.00 ((
% 132.79/23.00 (doubleComplementSub2) =>
% 132.79/23.00 ((
% 132.79/23.00 (doubleComplementEq) =>
% 132.79/23.00 ((
% 132.79/23.00 (complementTnotintersectT) =>
% 132.79/23.00 ((
% 132.79/23.00 (complementImpComplementIntersect) =>
% 132.79/23.00 ((
% 132.79/23.00 (complementSubsetComplementIntersect) =>
% 132.79/23.00 ((
% 132.79/23.00 (complementInPowersetComplementIntersect) =>
% 132.79/23.00 ((
% 132.79/23.00 (contraSubsetComplement) =>
% 132.79/23.00 ((
% 132.79/23.00 (complementTcontraSubset) =>
% 132.79/23.00 ((
% 132.79/23.00 (binunionTILcontra) =>
% 132.79/23.00 ((
% 132.79/23.00 (binunionTIRcontra) =>
% 132.79/23.00 ((
% 132.79/23.00 (inIntersectImpInUnion) =>
% 132.79/23.00 ((
% 132.79/23.00 (inIntersectImpInUnion2) =>
% 132.79/23.00 ((
% 132.79/23.00 (inIntersectImpInIntersectUnions) =>
% 132.79/23.00 ((
% 132.79/23.00 (intersectInPowersetIntersectUnions) =>
% 132.79/23.00 ((
% 132.79/23.00 (inComplementUnionImpNotIn1) =>
% 132.79/23.00 ((
% 132.79/23.00 (inComplementUnionImpInComplement1) =>
% 132.79/23.00 ((
% 132.79/23.00 (binunionTE) =>
% 132.79/23.00 ((
% 132.79/23.00 (binunionTEcontra) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2a1) =>
% 132.79/23.00 ((
% 132.79/23.00 (complementUnionInPowersetComplement) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2a2) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan1a) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan1b) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan1) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2a) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2b2) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2b) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule0) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule1) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule2) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule3) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule4) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_1) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_2) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_3) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_4) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_5) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1all2) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1SetBreln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (choice2fnsingleton) =>
% 132.79/23.00 ((
% 132.79/23.00 (setOfPairsIsBReln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1all1) =>
% 132.79/23.00 ((
% 132.79/23.00 (subbreln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (eqbreln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1invprop) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1invI) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1invE) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compprop) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compI) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compE) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compEex) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionprop) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionIL) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionIR) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionI) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionE) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionEcases) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionCommutes) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2Ex) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2W) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2A) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2B) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1Ex) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1Ex1) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1Equiv) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1E) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1I) =>
% 132.79/23.00 ((
% 132.79/23.00 (injFuncInInjFuncSet) =>
% 132.79/23.00 ((
% 132.79/23.00 (injFuncSetFuncIn) =>
% 132.79/23.00 ((
% 132.79/23.00 (injFuncSetFuncInj) =>
% 132.79/23.00 ((
% 132.79/23.00 (surjFuncSetFuncIn) =>
% 132.79/23.00 ((
% 132.79/23.00 (surjFuncSetFuncSurj) =>
% 132.79/23.00 ((
% 132.79/23.00 (leftInvIsSurj) =>
% 132.79/23.00 ((
% 132.79/23.00 (surjCantorThm) =>
% 132.79/23.00 ((
% 132.79/23.00 (foundation2) =>
% 132.79/23.00 ((
% 132.79/23.00 (notinself) =>
% 132.79/23.00 ((
% 132.79/23.00 (notinself2) =>
% 132.79/23.00 ((
% 132.79/23.00 (omegaSp) =>
% 132.79/23.00 ((
% 132.79/23.00 (omegaSclos) =>
% 132.79/23.00 ((
% 132.79/23.00 (peano0notS) =>
% 132.79/23.00 ((
% 132.79/23.00 (peanoSinj) =>
% 132.79/23.00 ((
% 132.79/23.00 (transitivesetOp1) =>
% 132.79/23.00 ((
% 132.79/23.00 (binintTransitive) =>
% 132.79/23.00 ((
% 132.79/23.00 (transitivesetOp2) =>
% 132.79/23.00 ((
% 132.79/23.00 (setunionTransitive) =>
% 132.79/23.00 ((
% 132.79/23.00 (ordinalMinLem1) =>
% 132.79/23.00 ((
% 132.79/23.00 (ordinalTransSet) =>
% 132.79/23.00 ((
% 132.79/23.00 (ordinalTransSet1) =>
% 132.79/23.00 ((
% 132.79/23.00 (setunionOrdinalLem1) =>
% 132.79/23.00 (ordinal @
% 132.79/23.00 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/23.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1930])).
% 132.79/23.00 thf(zip_derived_cl1960, plain,
% 132.79/23.00 (~ (((iffalseProp2) =>
% 132.79/23.00 (((iftrueProp1) =>
% 132.79/23.00 (((iftrueProp2) =>
% 132.79/23.00 (((ifSingleton) =>
% 132.79/23.00 (((ifp) =>
% 132.79/23.00 (((theeq) =>
% 132.79/23.00 (((iftrue) =>
% 132.79/23.00 (((iffalse) =>
% 132.79/23.00 (((iftrueorfalse) =>
% 132.79/23.00 (((binintersectT_lem) =>
% 132.79/23.00 (((binunionT_lem) =>
% 132.79/23.00 (((powersetT_lem) =>
% 132.79/23.00 (((setminusT_lem) =>
% 132.79/23.00 (((complementT_lem) =>
% 132.79/23.00 (((setextT) =>
% 132.79/23.00 (((subsetTI) =>
% 132.79/23.00 (((powersetTI1) =>
% 132.79/23.00 (((powersetTE1) =>
% 132.79/23.00 (((complementTI1) =>
% 132.79/23.00 (((complementTE1) =>
% 132.79/23.00 (((binintersectTELcontra) =>
% 132.79/23.00 (((binintersectTERcontra) =>
% 132.79/23.00 (((contrasubsetT) =>
% 132.79/23.00 (((contrasubsetT1) =>
% 132.79/23.00 (((contrasubsetT2) =>
% 132.79/23.00 (((contrasubsetT3) =>
% 132.79/23.00 (((doubleComplementI1) =>
% 132.79/23.00 (((doubleComplementE1) =>
% 132.79/23.00 (((doubleComplementSub1) =>
% 132.79/23.00 (((doubleComplementSub2) =>
% 132.79/23.00 ((
% 132.79/23.00 (doubleComplementEq) =>
% 132.79/23.00 ((
% 132.79/23.00 (complementTnotintersectT) =>
% 132.79/23.00 ((
% 132.79/23.00 (complementImpComplementIntersect) =>
% 132.79/23.00 ((
% 132.79/23.00 (complementSubsetComplementIntersect) =>
% 132.79/23.00 ((
% 132.79/23.00 (complementInPowersetComplementIntersect) =>
% 132.79/23.00 ((
% 132.79/23.00 (contraSubsetComplement) =>
% 132.79/23.00 ((
% 132.79/23.00 (complementTcontraSubset) =>
% 132.79/23.00 ((
% 132.79/23.00 (binunionTILcontra) =>
% 132.79/23.00 ((
% 132.79/23.00 (binunionTIRcontra) =>
% 132.79/23.00 ((
% 132.79/23.00 (inIntersectImpInUnion) =>
% 132.79/23.00 ((
% 132.79/23.00 (inIntersectImpInUnion2) =>
% 132.79/23.00 ((
% 132.79/23.00 (inIntersectImpInIntersectUnions) =>
% 132.79/23.00 ((
% 132.79/23.00 (intersectInPowersetIntersectUnions) =>
% 132.79/23.00 ((
% 132.79/23.00 (inComplementUnionImpNotIn1) =>
% 132.79/23.00 ((
% 132.79/23.00 (inComplementUnionImpInComplement1) =>
% 132.79/23.00 ((
% 132.79/23.00 (binunionTE) =>
% 132.79/23.00 ((
% 132.79/23.00 (binunionTEcontra) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2a1) =>
% 132.79/23.00 ((
% 132.79/23.00 (complementUnionInPowersetComplement) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2a2) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan1a) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan1b) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan1) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2a) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2b2) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2b) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule0) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule1) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule2) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule3) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule4) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_1) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_2) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_3) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_4) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_5) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1all2) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1SetBreln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (choice2fnsingleton) =>
% 132.79/23.00 ((
% 132.79/23.00 (setOfPairsIsBReln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1all1) =>
% 132.79/23.00 ((
% 132.79/23.00 (subbreln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (eqbreln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1invprop) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1invI) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1invE) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compprop) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compI) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compE) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compEex) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionprop) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionIL) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionIR) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionI) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionE) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionEcases) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionCommutes) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2Ex) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2W) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2A) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2B) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1Ex) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1Ex1) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1Equiv) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1E) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1I) =>
% 132.79/23.00 ((
% 132.79/23.00 (injFuncInInjFuncSet) =>
% 132.79/23.00 ((
% 132.79/23.00 (injFuncSetFuncIn) =>
% 132.79/23.00 ((
% 132.79/23.00 (injFuncSetFuncInj) =>
% 132.79/23.00 ((
% 132.79/23.00 (surjFuncSetFuncIn) =>
% 132.79/23.00 ((
% 132.79/23.00 (surjFuncSetFuncSurj) =>
% 132.79/23.00 ((
% 132.79/23.00 (leftInvIsSurj) =>
% 132.79/23.00 ((
% 132.79/23.00 (surjCantorThm) =>
% 132.79/23.00 ((
% 132.79/23.00 (foundation2) =>
% 132.79/23.00 ((
% 132.79/23.00 (notinself) =>
% 132.79/23.00 ((
% 132.79/23.00 (notinself2) =>
% 132.79/23.00 ((
% 132.79/23.00 (omegaSp) =>
% 132.79/23.00 ((
% 132.79/23.00 (omegaSclos) =>
% 132.79/23.00 ((
% 132.79/23.00 (peano0notS) =>
% 132.79/23.00 ((
% 132.79/23.00 (peanoSinj) =>
% 132.79/23.00 ((
% 132.79/23.00 (transitivesetOp1) =>
% 132.79/23.00 ((
% 132.79/23.00 (binintTransitive) =>
% 132.79/23.00 ((
% 132.79/23.00 (transitivesetOp2) =>
% 132.79/23.00 ((
% 132.79/23.00 (setunionTransitive) =>
% 132.79/23.00 ((
% 132.79/23.00 (ordinalMinLem1) =>
% 132.79/23.00 ((
% 132.79/23.00 (ordinalTransSet) =>
% 132.79/23.00 ((
% 132.79/23.00 (ordinalTransSet1) =>
% 132.79/23.00 ((
% 132.79/23.00 (setunionOrdinalLem1) =>
% 132.79/23.00 (ordinal @
% 132.79/23.00 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/23.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1945])).
% 132.79/23.00 thf(zip_derived_cl1982, plain,
% 132.79/23.00 (~ (((iftrueProp1) =>
% 132.79/23.00 (((iftrueProp2) =>
% 132.79/23.00 (((ifSingleton) =>
% 132.79/23.00 (((ifp) =>
% 132.79/23.00 (((theeq) =>
% 132.79/23.00 (((iftrue) =>
% 132.79/23.00 (((iffalse) =>
% 132.79/23.00 (((iftrueorfalse) =>
% 132.79/23.00 (((binintersectT_lem) =>
% 132.79/23.00 (((binunionT_lem) =>
% 132.79/23.00 (((powersetT_lem) =>
% 132.79/23.00 (((setminusT_lem) =>
% 132.79/23.00 (((complementT_lem) =>
% 132.79/23.00 (((setextT) =>
% 132.79/23.00 (((subsetTI) =>
% 132.79/23.00 (((powersetTI1) =>
% 132.79/23.00 (((powersetTE1) =>
% 132.79/23.00 (((complementTI1) =>
% 132.79/23.00 (((complementTE1) =>
% 132.79/23.00 (((binintersectTELcontra) =>
% 132.79/23.00 (((binintersectTERcontra) =>
% 132.79/23.00 (((contrasubsetT) =>
% 132.79/23.00 (((contrasubsetT1) =>
% 132.79/23.00 (((contrasubsetT2) =>
% 132.79/23.00 (((contrasubsetT3) =>
% 132.79/23.00 (((doubleComplementI1) =>
% 132.79/23.00 (((doubleComplementE1) =>
% 132.79/23.00 (((doubleComplementSub1) =>
% 132.79/23.00 (((doubleComplementSub2) =>
% 132.79/23.00 (((doubleComplementEq) =>
% 132.79/23.00 ((
% 132.79/23.00 (complementTnotintersectT) =>
% 132.79/23.00 ((
% 132.79/23.00 (complementImpComplementIntersect) =>
% 132.79/23.00 ((
% 132.79/23.00 (complementSubsetComplementIntersect) =>
% 132.79/23.00 ((
% 132.79/23.00 (complementInPowersetComplementIntersect) =>
% 132.79/23.00 ((
% 132.79/23.00 (contraSubsetComplement) =>
% 132.79/23.00 ((
% 132.79/23.00 (complementTcontraSubset) =>
% 132.79/23.00 ((
% 132.79/23.00 (binunionTILcontra) =>
% 132.79/23.00 ((
% 132.79/23.00 (binunionTIRcontra) =>
% 132.79/23.00 ((
% 132.79/23.00 (inIntersectImpInUnion) =>
% 132.79/23.00 ((
% 132.79/23.00 (inIntersectImpInUnion2) =>
% 132.79/23.00 ((
% 132.79/23.00 (inIntersectImpInIntersectUnions) =>
% 132.79/23.00 ((
% 132.79/23.00 (intersectInPowersetIntersectUnions) =>
% 132.79/23.00 ((
% 132.79/23.00 (inComplementUnionImpNotIn1) =>
% 132.79/23.00 ((
% 132.79/23.00 (inComplementUnionImpInComplement1) =>
% 132.79/23.00 ((
% 132.79/23.00 (binunionTE) =>
% 132.79/23.00 ((
% 132.79/23.00 (binunionTEcontra) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2a1) =>
% 132.79/23.00 ((
% 132.79/23.00 (complementUnionInPowersetComplement) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2a2) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan1a) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan1b) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan1) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2a) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2b2) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2b) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule0) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule1) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule2) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule3) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule4) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_1) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_2) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_3) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_4) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_5) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1all2) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1SetBreln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (choice2fnsingleton) =>
% 132.79/23.00 ((
% 132.79/23.00 (setOfPairsIsBReln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1all1) =>
% 132.79/23.00 ((
% 132.79/23.00 (subbreln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (eqbreln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1invprop) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1invI) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1invE) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compprop) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compI) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compE) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compEex) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionprop) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionIL) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionIR) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionI) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionE) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionEcases) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionCommutes) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2Ex) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2W) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2A) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2B) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1Ex) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1Ex1) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1Equiv) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1E) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1I) =>
% 132.79/23.00 ((
% 132.79/23.00 (injFuncInInjFuncSet) =>
% 132.79/23.00 ((
% 132.79/23.00 (injFuncSetFuncIn) =>
% 132.79/23.00 ((
% 132.79/23.00 (injFuncSetFuncInj) =>
% 132.79/23.00 ((
% 132.79/23.00 (surjFuncSetFuncIn) =>
% 132.79/23.00 ((
% 132.79/23.00 (surjFuncSetFuncSurj) =>
% 132.79/23.00 ((
% 132.79/23.00 (leftInvIsSurj) =>
% 132.79/23.00 ((
% 132.79/23.00 (surjCantorThm) =>
% 132.79/23.00 ((
% 132.79/23.00 (foundation2) =>
% 132.79/23.00 ((
% 132.79/23.00 (notinself) =>
% 132.79/23.00 ((
% 132.79/23.00 (notinself2) =>
% 132.79/23.00 ((
% 132.79/23.00 (omegaSp) =>
% 132.79/23.00 ((
% 132.79/23.00 (omegaSclos) =>
% 132.79/23.00 ((
% 132.79/23.00 (peano0notS) =>
% 132.79/23.00 ((
% 132.79/23.00 (peanoSinj) =>
% 132.79/23.00 ((
% 132.79/23.00 (transitivesetOp1) =>
% 132.79/23.00 ((
% 132.79/23.00 (binintTransitive) =>
% 132.79/23.00 ((
% 132.79/23.00 (transitivesetOp2) =>
% 132.79/23.00 ((
% 132.79/23.00 (setunionTransitive) =>
% 132.79/23.00 ((
% 132.79/23.00 (ordinalMinLem1) =>
% 132.79/23.00 ((
% 132.79/23.00 (ordinalTransSet) =>
% 132.79/23.00 ((
% 132.79/23.00 (ordinalTransSet1) =>
% 132.79/23.00 ((
% 132.79/23.00 (setunionOrdinalLem1) =>
% 132.79/23.00 (ordinal @
% 132.79/23.00 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/23.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1960])).
% 132.79/23.00 thf(zip_derived_cl2001, plain,
% 132.79/23.00 (~ (((iftrueProp2) =>
% 132.79/23.00 (((ifSingleton) =>
% 132.79/23.00 (((ifp) =>
% 132.79/23.00 (((theeq) =>
% 132.79/23.00 (((iftrue) =>
% 132.79/23.00 (((iffalse) =>
% 132.79/23.00 (((iftrueorfalse) =>
% 132.79/23.00 (((binintersectT_lem) =>
% 132.79/23.00 (((binunionT_lem) =>
% 132.79/23.00 (((powersetT_lem) =>
% 132.79/23.00 (((setminusT_lem) =>
% 132.79/23.00 (((complementT_lem) =>
% 132.79/23.00 (((setextT) =>
% 132.79/23.00 (((subsetTI) =>
% 132.79/23.00 (((powersetTI1) =>
% 132.79/23.00 (((powersetTE1) =>
% 132.79/23.00 (((complementTI1) =>
% 132.79/23.00 (((complementTE1) =>
% 132.79/23.00 (((binintersectTELcontra) =>
% 132.79/23.00 (((binintersectTERcontra) =>
% 132.79/23.00 (((contrasubsetT) =>
% 132.79/23.00 (((contrasubsetT1) =>
% 132.79/23.00 (((contrasubsetT2) =>
% 132.79/23.00 (((contrasubsetT3) =>
% 132.79/23.00 (((doubleComplementI1) =>
% 132.79/23.00 (((doubleComplementE1) =>
% 132.79/23.00 (((doubleComplementSub1) =>
% 132.79/23.00 (((doubleComplementSub2) =>
% 132.79/23.00 (((doubleComplementEq) =>
% 132.79/23.00 (((complementTnotintersectT) =>
% 132.79/23.00 ((
% 132.79/23.00 (complementImpComplementIntersect) =>
% 132.79/23.00 ((
% 132.79/23.00 (complementSubsetComplementIntersect) =>
% 132.79/23.00 ((
% 132.79/23.00 (complementInPowersetComplementIntersect) =>
% 132.79/23.00 ((
% 132.79/23.00 (contraSubsetComplement) =>
% 132.79/23.00 ((
% 132.79/23.00 (complementTcontraSubset) =>
% 132.79/23.00 ((
% 132.79/23.00 (binunionTILcontra) =>
% 132.79/23.00 ((
% 132.79/23.00 (binunionTIRcontra) =>
% 132.79/23.00 ((
% 132.79/23.00 (inIntersectImpInUnion) =>
% 132.79/23.00 ((
% 132.79/23.00 (inIntersectImpInUnion2) =>
% 132.79/23.00 ((
% 132.79/23.00 (inIntersectImpInIntersectUnions) =>
% 132.79/23.00 ((
% 132.79/23.00 (intersectInPowersetIntersectUnions) =>
% 132.79/23.00 ((
% 132.79/23.00 (inComplementUnionImpNotIn1) =>
% 132.79/23.00 ((
% 132.79/23.00 (inComplementUnionImpInComplement1) =>
% 132.79/23.00 ((
% 132.79/23.00 (binunionTE) =>
% 132.79/23.00 ((
% 132.79/23.00 (binunionTEcontra) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2a1) =>
% 132.79/23.00 ((
% 132.79/23.00 (complementUnionInPowersetComplement) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2a2) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan1a) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan1b) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan1) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2a) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2b2) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2b) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule0) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule1) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule2) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule3) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule4) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_1) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_2) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_3) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_4) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_5) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1all2) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1SetBreln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (choice2fnsingleton) =>
% 132.79/23.00 ((
% 132.79/23.00 (setOfPairsIsBReln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1all1) =>
% 132.79/23.00 ((
% 132.79/23.00 (subbreln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (eqbreln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1invprop) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1invI) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1invE) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compprop) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compI) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compE) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compEex) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionprop) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionIL) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionIR) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionI) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionE) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionEcases) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionCommutes) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2Ex) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2W) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2A) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2B) =>
% 132.79/23.00 ((
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% 132.79/23.00 ((
% 132.79/23.00 (image1Ex1) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1Equiv) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1E) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1I) =>
% 132.79/23.00 ((
% 132.79/23.00 (injFuncInInjFuncSet) =>
% 132.79/23.00 ((
% 132.79/23.00 (injFuncSetFuncIn) =>
% 132.79/23.00 ((
% 132.79/23.00 (injFuncSetFuncInj) =>
% 132.79/23.00 ((
% 132.79/23.00 (surjFuncSetFuncIn) =>
% 132.79/23.00 ((
% 132.79/23.00 (surjFuncSetFuncSurj) =>
% 132.79/23.00 ((
% 132.79/23.00 (leftInvIsSurj) =>
% 132.79/23.00 ((
% 132.79/23.00 (surjCantorThm) =>
% 132.79/23.00 ((
% 132.79/23.00 (foundation2) =>
% 132.79/23.00 ((
% 132.79/23.00 (notinself) =>
% 132.79/23.00 ((
% 132.79/23.00 (notinself2) =>
% 132.79/23.00 ((
% 132.79/23.00 (omegaSp) =>
% 132.79/23.00 ((
% 132.79/23.00 (omegaSclos) =>
% 132.79/23.00 ((
% 132.79/23.00 (peano0notS) =>
% 132.79/23.00 ((
% 132.79/23.00 (peanoSinj) =>
% 132.79/23.00 ((
% 132.79/23.00 (transitivesetOp1) =>
% 132.79/23.00 ((
% 132.79/23.00 (binintTransitive) =>
% 132.79/23.00 ((
% 132.79/23.00 (transitivesetOp2) =>
% 132.79/23.00 ((
% 132.79/23.00 (setunionTransitive) =>
% 132.79/23.00 ((
% 132.79/23.00 (ordinalMinLem1) =>
% 132.79/23.00 ((
% 132.79/23.00 (ordinalTransSet) =>
% 132.79/23.00 ((
% 132.79/23.00 (ordinalTransSet1) =>
% 132.79/23.00 ((
% 132.79/23.00 (setunionOrdinalLem1) =>
% 132.79/23.00 (ordinal @
% 132.79/23.00 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/23.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1982])).
% 132.79/23.00 thf(zip_derived_cl2017, plain,
% 132.79/23.00 (~ (((ifSingleton) =>
% 132.79/23.00 (((ifp) =>
% 132.79/23.00 (((theeq) =>
% 132.79/23.00 (((iftrue) =>
% 132.79/23.00 (((iffalse) =>
% 132.79/23.00 (((iftrueorfalse) =>
% 132.79/23.00 (((binintersectT_lem) =>
% 132.79/23.00 (((binunionT_lem) =>
% 132.79/23.00 (((powersetT_lem) =>
% 132.79/23.00 (((setminusT_lem) =>
% 132.79/23.00 (((complementT_lem) =>
% 132.79/23.00 (((setextT) =>
% 132.79/23.00 (((subsetTI) =>
% 132.79/23.00 (((powersetTI1) =>
% 132.79/23.00 (((powersetTE1) =>
% 132.79/23.00 (((complementTI1) =>
% 132.79/23.00 (((complementTE1) =>
% 132.79/23.00 (((binintersectTELcontra) =>
% 132.79/23.00 (((binintersectTERcontra) =>
% 132.79/23.00 (((contrasubsetT) =>
% 132.79/23.00 (((contrasubsetT1) =>
% 132.79/23.00 (((contrasubsetT2) =>
% 132.79/23.00 (((contrasubsetT3) =>
% 132.79/23.00 (((doubleComplementI1) =>
% 132.79/23.00 (((doubleComplementE1) =>
% 132.79/23.00 (((doubleComplementSub1) =>
% 132.79/23.00 (((doubleComplementSub2) =>
% 132.79/23.00 (((doubleComplementEq) =>
% 132.79/23.00 (((complementTnotintersectT) =>
% 132.79/23.00 (((complementImpComplementIntersect) =>
% 132.79/23.00 ((
% 132.79/23.00 (complementSubsetComplementIntersect) =>
% 132.79/23.00 ((
% 132.79/23.00 (complementInPowersetComplementIntersect) =>
% 132.79/23.00 ((
% 132.79/23.00 (contraSubsetComplement) =>
% 132.79/23.00 ((
% 132.79/23.00 (complementTcontraSubset) =>
% 132.79/23.00 ((
% 132.79/23.00 (binunionTILcontra) =>
% 132.79/23.00 ((
% 132.79/23.00 (binunionTIRcontra) =>
% 132.79/23.00 ((
% 132.79/23.00 (inIntersectImpInUnion) =>
% 132.79/23.00 ((
% 132.79/23.00 (inIntersectImpInUnion2) =>
% 132.79/23.00 ((
% 132.79/23.00 (inIntersectImpInIntersectUnions) =>
% 132.79/23.00 ((
% 132.79/23.00 (intersectInPowersetIntersectUnions) =>
% 132.79/23.00 ((
% 132.79/23.00 (inComplementUnionImpNotIn1) =>
% 132.79/23.00 ((
% 132.79/23.00 (inComplementUnionImpInComplement1) =>
% 132.79/23.00 ((
% 132.79/23.00 (binunionTE) =>
% 132.79/23.00 ((
% 132.79/23.00 (binunionTEcontra) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2a1) =>
% 132.79/23.00 ((
% 132.79/23.00 (complementUnionInPowersetComplement) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2a2) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan1a) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan1b) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan1) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2a) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2b2) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2b) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule0) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule1) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule2) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule3) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule4) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_1) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_2) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_3) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_4) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_5) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1all2) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1SetBreln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (choice2fnsingleton) =>
% 132.79/23.00 ((
% 132.79/23.00 (setOfPairsIsBReln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1all1) =>
% 132.79/23.00 ((
% 132.79/23.00 (subbreln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (eqbreln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1invprop) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1invI) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1invE) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compprop) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compI) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compE) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compEex) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionprop) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionIL) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionIR) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionI) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionE) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionEcases) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionCommutes) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2Ex) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2W) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2A) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2B) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1Ex) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1Ex1) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1Equiv) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1E) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1I) =>
% 132.79/23.00 ((
% 132.79/23.00 (injFuncInInjFuncSet) =>
% 132.79/23.00 ((
% 132.79/23.00 (injFuncSetFuncIn) =>
% 132.79/23.00 ((
% 132.79/23.00 (injFuncSetFuncInj) =>
% 132.79/23.00 ((
% 132.79/23.00 (surjFuncSetFuncIn) =>
% 132.79/23.00 ((
% 132.79/23.00 (surjFuncSetFuncSurj) =>
% 132.79/23.00 ((
% 132.79/23.00 (leftInvIsSurj) =>
% 132.79/23.00 ((
% 132.79/23.00 (surjCantorThm) =>
% 132.79/23.00 ((
% 132.79/23.00 (foundation2) =>
% 132.79/23.00 ((
% 132.79/23.00 (notinself) =>
% 132.79/23.00 ((
% 132.79/23.00 (notinself2) =>
% 132.79/23.00 ((
% 132.79/23.00 (omegaSp) =>
% 132.79/23.00 ((
% 132.79/23.00 (omegaSclos) =>
% 132.79/23.00 ((
% 132.79/23.00 (peano0notS) =>
% 132.79/23.00 ((
% 132.79/23.00 (peanoSinj) =>
% 132.79/23.00 ((
% 132.79/23.00 (transitivesetOp1) =>
% 132.79/23.00 ((
% 132.79/23.00 (binintTransitive) =>
% 132.79/23.00 ((
% 132.79/23.00 (transitivesetOp2) =>
% 132.79/23.00 ((
% 132.79/23.00 (setunionTransitive) =>
% 132.79/23.00 ((
% 132.79/23.00 (ordinalMinLem1) =>
% 132.79/23.00 ((
% 132.79/23.00 (ordinalTransSet) =>
% 132.79/23.00 ((
% 132.79/23.00 (ordinalTransSet1) =>
% 132.79/23.00 ((
% 132.79/23.00 (setunionOrdinalLem1) =>
% 132.79/23.00 (ordinal @
% 132.79/23.00 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/23.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2001])).
% 132.79/23.00 thf(zip_derived_cl2029, plain,
% 132.79/23.00 (~ (((ifp) =>
% 132.79/23.00 (((theeq) =>
% 132.79/23.00 (((iftrue) =>
% 132.79/23.00 (((iffalse) =>
% 132.79/23.00 (((iftrueorfalse) =>
% 132.79/23.00 (((binintersectT_lem) =>
% 132.79/23.00 (((binunionT_lem) =>
% 132.79/23.00 (((powersetT_lem) =>
% 132.79/23.00 (((setminusT_lem) =>
% 132.79/23.00 (((complementT_lem) =>
% 132.79/23.00 (((setextT) =>
% 132.79/23.00 (((subsetTI) =>
% 132.79/23.00 (((powersetTI1) =>
% 132.79/23.00 (((powersetTE1) =>
% 132.79/23.00 (((complementTI1) =>
% 132.79/23.00 (((complementTE1) =>
% 132.79/23.00 (((binintersectTELcontra) =>
% 132.79/23.00 (((binintersectTERcontra) =>
% 132.79/23.00 (((contrasubsetT) =>
% 132.79/23.00 (((contrasubsetT1) =>
% 132.79/23.00 (((contrasubsetT2) =>
% 132.79/23.00 (((contrasubsetT3) =>
% 132.79/23.00 (((doubleComplementI1) =>
% 132.79/23.00 (((doubleComplementE1) =>
% 132.79/23.00 (((doubleComplementSub1) =>
% 132.79/23.00 (((doubleComplementSub2) =>
% 132.79/23.00 (((doubleComplementEq) =>
% 132.79/23.00 (((complementTnotintersectT) =>
% 132.79/23.00 (((complementImpComplementIntersect) =>
% 132.79/23.00 (((complementSubsetComplementIntersect) =>
% 132.79/23.00 ((
% 132.79/23.00 (complementInPowersetComplementIntersect) =>
% 132.79/23.00 ((
% 132.79/23.00 (contraSubsetComplement) =>
% 132.79/23.00 ((
% 132.79/23.00 (complementTcontraSubset) =>
% 132.79/23.00 ((
% 132.79/23.00 (binunionTILcontra) =>
% 132.79/23.00 ((
% 132.79/23.00 (binunionTIRcontra) =>
% 132.79/23.00 ((
% 132.79/23.00 (inIntersectImpInUnion) =>
% 132.79/23.00 ((
% 132.79/23.00 (inIntersectImpInUnion2) =>
% 132.79/23.00 ((
% 132.79/23.00 (inIntersectImpInIntersectUnions) =>
% 132.79/23.00 ((
% 132.79/23.00 (intersectInPowersetIntersectUnions) =>
% 132.79/23.00 ((
% 132.79/23.00 (inComplementUnionImpNotIn1) =>
% 132.79/23.00 ((
% 132.79/23.00 (inComplementUnionImpInComplement1) =>
% 132.79/23.00 ((
% 132.79/23.00 (binunionTE) =>
% 132.79/23.00 ((
% 132.79/23.00 (binunionTEcontra) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2a1) =>
% 132.79/23.00 ((
% 132.79/23.00 (complementUnionInPowersetComplement) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2a2) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan1a) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan1b) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan1) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2a) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2b2) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2b) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule0) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule1) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule2) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule3) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule4) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_1) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_2) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_3) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_4) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_5) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1all2) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1SetBreln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (choice2fnsingleton) =>
% 132.79/23.00 ((
% 132.79/23.00 (setOfPairsIsBReln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1all1) =>
% 132.79/23.00 ((
% 132.79/23.00 (subbreln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (eqbreln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1invprop) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1invI) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1invE) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compprop) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compI) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compE) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compEex) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionprop) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionIL) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionIR) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionI) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionE) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionEcases) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionCommutes) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2Ex) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2W) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2A) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2B) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1Ex) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1Ex1) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1Equiv) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1E) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1I) =>
% 132.79/23.00 ((
% 132.79/23.00 (injFuncInInjFuncSet) =>
% 132.79/23.00 ((
% 132.79/23.00 (injFuncSetFuncIn) =>
% 132.79/23.00 ((
% 132.79/23.00 (injFuncSetFuncInj) =>
% 132.79/23.00 ((
% 132.79/23.00 (surjFuncSetFuncIn) =>
% 132.79/23.00 ((
% 132.79/23.00 (surjFuncSetFuncSurj) =>
% 132.79/23.00 ((
% 132.79/23.00 (leftInvIsSurj) =>
% 132.79/23.00 ((
% 132.79/23.00 (surjCantorThm) =>
% 132.79/23.00 ((
% 132.79/23.00 (foundation2) =>
% 132.79/23.00 ((
% 132.79/23.00 (notinself) =>
% 132.79/23.00 ((
% 132.79/23.00 (notinself2) =>
% 132.79/23.00 ((
% 132.79/23.00 (omegaSp) =>
% 132.79/23.00 ((
% 132.79/23.00 (omegaSclos) =>
% 132.79/23.00 ((
% 132.79/23.00 (peano0notS) =>
% 132.79/23.00 ((
% 132.79/23.00 (peanoSinj) =>
% 132.79/23.00 ((
% 132.79/23.00 (transitivesetOp1) =>
% 132.79/23.00 ((
% 132.79/23.00 (binintTransitive) =>
% 132.79/23.00 ((
% 132.79/23.00 (transitivesetOp2) =>
% 132.79/23.00 ((
% 132.79/23.00 (setunionTransitive) =>
% 132.79/23.00 ((
% 132.79/23.00 (ordinalMinLem1) =>
% 132.79/23.00 ((
% 132.79/23.00 (ordinalTransSet) =>
% 132.79/23.00 ((
% 132.79/23.00 (ordinalTransSet1) =>
% 132.79/23.00 ((
% 132.79/23.00 (setunionOrdinalLem1) =>
% 132.79/23.00 (ordinal @
% 132.79/23.00 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/23.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2017])).
% 132.79/23.00 thf(zip_derived_cl2041, plain,
% 132.79/23.00 (~ (((theeq) =>
% 132.79/23.00 (((iftrue) =>
% 132.79/23.00 (((iffalse) =>
% 132.79/23.00 (((iftrueorfalse) =>
% 132.79/23.00 (((binintersectT_lem) =>
% 132.79/23.00 (((binunionT_lem) =>
% 132.79/23.00 (((powersetT_lem) =>
% 132.79/23.00 (((setminusT_lem) =>
% 132.79/23.00 (((complementT_lem) =>
% 132.79/23.00 (((setextT) =>
% 132.79/23.00 (((subsetTI) =>
% 132.79/23.00 (((powersetTI1) =>
% 132.79/23.00 (((powersetTE1) =>
% 132.79/23.00 (((complementTI1) =>
% 132.79/23.00 (((complementTE1) =>
% 132.79/23.00 (((binintersectTELcontra) =>
% 132.79/23.00 (((binintersectTERcontra) =>
% 132.79/23.00 (((contrasubsetT) =>
% 132.79/23.00 (((contrasubsetT1) =>
% 132.79/23.00 (((contrasubsetT2) =>
% 132.79/23.00 (((contrasubsetT3) =>
% 132.79/23.00 (((doubleComplementI1) =>
% 132.79/23.00 (((doubleComplementE1) =>
% 132.79/23.00 (((doubleComplementSub1) =>
% 132.79/23.00 (((doubleComplementSub2) =>
% 132.79/23.00 (((doubleComplementEq) =>
% 132.79/23.00 (((complementTnotintersectT) =>
% 132.79/23.00 (((complementImpComplementIntersect) =>
% 132.79/23.00 (((complementSubsetComplementIntersect) =>
% 132.79/23.00 (((complementInPowersetComplementIntersect) =>
% 132.79/23.00 ((
% 132.79/23.00 (contraSubsetComplement) =>
% 132.79/23.00 ((
% 132.79/23.00 (complementTcontraSubset) =>
% 132.79/23.00 ((
% 132.79/23.00 (binunionTILcontra) =>
% 132.79/23.00 ((
% 132.79/23.00 (binunionTIRcontra) =>
% 132.79/23.00 ((
% 132.79/23.00 (inIntersectImpInUnion) =>
% 132.79/23.00 ((
% 132.79/23.00 (inIntersectImpInUnion2) =>
% 132.79/23.00 ((
% 132.79/23.00 (inIntersectImpInIntersectUnions) =>
% 132.79/23.00 ((
% 132.79/23.00 (intersectInPowersetIntersectUnions) =>
% 132.79/23.00 ((
% 132.79/23.00 (inComplementUnionImpNotIn1) =>
% 132.79/23.00 ((
% 132.79/23.00 (inComplementUnionImpInComplement1) =>
% 132.79/23.00 ((
% 132.79/23.00 (binunionTE) =>
% 132.79/23.00 ((
% 132.79/23.00 (binunionTEcontra) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2a1) =>
% 132.79/23.00 ((
% 132.79/23.00 (complementUnionInPowersetComplement) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2a2) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan1a) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan1b) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan1) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2a) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2b2) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2b) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule0) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule1) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule2) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule3) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule4) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_1) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_2) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_3) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_4) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_5) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1all2) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1SetBreln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (choice2fnsingleton) =>
% 132.79/23.00 ((
% 132.79/23.00 (setOfPairsIsBReln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1all1) =>
% 132.79/23.00 ((
% 132.79/23.00 (subbreln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (eqbreln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1invprop) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1invI) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1invE) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compprop) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compI) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compE) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compEex) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionprop) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionIL) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionIR) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionI) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionE) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionEcases) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionCommutes) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2Ex) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2W) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2A) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2B) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1Ex) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1Ex1) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1Equiv) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1E) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1I) =>
% 132.79/23.00 ((
% 132.79/23.00 (injFuncInInjFuncSet) =>
% 132.79/23.00 ((
% 132.79/23.00 (injFuncSetFuncIn) =>
% 132.79/23.00 ((
% 132.79/23.00 (injFuncSetFuncInj) =>
% 132.79/23.00 ((
% 132.79/23.00 (surjFuncSetFuncIn) =>
% 132.79/23.00 ((
% 132.79/23.00 (surjFuncSetFuncSurj) =>
% 132.79/23.00 ((
% 132.79/23.00 (leftInvIsSurj) =>
% 132.79/23.00 ((
% 132.79/23.00 (surjCantorThm) =>
% 132.79/23.00 ((
% 132.79/23.00 (foundation2) =>
% 132.79/23.00 ((
% 132.79/23.00 (notinself) =>
% 132.79/23.00 ((
% 132.79/23.00 (notinself2) =>
% 132.79/23.00 ((
% 132.79/23.00 (omegaSp) =>
% 132.79/23.00 ((
% 132.79/23.00 (omegaSclos) =>
% 132.79/23.00 ((
% 132.79/23.00 (peano0notS) =>
% 132.79/23.00 ((
% 132.79/23.00 (peanoSinj) =>
% 132.79/23.00 ((
% 132.79/23.00 (transitivesetOp1) =>
% 132.79/23.00 ((
% 132.79/23.00 (binintTransitive) =>
% 132.79/23.00 ((
% 132.79/23.00 (transitivesetOp2) =>
% 132.79/23.00 ((
% 132.79/23.00 (setunionTransitive) =>
% 132.79/23.00 ((
% 132.79/23.00 (ordinalMinLem1) =>
% 132.79/23.00 ((
% 132.79/23.00 (ordinalTransSet) =>
% 132.79/23.00 ((
% 132.79/23.00 (ordinalTransSet1) =>
% 132.79/23.00 ((
% 132.79/23.00 (setunionOrdinalLem1) =>
% 132.79/23.00 (ordinal @
% 132.79/23.00 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/23.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2029])).
% 132.79/23.00 thf(zip_derived_cl2053, plain,
% 132.79/23.00 (~ (((iftrue) =>
% 132.79/23.00 (((iffalse) =>
% 132.79/23.00 (((iftrueorfalse) =>
% 132.79/23.00 (((binintersectT_lem) =>
% 132.79/23.00 (((binunionT_lem) =>
% 132.79/23.00 (((powersetT_lem) =>
% 132.79/23.00 (((setminusT_lem) =>
% 132.79/23.00 (((complementT_lem) =>
% 132.79/23.00 (((setextT) =>
% 132.79/23.00 (((subsetTI) =>
% 132.79/23.00 (((powersetTI1) =>
% 132.79/23.00 (((powersetTE1) =>
% 132.79/23.00 (((complementTI1) =>
% 132.79/23.00 (((complementTE1) =>
% 132.79/23.00 (((binintersectTELcontra) =>
% 132.79/23.00 (((binintersectTERcontra) =>
% 132.79/23.00 (((contrasubsetT) =>
% 132.79/23.00 (((contrasubsetT1) =>
% 132.79/23.00 (((contrasubsetT2) =>
% 132.79/23.00 (((contrasubsetT3) =>
% 132.79/23.00 (((doubleComplementI1) =>
% 132.79/23.00 (((doubleComplementE1) =>
% 132.79/23.00 (((doubleComplementSub1) =>
% 132.79/23.00 (((doubleComplementSub2) =>
% 132.79/23.00 (((doubleComplementEq) =>
% 132.79/23.00 (((complementTnotintersectT) =>
% 132.79/23.00 (((complementImpComplementIntersect) =>
% 132.79/23.00 (((complementSubsetComplementIntersect) =>
% 132.79/23.00 (((complementInPowersetComplementIntersect) =>
% 132.79/23.00 (((contraSubsetComplement) =>
% 132.79/23.00 ((
% 132.79/23.00 (complementTcontraSubset) =>
% 132.79/23.00 ((
% 132.79/23.00 (binunionTILcontra) =>
% 132.79/23.00 ((
% 132.79/23.00 (binunionTIRcontra) =>
% 132.79/23.00 ((
% 132.79/23.00 (inIntersectImpInUnion) =>
% 132.79/23.00 ((
% 132.79/23.00 (inIntersectImpInUnion2) =>
% 132.79/23.00 ((
% 132.79/23.00 (inIntersectImpInIntersectUnions) =>
% 132.79/23.00 ((
% 132.79/23.00 (intersectInPowersetIntersectUnions) =>
% 132.79/23.00 ((
% 132.79/23.00 (inComplementUnionImpNotIn1) =>
% 132.79/23.00 ((
% 132.79/23.00 (inComplementUnionImpInComplement1) =>
% 132.79/23.00 ((
% 132.79/23.00 (binunionTE) =>
% 132.79/23.00 ((
% 132.79/23.00 (binunionTEcontra) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2a1) =>
% 132.79/23.00 ((
% 132.79/23.00 (complementUnionInPowersetComplement) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2a2) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan1a) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan1b) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan1) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2a) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2b2) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2b) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule0) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule1) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule2) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule3) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule4) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_1) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_2) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_3) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_4) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_5) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1all2) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1SetBreln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (choice2fnsingleton) =>
% 132.79/23.00 ((
% 132.79/23.00 (setOfPairsIsBReln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1all1) =>
% 132.79/23.00 ((
% 132.79/23.00 (subbreln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (eqbreln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1invprop) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1invI) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1invE) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compprop) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compI) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compE) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compEex) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionprop) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionIL) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionIR) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionI) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionE) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionEcases) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionCommutes) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2Ex) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2W) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2A) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2B) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1Ex) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1Ex1) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1Equiv) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1E) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1I) =>
% 132.79/23.00 ((
% 132.79/23.00 (injFuncInInjFuncSet) =>
% 132.79/23.00 ((
% 132.79/23.00 (injFuncSetFuncIn) =>
% 132.79/23.00 ((
% 132.79/23.00 (injFuncSetFuncInj) =>
% 132.79/23.00 ((
% 132.79/23.00 (surjFuncSetFuncIn) =>
% 132.79/23.00 ((
% 132.79/23.00 (surjFuncSetFuncSurj) =>
% 132.79/23.00 ((
% 132.79/23.00 (leftInvIsSurj) =>
% 132.79/23.00 ((
% 132.79/23.00 (surjCantorThm) =>
% 132.79/23.00 ((
% 132.79/23.00 (foundation2) =>
% 132.79/23.00 ((
% 132.79/23.00 (notinself) =>
% 132.79/23.00 ((
% 132.79/23.00 (notinself2) =>
% 132.79/23.00 ((
% 132.79/23.00 (omegaSp) =>
% 132.79/23.00 ((
% 132.79/23.00 (omegaSclos) =>
% 132.79/23.00 ((
% 132.79/23.00 (peano0notS) =>
% 132.79/23.00 ((
% 132.79/23.00 (peanoSinj) =>
% 132.79/23.00 ((
% 132.79/23.00 (transitivesetOp1) =>
% 132.79/23.00 ((
% 132.79/23.00 (binintTransitive) =>
% 132.79/23.00 ((
% 132.79/23.00 (transitivesetOp2) =>
% 132.79/23.00 ((
% 132.79/23.00 (setunionTransitive) =>
% 132.79/23.00 ((
% 132.79/23.00 (ordinalMinLem1) =>
% 132.79/23.00 ((
% 132.79/23.00 (ordinalTransSet) =>
% 132.79/23.00 ((
% 132.79/23.00 (ordinalTransSet1) =>
% 132.79/23.00 ((
% 132.79/23.00 (setunionOrdinalLem1) =>
% 132.79/23.00 (ordinal @
% 132.79/23.00 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/23.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2041])).
% 132.79/23.00 thf(zip_derived_cl2062, plain,
% 132.79/23.00 (~ (((iffalse) =>
% 132.79/23.00 (((iftrueorfalse) =>
% 132.79/23.00 (((binintersectT_lem) =>
% 132.79/23.00 (((binunionT_lem) =>
% 132.79/23.00 (((powersetT_lem) =>
% 132.79/23.00 (((setminusT_lem) =>
% 132.79/23.00 (((complementT_lem) =>
% 132.79/23.00 (((setextT) =>
% 132.79/23.00 (((subsetTI) =>
% 132.79/23.00 (((powersetTI1) =>
% 132.79/23.00 (((powersetTE1) =>
% 132.79/23.00 (((complementTI1) =>
% 132.79/23.00 (((complementTE1) =>
% 132.79/23.00 (((binintersectTELcontra) =>
% 132.79/23.00 (((binintersectTERcontra) =>
% 132.79/23.00 (((contrasubsetT) =>
% 132.79/23.00 (((contrasubsetT1) =>
% 132.79/23.00 (((contrasubsetT2) =>
% 132.79/23.00 (((contrasubsetT3) =>
% 132.79/23.00 (((doubleComplementI1) =>
% 132.79/23.00 (((doubleComplementE1) =>
% 132.79/23.00 (((doubleComplementSub1) =>
% 132.79/23.00 (((doubleComplementSub2) =>
% 132.79/23.00 (((doubleComplementEq) =>
% 132.79/23.00 (((complementTnotintersectT) =>
% 132.79/23.00 (((complementImpComplementIntersect) =>
% 132.79/23.00 (((complementSubsetComplementIntersect) =>
% 132.79/23.00 (((complementInPowersetComplementIntersect) =>
% 132.79/23.00 (((contraSubsetComplement) =>
% 132.79/23.00 (((complementTcontraSubset) =>
% 132.79/23.00 ((
% 132.79/23.00 (binunionTILcontra) =>
% 132.79/23.00 ((
% 132.79/23.00 (binunionTIRcontra) =>
% 132.79/23.00 ((
% 132.79/23.00 (inIntersectImpInUnion) =>
% 132.79/23.00 ((
% 132.79/23.00 (inIntersectImpInUnion2) =>
% 132.79/23.00 ((
% 132.79/23.00 (inIntersectImpInIntersectUnions) =>
% 132.79/23.00 ((
% 132.79/23.00 (intersectInPowersetIntersectUnions) =>
% 132.79/23.00 ((
% 132.79/23.00 (inComplementUnionImpNotIn1) =>
% 132.79/23.00 ((
% 132.79/23.00 (inComplementUnionImpInComplement1) =>
% 132.79/23.00 ((
% 132.79/23.00 (binunionTE) =>
% 132.79/23.00 ((
% 132.79/23.00 (binunionTEcontra) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2a1) =>
% 132.79/23.00 ((
% 132.79/23.00 (complementUnionInPowersetComplement) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2a2) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan1a) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan1b) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan1) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2a) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2b2) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2b) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule0) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule1) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule2) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule3) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule4) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_1) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_2) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_3) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_4) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_5) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1all2) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1SetBreln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (choice2fnsingleton) =>
% 132.79/23.00 ((
% 132.79/23.00 (setOfPairsIsBReln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1all1) =>
% 132.79/23.00 ((
% 132.79/23.00 (subbreln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (eqbreln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1invprop) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1invI) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1invE) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compprop) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compI) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compE) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compEex) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionprop) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionIL) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionIR) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionI) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionE) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionEcases) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionCommutes) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2Ex) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2W) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2A) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2B) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1Ex) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1Ex1) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1Equiv) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1E) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1I) =>
% 132.79/23.00 ((
% 132.79/23.00 (injFuncInInjFuncSet) =>
% 132.79/23.00 ((
% 132.79/23.00 (injFuncSetFuncIn) =>
% 132.79/23.00 ((
% 132.79/23.00 (injFuncSetFuncInj) =>
% 132.79/23.00 ((
% 132.79/23.00 (surjFuncSetFuncIn) =>
% 132.79/23.00 ((
% 132.79/23.00 (surjFuncSetFuncSurj) =>
% 132.79/23.00 ((
% 132.79/23.00 (leftInvIsSurj) =>
% 132.79/23.00 ((
% 132.79/23.00 (surjCantorThm) =>
% 132.79/23.00 ((
% 132.79/23.00 (foundation2) =>
% 132.79/23.00 ((
% 132.79/23.00 (notinself) =>
% 132.79/23.00 ((
% 132.79/23.00 (notinself2) =>
% 132.79/23.00 ((
% 132.79/23.00 (omegaSp) =>
% 132.79/23.00 ((
% 132.79/23.00 (omegaSclos) =>
% 132.79/23.00 ((
% 132.79/23.00 (peano0notS) =>
% 132.79/23.00 ((
% 132.79/23.00 (peanoSinj) =>
% 132.79/23.00 ((
% 132.79/23.00 (transitivesetOp1) =>
% 132.79/23.00 ((
% 132.79/23.00 (binintTransitive) =>
% 132.79/23.00 ((
% 132.79/23.00 (transitivesetOp2) =>
% 132.79/23.00 ((
% 132.79/23.00 (setunionTransitive) =>
% 132.79/23.00 ((
% 132.79/23.00 (ordinalMinLem1) =>
% 132.79/23.00 ((
% 132.79/23.00 (ordinalTransSet) =>
% 132.79/23.00 ((
% 132.79/23.00 (ordinalTransSet1) =>
% 132.79/23.00 ((
% 132.79/23.00 (setunionOrdinalLem1) =>
% 132.79/23.00 (ordinal @
% 132.79/23.00 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/23.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2053])).
% 132.79/23.00 thf(zip_derived_cl2072, plain,
% 132.79/23.00 (~ (((iftrueorfalse) =>
% 132.79/23.00 (((binintersectT_lem) =>
% 132.79/23.00 (((binunionT_lem) =>
% 132.79/23.00 (((powersetT_lem) =>
% 132.79/23.00 (((setminusT_lem) =>
% 132.79/23.00 (((complementT_lem) =>
% 132.79/23.00 (((setextT) =>
% 132.79/23.00 (((subsetTI) =>
% 132.79/23.00 (((powersetTI1) =>
% 132.79/23.00 (((powersetTE1) =>
% 132.79/23.00 (((complementTI1) =>
% 132.79/23.00 (((complementTE1) =>
% 132.79/23.00 (((binintersectTELcontra) =>
% 132.79/23.00 (((binintersectTERcontra) =>
% 132.79/23.00 (((contrasubsetT) =>
% 132.79/23.00 (((contrasubsetT1) =>
% 132.79/23.00 (((contrasubsetT2) =>
% 132.79/23.00 (((contrasubsetT3) =>
% 132.79/23.00 (((doubleComplementI1) =>
% 132.79/23.00 (((doubleComplementE1) =>
% 132.79/23.00 (((doubleComplementSub1) =>
% 132.79/23.00 (((doubleComplementSub2) =>
% 132.79/23.00 (((doubleComplementEq) =>
% 132.79/23.00 (((complementTnotintersectT) =>
% 132.79/23.00 (((complementImpComplementIntersect) =>
% 132.79/23.00 (((complementSubsetComplementIntersect) =>
% 132.79/23.00 (((complementInPowersetComplementIntersect) =>
% 132.79/23.00 (((contraSubsetComplement) =>
% 132.79/23.00 (((complementTcontraSubset) =>
% 132.79/23.00 (((binunionTILcontra) =>
% 132.79/23.00 ((
% 132.79/23.00 (binunionTIRcontra) =>
% 132.79/23.00 ((
% 132.79/23.00 (inIntersectImpInUnion) =>
% 132.79/23.00 ((
% 132.79/23.00 (inIntersectImpInUnion2) =>
% 132.79/23.00 ((
% 132.79/23.00 (inIntersectImpInIntersectUnions) =>
% 132.79/23.00 ((
% 132.79/23.00 (intersectInPowersetIntersectUnions) =>
% 132.79/23.00 ((
% 132.79/23.00 (inComplementUnionImpNotIn1) =>
% 132.79/23.00 ((
% 132.79/23.00 (inComplementUnionImpInComplement1) =>
% 132.79/23.00 ((
% 132.79/23.00 (binunionTE) =>
% 132.79/23.00 ((
% 132.79/23.00 (binunionTEcontra) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2a1) =>
% 132.79/23.00 ((
% 132.79/23.00 (complementUnionInPowersetComplement) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2a2) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan1a) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan1b) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan1) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2a) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2b2) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2b) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule0) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule1) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule2) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule3) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule4) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_1) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_2) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_3) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_4) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_5) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1all2) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1SetBreln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (choice2fnsingleton) =>
% 132.79/23.00 ((
% 132.79/23.00 (setOfPairsIsBReln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1all1) =>
% 132.79/23.00 ((
% 132.79/23.00 (subbreln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (eqbreln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1invprop) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1invI) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1invE) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compprop) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compI) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compE) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compEex) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionprop) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionIL) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionIR) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionI) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionE) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionEcases) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionCommutes) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2Ex) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2W) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2A) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2B) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1Ex) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1Ex1) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1Equiv) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1E) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1I) =>
% 132.79/23.00 ((
% 132.79/23.00 (injFuncInInjFuncSet) =>
% 132.79/23.00 ((
% 132.79/23.00 (injFuncSetFuncIn) =>
% 132.79/23.00 ((
% 132.79/23.00 (injFuncSetFuncInj) =>
% 132.79/23.00 ((
% 132.79/23.00 (surjFuncSetFuncIn) =>
% 132.79/23.00 ((
% 132.79/23.00 (surjFuncSetFuncSurj) =>
% 132.79/23.00 ((
% 132.79/23.00 (leftInvIsSurj) =>
% 132.79/23.00 ((
% 132.79/23.00 (surjCantorThm) =>
% 132.79/23.00 ((
% 132.79/23.00 (foundation2) =>
% 132.79/23.00 ((
% 132.79/23.00 (notinself) =>
% 132.79/23.00 ((
% 132.79/23.00 (notinself2) =>
% 132.79/23.00 ((
% 132.79/23.00 (omegaSp) =>
% 132.79/23.00 ((
% 132.79/23.00 (omegaSclos) =>
% 132.79/23.00 ((
% 132.79/23.00 (peano0notS) =>
% 132.79/23.00 ((
% 132.79/23.00 (peanoSinj) =>
% 132.79/23.00 ((
% 132.79/23.00 (transitivesetOp1) =>
% 132.79/23.00 ((
% 132.79/23.00 (binintTransitive) =>
% 132.79/23.00 ((
% 132.79/23.00 (transitivesetOp2) =>
% 132.79/23.00 ((
% 132.79/23.00 (setunionTransitive) =>
% 132.79/23.00 ((
% 132.79/23.00 (ordinalMinLem1) =>
% 132.79/23.00 ((
% 132.79/23.00 (ordinalTransSet) =>
% 132.79/23.00 ((
% 132.79/23.00 (ordinalTransSet1) =>
% 132.79/23.00 ((
% 132.79/23.00 (setunionOrdinalLem1) =>
% 132.79/23.00 (ordinal @
% 132.79/23.00 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/23.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2062])).
% 132.79/23.00 thf(zip_derived_cl2082, plain,
% 132.79/23.00 (~ (((binintersectT_lem) =>
% 132.79/23.00 (((binunionT_lem) =>
% 132.79/23.00 (((powersetT_lem) =>
% 132.79/23.00 (((setminusT_lem) =>
% 132.79/23.00 (((complementT_lem) =>
% 132.79/23.00 (((setextT) =>
% 132.79/23.00 (((subsetTI) =>
% 132.79/23.00 (((powersetTI1) =>
% 132.79/23.00 (((powersetTE1) =>
% 132.79/23.00 (((complementTI1) =>
% 132.79/23.00 (((complementTE1) =>
% 132.79/23.00 (((binintersectTELcontra) =>
% 132.79/23.00 (((binintersectTERcontra) =>
% 132.79/23.00 (((contrasubsetT) =>
% 132.79/23.00 (((contrasubsetT1) =>
% 132.79/23.00 (((contrasubsetT2) =>
% 132.79/23.00 (((contrasubsetT3) =>
% 132.79/23.00 (((doubleComplementI1) =>
% 132.79/23.00 (((doubleComplementE1) =>
% 132.79/23.00 (((doubleComplementSub1) =>
% 132.79/23.00 (((doubleComplementSub2) =>
% 132.79/23.00 (((doubleComplementEq) =>
% 132.79/23.00 (((complementTnotintersectT) =>
% 132.79/23.00 (((complementImpComplementIntersect) =>
% 132.79/23.00 (((complementSubsetComplementIntersect) =>
% 132.79/23.00 (((complementInPowersetComplementIntersect) =>
% 132.79/23.00 (((contraSubsetComplement) =>
% 132.79/23.00 (((complementTcontraSubset) =>
% 132.79/23.00 (((binunionTILcontra) =>
% 132.79/23.00 (((binunionTIRcontra) =>
% 132.79/23.00 ((
% 132.79/23.00 (inIntersectImpInUnion) =>
% 132.79/23.00 ((
% 132.79/23.00 (inIntersectImpInUnion2) =>
% 132.79/23.00 ((
% 132.79/23.00 (inIntersectImpInIntersectUnions) =>
% 132.79/23.00 ((
% 132.79/23.00 (intersectInPowersetIntersectUnions) =>
% 132.79/23.00 ((
% 132.79/23.00 (inComplementUnionImpNotIn1) =>
% 132.79/23.00 ((
% 132.79/23.00 (inComplementUnionImpInComplement1) =>
% 132.79/23.00 ((
% 132.79/23.00 (binunionTE) =>
% 132.79/23.00 ((
% 132.79/23.00 (binunionTEcontra) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2a1) =>
% 132.79/23.00 ((
% 132.79/23.00 (complementUnionInPowersetComplement) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2a2) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan1a) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan1b) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan1) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2a) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2b2) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2b) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule0) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule1) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule2) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule3) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule4) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_1) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_2) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_3) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_4) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_5) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1all2) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1SetBreln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (choice2fnsingleton) =>
% 132.79/23.00 ((
% 132.79/23.00 (setOfPairsIsBReln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1all1) =>
% 132.79/23.00 ((
% 132.79/23.00 (subbreln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (eqbreln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1invprop) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1invI) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1invE) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compprop) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compI) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compE) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compEex) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionprop) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionIL) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionIR) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionI) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionE) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionEcases) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionCommutes) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2Ex) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2W) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2A) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2B) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1Ex) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1Ex1) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1Equiv) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1E) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1I) =>
% 132.79/23.00 ((
% 132.79/23.00 (injFuncInInjFuncSet) =>
% 132.79/23.00 ((
% 132.79/23.00 (injFuncSetFuncIn) =>
% 132.79/23.00 ((
% 132.79/23.00 (injFuncSetFuncInj) =>
% 132.79/23.00 ((
% 132.79/23.00 (surjFuncSetFuncIn) =>
% 132.79/23.00 ((
% 132.79/23.00 (surjFuncSetFuncSurj) =>
% 132.79/23.00 ((
% 132.79/23.00 (leftInvIsSurj) =>
% 132.79/23.00 ((
% 132.79/23.00 (surjCantorThm) =>
% 132.79/23.00 ((
% 132.79/23.00 (foundation2) =>
% 132.79/23.00 ((
% 132.79/23.00 (notinself) =>
% 132.79/23.00 ((
% 132.79/23.00 (notinself2) =>
% 132.79/23.00 ((
% 132.79/23.00 (omegaSp) =>
% 132.79/23.00 ((
% 132.79/23.00 (omegaSclos) =>
% 132.79/23.00 ((
% 132.79/23.00 (peano0notS) =>
% 132.79/23.00 ((
% 132.79/23.00 (peanoSinj) =>
% 132.79/23.00 ((
% 132.79/23.00 (transitivesetOp1) =>
% 132.79/23.00 ((
% 132.79/23.00 (binintTransitive) =>
% 132.79/23.00 ((
% 132.79/23.00 (transitivesetOp2) =>
% 132.79/23.00 ((
% 132.79/23.00 (setunionTransitive) =>
% 132.79/23.00 ((
% 132.79/23.00 (ordinalMinLem1) =>
% 132.79/23.00 ((
% 132.79/23.00 (ordinalTransSet) =>
% 132.79/23.00 ((
% 132.79/23.00 (ordinalTransSet1) =>
% 132.79/23.00 ((
% 132.79/23.00 (setunionOrdinalLem1) =>
% 132.79/23.00 (ordinal @
% 132.79/23.00 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/23.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2072])).
% 132.79/23.00 thf(zip_derived_cl2093, plain,
% 132.79/23.00 (~ (((binunionT_lem) =>
% 132.79/23.00 (((powersetT_lem) =>
% 132.79/23.00 (((setminusT_lem) =>
% 132.79/23.00 (((complementT_lem) =>
% 132.79/23.00 (((setextT) =>
% 132.79/23.00 (((subsetTI) =>
% 132.79/23.00 (((powersetTI1) =>
% 132.79/23.00 (((powersetTE1) =>
% 132.79/23.00 (((complementTI1) =>
% 132.79/23.00 (((complementTE1) =>
% 132.79/23.00 (((binintersectTELcontra) =>
% 132.79/23.00 (((binintersectTERcontra) =>
% 132.79/23.00 (((contrasubsetT) =>
% 132.79/23.00 (((contrasubsetT1) =>
% 132.79/23.00 (((contrasubsetT2) =>
% 132.79/23.00 (((contrasubsetT3) =>
% 132.79/23.00 (((doubleComplementI1) =>
% 132.79/23.00 (((doubleComplementE1) =>
% 132.79/23.00 (((doubleComplementSub1) =>
% 132.79/23.00 (((doubleComplementSub2) =>
% 132.79/23.00 (((doubleComplementEq) =>
% 132.79/23.00 (((complementTnotintersectT) =>
% 132.79/23.00 (((complementImpComplementIntersect) =>
% 132.79/23.00 (((complementSubsetComplementIntersect) =>
% 132.79/23.00 (((complementInPowersetComplementIntersect) =>
% 132.79/23.00 (((contraSubsetComplement) =>
% 132.79/23.00 (((complementTcontraSubset) =>
% 132.79/23.00 (((binunionTILcontra) =>
% 132.79/23.00 (((binunionTIRcontra) =>
% 132.79/23.00 (((inIntersectImpInUnion) =>
% 132.79/23.00 ((
% 132.79/23.00 (inIntersectImpInUnion2) =>
% 132.79/23.00 ((
% 132.79/23.00 (inIntersectImpInIntersectUnions) =>
% 132.79/23.00 ((
% 132.79/23.00 (intersectInPowersetIntersectUnions) =>
% 132.79/23.00 ((
% 132.79/23.00 (inComplementUnionImpNotIn1) =>
% 132.79/23.00 ((
% 132.79/23.00 (inComplementUnionImpInComplement1) =>
% 132.79/23.00 ((
% 132.79/23.00 (binunionTE) =>
% 132.79/23.00 ((
% 132.79/23.00 (binunionTEcontra) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2a1) =>
% 132.79/23.00 ((
% 132.79/23.00 (complementUnionInPowersetComplement) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2a2) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan1a) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan1b) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan1) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2a) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2b2) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2b) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule0) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule1) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule2) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule3) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule4) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_1) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_2) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_3) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_4) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_5) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1all2) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1SetBreln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (choice2fnsingleton) =>
% 132.79/23.00 ((
% 132.79/23.00 (setOfPairsIsBReln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1all1) =>
% 132.79/23.00 ((
% 132.79/23.00 (subbreln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (eqbreln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1invprop) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1invI) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1invE) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compprop) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compI) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compE) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compEex) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionprop) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionIL) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionIR) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionI) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionE) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionEcases) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionCommutes) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2Ex) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2W) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2A) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2B) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1Ex) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1Ex1) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1Equiv) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1E) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1I) =>
% 132.79/23.00 ((
% 132.79/23.00 (injFuncInInjFuncSet) =>
% 132.79/23.00 ((
% 132.79/23.00 (injFuncSetFuncIn) =>
% 132.79/23.00 ((
% 132.79/23.00 (injFuncSetFuncInj) =>
% 132.79/23.00 ((
% 132.79/23.00 (surjFuncSetFuncIn) =>
% 132.79/23.00 ((
% 132.79/23.00 (surjFuncSetFuncSurj) =>
% 132.79/23.00 ((
% 132.79/23.00 (leftInvIsSurj) =>
% 132.79/23.00 ((
% 132.79/23.00 (surjCantorThm) =>
% 132.79/23.00 ((
% 132.79/23.00 (foundation2) =>
% 132.79/23.00 ((
% 132.79/23.00 (notinself) =>
% 132.79/23.00 ((
% 132.79/23.00 (notinself2) =>
% 132.79/23.00 ((
% 132.79/23.00 (omegaSp) =>
% 132.79/23.00 ((
% 132.79/23.00 (omegaSclos) =>
% 132.79/23.00 ((
% 132.79/23.00 (peano0notS) =>
% 132.79/23.00 ((
% 132.79/23.00 (peanoSinj) =>
% 132.79/23.00 ((
% 132.79/23.00 (transitivesetOp1) =>
% 132.79/23.00 ((
% 132.79/23.00 (binintTransitive) =>
% 132.79/23.00 ((
% 132.79/23.00 (transitivesetOp2) =>
% 132.79/23.00 ((
% 132.79/23.00 (setunionTransitive) =>
% 132.79/23.00 ((
% 132.79/23.00 (ordinalMinLem1) =>
% 132.79/23.00 ((
% 132.79/23.00 (ordinalTransSet) =>
% 132.79/23.00 ((
% 132.79/23.00 (ordinalTransSet1) =>
% 132.79/23.00 ((
% 132.79/23.00 (setunionOrdinalLem1) =>
% 132.79/23.00 (ordinal @
% 132.79/23.00 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/23.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2082])).
% 132.79/23.00 thf(zip_derived_cl2103, plain,
% 132.79/23.00 (~ (((powersetT_lem) =>
% 132.79/23.00 (((setminusT_lem) =>
% 132.79/23.00 (((complementT_lem) =>
% 132.79/23.00 (((setextT) =>
% 132.79/23.00 (((subsetTI) =>
% 132.79/23.00 (((powersetTI1) =>
% 132.79/23.00 (((powersetTE1) =>
% 132.79/23.00 (((complementTI1) =>
% 132.79/23.00 (((complementTE1) =>
% 132.79/23.00 (((binintersectTELcontra) =>
% 132.79/23.00 (((binintersectTERcontra) =>
% 132.79/23.00 (((contrasubsetT) =>
% 132.79/23.00 (((contrasubsetT1) =>
% 132.79/23.00 (((contrasubsetT2) =>
% 132.79/23.00 (((contrasubsetT3) =>
% 132.79/23.00 (((doubleComplementI1) =>
% 132.79/23.00 (((doubleComplementE1) =>
% 132.79/23.00 (((doubleComplementSub1) =>
% 132.79/23.00 (((doubleComplementSub2) =>
% 132.79/23.00 (((doubleComplementEq) =>
% 132.79/23.00 (((complementTnotintersectT) =>
% 132.79/23.00 (((complementImpComplementIntersect) =>
% 132.79/23.00 (((complementSubsetComplementIntersect) =>
% 132.79/23.00 (((complementInPowersetComplementIntersect) =>
% 132.79/23.00 (((contraSubsetComplement) =>
% 132.79/23.00 (((complementTcontraSubset) =>
% 132.79/23.00 (((binunionTILcontra) =>
% 132.79/23.00 (((binunionTIRcontra) =>
% 132.79/23.00 (((inIntersectImpInUnion) =>
% 132.79/23.00 (((inIntersectImpInUnion2) =>
% 132.79/23.00 ((
% 132.79/23.00 (inIntersectImpInIntersectUnions) =>
% 132.79/23.00 ((
% 132.79/23.00 (intersectInPowersetIntersectUnions) =>
% 132.79/23.00 ((
% 132.79/23.00 (inComplementUnionImpNotIn1) =>
% 132.79/23.00 ((
% 132.79/23.00 (inComplementUnionImpInComplement1) =>
% 132.79/23.00 ((
% 132.79/23.00 (binunionTE) =>
% 132.79/23.00 ((
% 132.79/23.00 (binunionTEcontra) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2a1) =>
% 132.79/23.00 ((
% 132.79/23.00 (complementUnionInPowersetComplement) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2a2) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan1a) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan1b) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan1) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2a) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2b2) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2b) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule0) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule1) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule2) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule3) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule4) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_1) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_2) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_3) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_4) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_5) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1all2) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1SetBreln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (choice2fnsingleton) =>
% 132.79/23.00 ((
% 132.79/23.00 (setOfPairsIsBReln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1all1) =>
% 132.79/23.00 ((
% 132.79/23.00 (subbreln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (eqbreln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1invprop) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1invI) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1invE) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compprop) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compI) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compE) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compEex) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionprop) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionIL) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionIR) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionI) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionE) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionEcases) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionCommutes) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2Ex) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2W) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2A) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2B) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1Ex) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1Ex1) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1Equiv) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1E) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1I) =>
% 132.79/23.00 ((
% 132.79/23.00 (injFuncInInjFuncSet) =>
% 132.79/23.00 ((
% 132.79/23.00 (injFuncSetFuncIn) =>
% 132.79/23.00 ((
% 132.79/23.00 (injFuncSetFuncInj) =>
% 132.79/23.00 ((
% 132.79/23.00 (surjFuncSetFuncIn) =>
% 132.79/23.00 ((
% 132.79/23.00 (surjFuncSetFuncSurj) =>
% 132.79/23.00 ((
% 132.79/23.00 (leftInvIsSurj) =>
% 132.79/23.00 ((
% 132.79/23.00 (surjCantorThm) =>
% 132.79/23.00 ((
% 132.79/23.00 (foundation2) =>
% 132.79/23.00 ((
% 132.79/23.00 (notinself) =>
% 132.79/23.00 ((
% 132.79/23.00 (notinself2) =>
% 132.79/23.00 ((
% 132.79/23.00 (omegaSp) =>
% 132.79/23.00 ((
% 132.79/23.00 (omegaSclos) =>
% 132.79/23.00 ((
% 132.79/23.00 (peano0notS) =>
% 132.79/23.00 ((
% 132.79/23.00 (peanoSinj) =>
% 132.79/23.00 ((
% 132.79/23.00 (transitivesetOp1) =>
% 132.79/23.00 ((
% 132.79/23.00 (binintTransitive) =>
% 132.79/23.00 ((
% 132.79/23.00 (transitivesetOp2) =>
% 132.79/23.00 ((
% 132.79/23.00 (setunionTransitive) =>
% 132.79/23.00 ((
% 132.79/23.00 (ordinalMinLem1) =>
% 132.79/23.00 ((
% 132.79/23.00 (ordinalTransSet) =>
% 132.79/23.00 ((
% 132.79/23.00 (ordinalTransSet1) =>
% 132.79/23.00 ((
% 132.79/23.00 (setunionOrdinalLem1) =>
% 132.79/23.00 (ordinal @
% 132.79/23.00 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/23.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2093])).
% 132.79/23.00 thf(zip_derived_cl2113, plain,
% 132.79/23.00 (~ (((setminusT_lem) =>
% 132.79/23.00 (((complementT_lem) =>
% 132.79/23.00 (((setextT) =>
% 132.79/23.00 (((subsetTI) =>
% 132.79/23.00 (((powersetTI1) =>
% 132.79/23.00 (((powersetTE1) =>
% 132.79/23.00 (((complementTI1) =>
% 132.79/23.00 (((complementTE1) =>
% 132.79/23.00 (((binintersectTELcontra) =>
% 132.79/23.00 (((binintersectTERcontra) =>
% 132.79/23.00 (((contrasubsetT) =>
% 132.79/23.00 (((contrasubsetT1) =>
% 132.79/23.00 (((contrasubsetT2) =>
% 132.79/23.00 (((contrasubsetT3) =>
% 132.79/23.00 (((doubleComplementI1) =>
% 132.79/23.00 (((doubleComplementE1) =>
% 132.79/23.00 (((doubleComplementSub1) =>
% 132.79/23.00 (((doubleComplementSub2) =>
% 132.79/23.00 (((doubleComplementEq) =>
% 132.79/23.00 (((complementTnotintersectT) =>
% 132.79/23.00 (((complementImpComplementIntersect) =>
% 132.79/23.00 (((complementSubsetComplementIntersect) =>
% 132.79/23.00 (((complementInPowersetComplementIntersect) =>
% 132.79/23.00 (((contraSubsetComplement) =>
% 132.79/23.00 (((complementTcontraSubset) =>
% 132.79/23.00 (((binunionTILcontra) =>
% 132.79/23.00 (((binunionTIRcontra) =>
% 132.79/23.00 (((inIntersectImpInUnion) =>
% 132.79/23.00 (((inIntersectImpInUnion2) =>
% 132.79/23.00 (((inIntersectImpInIntersectUnions) =>
% 132.79/23.00 ((
% 132.79/23.00 (intersectInPowersetIntersectUnions) =>
% 132.79/23.00 ((
% 132.79/23.00 (inComplementUnionImpNotIn1) =>
% 132.79/23.00 ((
% 132.79/23.00 (inComplementUnionImpInComplement1) =>
% 132.79/23.00 ((
% 132.79/23.00 (binunionTE) =>
% 132.79/23.00 ((
% 132.79/23.00 (binunionTEcontra) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2a1) =>
% 132.79/23.00 ((
% 132.79/23.00 (complementUnionInPowersetComplement) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2a2) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan1a) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan1b) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan1) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2a) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2b2) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2b) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule0) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule1) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule2) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule3) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule4) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_1) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_2) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_3) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_4) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_5) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1all2) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1SetBreln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (choice2fnsingleton) =>
% 132.79/23.00 ((
% 132.79/23.00 (setOfPairsIsBReln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1all1) =>
% 132.79/23.00 ((
% 132.79/23.00 (subbreln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (eqbreln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1invprop) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1invI) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1invE) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compprop) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compI) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compE) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compEex) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionprop) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionIL) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionIR) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionI) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionE) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionEcases) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionCommutes) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2Ex) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2W) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2A) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2B) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1Ex) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1Ex1) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1Equiv) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1E) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1I) =>
% 132.79/23.00 ((
% 132.79/23.00 (injFuncInInjFuncSet) =>
% 132.79/23.00 ((
% 132.79/23.00 (injFuncSetFuncIn) =>
% 132.79/23.00 ((
% 132.79/23.00 (injFuncSetFuncInj) =>
% 132.79/23.00 ((
% 132.79/23.00 (surjFuncSetFuncIn) =>
% 132.79/23.00 ((
% 132.79/23.00 (surjFuncSetFuncSurj) =>
% 132.79/23.00 ((
% 132.79/23.00 (leftInvIsSurj) =>
% 132.79/23.00 ((
% 132.79/23.00 (surjCantorThm) =>
% 132.79/23.00 ((
% 132.79/23.00 (foundation2) =>
% 132.79/23.00 ((
% 132.79/23.00 (notinself) =>
% 132.79/23.00 ((
% 132.79/23.00 (notinself2) =>
% 132.79/23.00 ((
% 132.79/23.00 (omegaSp) =>
% 132.79/23.00 ((
% 132.79/23.00 (omegaSclos) =>
% 132.79/23.00 ((
% 132.79/23.00 (peano0notS) =>
% 132.79/23.00 ((
% 132.79/23.00 (peanoSinj) =>
% 132.79/23.00 ((
% 132.79/23.00 (transitivesetOp1) =>
% 132.79/23.00 ((
% 132.79/23.00 (binintTransitive) =>
% 132.79/23.00 ((
% 132.79/23.00 (transitivesetOp2) =>
% 132.79/23.00 ((
% 132.79/23.00 (setunionTransitive) =>
% 132.79/23.00 ((
% 132.79/23.00 (ordinalMinLem1) =>
% 132.79/23.00 ((
% 132.79/23.00 (ordinalTransSet) =>
% 132.79/23.00 ((
% 132.79/23.00 (ordinalTransSet1) =>
% 132.79/23.00 ((
% 132.79/23.00 (setunionOrdinalLem1) =>
% 132.79/23.00 (ordinal @
% 132.79/23.00 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/23.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2103])).
% 132.79/23.00 thf(zip_derived_cl2121, plain,
% 132.79/23.00 (~ (((complementT_lem) =>
% 132.79/23.00 (((setextT) =>
% 132.79/23.00 (((subsetTI) =>
% 132.79/23.00 (((powersetTI1) =>
% 132.79/23.00 (((powersetTE1) =>
% 132.79/23.00 (((complementTI1) =>
% 132.79/23.00 (((complementTE1) =>
% 132.79/23.00 (((binintersectTELcontra) =>
% 132.79/23.00 (((binintersectTERcontra) =>
% 132.79/23.00 (((contrasubsetT) =>
% 132.79/23.00 (((contrasubsetT1) =>
% 132.79/23.00 (((contrasubsetT2) =>
% 132.79/23.00 (((contrasubsetT3) =>
% 132.79/23.00 (((doubleComplementI1) =>
% 132.79/23.00 (((doubleComplementE1) =>
% 132.79/23.00 (((doubleComplementSub1) =>
% 132.79/23.00 (((doubleComplementSub2) =>
% 132.79/23.00 (((doubleComplementEq) =>
% 132.79/23.00 (((complementTnotintersectT) =>
% 132.79/23.00 (((complementImpComplementIntersect) =>
% 132.79/23.00 (((complementSubsetComplementIntersect) =>
% 132.79/23.00 (((complementInPowersetComplementIntersect) =>
% 132.79/23.00 (((contraSubsetComplement) =>
% 132.79/23.00 (((complementTcontraSubset) =>
% 132.79/23.00 (((binunionTILcontra) =>
% 132.79/23.00 (((binunionTIRcontra) =>
% 132.79/23.00 (((inIntersectImpInUnion) =>
% 132.79/23.00 (((inIntersectImpInUnion2) =>
% 132.79/23.00 (((inIntersectImpInIntersectUnions) =>
% 132.79/23.00 (((intersectInPowersetIntersectUnions) =>
% 132.79/23.00 ((
% 132.79/23.00 (inComplementUnionImpNotIn1) =>
% 132.79/23.00 ((
% 132.79/23.00 (inComplementUnionImpInComplement1) =>
% 132.79/23.00 ((
% 132.79/23.00 (binunionTE) =>
% 132.79/23.00 ((
% 132.79/23.00 (binunionTEcontra) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2a1) =>
% 132.79/23.00 ((
% 132.79/23.00 (complementUnionInPowersetComplement) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2a2) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan1a) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan1b) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan1) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2a) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2b2) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2b) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule0) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule1) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule2) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule3) =>
% 132.79/23.00 ((
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% 132.79/23.00 ((
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% 132.79/23.00 ((
% 132.79/23.00 (woz1_2) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_3) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_4) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_5) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1all2) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1SetBreln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (choice2fnsingleton) =>
% 132.79/23.00 ((
% 132.79/23.00 (setOfPairsIsBReln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1all1) =>
% 132.79/23.00 ((
% 132.79/23.00 (subbreln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (eqbreln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1invprop) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1invI) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1invE) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compprop) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compI) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compE) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compEex) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionprop) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionIL) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionIR) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionI) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionE) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionEcases) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionCommutes) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2Ex) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2W) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2A) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2B) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1Ex) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1Ex1) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1Equiv) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1E) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1I) =>
% 132.79/23.00 ((
% 132.79/23.00 (injFuncInInjFuncSet) =>
% 132.79/23.00 ((
% 132.79/23.00 (injFuncSetFuncIn) =>
% 132.79/23.00 ((
% 132.79/23.00 (injFuncSetFuncInj) =>
% 132.79/23.00 ((
% 132.79/23.00 (surjFuncSetFuncIn) =>
% 132.79/23.00 ((
% 132.79/23.00 (surjFuncSetFuncSurj) =>
% 132.79/23.00 ((
% 132.79/23.00 (leftInvIsSurj) =>
% 132.79/23.00 ((
% 132.79/23.00 (surjCantorThm) =>
% 132.79/23.00 ((
% 132.79/23.00 (foundation2) =>
% 132.79/23.00 ((
% 132.79/23.00 (notinself) =>
% 132.79/23.00 ((
% 132.79/23.00 (notinself2) =>
% 132.79/23.00 ((
% 132.79/23.00 (omegaSp) =>
% 132.79/23.00 ((
% 132.79/23.00 (omegaSclos) =>
% 132.79/23.00 ((
% 132.79/23.00 (peano0notS) =>
% 132.79/23.00 ((
% 132.79/23.00 (peanoSinj) =>
% 132.79/23.00 ((
% 132.79/23.00 (transitivesetOp1) =>
% 132.79/23.00 ((
% 132.79/23.00 (binintTransitive) =>
% 132.79/23.00 ((
% 132.79/23.00 (transitivesetOp2) =>
% 132.79/23.00 ((
% 132.79/23.00 (setunionTransitive) =>
% 132.79/23.00 ((
% 132.79/23.00 (ordinalMinLem1) =>
% 132.79/23.00 ((
% 132.79/23.00 (ordinalTransSet) =>
% 132.79/23.00 ((
% 132.79/23.00 (ordinalTransSet1) =>
% 132.79/23.00 ((
% 132.79/23.00 (setunionOrdinalLem1) =>
% 132.79/23.00 (ordinal @
% 132.79/23.00 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/23.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2113])).
% 132.79/23.00 thf(zip_derived_cl2130, plain,
% 132.79/23.00 (~ (((setextT) =>
% 132.79/23.00 (((subsetTI) =>
% 132.79/23.00 (((powersetTI1) =>
% 132.79/23.00 (((powersetTE1) =>
% 132.79/23.00 (((complementTI1) =>
% 132.79/23.00 (((complementTE1) =>
% 132.79/23.00 (((binintersectTELcontra) =>
% 132.79/23.00 (((binintersectTERcontra) =>
% 132.79/23.00 (((contrasubsetT) =>
% 132.79/23.00 (((contrasubsetT1) =>
% 132.79/23.00 (((contrasubsetT2) =>
% 132.79/23.00 (((contrasubsetT3) =>
% 132.79/23.00 (((doubleComplementI1) =>
% 132.79/23.00 (((doubleComplementE1) =>
% 132.79/23.00 (((doubleComplementSub1) =>
% 132.79/23.00 (((doubleComplementSub2) =>
% 132.79/23.00 (((doubleComplementEq) =>
% 132.79/23.00 (((complementTnotintersectT) =>
% 132.79/23.00 (((complementImpComplementIntersect) =>
% 132.79/23.00 (((complementSubsetComplementIntersect) =>
% 132.79/23.00 (((complementInPowersetComplementIntersect) =>
% 132.79/23.00 (((contraSubsetComplement) =>
% 132.79/23.00 (((complementTcontraSubset) =>
% 132.79/23.00 (((binunionTILcontra) =>
% 132.79/23.00 (((binunionTIRcontra) =>
% 132.79/23.00 (((inIntersectImpInUnion) =>
% 132.79/23.00 (((inIntersectImpInUnion2) =>
% 132.79/23.00 (((inIntersectImpInIntersectUnions) =>
% 132.79/23.00 (((intersectInPowersetIntersectUnions) =>
% 132.79/23.00 (((inComplementUnionImpNotIn1) =>
% 132.79/23.00 ((
% 132.79/23.00 (inComplementUnionImpInComplement1) =>
% 132.79/23.00 ((
% 132.79/23.00 (binunionTE) =>
% 132.79/23.00 ((
% 132.79/23.00 (binunionTEcontra) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2a1) =>
% 132.79/23.00 ((
% 132.79/23.00 (complementUnionInPowersetComplement) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2a2) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan1a) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan1b) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan1) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2a) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2b2) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2b) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule0) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule1) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule2) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule3) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule4) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_1) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_2) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_3) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_4) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_5) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1all2) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1SetBreln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (choice2fnsingleton) =>
% 132.79/23.00 ((
% 132.79/23.00 (setOfPairsIsBReln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1all1) =>
% 132.79/23.00 ((
% 132.79/23.00 (subbreln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (eqbreln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1invprop) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1invI) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1invE) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compprop) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compI) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compE) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compEex) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionprop) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionIL) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionIR) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionI) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionE) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionEcases) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionCommutes) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2Ex) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2W) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2A) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2B) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1Ex) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1Ex1) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1Equiv) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1E) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1I) =>
% 132.79/23.00 ((
% 132.79/23.00 (injFuncInInjFuncSet) =>
% 132.79/23.00 ((
% 132.79/23.00 (injFuncSetFuncIn) =>
% 132.79/23.00 ((
% 132.79/23.00 (injFuncSetFuncInj) =>
% 132.79/23.00 ((
% 132.79/23.00 (surjFuncSetFuncIn) =>
% 132.79/23.00 ((
% 132.79/23.00 (surjFuncSetFuncSurj) =>
% 132.79/23.00 ((
% 132.79/23.00 (leftInvIsSurj) =>
% 132.79/23.00 ((
% 132.79/23.00 (surjCantorThm) =>
% 132.79/23.00 ((
% 132.79/23.00 (foundation2) =>
% 132.79/23.00 ((
% 132.79/23.00 (notinself) =>
% 132.79/23.00 ((
% 132.79/23.00 (notinself2) =>
% 132.79/23.00 ((
% 132.79/23.00 (omegaSp) =>
% 132.79/23.00 ((
% 132.79/23.00 (omegaSclos) =>
% 132.79/23.00 ((
% 132.79/23.00 (peano0notS) =>
% 132.79/23.00 ((
% 132.79/23.00 (peanoSinj) =>
% 132.79/23.00 ((
% 132.79/23.00 (transitivesetOp1) =>
% 132.79/23.00 ((
% 132.79/23.00 (binintTransitive) =>
% 132.79/23.00 ((
% 132.79/23.00 (transitivesetOp2) =>
% 132.79/23.00 ((
% 132.79/23.00 (setunionTransitive) =>
% 132.79/23.00 ((
% 132.79/23.00 (ordinalMinLem1) =>
% 132.79/23.00 ((
% 132.79/23.00 (ordinalTransSet) =>
% 132.79/23.00 ((
% 132.79/23.00 (ordinalTransSet1) =>
% 132.79/23.00 ((
% 132.79/23.00 (setunionOrdinalLem1) =>
% 132.79/23.00 (ordinal @
% 132.79/23.00 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/23.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2121])).
% 132.79/23.00 thf(zip_derived_cl2140, plain,
% 132.79/23.00 (~ (((subsetTI) =>
% 132.79/23.00 (((powersetTI1) =>
% 132.79/23.00 (((powersetTE1) =>
% 132.79/23.00 (((complementTI1) =>
% 132.79/23.00 (((complementTE1) =>
% 132.79/23.00 (((binintersectTELcontra) =>
% 132.79/23.00 (((binintersectTERcontra) =>
% 132.79/23.00 (((contrasubsetT) =>
% 132.79/23.00 (((contrasubsetT1) =>
% 132.79/23.00 (((contrasubsetT2) =>
% 132.79/23.00 (((contrasubsetT3) =>
% 132.79/23.00 (((doubleComplementI1) =>
% 132.79/23.00 (((doubleComplementE1) =>
% 132.79/23.00 (((doubleComplementSub1) =>
% 132.79/23.00 (((doubleComplementSub2) =>
% 132.79/23.00 (((doubleComplementEq) =>
% 132.79/23.00 (((complementTnotintersectT) =>
% 132.79/23.00 (((complementImpComplementIntersect) =>
% 132.79/23.00 (((complementSubsetComplementIntersect) =>
% 132.79/23.00 (((complementInPowersetComplementIntersect) =>
% 132.79/23.00 (((contraSubsetComplement) =>
% 132.79/23.00 (((complementTcontraSubset) =>
% 132.79/23.00 (((binunionTILcontra) =>
% 132.79/23.00 (((binunionTIRcontra) =>
% 132.79/23.00 (((inIntersectImpInUnion) =>
% 132.79/23.00 (((inIntersectImpInUnion2) =>
% 132.79/23.00 (((inIntersectImpInIntersectUnions) =>
% 132.79/23.00 (((intersectInPowersetIntersectUnions) =>
% 132.79/23.00 (((inComplementUnionImpNotIn1) =>
% 132.79/23.00 (((inComplementUnionImpInComplement1) =>
% 132.79/23.00 ((
% 132.79/23.00 (binunionTE) =>
% 132.79/23.00 ((
% 132.79/23.00 (binunionTEcontra) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2a1) =>
% 132.79/23.00 ((
% 132.79/23.00 (complementUnionInPowersetComplement) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2a2) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan1a) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan1b) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan1) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2a) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2b2) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2b) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule0) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule1) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule2) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule3) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule4) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_1) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_2) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_3) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_4) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_5) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1all2) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1SetBreln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (choice2fnsingleton) =>
% 132.79/23.00 ((
% 132.79/23.00 (setOfPairsIsBReln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1all1) =>
% 132.79/23.00 ((
% 132.79/23.00 (subbreln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (eqbreln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1invprop) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1invI) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1invE) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compprop) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compI) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compE) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compEex) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionprop) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionIL) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionIR) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionI) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionE) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionEcases) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionCommutes) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2Ex) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2W) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2A) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2B) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1Ex) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1Ex1) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1Equiv) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1E) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1I) =>
% 132.79/23.00 ((
% 132.79/23.00 (injFuncInInjFuncSet) =>
% 132.79/23.00 ((
% 132.79/23.00 (injFuncSetFuncIn) =>
% 132.79/23.00 ((
% 132.79/23.00 (injFuncSetFuncInj) =>
% 132.79/23.00 ((
% 132.79/23.00 (surjFuncSetFuncIn) =>
% 132.79/23.00 ((
% 132.79/23.00 (surjFuncSetFuncSurj) =>
% 132.79/23.00 ((
% 132.79/23.00 (leftInvIsSurj) =>
% 132.79/23.00 ((
% 132.79/23.00 (surjCantorThm) =>
% 132.79/23.00 ((
% 132.79/23.00 (foundation2) =>
% 132.79/23.00 ((
% 132.79/23.00 (notinself) =>
% 132.79/23.00 ((
% 132.79/23.00 (notinself2) =>
% 132.79/23.00 ((
% 132.79/23.00 (omegaSp) =>
% 132.79/23.00 ((
% 132.79/23.00 (omegaSclos) =>
% 132.79/23.00 ((
% 132.79/23.00 (peano0notS) =>
% 132.79/23.00 ((
% 132.79/23.00 (peanoSinj) =>
% 132.79/23.00 ((
% 132.79/23.00 (transitivesetOp1) =>
% 132.79/23.00 ((
% 132.79/23.00 (binintTransitive) =>
% 132.79/23.00 ((
% 132.79/23.00 (transitivesetOp2) =>
% 132.79/23.00 ((
% 132.79/23.00 (setunionTransitive) =>
% 132.79/23.00 ((
% 132.79/23.00 (ordinalMinLem1) =>
% 132.79/23.00 ((
% 132.79/23.00 (ordinalTransSet) =>
% 132.79/23.00 ((
% 132.79/23.00 (ordinalTransSet1) =>
% 132.79/23.00 ((
% 132.79/23.00 (setunionOrdinalLem1) =>
% 132.79/23.00 (ordinal @
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% 132.79/23.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2130])).
% 132.79/23.00 thf(zip_derived_cl2151, plain,
% 132.79/23.00 (~ (((powersetTI1) =>
% 132.79/23.00 (((powersetTE1) =>
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% 132.79/23.00 (((complementTE1) =>
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% 132.79/23.00 (((binintersectTERcontra) =>
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% 132.79/23.00 (((contrasubsetT1) =>
% 132.79/23.00 (((contrasubsetT2) =>
% 132.79/23.00 (((contrasubsetT3) =>
% 132.79/23.00 (((doubleComplementI1) =>
% 132.79/23.00 (((doubleComplementE1) =>
% 132.79/23.00 (((doubleComplementSub1) =>
% 132.79/23.00 (((doubleComplementSub2) =>
% 132.79/23.00 (((doubleComplementEq) =>
% 132.79/23.00 (((complementTnotintersectT) =>
% 132.79/23.00 (((complementImpComplementIntersect) =>
% 132.79/23.00 (((complementSubsetComplementIntersect) =>
% 132.79/23.00 (((complementInPowersetComplementIntersect) =>
% 132.79/23.00 (((contraSubsetComplement) =>
% 132.79/23.00 (((complementTcontraSubset) =>
% 132.79/23.00 (((binunionTILcontra) =>
% 132.79/23.00 (((binunionTIRcontra) =>
% 132.79/23.00 (((inIntersectImpInUnion) =>
% 132.79/23.00 (((inIntersectImpInUnion2) =>
% 132.79/23.00 (((inIntersectImpInIntersectUnions) =>
% 132.79/23.00 (((intersectInPowersetIntersectUnions) =>
% 132.79/23.00 (((inComplementUnionImpNotIn1) =>
% 132.79/23.00 (((inComplementUnionImpInComplement1) =>
% 132.79/23.00 (((binunionTE) =>
% 132.79/23.00 ((
% 132.79/23.00 (binunionTEcontra) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2a1) =>
% 132.79/23.00 ((
% 132.79/23.00 (complementUnionInPowersetComplement) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2a2) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan1a) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan1b) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan1) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2a) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2b2) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2b) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule0) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule1) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule2) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule3) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule4) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_1) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_2) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_3) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_4) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_5) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1all2) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1SetBreln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (choice2fnsingleton) =>
% 132.79/23.00 ((
% 132.79/23.00 (setOfPairsIsBReln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1all1) =>
% 132.79/23.00 ((
% 132.79/23.00 (subbreln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (eqbreln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1invprop) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1invI) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1invE) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compprop) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compI) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compE) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compEex) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionprop) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionIL) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionIR) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionI) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionE) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionEcases) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionCommutes) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2Ex) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2W) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2A) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2B) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1Ex) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1Ex1) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1Equiv) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1E) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1I) =>
% 132.79/23.00 ((
% 132.79/23.00 (injFuncInInjFuncSet) =>
% 132.79/23.00 ((
% 132.79/23.00 (injFuncSetFuncIn) =>
% 132.79/23.00 ((
% 132.79/23.00 (injFuncSetFuncInj) =>
% 132.79/23.00 ((
% 132.79/23.00 (surjFuncSetFuncIn) =>
% 132.79/23.00 ((
% 132.79/23.00 (surjFuncSetFuncSurj) =>
% 132.79/23.00 ((
% 132.79/23.00 (leftInvIsSurj) =>
% 132.79/23.00 ((
% 132.79/23.00 (surjCantorThm) =>
% 132.79/23.00 ((
% 132.79/23.00 (foundation2) =>
% 132.79/23.00 ((
% 132.79/23.00 (notinself) =>
% 132.79/23.00 ((
% 132.79/23.00 (notinself2) =>
% 132.79/23.00 ((
% 132.79/23.00 (omegaSp) =>
% 132.79/23.00 ((
% 132.79/23.00 (omegaSclos) =>
% 132.79/23.00 ((
% 132.79/23.00 (peano0notS) =>
% 132.79/23.00 ((
% 132.79/23.00 (peanoSinj) =>
% 132.79/23.00 ((
% 132.79/23.00 (transitivesetOp1) =>
% 132.79/23.00 ((
% 132.79/23.00 (binintTransitive) =>
% 132.79/23.00 ((
% 132.79/23.00 (transitivesetOp2) =>
% 132.79/23.00 ((
% 132.79/23.00 (setunionTransitive) =>
% 132.79/23.00 ((
% 132.79/23.00 (ordinalMinLem1) =>
% 132.79/23.00 ((
% 132.79/23.00 (ordinalTransSet) =>
% 132.79/23.00 ((
% 132.79/23.00 (ordinalTransSet1) =>
% 132.79/23.00 ((
% 132.79/23.00 (setunionOrdinalLem1) =>
% 132.79/23.00 (ordinal @
% 132.79/23.00 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/23.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2140])).
% 132.79/23.00 thf(zip_derived_cl2159, plain,
% 132.79/23.00 (~ (((powersetTE1) =>
% 132.79/23.00 (((complementTI1) =>
% 132.79/23.00 (((complementTE1) =>
% 132.79/23.00 (((binintersectTELcontra) =>
% 132.79/23.00 (((binintersectTERcontra) =>
% 132.79/23.00 (((contrasubsetT) =>
% 132.79/23.00 (((contrasubsetT1) =>
% 132.79/23.00 (((contrasubsetT2) =>
% 132.79/23.00 (((contrasubsetT3) =>
% 132.79/23.00 (((doubleComplementI1) =>
% 132.79/23.00 (((doubleComplementE1) =>
% 132.79/23.00 (((doubleComplementSub1) =>
% 132.79/23.00 (((doubleComplementSub2) =>
% 132.79/23.00 (((doubleComplementEq) =>
% 132.79/23.00 (((complementTnotintersectT) =>
% 132.79/23.00 (((complementImpComplementIntersect) =>
% 132.79/23.00 (((complementSubsetComplementIntersect) =>
% 132.79/23.00 (((complementInPowersetComplementIntersect) =>
% 132.79/23.00 (((contraSubsetComplement) =>
% 132.79/23.00 (((complementTcontraSubset) =>
% 132.79/23.00 (((binunionTILcontra) =>
% 132.79/23.00 (((binunionTIRcontra) =>
% 132.79/23.00 (((inIntersectImpInUnion) =>
% 132.79/23.00 (((inIntersectImpInUnion2) =>
% 132.79/23.00 (((inIntersectImpInIntersectUnions) =>
% 132.79/23.00 (((intersectInPowersetIntersectUnions) =>
% 132.79/23.00 (((inComplementUnionImpNotIn1) =>
% 132.79/23.00 (((inComplementUnionImpInComplement1) =>
% 132.79/23.00 (((binunionTE) =>
% 132.79/23.00 (((binunionTEcontra) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2a1) =>
% 132.79/23.00 ((
% 132.79/23.00 (complementUnionInPowersetComplement) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2a2) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan1a) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan1b) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan1) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2a) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2b2) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2b) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule0) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule1) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule2) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule3) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule4) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_1) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_2) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_3) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_4) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_5) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1all2) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1SetBreln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (choice2fnsingleton) =>
% 132.79/23.00 ((
% 132.79/23.00 (setOfPairsIsBReln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1all1) =>
% 132.79/23.00 ((
% 132.79/23.00 (subbreln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (eqbreln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1invprop) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1invI) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1invE) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compprop) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compI) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compE) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compEex) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionprop) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionIL) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionIR) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionI) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionE) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionEcases) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionCommutes) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2Ex) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2W) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2A) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2B) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1Ex) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1Ex1) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1Equiv) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1E) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1I) =>
% 132.79/23.00 ((
% 132.79/23.00 (injFuncInInjFuncSet) =>
% 132.79/23.00 ((
% 132.79/23.00 (injFuncSetFuncIn) =>
% 132.79/23.00 ((
% 132.79/23.00 (injFuncSetFuncInj) =>
% 132.79/23.00 ((
% 132.79/23.00 (surjFuncSetFuncIn) =>
% 132.79/23.00 ((
% 132.79/23.00 (surjFuncSetFuncSurj) =>
% 132.79/23.00 ((
% 132.79/23.00 (leftInvIsSurj) =>
% 132.79/23.00 ((
% 132.79/23.00 (surjCantorThm) =>
% 132.79/23.00 ((
% 132.79/23.00 (foundation2) =>
% 132.79/23.00 ((
% 132.79/23.00 (notinself) =>
% 132.79/23.00 ((
% 132.79/23.00 (notinself2) =>
% 132.79/23.00 ((
% 132.79/23.00 (omegaSp) =>
% 132.79/23.00 ((
% 132.79/23.00 (omegaSclos) =>
% 132.79/23.00 ((
% 132.79/23.00 (peano0notS) =>
% 132.79/23.00 ((
% 132.79/23.00 (peanoSinj) =>
% 132.79/23.00 ((
% 132.79/23.00 (transitivesetOp1) =>
% 132.79/23.00 ((
% 132.79/23.00 (binintTransitive) =>
% 132.79/23.00 ((
% 132.79/23.00 (transitivesetOp2) =>
% 132.79/23.00 ((
% 132.79/23.00 (setunionTransitive) =>
% 132.79/23.00 ((
% 132.79/23.00 (ordinalMinLem1) =>
% 132.79/23.00 ((
% 132.79/23.00 (ordinalTransSet) =>
% 132.79/23.00 ((
% 132.79/23.00 (ordinalTransSet1) =>
% 132.79/23.00 ((
% 132.79/23.00 (setunionOrdinalLem1) =>
% 132.79/23.00 (ordinal @
% 132.79/23.00 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/23.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2151])).
% 132.79/23.00 thf(zip_derived_cl2166, plain,
% 132.79/23.00 (~ (((complementTI1) =>
% 132.79/23.00 (((complementTE1) =>
% 132.79/23.00 (((binintersectTELcontra) =>
% 132.79/23.00 (((binintersectTERcontra) =>
% 132.79/23.00 (((contrasubsetT) =>
% 132.79/23.00 (((contrasubsetT1) =>
% 132.79/23.00 (((contrasubsetT2) =>
% 132.79/23.00 (((contrasubsetT3) =>
% 132.79/23.00 (((doubleComplementI1) =>
% 132.79/23.00 (((doubleComplementE1) =>
% 132.79/23.00 (((doubleComplementSub1) =>
% 132.79/23.00 (((doubleComplementSub2) =>
% 132.79/23.00 (((doubleComplementEq) =>
% 132.79/23.00 (((complementTnotintersectT) =>
% 132.79/23.00 (((complementImpComplementIntersect) =>
% 132.79/23.00 (((complementSubsetComplementIntersect) =>
% 132.79/23.00 (((complementInPowersetComplementIntersect) =>
% 132.79/23.00 (((contraSubsetComplement) =>
% 132.79/23.00 (((complementTcontraSubset) =>
% 132.79/23.00 (((binunionTILcontra) =>
% 132.79/23.00 (((binunionTIRcontra) =>
% 132.79/23.00 (((inIntersectImpInUnion) =>
% 132.79/23.00 (((inIntersectImpInUnion2) =>
% 132.79/23.00 (((inIntersectImpInIntersectUnions) =>
% 132.79/23.00 (((intersectInPowersetIntersectUnions) =>
% 132.79/23.00 (((inComplementUnionImpNotIn1) =>
% 132.79/23.00 (((inComplementUnionImpInComplement1) =>
% 132.79/23.00 (((binunionTE) =>
% 132.79/23.00 (((binunionTEcontra) =>
% 132.79/23.00 (((demorgan2a1) =>
% 132.79/23.00 ((
% 132.79/23.00 (complementUnionInPowersetComplement) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2a2) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan1a) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan1b) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan1) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2a) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2b2) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2b) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule0) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule1) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule2) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule3) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule4) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_1) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_2) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_3) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_4) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_5) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1all2) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1SetBreln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (choice2fnsingleton) =>
% 132.79/23.00 ((
% 132.79/23.00 (setOfPairsIsBReln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1all1) =>
% 132.79/23.00 ((
% 132.79/23.00 (subbreln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (eqbreln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1invprop) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1invI) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1invE) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compprop) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compI) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compE) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compEex) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionprop) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionIL) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionIR) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionI) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionE) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionEcases) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionCommutes) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2Ex) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2W) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2A) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2B) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1Ex) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1Ex1) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1Equiv) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1E) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1I) =>
% 132.79/23.00 ((
% 132.79/23.00 (injFuncInInjFuncSet) =>
% 132.79/23.00 ((
% 132.79/23.00 (injFuncSetFuncIn) =>
% 132.79/23.00 ((
% 132.79/23.00 (injFuncSetFuncInj) =>
% 132.79/23.00 ((
% 132.79/23.00 (surjFuncSetFuncIn) =>
% 132.79/23.00 ((
% 132.79/23.00 (surjFuncSetFuncSurj) =>
% 132.79/23.00 ((
% 132.79/23.00 (leftInvIsSurj) =>
% 132.79/23.00 ((
% 132.79/23.00 (surjCantorThm) =>
% 132.79/23.00 ((
% 132.79/23.00 (foundation2) =>
% 132.79/23.00 ((
% 132.79/23.00 (notinself) =>
% 132.79/23.00 ((
% 132.79/23.00 (notinself2) =>
% 132.79/23.00 ((
% 132.79/23.00 (omegaSp) =>
% 132.79/23.00 ((
% 132.79/23.00 (omegaSclos) =>
% 132.79/23.00 ((
% 132.79/23.00 (peano0notS) =>
% 132.79/23.00 ((
% 132.79/23.00 (peanoSinj) =>
% 132.79/23.00 ((
% 132.79/23.00 (transitivesetOp1) =>
% 132.79/23.00 ((
% 132.79/23.00 (binintTransitive) =>
% 132.79/23.00 ((
% 132.79/23.00 (transitivesetOp2) =>
% 132.79/23.00 ((
% 132.79/23.00 (setunionTransitive) =>
% 132.79/23.00 ((
% 132.79/23.00 (ordinalMinLem1) =>
% 132.79/23.00 ((
% 132.79/23.00 (ordinalTransSet) =>
% 132.79/23.00 ((
% 132.79/23.00 (ordinalTransSet1) =>
% 132.79/23.00 ((
% 132.79/23.00 (setunionOrdinalLem1) =>
% 132.79/23.00 (ordinal @
% 132.79/23.00 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/23.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2159])).
% 132.79/23.00 thf(zip_derived_cl2173, plain,
% 132.79/23.00 (~ (((complementTE1) =>
% 132.79/23.00 (((binintersectTELcontra) =>
% 132.79/23.00 (((binintersectTERcontra) =>
% 132.79/23.00 (((contrasubsetT) =>
% 132.79/23.00 (((contrasubsetT1) =>
% 132.79/23.00 (((contrasubsetT2) =>
% 132.79/23.00 (((contrasubsetT3) =>
% 132.79/23.00 (((doubleComplementI1) =>
% 132.79/23.00 (((doubleComplementE1) =>
% 132.79/23.00 (((doubleComplementSub1) =>
% 132.79/23.00 (((doubleComplementSub2) =>
% 132.79/23.00 (((doubleComplementEq) =>
% 132.79/23.00 (((complementTnotintersectT) =>
% 132.79/23.00 (((complementImpComplementIntersect) =>
% 132.79/23.00 (((complementSubsetComplementIntersect) =>
% 132.79/23.00 (((complementInPowersetComplementIntersect) =>
% 132.79/23.00 (((contraSubsetComplement) =>
% 132.79/23.00 (((complementTcontraSubset) =>
% 132.79/23.00 (((binunionTILcontra) =>
% 132.79/23.00 (((binunionTIRcontra) =>
% 132.79/23.00 (((inIntersectImpInUnion) =>
% 132.79/23.00 (((inIntersectImpInUnion2) =>
% 132.79/23.00 (((inIntersectImpInIntersectUnions) =>
% 132.79/23.00 (((intersectInPowersetIntersectUnions) =>
% 132.79/23.00 (((inComplementUnionImpNotIn1) =>
% 132.79/23.00 (((inComplementUnionImpInComplement1) =>
% 132.79/23.00 (((binunionTE) =>
% 132.79/23.00 (((binunionTEcontra) =>
% 132.79/23.00 (((demorgan2a1) =>
% 132.79/23.00 (((complementUnionInPowersetComplement) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2a2) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan1a) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan1b) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan1) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2a) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2b2) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2b) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule0) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule1) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule2) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule3) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule4) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_1) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_2) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_3) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_4) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_5) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1all2) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1SetBreln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (choice2fnsingleton) =>
% 132.79/23.00 ((
% 132.79/23.00 (setOfPairsIsBReln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1all1) =>
% 132.79/23.00 ((
% 132.79/23.00 (subbreln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (eqbreln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1invprop) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1invI) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1invE) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compprop) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compI) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compE) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compEex) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionprop) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionIL) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionIR) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionI) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionE) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionEcases) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionCommutes) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2Ex) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2W) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2A) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2B) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1Ex) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1Ex1) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1Equiv) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1E) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1I) =>
% 132.79/23.00 ((
% 132.79/23.00 (injFuncInInjFuncSet) =>
% 132.79/23.00 ((
% 132.79/23.00 (injFuncSetFuncIn) =>
% 132.79/23.00 ((
% 132.79/23.00 (injFuncSetFuncInj) =>
% 132.79/23.00 ((
% 132.79/23.00 (surjFuncSetFuncIn) =>
% 132.79/23.00 ((
% 132.79/23.00 (surjFuncSetFuncSurj) =>
% 132.79/23.00 ((
% 132.79/23.00 (leftInvIsSurj) =>
% 132.79/23.00 ((
% 132.79/23.00 (surjCantorThm) =>
% 132.79/23.00 ((
% 132.79/23.00 (foundation2) =>
% 132.79/23.00 ((
% 132.79/23.00 (notinself) =>
% 132.79/23.00 ((
% 132.79/23.00 (notinself2) =>
% 132.79/23.00 ((
% 132.79/23.00 (omegaSp) =>
% 132.79/23.00 ((
% 132.79/23.00 (omegaSclos) =>
% 132.79/23.00 ((
% 132.79/23.00 (peano0notS) =>
% 132.79/23.00 ((
% 132.79/23.00 (peanoSinj) =>
% 132.79/23.00 ((
% 132.79/23.00 (transitivesetOp1) =>
% 132.79/23.00 ((
% 132.79/23.00 (binintTransitive) =>
% 132.79/23.00 ((
% 132.79/23.00 (transitivesetOp2) =>
% 132.79/23.00 ((
% 132.79/23.00 (setunionTransitive) =>
% 132.79/23.00 ((
% 132.79/23.00 (ordinalMinLem1) =>
% 132.79/23.00 ((
% 132.79/23.00 (ordinalTransSet) =>
% 132.79/23.00 ((
% 132.79/23.00 (ordinalTransSet1) =>
% 132.79/23.00 ((
% 132.79/23.00 (setunionOrdinalLem1) =>
% 132.79/23.00 (ordinal @
% 132.79/23.00 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/23.00 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2166])).
% 132.79/23.00 thf(zip_derived_cl2180, plain,
% 132.79/23.00 (~ (((binintersectTELcontra) =>
% 132.79/23.00 (((binintersectTERcontra) =>
% 132.79/23.00 (((contrasubsetT) =>
% 132.79/23.00 (((contrasubsetT1) =>
% 132.79/23.00 (((contrasubsetT2) =>
% 132.79/23.00 (((contrasubsetT3) =>
% 132.79/23.00 (((doubleComplementI1) =>
% 132.79/23.00 (((doubleComplementE1) =>
% 132.79/23.00 (((doubleComplementSub1) =>
% 132.79/23.00 (((doubleComplementSub2) =>
% 132.79/23.00 (((doubleComplementEq) =>
% 132.79/23.00 (((complementTnotintersectT) =>
% 132.79/23.00 (((complementImpComplementIntersect) =>
% 132.79/23.00 (((complementSubsetComplementIntersect) =>
% 132.79/23.00 (((complementInPowersetComplementIntersect) =>
% 132.79/23.00 (((contraSubsetComplement) =>
% 132.79/23.00 (((complementTcontraSubset) =>
% 132.79/23.00 (((binunionTILcontra) =>
% 132.79/23.00 (((binunionTIRcontra) =>
% 132.79/23.00 (((inIntersectImpInUnion) =>
% 132.79/23.00 (((inIntersectImpInUnion2) =>
% 132.79/23.00 (((inIntersectImpInIntersectUnions) =>
% 132.79/23.00 (((intersectInPowersetIntersectUnions) =>
% 132.79/23.00 (((inComplementUnionImpNotIn1) =>
% 132.79/23.00 (((inComplementUnionImpInComplement1) =>
% 132.79/23.00 (((binunionTE) =>
% 132.79/23.00 (((binunionTEcontra) =>
% 132.79/23.00 (((demorgan2a1) =>
% 132.79/23.00 (((complementUnionInPowersetComplement) =>
% 132.79/23.00 (((demorgan2a2) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan1a) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan1b) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan1) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2a) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2b2) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2b) =>
% 132.79/23.00 ((
% 132.79/23.00 (demorgan2) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule0) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule1) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule2) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule3) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz13rule4) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_1) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_2) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_3) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_4) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz1_5) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1all2) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1SetBreln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (choice2fnsingleton) =>
% 132.79/23.00 ((
% 132.79/23.00 (setOfPairsIsBReln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1all1) =>
% 132.79/23.00 ((
% 132.79/23.00 (subbreln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (eqbreln1) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1invprop) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1invI) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1invE) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compprop) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compI) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compE) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1compEex) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionprop) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionIL) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionIR) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionI) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionE) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionEcases) =>
% 132.79/23.00 ((
% 132.79/23.00 (breln1unionCommutes) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2Ex) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2W) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2A) =>
% 132.79/23.00 ((
% 132.79/23.00 (woz2B) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1Ex) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1Ex1) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1Equiv) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1E) =>
% 132.79/23.00 ((
% 132.79/23.00 (image1I) =>
% 132.79/23.00 ((
% 132.79/23.00 (injFuncInInjFuncSet) =>
% 132.79/23.00 ((
% 132.79/23.00 (injFuncSetFuncIn) =>
% 132.79/23.00 ((
% 132.79/23.00 (injFuncSetFuncInj) =>
% 132.79/23.00 ((
% 132.79/23.00 (surjFuncSetFuncIn) =>
% 132.79/23.00 ((
% 132.79/23.00 (surjFuncSetFuncSurj) =>
% 132.79/23.00 ((
% 132.79/23.00 (leftInvIsSurj) =>
% 132.79/23.00 ((
% 132.79/23.00 (surjCantorThm) =>
% 132.79/23.00 ((
% 132.79/23.00 (foundation2) =>
% 132.79/23.00 ((
% 132.79/23.00 (notinself) =>
% 132.79/23.00 ((
% 132.79/23.00 (notinself2) =>
% 132.79/23.00 ((
% 132.79/23.01 (omegaSp) =>
% 132.79/23.01 ((
% 132.79/23.01 (omegaSclos) =>
% 132.79/23.01 ((
% 132.79/23.01 (peano0notS) =>
% 132.79/23.01 ((
% 132.79/23.01 (peanoSinj) =>
% 132.79/23.01 ((
% 132.79/23.01 (transitivesetOp1) =>
% 132.79/23.01 ((
% 132.79/23.01 (binintTransitive) =>
% 132.79/23.01 ((
% 132.79/23.01 (transitivesetOp2) =>
% 132.79/23.01 ((
% 132.79/23.01 (setunionTransitive) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalMinLem1) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalTransSet) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalTransSet1) =>
% 132.79/23.01 ((
% 132.79/23.01 (setunionOrdinalLem1) =>
% 132.79/23.01 (ordinal @
% 132.79/23.01 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/23.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2173])).
% 132.79/23.01 thf(zip_derived_cl2188, plain,
% 132.79/23.01 (~ (((binintersectTERcontra) =>
% 132.79/23.01 (((contrasubsetT) =>
% 132.79/23.01 (((contrasubsetT1) =>
% 132.79/23.01 (((contrasubsetT2) =>
% 132.79/23.01 (((contrasubsetT3) =>
% 132.79/23.01 (((doubleComplementI1) =>
% 132.79/23.01 (((doubleComplementE1) =>
% 132.79/23.01 (((doubleComplementSub1) =>
% 132.79/23.01 (((doubleComplementSub2) =>
% 132.79/23.01 (((doubleComplementEq) =>
% 132.79/23.01 (((complementTnotintersectT) =>
% 132.79/23.01 (((complementImpComplementIntersect) =>
% 132.79/23.01 (((complementSubsetComplementIntersect) =>
% 132.79/23.01 (((complementInPowersetComplementIntersect) =>
% 132.79/23.01 (((contraSubsetComplement) =>
% 132.79/23.01 (((complementTcontraSubset) =>
% 132.79/23.01 (((binunionTILcontra) =>
% 132.79/23.01 (((binunionTIRcontra) =>
% 132.79/23.01 (((inIntersectImpInUnion) =>
% 132.79/23.01 (((inIntersectImpInUnion2) =>
% 132.79/23.01 (((inIntersectImpInIntersectUnions) =>
% 132.79/23.01 (((intersectInPowersetIntersectUnions) =>
% 132.79/23.01 (((inComplementUnionImpNotIn1) =>
% 132.79/23.01 (((inComplementUnionImpInComplement1) =>
% 132.79/23.01 (((binunionTE) =>
% 132.79/23.01 (((binunionTEcontra) =>
% 132.79/23.01 (((demorgan2a1) =>
% 132.79/23.01 (((complementUnionInPowersetComplement) =>
% 132.79/23.01 (((demorgan2a2) =>
% 132.79/23.01 (((demorgan1a) =>
% 132.79/23.01 ((
% 132.79/23.01 (demorgan1b) =>
% 132.79/23.01 ((
% 132.79/23.01 (demorgan1) =>
% 132.79/23.01 ((
% 132.79/23.01 (demorgan2a) =>
% 132.79/23.01 ((
% 132.79/23.01 (demorgan2b2) =>
% 132.79/23.01 ((
% 132.79/23.01 (demorgan2b) =>
% 132.79/23.01 ((
% 132.79/23.01 (demorgan2) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz13rule0) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz13rule1) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz13rule2) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz13rule3) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz13rule4) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz1_1) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz1_2) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz1_3) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz1_4) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz1_5) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1all2) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1SetBreln1) =>
% 132.79/23.01 ((
% 132.79/23.01 (choice2fnsingleton) =>
% 132.79/23.01 ((
% 132.79/23.01 (setOfPairsIsBReln1) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1all1) =>
% 132.79/23.01 ((
% 132.79/23.01 (subbreln1) =>
% 132.79/23.01 ((
% 132.79/23.01 (eqbreln1) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1invprop) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1invI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1invE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compprop) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compEex) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionprop) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionIL) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionIR) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionEcases) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionCommutes) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2Ex) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2W) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2A) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2B) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Ex) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Ex1) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Equiv) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1E) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1I) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncInInjFuncSet) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncSetFuncIn) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncSetFuncInj) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjFuncSetFuncIn) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjFuncSetFuncSurj) =>
% 132.79/23.01 ((
% 132.79/23.01 (leftInvIsSurj) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjCantorThm) =>
% 132.79/23.01 ((
% 132.79/23.01 (foundation2) =>
% 132.79/23.01 ((
% 132.79/23.01 (notinself) =>
% 132.79/23.01 ((
% 132.79/23.01 (notinself2) =>
% 132.79/23.01 ((
% 132.79/23.01 (omegaSp) =>
% 132.79/23.01 ((
% 132.79/23.01 (omegaSclos) =>
% 132.79/23.01 ((
% 132.79/23.01 (peano0notS) =>
% 132.79/23.01 ((
% 132.79/23.01 (peanoSinj) =>
% 132.79/23.01 ((
% 132.79/23.01 (transitivesetOp1) =>
% 132.79/23.01 ((
% 132.79/23.01 (binintTransitive) =>
% 132.79/23.01 ((
% 132.79/23.01 (transitivesetOp2) =>
% 132.79/23.01 ((
% 132.79/23.01 (setunionTransitive) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalMinLem1) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalTransSet) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalTransSet1) =>
% 132.79/23.01 ((
% 132.79/23.01 (setunionOrdinalLem1) =>
% 132.79/23.01 (ordinal @
% 132.79/23.01 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/23.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2180])).
% 132.79/23.01 thf(zip_derived_cl2197, plain,
% 132.79/23.01 (~ (((contrasubsetT) =>
% 132.79/23.01 (((contrasubsetT1) =>
% 132.79/23.01 (((contrasubsetT2) =>
% 132.79/23.01 (((contrasubsetT3) =>
% 132.79/23.01 (((doubleComplementI1) =>
% 132.79/23.01 (((doubleComplementE1) =>
% 132.79/23.01 (((doubleComplementSub1) =>
% 132.79/23.01 (((doubleComplementSub2) =>
% 132.79/23.01 (((doubleComplementEq) =>
% 132.79/23.01 (((complementTnotintersectT) =>
% 132.79/23.01 (((complementImpComplementIntersect) =>
% 132.79/23.01 (((complementSubsetComplementIntersect) =>
% 132.79/23.01 (((complementInPowersetComplementIntersect) =>
% 132.79/23.01 (((contraSubsetComplement) =>
% 132.79/23.01 (((complementTcontraSubset) =>
% 132.79/23.01 (((binunionTILcontra) =>
% 132.79/23.01 (((binunionTIRcontra) =>
% 132.79/23.01 (((inIntersectImpInUnion) =>
% 132.79/23.01 (((inIntersectImpInUnion2) =>
% 132.79/23.01 (((inIntersectImpInIntersectUnions) =>
% 132.79/23.01 (((intersectInPowersetIntersectUnions) =>
% 132.79/23.01 (((inComplementUnionImpNotIn1) =>
% 132.79/23.01 (((inComplementUnionImpInComplement1) =>
% 132.79/23.01 (((binunionTE) =>
% 132.79/23.01 (((binunionTEcontra) =>
% 132.79/23.01 (((demorgan2a1) =>
% 132.79/23.01 (((complementUnionInPowersetComplement) =>
% 132.79/23.01 (((demorgan2a2) =>
% 132.79/23.01 (((demorgan1a) =>
% 132.79/23.01 (((demorgan1b) =>
% 132.79/23.01 ((
% 132.79/23.01 (demorgan1) =>
% 132.79/23.01 ((
% 132.79/23.01 (demorgan2a) =>
% 132.79/23.01 ((
% 132.79/23.01 (demorgan2b2) =>
% 132.79/23.01 ((
% 132.79/23.01 (demorgan2b) =>
% 132.79/23.01 ((
% 132.79/23.01 (demorgan2) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz13rule0) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz13rule1) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz13rule2) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz13rule3) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz13rule4) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz1_1) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz1_2) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz1_3) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz1_4) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz1_5) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1all2) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1SetBreln1) =>
% 132.79/23.01 ((
% 132.79/23.01 (choice2fnsingleton) =>
% 132.79/23.01 ((
% 132.79/23.01 (setOfPairsIsBReln1) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1all1) =>
% 132.79/23.01 ((
% 132.79/23.01 (subbreln1) =>
% 132.79/23.01 ((
% 132.79/23.01 (eqbreln1) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1invprop) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1invI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1invE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compprop) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compEex) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionprop) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionIL) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionIR) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionEcases) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionCommutes) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2Ex) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2W) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2A) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2B) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Ex) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Ex1) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Equiv) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1E) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1I) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncInInjFuncSet) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncSetFuncIn) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncSetFuncInj) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjFuncSetFuncIn) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjFuncSetFuncSurj) =>
% 132.79/23.01 ((
% 132.79/23.01 (leftInvIsSurj) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjCantorThm) =>
% 132.79/23.01 ((
% 132.79/23.01 (foundation2) =>
% 132.79/23.01 ((
% 132.79/23.01 (notinself) =>
% 132.79/23.01 ((
% 132.79/23.01 (notinself2) =>
% 132.79/23.01 ((
% 132.79/23.01 (omegaSp) =>
% 132.79/23.01 ((
% 132.79/23.01 (omegaSclos) =>
% 132.79/23.01 ((
% 132.79/23.01 (peano0notS) =>
% 132.79/23.01 ((
% 132.79/23.01 (peanoSinj) =>
% 132.79/23.01 ((
% 132.79/23.01 (transitivesetOp1) =>
% 132.79/23.01 ((
% 132.79/23.01 (binintTransitive) =>
% 132.79/23.01 ((
% 132.79/23.01 (transitivesetOp2) =>
% 132.79/23.01 ((
% 132.79/23.01 (setunionTransitive) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalMinLem1) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalTransSet) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalTransSet1) =>
% 132.79/23.01 ((
% 132.79/23.01 (setunionOrdinalLem1) =>
% 132.79/23.01 (ordinal @
% 132.79/23.01 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/23.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2188])).
% 132.79/23.01 thf(zip_derived_cl2207, plain,
% 132.79/23.01 (~ (((contrasubsetT1) =>
% 132.79/23.01 (((contrasubsetT2) =>
% 132.79/23.01 (((contrasubsetT3) =>
% 132.79/23.01 (((doubleComplementI1) =>
% 132.79/23.01 (((doubleComplementE1) =>
% 132.79/23.01 (((doubleComplementSub1) =>
% 132.79/23.01 (((doubleComplementSub2) =>
% 132.79/23.01 (((doubleComplementEq) =>
% 132.79/23.01 (((complementTnotintersectT) =>
% 132.79/23.01 (((complementImpComplementIntersect) =>
% 132.79/23.01 (((complementSubsetComplementIntersect) =>
% 132.79/23.01 (((complementInPowersetComplementIntersect) =>
% 132.79/23.01 (((contraSubsetComplement) =>
% 132.79/23.01 (((complementTcontraSubset) =>
% 132.79/23.01 (((binunionTILcontra) =>
% 132.79/23.01 (((binunionTIRcontra) =>
% 132.79/23.01 (((inIntersectImpInUnion) =>
% 132.79/23.01 (((inIntersectImpInUnion2) =>
% 132.79/23.01 (((inIntersectImpInIntersectUnions) =>
% 132.79/23.01 (((intersectInPowersetIntersectUnions) =>
% 132.79/23.01 (((inComplementUnionImpNotIn1) =>
% 132.79/23.01 (((inComplementUnionImpInComplement1) =>
% 132.79/23.01 (((binunionTE) =>
% 132.79/23.01 (((binunionTEcontra) =>
% 132.79/23.01 (((demorgan2a1) =>
% 132.79/23.01 (((complementUnionInPowersetComplement) =>
% 132.79/23.01 (((demorgan2a2) =>
% 132.79/23.01 (((demorgan1a) =>
% 132.79/23.01 (((demorgan1b) =>
% 132.79/23.01 (((demorgan1) =>
% 132.79/23.01 ((
% 132.79/23.01 (demorgan2a) =>
% 132.79/23.01 ((
% 132.79/23.01 (demorgan2b2) =>
% 132.79/23.01 ((
% 132.79/23.01 (demorgan2b) =>
% 132.79/23.01 ((
% 132.79/23.01 (demorgan2) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz13rule0) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz13rule1) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz13rule2) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz13rule3) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz13rule4) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz1_1) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz1_2) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz1_3) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz1_4) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz1_5) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1all2) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1SetBreln1) =>
% 132.79/23.01 ((
% 132.79/23.01 (choice2fnsingleton) =>
% 132.79/23.01 ((
% 132.79/23.01 (setOfPairsIsBReln1) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1all1) =>
% 132.79/23.01 ((
% 132.79/23.01 (subbreln1) =>
% 132.79/23.01 ((
% 132.79/23.01 (eqbreln1) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1invprop) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1invI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1invE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compprop) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compEex) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionprop) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionIL) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionIR) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionEcases) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionCommutes) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2Ex) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2W) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2A) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2B) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Ex) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Ex1) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Equiv) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1E) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1I) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncInInjFuncSet) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncSetFuncIn) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncSetFuncInj) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjFuncSetFuncIn) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjFuncSetFuncSurj) =>
% 132.79/23.01 ((
% 132.79/23.01 (leftInvIsSurj) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjCantorThm) =>
% 132.79/23.01 ((
% 132.79/23.01 (foundation2) =>
% 132.79/23.01 ((
% 132.79/23.01 (notinself) =>
% 132.79/23.01 ((
% 132.79/23.01 (notinself2) =>
% 132.79/23.01 ((
% 132.79/23.01 (omegaSp) =>
% 132.79/23.01 ((
% 132.79/23.01 (omegaSclos) =>
% 132.79/23.01 ((
% 132.79/23.01 (peano0notS) =>
% 132.79/23.01 ((
% 132.79/23.01 (peanoSinj) =>
% 132.79/23.01 ((
% 132.79/23.01 (transitivesetOp1) =>
% 132.79/23.01 ((
% 132.79/23.01 (binintTransitive) =>
% 132.79/23.01 ((
% 132.79/23.01 (transitivesetOp2) =>
% 132.79/23.01 ((
% 132.79/23.01 (setunionTransitive) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalMinLem1) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalTransSet) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalTransSet1) =>
% 132.79/23.01 ((
% 132.79/23.01 (setunionOrdinalLem1) =>
% 132.79/23.01 (ordinal @
% 132.79/23.01 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/23.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2197])).
% 132.79/23.01 thf(zip_derived_cl2219, plain,
% 132.79/23.01 (~ (((contrasubsetT2) =>
% 132.79/23.01 (((contrasubsetT3) =>
% 132.79/23.01 (((doubleComplementI1) =>
% 132.79/23.01 (((doubleComplementE1) =>
% 132.79/23.01 (((doubleComplementSub1) =>
% 132.79/23.01 (((doubleComplementSub2) =>
% 132.79/23.01 (((doubleComplementEq) =>
% 132.79/23.01 (((complementTnotintersectT) =>
% 132.79/23.01 (((complementImpComplementIntersect) =>
% 132.79/23.01 (((complementSubsetComplementIntersect) =>
% 132.79/23.01 (((complementInPowersetComplementIntersect) =>
% 132.79/23.01 (((contraSubsetComplement) =>
% 132.79/23.01 (((complementTcontraSubset) =>
% 132.79/23.01 (((binunionTILcontra) =>
% 132.79/23.01 (((binunionTIRcontra) =>
% 132.79/23.01 (((inIntersectImpInUnion) =>
% 132.79/23.01 (((inIntersectImpInUnion2) =>
% 132.79/23.01 (((inIntersectImpInIntersectUnions) =>
% 132.79/23.01 (((intersectInPowersetIntersectUnions) =>
% 132.79/23.01 (((inComplementUnionImpNotIn1) =>
% 132.79/23.01 (((inComplementUnionImpInComplement1) =>
% 132.79/23.01 (((binunionTE) =>
% 132.79/23.01 (((binunionTEcontra) =>
% 132.79/23.01 (((demorgan2a1) =>
% 132.79/23.01 (((complementUnionInPowersetComplement) =>
% 132.79/23.01 (((demorgan2a2) =>
% 132.79/23.01 (((demorgan1a) =>
% 132.79/23.01 (((demorgan1b) =>
% 132.79/23.01 (((demorgan1) =>
% 132.79/23.01 (((demorgan2a) =>
% 132.79/23.01 ((
% 132.79/23.01 (demorgan2b2) =>
% 132.79/23.01 ((
% 132.79/23.01 (demorgan2b) =>
% 132.79/23.01 ((
% 132.79/23.01 (demorgan2) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz13rule0) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz13rule1) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz13rule2) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz13rule3) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz13rule4) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz1_1) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz1_2) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz1_3) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz1_4) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz1_5) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1all2) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1SetBreln1) =>
% 132.79/23.01 ((
% 132.79/23.01 (choice2fnsingleton) =>
% 132.79/23.01 ((
% 132.79/23.01 (setOfPairsIsBReln1) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1all1) =>
% 132.79/23.01 ((
% 132.79/23.01 (subbreln1) =>
% 132.79/23.01 ((
% 132.79/23.01 (eqbreln1) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1invprop) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1invI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1invE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compprop) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compEex) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionprop) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionIL) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionIR) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionEcases) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionCommutes) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2Ex) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2W) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2A) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2B) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Ex) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Ex1) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Equiv) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1E) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1I) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncInInjFuncSet) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncSetFuncIn) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncSetFuncInj) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjFuncSetFuncIn) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjFuncSetFuncSurj) =>
% 132.79/23.01 ((
% 132.79/23.01 (leftInvIsSurj) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjCantorThm) =>
% 132.79/23.01 ((
% 132.79/23.01 (foundation2) =>
% 132.79/23.01 ((
% 132.79/23.01 (notinself) =>
% 132.79/23.01 ((
% 132.79/23.01 (notinself2) =>
% 132.79/23.01 ((
% 132.79/23.01 (omegaSp) =>
% 132.79/23.01 ((
% 132.79/23.01 (omegaSclos) =>
% 132.79/23.01 ((
% 132.79/23.01 (peano0notS) =>
% 132.79/23.01 ((
% 132.79/23.01 (peanoSinj) =>
% 132.79/23.01 ((
% 132.79/23.01 (transitivesetOp1) =>
% 132.79/23.01 ((
% 132.79/23.01 (binintTransitive) =>
% 132.79/23.01 ((
% 132.79/23.01 (transitivesetOp2) =>
% 132.79/23.01 ((
% 132.79/23.01 (setunionTransitive) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalMinLem1) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalTransSet) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalTransSet1) =>
% 132.79/23.01 ((
% 132.79/23.01 (setunionOrdinalLem1) =>
% 132.79/23.01 (ordinal @
% 132.79/23.01 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/23.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2207])).
% 132.79/23.01 thf(zip_derived_cl2235, plain,
% 132.79/23.01 (~ (((contrasubsetT3) =>
% 132.79/23.01 (((doubleComplementI1) =>
% 132.79/23.01 (((doubleComplementE1) =>
% 132.79/23.01 (((doubleComplementSub1) =>
% 132.79/23.01 (((doubleComplementSub2) =>
% 132.79/23.01 (((doubleComplementEq) =>
% 132.79/23.01 (((complementTnotintersectT) =>
% 132.79/23.01 (((complementImpComplementIntersect) =>
% 132.79/23.01 (((complementSubsetComplementIntersect) =>
% 132.79/23.01 (((complementInPowersetComplementIntersect) =>
% 132.79/23.01 (((contraSubsetComplement) =>
% 132.79/23.01 (((complementTcontraSubset) =>
% 132.79/23.01 (((binunionTILcontra) =>
% 132.79/23.01 (((binunionTIRcontra) =>
% 132.79/23.01 (((inIntersectImpInUnion) =>
% 132.79/23.01 (((inIntersectImpInUnion2) =>
% 132.79/23.01 (((inIntersectImpInIntersectUnions) =>
% 132.79/23.01 (((intersectInPowersetIntersectUnions) =>
% 132.79/23.01 (((inComplementUnionImpNotIn1) =>
% 132.79/23.01 (((inComplementUnionImpInComplement1) =>
% 132.79/23.01 (((binunionTE) =>
% 132.79/23.01 (((binunionTEcontra) =>
% 132.79/23.01 (((demorgan2a1) =>
% 132.79/23.01 (((complementUnionInPowersetComplement) =>
% 132.79/23.01 (((demorgan2a2) =>
% 132.79/23.01 (((demorgan1a) =>
% 132.79/23.01 (((demorgan1b) =>
% 132.79/23.01 (((demorgan1) =>
% 132.79/23.01 (((demorgan2a) =>
% 132.79/23.01 (((demorgan2b2) =>
% 132.79/23.01 ((
% 132.79/23.01 (demorgan2b) =>
% 132.79/23.01 ((
% 132.79/23.01 (demorgan2) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz13rule0) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz13rule1) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz13rule2) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz13rule3) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz13rule4) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz1_1) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz1_2) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz1_3) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz1_4) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz1_5) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1all2) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1SetBreln1) =>
% 132.79/23.01 ((
% 132.79/23.01 (choice2fnsingleton) =>
% 132.79/23.01 ((
% 132.79/23.01 (setOfPairsIsBReln1) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1all1) =>
% 132.79/23.01 ((
% 132.79/23.01 (subbreln1) =>
% 132.79/23.01 ((
% 132.79/23.01 (eqbreln1) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1invprop) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1invI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1invE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compprop) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compEex) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionprop) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionIL) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionIR) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionEcases) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionCommutes) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2Ex) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2W) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2A) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2B) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Ex) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Ex1) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Equiv) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1E) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1I) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncInInjFuncSet) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncSetFuncIn) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncSetFuncInj) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjFuncSetFuncIn) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjFuncSetFuncSurj) =>
% 132.79/23.01 ((
% 132.79/23.01 (leftInvIsSurj) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjCantorThm) =>
% 132.79/23.01 ((
% 132.79/23.01 (foundation2) =>
% 132.79/23.01 ((
% 132.79/23.01 (notinself) =>
% 132.79/23.01 ((
% 132.79/23.01 (notinself2) =>
% 132.79/23.01 ((
% 132.79/23.01 (omegaSp) =>
% 132.79/23.01 ((
% 132.79/23.01 (omegaSclos) =>
% 132.79/23.01 ((
% 132.79/23.01 (peano0notS) =>
% 132.79/23.01 ((
% 132.79/23.01 (peanoSinj) =>
% 132.79/23.01 ((
% 132.79/23.01 (transitivesetOp1) =>
% 132.79/23.01 ((
% 132.79/23.01 (binintTransitive) =>
% 132.79/23.01 ((
% 132.79/23.01 (transitivesetOp2) =>
% 132.79/23.01 ((
% 132.79/23.01 (setunionTransitive) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalMinLem1) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalTransSet) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalTransSet1) =>
% 132.79/23.01 ((
% 132.79/23.01 (setunionOrdinalLem1) =>
% 132.79/23.01 (ordinal @
% 132.79/23.01 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/23.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2219])).
% 132.79/23.01 thf(zip_derived_cl2254, plain,
% 132.79/23.01 (~ (((doubleComplementI1) =>
% 132.79/23.01 (((doubleComplementE1) =>
% 132.79/23.01 (((doubleComplementSub1) =>
% 132.79/23.01 (((doubleComplementSub2) =>
% 132.79/23.01 (((doubleComplementEq) =>
% 132.79/23.01 (((complementTnotintersectT) =>
% 132.79/23.01 (((complementImpComplementIntersect) =>
% 132.79/23.01 (((complementSubsetComplementIntersect) =>
% 132.79/23.01 (((complementInPowersetComplementIntersect) =>
% 132.79/23.01 (((contraSubsetComplement) =>
% 132.79/23.01 (((complementTcontraSubset) =>
% 132.79/23.01 (((binunionTILcontra) =>
% 132.79/23.01 (((binunionTIRcontra) =>
% 132.79/23.01 (((inIntersectImpInUnion) =>
% 132.79/23.01 (((inIntersectImpInUnion2) =>
% 132.79/23.01 (((inIntersectImpInIntersectUnions) =>
% 132.79/23.01 (((intersectInPowersetIntersectUnions) =>
% 132.79/23.01 (((inComplementUnionImpNotIn1) =>
% 132.79/23.01 (((inComplementUnionImpInComplement1) =>
% 132.79/23.01 (((binunionTE) =>
% 132.79/23.01 (((binunionTEcontra) =>
% 132.79/23.01 (((demorgan2a1) =>
% 132.79/23.01 (((complementUnionInPowersetComplement) =>
% 132.79/23.01 (((demorgan2a2) =>
% 132.79/23.01 (((demorgan1a) =>
% 132.79/23.01 (((demorgan1b) =>
% 132.79/23.01 (((demorgan1) =>
% 132.79/23.01 (((demorgan2a) =>
% 132.79/23.01 (((demorgan2b2) =>
% 132.79/23.01 (((demorgan2b) =>
% 132.79/23.01 ((
% 132.79/23.01 (demorgan2) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz13rule0) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz13rule1) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz13rule2) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz13rule3) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz13rule4) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz1_1) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz1_2) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz1_3) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz1_4) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz1_5) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1all2) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1SetBreln1) =>
% 132.79/23.01 ((
% 132.79/23.01 (choice2fnsingleton) =>
% 132.79/23.01 ((
% 132.79/23.01 (setOfPairsIsBReln1) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1all1) =>
% 132.79/23.01 ((
% 132.79/23.01 (subbreln1) =>
% 132.79/23.01 ((
% 132.79/23.01 (eqbreln1) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1invprop) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1invI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1invE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compprop) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compEex) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionprop) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionIL) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionIR) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionEcases) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionCommutes) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2Ex) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2W) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2A) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2B) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Ex) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Ex1) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Equiv) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1E) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1I) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncInInjFuncSet) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncSetFuncIn) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncSetFuncInj) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjFuncSetFuncIn) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjFuncSetFuncSurj) =>
% 132.79/23.01 ((
% 132.79/23.01 (leftInvIsSurj) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjCantorThm) =>
% 132.79/23.01 ((
% 132.79/23.01 (foundation2) =>
% 132.79/23.01 ((
% 132.79/23.01 (notinself) =>
% 132.79/23.01 ((
% 132.79/23.01 (notinself2) =>
% 132.79/23.01 ((
% 132.79/23.01 (omegaSp) =>
% 132.79/23.01 ((
% 132.79/23.01 (omegaSclos) =>
% 132.79/23.01 ((
% 132.79/23.01 (peano0notS) =>
% 132.79/23.01 ((
% 132.79/23.01 (peanoSinj) =>
% 132.79/23.01 ((
% 132.79/23.01 (transitivesetOp1) =>
% 132.79/23.01 ((
% 132.79/23.01 (binintTransitive) =>
% 132.79/23.01 ((
% 132.79/23.01 (transitivesetOp2) =>
% 132.79/23.01 ((
% 132.79/23.01 (setunionTransitive) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalMinLem1) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalTransSet) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalTransSet1) =>
% 132.79/23.01 ((
% 132.79/23.01 (setunionOrdinalLem1) =>
% 132.79/23.01 (ordinal @
% 132.79/23.01 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/23.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2235])).
% 132.79/23.01 thf(zip_derived_cl2267, plain,
% 132.79/23.01 (~ (((doubleComplementE1) =>
% 132.79/23.01 (((doubleComplementSub1) =>
% 132.79/23.01 (((doubleComplementSub2) =>
% 132.79/23.01 (((doubleComplementEq) =>
% 132.79/23.01 (((complementTnotintersectT) =>
% 132.79/23.01 (((complementImpComplementIntersect) =>
% 132.79/23.01 (((complementSubsetComplementIntersect) =>
% 132.79/23.01 (((complementInPowersetComplementIntersect) =>
% 132.79/23.01 (((contraSubsetComplement) =>
% 132.79/23.01 (((complementTcontraSubset) =>
% 132.79/23.01 (((binunionTILcontra) =>
% 132.79/23.01 (((binunionTIRcontra) =>
% 132.79/23.01 (((inIntersectImpInUnion) =>
% 132.79/23.01 (((inIntersectImpInUnion2) =>
% 132.79/23.01 (((inIntersectImpInIntersectUnions) =>
% 132.79/23.01 (((intersectInPowersetIntersectUnions) =>
% 132.79/23.01 (((inComplementUnionImpNotIn1) =>
% 132.79/23.01 (((inComplementUnionImpInComplement1) =>
% 132.79/23.01 (((binunionTE) =>
% 132.79/23.01 (((binunionTEcontra) =>
% 132.79/23.01 (((demorgan2a1) =>
% 132.79/23.01 (((complementUnionInPowersetComplement) =>
% 132.79/23.01 (((demorgan2a2) =>
% 132.79/23.01 (((demorgan1a) =>
% 132.79/23.01 (((demorgan1b) =>
% 132.79/23.01 (((demorgan1) =>
% 132.79/23.01 (((demorgan2a) =>
% 132.79/23.01 (((demorgan2b2) =>
% 132.79/23.01 (((demorgan2b) =>
% 132.79/23.01 (((demorgan2) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz13rule0) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz13rule1) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz13rule2) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz13rule3) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz13rule4) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz1_1) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz1_2) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz1_3) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz1_4) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz1_5) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1all2) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1SetBreln1) =>
% 132.79/23.01 ((
% 132.79/23.01 (choice2fnsingleton) =>
% 132.79/23.01 ((
% 132.79/23.01 (setOfPairsIsBReln1) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1all1) =>
% 132.79/23.01 ((
% 132.79/23.01 (subbreln1) =>
% 132.79/23.01 ((
% 132.79/23.01 (eqbreln1) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1invprop) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1invI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1invE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compprop) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compEex) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionprop) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionIL) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionIR) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionEcases) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionCommutes) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2Ex) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2W) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2A) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2B) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Ex) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Ex1) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Equiv) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1E) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1I) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncInInjFuncSet) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncSetFuncIn) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncSetFuncInj) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjFuncSetFuncIn) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjFuncSetFuncSurj) =>
% 132.79/23.01 ((
% 132.79/23.01 (leftInvIsSurj) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjCantorThm) =>
% 132.79/23.01 ((
% 132.79/23.01 (foundation2) =>
% 132.79/23.01 ((
% 132.79/23.01 (notinself) =>
% 132.79/23.01 ((
% 132.79/23.01 (notinself2) =>
% 132.79/23.01 ((
% 132.79/23.01 (omegaSp) =>
% 132.79/23.01 ((
% 132.79/23.01 (omegaSclos) =>
% 132.79/23.01 ((
% 132.79/23.01 (peano0notS) =>
% 132.79/23.01 ((
% 132.79/23.01 (peanoSinj) =>
% 132.79/23.01 ((
% 132.79/23.01 (transitivesetOp1) =>
% 132.79/23.01 ((
% 132.79/23.01 (binintTransitive) =>
% 132.79/23.01 ((
% 132.79/23.01 (transitivesetOp2) =>
% 132.79/23.01 ((
% 132.79/23.01 (setunionTransitive) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalMinLem1) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalTransSet) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalTransSet1) =>
% 132.79/23.01 ((
% 132.79/23.01 (setunionOrdinalLem1) =>
% 132.79/23.01 (ordinal @
% 132.79/23.01 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/23.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2254])).
% 132.79/23.01 thf(zip_derived_cl2278, plain,
% 132.79/23.01 (~ (((doubleComplementSub1) =>
% 132.79/23.01 (((doubleComplementSub2) =>
% 132.79/23.01 (((doubleComplementEq) =>
% 132.79/23.01 (((complementTnotintersectT) =>
% 132.79/23.01 (((complementImpComplementIntersect) =>
% 132.79/23.01 (((complementSubsetComplementIntersect) =>
% 132.79/23.01 (((complementInPowersetComplementIntersect) =>
% 132.79/23.01 (((contraSubsetComplement) =>
% 132.79/23.01 (((complementTcontraSubset) =>
% 132.79/23.01 (((binunionTILcontra) =>
% 132.79/23.01 (((binunionTIRcontra) =>
% 132.79/23.01 (((inIntersectImpInUnion) =>
% 132.79/23.01 (((inIntersectImpInUnion2) =>
% 132.79/23.01 (((inIntersectImpInIntersectUnions) =>
% 132.79/23.01 (((intersectInPowersetIntersectUnions) =>
% 132.79/23.01 (((inComplementUnionImpNotIn1) =>
% 132.79/23.01 (((inComplementUnionImpInComplement1) =>
% 132.79/23.01 (((binunionTE) =>
% 132.79/23.01 (((binunionTEcontra) =>
% 132.79/23.01 (((demorgan2a1) =>
% 132.79/23.01 (((complementUnionInPowersetComplement) =>
% 132.79/23.01 (((demorgan2a2) =>
% 132.79/23.01 (((demorgan1a) =>
% 132.79/23.01 (((demorgan1b) =>
% 132.79/23.01 (((demorgan1) =>
% 132.79/23.01 (((demorgan2a) =>
% 132.79/23.01 (((demorgan2b2) =>
% 132.79/23.01 (((demorgan2b) =>
% 132.79/23.01 (((demorgan2) =>
% 132.79/23.01 (((woz13rule0) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz13rule1) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz13rule2) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz13rule3) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz13rule4) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz1_1) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz1_2) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz1_3) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz1_4) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz1_5) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1all2) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1SetBreln1) =>
% 132.79/23.01 ((
% 132.79/23.01 (choice2fnsingleton) =>
% 132.79/23.01 ((
% 132.79/23.01 (setOfPairsIsBReln1) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1all1) =>
% 132.79/23.01 ((
% 132.79/23.01 (subbreln1) =>
% 132.79/23.01 ((
% 132.79/23.01 (eqbreln1) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1invprop) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1invI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1invE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compprop) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compEex) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionprop) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionIL) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionIR) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionEcases) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionCommutes) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2Ex) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2W) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2A) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2B) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Ex) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Ex1) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Equiv) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1E) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1I) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncInInjFuncSet) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncSetFuncIn) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncSetFuncInj) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjFuncSetFuncIn) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjFuncSetFuncSurj) =>
% 132.79/23.01 ((
% 132.79/23.01 (leftInvIsSurj) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjCantorThm) =>
% 132.79/23.01 ((
% 132.79/23.01 (foundation2) =>
% 132.79/23.01 ((
% 132.79/23.01 (notinself) =>
% 132.79/23.01 ((
% 132.79/23.01 (notinself2) =>
% 132.79/23.01 ((
% 132.79/23.01 (omegaSp) =>
% 132.79/23.01 ((
% 132.79/23.01 (omegaSclos) =>
% 132.79/23.01 ((
% 132.79/23.01 (peano0notS) =>
% 132.79/23.01 ((
% 132.79/23.01 (peanoSinj) =>
% 132.79/23.01 ((
% 132.79/23.01 (transitivesetOp1) =>
% 132.79/23.01 ((
% 132.79/23.01 (binintTransitive) =>
% 132.79/23.01 ((
% 132.79/23.01 (transitivesetOp2) =>
% 132.79/23.01 ((
% 132.79/23.01 (setunionTransitive) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalMinLem1) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalTransSet) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalTransSet1) =>
% 132.79/23.01 ((
% 132.79/23.01 (setunionOrdinalLem1) =>
% 132.79/23.01 (ordinal @
% 132.79/23.01 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/23.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2267])).
% 132.79/23.01 thf(zip_derived_cl2288, plain,
% 132.79/23.01 (~ (((doubleComplementSub2) =>
% 132.79/23.01 (((doubleComplementEq) =>
% 132.79/23.01 (((complementTnotintersectT) =>
% 132.79/23.01 (((complementImpComplementIntersect) =>
% 132.79/23.01 (((complementSubsetComplementIntersect) =>
% 132.79/23.01 (((complementInPowersetComplementIntersect) =>
% 132.79/23.01 (((contraSubsetComplement) =>
% 132.79/23.01 (((complementTcontraSubset) =>
% 132.79/23.01 (((binunionTILcontra) =>
% 132.79/23.01 (((binunionTIRcontra) =>
% 132.79/23.01 (((inIntersectImpInUnion) =>
% 132.79/23.01 (((inIntersectImpInUnion2) =>
% 132.79/23.01 (((inIntersectImpInIntersectUnions) =>
% 132.79/23.01 (((intersectInPowersetIntersectUnions) =>
% 132.79/23.01 (((inComplementUnionImpNotIn1) =>
% 132.79/23.01 (((inComplementUnionImpInComplement1) =>
% 132.79/23.01 (((binunionTE) =>
% 132.79/23.01 (((binunionTEcontra) =>
% 132.79/23.01 (((demorgan2a1) =>
% 132.79/23.01 (((complementUnionInPowersetComplement) =>
% 132.79/23.01 (((demorgan2a2) =>
% 132.79/23.01 (((demorgan1a) =>
% 132.79/23.01 (((demorgan1b) =>
% 132.79/23.01 (((demorgan1) =>
% 132.79/23.01 (((demorgan2a) =>
% 132.79/23.01 (((demorgan2b2) =>
% 132.79/23.01 (((demorgan2b) =>
% 132.79/23.01 (((demorgan2) =>
% 132.79/23.01 (((woz13rule0) =>
% 132.79/23.01 (((woz13rule1) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz13rule2) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz13rule3) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz13rule4) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz1_1) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz1_2) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz1_3) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz1_4) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz1_5) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1all2) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1SetBreln1) =>
% 132.79/23.01 ((
% 132.79/23.01 (choice2fnsingleton) =>
% 132.79/23.01 ((
% 132.79/23.01 (setOfPairsIsBReln1) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1all1) =>
% 132.79/23.01 ((
% 132.79/23.01 (subbreln1) =>
% 132.79/23.01 ((
% 132.79/23.01 (eqbreln1) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1invprop) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1invI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1invE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compprop) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compEex) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionprop) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionIL) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionIR) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionEcases) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionCommutes) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2Ex) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2W) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2A) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2B) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Ex) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Ex1) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Equiv) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1E) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1I) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncInInjFuncSet) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncSetFuncIn) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncSetFuncInj) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjFuncSetFuncIn) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjFuncSetFuncSurj) =>
% 132.79/23.01 ((
% 132.79/23.01 (leftInvIsSurj) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjCantorThm) =>
% 132.79/23.01 ((
% 132.79/23.01 (foundation2) =>
% 132.79/23.01 ((
% 132.79/23.01 (notinself) =>
% 132.79/23.01 ((
% 132.79/23.01 (notinself2) =>
% 132.79/23.01 ((
% 132.79/23.01 (omegaSp) =>
% 132.79/23.01 ((
% 132.79/23.01 (omegaSclos) =>
% 132.79/23.01 ((
% 132.79/23.01 (peano0notS) =>
% 132.79/23.01 ((
% 132.79/23.01 (peanoSinj) =>
% 132.79/23.01 ((
% 132.79/23.01 (transitivesetOp1) =>
% 132.79/23.01 ((
% 132.79/23.01 (binintTransitive) =>
% 132.79/23.01 ((
% 132.79/23.01 (transitivesetOp2) =>
% 132.79/23.01 ((
% 132.79/23.01 (setunionTransitive) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalMinLem1) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalTransSet) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalTransSet1) =>
% 132.79/23.01 ((
% 132.79/23.01 (setunionOrdinalLem1) =>
% 132.79/23.01 (ordinal @
% 132.79/23.01 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/23.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2278])).
% 132.79/23.01 thf(zip_derived_cl2299, plain,
% 132.79/23.01 (~ (((doubleComplementEq) =>
% 132.79/23.01 (((complementTnotintersectT) =>
% 132.79/23.01 (((complementImpComplementIntersect) =>
% 132.79/23.01 (((complementSubsetComplementIntersect) =>
% 132.79/23.01 (((complementInPowersetComplementIntersect) =>
% 132.79/23.01 (((contraSubsetComplement) =>
% 132.79/23.01 (((complementTcontraSubset) =>
% 132.79/23.01 (((binunionTILcontra) =>
% 132.79/23.01 (((binunionTIRcontra) =>
% 132.79/23.01 (((inIntersectImpInUnion) =>
% 132.79/23.01 (((inIntersectImpInUnion2) =>
% 132.79/23.01 (((inIntersectImpInIntersectUnions) =>
% 132.79/23.01 (((intersectInPowersetIntersectUnions) =>
% 132.79/23.01 (((inComplementUnionImpNotIn1) =>
% 132.79/23.01 (((inComplementUnionImpInComplement1) =>
% 132.79/23.01 (((binunionTE) =>
% 132.79/23.01 (((binunionTEcontra) =>
% 132.79/23.01 (((demorgan2a1) =>
% 132.79/23.01 (((complementUnionInPowersetComplement) =>
% 132.79/23.01 (((demorgan2a2) =>
% 132.79/23.01 (((demorgan1a) =>
% 132.79/23.01 (((demorgan1b) =>
% 132.79/23.01 (((demorgan1) =>
% 132.79/23.01 (((demorgan2a) =>
% 132.79/23.01 (((demorgan2b2) =>
% 132.79/23.01 (((demorgan2b) =>
% 132.79/23.01 (((demorgan2) =>
% 132.79/23.01 (((woz13rule0) =>
% 132.79/23.01 (((woz13rule1) =>
% 132.79/23.01 (((woz13rule2) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz13rule3) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz13rule4) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz1_1) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz1_2) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz1_3) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz1_4) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz1_5) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1all2) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1SetBreln1) =>
% 132.79/23.01 ((
% 132.79/23.01 (choice2fnsingleton) =>
% 132.79/23.01 ((
% 132.79/23.01 (setOfPairsIsBReln1) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1all1) =>
% 132.79/23.01 ((
% 132.79/23.01 (subbreln1) =>
% 132.79/23.01 ((
% 132.79/23.01 (eqbreln1) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1invprop) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1invI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1invE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compprop) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compEex) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionprop) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionIL) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionIR) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionEcases) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionCommutes) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2Ex) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2W) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2A) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2B) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Ex) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Ex1) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Equiv) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1E) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1I) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncInInjFuncSet) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncSetFuncIn) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncSetFuncInj) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjFuncSetFuncIn) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjFuncSetFuncSurj) =>
% 132.79/23.01 ((
% 132.79/23.01 (leftInvIsSurj) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjCantorThm) =>
% 132.79/23.01 ((
% 132.79/23.01 (foundation2) =>
% 132.79/23.01 ((
% 132.79/23.01 (notinself) =>
% 132.79/23.01 ((
% 132.79/23.01 (notinself2) =>
% 132.79/23.01 ((
% 132.79/23.01 (omegaSp) =>
% 132.79/23.01 ((
% 132.79/23.01 (omegaSclos) =>
% 132.79/23.01 ((
% 132.79/23.01 (peano0notS) =>
% 132.79/23.01 ((
% 132.79/23.01 (peanoSinj) =>
% 132.79/23.01 ((
% 132.79/23.01 (transitivesetOp1) =>
% 132.79/23.01 ((
% 132.79/23.01 (binintTransitive) =>
% 132.79/23.01 ((
% 132.79/23.01 (transitivesetOp2) =>
% 132.79/23.01 ((
% 132.79/23.01 (setunionTransitive) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalMinLem1) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalTransSet) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalTransSet1) =>
% 132.79/23.01 ((
% 132.79/23.01 (setunionOrdinalLem1) =>
% 132.79/23.01 (ordinal @
% 132.79/23.01 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/23.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2288])).
% 132.79/23.01 thf(zip_derived_cl2310, plain,
% 132.79/23.01 (~ (((complementTnotintersectT) =>
% 132.79/23.01 (((complementImpComplementIntersect) =>
% 132.79/23.01 (((complementSubsetComplementIntersect) =>
% 132.79/23.01 (((complementInPowersetComplementIntersect) =>
% 132.79/23.01 (((contraSubsetComplement) =>
% 132.79/23.01 (((complementTcontraSubset) =>
% 132.79/23.01 (((binunionTILcontra) =>
% 132.79/23.01 (((binunionTIRcontra) =>
% 132.79/23.01 (((inIntersectImpInUnion) =>
% 132.79/23.01 (((inIntersectImpInUnion2) =>
% 132.79/23.01 (((inIntersectImpInIntersectUnions) =>
% 132.79/23.01 (((intersectInPowersetIntersectUnions) =>
% 132.79/23.01 (((inComplementUnionImpNotIn1) =>
% 132.79/23.01 (((inComplementUnionImpInComplement1) =>
% 132.79/23.01 (((binunionTE) =>
% 132.79/23.01 (((binunionTEcontra) =>
% 132.79/23.01 (((demorgan2a1) =>
% 132.79/23.01 (((complementUnionInPowersetComplement) =>
% 132.79/23.01 (((demorgan2a2) =>
% 132.79/23.01 (((demorgan1a) =>
% 132.79/23.01 (((demorgan1b) =>
% 132.79/23.01 (((demorgan1) =>
% 132.79/23.01 (((demorgan2a) =>
% 132.79/23.01 (((demorgan2b2) =>
% 132.79/23.01 (((demorgan2b) =>
% 132.79/23.01 (((demorgan2) =>
% 132.79/23.01 (((woz13rule0) =>
% 132.79/23.01 (((woz13rule1) =>
% 132.79/23.01 (((woz13rule2) =>
% 132.79/23.01 (((woz13rule3) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz13rule4) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz1_1) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz1_2) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz1_3) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz1_4) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz1_5) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1all2) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1SetBreln1) =>
% 132.79/23.01 ((
% 132.79/23.01 (choice2fnsingleton) =>
% 132.79/23.01 ((
% 132.79/23.01 (setOfPairsIsBReln1) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1all1) =>
% 132.79/23.01 ((
% 132.79/23.01 (subbreln1) =>
% 132.79/23.01 ((
% 132.79/23.01 (eqbreln1) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1invprop) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1invI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1invE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compprop) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compEex) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionprop) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionIL) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionIR) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionEcases) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionCommutes) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2Ex) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2W) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2A) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2B) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Ex) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Ex1) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Equiv) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1E) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1I) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncInInjFuncSet) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncSetFuncIn) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncSetFuncInj) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjFuncSetFuncIn) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjFuncSetFuncSurj) =>
% 132.79/23.01 ((
% 132.79/23.01 (leftInvIsSurj) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjCantorThm) =>
% 132.79/23.01 ((
% 132.79/23.01 (foundation2) =>
% 132.79/23.01 ((
% 132.79/23.01 (notinself) =>
% 132.79/23.01 ((
% 132.79/23.01 (notinself2) =>
% 132.79/23.01 ((
% 132.79/23.01 (omegaSp) =>
% 132.79/23.01 ((
% 132.79/23.01 (omegaSclos) =>
% 132.79/23.01 ((
% 132.79/23.01 (peano0notS) =>
% 132.79/23.01 ((
% 132.79/23.01 (peanoSinj) =>
% 132.79/23.01 ((
% 132.79/23.01 (transitivesetOp1) =>
% 132.79/23.01 ((
% 132.79/23.01 (binintTransitive) =>
% 132.79/23.01 ((
% 132.79/23.01 (transitivesetOp2) =>
% 132.79/23.01 ((
% 132.79/23.01 (setunionTransitive) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalMinLem1) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalTransSet) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalTransSet1) =>
% 132.79/23.01 ((
% 132.79/23.01 (setunionOrdinalLem1) =>
% 132.79/23.01 (ordinal @
% 132.79/23.01 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/23.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2299])).
% 132.79/23.01 thf(zip_derived_cl2321, plain,
% 132.79/23.01 (~ (((complementImpComplementIntersect) =>
% 132.79/23.01 (((complementSubsetComplementIntersect) =>
% 132.79/23.01 (((complementInPowersetComplementIntersect) =>
% 132.79/23.01 (((contraSubsetComplement) =>
% 132.79/23.01 (((complementTcontraSubset) =>
% 132.79/23.01 (((binunionTILcontra) =>
% 132.79/23.01 (((binunionTIRcontra) =>
% 132.79/23.01 (((inIntersectImpInUnion) =>
% 132.79/23.01 (((inIntersectImpInUnion2) =>
% 132.79/23.01 (((inIntersectImpInIntersectUnions) =>
% 132.79/23.01 (((intersectInPowersetIntersectUnions) =>
% 132.79/23.01 (((inComplementUnionImpNotIn1) =>
% 132.79/23.01 (((inComplementUnionImpInComplement1) =>
% 132.79/23.01 (((binunionTE) =>
% 132.79/23.01 (((binunionTEcontra) =>
% 132.79/23.01 (((demorgan2a1) =>
% 132.79/23.01 (((complementUnionInPowersetComplement) =>
% 132.79/23.01 (((demorgan2a2) =>
% 132.79/23.01 (((demorgan1a) =>
% 132.79/23.01 (((demorgan1b) =>
% 132.79/23.01 (((demorgan1) =>
% 132.79/23.01 (((demorgan2a) =>
% 132.79/23.01 (((demorgan2b2) =>
% 132.79/23.01 (((demorgan2b) =>
% 132.79/23.01 (((demorgan2) =>
% 132.79/23.01 (((woz13rule0) =>
% 132.79/23.01 (((woz13rule1) =>
% 132.79/23.01 (((woz13rule2) =>
% 132.79/23.01 (((woz13rule3) =>
% 132.79/23.01 (((woz13rule4) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz1_1) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz1_2) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz1_3) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz1_4) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz1_5) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1all2) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1SetBreln1) =>
% 132.79/23.01 ((
% 132.79/23.01 (choice2fnsingleton) =>
% 132.79/23.01 ((
% 132.79/23.01 (setOfPairsIsBReln1) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1all1) =>
% 132.79/23.01 ((
% 132.79/23.01 (subbreln1) =>
% 132.79/23.01 ((
% 132.79/23.01 (eqbreln1) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1invprop) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1invI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1invE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compprop) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compEex) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionprop) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionIL) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionIR) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionEcases) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionCommutes) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2Ex) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2W) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2A) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2B) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Ex) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Ex1) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Equiv) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1E) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1I) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncInInjFuncSet) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncSetFuncIn) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncSetFuncInj) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjFuncSetFuncIn) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjFuncSetFuncSurj) =>
% 132.79/23.01 ((
% 132.79/23.01 (leftInvIsSurj) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjCantorThm) =>
% 132.79/23.01 ((
% 132.79/23.01 (foundation2) =>
% 132.79/23.01 ((
% 132.79/23.01 (notinself) =>
% 132.79/23.01 ((
% 132.79/23.01 (notinself2) =>
% 132.79/23.01 ((
% 132.79/23.01 (omegaSp) =>
% 132.79/23.01 ((
% 132.79/23.01 (omegaSclos) =>
% 132.79/23.01 ((
% 132.79/23.01 (peano0notS) =>
% 132.79/23.01 ((
% 132.79/23.01 (peanoSinj) =>
% 132.79/23.01 ((
% 132.79/23.01 (transitivesetOp1) =>
% 132.79/23.01 ((
% 132.79/23.01 (binintTransitive) =>
% 132.79/23.01 ((
% 132.79/23.01 (transitivesetOp2) =>
% 132.79/23.01 ((
% 132.79/23.01 (setunionTransitive) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalMinLem1) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalTransSet) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalTransSet1) =>
% 132.79/23.01 ((
% 132.79/23.01 (setunionOrdinalLem1) =>
% 132.79/23.01 (ordinal @
% 132.79/23.01 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/23.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2310])).
% 132.79/23.01 thf(zip_derived_cl2332, plain,
% 132.79/23.01 (~ (((complementSubsetComplementIntersect) =>
% 132.79/23.01 (((complementInPowersetComplementIntersect) =>
% 132.79/23.01 (((contraSubsetComplement) =>
% 132.79/23.01 (((complementTcontraSubset) =>
% 132.79/23.01 (((binunionTILcontra) =>
% 132.79/23.01 (((binunionTIRcontra) =>
% 132.79/23.01 (((inIntersectImpInUnion) =>
% 132.79/23.01 (((inIntersectImpInUnion2) =>
% 132.79/23.01 (((inIntersectImpInIntersectUnions) =>
% 132.79/23.01 (((intersectInPowersetIntersectUnions) =>
% 132.79/23.01 (((inComplementUnionImpNotIn1) =>
% 132.79/23.01 (((inComplementUnionImpInComplement1) =>
% 132.79/23.01 (((binunionTE) =>
% 132.79/23.01 (((binunionTEcontra) =>
% 132.79/23.01 (((demorgan2a1) =>
% 132.79/23.01 (((complementUnionInPowersetComplement) =>
% 132.79/23.01 (((demorgan2a2) =>
% 132.79/23.01 (((demorgan1a) =>
% 132.79/23.01 (((demorgan1b) =>
% 132.79/23.01 (((demorgan1) =>
% 132.79/23.01 (((demorgan2a) =>
% 132.79/23.01 (((demorgan2b2) =>
% 132.79/23.01 (((demorgan2b) =>
% 132.79/23.01 (((demorgan2) =>
% 132.79/23.01 (((woz13rule0) =>
% 132.79/23.01 (((woz13rule1) =>
% 132.79/23.01 (((woz13rule2) =>
% 132.79/23.01 (((woz13rule3) =>
% 132.79/23.01 (((woz13rule4) =>
% 132.79/23.01 (((woz1_1) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz1_2) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz1_3) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz1_4) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz1_5) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1all2) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1SetBreln1) =>
% 132.79/23.01 ((
% 132.79/23.01 (choice2fnsingleton) =>
% 132.79/23.01 ((
% 132.79/23.01 (setOfPairsIsBReln1) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1all1) =>
% 132.79/23.01 ((
% 132.79/23.01 (subbreln1) =>
% 132.79/23.01 ((
% 132.79/23.01 (eqbreln1) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1invprop) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1invI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1invE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compprop) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compEex) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionprop) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionIL) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionIR) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionEcases) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionCommutes) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2Ex) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2W) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2A) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2B) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Ex) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Ex1) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Equiv) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1E) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1I) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncInInjFuncSet) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncSetFuncIn) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncSetFuncInj) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjFuncSetFuncIn) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjFuncSetFuncSurj) =>
% 132.79/23.01 ((
% 132.79/23.01 (leftInvIsSurj) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjCantorThm) =>
% 132.79/23.01 ((
% 132.79/23.01 (foundation2) =>
% 132.79/23.01 ((
% 132.79/23.01 (notinself) =>
% 132.79/23.01 ((
% 132.79/23.01 (notinself2) =>
% 132.79/23.01 ((
% 132.79/23.01 (omegaSp) =>
% 132.79/23.01 ((
% 132.79/23.01 (omegaSclos) =>
% 132.79/23.01 ((
% 132.79/23.01 (peano0notS) =>
% 132.79/23.01 ((
% 132.79/23.01 (peanoSinj) =>
% 132.79/23.01 ((
% 132.79/23.01 (transitivesetOp1) =>
% 132.79/23.01 ((
% 132.79/23.01 (binintTransitive) =>
% 132.79/23.01 ((
% 132.79/23.01 (transitivesetOp2) =>
% 132.79/23.01 ((
% 132.79/23.01 (setunionTransitive) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalMinLem1) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalTransSet) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalTransSet1) =>
% 132.79/23.01 ((
% 132.79/23.01 (setunionOrdinalLem1) =>
% 132.79/23.01 (ordinal @
% 132.79/23.01 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/23.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2321])).
% 132.79/23.01 thf(zip_derived_cl2341, plain,
% 132.79/23.01 (~ (((complementInPowersetComplementIntersect) =>
% 132.79/23.01 (((contraSubsetComplement) =>
% 132.79/23.01 (((complementTcontraSubset) =>
% 132.79/23.01 (((binunionTILcontra) =>
% 132.79/23.01 (((binunionTIRcontra) =>
% 132.79/23.01 (((inIntersectImpInUnion) =>
% 132.79/23.01 (((inIntersectImpInUnion2) =>
% 132.79/23.01 (((inIntersectImpInIntersectUnions) =>
% 132.79/23.01 (((intersectInPowersetIntersectUnions) =>
% 132.79/23.01 (((inComplementUnionImpNotIn1) =>
% 132.79/23.01 (((inComplementUnionImpInComplement1) =>
% 132.79/23.01 (((binunionTE) =>
% 132.79/23.01 (((binunionTEcontra) =>
% 132.79/23.01 (((demorgan2a1) =>
% 132.79/23.01 (((complementUnionInPowersetComplement) =>
% 132.79/23.01 (((demorgan2a2) =>
% 132.79/23.01 (((demorgan1a) =>
% 132.79/23.01 (((demorgan1b) =>
% 132.79/23.01 (((demorgan1) =>
% 132.79/23.01 (((demorgan2a) =>
% 132.79/23.01 (((demorgan2b2) =>
% 132.79/23.01 (((demorgan2b) =>
% 132.79/23.01 (((demorgan2) =>
% 132.79/23.01 (((woz13rule0) =>
% 132.79/23.01 (((woz13rule1) =>
% 132.79/23.01 (((woz13rule2) =>
% 132.79/23.01 (((woz13rule3) =>
% 132.79/23.01 (((woz13rule4) =>
% 132.79/23.01 (((woz1_1) =>
% 132.79/23.01 (((woz1_2) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz1_3) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz1_4) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz1_5) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1all2) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1SetBreln1) =>
% 132.79/23.01 ((
% 132.79/23.01 (choice2fnsingleton) =>
% 132.79/23.01 ((
% 132.79/23.01 (setOfPairsIsBReln1) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1all1) =>
% 132.79/23.01 ((
% 132.79/23.01 (subbreln1) =>
% 132.79/23.01 ((
% 132.79/23.01 (eqbreln1) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1invprop) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1invI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1invE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compprop) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compEex) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionprop) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionIL) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionIR) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionEcases) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionCommutes) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2Ex) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2W) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2A) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2B) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Ex) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Ex1) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Equiv) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1E) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1I) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncInInjFuncSet) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncSetFuncIn) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncSetFuncInj) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjFuncSetFuncIn) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjFuncSetFuncSurj) =>
% 132.79/23.01 ((
% 132.79/23.01 (leftInvIsSurj) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjCantorThm) =>
% 132.79/23.01 ((
% 132.79/23.01 (foundation2) =>
% 132.79/23.01 ((
% 132.79/23.01 (notinself) =>
% 132.79/23.01 ((
% 132.79/23.01 (notinself2) =>
% 132.79/23.01 ((
% 132.79/23.01 (omegaSp) =>
% 132.79/23.01 ((
% 132.79/23.01 (omegaSclos) =>
% 132.79/23.01 ((
% 132.79/23.01 (peano0notS) =>
% 132.79/23.01 ((
% 132.79/23.01 (peanoSinj) =>
% 132.79/23.01 ((
% 132.79/23.01 (transitivesetOp1) =>
% 132.79/23.01 ((
% 132.79/23.01 (binintTransitive) =>
% 132.79/23.01 ((
% 132.79/23.01 (transitivesetOp2) =>
% 132.79/23.01 ((
% 132.79/23.01 (setunionTransitive) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalMinLem1) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalTransSet) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalTransSet1) =>
% 132.79/23.01 ((
% 132.79/23.01 (setunionOrdinalLem1) =>
% 132.79/23.01 (ordinal @
% 132.79/23.01 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/23.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2332])).
% 132.79/23.01 thf(zip_derived_cl2348, plain,
% 132.79/23.01 (~ (((contraSubsetComplement) =>
% 132.79/23.01 (((complementTcontraSubset) =>
% 132.79/23.01 (((binunionTILcontra) =>
% 132.79/23.01 (((binunionTIRcontra) =>
% 132.79/23.01 (((inIntersectImpInUnion) =>
% 132.79/23.01 (((inIntersectImpInUnion2) =>
% 132.79/23.01 (((inIntersectImpInIntersectUnions) =>
% 132.79/23.01 (((intersectInPowersetIntersectUnions) =>
% 132.79/23.01 (((inComplementUnionImpNotIn1) =>
% 132.79/23.01 (((inComplementUnionImpInComplement1) =>
% 132.79/23.01 (((binunionTE) =>
% 132.79/23.01 (((binunionTEcontra) =>
% 132.79/23.01 (((demorgan2a1) =>
% 132.79/23.01 (((complementUnionInPowersetComplement) =>
% 132.79/23.01 (((demorgan2a2) =>
% 132.79/23.01 (((demorgan1a) =>
% 132.79/23.01 (((demorgan1b) =>
% 132.79/23.01 (((demorgan1) =>
% 132.79/23.01 (((demorgan2a) =>
% 132.79/23.01 (((demorgan2b2) =>
% 132.79/23.01 (((demorgan2b) =>
% 132.79/23.01 (((demorgan2) =>
% 132.79/23.01 (((woz13rule0) =>
% 132.79/23.01 (((woz13rule1) =>
% 132.79/23.01 (((woz13rule2) =>
% 132.79/23.01 (((woz13rule3) =>
% 132.79/23.01 (((woz13rule4) =>
% 132.79/23.01 (((woz1_1) =>
% 132.79/23.01 (((woz1_2) =>
% 132.79/23.01 (((woz1_3) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz1_4) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz1_5) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1all2) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1SetBreln1) =>
% 132.79/23.01 ((
% 132.79/23.01 (choice2fnsingleton) =>
% 132.79/23.01 ((
% 132.79/23.01 (setOfPairsIsBReln1) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1all1) =>
% 132.79/23.01 ((
% 132.79/23.01 (subbreln1) =>
% 132.79/23.01 ((
% 132.79/23.01 (eqbreln1) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1invprop) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1invI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1invE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compprop) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compEex) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionprop) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionIL) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionIR) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionEcases) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionCommutes) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2Ex) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2W) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2A) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2B) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Ex) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Ex1) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Equiv) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1E) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1I) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncInInjFuncSet) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncSetFuncIn) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncSetFuncInj) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjFuncSetFuncIn) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjFuncSetFuncSurj) =>
% 132.79/23.01 ((
% 132.79/23.01 (leftInvIsSurj) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjCantorThm) =>
% 132.79/23.01 ((
% 132.79/23.01 (foundation2) =>
% 132.79/23.01 ((
% 132.79/23.01 (notinself) =>
% 132.79/23.01 ((
% 132.79/23.01 (notinself2) =>
% 132.79/23.01 ((
% 132.79/23.01 (omegaSp) =>
% 132.79/23.01 ((
% 132.79/23.01 (omegaSclos) =>
% 132.79/23.01 ((
% 132.79/23.01 (peano0notS) =>
% 132.79/23.01 ((
% 132.79/23.01 (peanoSinj) =>
% 132.79/23.01 ((
% 132.79/23.01 (transitivesetOp1) =>
% 132.79/23.01 ((
% 132.79/23.01 (binintTransitive) =>
% 132.79/23.01 ((
% 132.79/23.01 (transitivesetOp2) =>
% 132.79/23.01 ((
% 132.79/23.01 (setunionTransitive) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalMinLem1) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalTransSet) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalTransSet1) =>
% 132.79/23.01 ((
% 132.79/23.01 (setunionOrdinalLem1) =>
% 132.79/23.01 (ordinal @
% 132.79/23.01 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/23.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2341])).
% 132.79/23.01 thf(zip_derived_cl2355, plain,
% 132.79/23.01 (~ (((complementTcontraSubset) =>
% 132.79/23.01 (((binunionTILcontra) =>
% 132.79/23.01 (((binunionTIRcontra) =>
% 132.79/23.01 (((inIntersectImpInUnion) =>
% 132.79/23.01 (((inIntersectImpInUnion2) =>
% 132.79/23.01 (((inIntersectImpInIntersectUnions) =>
% 132.79/23.01 (((intersectInPowersetIntersectUnions) =>
% 132.79/23.01 (((inComplementUnionImpNotIn1) =>
% 132.79/23.01 (((inComplementUnionImpInComplement1) =>
% 132.79/23.01 (((binunionTE) =>
% 132.79/23.01 (((binunionTEcontra) =>
% 132.79/23.01 (((demorgan2a1) =>
% 132.79/23.01 (((complementUnionInPowersetComplement) =>
% 132.79/23.01 (((demorgan2a2) =>
% 132.79/23.01 (((demorgan1a) =>
% 132.79/23.01 (((demorgan1b) =>
% 132.79/23.01 (((demorgan1) =>
% 132.79/23.01 (((demorgan2a) =>
% 132.79/23.01 (((demorgan2b2) =>
% 132.79/23.01 (((demorgan2b) =>
% 132.79/23.01 (((demorgan2) =>
% 132.79/23.01 (((woz13rule0) =>
% 132.79/23.01 (((woz13rule1) =>
% 132.79/23.01 (((woz13rule2) =>
% 132.79/23.01 (((woz13rule3) =>
% 132.79/23.01 (((woz13rule4) =>
% 132.79/23.01 (((woz1_1) =>
% 132.79/23.01 (((woz1_2) =>
% 132.79/23.01 (((woz1_3) =>
% 132.79/23.01 (((woz1_4) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz1_5) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1all2) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1SetBreln1) =>
% 132.79/23.01 ((
% 132.79/23.01 (choice2fnsingleton) =>
% 132.79/23.01 ((
% 132.79/23.01 (setOfPairsIsBReln1) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1all1) =>
% 132.79/23.01 ((
% 132.79/23.01 (subbreln1) =>
% 132.79/23.01 ((
% 132.79/23.01 (eqbreln1) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1invprop) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1invI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1invE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compprop) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compEex) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionprop) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionIL) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionIR) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionEcases) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionCommutes) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2Ex) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2W) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2A) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2B) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Ex) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Ex1) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Equiv) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1E) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1I) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncInInjFuncSet) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncSetFuncIn) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncSetFuncInj) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjFuncSetFuncIn) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjFuncSetFuncSurj) =>
% 132.79/23.01 ((
% 132.79/23.01 (leftInvIsSurj) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjCantorThm) =>
% 132.79/23.01 ((
% 132.79/23.01 (foundation2) =>
% 132.79/23.01 ((
% 132.79/23.01 (notinself) =>
% 132.79/23.01 ((
% 132.79/23.01 (notinself2) =>
% 132.79/23.01 ((
% 132.79/23.01 (omegaSp) =>
% 132.79/23.01 ((
% 132.79/23.01 (omegaSclos) =>
% 132.79/23.01 ((
% 132.79/23.01 (peano0notS) =>
% 132.79/23.01 ((
% 132.79/23.01 (peanoSinj) =>
% 132.79/23.01 ((
% 132.79/23.01 (transitivesetOp1) =>
% 132.79/23.01 ((
% 132.79/23.01 (binintTransitive) =>
% 132.79/23.01 ((
% 132.79/23.01 (transitivesetOp2) =>
% 132.79/23.01 ((
% 132.79/23.01 (setunionTransitive) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalMinLem1) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalTransSet) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalTransSet1) =>
% 132.79/23.01 ((
% 132.79/23.01 (setunionOrdinalLem1) =>
% 132.79/23.01 (ordinal @
% 132.79/23.01 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/23.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2348])).
% 132.79/23.01 thf(zip_derived_cl2362, plain,
% 132.79/23.01 (~ (((binunionTILcontra) =>
% 132.79/23.01 (((binunionTIRcontra) =>
% 132.79/23.01 (((inIntersectImpInUnion) =>
% 132.79/23.01 (((inIntersectImpInUnion2) =>
% 132.79/23.01 (((inIntersectImpInIntersectUnions) =>
% 132.79/23.01 (((intersectInPowersetIntersectUnions) =>
% 132.79/23.01 (((inComplementUnionImpNotIn1) =>
% 132.79/23.01 (((inComplementUnionImpInComplement1) =>
% 132.79/23.01 (((binunionTE) =>
% 132.79/23.01 (((binunionTEcontra) =>
% 132.79/23.01 (((demorgan2a1) =>
% 132.79/23.01 (((complementUnionInPowersetComplement) =>
% 132.79/23.01 (((demorgan2a2) =>
% 132.79/23.01 (((demorgan1a) =>
% 132.79/23.01 (((demorgan1b) =>
% 132.79/23.01 (((demorgan1) =>
% 132.79/23.01 (((demorgan2a) =>
% 132.79/23.01 (((demorgan2b2) =>
% 132.79/23.01 (((demorgan2b) =>
% 132.79/23.01 (((demorgan2) =>
% 132.79/23.01 (((woz13rule0) =>
% 132.79/23.01 (((woz13rule1) =>
% 132.79/23.01 (((woz13rule2) =>
% 132.79/23.01 (((woz13rule3) =>
% 132.79/23.01 (((woz13rule4) =>
% 132.79/23.01 (((woz1_1) =>
% 132.79/23.01 (((woz1_2) =>
% 132.79/23.01 (((woz1_3) =>
% 132.79/23.01 (((woz1_4) =>
% 132.79/23.01 (((woz1_5) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1all2) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1SetBreln1) =>
% 132.79/23.01 ((
% 132.79/23.01 (choice2fnsingleton) =>
% 132.79/23.01 ((
% 132.79/23.01 (setOfPairsIsBReln1) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1all1) =>
% 132.79/23.01 ((
% 132.79/23.01 (subbreln1) =>
% 132.79/23.01 ((
% 132.79/23.01 (eqbreln1) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1invprop) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1invI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1invE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compprop) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compEex) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionprop) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionIL) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionIR) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionEcases) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionCommutes) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2Ex) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2W) =>
% 132.79/23.01 ((
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% 132.79/23.01 ((
% 132.79/23.01 (woz2B) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Ex) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Ex1) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Equiv) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1E) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1I) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncInInjFuncSet) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncSetFuncIn) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncSetFuncInj) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjFuncSetFuncIn) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjFuncSetFuncSurj) =>
% 132.79/23.01 ((
% 132.79/23.01 (leftInvIsSurj) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjCantorThm) =>
% 132.79/23.01 ((
% 132.79/23.01 (foundation2) =>
% 132.79/23.01 ((
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% 132.79/23.01 ((
% 132.79/23.01 (notinself2) =>
% 132.79/23.01 ((
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% 132.79/23.01 ((
% 132.79/23.01 (omegaSclos) =>
% 132.79/23.01 ((
% 132.79/23.01 (peano0notS) =>
% 132.79/23.01 ((
% 132.79/23.01 (peanoSinj) =>
% 132.79/23.01 ((
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% 132.79/23.01 ((
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% 132.79/23.01 ((
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% 132.79/23.01 ((
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% 132.79/23.01 ((
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% 132.79/23.01 ((
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% 132.79/23.01 ((
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% 132.79/23.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2355])).
% 132.79/23.01 thf(zip_derived_cl2370, plain,
% 132.79/23.01 (~ (((binunionTIRcontra) =>
% 132.79/23.01 (((inIntersectImpInUnion) =>
% 132.79/23.01 (((inIntersectImpInUnion2) =>
% 132.79/23.01 (((inIntersectImpInIntersectUnions) =>
% 132.79/23.01 (((intersectInPowersetIntersectUnions) =>
% 132.79/23.01 (((inComplementUnionImpNotIn1) =>
% 132.79/23.01 (((inComplementUnionImpInComplement1) =>
% 132.79/23.01 (((binunionTE) =>
% 132.79/23.01 (((binunionTEcontra) =>
% 132.79/23.01 (((demorgan2a1) =>
% 132.79/23.01 (((complementUnionInPowersetComplement) =>
% 132.79/23.01 (((demorgan2a2) =>
% 132.79/23.01 (((demorgan1a) =>
% 132.79/23.01 (((demorgan1b) =>
% 132.79/23.01 (((demorgan1) =>
% 132.79/23.01 (((demorgan2a) =>
% 132.79/23.01 (((demorgan2b2) =>
% 132.79/23.01 (((demorgan2b) =>
% 132.79/23.01 (((demorgan2) =>
% 132.79/23.01 (((woz13rule0) =>
% 132.79/23.01 (((woz13rule1) =>
% 132.79/23.01 (((woz13rule2) =>
% 132.79/23.01 (((woz13rule3) =>
% 132.79/23.01 (((woz13rule4) =>
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% 132.79/23.01 (((woz1_2) =>
% 132.79/23.01 (((woz1_3) =>
% 132.79/23.01 (((woz1_4) =>
% 132.79/23.01 (((woz1_5) =>
% 132.79/23.01 (((breln1all2) =>
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% 132.79/23.01 (choice2fnsingleton) =>
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% 132.79/23.01 ((
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% 132.79/23.01 ((
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% 132.79/23.01 ((
% 132.79/23.01 (breln1invE) =>
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% 132.79/23.01 ((
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% 132.79/23.01 ((
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% 132.79/23.01 (breln1unionCommutes) =>
% 132.79/23.01 ((
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% 132.79/23.01 ((
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% 132.79/23.01 ((
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% 132.79/23.01 ((
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% 132.79/23.01 ((
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% 132.79/23.01 ((
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% 132.79/23.01 ((
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% 132.79/23.01 ((
% 132.79/23.01 (image1E) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1I) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncInInjFuncSet) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncSetFuncIn) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncSetFuncInj) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjFuncSetFuncIn) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjFuncSetFuncSurj) =>
% 132.79/23.01 ((
% 132.79/23.01 (leftInvIsSurj) =>
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% 132.79/23.01 ((
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% 132.79/23.01 ((
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% 132.79/23.01 ((
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% 132.79/23.01 ((
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% 132.79/23.01 ((
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% 132.79/23.01 ((
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% 132.79/23.01 ((
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% 132.79/23.01 ((
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% 132.79/23.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2362])).
% 132.79/23.01 thf(zip_derived_cl2379, plain,
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% 132.79/23.01 (((inComplementUnionImpInComplement1) =>
% 132.79/23.01 (((binunionTE) =>
% 132.79/23.01 (((binunionTEcontra) =>
% 132.79/23.01 (((demorgan2a1) =>
% 132.79/23.01 (((complementUnionInPowersetComplement) =>
% 132.79/23.01 (((demorgan2a2) =>
% 132.79/23.01 (((demorgan1a) =>
% 132.79/23.01 (((demorgan1b) =>
% 132.79/23.01 (((demorgan1) =>
% 132.79/23.01 (((demorgan2a) =>
% 132.79/23.01 (((demorgan2b2) =>
% 132.79/23.01 (((demorgan2b) =>
% 132.79/23.01 (((demorgan2) =>
% 132.79/23.01 (((woz13rule0) =>
% 132.79/23.01 (((woz13rule1) =>
% 132.79/23.01 (((woz13rule2) =>
% 132.79/23.01 (((woz13rule3) =>
% 132.79/23.01 (((woz13rule4) =>
% 132.79/23.01 (((woz1_1) =>
% 132.79/23.01 (((woz1_2) =>
% 132.79/23.01 (((woz1_3) =>
% 132.79/23.01 (((woz1_4) =>
% 132.79/23.01 (((woz1_5) =>
% 132.79/23.01 (((breln1all2) =>
% 132.79/23.01 (((breln1SetBreln1) =>
% 132.79/23.01 ((
% 132.79/23.01 (choice2fnsingleton) =>
% 132.79/23.01 ((
% 132.79/23.01 (setOfPairsIsBReln1) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1all1) =>
% 132.79/23.01 ((
% 132.79/23.01 (subbreln1) =>
% 132.79/23.01 ((
% 132.79/23.01 (eqbreln1) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1invprop) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1invI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1invE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compprop) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compEex) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionprop) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionIL) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionIR) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionEcases) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionCommutes) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2Ex) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2W) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2A) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2B) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Ex) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Ex1) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Equiv) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1E) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1I) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncInInjFuncSet) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncSetFuncIn) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncSetFuncInj) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjFuncSetFuncIn) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjFuncSetFuncSurj) =>
% 132.79/23.01 ((
% 132.79/23.01 (leftInvIsSurj) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjCantorThm) =>
% 132.79/23.01 ((
% 132.79/23.01 (foundation2) =>
% 132.79/23.01 ((
% 132.79/23.01 (notinself) =>
% 132.79/23.01 ((
% 132.79/23.01 (notinself2) =>
% 132.79/23.01 ((
% 132.79/23.01 (omegaSp) =>
% 132.79/23.01 ((
% 132.79/23.01 (omegaSclos) =>
% 132.79/23.01 ((
% 132.79/23.01 (peano0notS) =>
% 132.79/23.01 ((
% 132.79/23.01 (peanoSinj) =>
% 132.79/23.01 ((
% 132.79/23.01 (transitivesetOp1) =>
% 132.79/23.01 ((
% 132.79/23.01 (binintTransitive) =>
% 132.79/23.01 ((
% 132.79/23.01 (transitivesetOp2) =>
% 132.79/23.01 ((
% 132.79/23.01 (setunionTransitive) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalMinLem1) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalTransSet) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalTransSet1) =>
% 132.79/23.01 ((
% 132.79/23.01 (setunionOrdinalLem1) =>
% 132.79/23.01 (ordinal @
% 132.79/23.01 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/23.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2370])).
% 132.79/23.01 thf(zip_derived_cl2389, plain,
% 132.79/23.01 (~ (((inIntersectImpInUnion2) =>
% 132.79/23.01 (((inIntersectImpInIntersectUnions) =>
% 132.79/23.01 (((intersectInPowersetIntersectUnions) =>
% 132.79/23.01 (((inComplementUnionImpNotIn1) =>
% 132.79/23.01 (((inComplementUnionImpInComplement1) =>
% 132.79/23.01 (((binunionTE) =>
% 132.79/23.01 (((binunionTEcontra) =>
% 132.79/23.01 (((demorgan2a1) =>
% 132.79/23.01 (((complementUnionInPowersetComplement) =>
% 132.79/23.01 (((demorgan2a2) =>
% 132.79/23.01 (((demorgan1a) =>
% 132.79/23.01 (((demorgan1b) =>
% 132.79/23.01 (((demorgan1) =>
% 132.79/23.01 (((demorgan2a) =>
% 132.79/23.01 (((demorgan2b2) =>
% 132.79/23.01 (((demorgan2b) =>
% 132.79/23.01 (((demorgan2) =>
% 132.79/23.01 (((woz13rule0) =>
% 132.79/23.01 (((woz13rule1) =>
% 132.79/23.01 (((woz13rule2) =>
% 132.79/23.01 (((woz13rule3) =>
% 132.79/23.01 (((woz13rule4) =>
% 132.79/23.01 (((woz1_1) =>
% 132.79/23.01 (((woz1_2) =>
% 132.79/23.01 (((woz1_3) =>
% 132.79/23.01 (((woz1_4) =>
% 132.79/23.01 (((woz1_5) =>
% 132.79/23.01 (((breln1all2) =>
% 132.79/23.01 (((breln1SetBreln1) =>
% 132.79/23.01 (((choice2fnsingleton) =>
% 132.79/23.01 ((
% 132.79/23.01 (setOfPairsIsBReln1) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1all1) =>
% 132.79/23.01 ((
% 132.79/23.01 (subbreln1) =>
% 132.79/23.01 ((
% 132.79/23.01 (eqbreln1) =>
% 132.79/23.01 ((
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% 132.79/23.01 ((
% 132.79/23.01 (breln1invI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1invE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compprop) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compEex) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionprop) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionIL) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionIR) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionEcases) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionCommutes) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2Ex) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2W) =>
% 132.79/23.01 ((
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% 132.79/23.01 ((
% 132.79/23.01 (woz2B) =>
% 132.79/23.01 ((
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% 132.79/23.01 ((
% 132.79/23.01 (image1Ex1) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Equiv) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1E) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1I) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncInInjFuncSet) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncSetFuncIn) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncSetFuncInj) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjFuncSetFuncIn) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjFuncSetFuncSurj) =>
% 132.79/23.01 ((
% 132.79/23.01 (leftInvIsSurj) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjCantorThm) =>
% 132.79/23.01 ((
% 132.79/23.01 (foundation2) =>
% 132.79/23.01 ((
% 132.79/23.01 (notinself) =>
% 132.79/23.01 ((
% 132.79/23.01 (notinself2) =>
% 132.79/23.01 ((
% 132.79/23.01 (omegaSp) =>
% 132.79/23.01 ((
% 132.79/23.01 (omegaSclos) =>
% 132.79/23.01 ((
% 132.79/23.01 (peano0notS) =>
% 132.79/23.01 ((
% 132.79/23.01 (peanoSinj) =>
% 132.79/23.01 ((
% 132.79/23.01 (transitivesetOp1) =>
% 132.79/23.01 ((
% 132.79/23.01 (binintTransitive) =>
% 132.79/23.01 ((
% 132.79/23.01 (transitivesetOp2) =>
% 132.79/23.01 ((
% 132.79/23.01 (setunionTransitive) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalMinLem1) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalTransSet) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalTransSet1) =>
% 132.79/23.01 ((
% 132.79/23.01 (setunionOrdinalLem1) =>
% 132.79/23.01 (ordinal @
% 132.79/23.01 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/23.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2379])).
% 132.79/23.01 thf(zip_derived_cl2399, plain,
% 132.79/23.01 (~ (((inIntersectImpInIntersectUnions) =>
% 132.79/23.01 (((intersectInPowersetIntersectUnions) =>
% 132.79/23.01 (((inComplementUnionImpNotIn1) =>
% 132.79/23.01 (((inComplementUnionImpInComplement1) =>
% 132.79/23.01 (((binunionTE) =>
% 132.79/23.01 (((binunionTEcontra) =>
% 132.79/23.01 (((demorgan2a1) =>
% 132.79/23.01 (((complementUnionInPowersetComplement) =>
% 132.79/23.01 (((demorgan2a2) =>
% 132.79/23.01 (((demorgan1a) =>
% 132.79/23.01 (((demorgan1b) =>
% 132.79/23.01 (((demorgan1) =>
% 132.79/23.01 (((demorgan2a) =>
% 132.79/23.01 (((demorgan2b2) =>
% 132.79/23.01 (((demorgan2b) =>
% 132.79/23.01 (((demorgan2) =>
% 132.79/23.01 (((woz13rule0) =>
% 132.79/23.01 (((woz13rule1) =>
% 132.79/23.01 (((woz13rule2) =>
% 132.79/23.01 (((woz13rule3) =>
% 132.79/23.01 (((woz13rule4) =>
% 132.79/23.01 (((woz1_1) =>
% 132.79/23.01 (((woz1_2) =>
% 132.79/23.01 (((woz1_3) =>
% 132.79/23.01 (((woz1_4) =>
% 132.79/23.01 (((woz1_5) =>
% 132.79/23.01 (((breln1all2) =>
% 132.79/23.01 (((breln1SetBreln1) =>
% 132.79/23.01 (((choice2fnsingleton) =>
% 132.79/23.01 (((setOfPairsIsBReln1) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1all1) =>
% 132.79/23.01 ((
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% 132.79/23.01 ((
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% 132.79/23.01 ((
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% 132.79/23.01 ((
% 132.79/23.01 (breln1invI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1invE) =>
% 132.79/23.01 ((
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% 132.79/23.01 ((
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% 132.79/23.01 ((
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% 132.79/23.01 ((
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% 132.79/23.01 ((
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% 132.79/23.01 ((
% 132.79/23.01 (breln1unionI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionEcases) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionCommutes) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2Ex) =>
% 132.79/23.01 ((
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% 132.79/23.01 ((
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% 132.79/23.01 ((
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% 132.79/23.01 ((
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% 132.79/23.01 ((
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% 132.79/23.01 ((
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% 132.79/23.01 ((
% 132.79/23.01 (image1E) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1I) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncInInjFuncSet) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncSetFuncIn) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncSetFuncInj) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjFuncSetFuncIn) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjFuncSetFuncSurj) =>
% 132.79/23.01 ((
% 132.79/23.01 (leftInvIsSurj) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjCantorThm) =>
% 132.79/23.01 ((
% 132.79/23.01 (foundation2) =>
% 132.79/23.01 ((
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% 132.79/23.01 ((
% 132.79/23.01 (notinself2) =>
% 132.79/23.01 ((
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% 132.79/23.01 ((
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% 132.79/23.01 ((
% 132.79/23.01 (peano0notS) =>
% 132.79/23.01 ((
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% 132.79/23.01 ((
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% 132.79/23.01 ((
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% 132.79/23.01 ((
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% 132.79/23.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2389])).
% 132.79/23.01 thf(zip_derived_cl2408, plain,
% 132.79/23.01 (~ (((intersectInPowersetIntersectUnions) =>
% 132.79/23.01 (((inComplementUnionImpNotIn1) =>
% 132.79/23.01 (((inComplementUnionImpInComplement1) =>
% 132.79/23.01 (((binunionTE) =>
% 132.79/23.01 (((binunionTEcontra) =>
% 132.79/23.01 (((demorgan2a1) =>
% 132.79/23.01 (((complementUnionInPowersetComplement) =>
% 132.79/23.01 (((demorgan2a2) =>
% 132.79/23.01 (((demorgan1a) =>
% 132.79/23.01 (((demorgan1b) =>
% 132.79/23.01 (((demorgan1) =>
% 132.79/23.01 (((demorgan2a) =>
% 132.79/23.01 (((demorgan2b2) =>
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% 132.79/23.01 (((demorgan2) =>
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% 132.79/23.01 (((woz1_3) =>
% 132.79/23.01 (((woz1_4) =>
% 132.79/23.01 (((woz1_5) =>
% 132.79/23.01 (((breln1all2) =>
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% 132.79/23.01 (((choice2fnsingleton) =>
% 132.79/23.01 (((setOfPairsIsBReln1) =>
% 132.79/23.01 (((breln1all1) =>
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% 132.79/23.01 ((
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% 132.79/23.01 ((
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% 132.79/23.01 ((
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% 132.79/23.01 (image1E) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1I) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncInInjFuncSet) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncSetFuncIn) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncSetFuncInj) =>
% 132.79/23.01 ((
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% 132.79/23.01 ((
% 132.79/23.01 (surjFuncSetFuncSurj) =>
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% 132.79/23.01 ((
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% 132.79/23.01 ((
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% 132.79/23.01 ((
% 132.79/23.01 (notinself2) =>
% 132.79/23.01 ((
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% 132.79/23.01 ((
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% 132.79/23.01 ((
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% 132.79/23.01 ((
% 132.79/23.01 (peanoSinj) =>
% 132.79/23.01 ((
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% 132.79/23.01 ((
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% 132.79/23.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2399])).
% 132.79/23.01 thf(zip_derived_cl2417, plain,
% 132.79/23.01 (~ (((inComplementUnionImpNotIn1) =>
% 132.79/23.01 (((inComplementUnionImpInComplement1) =>
% 132.79/23.01 (((binunionTE) =>
% 132.79/23.01 (((binunionTEcontra) =>
% 132.79/23.01 (((demorgan2a1) =>
% 132.79/23.01 (((complementUnionInPowersetComplement) =>
% 132.79/23.01 (((demorgan2a2) =>
% 132.79/23.01 (((demorgan1a) =>
% 132.79/23.01 (((demorgan1b) =>
% 132.79/23.01 (((demorgan1) =>
% 132.79/23.01 (((demorgan2a) =>
% 132.79/23.01 (((demorgan2b2) =>
% 132.79/23.01 (((demorgan2b) =>
% 132.79/23.01 (((demorgan2) =>
% 132.79/23.01 (((woz13rule0) =>
% 132.79/23.01 (((woz13rule1) =>
% 132.79/23.01 (((woz13rule2) =>
% 132.79/23.01 (((woz13rule3) =>
% 132.79/23.01 (((woz13rule4) =>
% 132.79/23.01 (((woz1_1) =>
% 132.79/23.01 (((woz1_2) =>
% 132.79/23.01 (((woz1_3) =>
% 132.79/23.01 (((woz1_4) =>
% 132.79/23.01 (((woz1_5) =>
% 132.79/23.01 (((breln1all2) =>
% 132.79/23.01 (((breln1SetBreln1) =>
% 132.79/23.01 (((choice2fnsingleton) =>
% 132.79/23.01 (((setOfPairsIsBReln1) =>
% 132.79/23.01 (((breln1all1) =>
% 132.79/23.01 (((subbreln1) =>
% 132.79/23.01 ((
% 132.79/23.01 (eqbreln1) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1invprop) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1invI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1invE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compprop) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compEex) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionprop) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionIL) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionIR) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionEcases) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionCommutes) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2Ex) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2W) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2A) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2B) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Ex) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Ex1) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Equiv) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1E) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1I) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncInInjFuncSet) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncSetFuncIn) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncSetFuncInj) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjFuncSetFuncIn) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjFuncSetFuncSurj) =>
% 132.79/23.01 ((
% 132.79/23.01 (leftInvIsSurj) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjCantorThm) =>
% 132.79/23.01 ((
% 132.79/23.01 (foundation2) =>
% 132.79/23.01 ((
% 132.79/23.01 (notinself) =>
% 132.79/23.01 ((
% 132.79/23.01 (notinself2) =>
% 132.79/23.01 ((
% 132.79/23.01 (omegaSp) =>
% 132.79/23.01 ((
% 132.79/23.01 (omegaSclos) =>
% 132.79/23.01 ((
% 132.79/23.01 (peano0notS) =>
% 132.79/23.01 ((
% 132.79/23.01 (peanoSinj) =>
% 132.79/23.01 ((
% 132.79/23.01 (transitivesetOp1) =>
% 132.79/23.01 ((
% 132.79/23.01 (binintTransitive) =>
% 132.79/23.01 ((
% 132.79/23.01 (transitivesetOp2) =>
% 132.79/23.01 ((
% 132.79/23.01 (setunionTransitive) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalMinLem1) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalTransSet) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalTransSet1) =>
% 132.79/23.01 ((
% 132.79/23.01 (setunionOrdinalLem1) =>
% 132.79/23.01 (ordinal @
% 132.79/23.01 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/23.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2408])).
% 132.79/23.01 thf(zip_derived_cl2427, plain,
% 132.79/23.01 (~ (((inComplementUnionImpInComplement1) =>
% 132.79/23.01 (((binunionTE) =>
% 132.79/23.01 (((binunionTEcontra) =>
% 132.79/23.01 (((demorgan2a1) =>
% 132.79/23.01 (((complementUnionInPowersetComplement) =>
% 132.79/23.01 (((demorgan2a2) =>
% 132.79/23.01 (((demorgan1a) =>
% 132.79/23.01 (((demorgan1b) =>
% 132.79/23.01 (((demorgan1) =>
% 132.79/23.01 (((demorgan2a) =>
% 132.79/23.01 (((demorgan2b2) =>
% 132.79/23.01 (((demorgan2b) =>
% 132.79/23.01 (((demorgan2) =>
% 132.79/23.01 (((woz13rule0) =>
% 132.79/23.01 (((woz13rule1) =>
% 132.79/23.01 (((woz13rule2) =>
% 132.79/23.01 (((woz13rule3) =>
% 132.79/23.01 (((woz13rule4) =>
% 132.79/23.01 (((woz1_1) =>
% 132.79/23.01 (((woz1_2) =>
% 132.79/23.01 (((woz1_3) =>
% 132.79/23.01 (((woz1_4) =>
% 132.79/23.01 (((woz1_5) =>
% 132.79/23.01 (((breln1all2) =>
% 132.79/23.01 (((breln1SetBreln1) =>
% 132.79/23.01 (((choice2fnsingleton) =>
% 132.79/23.01 (((setOfPairsIsBReln1) =>
% 132.79/23.01 (((breln1all1) =>
% 132.79/23.01 (((subbreln1) =>
% 132.79/23.01 (((eqbreln1) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1invprop) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1invI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1invE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compprop) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compEex) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionprop) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionIL) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionIR) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionEcases) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionCommutes) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2Ex) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2W) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2A) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2B) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Ex) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Ex1) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Equiv) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1E) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1I) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncInInjFuncSet) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncSetFuncIn) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncSetFuncInj) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjFuncSetFuncIn) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjFuncSetFuncSurj) =>
% 132.79/23.01 ((
% 132.79/23.01 (leftInvIsSurj) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjCantorThm) =>
% 132.79/23.01 ((
% 132.79/23.01 (foundation2) =>
% 132.79/23.01 ((
% 132.79/23.01 (notinself) =>
% 132.79/23.01 ((
% 132.79/23.01 (notinself2) =>
% 132.79/23.01 ((
% 132.79/23.01 (omegaSp) =>
% 132.79/23.01 ((
% 132.79/23.01 (omegaSclos) =>
% 132.79/23.01 ((
% 132.79/23.01 (peano0notS) =>
% 132.79/23.01 ((
% 132.79/23.01 (peanoSinj) =>
% 132.79/23.01 ((
% 132.79/23.01 (transitivesetOp1) =>
% 132.79/23.01 ((
% 132.79/23.01 (binintTransitive) =>
% 132.79/23.01 ((
% 132.79/23.01 (transitivesetOp2) =>
% 132.79/23.01 ((
% 132.79/23.01 (setunionTransitive) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalMinLem1) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalTransSet) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalTransSet1) =>
% 132.79/23.01 ((
% 132.79/23.01 (setunionOrdinalLem1) =>
% 132.79/23.01 (ordinal @
% 132.79/23.01 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/23.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2417])).
% 132.79/23.01 thf(zip_derived_cl2437, plain,
% 132.79/23.01 (~ (((binunionTE) =>
% 132.79/23.01 (((binunionTEcontra) =>
% 132.79/23.01 (((demorgan2a1) =>
% 132.79/23.01 (((complementUnionInPowersetComplement) =>
% 132.79/23.01 (((demorgan2a2) =>
% 132.79/23.01 (((demorgan1a) =>
% 132.79/23.01 (((demorgan1b) =>
% 132.79/23.01 (((demorgan1) =>
% 132.79/23.01 (((demorgan2a) =>
% 132.79/23.01 (((demorgan2b2) =>
% 132.79/23.01 (((demorgan2b) =>
% 132.79/23.01 (((demorgan2) =>
% 132.79/23.01 (((woz13rule0) =>
% 132.79/23.01 (((woz13rule1) =>
% 132.79/23.01 (((woz13rule2) =>
% 132.79/23.01 (((woz13rule3) =>
% 132.79/23.01 (((woz13rule4) =>
% 132.79/23.01 (((woz1_1) =>
% 132.79/23.01 (((woz1_2) =>
% 132.79/23.01 (((woz1_3) =>
% 132.79/23.01 (((woz1_4) =>
% 132.79/23.01 (((woz1_5) =>
% 132.79/23.01 (((breln1all2) =>
% 132.79/23.01 (((breln1SetBreln1) =>
% 132.79/23.01 (((choice2fnsingleton) =>
% 132.79/23.01 (((setOfPairsIsBReln1) =>
% 132.79/23.01 (((breln1all1) =>
% 132.79/23.01 (((subbreln1) =>
% 132.79/23.01 (((eqbreln1) =>
% 132.79/23.01 (((breln1invprop) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1invI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1invE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compprop) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compEex) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionprop) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionIL) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionIR) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionEcases) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionCommutes) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2Ex) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2W) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2A) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2B) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Ex) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Ex1) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Equiv) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1E) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1I) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncInInjFuncSet) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncSetFuncIn) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncSetFuncInj) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjFuncSetFuncIn) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjFuncSetFuncSurj) =>
% 132.79/23.01 ((
% 132.79/23.01 (leftInvIsSurj) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjCantorThm) =>
% 132.79/23.01 ((
% 132.79/23.01 (foundation2) =>
% 132.79/23.01 ((
% 132.79/23.01 (notinself) =>
% 132.79/23.01 ((
% 132.79/23.01 (notinself2) =>
% 132.79/23.01 ((
% 132.79/23.01 (omegaSp) =>
% 132.79/23.01 ((
% 132.79/23.01 (omegaSclos) =>
% 132.79/23.01 ((
% 132.79/23.01 (peano0notS) =>
% 132.79/23.01 ((
% 132.79/23.01 (peanoSinj) =>
% 132.79/23.01 ((
% 132.79/23.01 (transitivesetOp1) =>
% 132.79/23.01 ((
% 132.79/23.01 (binintTransitive) =>
% 132.79/23.01 ((
% 132.79/23.01 (transitivesetOp2) =>
% 132.79/23.01 ((
% 132.79/23.01 (setunionTransitive) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalMinLem1) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalTransSet) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalTransSet1) =>
% 132.79/23.01 ((
% 132.79/23.01 (setunionOrdinalLem1) =>
% 132.79/23.01 (ordinal @
% 132.79/23.01 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/23.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2427])).
% 132.79/23.01 thf(zip_derived_cl2448, plain,
% 132.79/23.01 (~ (((binunionTEcontra) =>
% 132.79/23.01 (((demorgan2a1) =>
% 132.79/23.01 (((complementUnionInPowersetComplement) =>
% 132.79/23.01 (((demorgan2a2) =>
% 132.79/23.01 (((demorgan1a) =>
% 132.79/23.01 (((demorgan1b) =>
% 132.79/23.01 (((demorgan1) =>
% 132.79/23.01 (((demorgan2a) =>
% 132.79/23.01 (((demorgan2b2) =>
% 132.79/23.01 (((demorgan2b) =>
% 132.79/23.01 (((demorgan2) =>
% 132.79/23.01 (((woz13rule0) =>
% 132.79/23.01 (((woz13rule1) =>
% 132.79/23.01 (((woz13rule2) =>
% 132.79/23.01 (((woz13rule3) =>
% 132.79/23.01 (((woz13rule4) =>
% 132.79/23.01 (((woz1_1) =>
% 132.79/23.01 (((woz1_2) =>
% 132.79/23.01 (((woz1_3) =>
% 132.79/23.01 (((woz1_4) =>
% 132.79/23.01 (((woz1_5) =>
% 132.79/23.01 (((breln1all2) =>
% 132.79/23.01 (((breln1SetBreln1) =>
% 132.79/23.01 (((choice2fnsingleton) =>
% 132.79/23.01 (((setOfPairsIsBReln1) =>
% 132.79/23.01 (((breln1all1) =>
% 132.79/23.01 (((subbreln1) =>
% 132.79/23.01 (((eqbreln1) =>
% 132.79/23.01 (((breln1invprop) =>
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% 132.79/23.01 (breln1invE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compprop) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compEex) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionprop) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionIL) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionIR) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionEcases) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionCommutes) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2Ex) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2W) =>
% 132.79/23.01 ((
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% 132.79/23.01 ((
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% 132.79/23.01 ((
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% 132.79/23.01 ((
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% 132.79/23.01 ((
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% 132.79/23.01 ((
% 132.79/23.01 (image1E) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1I) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncInInjFuncSet) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncSetFuncIn) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncSetFuncInj) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjFuncSetFuncIn) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjFuncSetFuncSurj) =>
% 132.79/23.01 ((
% 132.79/23.01 (leftInvIsSurj) =>
% 132.79/23.01 ((
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% 132.79/23.01 ((
% 132.79/23.01 (foundation2) =>
% 132.79/23.01 ((
% 132.79/23.01 (notinself) =>
% 132.79/23.01 ((
% 132.79/23.01 (notinself2) =>
% 132.79/23.01 ((
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% 132.79/23.01 ((
% 132.79/23.01 (omegaSclos) =>
% 132.79/23.01 ((
% 132.79/23.01 (peano0notS) =>
% 132.79/23.01 ((
% 132.79/23.01 (peanoSinj) =>
% 132.79/23.01 ((
% 132.79/23.01 (transitivesetOp1) =>
% 132.79/23.01 ((
% 132.79/23.01 (binintTransitive) =>
% 132.79/23.01 ((
% 132.79/23.01 (transitivesetOp2) =>
% 132.79/23.01 ((
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% 132.79/23.01 ((
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% 132.79/23.01 ((
% 132.79/23.01 (ordinalTransSet) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalTransSet1) =>
% 132.79/23.01 ((
% 132.79/23.01 (setunionOrdinalLem1) =>
% 132.79/23.01 (ordinal @
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% 132.79/23.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2437])).
% 132.79/23.01 thf(zip_derived_cl2459, plain,
% 132.79/23.01 (~ (((demorgan2a1) =>
% 132.79/23.01 (((complementUnionInPowersetComplement) =>
% 132.79/23.01 (((demorgan2a2) =>
% 132.79/23.01 (((demorgan1a) =>
% 132.79/23.01 (((demorgan1b) =>
% 132.79/23.01 (((demorgan1) =>
% 132.79/23.01 (((demorgan2a) =>
% 132.79/23.01 (((demorgan2b2) =>
% 132.79/23.01 (((demorgan2b) =>
% 132.79/23.01 (((demorgan2) =>
% 132.79/23.01 (((woz13rule0) =>
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% 132.79/23.01 (((woz13rule2) =>
% 132.79/23.01 (((woz13rule3) =>
% 132.79/23.01 (((woz13rule4) =>
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% 132.79/23.01 (((woz1_2) =>
% 132.79/23.01 (((woz1_3) =>
% 132.79/23.01 (((woz1_4) =>
% 132.79/23.01 (((woz1_5) =>
% 132.79/23.01 (((breln1all2) =>
% 132.79/23.01 (((breln1SetBreln1) =>
% 132.79/23.01 (((choice2fnsingleton) =>
% 132.79/23.01 (((setOfPairsIsBReln1) =>
% 132.79/23.01 (((breln1all1) =>
% 132.79/23.01 (((subbreln1) =>
% 132.79/23.01 (((eqbreln1) =>
% 132.79/23.01 (((breln1invprop) =>
% 132.79/23.01 (((breln1invI) =>
% 132.79/23.01 (((breln1invE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compprop) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compEex) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionprop) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionIL) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionIR) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionEcases) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionCommutes) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2Ex) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2W) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2A) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2B) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Ex) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Ex1) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Equiv) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1E) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1I) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncInInjFuncSet) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncSetFuncIn) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncSetFuncInj) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjFuncSetFuncIn) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjFuncSetFuncSurj) =>
% 132.79/23.01 ((
% 132.79/23.01 (leftInvIsSurj) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjCantorThm) =>
% 132.79/23.01 ((
% 132.79/23.01 (foundation2) =>
% 132.79/23.01 ((
% 132.79/23.01 (notinself) =>
% 132.79/23.01 ((
% 132.79/23.01 (notinself2) =>
% 132.79/23.01 ((
% 132.79/23.01 (omegaSp) =>
% 132.79/23.01 ((
% 132.79/23.01 (omegaSclos) =>
% 132.79/23.01 ((
% 132.79/23.01 (peano0notS) =>
% 132.79/23.01 ((
% 132.79/23.01 (peanoSinj) =>
% 132.79/23.01 ((
% 132.79/23.01 (transitivesetOp1) =>
% 132.79/23.01 ((
% 132.79/23.01 (binintTransitive) =>
% 132.79/23.01 ((
% 132.79/23.01 (transitivesetOp2) =>
% 132.79/23.01 ((
% 132.79/23.01 (setunionTransitive) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalMinLem1) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalTransSet) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalTransSet1) =>
% 132.79/23.01 ((
% 132.79/23.01 (setunionOrdinalLem1) =>
% 132.79/23.01 (ordinal @
% 132.79/23.01 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/23.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2448])).
% 132.79/23.01 thf(zip_derived_cl2470, plain,
% 132.79/23.01 (~ (((complementUnionInPowersetComplement) =>
% 132.79/23.01 (((demorgan2a2) =>
% 132.79/23.01 (((demorgan1a) =>
% 132.79/23.01 (((demorgan1b) =>
% 132.79/23.01 (((demorgan1) =>
% 132.79/23.01 (((demorgan2a) =>
% 132.79/23.01 (((demorgan2b2) =>
% 132.79/23.01 (((demorgan2b) =>
% 132.79/23.01 (((demorgan2) =>
% 132.79/23.01 (((woz13rule0) =>
% 132.79/23.01 (((woz13rule1) =>
% 132.79/23.01 (((woz13rule2) =>
% 132.79/23.01 (((woz13rule3) =>
% 132.79/23.01 (((woz13rule4) =>
% 132.79/23.01 (((woz1_1) =>
% 132.79/23.01 (((woz1_2) =>
% 132.79/23.01 (((woz1_3) =>
% 132.79/23.01 (((woz1_4) =>
% 132.79/23.01 (((woz1_5) =>
% 132.79/23.01 (((breln1all2) =>
% 132.79/23.01 (((breln1SetBreln1) =>
% 132.79/23.01 (((choice2fnsingleton) =>
% 132.79/23.01 (((setOfPairsIsBReln1) =>
% 132.79/23.01 (((breln1all1) =>
% 132.79/23.01 (((subbreln1) =>
% 132.79/23.01 (((eqbreln1) =>
% 132.79/23.01 (((breln1invprop) =>
% 132.79/23.01 (((breln1invI) =>
% 132.79/23.01 (((breln1invE) =>
% 132.79/23.01 (((breln1compprop) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compEex) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionprop) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionIL) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionIR) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionEcases) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionCommutes) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2Ex) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2W) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2A) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2B) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Ex) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Ex1) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Equiv) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1E) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1I) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncInInjFuncSet) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncSetFuncIn) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncSetFuncInj) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjFuncSetFuncIn) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjFuncSetFuncSurj) =>
% 132.79/23.01 ((
% 132.79/23.01 (leftInvIsSurj) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjCantorThm) =>
% 132.79/23.01 ((
% 132.79/23.01 (foundation2) =>
% 132.79/23.01 ((
% 132.79/23.01 (notinself) =>
% 132.79/23.01 ((
% 132.79/23.01 (notinself2) =>
% 132.79/23.01 ((
% 132.79/23.01 (omegaSp) =>
% 132.79/23.01 ((
% 132.79/23.01 (omegaSclos) =>
% 132.79/23.01 ((
% 132.79/23.01 (peano0notS) =>
% 132.79/23.01 ((
% 132.79/23.01 (peanoSinj) =>
% 132.79/23.01 ((
% 132.79/23.01 (transitivesetOp1) =>
% 132.79/23.01 ((
% 132.79/23.01 (binintTransitive) =>
% 132.79/23.01 ((
% 132.79/23.01 (transitivesetOp2) =>
% 132.79/23.01 ((
% 132.79/23.01 (setunionTransitive) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalMinLem1) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalTransSet) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalTransSet1) =>
% 132.79/23.01 ((
% 132.79/23.01 (setunionOrdinalLem1) =>
% 132.79/23.01 (ordinal @
% 132.79/23.01 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/23.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2459])).
% 132.79/23.01 thf(zip_derived_cl2481, plain,
% 132.79/23.01 (~ (((demorgan2a2) =>
% 132.79/23.01 (((demorgan1a) =>
% 132.79/23.01 (((demorgan1b) =>
% 132.79/23.01 (((demorgan1) =>
% 132.79/23.01 (((demorgan2a) =>
% 132.79/23.01 (((demorgan2b2) =>
% 132.79/23.01 (((demorgan2b) =>
% 132.79/23.01 (((demorgan2) =>
% 132.79/23.01 (((woz13rule0) =>
% 132.79/23.01 (((woz13rule1) =>
% 132.79/23.01 (((woz13rule2) =>
% 132.79/23.01 (((woz13rule3) =>
% 132.79/23.01 (((woz13rule4) =>
% 132.79/23.01 (((woz1_1) =>
% 132.79/23.01 (((woz1_2) =>
% 132.79/23.01 (((woz1_3) =>
% 132.79/23.01 (((woz1_4) =>
% 132.79/23.01 (((woz1_5) =>
% 132.79/23.01 (((breln1all2) =>
% 132.79/23.01 (((breln1SetBreln1) =>
% 132.79/23.01 (((choice2fnsingleton) =>
% 132.79/23.01 (((setOfPairsIsBReln1) =>
% 132.79/23.01 (((breln1all1) =>
% 132.79/23.01 (((subbreln1) =>
% 132.79/23.01 (((eqbreln1) =>
% 132.79/23.01 (((breln1invprop) =>
% 132.79/23.01 (((breln1invI) =>
% 132.79/23.01 (((breln1invE) =>
% 132.79/23.01 (((breln1compprop) =>
% 132.79/23.01 (((breln1compI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compEex) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionprop) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionIL) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionIR) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionEcases) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionCommutes) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2Ex) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2W) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2A) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2B) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Ex) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Ex1) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Equiv) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1E) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1I) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncInInjFuncSet) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncSetFuncIn) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncSetFuncInj) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjFuncSetFuncIn) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjFuncSetFuncSurj) =>
% 132.79/23.01 ((
% 132.79/23.01 (leftInvIsSurj) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjCantorThm) =>
% 132.79/23.01 ((
% 132.79/23.01 (foundation2) =>
% 132.79/23.01 ((
% 132.79/23.01 (notinself) =>
% 132.79/23.01 ((
% 132.79/23.01 (notinself2) =>
% 132.79/23.01 ((
% 132.79/23.01 (omegaSp) =>
% 132.79/23.01 ((
% 132.79/23.01 (omegaSclos) =>
% 132.79/23.01 ((
% 132.79/23.01 (peano0notS) =>
% 132.79/23.01 ((
% 132.79/23.01 (peanoSinj) =>
% 132.79/23.01 ((
% 132.79/23.01 (transitivesetOp1) =>
% 132.79/23.01 ((
% 132.79/23.01 (binintTransitive) =>
% 132.79/23.01 ((
% 132.79/23.01 (transitivesetOp2) =>
% 132.79/23.01 ((
% 132.79/23.01 (setunionTransitive) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalMinLem1) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalTransSet) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalTransSet1) =>
% 132.79/23.01 ((
% 132.79/23.01 (setunionOrdinalLem1) =>
% 132.79/23.01 (ordinal @
% 132.79/23.01 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/23.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2470])).
% 132.79/23.01 thf(zip_derived_cl2493, plain,
% 132.79/23.01 (~ (((demorgan1a) =>
% 132.79/23.01 (((demorgan1b) =>
% 132.79/23.01 (((demorgan1) =>
% 132.79/23.01 (((demorgan2a) =>
% 132.79/23.01 (((demorgan2b2) =>
% 132.79/23.01 (((demorgan2b) =>
% 132.79/23.01 (((demorgan2) =>
% 132.79/23.01 (((woz13rule0) =>
% 132.79/23.01 (((woz13rule1) =>
% 132.79/23.01 (((woz13rule2) =>
% 132.79/23.01 (((woz13rule3) =>
% 132.79/23.01 (((woz13rule4) =>
% 132.79/23.01 (((woz1_1) =>
% 132.79/23.01 (((woz1_2) =>
% 132.79/23.01 (((woz1_3) =>
% 132.79/23.01 (((woz1_4) =>
% 132.79/23.01 (((woz1_5) =>
% 132.79/23.01 (((breln1all2) =>
% 132.79/23.01 (((breln1SetBreln1) =>
% 132.79/23.01 (((choice2fnsingleton) =>
% 132.79/23.01 (((setOfPairsIsBReln1) =>
% 132.79/23.01 (((breln1all1) =>
% 132.79/23.01 (((subbreln1) =>
% 132.79/23.01 (((eqbreln1) =>
% 132.79/23.01 (((breln1invprop) =>
% 132.79/23.01 (((breln1invI) =>
% 132.79/23.01 (((breln1invE) =>
% 132.79/23.01 (((breln1compprop) =>
% 132.79/23.01 (((breln1compI) =>
% 132.79/23.01 (((breln1compE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1compEex) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionprop) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionIL) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionIR) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionEcases) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionCommutes) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2Ex) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2W) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2A) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2B) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Ex) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Ex1) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Equiv) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1E) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1I) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncInInjFuncSet) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncSetFuncIn) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncSetFuncInj) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjFuncSetFuncIn) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjFuncSetFuncSurj) =>
% 132.79/23.01 ((
% 132.79/23.01 (leftInvIsSurj) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjCantorThm) =>
% 132.79/23.01 ((
% 132.79/23.01 (foundation2) =>
% 132.79/23.01 ((
% 132.79/23.01 (notinself) =>
% 132.79/23.01 ((
% 132.79/23.01 (notinself2) =>
% 132.79/23.01 ((
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% 132.79/23.01 ((
% 132.79/23.01 (omegaSclos) =>
% 132.79/23.01 ((
% 132.79/23.01 (peano0notS) =>
% 132.79/23.01 ((
% 132.79/23.01 (peanoSinj) =>
% 132.79/23.01 ((
% 132.79/23.01 (transitivesetOp1) =>
% 132.79/23.01 ((
% 132.79/23.01 (binintTransitive) =>
% 132.79/23.01 ((
% 132.79/23.01 (transitivesetOp2) =>
% 132.79/23.01 ((
% 132.79/23.01 (setunionTransitive) =>
% 132.79/23.01 ((
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% 132.79/23.01 ((
% 132.79/23.01 (ordinalTransSet) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalTransSet1) =>
% 132.79/23.01 ((
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% 132.79/23.01 (ordinal @
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% 132.79/23.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2481])).
% 132.79/23.01 thf(zip_derived_cl2506, plain,
% 132.79/23.01 (~ (((demorgan1b) =>
% 132.79/23.01 (((demorgan1) =>
% 132.79/23.01 (((demorgan2a) =>
% 132.79/23.01 (((demorgan2b2) =>
% 132.79/23.01 (((demorgan2b) =>
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% 132.79/23.01 (((woz13rule1) =>
% 132.79/23.01 (((woz13rule2) =>
% 132.79/23.01 (((woz13rule3) =>
% 132.79/23.01 (((woz13rule4) =>
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% 132.79/23.01 (((woz1_2) =>
% 132.79/23.01 (((woz1_3) =>
% 132.79/23.01 (((woz1_4) =>
% 132.79/23.01 (((woz1_5) =>
% 132.79/23.01 (((breln1all2) =>
% 132.79/23.01 (((breln1SetBreln1) =>
% 132.79/23.01 (((choice2fnsingleton) =>
% 132.79/23.01 (((setOfPairsIsBReln1) =>
% 132.79/23.01 (((breln1all1) =>
% 132.79/23.01 (((subbreln1) =>
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% 132.79/23.01 (((breln1invE) =>
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% 132.79/23.01 ((
% 132.79/23.01 (breln1unionIR) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionEcases) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionCommutes) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2Ex) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2W) =>
% 132.79/23.01 ((
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% 132.79/23.01 ((
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% 132.79/23.01 ((
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% 132.79/23.01 ((
% 132.79/23.01 (image1Ex1) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Equiv) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1E) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1I) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncInInjFuncSet) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncSetFuncIn) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncSetFuncInj) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjFuncSetFuncIn) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjFuncSetFuncSurj) =>
% 132.79/23.01 ((
% 132.79/23.01 (leftInvIsSurj) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjCantorThm) =>
% 132.79/23.01 ((
% 132.79/23.01 (foundation2) =>
% 132.79/23.01 ((
% 132.79/23.01 (notinself) =>
% 132.79/23.01 ((
% 132.79/23.01 (notinself2) =>
% 132.79/23.01 ((
% 132.79/23.01 (omegaSp) =>
% 132.79/23.01 ((
% 132.79/23.01 (omegaSclos) =>
% 132.79/23.01 ((
% 132.79/23.01 (peano0notS) =>
% 132.79/23.01 ((
% 132.79/23.01 (peanoSinj) =>
% 132.79/23.01 ((
% 132.79/23.01 (transitivesetOp1) =>
% 132.79/23.01 ((
% 132.79/23.01 (binintTransitive) =>
% 132.79/23.01 ((
% 132.79/23.01 (transitivesetOp2) =>
% 132.79/23.01 ((
% 132.79/23.01 (setunionTransitive) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalMinLem1) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalTransSet) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalTransSet1) =>
% 132.79/23.01 ((
% 132.79/23.01 (setunionOrdinalLem1) =>
% 132.79/23.01 (ordinal @
% 132.79/23.01 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/23.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2493])).
% 132.79/23.01 thf(zip_derived_cl2518, plain,
% 132.79/23.01 (~ (((demorgan1) =>
% 132.79/23.01 (((demorgan2a) =>
% 132.79/23.01 (((demorgan2b2) =>
% 132.79/23.01 (((demorgan2b) =>
% 132.79/23.01 (((demorgan2) =>
% 132.79/23.01 (((woz13rule0) =>
% 132.79/23.01 (((woz13rule1) =>
% 132.79/23.01 (((woz13rule2) =>
% 132.79/23.01 (((woz13rule3) =>
% 132.79/23.01 (((woz13rule4) =>
% 132.79/23.01 (((woz1_1) =>
% 132.79/23.01 (((woz1_2) =>
% 132.79/23.01 (((woz1_3) =>
% 132.79/23.01 (((woz1_4) =>
% 132.79/23.01 (((woz1_5) =>
% 132.79/23.01 (((breln1all2) =>
% 132.79/23.01 (((breln1SetBreln1) =>
% 132.79/23.01 (((choice2fnsingleton) =>
% 132.79/23.01 (((setOfPairsIsBReln1) =>
% 132.79/23.01 (((breln1all1) =>
% 132.79/23.01 (((subbreln1) =>
% 132.79/23.01 (((eqbreln1) =>
% 132.79/23.01 (((breln1invprop) =>
% 132.79/23.01 (((breln1invI) =>
% 132.79/23.01 (((breln1invE) =>
% 132.79/23.01 (((breln1compprop) =>
% 132.79/23.01 (((breln1compI) =>
% 132.79/23.01 (((breln1compE) =>
% 132.79/23.01 (((breln1compEex) =>
% 132.79/23.01 (((breln1unionprop) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionIL) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionIR) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionEcases) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionCommutes) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2Ex) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2W) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2A) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2B) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Ex) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Ex1) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Equiv) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1E) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1I) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncInInjFuncSet) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncSetFuncIn) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncSetFuncInj) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjFuncSetFuncIn) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjFuncSetFuncSurj) =>
% 132.79/23.01 ((
% 132.79/23.01 (leftInvIsSurj) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjCantorThm) =>
% 132.79/23.01 ((
% 132.79/23.01 (foundation2) =>
% 132.79/23.01 ((
% 132.79/23.01 (notinself) =>
% 132.79/23.01 ((
% 132.79/23.01 (notinself2) =>
% 132.79/23.01 ((
% 132.79/23.01 (omegaSp) =>
% 132.79/23.01 ((
% 132.79/23.01 (omegaSclos) =>
% 132.79/23.01 ((
% 132.79/23.01 (peano0notS) =>
% 132.79/23.01 ((
% 132.79/23.01 (peanoSinj) =>
% 132.79/23.01 ((
% 132.79/23.01 (transitivesetOp1) =>
% 132.79/23.01 ((
% 132.79/23.01 (binintTransitive) =>
% 132.79/23.01 ((
% 132.79/23.01 (transitivesetOp2) =>
% 132.79/23.01 ((
% 132.79/23.01 (setunionTransitive) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalMinLem1) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalTransSet) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalTransSet1) =>
% 132.79/23.01 ((
% 132.79/23.01 (setunionOrdinalLem1) =>
% 132.79/23.01 (ordinal @
% 132.79/23.01 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/23.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2506])).
% 132.79/23.01 thf(zip_derived_cl2530, plain,
% 132.79/23.01 (~ (((demorgan2a) =>
% 132.79/23.01 (((demorgan2b2) =>
% 132.79/23.01 (((demorgan2b) =>
% 132.79/23.01 (((demorgan2) =>
% 132.79/23.01 (((woz13rule0) =>
% 132.79/23.01 (((woz13rule1) =>
% 132.79/23.01 (((woz13rule2) =>
% 132.79/23.01 (((woz13rule3) =>
% 132.79/23.01 (((woz13rule4) =>
% 132.79/23.01 (((woz1_1) =>
% 132.79/23.01 (((woz1_2) =>
% 132.79/23.01 (((woz1_3) =>
% 132.79/23.01 (((woz1_4) =>
% 132.79/23.01 (((woz1_5) =>
% 132.79/23.01 (((breln1all2) =>
% 132.79/23.01 (((breln1SetBreln1) =>
% 132.79/23.01 (((choice2fnsingleton) =>
% 132.79/23.01 (((setOfPairsIsBReln1) =>
% 132.79/23.01 (((breln1all1) =>
% 132.79/23.01 (((subbreln1) =>
% 132.79/23.01 (((eqbreln1) =>
% 132.79/23.01 (((breln1invprop) =>
% 132.79/23.01 (((breln1invI) =>
% 132.79/23.01 (((breln1invE) =>
% 132.79/23.01 (((breln1compprop) =>
% 132.79/23.01 (((breln1compI) =>
% 132.79/23.01 (((breln1compE) =>
% 132.79/23.01 (((breln1compEex) =>
% 132.79/23.01 (((breln1unionprop) =>
% 132.79/23.01 (((breln1unionIL) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionIR) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionEcases) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionCommutes) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2Ex) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2W) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2A) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2B) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Ex) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Ex1) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Equiv) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1E) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1I) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncInInjFuncSet) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncSetFuncIn) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncSetFuncInj) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjFuncSetFuncIn) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjFuncSetFuncSurj) =>
% 132.79/23.01 ((
% 132.79/23.01 (leftInvIsSurj) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjCantorThm) =>
% 132.79/23.01 ((
% 132.79/23.01 (foundation2) =>
% 132.79/23.01 ((
% 132.79/23.01 (notinself) =>
% 132.79/23.01 ((
% 132.79/23.01 (notinself2) =>
% 132.79/23.01 ((
% 132.79/23.01 (omegaSp) =>
% 132.79/23.01 ((
% 132.79/23.01 (omegaSclos) =>
% 132.79/23.01 ((
% 132.79/23.01 (peano0notS) =>
% 132.79/23.01 ((
% 132.79/23.01 (peanoSinj) =>
% 132.79/23.01 ((
% 132.79/23.01 (transitivesetOp1) =>
% 132.79/23.01 ((
% 132.79/23.01 (binintTransitive) =>
% 132.79/23.01 ((
% 132.79/23.01 (transitivesetOp2) =>
% 132.79/23.01 ((
% 132.79/23.01 (setunionTransitive) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalMinLem1) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalTransSet) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalTransSet1) =>
% 132.79/23.01 ((
% 132.79/23.01 (setunionOrdinalLem1) =>
% 132.79/23.01 (ordinal @
% 132.79/23.01 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/23.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2518])).
% 132.79/23.01 thf(zip_derived_cl2541, plain,
% 132.79/23.01 (~ (((demorgan2b2) =>
% 132.79/23.01 (((demorgan2b) =>
% 132.79/23.01 (((demorgan2) =>
% 132.79/23.01 (((woz13rule0) =>
% 132.79/23.01 (((woz13rule1) =>
% 132.79/23.01 (((woz13rule2) =>
% 132.79/23.01 (((woz13rule3) =>
% 132.79/23.01 (((woz13rule4) =>
% 132.79/23.01 (((woz1_1) =>
% 132.79/23.01 (((woz1_2) =>
% 132.79/23.01 (((woz1_3) =>
% 132.79/23.01 (((woz1_4) =>
% 132.79/23.01 (((woz1_5) =>
% 132.79/23.01 (((breln1all2) =>
% 132.79/23.01 (((breln1SetBreln1) =>
% 132.79/23.01 (((choice2fnsingleton) =>
% 132.79/23.01 (((setOfPairsIsBReln1) =>
% 132.79/23.01 (((breln1all1) =>
% 132.79/23.01 (((subbreln1) =>
% 132.79/23.01 (((eqbreln1) =>
% 132.79/23.01 (((breln1invprop) =>
% 132.79/23.01 (((breln1invI) =>
% 132.79/23.01 (((breln1invE) =>
% 132.79/23.01 (((breln1compprop) =>
% 132.79/23.01 (((breln1compI) =>
% 132.79/23.01 (((breln1compE) =>
% 132.79/23.01 (((breln1compEex) =>
% 132.79/23.01 (((breln1unionprop) =>
% 132.79/23.01 (((breln1unionIL) =>
% 132.79/23.01 (((breln1unionIR) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionEcases) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionCommutes) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2Ex) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2W) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2A) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2B) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Ex) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Ex1) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Equiv) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1E) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1I) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncInInjFuncSet) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncSetFuncIn) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncSetFuncInj) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjFuncSetFuncIn) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjFuncSetFuncSurj) =>
% 132.79/23.01 ((
% 132.79/23.01 (leftInvIsSurj) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjCantorThm) =>
% 132.79/23.01 ((
% 132.79/23.01 (foundation2) =>
% 132.79/23.01 ((
% 132.79/23.01 (notinself) =>
% 132.79/23.01 ((
% 132.79/23.01 (notinself2) =>
% 132.79/23.01 ((
% 132.79/23.01 (omegaSp) =>
% 132.79/23.01 ((
% 132.79/23.01 (omegaSclos) =>
% 132.79/23.01 ((
% 132.79/23.01 (peano0notS) =>
% 132.79/23.01 ((
% 132.79/23.01 (peanoSinj) =>
% 132.79/23.01 ((
% 132.79/23.01 (transitivesetOp1) =>
% 132.79/23.01 ((
% 132.79/23.01 (binintTransitive) =>
% 132.79/23.01 ((
% 132.79/23.01 (transitivesetOp2) =>
% 132.79/23.01 ((
% 132.79/23.01 (setunionTransitive) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalMinLem1) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalTransSet) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalTransSet1) =>
% 132.79/23.01 ((
% 132.79/23.01 (setunionOrdinalLem1) =>
% 132.79/23.01 (ordinal @
% 132.79/23.01 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/23.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2530])).
% 132.79/23.01 thf(zip_derived_cl2552, plain,
% 132.79/23.01 (~ (((demorgan2b) =>
% 132.79/23.01 (((demorgan2) =>
% 132.79/23.01 (((woz13rule0) =>
% 132.79/23.01 (((woz13rule1) =>
% 132.79/23.01 (((woz13rule2) =>
% 132.79/23.01 (((woz13rule3) =>
% 132.79/23.01 (((woz13rule4) =>
% 132.79/23.01 (((woz1_1) =>
% 132.79/23.01 (((woz1_2) =>
% 132.79/23.01 (((woz1_3) =>
% 132.79/23.01 (((woz1_4) =>
% 132.79/23.01 (((woz1_5) =>
% 132.79/23.01 (((breln1all2) =>
% 132.79/23.01 (((breln1SetBreln1) =>
% 132.79/23.01 (((choice2fnsingleton) =>
% 132.79/23.01 (((setOfPairsIsBReln1) =>
% 132.79/23.01 (((breln1all1) =>
% 132.79/23.01 (((subbreln1) =>
% 132.79/23.01 (((eqbreln1) =>
% 132.79/23.01 (((breln1invprop) =>
% 132.79/23.01 (((breln1invI) =>
% 132.79/23.01 (((breln1invE) =>
% 132.79/23.01 (((breln1compprop) =>
% 132.79/23.01 (((breln1compI) =>
% 132.79/23.01 (((breln1compE) =>
% 132.79/23.01 (((breln1compEex) =>
% 132.79/23.01 (((breln1unionprop) =>
% 132.79/23.01 (((breln1unionIL) =>
% 132.79/23.01 (((breln1unionIR) =>
% 132.79/23.01 (((breln1unionI) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionEcases) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionCommutes) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2Ex) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2W) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2A) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2B) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Ex) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Ex1) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1Equiv) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1E) =>
% 132.79/23.01 ((
% 132.79/23.01 (image1I) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncInInjFuncSet) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncSetFuncIn) =>
% 132.79/23.01 ((
% 132.79/23.01 (injFuncSetFuncInj) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjFuncSetFuncIn) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjFuncSetFuncSurj) =>
% 132.79/23.01 ((
% 132.79/23.01 (leftInvIsSurj) =>
% 132.79/23.01 ((
% 132.79/23.01 (surjCantorThm) =>
% 132.79/23.01 ((
% 132.79/23.01 (foundation2) =>
% 132.79/23.01 ((
% 132.79/23.01 (notinself) =>
% 132.79/23.01 ((
% 132.79/23.01 (notinself2) =>
% 132.79/23.01 ((
% 132.79/23.01 (omegaSp) =>
% 132.79/23.01 ((
% 132.79/23.01 (omegaSclos) =>
% 132.79/23.01 ((
% 132.79/23.01 (peano0notS) =>
% 132.79/23.01 ((
% 132.79/23.01 (peanoSinj) =>
% 132.79/23.01 ((
% 132.79/23.01 (transitivesetOp1) =>
% 132.79/23.01 ((
% 132.79/23.01 (binintTransitive) =>
% 132.79/23.01 ((
% 132.79/23.01 (transitivesetOp2) =>
% 132.79/23.01 ((
% 132.79/23.01 (setunionTransitive) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalMinLem1) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalTransSet) =>
% 132.79/23.01 ((
% 132.79/23.01 (ordinalTransSet1) =>
% 132.79/23.01 ((
% 132.79/23.01 (setunionOrdinalLem1) =>
% 132.79/23.01 (ordinal @
% 132.79/23.01 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/23.01 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2541])).
% 132.79/23.01 thf(zip_derived_cl2563, plain,
% 132.79/23.01 (~ (((demorgan2) =>
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% 132.79/23.01 (((woz13rule1) =>
% 132.79/23.01 (((woz13rule2) =>
% 132.79/23.01 (((woz13rule3) =>
% 132.79/23.01 (((woz13rule4) =>
% 132.79/23.01 (((woz1_1) =>
% 132.79/23.01 (((woz1_2) =>
% 132.79/23.01 (((woz1_3) =>
% 132.79/23.01 (((woz1_4) =>
% 132.79/23.01 (((woz1_5) =>
% 132.79/23.01 (((breln1all2) =>
% 132.79/23.01 (((breln1SetBreln1) =>
% 132.79/23.01 (((choice2fnsingleton) =>
% 132.79/23.01 (((setOfPairsIsBReln1) =>
% 132.79/23.01 (((breln1all1) =>
% 132.79/23.01 (((subbreln1) =>
% 132.79/23.01 (((eqbreln1) =>
% 132.79/23.01 (((breln1invprop) =>
% 132.79/23.01 (((breln1invI) =>
% 132.79/23.01 (((breln1invE) =>
% 132.79/23.01 (((breln1compprop) =>
% 132.79/23.01 (((breln1compI) =>
% 132.79/23.01 (((breln1compE) =>
% 132.79/23.01 (((breln1compEex) =>
% 132.79/23.01 (((breln1unionprop) =>
% 132.79/23.01 (((breln1unionIL) =>
% 132.79/23.01 (((breln1unionIR) =>
% 132.79/23.01 (((breln1unionI) =>
% 132.79/23.01 (((breln1unionE) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionEcases) =>
% 132.79/23.01 ((
% 132.79/23.01 (breln1unionCommutes) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2Ex) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2W) =>
% 132.79/23.01 ((
% 132.79/23.01 (woz2A) =>
% 132.79/23.01 ((
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% 132.79/23.01 ((
% 132.79/23.01 (omegaSclos) =>
% 132.79/23.01 ((
% 132.79/23.01 (peano0notS) =>
% 132.79/23.01 ((
% 132.79/23.01 (peanoSinj) =>
% 132.79/23.01 ((
% 132.79/23.01 (transitivesetOp1) =>
% 132.79/23.01 ((
% 132.79/23.01 (binintTransitive) =>
% 132.79/23.01 ((
% 132.79/23.02 (transitivesetOp2) =>
% 132.79/23.02 ((
% 132.79/23.02 (setunionTransitive) =>
% 132.79/23.02 ((
% 132.79/23.02 (ordinalMinLem1) =>
% 132.79/23.02 ((
% 132.79/23.02 (ordinalTransSet) =>
% 132.79/23.02 ((
% 132.79/23.02 (ordinalTransSet1) =>
% 132.79/23.02 ((
% 132.79/23.02 (setunionOrdinalLem1) =>
% 132.79/23.02 (ordinal @
% 132.79/23.02 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/23.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2610])).
% 132.79/23.02 thf(zip_derived_cl2630, plain,
% 132.79/23.02 (~ (((woz1_1) =>
% 132.79/23.02 (((woz1_2) =>
% 132.79/23.02 (((woz1_3) =>
% 132.79/23.02 (((woz1_4) =>
% 132.79/23.02 (((woz1_5) =>
% 132.79/23.02 (((breln1all2) =>
% 132.79/23.02 (((breln1SetBreln1) =>
% 132.79/23.02 (((choice2fnsingleton) =>
% 132.79/23.02 (((setOfPairsIsBReln1) =>
% 132.79/23.02 (((breln1all1) =>
% 132.79/23.02 (((subbreln1) =>
% 132.79/23.02 (((eqbreln1) =>
% 132.79/23.02 (((breln1invprop) =>
% 132.79/23.02 (((breln1invI) =>
% 132.79/23.02 (((breln1invE) =>
% 132.79/23.02 (((breln1compprop) =>
% 132.79/23.02 (((breln1compI) =>
% 132.79/23.02 (((breln1compE) =>
% 132.79/23.02 (((breln1compEex) =>
% 132.79/23.02 (((breln1unionprop) =>
% 132.79/23.02 (((breln1unionIL) =>
% 132.79/23.02 (((breln1unionIR) =>
% 132.79/23.02 (((breln1unionI) =>
% 132.79/23.02 (((breln1unionE) =>
% 132.79/23.02 (((breln1unionEcases) =>
% 132.79/23.02 (((breln1unionCommutes) =>
% 132.79/23.02 (((woz2Ex) =>
% 132.79/23.02 (((woz2W) =>
% 132.79/23.02 (((woz2A) =>
% 132.79/23.02 (((woz2B) =>
% 132.79/23.02 ((
% 132.79/23.02 (image1Ex) =>
% 132.79/23.02 ((
% 132.79/23.02 (image1Ex1) =>
% 132.79/23.02 ((
% 132.79/23.02 (image1Equiv) =>
% 132.79/23.02 ((
% 132.79/23.02 (image1E) =>
% 132.79/23.02 ((
% 132.79/23.02 (image1I) =>
% 132.79/23.02 ((
% 132.79/23.02 (injFuncInInjFuncSet) =>
% 132.79/23.02 ((
% 132.79/23.02 (injFuncSetFuncIn) =>
% 132.79/23.02 ((
% 132.79/23.02 (injFuncSetFuncInj) =>
% 132.79/23.02 ((
% 132.79/23.02 (surjFuncSetFuncIn) =>
% 132.79/23.02 ((
% 132.79/23.02 (surjFuncSetFuncSurj) =>
% 132.79/23.02 ((
% 132.79/23.02 (leftInvIsSurj) =>
% 132.79/23.02 ((
% 132.79/23.02 (surjCantorThm) =>
% 132.79/23.02 ((
% 132.79/23.02 (foundation2) =>
% 132.79/23.02 ((
% 132.79/23.02 (notinself) =>
% 132.79/23.02 ((
% 132.79/23.02 (notinself2) =>
% 132.79/23.02 ((
% 132.79/23.02 (omegaSp) =>
% 132.79/23.02 ((
% 132.79/23.02 (omegaSclos) =>
% 132.79/23.02 ((
% 132.79/23.02 (peano0notS) =>
% 132.79/23.02 ((
% 132.79/23.02 (peanoSinj) =>
% 132.79/23.02 ((
% 132.79/23.02 (transitivesetOp1) =>
% 132.79/23.02 ((
% 132.79/23.02 (binintTransitive) =>
% 132.79/23.02 ((
% 132.79/23.02 (transitivesetOp2) =>
% 132.79/23.02 ((
% 132.79/23.02 (setunionTransitive) =>
% 132.79/23.02 ((
% 132.79/23.02 (ordinalMinLem1) =>
% 132.79/23.02 ((
% 132.79/23.02 (ordinalTransSet) =>
% 132.79/23.02 ((
% 132.79/23.02 (ordinalTransSet1) =>
% 132.79/23.02 ((
% 132.79/23.02 (setunionOrdinalLem1) =>
% 132.79/23.02 (ordinal @
% 132.79/23.02 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/23.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2620])).
% 132.79/23.02 thf(zip_derived_cl2641, plain,
% 132.79/23.02 (~ (((woz1_2) =>
% 132.79/23.02 (((woz1_3) =>
% 132.79/23.02 (((woz1_4) =>
% 132.79/23.02 (((woz1_5) =>
% 132.79/23.02 (((breln1all2) =>
% 132.79/23.02 (((breln1SetBreln1) =>
% 132.79/23.02 (((choice2fnsingleton) =>
% 132.79/23.02 (((setOfPairsIsBReln1) =>
% 132.79/23.02 (((breln1all1) =>
% 132.79/23.02 (((subbreln1) =>
% 132.79/23.02 (((eqbreln1) =>
% 132.79/23.02 (((breln1invprop) =>
% 132.79/23.02 (((breln1invI) =>
% 132.79/23.02 (((breln1invE) =>
% 132.79/23.02 (((breln1compprop) =>
% 132.79/23.02 (((breln1compI) =>
% 132.79/23.02 (((breln1compE) =>
% 132.79/23.02 (((breln1compEex) =>
% 132.79/23.02 (((breln1unionprop) =>
% 132.79/23.02 (((breln1unionIL) =>
% 132.79/23.02 (((breln1unionIR) =>
% 132.79/23.02 (((breln1unionI) =>
% 132.79/23.02 (((breln1unionE) =>
% 132.79/23.02 (((breln1unionEcases) =>
% 132.79/23.02 (((breln1unionCommutes) =>
% 132.79/23.02 (((woz2Ex) =>
% 132.79/23.02 (((woz2W) =>
% 132.79/23.02 (((woz2A) =>
% 132.79/23.02 (((woz2B) =>
% 132.79/23.02 (((image1Ex) =>
% 132.79/23.02 ((
% 132.79/23.02 (image1Ex1) =>
% 132.79/23.02 ((
% 132.79/23.02 (image1Equiv) =>
% 132.79/23.02 ((
% 132.79/23.02 (image1E) =>
% 132.79/23.02 ((
% 132.79/23.02 (image1I) =>
% 132.79/23.02 ((
% 132.79/23.02 (injFuncInInjFuncSet) =>
% 132.79/23.02 ((
% 132.79/23.02 (injFuncSetFuncIn) =>
% 132.79/23.02 ((
% 132.79/23.02 (injFuncSetFuncInj) =>
% 132.79/23.02 ((
% 132.79/23.02 (surjFuncSetFuncIn) =>
% 132.79/23.02 ((
% 132.79/23.02 (surjFuncSetFuncSurj) =>
% 132.79/23.02 ((
% 132.79/23.02 (leftInvIsSurj) =>
% 132.79/23.02 ((
% 132.79/23.02 (surjCantorThm) =>
% 132.79/23.02 ((
% 132.79/23.02 (foundation2) =>
% 132.79/23.02 ((
% 132.79/23.02 (notinself) =>
% 132.79/23.02 ((
% 132.79/23.02 (notinself2) =>
% 132.79/23.02 ((
% 132.79/23.02 (omegaSp) =>
% 132.79/23.02 ((
% 132.79/23.02 (omegaSclos) =>
% 132.79/23.02 ((
% 132.79/23.02 (peano0notS) =>
% 132.79/23.02 ((
% 132.79/23.02 (peanoSinj) =>
% 132.79/23.02 ((
% 132.79/23.02 (transitivesetOp1) =>
% 132.79/23.02 ((
% 132.79/23.02 (binintTransitive) =>
% 132.79/23.02 ((
% 132.79/23.02 (transitivesetOp2) =>
% 132.79/23.02 ((
% 132.79/23.02 (setunionTransitive) =>
% 132.79/23.02 ((
% 132.79/23.02 (ordinalMinLem1) =>
% 132.79/23.02 ((
% 132.79/23.02 (ordinalTransSet) =>
% 132.79/23.02 ((
% 132.79/23.02 (ordinalTransSet1) =>
% 132.79/23.02 ((
% 132.79/23.02 (setunionOrdinalLem1) =>
% 132.79/23.02 (ordinal @
% 132.79/23.02 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/23.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2630])).
% 132.79/23.02 thf(zip_derived_cl2652, plain,
% 132.79/23.02 (~ (((woz1_3) =>
% 132.79/23.02 (((woz1_4) =>
% 132.79/23.02 (((woz1_5) =>
% 132.79/23.02 (((breln1all2) =>
% 132.79/23.02 (((breln1SetBreln1) =>
% 132.79/23.02 (((choice2fnsingleton) =>
% 132.79/23.02 (((setOfPairsIsBReln1) =>
% 132.79/23.02 (((breln1all1) =>
% 132.79/23.02 (((subbreln1) =>
% 132.79/23.02 (((eqbreln1) =>
% 132.79/23.02 (((breln1invprop) =>
% 132.79/23.02 (((breln1invI) =>
% 132.79/23.02 (((breln1invE) =>
% 132.79/23.02 (((breln1compprop) =>
% 132.79/23.02 (((breln1compI) =>
% 132.79/23.02 (((breln1compE) =>
% 132.79/23.02 (((breln1compEex) =>
% 132.79/23.02 (((breln1unionprop) =>
% 132.79/23.02 (((breln1unionIL) =>
% 132.79/23.02 (((breln1unionIR) =>
% 132.79/23.02 (((breln1unionI) =>
% 132.79/23.02 (((breln1unionE) =>
% 132.79/23.02 (((breln1unionEcases) =>
% 132.79/23.02 (((breln1unionCommutes) =>
% 132.79/23.02 (((woz2Ex) =>
% 132.79/23.02 (((woz2W) =>
% 132.79/23.02 (((woz2A) =>
% 132.79/23.02 (((woz2B) =>
% 132.79/23.02 (((image1Ex) =>
% 132.79/23.02 (((image1Ex1) =>
% 132.79/23.02 ((
% 132.79/23.02 (image1Equiv) =>
% 132.79/23.02 ((
% 132.79/23.02 (image1E) =>
% 132.79/23.02 ((
% 132.79/23.02 (image1I) =>
% 132.79/23.02 ((
% 132.79/23.02 (injFuncInInjFuncSet) =>
% 132.79/23.02 ((
% 132.79/23.02 (injFuncSetFuncIn) =>
% 132.79/23.02 ((
% 132.79/23.02 (injFuncSetFuncInj) =>
% 132.79/23.02 ((
% 132.79/23.02 (surjFuncSetFuncIn) =>
% 132.79/23.02 ((
% 132.79/23.02 (surjFuncSetFuncSurj) =>
% 132.79/23.02 ((
% 132.79/23.02 (leftInvIsSurj) =>
% 132.79/23.02 ((
% 132.79/23.02 (surjCantorThm) =>
% 132.79/23.02 ((
% 132.79/23.02 (foundation2) =>
% 132.79/23.02 ((
% 132.79/23.02 (notinself) =>
% 132.79/23.02 ((
% 132.79/23.02 (notinself2) =>
% 132.79/23.02 ((
% 132.79/23.02 (omegaSp) =>
% 132.79/23.02 ((
% 132.79/23.02 (omegaSclos) =>
% 132.79/23.02 ((
% 132.79/23.02 (peano0notS) =>
% 132.79/23.02 ((
% 132.79/23.02 (peanoSinj) =>
% 132.79/23.02 ((
% 132.79/23.02 (transitivesetOp1) =>
% 132.79/23.02 ((
% 132.79/23.02 (binintTransitive) =>
% 132.79/23.02 ((
% 132.79/23.02 (transitivesetOp2) =>
% 132.79/23.02 ((
% 132.79/23.02 (setunionTransitive) =>
% 132.79/23.02 ((
% 132.79/23.02 (ordinalMinLem1) =>
% 132.79/23.02 ((
% 132.79/23.02 (ordinalTransSet) =>
% 132.79/23.02 ((
% 132.79/23.02 (ordinalTransSet1) =>
% 132.79/23.02 ((
% 132.79/23.02 (setunionOrdinalLem1) =>
% 132.79/23.02 (ordinal @
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% 132.79/23.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2641])).
% 132.79/23.02 thf(zip_derived_cl2663, plain,
% 132.79/23.02 (~ (((woz1_4) =>
% 132.79/23.02 (((woz1_5) =>
% 132.79/23.02 (((breln1all2) =>
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% 132.79/23.02 (((choice2fnsingleton) =>
% 132.79/23.02 (((setOfPairsIsBReln1) =>
% 132.79/23.02 (((breln1all1) =>
% 132.79/23.02 (((subbreln1) =>
% 132.79/23.02 (((eqbreln1) =>
% 132.79/23.02 (((breln1invprop) =>
% 132.79/23.02 (((breln1invI) =>
% 132.79/23.02 (((breln1invE) =>
% 132.79/23.02 (((breln1compprop) =>
% 132.79/23.02 (((breln1compI) =>
% 132.79/23.02 (((breln1compE) =>
% 132.79/23.02 (((breln1compEex) =>
% 132.79/23.02 (((breln1unionprop) =>
% 132.79/23.02 (((breln1unionIL) =>
% 132.79/23.02 (((breln1unionIR) =>
% 132.79/23.02 (((breln1unionI) =>
% 132.79/23.02 (((breln1unionE) =>
% 132.79/23.02 (((breln1unionEcases) =>
% 132.79/23.02 (((breln1unionCommutes) =>
% 132.79/23.02 (((woz2Ex) =>
% 132.79/23.02 (((woz2W) =>
% 132.79/23.02 (((woz2A) =>
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% 132.79/23.02 (((image1Ex1) =>
% 132.79/23.02 (((image1Equiv) =>
% 132.79/23.02 ((
% 132.79/23.02 (image1E) =>
% 132.79/23.02 ((
% 132.79/23.02 (image1I) =>
% 132.79/23.02 ((
% 132.79/23.02 (injFuncInInjFuncSet) =>
% 132.79/23.02 ((
% 132.79/23.02 (injFuncSetFuncIn) =>
% 132.79/23.02 ((
% 132.79/23.02 (injFuncSetFuncInj) =>
% 132.79/23.02 ((
% 132.79/23.02 (surjFuncSetFuncIn) =>
% 132.79/23.02 ((
% 132.79/23.02 (surjFuncSetFuncSurj) =>
% 132.79/23.02 ((
% 132.79/23.02 (leftInvIsSurj) =>
% 132.79/23.02 ((
% 132.79/23.02 (surjCantorThm) =>
% 132.79/23.02 ((
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% 132.79/23.02 ((
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% 132.79/23.02 ((
% 132.79/23.02 (notinself2) =>
% 132.79/23.02 ((
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% 132.79/23.02 ((
% 132.79/23.02 (omegaSclos) =>
% 132.79/23.02 ((
% 132.79/23.02 (peano0notS) =>
% 132.79/23.02 ((
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% 132.79/23.02 ((
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% 132.79/23.02 ((
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% 132.79/23.02 ((
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% 132.79/23.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2652])).
% 132.79/23.02 thf(zip_derived_cl2672, plain,
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% 132.79/23.02 (((image1E) =>
% 132.79/23.02 ((
% 132.79/23.02 (image1I) =>
% 132.79/23.02 ((
% 132.79/23.02 (injFuncInInjFuncSet) =>
% 132.79/23.02 ((
% 132.79/23.02 (injFuncSetFuncIn) =>
% 132.79/23.02 ((
% 132.79/23.02 (injFuncSetFuncInj) =>
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% 132.79/23.02 ((
% 132.79/23.02 (surjCantorThm) =>
% 132.79/23.02 ((
% 132.79/23.02 (foundation2) =>
% 132.79/23.02 ((
% 132.79/23.02 (notinself) =>
% 132.79/23.02 ((
% 132.79/23.02 (notinself2) =>
% 132.79/23.02 ((
% 132.79/23.02 (omegaSp) =>
% 132.79/23.02 ((
% 132.79/23.02 (omegaSclos) =>
% 132.79/23.02 ((
% 132.79/23.02 (peano0notS) =>
% 132.79/23.02 ((
% 132.79/23.02 (peanoSinj) =>
% 132.79/23.02 ((
% 132.79/23.02 (transitivesetOp1) =>
% 132.79/23.02 ((
% 132.79/23.02 (binintTransitive) =>
% 132.79/23.02 ((
% 132.79/23.02 (transitivesetOp2) =>
% 132.79/23.02 ((
% 132.79/23.02 (setunionTransitive) =>
% 132.79/23.02 ((
% 132.79/23.02 (ordinalMinLem1) =>
% 132.79/23.02 ((
% 132.79/23.02 (ordinalTransSet) =>
% 132.79/23.02 ((
% 132.79/23.02 (ordinalTransSet1) =>
% 132.79/23.02 ((
% 132.79/23.02 (setunionOrdinalLem1) =>
% 132.79/23.02 (ordinal @
% 132.79/23.02 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/23.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2672])).
% 132.79/23.02 thf(zip_derived_cl2693, plain,
% 132.79/23.02 (~ (((breln1SetBreln1) =>
% 132.79/23.02 (((choice2fnsingleton) =>
% 132.79/23.02 (((setOfPairsIsBReln1) =>
% 132.79/23.02 (((breln1all1) =>
% 132.79/23.02 (((subbreln1) =>
% 132.79/23.02 (((eqbreln1) =>
% 132.79/23.02 (((breln1invprop) =>
% 132.79/23.02 (((breln1invI) =>
% 132.79/23.02 (((breln1invE) =>
% 132.79/23.02 (((breln1compprop) =>
% 132.79/23.02 (((breln1compI) =>
% 132.79/23.02 (((breln1compE) =>
% 132.79/23.02 (((breln1compEex) =>
% 132.79/23.02 (((breln1unionprop) =>
% 132.79/23.02 (((breln1unionIL) =>
% 132.79/23.02 (((breln1unionIR) =>
% 132.79/23.02 (((breln1unionI) =>
% 132.79/23.02 (((breln1unionE) =>
% 132.79/23.02 (((breln1unionEcases) =>
% 132.79/23.02 (((breln1unionCommutes) =>
% 132.79/23.02 (((woz2Ex) =>
% 132.79/23.02 (((woz2W) =>
% 132.79/23.02 (((woz2A) =>
% 132.79/23.02 (((woz2B) =>
% 132.79/23.02 (((image1Ex) =>
% 132.79/23.02 (((image1Ex1) =>
% 132.79/23.02 (((image1Equiv) =>
% 132.79/23.02 (((image1E) =>
% 132.79/23.02 (((image1I) =>
% 132.79/23.02 (((injFuncInInjFuncSet) =>
% 132.79/23.02 ((
% 132.79/23.02 (injFuncSetFuncIn) =>
% 132.79/23.02 ((
% 132.79/23.02 (injFuncSetFuncInj) =>
% 132.79/23.02 ((
% 132.79/23.02 (surjFuncSetFuncIn) =>
% 132.79/23.02 ((
% 132.79/23.02 (surjFuncSetFuncSurj) =>
% 132.79/23.02 ((
% 132.79/23.02 (leftInvIsSurj) =>
% 132.79/23.02 ((
% 132.79/23.02 (surjCantorThm) =>
% 132.79/23.02 ((
% 132.79/23.02 (foundation2) =>
% 132.79/23.02 ((
% 132.79/23.02 (notinself) =>
% 132.79/23.02 ((
% 132.79/23.02 (notinself2) =>
% 132.79/23.02 ((
% 132.79/23.02 (omegaSp) =>
% 132.79/23.02 ((
% 132.79/23.02 (omegaSclos) =>
% 132.79/23.02 ((
% 132.79/23.02 (peano0notS) =>
% 132.79/23.02 ((
% 132.79/23.02 (peanoSinj) =>
% 132.79/23.02 ((
% 132.79/23.02 (transitivesetOp1) =>
% 132.79/23.02 ((
% 132.79/23.02 (binintTransitive) =>
% 132.79/23.02 ((
% 132.79/23.02 (transitivesetOp2) =>
% 132.79/23.02 ((
% 132.79/23.02 (setunionTransitive) =>
% 132.79/23.02 ((
% 132.79/23.02 (ordinalMinLem1) =>
% 132.79/23.02 ((
% 132.79/23.02 (ordinalTransSet) =>
% 132.79/23.02 ((
% 132.79/23.02 (ordinalTransSet1) =>
% 132.79/23.02 ((
% 132.79/23.02 (setunionOrdinalLem1) =>
% 132.79/23.02 (ordinal @
% 132.79/23.02 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/23.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2682])).
% 132.79/23.02 thf(zip_derived_cl2704, plain,
% 132.79/23.02 (~ (((choice2fnsingleton) =>
% 132.79/23.02 (((setOfPairsIsBReln1) =>
% 132.79/23.02 (((breln1all1) =>
% 132.79/23.02 (((subbreln1) =>
% 132.79/23.02 (((eqbreln1) =>
% 132.79/23.02 (((breln1invprop) =>
% 132.79/23.02 (((breln1invI) =>
% 132.79/23.02 (((breln1invE) =>
% 132.79/23.02 (((breln1compprop) =>
% 132.79/23.02 (((breln1compI) =>
% 132.79/23.02 (((breln1compE) =>
% 132.79/23.02 (((breln1compEex) =>
% 132.79/23.02 (((breln1unionprop) =>
% 132.79/23.02 (((breln1unionIL) =>
% 132.79/23.02 (((breln1unionIR) =>
% 132.79/23.02 (((breln1unionI) =>
% 132.79/23.02 (((breln1unionE) =>
% 132.79/23.02 (((breln1unionEcases) =>
% 132.79/23.02 (((breln1unionCommutes) =>
% 132.79/23.02 (((woz2Ex) =>
% 132.79/23.02 (((woz2W) =>
% 132.79/23.02 (((woz2A) =>
% 132.79/23.02 (((woz2B) =>
% 132.79/23.02 (((image1Ex) =>
% 132.79/23.02 (((image1Ex1) =>
% 132.79/23.02 (((image1Equiv) =>
% 132.79/23.02 (((image1E) =>
% 132.79/23.02 (((image1I) =>
% 132.79/23.02 (((injFuncInInjFuncSet) =>
% 132.79/23.02 (((injFuncSetFuncIn) =>
% 132.79/23.02 ((
% 132.79/23.02 (injFuncSetFuncInj) =>
% 132.79/23.02 ((
% 132.79/23.02 (surjFuncSetFuncIn) =>
% 132.79/23.02 ((
% 132.79/23.02 (surjFuncSetFuncSurj) =>
% 132.79/23.02 ((
% 132.79/23.02 (leftInvIsSurj) =>
% 132.79/23.02 ((
% 132.79/23.02 (surjCantorThm) =>
% 132.79/23.02 ((
% 132.79/23.02 (foundation2) =>
% 132.79/23.02 ((
% 132.79/23.02 (notinself) =>
% 132.79/23.02 ((
% 132.79/23.02 (notinself2) =>
% 132.79/23.02 ((
% 132.79/23.02 (omegaSp) =>
% 132.79/23.02 ((
% 132.79/23.02 (omegaSclos) =>
% 132.79/23.02 ((
% 132.79/23.02 (peano0notS) =>
% 132.79/23.02 ((
% 132.79/23.02 (peanoSinj) =>
% 132.79/23.02 ((
% 132.79/23.02 (transitivesetOp1) =>
% 132.79/23.02 ((
% 132.79/23.02 (binintTransitive) =>
% 132.79/23.02 ((
% 132.79/23.02 (transitivesetOp2) =>
% 132.79/23.02 ((
% 132.79/23.02 (setunionTransitive) =>
% 132.79/23.02 ((
% 132.79/23.02 (ordinalMinLem1) =>
% 132.79/23.02 ((
% 132.79/23.02 (ordinalTransSet) =>
% 132.79/23.02 ((
% 132.79/23.02 (ordinalTransSet1) =>
% 132.79/23.02 ((
% 132.79/23.02 (setunionOrdinalLem1) =>
% 132.79/23.02 (ordinal @
% 132.79/23.02 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/23.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2693])).
% 132.79/23.02 thf(zip_derived_cl2714, plain,
% 132.79/23.02 (~ (((setOfPairsIsBReln1) =>
% 132.79/23.02 (((breln1all1) =>
% 132.79/23.02 (((subbreln1) =>
% 132.79/23.02 (((eqbreln1) =>
% 132.79/23.02 (((breln1invprop) =>
% 132.79/23.02 (((breln1invI) =>
% 132.79/23.02 (((breln1invE) =>
% 132.79/23.02 (((breln1compprop) =>
% 132.79/23.02 (((breln1compI) =>
% 132.79/23.02 (((breln1compE) =>
% 132.79/23.02 (((breln1compEex) =>
% 132.79/23.02 (((breln1unionprop) =>
% 132.79/23.02 (((breln1unionIL) =>
% 132.79/23.02 (((breln1unionIR) =>
% 132.79/23.02 (((breln1unionI) =>
% 132.79/23.02 (((breln1unionE) =>
% 132.79/23.02 (((breln1unionEcases) =>
% 132.79/23.02 (((breln1unionCommutes) =>
% 132.79/23.02 (((woz2Ex) =>
% 132.79/23.02 (((woz2W) =>
% 132.79/23.02 (((woz2A) =>
% 132.79/23.02 (((woz2B) =>
% 132.79/23.02 (((image1Ex) =>
% 132.79/23.02 (((image1Ex1) =>
% 132.79/23.02 (((image1Equiv) =>
% 132.79/23.02 (((image1E) =>
% 132.79/23.02 (((image1I) =>
% 132.79/23.02 (((injFuncInInjFuncSet) =>
% 132.79/23.02 (((injFuncSetFuncIn) =>
% 132.79/23.02 (((injFuncSetFuncInj) =>
% 132.79/23.02 ((
% 132.79/23.02 (surjFuncSetFuncIn) =>
% 132.79/23.02 ((
% 132.79/23.02 (surjFuncSetFuncSurj) =>
% 132.79/23.02 ((
% 132.79/23.02 (leftInvIsSurj) =>
% 132.79/23.02 ((
% 132.79/23.02 (surjCantorThm) =>
% 132.79/23.02 ((
% 132.79/23.02 (foundation2) =>
% 132.79/23.02 ((
% 132.79/23.02 (notinself) =>
% 132.79/23.02 ((
% 132.79/23.02 (notinself2) =>
% 132.79/23.02 ((
% 132.79/23.02 (omegaSp) =>
% 132.79/23.02 ((
% 132.79/23.02 (omegaSclos) =>
% 132.79/23.02 ((
% 132.79/23.02 (peano0notS) =>
% 132.79/23.02 ((
% 132.79/23.02 (peanoSinj) =>
% 132.79/23.02 ((
% 132.79/23.02 (transitivesetOp1) =>
% 132.79/23.02 ((
% 132.79/23.02 (binintTransitive) =>
% 132.79/23.02 ((
% 132.79/23.02 (transitivesetOp2) =>
% 132.79/23.02 ((
% 132.79/23.02 (setunionTransitive) =>
% 132.79/23.02 ((
% 132.79/23.02 (ordinalMinLem1) =>
% 132.79/23.02 ((
% 132.79/23.02 (ordinalTransSet) =>
% 132.79/23.02 ((
% 132.79/23.02 (ordinalTransSet1) =>
% 132.79/23.02 ((
% 132.79/23.02 (setunionOrdinalLem1) =>
% 132.79/23.02 (ordinal @
% 132.79/23.02 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/23.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2704])).
% 132.79/23.02 thf(zip_derived_cl2725, plain,
% 132.79/23.02 (~ (((breln1all1) =>
% 132.79/23.02 (((subbreln1) =>
% 132.79/23.02 (((eqbreln1) =>
% 132.79/23.02 (((breln1invprop) =>
% 132.79/23.02 (((breln1invI) =>
% 132.79/23.02 (((breln1invE) =>
% 132.79/23.02 (((breln1compprop) =>
% 132.79/23.02 (((breln1compI) =>
% 132.79/23.02 (((breln1compE) =>
% 132.79/23.02 (((breln1compEex) =>
% 132.79/23.02 (((breln1unionprop) =>
% 132.79/23.02 (((breln1unionIL) =>
% 132.79/23.02 (((breln1unionIR) =>
% 132.79/23.02 (((breln1unionI) =>
% 132.79/23.02 (((breln1unionE) =>
% 132.79/23.02 (((breln1unionEcases) =>
% 132.79/23.02 (((breln1unionCommutes) =>
% 132.79/23.02 (((woz2Ex) =>
% 132.79/23.02 (((woz2W) =>
% 132.79/23.02 (((woz2A) =>
% 132.79/23.02 (((woz2B) =>
% 132.79/23.02 (((image1Ex) =>
% 132.79/23.02 (((image1Ex1) =>
% 132.79/23.02 (((image1Equiv) =>
% 132.79/23.02 (((image1E) =>
% 132.79/23.02 (((image1I) =>
% 132.79/23.02 (((injFuncInInjFuncSet) =>
% 132.79/23.02 (((injFuncSetFuncIn) =>
% 132.79/23.02 (((injFuncSetFuncInj) =>
% 132.79/23.02 (((surjFuncSetFuncIn) =>
% 132.79/23.02 ((
% 132.79/23.02 (surjFuncSetFuncSurj) =>
% 132.79/23.02 ((
% 132.79/23.02 (leftInvIsSurj) =>
% 132.79/23.02 ((
% 132.79/23.02 (surjCantorThm) =>
% 132.79/23.02 ((
% 132.79/23.02 (foundation2) =>
% 132.79/23.02 ((
% 132.79/23.02 (notinself) =>
% 132.79/23.02 ((
% 132.79/23.02 (notinself2) =>
% 132.79/23.02 ((
% 132.79/23.02 (omegaSp) =>
% 132.79/23.02 ((
% 132.79/23.02 (omegaSclos) =>
% 132.79/23.02 ((
% 132.79/23.02 (peano0notS) =>
% 132.79/23.02 ((
% 132.79/23.02 (peanoSinj) =>
% 132.79/23.02 ((
% 132.79/23.02 (transitivesetOp1) =>
% 132.79/23.02 ((
% 132.79/23.02 (binintTransitive) =>
% 132.79/23.02 ((
% 132.79/23.02 (transitivesetOp2) =>
% 132.79/23.02 ((
% 132.79/23.02 (setunionTransitive) =>
% 132.79/23.02 ((
% 132.79/23.02 (ordinalMinLem1) =>
% 132.79/23.02 ((
% 132.79/23.02 (ordinalTransSet) =>
% 132.79/23.02 ((
% 132.79/23.02 (ordinalTransSet1) =>
% 132.79/23.02 ((
% 132.79/23.02 (setunionOrdinalLem1) =>
% 132.79/23.02 (ordinal @
% 132.79/23.02 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/23.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2714])).
% 132.79/23.02 thf(zip_derived_cl2736, plain,
% 132.79/23.02 (~ (((subbreln1) =>
% 132.79/23.02 (((eqbreln1) =>
% 132.79/23.02 (((breln1invprop) =>
% 132.79/23.02 (((breln1invI) =>
% 132.79/23.02 (((breln1invE) =>
% 132.79/23.02 (((breln1compprop) =>
% 132.79/23.02 (((breln1compI) =>
% 132.79/23.02 (((breln1compE) =>
% 132.79/23.02 (((breln1compEex) =>
% 132.79/23.02 (((breln1unionprop) =>
% 132.79/23.02 (((breln1unionIL) =>
% 132.79/23.02 (((breln1unionIR) =>
% 132.79/23.02 (((breln1unionI) =>
% 132.79/23.02 (((breln1unionE) =>
% 132.79/23.02 (((breln1unionEcases) =>
% 132.79/23.02 (((breln1unionCommutes) =>
% 132.79/23.02 (((woz2Ex) =>
% 132.79/23.02 (((woz2W) =>
% 132.79/23.02 (((woz2A) =>
% 132.79/23.02 (((woz2B) =>
% 132.79/23.02 (((image1Ex) =>
% 132.79/23.02 (((image1Ex1) =>
% 132.79/23.02 (((image1Equiv) =>
% 132.79/23.02 (((image1E) =>
% 132.79/23.02 (((image1I) =>
% 132.79/23.02 (((injFuncInInjFuncSet) =>
% 132.79/23.02 (((injFuncSetFuncIn) =>
% 132.79/23.02 (((injFuncSetFuncInj) =>
% 132.79/23.02 (((surjFuncSetFuncIn) =>
% 132.79/23.02 (((surjFuncSetFuncSurj) =>
% 132.79/23.02 ((
% 132.79/23.02 (leftInvIsSurj) =>
% 132.79/23.02 ((
% 132.79/23.02 (surjCantorThm) =>
% 132.79/23.02 ((
% 132.79/23.02 (foundation2) =>
% 132.79/23.02 ((
% 132.79/23.02 (notinself) =>
% 132.79/23.02 ((
% 132.79/23.02 (notinself2) =>
% 132.79/23.02 ((
% 132.79/23.02 (omegaSp) =>
% 132.79/23.02 ((
% 132.79/23.02 (omegaSclos) =>
% 132.79/23.02 ((
% 132.79/23.02 (peano0notS) =>
% 132.79/23.02 ((
% 132.79/23.02 (peanoSinj) =>
% 132.79/23.02 ((
% 132.79/23.02 (transitivesetOp1) =>
% 132.79/23.02 ((
% 132.79/23.02 (binintTransitive) =>
% 132.79/23.02 ((
% 132.79/23.02 (transitivesetOp2) =>
% 132.79/23.02 ((
% 132.79/23.02 (setunionTransitive) =>
% 132.79/23.02 ((
% 132.79/23.02 (ordinalMinLem1) =>
% 132.79/23.02 ((
% 132.79/23.02 (ordinalTransSet) =>
% 132.79/23.02 ((
% 132.79/23.02 (ordinalTransSet1) =>
% 132.79/23.02 ((
% 132.79/23.02 (setunionOrdinalLem1) =>
% 132.79/23.02 (ordinal @
% 132.79/23.02 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/23.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2725])).
% 132.79/23.02 thf(zip_derived_cl2749, plain,
% 132.79/23.02 (~ (((eqbreln1) =>
% 132.79/23.02 (((breln1invprop) =>
% 132.79/23.02 (((breln1invI) =>
% 132.79/23.02 (((breln1invE) =>
% 132.79/23.02 (((breln1compprop) =>
% 132.79/23.02 (((breln1compI) =>
% 132.79/23.02 (((breln1compE) =>
% 132.79/23.02 (((breln1compEex) =>
% 132.79/23.02 (((breln1unionprop) =>
% 132.79/23.02 (((breln1unionIL) =>
% 132.79/23.02 (((breln1unionIR) =>
% 132.79/23.02 (((breln1unionI) =>
% 132.79/23.02 (((breln1unionE) =>
% 132.79/23.02 (((breln1unionEcases) =>
% 132.79/23.02 (((breln1unionCommutes) =>
% 132.79/23.02 (((woz2Ex) =>
% 132.79/23.02 (((woz2W) =>
% 132.79/23.02 (((woz2A) =>
% 132.79/23.02 (((woz2B) =>
% 132.79/23.02 (((image1Ex) =>
% 132.79/23.02 (((image1Ex1) =>
% 132.79/23.02 (((image1Equiv) =>
% 132.79/23.02 (((image1E) =>
% 132.79/23.02 (((image1I) =>
% 132.79/23.02 (((injFuncInInjFuncSet) =>
% 132.79/23.02 (((injFuncSetFuncIn) =>
% 132.79/23.02 (((injFuncSetFuncInj) =>
% 132.79/23.02 (((surjFuncSetFuncIn) =>
% 132.79/23.02 (((surjFuncSetFuncSurj) =>
% 132.79/23.02 (((leftInvIsSurj) =>
% 132.79/23.02 ((
% 132.79/23.02 (surjCantorThm) =>
% 132.79/23.02 ((
% 132.79/23.02 (foundation2) =>
% 132.79/23.02 ((
% 132.79/23.02 (notinself) =>
% 132.79/23.02 ((
% 132.79/23.02 (notinself2) =>
% 132.79/23.02 ((
% 132.79/23.02 (omegaSp) =>
% 132.79/23.02 ((
% 132.79/23.02 (omegaSclos) =>
% 132.79/23.02 ((
% 132.79/23.02 (peano0notS) =>
% 132.79/23.02 ((
% 132.79/23.02 (peanoSinj) =>
% 132.79/23.02 ((
% 132.79/23.02 (transitivesetOp1) =>
% 132.79/23.02 ((
% 132.79/23.02 (binintTransitive) =>
% 132.79/23.02 ((
% 132.79/23.02 (transitivesetOp2) =>
% 132.79/23.02 ((
% 132.79/23.02 (setunionTransitive) =>
% 132.79/23.02 ((
% 132.79/23.02 (ordinalMinLem1) =>
% 132.79/23.02 ((
% 132.79/23.02 (ordinalTransSet) =>
% 132.79/23.02 ((
% 132.79/23.02 (ordinalTransSet1) =>
% 132.79/23.02 ((
% 132.79/23.02 (setunionOrdinalLem1) =>
% 132.79/23.02 (ordinal @
% 132.79/23.02 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/23.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2736])).
% 132.79/23.02 thf(zip_derived_cl2758, plain,
% 132.79/23.02 (~ (((breln1invprop) =>
% 132.79/23.02 (((breln1invI) =>
% 132.79/23.02 (((breln1invE) =>
% 132.79/23.02 (((breln1compprop) =>
% 132.79/23.02 (((breln1compI) =>
% 132.79/23.02 (((breln1compE) =>
% 132.79/23.02 (((breln1compEex) =>
% 132.79/23.02 (((breln1unionprop) =>
% 132.79/23.02 (((breln1unionIL) =>
% 132.79/23.02 (((breln1unionIR) =>
% 132.79/23.02 (((breln1unionI) =>
% 132.79/23.02 (((breln1unionE) =>
% 132.79/23.02 (((breln1unionEcases) =>
% 132.79/23.02 (((breln1unionCommutes) =>
% 132.79/23.02 (((woz2Ex) =>
% 132.79/23.02 (((woz2W) =>
% 132.79/23.02 (((woz2A) =>
% 132.79/23.02 (((woz2B) =>
% 132.79/23.02 (((image1Ex) =>
% 132.79/23.02 (((image1Ex1) =>
% 132.79/23.02 (((image1Equiv) =>
% 132.79/23.02 (((image1E) =>
% 132.79/23.02 (((image1I) =>
% 132.79/23.02 (((injFuncInInjFuncSet) =>
% 132.79/23.02 (((injFuncSetFuncIn) =>
% 132.79/23.02 (((injFuncSetFuncInj) =>
% 132.79/23.02 (((surjFuncSetFuncIn) =>
% 132.79/23.02 (((surjFuncSetFuncSurj) =>
% 132.79/23.02 (((leftInvIsSurj) =>
% 132.79/23.02 (((surjCantorThm) =>
% 132.79/23.02 ((
% 132.79/23.02 (foundation2) =>
% 132.79/23.02 ((
% 132.79/23.02 (notinself) =>
% 132.79/23.02 ((
% 132.79/23.02 (notinself2) =>
% 132.79/23.02 ((
% 132.79/23.02 (omegaSp) =>
% 132.79/23.02 ((
% 132.79/23.02 (omegaSclos) =>
% 132.79/23.02 ((
% 132.79/23.02 (peano0notS) =>
% 132.79/23.02 ((
% 132.79/23.02 (peanoSinj) =>
% 132.79/23.02 ((
% 132.79/23.02 (transitivesetOp1) =>
% 132.79/23.02 ((
% 132.79/23.02 (binintTransitive) =>
% 132.79/23.02 ((
% 132.79/23.02 (transitivesetOp2) =>
% 132.79/23.02 ((
% 132.79/23.02 (setunionTransitive) =>
% 132.79/23.02 ((
% 132.79/23.02 (ordinalMinLem1) =>
% 132.79/23.02 ((
% 132.79/23.02 (ordinalTransSet) =>
% 132.79/23.02 ((
% 132.79/23.02 (ordinalTransSet1) =>
% 132.79/23.02 ((
% 132.79/23.02 (setunionOrdinalLem1) =>
% 132.79/23.02 (ordinal @
% 132.79/23.02 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/23.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2749])).
% 132.79/23.02 thf(zip_derived_cl2766, plain,
% 132.79/23.02 (~ (((breln1invI) =>
% 132.79/23.02 (((breln1invE) =>
% 132.79/23.02 (((breln1compprop) =>
% 132.79/23.02 (((breln1compI) =>
% 132.79/23.02 (((breln1compE) =>
% 132.79/23.02 (((breln1compEex) =>
% 132.79/23.02 (((breln1unionprop) =>
% 132.79/23.02 (((breln1unionIL) =>
% 132.79/23.02 (((breln1unionIR) =>
% 132.79/23.02 (((breln1unionI) =>
% 132.79/23.02 (((breln1unionE) =>
% 132.79/23.02 (((breln1unionEcases) =>
% 132.79/23.02 (((breln1unionCommutes) =>
% 132.79/23.02 (((woz2Ex) =>
% 132.79/23.02 (((woz2W) =>
% 132.79/23.02 (((woz2A) =>
% 132.79/23.02 (((woz2B) =>
% 132.79/23.02 (((image1Ex) =>
% 132.79/23.02 (((image1Ex1) =>
% 132.79/23.02 (((image1Equiv) =>
% 132.79/23.02 (((image1E) =>
% 132.79/23.02 (((image1I) =>
% 132.79/23.02 (((injFuncInInjFuncSet) =>
% 132.79/23.02 (((injFuncSetFuncIn) =>
% 132.79/23.02 (((injFuncSetFuncInj) =>
% 132.79/23.02 (((surjFuncSetFuncIn) =>
% 132.79/23.02 (((surjFuncSetFuncSurj) =>
% 132.79/23.02 (((leftInvIsSurj) =>
% 132.79/23.02 (((surjCantorThm) =>
% 132.79/23.02 (((foundation2) =>
% 132.79/23.02 ((
% 132.79/23.02 (notinself) =>
% 132.79/23.02 ((
% 132.79/23.02 (notinself2) =>
% 132.79/23.02 ((
% 132.79/23.02 (omegaSp) =>
% 132.79/23.02 ((
% 132.79/23.02 (omegaSclos) =>
% 132.79/23.02 ((
% 132.79/23.02 (peano0notS) =>
% 132.79/23.02 ((
% 132.79/23.02 (peanoSinj) =>
% 132.79/23.02 ((
% 132.79/23.02 (transitivesetOp1) =>
% 132.79/23.02 ((
% 132.79/23.02 (binintTransitive) =>
% 132.79/23.02 ((
% 132.79/23.02 (transitivesetOp2) =>
% 132.79/23.02 ((
% 132.79/23.02 (setunionTransitive) =>
% 132.79/23.02 ((
% 132.79/23.02 (ordinalMinLem1) =>
% 132.79/23.02 ((
% 132.79/23.02 (ordinalTransSet) =>
% 132.79/23.02 ((
% 132.79/23.02 (ordinalTransSet1) =>
% 132.79/23.02 ((
% 132.79/23.02 (setunionOrdinalLem1) =>
% 132.79/23.02 (ordinal @
% 132.79/23.02 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/23.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2758])).
% 132.79/23.02 thf(zip_derived_cl2775, plain,
% 132.79/23.02 (~ (((breln1invE) =>
% 132.79/23.02 (((breln1compprop) =>
% 132.79/23.02 (((breln1compI) =>
% 132.79/23.02 (((breln1compE) =>
% 132.79/23.02 (((breln1compEex) =>
% 132.79/23.02 (((breln1unionprop) =>
% 132.79/23.02 (((breln1unionIL) =>
% 132.79/23.02 (((breln1unionIR) =>
% 132.79/23.02 (((breln1unionI) =>
% 132.79/23.02 (((breln1unionE) =>
% 132.79/23.02 (((breln1unionEcases) =>
% 132.79/23.02 (((breln1unionCommutes) =>
% 132.79/23.02 (((woz2Ex) =>
% 132.79/23.02 (((woz2W) =>
% 132.79/23.02 (((woz2A) =>
% 132.79/23.02 (((woz2B) =>
% 132.79/23.02 (((image1Ex) =>
% 132.79/23.02 (((image1Ex1) =>
% 132.79/23.02 (((image1Equiv) =>
% 132.79/23.02 (((image1E) =>
% 132.79/23.02 (((image1I) =>
% 132.79/23.02 (((injFuncInInjFuncSet) =>
% 132.79/23.02 (((injFuncSetFuncIn) =>
% 132.79/23.02 (((injFuncSetFuncInj) =>
% 132.79/23.02 (((surjFuncSetFuncIn) =>
% 132.79/23.02 (((surjFuncSetFuncSurj) =>
% 132.79/23.02 (((leftInvIsSurj) =>
% 132.79/23.02 (((surjCantorThm) =>
% 132.79/23.02 (((foundation2) =>
% 132.79/23.02 (((notinself) =>
% 132.79/23.02 ((
% 132.79/23.02 (notinself2) =>
% 132.79/23.02 ((
% 132.79/23.02 (omegaSp) =>
% 132.79/23.02 ((
% 132.79/23.02 (omegaSclos) =>
% 132.79/23.02 ((
% 132.79/23.02 (peano0notS) =>
% 132.79/23.02 ((
% 132.79/23.02 (peanoSinj) =>
% 132.79/23.02 ((
% 132.79/23.02 (transitivesetOp1) =>
% 132.79/23.02 ((
% 132.79/23.02 (binintTransitive) =>
% 132.79/23.02 ((
% 132.79/23.02 (transitivesetOp2) =>
% 132.79/23.02 ((
% 132.79/23.02 (setunionTransitive) =>
% 132.79/23.02 ((
% 132.79/23.02 (ordinalMinLem1) =>
% 132.79/23.02 ((
% 132.79/23.02 (ordinalTransSet) =>
% 132.79/23.02 ((
% 132.79/23.02 (ordinalTransSet1) =>
% 132.79/23.02 ((
% 132.79/23.02 (setunionOrdinalLem1) =>
% 132.79/23.02 (ordinal @
% 132.79/23.02 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/23.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2766])).
% 132.79/23.02 thf(zip_derived_cl2786, plain,
% 132.79/23.02 (~ (((breln1compprop) =>
% 132.79/23.02 (((breln1compI) =>
% 132.79/23.02 (((breln1compE) =>
% 132.79/23.02 (((breln1compEex) =>
% 132.79/23.02 (((breln1unionprop) =>
% 132.79/23.02 (((breln1unionIL) =>
% 132.79/23.02 (((breln1unionIR) =>
% 132.79/23.02 (((breln1unionI) =>
% 132.79/23.02 (((breln1unionE) =>
% 132.79/23.02 (((breln1unionEcases) =>
% 132.79/23.02 (((breln1unionCommutes) =>
% 132.79/23.02 (((woz2Ex) =>
% 132.79/23.02 (((woz2W) =>
% 132.79/23.02 (((woz2A) =>
% 132.79/23.02 (((woz2B) =>
% 132.79/23.02 (((image1Ex) =>
% 132.79/23.02 (((image1Ex1) =>
% 132.79/23.02 (((image1Equiv) =>
% 132.79/23.02 (((image1E) =>
% 132.79/23.02 (((image1I) =>
% 132.79/23.02 (((injFuncInInjFuncSet) =>
% 132.79/23.02 (((injFuncSetFuncIn) =>
% 132.79/23.02 (((injFuncSetFuncInj) =>
% 132.79/23.02 (((surjFuncSetFuncIn) =>
% 132.79/23.02 (((surjFuncSetFuncSurj) =>
% 132.79/23.02 (((leftInvIsSurj) =>
% 132.79/23.02 (((surjCantorThm) =>
% 132.79/23.02 (((foundation2) =>
% 132.79/23.02 (((notinself) =>
% 132.79/23.02 (((notinself2) =>
% 132.79/23.02 ((
% 132.79/23.02 (omegaSp) =>
% 132.79/23.02 ((
% 132.79/23.02 (omegaSclos) =>
% 132.79/23.02 ((
% 132.79/23.02 (peano0notS) =>
% 132.79/23.02 ((
% 132.79/23.02 (peanoSinj) =>
% 132.79/23.02 ((
% 132.79/23.02 (transitivesetOp1) =>
% 132.79/23.02 ((
% 132.79/23.02 (binintTransitive) =>
% 132.79/23.02 ((
% 132.79/23.02 (transitivesetOp2) =>
% 132.79/23.02 ((
% 132.79/23.02 (setunionTransitive) =>
% 132.79/23.02 ((
% 132.79/23.02 (ordinalMinLem1) =>
% 132.79/23.02 ((
% 132.79/23.02 (ordinalTransSet) =>
% 132.79/23.02 ((
% 132.79/23.02 (ordinalTransSet1) =>
% 132.79/23.02 ((
% 132.79/23.02 (setunionOrdinalLem1) =>
% 132.79/23.02 (ordinal @
% 132.79/23.02 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/23.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2775])).
% 132.79/23.02 thf(zip_derived_cl2799, plain,
% 132.79/23.02 (~ (((breln1compI) =>
% 132.79/23.02 (((breln1compE) =>
% 132.79/23.02 (((breln1compEex) =>
% 132.79/23.02 (((breln1unionprop) =>
% 132.79/23.02 (((breln1unionIL) =>
% 132.79/23.02 (((breln1unionIR) =>
% 132.79/23.02 (((breln1unionI) =>
% 132.79/23.02 (((breln1unionE) =>
% 132.79/23.02 (((breln1unionEcases) =>
% 132.79/23.02 (((breln1unionCommutes) =>
% 132.79/23.02 (((woz2Ex) =>
% 132.79/23.02 (((woz2W) =>
% 132.79/23.02 (((woz2A) =>
% 132.79/23.02 (((woz2B) =>
% 132.79/23.02 (((image1Ex) =>
% 132.79/23.02 (((image1Ex1) =>
% 132.79/23.02 (((image1Equiv) =>
% 132.79/23.02 (((image1E) =>
% 132.79/23.02 (((image1I) =>
% 132.79/23.02 (((injFuncInInjFuncSet) =>
% 132.79/23.02 (((injFuncSetFuncIn) =>
% 132.79/23.02 (((injFuncSetFuncInj) =>
% 132.79/23.02 (((surjFuncSetFuncIn) =>
% 132.79/23.02 (((surjFuncSetFuncSurj) =>
% 132.79/23.02 (((leftInvIsSurj) =>
% 132.79/23.02 (((surjCantorThm) =>
% 132.79/23.02 (((foundation2) =>
% 132.79/23.02 (((notinself) =>
% 132.79/23.02 (((notinself2) =>
% 132.79/23.02 (((omegaSp) =>
% 132.79/23.02 ((
% 132.79/23.02 (omegaSclos) =>
% 132.79/23.02 ((
% 132.79/23.02 (peano0notS) =>
% 132.79/23.02 ((
% 132.79/23.02 (peanoSinj) =>
% 132.79/23.02 ((
% 132.79/23.02 (transitivesetOp1) =>
% 132.79/23.02 ((
% 132.79/23.02 (binintTransitive) =>
% 132.79/23.02 ((
% 132.79/23.02 (transitivesetOp2) =>
% 132.79/23.02 ((
% 132.79/23.02 (setunionTransitive) =>
% 132.79/23.02 ((
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% 132.79/23.02 ((
% 132.79/23.02 (ordinalTransSet) =>
% 132.79/23.02 ((
% 132.79/23.02 (ordinalTransSet1) =>
% 132.79/23.02 ((
% 132.79/23.02 (setunionOrdinalLem1) =>
% 132.79/23.02 (ordinal @
% 132.79/23.02 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/23.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2786])).
% 132.79/23.02 thf(zip_derived_cl2813, plain,
% 132.79/23.02 (~ (((breln1compE) =>
% 132.79/23.02 (((breln1compEex) =>
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% 132.79/23.02 (((breln1unionIL) =>
% 132.79/23.02 (((breln1unionIR) =>
% 132.79/23.02 (((breln1unionI) =>
% 132.79/23.02 (((breln1unionE) =>
% 132.79/23.02 (((breln1unionEcases) =>
% 132.79/23.02 (((breln1unionCommutes) =>
% 132.79/23.02 (((woz2Ex) =>
% 132.79/23.02 (((woz2W) =>
% 132.79/23.02 (((woz2A) =>
% 132.79/23.02 (((woz2B) =>
% 132.79/23.02 (((image1Ex) =>
% 132.79/23.02 (((image1Ex1) =>
% 132.79/23.02 (((image1Equiv) =>
% 132.79/23.02 (((image1E) =>
% 132.79/23.02 (((image1I) =>
% 132.79/23.02 (((injFuncInInjFuncSet) =>
% 132.79/23.02 (((injFuncSetFuncIn) =>
% 132.79/23.02 (((injFuncSetFuncInj) =>
% 132.79/23.02 (((surjFuncSetFuncIn) =>
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% 132.79/23.02 (((leftInvIsSurj) =>
% 132.79/23.02 (((surjCantorThm) =>
% 132.79/23.02 (((foundation2) =>
% 132.79/23.02 (((notinself) =>
% 132.79/23.02 (((notinself2) =>
% 132.79/23.02 (((omegaSp) =>
% 132.79/23.02 (((omegaSclos) =>
% 132.79/23.02 ((
% 132.79/23.02 (peano0notS) =>
% 132.79/23.02 ((
% 132.79/23.02 (peanoSinj) =>
% 132.79/23.02 ((
% 132.79/23.02 (transitivesetOp1) =>
% 132.79/23.02 ((
% 132.79/23.02 (binintTransitive) =>
% 132.79/23.02 ((
% 132.79/23.02 (transitivesetOp2) =>
% 132.79/23.02 ((
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% 132.79/23.02 ((
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% 132.79/23.02 ((
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% 132.79/23.02 ((
% 132.79/23.02 (ordinalTransSet1) =>
% 132.79/23.02 ((
% 132.79/23.02 (setunionOrdinalLem1) =>
% 132.79/23.02 (ordinal @
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% 132.79/23.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2799])).
% 132.79/23.02 thf(zip_derived_cl2828, plain,
% 132.79/23.02 (~ (((breln1compEex) =>
% 132.79/23.02 (((breln1unionprop) =>
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% 132.79/23.02 (((breln1unionIR) =>
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% 132.79/23.02 (((breln1unionE) =>
% 132.79/23.02 (((breln1unionEcases) =>
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% 132.79/23.02 (((woz2Ex) =>
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% 132.79/23.02 (((woz2B) =>
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% 132.79/23.02 (((image1Ex1) =>
% 132.79/23.02 (((image1Equiv) =>
% 132.79/23.02 (((image1E) =>
% 132.79/23.02 (((image1I) =>
% 132.79/23.02 (((injFuncInInjFuncSet) =>
% 132.79/23.02 (((injFuncSetFuncIn) =>
% 132.79/23.02 (((injFuncSetFuncInj) =>
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% 132.79/23.02 (((notinself2) =>
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% 132.79/23.02 (((peano0notS) =>
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% 132.79/23.02 (peanoSinj) =>
% 132.79/23.02 ((
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% 132.79/23.02 ((
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% 132.79/23.02 ((
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% 132.79/23.02 ((
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% 132.79/23.02 ((
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% 132.79/23.02 (ordinal @
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% 132.79/23.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2813])).
% 132.79/23.02 thf(zip_derived_cl2843, plain,
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% 132.79/23.02 (((image1Equiv) =>
% 132.79/23.02 (((image1E) =>
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% 132.79/23.02 (((injFuncInInjFuncSet) =>
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% 132.79/23.02 (((injFuncSetFuncInj) =>
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% 132.79/23.02 ((
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% 132.79/23.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2828])).
% 132.79/23.02 thf(zip_derived_cl2859, plain,
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% 132.79/23.02 (((leftInvIsSurj) =>
% 132.79/23.02 (((surjCantorThm) =>
% 132.79/23.02 (((foundation2) =>
% 132.79/23.02 (((notinself) =>
% 132.79/23.02 (((notinself2) =>
% 132.79/23.02 (((omegaSp) =>
% 132.79/23.02 (((omegaSclos) =>
% 132.79/23.02 (((peano0notS) =>
% 132.79/23.02 (((peanoSinj) =>
% 132.79/23.02 (((transitivesetOp1) =>
% 132.79/23.02 (((binintTransitive) =>
% 132.79/23.02 (((transitivesetOp2) =>
% 132.79/23.02 (((setunionTransitive) =>
% 132.79/23.02 (((ordinalMinLem1) =>
% 132.79/23.02 (((ordinalTransSet) =>
% 132.79/23.02 (((ordinalTransSet1) =>
% 132.79/23.02 (((setunionOrdinalLem1) =>
% 132.79/23.02 (ordinal @ emptyset)))))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/23.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3022])).
% 132.79/23.02 thf(zip_derived_cl3048, plain,
% 132.79/23.02 (~ (((image1I) =>
% 132.79/23.02 (((injFuncInInjFuncSet) =>
% 132.79/23.02 (((injFuncSetFuncIn) =>
% 132.79/23.02 (((injFuncSetFuncInj) =>
% 132.79/23.02 (((surjFuncSetFuncIn) =>
% 132.79/23.02 (((surjFuncSetFuncSurj) =>
% 132.79/23.02 (((leftInvIsSurj) =>
% 132.79/23.02 (((surjCantorThm) =>
% 132.79/23.02 (((foundation2) =>
% 132.79/23.02 (((notinself) =>
% 132.79/23.02 (((notinself2) =>
% 132.79/23.02 (((omegaSp) =>
% 132.79/23.02 (((omegaSclos) =>
% 132.79/23.02 (((peano0notS) =>
% 132.79/23.02 (((peanoSinj) =>
% 132.79/23.02 (((transitivesetOp1) =>
% 132.79/23.02 (((binintTransitive) =>
% 132.79/23.02 (((transitivesetOp2) =>
% 132.79/23.02 (((setunionTransitive) =>
% 132.79/23.02 (((ordinalMinLem1) =>
% 132.79/23.02 (((ordinalTransSet) =>
% 132.79/23.02 (((ordinalTransSet1) =>
% 132.79/23.02 (((setunionOrdinalLem1) =>
% 132.79/23.02 (ordinal @ emptyset)))))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/23.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3035])).
% 132.79/23.02 thf(zip_derived_cl3064, plain,
% 132.79/23.02 (~ (((injFuncInInjFuncSet) =>
% 132.79/23.02 (((injFuncSetFuncIn) =>
% 132.79/23.02 (((injFuncSetFuncInj) =>
% 132.79/23.02 (((surjFuncSetFuncIn) =>
% 132.79/23.02 (((surjFuncSetFuncSurj) =>
% 132.79/23.02 (((leftInvIsSurj) =>
% 132.79/23.02 (((surjCantorThm) =>
% 132.79/23.02 (((foundation2) =>
% 132.79/23.02 (((notinself) =>
% 132.79/23.02 (((notinself2) =>
% 132.79/23.02 (((omegaSp) =>
% 132.79/23.02 (((omegaSclos) =>
% 132.79/23.02 (((peano0notS) =>
% 132.79/23.02 (((peanoSinj) =>
% 132.79/23.02 (((transitivesetOp1) =>
% 132.79/23.02 (((binintTransitive) =>
% 132.79/23.02 (((transitivesetOp2) =>
% 132.79/23.02 (((setunionTransitive) =>
% 132.79/23.02 (((ordinalMinLem1) =>
% 132.79/23.02 (((ordinalTransSet) =>
% 132.79/23.02 (((ordinalTransSet1) =>
% 132.79/23.02 (((setunionOrdinalLem1) =>
% 132.79/23.02 (ordinal @ emptyset)))))))))))))))))))))))))))))))))))))))))))))),
% 132.79/23.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3048])).
% 132.79/23.02 thf(zip_derived_cl3078, plain,
% 132.79/23.02 (~ (((injFuncSetFuncIn) =>
% 132.79/23.02 (((injFuncSetFuncInj) =>
% 132.79/23.02 (((surjFuncSetFuncIn) =>
% 132.79/23.02 (((surjFuncSetFuncSurj) =>
% 132.79/23.02 (((leftInvIsSurj) =>
% 132.79/23.02 (((surjCantorThm) =>
% 132.79/23.02 (((foundation2) =>
% 132.79/23.02 (((notinself) =>
% 132.79/23.02 (((notinself2) =>
% 132.79/23.02 (((omegaSp) =>
% 132.79/23.02 (((omegaSclos) =>
% 132.79/23.02 (((peano0notS) =>
% 132.79/23.02 (((peanoSinj) =>
% 132.79/23.02 (((transitivesetOp1) =>
% 132.79/23.02 (((binintTransitive) =>
% 132.79/23.02 (((transitivesetOp2) =>
% 132.79/23.02 (((setunionTransitive) =>
% 132.79/23.02 (((ordinalMinLem1) =>
% 132.79/23.02 (((ordinalTransSet) =>
% 132.79/23.02 (((ordinalTransSet1) =>
% 132.79/23.02 (((setunionOrdinalLem1) =>
% 132.79/23.02 (ordinal @ emptyset)))))))))))))))))))))))))))))))))))))))))))),
% 132.79/23.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3064])).
% 132.79/23.02 thf(zip_derived_cl3091, plain,
% 132.79/23.02 (~ (((injFuncSetFuncInj) =>
% 132.79/23.02 (((surjFuncSetFuncIn) =>
% 132.79/23.02 (((surjFuncSetFuncSurj) =>
% 132.79/23.02 (((leftInvIsSurj) =>
% 132.79/23.02 (((surjCantorThm) =>
% 132.79/23.02 (((foundation2) =>
% 132.79/23.02 (((notinself) =>
% 132.79/23.02 (((notinself2) =>
% 132.79/23.02 (((omegaSp) =>
% 132.79/23.02 (((omegaSclos) =>
% 132.79/23.02 (((peano0notS) =>
% 132.79/23.02 (((peanoSinj) =>
% 132.79/23.02 (((transitivesetOp1) =>
% 132.79/23.02 (((binintTransitive) =>
% 132.79/23.02 (((transitivesetOp2) =>
% 132.79/23.02 (((setunionTransitive) =>
% 132.79/23.02 (((ordinalMinLem1) =>
% 132.79/23.02 (((ordinalTransSet) =>
% 132.79/23.02 (((ordinalTransSet1) =>
% 132.79/23.02 (((setunionOrdinalLem1) =>
% 132.79/23.02 (ordinal @ emptyset)))))))))))))))))))))))))))))))))))))))))),
% 132.79/23.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3078])).
% 132.79/23.02 thf(zip_derived_cl3103, plain,
% 132.79/23.02 (~ (((surjFuncSetFuncIn) =>
% 132.79/23.02 (((surjFuncSetFuncSurj) =>
% 132.79/23.02 (((leftInvIsSurj) =>
% 132.79/23.02 (((surjCantorThm) =>
% 132.79/23.02 (((foundation2) =>
% 132.79/23.02 (((notinself) =>
% 132.79/23.02 (((notinself2) =>
% 132.79/23.02 (((omegaSp) =>
% 132.79/23.02 (((omegaSclos) =>
% 132.79/23.02 (((peano0notS) =>
% 132.79/23.02 (((peanoSinj) =>
% 132.79/23.02 (((transitivesetOp1) =>
% 132.79/23.02 (((binintTransitive) =>
% 132.79/23.02 (((transitivesetOp2) =>
% 132.79/23.02 (((setunionTransitive) =>
% 132.79/23.02 (((ordinalMinLem1) =>
% 132.79/23.02 (((ordinalTransSet) =>
% 132.79/23.02 (((ordinalTransSet1) =>
% 132.79/23.02 (((setunionOrdinalLem1) =>
% 132.79/23.02 (ordinal @ emptyset)))))))))))))))))))))))))))))))))))))))),
% 132.79/23.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3091])).
% 132.79/23.02 thf(zip_derived_cl3114, plain,
% 132.79/23.02 (~ (((surjFuncSetFuncSurj) =>
% 132.79/23.02 (((leftInvIsSurj) =>
% 132.79/23.02 (((surjCantorThm) =>
% 132.79/23.02 (((foundation2) =>
% 132.79/23.02 (((notinself) =>
% 132.79/23.02 (((notinself2) =>
% 132.79/23.02 (((omegaSp) =>
% 132.79/23.02 (((omegaSclos) =>
% 132.79/23.02 (((peano0notS) =>
% 132.79/23.02 (((peanoSinj) =>
% 132.79/23.02 (((transitivesetOp1) =>
% 132.79/23.02 (((binintTransitive) =>
% 132.79/23.02 (((transitivesetOp2) =>
% 132.79/23.02 (((setunionTransitive) =>
% 132.79/23.02 (((ordinalMinLem1) =>
% 132.79/23.02 (((ordinalTransSet) =>
% 132.79/23.02 (((ordinalTransSet1) =>
% 132.79/23.02 (((setunionOrdinalLem1) =>
% 132.79/23.02 (ordinal @ emptyset)))))))))))))))))))))))))))))))))))))),
% 132.79/23.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3103])).
% 132.79/23.02 thf(zip_derived_cl3126, plain,
% 132.79/23.02 (~ (((leftInvIsSurj) =>
% 132.79/23.02 (((surjCantorThm) =>
% 132.79/23.02 (((foundation2) =>
% 132.79/23.02 (((notinself) =>
% 132.79/23.02 (((notinself2) =>
% 132.79/23.02 (((omegaSp) =>
% 132.79/23.02 (((omegaSclos) =>
% 132.79/23.02 (((peano0notS) =>
% 132.79/23.02 (((peanoSinj) =>
% 132.79/23.02 (((transitivesetOp1) =>
% 132.79/23.02 (((binintTransitive) =>
% 132.79/23.02 (((transitivesetOp2) =>
% 132.79/23.02 (((setunionTransitive) =>
% 132.79/23.02 (((ordinalMinLem1) =>
% 132.79/23.02 (((ordinalTransSet) =>
% 132.79/23.02 (((ordinalTransSet1) =>
% 132.79/23.02 (((setunionOrdinalLem1) => (ordinal @
% 132.79/23.02 emptyset)))))))))))))))))))))))))))))))))))),
% 132.79/23.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3114])).
% 132.79/23.02 thf(zip_derived_cl3138, plain,
% 132.79/23.02 (~ (((surjCantorThm) =>
% 132.79/23.02 (((foundation2) =>
% 132.79/23.02 (((notinself) =>
% 132.79/23.02 (((notinself2) =>
% 132.79/23.02 (((omegaSp) =>
% 132.79/23.02 (((omegaSclos) =>
% 132.79/23.02 (((peano0notS) =>
% 132.79/23.02 (((peanoSinj) =>
% 132.79/23.02 (((transitivesetOp1) =>
% 132.79/23.02 (((binintTransitive) =>
% 132.79/23.02 (((transitivesetOp2) =>
% 132.79/23.02 (((setunionTransitive) =>
% 132.79/23.02 (((ordinalMinLem1) =>
% 132.79/23.02 (((ordinalTransSet) =>
% 132.79/23.02 (((ordinalTransSet1) =>
% 132.79/23.02 (((setunionOrdinalLem1) => (ordinal @
% 132.79/23.02 emptyset)))))))))))))))))))))))))))))))))),
% 132.79/23.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3126])).
% 132.79/23.02 thf(zip_derived_cl3148, plain,
% 132.79/23.02 (~ (((foundation2) =>
% 132.79/23.02 (((notinself) =>
% 132.79/23.02 (((notinself2) =>
% 132.79/23.02 (((omegaSp) =>
% 132.79/23.02 (((omegaSclos) =>
% 132.79/23.02 (((peano0notS) =>
% 132.79/23.02 (((peanoSinj) =>
% 132.79/23.02 (((transitivesetOp1) =>
% 132.79/23.02 (((binintTransitive) =>
% 132.79/23.02 (((transitivesetOp2) =>
% 132.79/23.02 (((setunionTransitive) =>
% 132.79/23.02 (((ordinalMinLem1) =>
% 132.79/23.02 (((ordinalTransSet) =>
% 132.79/23.02 (((ordinalTransSet1) =>
% 132.79/23.02 (((setunionOrdinalLem1) => (ordinal @
% 132.79/23.02 emptyset)))))))))))))))))))))))))))))))),
% 132.79/23.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3138])).
% 132.79/23.02 thf(zip_derived_cl3157, plain,
% 132.79/23.02 (~ (((notinself) =>
% 132.79/23.02 (((notinself2) =>
% 132.79/23.02 (((omegaSp) =>
% 132.79/23.02 (((omegaSclos) =>
% 132.79/23.02 (((peano0notS) =>
% 132.79/23.02 (((peanoSinj) =>
% 132.79/23.02 (((transitivesetOp1) =>
% 132.79/23.02 (((binintTransitive) =>
% 132.79/23.02 (((transitivesetOp2) =>
% 132.79/23.02 (((setunionTransitive) =>
% 132.79/23.02 (((ordinalMinLem1) =>
% 132.79/23.02 (((ordinalTransSet) =>
% 132.79/23.02 (((ordinalTransSet1) =>
% 132.79/23.02 (((setunionOrdinalLem1) => (ordinal @
% 132.79/23.02 emptyset)))))))))))))))))))))))))))))),
% 132.79/23.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3148])).
% 132.79/23.02 thf(zip_derived_cl3163, plain,
% 132.79/23.02 (~ (((notinself2) =>
% 132.79/23.02 (((omegaSp) =>
% 132.79/23.02 (((omegaSclos) =>
% 132.79/23.02 (((peano0notS) =>
% 132.79/23.02 (((peanoSinj) =>
% 132.79/23.02 (((transitivesetOp1) =>
% 132.79/23.02 (((binintTransitive) =>
% 132.79/23.02 (((transitivesetOp2) =>
% 132.79/23.02 (((setunionTransitive) =>
% 132.79/23.02 (((ordinalMinLem1) =>
% 132.79/23.02 (((ordinalTransSet) =>
% 132.79/23.02 (((ordinalTransSet1) =>
% 132.79/23.02 (((setunionOrdinalLem1) => (ordinal @
% 132.79/23.02 emptyset)))))))))))))))))))))))))))),
% 132.79/23.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3157])).
% 132.79/23.02 thf(zip_derived_cl3170, plain,
% 132.79/23.02 (~ (((omegaSp) =>
% 132.79/23.02 (((omegaSclos) =>
% 132.79/23.02 (((peano0notS) =>
% 132.79/23.02 (((peanoSinj) =>
% 132.79/23.02 (((transitivesetOp1) =>
% 132.79/23.02 (((binintTransitive) =>
% 132.79/23.02 (((transitivesetOp2) =>
% 132.79/23.02 (((setunionTransitive) =>
% 132.79/23.02 (((ordinalMinLem1) =>
% 132.79/23.02 (((ordinalTransSet) =>
% 132.79/23.02 (((ordinalTransSet1) =>
% 132.79/23.02 (((setunionOrdinalLem1) => (ordinal @ emptyset)))))))))))))))))))))))))),
% 132.79/23.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3163])).
% 132.79/23.02 thf(zip_derived_cl3177, plain,
% 132.79/23.02 (~ (((omegaSclos) =>
% 132.79/23.02 (((peano0notS) =>
% 132.79/23.02 (((peanoSinj) =>
% 132.79/23.02 (((transitivesetOp1) =>
% 132.79/23.02 (((binintTransitive) =>
% 132.79/23.02 (((transitivesetOp2) =>
% 132.79/23.02 (((setunionTransitive) =>
% 132.79/23.02 (((ordinalMinLem1) =>
% 132.79/23.02 (((ordinalTransSet) =>
% 132.79/23.02 (((ordinalTransSet1) =>
% 132.79/23.02 (((setunionOrdinalLem1) => (ordinal @ emptyset)))))))))))))))))))))))),
% 132.79/23.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3170])).
% 132.79/23.02 thf(zip_derived_cl3185, plain,
% 132.79/23.02 (~ (((peano0notS) =>
% 132.79/23.02 (((peanoSinj) =>
% 132.79/23.02 (((transitivesetOp1) =>
% 132.79/23.02 (((binintTransitive) =>
% 132.79/23.02 (((transitivesetOp2) =>
% 132.79/23.02 (((setunionTransitive) =>
% 132.79/23.02 (((ordinalMinLem1) =>
% 132.79/23.02 (((ordinalTransSet) =>
% 132.79/23.02 (((ordinalTransSet1) =>
% 132.79/23.02 (((setunionOrdinalLem1) => (ordinal @ emptyset)))))))))))))))))))))),
% 132.79/23.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3177])).
% 132.79/23.02 thf(zip_derived_cl3196, plain,
% 132.79/23.02 (~ (((peanoSinj) =>
% 132.79/23.02 (((transitivesetOp1) =>
% 132.79/23.02 (((binintTransitive) =>
% 132.79/23.02 (((transitivesetOp2) =>
% 132.79/23.02 (((setunionTransitive) =>
% 132.79/23.02 (((ordinalMinLem1) =>
% 132.79/23.02 (((ordinalTransSet) =>
% 132.79/23.02 (((ordinalTransSet1) =>
% 132.79/23.02 (((setunionOrdinalLem1) => (ordinal @ emptyset)))))))))))))))))))),
% 132.79/23.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3185])).
% 132.79/23.02 thf(zip_derived_cl3205, plain,
% 132.79/23.02 (~ (((transitivesetOp1) =>
% 132.79/23.02 (((binintTransitive) =>
% 132.79/23.02 (((transitivesetOp2) =>
% 132.79/23.02 (((setunionTransitive) =>
% 132.79/23.02 (((ordinalMinLem1) =>
% 132.79/23.02 (((ordinalTransSet) =>
% 132.79/23.02 (((ordinalTransSet1) =>
% 132.79/23.02 (((setunionOrdinalLem1) => (ordinal @ emptyset)))))))))))))))))),
% 132.79/23.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3196])).
% 132.79/23.02 thf(zip_derived_cl3211, plain,
% 132.79/23.02 (~ (((binintTransitive) =>
% 132.79/23.02 (((transitivesetOp2) =>
% 132.79/23.02 (((setunionTransitive) =>
% 132.79/23.02 (((ordinalMinLem1) =>
% 132.79/23.02 (((ordinalTransSet) =>
% 132.79/23.02 (((ordinalTransSet1) =>
% 132.79/23.02 (((setunionOrdinalLem1) => (ordinal @ emptyset)))))))))))))))),
% 132.79/23.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3205])).
% 132.79/23.02 thf(zip_derived_cl3217, plain,
% 132.79/23.02 (~ (((transitivesetOp2) =>
% 132.79/23.02 (((setunionTransitive) =>
% 132.79/23.02 (((ordinalMinLem1) =>
% 132.79/23.02 (((ordinalTransSet) =>
% 132.79/23.02 (((ordinalTransSet1) =>
% 132.79/23.02 (((setunionOrdinalLem1) => (ordinal @ emptyset)))))))))))))),
% 132.79/23.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3211])).
% 132.79/23.02 thf(zip_derived_cl3225, plain,
% 132.79/23.02 (~ (((setunionTransitive) =>
% 132.79/23.02 (((ordinalMinLem1) =>
% 132.79/23.02 (((ordinalTransSet) =>
% 132.79/23.02 (((ordinalTransSet1) =>
% 132.79/23.02 (((setunionOrdinalLem1) => (ordinal @ emptyset)))))))))))),
% 132.79/23.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3217])).
% 132.79/23.02 thf(zip_derived_cl3232, plain,
% 132.79/23.02 (~ (((ordinalMinLem1) =>
% 132.79/23.02 (((ordinalTransSet) =>
% 132.79/23.02 (((ordinalTransSet1) =>
% 132.79/23.02 (((setunionOrdinalLem1) => (ordinal @ emptyset)))))))))),
% 132.79/23.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3225])).
% 132.79/23.02 thf(zip_derived_cl3239, plain,
% 132.79/23.02 (~ (((ordinalTransSet) =>
% 132.79/23.02 (((ordinalTransSet1) =>
% 132.79/23.02 (((setunionOrdinalLem1) => (ordinal @ emptyset)))))))),
% 132.79/23.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3232])).
% 132.79/23.02 thf(zip_derived_cl3247, plain,
% 132.79/23.02 (~ (((ordinalTransSet1) =>
% 132.79/23.02 (((setunionOrdinalLem1) => (ordinal @ emptyset)))))),
% 132.79/23.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3239])).
% 132.79/23.02 thf(zip_derived_cl3259, plain,
% 132.79/23.02 (~ (((setunionOrdinalLem1) => (ordinal @ emptyset)))),
% 132.79/23.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3247])).
% 132.79/23.02 thf(zip_derived_cl3273, plain, (~ (ordinal @ emptyset)),
% 132.79/23.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3259])).
% 132.79/23.02 thf(ordinal, axiom, ~ (ordinal @ X0) =>
% 132.79/23.02 ((((transitiveset @ X0) & (wellorderedByIn @ X0))) != ($true))).
% 132.79/23.02 thf('4', plain,
% 132.79/23.02 (![X0:$i]:
% 132.79/23.02 ( ( ~( ordinal @ X0 ) ) <=>
% 132.79/23.02 ( ~( ( transitiveset @ X0 ) & ( wellorderedByIn @ X0 ) ) ) )),
% 132.79/23.02 inference('rw.lit', [status(esa)], [ordinal])).
% 132.79/23.02 thf(zip_derived_cl3282, plain,
% 132.79/23.02 (~ (((transitiveset @ emptyset) & (wellorderedByIn @ emptyset)))),
% 132.79/23.02 inference('rw_clause', [status(thm)], [zip_derived_cl3273, '4'])).
% 132.79/23.02 thf(zip_derived_cl3290, plain,
% 132.79/23.02 ((~ (transitiveset @ emptyset) | ~ (wellorderedByIn @ emptyset))),
% 132.79/23.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl3282])).
% 132.79/23.02 thf(transitiveset, axiom, ~ (transitiveset @ X0) =>
% 132.79/23.02 ((((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X0) => (subset @ Y0 @ X0)))))) !=
% 132.79/23.02 ($true))).
% 132.79/23.02 thf('5', plain,
% 132.79/23.02 (![X0:$i]:
% 132.79/23.02 ( ( ~( transitiveset @ X0 ) ) <=>
% 132.79/23.02 ( ~( ![X5:$i]: ( ( in @ X5 @ X0 ) => ( subset @ X5 @ X0 ) ) ) ) )),
% 132.79/23.02 inference('rw.lit', [status(esa)], [transitiveset])).
% 132.79/23.02 thf(zip_derived_cl3299, plain,
% 132.79/23.02 ((~ (((!!) @ (^[Y0 : $i]:
% 132.79/23.02 (((in @ Y0 @ emptyset) => (subset @ Y0 @ emptyset))))))
% 132.79/23.02 | ~ (wellorderedByIn @ emptyset))),
% 132.79/23.02 inference('rw_clause', [status(thm)], [zip_derived_cl3290, '5'])).
% 132.79/23.02 thf(zip_derived_cl3210, plain, ( (transitivesetOp1)),
% 132.79/23.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3205])).
% 132.79/23.02 thf(transitivesetOp1, axiom, (transitivesetOp1) =>
% 132.79/23.02 ((((!!) @ (^[Y0 : $i]:
% 132.79/23.02 (((transitiveset @ Y0) =>
% 132.79/23.02 (((!!) @ (^[Y1 : $i]:
% 132.79/23.02 (((in @ Y1 @ Y0) => (subset @ Y1 @ Y0)))))))))))
% 132.79/23.02 = ($true))).
% 132.79/23.02 thf('6', plain,
% 132.79/23.02 (( transitivesetOp1 ) <=>
% 132.79/23.02 ( ![X5:$i]:
% 132.79/23.02 ( ( transitiveset @ X5 ) =>
% 132.79/23.02 ( ![X7:$i]: ( ( in @ X7 @ X5 ) => ( subset @ X7 @ X5 ) ) ) ) )),
% 132.79/23.02 inference('rw.lit', [status(esa)], [transitivesetOp1])).
% 132.79/23.02 thf(zip_derived_cl3215, plain,
% 132.79/23.02 ( (((!!) @ (^[Y0 : $i]:
% 132.79/23.02 (((transitiveset @ Y0) =>
% 132.79/23.02 (((!!) @ (^[Y1 : $i]:
% 132.79/23.02 (((in @ Y1 @ Y0) => (subset @ Y1 @ Y0)))))))))))),
% 132.79/23.02 inference('rw_clause', [status(thm)], [zip_derived_cl3210, '6'])).
% 132.79/23.02 thf(zip_derived_cl3222, plain,
% 132.79/23.02 (![X2 : $i]:
% 132.79/23.02 (((transitiveset @ X2) =>
% 132.79/23.02 (((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X2) => (subset @ Y0 @ X2))))))))),
% 132.79/23.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl3215])).
% 132.79/23.02 thf(zip_derived_cl3228, plain,
% 132.79/23.02 (![X2 : $i]:
% 132.79/23.02 (~ (transitiveset @ X2)
% 132.79/23.02 | (((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X2) => (subset @ Y0 @ X2)))))))),
% 132.79/23.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3222])).
% 132.79/23.02 thf(zip_derived_cl3234, plain,
% 132.79/23.02 (![X0 : $i]:
% 132.79/23.02 (~ (((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X0) => (subset @ Y0 @ X0))))))
% 132.79/23.02 | (((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X0) => (subset @ Y0 @ X0)))))))),
% 132.79/23.02 inference('rw_clause', [status(thm)], [zip_derived_cl3228, '5'])).
% 132.79/23.02 thf(zip_derived_cl3241, plain,
% 132.79/23.02 (![X0 : $i]:
% 132.79/23.02 (~ (((in @ ('#sk337' @ X0 @ (^[Y0 : $i]: (subset @ Y0 @ X0))) @ X0) =>
% 132.79/23.02 (subset @ ('#sk337' @ X0 @ (^[Y0 : $i]: (subset @ Y0 @ X0))) @
% 132.79/23.02 X0)))
% 132.79/23.02 | (((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X0) => (subset @ Y0 @ X0)))))))),
% 132.79/23.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl3234])).
% 132.79/23.02 thf(zip_derived_cl3249, plain,
% 132.79/23.02 (![X0 : $i]:
% 132.79/23.02 ( (in @ ('#sk337' @ X0 @ (^[Y0 : $i]: (subset @ Y0 @ X0))) @ X0)
% 132.79/23.02 | (((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X0) => (subset @ Y0 @ X0)))))))),
% 132.79/23.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3241])).
% 132.79/23.02 thf(zip_derived_cl3260, plain,
% 132.79/23.02 (![X0 : $i]:
% 132.79/23.02 (~ ('#form1597' @ X0)
% 132.79/23.02 | (((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X0) => (subset @ Y0 @ X0)))))))),
% 132.79/23.02 define([status(thm)])).
% 132.79/23.02 thf(zip_derived_cl3216, plain, ( (binintTransitive)),
% 132.79/23.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3211])).
% 132.79/23.02 thf(binintTransitive, axiom, (binintTransitive) =>
% 132.79/23.02 ((((!!) @ (^[Y0 : $i]:
% 132.79/23.02 (((transitiveset @ Y0) =>
% 132.79/23.02 (((!!) @ (^[Y1 : $i]:
% 132.79/23.02 (((transitiveset @ Y1) => (transitiveset @
% 132.79/23.02 (binintersect @ Y0 @ Y1))))))))))))
% 132.79/23.02 = ($true))).
% 132.79/23.02 thf('7', plain,
% 132.79/23.02 (( binintTransitive ) <=>
% 132.79/23.02 ( ![X5:$i]:
% 132.79/23.02 ( ( transitiveset @ X5 ) =>
% 132.79/23.02 ( ![X7:$i]:
% 132.79/23.02 ( ( transitiveset @ X7 ) =>
% 132.79/23.02 ( transitiveset @ ( binintersect @ X5 @ X7 ) ) ) ) ) )),
% 132.79/23.02 inference('rw.lit', [status(esa)], [binintTransitive])).
% 132.79/23.02 thf(zip_derived_cl3223, plain,
% 132.79/23.02 ( (((!!) @ (^[Y0 : $i]:
% 132.79/23.02 (((transitiveset @ Y0) =>
% 132.79/23.02 (((!!) @ (^[Y1 : $i]:
% 132.79/23.02 (((transitiveset @ Y1) => (transitiveset @
% 132.79/23.02 (binintersect @ Y0 @ Y1))))))))))))),
% 132.79/23.02 inference('rw_clause', [status(thm)], [zip_derived_cl3216, '7'])).
% 132.79/23.02 thf(zip_derived_cl3229, plain,
% 132.79/23.02 (![X2 : $i]:
% 132.79/23.02 (((transitiveset @ X2) =>
% 132.79/23.02 (((!!) @ (^[Y0 : $i]:
% 132.79/23.02 (((transitiveset @ Y0) => (transitiveset @
% 132.79/23.02 (binintersect @ X2 @ Y0)))))))))),
% 132.79/23.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl3223])).
% 132.79/23.02 thf(zip_derived_cl3235, plain,
% 132.79/23.02 (![X2 : $i]:
% 132.79/23.02 (~ (transitiveset @ X2)
% 132.79/23.02 | (((!!) @ (^[Y0 : $i]:
% 132.79/23.02 (((transitiveset @ Y0) => (transitiveset @
% 132.79/23.02 (binintersect @ X2 @ Y0))))))))),
% 132.79/23.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3229])).
% 132.79/23.02 thf(zip_derived_cl3242, plain,
% 132.79/23.02 (![X0 : $i]:
% 132.79/23.02 (~ (((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X0) => (subset @ Y0 @ X0))))))
% 132.79/23.02 | (((!!) @ (^[Y0 : $i]:
% 132.79/23.02 (((transitiveset @ Y0) => (transitiveset @
% 132.79/23.02 (binintersect @ X0 @ Y0))))))))),
% 132.79/23.02 inference('rw_clause', [status(thm)], [zip_derived_cl3235, '5'])).
% 132.79/23.02 thf(zip_derived_cl3251, plain,
% 132.79/23.02 (![X0 : $i]:
% 132.79/23.02 ( ('#form1597' @ X0)
% 132.79/23.02 | ~ (((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X0) => (subset @ Y0 @ X0)))))))),
% 132.79/23.02 define([status(thm)])).
% 132.79/23.02 thf(zip_derived_cl3307, plain,
% 132.79/23.02 ((~ ('#form1597' @ emptyset) | ~ (wellorderedByIn @ emptyset))),
% 132.79/23.02 inference('renaming', [status(thm)],
% 132.79/23.02 [zip_derived_cl3299, zip_derived_cl3260, zip_derived_cl3251])).
% 132.79/23.02 thf(wellorderedByIn, axiom, ~ (wellorderedByIn @ X0) =>
% 132.79/23.02 ((((stricttotalorderedByIn @ X0) &
% 132.79/23.02 (((!!) @ (^[Y0 : $i]:
% 132.79/23.02 (((in @ Y0 @ (powerset @ X0)) =>
% 132.79/23.02 (((nonempty @ Y0) =>
% 132.79/23.02 (((??) @ (^[Y1 : $i]:
% 132.79/23.02 (((in @ Y1 @ Y0) &
% 132.79/23.02 (((!!) @ (^[Y2 : $i]:
% 132.79/23.02 (((in @ Y2 @ Y0) =>
% 132.79/23.02 (((in @ Y1 @ Y2) |
% 132.79/23.02 (((Y1) = (Y2))))))))))))))))))))))))
% 132.79/23.02 != ($true))).
% 132.79/23.02 thf('8', plain,
% 132.79/23.02 (![X0:$i]:
% 132.79/23.02 ( ( ~( wellorderedByIn @ X0 ) ) <=>
% 132.79/23.02 ( ~( ( stricttotalorderedByIn @ X0 ) &
% 132.79/23.02 ( ![X5:$i]:
% 132.79/23.02 ( ( in @ X5 @ ( powerset @ X0 ) ) =>
% 132.79/23.02 ( ( nonempty @ X5 ) =>
% 132.79/23.02 ( ?[X7:$i]:
% 132.79/23.02 ( ( in @ X7 @ X5 ) &
% 132.79/23.02 ( ![X9:$i]:
% 132.79/23.02 ( ( in @ X9 @ X5 ) =>
% 132.79/23.02 ( ( in @ X7 @ X9 ) | ( ( X7 ) = ( X9 ) ) ) ) ) ) ) ) ) ) ) ) )),
% 132.79/23.02 inference('rw.lit', [status(esa)], [wellorderedByIn])).
% 132.79/23.02 thf(zip_derived_cl3314, plain,
% 132.79/23.02 ((~ (((stricttotalorderedByIn @ emptyset) &
% 132.79/23.02 (((!!) @ (^[Y0 : $i]:
% 132.79/23.02 (((in @ Y0 @ (powerset @ emptyset)) =>
% 132.79/23.02 (((nonempty @ Y0) =>
% 132.79/23.02 (((??) @ (^[Y1 : $i]:
% 132.79/23.02 (((in @ Y1 @ Y0) &
% 132.79/23.02 (((!!) @ (^[Y2 : $i]:
% 132.79/23.02 (((in @ Y2 @ Y0) =>
% 132.79/23.02 (((in @ Y1 @ Y2) |
% 132.79/23.02 (((Y1) = (Y2))))))))))))))))))))))))
% 132.79/23.02 | ~ ('#form1597' @ emptyset))),
% 132.79/23.02 inference('rw_clause', [status(thm)], [zip_derived_cl3307, '8'])).
% 132.79/23.02 thf(zip_derived_cl3321, plain,
% 132.79/23.02 ((~ (stricttotalorderedByIn @ emptyset)
% 132.79/23.02 | ~ (((!!) @ (^[Y0 : $i]:
% 132.79/23.02 (((in @ Y0 @ (powerset @ emptyset)) =>
% 132.79/23.02 (((nonempty @ Y0) =>
% 132.79/23.02 (((??) @ (^[Y1 : $i]:
% 132.79/23.02 (((in @ Y1 @ Y0) &
% 132.79/23.02 (((!!) @ (^[Y2 : $i]:
% 132.79/23.02 (((in @ Y2 @ Y0) =>
% 132.79/23.02 (((in @ Y1 @ Y2) |
% 132.79/23.02 (((Y1) = (Y2))))))))))))))))))))))
% 132.79/23.02 | ~ ('#form1597' @ emptyset))),
% 132.79/23.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl3314])).
% 132.79/23.02 thf(stricttotalorderedByIn, axiom, ~ (stricttotalorderedByIn @ X0) =>
% 132.79/23.02 ((((((!!) @ (^[Y0 : $i]:
% 132.79/23.02 (((in @ Y0 @ X0) =>
% 132.79/23.02 (((!!) @ (^[Y1 : $i]:
% 132.79/23.02 (((in @ Y1 @ X0) =>
% 132.79/23.02 (((!!) @ (^[Y2 : $i]:
% 132.79/23.02 (((in @ Y2 @ X0) =>
% 132.79/23.02 (((((in @ Y1 @ Y2) & (in @
% 132.79/23.02 Y0 @ Y1))) =>
% 132.79/23.02 (in @ Y0 @ Y2)))))))))))))))))) &
% 132.79/23.02 (((!!) @ (^[Y0 : $i]:
% 132.79/23.02 (((in @ Y0 @ X0) =>
% 132.79/23.02 (((!!) @ (^[Y1 : $i]:
% 132.79/23.02 (((in @ Y1 @ X0) =>
% 132.79/23.02 (((in @ Y1 @ Y0) | (in @ Y0 @ Y1) |
% 132.79/23.02 (((Y0) = (Y1))))))))))))))) &
% 132.79/23.02 (((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X0) => (((~) @ (in @ Y0 @ Y0))))))))))
% 132.79/23.02 != ($true))).
% 132.79/23.02 thf('9', plain,
% 132.79/23.02 (![X0:$i]:
% 132.79/23.02 ( ( ~( stricttotalorderedByIn @ X0 ) ) <=>
% 132.79/23.02 ( ~( ( ![X5:$i]:
% 132.79/23.02 ( ( in @ X5 @ X0 ) =>
% 132.79/23.02 ( ![X7:$i]:
% 132.79/23.02 ( ( in @ X7 @ X0 ) =>
% 132.79/23.02 ( ![X9:$i]:
% 132.79/23.02 ( ( in @ X9 @ X0 ) =>
% 132.79/23.02 ( ( ( in @ X7 @ X9 ) & ( in @ X5 @ X7 ) ) =>
% 132.79/23.02 ( in @ X5 @ X9 ) ) ) ) ) ) ) ) &
% 132.79/23.02 ( ![X11:$i]:
% 132.79/23.02 ( ( in @ X11 @ X0 ) =>
% 132.79/23.02 ( ![X13:$i]:
% 132.79/23.02 ( ( in @ X13 @ X0 ) =>
% 132.79/23.02 ( ( in @ X13 @ X11 ) | ( in @ X11 @ X13 ) |
% 132.79/23.02 ( ( X11 ) = ( X13 ) ) ) ) ) ) ) &
% 132.79/23.02 ( ![X15:$i]: ( ( in @ X15 @ X0 ) => ( ~( in @ X15 @ X15 ) ) ) ) ) ) )),
% 132.79/23.02 inference('rw.lit', [status(esa)], [stricttotalorderedByIn])).
% 132.79/23.02 thf(zip_derived_cl3327, plain,
% 132.79/23.02 ((~ (((((!!) @ (^[Y0 : $i]:
% 132.79/23.02 (((in @ Y0 @ emptyset) =>
% 132.79/23.02 (((!!) @ (^[Y1 : $i]:
% 132.79/23.02 (((in @ Y1 @ emptyset) =>
% 132.79/23.02 (((!!) @ (^[Y2 : $i]:
% 132.79/23.02 (((in @ Y2 @ emptyset) =>
% 132.79/23.02 (((((in @ Y1 @ Y2) &
% 132.79/23.02 (in @ Y0 @ Y1))) =>
% 132.79/23.02 (in @ Y0 @ Y2)))))))))))))))))) &
% 132.79/23.02 (((!!) @ (^[Y0 : $i]:
% 132.79/23.02 (((in @ Y0 @ emptyset) =>
% 132.79/23.02 (((!!) @ (^[Y1 : $i]:
% 132.79/23.02 (((in @ Y1 @ emptyset) =>
% 132.79/23.02 (((in @ Y1 @ Y0) | (in @ Y0 @ Y1) |
% 132.79/23.02 (((Y0) = (Y1))))))))))))))) &
% 132.79/23.02 (((!!) @ (^[Y0 : $i]:
% 132.79/23.02 (((in @ Y0 @ emptyset) => (((~) @ (in @ Y0 @ Y0))))))))))
% 132.79/23.02 | ~ ('#form1597' @ emptyset)
% 132.79/23.02 | ~ (((!!) @ (^[Y0 : $i]:
% 132.79/23.02 (((in @ Y0 @ (powerset @ emptyset)) =>
% 132.79/23.02 (((nonempty @ Y0) =>
% 132.79/23.02 (((??) @ (^[Y1 : $i]:
% 132.79/23.02 (((in @ Y1 @ Y0) &
% 132.79/23.02 (((!!) @ (^[Y2 : $i]:
% 132.79/23.02 (((in @ Y2 @ Y0) =>
% 132.79/23.02 (((in @ Y1 @ Y2) |
% 132.79/23.02 (((Y1) = (Y2)))))))))))))))))))))))),
% 132.79/23.02 inference('rw_clause', [status(thm)], [zip_derived_cl3321, '9'])).
% 132.79/23.02 thf(zip_derived_cl3238, plain, ( (ordinalMinLem1)),
% 132.79/23.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3232])).
% 132.79/23.02 thf(ordinalMinLem1, axiom, (ordinalMinLem1) =>
% 132.79/23.02 ((((!!) @ (^[Y0 : $i]:
% 132.79/23.02 (((ordinal @ Y0) =>
% 132.79/23.02 (((!!) @ (^[Y1 : $i]:
% 132.79/23.02 (((ordinal @ Y1) => (transitiveset @
% 132.79/23.02 (binintersect @ Y0 @ Y1))))))))))))
% 132.79/23.02 = ($true))).
% 132.79/23.02 thf('10', plain,
% 132.79/23.02 (( ordinalMinLem1 ) <=>
% 132.79/23.02 ( ![X5:$i]:
% 132.79/23.02 ( ( ordinal @ X5 ) =>
% 132.79/23.02 ( ![X7:$i]:
% 132.79/23.02 ( ( ordinal @ X7 ) =>
% 132.79/23.02 ( transitiveset @ ( binintersect @ X5 @ X7 ) ) ) ) ) )),
% 132.79/23.02 inference('rw.lit', [status(esa)], [ordinalMinLem1])).
% 132.79/23.02 thf(zip_derived_cl3245, plain,
% 132.79/23.02 ( (((!!) @ (^[Y0 : $i]:
% 132.79/23.02 (((ordinal @ Y0) =>
% 132.79/23.02 (((!!) @ (^[Y1 : $i]:
% 132.79/23.02 (((ordinal @ Y1) => (transitiveset @
% 132.79/23.02 (binintersect @ Y0 @ Y1))))))))))))),
% 132.79/23.02 inference('rw_clause', [status(thm)], [zip_derived_cl3238, '10'])).
% 132.79/23.02 thf(zip_derived_cl3256, plain,
% 132.79/23.02 (![X2 : $i]:
% 132.79/23.02 (((ordinal @ X2) =>
% 132.79/23.02 (((!!) @ (^[Y0 : $i]:
% 132.79/23.02 (((ordinal @ Y0) => (transitiveset @
% 132.79/23.02 (binintersect @ X2 @ Y0)))))))))),
% 132.79/23.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl3245])).
% 132.79/23.02 thf(zip_derived_cl3269, plain,
% 132.79/23.02 (![X2 : $i]:
% 132.79/23.02 (~ (ordinal @ X2)
% 132.79/23.02 | (((!!) @ (^[Y0 : $i]:
% 132.79/23.02 (((ordinal @ Y0) => (transitiveset @
% 132.79/23.02 (binintersect @ X2 @ Y0))))))))),
% 132.79/23.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3256])).
% 132.79/23.02 thf(zip_derived_cl3278, plain,
% 132.79/23.02 (![X0 : $i]:
% 132.79/23.02 (~ (((transitiveset @ X0) & (wellorderedByIn @ X0)))
% 132.79/23.02 | (((!!) @ (^[Y0 : $i]:
% 132.79/23.02 (((ordinal @ Y0) => (transitiveset @
% 132.79/23.02 (binintersect @ X0 @ Y0))))))))),
% 132.79/23.02 inference('rw_clause', [status(thm)], [zip_derived_cl3269, '4'])).
% 132.79/23.02 thf(zip_derived_cl3286, plain,
% 132.79/23.02 (![X0 : $i]:
% 132.79/23.02 (~ (transitiveset @ X0)
% 132.79/23.02 | ~ (wellorderedByIn @ X0)
% 132.79/23.02 | (((!!) @ (^[Y0 : $i]:
% 132.79/23.02 (((ordinal @ Y0) => (transitiveset @
% 132.79/23.02 (binintersect @ X0 @ Y0))))))))),
% 132.79/23.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl3278])).
% 132.79/23.02 thf(zip_derived_cl3295, plain,
% 132.79/23.02 (![X0 : $i]:
% 132.79/23.02 (~ (((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X0) => (subset @ Y0 @ X0))))))
% 132.79/23.02 | (((!!) @ (^[Y0 : $i]:
% 132.79/23.02 (((ordinal @ Y0) => (transitiveset @
% 132.79/23.02 (binintersect @ X0 @ Y0)))))))
% 132.79/23.02 | ~ (wellorderedByIn @ X0))),
% 132.79/23.02 inference('rw_clause', [status(thm)], [zip_derived_cl3286, '5'])).
% 132.79/23.02 thf(zip_derived_cl3260, plain,
% 132.79/23.02 (![X0 : $i]:
% 132.79/23.02 (~ ('#form1597' @ X0)
% 132.79/23.02 | (((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X0) => (subset @ Y0 @ X0)))))))),
% 132.79/23.02 define([status(thm)])).
% 132.79/23.02 thf(zip_derived_cl3251, plain,
% 132.79/23.02 (![X0 : $i]:
% 132.79/23.02 ( ('#form1597' @ X0)
% 132.79/23.02 | ~ (((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X0) => (subset @ Y0 @ X0)))))))),
% 132.79/23.02 define([status(thm)])).
% 132.79/23.02 thf(zip_derived_cl3303, plain,
% 132.79/23.02 (![X0 : $i]:
% 132.79/23.02 (~ ('#form1597' @ X0)
% 132.79/23.02 | ~ (wellorderedByIn @ X0)
% 132.79/23.02 | (((!!) @ (^[Y0 : $i]:
% 132.79/23.02 (((ordinal @ Y0) => (transitiveset @
% 132.79/23.02 (binintersect @ X0 @ Y0))))))))),
% 132.79/23.02 inference('renaming', [status(thm)],
% 132.79/23.02 [zip_derived_cl3295, zip_derived_cl3260, zip_derived_cl3251])).
% 132.79/23.02 thf(zip_derived_cl3310, plain,
% 132.79/23.02 (![X0 : $i]:
% 132.79/23.02 (~ (((stricttotalorderedByIn @ X0) &
% 132.79/23.02 (((!!) @ (^[Y0 : $i]:
% 132.79/23.02 (((in @ Y0 @ (powerset @ X0)) =>
% 132.79/23.02 (((nonempty @ Y0) =>
% 132.79/23.02 (((??) @ (^[Y1 : $i]:
% 132.79/23.02 (((in @ Y1 @ Y0) &
% 132.79/23.02 (((!!) @ (^[Y2 : $i]:
% 132.79/23.02 (((in @ Y2 @ Y0) =>
% 132.79/23.02 (((in @ Y1 @ Y2) |
% 132.79/23.02 (((Y1) = (Y2))))))))))))))))))))))))
% 132.79/23.02 | (((!!) @ (^[Y0 : $i]:
% 132.79/23.02 (((ordinal @ Y0) => (transitiveset @
% 132.79/23.02 (binintersect @ X0 @ Y0)))))))
% 132.79/23.02 | ~ ('#form1597' @ X0))),
% 132.79/23.02 inference('rw_clause', [status(thm)], [zip_derived_cl3303, '8'])).
% 132.79/23.02 thf(zip_derived_cl3317, plain,
% 132.79/23.02 (![X0 : $i]:
% 132.79/23.02 (~ (stricttotalorderedByIn @ X0)
% 132.79/23.02 | ~ (((!!) @ (^[Y0 : $i]:
% 132.79/23.02 (((in @ Y0 @ (powerset @ X0)) =>
% 132.79/23.02 (((nonempty @ Y0) =>
% 132.79/23.02 (((??) @ (^[Y1 : $i]:
% 132.79/23.02 (((in @ Y1 @ Y0) &
% 132.79/23.02 (((!!) @ (^[Y2 : $i]:
% 132.79/23.02 (((in @ Y2 @ Y0) =>
% 132.79/23.02 (((in @ Y1 @ Y2) |
% 132.79/23.02 (((Y1) = (Y2))))))))))))))))))))))
% 132.79/23.02 | ~ ('#form1597' @ X0)
% 132.79/23.02 | (((!!) @ (^[Y0 : $i]:
% 132.79/23.02 (((ordinal @ Y0) => (transitiveset @
% 132.79/23.02 (binintersect @ X0 @ Y0))))))))),
% 132.79/23.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl3310])).
% 132.79/23.02 thf(zip_derived_cl3322, plain,
% 132.79/23.02 (![X0 : $i]:
% 132.79/23.02 (~ (((((!!) @ (^[Y0 : $i]:
% 132.79/23.02 (((in @ Y0 @ X0) =>
% 132.79/23.02 (((!!) @ (^[Y1 : $i]:
% 132.79/23.02 (((in @ Y1 @ X0) =>
% 132.79/23.02 (((!!) @ (^[Y2 : $i]:
% 132.79/23.02 (((in @ Y2 @ X0) =>
% 132.79/23.02 (((((in @ Y1 @ Y2) &
% 132.79/23.02 (in @ Y0 @ Y1))) =>
% 132.79/23.02 (in @ Y0 @ Y2)))))))))))))))))) &
% 132.79/23.02 (((!!) @ (^[Y0 : $i]:
% 132.79/23.02 (((in @ Y0 @ X0) =>
% 132.79/23.02 (((!!) @ (^[Y1 : $i]:
% 132.79/23.02 (((in @ Y1 @ X0) =>
% 132.79/23.02 (((in @ Y1 @ Y0) | (in @ Y0 @ Y1) |
% 132.79/23.02 (((Y0) = (Y1))))))))))))))) &
% 132.79/23.02 (((!!) @ (^[Y0 : $i]:
% 132.79/23.02 (((in @ Y0 @ X0) => (((~) @ (in @ Y0 @ Y0))))))))))
% 132.79/23.02 | (((!!) @ (^[Y0 : $i]:
% 132.79/23.02 (((ordinal @ Y0) => (transitiveset @
% 132.79/23.02 (binintersect @ X0 @ Y0)))))))
% 132.79/23.02 | ~ ('#form1597' @ X0)
% 132.79/23.02 | ~ (((!!) @ (^[Y0 : $i]:
% 132.79/23.02 (((in @ Y0 @ (powerset @ X0)) =>
% 132.79/23.02 (((nonempty @ Y0) =>
% 132.79/23.02 (((??) @ (^[Y1 : $i]:
% 132.79/23.02 (((in @ Y1 @ Y0) &
% 132.79/23.02 (((!!) @ (^[Y2 : $i]:
% 132.79/23.02 (((in @ Y2 @ Y0) =>
% 132.79/23.02 (((in @ Y1 @ Y2) |
% 132.79/23.02 (((Y1) = (Y2)))))))))))))))))))))))),
% 132.79/23.02 inference('rw_clause', [status(thm)], [zip_derived_cl3317, '9'])).
% 132.79/23.02 thf(zip_derived_cl3328, plain,
% 132.79/23.02 (![X0 : $i]:
% 132.79/23.02 ( ('#form1598' @ X0)
% 132.79/23.02 | ~ (((!!) @ (^[Y0 : $i]:
% 132.79/23.02 (((in @ Y0 @ (powerset @ X0)) =>
% 132.79/23.02 (((nonempty @ Y0) =>
% 132.79/23.02 (((??) @ (^[Y1 : $i]:
% 132.79/23.02 (((in @ Y1 @ Y0) &
% 132.79/23.02 (((!!) @ (^[Y2 : $i]:
% 132.79/23.02 (((in @ Y2 @ Y0) =>
% 132.79/23.02 (((in @ Y1 @ Y2) |
% 132.79/23.02 (((Y1) = (Y2)))))))))))))))))))))))),
% 132.79/23.02 define([status(thm)])).
% 132.79/23.02 thf(zip_derived_cl3334, plain,
% 132.79/23.02 ((~ ('#form1598' @ emptyset)
% 132.79/23.02 | ~ ('#form1597' @ emptyset)
% 132.79/23.02 | ~ (((((!!) @ (^[Y0 : $i]:
% 132.79/23.02 (((in @ Y0 @ emptyset) =>
% 132.79/23.02 (((!!) @ (^[Y1 : $i]:
% 132.79/23.02 (((in @ Y1 @ emptyset) =>
% 132.79/23.02 (((!!) @ (^[Y2 : $i]:
% 132.79/23.02 (((in @ Y2 @ emptyset) =>
% 132.79/23.02 (((((in @ Y1 @ Y2) &
% 132.79/23.02 (in @ Y0 @ Y1))) =>
% 132.79/23.02 (in @ Y0 @ Y2)))))))))))))))))) &
% 132.79/23.02 (((!!) @ (^[Y0 : $i]:
% 132.79/23.02 (((in @ Y0 @ emptyset) =>
% 132.79/23.02 (((!!) @ (^[Y1 : $i]:
% 132.79/23.02 (((in @ Y1 @ emptyset) =>
% 132.79/23.02 (((in @ Y1 @ Y0) | (in @ Y0 @ Y1) |
% 132.79/23.02 (((Y0) = (Y1))))))))))))))) &
% 132.79/23.02 (((!!) @ (^[Y0 : $i]:
% 132.79/23.02 (((in @ Y0 @ emptyset) => (((~) @ (in @ Y0 @ Y0)))))))))))),
% 132.79/23.02 inference('renaming', [status(thm)],
% 132.79/23.02 [zip_derived_cl3327, zip_derived_cl3328])).
% 132.79/23.02 thf(zip_derived_cl3341, plain,
% 132.79/23.02 ((~ (((!!) @ (^[Y0 : $i]:
% 132.79/23.02 (((in @ Y0 @ emptyset) =>
% 132.79/23.02 (((!!) @ (^[Y1 : $i]:
% 132.79/23.02 (((in @ Y1 @ emptyset) =>
% 132.79/23.02 (((!!) @ (^[Y2 : $i]:
% 132.79/23.02 (((in @ Y2 @ emptyset) =>
% 132.79/23.02 (((((in @ Y1 @ Y2) & (in @
% 132.79/23.02 Y0 @ Y1))) =>
% 132.79/23.02 (in @ Y0 @ Y2))))))))))))))))))
% 132.79/23.02 | ~ (((!!) @ (^[Y0 : $i]:
% 132.79/23.02 (((in @ Y0 @ emptyset) =>
% 132.79/23.02 (((!!) @ (^[Y1 : $i]:
% 132.79/23.02 (((in @ Y1 @ emptyset) =>
% 132.79/23.02 (((in @ Y1 @ Y0) | (in @ Y0 @ Y1) |
% 132.79/23.02 (((Y0) = (Y1)))))))))))))))
% 132.79/23.02 | ~ (((!!) @ (^[Y0 : $i]:
% 132.79/23.02 (((in @ Y0 @ emptyset) => (((~) @ (in @ Y0 @ Y0))))))))
% 132.79/23.02 | ~ ('#form1597' @ emptyset)
% 132.79/23.02 | ~ ('#form1598' @ emptyset))),
% 132.79/23.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl3334])).
% 132.79/23.02 thf(zip_derived_cl3348, plain,
% 132.79/23.02 ((~ (((in @ '#sk1600' @ emptyset) =>
% 132.79/23.02 (((!!) @ (^[Y0 : $i]:
% 132.79/23.02 (((in @ Y0 @ emptyset) =>
% 132.79/23.02 (((!!) @ (^[Y1 : $i]:
% 132.79/23.02 (((in @ Y1 @ emptyset) =>
% 132.79/23.02 (((((in @ Y0 @ Y1) & (in @ '#sk1600' @
% 132.79/23.02 Y0))) =>
% 132.79/23.02 (in @ '#sk1600' @ Y1)))))))))))))))
% 132.79/23.02 | ~ ('#form1598' @ emptyset)
% 132.79/23.02 | ~ ('#form1597' @ emptyset)
% 132.79/23.02 | ~ (((!!) @ (^[Y0 : $i]:
% 132.79/23.02 (((in @ Y0 @ emptyset) => (((~) @ (in @ Y0 @ Y0))))))))
% 132.79/23.02 | ~ (((!!) @ (^[Y0 : $i]:
% 132.79/23.02 (((in @ Y0 @ emptyset) =>
% 132.79/23.02 (((!!) @ (^[Y1 : $i]:
% 132.79/23.02 (((in @ Y1 @ emptyset) =>
% 132.79/23.02 (((in @ Y1 @ Y0) | (in @ Y0 @ Y1) |
% 132.79/23.02 (((Y0) = (Y1))))))))))))))))),
% 132.79/23.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl3341])).
% 132.79/23.02 thf(zip_derived_cl3355, plain,
% 132.79/23.02 (( (in @ '#sk1600' @ emptyset)
% 132.79/23.02 | ~ (((!!) @ (^[Y0 : $i]:
% 132.79/23.02 (((in @ Y0 @ emptyset) =>
% 132.79/23.02 (((!!) @ (^[Y1 : $i]:
% 132.79/23.02 (((in @ Y1 @ emptyset) =>
% 132.79/23.02 (((in @ Y1 @ Y0) | (in @ Y0 @ Y1) |
% 132.79/23.02 (((Y0) = (Y1)))))))))))))))
% 132.79/23.02 | ~ (((!!) @ (^[Y0 : $i]:
% 132.79/23.02 (((in @ Y0 @ emptyset) => (((~) @ (in @ Y0 @ Y0))))))))
% 132.79/23.02 | ~ ('#form1597' @ emptyset)
% 132.79/23.02 | ~ ('#form1598' @ emptyset))),
% 132.79/23.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3348])).
% 132.79/23.02 thf(zip_derived_cl3355, plain,
% 132.79/23.02 (( (in @ '#sk1600' @ emptyset)
% 132.79/23.02 | ~ (((!!) @ (^[Y0 : $i]:
% 132.79/23.02 (((in @ Y0 @ emptyset) =>
% 132.79/23.02 (((!!) @ (^[Y1 : $i]:
% 132.79/23.02 (((in @ Y1 @ emptyset) =>
% 132.79/23.02 (((in @ Y1 @ Y0) | (in @ Y0 @ Y1) |
% 132.79/23.02 (((Y0) = (Y1)))))))))))))))
% 132.79/23.02 | ~ (((!!) @ (^[Y0 : $i]:
% 132.79/23.02 (((in @ Y0 @ emptyset) => (((~) @ (in @ Y0 @ Y0))))))))
% 132.79/23.02 | ~ ('#form1597' @ emptyset)
% 132.79/23.02 | ~ ('#form1598' @ emptyset))),
% 132.79/23.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3348])).
% 132.79/23.02 thf(zip_derived_cl3363, plain,
% 132.79/23.02 (( ('#form1602')
% 132.79/23.02 | ~ (((!!) @ (^[Y0 : $i]:
% 132.79/23.02 (((in @ Y0 @ emptyset) =>
% 132.79/23.02 (((!!) @ (^[Y1 : $i]:
% 132.79/23.02 (((in @ Y1 @ emptyset) =>
% 132.79/23.02 (((in @ Y1 @ Y0) | (in @ Y0 @ Y1) |
% 132.79/23.02 (((Y0) = (Y1))))))))))))))))),
% 132.79/23.02 define([status(thm)])).
% 132.79/23.02 thf(zip_derived_cl3365, plain,
% 132.79/23.02 ((~ ('#form1602')
% 132.79/23.02 | ~ ('#form1598' @ emptyset)
% 132.79/23.02 | ~ ('#form1597' @ emptyset)
% 132.79/23.02 | ~ (((!!) @ (^[Y0 : $i]:
% 132.79/23.02 (((in @ Y0 @ emptyset) => (((~) @ (in @ Y0 @ Y0))))))))
% 132.79/23.02 | (in @ '#sk1600' @ emptyset))),
% 132.79/23.02 inference('renaming', [status(thm)],
% 132.79/23.02 [zip_derived_cl3355, zip_derived_cl3363])).
% 132.79/23.02 thf(zip_derived_cl3365, plain,
% 132.79/23.02 ((~ ('#form1602')
% 132.79/23.02 | ~ ('#form1598' @ emptyset)
% 132.79/23.02 | ~ ('#form1597' @ emptyset)
% 132.79/23.02 | ~ (((!!) @ (^[Y0 : $i]:
% 132.79/23.02 (((in @ Y0 @ emptyset) => (((~) @ (in @ Y0 @ Y0))))))))
% 132.79/23.02 | (in @ '#sk1600' @ emptyset))),
% 132.79/23.02 inference('renaming', [status(thm)],
% 132.79/23.02 [zip_derived_cl3355, zip_derived_cl3363])).
% 132.79/23.02 thf(zip_derived_cl3375, plain,
% 132.79/23.02 (( ('#form1607')
% 132.79/23.02 | ~ (((!!) @ (^[Y0 : $i]:
% 132.79/23.02 (((in @ Y0 @ emptyset) => (((~) @ (in @ Y0 @ Y0)))))))))),
% 132.79/23.02 define([status(thm)])).
% 132.79/23.02 thf(zip_derived_cl3377, plain,
% 132.79/23.02 ((~ ('#form1607')
% 132.79/23.02 | (in @ '#sk1600' @ emptyset)
% 132.79/23.02 | ~ ('#form1597' @ emptyset)
% 132.79/23.02 | ~ ('#form1598' @ emptyset)
% 132.79/23.02 | ~ ('#form1602'))),
% 132.79/23.02 inference('renaming', [status(thm)],
% 132.79/23.02 [zip_derived_cl3365, zip_derived_cl3375])).
% 132.79/23.02 thf(zip_derived_cl3363, plain,
% 132.79/23.02 (( ('#form1602')
% 132.79/23.02 | ~ (((!!) @ (^[Y0 : $i]:
% 132.79/23.02 (((in @ Y0 @ emptyset) =>
% 132.79/23.02 (((!!) @ (^[Y1 : $i]:
% 132.79/23.02 (((in @ Y1 @ emptyset) =>
% 132.79/23.02 (((in @ Y1 @ Y0) | (in @ Y0 @ Y1) |
% 132.79/23.02 (((Y0) = (Y1))))))))))))))))),
% 132.79/23.02 define([status(thm)])).
% 132.79/23.02 thf(zip_derived_cl3364, plain,
% 132.79/23.02 ((~ (((in @ '#sk1603' @ emptyset) =>
% 132.79/23.02 (((!!) @ (^[Y0 : $i]:
% 132.79/23.02 (((in @ Y0 @ emptyset) =>
% 132.79/23.02 (((in @ Y0 @ '#sk1603') | (in @ '#sk1603' @ Y0) |
% 132.79/23.02 ((('#sk1603') = (Y0))))))))))))
% 132.79/23.02 | ('#form1602'))),
% 132.79/23.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl3363])).
% 132.79/23.02 thf(zip_derived_cl3378, plain,
% 132.79/23.02 (( (in @ '#sk1603' @ emptyset) | ('#form1602'))),
% 132.79/23.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3364])).
% 132.79/23.02 thf(zip_derived_cl6, plain, ( (emptysetAx)),
% 132.79/23.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl4])).
% 132.79/23.02 thf(emptysetAx, axiom, (emptysetAx) =>
% 132.79/23.02 ((((!!) @ (^[Y0 : $i]: (((~) @ (in @ Y0 @ emptyset)))))) = ($true))).
% 132.79/23.02 thf('11', plain,
% 132.79/23.02 (( emptysetAx ) <=> ( ![X5:$i]: ( ~( in @ X5 @ emptyset ) ) )),
% 132.79/23.02 inference('rw.lit', [status(esa)], [emptysetAx])).
% 132.79/23.02 thf(zip_derived_cl9, plain,
% 132.79/23.02 ( (((!!) @ (^[Y0 : $i]: (((~) @ (in @ Y0 @ emptyset))))))),
% 132.79/23.02 inference('rw_clause', [status(thm)], [zip_derived_cl6, '11'])).
% 132.79/23.02 thf(zip_derived_cl13, plain, (![X2 : $i]: ~ (in @ X2 @ emptyset)),
% 132.79/23.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl9])).
% 132.79/23.02 thf(zip_derived_cl3494, plain, ( ('#form1602')),
% 132.79/23.02 inference('clc', [status(thm)], [zip_derived_cl3378, zip_derived_cl13])).
% 132.79/23.02 thf(zip_derived_cl3498, plain,
% 132.79/23.02 ((~ ('#form1607')
% 132.79/23.02 | (in @ '#sk1600' @ emptyset)
% 132.79/23.02 | ~ ('#form1597' @ emptyset)
% 132.79/23.02 | ~ ('#form1598' @ emptyset))),
% 132.79/23.02 inference('demod', [status(thm)],
% 132.79/23.02 [zip_derived_cl3377, zip_derived_cl3494])).
% 132.79/23.02 thf(zip_derived_cl13, plain, (![X2 : $i]: ~ (in @ X2 @ emptyset)),
% 132.79/23.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl9])).
% 132.79/23.02 thf(zip_derived_cl3499, plain,
% 132.79/23.02 ((~ ('#form1598' @ emptyset)
% 132.79/23.02 | ~ ('#form1597' @ emptyset)
% 132.79/23.02 | ~ ('#form1607'))),
% 132.79/23.02 inference('clc', [status(thm)], [zip_derived_cl3498, zip_derived_cl13])).
% 132.79/23.02 thf(zip_derived_cl3375, plain,
% 132.79/23.02 (( ('#form1607')
% 132.79/23.02 | ~ (((!!) @ (^[Y0 : $i]:
% 132.79/23.02 (((in @ Y0 @ emptyset) => (((~) @ (in @ Y0 @ Y0)))))))))),
% 132.79/23.02 define([status(thm)])).
% 132.79/23.02 thf(zip_derived_cl3376, plain,
% 132.79/23.02 ((~ (((in @ ('#sk290' @ emptyset @ (^[Y0 : $i]: (in @ Y0 @ Y0))) @
% 132.79/23.02 emptyset) =>
% 132.79/23.02 (((~) @ (in @
% 132.79/23.02 ('#sk290' @ emptyset @ (^[Y0 : $i]: (in @ Y0 @ Y0))) @
% 132.79/23.02 ('#sk290' @ emptyset @ (^[Y0 : $i]: (in @ Y0 @ Y0))))))))
% 132.79/23.02 | ('#form1607'))),
% 132.79/23.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl3375])).
% 132.79/23.02 thf(zip_derived_cl3392, plain,
% 132.79/23.02 (( (in @ ('#sk290' @ emptyset @ (^[Y0 : $i]: (in @ Y0 @ Y0))) @ emptyset)
% 132.79/23.02 | ('#form1607'))),
% 132.79/23.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3376])).
% 132.79/23.02 thf(zip_derived_cl13, plain, (![X2 : $i]: ~ (in @ X2 @ emptyset)),
% 132.79/23.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl9])).
% 132.79/23.02 thf(zip_derived_cl3522, plain, ( ('#form1607')),
% 132.79/23.02 inference('clc', [status(thm)], [zip_derived_cl3392, zip_derived_cl13])).
% 132.79/23.02 thf(zip_derived_cl3523, plain,
% 132.79/23.02 ((~ ('#form1598' @ emptyset) | ~ ('#form1597' @ emptyset))),
% 132.79/23.02 inference('demod', [status(thm)],
% 132.79/23.02 [zip_derived_cl3499, zip_derived_cl3522])).
% 132.79/23.02 thf(zip_derived_cl3231, plain, ( (setunionTransitive)),
% 132.79/23.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3225])).
% 132.79/23.02 thf(setunionTransitive, axiom, (setunionTransitive) =>
% 132.79/23.02 ((((!!) @ (^[Y0 : $i]:
% 132.79/23.02 (((((!!) @ (^[Y1 : $i]:
% 132.79/23.02 (((in @ Y1 @ Y0) => (transitiveset @ Y1)))))) =>
% 132.79/23.02 (transitiveset @ (setunion @ Y0)))))))
% 132.79/23.02 = ($true))).
% 132.79/23.02 thf('12', plain,
% 132.79/23.02 (( setunionTransitive ) <=>
% 132.79/23.02 ( ![X5:$i]:
% 132.79/23.02 ( ( ![X7:$i]: ( ( in @ X7 @ X5 ) => ( transitiveset @ X7 ) ) ) =>
% 132.79/23.02 ( transitiveset @ ( setunion @ X5 ) ) ) )),
% 132.79/23.02 inference('rw.lit', [status(esa)], [setunionTransitive])).
% 132.79/23.02 thf(zip_derived_cl3237, plain,
% 132.79/23.02 ( (((!!) @ (^[Y0 : $i]:
% 132.79/23.02 (((((!!) @ (^[Y1 : $i]:
% 132.79/23.02 (((in @ Y1 @ Y0) => (transitiveset @ Y1)))))) =>
% 132.79/23.02 (transitiveset @ (setunion @ Y0)))))))),
% 132.79/23.02 inference('rw_clause', [status(thm)], [zip_derived_cl3231, '12'])).
% 132.79/23.02 thf(zip_derived_cl3244, plain,
% 132.79/23.02 (![X2 : $i]:
% 132.79/23.02 (((((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X2) => (transitiveset @ Y0)))))) =>
% 132.79/23.02 (transitiveset @ (setunion @ X2))))),
% 132.79/23.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl3237])).
% 132.79/23.02 thf(zip_derived_cl3255, plain,
% 132.79/23.02 (![X2 : $i]:
% 132.79/23.02 (~ (((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X2) => (transitiveset @ Y0))))))
% 132.79/23.02 | (transitiveset @ (setunion @ X2)))),
% 132.79/23.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3244])).
% 132.79/23.02 thf(transitiveset, axiom, (transitiveset @ X0) =>
% 132.79/23.02 ((((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X0) => (subset @ Y0 @ X0)))))) =
% 132.79/23.02 ($true))).
% 132.79/23.02 thf('13', plain,
% 132.79/23.02 (![X0:$i]:
% 132.79/23.02 ( ( transitiveset @ X0 ) <=>
% 132.79/23.02 ( ![X5:$i]: ( ( in @ X5 @ X0 ) => ( subset @ X5 @ X0 ) ) ) )),
% 132.79/23.02 inference('rw.lit', [status(esa)], [transitiveset])).
% 132.79/23.02 thf(zip_derived_cl3268, plain,
% 132.79/23.02 (![X0 : $i]:
% 132.79/23.02 ( (((!!) @ (^[Y0 : $i]:
% 132.79/23.02 (((in @ Y0 @ (setunion @ X0)) => (subset @ Y0 @
% 132.79/23.02 (setunion @ X0)))))))
% 132.79/23.02 | ~ (((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X0) => (transitiveset @ Y0)))))))),
% 132.79/23.02 inference('rw_clause', [status(thm)], [zip_derived_cl3255, '13'])).
% 132.79/23.02 thf(zip_derived_cl3260, plain,
% 132.79/23.02 (![X0 : $i]:
% 132.79/23.02 (~ ('#form1597' @ X0)
% 132.79/23.02 | (((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X0) => (subset @ Y0 @ X0)))))))),
% 132.79/23.02 define([status(thm)])).
% 132.79/23.02 thf(zip_derived_cl3251, plain,
% 132.79/23.02 (![X0 : $i]:
% 132.79/23.02 ( ('#form1597' @ X0)
% 132.79/23.02 | ~ (((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X0) => (subset @ Y0 @ X0)))))))),
% 132.79/23.02 define([status(thm)])).
% 132.79/23.02 thf(zip_derived_cl3277, plain,
% 132.79/23.02 (![X0 : $i]:
% 132.79/23.02 ( ('#form1597' @ (setunion @ X0))
% 132.79/23.02 | ~ (((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X0) => (transitiveset @ Y0)))))))),
% 132.79/23.02 inference('renaming', [status(thm)],
% 132.79/23.02 [zip_derived_cl3268, zip_derived_cl3260, zip_derived_cl3251])).
% 132.79/23.02 thf(zip_derived_cl3285, plain,
% 132.79/23.02 (![X0 : $i]:
% 132.79/23.02 (~ (((in @ ('#sk337' @ X0 @ transitiveset) @ X0) => (transitiveset @
% 132.79/23.02 ('#sk337' @ X0 @ transitiveset))))
% 132.79/23.02 | ('#form1597' @ (setunion @ X0)))),
% 132.79/23.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl3277])).
% 132.79/23.02 thf(zip_derived_cl3293, plain,
% 132.79/23.02 (![X0 : $i]:
% 132.79/23.02 ( (in @ ('#sk337' @ X0 @ transitiveset) @ X0)
% 132.79/23.02 | ('#form1597' @ (setunion @ X0)))),
% 132.79/23.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3285])).
% 132.79/23.02 thf(zip_derived_cl3328, plain,
% 132.79/23.02 (![X0 : $i]:
% 132.79/23.02 ( ('#form1598' @ X0)
% 132.79/23.02 | ~ (((!!) @ (^[Y0 : $i]:
% 132.79/23.02 (((in @ Y0 @ (powerset @ X0)) =>
% 132.79/23.02 (((nonempty @ Y0) =>
% 132.79/23.02 (((??) @ (^[Y1 : $i]:
% 132.79/23.02 (((in @ Y1 @ Y0) &
% 132.79/23.02 (((!!) @ (^[Y2 : $i]:
% 132.79/23.02 (((in @ Y2 @ Y0) =>
% 132.79/23.02 (((in @ Y1 @ Y2) |
% 132.79/23.02 (((Y1) = (Y2)))))))))))))))))))))))),
% 132.79/23.02 define([status(thm)])).
% 132.79/23.02 thf(zip_derived_cl3329, plain,
% 132.79/23.02 (![X0 : $i]:
% 132.79/23.02 (~ (((in @ ('#sk1599' @ X0) @ (powerset @ X0)) =>
% 132.79/23.02 (((nonempty @ ('#sk1599' @ X0)) =>
% 132.79/23.02 (((??) @ (^[Y0 : $i]:
% 132.79/23.02 (((in @ Y0 @ ('#sk1599' @ X0)) &
% 132.79/23.02 (((!!) @ (^[Y1 : $i]:
% 132.79/23.02 (((in @ Y1 @ ('#sk1599' @ X0)) =>
% 132.79/23.02 (((in @ Y0 @ Y1) | (((Y0) = (Y1)))))))))))))))))))
% 132.79/23.02 | ('#form1598' @ X0))),
% 132.79/23.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl3328])).
% 132.79/23.02 thf(zip_derived_cl3337, plain,
% 132.79/23.02 (![X0 : $i]:
% 132.79/23.02 (~ (((nonempty @ ('#sk1599' @ X0)) =>
% 132.79/23.02 (((??) @ (^[Y0 : $i]:
% 132.79/23.02 (((in @ Y0 @ ('#sk1599' @ X0)) &
% 132.79/23.02 (((!!) @ (^[Y1 : $i]:
% 132.79/23.02 (((in @ Y1 @ ('#sk1599' @ X0)) =>
% 132.79/23.02 (((in @ Y0 @ Y1) | (((Y0) = (Y1)))))))))))))))))
% 132.79/23.02 | ('#form1598' @ X0))),
% 132.79/23.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3329])).
% 132.79/23.02 thf(zip_derived_cl3343, plain,
% 132.79/23.02 (![X0 : $i]: ( (nonempty @ ('#sk1599' @ X0)) | ('#form1598' @ X0))),
% 132.79/23.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3337])).
% 132.79/23.02 thf(nonempty, axiom, (nonempty @ X0) => ((X0) != (emptyset))).
% 132.79/23.02 thf('14', plain,
% 132.79/23.02 (![X0:$i]: ( ( nonempty @ X0 ) <=> ( ( X0 ) != ( emptyset ) ) )),
% 132.79/23.02 inference('rw.lit', [status(esa)], [nonempty])).
% 132.79/23.02 thf(zip_derived_cl3350, plain,
% 132.79/23.02 (![X0 : $i]: ((('#sk1599' @ X0) != (emptyset)) | ('#form1598' @ X0))),
% 132.79/23.02 inference('rw_clause', [status(thm)], [zip_derived_cl3343, '14'])).
% 132.79/23.02 thf(zip_derived_cl3156, plain, ( (foundation2)),
% 132.79/23.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3148])).
% 132.79/23.02 thf(foundation2, axiom, (foundation2) =>
% 132.79/23.02 ((((!!) @ (^[Y0 : $i]:
% 132.79/23.02 (((nonempty @ Y0) =>
% 132.79/23.02 (((??) @ (^[Y1 : $i]:
% 132.79/23.02 (((in @ Y1 @ Y0) &
% 132.79/23.02 (((binintersect @ Y1 @ Y0) = (emptyset)))))))))))))
% 132.79/23.02 = ($true))).
% 132.79/23.02 thf('15', plain,
% 132.79/23.02 (( foundation2 ) <=>
% 132.79/23.02 ( ![X5:$i]:
% 132.79/23.02 ( ( nonempty @ X5 ) =>
% 132.79/23.02 ( ?[X7:$i]:
% 132.79/23.02 ( ( in @ X7 @ X5 ) & ( ( binintersect @ X7 @ X5 ) = ( emptyset ) ) ) ) ) )),
% 132.79/23.02 inference('rw.lit', [status(esa)], [foundation2])).
% 132.79/23.02 thf(zip_derived_cl3161, plain,
% 132.79/23.02 ( (((!!) @ (^[Y0 : $i]:
% 132.79/23.02 (((nonempty @ Y0) =>
% 132.79/23.02 (((??) @ (^[Y1 : $i]:
% 132.79/23.02 (((in @ Y1 @ Y0) &
% 132.79/23.02 (((binintersect @ Y1 @ Y0) = (emptyset)))))))))))))),
% 132.79/23.02 inference('rw_clause', [status(thm)], [zip_derived_cl3156, '15'])).
% 132.79/23.02 thf(zip_derived_cl3167, plain,
% 132.79/23.02 (![X2 : $i]:
% 132.79/23.02 (((nonempty @ X2) =>
% 132.79/23.02 (((??) @ (^[Y0 : $i]:
% 132.79/23.02 (((in @ Y0 @ X2) &
% 132.79/23.02 (((binintersect @ Y0 @ X2) = (emptyset))))))))))),
% 132.79/23.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl3161])).
% 132.79/23.02 thf(zip_derived_cl3173, plain,
% 132.79/23.02 (![X2 : $i]:
% 132.79/23.02 (~ (nonempty @ X2)
% 132.79/23.02 | (((??) @ (^[Y0 : $i]:
% 132.79/23.02 (((in @ Y0 @ X2) &
% 132.79/23.02 (((binintersect @ Y0 @ X2) = (emptyset)))))))))),
% 132.79/23.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3167])).
% 132.79/23.02 thf(nonempty, axiom, ~ (nonempty @ X0) => ((X0) = (emptyset))).
% 132.79/23.02 thf('16', plain,
% 132.79/23.02 (![X0:$i]: ( ( ~( nonempty @ X0 ) ) <=> ( ( X0 ) = ( emptyset ) ) )),
% 132.79/23.02 inference('rw.lit', [status(esa)], [nonempty])).
% 132.79/23.02 thf(zip_derived_cl3181, plain,
% 132.79/23.02 (![X0 : $i]:
% 132.79/23.02 (((X0) = (emptyset))
% 132.79/23.02 | (((??) @ (^[Y0 : $i]:
% 132.79/23.02 (((in @ Y0 @ X0) &
% 132.79/23.02 (((binintersect @ Y0 @ X0) = (emptyset)))))))))),
% 132.79/23.02 inference('rw_clause', [status(thm)], [zip_derived_cl3173, '16'])).
% 132.79/23.02 thf(zip_derived_cl3189, plain,
% 132.79/23.02 (![X0 : $i]:
% 132.79/23.02 ( (((in @ ('#sk1571' @ X0) @ X0) &
% 132.79/23.02 (((binintersect @ ('#sk1571' @ X0) @ X0) = (emptyset)))))
% 132.79/23.02 | ((X0) = (emptyset)))),
% 132.79/23.02 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl3181])).
% 132.79/23.02 thf(zip_derived_cl3198, plain,
% 132.79/23.02 (![X0 : $i]: ( (in @ ('#sk1571' @ X0) @ X0) | ((X0) = (emptyset)))),
% 132.79/23.02 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl3189])).
% 132.79/23.02 thf(zip_derived_cl13, plain, (![X2 : $i]: ~ (in @ X2 @ emptyset)),
% 132.79/23.02 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl9])).
% 132.79/23.02 thf(zip_derived_cl3336, plain,
% 132.79/23.02 (![X0 : $i]:
% 132.79/23.02 ( (in @ ('#sk1599' @ X0) @ (powerset @ X0)) | ('#form1598' @ X0))),
% 132.79/23.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3329])).
% 132.79/23.02 thf(zip_derived_cl15, plain, ( (powersetAx)),
% 132.79/23.02 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl11])).
% 132.79/23.02 thf(powersetAx, axiom, (powersetAx) =>
% 132.79/23.02 ((((!!) @ (^[Y0 : $i]:
% 132.79/23.02 (((!!) @ (^[Y1 : $i]:
% 132.79/23.02 (((in @ Y1 @ (powerset @ Y0)) <=>
% 132.79/23.02 (((!!) @ (^[Y2 : $i]:
% 132.79/23.02 (((in @ Y2 @ Y1) =>